DT2H2X---1.9.5.THM-Ref.s

%------------------------------------------------------------------------------
% File     : DT2H2X---1.9.5
% Problem  : ITP271^3 : TPTP v9.2.1. Bugfixed v9.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300

% Computer : n001.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sat Feb 28 09:15:16 AM UTC 2026

% Result   : Theorem 168.03s 28.52s
% Output   : Refutation 168.03s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   15
% Syntax   : Number of formulae    :  102 ( 102 unt;   0 typ;   0 def)
%            Number of atoms       :  252 ( 158 equ;   0 cnn)
%            Maximal formula atoms :    1 (   2 avg)
%            Number of connectives : 13424 (  18   ~;   0   |;   0   &;13398   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   2 avg)
%            Number of types       :   93 (  92 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  985 ( 981 usr;  85 con; 0-8 aty)
%                                         (   8  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  163 ( 134   ^;  29   !;   0   ?; 163   :)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_5,type,
    rat: $tType ).

thf(type_def_6,type,
    int: $tType ).

thf(type_def_8,type,
    real: $tType ).

thf(type_def_9,type,
    set_Pr1261947904930325089at_nat: $tType ).

thf(type_def_10,type,
    nat: $tType ).

thf(type_def_11,type,
    complex: $tType ).

thf(type_def_12,type,
    product_prod_int_int: $tType ).

thf(type_def_13,type,
    num: $tType ).

thf(type_def_14,type,
    option_num: $tType ).

thf(type_def_15,type,
    product_prod_num_num: $tType ).

thf(type_def_16,type,
    code_integer: $tType ).

thf(type_def_17,type,
    produc6271795597528267376eger_o: $tType ).

thf(type_def_18,type,
    produc8923325533196201883nteger: $tType ).

thf(type_def_19,type,
    set_fi4554929511873752355omplex: $tType ).

thf(type_def_20,type,
    filter6041513312241820739omplex: $tType ).

thf(type_def_21,type,
    set_fi7789364187291644575l_real: $tType ).

thf(type_def_22,type,
    filter2146258269922977983l_real: $tType ).

thf(type_def_23,type,
    set_real: $tType ).

thf(type_def_24,type,
    filter_real: $tType ).

thf(type_def_25,type,
    product_prod_nat_nat: $tType ).

thf(type_def_26,type,
    filter_nat: $tType ).

thf(type_def_27,type,
    filter1242075044329608583at_nat: $tType ).

thf(type_def_28,type,
    set_Pr5085853215250843933omplex: $tType ).

thf(type_def_29,type,
    set_Pr6218003697084177305l_real: $tType ).

thf(type_def_30,type,
    set_o: $tType ).

thf(type_def_31,type,
    set_complex: $tType ).

thf(type_def_32,type,
    set_int: $tType ).

thf(type_def_33,type,
    set_list_nat: $tType ).

thf(type_def_34,type,
    set_nat: $tType ).

thf(type_def_35,type,
    set_Product_unit: $tType ).

thf(type_def_36,type,
    set_char: $tType ).

thf(type_def_37,type,
    set_list_o: $tType ).

thf(type_def_38,type,
    set_list_complex: $tType ).

thf(type_def_39,type,
    set_list_int: $tType ).

thf(type_def_40,type,
    set_list_real: $tType ).

thf(type_def_41,type,
    set_list_VEBT_VEBT: $tType ).

thf(type_def_42,type,
    set_num: $tType ).

thf(type_def_43,type,
    set_rat: $tType ).

thf(type_def_44,type,
    set_set_nat: $tType ).

thf(type_def_45,type,
    set_set_real: $tType ).

thf(type_def_46,type,
    set_VEBT_VEBT: $tType ).

thf(type_def_47,type,
    char: $tType ).

thf(type_def_48,type,
    set_Pr8693737435421807431at_nat: $tType ).

thf(type_def_49,type,
    list_nat: $tType ).

thf(type_def_50,type,
    extended_enat: $tType ).

thf(type_def_51,type,
    vEBT_VEBT: $tType ).

thf(type_def_52,type,
    list_o: $tType ).

thf(type_def_53,type,
    list_int: $tType ).

thf(type_def_54,type,
    option_nat: $tType ).

thf(type_def_55,type,
    list_complex: $tType ).

thf(type_def_56,type,
    list_P6011104703257516679at_nat: $tType ).

thf(type_def_57,type,
    list_real: $tType ).

thf(type_def_58,type,
    list_VEBT_VEBT: $tType ).

thf(type_def_59,type,
    list_num: $tType ).

thf(type_def_60,type,
    list_P4002435161011370285od_o_o: $tType ).

thf(type_def_61,type,
    product_prod_o_o: $tType ).

thf(type_def_62,type,
    list_P3795440434834930179_o_int: $tType ).

thf(type_def_63,type,
    product_prod_o_int: $tType ).

thf(type_def_64,type,
    list_P6285523579766656935_o_nat: $tType ).

thf(type_def_65,type,
    product_prod_o_nat: $tType ).

thf(type_def_66,type,
    list_P7495141550334521929T_VEBT: $tType ).

thf(type_def_67,type,
    produc2504756804600209347T_VEBT: $tType ).

thf(type_def_68,type,
    list_P1726324292696863441at_num: $tType ).

thf(type_def_69,type,
    product_prod_nat_num: $tType ).

thf(type_def_70,type,
    list_P3744719386663036955um_num: $tType ).

thf(type_def_71,type,
    list_P3126845725202233233VEBT_o: $tType ).

thf(type_def_72,type,
    produc334124729049499915VEBT_o: $tType ).

thf(type_def_73,type,
    list_P4547456442757143711BT_int: $tType ).

thf(type_def_74,type,
    produc4894624898956917775BT_int: $tType ).

thf(type_def_75,type,
    list_P7037539587688870467BT_nat: $tType ).

thf(type_def_76,type,
    produc9072475918466114483BT_nat: $tType ).

thf(type_def_77,type,
    list_P7413028617227757229T_VEBT: $tType ).

thf(type_def_78,type,
    produc8243902056947475879T_VEBT: $tType ).

thf(type_def_79,type,
    list_P7333126701944960589_nat_o: $tType ).

thf(type_def_80,type,
    list_P5647936690300460905T_VEBT: $tType ).

thf(type_def_81,type,
    option4927543243414619207at_nat: $tType ).

thf(type_def_82,type,
    produc4953844613479565601on_nat: $tType ).

thf(type_def_83,type,
    produc2233624965454879586on_nat: $tType ).

thf(type_def_84,type,
    produc7248412053542808358at_nat: $tType ).

thf(type_def_85,type,
    produc4471711990508489141at_nat: $tType ).

thf(type_def_86,type,
    produc8306885398267862888on_nat: $tType ).

thf(type_def_87,type,
    produc2963631642982155120at_num: $tType ).

thf(type_def_88,type,
    produc3368934014287244435at_num: $tType ).

thf(type_def_89,type,
    produc3447558737645232053on_num: $tType ).

thf(type_def_90,type,
    produc7036089656553540234on_num: $tType ).

thf(type_def_91,type,
    produc1193250871479095198on_num: $tType ).

thf(type_def_92,type,
    produc6121120109295599847at_nat: $tType ).

thf(type_def_93,type,
    produc5491161045314408544at_nat: $tType ).

thf(type_def_94,type,
    produc5542196010084753463at_nat: $tType ).

thf(type_def_95,type,
    produc859450856879609959at_nat: $tType ).

thf(type_def_96,type,
    produc4411394909380815293omplex: $tType ).

thf(type_def_97,type,
    produc2422161461964618553l_real: $tType ).

thf(func_def_0,type,
    produc5542196010084753463at_nat: $tType ).

thf(func_def_1,type,
    produc5491161045314408544at_nat: $tType ).

thf(func_def_2,type,
    produc1193250871479095198on_num: $tType ).

thf(func_def_3,type,
    produc8306885398267862888on_nat: $tType ).

thf(func_def_4,type,
    produc6121120109295599847at_nat: $tType ).

thf(func_def_5,type,
    produc3368934014287244435at_num: $tType ).

thf(func_def_6,type,
    produc4471711990508489141at_nat: $tType ).

thf(func_def_7,type,
    produc7036089656553540234on_num: $tType ).

thf(func_def_8,type,
    produc2233624965454879586on_nat: $tType ).

thf(func_def_9,type,
    set_Pr8693737435421807431at_nat: $tType ).

thf(func_def_10,type,
    produc859450856879609959at_nat: $tType ).

thf(func_def_11,type,
    set_fi4554929511873752355omplex: $tType ).

thf(func_def_12,type,
    list_P7413028617227757229T_VEBT: $tType ).

thf(func_def_13,type,
    produc3447558737645232053on_num: $tType ).

thf(func_def_14,type,
    produc4953844613479565601on_nat: $tType ).

thf(func_def_15,type,
    produc2963631642982155120at_num: $tType ).

thf(func_def_16,type,
    produc7248412053542808358at_nat: $tType ).

thf(func_def_17,type,
    set_fi7789364187291644575l_real: $tType ).

thf(func_def_18,type,
    filter6041513312241820739omplex: $tType ).

thf(func_def_19,type,
    list_P7037539587688870467BT_nat: $tType ).

thf(func_def_20,type,
    list_P4547456442757143711BT_int: $tType ).

thf(func_def_21,type,
    list_P5647936690300460905T_VEBT: $tType ).

thf(func_def_22,type,
    produc8243902056947475879T_VEBT: $tType ).

thf(func_def_23,type,
    set_Pr5085853215250843933omplex: $tType ).

thf(func_def_24,type,
    produc8923325533196201883nteger: $tType ).

thf(func_def_25,type,
    list_P3126845725202233233VEBT_o: $tType ).

thf(func_def_26,type,
    list_P7495141550334521929T_VEBT: $tType ).

thf(func_def_27,type,
    filter2146258269922977983l_real: $tType ).

thf(func_def_28,type,
    option4927543243414619207at_nat: $tType ).

thf(func_def_29,type,
    filter1242075044329608583at_nat: $tType ).

thf(func_def_30,type,
    set_Pr6218003697084177305l_real: $tType ).

thf(func_def_31,type,
    list_P3744719386663036955um_num: $tType ).

thf(func_def_32,type,
    list_P1726324292696863441at_num: $tType ).

thf(func_def_33,type,
    list_P6011104703257516679at_nat: $tType ).

thf(func_def_34,type,
    produc9072475918466114483BT_nat: $tType ).

thf(func_def_35,type,
    produc4894624898956917775BT_int: $tType ).

thf(func_def_36,type,
    set_Pr1261947904930325089at_nat: $tType ).

thf(func_def_37,type,
    produc4411394909380815293omplex: $tType ).

thf(func_def_38,type,
    list_P7333126701944960589_nat_o: $tType ).

thf(func_def_39,type,
    list_P6285523579766656935_o_nat: $tType ).

thf(func_def_40,type,
    list_P3795440434834930179_o_int: $tType ).

thf(func_def_41,type,
    set_list_VEBT_VEBT: $tType ).

thf(func_def_42,type,
    produc334124729049499915VEBT_o: $tType ).

thf(func_def_43,type,
    produc2504756804600209347T_VEBT: $tType ).

thf(func_def_44,type,
    produc6271795597528267376eger_o: $tType ).

thf(func_def_45,type,
    produc2422161461964618553l_real: $tType ).

thf(func_def_46,type,
    product_prod_num_num: $tType ).

thf(func_def_47,type,
    product_prod_nat_num: $tType ).

thf(func_def_48,type,
    product_prod_nat_nat: $tType ).

thf(func_def_49,type,
    product_prod_int_int: $tType ).

thf(func_def_50,type,
    list_P4002435161011370285od_o_o: $tType ).

thf(func_def_51,type,
    set_list_complex: $tType ).

thf(func_def_52,type,
    set_list_real: $tType ).

thf(func_def_53,type,
    list_VEBT_VEBT: $tType ).

thf(func_def_54,type,
    set_set_real: $tType ).

thf(func_def_55,type,
    set_list_nat: $tType ).

thf(func_def_56,type,
    set_list_int: $tType ).

thf(func_def_57,type,
    product_prod_o_nat: $tType ).

thf(func_def_58,type,
    product_prod_o_int: $tType ).

thf(func_def_59,type,
    set_VEBT_VEBT: $tType ).

thf(func_def_60,type,
    set_set_nat: $tType ).

thf(func_def_61,type,
    set_Product_unit: $tType ).

thf(func_def_62,type,
    list_complex: $tType ).

thf(func_def_63,type,
    set_list_o: $tType ).

thf(func_def_64,type,
    product_prod_o_o: $tType ).

thf(func_def_65,type,
    set_complex: $tType ).

thf(func_def_66,type,
    filter_real: $tType ).

thf(func_def_67,type,
    option_num: $tType ).

thf(func_def_68,type,
    option_nat: $tType ).

thf(func_def_69,type,
    filter_nat: $tType ).

thf(func_def_70,type,
    set_char: $tType ).

thf(func_def_71,type,
    list_real: $tType ).

thf(func_def_72,type,
    set_real: $tType ).

thf(func_def_73,type,
    list_num: $tType ).

thf(func_def_74,type,
    list_nat: $tType ).

thf(func_def_75,type,
    list_int: $tType ).

thf(func_def_76,type,
    vEBT_VEBT: $tType ).

thf(func_def_77,type,
    set_rat: $tType ).

thf(func_def_78,type,
    set_num: $tType ).

thf(func_def_79,type,
    set_nat: $tType ).

thf(func_def_80,type,
    set_int: $tType ).

thf(func_def_81,type,
    code_integer: $tType ).

thf(func_def_82,type,
    extended_enat: $tType ).

thf(func_def_83,type,
    list_o: $tType ).

thf(func_def_84,type,
    complex: $tType ).

thf(func_def_85,type,
    set_o: $tType ).

thf(func_def_86,type,
    char: $tType ).

thf(func_def_87,type,
    real: $tType ).

thf(func_def_88,type,
    rat: $tType ).

thf(func_def_89,type,
    num: $tType ).

thf(func_def_90,type,
    nat: $tType ).

thf(func_def_91,type,
    int: $tType ).

thf(func_def_92,type,
    archim2889992004027027881ng_rat: rat > int ).

thf(func_def_93,type,
    archim7802044766580827645g_real: real > int ).

thf(func_def_94,type,
    archim3151403230148437115or_rat: rat > int ).

thf(func_def_95,type,
    archim6058952711729229775r_real: real > int ).

thf(func_def_96,type,
    archimedean_frac_rat: rat > rat ).

thf(func_def_97,type,
    archim2898591450579166408c_real: real > real ).

thf(func_def_98,type,
    archim7778729529865785530nd_rat: rat > int ).

thf(func_def_99,type,
    archim8280529875227126926d_real: real > int ).

thf(func_def_100,type,
    bNF_Ca8665028551170535155natLeq: set_Pr1261947904930325089at_nat ).

thf(func_def_101,type,
    bNF_Ca8459412986667044542atLess: set_Pr1261947904930325089at_nat ).

thf(func_def_102,type,
    bNF_We3818239936649020644el_nat: set_Pr1261947904930325089at_nat > $o ).

thf(func_def_103,type,
    binomial: nat > nat > nat ).

thf(func_def_104,type,
    gbinomial_complex: complex > nat > complex ).

thf(func_def_105,type,
    gbinomial_int: int > nat > int ).

thf(func_def_106,type,
    gbinomial_nat: nat > nat > nat ).

thf(func_def_107,type,
    gbinomial_rat: rat > nat > rat ).

thf(func_def_108,type,
    gbinomial_real: real > nat > real ).

thf(func_def_109,type,
    bit_and_int_rel: product_prod_int_int > product_prod_int_int > $o ).

thf(func_def_110,type,
    bit_and_not_num: num > num > option_num ).

thf(func_def_111,type,
    bit_and_not_num_rel: product_prod_num_num > product_prod_num_num > $o ).

thf(func_def_112,type,
    bit_concat_bit: nat > int > int > int ).

thf(func_def_113,type,
    bit_or_not_num_neg: num > num > num ).

thf(func_def_114,type,
    bit_or3848514188828904588eg_rel: product_prod_num_num > product_prod_num_num > $o ).

thf(func_def_115,type,
    bit_ri7919022796975470100ot_int: int > int ).

thf(func_def_116,type,
    bit_ri6519982836138164636nteger: nat > code_integer > code_integer ).

thf(func_def_117,type,
    bit_ri631733984087533419it_int: nat > int > int ).

thf(func_def_118,type,
    bit_se3949692690581998587nteger: code_integer > code_integer > code_integer ).

thf(func_def_119,type,
    bit_se725231765392027082nd_int: int > int > int ).

thf(func_def_120,type,
    bit_se727722235901077358nd_nat: nat > nat > nat ).

thf(func_def_121,type,
    bit_se8568078237143864401it_int: nat > int > int ).

thf(func_def_122,type,
    bit_se8570568707652914677it_nat: nat > nat > nat ).

thf(func_def_123,type,
    bit_se1345352211410354436nteger: nat > code_integer > code_integer ).

thf(func_def_124,type,
    bit_se2159334234014336723it_int: nat > int > int ).

thf(func_def_125,type,
    bit_se2161824704523386999it_nat: nat > nat > nat ).

thf(func_def_126,type,
    bit_se2119862282449309892nteger: nat > code_integer ).

thf(func_def_127,type,
    bit_se2000444600071755411sk_int: nat > int ).

thf(func_def_128,type,
    bit_se2002935070580805687sk_nat: nat > nat ).

thf(func_def_129,type,
    bit_se1080825931792720795nteger: code_integer > code_integer > code_integer ).

thf(func_def_130,type,
    bit_se1409905431419307370or_int: int > int > int ).

thf(func_def_131,type,
    bit_se1412395901928357646or_nat: nat > nat > nat ).

thf(func_def_132,type,
    bit_se545348938243370406it_int: nat > int > int ).

thf(func_def_133,type,
    bit_se547839408752420682it_nat: nat > nat > nat ).

thf(func_def_134,type,
    bit_se2793503036327961859nteger: nat > code_integer > code_integer ).

thf(func_def_135,type,
    bit_se7879613467334960850it_int: nat > int > int ).

thf(func_def_136,type,
    bit_se7882103937844011126it_nat: nat > nat > nat ).

thf(func_def_137,type,
    bit_se1745604003318907178nteger: nat > code_integer > code_integer ).

thf(func_def_138,type,
    bit_se2923211474154528505it_int: nat > int > int ).

thf(func_def_139,type,
    bit_se2925701944663578781it_nat: nat > nat > nat ).

thf(func_def_140,type,
    bit_se8260200283734997820nteger: nat > code_integer > code_integer ).

thf(func_def_141,type,
    bit_se4203085406695923979it_int: nat > int > int ).

thf(func_def_142,type,
    bit_se4205575877204974255it_nat: nat > nat > nat ).

thf(func_def_143,type,
    bit_se6526347334894502574or_int: int > int > int ).

thf(func_def_144,type,
    bit_se6528837805403552850or_nat: nat > nat > nat ).

thf(func_def_145,type,
    bit_se1146084159140164899it_int: int > nat > $o ).

thf(func_def_146,type,
    bit_se1148574629649215175it_nat: nat > nat > $o ).

thf(func_def_147,type,
    bit_take_bit_num: nat > num > option_num ).

thf(func_def_148,type,
    bit_un1837492267222099188nd_num: num > num > option_num ).

thf(func_def_149,type,
    bit_un5425074673868309765um_rel: product_prod_num_num > product_prod_num_num > $o ).

thf(func_def_150,type,
    bit_un6178654185764691216or_num: num > num > option_num ).

thf(func_def_151,type,
    bit_un3595099601533988841um_rel: product_prod_num_num > product_prod_num_num > $o ).

thf(func_def_152,type,
    bit_un7362597486090784418nd_num: num > num > option_num ).

thf(func_def_153,type,
    bit_un4731106466462545111um_rel: product_prod_num_num > product_prod_num_num > $o ).

thf(func_def_154,type,
    bit_un2480387367778600638or_num: num > num > option_num ).

thf(func_def_155,type,
    bit_un2901131394128224187um_rel: product_prod_num_num > product_prod_num_num > $o ).

thf(func_def_156,type,
    code_bit_cut_integer: code_integer > produc6271795597528267376eger_o ).

thf(func_def_157,type,
    code_divmod_abs: code_integer > code_integer > produc8923325533196201883nteger ).

thf(func_def_158,type,
    code_divmod_integer: code_integer > code_integer > produc8923325533196201883nteger ).

thf(func_def_159,type,
    code_int_of_integer: code_integer > int ).

thf(func_def_160,type,
    code_integer_of_int: int > code_integer ).

thf(func_def_161,type,
    code_integer_of_num: num > code_integer ).

thf(func_def_162,type,
    code_nat_of_integer: code_integer > nat ).

thf(func_def_163,type,
    code_num_of_integer: code_integer > num ).

thf(func_def_164,type,
    code_Target_negative: num > int ).

thf(func_def_165,type,
    code_Target_positive: num > int ).

thf(func_def_166,type,
    comple8358262395181532106omplex: set_fi4554929511873752355omplex > filter6041513312241820739omplex ).

thf(func_def_167,type,
    comple2936214249959783750l_real: set_fi7789364187291644575l_real > filter2146258269922977983l_real ).

thf(func_def_168,type,
    comple4887499456419720421f_real: set_real > real ).

thf(func_def_169,type,
    comple1385675409528146559p_real: set_real > real ).

thf(func_def_170,type,
    arg: complex > real ).

thf(func_def_171,type,
    cis: real > complex ).

thf(func_def_172,type,
    cnj: complex > complex ).

thf(func_def_173,type,
    complex2: real > real > complex ).

thf(func_def_174,type,
    im: complex > real ).

thf(func_def_175,type,
    re: complex > real ).

thf(func_def_176,type,
    csqrt: complex > complex ).

thf(func_def_177,type,
    imaginary_unit: complex ).

thf(func_def_178,type,
    rcis: real > real > complex ).

thf(func_def_179,type,
    differ6690327859849518006l_real: ( real > real ) > filter_real > $o ).

thf(func_def_180,type,
    has_de1759254742604945161l_real: ( real > real ) > ( real > real ) > filter_real > $o ).

thf(func_def_181,type,
    has_fi5821293074295781190e_real: ( real > real ) > real > filter_real > $o ).

thf(func_def_182,type,
    adjust_div: product_prod_int_int > int ).

thf(func_def_183,type,
    adjust_mod: int > int > int ).

thf(func_def_184,type,
    divmod_nat: nat > nat > product_prod_nat_nat ).

thf(func_def_185,type,
    eucl_rel_int: int > int > product_prod_int_int > $o ).

thf(func_def_186,type,
    unique5706413561485394159nteger: produc8923325533196201883nteger > $o ).

thf(func_def_187,type,
    unique6319869463603278526ux_int: product_prod_int_int > $o ).

thf(func_def_188,type,
    unique6322359934112328802ux_nat: product_prod_nat_nat > $o ).

thf(func_def_189,type,
    unique3479559517661332726nteger: num > num > produc8923325533196201883nteger ).

thf(func_def_190,type,
    unique5052692396658037445od_int: num > num > product_prod_int_int ).

thf(func_def_191,type,
    unique5055182867167087721od_nat: num > num > product_prod_nat_nat ).

thf(func_def_192,type,
    unique4921790084139445826nteger: num > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(func_def_193,type,
    unique5024387138958732305ep_int: num > product_prod_int_int > product_prod_int_int ).

thf(func_def_194,type,
    unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat ).

thf(func_def_195,type,
    euclid4774559944035922753ze_int: int > nat ).

thf(func_def_196,type,
    euclid4777050414544973029ze_nat: nat > nat ).

thf(func_def_197,type,
    euclid3395696857347342551nt_int: int > int ).

thf(func_def_198,type,
    comm_s8582702949713902594nteger: code_integer > nat > code_integer ).

thf(func_def_199,type,
    comm_s2602460028002588243omplex: complex > nat > complex ).

thf(func_def_200,type,
    comm_s4660882817536571857er_int: int > nat > int ).

thf(func_def_201,type,
    comm_s4663373288045622133er_nat: nat > nat > nat ).

thf(func_def_202,type,
    comm_s4028243227959126397er_rat: rat > nat > rat ).

thf(func_def_203,type,
    comm_s7457072308508201937r_real: real > nat > real ).

thf(func_def_204,type,
    semiri3624122377584611663nteger: nat > code_integer ).

thf(func_def_205,type,
    semiri5044797733671781792omplex: nat > complex ).

thf(func_def_206,type,
    semiri1406184849735516958ct_int: nat > int ).

thf(func_def_207,type,
    semiri1408675320244567234ct_nat: nat > nat ).

thf(func_def_208,type,
    semiri773545260158071498ct_rat: nat > rat ).

thf(func_def_209,type,
    semiri2265585572941072030t_real: nat > real ).

thf(func_def_210,type,
    invers8013647133539491842omplex: complex > complex ).

thf(func_def_211,type,
    inverse_inverse_rat: rat > rat ).

thf(func_def_212,type,
    inverse_inverse_real: real > real ).

thf(func_def_213,type,
    at_bot_real: filter_real ).

thf(func_def_214,type,
    at_top_nat: filter_nat ).

thf(func_def_215,type,
    at_top_real: filter_real ).

thf(func_def_216,type,
    eventually_nat: ( nat > $o ) > filter_nat > $o ).

thf(func_def_217,type,
    eventu1038000079068216329at_nat: ( product_prod_nat_nat > $o ) > filter1242075044329608583at_nat > $o ).

thf(func_def_218,type,
    eventually_real: ( real > $o ) > filter_real > $o ).

thf(func_def_219,type,
    filterlim_nat_nat: ( nat > nat ) > filter_nat > filter_nat > $o ).

thf(func_def_220,type,
    filterlim_nat_real: ( nat > real ) > filter_real > filter_nat > $o ).

thf(func_def_221,type,
    filterlim_real_real: ( real > real ) > filter_real > filter_real > $o ).

thf(func_def_222,type,
    filtermap_real_real: ( real > real ) > filter_real > filter_real ).

thf(func_def_223,type,
    princi3496590319149328850omplex: set_Pr5085853215250843933omplex > filter6041513312241820739omplex ).

thf(func_def_224,type,
    princi6114159922880469582l_real: set_Pr6218003697084177305l_real > filter2146258269922977983l_real ).

thf(func_def_225,type,
    prod_filter_nat_nat: filter_nat > filter_nat > filter1242075044329608583at_nat ).

thf(func_def_226,type,
    finite_card_o: set_o > nat ).

thf(func_def_227,type,
    finite_card_complex: set_complex > nat ).

thf(func_def_228,type,
    finite_card_int: set_int > nat ).

thf(func_def_229,type,
    finite_card_list_nat: set_list_nat > nat ).

thf(func_def_230,type,
    finite_card_nat: set_nat > nat ).

thf(func_def_231,type,
    finite410649719033368117t_unit: set_Product_unit > nat ).

thf(func_def_232,type,
    finite_card_char: set_char > nat ).

thf(func_def_233,type,
    finite_finite_o: set_o > $o ).

thf(func_def_234,type,
    finite3207457112153483333omplex: set_complex > $o ).

thf(func_def_235,type,
    finite_finite_int: set_int > $o ).

thf(func_def_236,type,
    finite_finite_list_o: set_list_o > $o ).

thf(func_def_237,type,
    finite8712137658972009173omplex: set_list_complex > $o ).

thf(func_def_238,type,
    finite3922522038869484883st_int: set_list_int > $o ).

thf(func_def_239,type,
    finite8100373058378681591st_nat: set_list_nat > $o ).

thf(func_def_240,type,
    finite306553202115118035t_real: set_list_real > $o ).

thf(func_def_241,type,
    finite3004134309566078307T_VEBT: set_list_VEBT_VEBT > $o ).

thf(func_def_242,type,
    finite_finite_nat: set_nat > $o ).

thf(func_def_243,type,
    finite_finite_num: set_num > $o ).

thf(func_def_244,type,
    finite6177210948735845034at_nat: set_Pr1261947904930325089at_nat > $o ).

thf(func_def_245,type,
    finite_finite_rat: set_rat > $o ).

thf(func_def_246,type,
    finite_finite_real: set_real > $o ).

thf(func_def_247,type,
    finite1152437895449049373et_nat: set_set_nat > $o ).

thf(func_def_248,type,
    finite9007344921179782393t_real: set_set_real > $o ).

thf(func_def_249,type,
    finite5795047828879050333T_VEBT: set_VEBT_VEBT > $o ).

thf(func_def_250,type,
    bij_be1856998921033663316omplex: ( complex > complex ) > set_complex > set_complex > $o ).

thf(func_def_251,type,
    bij_betw_nat_complex: ( nat > complex ) > set_nat > set_complex > $o ).

thf(func_def_252,type,
    bij_betw_nat_nat: ( nat > nat ) > set_nat > set_nat > $o ).

thf(func_def_253,type,
    comp_C8797469213163452608nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(func_def_254,type,
    comp_C1593894019821074884nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(func_def_255,type,
    comp_int_int_num: ( int > int ) > ( num > int ) > num > int ).

thf(func_def_256,type,
    comp_int_nat_int: ( int > nat ) > ( int > int ) > int > nat ).

thf(func_def_257,type,
    comp_nat_nat_nat: ( nat > nat ) > ( nat > nat ) > nat > nat ).

thf(func_def_258,type,
    comp_nat_real_nat: ( nat > real ) > ( nat > nat ) > nat > real ).

thf(func_def_259,type,
    id_o: $o > $o ).

thf(func_def_260,type,
    id_nat: nat > nat ).

thf(func_def_261,type,
    inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).

thf(func_def_262,type,
    inj_on_nat_char: ( nat > char ) > set_nat > $o ).

thf(func_def_263,type,
    inj_on_real_real: ( real > real ) > set_real > $o ).

thf(func_def_264,type,
    map_fu434086159418415080_int_o: ( int > product_prod_nat_nat ) > ( ( product_prod_nat_nat > $o ) > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > int > int > $o ).

thf(func_def_265,type,
    map_fu4960017516451851995nt_int: ( int > product_prod_nat_nat ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > int > int > int ).

thf(func_def_266,type,
    map_fu4826362097070443709at_o_o: ( int > product_prod_nat_nat ) > ( $o > $o ) > ( product_prod_nat_nat > $o ) > int > $o ).

thf(func_def_267,type,
    map_fu2345160673673942751at_nat: ( int > product_prod_nat_nat ) > ( nat > nat ) > ( product_prod_nat_nat > nat ) > int > nat ).

thf(func_def_268,type,
    map_fu3667384564859982768at_int: ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ).

thf(func_def_269,type,
    strict1292158309912662752at_nat: ( nat > nat ) > set_nat > $o ).

thf(func_def_270,type,
    the_in5290026491893676941l_real: set_real > ( real > real ) > real > real ).

thf(func_def_271,type,
    fun_pair_leq: set_Pr8693737435421807431at_nat ).

thf(func_def_272,type,
    fun_pair_less: set_Pr8693737435421807431at_nat ).

thf(func_def_273,type,
    gcd_Gcd_nat: set_nat > nat ).

thf(func_def_274,type,
    bezw: nat > nat > product_prod_int_int ).

thf(func_def_275,type,
    bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(func_def_276,type,
    gcd_gcd_int: int > int > int ).

thf(func_def_277,type,
    gcd_gcd_nat: nat > nat > nat ).

thf(func_def_278,type,
    gcd_nat_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(func_def_279,type,
    abs_abs_Code_integer: code_integer > code_integer ).

thf(func_def_280,type,
    abs_abs_complex: complex > complex ).

thf(func_def_281,type,
    abs_abs_int: int > int ).

thf(func_def_282,type,
    abs_abs_rat: rat > rat ).

thf(func_def_283,type,
    abs_abs_real: real > real ).

thf(func_def_284,type,
    minus_8727706125548526216plex_o: ( complex > $o ) > ( complex > $o ) > complex > $o ).

thf(func_def_285,type,
    minus_minus_int_o: ( int > $o ) > ( int > $o ) > int > $o ).

thf(func_def_286,type,
    minus_1139252259498527702_nat_o: ( list_nat > $o ) > ( list_nat > $o ) > list_nat > $o ).

thf(func_def_287,type,
    minus_minus_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).

thf(func_def_288,type,
    minus_2270307095948843157_nat_o: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).

thf(func_def_289,type,
    minus_minus_real_o: ( real > $o ) > ( real > $o ) > real > $o ).

thf(func_def_290,type,
    minus_8373710615458151222nteger: code_integer > code_integer > code_integer ).

thf(func_def_291,type,
    minus_minus_complex: complex > complex > complex ).

thf(func_def_292,type,
    minus_3235023915231533773d_enat: extended_enat > extended_enat > extended_enat ).

thf(func_def_293,type,
    minus_minus_int: int > int > int ).

thf(func_def_294,type,
    minus_minus_nat: nat > nat > nat ).

thf(func_def_295,type,
    minus_minus_rat: rat > rat > rat ).

thf(func_def_296,type,
    minus_minus_real: real > real > real ).

thf(func_def_297,type,
    minus_811609699411566653omplex: set_complex > set_complex > set_complex ).

thf(func_def_298,type,
    minus_minus_set_int: set_int > set_int > set_int ).

thf(func_def_299,type,
    minus_7954133019191499631st_nat: set_list_nat > set_list_nat > set_list_nat ).

thf(func_def_300,type,
    minus_minus_set_nat: set_nat > set_nat > set_nat ).

thf(func_def_301,type,
    minus_1356011639430497352at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).

thf(func_def_302,type,
    minus_minus_set_real: set_real > set_real > set_real ).

thf(func_def_303,type,
    minus_5127226145743854075T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > set_VEBT_VEBT ).

thf(func_def_304,type,
    one_one_Code_integer: code_integer ).

thf(func_def_305,type,
    one_one_complex: complex ).

thf(func_def_306,type,
    one_on7984719198319812577d_enat: extended_enat ).

thf(func_def_307,type,
    one_one_int: int ).

thf(func_def_308,type,
    one_one_nat: nat ).

thf(func_def_309,type,
    one_one_rat: rat ).

thf(func_def_310,type,
    one_one_real: real ).

thf(func_def_311,type,
    plus_p5714425477246183910nteger: code_integer > code_integer > code_integer ).

thf(func_def_312,type,
    plus_plus_complex: complex > complex > complex ).

thf(func_def_313,type,
    plus_p3455044024723400733d_enat: extended_enat > extended_enat > extended_enat ).

thf(func_def_314,type,
    plus_plus_int: int > int > int ).

thf(func_def_315,type,
    plus_plus_nat: nat > nat > nat ).

thf(func_def_316,type,
    plus_plus_num: num > num > num ).

thf(func_def_317,type,
    plus_plus_rat: rat > rat > rat ).

thf(func_def_318,type,
    plus_plus_real: real > real > real ).

thf(func_def_319,type,
    sgn_sgn_Code_integer: code_integer > code_integer ).

thf(func_def_320,type,
    sgn_sgn_complex: complex > complex ).

thf(func_def_321,type,
    sgn_sgn_int: int > int ).

thf(func_def_322,type,
    sgn_sgn_real: real > real ).

thf(func_def_323,type,
    times_3573771949741848930nteger: code_integer > code_integer > code_integer ).

thf(func_def_324,type,
    times_times_complex: complex > complex > complex ).

thf(func_def_325,type,
    times_7803423173614009249d_enat: extended_enat > extended_enat > extended_enat ).

thf(func_def_326,type,
    times_times_int: int > int > int ).

thf(func_def_327,type,
    times_times_nat: nat > nat > nat ).

thf(func_def_328,type,
    times_times_num: num > num > num ).

thf(func_def_329,type,
    times_times_rat: rat > rat > rat ).

thf(func_def_330,type,
    times_times_real: real > real > real ).

thf(func_def_331,type,
    uminus1351360451143612070nteger: code_integer > code_integer ).

thf(func_def_332,type,
    uminus1482373934393186551omplex: complex > complex ).

thf(func_def_333,type,
    uminus_uminus_int: int > int ).

thf(func_def_334,type,
    uminus_uminus_rat: rat > rat ).

thf(func_def_335,type,
    uminus_uminus_real: real > real ).

thf(func_def_336,type,
    uminus1532241313380277803et_int: set_int > set_int ).

thf(func_def_337,type,
    uminus5710092332889474511et_nat: set_nat > set_nat ).

thf(func_def_338,type,
    uminus6524753893492686040at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).

thf(func_def_339,type,
    uminus612125837232591019t_real: set_real > set_real ).

thf(func_def_340,type,
    uminus8041839845116263051T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT ).

thf(func_def_341,type,
    zero_z3403309356797280102nteger: code_integer ).

thf(func_def_342,type,
    zero_zero_complex: complex ).

thf(func_def_343,type,
    zero_z5237406670263579293d_enat: extended_enat ).

thf(func_def_344,type,
    zero_zero_int: int ).

thf(func_def_345,type,
    zero_zero_nat: nat ).

thf(func_def_346,type,
    zero_zero_rat: rat ).

thf(func_def_347,type,
    zero_zero_real: real ).

thf(func_def_348,type,
    groups6621422865394947399nteger: ( complex > code_integer ) > set_complex > code_integer ).

thf(func_def_349,type,
    groups7754918857620584856omplex: ( complex > complex ) > set_complex > complex ).

thf(func_def_350,type,
    groups5690904116761175830ex_int: ( complex > int ) > set_complex > int ).

thf(func_def_351,type,
    groups5693394587270226106ex_nat: ( complex > nat ) > set_complex > nat ).

thf(func_def_352,type,
    groups5058264527183730370ex_rat: ( complex > rat ) > set_complex > rat ).

thf(func_def_353,type,
    groups5808333547571424918x_real: ( complex > real ) > set_complex > real ).

thf(func_def_354,type,
    groups7873554091576472773nteger: ( int > code_integer ) > set_int > code_integer ).

thf(func_def_355,type,
    groups3049146728041665814omplex: ( int > complex ) > set_int > complex ).

thf(func_def_356,type,
    groups4538972089207619220nt_int: ( int > int ) > set_int > int ).

thf(func_def_357,type,
    groups4541462559716669496nt_nat: ( int > nat ) > set_int > nat ).

thf(func_def_358,type,
    groups3906332499630173760nt_rat: ( int > rat ) > set_int > rat ).

thf(func_def_359,type,
    groups8778361861064173332t_real: ( int > real ) > set_int > real ).

thf(func_def_360,type,
    groups7501900531339628137nteger: ( nat > code_integer ) > set_nat > code_integer ).

thf(func_def_361,type,
    groups2073611262835488442omplex: ( nat > complex ) > set_nat > complex ).

thf(func_def_362,type,
    groups3539618377306564664at_int: ( nat > int ) > set_nat > int ).

thf(func_def_363,type,
    groups3542108847815614940at_nat: ( nat > nat ) > set_nat > nat ).

thf(func_def_364,type,
    groups2906978787729119204at_rat: ( nat > rat ) > set_nat > rat ).

thf(func_def_365,type,
    groups6591440286371151544t_real: ( nat > real ) > set_nat > real ).

thf(func_def_366,type,
    groups6381953495645901045omplex: ( product_prod_nat_nat > complex ) > set_Pr1261947904930325089at_nat > complex ).

thf(func_def_367,type,
    groups977919841031483927at_nat: ( product_prod_nat_nat > nat ) > set_Pr1261947904930325089at_nat > nat ).

thf(func_def_368,type,
    groups342789780944988191at_rat: ( product_prod_nat_nat > rat ) > set_Pr1261947904930325089at_nat > rat ).

thf(func_def_369,type,
    groups4567486121110086003t_real: ( product_prod_nat_nat > real ) > set_Pr1261947904930325089at_nat > real ).

thf(func_def_370,type,
    groups7713935264441627589nteger: ( real > code_integer ) > set_real > code_integer ).

thf(func_def_371,type,
    groups5754745047067104278omplex: ( real > complex ) > set_real > complex ).

thf(func_def_372,type,
    groups1932886352136224148al_int: ( real > int ) > set_real > int ).

thf(func_def_373,type,
    groups1935376822645274424al_nat: ( real > nat ) > set_real > nat ).

thf(func_def_374,type,
    groups1300246762558778688al_rat: ( real > rat ) > set_real > rat ).

thf(func_def_375,type,
    groups8097168146408367636l_real: ( real > real ) > set_real > real ).

thf(func_def_376,type,
    groups1794756597179926696omplex: ( vEBT_VEBT > complex ) > set_VEBT_VEBT > complex ).

thf(func_def_377,type,
    groups769130701875090982BT_int: ( vEBT_VEBT > int ) > set_VEBT_VEBT > int ).

thf(func_def_378,type,
    groups771621172384141258BT_nat: ( vEBT_VEBT > nat ) > set_VEBT_VEBT > nat ).

thf(func_def_379,type,
    groups136491112297645522BT_rat: ( vEBT_VEBT > rat ) > set_VEBT_VEBT > rat ).

thf(func_def_380,type,
    groups2240296850493347238T_real: ( vEBT_VEBT > real ) > set_VEBT_VEBT > real ).

thf(func_def_381,type,
    groups8682486955453173170nteger: ( complex > code_integer ) > set_complex > code_integer ).

thf(func_def_382,type,
    groups3708469109370488835omplex: ( complex > complex ) > set_complex > complex ).

thf(func_def_383,type,
    groups858564598930262913ex_int: ( complex > int ) > set_complex > int ).

thf(func_def_384,type,
    groups861055069439313189ex_nat: ( complex > nat ) > set_complex > nat ).

thf(func_def_385,type,
    groups225925009352817453ex_rat: ( complex > rat ) > set_complex > rat ).

thf(func_def_386,type,
    groups766887009212190081x_real: ( complex > real ) > set_complex > real ).

thf(func_def_387,type,
    groups7440179247065528705omplex: ( int > complex ) > set_int > complex ).

thf(func_def_388,type,
    groups1705073143266064639nt_int: ( int > int ) > set_int > int ).

thf(func_def_389,type,
    groups1707563613775114915nt_nat: ( int > nat ) > set_int > nat ).

thf(func_def_390,type,
    groups1072433553688619179nt_rat: ( int > rat ) > set_int > rat ).

thf(func_def_391,type,
    groups2316167850115554303t_real: ( int > real ) > set_int > real ).

thf(func_def_392,type,
    groups3455450783089532116nteger: ( nat > code_integer ) > set_nat > code_integer ).

thf(func_def_393,type,
    groups6464643781859351333omplex: ( nat > complex ) > set_nat > complex ).

thf(func_def_394,type,
    groups705719431365010083at_int: ( nat > int ) > set_nat > int ).

thf(func_def_395,type,
    groups708209901874060359at_nat: ( nat > nat ) > set_nat > nat ).

thf(func_def_396,type,
    groups73079841787564623at_rat: ( nat > rat ) > set_nat > rat ).

thf(func_def_397,type,
    groups129246275422532515t_real: ( nat > real ) > set_nat > real ).

thf(func_def_398,type,
    groups8110221916422527690omplex: ( product_prod_nat_nat > complex ) > set_Pr1261947904930325089at_nat > complex ).

thf(func_def_399,type,
    groups713298508707869441omplex: ( real > complex ) > set_real > complex ).

thf(func_def_400,type,
    groups4694064378042380927al_int: ( real > int ) > set_real > int ).

thf(func_def_401,type,
    groups4696554848551431203al_nat: ( real > nat ) > set_real > nat ).

thf(func_def_402,type,
    groups4061424788464935467al_rat: ( real > rat ) > set_real > rat ).

thf(func_def_403,type,
    groups1681761925125756287l_real: ( real > real ) > set_real > real ).

thf(func_def_404,type,
    groups127312072573709053omplex: ( vEBT_VEBT > complex ) > set_VEBT_VEBT > complex ).

thf(func_def_405,type,
    groups2703838992350267259T_real: ( vEBT_VEBT > real ) > set_VEBT_VEBT > real ).

thf(func_def_406,type,
    groups9116527308978886569_o_int: ( $o > int ) > int > list_o > int ).

thf(func_def_407,type,
    groups4561878855575611511st_nat: list_nat > nat ).

thf(func_def_408,type,
    the_int: ( int > $o ) > int ).

thf(func_def_409,type,
    the_real: ( real > $o ) > real ).

thf(func_def_410,type,
    if_int_int: $o > ( int > int ) > ( int > int ) > int > int ).

thf(func_def_411,type,
    if_Code_integer: $o > code_integer > code_integer > code_integer ).

thf(func_def_412,type,
    if_complex: $o > complex > complex > complex ).

thf(func_def_413,type,
    if_Extended_enat: $o > extended_enat > extended_enat > extended_enat ).

thf(func_def_414,type,
    if_int: $o > int > int > int ).

thf(func_def_415,type,
    if_list_int: $o > list_int > list_int > list_int ).

thf(func_def_416,type,
    if_list_nat: $o > list_nat > list_nat > list_nat ).

thf(func_def_417,type,
    if_nat: $o > nat > nat > nat ).

thf(func_def_418,type,
    if_num: $o > num > num > num ).

thf(func_def_419,type,
    if_option_nat: $o > option_nat > option_nat > option_nat ).

thf(func_def_420,type,
    if_option_num: $o > option_num > option_num > option_num ).

thf(func_def_421,type,
    if_Pro5737122678794959658eger_o: $o > produc6271795597528267376eger_o > produc6271795597528267376eger_o > produc6271795597528267376eger_o ).

thf(func_def_422,type,
    if_Pro6119634080678213985nteger: $o > produc8923325533196201883nteger > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(func_def_423,type,
    if_Pro3027730157355071871nt_int: $o > product_prod_int_int > product_prod_int_int > product_prod_int_int ).

thf(func_def_424,type,
    if_Pro6206227464963214023at_nat: $o > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).

thf(func_def_425,type,
    if_rat: $o > rat > rat > rat ).

thf(func_def_426,type,
    if_real: $o > real > real > real ).

thf(func_def_427,type,
    if_set_nat: $o > set_nat > set_nat > set_nat ).

thf(func_def_428,type,
    if_set_real: $o > set_real > set_real > set_real ).

thf(func_def_429,type,
    if_VEBT_VEBT: $o > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_430,type,
    infini8530281810654367211te_nat: set_nat > nat > nat ).

thf(func_def_431,type,
    abs_Integ: product_prod_nat_nat > int ).

thf(func_def_432,type,
    rep_Integ: int > product_prod_nat_nat ).

thf(func_def_433,type,
    nat2: int > nat ).

thf(func_def_434,type,
    power_int_real: real > int > real ).

thf(func_def_435,type,
    ring_1_Ints_real: set_real ).

thf(func_def_436,type,
    ring_18347121197199848620nteger: int > code_integer ).

thf(func_def_437,type,
    ring_17405671764205052669omplex: int > complex ).

thf(func_def_438,type,
    ring_1_of_int_int: int > int ).

thf(func_def_439,type,
    ring_1_of_int_rat: int > rat ).

thf(func_def_440,type,
    ring_1_of_int_real: int > real ).

thf(func_def_441,type,
    inf_in1870772243966228564d_enat: extended_enat > extended_enat > extended_enat ).

thf(func_def_442,type,
    inf_inf_nat: nat > nat > nat ).

thf(func_def_443,type,
    inf_in2572325071724192079at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).

thf(func_def_444,type,
    semila1623282765462674594er_nat: ( nat > nat > nat ) > nat > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).

thf(func_def_445,type,
    sup_su3973961784419623482d_enat: extended_enat > extended_enat > extended_enat ).

thf(func_def_446,type,
    sup_sup_nat: nat > nat > nat ).

thf(func_def_447,type,
    sup_sup_set_nat: set_nat > set_nat > set_nat ).

thf(func_def_448,type,
    sup_su6327502436637775413at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).

thf(func_def_449,type,
    lattic8265883725875713057ax_nat: set_nat > nat ).

thf(func_def_450,type,
    bfun_nat_real: ( nat > real ) > filter_nat > $o ).

thf(func_def_451,type,
    append_int: list_int > list_int > list_int ).

thf(func_def_452,type,
    append_nat: list_nat > list_nat > list_nat ).

thf(func_def_453,type,
    drop_nat: nat > list_nat > list_nat ).

thf(func_def_454,type,
    last_nat: list_nat > nat ).

thf(func_def_455,type,
    linord2614967742042102400et_nat: set_nat > list_nat ).

thf(func_def_456,type,
    cons_int: int > list_int > list_int ).

thf(func_def_457,type,
    cons_nat: nat > list_nat > list_nat ).

thf(func_def_458,type,
    nil_int: list_int ).

thf(func_def_459,type,
    nil_nat: list_nat ).

thf(func_def_460,type,
    hd_nat: list_nat > nat ).

thf(func_def_461,type,
    map_nat_nat: ( nat > nat ) > list_nat > list_nat ).

thf(func_def_462,type,
    set_o2: list_o > set_o ).

thf(func_def_463,type,
    set_complex2: list_complex > set_complex ).

thf(func_def_464,type,
    set_int2: list_int > set_int ).

thf(func_def_465,type,
    set_nat2: list_nat > set_nat ).

thf(func_def_466,type,
    set_Pr5648618587558075414at_nat: list_P6011104703257516679at_nat > set_Pr1261947904930325089at_nat ).

thf(func_def_467,type,
    set_real2: list_real > set_real ).

thf(func_def_468,type,
    set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).

thf(func_def_469,type,
    size_list_VEBT_VEBT: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > nat ).

thf(func_def_470,type,
    tl_nat: list_nat > list_nat ).

thf(func_def_471,type,
    list_update_o: list_o > nat > $o > list_o ).

thf(func_def_472,type,
    list_update_complex: list_complex > nat > complex > list_complex ).

thf(func_def_473,type,
    list_update_int: list_int > nat > int > list_int ).

thf(func_def_474,type,
    list_update_nat: list_nat > nat > nat > list_nat ).

thf(func_def_475,type,
    list_u6180841689913720943at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat > list_P6011104703257516679at_nat ).

thf(func_def_476,type,
    list_update_real: list_real > nat > real > list_real ).

thf(func_def_477,type,
    list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_478,type,
    nth_o: list_o > nat > $o ).

thf(func_def_479,type,
    nth_complex: list_complex > nat > complex ).

thf(func_def_480,type,
    nth_int: list_int > nat > int ).

thf(func_def_481,type,
    nth_nat: list_nat > nat > nat ).

thf(func_def_482,type,
    nth_num: list_num > nat > num ).

thf(func_def_483,type,
    nth_Product_prod_o_o: list_P4002435161011370285od_o_o > nat > product_prod_o_o ).

thf(func_def_484,type,
    nth_Pr1649062631805364268_o_int: list_P3795440434834930179_o_int > nat > product_prod_o_int ).

thf(func_def_485,type,
    nth_Pr5826913651314560976_o_nat: list_P6285523579766656935_o_nat > nat > product_prod_o_nat ).

thf(func_def_486,type,
    nth_Pr6777367263587873994T_VEBT: list_P7495141550334521929T_VEBT > nat > produc2504756804600209347T_VEBT ).

thf(func_def_487,type,
    nth_Pr7617993195940197384at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat ).

thf(func_def_488,type,
    nth_Pr8326237132889035090at_num: list_P1726324292696863441at_num > nat > product_prod_nat_num ).

thf(func_def_489,type,
    nth_Pr6456567536196504476um_num: list_P3744719386663036955um_num > nat > product_prod_num_num ).

thf(func_def_490,type,
    nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o ).

thf(func_def_491,type,
    nth_Pr6837108013167703752BT_int: list_P4547456442757143711BT_int > nat > produc4894624898956917775BT_int ).

thf(func_def_492,type,
    nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat ).

thf(func_def_493,type,
    nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).

thf(func_def_494,type,
    nth_real: list_real > nat > real ).

thf(func_def_495,type,
    nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_496,type,
    product_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).

thf(func_def_497,type,
    product_o_int: list_o > list_int > list_P3795440434834930179_o_int ).

thf(func_def_498,type,
    product_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).

thf(func_def_499,type,
    product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).

thf(func_def_500,type,
    product_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o ).

thf(func_def_501,type,
    product_nat_num: list_nat > list_num > list_P1726324292696863441at_num ).

thf(func_def_502,type,
    produc7156399406898700509T_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).

thf(func_def_503,type,
    product_num_num: list_num > list_num > list_P3744719386663036955um_num ).

thf(func_def_504,type,
    product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).

thf(func_def_505,type,
    produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).

thf(func_def_506,type,
    produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).

thf(func_def_507,type,
    produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).

thf(func_def_508,type,
    replicate_o: nat > $o > list_o ).

thf(func_def_509,type,
    replicate_complex: nat > complex > list_complex ).

thf(func_def_510,type,
    replicate_int: nat > int > list_int ).

thf(func_def_511,type,
    replicate_nat: nat > nat > list_nat ).

thf(func_def_512,type,
    replic4235873036481779905at_nat: nat > product_prod_nat_nat > list_P6011104703257516679at_nat ).

thf(func_def_513,type,
    replicate_real: nat > real > list_real ).

thf(func_def_514,type,
    replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_515,type,
    sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).

thf(func_def_516,type,
    take_nat: nat > list_nat > list_nat ).

thf(func_def_517,type,
    upt: nat > nat > list_nat ).

thf(func_def_518,type,
    upto: int > int > list_int ).

thf(func_def_519,type,
    upto_aux: int > int > list_int > list_int ).

thf(func_def_520,type,
    suc: nat > nat ).

thf(func_def_521,type,
    compow_nat_nat: nat > ( nat > nat ) > nat > nat ).

thf(func_def_522,type,
    case_nat_o: $o > ( nat > $o ) > nat > $o ).

thf(func_def_523,type,
    case_nat_nat: nat > ( nat > nat ) > nat > nat ).

thf(func_def_524,type,
    case_nat_option_num: option_num > ( nat > option_num ) > nat > option_num ).

thf(func_def_525,type,
    pred: nat > nat ).

thf(func_def_526,type,
    semiri4939895301339042750nteger: nat > code_integer ).

thf(func_def_527,type,
    semiri8010041392384452111omplex: nat > complex ).

thf(func_def_528,type,
    semiri4216267220026989637d_enat: nat > extended_enat ).

thf(func_def_529,type,
    semiri1314217659103216013at_int: nat > int ).

thf(func_def_530,type,
    semiri1316708129612266289at_nat: nat > nat ).

thf(func_def_531,type,
    semiri681578069525770553at_rat: nat > rat ).

thf(func_def_532,type,
    semiri5074537144036343181t_real: nat > real ).

thf(func_def_533,type,
    semiri2816024913162550771omplex: ( complex > complex ) > nat > complex > complex ).

thf(func_def_534,type,
    semiri8420488043553186161ux_int: ( int > int ) > nat > int > int ).

thf(func_def_535,type,
    semiri8422978514062236437ux_nat: ( nat > nat ) > nat > nat > nat ).

thf(func_def_536,type,
    semiri7787848453975740701ux_rat: ( rat > rat ) > nat > rat > rat ).

thf(func_def_537,type,
    semiri7260567687927622513x_real: ( real > real ) > nat > real > real ).

thf(func_def_538,type,
    size_size_list_o: list_o > nat ).

thf(func_def_539,type,
    size_s3451745648224563538omplex: list_complex > nat ).

thf(func_def_540,type,
    size_size_list_int: list_int > nat ).

thf(func_def_541,type,
    size_size_list_nat: list_nat > nat ).

thf(func_def_542,type,
    size_size_list_num: list_num > nat ).

thf(func_def_543,type,
    size_s1515746228057227161od_o_o: list_P4002435161011370285od_o_o > nat ).

thf(func_def_544,type,
    size_s2953683556165314199_o_int: list_P3795440434834930179_o_int > nat ).

thf(func_def_545,type,
    size_s5443766701097040955_o_nat: list_P6285523579766656935_o_nat > nat ).

thf(func_def_546,type,
    size_s4313452262239582901T_VEBT: list_P7495141550334521929T_VEBT > nat ).

thf(func_def_547,type,
    size_s6491369823275344609_nat_o: list_P7333126701944960589_nat_o > nat ).

thf(func_def_548,type,
    size_s5460976970255530739at_nat: list_P6011104703257516679at_nat > nat ).

thf(func_def_549,type,
    size_s4762443039079500285T_VEBT: list_P5647936690300460905T_VEBT > nat ).

thf(func_def_550,type,
    size_s9168528473962070013VEBT_o: list_P3126845725202233233VEBT_o > nat ).

thf(func_def_551,type,
    size_s3661962791536183091BT_int: list_P4547456442757143711BT_int > nat ).

thf(func_def_552,type,
    size_s6152045936467909847BT_nat: list_P7037539587688870467BT_nat > nat ).

thf(func_def_553,type,
    size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat ).

thf(func_def_554,type,
    size_size_list_real: list_real > nat ).

thf(func_def_555,type,
    size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).

thf(func_def_556,type,
    size_size_num: num > nat ).

thf(func_def_557,type,
    size_size_option_nat: option_nat > nat ).

thf(func_def_558,type,
    size_size_option_num: option_num > nat ).

thf(func_def_559,type,
    size_s170228958280169651at_nat: option4927543243414619207at_nat > nat ).

thf(func_def_560,type,
    size_size_VEBT_VEBT: vEBT_VEBT > nat ).

thf(func_def_561,type,
    nat_list_encode: list_nat > nat ).

thf(func_def_562,type,
    nat_list_encode_rel: list_nat > list_nat > $o ).

thf(func_def_563,type,
    nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).

thf(func_def_564,type,
    nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(func_def_565,type,
    nat_prod_encode: product_prod_nat_nat > nat ).

thf(func_def_566,type,
    nat_set_decode: nat > set_nat ).

thf(func_def_567,type,
    nat_set_encode: set_nat > nat ).

thf(func_def_568,type,
    nat_triangle: nat > nat ).

thf(func_def_569,type,
    root: nat > real > real ).

thf(func_def_570,type,
    sqrt: real > real ).

thf(func_def_571,type,
    bitM: num > num ).

thf(func_def_572,type,
    inc: num > num ).

thf(func_def_573,type,
    neg_nu8804712462038260780nteger: code_integer > code_integer ).

thf(func_def_574,type,
    neg_nu7009210354673126013omplex: complex > complex ).

thf(func_def_575,type,
    neg_numeral_dbl_int: int > int ).

thf(func_def_576,type,
    neg_numeral_dbl_rat: rat > rat ).

thf(func_def_577,type,
    neg_numeral_dbl_real: real > real ).

thf(func_def_578,type,
    neg_nu7757733837767384882nteger: code_integer > code_integer ).

thf(func_def_579,type,
    neg_nu6511756317524482435omplex: complex > complex ).

thf(func_def_580,type,
    neg_nu3811975205180677377ec_int: int > int ).

thf(func_def_581,type,
    neg_nu3179335615603231917ec_rat: rat > rat ).

thf(func_def_582,type,
    neg_nu6075765906172075777c_real: real > real ).

thf(func_def_583,type,
    neg_nu5831290666863070958nteger: code_integer > code_integer ).

thf(func_def_584,type,
    neg_nu8557863876264182079omplex: complex > complex ).

thf(func_def_585,type,
    neg_nu5851722552734809277nc_int: int > int ).

thf(func_def_586,type,
    neg_nu5219082963157363817nc_rat: rat > rat ).

thf(func_def_587,type,
    neg_nu8295874005876285629c_real: real > real ).

thf(func_def_588,type,
    neg_numeral_sub_int: num > num > int ).

thf(func_def_589,type,
    bit0: num > num ).

thf(func_def_590,type,
    bit1: num > num ).

thf(func_def_591,type,
    one: num ).

thf(func_def_592,type,
    case_num_option_num: option_num > ( num > option_num ) > ( num > option_num ) > num > option_num ).

thf(func_def_593,type,
    size_num: num > nat ).

thf(func_def_594,type,
    num_of_nat: nat > num ).

thf(func_def_595,type,
    numera6620942414471956472nteger: num > code_integer ).

thf(func_def_596,type,
    numera6690914467698888265omplex: num > complex ).

thf(func_def_597,type,
    numera1916890842035813515d_enat: num > extended_enat ).

thf(func_def_598,type,
    numeral_numeral_int: num > int ).

thf(func_def_599,type,
    numeral_numeral_nat: num > nat ).

thf(func_def_600,type,
    numeral_numeral_rat: num > rat ).

thf(func_def_601,type,
    numeral_numeral_real: num > real ).

thf(func_def_602,type,
    pow: num > num > num ).

thf(func_def_603,type,
    pred_numeral: num > nat ).

thf(func_def_604,type,
    sqr: num > num ).

thf(func_def_605,type,
    none_nat: option_nat ).

thf(func_def_606,type,
    none_num: option_num ).

thf(func_def_607,type,
    none_P5556105721700978146at_nat: option4927543243414619207at_nat ).

thf(func_def_608,type,
    some_nat: nat > option_nat ).

thf(func_def_609,type,
    some_num: num > option_num ).

thf(func_def_610,type,
    some_P7363390416028606310at_nat: product_prod_nat_nat > option4927543243414619207at_nat ).

thf(func_def_611,type,
    case_o184042715313410164at_nat: $o > ( product_prod_nat_nat > $o ) > option4927543243414619207at_nat > $o ).

thf(func_def_612,type,
    case_option_int_num: int > ( num > int ) > option_num > int ).

thf(func_def_613,type,
    case_option_num_num: num > ( num > num ) > option_num > num ).

thf(func_def_614,type,
    case_o6005452278849405969um_num: option_num > ( num > option_num ) > option_num > option_num ).

thf(func_def_615,type,
    map_option_num_num: ( num > num ) > option_num > option_num ).

thf(func_def_616,type,
    size_option_nat: ( nat > nat ) > option_nat > nat ).

thf(func_def_617,type,
    size_option_num: ( num > nat ) > option_num > nat ).

thf(func_def_618,type,
    size_o8335143837870341156at_nat: ( product_prod_nat_nat > nat ) > option4927543243414619207at_nat > nat ).

thf(func_def_619,type,
    the_nat: option_nat > nat ).

thf(func_def_620,type,
    the_num: option_num > num ).

thf(func_def_621,type,
    the_Pr8591224930841456533at_nat: option4927543243414619207at_nat > product_prod_nat_nat ).

thf(func_def_622,type,
    order_underS_nat: set_Pr1261947904930325089at_nat > nat > set_nat ).

thf(func_def_623,type,
    bot_bo4199563552545308370d_enat: extended_enat ).

thf(func_def_624,type,
    bot_bot_nat: nat ).

thf(func_def_625,type,
    bot_bot_set_complex: set_complex ).

thf(func_def_626,type,
    bot_bot_set_int: set_int ).

thf(func_def_627,type,
    bot_bot_set_nat: set_nat ).

thf(func_def_628,type,
    bot_bot_set_num: set_num ).

thf(func_def_629,type,
    bot_bo2099793752762293965at_nat: set_Pr1261947904930325089at_nat ).

thf(func_def_630,type,
    bot_bot_set_rat: set_rat ).

thf(func_def_631,type,
    bot_bot_set_real: set_real ).

thf(func_def_632,type,
    bot_bot_set_set_nat: set_set_nat ).

thf(func_def_633,type,
    bot_bot_set_set_real: set_set_real ).

thf(func_def_634,type,
    bot_bo8194388402131092736T_VEBT: set_VEBT_VEBT ).

thf(func_def_635,type,
    ord_Least_nat: ( nat > $o ) > nat ).

thf(func_def_636,type,
    ord_Least_real: ( real > $o ) > real ).

thf(func_def_637,type,
    ord_le6747313008572928689nteger: code_integer > code_integer > $o ).

thf(func_def_638,type,
    ord_le72135733267957522d_enat: extended_enat > extended_enat > $o ).

thf(func_def_639,type,
    ord_less_int: int > int > $o ).

thf(func_def_640,type,
    ord_less_nat: nat > nat > $o ).

thf(func_def_641,type,
    ord_less_num: num > num > $o ).

thf(func_def_642,type,
    ord_less_rat: rat > rat > $o ).

thf(func_def_643,type,
    ord_less_real: real > real > $o ).

thf(func_def_644,type,
    ord_less_set_complex: set_complex > set_complex > $o ).

thf(func_def_645,type,
    ord_less_set_int: set_int > set_int > $o ).

thf(func_def_646,type,
    ord_less_set_nat: set_nat > set_nat > $o ).

thf(func_def_647,type,
    ord_less_set_num: set_num > set_num > $o ).

thf(func_def_648,type,
    ord_le7866589430770878221at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).

thf(func_def_649,type,
    ord_less_set_rat: set_rat > set_rat > $o ).

thf(func_def_650,type,
    ord_less_set_real: set_real > set_real > $o ).

thf(func_def_651,type,
    ord_less_set_set_nat: set_set_nat > set_set_nat > $o ).

thf(func_def_652,type,
    ord_le7926960851185191020t_real: set_set_real > set_set_real > $o ).

thf(func_def_653,type,
    ord_le3480810397992357184T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > $o ).

thf(func_def_654,type,
    ord_le3102999989581377725nteger: code_integer > code_integer > $o ).

thf(func_def_655,type,
    ord_le2932123472753598470d_enat: extended_enat > extended_enat > $o ).

thf(func_def_656,type,
    ord_le2510731241096832064er_nat: filter_nat > filter_nat > $o ).

thf(func_def_657,type,
    ord_less_eq_int: int > int > $o ).

thf(func_def_658,type,
    ord_less_eq_nat: nat > nat > $o ).

thf(func_def_659,type,
    ord_less_eq_num: num > num > $o ).

thf(func_def_660,type,
    ord_less_eq_rat: rat > rat > $o ).

thf(func_def_661,type,
    ord_less_eq_real: real > real > $o ).

thf(func_def_662,type,
    ord_less_eq_set_o: set_o > set_o > $o ).

thf(func_def_663,type,
    ord_le211207098394363844omplex: set_complex > set_complex > $o ).

thf(func_def_664,type,
    ord_less_eq_set_int: set_int > set_int > $o ).

thf(func_def_665,type,
    ord_less_eq_set_nat: set_nat > set_nat > $o ).

thf(func_def_666,type,
    ord_less_eq_set_num: set_num > set_num > $o ).

thf(func_def_667,type,
    ord_le3146513528884898305at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).

thf(func_def_668,type,
    ord_less_eq_set_real: set_real > set_real > $o ).

thf(func_def_669,type,
    ord_le6893508408891458716et_nat: set_set_nat > set_set_nat > $o ).

thf(func_def_670,type,
    ord_le3558479182127378552t_real: set_set_real > set_set_real > $o ).

thf(func_def_671,type,
    ord_le4337996190870823476T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > $o ).

thf(func_def_672,type,
    ord_max_Code_integer: code_integer > code_integer > code_integer ).

thf(func_def_673,type,
    ord_ma741700101516333627d_enat: extended_enat > extended_enat > extended_enat ).

thf(func_def_674,type,
    ord_max_int: int > int > int ).

thf(func_def_675,type,
    ord_max_nat: nat > nat > nat ).

thf(func_def_676,type,
    ord_max_num: num > num > num ).

thf(func_def_677,type,
    ord_max_rat: rat > rat > rat ).

thf(func_def_678,type,
    ord_max_real: real > real > real ).

thf(func_def_679,type,
    ord_max_set_nat: set_nat > set_nat > set_nat ).

thf(func_def_680,type,
    ord_max_set_real: set_real > set_real > set_real ).

thf(func_def_681,type,
    ord_mi8085742599997312461d_enat: extended_enat > extended_enat > extended_enat ).

thf(func_def_682,type,
    ord_min_nat: nat > nat > nat ).

thf(func_def_683,type,
    order_Greatest_nat: ( nat > $o ) > nat ).

thf(func_def_684,type,
    order_9091379641038594480t_real: ( nat > real ) > $o ).

thf(func_def_685,type,
    order_mono_nat_nat: ( nat > nat ) > $o ).

thf(func_def_686,type,
    order_mono_nat_real: ( nat > real ) > $o ).

thf(func_def_687,type,
    order_5726023648592871131at_nat: ( nat > nat ) > $o ).

thf(func_def_688,type,
    order_7092887310737990675l_real: ( real > real ) > $o ).

thf(func_def_689,type,
    ordering_top_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > nat > $o ).

thf(func_def_690,type,
    top_top_set_o: set_o ).

thf(func_def_691,type,
    top_top_set_nat: set_nat ).

thf(func_def_692,type,
    top_to1996260823553986621t_unit: set_Product_unit ).

thf(func_def_693,type,
    top_top_set_real: set_real ).

thf(func_def_694,type,
    top_top_set_char: set_char ).

thf(func_def_695,type,
    power_8256067586552552935nteger: code_integer > nat > code_integer ).

thf(func_def_696,type,
    power_power_complex: complex > nat > complex ).

thf(func_def_697,type,
    power_power_int: int > nat > int ).

thf(func_def_698,type,
    power_power_nat: nat > nat > nat ).

thf(func_def_699,type,
    power_power_rat: rat > nat > rat ).

thf(func_def_700,type,
    power_power_real: real > nat > real ).

thf(func_def_701,type,
    produc4035269172776083154on_nat: ( nat > nat > $o ) > produc4953844613479565601on_nat > produc2233624965454879586on_nat ).

thf(func_def_702,type,
    produc3209952032786966637at_nat: ( nat > nat > nat ) > produc7248412053542808358at_nat > produc4471711990508489141at_nat ).

thf(func_def_703,type,
    produc8929957630744042906on_nat: ( nat > nat > nat ) > produc4953844613479565601on_nat > produc8306885398267862888on_nat ).

thf(func_def_704,type,
    produc851828971589881931at_num: ( nat > num > num ) > produc2963631642982155120at_num > produc3368934014287244435at_num ).

thf(func_def_705,type,
    produc3576312749637752826on_num: ( num > num > $o ) > produc3447558737645232053on_num > produc7036089656553540234on_num ).

thf(func_def_706,type,
    produc5778274026573060048on_num: ( num > num > num ) > produc3447558737645232053on_num > produc1193250871479095198on_num ).

thf(func_def_707,type,
    produc3994169339658061776at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > produc6121120109295599847at_nat > produc5491161045314408544at_nat ).

thf(func_def_708,type,
    produc2899441246263362727at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > produc6121120109295599847at_nat > produc5542196010084753463at_nat ).

thf(func_def_709,type,
    product_Pair_o_o: $o > $o > product_prod_o_o ).

thf(func_def_710,type,
    product_Pair_o_int: $o > int > product_prod_o_int ).

thf(func_def_711,type,
    product_Pair_o_nat: $o > nat > product_prod_o_nat ).

thf(func_def_712,type,
    produc2982872950893828659T_VEBT: $o > vEBT_VEBT > produc2504756804600209347T_VEBT ).

thf(func_def_713,type,
    produc6677183202524767010eger_o: code_integer > $o > produc6271795597528267376eger_o ).

thf(func_def_714,type,
    produc1086072967326762835nteger: code_integer > code_integer > produc8923325533196201883nteger ).

thf(func_def_715,type,
    product_Pair_int_int: int > int > product_prod_int_int ).

thf(func_def_716,type,
    product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).

thf(func_def_717,type,
    product_Pair_nat_num: nat > num > product_prod_nat_num ).

thf(func_def_718,type,
    produc487386426758144856at_nat: nat > product_prod_nat_nat > produc7248412053542808358at_nat ).

thf(func_def_719,type,
    produc1195630363706982562at_num: nat > product_prod_nat_num > produc2963631642982155120at_num ).

thf(func_def_720,type,
    product_Pair_num_num: num > num > product_prod_num_num ).

thf(func_def_721,type,
    produc5098337634421038937on_nat: option_nat > option_nat > produc4953844613479565601on_nat ).

thf(func_def_722,type,
    produc8585076106096196333on_num: option_num > option_num > produc3447558737645232053on_num ).

thf(func_def_723,type,
    produc488173922507101015at_nat: option4927543243414619207at_nat > option4927543243414619207at_nat > produc6121120109295599847at_nat ).

thf(func_def_724,type,
    produc6161850002892822231at_nat: product_prod_nat_nat > product_prod_nat_nat > produc859450856879609959at_nat ).

thf(func_def_725,type,
    produc8721562602347293563VEBT_o: vEBT_VEBT > $o > produc334124729049499915VEBT_o ).

thf(func_def_726,type,
    produc736041933913180425BT_int: vEBT_VEBT > int > produc4894624898956917775BT_int ).

thf(func_def_727,type,
    produc738532404422230701BT_nat: vEBT_VEBT > nat > produc9072475918466114483BT_nat ).

thf(func_def_728,type,
    produc537772716801021591T_VEBT: vEBT_VEBT > vEBT_VEBT > produc8243902056947475879T_VEBT ).

thf(func_def_729,type,
    produc457027306803732586at_nat: set_nat > ( nat > set_nat ) > set_Pr1261947904930325089at_nat ).

thf(func_def_730,type,
    produc6499014454317279255nteger: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(func_def_731,type,
    produc1553301316500091796er_int: ( code_integer > code_integer > int ) > produc8923325533196201883nteger > int ).

thf(func_def_732,type,
    produc1555791787009142072er_nat: ( code_integer > code_integer > nat ) > produc8923325533196201883nteger > nat ).

thf(func_def_733,type,
    produc7336495610019696514er_num: ( code_integer > code_integer > num ) > produc8923325533196201883nteger > num ).

thf(func_def_734,type,
    produc9125791028180074456eger_o: ( code_integer > code_integer > produc6271795597528267376eger_o ) > produc8923325533196201883nteger > produc6271795597528267376eger_o ).

thf(func_def_735,type,
    produc6916734918728496179nteger: ( code_integer > code_integer > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(func_def_736,type,
    produc6771430404735790350plex_o: ( complex > complex > $o ) > produc4411394909380815293omplex > $o ).

thf(func_def_737,type,
    produc4947309494688390418_int_o: ( int > int > $o ) > product_prod_int_int > $o ).

thf(func_def_738,type,
    produc8211389475949308722nt_int: ( int > int > int ) > product_prod_int_int > int ).

thf(func_def_739,type,
    produc4245557441103728435nt_int: ( int > int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).

thf(func_def_740,type,
    produc8739625826339149834_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(func_def_741,type,
    produc27273713700761075at_nat: ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).

thf(func_def_742,type,
    produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).

thf(func_def_743,type,
    produc1917071388513777916omplex: ( nat > nat > complex ) > product_prod_nat_nat > complex ).

thf(func_def_744,type,
    produc6840382203811409530at_int: ( nat > nat > int ) > product_prod_nat_nat > int ).

thf(func_def_745,type,
    produc6842872674320459806at_nat: ( nat > nat > nat ) > product_prod_nat_nat > nat ).

thf(func_def_746,type,
    produc2626176000494625587at_nat: ( nat > nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).

thf(func_def_747,type,
    produc6207742614233964070at_rat: ( nat > nat > rat ) > product_prod_nat_nat > rat ).

thf(func_def_748,type,
    produc1703576794950452218t_real: ( nat > nat > real ) > product_prod_nat_nat > real ).

thf(func_def_749,type,
    produc3453488052772718514omplex: ( nat > nat > set_complex ) > product_prod_nat_nat > set_complex ).

thf(func_def_750,type,
    produc3668448655016342576t_real: ( nat > nat > set_real ) > product_prod_nat_nat > set_real ).

thf(func_def_751,type,
    produc4927758841916487424_num_o: ( nat > num > $o ) > product_prod_nat_num > $o ).

thf(func_def_752,type,
    produc478579273971653890on_num: ( nat > num > option_num ) > product_prod_nat_num > option_num ).

thf(func_def_753,type,
    produc6231982587499038204omplex: ( nat > num > set_complex ) > product_prod_nat_num > set_complex ).

thf(func_def_754,type,
    produc9175805072616146554et_int: ( nat > num > set_int ) > product_prod_nat_num > set_int ).

thf(func_def_755,type,
    produc4130284055270567454et_nat: ( nat > num > set_nat ) > product_prod_nat_num > set_nat ).

thf(func_def_756,type,
    produc1435849484188172666t_real: ( nat > num > set_real ) > product_prod_nat_num > set_real ).

thf(func_def_757,type,
    produc5703948589228662326_num_o: ( num > num > $o ) > product_prod_num_num > $o ).

thf(func_def_758,type,
    produc2866383454006189126omplex: ( num > num > set_complex ) > product_prod_num_num > set_complex ).

thf(func_def_759,type,
    produc6406642877701697732et_int: ( num > num > set_int ) > product_prod_num_num > set_int ).

thf(func_def_760,type,
    produc1361121860356118632et_nat: ( num > num > set_nat ) > product_prod_num_num > set_nat ).

thf(func_def_761,type,
    produc8296048397933160132t_real: ( num > num > set_real ) > product_prod_num_num > set_real ).

thf(func_def_762,type,
    produc6590410687421337004_nat_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > produc859450856879609959at_nat > $o ).

thf(func_def_763,type,
    produc5414030515140494994real_o: ( real > real > $o ) > produc2422161461964618553l_real > $o ).

thf(func_def_764,type,
    product_fst_int_int: product_prod_int_int > int ).

thf(func_def_765,type,
    product_fst_nat_nat: product_prod_nat_nat > nat ).

thf(func_def_766,type,
    product_snd_int_int: product_prod_int_int > int ).

thf(func_def_767,type,
    product_snd_nat_nat: product_prod_nat_nat > nat ).

thf(func_def_768,type,
    frct: product_prod_int_int > rat ).

thf(func_def_769,type,
    field_5140801741446780682s_real: set_real ).

thf(func_def_770,type,
    field_7254667332652039916t_real: rat > real ).

thf(func_def_771,type,
    normalize: product_prod_int_int > product_prod_int_int ).

thf(func_def_772,type,
    quotient_of: rat > product_prod_int_int ).

thf(func_def_773,type,
    real_V2521375963428798218omplex: set_complex ).

thf(func_def_774,type,
    real_V5970128139526366754l_real: ( real > real ) > $o ).

thf(func_def_775,type,
    real_V3694042436643373181omplex: complex > complex > real ).

thf(func_def_776,type,
    real_V975177566351809787t_real: real > real > real ).

thf(func_def_777,type,
    real_V1022390504157884413omplex: complex > real ).

thf(func_def_778,type,
    real_V7735802525324610683m_real: real > real ).

thf(func_def_779,type,
    real_V4546457046886955230omplex: real > complex ).

thf(func_def_780,type,
    real_V1803761363581548252l_real: real > real ).

thf(func_def_781,type,
    real_V2046097035970521341omplex: real > complex > complex ).

thf(func_def_782,type,
    real_V1485227260804924795R_real: real > real > real ).

thf(func_def_783,type,
    field_nat: set_Pr1261947904930325089at_nat > set_nat ).

thf(func_def_784,type,
    id_nat2: set_Pr1261947904930325089at_nat ).

thf(func_def_785,type,
    divide6298287555418463151nteger: code_integer > code_integer > code_integer ).

thf(func_def_786,type,
    divide1717551699836669952omplex: complex > complex > complex ).

thf(func_def_787,type,
    divide_divide_int: int > int > int ).

thf(func_def_788,type,
    divide_divide_nat: nat > nat > nat ).

thf(func_def_789,type,
    divide_divide_rat: rat > rat > rat ).

thf(func_def_790,type,
    divide_divide_real: real > real > real ).

thf(func_def_791,type,
    dvd_dvd_Code_integer: code_integer > code_integer > $o ).

thf(func_def_792,type,
    dvd_dvd_complex: complex > complex > $o ).

thf(func_def_793,type,
    dvd_dvd_int: int > int > $o ).

thf(func_def_794,type,
    dvd_dvd_nat: nat > nat > $o ).

thf(func_def_795,type,
    dvd_dvd_rat: rat > rat > $o ).

thf(func_def_796,type,
    dvd_dvd_real: real > real > $o ).

thf(func_def_797,type,
    modulo364778990260209775nteger: code_integer > code_integer > code_integer ).

thf(func_def_798,type,
    modulo_modulo_int: int > int > int ).

thf(func_def_799,type,
    modulo_modulo_nat: nat > nat > nat ).

thf(func_def_800,type,
    zero_n356916108424825756nteger: $o > code_integer ).

thf(func_def_801,type,
    zero_n1201886186963655149omplex: $o > complex ).

thf(func_def_802,type,
    zero_n2684676970156552555ol_int: $o > int ).

thf(func_def_803,type,
    zero_n2687167440665602831ol_nat: $o > nat ).

thf(func_def_804,type,
    zero_n2052037380579107095ol_rat: $o > rat ).

thf(func_def_805,type,
    zero_n3304061248610475627l_real: $o > real ).

thf(func_def_806,type,
    suminf_complex: ( nat > complex ) > complex ).

thf(func_def_807,type,
    suminf_int: ( nat > int ) > int ).

thf(func_def_808,type,
    suminf_nat: ( nat > nat ) > nat ).

thf(func_def_809,type,
    suminf_real: ( nat > real ) > real ).

thf(func_def_810,type,
    summable_complex: ( nat > complex ) > $o ).

thf(func_def_811,type,
    summable_int: ( nat > int ) > $o ).

thf(func_def_812,type,
    summable_nat: ( nat > nat ) > $o ).

thf(func_def_813,type,
    summable_real: ( nat > real ) > $o ).

thf(func_def_814,type,
    sums_complex: ( nat > complex ) > complex > $o ).

thf(func_def_815,type,
    sums_int: ( nat > int ) > int > $o ).

thf(func_def_816,type,
    sums_nat: ( nat > nat ) > nat > $o ).

thf(func_def_817,type,
    sums_real: ( nat > real ) > real > $o ).

thf(func_def_818,type,
    collect_complex: ( complex > $o ) > set_complex ).

thf(func_def_819,type,
    collect_int: ( int > $o ) > set_int ).

thf(func_def_820,type,
    collect_list_o: ( list_o > $o ) > set_list_o ).

thf(func_def_821,type,
    collect_list_complex: ( list_complex > $o ) > set_list_complex ).

thf(func_def_822,type,
    collect_list_int: ( list_int > $o ) > set_list_int ).

thf(func_def_823,type,
    collect_list_nat: ( list_nat > $o ) > set_list_nat ).

thf(func_def_824,type,
    collect_list_real: ( list_real > $o ) > set_list_real ).

thf(func_def_825,type,
    collec5608196760682091941T_VEBT: ( list_VEBT_VEBT > $o ) > set_list_VEBT_VEBT ).

thf(func_def_826,type,
    collect_nat: ( nat > $o ) > set_nat ).

thf(func_def_827,type,
    collect_num: ( num > $o ) > set_num ).

thf(func_def_828,type,
    collec8663557070575231912omplex: ( produc4411394909380815293omplex > $o ) > set_Pr5085853215250843933omplex ).

thf(func_def_829,type,
    collec3392354462482085612at_nat: ( product_prod_nat_nat > $o ) > set_Pr1261947904930325089at_nat ).

thf(func_def_830,type,
    collec3799799289383736868l_real: ( produc2422161461964618553l_real > $o ) > set_Pr6218003697084177305l_real ).

thf(func_def_831,type,
    collect_rat: ( rat > $o ) > set_rat ).

thf(func_def_832,type,
    collect_real: ( real > $o ) > set_real ).

thf(func_def_833,type,
    image_int_int: ( int > int ) > set_int > set_int ).

thf(func_def_834,type,
    image_nat_nat: ( nat > nat ) > set_nat > set_nat ).

thf(func_def_835,type,
    image_nat_real: ( nat > real ) > set_nat > set_real ).

thf(func_def_836,type,
    image_nat_char: ( nat > char ) > set_nat > set_char ).

thf(func_def_837,type,
    image_5971271580939081552omplex: ( real > filter6041513312241820739omplex ) > set_real > set_fi4554929511873752355omplex ).

thf(func_def_838,type,
    image_2178119161166701260l_real: ( real > filter2146258269922977983l_real ) > set_real > set_fi7789364187291644575l_real ).

thf(func_def_839,type,
    image_real_real: ( real > real ) > set_real > set_real ).

thf(func_def_840,type,
    image_char_nat: ( char > nat ) > set_char > set_nat ).

thf(func_def_841,type,
    image_VEBT_VEBT_nat: ( vEBT_VEBT > nat ) > set_VEBT_VEBT > set_nat ).

thf(func_def_842,type,
    insert_complex: complex > set_complex > set_complex ).

thf(func_def_843,type,
    insert_int: int > set_int > set_int ).

thf(func_def_844,type,
    insert_nat: nat > set_nat > set_nat ).

thf(func_def_845,type,
    insert_num: num > set_num > set_num ).

thf(func_def_846,type,
    insert8211810215607154385at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).

thf(func_def_847,type,
    insert_rat: rat > set_rat > set_rat ).

thf(func_def_848,type,
    insert_real: real > set_real > set_real ).

thf(func_def_849,type,
    insert_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > set_VEBT_VEBT ).

thf(func_def_850,type,
    vimage_nat_nat: ( nat > nat ) > set_nat > set_nat ).

thf(func_def_851,type,
    set_fo1517530859248394432omplex: ( nat > complex > complex ) > nat > nat > complex > complex ).

thf(func_def_852,type,
    set_fo2581907887559384638at_int: ( nat > int > int ) > nat > nat > int > int ).

thf(func_def_853,type,
    set_fo2584398358068434914at_nat: ( nat > nat > nat ) > nat > nat > nat > nat ).

thf(func_def_854,type,
    set_fo1949268297981939178at_rat: ( nat > rat > rat ) > nat > nat > rat > rat ).

thf(func_def_855,type,
    set_fo3111899725591712190t_real: ( nat > real > real ) > nat > nat > real > real ).

thf(func_def_856,type,
    set_or1266510415728281911st_int: int > int > set_int ).

thf(func_def_857,type,
    set_or1269000886237332187st_nat: nat > nat > set_nat ).

thf(func_def_858,type,
    set_or7049704709247886629st_num: num > num > set_num ).

thf(func_def_859,type,
    set_or633870826150836451st_rat: rat > rat > set_rat ).

thf(func_def_860,type,
    set_or1222579329274155063t_real: real > real > set_real ).

thf(func_def_861,type,
    set_or4548717258645045905et_nat: set_nat > set_nat > set_set_nat ).

thf(func_def_862,type,
    set_or7743017856606604397t_real: set_real > set_real > set_set_real ).

thf(func_def_863,type,
    set_or4662586982721622107an_int: int > int > set_int ).

thf(func_def_864,type,
    set_or4665077453230672383an_nat: nat > nat > set_nat ).

thf(func_def_865,type,
    set_ord_atLeast_nat: nat > set_nat ).

thf(func_def_866,type,
    set_ord_atLeast_real: real > set_real ).

thf(func_def_867,type,
    set_ord_atMost_nat: nat > set_nat ).

thf(func_def_868,type,
    set_or6656581121297822940st_int: int > int > set_int ).

thf(func_def_869,type,
    set_or6659071591806873216st_nat: nat > nat > set_nat ).

thf(func_def_870,type,
    set_or5832277885323065728an_int: int > int > set_int ).

thf(func_def_871,type,
    set_or5834768355832116004an_nat: nat > nat > set_nat ).

thf(func_def_872,type,
    set_or1633881224788618240n_real: real > real > set_real ).

thf(func_def_873,type,
    set_or1210151606488870762an_nat: nat > set_nat ).

thf(func_def_874,type,
    set_or5849166863359141190n_real: real > set_real ).

thf(func_def_875,type,
    set_ord_lessThan_int: int > set_int ).

thf(func_def_876,type,
    set_ord_lessThan_nat: nat > set_nat ).

thf(func_def_877,type,
    set_ord_lessThan_num: num > set_num ).

thf(func_def_878,type,
    set_ord_lessThan_rat: rat > set_rat ).

thf(func_def_879,type,
    set_or5984915006950818249n_real: real > set_real ).

thf(func_def_880,type,
    ascii_of: char > char ).

thf(func_def_881,type,
    char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).

thf(func_def_882,type,
    comm_s629917340098488124ar_nat: char > nat ).

thf(func_def_883,type,
    integer_of_char: char > code_integer ).

thf(func_def_884,type,
    unique3096191561947761185of_nat: nat > char ).

thf(func_def_885,type,
    topolo4422821103128117721l_real: filter_real > ( real > real ) > $o ).

thf(func_def_886,type,
    topolo5044208981011980120l_real: set_real > ( real > real ) > $o ).

thf(func_def_887,type,
    topolo4899668324122417113eq_int: ( nat > int ) > $o ).

thf(func_def_888,type,
    topolo4902158794631467389eq_nat: ( nat > nat ) > $o ).

thf(func_def_889,type,
    topolo1459490580787246023eq_num: ( nat > num ) > $o ).

thf(func_def_890,type,
    topolo6980174941875973593q_real: ( nat > real ) > $o ).

thf(func_def_891,type,
    topolo7278393974255667507et_nat: ( nat > set_nat ) > $o ).

thf(func_def_892,type,
    topolo2489691266198938127t_real: ( nat > set_real ) > $o ).

thf(func_def_893,type,
    topolo2177554685111907308n_real: real > set_real > filter_real ).

thf(func_def_894,type,
    topolo7531315842566124627t_real: ( nat > real ) > $o ).

thf(func_def_895,type,
    topolo2815343760600316023s_real: real > filter_real ).

thf(func_def_896,type,
    topolo4055970368930404560y_real: ( nat > real ) > $o ).

thf(func_def_897,type,
    topolo896644834953643431omplex: filter6041513312241820739omplex ).

thf(func_def_898,type,
    topolo1511823702728130853y_real: filter2146258269922977983l_real ).

thf(func_def_899,type,
    arccos: real > real ).

thf(func_def_900,type,
    arcosh_real: real > real ).

thf(func_def_901,type,
    arcsin: real > real ).

thf(func_def_902,type,
    arctan: real > real ).

thf(func_def_903,type,
    arsinh_real: real > real ).

thf(func_def_904,type,
    artanh_real: real > real ).

thf(func_def_905,type,
    cos_complex: complex > complex ).

thf(func_def_906,type,
    cos_real: real > real ).

thf(func_def_907,type,
    cos_coeff: nat > real ).

thf(func_def_908,type,
    cosh_real: real > real ).

thf(func_def_909,type,
    cot_real: real > real ).

thf(func_def_910,type,
    diffs_complex: ( nat > complex ) > nat > complex ).

thf(func_def_911,type,
    diffs_int: ( nat > int ) > nat > int ).

thf(func_def_912,type,
    diffs_real: ( nat > real ) > nat > real ).

thf(func_def_913,type,
    exp_complex: complex > complex ).

thf(func_def_914,type,
    exp_real: real > real ).

thf(func_def_915,type,
    ln_ln_real: real > real ).

thf(func_def_916,type,
    log: real > real > real ).

thf(func_def_917,type,
    pi: real ).

thf(func_def_918,type,
    powr_real: real > real > real ).

thf(func_def_919,type,
    sin_complex: complex > complex ).

thf(func_def_920,type,
    sin_real: real > real ).

thf(func_def_921,type,
    sin_coeff: nat > real ).

thf(func_def_922,type,
    sinh_real: real > real ).

thf(func_def_923,type,
    tan_complex: complex > complex ).

thf(func_def_924,type,
    tan_real: real > real ).

thf(func_def_925,type,
    tanh_complex: complex > complex ).

thf(func_def_926,type,
    tanh_real: real > real ).

thf(func_def_927,type,
    transi2905341329935302413cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).

thf(func_def_928,type,
    transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).

thf(func_def_929,type,
    vEBT_T_i_n_s_e_r_t: vEBT_VEBT > nat > nat ).

thf(func_def_930,type,
    vEBT_T_i_n_s_e_r_t2: vEBT_VEBT > nat > nat ).

thf(func_def_931,type,
    vEBT_T5076183648494686801_t_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_932,type,
    vEBT_T9217963907923527482_t_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_933,type,
    vEBT_T_m_a_x_t: vEBT_VEBT > nat ).

thf(func_def_934,type,
    vEBT_T_m_a_x_t_rel: vEBT_VEBT > vEBT_VEBT > $o ).

thf(func_def_935,type,
    vEBT_T_m_e_m_b_e_r: vEBT_VEBT > nat > nat ).

thf(func_def_936,type,
    vEBT_T_m_e_m_b_e_r2: vEBT_VEBT > nat > nat ).

thf(func_def_937,type,
    vEBT_T8099345112685741742_r_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_938,type,
    vEBT_T5837161174952499735_r_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_939,type,
    vEBT_T_m_i_n_N_u_l_l: vEBT_VEBT > nat ).

thf(func_def_940,type,
    vEBT_T5462971552011256508_l_rel: vEBT_VEBT > vEBT_VEBT > $o ).

thf(func_def_941,type,
    vEBT_T_m_i_n_t: vEBT_VEBT > nat ).

thf(func_def_942,type,
    vEBT_T_m_i_n_t_rel: vEBT_VEBT > vEBT_VEBT > $o ).

thf(func_def_943,type,
    vEBT_T_p_r_e_d: vEBT_VEBT > nat > nat ).

thf(func_def_944,type,
    vEBT_T_p_r_e_d2: vEBT_VEBT > nat > nat ).

thf(func_def_945,type,
    vEBT_T_p_r_e_d_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_946,type,
    vEBT_T_p_r_e_d_rel2: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_947,type,
    vEBT_T_s_u_c_c: vEBT_VEBT > nat > nat ).

thf(func_def_948,type,
    vEBT_T_s_u_c_c2: vEBT_VEBT > nat > nat ).

thf(func_def_949,type,
    vEBT_T_s_u_c_c_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_950,type,
    vEBT_T_s_u_c_c_rel2: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_951,type,
    vEBT_Leaf: $o > $o > vEBT_VEBT ).

thf(func_def_952,type,
    vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_953,type,
    vEBT_size_VEBT: vEBT_VEBT > nat ).

thf(func_def_954,type,
    vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).

thf(func_def_955,type,
    vEBT_VEBT_high: nat > nat > nat ).

thf(func_def_956,type,
    vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).

thf(func_def_957,type,
    vEBT_VEBT_low: nat > nat > nat ).

thf(func_def_958,type,
    vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).

thf(func_def_959,type,
    vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_960,type,
    vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).

thf(func_def_961,type,
    vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_962,type,
    vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).

thf(func_def_963,type,
    vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_964,type,
    vEBT_invar_vebt: vEBT_VEBT > nat > $o ).

thf(func_def_965,type,
    vEBT_set_vebt: vEBT_VEBT > set_nat ).

thf(func_def_966,type,
    vEBT_vebt_buildup: nat > vEBT_VEBT ).

thf(func_def_967,type,
    vEBT_v4011308405150292612up_rel: nat > nat > $o ).

thf(func_def_968,type,
    vEBT_T_d_e_l_e_t_e: vEBT_VEBT > nat > nat ).

thf(func_def_969,type,
    vEBT_T8441311223069195367_e_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_970,type,
    vEBT_vebt_delete: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_971,type,
    vEBT_vebt_delete_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_972,type,
    vEBT_VEBT_height: vEBT_VEBT > nat ).

thf(func_def_973,type,
    vEBT_VEBT_height_rel: vEBT_VEBT > vEBT_VEBT > $o ).

thf(func_def_974,type,
    vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_975,type,
    vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_976,type,
    vEBT_VEBT_bit_concat: nat > nat > nat > nat ).

thf(func_def_977,type,
    vEBT_VEBT_minNull: vEBT_VEBT > $o ).

thf(func_def_978,type,
    vEBT_V6963167321098673237ll_rel: vEBT_VEBT > vEBT_VEBT > $o ).

thf(func_def_979,type,
    vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).

thf(func_def_980,type,
    vEBT_vebt_member: vEBT_VEBT > nat > $o ).

thf(func_def_981,type,
    vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_982,type,
    vEBT_VEBT_add: option_nat > option_nat > option_nat ).

thf(func_def_983,type,
    vEBT_VEBT_greater: option_nat > option_nat > $o ).

thf(func_def_984,type,
    vEBT_VEBT_less: option_nat > option_nat > $o ).

thf(func_def_985,type,
    vEBT_VEBT_lesseq: option_nat > option_nat > $o ).

thf(func_def_986,type,
    vEBT_VEBT_max_in_set: set_nat > nat > $o ).

thf(func_def_987,type,
    vEBT_VEBT_min_in_set: set_nat > nat > $o ).

thf(func_def_988,type,
    vEBT_VEBT_mul: option_nat > option_nat > option_nat ).

thf(func_def_989,type,
    vEBT_V4262088993061758097ft_nat: ( nat > nat > nat ) > option_nat > option_nat > option_nat ).

thf(func_def_990,type,
    vEBT_V819420779217536731ft_num: ( num > num > num ) > option_num > option_num > option_num ).

thf(func_def_991,type,
    vEBT_V1502963449132264192at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > option4927543243414619207at_nat > option4927543243414619207at_nat > option4927543243414619207at_nat ).

thf(func_def_992,type,
    vEBT_VEBT_power: option_nat > option_nat > option_nat ).

thf(func_def_993,type,
    vEBT_vebt_maxt: vEBT_VEBT > option_nat ).

thf(func_def_994,type,
    vEBT_vebt_maxt_rel: vEBT_VEBT > vEBT_VEBT > $o ).

thf(func_def_995,type,
    vEBT_vebt_mint: vEBT_VEBT > option_nat ).

thf(func_def_996,type,
    vEBT_vebt_mint_rel: vEBT_VEBT > vEBT_VEBT > $o ).

thf(func_def_997,type,
    vEBT_is_pred_in_set: set_nat > nat > nat > $o ).

thf(func_def_998,type,
    vEBT_vebt_pred: vEBT_VEBT > nat > option_nat ).

thf(func_def_999,type,
    vEBT_vebt_pred_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_1000,type,
    vEBT_is_succ_in_set: set_nat > nat > nat > $o ).

thf(func_def_1001,type,
    vEBT_vebt_succ: vEBT_VEBT > nat > option_nat ).

thf(func_def_1002,type,
    vEBT_vebt_succ_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_1003,type,
    accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).

thf(func_def_1004,type,
    accp_nat: ( nat > nat > $o ) > nat > $o ).

thf(func_def_1005,type,
    accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).

thf(func_def_1006,type,
    accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).

thf(func_def_1007,type,
    accp_P3113834385874906142um_num: ( product_prod_num_num > product_prod_num_num > $o ) > product_prod_num_num > $o ).

thf(func_def_1008,type,
    accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).

thf(func_def_1009,type,
    accp_VEBT_VEBT: ( vEBT_VEBT > vEBT_VEBT > $o ) > vEBT_VEBT > $o ).

thf(func_def_1010,type,
    pred_nat: set_Pr1261947904930325089at_nat ).

thf(func_def_1011,type,
    wf_nat: set_Pr1261947904930325089at_nat > $o ).

thf(func_def_1012,type,
    fChoice_real: ( real > $o ) > real ).

thf(func_def_1013,type,
    member_o: $o > set_o > $o ).

thf(func_def_1014,type,
    member_complex: complex > set_complex > $o ).

thf(func_def_1015,type,
    member_int: int > set_int > $o ).

thf(func_def_1016,type,
    member_list_o: list_o > set_list_o > $o ).

thf(func_def_1017,type,
    member_list_int: list_int > set_list_int > $o ).

thf(func_def_1018,type,
    member_list_nat: list_nat > set_list_nat > $o ).

thf(func_def_1019,type,
    member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o ).

thf(func_def_1020,type,
    member_nat: nat > set_nat > $o ).

thf(func_def_1021,type,
    member_num: num > set_num > $o ).

thf(func_def_1022,type,
    member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).

thf(func_def_1023,type,
    member8206827879206165904at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > $o ).

thf(func_def_1024,type,
    member_rat: rat > set_rat > $o ).

thf(func_def_1025,type,
    member_real: real > set_real > $o ).

thf(func_def_1026,type,
    member_set_nat: set_nat > set_set_nat > $o ).

thf(func_def_1027,type,
    member_set_real: set_real > set_set_real > $o ).

thf(func_def_1028,type,
    member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).

thf(func_def_1029,type,
    deg: nat ).

thf(func_def_1030,type,
    m: nat ).

thf(func_def_1031,type,
    ma: nat ).

thf(func_def_1032,type,
    mi: nat ).

thf(func_def_1033,type,
    na: nat ).

thf(func_def_1034,type,
    summary: vEBT_VEBT ).

thf(func_def_1035,type,
    treeList: list_VEBT_VEBT ).

thf(func_def_1036,type,
    xa: nat ).

thf(func_def_1061,type,
    ph1: 
      !>[X0: $tType] : X0 ).

thf(func_def_1062,type,
    sK2: rat > rat ).

thf(func_def_1063,type,
    sK3: real > real ).

thf(func_def_1064,type,
    sK4: rat > rat ).

thf(func_def_1065,type,
    sK5: real > real ).

thf(func_def_1066,type,
    sK6: real > nat ).

thf(func_def_1067,type,
    sK7: int ).

thf(func_def_1068,type,
    sK8: int ).

thf(func_def_1069,type,
    sK9: int ).

thf(func_def_1070,type,
    sK10: int ).

thf(func_def_1071,type,
    sK11: int ).

thf(func_def_1072,type,
    sK12: nat > list_VEBT_VEBT ).

thf(func_def_1073,type,
    sK13: nat ).

thf(func_def_1074,type,
    sK14: nat ).

thf(func_def_1075,type,
    sK15: nat ).

thf(func_def_1076,type,
    sK16: nat ).

thf(func_def_1077,type,
    sK17: nat ).

thf(func_def_1078,type,
    sK18: nat ).

thf(func_def_1079,type,
    sK19: nat ).

thf(func_def_1080,type,
    sK20: nat ).

thf(func_def_1081,type,
    sK21: real ).

thf(func_def_1082,type,
    sK22: real ).

thf(func_def_1083,type,
    sK23: real ).

thf(func_def_1084,type,
    sK24: real ).

thf(func_def_1085,type,
    sK25: real ).

thf(func_def_1086,type,
    sK26: real ).

thf(func_def_1087,type,
    sK27: vEBT_VEBT > nat ).

thf(func_def_1088,type,
    sK28: nat > nat ).

thf(func_def_1089,type,
    sK29: nat > nat ).

thf(func_def_1090,type,
    sK30: int > int ).

thf(func_def_1091,type,
    sK31: int > int ).

thf(func_def_1092,type,
    sK32: real > real ).

thf(func_def_1093,type,
    sK33: nat > nat ).

thf(func_def_1094,type,
    sK34: nat ).

thf(func_def_1095,type,
    sK35: nat ).

thf(func_def_1096,type,
    sK36: real > real ).

thf(f37304,plain,
    $false,
    inference(subsumption_resolution,[status(thm)],[f37303,f36976]) ).

thf(f36976,plain,
    ( ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ summary ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) @ ( numeral_numeral_nat @ one ) )
   != ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ mi ) ),
    inference(forward_demodulation,[status(thm)],[f36975,f36213]) ).

thf(f36213,plain,
    ! [X2: nat,X1: nat] :
      ( ( plus_plus_nat @ X1 @ X2 )
      = ( plus_plus_nat @ X2 @ X1 ) ),
    inference(beta_eta_normalization,[status(thm)],[f36209]) ).

thf(f36209,plain,
    ! [X2: nat,X1: nat] :
      ( ( ^ [Y0: nat] : ( plus_plus_nat @ Y0 @ X1 )
        @ X2 )
      = ( plus_plus_nat @ X1 @ X2 ) ),
    inference(argument_congruence,[status(thm)],[f36208]) ).

thf(f36208,plain,
    ! [X1: nat] :
      ( ( plus_plus_nat @ X1 )
      = ( ^ [Y0: nat] : ( plus_plus_nat @ Y0 @ X1 ) ) ),
    inference(beta_eta_normalization,[status(thm)],[f36207]) ).

thf(f36207,plain,
    ! [X1: nat] :
      ( ( plus_plus_nat @ X1 )
      = ( ^ [Y0: nat,Y1: nat] : ( plus_plus_nat @ Y1 @ Y0 )
        @ X1 ) ),
    inference(argument_congruence,[status(thm)],[f30366]) ).

thf(f30366,plain,
    ( plus_plus_nat
    = ( ^ [Y0: nat,Y1: nat] : ( plus_plus_nat @ Y1 @ Y0 ) ) ),
    inference(cnf_transformation,[status(thm)],[f15701]) ).

thf(f15701,plain,
    ( plus_plus_nat
    = ( ^ [Y0: nat,Y1: nat] : ( plus_plus_nat @ Y1 @ Y0 ) ) ),
    inference(fool_elimination,[status(thm)],[f15700]) ).

thf(f15700,plain,
    ( plus_plus_nat
    = ( ^ [X0: nat,X1: nat] : ( plus_plus_nat @ X1 @ X0 ) ) ),
    inference(rectify,[status(thm)],[f1291]) ).

thf(f1291,axiom,
    ( plus_plus_nat
    = ( ^ [X93: nat,X118: nat] : ( plus_plus_nat @ X118 @ X93 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.T5XVM49IAI/DTF2THF_21656.p',fact_1290_add_Ocommute) ).

thf(f36975,plain,
    ( ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ summary ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) @ ( numeral_numeral_nat @ one ) )
   != ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ mi ) ),
    inference(backward_demodulation,[status(thm)],[f36249,f36971]) ).

thf(f36971,plain,
    ! [X1: num] :
      ( ( plus_plus_nat @ ( numeral_numeral_nat @ X1 ) @ ( numeral_numeral_nat @ X1 ) )
      = ( numeral_numeral_nat @ ( bit0 @ X1 ) ) ),
    inference(equality_proxy_clausification,[status(thm)],[f36970]) ).

thf(f36970,plain,
    ! [X1: num] :
      ( $true
      = ( ( numeral_numeral_nat @ ( bit0 @ X1 ) )
        = ( plus_plus_nat @ ( numeral_numeral_nat @ X1 ) @ ( numeral_numeral_nat @ X1 ) ) ) ),
    inference(beta_eta_normalization,[status(thm)],[f36969]) ).

thf(f36969,plain,
    ! [X1: num] :
      ( ( ^ [Y0: num] :
            ( ( numeral_numeral_nat @ ( bit0 @ Y0 ) )
            = ( plus_plus_nat @ ( numeral_numeral_nat @ Y0 ) @ ( numeral_numeral_nat @ Y0 ) ) )
        @ X1 )
      = $true ),
    inference(pi_clausification,[status(thm)],[f30340]) ).

thf(f30340,plain,
    ( ( !! @ num
      @ ^ [Y0: num] :
          ( ( numeral_numeral_nat @ ( bit0 @ Y0 ) )
          = ( plus_plus_nat @ ( numeral_numeral_nat @ Y0 ) @ ( numeral_numeral_nat @ Y0 ) ) ) )
    = $true ),
    inference(cnf_transformation,[status(thm)],[f19285]) ).

thf(f19285,plain,
    ( ( !! @ num
      @ ^ [Y0: num] :
          ( ( numeral_numeral_nat @ ( bit0 @ Y0 ) )
          = ( plus_plus_nat @ ( numeral_numeral_nat @ Y0 ) @ ( numeral_numeral_nat @ Y0 ) ) ) )
    = $true ),
    inference(fool_elimination,[status(thm)],[f19284]) ).

thf(f19284,plain,
    ! [X0: num] :
      ( ( numeral_numeral_nat @ ( bit0 @ X0 ) )
      = ( plus_plus_nat @ ( numeral_numeral_nat @ X0 ) @ ( numeral_numeral_nat @ X0 ) ) ),
    inference(rectify,[status(thm)],[f1547]) ).

thf(f1547,axiom,
    ! [X2: num] :
      ( ( numeral_numeral_nat @ ( bit0 @ X2 ) )
      = ( plus_plus_nat @ ( numeral_numeral_nat @ X2 ) @ ( numeral_numeral_nat @ X2 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.T5XVM49IAI/DTF2THF_21656.p',fact_1546_numeral__code_I2_J) ).

thf(f36249,plain,
    ( ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ summary ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ) ) ) ) @ ( numeral_numeral_nat @ one ) )
   != ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ mi ) ),
    inference(forward_demodulation,[status(thm)],[f36248,f36213]) ).

thf(f36248,plain,
    ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ mi )
   != ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ summary ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) @ ( numeral_numeral_nat @ one ) ) ),
    inference(forward_demodulation,[status(thm)],[f36247,f36213]) ).

thf(f36247,plain,
    ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ mi )
   != ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_t @ summary ) ) ) ) ) @ ( numeral_numeral_nat @ one ) ) ),
    inference(forward_demodulation,[status(thm)],[f36246,f36213]) ).

thf(f36246,plain,
    ( ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_t @ summary ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) ) @ ( numeral_numeral_nat @ one ) )
   != ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ mi ) ),
    inference(forward_demodulation,[status(thm)],[f36222,f36213]) ).

thf(f36222,plain,
    ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ mi )
   != ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_t @ summary ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) ) @ ( numeral_numeral_nat @ one ) ) ),
    inference(backward_demodulation,[status(thm)],[f36124,f36213]) ).

thf(f36124,plain,
    ( ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_t @ summary ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ ( numeral_numeral_nat @ one ) ) @ ( numeral_numeral_nat @ one ) )
   != ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ mi ) ),
    inference(equality_proxy_clausification,[status(thm)],[f36123]) ).

thf(f36123,plain,
    ( ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ mi )
      = ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_t @ summary ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ ( numeral_numeral_nat @ one ) ) @ ( numeral_numeral_nat @ one ) ) )
    = $false ),
    inference(not_proxy_clausification,[status(thm)],[f33948]) ).

thf(f33948,plain,
    ( $true
    = ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ mi )
     != ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_t @ summary ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ ( numeral_numeral_nat @ one ) ) @ ( numeral_numeral_nat @ one ) ) ) ),
    inference(definition_unfolding,[status(thm)],[f31669,f30958,f30783,f30783]) ).

thf(f30783,plain,
    ( one_one_nat
    = ( numeral_numeral_nat @ one ) ),
    inference(cnf_transformation,[status(thm)],[f28081]) ).

thf(f28081,plain,
    ( one_one_nat
    = ( numeral_numeral_nat @ one ) ),
    inference(fool_elimination,[status(thm)],[f206]) ).

thf(f206,axiom,
    ( one_one_nat
    = ( numeral_numeral_nat @ one ) ),
    file('/export/starexec/sandbox2/tmp/tmp.T5XVM49IAI/DTF2THF_21656.p',fact_205_numerals_I1_J) ).

thf(f30958,plain,
    xa = mi,
    inference(cnf_transformation,[status(thm)],[f27728]) ).

thf(f27728,plain,
    xa = mi,
    inference(fool_elimination,[status(thm)],[f1]) ).

thf(f1,axiom,
    xa = mi,
    file('/export/starexec/sandbox2/tmp/tmp.T5XVM49IAI/DTF2THF_21656.p',fact_0_True) ).

thf(f31669,plain,
    ( $true
    = ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
     != ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_t @ summary ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat ) @ one_one_nat ) ) ),
    inference(cnf_transformation,[status(thm)],[f17484]) ).

thf(f17484,plain,
    ( $true
    = ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
     != ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_t @ summary ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat ) @ one_one_nat ) ) ),
    inference(fool_elimination,[status(thm)],[f10255]) ).

thf(f10255,negated_conjecture,
    ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
   != ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_t @ summary ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat ) @ one_one_nat ) ),
    inference(negated_conjecture,[status(cth)],[f10254]) ).

thf(f10254,conjecture,
    ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
    = ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_t @ summary ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat ) @ one_one_nat ) ),
    file('/export/starexec/sandbox2/tmp/tmp.T5XVM49IAI/DTF2THF_21656.p',conj_0) ).

thf(f37303,plain,
    ( ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ summary ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) @ ( numeral_numeral_nat @ one ) )
    = ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ mi ) ),
    inference(backward_demodulation,[status(thm)],[f36978,f37302]) ).

thf(f37302,plain,
    ! [X2: nat,X1: nat] :
      ( ( if_nat @ $false @ X1 @ X2 )
      = X2 ),
    inference(equality_proxy_clausification,[status(thm)],[f37301]) ).

thf(f37301,plain,
    ! [X2: nat,X1: nat] :
      ( $true
      = ( ( if_nat @ $false @ X1 @ X2 )
        = X2 ) ),
    inference(beta_eta_normalization,[status(thm)],[f37300]) ).

thf(f37300,plain,
    ! [X2: nat,X1: nat] :
      ( $true
      = ( ^ [Y0: nat] :
            ( ( if_nat @ $false @ X1 @ Y0 )
            = Y0 )
        @ X2 ) ),
    inference(pi_clausification,[status(thm)],[f37297]) ).

thf(f37297,plain,
    ! [X1: nat] :
      ( ( !! @ nat
        @ ^ [Y0: nat] :
            ( ( if_nat @ $false @ X1 @ Y0 )
            = Y0 ) )
      = $true ),
    inference(beta_eta_normalization,[status(thm)],[f37296]) ).

thf(f37296,plain,
    ! [X1: nat] :
      ( $true
      = ( ^ [Y0: nat] :
            ( !! @ nat
            @ ^ [Y1: nat] :
                ( ( if_nat @ $false @ Y0 @ Y1 )
                = Y1 ) )
        @ X1 ) ),
    inference(pi_clausification,[status(thm)],[f29963]) ).

thf(f29963,plain,
    ( ( !! @ nat
      @ ^ [Y0: nat] :
          ( !! @ nat
          @ ^ [Y1: nat] :
              ( ( if_nat @ $false @ Y0 @ Y1 )
              = Y1 ) ) )
    = $true ),
    inference(cnf_transformation,[status(thm)],[f24490]) ).

thf(f24490,plain,
    ( ( !! @ nat
      @ ^ [Y0: nat] :
          ( !! @ nat
          @ ^ [Y1: nat] :
              ( ( if_nat @ $false @ Y0 @ Y1 )
              = Y1 ) ) )
    = $true ),
    inference(fool_elimination,[status(thm)],[f24489]) ).

thf(f24489,plain,
    ! [X0: nat,X1: nat] :
      ( ( if_nat @ $false @ X1 @ X0 )
      = X0 ),
    inference(rectify,[status(thm)],[f10214]) ).

thf(f10214,axiom,
    ! [X20: nat,X12: nat] :
      ( ( if_nat @ $false @ X12 @ X20 )
      = X20 ),
    file('/export/starexec/sandbox2/tmp/tmp.T5XVM49IAI/DTF2THF_21656.p',help_If_2_1_If_001t__Nat__Onat_T) ).

thf(f36978,plain,
    ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ mi )
    = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ summary ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) )
      @ ( if_nat @ $false
        @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
          @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) )
            @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
              @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( vEBT_T_d_e_l_e_t_e @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
                  @ ( if_nat
                    @ ( ma
                      = ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
                    @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
                      @ ( plus_plus_nat @ ( numeral_numeral_nat @ one )
                        @ ( if_nat
                          @ ( none_nat
                            = ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
                          @ ( numeral_numeral_nat @ one )
                          @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
                    @ ( numeral_numeral_nat @ one ) ) ) )
              @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
                @ ( if_nat
                  @ ( ma
                    = ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
                  @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
                  @ ( numeral_numeral_nat @ one ) ) ) ) ) )
        @ ( numeral_numeral_nat @ one ) ) ) ),
    inference(forward_demodulation,[status(thm)],[f36974,f36213]) ).

thf(f36974,plain,
    ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ mi )
    = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ summary ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) )
      @ ( if_nat @ $false
        @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
          @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) )
            @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
              @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( vEBT_T_d_e_l_e_t_e @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
                  @ ( if_nat
                    @ ( ma
                      = ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
                    @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
                      @ ( plus_plus_nat @ ( numeral_numeral_nat @ one )
                        @ ( if_nat
                          @ ( none_nat
                            = ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
                          @ ( numeral_numeral_nat @ one )
                          @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
                    @ ( numeral_numeral_nat @ one ) ) ) )
              @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
                @ ( if_nat
                  @ ( ma
                    = ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
                  @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
                  @ ( numeral_numeral_nat @ one ) ) ) ) ) )
        @ ( numeral_numeral_nat @ one ) ) ) ),
    inference(backward_demodulation,[status(thm)],[f36390,f36971]) ).

thf(f36390,plain,
    ( ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ summary ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ) ) ) )
      @ ( if_nat @ $false
        @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
          @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) )
            @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
              @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( vEBT_T_d_e_l_e_t_e @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
                  @ ( if_nat
                    @ ( ma
                      = ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
                    @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
                      @ ( plus_plus_nat @ ( numeral_numeral_nat @ one )
                        @ ( if_nat
                          @ ( none_nat
                            = ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
                          @ ( numeral_numeral_nat @ one )
                          @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
                    @ ( numeral_numeral_nat @ one ) ) ) )
              @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
                @ ( if_nat
                  @ ( ma
                    = ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
                  @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
                  @ ( numeral_numeral_nat @ one ) ) ) ) ) )
        @ ( numeral_numeral_nat @ one ) ) )
    = ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ mi ) ),
    inference(backward_demodulation,[status(thm)],[f36237,f36385]) ).

thf(f36385,plain,
    ! [X2: nat,X1: nat] :
      ( ( times_times_nat @ X1 @ X2 )
      = ( times_times_nat @ X2 @ X1 ) ),
    inference(beta_eta_normalization,[status(thm)],[f36379]) ).

thf(f36379,plain,
    ! [X2: nat,X1: nat] :
      ( ( ^ [Y0: nat] : ( times_times_nat @ Y0 @ X1 )
        @ X2 )
      = ( times_times_nat @ X1 @ X2 ) ),
    inference(argument_congruence,[status(thm)],[f36287]) ).

thf(f36287,plain,
    ! [X1: nat] :
      ( ( times_times_nat @ X1 )
      = ( ^ [Y0: nat] : ( times_times_nat @ Y0 @ X1 ) ) ),
    inference(beta_eta_normalization,[status(thm)],[f36284]) ).

thf(f36284,plain,
    ! [X1: nat] :
      ( ( times_times_nat @ X1 )
      = ( ^ [Y0: nat,Y1: nat] : ( times_times_nat @ Y1 @ Y0 )
        @ X1 ) ),
    inference(argument_congruence,[status(thm)],[f31577]) ).

thf(f31577,plain,
    ( times_times_nat
    = ( ^ [Y0: nat,Y1: nat] : ( times_times_nat @ Y1 @ Y0 ) ) ),
    inference(cnf_transformation,[status(thm)],[f15240]) ).

thf(f15240,plain,
    ( times_times_nat
    = ( ^ [Y0: nat,Y1: nat] : ( times_times_nat @ Y1 @ Y0 ) ) ),
    inference(fool_elimination,[status(thm)],[f15239]) ).

thf(f15239,plain,
    ( ( ^ [X0: nat,X1: nat] : ( times_times_nat @ X1 @ X0 ) )
    = times_times_nat ),
    inference(rectify,[status(thm)],[f1242]) ).

thf(f1242,axiom,
    ( ( ^ [X93: nat,X118: nat] : ( times_times_nat @ X118 @ X93 ) )
    = times_times_nat ),
    file('/export/starexec/sandbox2/tmp/tmp.T5XVM49IAI/DTF2THF_21656.p',fact_1241_mult_Ocommute) ).

thf(f36237,plain,
    ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ mi )
    = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ summary ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ) ) ) )
      @ ( if_nat @ $false
        @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
          @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
            @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
              @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( vEBT_T_d_e_l_e_t_e @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
                  @ ( if_nat
                    @ ( ma
                      = ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
                    @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
                      @ ( plus_plus_nat @ ( numeral_numeral_nat @ one )
                        @ ( if_nat
                          @ ( none_nat
                            = ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
                          @ ( numeral_numeral_nat @ one )
                          @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
                    @ ( numeral_numeral_nat @ one ) ) ) )
              @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
                @ ( if_nat
                  @ ( ma
                    = ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
                  @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
                  @ ( numeral_numeral_nat @ one ) ) ) ) ) )
        @ ( numeral_numeral_nat @ one ) ) ) ),
    inference(forward_demodulation,[status(thm)],[f36236,f36213]) ).

thf(f36236,plain,
    ( ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ summary ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ) ) ) )
      @ ( if_nat @ $false
        @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
          @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
            @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
              @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( vEBT_T_d_e_l_e_t_e @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
                  @ ( if_nat
                    @ ( ma
                      = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) )
                    @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
                      @ ( plus_plus_nat @ ( numeral_numeral_nat @ one )
                        @ ( if_nat
                          @ ( none_nat
                            = ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
                          @ ( numeral_numeral_nat @ one )
                          @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
                    @ ( numeral_numeral_nat @ one ) ) ) )
              @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
                @ ( if_nat
                  @ ( ma
                    = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) )
                  @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
                  @ ( numeral_numeral_nat @ one ) ) ) ) ) )
        @ ( numeral_numeral_nat @ one ) ) )
    = ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ mi ) ),
    inference(forward_demodulation,[status(thm)],[f36235,f36213]) ).

thf(f36235,plain,
    ( ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ summary ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) )
      @ ( if_nat @ $false
        @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
          @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
            @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
              @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( vEBT_T_d_e_l_e_t_e @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
                  @ ( if_nat
                    @ ( ma
                      = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) )
                    @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
                      @ ( plus_plus_nat @ ( numeral_numeral_nat @ one )
                        @ ( if_nat
                          @ ( none_nat
                            = ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
                          @ ( numeral_numeral_nat @ one )
                          @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
                    @ ( numeral_numeral_nat @ one ) ) ) )
              @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
                @ ( if_nat
                  @ ( ma
                    = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) )
                  @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
                  @ ( numeral_numeral_nat @ one ) ) ) ) ) )
        @ ( numeral_numeral_nat @ one ) ) )
    = ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ mi ) ),
    inference(forward_demodulation,[status(thm)],[f36234,f36213]) ).

thf(f36234,plain,
    ( ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_t @ summary ) ) ) ) )
      @ ( if_nat @ $false
        @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
          @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
            @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
              @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( vEBT_T_d_e_l_e_t_e @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
                  @ ( if_nat
                    @ ( ma
                      = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) )
                    @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
                      @ ( plus_plus_nat @ ( numeral_numeral_nat @ one )
                        @ ( if_nat
                          @ ( none_nat
                            = ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
                          @ ( numeral_numeral_nat @ one )
                          @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
                    @ ( numeral_numeral_nat @ one ) ) ) )
              @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
                @ ( if_nat
                  @ ( ma
                    = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) )
                  @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
                  @ ( numeral_numeral_nat @ one ) ) ) ) ) )
        @ ( numeral_numeral_nat @ one ) ) )
    = ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ mi ) ),
    inference(forward_demodulation,[status(thm)],[f36233,f36213]) ).

thf(f36233,plain,
    ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ mi )
    = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_t @ summary ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) )
      @ ( if_nat @ $false
        @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
          @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
            @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
              @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( vEBT_T_d_e_l_e_t_e @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
                  @ ( if_nat
                    @ ( ma
                      = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) )
                    @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
                      @ ( plus_plus_nat @ ( numeral_numeral_nat @ one )
                        @ ( if_nat
                          @ ( none_nat
                            = ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
                          @ ( numeral_numeral_nat @ one )
                          @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
                    @ ( numeral_numeral_nat @ one ) ) ) )
              @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
                @ ( if_nat
                  @ ( ma
                    = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) )
                  @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
                  @ ( numeral_numeral_nat @ one ) ) ) ) ) )
        @ ( numeral_numeral_nat @ one ) ) ) ),
    inference(forward_demodulation,[status(thm)],[f36223,f36213]) ).

thf(f36223,plain,
    ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ mi )
    = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_t @ summary ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) )
      @ ( if_nat @ $false
        @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
          @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
            @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
              @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( vEBT_T_d_e_l_e_t_e @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
                  @ ( if_nat
                    @ ( ma
                      = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) )
                    @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
                      @ ( plus_plus_nat @ ( numeral_numeral_nat @ one )
                        @ ( if_nat
                          @ ( none_nat
                            = ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
                          @ ( numeral_numeral_nat @ one )
                          @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
                    @ ( numeral_numeral_nat @ one ) ) ) )
              @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
                @ ( if_nat
                  @ ( ma
                    = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) )
                  @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
                  @ ( numeral_numeral_nat @ one ) ) ) ) ) )
        @ ( numeral_numeral_nat @ one ) ) ) ),
    inference(backward_demodulation,[status(thm)],[f36069,f36213]) ).

thf(f36069,plain,
    ( ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_t @ summary ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ ( numeral_numeral_nat @ one ) )
      @ ( if_nat @ $false
        @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
          @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
            @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
              @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( vEBT_T_d_e_l_e_t_e @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
                  @ ( if_nat
                    @ ( ma
                      = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) )
                    @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
                      @ ( plus_plus_nat @ ( numeral_numeral_nat @ one )
                        @ ( if_nat
                          @ ( none_nat
                            = ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
                          @ ( numeral_numeral_nat @ one )
                          @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
                    @ ( numeral_numeral_nat @ one ) ) ) )
              @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
                @ ( if_nat
                  @ ( ma
                    = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) )
                  @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
                  @ ( numeral_numeral_nat @ one ) ) ) ) ) )
        @ ( numeral_numeral_nat @ one ) ) )
    = ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ mi ) ),
    inference(forward_demodulation,[status(thm)],[f35323,f36015]) ).

thf(f36015,plain,
    ( ( ord_less_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( numeral_numeral_nat @ one ) ) ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ ( size_s6755466524823107622T_VEBT @ treeList ) ) @ ( numeral_numeral_real @ one ) ) )
    = $false ),
    inference(not_proxy_clausification,[status(thm)],[f35757]) ).

thf(f35757,plain,
    ( ( ~ ( ord_less_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( numeral_numeral_nat @ one ) ) ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ ( size_s6755466524823107622T_VEBT @ treeList ) ) @ ( numeral_numeral_real @ one ) ) ) )
    = $true ),
    inference(beta_eta_normalization,[status(thm)],[f33566]) ).

thf(f33566,plain,
    ( $true
    = ( ~ ( ^ [Y0: nat] :
              ( ^ [Y1: nat,Y2: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ Y1 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ Y2 ) @ ( numeral_numeral_real @ one ) ) )
              @ ( plus_plus_nat @ Y0 @ ( numeral_numeral_nat @ one ) ) )
          @ ( ^ [Y0: nat,Y1: nat] : ( divide_divide_nat @ Y0 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y1 ) )
            @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) )
            @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
          @ ( size_s6755466524823107622T_VEBT @ treeList ) ) ) ),
    inference(definition_unfolding,[status(thm)],[f31231,f32416,f30037]) ).

thf(f30037,plain,
    ( vEBT_VEBT_high
    = ( ^ [Y0: nat,Y1: nat] : ( divide_divide_nat @ Y0 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y1 ) ) ) ),
    inference(cnf_transformation,[status(thm)],[f29609]) ).

thf(f29609,plain,
    ( vEBT_VEBT_high
    = ( ^ [Y0: nat,Y1: nat] : ( divide_divide_nat @ Y0 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y1 ) ) ) ),
    inference(fool_elimination,[status(thm)],[f29608]) ).

thf(f29608,plain,
    ( vEBT_VEBT_high
    = ( ^ [X0: nat,X1: nat] : ( divide_divide_nat @ X0 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X1 ) ) ) ),
    inference(rectify,[status(thm)],[f35]) ).

thf(f35,axiom,
    ( vEBT_VEBT_high
    = ( ^ [X13: nat,X14: nat] : ( divide_divide_nat @ X13 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X14 ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.T5XVM49IAI/DTF2THF_21656.p',fact_34_high__def) ).

thf(f32416,plain,
    ( ord_less_nat
    = ( ^ [Y0: nat] :
          ( ^ [Y1: nat,Y2: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ Y1 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ Y2 ) @ ( numeral_numeral_real @ one ) ) )
          @ ( plus_plus_nat @ Y0 @ ( numeral_numeral_nat @ one ) ) ) ) ),
    inference(definition_unfolding,[status(thm)],[f29859,f32415,f30783]) ).

thf(f32415,plain,
    ( ord_less_eq_nat
    = ( ^ [Y0: nat,Y1: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ Y0 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ Y1 ) @ ( numeral_numeral_real @ one ) ) ) ) ),
    inference(definition_unfolding,[status(thm)],[f30830,f30031]) ).

thf(f30031,plain,
    ( one_one_real
    = ( numeral_numeral_real @ one ) ),
    inference(cnf_transformation,[status(thm)],[f21614]) ).

thf(f21614,plain,
    ( one_one_real
    = ( numeral_numeral_real @ one ) ),
    inference(fool_elimination,[status(thm)],[f201]) ).

thf(f201,axiom,
    ( one_one_real
    = ( numeral_numeral_real @ one ) ),
    file('/export/starexec/sandbox2/tmp/tmp.T5XVM49IAI/DTF2THF_21656.p',fact_200_numeral__One) ).

thf(f30830,plain,
    ( ord_less_eq_nat
    = ( ^ [Y0: nat,Y1: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ Y0 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ Y1 ) @ one_one_real ) ) ) ),
    inference(cnf_transformation,[status(thm)],[f27880]) ).

thf(f27880,plain,
    ( ord_less_eq_nat
    = ( ^ [Y0: nat,Y1: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ Y0 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ Y1 ) @ one_one_real ) ) ) ),
    inference(fool_elimination,[status(thm)],[f27879]) ).

thf(f27879,plain,
    ( ord_less_eq_nat
    = ( ^ [X0: nat,X1: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ X0 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ X1 ) @ one_one_real ) ) ) ),
    inference(rectify,[status(thm)],[f7407]) ).

thf(f7407,axiom,
    ( ord_less_eq_nat
    = ( ^ [X14: nat,X73: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ X14 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ X73 ) @ one_one_real ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.T5XVM49IAI/DTF2THF_21656.p',fact_7406_nat__le__real__less) ).

thf(f29859,plain,
    ( ord_less_nat
    = ( ^ [Y0: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y0 @ one_one_nat ) ) ) ),
    inference(cnf_transformation,[status(thm)],[f16609]) ).

thf(f16609,plain,
    ( ord_less_nat
    = ( ^ [Y0: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y0 @ one_one_nat ) ) ) ),
    inference(fool_elimination,[status(thm)],[f16608]) ).

thf(f16608,plain,
    ( ord_less_nat
    = ( ^ [X0: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X0 @ one_one_nat ) ) ) ),
    inference(rectify,[status(thm)],[f625]) ).

thf(f625,axiom,
    ( ord_less_nat
    = ( ^ [X93: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X93 @ one_one_nat ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.T5XVM49IAI/DTF2THF_21656.p',fact_624_discrete) ).

thf(f31231,plain,
    ( ( ~ ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) ) )
    = $true ),
    inference(cnf_transformation,[status(thm)],[f24835]) ).

thf(f24835,plain,
    ( ( ~ ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) ) )
    = $true ),
    inference(fool_elimination,[status(thm)],[f24834]) ).

thf(f24834,plain,
    ~ ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) ),
    inference(rectify,[status(thm)],[f5]) ).

thf(f5,axiom,
    ~ ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) ),
    file('/export/starexec/sandbox2/tmp/tmp.T5XVM49IAI/DTF2THF_21656.p',fact_4_False) ).

thf(f35323,plain,
    ( ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_t @ summary ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ ( numeral_numeral_nat @ one ) )
      @ ( if_nat @ ( ord_less_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( numeral_numeral_nat @ one ) ) ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ ( size_s6755466524823107622T_VEBT @ treeList ) ) @ ( numeral_numeral_real @ one ) ) )
        @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
          @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
            @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
              @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( vEBT_T_d_e_l_e_t_e @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
                  @ ( if_nat
                    @ ( ma
                      = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) )
                    @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ one ) @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
                      @ ( plus_plus_nat @ ( numeral_numeral_nat @ one )
                        @ ( if_nat
                          @ ( none_nat
                            = ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
                          @ ( numeral_numeral_nat @ one )
                          @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
                    @ ( numeral_numeral_nat @ one ) ) ) )
              @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
                @ ( if_nat
                  @ ( ma
                    = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) )
                  @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( times_times_nat @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
                  @ ( numeral_numeral_nat @ one ) ) ) ) ) )
        @ ( numeral_numeral_nat @ one ) ) )
    = ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ mi ) ),
    inference(beta_eta_normalization,[status(thm)],[f33334]) ).

thf(f33334,plain,
    ( ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_t @ summary ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ ( numeral_numeral_nat @ one ) )
      @ ( if_nat
        @ ( ^ [Y0: nat] :
              ( ^ [Y1: nat,Y2: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ Y1 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ Y2 ) @ ( numeral_numeral_real @ one ) ) )
              @ ( plus_plus_nat @ Y0 @ ( numeral_numeral_nat @ one ) ) )
          @ ( ^ [Y0: nat,Y1: nat] : ( divide_divide_nat @ Y0 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y1 ) )
            @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) )
            @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
          @ ( size_s6755466524823107622T_VEBT @ treeList ) )
        @ ( plus_plus_nat
          @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) )
            @ ( vEBT_T_d_e_l_e_t_e
              @ ( nth_VEBT_VEBT @ treeList
                @ ( ^ [Y0: nat,Y1: nat] : ( divide_divide_nat @ Y0 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y1 ) )
                  @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) )
                  @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
              @ ( ^ [Y0: nat,Y1: nat] :
                    ( ^ [Y2: nat,Y3: nat] : ( minus_minus_nat @ Y2 @ ( times_times_nat @ ( divide_divide_nat @ Y2 @ Y3 ) @ Y3 ) )
                    @ Y0
                    @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y1 ) )
                @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) )
                @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
          @ ( plus_plus_nat
            @ ( plus_plus_nat @ ( numeral_numeral_nat @ one )
              @ ( vEBT_T_m_i_n_N_u_l_l
                @ ( vEBT_vebt_delete
                  @ ( nth_VEBT_VEBT @ treeList
                    @ ( ^ [Y0: nat,Y1: nat] : ( divide_divide_nat @ Y0 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y1 ) )
                      @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) )
                      @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
                  @ ( ^ [Y0: nat,Y1: nat] :
                        ( ^ [Y2: nat,Y3: nat] : ( minus_minus_nat @ Y2 @ ( times_times_nat @ ( divide_divide_nat @ Y2 @ Y3 ) @ Y3 ) )
                        @ Y0
                        @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y1 ) )
                    @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) )
                    @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
            @ ( if_nat
              @ ( vEBT_VEBT_minNull
                @ ( vEBT_vebt_delete
                  @ ( nth_VEBT_VEBT @ treeList
                    @ ( ^ [Y0: nat,Y1: nat] : ( divide_divide_nat @ Y0 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y1 ) )
                      @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) )
                      @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
                  @ ( ^ [Y0: nat,Y1: nat] :
                        ( ^ [Y2: nat,Y3: nat] : ( minus_minus_nat @ Y2 @ ( times_times_nat @ ( divide_divide_nat @ Y2 @ Y3 ) @ Y3 ) )
                        @ Y0
                        @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y1 ) )
                    @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) )
                    @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
              @ ( plus_plus_nat
                @ ( plus_plus_nat @ ( numeral_numeral_nat @ one )
                  @ ( vEBT_T_d_e_l_e_t_e @ summary
                    @ ( ^ [Y0: nat,Y1: nat] : ( divide_divide_nat @ Y0 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y1 ) )
                      @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) )
                      @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
                  @ ( if_nat
                    @ ( ma
                      = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) )
                    @ ( plus_plus_nat
                      @ ( plus_plus_nat @ ( numeral_numeral_nat @ one )
                        @ ( vEBT_T_m_a_x_t
                          @ ( vEBT_vebt_delete @ summary
                            @ ( ^ [Y0: nat,Y1: nat] : ( divide_divide_nat @ Y0 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y1 ) )
                              @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) )
                              @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
                      @ ( plus_plus_nat @ ( numeral_numeral_nat @ one )
                        @ ( if_nat
                          @ ( none_nat
                            = ( vEBT_vebt_maxt
                              @ ( vEBT_vebt_delete @ summary
                                @ ( ^ [Y0: nat,Y1: nat] : ( divide_divide_nat @ Y0 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y1 ) )
                                  @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) )
                                  @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
                          @ ( numeral_numeral_nat @ one )
                          @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) )
                            @ ( vEBT_T_m_a_x_t
                              @ ( nth_VEBT_VEBT
                                @ ( list_u1324408373059187874T_VEBT @ treeList
                                  @ ( ^ [Y0: nat,Y1: nat] : ( divide_divide_nat @ Y0 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y1 ) )
                                    @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) )
                                    @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
                                  @ ( vEBT_vebt_delete
                                    @ ( nth_VEBT_VEBT @ treeList
                                      @ ( ^ [Y0: nat,Y1: nat] : ( divide_divide_nat @ Y0 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y1 ) )
                                        @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) )
                                        @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
                                    @ ( ^ [Y0: nat,Y1: nat] :
                                          ( ^ [Y2: nat,Y3: nat] : ( minus_minus_nat @ Y2 @ ( times_times_nat @ ( divide_divide_nat @ Y2 @ Y3 ) @ Y3 ) )
                                          @ Y0
                                          @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y1 ) )
                                      @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) )
                                      @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
                                @ ( the_nat
                                  @ ( vEBT_vebt_maxt
                                    @ ( vEBT_vebt_delete @ summary
                                      @ ( ^ [Y0: nat,Y1: nat] : ( divide_divide_nat @ Y0 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y1 ) )
                                        @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) )
                                        @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
                    @ ( numeral_numeral_nat @ one ) ) ) )
              @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
                @ ( if_nat
                  @ ( ma
                    = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) )
                  @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) )
                    @ ( vEBT_T_m_a_x_t
                      @ ( nth_VEBT_VEBT
                        @ ( list_u1324408373059187874T_VEBT @ treeList
                          @ ( ^ [Y0: nat,Y1: nat] : ( divide_divide_nat @ Y0 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y1 ) )
                            @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) )
                            @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
                          @ ( vEBT_vebt_delete
                            @ ( nth_VEBT_VEBT @ treeList
                              @ ( ^ [Y0: nat,Y1: nat] : ( divide_divide_nat @ Y0 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y1 ) )
                                @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) )
                                @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
                            @ ( ^ [Y0: nat,Y1: nat] :
                                  ( ^ [Y2: nat,Y3: nat] : ( minus_minus_nat @ Y2 @ ( times_times_nat @ ( divide_divide_nat @ Y2 @ Y3 ) @ Y3 ) )
                                  @ Y0
                                  @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y1 ) )
                              @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) )
                              @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
                        @ ( ^ [Y0: nat,Y1: nat] : ( divide_divide_nat @ Y0 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y1 ) )
                          @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) )
                          @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
                  @ ( numeral_numeral_nat @ one ) ) ) ) ) )
        @ ( numeral_numeral_nat @ one ) ) )
    = ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ mi ) ),
    inference(definition_unfolding,[status(thm)],[f30946,f30958,f30783,f32416,f30037,f30037,f32420,f30783,f30037,f32420,f30037,f32420,f30783,f30037,f30783,f30037,f30783,f30037,f30783,f30037,f30037,f32420,f30037,f30783,f30037,f30037,f32420,f30037,f30783,f30783]) ).

thf(f32420,plain,
    ( vEBT_VEBT_low
    = ( ^ [Y0: nat,Y1: nat] :
          ( ^ [Y2: nat,Y3: nat] : ( minus_minus_nat @ Y2 @ ( times_times_nat @ ( divide_divide_nat @ Y2 @ Y3 ) @ Y3 ) )
          @ Y0
          @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y1 ) ) ) ),
    inference(definition_unfolding,[status(thm)],[f31018,f30425]) ).

thf(f30425,plain,
    ( modulo_modulo_nat
    = ( ^ [Y0: nat,Y1: nat] : ( minus_minus_nat @ Y0 @ ( times_times_nat @ ( divide_divide_nat @ Y0 @ Y1 ) @ Y1 ) ) ) ),
    inference(cnf_transformation,[status(thm)],[f29241]) ).

thf(f29241,plain,
    ( modulo_modulo_nat
    = ( ^ [Y0: nat,Y1: nat] : ( minus_minus_nat @ Y0 @ ( times_times_nat @ ( divide_divide_nat @ Y0 @ Y1 ) @ Y1 ) ) ) ),
    inference(fool_elimination,[status(thm)],[f29240]) ).

thf(f29240,plain,
    ( modulo_modulo_nat
    = ( ^ [X0: nat,X1: nat] : ( minus_minus_nat @ X0 @ ( times_times_nat @ ( divide_divide_nat @ X0 @ X1 ) @ X1 ) ) ) ),
    inference(rectify,[status(thm)],[f3655]) ).

thf(f3655,axiom,
    ( modulo_modulo_nat
    = ( ^ [X73: nat,X14: nat] : ( minus_minus_nat @ X73 @ ( times_times_nat @ ( divide_divide_nat @ X73 @ X14 ) @ X14 ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.T5XVM49IAI/DTF2THF_21656.p',fact_3654_modulo__nat__def) ).

thf(f31018,plain,
    ( vEBT_VEBT_low
    = ( ^ [Y0: nat,Y1: nat] : ( modulo_modulo_nat @ Y0 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y1 ) ) ) ),
    inference(cnf_transformation,[status(thm)],[f18603]) ).

thf(f18603,plain,
    ( vEBT_VEBT_low
    = ( ^ [Y0: nat,Y1: nat] : ( modulo_modulo_nat @ Y0 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y1 ) ) ) ),
    inference(fool_elimination,[status(thm)],[f18602]) ).

thf(f18602,plain,
    ( ( ^ [X0: nat,X1: nat] : ( modulo_modulo_nat @ X0 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X1 ) ) )
    = vEBT_VEBT_low ),
    inference(rectify,[status(thm)],[f3448]) ).

thf(f3448,axiom,
    ( ( ^ [X13: nat,X14: nat] : ( modulo_modulo_nat @ X13 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X14 ) ) )
    = vEBT_VEBT_low ),
    file('/export/starexec/sandbox2/tmp/tmp.T5XVM49IAI/DTF2THF_21656.p',fact_3447_low__def) ).

thf(f30946,plain,
    ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
    = ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_t @ summary ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat )
      @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) )
        @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
          @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
            @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
              @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_d_e_l_e_t_e @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
                  @ ( if_nat
                    @ ( ma
                      = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) )
                    @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
                      @ ( plus_plus_nat @ one_one_nat
                        @ ( if_nat
                          @ ( none_nat
                            = ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
                          @ one_one_nat
                          @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
                    @ one_one_nat ) ) )
              @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
                @ ( if_nat
                  @ ( ma
                    = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) )
                  @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
                  @ one_one_nat ) ) ) ) )
        @ one_one_nat ) ) ),
    inference(cnf_transformation,[status(thm)],[f19767]) ).

thf(f19767,plain,
    ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
    = ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_t @ summary ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat )
      @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) )
        @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
          @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
            @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
              @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_d_e_l_e_t_e @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
                  @ ( if_nat
                    @ ( ma
                      = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) )
                    @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
                      @ ( plus_plus_nat @ one_one_nat
                        @ ( if_nat
                          @ ( none_nat
                            = ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
                          @ one_one_nat
                          @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
                    @ one_one_nat ) ) )
              @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
                @ ( if_nat
                  @ ( ma
                    = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) )
                  @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
                  @ one_one_nat ) ) ) ) )
        @ one_one_nat ) ) ),
    inference(fool_elimination,[status(thm)],[f1572]) ).

thf(f1572,axiom,
    ( ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_t @ summary ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat )
      @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) )
        @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
          @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
            @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
              @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_d_e_l_e_t_e @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
                  @ ( if_nat
                    @ ( ma
                      = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) )
                    @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
                      @ ( plus_plus_nat @ one_one_nat
                        @ ( if_nat
                          @ ( none_nat
                            = ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
                          @ one_one_nat
                          @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
                    @ one_one_nat ) ) )
              @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
                @ ( if_nat
                  @ ( ma
                    = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) )
                  @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
                  @ one_one_nat ) ) ) ) )
        @ one_one_nat ) )
    = ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa ) ),
    file('/export/starexec/sandbox2/tmp/tmp.T5XVM49IAI/DTF2THF_21656.p',fact_1571__C3_C) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ITP271^3 : TPTP v9.2.1. Bugfixed v9.2.1.
% 0.13/0.14  % Command  : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.35  % Computer : n001.cluster.edu
% 0.17/0.35  % Model    : x86_64 x86_64
% 0.17/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35  % Memory   : 8042.1875MB
% 0.17/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35  % CPULimit : 300
% 0.17/0.35  % WCLimit  : 300
% 0.17/0.35  % DateTime : Fri Feb 27 11:07:20 EST 2026
% 0.17/0.35  % CPUTime  : 
% 0.17/0.35  Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.48  ---- Original DTF file ---
% 0.29/0.48  thf(spec,logic,$$dhol).
% 0.29/0.48  %------------------------------------------------------------------------------
% 0.29/0.48  % File     : ITP271^3 : TPTP v9.2.1. Bugfixed v9.2.1.
% 0.29/0.48  % Domain   : Interactive Theorem Proving
% 0.29/0.48  % Problem  : Sledgehammer problem VEBT_DeleteBounds 00599_037420
% 0.29/0.48  % Version  : [Des22] axioms.
% 0.29/0.48  % English  :
% 0.29/0.48  
% 0.29/0.48  % Refs     : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.29/0.48  %          : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 0.29/0.48  % Source   : [Des22]
% 0.29/0.48  % Names    : 0074_VEBT_DeleteBounds_00599_037420 [Des22]
% 0.29/0.48  
% 0.29/0.48  % Status   : Theorem
% 0.29/0.48  % Rating   : ? v9.2.1
% 0.29/0.48  % Syntax   : Number of formulae    : 11291 (5760 unt;1037 typ;   0 def)
% 0.29/0.48  %            Number of atoms       : 29342 (13266 equ;   0 cnn)
% 0.29/0.48  %            Maximal formula atoms :   71 (   2 avg)
% 0.29/0.48  %            Number of connectives : 133906 (2961   ~; 473   |;1908   &;116900   @)
% 0.29/0.48  %                                         (   0 <=>;11664  =>;   0  <=;   0 <~>)
% 0.29/0.48  %            Maximal formula depth :   39 (   6 avg)
% 0.29/0.48  %            Number of types       :   93 (  92 usr)
% 0.29/0.48  %            Number of type conns  : 4290 (4290   >;   0   *;   0   +;   0  <<)
% 0.29/0.48  %            Number of symbols     :  948 ( 945 usr;  63 con; 0-8 aty)
% 0.29/0.48  %            Number of variables   : 26656 (1747   ^;24029   !; 880   ?;26656   :)
% 0.29/0.48  % SPC      : TH0_THM_EQU_NAR
% 0.29/0.48  
% 0.29/0.48  % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.29/0.48  %            from the van Emde Boas Trees session in the Archive of Formal
% 0.29/0.48  %            proofs - 
% 0.29/0.48  %            www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 0.29/0.48  %            2022-02-18 12:46:42.717
% 0.29/0.48  % Bugfixes : Added ()s around negated sides of equations.
% 0.29/0.48  %------------------------------------------------------------------------------
% 0.29/0.48  % Could-be-implicit typings (92)
% 0.29/0.48  thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 0.29/0.48      produc5542196010084753463at_nat: $tType ).
% 0.29/0.48  
% 0.29/0.48  thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 0.29/0.48      produc5491161045314408544at_nat: $tType ).
% 0.29/0.48  
% 0.29/0.48  thf(ty_n_t__Product____Type__Oprod_I_062_It__Num__Onum_M_062_It__Num__Onum_Mt__Num__Onum_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Num__Onum_J_Mt__Option__Ooption_It__Num__Onum_J_J_J,type,
% 0.29/0.48      produc1193250871479095198on_num: $tType ).
% 0.29/0.48  
% 0.29/0.48  thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Nat__Onat_J_Mt__Option__Ooption_It__Nat__Onat_J_J_J,type,
% 0.29/0.48      produc8306885398267862888on_nat: $tType ).
% 0.29/0.48  
% 0.29/0.48  thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 0.29/0.48      produc6121120109295599847at_nat: $tType ).
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% 0.29/0.48  thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_M_062_It__Num__Onum_Mt__Num__Onum_J_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J_J_J,type,
% 0.29/0.48      produc3368934014287244435at_num: $tType ).
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% 0.29/0.48  thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 0.29/0.48      produc4471711990508489141at_nat: $tType ).
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% 0.29/0.48  thf(ty_n_t__Product____Type__Oprod_I_062_It__Num__Onum_M_062_It__Num__Onum_M_Eo_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Num__Onum_J_Mt__Option__Ooption_It__Num__Onum_J_J_J,type,
% 0.29/0.48      produc7036089656553540234on_num: $tType ).
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% 0.29/0.48  thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Nat__Onat_J_Mt__Option__Ooption_It__Nat__Onat_J_J_J,type,
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% 0.29/0.48  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
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% 0.29/0.48  thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.29/0.48      produc859450856879609959at_nat: $tType ).
% 0.29/0.48  
% 0.29/0.48  thf(ty_n_t__Set__Oset_It__Filter__Ofilter_It__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J_J_J,type,
% 0.29/0.48      set_fi4554929511873752355omplex: $tType ).
% 0.29/0.48  
% 0.29/0.48  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 0.29/0.48      list_P7413028617227757229T_VEBT: $tType ).
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% 0.29/0.48  thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J_J,type,
% 0.29/0.48      produc2963631642982155120at_num: $tType ).
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% 0.29/0.48  thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
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% 0.29/0.48  
% 0.29/0.48  thf(ty_n_t__Set__Oset_It__Filter__Ofilter_It__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_J_J,type,
% 0.29/0.48      set_fi7789364187291644575l_real: $tType ).
% 0.29/0.48  
% 0.29/0.48  thf(ty_n_t__Filter__Ofilter_It__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J_J,type,
% 0.29/0.48      filter6041513312241820739omplex: $tType ).
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% 0.29/0.49      replicate_complex: nat > complex > list_complex ).
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% 0.29/0.49      suc: nat > nat ).
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% 0.29/0.49  
% 0.29/0.49  thf(sy_c_Transcendental_Oarcosh_001t__Real__Oreal,type,
% 0.29/0.49      arcosh_real: real > real ).
% 0.29/0.49  
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% 0.29/0.49  
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% 0.29/0.49      arctan: real > real ).
% 0.29/0.49  
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% 0.29/0.49  
% 0.29/0.49  thf(sy_c_Transcendental_Oartanh_001t__Real__Oreal,type,
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% 0.29/0.49  
% 0.29/0.49  thf(sy_c_Transcendental_Ocos_001t__Complex__Ocomplex,type,
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% 0.29/0.49  
% 0.29/0.49  thf(sy_c_Transcendental_Ocos_001t__Real__Oreal,type,
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% 0.29/0.49      cos_coeff: nat > real ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_Transcendental_Ocosh_001t__Real__Oreal,type,
% 0.29/0.49      cosh_real: real > real ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_Transcendental_Ocot_001t__Real__Oreal,type,
% 0.29/0.49      cot_real: real > real ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_Transcendental_Odiffs_001t__Complex__Ocomplex,type,
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% 0.29/0.49  thf(sy_c_Transcendental_Odiffs_001t__Int__Oint,type,
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% 0.29/0.49  thf(sy_c_Transcendental_Oexp_001t__Complex__Ocomplex,type,
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% 0.29/0.49  
% 0.29/0.49  thf(sy_c_Transcendental_Oexp_001t__Real__Oreal,type,
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% 0.29/0.49  
% 0.29/0.49  thf(sy_c_Transcendental_Oln__class_Oln_001t__Real__Oreal,type,
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% 0.29/0.49  thf(sy_c_Transcendental_Olog,type,
% 0.29/0.49      log: real > real > real ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_Transcendental_Opi,type,
% 0.29/0.49      pi: real ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_Transcendental_Opowr_001t__Real__Oreal,type,
% 0.29/0.49      powr_real: real > real > real ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_Transcendental_Osin_001t__Complex__Ocomplex,type,
% 0.29/0.49      sin_complex: complex > complex ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_Transcendental_Osin_001t__Real__Oreal,type,
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% 0.29/0.49  
% 0.29/0.49  thf(sy_c_Transcendental_Osinh_001t__Real__Oreal,type,
% 0.29/0.49      sinh_real: real > real ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_Transcendental_Otan_001t__Complex__Ocomplex,type,
% 0.29/0.49      tan_complex: complex > complex ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_Transcendental_Otan_001t__Real__Oreal,type,
% 0.29/0.49      tan_real: real > real ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_Transcendental_Otanh_001t__Complex__Ocomplex,type,
% 0.29/0.49      tanh_complex: complex > complex ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_Transcendental_Otanh_001t__Real__Oreal,type,
% 0.29/0.49      tanh_real: real > real ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_Transitive__Closure_Ortrancl_001t__Nat__Onat,type,
% 0.29/0.49      transi2905341329935302413cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_Transitive__Closure_Otrancl_001t__Nat__Onat,type,
% 0.29/0.49      transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
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% 0.29/0.49  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t,type,
% 0.29/0.49      vEBT_T_i_n_s_e_r_t: vEBT_VEBT > nat > nat ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H,type,
% 0.29/0.49      vEBT_T_i_n_s_e_r_t2: vEBT_VEBT > nat > nat ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H__rel,type,
% 0.29/0.49      vEBT_T5076183648494686801_t_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t__rel,type,
% 0.29/0.49      vEBT_T9217963907923527482_t_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t,type,
% 0.29/0.49      vEBT_T_m_a_x_t: vEBT_VEBT > nat ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t__rel,type,
% 0.29/0.49      vEBT_T_m_a_x_t_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r,type,
% 0.29/0.49      vEBT_T_m_e_m_b_e_r: vEBT_VEBT > nat > nat ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H,type,
% 0.29/0.49      vEBT_T_m_e_m_b_e_r2: vEBT_VEBT > nat > nat ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H__rel,type,
% 0.29/0.49      vEBT_T8099345112685741742_r_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r__rel,type,
% 0.29/0.49      vEBT_T5837161174952499735_r_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l,type,
% 0.29/0.49      vEBT_T_m_i_n_N_u_l_l: vEBT_VEBT > nat ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l__rel,type,
% 0.29/0.49      vEBT_T5462971552011256508_l_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t,type,
% 0.29/0.49      vEBT_T_m_i_n_t: vEBT_VEBT > nat ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t__rel,type,
% 0.29/0.49      vEBT_T_m_i_n_t_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d,type,
% 0.29/0.49      vEBT_T_p_r_e_d: vEBT_VEBT > nat > nat ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H,type,
% 0.29/0.49      vEBT_T_p_r_e_d2: vEBT_VEBT > nat > nat ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H__rel,type,
% 0.29/0.49      vEBT_T_p_r_e_d_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d__rel,type,
% 0.29/0.49      vEBT_T_p_r_e_d_rel2: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c,type,
% 0.29/0.49      vEBT_T_s_u_c_c: vEBT_VEBT > nat > nat ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H,type,
% 0.29/0.49      vEBT_T_s_u_c_c2: vEBT_VEBT > nat > nat ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H__rel,type,
% 0.29/0.49      vEBT_T_s_u_c_c_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c__rel,type,
% 0.29/0.49      vEBT_T_s_u_c_c_rel2: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Definitions_OVEBT_OLeaf,type,
% 0.29/0.49      vEBT_Leaf: $o > $o > vEBT_VEBT ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Definitions_OVEBT_ONode,type,
% 0.29/0.49      vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Definitions_OVEBT_Osize__VEBT,type,
% 0.29/0.49      vEBT_size_VEBT: vEBT_VEBT > nat ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Definitions_OVEBT__internal_Oboth__member__options,type,
% 0.29/0.49      vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Definitions_OVEBT__internal_Ohigh,type,
% 0.29/0.49      vEBT_VEBT_high: nat > nat > nat ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Definitions_OVEBT__internal_Oin__children,type,
% 0.29/0.49      vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Definitions_OVEBT__internal_Olow,type,
% 0.29/0.49      vEBT_VEBT_low: nat > nat > nat ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima,type,
% 0.29/0.49      vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima__rel,type,
% 0.29/0.49      vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member,type,
% 0.29/0.49      vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member__rel,type,
% 0.29/0.49      vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H,type,
% 0.29/0.49      vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H__rel,type,
% 0.29/0.49      vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Definitions_Oinvar__vebt,type,
% 0.29/0.49      vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Definitions_Oset__vebt,type,
% 0.29/0.49      vEBT_set_vebt: vEBT_VEBT > set_nat ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Definitions_Ovebt__buildup,type,
% 0.29/0.49      vEBT_vebt_buildup: nat > vEBT_VEBT ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Definitions_Ovebt__buildup__rel,type,
% 0.29/0.49      vEBT_v4011308405150292612up_rel: nat > nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__DeleteBounds_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e,type,
% 0.29/0.49      vEBT_T_d_e_l_e_t_e: vEBT_VEBT > nat > nat ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__DeleteBounds_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e__rel,type,
% 0.29/0.49      vEBT_T8441311223069195367_e_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Delete_Ovebt__delete,type,
% 0.29/0.49      vEBT_vebt_delete: vEBT_VEBT > nat > vEBT_VEBT ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Delete_Ovebt__delete__rel,type,
% 0.29/0.49      vEBT_vebt_delete_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Height_OVEBT__internal_Oheight,type,
% 0.29/0.49      vEBT_VEBT_height: vEBT_VEBT > nat ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Height_OVEBT__internal_Oheight__rel,type,
% 0.29/0.49      vEBT_VEBT_height_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Insert_Ovebt__insert,type,
% 0.29/0.49      vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Insert_Ovebt__insert__rel,type,
% 0.29/0.49      vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Member_OVEBT__internal_Obit__concat,type,
% 0.29/0.49      vEBT_VEBT_bit_concat: nat > nat > nat > nat ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Member_OVEBT__internal_OminNull,type,
% 0.29/0.49      vEBT_VEBT_minNull: vEBT_VEBT > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Member_OVEBT__internal_OminNull__rel,type,
% 0.29/0.49      vEBT_V6963167321098673237ll_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Member_OVEBT__internal_Oset__vebt_H,type,
% 0.29/0.49      vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Member_Ovebt__member,type,
% 0.29/0.49      vEBT_vebt_member: vEBT_VEBT > nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Member_Ovebt__member__rel,type,
% 0.29/0.49      vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__MinMax_OVEBT__internal_Oadd,type,
% 0.29/0.49      vEBT_VEBT_add: option_nat > option_nat > option_nat ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__MinMax_OVEBT__internal_Ogreater,type,
% 0.29/0.49      vEBT_VEBT_greater: option_nat > option_nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__MinMax_OVEBT__internal_Oless,type,
% 0.29/0.49      vEBT_VEBT_less: option_nat > option_nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__MinMax_OVEBT__internal_Olesseq,type,
% 0.29/0.49      vEBT_VEBT_lesseq: option_nat > option_nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__MinMax_OVEBT__internal_Omax__in__set,type,
% 0.29/0.49      vEBT_VEBT_max_in_set: set_nat > nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__MinMax_OVEBT__internal_Omin__in__set,type,
% 0.29/0.49      vEBT_VEBT_min_in_set: set_nat > nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__MinMax_OVEBT__internal_Omul,type,
% 0.29/0.49      vEBT_VEBT_mul: option_nat > option_nat > option_nat ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Nat__Onat,type,
% 0.29/0.49      vEBT_V4262088993061758097ft_nat: ( nat > nat > nat ) > option_nat > option_nat > option_nat ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Num__Onum,type,
% 0.29/0.49      vEBT_V819420779217536731ft_num: ( num > num > num ) > option_num > option_num > option_num ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.29/0.49      vEBT_V1502963449132264192at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > option4927543243414619207at_nat > option4927543243414619207at_nat > option4927543243414619207at_nat ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__MinMax_OVEBT__internal_Opower,type,
% 0.29/0.49      vEBT_VEBT_power: option_nat > option_nat > option_nat ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__MinMax_Ovebt__maxt,type,
% 0.29/0.49      vEBT_vebt_maxt: vEBT_VEBT > option_nat ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__MinMax_Ovebt__maxt__rel,type,
% 0.29/0.49      vEBT_vebt_maxt_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__MinMax_Ovebt__mint,type,
% 0.29/0.49      vEBT_vebt_mint: vEBT_VEBT > option_nat ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__MinMax_Ovebt__mint__rel,type,
% 0.29/0.49      vEBT_vebt_mint_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Pred_Ois__pred__in__set,type,
% 0.29/0.49      vEBT_is_pred_in_set: set_nat > nat > nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Pred_Ovebt__pred,type,
% 0.29/0.49      vEBT_vebt_pred: vEBT_VEBT > nat > option_nat ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Pred_Ovebt__pred__rel,type,
% 0.29/0.49      vEBT_vebt_pred_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Succ_Ois__succ__in__set,type,
% 0.29/0.49      vEBT_is_succ_in_set: set_nat > nat > nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Succ_Ovebt__succ,type,
% 0.29/0.49      vEBT_vebt_succ: vEBT_VEBT > nat > option_nat ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_VEBT__Succ_Ovebt__succ__rel,type,
% 0.29/0.49      vEBT_vebt_succ_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_Wellfounded_Oaccp_001t__List__Olist_It__Nat__Onat_J,type,
% 0.29/0.49      accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_Wellfounded_Oaccp_001t__Nat__Onat,type,
% 0.29/0.49      accp_nat: ( nat > nat > $o ) > nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.29/0.49      accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.29/0.49      accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 0.29/0.49      accp_P3113834385874906142um_num: ( product_prod_num_num > product_prod_num_num > $o ) > product_prod_num_num > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 0.29/0.49      accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_Wellfounded_Oaccp_001t__VEBT____Definitions__OVEBT,type,
% 0.29/0.49      accp_VEBT_VEBT: ( vEBT_VEBT > vEBT_VEBT > $o ) > vEBT_VEBT > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_Wellfounded_Opred__nat,type,
% 0.29/0.49      pred_nat: set_Pr1261947904930325089at_nat ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_Wellfounded_Owf_001t__Nat__Onat,type,
% 0.29/0.49      wf_nat: set_Pr1261947904930325089at_nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_fChoice_001t__Real__Oreal,type,
% 0.29/0.49      fChoice_real: ( real > $o ) > real ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_member_001_Eo,type,
% 0.29/0.49      member_o: $o > set_o > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_member_001t__Complex__Ocomplex,type,
% 0.29/0.49      member_complex: complex > set_complex > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_member_001t__Int__Oint,type,
% 0.29/0.49      member_int: int > set_int > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_member_001t__List__Olist_I_Eo_J,type,
% 0.29/0.49      member_list_o: list_o > set_list_o > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_member_001t__List__Olist_It__Int__Oint_J,type,
% 0.29/0.49      member_list_int: list_int > set_list_int > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 0.29/0.49      member_list_nat: list_nat > set_list_nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_member_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 0.29/0.49      member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_member_001t__Nat__Onat,type,
% 0.29/0.49      member_nat: nat > set_nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_member_001t__Num__Onum,type,
% 0.29/0.49      member_num: num > set_num > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.29/0.49      member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.29/0.49      member8206827879206165904at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_member_001t__Rat__Orat,type,
% 0.29/0.49      member_rat: rat > set_rat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_member_001t__Real__Oreal,type,
% 0.29/0.49      member_real: real > set_real > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.29/0.49      member_set_nat: set_nat > set_set_nat > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_member_001t__Set__Oset_It__Real__Oreal_J,type,
% 0.29/0.49      member_set_real: set_real > set_set_real > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_c_member_001t__VEBT____Definitions__OVEBT,type,
% 0.29/0.49      member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_v_deg____,type,
% 0.29/0.49      deg: nat ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_v_m____,type,
% 0.29/0.49      m: nat ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_v_ma____,type,
% 0.29/0.49      ma: nat ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_v_mi____,type,
% 0.29/0.49      mi: nat ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_v_na____,type,
% 0.29/0.49      na: nat ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_v_summary____,type,
% 0.29/0.49      summary: vEBT_VEBT ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_v_treeList____,type,
% 0.29/0.49      treeList: list_VEBT_VEBT ).
% 0.29/0.49  
% 0.29/0.49  thf(sy_v_xa____,type,
% 0.29/0.49      xa: nat ).
% 0.29/0.49  
% 0.29/0.49  % Relevant facts (10211)
% 0.29/0.49  thf(fact_0_True,axiom,
% 0.29/0.49      xa = mi ).
% 0.29/0.49  
% 0.29/0.49  % True
% 0.29/0.49  thf(fact_1__C4_Ohyps_C_I8_J,axiom,
% 0.29/0.49      ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 0.29/0.49  
% 0.29/0.49  % "4.hyps"(8)
% 0.29/0.49  thf(fact_2__C4_Ohyps_C_I7_J,axiom,
% 0.29/0.49      ord_less_eq_nat @ mi @ ma ).
% 0.29/0.49  
% 0.29/0.49  % "4.hyps"(7)
% 0.29/0.49  thf(fact_3_pow__sum,axiom,
% 0.29/0.49      ! [A: nat,B: nat] :
% 0.29/0.49        ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 0.29/0.49        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ).
% 0.29/0.49  
% 0.29/0.49  % pow_sum
% 0.29/0.49  thf(fact_4_False,axiom,
% 0.29/0.49      ~ ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) ) ).
% 0.29/0.49  
% 0.29/0.49  % False
% 0.29/0.49  thf(fact_5__C4_Ohyps_C_I2_J,axiom,
% 0.29/0.49      ( ( size_s6755466524823107622T_VEBT @ treeList )
% 0.29/0.49      = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ).
% 0.29/0.49  
% 0.29/0.49  % "4.hyps"(2)
% 0.29/0.49  thf(fact_6_one__add__one,axiom,
% 0.29/0.49      ( ( plus_plus_complex @ one_one_complex @ one_one_complex )
% 0.29/0.49      = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % one_add_one
% 0.29/0.49  thf(fact_7_one__add__one,axiom,
% 0.29/0.49      ( ( plus_plus_real @ one_one_real @ one_one_real )
% 0.29/0.49      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % one_add_one
% 0.29/0.49  thf(fact_8_one__add__one,axiom,
% 0.29/0.49      ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 0.29/0.49      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % one_add_one
% 0.29/0.49  thf(fact_9_one__add__one,axiom,
% 0.29/0.49      ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 0.29/0.49      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % one_add_one
% 0.29/0.49  thf(fact_10_one__add__one,axiom,
% 0.29/0.49      ( ( plus_plus_int @ one_one_int @ one_one_int )
% 0.29/0.49      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % one_add_one
% 0.29/0.49  thf(fact_11_numeral__plus__one,axiom,
% 0.29/0.49      ! [N: num] :
% 0.29/0.49        ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ one_one_complex )
% 0.29/0.49        = ( numera6690914467698888265omplex @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % numeral_plus_one
% 0.29/0.49  thf(fact_12_numeral__plus__one,axiom,
% 0.29/0.49      ! [N: num] :
% 0.29/0.49        ( ( plus_plus_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 0.29/0.49        = ( numeral_numeral_real @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % numeral_plus_one
% 0.29/0.49  thf(fact_13_numeral__plus__one,axiom,
% 0.29/0.49      ! [N: num] :
% 0.29/0.49        ( ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 0.29/0.49        = ( numeral_numeral_rat @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % numeral_plus_one
% 0.29/0.49  thf(fact_14_numeral__plus__one,axiom,
% 0.29/0.49      ! [N: num] :
% 0.29/0.49        ( ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 0.29/0.49        = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % numeral_plus_one
% 0.29/0.49  thf(fact_15_numeral__plus__one,axiom,
% 0.29/0.49      ! [N: num] :
% 0.29/0.49        ( ( plus_plus_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 0.29/0.49        = ( numeral_numeral_int @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % numeral_plus_one
% 0.29/0.49  thf(fact_16_one__plus__numeral,axiom,
% 0.29/0.49      ! [N: num] :
% 0.29/0.49        ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ N ) )
% 0.29/0.49        = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % one_plus_numeral
% 0.29/0.49  thf(fact_17_one__plus__numeral,axiom,
% 0.29/0.49      ! [N: num] :
% 0.29/0.49        ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 0.29/0.49        = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % one_plus_numeral
% 0.29/0.49  thf(fact_18_one__plus__numeral,axiom,
% 0.29/0.49      ! [N: num] :
% 0.29/0.49        ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 0.29/0.49        = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % one_plus_numeral
% 0.29/0.49  thf(fact_19_one__plus__numeral,axiom,
% 0.29/0.49      ! [N: num] :
% 0.29/0.49        ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 0.29/0.49        = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % one_plus_numeral
% 0.29/0.49  thf(fact_20_one__plus__numeral,axiom,
% 0.29/0.49      ! [N: num] :
% 0.29/0.49        ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 0.29/0.49        = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % one_plus_numeral
% 0.29/0.49  thf(fact_21_bit__concat__def,axiom,
% 0.29/0.49      ( vEBT_VEBT_bit_concat
% 0.29/0.49      = ( ^ [H: nat,L: nat,D: nat] : ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ D ) ) @ L ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % bit_concat_def
% 0.29/0.49  thf(fact_22_high__bound__aux,axiom,
% 0.29/0.49      ! [Ma: nat,N: nat,M: nat] :
% 0.29/0.49        ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 0.29/0.49       => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % high_bound_aux
% 0.29/0.49  thf(fact_23_numeral__eq__one__iff,axiom,
% 0.29/0.49      ! [N: num] :
% 0.29/0.49        ( ( ( numera6690914467698888265omplex @ N )
% 0.29/0.49          = one_one_complex )
% 0.29/0.49        = ( N = one ) ) ).
% 0.29/0.49  
% 0.29/0.49  % numeral_eq_one_iff
% 0.29/0.49  thf(fact_24_numeral__eq__one__iff,axiom,
% 0.29/0.49      ! [N: num] :
% 0.29/0.49        ( ( ( numeral_numeral_real @ N )
% 0.29/0.49          = one_one_real )
% 0.29/0.49        = ( N = one ) ) ).
% 0.29/0.49  
% 0.29/0.49  % numeral_eq_one_iff
% 0.29/0.49  thf(fact_25_numeral__eq__one__iff,axiom,
% 0.29/0.49      ! [N: num] :
% 0.29/0.49        ( ( ( numeral_numeral_rat @ N )
% 0.29/0.49          = one_one_rat )
% 0.29/0.49        = ( N = one ) ) ).
% 0.29/0.49  
% 0.29/0.49  % numeral_eq_one_iff
% 0.29/0.49  thf(fact_26_numeral__eq__one__iff,axiom,
% 0.29/0.49      ! [N: num] :
% 0.29/0.49        ( ( ( numeral_numeral_nat @ N )
% 0.29/0.49          = one_one_nat )
% 0.29/0.49        = ( N = one ) ) ).
% 0.29/0.49  
% 0.29/0.49  % numeral_eq_one_iff
% 0.29/0.49  thf(fact_27_numeral__eq__one__iff,axiom,
% 0.29/0.49      ! [N: num] :
% 0.29/0.49        ( ( ( numeral_numeral_int @ N )
% 0.29/0.49          = one_one_int )
% 0.29/0.49        = ( N = one ) ) ).
% 0.29/0.49  
% 0.29/0.49  % numeral_eq_one_iff
% 0.29/0.49  thf(fact_28_one__eq__numeral__iff,axiom,
% 0.29/0.49      ! [N: num] :
% 0.29/0.49        ( ( one_one_complex
% 0.29/0.49          = ( numera6690914467698888265omplex @ N ) )
% 0.29/0.49        = ( one = N ) ) ).
% 0.29/0.49  
% 0.29/0.49  % one_eq_numeral_iff
% 0.29/0.49  thf(fact_29_one__eq__numeral__iff,axiom,
% 0.29/0.49      ! [N: num] :
% 0.29/0.49        ( ( one_one_real
% 0.29/0.49          = ( numeral_numeral_real @ N ) )
% 0.29/0.49        = ( one = N ) ) ).
% 0.29/0.49  
% 0.29/0.49  % one_eq_numeral_iff
% 0.29/0.49  thf(fact_30_one__eq__numeral__iff,axiom,
% 0.29/0.49      ! [N: num] :
% 0.29/0.49        ( ( one_one_rat
% 0.29/0.49          = ( numeral_numeral_rat @ N ) )
% 0.29/0.49        = ( one = N ) ) ).
% 0.29/0.49  
% 0.29/0.49  % one_eq_numeral_iff
% 0.29/0.49  thf(fact_31_one__eq__numeral__iff,axiom,
% 0.29/0.49      ! [N: num] :
% 0.29/0.49        ( ( one_one_nat
% 0.29/0.49          = ( numeral_numeral_nat @ N ) )
% 0.29/0.49        = ( one = N ) ) ).
% 0.29/0.49  
% 0.29/0.49  % one_eq_numeral_iff
% 0.29/0.49  thf(fact_32_one__eq__numeral__iff,axiom,
% 0.29/0.49      ! [N: num] :
% 0.29/0.49        ( ( one_one_int
% 0.29/0.49          = ( numeral_numeral_int @ N ) )
% 0.29/0.49        = ( one = N ) ) ).
% 0.29/0.49  
% 0.29/0.49  % one_eq_numeral_iff
% 0.29/0.49  thf(fact_33_tdeletemimi,axiom,
% 0.29/0.49      ! [Deg: nat,Mi: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.29/0.49        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.29/0.49       => ( ord_less_eq_nat @ ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Mi ) ) @ Deg @ TreeList @ Summary ) @ X ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % tdeletemimi
% 0.29/0.49  thf(fact_34_high__def,axiom,
% 0.29/0.49      ( vEBT_VEBT_high
% 0.29/0.49      = ( ^ [X2: nat,N2: nat] : ( divide_divide_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % high_def
% 0.29/0.49  thf(fact_35_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Osimps_I3_J,axiom,
% 0.29/0.49      ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 0.29/0.49        ( ( vEBT_T_m_i_n_t @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 0.29/0.49        = one_one_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.simps(3)
% 0.29/0.49  thf(fact_36_semiring__norm_I86_J,axiom,
% 0.29/0.49      ! [M: num] :
% 0.29/0.49        ( ( bit1 @ M )
% 0.29/0.49       != one ) ).
% 0.29/0.49  
% 0.29/0.49  % semiring_norm(86)
% 0.29/0.49  thf(fact_37__C4_Ohyps_C_I3_J,axiom,
% 0.29/0.49      m = na ).
% 0.29/0.49  
% 0.29/0.49  % "4.hyps"(3)
% 0.29/0.49  thf(fact_38_max__in__set__def,axiom,
% 0.29/0.49      ( vEBT_VEBT_max_in_set
% 0.29/0.49      = ( ^ [Xs: set_nat,X2: nat] :
% 0.29/0.49            ( ( member_nat @ X2 @ Xs )
% 0.29/0.49            & ! [Y: nat] :
% 0.29/0.49                ( ( member_nat @ Y @ Xs )
% 0.29/0.49               => ( ord_less_eq_nat @ Y @ X2 ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % max_in_set_def
% 0.29/0.49  thf(fact_39_min__in__set__def,axiom,
% 0.29/0.49      ( vEBT_VEBT_min_in_set
% 0.29/0.49      = ( ^ [Xs: set_nat,X2: nat] :
% 0.29/0.49            ( ( member_nat @ X2 @ Xs )
% 0.29/0.49            & ! [Y: nat] :
% 0.29/0.49                ( ( member_nat @ Y @ Xs )
% 0.29/0.49               => ( ord_less_eq_nat @ X2 @ Y ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % min_in_set_def
% 0.29/0.49  thf(fact_40_numeral__eq__iff,axiom,
% 0.29/0.49      ! [M: num,N: num] :
% 0.29/0.49        ( ( ( numera6690914467698888265omplex @ M )
% 0.29/0.49          = ( numera6690914467698888265omplex @ N ) )
% 0.29/0.49        = ( M = N ) ) ).
% 0.29/0.49  
% 0.29/0.49  % numeral_eq_iff
% 0.29/0.49  thf(fact_41_numeral__eq__iff,axiom,
% 0.29/0.49      ! [M: num,N: num] :
% 0.29/0.49        ( ( ( numeral_numeral_real @ M )
% 0.29/0.49          = ( numeral_numeral_real @ N ) )
% 0.29/0.49        = ( M = N ) ) ).
% 0.29/0.49  
% 0.29/0.49  % numeral_eq_iff
% 0.29/0.49  thf(fact_42_numeral__eq__iff,axiom,
% 0.29/0.49      ! [M: num,N: num] :
% 0.29/0.49        ( ( ( numeral_numeral_rat @ M )
% 0.29/0.49          = ( numeral_numeral_rat @ N ) )
% 0.29/0.49        = ( M = N ) ) ).
% 0.29/0.49  
% 0.29/0.49  % numeral_eq_iff
% 0.29/0.49  thf(fact_43_numeral__eq__iff,axiom,
% 0.29/0.49      ! [M: num,N: num] :
% 0.29/0.49        ( ( ( numeral_numeral_nat @ M )
% 0.29/0.49          = ( numeral_numeral_nat @ N ) )
% 0.29/0.49        = ( M = N ) ) ).
% 0.29/0.49  
% 0.29/0.49  % numeral_eq_iff
% 0.29/0.49  thf(fact_44_numeral__eq__iff,axiom,
% 0.29/0.49      ! [M: num,N: num] :
% 0.29/0.49        ( ( ( numeral_numeral_int @ M )
% 0.29/0.49          = ( numeral_numeral_int @ N ) )
% 0.29/0.49        = ( M = N ) ) ).
% 0.29/0.49  
% 0.29/0.49  % numeral_eq_iff
% 0.29/0.49  thf(fact_45_semiring__norm_I87_J,axiom,
% 0.29/0.49      ! [M: num,N: num] :
% 0.29/0.49        ( ( ( bit0 @ M )
% 0.29/0.49          = ( bit0 @ N ) )
% 0.29/0.49        = ( M = N ) ) ).
% 0.29/0.49  
% 0.29/0.49  % semiring_norm(87)
% 0.29/0.49  thf(fact_46_semiring__norm_I90_J,axiom,
% 0.29/0.49      ! [M: num,N: num] :
% 0.29/0.49        ( ( ( bit1 @ M )
% 0.29/0.49          = ( bit1 @ N ) )
% 0.29/0.49        = ( M = N ) ) ).
% 0.29/0.49  
% 0.29/0.49  % semiring_norm(90)
% 0.29/0.49  thf(fact_47_deggy,axiom,
% 0.29/0.49      ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ).
% 0.29/0.49  
% 0.29/0.49  % deggy
% 0.29/0.49  thf(fact_48__092_060open_062mi_A_092_060le_062_Ax_A_092_060and_062_Ax_A_092_060le_062_Ama_092_060close_062,axiom,
% 0.29/0.49      ( ( ord_less_eq_nat @ mi @ xa )
% 0.29/0.49      & ( ord_less_eq_nat @ xa @ ma ) ) ).
% 0.29/0.49  
% 0.29/0.49  % \<open>mi \<le> x \<and> x \<le> ma\<close>
% 0.29/0.49  thf(fact_49__C4_Ohyps_C_I4_J,axiom,
% 0.29/0.49      ( deg
% 0.29/0.49      = ( plus_plus_nat @ na @ m ) ) ).
% 0.29/0.49  
% 0.29/0.49  % "4.hyps"(4)
% 0.29/0.49  thf(fact_50_numeral__le__iff,axiom,
% 0.29/0.49      ! [M: num,N: num] :
% 0.29/0.49        ( ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 0.29/0.49        = ( ord_less_eq_num @ M @ N ) ) ).
% 0.29/0.49  
% 0.29/0.49  % numeral_le_iff
% 0.29/0.49  thf(fact_51_numeral__le__iff,axiom,
% 0.29/0.49      ! [M: num,N: num] :
% 0.29/0.49        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 0.29/0.49        = ( ord_less_eq_num @ M @ N ) ) ).
% 0.29/0.49  
% 0.29/0.49  % numeral_le_iff
% 0.29/0.49  thf(fact_52_numeral__le__iff,axiom,
% 0.29/0.49      ! [M: num,N: num] :
% 0.29/0.49        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.29/0.49        = ( ord_less_eq_num @ M @ N ) ) ).
% 0.29/0.49  
% 0.29/0.49  % numeral_le_iff
% 0.29/0.49  thf(fact_53_numeral__le__iff,axiom,
% 0.29/0.49      ! [M: num,N: num] :
% 0.29/0.49        ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.29/0.49        = ( ord_less_eq_num @ M @ N ) ) ).
% 0.29/0.49  
% 0.29/0.49  % numeral_le_iff
% 0.29/0.49  thf(fact_54_high__inv,axiom,
% 0.29/0.49      ! [X: nat,N: nat,Y2: nat] :
% 0.29/0.49        ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.29/0.49       => ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ Y2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X ) @ N )
% 0.29/0.49          = Y2 ) ) ).
% 0.29/0.49  
% 0.29/0.49  % high_inv
% 0.29/0.49  thf(fact_55_numeral__less__iff,axiom,
% 0.29/0.49      ! [M: num,N: num] :
% 0.29/0.49        ( ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 0.29/0.49        = ( ord_less_num @ M @ N ) ) ).
% 0.29/0.49  
% 0.29/0.49  % numeral_less_iff
% 0.29/0.49  thf(fact_56_numeral__less__iff,axiom,
% 0.29/0.49      ! [M: num,N: num] :
% 0.29/0.49        ( ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 0.29/0.49        = ( ord_less_num @ M @ N ) ) ).
% 0.29/0.49  
% 0.29/0.49  % numeral_less_iff
% 0.29/0.49  thf(fact_57_numeral__less__iff,axiom,
% 0.29/0.49      ! [M: num,N: num] :
% 0.29/0.49        ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.29/0.49        = ( ord_less_num @ M @ N ) ) ).
% 0.29/0.49  
% 0.29/0.49  % numeral_less_iff
% 0.29/0.49  thf(fact_58_numeral__less__iff,axiom,
% 0.29/0.49      ! [M: num,N: num] :
% 0.29/0.49        ( ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.29/0.49        = ( ord_less_num @ M @ N ) ) ).
% 0.29/0.49  
% 0.29/0.49  % numeral_less_iff
% 0.29/0.49  thf(fact_59_mult__numeral__left__semiring__numeral,axiom,
% 0.29/0.49      ! [V: num,W: num,Z: complex] :
% 0.29/0.49        ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 0.29/0.49        = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mult_numeral_left_semiring_numeral
% 0.29/0.49  thf(fact_60_mult__numeral__left__semiring__numeral,axiom,
% 0.29/0.49      ! [V: num,W: num,Z: real] :
% 0.29/0.49        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 0.29/0.49        = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mult_numeral_left_semiring_numeral
% 0.29/0.49  thf(fact_61_mult__numeral__left__semiring__numeral,axiom,
% 0.29/0.49      ! [V: num,W: num,Z: rat] :
% 0.29/0.49        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 0.29/0.49        = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mult_numeral_left_semiring_numeral
% 0.29/0.49  thf(fact_62_mult__numeral__left__semiring__numeral,axiom,
% 0.29/0.49      ! [V: num,W: num,Z: nat] :
% 0.29/0.49        ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 0.29/0.49        = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mult_numeral_left_semiring_numeral
% 0.29/0.49  thf(fact_63_mult__numeral__left__semiring__numeral,axiom,
% 0.29/0.49      ! [V: num,W: num,Z: int] :
% 0.29/0.49        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 0.29/0.49        = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mult_numeral_left_semiring_numeral
% 0.29/0.49  thf(fact_64_numeral__times__numeral,axiom,
% 0.29/0.49      ! [M: num,N: num] :
% 0.29/0.49        ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) )
% 0.29/0.49        = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % numeral_times_numeral
% 0.29/0.49  thf(fact_65_numeral__times__numeral,axiom,
% 0.29/0.49      ! [M: num,N: num] :
% 0.29/0.49        ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 0.29/0.49        = ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % numeral_times_numeral
% 0.29/0.49  thf(fact_66_numeral__times__numeral,axiom,
% 0.29/0.49      ! [M: num,N: num] :
% 0.29/0.49        ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 0.29/0.49        = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % numeral_times_numeral
% 0.29/0.49  thf(fact_67_numeral__times__numeral,axiom,
% 0.29/0.49      ! [M: num,N: num] :
% 0.29/0.49        ( ( times_times_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.29/0.49        = ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % numeral_times_numeral
% 0.29/0.49  thf(fact_68_numeral__times__numeral,axiom,
% 0.29/0.49      ! [M: num,N: num] :
% 0.29/0.49        ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.29/0.49        = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % numeral_times_numeral
% 0.29/0.49  thf(fact_69_semiring__norm_I83_J,axiom,
% 0.29/0.49      ! [N: num] :
% 0.29/0.49        ( one
% 0.29/0.49       != ( bit0 @ N ) ) ).
% 0.29/0.49  
% 0.29/0.49  % semiring_norm(83)
% 0.29/0.49  thf(fact_70_semiring__norm_I85_J,axiom,
% 0.29/0.49      ! [M: num] :
% 0.29/0.49        ( ( bit0 @ M )
% 0.29/0.49       != one ) ).
% 0.29/0.49  
% 0.29/0.49  % semiring_norm(85)
% 0.29/0.49  thf(fact_71_semiring__norm_I88_J,axiom,
% 0.29/0.49      ! [M: num,N: num] :
% 0.29/0.49        ( ( bit0 @ M )
% 0.29/0.49       != ( bit1 @ N ) ) ).
% 0.29/0.49  
% 0.29/0.49  % semiring_norm(88)
% 0.29/0.49  thf(fact_72_semiring__norm_I89_J,axiom,
% 0.29/0.49      ! [M: num,N: num] :
% 0.29/0.49        ( ( bit1 @ M )
% 0.29/0.49       != ( bit0 @ N ) ) ).
% 0.29/0.49  
% 0.29/0.49  % semiring_norm(89)
% 0.29/0.49  thf(fact_73_semiring__norm_I84_J,axiom,
% 0.29/0.49      ! [N: num] :
% 0.29/0.49        ( one
% 0.29/0.49       != ( bit1 @ N ) ) ).
% 0.29/0.49  
% 0.29/0.49  % semiring_norm(84)
% 0.29/0.49  thf(fact_74_semiring__norm_I6_J,axiom,
% 0.29/0.49      ! [M: num,N: num] :
% 0.29/0.49        ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.29/0.49        = ( bit0 @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % semiring_norm(6)
% 0.29/0.49  thf(fact_75_distrib__right__numeral,axiom,
% 0.29/0.49      ! [A: complex,B: complex,V: num] :
% 0.29/0.49        ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 0.29/0.49        = ( plus_plus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % distrib_right_numeral
% 0.29/0.49  thf(fact_76_distrib__right__numeral,axiom,
% 0.29/0.49      ! [A: real,B: real,V: num] :
% 0.29/0.49        ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 0.29/0.49        = ( plus_plus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % distrib_right_numeral
% 0.29/0.49  thf(fact_77_distrib__right__numeral,axiom,
% 0.29/0.49      ! [A: rat,B: rat,V: num] :
% 0.29/0.49        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 0.29/0.49        = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % distrib_right_numeral
% 0.29/0.49  thf(fact_78_distrib__right__numeral,axiom,
% 0.29/0.49      ! [A: nat,B: nat,V: num] :
% 0.29/0.49        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
% 0.29/0.49        = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % distrib_right_numeral
% 0.29/0.49  thf(fact_79_distrib__right__numeral,axiom,
% 0.29/0.49      ! [A: int,B: int,V: num] :
% 0.29/0.49        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 0.29/0.49        = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % distrib_right_numeral
% 0.29/0.49  thf(fact_80_distrib__left__numeral,axiom,
% 0.29/0.49      ! [V: num,B: complex,C: complex] :
% 0.29/0.49        ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ B @ C ) )
% 0.29/0.49        = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % distrib_left_numeral
% 0.29/0.49  thf(fact_81_distrib__left__numeral,axiom,
% 0.29/0.49      ! [V: num,B: real,C: real] :
% 0.29/0.49        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ B @ C ) )
% 0.29/0.49        = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % distrib_left_numeral
% 0.29/0.49  thf(fact_82_distrib__left__numeral,axiom,
% 0.29/0.49      ! [V: num,B: rat,C: rat] :
% 0.29/0.49        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ B @ C ) )
% 0.29/0.49        = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % distrib_left_numeral
% 0.29/0.49  thf(fact_83_distrib__left__numeral,axiom,
% 0.29/0.49      ! [V: num,B: nat,C: nat] :
% 0.29/0.49        ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
% 0.29/0.49        = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % distrib_left_numeral
% 0.29/0.49  thf(fact_84_distrib__left__numeral,axiom,
% 0.29/0.49      ! [V: num,B: int,C: int] :
% 0.29/0.49        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B @ C ) )
% 0.29/0.49        = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % distrib_left_numeral
% 0.29/0.49  thf(fact_85_add__numeral__left,axiom,
% 0.29/0.49      ! [V: num,W: num,Z: complex] :
% 0.29/0.49        ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 0.29/0.49        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_numeral_left
% 0.29/0.49  thf(fact_86_add__numeral__left,axiom,
% 0.29/0.49      ! [V: num,W: num,Z: real] :
% 0.29/0.49        ( ( plus_plus_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 0.29/0.49        = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_numeral_left
% 0.29/0.49  thf(fact_87_add__numeral__left,axiom,
% 0.29/0.49      ! [V: num,W: num,Z: rat] :
% 0.29/0.49        ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 0.29/0.49        = ( plus_plus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_numeral_left
% 0.29/0.49  thf(fact_88_add__numeral__left,axiom,
% 0.29/0.49      ! [V: num,W: num,Z: nat] :
% 0.29/0.49        ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 0.29/0.49        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_numeral_left
% 0.29/0.49  thf(fact_89_add__numeral__left,axiom,
% 0.29/0.49      ! [V: num,W: num,Z: int] :
% 0.29/0.49        ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 0.29/0.49        = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_numeral_left
% 0.29/0.49  thf(fact_90_numeral__plus__numeral,axiom,
% 0.29/0.49      ! [M: num,N: num] :
% 0.29/0.49        ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) )
% 0.29/0.49        = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % numeral_plus_numeral
% 0.29/0.49  thf(fact_91_numeral__plus__numeral,axiom,
% 0.29/0.49      ! [M: num,N: num] :
% 0.29/0.49        ( ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 0.29/0.49        = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % numeral_plus_numeral
% 0.29/0.49  thf(fact_92_numeral__plus__numeral,axiom,
% 0.29/0.49      ! [M: num,N: num] :
% 0.29/0.49        ( ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 0.29/0.49        = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % numeral_plus_numeral
% 0.29/0.49  thf(fact_93_numeral__plus__numeral,axiom,
% 0.29/0.49      ! [M: num,N: num] :
% 0.29/0.49        ( ( plus_plus_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.29/0.49        = ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % numeral_plus_numeral
% 0.29/0.49  thf(fact_94_numeral__plus__numeral,axiom,
% 0.29/0.49      ! [M: num,N: num] :
% 0.29/0.49        ( ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.29/0.49        = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % numeral_plus_numeral
% 0.29/0.49  thf(fact_95_semiring__norm_I2_J,axiom,
% 0.29/0.49      ( ( plus_plus_num @ one @ one )
% 0.29/0.49      = ( bit0 @ one ) ) ).
% 0.29/0.49  
% 0.29/0.49  % semiring_norm(2)
% 0.29/0.49  thf(fact_96_semiring__norm_I7_J,axiom,
% 0.29/0.49      ! [M: num,N: num] :
% 0.29/0.49        ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.29/0.49        = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % semiring_norm(7)
% 0.29/0.49  thf(fact_97_semiring__norm_I9_J,axiom,
% 0.29/0.49      ! [M: num,N: num] :
% 0.29/0.49        ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.29/0.49        = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % semiring_norm(9)
% 0.29/0.49  thf(fact_98_mem__Collect__eq,axiom,
% 0.29/0.49      ! [A: int,P: int > $o] :
% 0.29/0.49        ( ( member_int @ A @ ( collect_int @ P ) )
% 0.29/0.49        = ( P @ A ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mem_Collect_eq
% 0.29/0.49  thf(fact_99_mem__Collect__eq,axiom,
% 0.29/0.49      ! [A: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 0.29/0.49        ( ( member8440522571783428010at_nat @ A @ ( collec3392354462482085612at_nat @ P ) )
% 0.29/0.49        = ( P @ A ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mem_Collect_eq
% 0.29/0.49  thf(fact_100_mem__Collect__eq,axiom,
% 0.29/0.49      ! [A: complex,P: complex > $o] :
% 0.29/0.49        ( ( member_complex @ A @ ( collect_complex @ P ) )
% 0.29/0.49        = ( P @ A ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mem_Collect_eq
% 0.29/0.49  thf(fact_101_mem__Collect__eq,axiom,
% 0.29/0.49      ! [A: real,P: real > $o] :
% 0.29/0.49        ( ( member_real @ A @ ( collect_real @ P ) )
% 0.29/0.49        = ( P @ A ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mem_Collect_eq
% 0.29/0.49  thf(fact_102_mem__Collect__eq,axiom,
% 0.29/0.49      ! [A: list_nat,P: list_nat > $o] :
% 0.29/0.49        ( ( member_list_nat @ A @ ( collect_list_nat @ P ) )
% 0.29/0.49        = ( P @ A ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mem_Collect_eq
% 0.29/0.49  thf(fact_103_mem__Collect__eq,axiom,
% 0.29/0.49      ! [A: nat,P: nat > $o] :
% 0.29/0.49        ( ( member_nat @ A @ ( collect_nat @ P ) )
% 0.29/0.49        = ( P @ A ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mem_Collect_eq
% 0.29/0.49  thf(fact_104_Collect__mem__eq,axiom,
% 0.29/0.49      ! [A2: set_int] :
% 0.29/0.49        ( ( collect_int
% 0.29/0.49          @ ^ [X2: int] : ( member_int @ X2 @ A2 ) )
% 0.29/0.49        = A2 ) ).
% 0.29/0.49  
% 0.29/0.49  % Collect_mem_eq
% 0.29/0.49  thf(fact_105_Collect__mem__eq,axiom,
% 0.29/0.49      ! [A2: set_Pr1261947904930325089at_nat] :
% 0.29/0.49        ( ( collec3392354462482085612at_nat
% 0.29/0.49          @ ^ [X2: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X2 @ A2 ) )
% 0.29/0.49        = A2 ) ).
% 0.29/0.49  
% 0.29/0.49  % Collect_mem_eq
% 0.29/0.49  thf(fact_106_Collect__mem__eq,axiom,
% 0.29/0.49      ! [A2: set_complex] :
% 0.29/0.49        ( ( collect_complex
% 0.29/0.49          @ ^ [X2: complex] : ( member_complex @ X2 @ A2 ) )
% 0.29/0.49        = A2 ) ).
% 0.29/0.49  
% 0.29/0.49  % Collect_mem_eq
% 0.29/0.49  thf(fact_107_Collect__mem__eq,axiom,
% 0.29/0.49      ! [A2: set_real] :
% 0.29/0.49        ( ( collect_real
% 0.29/0.49          @ ^ [X2: real] : ( member_real @ X2 @ A2 ) )
% 0.29/0.49        = A2 ) ).
% 0.29/0.49  
% 0.29/0.49  % Collect_mem_eq
% 0.29/0.49  thf(fact_108_Collect__mem__eq,axiom,
% 0.29/0.49      ! [A2: set_list_nat] :
% 0.29/0.49        ( ( collect_list_nat
% 0.29/0.49          @ ^ [X2: list_nat] : ( member_list_nat @ X2 @ A2 ) )
% 0.29/0.49        = A2 ) ).
% 0.29/0.49  
% 0.29/0.49  % Collect_mem_eq
% 0.29/0.49  thf(fact_109_Collect__mem__eq,axiom,
% 0.29/0.49      ! [A2: set_nat] :
% 0.29/0.49        ( ( collect_nat
% 0.29/0.49          @ ^ [X2: nat] : ( member_nat @ X2 @ A2 ) )
% 0.29/0.49        = A2 ) ).
% 0.29/0.49  
% 0.29/0.49  % Collect_mem_eq
% 0.29/0.49  thf(fact_110_Collect__cong,axiom,
% 0.29/0.49      ! [P: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
% 0.29/0.49        ( ! [X3: product_prod_nat_nat] :
% 0.29/0.49            ( ( P @ X3 )
% 0.29/0.49            = ( Q @ X3 ) )
% 0.29/0.49       => ( ( collec3392354462482085612at_nat @ P )
% 0.29/0.49          = ( collec3392354462482085612at_nat @ Q ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % Collect_cong
% 0.29/0.49  thf(fact_111_Collect__cong,axiom,
% 0.29/0.49      ! [P: complex > $o,Q: complex > $o] :
% 0.29/0.49        ( ! [X3: complex] :
% 0.29/0.49            ( ( P @ X3 )
% 0.29/0.49            = ( Q @ X3 ) )
% 0.29/0.49       => ( ( collect_complex @ P )
% 0.29/0.49          = ( collect_complex @ Q ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % Collect_cong
% 0.29/0.49  thf(fact_112_Collect__cong,axiom,
% 0.29/0.49      ! [P: real > $o,Q: real > $o] :
% 0.29/0.49        ( ! [X3: real] :
% 0.29/0.49            ( ( P @ X3 )
% 0.29/0.49            = ( Q @ X3 ) )
% 0.29/0.49       => ( ( collect_real @ P )
% 0.29/0.49          = ( collect_real @ Q ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % Collect_cong
% 0.29/0.49  thf(fact_113_Collect__cong,axiom,
% 0.29/0.49      ! [P: list_nat > $o,Q: list_nat > $o] :
% 0.29/0.49        ( ! [X3: list_nat] :
% 0.29/0.49            ( ( P @ X3 )
% 0.29/0.49            = ( Q @ X3 ) )
% 0.29/0.49       => ( ( collect_list_nat @ P )
% 0.29/0.49          = ( collect_list_nat @ Q ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % Collect_cong
% 0.29/0.49  thf(fact_114_Collect__cong,axiom,
% 0.29/0.49      ! [P: nat > $o,Q: nat > $o] :
% 0.29/0.49        ( ! [X3: nat] :
% 0.29/0.49            ( ( P @ X3 )
% 0.29/0.49            = ( Q @ X3 ) )
% 0.29/0.49       => ( ( collect_nat @ P )
% 0.29/0.49          = ( collect_nat @ Q ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % Collect_cong
% 0.29/0.49  thf(fact_115_numeral__le__one__iff,axiom,
% 0.29/0.49      ! [N: num] :
% 0.29/0.49        ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 0.29/0.49        = ( ord_less_eq_num @ N @ one ) ) ).
% 0.29/0.49  
% 0.29/0.49  % numeral_le_one_iff
% 0.29/0.49  thf(fact_116_numeral__le__one__iff,axiom,
% 0.29/0.49      ! [N: num] :
% 0.29/0.49        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 0.29/0.49        = ( ord_less_eq_num @ N @ one ) ) ).
% 0.29/0.49  
% 0.29/0.49  % numeral_le_one_iff
% 0.29/0.49  thf(fact_117_numeral__le__one__iff,axiom,
% 0.29/0.49      ! [N: num] :
% 0.29/0.49        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 0.29/0.49        = ( ord_less_eq_num @ N @ one ) ) ).
% 0.29/0.49  
% 0.29/0.49  % numeral_le_one_iff
% 0.29/0.49  thf(fact_118_numeral__le__one__iff,axiom,
% 0.29/0.49      ! [N: num] :
% 0.29/0.49        ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 0.29/0.49        = ( ord_less_eq_num @ N @ one ) ) ).
% 0.29/0.49  
% 0.29/0.49  % numeral_le_one_iff
% 0.29/0.49  thf(fact_119_one__less__numeral__iff,axiom,
% 0.29/0.49      ! [N: num] :
% 0.29/0.49        ( ( ord_less_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 0.29/0.49        = ( ord_less_num @ one @ N ) ) ).
% 0.29/0.49  
% 0.29/0.49  % one_less_numeral_iff
% 0.29/0.49  thf(fact_120_one__less__numeral__iff,axiom,
% 0.29/0.49      ! [N: num] :
% 0.29/0.49        ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 0.29/0.49        = ( ord_less_num @ one @ N ) ) ).
% 0.29/0.49  
% 0.29/0.49  % one_less_numeral_iff
% 0.29/0.49  thf(fact_121_one__less__numeral__iff,axiom,
% 0.29/0.49      ! [N: num] :
% 0.29/0.49        ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 0.29/0.49        = ( ord_less_num @ one @ N ) ) ).
% 0.29/0.49  
% 0.29/0.49  % one_less_numeral_iff
% 0.29/0.49  thf(fact_122_one__less__numeral__iff,axiom,
% 0.29/0.49      ! [N: num] :
% 0.29/0.49        ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 0.29/0.49        = ( ord_less_num @ one @ N ) ) ).
% 0.29/0.49  
% 0.29/0.49  % one_less_numeral_iff
% 0.29/0.49  thf(fact_123_le__divide__eq__numeral1_I1_J,axiom,
% 0.29/0.49      ! [A: real,B: real,W: num] :
% 0.29/0.49        ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 0.29/0.49        = ( ord_less_eq_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 0.29/0.49  
% 0.29/0.49  % le_divide_eq_numeral1(1)
% 0.29/0.49  thf(fact_124_le__divide__eq__numeral1_I1_J,axiom,
% 0.29/0.49      ! [A: rat,B: rat,W: num] :
% 0.29/0.49        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 0.29/0.49        = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 0.29/0.49  
% 0.29/0.49  % le_divide_eq_numeral1(1)
% 0.29/0.49  thf(fact_125_divide__le__eq__numeral1_I1_J,axiom,
% 0.29/0.49      ! [B: real,W: num,A: real] :
% 0.29/0.49        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 0.29/0.49        = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % divide_le_eq_numeral1(1)
% 0.29/0.49  thf(fact_126_divide__le__eq__numeral1_I1_J,axiom,
% 0.29/0.49      ! [B: rat,W: num,A: rat] :
% 0.29/0.49        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 0.29/0.49        = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % divide_le_eq_numeral1(1)
% 0.29/0.49  thf(fact_127_less__divide__eq__numeral1_I1_J,axiom,
% 0.29/0.49      ! [A: real,B: real,W: num] :
% 0.29/0.49        ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 0.29/0.49        = ( ord_less_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 0.29/0.49  
% 0.29/0.49  % less_divide_eq_numeral1(1)
% 0.29/0.49  thf(fact_128_less__divide__eq__numeral1_I1_J,axiom,
% 0.29/0.49      ! [A: rat,B: rat,W: num] :
% 0.29/0.49        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 0.29/0.49        = ( ord_less_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 0.29/0.49  
% 0.29/0.49  % less_divide_eq_numeral1(1)
% 0.29/0.49  thf(fact_129_divide__less__eq__numeral1_I1_J,axiom,
% 0.29/0.49      ! [B: real,W: num,A: real] :
% 0.29/0.49        ( ( ord_less_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 0.29/0.49        = ( ord_less_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % divide_less_eq_numeral1(1)
% 0.29/0.49  thf(fact_130_divide__less__eq__numeral1_I1_J,axiom,
% 0.29/0.49      ! [B: rat,W: num,A: rat] :
% 0.29/0.49        ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 0.29/0.49        = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % divide_less_eq_numeral1(1)
% 0.29/0.49  thf(fact_131_semiring__norm_I3_J,axiom,
% 0.29/0.49      ! [N: num] :
% 0.29/0.49        ( ( plus_plus_num @ one @ ( bit0 @ N ) )
% 0.29/0.49        = ( bit1 @ N ) ) ).
% 0.29/0.49  
% 0.29/0.49  % semiring_norm(3)
% 0.29/0.49  thf(fact_132_semiring__norm_I4_J,axiom,
% 0.29/0.49      ! [N: num] :
% 0.29/0.49        ( ( plus_plus_num @ one @ ( bit1 @ N ) )
% 0.29/0.49        = ( bit0 @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % semiring_norm(4)
% 0.29/0.49  thf(fact_133_semiring__norm_I5_J,axiom,
% 0.29/0.49      ! [M: num] :
% 0.29/0.49        ( ( plus_plus_num @ ( bit0 @ M ) @ one )
% 0.29/0.49        = ( bit1 @ M ) ) ).
% 0.29/0.49  
% 0.29/0.49  % semiring_norm(5)
% 0.29/0.49  thf(fact_134_semiring__norm_I8_J,axiom,
% 0.29/0.49      ! [M: num] :
% 0.29/0.49        ( ( plus_plus_num @ ( bit1 @ M ) @ one )
% 0.29/0.49        = ( bit0 @ ( plus_plus_num @ M @ one ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % semiring_norm(8)
% 0.29/0.49  thf(fact_135_semiring__norm_I10_J,axiom,
% 0.29/0.49      ! [M: num,N: num] :
% 0.29/0.49        ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.29/0.49        = ( bit0 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ one ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % semiring_norm(10)
% 0.29/0.49  thf(fact_136__C4_Ohyps_C_I1_J,axiom,
% 0.29/0.49      vEBT_invar_vebt @ summary @ m ).
% 0.29/0.49  
% 0.29/0.49  % "4.hyps"(1)
% 0.29/0.49  thf(fact_137__C4_Ohyps_C_I5_J,axiom,
% 0.29/0.49      ! [I: nat] :
% 0.29/0.49        ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 0.29/0.49       => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ X4 ) )
% 0.29/0.49          = ( vEBT_V8194947554948674370ptions @ summary @ I ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % "4.hyps"(5)
% 0.29/0.49  thf(fact_138_add__One__commute,axiom,
% 0.29/0.49      ! [N: num] :
% 0.29/0.49        ( ( plus_plus_num @ one @ N )
% 0.29/0.49        = ( plus_plus_num @ N @ one ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_One_commute
% 0.29/0.49  thf(fact_139_le__numeral__extra_I4_J,axiom,
% 0.29/0.49      ord_less_eq_real @ one_one_real @ one_one_real ).
% 0.29/0.49  
% 0.29/0.49  % le_numeral_extra(4)
% 0.29/0.49  thf(fact_140_le__numeral__extra_I4_J,axiom,
% 0.29/0.49      ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 0.29/0.49  
% 0.29/0.49  % le_numeral_extra(4)
% 0.29/0.49  thf(fact_141_le__numeral__extra_I4_J,axiom,
% 0.29/0.49      ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 0.29/0.49  
% 0.29/0.49  % le_numeral_extra(4)
% 0.29/0.49  thf(fact_142_le__numeral__extra_I4_J,axiom,
% 0.29/0.49      ord_less_eq_int @ one_one_int @ one_one_int ).
% 0.29/0.49  
% 0.29/0.49  % le_numeral_extra(4)
% 0.29/0.49  thf(fact_143_one__le__numeral,axiom,
% 0.29/0.49      ! [N: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ N ) ) ).
% 0.29/0.49  
% 0.29/0.49  % one_le_numeral
% 0.29/0.49  thf(fact_144_one__le__numeral,axiom,
% 0.29/0.49      ! [N: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) ) ).
% 0.29/0.49  
% 0.29/0.49  % one_le_numeral
% 0.29/0.49  thf(fact_145_one__le__numeral,axiom,
% 0.29/0.49      ! [N: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 0.29/0.49  
% 0.29/0.49  % one_le_numeral
% 0.29/0.49  thf(fact_146_one__le__numeral,axiom,
% 0.29/0.49      ! [N: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N ) ) ).
% 0.29/0.49  
% 0.29/0.49  % one_le_numeral
% 0.29/0.49  thf(fact_147_less__numeral__extra_I4_J,axiom,
% 0.29/0.49      ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 0.29/0.49  
% 0.29/0.49  % less_numeral_extra(4)
% 0.29/0.49  thf(fact_148_less__numeral__extra_I4_J,axiom,
% 0.29/0.49      ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 0.29/0.49  
% 0.29/0.49  % less_numeral_extra(4)
% 0.29/0.49  thf(fact_149_less__numeral__extra_I4_J,axiom,
% 0.29/0.50      ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % less_numeral_extra(4)
% 0.29/0.50  thf(fact_150_less__numeral__extra_I4_J,axiom,
% 0.29/0.50      ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 0.29/0.50  
% 0.29/0.50  % less_numeral_extra(4)
% 0.29/0.50  thf(fact_151_left__add__mult__distrib,axiom,
% 0.29/0.50      ! [I2: nat,U: nat,J: nat,K: nat] :
% 0.29/0.50        ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
% 0.29/0.50        = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I2 @ J ) @ U ) @ K ) ) ).
% 0.29/0.50  
% 0.29/0.50  % left_add_mult_distrib
% 0.29/0.50  thf(fact_152_mint__bound,axiom,
% 0.29/0.50      ! [T: vEBT_VEBT] : ( ord_less_eq_nat @ ( vEBT_T_m_i_n_t @ T ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % mint_bound
% 0.29/0.50  thf(fact_153_is__num__normalize_I1_J,axiom,
% 0.29/0.50      ! [A: real,B: real,C: real] :
% 0.29/0.50        ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.29/0.50        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % is_num_normalize(1)
% 0.29/0.50  thf(fact_154_is__num__normalize_I1_J,axiom,
% 0.29/0.50      ! [A: rat,B: rat,C: rat] :
% 0.29/0.50        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.29/0.50        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % is_num_normalize(1)
% 0.29/0.50  thf(fact_155_is__num__normalize_I1_J,axiom,
% 0.29/0.50      ! [A: int,B: int,C: int] :
% 0.29/0.50        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.29/0.50        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % is_num_normalize(1)
% 0.29/0.50  thf(fact_156_is__num__normalize_I1_J,axiom,
% 0.29/0.50      ! [A: complex,B: complex,C: complex] :
% 0.29/0.50        ( ( plus_plus_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 0.29/0.50        = ( plus_plus_complex @ A @ ( plus_plus_complex @ B @ C ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % is_num_normalize(1)
% 0.29/0.50  thf(fact_157_divide__numeral__1,axiom,
% 0.29/0.50      ! [A: complex] :
% 0.29/0.50        ( ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ one ) )
% 0.29/0.50        = A ) ).
% 0.29/0.50  
% 0.29/0.50  % divide_numeral_1
% 0.29/0.50  thf(fact_158_divide__numeral__1,axiom,
% 0.29/0.50      ! [A: real] :
% 0.29/0.50        ( ( divide_divide_real @ A @ ( numeral_numeral_real @ one ) )
% 0.29/0.50        = A ) ).
% 0.29/0.50  
% 0.29/0.50  % divide_numeral_1
% 0.29/0.50  thf(fact_159_divide__numeral__1,axiom,
% 0.29/0.50      ! [A: rat] :
% 0.29/0.50        ( ( divide_divide_rat @ A @ ( numeral_numeral_rat @ one ) )
% 0.29/0.50        = A ) ).
% 0.29/0.50  
% 0.29/0.50  % divide_numeral_1
% 0.29/0.50  thf(fact_160_not__numeral__less__one,axiom,
% 0.29/0.50      ! [N: num] :
% 0.29/0.50        ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ one_one_real ) ).
% 0.29/0.50  
% 0.29/0.50  % not_numeral_less_one
% 0.29/0.50  thf(fact_161_not__numeral__less__one,axiom,
% 0.29/0.50      ! [N: num] :
% 0.29/0.50        ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat ) ).
% 0.29/0.50  
% 0.29/0.50  % not_numeral_less_one
% 0.29/0.50  thf(fact_162_not__numeral__less__one,axiom,
% 0.29/0.50      ! [N: num] :
% 0.29/0.50        ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % not_numeral_less_one
% 0.29/0.50  thf(fact_163_not__numeral__less__one,axiom,
% 0.29/0.50      ! [N: num] :
% 0.29/0.50        ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ).
% 0.29/0.50  
% 0.29/0.50  % not_numeral_less_one
% 0.29/0.50  thf(fact_164_mult__numeral__1__right,axiom,
% 0.29/0.50      ! [A: complex] :
% 0.29/0.50        ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ one ) )
% 0.29/0.50        = A ) ).
% 0.29/0.50  
% 0.29/0.50  % mult_numeral_1_right
% 0.29/0.50  thf(fact_165_mult__numeral__1__right,axiom,
% 0.29/0.50      ! [A: real] :
% 0.29/0.50        ( ( times_times_real @ A @ ( numeral_numeral_real @ one ) )
% 0.29/0.50        = A ) ).
% 0.29/0.50  
% 0.29/0.50  % mult_numeral_1_right
% 0.29/0.50  thf(fact_166_mult__numeral__1__right,axiom,
% 0.29/0.50      ! [A: rat] :
% 0.29/0.50        ( ( times_times_rat @ A @ ( numeral_numeral_rat @ one ) )
% 0.29/0.50        = A ) ).
% 0.29/0.50  
% 0.29/0.50  % mult_numeral_1_right
% 0.29/0.50  thf(fact_167_mult__numeral__1__right,axiom,
% 0.29/0.50      ! [A: nat] :
% 0.29/0.50        ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
% 0.29/0.50        = A ) ).
% 0.29/0.50  
% 0.29/0.50  % mult_numeral_1_right
% 0.29/0.50  thf(fact_168_mult__numeral__1__right,axiom,
% 0.29/0.50      ! [A: int] :
% 0.29/0.50        ( ( times_times_int @ A @ ( numeral_numeral_int @ one ) )
% 0.29/0.50        = A ) ).
% 0.29/0.50  
% 0.29/0.50  % mult_numeral_1_right
% 0.29/0.50  thf(fact_169_mult__numeral__1,axiom,
% 0.29/0.50      ! [A: complex] :
% 0.29/0.50        ( ( times_times_complex @ ( numera6690914467698888265omplex @ one ) @ A )
% 0.29/0.50        = A ) ).
% 0.29/0.50  
% 0.29/0.50  % mult_numeral_1
% 0.29/0.50  thf(fact_170_mult__numeral__1,axiom,
% 0.29/0.50      ! [A: real] :
% 0.29/0.50        ( ( times_times_real @ ( numeral_numeral_real @ one ) @ A )
% 0.29/0.50        = A ) ).
% 0.29/0.50  
% 0.29/0.50  % mult_numeral_1
% 0.29/0.50  thf(fact_171_mult__numeral__1,axiom,
% 0.29/0.50      ! [A: rat] :
% 0.29/0.50        ( ( times_times_rat @ ( numeral_numeral_rat @ one ) @ A )
% 0.29/0.50        = A ) ).
% 0.29/0.50  
% 0.29/0.50  % mult_numeral_1
% 0.29/0.50  thf(fact_172_mult__numeral__1,axiom,
% 0.29/0.50      ! [A: nat] :
% 0.29/0.50        ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
% 0.29/0.50        = A ) ).
% 0.29/0.50  
% 0.29/0.50  % mult_numeral_1
% 0.29/0.50  thf(fact_173_mult__numeral__1,axiom,
% 0.29/0.50      ! [A: int] :
% 0.29/0.50        ( ( times_times_int @ ( numeral_numeral_int @ one ) @ A )
% 0.29/0.50        = A ) ).
% 0.29/0.50  
% 0.29/0.50  % mult_numeral_1
% 0.29/0.50  thf(fact_174_left__add__twice,axiom,
% 0.29/0.50      ! [A: complex,B: complex] :
% 0.29/0.50        ( ( plus_plus_complex @ A @ ( plus_plus_complex @ A @ B ) )
% 0.29/0.50        = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.29/0.50  
% 0.29/0.50  % left_add_twice
% 0.29/0.50  thf(fact_175_left__add__twice,axiom,
% 0.29/0.50      ! [A: real,B: real] :
% 0.29/0.50        ( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B ) )
% 0.29/0.50        = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.29/0.50  
% 0.29/0.50  % left_add_twice
% 0.29/0.50  thf(fact_176_left__add__twice,axiom,
% 0.29/0.50      ! [A: rat,B: rat] :
% 0.29/0.50        ( ( plus_plus_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 0.29/0.50        = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.29/0.50  
% 0.29/0.50  % left_add_twice
% 0.29/0.50  thf(fact_177_left__add__twice,axiom,
% 0.29/0.50      ! [A: nat,B: nat] :
% 0.29/0.50        ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.29/0.50        = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.29/0.50  
% 0.29/0.50  % left_add_twice
% 0.29/0.50  thf(fact_178_left__add__twice,axiom,
% 0.29/0.50      ! [A: int,B: int] :
% 0.29/0.50        ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B ) )
% 0.29/0.50        = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.29/0.50  
% 0.29/0.50  % left_add_twice
% 0.29/0.50  thf(fact_179_mult__2__right,axiom,
% 0.29/0.50      ! [Z: complex] :
% 0.29/0.50        ( ( times_times_complex @ Z @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) )
% 0.29/0.50        = ( plus_plus_complex @ Z @ Z ) ) ).
% 0.29/0.50  
% 0.29/0.50  % mult_2_right
% 0.29/0.50  thf(fact_180_mult__2__right,axiom,
% 0.29/0.50      ! [Z: real] :
% 0.29/0.50        ( ( times_times_real @ Z @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.29/0.50        = ( plus_plus_real @ Z @ Z ) ) ).
% 0.29/0.50  
% 0.29/0.50  % mult_2_right
% 0.29/0.50  thf(fact_181_mult__2__right,axiom,
% 0.29/0.50      ! [Z: rat] :
% 0.29/0.50        ( ( times_times_rat @ Z @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 0.29/0.50        = ( plus_plus_rat @ Z @ Z ) ) ).
% 0.29/0.50  
% 0.29/0.50  % mult_2_right
% 0.29/0.50  thf(fact_182_mult__2__right,axiom,
% 0.29/0.50      ! [Z: nat] :
% 0.29/0.50        ( ( times_times_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.50        = ( plus_plus_nat @ Z @ Z ) ) ).
% 0.29/0.50  
% 0.29/0.50  % mult_2_right
% 0.29/0.50  thf(fact_183_mult__2__right,axiom,
% 0.29/0.50      ! [Z: int] :
% 0.29/0.50        ( ( times_times_int @ Z @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.50        = ( plus_plus_int @ Z @ Z ) ) ).
% 0.29/0.50  
% 0.29/0.50  % mult_2_right
% 0.29/0.50  thf(fact_184_mult__2,axiom,
% 0.29/0.50      ! [Z: complex] :
% 0.29/0.50        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z )
% 0.29/0.50        = ( plus_plus_complex @ Z @ Z ) ) ).
% 0.29/0.50  
% 0.29/0.50  % mult_2
% 0.29/0.50  thf(fact_185_mult__2,axiom,
% 0.29/0.50      ! [Z: real] :
% 0.29/0.50        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z )
% 0.29/0.50        = ( plus_plus_real @ Z @ Z ) ) ).
% 0.29/0.50  
% 0.29/0.50  % mult_2
% 0.29/0.50  thf(fact_186_mult__2,axiom,
% 0.29/0.50      ! [Z: rat] :
% 0.29/0.50        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z )
% 0.29/0.50        = ( plus_plus_rat @ Z @ Z ) ) ).
% 0.29/0.50  
% 0.29/0.50  % mult_2
% 0.29/0.50  thf(fact_187_mult__2,axiom,
% 0.29/0.50      ! [Z: nat] :
% 0.29/0.50        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z )
% 0.29/0.50        = ( plus_plus_nat @ Z @ Z ) ) ).
% 0.29/0.50  
% 0.29/0.50  % mult_2
% 0.29/0.50  thf(fact_188_mult__2,axiom,
% 0.29/0.50      ! [Z: int] :
% 0.29/0.50        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z )
% 0.29/0.50        = ( plus_plus_int @ Z @ Z ) ) ).
% 0.29/0.50  
% 0.29/0.50  % mult_2
% 0.29/0.50  thf(fact_189_numeral__Bit0,axiom,
% 0.29/0.50      ! [N: num] :
% 0.29/0.50        ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 0.29/0.50        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % numeral_Bit0
% 0.29/0.50  thf(fact_190_numeral__Bit0,axiom,
% 0.29/0.50      ! [N: num] :
% 0.29/0.50        ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 0.29/0.50        = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % numeral_Bit0
% 0.29/0.50  thf(fact_191_numeral__Bit0,axiom,
% 0.29/0.50      ! [N: num] :
% 0.29/0.50        ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 0.29/0.50        = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % numeral_Bit0
% 0.29/0.50  thf(fact_192_numeral__Bit0,axiom,
% 0.29/0.50      ! [N: num] :
% 0.29/0.50        ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 0.29/0.50        = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % numeral_Bit0
% 0.29/0.50  thf(fact_193_numeral__Bit0,axiom,
% 0.29/0.50      ! [N: num] :
% 0.29/0.50        ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 0.29/0.50        = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % numeral_Bit0
% 0.29/0.50  thf(fact_194_one__plus__numeral__commute,axiom,
% 0.29/0.50      ! [X: num] :
% 0.29/0.50        ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ X ) )
% 0.29/0.50        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X ) @ one_one_complex ) ) ).
% 0.29/0.50  
% 0.29/0.50  % one_plus_numeral_commute
% 0.29/0.50  thf(fact_195_one__plus__numeral__commute,axiom,
% 0.29/0.50      ! [X: num] :
% 0.29/0.50        ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ X ) )
% 0.29/0.50        = ( plus_plus_real @ ( numeral_numeral_real @ X ) @ one_one_real ) ) ).
% 0.29/0.50  
% 0.29/0.50  % one_plus_numeral_commute
% 0.29/0.50  thf(fact_196_one__plus__numeral__commute,axiom,
% 0.29/0.50      ! [X: num] :
% 0.29/0.50        ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 0.29/0.50        = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 0.29/0.50  
% 0.29/0.50  % one_plus_numeral_commute
% 0.29/0.50  thf(fact_197_one__plus__numeral__commute,axiom,
% 0.29/0.50      ! [X: num] :
% 0.29/0.50        ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 0.29/0.50        = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 0.29/0.50  
% 0.29/0.50  % one_plus_numeral_commute
% 0.29/0.50  thf(fact_198_one__plus__numeral__commute,axiom,
% 0.29/0.50      ! [X: num] :
% 0.29/0.50        ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 0.29/0.50        = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 0.29/0.50  
% 0.29/0.50  % one_plus_numeral_commute
% 0.29/0.50  thf(fact_199_numeral__One,axiom,
% 0.29/0.50      ( ( numera6690914467698888265omplex @ one )
% 0.29/0.50      = one_one_complex ) ).
% 0.29/0.50  
% 0.29/0.50  % numeral_One
% 0.29/0.50  thf(fact_200_numeral__One,axiom,
% 0.29/0.50      ( ( numeral_numeral_real @ one )
% 0.29/0.50      = one_one_real ) ).
% 0.29/0.50  
% 0.29/0.50  % numeral_One
% 0.29/0.50  thf(fact_201_numeral__One,axiom,
% 0.29/0.50      ( ( numeral_numeral_rat @ one )
% 0.29/0.50      = one_one_rat ) ).
% 0.29/0.50  
% 0.29/0.50  % numeral_One
% 0.29/0.50  thf(fact_202_numeral__One,axiom,
% 0.29/0.50      ( ( numeral_numeral_nat @ one )
% 0.29/0.50      = one_one_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % numeral_One
% 0.29/0.50  thf(fact_203_numeral__One,axiom,
% 0.29/0.50      ( ( numeral_numeral_int @ one )
% 0.29/0.50      = one_one_int ) ).
% 0.29/0.50  
% 0.29/0.50  % numeral_One
% 0.29/0.50  thf(fact_204_num_Oexhaust,axiom,
% 0.29/0.50      ! [Y2: num] :
% 0.29/0.50        ( ( Y2 != one )
% 0.29/0.50       => ( ! [X22: num] :
% 0.29/0.50              ( Y2
% 0.29/0.50             != ( bit0 @ X22 ) )
% 0.29/0.50         => ~ ! [X32: num] :
% 0.29/0.50                ( Y2
% 0.29/0.50               != ( bit1 @ X32 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % num.exhaust
% 0.29/0.50  thf(fact_205_numerals_I1_J,axiom,
% 0.29/0.50      ( ( numeral_numeral_nat @ one )
% 0.29/0.50      = one_one_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % numerals(1)
% 0.29/0.50  thf(fact_206_numeral__Bit1,axiom,
% 0.29/0.50      ! [N: num] :
% 0.29/0.50        ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 0.29/0.50        = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 0.29/0.50  
% 0.29/0.50  % numeral_Bit1
% 0.29/0.50  thf(fact_207_numeral__Bit1,axiom,
% 0.29/0.50      ! [N: num] :
% 0.29/0.50        ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 0.29/0.50        = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 0.29/0.50  
% 0.29/0.50  % numeral_Bit1
% 0.29/0.50  thf(fact_208_numeral__Bit1,axiom,
% 0.29/0.50      ! [N: num] :
% 0.29/0.50        ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 0.29/0.50        = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 0.29/0.50  
% 0.29/0.50  % numeral_Bit1
% 0.29/0.50  thf(fact_209_numeral__Bit1,axiom,
% 0.29/0.50      ! [N: num] :
% 0.29/0.50        ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 0.29/0.50        = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 0.29/0.50  
% 0.29/0.50  % numeral_Bit1
% 0.29/0.50  thf(fact_210_numeral__Bit1,axiom,
% 0.29/0.50      ! [N: num] :
% 0.29/0.50        ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 0.29/0.50        = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 0.29/0.50  
% 0.29/0.50  % numeral_Bit1
% 0.29/0.50  thf(fact_211_nat__1__add__1,axiom,
% 0.29/0.50      ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 0.29/0.50      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % nat_1_add_1
% 0.29/0.50  thf(fact_212_insert__simp__mima,axiom,
% 0.29/0.50      ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.29/0.50        ( ( ( X = Mi )
% 0.29/0.50          | ( X = Ma ) )
% 0.29/0.50       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.29/0.50         => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.29/0.50            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % insert_simp_mima
% 0.29/0.50  thf(fact_213_add__self__div__2,axiom,
% 0.29/0.50      ! [M: nat] :
% 0.29/0.50        ( ( divide_divide_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.50        = M ) ).
% 0.29/0.50  
% 0.29/0.50  % add_self_div_2
% 0.29/0.50  thf(fact_214_power__increasing__iff,axiom,
% 0.29/0.50      ! [B: real,X: nat,Y2: nat] :
% 0.29/0.50        ( ( ord_less_real @ one_one_real @ B )
% 0.29/0.50       => ( ( ord_less_eq_real @ ( power_power_real @ B @ X ) @ ( power_power_real @ B @ Y2 ) )
% 0.29/0.50          = ( ord_less_eq_nat @ X @ Y2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_increasing_iff
% 0.29/0.50  thf(fact_215_power__increasing__iff,axiom,
% 0.29/0.50      ! [B: rat,X: nat,Y2: nat] :
% 0.29/0.50        ( ( ord_less_rat @ one_one_rat @ B )
% 0.29/0.50       => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y2 ) )
% 0.29/0.50          = ( ord_less_eq_nat @ X @ Y2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_increasing_iff
% 0.29/0.50  thf(fact_216_power__increasing__iff,axiom,
% 0.29/0.50      ! [B: nat,X: nat,Y2: nat] :
% 0.29/0.50        ( ( ord_less_nat @ one_one_nat @ B )
% 0.29/0.50       => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y2 ) )
% 0.29/0.50          = ( ord_less_eq_nat @ X @ Y2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_increasing_iff
% 0.29/0.50  thf(fact_217_power__increasing__iff,axiom,
% 0.29/0.50      ! [B: int,X: nat,Y2: nat] :
% 0.29/0.50        ( ( ord_less_int @ one_one_int @ B )
% 0.29/0.50       => ( ( ord_less_eq_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y2 ) )
% 0.29/0.50          = ( ord_less_eq_nat @ X @ Y2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_increasing_iff
% 0.29/0.50  thf(fact_218__C4_OIH_C_I2_J,axiom,
% 0.29/0.50      ! [X: nat] : ( ord_less_eq_nat @ ( vEBT_T_d_e_l_e_t_e @ summary @ X ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ summary ) ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % "4.IH"(2)
% 0.29/0.50  thf(fact_219_power__add__numeral2,axiom,
% 0.29/0.50      ! [A: complex,M: num,N: num,B: complex] :
% 0.29/0.50        ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 0.29/0.50        = ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_add_numeral2
% 0.29/0.50  thf(fact_220_power__add__numeral2,axiom,
% 0.29/0.50      ! [A: real,M: num,N: num,B: real] :
% 0.29/0.50        ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 0.29/0.50        = ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_add_numeral2
% 0.29/0.50  thf(fact_221_power__add__numeral2,axiom,
% 0.29/0.50      ! [A: nat,M: num,N: num,B: nat] :
% 0.29/0.50        ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 0.29/0.50        = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_add_numeral2
% 0.29/0.50  thf(fact_222_power__add__numeral2,axiom,
% 0.29/0.50      ! [A: int,M: num,N: num,B: int] :
% 0.29/0.50        ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 0.29/0.50        = ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_add_numeral2
% 0.29/0.50  thf(fact_223_power__add__numeral,axiom,
% 0.29/0.50      ! [A: complex,M: num,N: num] :
% 0.29/0.50        ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) )
% 0.29/0.50        = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_add_numeral
% 0.29/0.50  thf(fact_224_power__add__numeral,axiom,
% 0.29/0.50      ! [A: real,M: num,N: num] :
% 0.29/0.50        ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) )
% 0.29/0.50        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_add_numeral
% 0.29/0.50  thf(fact_225_power__add__numeral,axiom,
% 0.29/0.50      ! [A: nat,M: num,N: num] :
% 0.29/0.50        ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) )
% 0.29/0.50        = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_add_numeral
% 0.29/0.50  thf(fact_226_power__add__numeral,axiom,
% 0.29/0.50      ! [A: int,M: num,N: num] :
% 0.29/0.50        ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) )
% 0.29/0.50        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_add_numeral
% 0.29/0.50  thf(fact_227_power__strict__increasing__iff,axiom,
% 0.29/0.50      ! [B: real,X: nat,Y2: nat] :
% 0.29/0.50        ( ( ord_less_real @ one_one_real @ B )
% 0.29/0.50       => ( ( ord_less_real @ ( power_power_real @ B @ X ) @ ( power_power_real @ B @ Y2 ) )
% 0.29/0.50          = ( ord_less_nat @ X @ Y2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_strict_increasing_iff
% 0.29/0.50  thf(fact_228_power__strict__increasing__iff,axiom,
% 0.29/0.50      ! [B: rat,X: nat,Y2: nat] :
% 0.29/0.50        ( ( ord_less_rat @ one_one_rat @ B )
% 0.29/0.50       => ( ( ord_less_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y2 ) )
% 0.29/0.50          = ( ord_less_nat @ X @ Y2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_strict_increasing_iff
% 0.29/0.50  thf(fact_229_power__strict__increasing__iff,axiom,
% 0.29/0.50      ! [B: nat,X: nat,Y2: nat] :
% 0.29/0.50        ( ( ord_less_nat @ one_one_nat @ B )
% 0.29/0.50       => ( ( ord_less_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y2 ) )
% 0.29/0.50          = ( ord_less_nat @ X @ Y2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_strict_increasing_iff
% 0.29/0.50  thf(fact_230_power__strict__increasing__iff,axiom,
% 0.29/0.50      ! [B: int,X: nat,Y2: nat] :
% 0.29/0.50        ( ( ord_less_int @ one_one_int @ B )
% 0.29/0.50       => ( ( ord_less_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y2 ) )
% 0.29/0.50          = ( ord_less_nat @ X @ Y2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_strict_increasing_iff
% 0.29/0.50  thf(fact_231_ex__power__ivl2,axiom,
% 0.29/0.50      ! [B: nat,K: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.29/0.50       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 0.29/0.50         => ? [N3: nat] :
% 0.29/0.50              ( ( ord_less_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 0.29/0.50              & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ex_power_ivl2
% 0.29/0.50  thf(fact_232_ex__power__ivl1,axiom,
% 0.29/0.50      ! [B: nat,K: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.29/0.50       => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 0.29/0.50         => ? [N3: nat] :
% 0.29/0.50              ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 0.29/0.50              & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ex_power_ivl1
% 0.29/0.50  thf(fact_233_sum__squares__bound,axiom,
% 0.29/0.50      ! [X: real,Y2: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y2 ) @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % sum_squares_bound
% 0.29/0.50  thf(fact_234_sum__squares__bound,axiom,
% 0.29/0.50      ! [X: rat,Y2: rat] : ( ord_less_eq_rat @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y2 ) @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % sum_squares_bound
% 0.29/0.50  thf(fact_235_power__inject__exp,axiom,
% 0.29/0.50      ! [A: real,M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_real @ one_one_real @ A )
% 0.29/0.50       => ( ( ( power_power_real @ A @ M )
% 0.29/0.50            = ( power_power_real @ A @ N ) )
% 0.29/0.50          = ( M = N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_inject_exp
% 0.29/0.50  thf(fact_236_power__inject__exp,axiom,
% 0.29/0.50      ! [A: rat,M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_rat @ one_one_rat @ A )
% 0.29/0.50       => ( ( ( power_power_rat @ A @ M )
% 0.29/0.50            = ( power_power_rat @ A @ N ) )
% 0.29/0.50          = ( M = N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_inject_exp
% 0.29/0.50  thf(fact_237_power__inject__exp,axiom,
% 0.29/0.50      ! [A: nat,M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_nat @ one_one_nat @ A )
% 0.29/0.50       => ( ( ( power_power_nat @ A @ M )
% 0.29/0.50            = ( power_power_nat @ A @ N ) )
% 0.29/0.50          = ( M = N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_inject_exp
% 0.29/0.50  thf(fact_238_power__inject__exp,axiom,
% 0.29/0.50      ! [A: int,M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_int @ one_one_int @ A )
% 0.29/0.50       => ( ( ( power_power_int @ A @ M )
% 0.29/0.50            = ( power_power_int @ A @ N ) )
% 0.29/0.50          = ( M = N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_inject_exp
% 0.29/0.50  thf(fact_239_power2__sum,axiom,
% 0.29/0.50      ! [X: complex,Y2: complex] :
% 0.29/0.50        ( ( power_power_complex @ ( plus_plus_complex @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.50        = ( plus_plus_complex @ ( plus_plus_complex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) @ Y2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power2_sum
% 0.29/0.50  thf(fact_240_power2__sum,axiom,
% 0.29/0.50      ! [X: real,Y2: real] :
% 0.29/0.50        ( ( power_power_real @ ( plus_plus_real @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.50        = ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power2_sum
% 0.29/0.50  thf(fact_241_power2__sum,axiom,
% 0.29/0.50      ! [X: rat,Y2: rat] :
% 0.29/0.50        ( ( power_power_rat @ ( plus_plus_rat @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.50        = ( plus_plus_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power2_sum
% 0.29/0.50  thf(fact_242_power2__sum,axiom,
% 0.29/0.50      ! [X: nat,Y2: nat] :
% 0.29/0.50        ( ( power_power_nat @ ( plus_plus_nat @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.50        = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) @ Y2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power2_sum
% 0.29/0.50  thf(fact_243_power2__sum,axiom,
% 0.29/0.50      ! [X: int,Y2: int] :
% 0.29/0.50        ( ( power_power_int @ ( plus_plus_int @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.50        = ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X ) @ Y2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power2_sum
% 0.29/0.50  thf(fact_244_deg__deg__n,axiom,
% 0.29/0.50      ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 0.29/0.50        ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N )
% 0.29/0.50       => ( Deg = N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % deg_deg_n
% 0.29/0.50  thf(fact_245_height__compose__summary,axiom,
% 0.29/0.50      ! [Summary: vEBT_VEBT,Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT] : ( ord_less_eq_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ Summary ) ) @ ( vEBT_VEBT_height @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % height_compose_summary
% 0.29/0.50  thf(fact_246_power__one,axiom,
% 0.29/0.50      ! [N: nat] :
% 0.29/0.50        ( ( power_power_rat @ one_one_rat @ N )
% 0.29/0.50        = one_one_rat ) ).
% 0.29/0.50  
% 0.29/0.50  % power_one
% 0.29/0.50  thf(fact_247_power__one,axiom,
% 0.29/0.50      ! [N: nat] :
% 0.29/0.50        ( ( power_power_nat @ one_one_nat @ N )
% 0.29/0.50        = one_one_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % power_one
% 0.29/0.50  thf(fact_248_power__one,axiom,
% 0.29/0.50      ! [N: nat] :
% 0.29/0.50        ( ( power_power_real @ one_one_real @ N )
% 0.29/0.50        = one_one_real ) ).
% 0.29/0.50  
% 0.29/0.50  % power_one
% 0.29/0.50  thf(fact_249_power__one,axiom,
% 0.29/0.50      ! [N: nat] :
% 0.29/0.50        ( ( power_power_int @ one_one_int @ N )
% 0.29/0.50        = one_one_int ) ).
% 0.29/0.50  
% 0.29/0.50  % power_one
% 0.29/0.50  thf(fact_250_power__one,axiom,
% 0.29/0.50      ! [N: nat] :
% 0.29/0.50        ( ( power_power_complex @ one_one_complex @ N )
% 0.29/0.50        = one_one_complex ) ).
% 0.29/0.50  
% 0.29/0.50  % power_one
% 0.29/0.50  thf(fact_251_two__powr__height__bound__deg,axiom,
% 0.29/0.50      ! [T: vEBT_VEBT,N: nat] :
% 0.29/0.50        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.50       => ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( vEBT_VEBT_height @ T ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % two_powr_height_bound_deg
% 0.29/0.50  thf(fact_252_power__one__right,axiom,
% 0.29/0.50      ! [A: nat] :
% 0.29/0.50        ( ( power_power_nat @ A @ one_one_nat )
% 0.29/0.50        = A ) ).
% 0.29/0.50  
% 0.29/0.50  % power_one_right
% 0.29/0.50  thf(fact_253_power__one__right,axiom,
% 0.29/0.50      ! [A: real] :
% 0.29/0.50        ( ( power_power_real @ A @ one_one_nat )
% 0.29/0.50        = A ) ).
% 0.29/0.50  
% 0.29/0.50  % power_one_right
% 0.29/0.50  thf(fact_254_power__one__right,axiom,
% 0.29/0.50      ! [A: int] :
% 0.29/0.50        ( ( power_power_int @ A @ one_one_nat )
% 0.29/0.50        = A ) ).
% 0.29/0.50  
% 0.29/0.50  % power_one_right
% 0.29/0.50  thf(fact_255_power__one__right,axiom,
% 0.29/0.50      ! [A: complex] :
% 0.29/0.50        ( ( power_power_complex @ A @ one_one_nat )
% 0.29/0.50        = A ) ).
% 0.29/0.50  
% 0.29/0.50  % power_one_right
% 0.29/0.50  thf(fact_256_valid__insert__both__member__options__add,axiom,
% 0.29/0.50      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.50        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.50       => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.29/0.50         => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ X ) @ X ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % valid_insert_both_member_options_add
% 0.29/0.50  thf(fact_257_valid__insert__both__member__options__pres,axiom,
% 0.29/0.50      ! [T: vEBT_VEBT,N: nat,X: nat,Y2: nat] :
% 0.29/0.50        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.50       => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.29/0.50         => ( ( ord_less_nat @ Y2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.29/0.50           => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 0.29/0.50             => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ Y2 ) @ X ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % valid_insert_both_member_options_pres
% 0.29/0.50  thf(fact_258_semiring__norm_I13_J,axiom,
% 0.29/0.50      ! [M: num,N: num] :
% 0.29/0.50        ( ( times_times_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.29/0.50        = ( bit0 @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % semiring_norm(13)
% 0.29/0.50  thf(fact_259_semiring__norm_I12_J,axiom,
% 0.29/0.50      ! [N: num] :
% 0.29/0.50        ( ( times_times_num @ one @ N )
% 0.29/0.50        = N ) ).
% 0.29/0.50  
% 0.29/0.50  % semiring_norm(12)
% 0.29/0.50  thf(fact_260_semiring__norm_I11_J,axiom,
% 0.29/0.50      ! [M: num] :
% 0.29/0.50        ( ( times_times_num @ M @ one )
% 0.29/0.50        = M ) ).
% 0.29/0.50  
% 0.29/0.50  % semiring_norm(11)
% 0.29/0.50  thf(fact_261_semiring__norm_I78_J,axiom,
% 0.29/0.50      ! [M: num,N: num] :
% 0.29/0.50        ( ( ord_less_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.29/0.50        = ( ord_less_num @ M @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % semiring_norm(78)
% 0.29/0.50  thf(fact_262_semiring__norm_I71_J,axiom,
% 0.29/0.50      ! [M: num,N: num] :
% 0.29/0.50        ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.29/0.50        = ( ord_less_eq_num @ M @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % semiring_norm(71)
% 0.29/0.50  thf(fact_263_semiring__norm_I75_J,axiom,
% 0.29/0.50      ! [M: num] :
% 0.29/0.50        ~ ( ord_less_num @ M @ one ) ).
% 0.29/0.50  
% 0.29/0.50  % semiring_norm(75)
% 0.29/0.50  thf(fact_264_semiring__norm_I68_J,axiom,
% 0.29/0.50      ! [N: num] : ( ord_less_eq_num @ one @ N ) ).
% 0.29/0.50  
% 0.29/0.50  % semiring_norm(68)
% 0.29/0.50  thf(fact_265_semiring__norm_I80_J,axiom,
% 0.29/0.50      ! [M: num,N: num] :
% 0.29/0.50        ( ( ord_less_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.29/0.50        = ( ord_less_num @ M @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % semiring_norm(80)
% 0.29/0.50  thf(fact_266_semiring__norm_I73_J,axiom,
% 0.29/0.50      ! [M: num,N: num] :
% 0.29/0.50        ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.29/0.50        = ( ord_less_eq_num @ M @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % semiring_norm(73)
% 0.29/0.50  thf(fact_267_mi__ma__2__deg,axiom,
% 0.29/0.50      ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 0.29/0.50        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 0.29/0.50       => ( ( ord_less_eq_nat @ Mi @ Ma )
% 0.29/0.50          & ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % mi_ma_2_deg
% 0.29/0.50  thf(fact_268_num__double,axiom,
% 0.29/0.50      ! [N: num] :
% 0.29/0.50        ( ( times_times_num @ ( bit0 @ one ) @ N )
% 0.29/0.50        = ( bit0 @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % num_double
% 0.29/0.50  thf(fact_269_power__mult__numeral,axiom,
% 0.29/0.50      ! [A: nat,M: num,N: num] :
% 0.29/0.50        ( ( power_power_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 0.29/0.50        = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_mult_numeral
% 0.29/0.50  thf(fact_270_power__mult__numeral,axiom,
% 0.29/0.50      ! [A: real,M: num,N: num] :
% 0.29/0.50        ( ( power_power_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 0.29/0.50        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_mult_numeral
% 0.29/0.50  thf(fact_271_power__mult__numeral,axiom,
% 0.29/0.50      ! [A: int,M: num,N: num] :
% 0.29/0.50        ( ( power_power_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 0.29/0.50        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_mult_numeral
% 0.29/0.50  thf(fact_272_power__mult__numeral,axiom,
% 0.29/0.50      ! [A: complex,M: num,N: num] :
% 0.29/0.50        ( ( power_power_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 0.29/0.50        = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_mult_numeral
% 0.29/0.50  thf(fact_273_semiring__norm_I15_J,axiom,
% 0.29/0.50      ! [M: num,N: num] :
% 0.29/0.50        ( ( times_times_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.29/0.50        = ( bit0 @ ( times_times_num @ ( bit1 @ M ) @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % semiring_norm(15)
% 0.29/0.50  thf(fact_274_semiring__norm_I14_J,axiom,
% 0.29/0.50      ! [M: num,N: num] :
% 0.29/0.50        ( ( times_times_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.29/0.50        = ( bit0 @ ( times_times_num @ M @ ( bit1 @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % semiring_norm(14)
% 0.29/0.50  thf(fact_275_semiring__norm_I76_J,axiom,
% 0.29/0.50      ! [N: num] : ( ord_less_num @ one @ ( bit0 @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % semiring_norm(76)
% 0.29/0.50  thf(fact_276_semiring__norm_I69_J,axiom,
% 0.29/0.50      ! [M: num] :
% 0.29/0.50        ~ ( ord_less_eq_num @ ( bit0 @ M ) @ one ) ).
% 0.29/0.50  
% 0.29/0.50  % semiring_norm(69)
% 0.29/0.50  thf(fact_277_semiring__norm_I81_J,axiom,
% 0.29/0.50      ! [M: num,N: num] :
% 0.29/0.50        ( ( ord_less_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.29/0.50        = ( ord_less_num @ M @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % semiring_norm(81)
% 0.29/0.50  thf(fact_278_semiring__norm_I72_J,axiom,
% 0.29/0.50      ! [M: num,N: num] :
% 0.29/0.50        ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.29/0.50        = ( ord_less_eq_num @ M @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % semiring_norm(72)
% 0.29/0.50  thf(fact_279_semiring__norm_I77_J,axiom,
% 0.29/0.50      ! [N: num] : ( ord_less_num @ one @ ( bit1 @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % semiring_norm(77)
% 0.29/0.50  thf(fact_280_semiring__norm_I70_J,axiom,
% 0.29/0.50      ! [M: num] :
% 0.29/0.50        ~ ( ord_less_eq_num @ ( bit1 @ M ) @ one ) ).
% 0.29/0.50  
% 0.29/0.50  % semiring_norm(70)
% 0.29/0.50  thf(fact_281_semiring__norm_I16_J,axiom,
% 0.29/0.50      ! [M: num,N: num] :
% 0.29/0.50        ( ( times_times_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.29/0.50        = ( bit1 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % semiring_norm(16)
% 0.29/0.50  thf(fact_282_semiring__norm_I79_J,axiom,
% 0.29/0.50      ! [M: num,N: num] :
% 0.29/0.50        ( ( ord_less_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.29/0.50        = ( ord_less_eq_num @ M @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % semiring_norm(79)
% 0.29/0.50  thf(fact_283_semiring__norm_I74_J,axiom,
% 0.29/0.50      ! [M: num,N: num] :
% 0.29/0.50        ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.29/0.50        = ( ord_less_num @ M @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % semiring_norm(74)
% 0.29/0.50  thf(fact_284__C4_Ohyps_C_I6_J,axiom,
% 0.29/0.50      ( ( mi = ma )
% 0.29/0.50     => ! [X5: vEBT_VEBT] :
% 0.29/0.50          ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ treeList ) )
% 0.29/0.50         => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % "4.hyps"(6)
% 0.29/0.50  thf(fact_285__C4_OIH_C_I1_J,axiom,
% 0.29/0.50      ! [X5: vEBT_VEBT] :
% 0.29/0.50        ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ treeList ) )
% 0.29/0.50       => ( ( vEBT_invar_vebt @ X5 @ na )
% 0.29/0.50          & ! [Xa: nat] : ( ord_less_eq_nat @ ( vEBT_T_d_e_l_e_t_e @ X5 @ Xa ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ X5 ) ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % "4.IH"(1)
% 0.29/0.50  thf(fact_286__C4_Ohyps_C_I9_J,axiom,
% 0.29/0.50      ( ( mi != ma )
% 0.29/0.50     => ! [I: nat] :
% 0.29/0.50          ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 0.29/0.50         => ( ( ( ( vEBT_VEBT_high @ ma @ na )
% 0.29/0.50                = I )
% 0.29/0.50             => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
% 0.29/0.50            & ! [X5: nat] :
% 0.29/0.50                ( ( ( ( vEBT_VEBT_high @ X5 @ na )
% 0.29/0.50                    = I )
% 0.29/0.50                  & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ ( vEBT_VEBT_low @ X5 @ na ) ) )
% 0.29/0.50               => ( ( ord_less_nat @ mi @ X5 )
% 0.29/0.50                  & ( ord_less_eq_nat @ X5 @ ma ) ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % "4.hyps"(9)
% 0.29/0.50  thf(fact_287_L2__set__mult__ineq__lemma,axiom,
% 0.29/0.50      ! [A: real,C: real,B: real,D2: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_real @ A @ C ) ) @ ( times_times_real @ B @ D2 ) ) @ ( plus_plus_real @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ D2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ C @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % L2_set_mult_ineq_lemma
% 0.29/0.50  thf(fact_288_four__x__squared,axiom,
% 0.29/0.50      ! [X: real] :
% 0.29/0.50        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.50        = ( power_power_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % four_x_squared
% 0.29/0.50  thf(fact_289_le__num__One__iff,axiom,
% 0.29/0.50      ! [X: num] :
% 0.29/0.50        ( ( ord_less_eq_num @ X @ one )
% 0.29/0.50        = ( X = one ) ) ).
% 0.29/0.50  
% 0.29/0.50  % le_num_One_iff
% 0.29/0.50  thf(fact_290_div__mult2__numeral__eq,axiom,
% 0.29/0.50      ! [A: nat,K: num,L2: num] :
% 0.29/0.50        ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ L2 ) )
% 0.29/0.50        = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ K @ L2 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % div_mult2_numeral_eq
% 0.29/0.50  thf(fact_291_div__mult2__numeral__eq,axiom,
% 0.29/0.50      ! [A: int,K: num,L2: num] :
% 0.29/0.50        ( ( divide_divide_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ L2 ) )
% 0.29/0.50        = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( times_times_num @ K @ L2 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % div_mult2_numeral_eq
% 0.29/0.50  thf(fact_292_height__node,axiom,
% 0.29/0.50      ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 0.29/0.50        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 0.29/0.50       => ( ord_less_eq_nat @ one_one_nat @ ( vEBT_VEBT_height @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % height_node
% 0.29/0.50  thf(fact_293_power__commuting__commutes,axiom,
% 0.29/0.50      ! [X: complex,Y2: complex,N: nat] :
% 0.29/0.50        ( ( ( times_times_complex @ X @ Y2 )
% 0.29/0.50          = ( times_times_complex @ Y2 @ X ) )
% 0.29/0.50       => ( ( times_times_complex @ ( power_power_complex @ X @ N ) @ Y2 )
% 0.29/0.50          = ( times_times_complex @ Y2 @ ( power_power_complex @ X @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_commuting_commutes
% 0.29/0.50  thf(fact_294_power__commuting__commutes,axiom,
% 0.29/0.50      ! [X: real,Y2: real,N: nat] :
% 0.29/0.50        ( ( ( times_times_real @ X @ Y2 )
% 0.29/0.50          = ( times_times_real @ Y2 @ X ) )
% 0.29/0.50       => ( ( times_times_real @ ( power_power_real @ X @ N ) @ Y2 )
% 0.29/0.50          = ( times_times_real @ Y2 @ ( power_power_real @ X @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_commuting_commutes
% 0.29/0.50  thf(fact_295_power__commuting__commutes,axiom,
% 0.29/0.50      ! [X: nat,Y2: nat,N: nat] :
% 0.29/0.50        ( ( ( times_times_nat @ X @ Y2 )
% 0.29/0.50          = ( times_times_nat @ Y2 @ X ) )
% 0.29/0.50       => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ Y2 )
% 0.29/0.50          = ( times_times_nat @ Y2 @ ( power_power_nat @ X @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_commuting_commutes
% 0.29/0.50  thf(fact_296_power__commuting__commutes,axiom,
% 0.29/0.50      ! [X: int,Y2: int,N: nat] :
% 0.29/0.50        ( ( ( times_times_int @ X @ Y2 )
% 0.29/0.50          = ( times_times_int @ Y2 @ X ) )
% 0.29/0.50       => ( ( times_times_int @ ( power_power_int @ X @ N ) @ Y2 )
% 0.29/0.50          = ( times_times_int @ Y2 @ ( power_power_int @ X @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_commuting_commutes
% 0.29/0.50  thf(fact_297_power__mult__distrib,axiom,
% 0.29/0.50      ! [A: complex,B: complex,N: nat] :
% 0.29/0.50        ( ( power_power_complex @ ( times_times_complex @ A @ B ) @ N )
% 0.29/0.50        = ( times_times_complex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_mult_distrib
% 0.29/0.50  thf(fact_298_power__mult__distrib,axiom,
% 0.29/0.50      ! [A: real,B: real,N: nat] :
% 0.29/0.50        ( ( power_power_real @ ( times_times_real @ A @ B ) @ N )
% 0.29/0.50        = ( times_times_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_mult_distrib
% 0.29/0.50  thf(fact_299_power__mult__distrib,axiom,
% 0.29/0.50      ! [A: nat,B: nat,N: nat] :
% 0.29/0.50        ( ( power_power_nat @ ( times_times_nat @ A @ B ) @ N )
% 0.29/0.50        = ( times_times_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_mult_distrib
% 0.29/0.50  thf(fact_300_power__mult__distrib,axiom,
% 0.29/0.50      ! [A: int,B: int,N: nat] :
% 0.29/0.50        ( ( power_power_int @ ( times_times_int @ A @ B ) @ N )
% 0.29/0.50        = ( times_times_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_mult_distrib
% 0.29/0.50  thf(fact_301_power__commutes,axiom,
% 0.29/0.50      ! [A: complex,N: nat] :
% 0.29/0.50        ( ( times_times_complex @ ( power_power_complex @ A @ N ) @ A )
% 0.29/0.50        = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_commutes
% 0.29/0.50  thf(fact_302_power__commutes,axiom,
% 0.29/0.50      ! [A: real,N: nat] :
% 0.29/0.50        ( ( times_times_real @ ( power_power_real @ A @ N ) @ A )
% 0.29/0.50        = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_commutes
% 0.29/0.50  thf(fact_303_power__commutes,axiom,
% 0.29/0.50      ! [A: nat,N: nat] :
% 0.29/0.50        ( ( times_times_nat @ ( power_power_nat @ A @ N ) @ A )
% 0.29/0.50        = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_commutes
% 0.29/0.50  thf(fact_304_power__commutes,axiom,
% 0.29/0.50      ! [A: int,N: nat] :
% 0.29/0.50        ( ( times_times_int @ ( power_power_int @ A @ N ) @ A )
% 0.29/0.50        = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_commutes
% 0.29/0.50  thf(fact_305_power__divide,axiom,
% 0.29/0.50      ! [A: complex,B: complex,N: nat] :
% 0.29/0.50        ( ( power_power_complex @ ( divide1717551699836669952omplex @ A @ B ) @ N )
% 0.29/0.50        = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_divide
% 0.29/0.50  thf(fact_306_power__divide,axiom,
% 0.29/0.50      ! [A: real,B: real,N: nat] :
% 0.29/0.50        ( ( power_power_real @ ( divide_divide_real @ A @ B ) @ N )
% 0.29/0.50        = ( divide_divide_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_divide
% 0.29/0.50  thf(fact_307_power__divide,axiom,
% 0.29/0.50      ! [A: rat,B: rat,N: nat] :
% 0.29/0.50        ( ( power_power_rat @ ( divide_divide_rat @ A @ B ) @ N )
% 0.29/0.50        = ( divide_divide_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_divide
% 0.29/0.50  thf(fact_308_power__mult,axiom,
% 0.29/0.50      ! [A: nat,M: nat,N: nat] :
% 0.29/0.50        ( ( power_power_nat @ A @ ( times_times_nat @ M @ N ) )
% 0.29/0.50        = ( power_power_nat @ ( power_power_nat @ A @ M ) @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_mult
% 0.29/0.50  thf(fact_309_power__mult,axiom,
% 0.29/0.50      ! [A: real,M: nat,N: nat] :
% 0.29/0.50        ( ( power_power_real @ A @ ( times_times_nat @ M @ N ) )
% 0.29/0.50        = ( power_power_real @ ( power_power_real @ A @ M ) @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_mult
% 0.29/0.50  thf(fact_310_power__mult,axiom,
% 0.29/0.50      ! [A: int,M: nat,N: nat] :
% 0.29/0.50        ( ( power_power_int @ A @ ( times_times_nat @ M @ N ) )
% 0.29/0.50        = ( power_power_int @ ( power_power_int @ A @ M ) @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_mult
% 0.29/0.50  thf(fact_311_power__mult,axiom,
% 0.29/0.50      ! [A: complex,M: nat,N: nat] :
% 0.29/0.50        ( ( power_power_complex @ A @ ( times_times_nat @ M @ N ) )
% 0.29/0.50        = ( power_power_complex @ ( power_power_complex @ A @ M ) @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_mult
% 0.29/0.50  thf(fact_312_div__le__dividend,axiom,
% 0.29/0.50      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ M ) ).
% 0.29/0.50  
% 0.29/0.50  % div_le_dividend
% 0.29/0.50  thf(fact_313_div__le__mono,axiom,
% 0.29/0.50      ! [M: nat,N: nat,K: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.50       => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N @ K ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % div_le_mono
% 0.29/0.50  thf(fact_314_div__mult2__eq,axiom,
% 0.29/0.50      ! [M: nat,N: nat,Q2: nat] :
% 0.29/0.50        ( ( divide_divide_nat @ M @ ( times_times_nat @ N @ Q2 ) )
% 0.29/0.50        = ( divide_divide_nat @ ( divide_divide_nat @ M @ N ) @ Q2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % div_mult2_eq
% 0.29/0.50  thf(fact_315_one__le__power,axiom,
% 0.29/0.50      ! [A: rat,N: nat] :
% 0.29/0.50        ( ( ord_less_eq_rat @ one_one_rat @ A )
% 0.29/0.50       => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % one_le_power
% 0.29/0.50  thf(fact_316_one__le__power,axiom,
% 0.29/0.50      ! [A: real,N: nat] :
% 0.29/0.50        ( ( ord_less_eq_real @ one_one_real @ A )
% 0.29/0.50       => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % one_le_power
% 0.29/0.50  thf(fact_317_one__le__power,axiom,
% 0.29/0.50      ! [A: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ one_one_nat @ A )
% 0.29/0.50       => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % one_le_power
% 0.29/0.50  thf(fact_318_one__le__power,axiom,
% 0.29/0.50      ! [A: int,N: nat] :
% 0.29/0.50        ( ( ord_less_eq_int @ one_one_int @ A )
% 0.29/0.50       => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % one_le_power
% 0.29/0.50  thf(fact_319_left__right__inverse__power,axiom,
% 0.29/0.50      ! [X: rat,Y2: rat,N: nat] :
% 0.29/0.50        ( ( ( times_times_rat @ X @ Y2 )
% 0.29/0.50          = one_one_rat )
% 0.29/0.50       => ( ( times_times_rat @ ( power_power_rat @ X @ N ) @ ( power_power_rat @ Y2 @ N ) )
% 0.29/0.50          = one_one_rat ) ) ).
% 0.29/0.50  
% 0.29/0.50  % left_right_inverse_power
% 0.29/0.50  thf(fact_320_left__right__inverse__power,axiom,
% 0.29/0.50      ! [X: complex,Y2: complex,N: nat] :
% 0.29/0.50        ( ( ( times_times_complex @ X @ Y2 )
% 0.29/0.50          = one_one_complex )
% 0.29/0.50       => ( ( times_times_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y2 @ N ) )
% 0.29/0.50          = one_one_complex ) ) ).
% 0.29/0.50  
% 0.29/0.50  % left_right_inverse_power
% 0.29/0.50  thf(fact_321_left__right__inverse__power,axiom,
% 0.29/0.50      ! [X: real,Y2: real,N: nat] :
% 0.29/0.50        ( ( ( times_times_real @ X @ Y2 )
% 0.29/0.50          = one_one_real )
% 0.29/0.50       => ( ( times_times_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y2 @ N ) )
% 0.29/0.50          = one_one_real ) ) ).
% 0.29/0.50  
% 0.29/0.50  % left_right_inverse_power
% 0.29/0.50  thf(fact_322_left__right__inverse__power,axiom,
% 0.29/0.50      ! [X: nat,Y2: nat,N: nat] :
% 0.29/0.50        ( ( ( times_times_nat @ X @ Y2 )
% 0.29/0.50          = one_one_nat )
% 0.29/0.50       => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y2 @ N ) )
% 0.29/0.50          = one_one_nat ) ) ).
% 0.29/0.50  
% 0.29/0.50  % left_right_inverse_power
% 0.29/0.50  thf(fact_323_left__right__inverse__power,axiom,
% 0.29/0.50      ! [X: int,Y2: int,N: nat] :
% 0.29/0.50        ( ( ( times_times_int @ X @ Y2 )
% 0.29/0.50          = one_one_int )
% 0.29/0.50       => ( ( times_times_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y2 @ N ) )
% 0.29/0.50          = one_one_int ) ) ).
% 0.29/0.50  
% 0.29/0.50  % left_right_inverse_power
% 0.29/0.50  thf(fact_324_power__one__over,axiom,
% 0.29/0.50      ! [A: complex,N: nat] :
% 0.29/0.50        ( ( power_power_complex @ ( divide1717551699836669952omplex @ one_one_complex @ A ) @ N )
% 0.29/0.50        = ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ A @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_one_over
% 0.29/0.50  thf(fact_325_power__one__over,axiom,
% 0.29/0.50      ! [A: real,N: nat] :
% 0.29/0.50        ( ( power_power_real @ ( divide_divide_real @ one_one_real @ A ) @ N )
% 0.29/0.50        = ( divide_divide_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_one_over
% 0.29/0.50  thf(fact_326_power__one__over,axiom,
% 0.29/0.50      ! [A: rat,N: nat] :
% 0.29/0.50        ( ( power_power_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ N )
% 0.29/0.50        = ( divide_divide_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_one_over
% 0.29/0.50  thf(fact_327_power__add,axiom,
% 0.29/0.50      ! [A: complex,M: nat,N: nat] :
% 0.29/0.50        ( ( power_power_complex @ A @ ( plus_plus_nat @ M @ N ) )
% 0.29/0.50        = ( times_times_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_add
% 0.29/0.50  thf(fact_328_power__add,axiom,
% 0.29/0.50      ! [A: real,M: nat,N: nat] :
% 0.29/0.50        ( ( power_power_real @ A @ ( plus_plus_nat @ M @ N ) )
% 0.29/0.50        = ( times_times_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_add
% 0.29/0.50  thf(fact_329_power__add,axiom,
% 0.29/0.50      ! [A: nat,M: nat,N: nat] :
% 0.29/0.50        ( ( power_power_nat @ A @ ( plus_plus_nat @ M @ N ) )
% 0.29/0.50        = ( times_times_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_add
% 0.29/0.50  thf(fact_330_power__add,axiom,
% 0.29/0.50      ! [A: int,M: nat,N: nat] :
% 0.29/0.50        ( ( power_power_int @ A @ ( plus_plus_nat @ M @ N ) )
% 0.29/0.50        = ( times_times_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_add
% 0.29/0.50  thf(fact_331_less__mult__imp__div__less,axiom,
% 0.29/0.50      ! [M: nat,I2: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_nat @ M @ ( times_times_nat @ I2 @ N ) )
% 0.29/0.50       => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ I2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % less_mult_imp_div_less
% 0.29/0.50  thf(fact_332_times__div__less__eq__dividend,axiom,
% 0.29/0.50      ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) @ M ) ).
% 0.29/0.50  
% 0.29/0.50  % times_div_less_eq_dividend
% 0.29/0.50  thf(fact_333_div__times__less__eq__dividend,axiom,
% 0.29/0.50      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) @ M ) ).
% 0.29/0.50  
% 0.29/0.50  % div_times_less_eq_dividend
% 0.29/0.50  thf(fact_334_numeral__Bit0__div__2,axiom,
% 0.29/0.50      ! [N: num] :
% 0.29/0.50        ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.50        = ( numeral_numeral_nat @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % numeral_Bit0_div_2
% 0.29/0.50  thf(fact_335_numeral__Bit0__div__2,axiom,
% 0.29/0.50      ! [N: num] :
% 0.29/0.50        ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.50        = ( numeral_numeral_int @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % numeral_Bit0_div_2
% 0.29/0.50  thf(fact_336_power__gt1__lemma,axiom,
% 0.29/0.50      ! [A: real,N: nat] :
% 0.29/0.50        ( ( ord_less_real @ one_one_real @ A )
% 0.29/0.50       => ( ord_less_real @ one_one_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_gt1_lemma
% 0.29/0.50  thf(fact_337_power__gt1__lemma,axiom,
% 0.29/0.50      ! [A: rat,N: nat] :
% 0.29/0.50        ( ( ord_less_rat @ one_one_rat @ A )
% 0.29/0.50       => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_gt1_lemma
% 0.29/0.50  thf(fact_338_power__gt1__lemma,axiom,
% 0.29/0.50      ! [A: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_nat @ one_one_nat @ A )
% 0.29/0.50       => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_gt1_lemma
% 0.29/0.50  thf(fact_339_power__gt1__lemma,axiom,
% 0.29/0.50      ! [A: int,N: nat] :
% 0.29/0.50        ( ( ord_less_int @ one_one_int @ A )
% 0.29/0.50       => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_gt1_lemma
% 0.29/0.50  thf(fact_340_power__less__power__Suc,axiom,
% 0.29/0.50      ! [A: real,N: nat] :
% 0.29/0.50        ( ( ord_less_real @ one_one_real @ A )
% 0.29/0.50       => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_less_power_Suc
% 0.29/0.50  thf(fact_341_power__less__power__Suc,axiom,
% 0.29/0.50      ! [A: rat,N: nat] :
% 0.29/0.50        ( ( ord_less_rat @ one_one_rat @ A )
% 0.29/0.50       => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_less_power_Suc
% 0.29/0.50  thf(fact_342_power__less__power__Suc,axiom,
% 0.29/0.50      ! [A: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_nat @ one_one_nat @ A )
% 0.29/0.50       => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_less_power_Suc
% 0.29/0.50  thf(fact_343_power__less__power__Suc,axiom,
% 0.29/0.50      ! [A: int,N: nat] :
% 0.29/0.50        ( ( ord_less_int @ one_one_int @ A )
% 0.29/0.50       => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_less_power_Suc
% 0.29/0.50  thf(fact_344_power__less__imp__less__exp,axiom,
% 0.29/0.50      ! [A: real,M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_real @ one_one_real @ A )
% 0.29/0.50       => ( ( ord_less_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 0.29/0.50         => ( ord_less_nat @ M @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_less_imp_less_exp
% 0.29/0.50  thf(fact_345_power__less__imp__less__exp,axiom,
% 0.29/0.50      ! [A: rat,M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_rat @ one_one_rat @ A )
% 0.29/0.50       => ( ( ord_less_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 0.29/0.50         => ( ord_less_nat @ M @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_less_imp_less_exp
% 0.29/0.50  thf(fact_346_power__less__imp__less__exp,axiom,
% 0.29/0.50      ! [A: nat,M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_nat @ one_one_nat @ A )
% 0.29/0.50       => ( ( ord_less_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 0.29/0.50         => ( ord_less_nat @ M @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_less_imp_less_exp
% 0.29/0.50  thf(fact_347_power__less__imp__less__exp,axiom,
% 0.29/0.50      ! [A: int,M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_int @ one_one_int @ A )
% 0.29/0.50       => ( ( ord_less_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 0.29/0.50         => ( ord_less_nat @ M @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_less_imp_less_exp
% 0.29/0.50  thf(fact_348_power__strict__increasing,axiom,
% 0.29/0.50      ! [N: nat,N4: nat,A: real] :
% 0.29/0.50        ( ( ord_less_nat @ N @ N4 )
% 0.29/0.50       => ( ( ord_less_real @ one_one_real @ A )
% 0.29/0.50         => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N4 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_strict_increasing
% 0.29/0.50  thf(fact_349_power__strict__increasing,axiom,
% 0.29/0.50      ! [N: nat,N4: nat,A: rat] :
% 0.29/0.50        ( ( ord_less_nat @ N @ N4 )
% 0.29/0.50       => ( ( ord_less_rat @ one_one_rat @ A )
% 0.29/0.50         => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_strict_increasing
% 0.29/0.50  thf(fact_350_power__strict__increasing,axiom,
% 0.29/0.50      ! [N: nat,N4: nat,A: nat] :
% 0.29/0.50        ( ( ord_less_nat @ N @ N4 )
% 0.29/0.50       => ( ( ord_less_nat @ one_one_nat @ A )
% 0.29/0.50         => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_strict_increasing
% 0.29/0.50  thf(fact_351_power__strict__increasing,axiom,
% 0.29/0.50      ! [N: nat,N4: nat,A: int] :
% 0.29/0.50        ( ( ord_less_nat @ N @ N4 )
% 0.29/0.50       => ( ( ord_less_int @ one_one_int @ A )
% 0.29/0.50         => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_strict_increasing
% 0.29/0.50  thf(fact_352_power__increasing,axiom,
% 0.29/0.50      ! [N: nat,N4: nat,A: rat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ N @ N4 )
% 0.29/0.50       => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 0.29/0.50         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_increasing
% 0.29/0.50  thf(fact_353_power__increasing,axiom,
% 0.29/0.50      ! [N: nat,N4: nat,A: real] :
% 0.29/0.50        ( ( ord_less_eq_nat @ N @ N4 )
% 0.29/0.50       => ( ( ord_less_eq_real @ one_one_real @ A )
% 0.29/0.50         => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N4 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_increasing
% 0.29/0.50  thf(fact_354_power__increasing,axiom,
% 0.29/0.50      ! [N: nat,N4: nat,A: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ N @ N4 )
% 0.29/0.50       => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 0.29/0.50         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_increasing
% 0.29/0.50  thf(fact_355_power__increasing,axiom,
% 0.29/0.50      ! [N: nat,N4: nat,A: int] :
% 0.29/0.50        ( ( ord_less_eq_nat @ N @ N4 )
% 0.29/0.50       => ( ( ord_less_eq_int @ one_one_int @ A )
% 0.29/0.50         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_increasing
% 0.29/0.50  thf(fact_356_power__le__imp__le__exp,axiom,
% 0.29/0.50      ! [A: real,M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_real @ one_one_real @ A )
% 0.29/0.50       => ( ( ord_less_eq_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 0.29/0.50         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_le_imp_le_exp
% 0.29/0.50  thf(fact_357_power__le__imp__le__exp,axiom,
% 0.29/0.50      ! [A: rat,M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_rat @ one_one_rat @ A )
% 0.29/0.50       => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 0.29/0.50         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_le_imp_le_exp
% 0.29/0.50  thf(fact_358_power__le__imp__le__exp,axiom,
% 0.29/0.50      ! [A: nat,M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_nat @ one_one_nat @ A )
% 0.29/0.50       => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 0.29/0.50         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_le_imp_le_exp
% 0.29/0.50  thf(fact_359_power__le__imp__le__exp,axiom,
% 0.29/0.50      ! [A: int,M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_int @ one_one_int @ A )
% 0.29/0.50       => ( ( ord_less_eq_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 0.29/0.50         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_le_imp_le_exp
% 0.29/0.50  thf(fact_360_power4__eq__xxxx,axiom,
% 0.29/0.50      ! [X: complex] :
% 0.29/0.50        ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.29/0.50        = ( times_times_complex @ ( times_times_complex @ ( times_times_complex @ X @ X ) @ X ) @ X ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power4_eq_xxxx
% 0.29/0.50  thf(fact_361_power4__eq__xxxx,axiom,
% 0.29/0.50      ! [X: real] :
% 0.29/0.50        ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.29/0.50        = ( times_times_real @ ( times_times_real @ ( times_times_real @ X @ X ) @ X ) @ X ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power4_eq_xxxx
% 0.29/0.50  thf(fact_362_power4__eq__xxxx,axiom,
% 0.29/0.50      ! [X: nat] :
% 0.29/0.50        ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.29/0.50        = ( times_times_nat @ ( times_times_nat @ ( times_times_nat @ X @ X ) @ X ) @ X ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power4_eq_xxxx
% 0.29/0.50  thf(fact_363_power4__eq__xxxx,axiom,
% 0.29/0.50      ! [X: int] :
% 0.29/0.50        ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.29/0.50        = ( times_times_int @ ( times_times_int @ ( times_times_int @ X @ X ) @ X ) @ X ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power4_eq_xxxx
% 0.29/0.50  thf(fact_364_power2__eq__square,axiom,
% 0.29/0.50      ! [A: complex] :
% 0.29/0.50        ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.50        = ( times_times_complex @ A @ A ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power2_eq_square
% 0.29/0.50  thf(fact_365_power2__eq__square,axiom,
% 0.29/0.50      ! [A: real] :
% 0.29/0.50        ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.50        = ( times_times_real @ A @ A ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power2_eq_square
% 0.29/0.50  thf(fact_366_power2__eq__square,axiom,
% 0.29/0.50      ! [A: nat] :
% 0.29/0.50        ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.50        = ( times_times_nat @ A @ A ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power2_eq_square
% 0.29/0.50  thf(fact_367_power2__eq__square,axiom,
% 0.29/0.50      ! [A: int] :
% 0.29/0.50        ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.50        = ( times_times_int @ A @ A ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power2_eq_square
% 0.29/0.50  thf(fact_368_one__power2,axiom,
% 0.29/0.50      ( ( power_power_rat @ one_one_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.50      = one_one_rat ) ).
% 0.29/0.50  
% 0.29/0.50  % one_power2
% 0.29/0.50  thf(fact_369_one__power2,axiom,
% 0.29/0.50      ( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.50      = one_one_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % one_power2
% 0.29/0.50  thf(fact_370_one__power2,axiom,
% 0.29/0.50      ( ( power_power_real @ one_one_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.50      = one_one_real ) ).
% 0.29/0.50  
% 0.29/0.50  % one_power2
% 0.29/0.50  thf(fact_371_one__power2,axiom,
% 0.29/0.50      ( ( power_power_int @ one_one_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.50      = one_one_int ) ).
% 0.29/0.50  
% 0.29/0.50  % one_power2
% 0.29/0.50  thf(fact_372_one__power2,axiom,
% 0.29/0.50      ( ( power_power_complex @ one_one_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.50      = one_one_complex ) ).
% 0.29/0.50  
% 0.29/0.50  % one_power2
% 0.29/0.50  thf(fact_373_numeral__Bit1__div__2,axiom,
% 0.29/0.50      ! [N: num] :
% 0.29/0.50        ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.50        = ( numeral_numeral_nat @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % numeral_Bit1_div_2
% 0.29/0.50  thf(fact_374_numeral__Bit1__div__2,axiom,
% 0.29/0.50      ! [N: num] :
% 0.29/0.50        ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.50        = ( numeral_numeral_int @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % numeral_Bit1_div_2
% 0.29/0.50  thf(fact_375_power3__eq__cube,axiom,
% 0.29/0.50      ! [A: complex] :
% 0.29/0.50        ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.29/0.50        = ( times_times_complex @ ( times_times_complex @ A @ A ) @ A ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power3_eq_cube
% 0.29/0.50  thf(fact_376_power3__eq__cube,axiom,
% 0.29/0.50      ! [A: real] :
% 0.29/0.50        ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.29/0.50        = ( times_times_real @ ( times_times_real @ A @ A ) @ A ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power3_eq_cube
% 0.29/0.50  thf(fact_377_power3__eq__cube,axiom,
% 0.29/0.50      ! [A: nat] :
% 0.29/0.50        ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.29/0.50        = ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power3_eq_cube
% 0.29/0.50  thf(fact_378_power3__eq__cube,axiom,
% 0.29/0.50      ! [A: int] :
% 0.29/0.50        ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.29/0.50        = ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power3_eq_cube
% 0.29/0.50  thf(fact_379_power__even__eq,axiom,
% 0.29/0.50      ! [A: nat,N: nat] :
% 0.29/0.50        ( ( power_power_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.29/0.50        = ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_even_eq
% 0.29/0.50  thf(fact_380_power__even__eq,axiom,
% 0.29/0.50      ! [A: real,N: nat] :
% 0.29/0.50        ( ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.29/0.50        = ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_even_eq
% 0.29/0.50  thf(fact_381_power__even__eq,axiom,
% 0.29/0.50      ! [A: int,N: nat] :
% 0.29/0.50        ( ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.29/0.50        = ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_even_eq
% 0.29/0.50  thf(fact_382_power__even__eq,axiom,
% 0.29/0.50      ! [A: complex,N: nat] :
% 0.29/0.50        ( ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.29/0.50        = ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_even_eq
% 0.29/0.50  thf(fact_383_less__exp,axiom,
% 0.29/0.50      ! [N: nat] : ( ord_less_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % less_exp
% 0.29/0.50  thf(fact_384_self__le__ge2__pow,axiom,
% 0.29/0.50      ! [K: nat,M: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 0.29/0.50       => ( ord_less_eq_nat @ M @ ( power_power_nat @ K @ M ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % self_le_ge2_pow
% 0.29/0.50  thf(fact_385_power2__nat__le__eq__le,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.50        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power2_nat_le_eq_le
% 0.29/0.50  thf(fact_386_power2__nat__le__imp__le,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N )
% 0.29/0.50       => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power2_nat_le_imp_le
% 0.29/0.50  thf(fact_387_nested__mint,axiom,
% 0.29/0.50      ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,Va: nat] :
% 0.29/0.50        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 0.29/0.50       => ( ( N
% 0.29/0.50            = ( suc @ ( suc @ Va ) ) )
% 0.29/0.50         => ( ~ ( ord_less_nat @ Ma @ Mi )
% 0.29/0.50           => ( ( Ma != Mi )
% 0.29/0.50             => ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( suc @ ( divide_divide_nat @ Va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % nested_mint
% 0.29/0.50  thf(fact_388_both__member__options__from__chilf__to__complete__tree,axiom,
% 0.29/0.50      ! [X: nat,Deg: nat,TreeList: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 0.29/0.50        ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.29/0.50       => ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 0.29/0.50         => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.50           => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % both_member_options_from_chilf_to_complete_tree
% 0.29/0.50  thf(fact_389_post__member__pre__member,axiom,
% 0.29/0.50      ! [T: vEBT_VEBT,N: nat,X: nat,Y2: nat] :
% 0.29/0.50        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.50       => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.29/0.50         => ( ( ord_less_nat @ Y2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.29/0.50           => ( ( vEBT_vebt_member @ ( vEBT_vebt_insert @ T @ X ) @ Y2 )
% 0.29/0.50             => ( ( vEBT_vebt_member @ T @ Y2 )
% 0.29/0.50                | ( X = Y2 ) ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % post_member_pre_member
% 0.29/0.50  thf(fact_390_both__member__options__from__complete__tree__to__child,axiom,
% 0.29/0.50      ! [Deg: nat,Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 0.29/0.50       => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.29/0.50         => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.50            | ( X = Mi )
% 0.29/0.50            | ( X = Ma ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % both_member_options_from_complete_tree_to_child
% 0.29/0.50  thf(fact_391_summaxma,axiom,
% 0.29/0.50      ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.29/0.50        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg )
% 0.29/0.50       => ( ( Mi != Ma )
% 0.29/0.50         => ( ( the_nat @ ( vEBT_vebt_maxt @ Summary ) )
% 0.29/0.50            = ( vEBT_VEBT_high @ Ma @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % summaxma
% 0.29/0.50  thf(fact_392_both__member__options__ding,axiom,
% 0.29/0.50      ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.50        ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N )
% 0.29/0.50       => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 0.29/0.50         => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.50           => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ X ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % both_member_options_ding
% 0.29/0.50  thf(fact_393_member__bound,axiom,
% 0.29/0.50      ! [Tree: vEBT_VEBT,X: nat,N: nat] :
% 0.29/0.50        ( ( vEBT_vebt_member @ Tree @ X )
% 0.29/0.50       => ( ( vEBT_invar_vebt @ Tree @ N )
% 0.29/0.50         => ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % member_bound
% 0.29/0.50  thf(fact_394_div__exp__eq,axiom,
% 0.29/0.50      ! [A: nat,M: nat,N: nat] :
% 0.29/0.50        ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.29/0.50        = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % div_exp_eq
% 0.29/0.50  thf(fact_395_div__exp__eq,axiom,
% 0.29/0.50      ! [A: int,M: nat,N: nat] :
% 0.29/0.50        ( ( divide_divide_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.29/0.50        = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % div_exp_eq
% 0.29/0.50  thf(fact_396_set__n__deg__not__0,axiom,
% 0.29/0.50      ! [TreeList: list_VEBT_VEBT,N: nat,M: nat] :
% 0.29/0.50        ( ! [X3: vEBT_VEBT] :
% 0.29/0.50            ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.29/0.50           => ( vEBT_invar_vebt @ X3 @ N ) )
% 0.29/0.50       => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.29/0.50            = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.29/0.50         => ( ord_less_eq_nat @ one_one_nat @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % set_n_deg_not_0
% 0.29/0.50  thf(fact_397_field__less__half__sum,axiom,
% 0.29/0.50      ! [X: real,Y2: real] :
% 0.29/0.50        ( ( ord_less_real @ X @ Y2 )
% 0.29/0.50       => ( ord_less_real @ X @ ( divide_divide_real @ ( plus_plus_real @ X @ Y2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % field_less_half_sum
% 0.29/0.50  thf(fact_398_field__less__half__sum,axiom,
% 0.29/0.50      ! [X: rat,Y2: rat] :
% 0.29/0.50        ( ( ord_less_rat @ X @ Y2 )
% 0.29/0.50       => ( ord_less_rat @ X @ ( divide_divide_rat @ ( plus_plus_rat @ X @ Y2 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % field_less_half_sum
% 0.29/0.50  thf(fact_399_delt__out__of__range,axiom,
% 0.29/0.50      ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.29/0.50        ( ( ( ord_less_nat @ X @ Mi )
% 0.29/0.50          | ( ord_less_nat @ Ma @ X ) )
% 0.29/0.50       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.29/0.50         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.29/0.50            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % delt_out_of_range
% 0.29/0.50  thf(fact_400_nat__1__eq__mult__iff,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( one_one_nat
% 0.29/0.50          = ( times_times_nat @ M @ N ) )
% 0.29/0.50        = ( ( M = one_one_nat )
% 0.29/0.50          & ( N = one_one_nat ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % nat_1_eq_mult_iff
% 0.29/0.50  thf(fact_401_even__odd__cases,axiom,
% 0.29/0.50      ! [X: nat] :
% 0.29/0.50        ( ! [N3: nat] :
% 0.29/0.50            ( X
% 0.29/0.50           != ( plus_plus_nat @ N3 @ N3 ) )
% 0.29/0.50       => ~ ! [N3: nat] :
% 0.29/0.50              ( X
% 0.29/0.50             != ( plus_plus_nat @ N3 @ ( suc @ N3 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % even_odd_cases
% 0.29/0.50  thf(fact_402_delete__pres__valid,axiom,
% 0.29/0.50      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.50        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.50       => ( vEBT_invar_vebt @ ( vEBT_vebt_delete @ T @ X ) @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % delete_pres_valid
% 0.29/0.50  thf(fact_403_deg__SUcn__Node,axiom,
% 0.29/0.50      ! [Tree: vEBT_VEBT,N: nat] :
% 0.29/0.50        ( ( vEBT_invar_vebt @ Tree @ ( suc @ ( suc @ N ) ) )
% 0.29/0.50       => ? [Info2: option4927543243414619207at_nat,TreeList2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 0.29/0.50            ( Tree
% 0.29/0.50            = ( vEBT_Node @ Info2 @ ( suc @ ( suc @ N ) ) @ TreeList2 @ S ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % deg_SUcn_Node
% 0.29/0.50  thf(fact_404_dele__bmo__cont__corr,axiom,
% 0.29/0.50      ! [T: vEBT_VEBT,N: nat,X: nat,Y2: nat] :
% 0.29/0.50        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.50       => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ T @ X ) @ Y2 )
% 0.29/0.50          = ( ( X != Y2 )
% 0.29/0.50            & ( vEBT_V8194947554948674370ptions @ T @ Y2 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % dele_bmo_cont_corr
% 0.29/0.50  thf(fact_405_both__member__options__equiv__member,axiom,
% 0.29/0.50      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.50        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.50       => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 0.29/0.50          = ( vEBT_vebt_member @ T @ X ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % both_member_options_equiv_member
% 0.29/0.50  thf(fact_406_valid__member__both__member__options,axiom,
% 0.29/0.50      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.50        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.50       => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 0.29/0.50         => ( vEBT_vebt_member @ T @ X ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % valid_member_both_member_options
% 0.29/0.50  thf(fact_407_dele__member__cont__corr,axiom,
% 0.29/0.50      ! [T: vEBT_VEBT,N: nat,X: nat,Y2: nat] :
% 0.29/0.50        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.50       => ( ( vEBT_vebt_member @ ( vEBT_vebt_delete @ T @ X ) @ Y2 )
% 0.29/0.50          = ( ( X != Y2 )
% 0.29/0.50            & ( vEBT_vebt_member @ T @ Y2 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % dele_member_cont_corr
% 0.29/0.50  thf(fact_408_inthall,axiom,
% 0.29/0.50      ! [Xs2: list_P6011104703257516679at_nat,P: product_prod_nat_nat > $o,N: nat] :
% 0.29/0.50        ( ! [X3: product_prod_nat_nat] :
% 0.29/0.50            ( ( member8440522571783428010at_nat @ X3 @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 0.29/0.50           => ( P @ X3 ) )
% 0.29/0.50       => ( ( ord_less_nat @ N @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 0.29/0.50         => ( P @ ( nth_Pr7617993195940197384at_nat @ Xs2 @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % inthall
% 0.29/0.50  thf(fact_409_inthall,axiom,
% 0.29/0.50      ! [Xs2: list_complex,P: complex > $o,N: nat] :
% 0.29/0.50        ( ! [X3: complex] :
% 0.29/0.50            ( ( member_complex @ X3 @ ( set_complex2 @ Xs2 ) )
% 0.29/0.50           => ( P @ X3 ) )
% 0.29/0.50       => ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 0.29/0.50         => ( P @ ( nth_complex @ Xs2 @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % inthall
% 0.29/0.50  thf(fact_410_inthall,axiom,
% 0.29/0.50      ! [Xs2: list_real,P: real > $o,N: nat] :
% 0.29/0.50        ( ! [X3: real] :
% 0.29/0.50            ( ( member_real @ X3 @ ( set_real2 @ Xs2 ) )
% 0.29/0.50           => ( P @ X3 ) )
% 0.29/0.50       => ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 0.29/0.50         => ( P @ ( nth_real @ Xs2 @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % inthall
% 0.29/0.50  thf(fact_411_inthall,axiom,
% 0.29/0.50      ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o,N: nat] :
% 0.29/0.50        ( ! [X3: vEBT_VEBT] :
% 0.29/0.50            ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 0.29/0.50           => ( P @ X3 ) )
% 0.29/0.50       => ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.29/0.50         => ( P @ ( nth_VEBT_VEBT @ Xs2 @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % inthall
% 0.29/0.50  thf(fact_412_inthall,axiom,
% 0.29/0.50      ! [Xs2: list_o,P: $o > $o,N: nat] :
% 0.29/0.50        ( ! [X3: $o] :
% 0.29/0.50            ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 0.29/0.50           => ( P @ X3 ) )
% 0.29/0.50       => ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 0.29/0.50         => ( P @ ( nth_o @ Xs2 @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % inthall
% 0.29/0.50  thf(fact_413_inthall,axiom,
% 0.29/0.50      ! [Xs2: list_nat,P: nat > $o,N: nat] :
% 0.29/0.50        ( ! [X3: nat] :
% 0.29/0.50            ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 0.29/0.50           => ( P @ X3 ) )
% 0.29/0.50       => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 0.29/0.50         => ( P @ ( nth_nat @ Xs2 @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % inthall
% 0.29/0.50  thf(fact_414_inthall,axiom,
% 0.29/0.50      ! [Xs2: list_int,P: int > $o,N: nat] :
% 0.29/0.50        ( ! [X3: int] :
% 0.29/0.50            ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 0.29/0.50           => ( P @ X3 ) )
% 0.29/0.50       => ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 0.29/0.50         => ( P @ ( nth_int @ Xs2 @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % inthall
% 0.29/0.50  thf(fact_415_bit__split__inv,axiom,
% 0.29/0.50      ! [X: nat,D2: nat] :
% 0.29/0.50        ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X @ D2 ) @ ( vEBT_VEBT_low @ X @ D2 ) @ D2 )
% 0.29/0.50        = X ) ).
% 0.29/0.50  
% 0.29/0.50  % bit_split_inv
% 0.29/0.50  thf(fact_416_nat_Oinject,axiom,
% 0.29/0.50      ! [X23: nat,Y22: nat] :
% 0.29/0.50        ( ( ( suc @ X23 )
% 0.29/0.50          = ( suc @ Y22 ) )
% 0.29/0.50        = ( X23 = Y22 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % nat.inject
% 0.29/0.50  thf(fact_417_old_Onat_Oinject,axiom,
% 0.29/0.50      ! [Nat: nat,Nat2: nat] :
% 0.29/0.50        ( ( ( suc @ Nat )
% 0.29/0.50          = ( suc @ Nat2 ) )
% 0.29/0.50        = ( Nat = Nat2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % old.nat.inject
% 0.29/0.50  thf(fact_418_real__divide__square__eq,axiom,
% 0.29/0.50      ! [R: real,A: real] :
% 0.29/0.50        ( ( divide_divide_real @ ( times_times_real @ R @ A ) @ ( times_times_real @ R @ R ) )
% 0.29/0.50        = ( divide_divide_real @ A @ R ) ) ).
% 0.29/0.50  
% 0.29/0.50  % real_divide_square_eq
% 0.29/0.50  thf(fact_419_height__compose__child,axiom,
% 0.29/0.50      ! [T: vEBT_VEBT,TreeList: list_VEBT_VEBT,Info: option4927543243414619207at_nat,Deg: nat,Summary: vEBT_VEBT] :
% 0.29/0.50        ( ( member_VEBT_VEBT @ T @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.29/0.50       => ( ord_less_eq_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( vEBT_VEBT_height @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % height_compose_child
% 0.29/0.50  thf(fact_420_mi__eq__ma__no__ch,axiom,
% 0.29/0.50      ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.29/0.50        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg )
% 0.29/0.50       => ( ( Mi = Ma )
% 0.29/0.50         => ( ! [X5: vEBT_VEBT] :
% 0.29/0.50                ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.29/0.50               => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) )
% 0.29/0.50            & ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % mi_eq_ma_no_ch
% 0.29/0.50  thf(fact_421_low__inv,axiom,
% 0.29/0.50      ! [X: nat,N: nat,Y2: nat] :
% 0.29/0.50        ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.29/0.50       => ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ Y2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X ) @ N )
% 0.29/0.50          = X ) ) ).
% 0.29/0.50  
% 0.29/0.50  % low_inv
% 0.29/0.50  thf(fact_422_bits__div__by__1,axiom,
% 0.29/0.50      ! [A: nat] :
% 0.29/0.50        ( ( divide_divide_nat @ A @ one_one_nat )
% 0.29/0.50        = A ) ).
% 0.29/0.50  
% 0.29/0.50  % bits_div_by_1
% 0.29/0.50  thf(fact_423_bits__div__by__1,axiom,
% 0.29/0.50      ! [A: int] :
% 0.29/0.50        ( ( divide_divide_int @ A @ one_one_int )
% 0.29/0.50        = A ) ).
% 0.29/0.50  
% 0.29/0.50  % bits_div_by_1
% 0.29/0.50  thf(fact_424_lessI,axiom,
% 0.29/0.50      ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % lessI
% 0.29/0.50  thf(fact_425_Suc__mono,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_nat @ M @ N )
% 0.29/0.50       => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Suc_mono
% 0.29/0.50  thf(fact_426_Suc__less__eq,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.29/0.50        = ( ord_less_nat @ M @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Suc_less_eq
% 0.29/0.50  thf(fact_427_add__Suc__right,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( plus_plus_nat @ M @ ( suc @ N ) )
% 0.29/0.50        = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % add_Suc_right
% 0.29/0.50  thf(fact_428_Suc__le__mono,axiom,
% 0.29/0.50      ! [N: nat,M: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
% 0.29/0.50        = ( ord_less_eq_nat @ N @ M ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Suc_le_mono
% 0.29/0.50  thf(fact_429_nat__add__left__cancel__less,axiom,
% 0.29/0.50      ! [K: nat,M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.29/0.50        = ( ord_less_nat @ M @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % nat_add_left_cancel_less
% 0.29/0.50  thf(fact_430_nat__add__left__cancel__le,axiom,
% 0.29/0.50      ! [K: nat,M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.29/0.50        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % nat_add_left_cancel_le
% 0.29/0.50  thf(fact_431_nat__mult__eq__1__iff,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( ( times_times_nat @ M @ N )
% 0.29/0.50          = one_one_nat )
% 0.29/0.50        = ( ( M = one_one_nat )
% 0.29/0.50          & ( N = one_one_nat ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % nat_mult_eq_1_iff
% 0.29/0.50  thf(fact_432_member__correct,axiom,
% 0.29/0.50      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.50        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.50       => ( ( vEBT_vebt_member @ T @ X )
% 0.29/0.50          = ( member_nat @ X @ ( vEBT_set_vebt @ T ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % member_correct
% 0.29/0.50  thf(fact_433_mult__Suc__right,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( times_times_nat @ M @ ( suc @ N ) )
% 0.29/0.50        = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % mult_Suc_right
% 0.29/0.50  thf(fact_434_member__inv,axiom,
% 0.29/0.50      ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.29/0.50        ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.29/0.50       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.29/0.50          & ( ( X = Mi )
% 0.29/0.50            | ( X = Ma )
% 0.29/0.50            | ( ( ord_less_nat @ X @ Ma )
% 0.29/0.50              & ( ord_less_nat @ Mi @ X )
% 0.29/0.50              & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.29/0.50              & ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % member_inv
% 0.29/0.50  thf(fact_435_Suc__numeral,axiom,
% 0.29/0.50      ! [N: num] :
% 0.29/0.50        ( ( suc @ ( numeral_numeral_nat @ N ) )
% 0.29/0.50        = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Suc_numeral
% 0.29/0.50  thf(fact_436_add__2__eq__Suc_H,axiom,
% 0.29/0.50      ! [N: nat] :
% 0.29/0.50        ( ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.50        = ( suc @ ( suc @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % add_2_eq_Suc'
% 0.29/0.50  thf(fact_437_add__2__eq__Suc,axiom,
% 0.29/0.50      ! [N: nat] :
% 0.29/0.50        ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.29/0.50        = ( suc @ ( suc @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % add_2_eq_Suc
% 0.29/0.50  thf(fact_438_Suc__1,axiom,
% 0.29/0.50      ( ( suc @ one_one_nat )
% 0.29/0.50      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Suc_1
% 0.29/0.50  thf(fact_439_div2__Suc__Suc,axiom,
% 0.29/0.50      ! [M: nat] :
% 0.29/0.50        ( ( divide_divide_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.50        = ( suc @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % div2_Suc_Suc
% 0.29/0.50  thf(fact_440_Suc__div__eq__add3__div__numeral,axiom,
% 0.29/0.50      ! [M: nat,V: num] :
% 0.29/0.50        ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 0.29/0.50        = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Suc_div_eq_add3_div_numeral
% 0.29/0.50  thf(fact_441_div__Suc__eq__div__add3,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( divide_divide_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 0.29/0.50        = ( divide_divide_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % div_Suc_eq_div_add3
% 0.29/0.50  thf(fact_442_complete__real,axiom,
% 0.29/0.50      ! [S2: set_real] :
% 0.29/0.50        ( ? [X5: real] : ( member_real @ X5 @ S2 )
% 0.29/0.50       => ( ? [Z2: real] :
% 0.29/0.50            ! [X3: real] :
% 0.29/0.50              ( ( member_real @ X3 @ S2 )
% 0.29/0.50             => ( ord_less_eq_real @ X3 @ Z2 ) )
% 0.29/0.50         => ? [Y3: real] :
% 0.29/0.50              ( ! [X5: real] :
% 0.29/0.50                  ( ( member_real @ X5 @ S2 )
% 0.29/0.50                 => ( ord_less_eq_real @ X5 @ Y3 ) )
% 0.29/0.50              & ! [Z2: real] :
% 0.29/0.50                  ( ! [X3: real] :
% 0.29/0.50                      ( ( member_real @ X3 @ S2 )
% 0.29/0.50                     => ( ord_less_eq_real @ X3 @ Z2 ) )
% 0.29/0.50                 => ( ord_less_eq_real @ Y3 @ Z2 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % complete_real
% 0.29/0.50  thf(fact_443_real__arch__pow,axiom,
% 0.29/0.50      ! [X: real,Y2: real] :
% 0.29/0.50        ( ( ord_less_real @ one_one_real @ X )
% 0.29/0.50       => ? [N3: nat] : ( ord_less_real @ Y2 @ ( power_power_real @ X @ N3 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % real_arch_pow
% 0.29/0.50  thf(fact_444_less__eq__real__def,axiom,
% 0.29/0.50      ( ord_less_eq_real
% 0.29/0.50      = ( ^ [X2: real,Y: real] :
% 0.29/0.50            ( ( ord_less_real @ X2 @ Y )
% 0.29/0.50            | ( X2 = Y ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % less_eq_real_def
% 0.29/0.50  thf(fact_445_Suc__inject,axiom,
% 0.29/0.50      ! [X: nat,Y2: nat] :
% 0.29/0.50        ( ( ( suc @ X )
% 0.29/0.50          = ( suc @ Y2 ) )
% 0.29/0.50       => ( X = Y2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Suc_inject
% 0.29/0.50  thf(fact_446_n__not__Suc__n,axiom,
% 0.29/0.50      ! [N: nat] :
% 0.29/0.50        ( N
% 0.29/0.50       != ( suc @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % n_not_Suc_n
% 0.29/0.50  thf(fact_447_Nat_OlessE,axiom,
% 0.29/0.50      ! [I2: nat,K: nat] :
% 0.29/0.50        ( ( ord_less_nat @ I2 @ K )
% 0.29/0.50       => ( ( K
% 0.29/0.50           != ( suc @ I2 ) )
% 0.29/0.50         => ~ ! [J2: nat] :
% 0.29/0.50                ( ( ord_less_nat @ I2 @ J2 )
% 0.29/0.50               => ( K
% 0.29/0.50                 != ( suc @ J2 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Nat.lessE
% 0.29/0.50  thf(fact_448_Suc__lessD,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_nat @ ( suc @ M ) @ N )
% 0.29/0.50       => ( ord_less_nat @ M @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Suc_lessD
% 0.29/0.50  thf(fact_449_Suc__lessE,axiom,
% 0.29/0.50      ! [I2: nat,K: nat] :
% 0.29/0.50        ( ( ord_less_nat @ ( suc @ I2 ) @ K )
% 0.29/0.50       => ~ ! [J2: nat] :
% 0.29/0.50              ( ( ord_less_nat @ I2 @ J2 )
% 0.29/0.50             => ( K
% 0.29/0.50               != ( suc @ J2 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Suc_lessE
% 0.29/0.50  thf(fact_450_Suc__lessI,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_nat @ M @ N )
% 0.29/0.50       => ( ( ( suc @ M )
% 0.29/0.50           != N )
% 0.29/0.50         => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Suc_lessI
% 0.29/0.50  thf(fact_451_less__SucE,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.29/0.50       => ( ~ ( ord_less_nat @ M @ N )
% 0.29/0.50         => ( M = N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % less_SucE
% 0.29/0.50  thf(fact_452_less__SucI,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_nat @ M @ N )
% 0.29/0.50       => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % less_SucI
% 0.29/0.50  thf(fact_453_Ex__less__Suc,axiom,
% 0.29/0.50      ! [N: nat,P: nat > $o] :
% 0.29/0.50        ( ( ? [I3: nat] :
% 0.29/0.50              ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 0.29/0.50              & ( P @ I3 ) ) )
% 0.29/0.50        = ( ( P @ N )
% 0.29/0.50          | ? [I3: nat] :
% 0.29/0.50              ( ( ord_less_nat @ I3 @ N )
% 0.29/0.50              & ( P @ I3 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Ex_less_Suc
% 0.29/0.50  thf(fact_454_less__Suc__eq,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.29/0.50        = ( ( ord_less_nat @ M @ N )
% 0.29/0.50          | ( M = N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % less_Suc_eq
% 0.29/0.50  thf(fact_455_not__less__eq,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( ~ ( ord_less_nat @ M @ N ) )
% 0.29/0.50        = ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % not_less_eq
% 0.29/0.50  thf(fact_456_All__less__Suc,axiom,
% 0.29/0.50      ! [N: nat,P: nat > $o] :
% 0.29/0.50        ( ( ! [I3: nat] :
% 0.29/0.50              ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 0.29/0.50             => ( P @ I3 ) ) )
% 0.29/0.50        = ( ( P @ N )
% 0.29/0.50          & ! [I3: nat] :
% 0.29/0.50              ( ( ord_less_nat @ I3 @ N )
% 0.29/0.50             => ( P @ I3 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % All_less_Suc
% 0.29/0.50  thf(fact_457_Suc__less__eq2,axiom,
% 0.29/0.50      ! [N: nat,M: nat] :
% 0.29/0.50        ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.29/0.50        = ( ? [M2: nat] :
% 0.29/0.50              ( ( M
% 0.29/0.50                = ( suc @ M2 ) )
% 0.29/0.50              & ( ord_less_nat @ N @ M2 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Suc_less_eq2
% 0.29/0.50  thf(fact_458_less__antisym,axiom,
% 0.29/0.50      ! [N: nat,M: nat] :
% 0.29/0.50        ( ~ ( ord_less_nat @ N @ M )
% 0.29/0.50       => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.29/0.50         => ( M = N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % less_antisym
% 0.29/0.50  thf(fact_459_Suc__less__SucD,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.29/0.50       => ( ord_less_nat @ M @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Suc_less_SucD
% 0.29/0.50  thf(fact_460_less__trans__Suc,axiom,
% 0.29/0.50      ! [I2: nat,J: nat,K: nat] :
% 0.29/0.50        ( ( ord_less_nat @ I2 @ J )
% 0.29/0.50       => ( ( ord_less_nat @ J @ K )
% 0.29/0.50         => ( ord_less_nat @ ( suc @ I2 ) @ K ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % less_trans_Suc
% 0.29/0.50  thf(fact_461_less__Suc__induct,axiom,
% 0.29/0.50      ! [I2: nat,J: nat,P: nat > nat > $o] :
% 0.29/0.50        ( ( ord_less_nat @ I2 @ J )
% 0.29/0.50       => ( ! [I4: nat] : ( P @ I4 @ ( suc @ I4 ) )
% 0.29/0.50         => ( ! [I4: nat,J2: nat,K2: nat] :
% 0.29/0.50                ( ( ord_less_nat @ I4 @ J2 )
% 0.29/0.50               => ( ( ord_less_nat @ J2 @ K2 )
% 0.29/0.50                 => ( ( P @ I4 @ J2 )
% 0.29/0.50                   => ( ( P @ J2 @ K2 )
% 0.29/0.50                     => ( P @ I4 @ K2 ) ) ) ) )
% 0.29/0.50           => ( P @ I2 @ J ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % less_Suc_induct
% 0.29/0.50  thf(fact_462_strict__inc__induct,axiom,
% 0.29/0.50      ! [I2: nat,J: nat,P: nat > $o] :
% 0.29/0.50        ( ( ord_less_nat @ I2 @ J )
% 0.29/0.50       => ( ! [I4: nat] :
% 0.29/0.50              ( ( J
% 0.29/0.50                = ( suc @ I4 ) )
% 0.29/0.50             => ( P @ I4 ) )
% 0.29/0.50         => ( ! [I4: nat] :
% 0.29/0.50                ( ( ord_less_nat @ I4 @ J )
% 0.29/0.50               => ( ( P @ ( suc @ I4 ) )
% 0.29/0.50                 => ( P @ I4 ) ) )
% 0.29/0.50           => ( P @ I2 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % strict_inc_induct
% 0.29/0.50  thf(fact_463_not__less__less__Suc__eq,axiom,
% 0.29/0.50      ! [N: nat,M: nat] :
% 0.29/0.50        ( ~ ( ord_less_nat @ N @ M )
% 0.29/0.50       => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.29/0.50          = ( N = M ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % not_less_less_Suc_eq
% 0.29/0.50  thf(fact_464_add__Suc__shift,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 0.29/0.50        = ( plus_plus_nat @ M @ ( suc @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % add_Suc_shift
% 0.29/0.50  thf(fact_465_add__Suc,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 0.29/0.50        = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % add_Suc
% 0.29/0.50  thf(fact_466_nat__arith_Osuc1,axiom,
% 0.29/0.50      ! [A2: nat,K: nat,A: nat] :
% 0.29/0.50        ( ( A2
% 0.29/0.50          = ( plus_plus_nat @ K @ A ) )
% 0.29/0.50       => ( ( suc @ A2 )
% 0.29/0.50          = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % nat_arith.suc1
% 0.29/0.50  thf(fact_467_Suc__leD,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.29/0.50       => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Suc_leD
% 0.29/0.50  thf(fact_468_le__SucE,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.29/0.50       => ( ~ ( ord_less_eq_nat @ M @ N )
% 0.29/0.50         => ( M
% 0.29/0.50            = ( suc @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % le_SucE
% 0.29/0.50  thf(fact_469_le__SucI,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.50       => ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % le_SucI
% 0.29/0.50  thf(fact_470_Suc__le__D,axiom,
% 0.29/0.50      ! [N: nat,M3: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ ( suc @ N ) @ M3 )
% 0.29/0.50       => ? [M4: nat] :
% 0.29/0.50            ( M3
% 0.29/0.50            = ( suc @ M4 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Suc_le_D
% 0.29/0.50  thf(fact_471_le__Suc__eq,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.29/0.50        = ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.50          | ( M
% 0.29/0.50            = ( suc @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % le_Suc_eq
% 0.29/0.50  thf(fact_472_Suc__n__not__le__n,axiom,
% 0.29/0.50      ! [N: nat] :
% 0.29/0.50        ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 0.29/0.50  
% 0.29/0.50  % Suc_n_not_le_n
% 0.29/0.50  thf(fact_473_not__less__eq__eq,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( ~ ( ord_less_eq_nat @ M @ N ) )
% 0.29/0.50        = ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 0.29/0.50  
% 0.29/0.50  % not_less_eq_eq
% 0.29/0.50  thf(fact_474_full__nat__induct,axiom,
% 0.29/0.50      ! [P: nat > $o,N: nat] :
% 0.29/0.50        ( ! [N3: nat] :
% 0.29/0.50            ( ! [M5: nat] :
% 0.29/0.50                ( ( ord_less_eq_nat @ ( suc @ M5 ) @ N3 )
% 0.29/0.50               => ( P @ M5 ) )
% 0.29/0.50           => ( P @ N3 ) )
% 0.29/0.50       => ( P @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % full_nat_induct
% 0.29/0.50  thf(fact_475_nat__induct__at__least,axiom,
% 0.29/0.50      ! [M: nat,N: nat,P: nat > $o] :
% 0.29/0.50        ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.50       => ( ( P @ M )
% 0.29/0.50         => ( ! [N3: nat] :
% 0.29/0.50                ( ( ord_less_eq_nat @ M @ N3 )
% 0.29/0.50               => ( ( P @ N3 )
% 0.29/0.50                 => ( P @ ( suc @ N3 ) ) ) )
% 0.29/0.50           => ( P @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % nat_induct_at_least
% 0.29/0.50  thf(fact_476_transitive__stepwise__le,axiom,
% 0.29/0.50      ! [M: nat,N: nat,R2: nat > nat > $o] :
% 0.29/0.50        ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.50       => ( ! [X3: nat] : ( R2 @ X3 @ X3 )
% 0.29/0.50         => ( ! [X3: nat,Y3: nat,Z3: nat] :
% 0.29/0.50                ( ( R2 @ X3 @ Y3 )
% 0.29/0.50               => ( ( R2 @ Y3 @ Z3 )
% 0.29/0.50                 => ( R2 @ X3 @ Z3 ) ) )
% 0.29/0.50           => ( ! [N3: nat] : ( R2 @ N3 @ ( suc @ N3 ) )
% 0.29/0.50             => ( R2 @ M @ N ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % transitive_stepwise_le
% 0.29/0.50  thf(fact_477_Suc__mult__cancel1,axiom,
% 0.29/0.50      ! [K: nat,M: nat,N: nat] :
% 0.29/0.50        ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 0.29/0.50          = ( times_times_nat @ ( suc @ K ) @ N ) )
% 0.29/0.50        = ( M = N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Suc_mult_cancel1
% 0.29/0.50  thf(fact_478_lift__Suc__mono__less,axiom,
% 0.29/0.50      ! [F: nat > real,N: nat,N5: nat] :
% 0.29/0.50        ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.29/0.50       => ( ( ord_less_nat @ N @ N5 )
% 0.29/0.50         => ( ord_less_real @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % lift_Suc_mono_less
% 0.29/0.50  thf(fact_479_lift__Suc__mono__less,axiom,
% 0.29/0.50      ! [F: nat > rat,N: nat,N5: nat] :
% 0.29/0.50        ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.29/0.50       => ( ( ord_less_nat @ N @ N5 )
% 0.29/0.50         => ( ord_less_rat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % lift_Suc_mono_less
% 0.29/0.50  thf(fact_480_lift__Suc__mono__less,axiom,
% 0.29/0.50      ! [F: nat > num,N: nat,N5: nat] :
% 0.29/0.50        ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.29/0.50       => ( ( ord_less_nat @ N @ N5 )
% 0.29/0.50         => ( ord_less_num @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % lift_Suc_mono_less
% 0.29/0.50  thf(fact_481_lift__Suc__mono__less,axiom,
% 0.29/0.50      ! [F: nat > nat,N: nat,N5: nat] :
% 0.29/0.50        ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.29/0.50       => ( ( ord_less_nat @ N @ N5 )
% 0.29/0.50         => ( ord_less_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % lift_Suc_mono_less
% 0.29/0.50  thf(fact_482_lift__Suc__mono__less,axiom,
% 0.29/0.50      ! [F: nat > int,N: nat,N5: nat] :
% 0.29/0.50        ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.29/0.50       => ( ( ord_less_nat @ N @ N5 )
% 0.29/0.50         => ( ord_less_int @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % lift_Suc_mono_less
% 0.29/0.50  thf(fact_483_lift__Suc__mono__less__iff,axiom,
% 0.29/0.50      ! [F: nat > real,N: nat,M: nat] :
% 0.29/0.50        ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.29/0.50       => ( ( ord_less_real @ ( F @ N ) @ ( F @ M ) )
% 0.29/0.50          = ( ord_less_nat @ N @ M ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % lift_Suc_mono_less_iff
% 0.29/0.50  thf(fact_484_lift__Suc__mono__less__iff,axiom,
% 0.29/0.50      ! [F: nat > rat,N: nat,M: nat] :
% 0.29/0.50        ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.29/0.50       => ( ( ord_less_rat @ ( F @ N ) @ ( F @ M ) )
% 0.29/0.50          = ( ord_less_nat @ N @ M ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % lift_Suc_mono_less_iff
% 0.29/0.50  thf(fact_485_lift__Suc__mono__less__iff,axiom,
% 0.29/0.50      ! [F: nat > num,N: nat,M: nat] :
% 0.29/0.50        ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.29/0.50       => ( ( ord_less_num @ ( F @ N ) @ ( F @ M ) )
% 0.29/0.50          = ( ord_less_nat @ N @ M ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % lift_Suc_mono_less_iff
% 0.29/0.50  thf(fact_486_lift__Suc__mono__less__iff,axiom,
% 0.29/0.50      ! [F: nat > nat,N: nat,M: nat] :
% 0.29/0.50        ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.29/0.50       => ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
% 0.29/0.50          = ( ord_less_nat @ N @ M ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % lift_Suc_mono_less_iff
% 0.29/0.50  thf(fact_487_lift__Suc__mono__less__iff,axiom,
% 0.29/0.50      ! [F: nat > int,N: nat,M: nat] :
% 0.29/0.50        ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.29/0.50       => ( ( ord_less_int @ ( F @ N ) @ ( F @ M ) )
% 0.29/0.50          = ( ord_less_nat @ N @ M ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % lift_Suc_mono_less_iff
% 0.29/0.50  thf(fact_488_lift__Suc__mono__le,axiom,
% 0.29/0.50      ! [F: nat > set_real,N: nat,N5: nat] :
% 0.29/0.50        ( ! [N3: nat] : ( ord_less_eq_set_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.29/0.50       => ( ( ord_less_eq_nat @ N @ N5 )
% 0.29/0.50         => ( ord_less_eq_set_real @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % lift_Suc_mono_le
% 0.29/0.50  thf(fact_489_lift__Suc__mono__le,axiom,
% 0.29/0.50      ! [F: nat > set_nat,N: nat,N5: nat] :
% 0.29/0.50        ( ! [N3: nat] : ( ord_less_eq_set_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.29/0.50       => ( ( ord_less_eq_nat @ N @ N5 )
% 0.29/0.50         => ( ord_less_eq_set_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % lift_Suc_mono_le
% 0.29/0.50  thf(fact_490_lift__Suc__mono__le,axiom,
% 0.29/0.50      ! [F: nat > num,N: nat,N5: nat] :
% 0.29/0.50        ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.29/0.50       => ( ( ord_less_eq_nat @ N @ N5 )
% 0.29/0.50         => ( ord_less_eq_num @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % lift_Suc_mono_le
% 0.29/0.50  thf(fact_491_lift__Suc__mono__le,axiom,
% 0.29/0.50      ! [F: nat > nat,N: nat,N5: nat] :
% 0.29/0.50        ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.29/0.50       => ( ( ord_less_eq_nat @ N @ N5 )
% 0.29/0.50         => ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % lift_Suc_mono_le
% 0.29/0.50  thf(fact_492_lift__Suc__mono__le,axiom,
% 0.29/0.50      ! [F: nat > int,N: nat,N5: nat] :
% 0.29/0.50        ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.29/0.50       => ( ( ord_less_eq_nat @ N @ N5 )
% 0.29/0.50         => ( ord_less_eq_int @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % lift_Suc_mono_le
% 0.29/0.50  thf(fact_493_lift__Suc__antimono__le,axiom,
% 0.29/0.50      ! [F: nat > set_real,N: nat,N5: nat] :
% 0.29/0.50        ( ! [N3: nat] : ( ord_less_eq_set_real @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 0.29/0.50       => ( ( ord_less_eq_nat @ N @ N5 )
% 0.29/0.50         => ( ord_less_eq_set_real @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % lift_Suc_antimono_le
% 0.29/0.50  thf(fact_494_lift__Suc__antimono__le,axiom,
% 0.29/0.50      ! [F: nat > set_nat,N: nat,N5: nat] :
% 0.29/0.50        ( ! [N3: nat] : ( ord_less_eq_set_nat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 0.29/0.50       => ( ( ord_less_eq_nat @ N @ N5 )
% 0.29/0.50         => ( ord_less_eq_set_nat @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % lift_Suc_antimono_le
% 0.29/0.50  thf(fact_495_lift__Suc__antimono__le,axiom,
% 0.29/0.50      ! [F: nat > num,N: nat,N5: nat] :
% 0.29/0.50        ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 0.29/0.50       => ( ( ord_less_eq_nat @ N @ N5 )
% 0.29/0.50         => ( ord_less_eq_num @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % lift_Suc_antimono_le
% 0.29/0.50  thf(fact_496_lift__Suc__antimono__le,axiom,
% 0.29/0.50      ! [F: nat > nat,N: nat,N5: nat] :
% 0.29/0.50        ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 0.29/0.50       => ( ( ord_less_eq_nat @ N @ N5 )
% 0.29/0.50         => ( ord_less_eq_nat @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % lift_Suc_antimono_le
% 0.29/0.50  thf(fact_497_lift__Suc__antimono__le,axiom,
% 0.29/0.50      ! [F: nat > int,N: nat,N5: nat] :
% 0.29/0.50        ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 0.29/0.50       => ( ( ord_less_eq_nat @ N @ N5 )
% 0.29/0.50         => ( ord_less_eq_int @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % lift_Suc_antimono_le
% 0.29/0.50  thf(fact_498_less__imp__Suc__add,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_nat @ M @ N )
% 0.29/0.50       => ? [K2: nat] :
% 0.29/0.50            ( N
% 0.29/0.50            = ( suc @ ( plus_plus_nat @ M @ K2 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % less_imp_Suc_add
% 0.29/0.50  thf(fact_499_less__iff__Suc__add,axiom,
% 0.29/0.50      ( ord_less_nat
% 0.29/0.50      = ( ^ [M6: nat,N2: nat] :
% 0.29/0.50          ? [K3: nat] :
% 0.29/0.50            ( N2
% 0.29/0.50            = ( suc @ ( plus_plus_nat @ M6 @ K3 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % less_iff_Suc_add
% 0.29/0.50  thf(fact_500_less__add__Suc2,axiom,
% 0.29/0.50      ! [I2: nat,M: nat] : ( ord_less_nat @ I2 @ ( suc @ ( plus_plus_nat @ M @ I2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % less_add_Suc2
% 0.29/0.50  thf(fact_501_less__add__Suc1,axiom,
% 0.29/0.50      ! [I2: nat,M: nat] : ( ord_less_nat @ I2 @ ( suc @ ( plus_plus_nat @ I2 @ M ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % less_add_Suc1
% 0.29/0.50  thf(fact_502_less__natE,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_nat @ M @ N )
% 0.29/0.50       => ~ ! [Q3: nat] :
% 0.29/0.50              ( N
% 0.29/0.50             != ( suc @ ( plus_plus_nat @ M @ Q3 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % less_natE
% 0.29/0.50  thf(fact_503_Suc__leI,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_nat @ M @ N )
% 0.29/0.50       => ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Suc_leI
% 0.29/0.50  thf(fact_504_Suc__le__eq,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.29/0.50        = ( ord_less_nat @ M @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Suc_le_eq
% 0.29/0.50  thf(fact_505_dec__induct,axiom,
% 0.29/0.50      ! [I2: nat,J: nat,P: nat > $o] :
% 0.29/0.50        ( ( ord_less_eq_nat @ I2 @ J )
% 0.29/0.50       => ( ( P @ I2 )
% 0.29/0.50         => ( ! [N3: nat] :
% 0.29/0.50                ( ( ord_less_eq_nat @ I2 @ N3 )
% 0.29/0.50               => ( ( ord_less_nat @ N3 @ J )
% 0.29/0.50                 => ( ( P @ N3 )
% 0.29/0.50                   => ( P @ ( suc @ N3 ) ) ) ) )
% 0.29/0.50           => ( P @ J ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % dec_induct
% 0.29/0.50  thf(fact_506_inc__induct,axiom,
% 0.29/0.50      ! [I2: nat,J: nat,P: nat > $o] :
% 0.29/0.50        ( ( ord_less_eq_nat @ I2 @ J )
% 0.29/0.50       => ( ( P @ J )
% 0.29/0.50         => ( ! [N3: nat] :
% 0.29/0.50                ( ( ord_less_eq_nat @ I2 @ N3 )
% 0.29/0.50               => ( ( ord_less_nat @ N3 @ J )
% 0.29/0.50                 => ( ( P @ ( suc @ N3 ) )
% 0.29/0.50                   => ( P @ N3 ) ) ) )
% 0.29/0.50           => ( P @ I2 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % inc_induct
% 0.29/0.50  thf(fact_507_Suc__le__lessD,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.29/0.50       => ( ord_less_nat @ M @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Suc_le_lessD
% 0.29/0.50  thf(fact_508_le__less__Suc__eq,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.50       => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.29/0.50          = ( N = M ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % le_less_Suc_eq
% 0.29/0.50  thf(fact_509_less__Suc__eq__le,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.29/0.50        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % less_Suc_eq_le
% 0.29/0.50  thf(fact_510_less__eq__Suc__le,axiom,
% 0.29/0.50      ( ord_less_nat
% 0.29/0.50      = ( ^ [N2: nat] : ( ord_less_eq_nat @ ( suc @ N2 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % less_eq_Suc_le
% 0.29/0.50  thf(fact_511_le__imp__less__Suc,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.50       => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % le_imp_less_Suc
% 0.29/0.50  thf(fact_512_Suc__eq__plus1__left,axiom,
% 0.29/0.50      ( suc
% 0.29/0.50      = ( plus_plus_nat @ one_one_nat ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Suc_eq_plus1_left
% 0.29/0.50  thf(fact_513_plus__1__eq__Suc,axiom,
% 0.29/0.50      ( ( plus_plus_nat @ one_one_nat )
% 0.29/0.50      = suc ) ).
% 0.29/0.50  
% 0.29/0.50  % plus_1_eq_Suc
% 0.29/0.50  thf(fact_514_Suc__eq__plus1,axiom,
% 0.29/0.50      ( suc
% 0.29/0.50      = ( ^ [N2: nat] : ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Suc_eq_plus1
% 0.29/0.50  thf(fact_515_Suc__mult__less__cancel1,axiom,
% 0.29/0.50      ! [K: nat,M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 0.29/0.50        = ( ord_less_nat @ M @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Suc_mult_less_cancel1
% 0.29/0.50  thf(fact_516_mult__Suc,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( times_times_nat @ ( suc @ M ) @ N )
% 0.29/0.50        = ( plus_plus_nat @ N @ ( times_times_nat @ M @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % mult_Suc
% 0.29/0.50  thf(fact_517_Suc__mult__le__cancel1,axiom,
% 0.29/0.50      ! [K: nat,M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 0.29/0.50        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Suc_mult_le_cancel1
% 0.29/0.50  thf(fact_518_power__Suc,axiom,
% 0.29/0.50      ! [A: complex,N: nat] :
% 0.29/0.50        ( ( power_power_complex @ A @ ( suc @ N ) )
% 0.29/0.50        = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_Suc
% 0.29/0.50  thf(fact_519_power__Suc,axiom,
% 0.29/0.50      ! [A: real,N: nat] :
% 0.29/0.50        ( ( power_power_real @ A @ ( suc @ N ) )
% 0.29/0.50        = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_Suc
% 0.29/0.50  thf(fact_520_power__Suc,axiom,
% 0.29/0.50      ! [A: nat,N: nat] :
% 0.29/0.50        ( ( power_power_nat @ A @ ( suc @ N ) )
% 0.29/0.50        = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_Suc
% 0.29/0.50  thf(fact_521_power__Suc,axiom,
% 0.29/0.50      ! [A: int,N: nat] :
% 0.29/0.50        ( ( power_power_int @ A @ ( suc @ N ) )
% 0.29/0.50        = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_Suc
% 0.29/0.50  thf(fact_522_power__Suc2,axiom,
% 0.29/0.50      ! [A: complex,N: nat] :
% 0.29/0.50        ( ( power_power_complex @ A @ ( suc @ N ) )
% 0.29/0.50        = ( times_times_complex @ ( power_power_complex @ A @ N ) @ A ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_Suc2
% 0.29/0.50  thf(fact_523_power__Suc2,axiom,
% 0.29/0.50      ! [A: real,N: nat] :
% 0.29/0.50        ( ( power_power_real @ A @ ( suc @ N ) )
% 0.29/0.50        = ( times_times_real @ ( power_power_real @ A @ N ) @ A ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_Suc2
% 0.29/0.50  thf(fact_524_power__Suc2,axiom,
% 0.29/0.50      ! [A: nat,N: nat] :
% 0.29/0.50        ( ( power_power_nat @ A @ ( suc @ N ) )
% 0.29/0.50        = ( times_times_nat @ ( power_power_nat @ A @ N ) @ A ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_Suc2
% 0.29/0.50  thf(fact_525_power__Suc2,axiom,
% 0.29/0.50      ! [A: int,N: nat] :
% 0.29/0.50        ( ( power_power_int @ A @ ( suc @ N ) )
% 0.29/0.50        = ( times_times_int @ ( power_power_int @ A @ N ) @ A ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_Suc2
% 0.29/0.50  thf(fact_526_Suc__div__le__mono,axiom,
% 0.29/0.50      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ ( divide_divide_nat @ ( suc @ M ) @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Suc_div_le_mono
% 0.29/0.50  thf(fact_527_power__gt1,axiom,
% 0.29/0.50      ! [A: real,N: nat] :
% 0.29/0.50        ( ( ord_less_real @ one_one_real @ A )
% 0.29/0.50       => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ ( suc @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_gt1
% 0.29/0.50  thf(fact_528_power__gt1,axiom,
% 0.29/0.50      ! [A: rat,N: nat] :
% 0.29/0.50        ( ( ord_less_rat @ one_one_rat @ A )
% 0.29/0.50       => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_gt1
% 0.29/0.50  thf(fact_529_power__gt1,axiom,
% 0.29/0.50      ! [A: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_nat @ one_one_nat @ A )
% 0.29/0.50       => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_gt1
% 0.29/0.50  thf(fact_530_power__gt1,axiom,
% 0.29/0.50      ! [A: int,N: nat] :
% 0.29/0.50        ( ( ord_less_int @ one_one_int @ A )
% 0.29/0.50       => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_gt1
% 0.29/0.50  thf(fact_531_eval__nat__numeral_I3_J,axiom,
% 0.29/0.50      ! [N: num] :
% 0.29/0.50        ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 0.29/0.50        = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % eval_nat_numeral(3)
% 0.29/0.50  thf(fact_532_nat__neq__iff,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( M != N )
% 0.29/0.50        = ( ( ord_less_nat @ M @ N )
% 0.29/0.50          | ( ord_less_nat @ N @ M ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % nat_neq_iff
% 0.29/0.50  thf(fact_533_less__not__refl,axiom,
% 0.29/0.50      ! [N: nat] :
% 0.29/0.50        ~ ( ord_less_nat @ N @ N ) ).
% 0.29/0.50  
% 0.29/0.50  % less_not_refl
% 0.29/0.50  thf(fact_534_less__not__refl2,axiom,
% 0.29/0.50      ! [N: nat,M: nat] :
% 0.29/0.50        ( ( ord_less_nat @ N @ M )
% 0.29/0.50       => ( M != N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % less_not_refl2
% 0.29/0.50  thf(fact_535_less__not__refl3,axiom,
% 0.29/0.50      ! [S3: nat,T: nat] :
% 0.29/0.50        ( ( ord_less_nat @ S3 @ T )
% 0.29/0.50       => ( S3 != T ) ) ).
% 0.29/0.50  
% 0.29/0.50  % less_not_refl3
% 0.29/0.50  thf(fact_536_less__irrefl__nat,axiom,
% 0.29/0.50      ! [N: nat] :
% 0.29/0.50        ~ ( ord_less_nat @ N @ N ) ).
% 0.29/0.50  
% 0.29/0.50  % less_irrefl_nat
% 0.29/0.50  thf(fact_537_nat__less__induct,axiom,
% 0.29/0.50      ! [P: nat > $o,N: nat] :
% 0.29/0.50        ( ! [N3: nat] :
% 0.29/0.50            ( ! [M5: nat] :
% 0.29/0.50                ( ( ord_less_nat @ M5 @ N3 )
% 0.29/0.50               => ( P @ M5 ) )
% 0.29/0.50           => ( P @ N3 ) )
% 0.29/0.50       => ( P @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % nat_less_induct
% 0.29/0.50  thf(fact_538_infinite__descent,axiom,
% 0.29/0.50      ! [P: nat > $o,N: nat] :
% 0.29/0.50        ( ! [N3: nat] :
% 0.29/0.50            ( ~ ( P @ N3 )
% 0.29/0.50           => ? [M5: nat] :
% 0.29/0.50                ( ( ord_less_nat @ M5 @ N3 )
% 0.29/0.50                & ~ ( P @ M5 ) ) )
% 0.29/0.50       => ( P @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % infinite_descent
% 0.29/0.50  thf(fact_539_linorder__neqE__nat,axiom,
% 0.29/0.50      ! [X: nat,Y2: nat] :
% 0.29/0.50        ( ( X != Y2 )
% 0.29/0.50       => ( ~ ( ord_less_nat @ X @ Y2 )
% 0.29/0.50         => ( ord_less_nat @ Y2 @ X ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_neqE_nat
% 0.29/0.50  thf(fact_540_le__refl,axiom,
% 0.29/0.50      ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 0.29/0.50  
% 0.29/0.50  % le_refl
% 0.29/0.50  thf(fact_541_le__trans,axiom,
% 0.29/0.50      ! [I2: nat,J: nat,K: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ I2 @ J )
% 0.29/0.50       => ( ( ord_less_eq_nat @ J @ K )
% 0.29/0.50         => ( ord_less_eq_nat @ I2 @ K ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % le_trans
% 0.29/0.50  thf(fact_542_eq__imp__le,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( M = N )
% 0.29/0.50       => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % eq_imp_le
% 0.29/0.50  thf(fact_543_le__antisym,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.50       => ( ( ord_less_eq_nat @ N @ M )
% 0.29/0.50         => ( M = N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % le_antisym
% 0.29/0.50  thf(fact_544_nat__le__linear,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.50        | ( ord_less_eq_nat @ N @ M ) ) ).
% 0.29/0.50  
% 0.29/0.50  % nat_le_linear
% 0.29/0.50  thf(fact_545_Nat_Oex__has__greatest__nat,axiom,
% 0.29/0.50      ! [P: nat > $o,K: nat,B: nat] :
% 0.29/0.50        ( ( P @ K )
% 0.29/0.50       => ( ! [Y3: nat] :
% 0.29/0.50              ( ( P @ Y3 )
% 0.29/0.50             => ( ord_less_eq_nat @ Y3 @ B ) )
% 0.29/0.50         => ? [X3: nat] :
% 0.29/0.50              ( ( P @ X3 )
% 0.29/0.50              & ! [Y4: nat] :
% 0.29/0.50                  ( ( P @ Y4 )
% 0.29/0.50                 => ( ord_less_eq_nat @ Y4 @ X3 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Nat.ex_has_greatest_nat
% 0.29/0.50  thf(fact_546_size__neq__size__imp__neq,axiom,
% 0.29/0.50      ! [X: list_VEBT_VEBT,Y2: list_VEBT_VEBT] :
% 0.29/0.50        ( ( ( size_s6755466524823107622T_VEBT @ X )
% 0.29/0.50         != ( size_s6755466524823107622T_VEBT @ Y2 ) )
% 0.29/0.50       => ( X != Y2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % size_neq_size_imp_neq
% 0.29/0.50  thf(fact_547_size__neq__size__imp__neq,axiom,
% 0.29/0.50      ! [X: list_o,Y2: list_o] :
% 0.29/0.50        ( ( ( size_size_list_o @ X )
% 0.29/0.50         != ( size_size_list_o @ Y2 ) )
% 0.29/0.50       => ( X != Y2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % size_neq_size_imp_neq
% 0.29/0.50  thf(fact_548_size__neq__size__imp__neq,axiom,
% 0.29/0.50      ! [X: list_nat,Y2: list_nat] :
% 0.29/0.50        ( ( ( size_size_list_nat @ X )
% 0.29/0.50         != ( size_size_list_nat @ Y2 ) )
% 0.29/0.50       => ( X != Y2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % size_neq_size_imp_neq
% 0.29/0.50  thf(fact_549_size__neq__size__imp__neq,axiom,
% 0.29/0.50      ! [X: list_int,Y2: list_int] :
% 0.29/0.50        ( ( ( size_size_list_int @ X )
% 0.29/0.50         != ( size_size_list_int @ Y2 ) )
% 0.29/0.50       => ( X != Y2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % size_neq_size_imp_neq
% 0.29/0.50  thf(fact_550_size__neq__size__imp__neq,axiom,
% 0.29/0.50      ! [X: num,Y2: num] :
% 0.29/0.50        ( ( ( size_size_num @ X )
% 0.29/0.50         != ( size_size_num @ Y2 ) )
% 0.29/0.50       => ( X != Y2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % size_neq_size_imp_neq
% 0.29/0.50  thf(fact_551_Suc3__eq__add__3,axiom,
% 0.29/0.50      ! [N: nat] :
% 0.29/0.50        ( ( suc @ ( suc @ ( suc @ N ) ) )
% 0.29/0.50        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Suc3_eq_add_3
% 0.29/0.50  thf(fact_552_div__nat__eqI,axiom,
% 0.29/0.50      ! [N: nat,Q2: nat,M: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q2 ) @ M )
% 0.29/0.50       => ( ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q2 ) ) )
% 0.29/0.50         => ( ( divide_divide_nat @ M @ N )
% 0.29/0.50            = Q2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % div_nat_eqI
% 0.29/0.50  thf(fact_553_Suc__nat__number__of__add,axiom,
% 0.29/0.50      ! [V: num,N: nat] :
% 0.29/0.50        ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N ) )
% 0.29/0.50        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ one ) ) @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Suc_nat_number_of_add
% 0.29/0.50  thf(fact_554_Suc__div__eq__add3__div,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 0.29/0.50        = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Suc_div_eq_add3_div
% 0.29/0.50  thf(fact_555_power__odd__eq,axiom,
% 0.29/0.50      ! [A: complex,N: nat] :
% 0.29/0.50        ( ( power_power_complex @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.29/0.50        = ( times_times_complex @ A @ ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_odd_eq
% 0.29/0.50  thf(fact_556_power__odd__eq,axiom,
% 0.29/0.50      ! [A: real,N: nat] :
% 0.29/0.50        ( ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.29/0.50        = ( times_times_real @ A @ ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_odd_eq
% 0.29/0.50  thf(fact_557_power__odd__eq,axiom,
% 0.29/0.50      ! [A: nat,N: nat] :
% 0.29/0.50        ( ( power_power_nat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.29/0.50        = ( times_times_nat @ A @ ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_odd_eq
% 0.29/0.50  thf(fact_558_power__odd__eq,axiom,
% 0.29/0.50      ! [A: int,N: nat] :
% 0.29/0.50        ( ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.29/0.50        = ( times_times_int @ A @ ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_odd_eq
% 0.29/0.50  thf(fact_559_two__realpow__ge__one,axiom,
% 0.29/0.50      ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % two_realpow_ge_one
% 0.29/0.50  thf(fact_560_less__add__eq__less,axiom,
% 0.29/0.50      ! [K: nat,L2: nat,M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_nat @ K @ L2 )
% 0.29/0.50       => ( ( ( plus_plus_nat @ M @ L2 )
% 0.29/0.50            = ( plus_plus_nat @ K @ N ) )
% 0.29/0.50         => ( ord_less_nat @ M @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % less_add_eq_less
% 0.29/0.50  thf(fact_561_trans__less__add2,axiom,
% 0.29/0.50      ! [I2: nat,J: nat,M: nat] :
% 0.29/0.50        ( ( ord_less_nat @ I2 @ J )
% 0.29/0.50       => ( ord_less_nat @ I2 @ ( plus_plus_nat @ M @ J ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % trans_less_add2
% 0.29/0.50  thf(fact_562_trans__less__add1,axiom,
% 0.29/0.50      ! [I2: nat,J: nat,M: nat] :
% 0.29/0.50        ( ( ord_less_nat @ I2 @ J )
% 0.29/0.50       => ( ord_less_nat @ I2 @ ( plus_plus_nat @ J @ M ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % trans_less_add1
% 0.29/0.50  thf(fact_563_add__less__mono1,axiom,
% 0.29/0.50      ! [I2: nat,J: nat,K: nat] :
% 0.29/0.50        ( ( ord_less_nat @ I2 @ J )
% 0.29/0.50       => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % add_less_mono1
% 0.29/0.50  thf(fact_564_not__add__less2,axiom,
% 0.29/0.50      ! [J: nat,I2: nat] :
% 0.29/0.50        ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I2 ) @ I2 ) ).
% 0.29/0.50  
% 0.29/0.50  % not_add_less2
% 0.29/0.50  thf(fact_565_not__add__less1,axiom,
% 0.29/0.50      ! [I2: nat,J: nat] :
% 0.29/0.50        ~ ( ord_less_nat @ ( plus_plus_nat @ I2 @ J ) @ I2 ) ).
% 0.29/0.50  
% 0.29/0.50  % not_add_less1
% 0.29/0.50  thf(fact_566_add__less__mono,axiom,
% 0.29/0.50      ! [I2: nat,J: nat,K: nat,L2: nat] :
% 0.29/0.50        ( ( ord_less_nat @ I2 @ J )
% 0.29/0.50       => ( ( ord_less_nat @ K @ L2 )
% 0.29/0.50         => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % add_less_mono
% 0.29/0.50  thf(fact_567_add__lessD1,axiom,
% 0.29/0.50      ! [I2: nat,J: nat,K: nat] :
% 0.29/0.50        ( ( ord_less_nat @ ( plus_plus_nat @ I2 @ J ) @ K )
% 0.29/0.50       => ( ord_less_nat @ I2 @ K ) ) ).
% 0.29/0.50  
% 0.29/0.50  % add_lessD1
% 0.29/0.50  thf(fact_568_nat__less__le,axiom,
% 0.29/0.50      ( ord_less_nat
% 0.29/0.50      = ( ^ [M6: nat,N2: nat] :
% 0.29/0.50            ( ( ord_less_eq_nat @ M6 @ N2 )
% 0.29/0.50            & ( M6 != N2 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % nat_less_le
% 0.29/0.50  thf(fact_569_less__imp__le__nat,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_nat @ M @ N )
% 0.29/0.50       => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % less_imp_le_nat
% 0.29/0.50  thf(fact_570_le__eq__less__or__eq,axiom,
% 0.29/0.50      ( ord_less_eq_nat
% 0.29/0.50      = ( ^ [M6: nat,N2: nat] :
% 0.29/0.50            ( ( ord_less_nat @ M6 @ N2 )
% 0.29/0.50            | ( M6 = N2 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % le_eq_less_or_eq
% 0.29/0.50  thf(fact_571_less__or__eq__imp__le,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( ( ord_less_nat @ M @ N )
% 0.29/0.50          | ( M = N ) )
% 0.29/0.50       => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % less_or_eq_imp_le
% 0.29/0.50  thf(fact_572_le__neq__implies__less,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.50       => ( ( M != N )
% 0.29/0.50         => ( ord_less_nat @ M @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % le_neq_implies_less
% 0.29/0.50  thf(fact_573_less__mono__imp__le__mono,axiom,
% 0.29/0.50      ! [F: nat > nat,I2: nat,J: nat] :
% 0.29/0.50        ( ! [I4: nat,J2: nat] :
% 0.29/0.50            ( ( ord_less_nat @ I4 @ J2 )
% 0.29/0.50           => ( ord_less_nat @ ( F @ I4 ) @ ( F @ J2 ) ) )
% 0.29/0.50       => ( ( ord_less_eq_nat @ I2 @ J )
% 0.29/0.50         => ( ord_less_eq_nat @ ( F @ I2 ) @ ( F @ J ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % less_mono_imp_le_mono
% 0.29/0.50  thf(fact_574_nat__le__iff__add,axiom,
% 0.29/0.50      ( ord_less_eq_nat
% 0.29/0.50      = ( ^ [M6: nat,N2: nat] :
% 0.29/0.50          ? [K3: nat] :
% 0.29/0.50            ( N2
% 0.29/0.50            = ( plus_plus_nat @ M6 @ K3 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % nat_le_iff_add
% 0.29/0.50  thf(fact_575_trans__le__add2,axiom,
% 0.29/0.50      ! [I2: nat,J: nat,M: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ I2 @ J )
% 0.29/0.50       => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ M @ J ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % trans_le_add2
% 0.29/0.50  thf(fact_576_trans__le__add1,axiom,
% 0.29/0.50      ! [I2: nat,J: nat,M: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ I2 @ J )
% 0.29/0.50       => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ J @ M ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % trans_le_add1
% 0.29/0.50  thf(fact_577_add__le__mono1,axiom,
% 0.29/0.50      ! [I2: nat,J: nat,K: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ I2 @ J )
% 0.29/0.50       => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % add_le_mono1
% 0.29/0.50  thf(fact_578_add__le__mono,axiom,
% 0.29/0.50      ! [I2: nat,J: nat,K: nat,L2: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ I2 @ J )
% 0.29/0.50       => ( ( ord_less_eq_nat @ K @ L2 )
% 0.29/0.50         => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % add_le_mono
% 0.29/0.50  thf(fact_579_le__Suc__ex,axiom,
% 0.29/0.50      ! [K: nat,L2: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ K @ L2 )
% 0.29/0.50       => ? [N3: nat] :
% 0.29/0.50            ( L2
% 0.29/0.50            = ( plus_plus_nat @ K @ N3 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % le_Suc_ex
% 0.29/0.50  thf(fact_580_add__leD2,axiom,
% 0.29/0.50      ! [M: nat,K: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.29/0.50       => ( ord_less_eq_nat @ K @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % add_leD2
% 0.29/0.50  thf(fact_581_add__leD1,axiom,
% 0.29/0.50      ! [M: nat,K: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.29/0.50       => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % add_leD1
% 0.29/0.50  thf(fact_582_le__add2,axiom,
% 0.29/0.50      ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % le_add2
% 0.29/0.50  thf(fact_583_le__add1,axiom,
% 0.29/0.50      ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 0.29/0.50  
% 0.29/0.50  % le_add1
% 0.29/0.50  thf(fact_584_add__leE,axiom,
% 0.29/0.50      ! [M: nat,K: nat,N: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.29/0.50       => ~ ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.50           => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % add_leE
% 0.29/0.50  thf(fact_585_add__mult__distrib2,axiom,
% 0.29/0.50      ! [K: nat,M: nat,N: nat] :
% 0.29/0.50        ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N ) )
% 0.29/0.50        = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % add_mult_distrib2
% 0.29/0.50  thf(fact_586_add__mult__distrib,axiom,
% 0.29/0.50      ! [M: nat,N: nat,K: nat] :
% 0.29/0.50        ( ( times_times_nat @ ( plus_plus_nat @ M @ N ) @ K )
% 0.29/0.50        = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % add_mult_distrib
% 0.29/0.50  thf(fact_587_le__cube,axiom,
% 0.29/0.50      ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % le_cube
% 0.29/0.50  thf(fact_588_le__square,axiom,
% 0.29/0.50      ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 0.29/0.50  
% 0.29/0.50  % le_square
% 0.29/0.50  thf(fact_589_mult__le__mono,axiom,
% 0.29/0.50      ! [I2: nat,J: nat,K: nat,L2: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ I2 @ J )
% 0.29/0.50       => ( ( ord_less_eq_nat @ K @ L2 )
% 0.29/0.50         => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ L2 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % mult_le_mono
% 0.29/0.50  thf(fact_590_mult__le__mono1,axiom,
% 0.29/0.50      ! [I2: nat,J: nat,K: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ I2 @ J )
% 0.29/0.50       => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % mult_le_mono1
% 0.29/0.50  thf(fact_591_mult__le__mono2,axiom,
% 0.29/0.50      ! [I2: nat,J: nat,K: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ I2 @ J )
% 0.29/0.50       => ( ord_less_eq_nat @ ( times_times_nat @ K @ I2 ) @ ( times_times_nat @ K @ J ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % mult_le_mono2
% 0.29/0.50  thf(fact_592_nat__mult__1__right,axiom,
% 0.29/0.50      ! [N: nat] :
% 0.29/0.50        ( ( times_times_nat @ N @ one_one_nat )
% 0.29/0.50        = N ) ).
% 0.29/0.50  
% 0.29/0.50  % nat_mult_1_right
% 0.29/0.50  thf(fact_593_nat__mult__1,axiom,
% 0.29/0.50      ! [N: nat] :
% 0.29/0.50        ( ( times_times_nat @ one_one_nat @ N )
% 0.29/0.50        = N ) ).
% 0.29/0.50  
% 0.29/0.50  % nat_mult_1
% 0.29/0.50  thf(fact_594_mono__nat__linear__lb,axiom,
% 0.29/0.50      ! [F: nat > nat,M: nat,K: nat] :
% 0.29/0.50        ( ! [M4: nat,N3: nat] :
% 0.29/0.50            ( ( ord_less_nat @ M4 @ N3 )
% 0.29/0.50           => ( ord_less_nat @ ( F @ M4 ) @ ( F @ N3 ) ) )
% 0.29/0.50       => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % mono_nat_linear_lb
% 0.29/0.50  thf(fact_595_field__sum__of__halves,axiom,
% 0.29/0.50      ! [X: real] :
% 0.29/0.50        ( ( plus_plus_real @ ( divide_divide_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.50        = X ) ).
% 0.29/0.50  
% 0.29/0.50  % field_sum_of_halves
% 0.29/0.50  thf(fact_596_field__sum__of__halves,axiom,
% 0.29/0.50      ! [X: rat] :
% 0.29/0.50        ( ( plus_plus_rat @ ( divide_divide_rat @ X @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( divide_divide_rat @ X @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 0.29/0.50        = X ) ).
% 0.29/0.50  
% 0.29/0.50  % field_sum_of_halves
% 0.29/0.50  thf(fact_597_in__children__def,axiom,
% 0.29/0.50      ( vEBT_V5917875025757280293ildren
% 0.29/0.50      = ( ^ [N2: nat,TreeList3: list_VEBT_VEBT,X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ X2 @ N2 ) ) @ ( vEBT_VEBT_low @ X2 @ N2 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % in_children_def
% 0.29/0.50  thf(fact_598_invar__vebt_Ointros_I5_J,axiom,
% 0.29/0.50      ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 0.29/0.50        ( ! [X3: vEBT_VEBT] :
% 0.29/0.50            ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.29/0.50           => ( vEBT_invar_vebt @ X3 @ N ) )
% 0.29/0.50       => ( ( vEBT_invar_vebt @ Summary @ M )
% 0.29/0.50         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.29/0.50              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.29/0.50           => ( ( M
% 0.29/0.50                = ( suc @ N ) )
% 0.29/0.50             => ( ( Deg
% 0.29/0.50                  = ( plus_plus_nat @ N @ M ) )
% 0.29/0.50               => ( ! [I4: nat] :
% 0.29/0.50                      ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.29/0.50                     => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ X4 ) )
% 0.29/0.50                        = ( vEBT_V8194947554948674370ptions @ Summary @ I4 ) ) )
% 0.29/0.50                 => ( ( ( Mi = Ma )
% 0.29/0.50                     => ! [X3: vEBT_VEBT] :
% 0.29/0.50                          ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.29/0.50                         => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_12 ) ) )
% 0.29/0.50                   => ( ( ord_less_eq_nat @ Mi @ Ma )
% 0.29/0.50                     => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 0.29/0.50                       => ( ( ( Mi != Ma )
% 0.29/0.50                           => ! [I4: nat] :
% 0.29/0.50                                ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.29/0.50                               => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 0.29/0.50                                      = I4 )
% 0.29/0.50                                   => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 0.29/0.50                                  & ! [X3: nat] :
% 0.29/0.50                                      ( ( ( ( vEBT_VEBT_high @ X3 @ N )
% 0.29/0.50                                          = I4 )
% 0.29/0.50                                        & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ X3 @ N ) ) )
% 0.29/0.50                                     => ( ( ord_less_nat @ Mi @ X3 )
% 0.29/0.50                                        & ( ord_less_eq_nat @ X3 @ Ma ) ) ) ) ) )
% 0.29/0.50                         => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % invar_vebt.intros(5)
% 0.29/0.50  thf(fact_599_invar__vebt_Ointros_I4_J,axiom,
% 0.29/0.50      ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 0.29/0.50        ( ! [X3: vEBT_VEBT] :
% 0.29/0.50            ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.29/0.50           => ( vEBT_invar_vebt @ X3 @ N ) )
% 0.29/0.50       => ( ( vEBT_invar_vebt @ Summary @ M )
% 0.29/0.50         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.29/0.50              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.29/0.50           => ( ( M = N )
% 0.29/0.50             => ( ( Deg
% 0.29/0.50                  = ( plus_plus_nat @ N @ M ) )
% 0.29/0.50               => ( ! [I4: nat] :
% 0.29/0.50                      ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.29/0.50                     => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ X4 ) )
% 0.29/0.50                        = ( vEBT_V8194947554948674370ptions @ Summary @ I4 ) ) )
% 0.29/0.50                 => ( ( ( Mi = Ma )
% 0.29/0.50                     => ! [X3: vEBT_VEBT] :
% 0.29/0.50                          ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.29/0.50                         => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_12 ) ) )
% 0.29/0.50                   => ( ( ord_less_eq_nat @ Mi @ Ma )
% 0.29/0.50                     => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 0.29/0.50                       => ( ( ( Mi != Ma )
% 0.29/0.50                           => ! [I4: nat] :
% 0.29/0.50                                ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.29/0.50                               => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 0.29/0.50                                      = I4 )
% 0.29/0.50                                   => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 0.29/0.50                                  & ! [X3: nat] :
% 0.29/0.50                                      ( ( ( ( vEBT_VEBT_high @ X3 @ N )
% 0.29/0.50                                          = I4 )
% 0.29/0.50                                        & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ X3 @ N ) ) )
% 0.29/0.50                                     => ( ( ord_less_nat @ Mi @ X3 )
% 0.29/0.50                                        & ( ord_less_eq_nat @ X3 @ Ma ) ) ) ) ) )
% 0.29/0.50                         => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % invar_vebt.intros(4)
% 0.29/0.50  thf(fact_600_minNull__delete__time__bound,axiom,
% 0.29/0.50      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.50        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.50       => ( ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ T @ X ) )
% 0.29/0.50         => ( ord_less_eq_nat @ ( vEBT_T_d_e_l_e_t_e @ T @ X ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % minNull_delete_time_bound
% 0.29/0.50  thf(fact_601_del__single__cont,axiom,
% 0.29/0.50      ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.29/0.50        ( ( ( X = Mi )
% 0.29/0.50          & ( X = Ma ) )
% 0.29/0.50       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.29/0.50         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.29/0.50            = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % del_single_cont
% 0.29/0.50  thf(fact_602_enat__ord__number_I1_J,axiom,
% 0.29/0.50      ! [M: num,N: num] :
% 0.29/0.50        ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 0.29/0.50        = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % enat_ord_number(1)
% 0.29/0.50  thf(fact_603_enat__ord__number_I2_J,axiom,
% 0.29/0.50      ! [M: num,N: num] :
% 0.29/0.50        ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 0.29/0.50        = ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % enat_ord_number(2)
% 0.29/0.50  thf(fact_604_zdiv__numeral__Bit1,axiom,
% 0.29/0.50      ! [V: num,W: num] :
% 0.29/0.50        ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 0.29/0.50        = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % zdiv_numeral_Bit1
% 0.29/0.50  thf(fact_605_double__not__eq__Suc__double,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 0.29/0.50       != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % double_not_eq_Suc_double
% 0.29/0.50  thf(fact_606_Suc__double__not__eq__double,axiom,
% 0.29/0.50      ! [M: nat,N: nat] :
% 0.29/0.50        ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.29/0.50       != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Suc_double_not_eq_double
% 0.29/0.50  thf(fact_607_misiz,axiom,
% 0.29/0.50      ! [T: vEBT_VEBT,N: nat,M: nat] :
% 0.29/0.50        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.50       => ( ( ( some_nat @ M )
% 0.29/0.50            = ( vEBT_vebt_mint @ T ) )
% 0.29/0.50         => ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % misiz
% 0.29/0.50  thf(fact_608_not__min__Null__member,axiom,
% 0.29/0.50      ! [T: vEBT_VEBT] :
% 0.29/0.50        ( ~ ( vEBT_VEBT_minNull @ T )
% 0.29/0.50       => ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_12 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % not_min_Null_member
% 0.29/0.50  thf(fact_609_min__Null__member,axiom,
% 0.29/0.50      ! [T: vEBT_VEBT,X: nat] :
% 0.29/0.50        ( ( vEBT_VEBT_minNull @ T )
% 0.29/0.50       => ~ ( vEBT_vebt_member @ T @ X ) ) ).
% 0.29/0.50  
% 0.29/0.50  % min_Null_member
% 0.29/0.50  thf(fact_610_maxbmo,axiom,
% 0.29/0.50      ! [T: vEBT_VEBT,X: nat] :
% 0.29/0.51        ( ( ( vEBT_vebt_maxt @ T )
% 0.29/0.51          = ( some_nat @ X ) )
% 0.29/0.51       => ( vEBT_V8194947554948674370ptions @ T @ X ) ) ).
% 0.29/0.51  
% 0.29/0.51  % maxbmo
% 0.29/0.51  thf(fact_611_power__shift,axiom,
% 0.29/0.51      ! [X: nat,Y2: nat,Z: nat] :
% 0.29/0.51        ( ( ( power_power_nat @ X @ Y2 )
% 0.29/0.51          = Z )
% 0.29/0.51        = ( ( vEBT_VEBT_power @ ( some_nat @ X ) @ ( some_nat @ Y2 ) )
% 0.29/0.51          = ( some_nat @ Z ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power_shift
% 0.29/0.51  thf(fact_612_mint__member,axiom,
% 0.29/0.51      ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 0.29/0.51        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.51       => ( ( ( vEBT_vebt_mint @ T )
% 0.29/0.51            = ( some_nat @ Maxi ) )
% 0.29/0.51         => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mint_member
% 0.29/0.51  thf(fact_613_maxt__member,axiom,
% 0.29/0.51      ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 0.29/0.51        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.51       => ( ( ( vEBT_vebt_maxt @ T )
% 0.29/0.51            = ( some_nat @ Maxi ) )
% 0.29/0.51         => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % maxt_member
% 0.29/0.51  thf(fact_614_VEBT_Oinject_I1_J,axiom,
% 0.29/0.51      ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,Y11: option4927543243414619207at_nat,Y12: nat,Y13: list_VEBT_VEBT,Y14: vEBT_VEBT] :
% 0.29/0.51        ( ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 0.29/0.51          = ( vEBT_Node @ Y11 @ Y12 @ Y13 @ Y14 ) )
% 0.29/0.51        = ( ( X11 = Y11 )
% 0.29/0.51          & ( X12 = Y12 )
% 0.29/0.51          & ( X13 = Y13 )
% 0.29/0.51          & ( X14 = Y14 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % VEBT.inject(1)
% 0.29/0.51  thf(fact_615_mint__corr__help,axiom,
% 0.29/0.51      ! [T: vEBT_VEBT,N: nat,Mini: nat,X: nat] :
% 0.29/0.51        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.51       => ( ( ( vEBT_vebt_mint @ T )
% 0.29/0.51            = ( some_nat @ Mini ) )
% 0.29/0.51         => ( ( vEBT_vebt_member @ T @ X )
% 0.29/0.51           => ( ord_less_eq_nat @ Mini @ X ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mint_corr_help
% 0.29/0.51  thf(fact_616_maxt__corr__help,axiom,
% 0.29/0.51      ! [T: vEBT_VEBT,N: nat,Maxi: nat,X: nat] :
% 0.29/0.51        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.51       => ( ( ( vEBT_vebt_maxt @ T )
% 0.29/0.51            = ( some_nat @ Maxi ) )
% 0.29/0.51         => ( ( vEBT_vebt_member @ T @ X )
% 0.29/0.51           => ( ord_less_eq_nat @ X @ Maxi ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % maxt_corr_help
% 0.29/0.51  thf(fact_617_zdiv__numeral__Bit0,axiom,
% 0.29/0.51      ! [V: num,W: num] :
% 0.29/0.51        ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 0.29/0.51        = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % zdiv_numeral_Bit0
% 0.29/0.51  thf(fact_618_lesseq__shift,axiom,
% 0.29/0.51      ( ord_less_eq_nat
% 0.29/0.51      = ( ^ [X2: nat,Y: nat] : ( vEBT_VEBT_lesseq @ ( some_nat @ X2 ) @ ( some_nat @ Y ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % lesseq_shift
% 0.29/0.51  thf(fact_619_enat__less__induct,axiom,
% 0.29/0.51      ! [P: extended_enat > $o,N: extended_enat] :
% 0.29/0.51        ( ! [N3: extended_enat] :
% 0.29/0.51            ( ! [M5: extended_enat] :
% 0.29/0.51                ( ( ord_le72135733267957522d_enat @ M5 @ N3 )
% 0.29/0.51               => ( P @ M5 ) )
% 0.29/0.51           => ( P @ N3 ) )
% 0.29/0.51       => ( P @ N ) ) ).
% 0.29/0.51  
% 0.29/0.51  % enat_less_induct
% 0.29/0.51  thf(fact_620_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I4_J,axiom,
% 0.29/0.51      ! [Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Uu: nat] :
% 0.29/0.51        ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Uu )
% 0.29/0.51        = one_one_nat ) ).
% 0.29/0.51  
% 0.29/0.51  % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.simps(4)
% 0.29/0.51  thf(fact_621_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Osimps_I2_J,axiom,
% 0.29/0.51      ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.29/0.51        ( ( vEBT_T_m_i_n_t @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.29/0.51        = one_one_nat ) ).
% 0.29/0.51  
% 0.29/0.51  % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.simps(2)
% 0.29/0.51  thf(fact_622_invar__vebt_Ointros_I2_J,axiom,
% 0.29/0.51      ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 0.29/0.51        ( ! [X3: vEBT_VEBT] :
% 0.29/0.51            ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.29/0.51           => ( vEBT_invar_vebt @ X3 @ N ) )
% 0.29/0.51       => ( ( vEBT_invar_vebt @ Summary @ M )
% 0.29/0.51         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.29/0.51              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.29/0.51           => ( ( M = N )
% 0.29/0.51             => ( ( Deg
% 0.29/0.51                  = ( plus_plus_nat @ N @ M ) )
% 0.29/0.51               => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 )
% 0.29/0.51                 => ( ! [X3: vEBT_VEBT] :
% 0.29/0.51                        ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.29/0.51                       => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_12 ) )
% 0.29/0.51                   => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % invar_vebt.intros(2)
% 0.29/0.51  thf(fact_623_invar__vebt_Ointros_I3_J,axiom,
% 0.29/0.51      ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 0.29/0.51        ( ! [X3: vEBT_VEBT] :
% 0.29/0.51            ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.29/0.51           => ( vEBT_invar_vebt @ X3 @ N ) )
% 0.29/0.51       => ( ( vEBT_invar_vebt @ Summary @ M )
% 0.29/0.51         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.29/0.51              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.29/0.51           => ( ( M
% 0.29/0.51                = ( suc @ N ) )
% 0.29/0.51             => ( ( Deg
% 0.29/0.51                  = ( plus_plus_nat @ N @ M ) )
% 0.29/0.51               => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 )
% 0.29/0.51                 => ( ! [X3: vEBT_VEBT] :
% 0.29/0.51                        ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.29/0.51                       => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_12 ) )
% 0.29/0.51                   => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % invar_vebt.intros(3)
% 0.29/0.51  thf(fact_624_discrete,axiom,
% 0.29/0.51      ( ord_less_nat
% 0.29/0.51      = ( ^ [A3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A3 @ one_one_nat ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % discrete
% 0.29/0.51  thf(fact_625_discrete,axiom,
% 0.29/0.51      ( ord_less_int
% 0.29/0.51      = ( ^ [A3: int] : ( ord_less_eq_int @ ( plus_plus_int @ A3 @ one_one_int ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % discrete
% 0.29/0.51  thf(fact_626_maxt__sound,axiom,
% 0.29/0.51      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.51        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.51       => ( ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X )
% 0.29/0.51         => ( ( vEBT_vebt_maxt @ T )
% 0.29/0.51            = ( some_nat @ X ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % maxt_sound
% 0.29/0.51  thf(fact_627_maxt__corr,axiom,
% 0.29/0.51      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.51        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.51       => ( ( ( vEBT_vebt_maxt @ T )
% 0.29/0.51            = ( some_nat @ X ) )
% 0.29/0.51         => ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % maxt_corr
% 0.29/0.51  thf(fact_628_mint__sound,axiom,
% 0.29/0.51      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.51        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.51       => ( ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X )
% 0.29/0.51         => ( ( vEBT_vebt_mint @ T )
% 0.29/0.51            = ( some_nat @ X ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mint_sound
% 0.29/0.51  thf(fact_629_mint__corr,axiom,
% 0.29/0.51      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.51        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.51       => ( ( ( vEBT_vebt_mint @ T )
% 0.29/0.51            = ( some_nat @ X ) )
% 0.29/0.51         => ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mint_corr
% 0.29/0.51  thf(fact_630_del__x__mi__lets__in__not__minNull,axiom,
% 0.29/0.51      ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList: list_VEBT_VEBT,L2: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 0.29/0.51        ( ( ( X = Mi )
% 0.29/0.51          & ( ord_less_nat @ X @ Ma ) )
% 0.29/0.51       => ( ( Mi != Ma )
% 0.29/0.51         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.29/0.51           => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.51                = H2 )
% 0.29/0.51             => ( ( Xn
% 0.29/0.51                  = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 0.29/0.51               => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.51                    = L2 )
% 0.29/0.51                 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.29/0.51                   => ( ( Newnode
% 0.29/0.51                        = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) )
% 0.29/0.51                     => ( ( Newlist
% 0.29/0.51                          = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 0.29/0.51                       => ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 0.29/0.51                         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.29/0.51                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % del_x_mi_lets_in_not_minNull
% 0.29/0.51  thf(fact_631_del__x__not__mi__newnode__not__nil,axiom,
% 0.29/0.51      ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L2: nat,Newnode: vEBT_VEBT,TreeList: list_VEBT_VEBT,Newlist: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.29/0.51        ( ( ( ord_less_nat @ Mi @ X )
% 0.29/0.51          & ( ord_less_eq_nat @ X @ Ma ) )
% 0.29/0.51       => ( ( Mi != Ma )
% 0.29/0.51         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.29/0.51           => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.51                = H2 )
% 0.29/0.51             => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.51                  = L2 )
% 0.29/0.51               => ( ( Newnode
% 0.29/0.51                    = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) )
% 0.29/0.51                 => ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 0.29/0.51                   => ( ( Newlist
% 0.29/0.51                        = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 0.29/0.51                     => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.29/0.51                       => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.29/0.51                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % del_x_not_mi_newnode_not_nil
% 0.29/0.51  thf(fact_632_pred__max,axiom,
% 0.29/0.51      ! [Deg: nat,Ma: nat,X: nat,Mi: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.29/0.51        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.29/0.51       => ( ( ord_less_nat @ Ma @ X )
% 0.29/0.51         => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.29/0.51            = ( some_nat @ Ma ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % pred_max
% 0.29/0.51  thf(fact_633_succ__min,axiom,
% 0.29/0.51      ! [Deg: nat,X: nat,Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.29/0.51        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.29/0.51       => ( ( ord_less_nat @ X @ Mi )
% 0.29/0.51         => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.29/0.51            = ( some_nat @ Mi ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % succ_min
% 0.29/0.51  thf(fact_634_mintlistlength,axiom,
% 0.29/0.51      ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 0.29/0.51        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 0.29/0.51       => ( ( Mi != Ma )
% 0.29/0.51         => ( ( ord_less_nat @ Mi @ Ma )
% 0.29/0.51            & ? [M4: nat] :
% 0.29/0.51                ( ( ( some_nat @ M4 )
% 0.29/0.51                  = ( vEBT_vebt_mint @ Summary ) )
% 0.29/0.51                & ( ord_less_nat @ M4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mintlistlength
% 0.29/0.51  thf(fact_635_set__vebt__set__vebt_H__valid,axiom,
% 0.29/0.51      ! [T: vEBT_VEBT,N: nat] :
% 0.29/0.51        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.51       => ( ( vEBT_set_vebt @ T )
% 0.29/0.51          = ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % set_vebt_set_vebt'_valid
% 0.29/0.51  thf(fact_636_helpyd,axiom,
% 0.29/0.51      ! [T: vEBT_VEBT,N: nat,X: nat,Y2: nat] :
% 0.29/0.51        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.51       => ( ( ( vEBT_vebt_succ @ T @ X )
% 0.29/0.51            = ( some_nat @ Y2 ) )
% 0.29/0.51         => ( ord_less_nat @ Y2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % helpyd
% 0.29/0.51  thf(fact_637_power__minus__is__div,axiom,
% 0.29/0.51      ! [B: nat,A: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.51       => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ A @ B ) )
% 0.29/0.51          = ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power_minus_is_div
% 0.29/0.51  thf(fact_638_helpypredd,axiom,
% 0.29/0.51      ! [T: vEBT_VEBT,N: nat,X: nat,Y2: nat] :
% 0.29/0.51        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.51       => ( ( ( vEBT_vebt_pred @ T @ X )
% 0.29/0.51            = ( some_nat @ Y2 ) )
% 0.29/0.51         => ( ord_less_nat @ Y2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % helpypredd
% 0.29/0.51  thf(fact_639_diff__Suc__Suc,axiom,
% 0.29/0.51      ! [M: nat,N: nat] :
% 0.29/0.51        ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.29/0.51        = ( minus_minus_nat @ M @ N ) ) ).
% 0.29/0.51  
% 0.29/0.51  % diff_Suc_Suc
% 0.29/0.51  thf(fact_640_Suc__diff__diff,axiom,
% 0.29/0.51      ! [M: nat,N: nat,K: nat] :
% 0.29/0.51        ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 0.29/0.51        = ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Suc_diff_diff
% 0.29/0.51  thf(fact_641_diff__diff__left,axiom,
% 0.29/0.51      ! [I2: nat,J: nat,K: nat] :
% 0.29/0.51        ( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J ) @ K )
% 0.29/0.51        = ( minus_minus_nat @ I2 @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % diff_diff_left
% 0.29/0.51  thf(fact_642_diff__diff__cancel,axiom,
% 0.29/0.51      ! [I2: nat,N: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ I2 @ N )
% 0.29/0.51       => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I2 ) )
% 0.29/0.51          = I2 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % diff_diff_cancel
% 0.29/0.51  thf(fact_643_right__diff__distrib__numeral,axiom,
% 0.29/0.51      ! [V: num,B: complex,C: complex] :
% 0.29/0.51        ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( minus_minus_complex @ B @ C ) )
% 0.29/0.51        = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % right_diff_distrib_numeral
% 0.29/0.51  thf(fact_644_right__diff__distrib__numeral,axiom,
% 0.29/0.51      ! [V: num,B: real,C: real] :
% 0.29/0.51        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( minus_minus_real @ B @ C ) )
% 0.29/0.51        = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % right_diff_distrib_numeral
% 0.29/0.51  thf(fact_645_right__diff__distrib__numeral,axiom,
% 0.29/0.51      ! [V: num,B: rat,C: rat] :
% 0.29/0.51        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( minus_minus_rat @ B @ C ) )
% 0.29/0.51        = ( minus_minus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % right_diff_distrib_numeral
% 0.29/0.51  thf(fact_646_right__diff__distrib__numeral,axiom,
% 0.29/0.51      ! [V: num,B: int,C: int] :
% 0.29/0.51        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( minus_minus_int @ B @ C ) )
% 0.29/0.51        = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % right_diff_distrib_numeral
% 0.29/0.51  thf(fact_647_left__diff__distrib__numeral,axiom,
% 0.29/0.51      ! [A: complex,B: complex,V: num] :
% 0.29/0.51        ( ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 0.29/0.51        = ( minus_minus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % left_diff_distrib_numeral
% 0.29/0.51  thf(fact_648_left__diff__distrib__numeral,axiom,
% 0.29/0.51      ! [A: real,B: real,V: num] :
% 0.29/0.51        ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 0.29/0.51        = ( minus_minus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % left_diff_distrib_numeral
% 0.29/0.51  thf(fact_649_left__diff__distrib__numeral,axiom,
% 0.29/0.51      ! [A: rat,B: rat,V: num] :
% 0.29/0.51        ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 0.29/0.51        = ( minus_minus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % left_diff_distrib_numeral
% 0.29/0.51  thf(fact_650_left__diff__distrib__numeral,axiom,
% 0.29/0.51      ! [A: int,B: int,V: num] :
% 0.29/0.51        ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 0.29/0.51        = ( minus_minus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % left_diff_distrib_numeral
% 0.29/0.51  thf(fact_651_diff__Suc__1,axiom,
% 0.29/0.51      ! [N: nat] :
% 0.29/0.51        ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 0.29/0.51        = N ) ).
% 0.29/0.51  
% 0.29/0.51  % diff_Suc_1
% 0.29/0.51  thf(fact_652_Nat_Oadd__diff__assoc,axiom,
% 0.29/0.51      ! [K: nat,J: nat,I2: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ K @ J )
% 0.29/0.51       => ( ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 0.29/0.51          = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J ) @ K ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Nat.add_diff_assoc
% 0.29/0.51  thf(fact_653_Nat_Oadd__diff__assoc2,axiom,
% 0.29/0.51      ! [K: nat,J: nat,I2: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ K @ J )
% 0.29/0.51       => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
% 0.29/0.51          = ( minus_minus_nat @ ( plus_plus_nat @ J @ I2 ) @ K ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Nat.add_diff_assoc2
% 0.29/0.51  thf(fact_654_Nat_Odiff__diff__right,axiom,
% 0.29/0.51      ! [K: nat,J: nat,I2: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ K @ J )
% 0.29/0.51       => ( ( minus_minus_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 0.29/0.51          = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Nat.diff_diff_right
% 0.29/0.51  thf(fact_655_diff__Suc__diff__eq1,axiom,
% 0.29/0.51      ! [K: nat,J: nat,I2: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ K @ J )
% 0.29/0.51       => ( ( minus_minus_nat @ I2 @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 0.29/0.51          = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ K ) @ ( suc @ J ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % diff_Suc_diff_eq1
% 0.29/0.51  thf(fact_656_diff__Suc__diff__eq2,axiom,
% 0.29/0.51      ! [K: nat,J: nat,I2: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ K @ J )
% 0.29/0.51       => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I2 )
% 0.29/0.51          = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % diff_Suc_diff_eq2
% 0.29/0.51  thf(fact_657_pred__member,axiom,
% 0.29/0.51      ! [T: vEBT_VEBT,X: nat,Y2: nat] :
% 0.29/0.51        ( ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Y2 )
% 0.29/0.51        = ( ( vEBT_vebt_member @ T @ Y2 )
% 0.29/0.51          & ( ord_less_nat @ Y2 @ X )
% 0.29/0.51          & ! [Z4: nat] :
% 0.29/0.51              ( ( ( vEBT_vebt_member @ T @ Z4 )
% 0.29/0.51                & ( ord_less_nat @ Z4 @ X ) )
% 0.29/0.51             => ( ord_less_eq_nat @ Z4 @ Y2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % pred_member
% 0.29/0.51  thf(fact_658_succ__member,axiom,
% 0.29/0.51      ! [T: vEBT_VEBT,X: nat,Y2: nat] :
% 0.29/0.51        ( ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Y2 )
% 0.29/0.51        = ( ( vEBT_vebt_member @ T @ Y2 )
% 0.29/0.51          & ( ord_less_nat @ X @ Y2 )
% 0.29/0.51          & ! [Z4: nat] :
% 0.29/0.51              ( ( ( vEBT_vebt_member @ T @ Z4 )
% 0.29/0.51                & ( ord_less_nat @ X @ Z4 ) )
% 0.29/0.51             => ( ord_less_eq_nat @ Y2 @ Z4 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % succ_member
% 0.29/0.51  thf(fact_659_succ__corr,axiom,
% 0.29/0.51      ! [T: vEBT_VEBT,N: nat,X: nat,Sx: nat] :
% 0.29/0.51        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.51       => ( ( ( vEBT_vebt_succ @ T @ X )
% 0.29/0.51            = ( some_nat @ Sx ) )
% 0.29/0.51          = ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % succ_corr
% 0.29/0.51  thf(fact_660_pred__corr,axiom,
% 0.29/0.51      ! [T: vEBT_VEBT,N: nat,X: nat,Px: nat] :
% 0.29/0.51        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.51       => ( ( ( vEBT_vebt_pred @ T @ X )
% 0.29/0.51            = ( some_nat @ Px ) )
% 0.29/0.51          = ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Px ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % pred_corr
% 0.29/0.51  thf(fact_661_pred__correct,axiom,
% 0.29/0.51      ! [T: vEBT_VEBT,N: nat,X: nat,Sx: nat] :
% 0.29/0.51        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.51       => ( ( ( vEBT_vebt_pred @ T @ X )
% 0.29/0.51            = ( some_nat @ Sx ) )
% 0.29/0.51          = ( vEBT_is_pred_in_set @ ( vEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % pred_correct
% 0.29/0.51  thf(fact_662_succ__correct,axiom,
% 0.29/0.51      ! [T: vEBT_VEBT,N: nat,X: nat,Sx: nat] :
% 0.29/0.51        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.51       => ( ( ( vEBT_vebt_succ @ T @ X )
% 0.29/0.51            = ( some_nat @ Sx ) )
% 0.29/0.51          = ( vEBT_is_succ_in_set @ ( vEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % succ_correct
% 0.29/0.51  thf(fact_663_local_Opower__def,axiom,
% 0.29/0.51      ( vEBT_VEBT_power
% 0.29/0.51      = ( vEBT_V4262088993061758097ft_nat @ power_power_nat ) ) ).
% 0.29/0.51  
% 0.29/0.51  % local.power_def
% 0.29/0.51  thf(fact_664_diff__commute,axiom,
% 0.29/0.51      ! [I2: nat,J: nat,K: nat] :
% 0.29/0.51        ( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J ) @ K )
% 0.29/0.51        = ( minus_minus_nat @ ( minus_minus_nat @ I2 @ K ) @ J ) ) ).
% 0.29/0.51  
% 0.29/0.51  % diff_commute
% 0.29/0.51  thf(fact_665_add__diff__add,axiom,
% 0.29/0.51      ! [A: real,C: real,B: real,D2: real] :
% 0.29/0.51        ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D2 ) )
% 0.29/0.51        = ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ ( minus_minus_real @ C @ D2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % add_diff_add
% 0.29/0.51  thf(fact_666_add__diff__add,axiom,
% 0.29/0.51      ! [A: complex,C: complex,B: complex,D2: complex] :
% 0.29/0.51        ( ( minus_minus_complex @ ( plus_plus_complex @ A @ C ) @ ( plus_plus_complex @ B @ D2 ) )
% 0.29/0.51        = ( plus_plus_complex @ ( minus_minus_complex @ A @ B ) @ ( minus_minus_complex @ C @ D2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % add_diff_add
% 0.29/0.51  thf(fact_667_add__diff__add,axiom,
% 0.29/0.51      ! [A: rat,C: rat,B: rat,D2: rat] :
% 0.29/0.51        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) )
% 0.29/0.51        = ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ ( minus_minus_rat @ C @ D2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % add_diff_add
% 0.29/0.51  thf(fact_668_add__diff__add,axiom,
% 0.29/0.51      ! [A: int,C: int,B: int,D2: int] :
% 0.29/0.51        ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) )
% 0.29/0.51        = ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ ( minus_minus_int @ C @ D2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % add_diff_add
% 0.29/0.51  thf(fact_669_zero__induct__lemma,axiom,
% 0.29/0.51      ! [P: nat > $o,K: nat,I2: nat] :
% 0.29/0.51        ( ( P @ K )
% 0.29/0.51       => ( ! [N3: nat] :
% 0.29/0.51              ( ( P @ ( suc @ N3 ) )
% 0.29/0.51             => ( P @ N3 ) )
% 0.29/0.51         => ( P @ ( minus_minus_nat @ K @ I2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % zero_induct_lemma
% 0.29/0.51  thf(fact_670_diff__less__mono2,axiom,
% 0.29/0.51      ! [M: nat,N: nat,L2: nat] :
% 0.29/0.51        ( ( ord_less_nat @ M @ N )
% 0.29/0.51       => ( ( ord_less_nat @ M @ L2 )
% 0.29/0.51         => ( ord_less_nat @ ( minus_minus_nat @ L2 @ N ) @ ( minus_minus_nat @ L2 @ M ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % diff_less_mono2
% 0.29/0.51  thf(fact_671_less__imp__diff__less,axiom,
% 0.29/0.51      ! [J: nat,K: nat,N: nat] :
% 0.29/0.51        ( ( ord_less_nat @ J @ K )
% 0.29/0.51       => ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K ) ) ).
% 0.29/0.51  
% 0.29/0.51  % less_imp_diff_less
% 0.29/0.51  thf(fact_672_diff__add__inverse2,axiom,
% 0.29/0.51      ! [M: nat,N: nat] :
% 0.29/0.51        ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
% 0.29/0.51        = M ) ).
% 0.29/0.51  
% 0.29/0.51  % diff_add_inverse2
% 0.29/0.51  thf(fact_673_diff__add__inverse,axiom,
% 0.29/0.51      ! [N: nat,M: nat] :
% 0.29/0.51        ( ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ N )
% 0.29/0.51        = M ) ).
% 0.29/0.51  
% 0.29/0.51  % diff_add_inverse
% 0.29/0.51  thf(fact_674_diff__cancel2,axiom,
% 0.29/0.51      ! [M: nat,K: nat,N: nat] :
% 0.29/0.51        ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) )
% 0.29/0.51        = ( minus_minus_nat @ M @ N ) ) ).
% 0.29/0.51  
% 0.29/0.51  % diff_cancel2
% 0.29/0.51  thf(fact_675_Nat_Odiff__cancel,axiom,
% 0.29/0.51      ! [K: nat,M: nat,N: nat] :
% 0.29/0.51        ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.29/0.51        = ( minus_minus_nat @ M @ N ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Nat.diff_cancel
% 0.29/0.51  thf(fact_676_eq__diff__iff,axiom,
% 0.29/0.51      ! [K: nat,M: nat,N: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ K @ M )
% 0.29/0.51       => ( ( ord_less_eq_nat @ K @ N )
% 0.29/0.51         => ( ( ( minus_minus_nat @ M @ K )
% 0.29/0.51              = ( minus_minus_nat @ N @ K ) )
% 0.29/0.51            = ( M = N ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % eq_diff_iff
% 0.29/0.51  thf(fact_677_le__diff__iff,axiom,
% 0.29/0.51      ! [K: nat,M: nat,N: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ K @ M )
% 0.29/0.51       => ( ( ord_less_eq_nat @ K @ N )
% 0.29/0.51         => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.29/0.51            = ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % le_diff_iff
% 0.29/0.51  thf(fact_678_Nat_Odiff__diff__eq,axiom,
% 0.29/0.51      ! [K: nat,M: nat,N: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ K @ M )
% 0.29/0.51       => ( ( ord_less_eq_nat @ K @ N )
% 0.29/0.51         => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.29/0.51            = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Nat.diff_diff_eq
% 0.29/0.51  thf(fact_679_diff__le__mono,axiom,
% 0.29/0.51      ! [M: nat,N: nat,L2: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.51       => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L2 ) @ ( minus_minus_nat @ N @ L2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % diff_le_mono
% 0.29/0.51  thf(fact_680_diff__le__self,axiom,
% 0.29/0.51      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 0.29/0.51  
% 0.29/0.51  % diff_le_self
% 0.29/0.51  thf(fact_681_le__diff__iff_H,axiom,
% 0.29/0.51      ! [A: nat,C: nat,B: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ A @ C )
% 0.29/0.51       => ( ( ord_less_eq_nat @ B @ C )
% 0.29/0.51         => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 0.29/0.51            = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % le_diff_iff'
% 0.29/0.51  thf(fact_682_diff__le__mono2,axiom,
% 0.29/0.51      ! [M: nat,N: nat,L2: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.51       => ( ord_less_eq_nat @ ( minus_minus_nat @ L2 @ N ) @ ( minus_minus_nat @ L2 @ M ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % diff_le_mono2
% 0.29/0.51  thf(fact_683_diff__mult__distrib,axiom,
% 0.29/0.51      ! [M: nat,N: nat,K: nat] :
% 0.29/0.51        ( ( times_times_nat @ ( minus_minus_nat @ M @ N ) @ K )
% 0.29/0.51        = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % diff_mult_distrib
% 0.29/0.51  thf(fact_684_diff__mult__distrib2,axiom,
% 0.29/0.51      ! [K: nat,M: nat,N: nat] :
% 0.29/0.51        ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 0.29/0.51        = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % diff_mult_distrib2
% 0.29/0.51  thf(fact_685_mult__diff__mult,axiom,
% 0.29/0.51      ! [X: rat,Y2: rat,A: rat,B: rat] :
% 0.29/0.51        ( ( minus_minus_rat @ ( times_times_rat @ X @ Y2 ) @ ( times_times_rat @ A @ B ) )
% 0.29/0.51        = ( plus_plus_rat @ ( times_times_rat @ X @ ( minus_minus_rat @ Y2 @ B ) ) @ ( times_times_rat @ ( minus_minus_rat @ X @ A ) @ B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_diff_mult
% 0.29/0.51  thf(fact_686_mult__diff__mult,axiom,
% 0.29/0.51      ! [X: complex,Y2: complex,A: complex,B: complex] :
% 0.29/0.51        ( ( minus_minus_complex @ ( times_times_complex @ X @ Y2 ) @ ( times_times_complex @ A @ B ) )
% 0.29/0.51        = ( plus_plus_complex @ ( times_times_complex @ X @ ( minus_minus_complex @ Y2 @ B ) ) @ ( times_times_complex @ ( minus_minus_complex @ X @ A ) @ B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_diff_mult
% 0.29/0.51  thf(fact_687_mult__diff__mult,axiom,
% 0.29/0.51      ! [X: real,Y2: real,A: real,B: real] :
% 0.29/0.51        ( ( minus_minus_real @ ( times_times_real @ X @ Y2 ) @ ( times_times_real @ A @ B ) )
% 0.29/0.51        = ( plus_plus_real @ ( times_times_real @ X @ ( minus_minus_real @ Y2 @ B ) ) @ ( times_times_real @ ( minus_minus_real @ X @ A ) @ B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_diff_mult
% 0.29/0.51  thf(fact_688_mult__diff__mult,axiom,
% 0.29/0.51      ! [X: int,Y2: int,A: int,B: int] :
% 0.29/0.51        ( ( minus_minus_int @ ( times_times_int @ X @ Y2 ) @ ( times_times_int @ A @ B ) )
% 0.29/0.51        = ( plus_plus_int @ ( times_times_int @ X @ ( minus_minus_int @ Y2 @ B ) ) @ ( times_times_int @ ( minus_minus_int @ X @ A ) @ B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_diff_mult
% 0.29/0.51  thf(fact_689_Suc__diff__Suc,axiom,
% 0.29/0.51      ! [N: nat,M: nat] :
% 0.29/0.51        ( ( ord_less_nat @ N @ M )
% 0.29/0.51       => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N ) ) )
% 0.29/0.51          = ( minus_minus_nat @ M @ N ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Suc_diff_Suc
% 0.29/0.51  thf(fact_690_diff__less__Suc,axiom,
% 0.29/0.51      ! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% 0.29/0.51  
% 0.29/0.51  % diff_less_Suc
% 0.29/0.51  thf(fact_691_Suc__diff__le,axiom,
% 0.29/0.51      ! [N: nat,M: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ N @ M )
% 0.29/0.51       => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 0.29/0.51          = ( suc @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Suc_diff_le
% 0.29/0.51  thf(fact_692_diff__Suc__eq__diff__pred,axiom,
% 0.29/0.51      ! [M: nat,N: nat] :
% 0.29/0.51        ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 0.29/0.51        = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
% 0.29/0.51  
% 0.29/0.51  % diff_Suc_eq_diff_pred
% 0.29/0.51  thf(fact_693_add__diff__inverse__nat,axiom,
% 0.29/0.51      ! [M: nat,N: nat] :
% 0.29/0.51        ( ~ ( ord_less_nat @ M @ N )
% 0.29/0.51       => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
% 0.29/0.51          = M ) ) ).
% 0.29/0.51  
% 0.29/0.51  % add_diff_inverse_nat
% 0.29/0.51  thf(fact_694_less__diff__conv,axiom,
% 0.29/0.51      ! [I2: nat,J: nat,K: nat] :
% 0.29/0.51        ( ( ord_less_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 0.29/0.51        = ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ).
% 0.29/0.51  
% 0.29/0.51  % less_diff_conv
% 0.29/0.51  thf(fact_695_less__diff__iff,axiom,
% 0.29/0.51      ! [K: nat,M: nat,N: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ K @ M )
% 0.29/0.51       => ( ( ord_less_eq_nat @ K @ N )
% 0.29/0.51         => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.29/0.51            = ( ord_less_nat @ M @ N ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % less_diff_iff
% 0.29/0.51  thf(fact_696_diff__less__mono,axiom,
% 0.29/0.51      ! [A: nat,B: nat,C: nat] :
% 0.29/0.51        ( ( ord_less_nat @ A @ B )
% 0.29/0.51       => ( ( ord_less_eq_nat @ C @ A )
% 0.29/0.51         => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % diff_less_mono
% 0.29/0.51  thf(fact_697_le__diff__conv,axiom,
% 0.29/0.51      ! [J: nat,K: nat,I2: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
% 0.29/0.51        = ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I2 @ K ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % le_diff_conv
% 0.29/0.51  thf(fact_698_Nat_Ole__diff__conv2,axiom,
% 0.29/0.51      ! [K: nat,J: nat,I2: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ K @ J )
% 0.29/0.51       => ( ( ord_less_eq_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 0.29/0.51          = ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Nat.le_diff_conv2
% 0.29/0.51  thf(fact_699_Nat_Odiff__add__assoc,axiom,
% 0.29/0.51      ! [K: nat,J: nat,I2: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ K @ J )
% 0.29/0.51       => ( ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J ) @ K )
% 0.29/0.51          = ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Nat.diff_add_assoc
% 0.29/0.51  thf(fact_700_Nat_Odiff__add__assoc2,axiom,
% 0.29/0.51      ! [K: nat,J: nat,I2: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ K @ J )
% 0.29/0.51       => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I2 ) @ K )
% 0.29/0.51          = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Nat.diff_add_assoc2
% 0.29/0.51  thf(fact_701_Nat_Ole__imp__diff__is__add,axiom,
% 0.29/0.51      ! [I2: nat,J: nat,K: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ I2 @ J )
% 0.29/0.51       => ( ( ( minus_minus_nat @ J @ I2 )
% 0.29/0.51            = K )
% 0.29/0.51          = ( J
% 0.29/0.51            = ( plus_plus_nat @ K @ I2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Nat.le_imp_diff_is_add
% 0.29/0.51  thf(fact_702_less__diff__conv2,axiom,
% 0.29/0.51      ! [K: nat,J: nat,I2: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ K @ J )
% 0.29/0.51       => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
% 0.29/0.51          = ( ord_less_nat @ J @ ( plus_plus_nat @ I2 @ K ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % less_diff_conv2
% 0.29/0.51  thf(fact_703_nat__eq__add__iff1,axiom,
% 0.29/0.51      ! [J: nat,I2: nat,U: nat,M: nat,N: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ J @ I2 )
% 0.29/0.51       => ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M )
% 0.29/0.51            = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.29/0.51          = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M )
% 0.29/0.51            = N ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nat_eq_add_iff1
% 0.29/0.51  thf(fact_704_nat__eq__add__iff2,axiom,
% 0.29/0.51      ! [I2: nat,J: nat,U: nat,M: nat,N: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ I2 @ J )
% 0.29/0.51       => ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M )
% 0.29/0.51            = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.29/0.51          = ( M
% 0.29/0.51            = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nat_eq_add_iff2
% 0.29/0.51  thf(fact_705_nat__le__add__iff1,axiom,
% 0.29/0.51      ! [J: nat,I2: nat,U: nat,M: nat,N: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ J @ I2 )
% 0.29/0.51       => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.29/0.51          = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nat_le_add_iff1
% 0.29/0.51  thf(fact_706_nat__le__add__iff2,axiom,
% 0.29/0.51      ! [I2: nat,J: nat,U: nat,M: nat,N: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ I2 @ J )
% 0.29/0.51       => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.29/0.51          = ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nat_le_add_iff2
% 0.29/0.51  thf(fact_707_nat__diff__add__eq1,axiom,
% 0.29/0.51      ! [J: nat,I2: nat,U: nat,M: nat,N: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ J @ I2 )
% 0.29/0.51       => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.29/0.51          = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nat_diff_add_eq1
% 0.29/0.51  thf(fact_708_nat__diff__add__eq2,axiom,
% 0.29/0.51      ! [I2: nat,J: nat,U: nat,M: nat,N: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ I2 @ J )
% 0.29/0.51       => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.29/0.51          = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nat_diff_add_eq2
% 0.29/0.51  thf(fact_709_power2__commute,axiom,
% 0.29/0.51      ! [X: real,Y2: real] :
% 0.29/0.51        ( ( power_power_real @ ( minus_minus_real @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.51        = ( power_power_real @ ( minus_minus_real @ Y2 @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power2_commute
% 0.29/0.51  thf(fact_710_power2__commute,axiom,
% 0.29/0.51      ! [X: complex,Y2: complex] :
% 0.29/0.51        ( ( power_power_complex @ ( minus_minus_complex @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.51        = ( power_power_complex @ ( minus_minus_complex @ Y2 @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power2_commute
% 0.29/0.51  thf(fact_711_power2__commute,axiom,
% 0.29/0.51      ! [X: rat,Y2: rat] :
% 0.29/0.51        ( ( power_power_rat @ ( minus_minus_rat @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.51        = ( power_power_rat @ ( minus_minus_rat @ Y2 @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power2_commute
% 0.29/0.51  thf(fact_712_power2__commute,axiom,
% 0.29/0.51      ! [X: int,Y2: int] :
% 0.29/0.51        ( ( power_power_int @ ( minus_minus_int @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.51        = ( power_power_int @ ( minus_minus_int @ Y2 @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power2_commute
% 0.29/0.51  thf(fact_713_nat__less__add__iff1,axiom,
% 0.29/0.51      ! [J: nat,I2: nat,U: nat,M: nat,N: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ J @ I2 )
% 0.29/0.51       => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.29/0.51          = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nat_less_add_iff1
% 0.29/0.51  thf(fact_714_nat__less__add__iff2,axiom,
% 0.29/0.51      ! [I2: nat,J: nat,U: nat,M: nat,N: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ I2 @ J )
% 0.29/0.51       => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.29/0.51          = ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nat_less_add_iff2
% 0.29/0.51  thf(fact_715_diff__le__diff__pow,axiom,
% 0.29/0.51      ! [K: nat,M: nat,N: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 0.29/0.51       => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ ( minus_minus_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % diff_le_diff_pow
% 0.29/0.51  thf(fact_716_power2__diff,axiom,
% 0.29/0.51      ! [X: complex,Y2: complex] :
% 0.29/0.51        ( ( power_power_complex @ ( minus_minus_complex @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.51        = ( minus_minus_complex @ ( plus_plus_complex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) @ Y2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power2_diff
% 0.29/0.51  thf(fact_717_power2__diff,axiom,
% 0.29/0.51      ! [X: real,Y2: real] :
% 0.29/0.51        ( ( power_power_real @ ( minus_minus_real @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.51        = ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power2_diff
% 0.29/0.51  thf(fact_718_power2__diff,axiom,
% 0.29/0.51      ! [X: rat,Y2: rat] :
% 0.29/0.51        ( ( power_power_rat @ ( minus_minus_rat @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.51        = ( minus_minus_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power2_diff
% 0.29/0.51  thf(fact_719_power2__diff,axiom,
% 0.29/0.51      ! [X: int,Y2: int] :
% 0.29/0.51        ( ( power_power_int @ ( minus_minus_int @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.51        = ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X ) @ Y2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power2_diff
% 0.29/0.51  thf(fact_720_set__swap,axiom,
% 0.29/0.51      ! [I2: nat,Xs2: list_VEBT_VEBT,J: nat] :
% 0.29/0.51        ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.29/0.51       => ( ( ord_less_nat @ J @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.29/0.51         => ( ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ ( nth_VEBT_VEBT @ Xs2 @ J ) ) @ J @ ( nth_VEBT_VEBT @ Xs2 @ I2 ) ) )
% 0.29/0.51            = ( set_VEBT_VEBT2 @ Xs2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % set_swap
% 0.29/0.51  thf(fact_721_set__swap,axiom,
% 0.29/0.51      ! [I2: nat,Xs2: list_o,J: nat] :
% 0.29/0.51        ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 0.29/0.51       => ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs2 ) )
% 0.29/0.51         => ( ( set_o2 @ ( list_update_o @ ( list_update_o @ Xs2 @ I2 @ ( nth_o @ Xs2 @ J ) ) @ J @ ( nth_o @ Xs2 @ I2 ) ) )
% 0.29/0.51            = ( set_o2 @ Xs2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % set_swap
% 0.29/0.51  thf(fact_722_set__swap,axiom,
% 0.29/0.51      ! [I2: nat,Xs2: list_nat,J: nat] :
% 0.29/0.51        ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 0.29/0.51       => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 0.29/0.51         => ( ( set_nat2 @ ( list_update_nat @ ( list_update_nat @ Xs2 @ I2 @ ( nth_nat @ Xs2 @ J ) ) @ J @ ( nth_nat @ Xs2 @ I2 ) ) )
% 0.29/0.51            = ( set_nat2 @ Xs2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % set_swap
% 0.29/0.51  thf(fact_723_set__swap,axiom,
% 0.29/0.51      ! [I2: nat,Xs2: list_int,J: nat] :
% 0.29/0.51        ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 0.29/0.51       => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs2 ) )
% 0.29/0.51         => ( ( set_int2 @ ( list_update_int @ ( list_update_int @ Xs2 @ I2 @ ( nth_int @ Xs2 @ J ) ) @ J @ ( nth_int @ Xs2 @ I2 ) ) )
% 0.29/0.51            = ( set_int2 @ Xs2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % set_swap
% 0.29/0.51  thf(fact_724_insert__simp__norm,axiom,
% 0.29/0.51      ! [X: nat,Deg: nat,TreeList: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 0.29/0.51        ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.29/0.51       => ( ( ord_less_nat @ Mi @ X )
% 0.29/0.51         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.29/0.51           => ( ( X != Ma )
% 0.29/0.51             => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.29/0.51                = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( ord_max_nat @ X @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % insert_simp_norm
% 0.29/0.51  thf(fact_725_insert__simp__excp,axiom,
% 0.29/0.51      ! [Mi: nat,Deg: nat,TreeList: list_VEBT_VEBT,X: nat,Ma: nat,Summary: vEBT_VEBT] :
% 0.29/0.51        ( ( ord_less_nat @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.29/0.51       => ( ( ord_less_nat @ X @ Mi )
% 0.29/0.51         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.29/0.51           => ( ( X != Ma )
% 0.29/0.51             => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.29/0.51                = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ ( ord_max_nat @ Mi @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % insert_simp_excp
% 0.29/0.51  thf(fact_726_nth__list__update__eq,axiom,
% 0.29/0.51      ! [I2: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 0.29/0.51        ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.29/0.51       => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ I2 )
% 0.29/0.51          = X ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nth_list_update_eq
% 0.29/0.51  thf(fact_727_nth__list__update__eq,axiom,
% 0.29/0.51      ! [I2: nat,Xs2: list_o,X: $o] :
% 0.29/0.51        ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 0.29/0.51       => ( ( nth_o @ ( list_update_o @ Xs2 @ I2 @ X ) @ I2 )
% 0.29/0.51          = X ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nth_list_update_eq
% 0.29/0.51  thf(fact_728_nth__list__update__eq,axiom,
% 0.29/0.51      ! [I2: nat,Xs2: list_nat,X: nat] :
% 0.29/0.51        ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 0.29/0.51       => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) @ I2 )
% 0.29/0.51          = X ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nth_list_update_eq
% 0.29/0.51  thf(fact_729_nth__list__update__eq,axiom,
% 0.29/0.51      ! [I2: nat,Xs2: list_int,X: int] :
% 0.29/0.51        ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 0.29/0.51       => ( ( nth_int @ ( list_update_int @ Xs2 @ I2 @ X ) @ I2 )
% 0.29/0.51          = X ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nth_list_update_eq
% 0.29/0.51  thf(fact_730_divmod__step__eq,axiom,
% 0.29/0.51      ! [L2: num,R: nat,Q2: nat] :
% 0.29/0.51        ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R )
% 0.29/0.51         => ( ( unique5026877609467782581ep_nat @ L2 @ ( product_Pair_nat_nat @ Q2 @ R ) )
% 0.29/0.51            = ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ one_one_nat ) @ ( minus_minus_nat @ R @ ( numeral_numeral_nat @ L2 ) ) ) ) )
% 0.29/0.51        & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R )
% 0.29/0.51         => ( ( unique5026877609467782581ep_nat @ L2 @ ( product_Pair_nat_nat @ Q2 @ R ) )
% 0.29/0.51            = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ R ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % divmod_step_eq
% 0.29/0.51  thf(fact_731_divmod__step__eq,axiom,
% 0.29/0.51      ! [L2: num,R: int,Q2: int] :
% 0.29/0.51        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R )
% 0.29/0.51         => ( ( unique5024387138958732305ep_int @ L2 @ ( product_Pair_int_int @ Q2 @ R ) )
% 0.29/0.51            = ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ one_one_int ) @ ( minus_minus_int @ R @ ( numeral_numeral_int @ L2 ) ) ) ) )
% 0.29/0.51        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R )
% 0.29/0.51         => ( ( unique5024387138958732305ep_int @ L2 @ ( product_Pair_int_int @ Q2 @ R ) )
% 0.29/0.51            = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ R ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % divmod_step_eq
% 0.29/0.51  thf(fact_732_divmod__step__eq,axiom,
% 0.29/0.51      ! [L2: num,R: code_integer,Q2: code_integer] :
% 0.29/0.51        ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R )
% 0.29/0.51         => ( ( unique4921790084139445826nteger @ L2 @ ( produc1086072967326762835nteger @ Q2 @ R ) )
% 0.29/0.51            = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R @ ( numera6620942414471956472nteger @ L2 ) ) ) ) )
% 0.29/0.51        & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R )
% 0.29/0.51         => ( ( unique4921790084139445826nteger @ L2 @ ( produc1086072967326762835nteger @ Q2 @ R ) )
% 0.29/0.51            = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ R ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % divmod_step_eq
% 0.29/0.51  thf(fact_733_succ__list__to__short,axiom,
% 0.29/0.51      ! [Deg: nat,Mi: nat,X: nat,TreeList: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 0.29/0.51        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.29/0.51       => ( ( ord_less_eq_nat @ Mi @ X )
% 0.29/0.51         => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.51           => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.29/0.51              = none_nat ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % succ_list_to_short
% 0.29/0.51  thf(fact_734_pred__list__to__short,axiom,
% 0.29/0.51      ! [Deg: nat,X: nat,Ma: nat,TreeList: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 0.29/0.51        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.29/0.51       => ( ( ord_less_eq_nat @ X @ Ma )
% 0.29/0.51         => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.51           => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.29/0.51              = none_nat ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % pred_list_to_short
% 0.29/0.51  thf(fact_735_list__update__beyond,axiom,
% 0.29/0.51      ! [Xs2: list_VEBT_VEBT,I2: nat,X: vEBT_VEBT] :
% 0.29/0.51        ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ I2 )
% 0.29/0.51       => ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X )
% 0.29/0.51          = Xs2 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % list_update_beyond
% 0.29/0.51  thf(fact_736_list__update__beyond,axiom,
% 0.29/0.51      ! [Xs2: list_o,I2: nat,X: $o] :
% 0.29/0.51        ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs2 ) @ I2 )
% 0.29/0.51       => ( ( list_update_o @ Xs2 @ I2 @ X )
% 0.29/0.51          = Xs2 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % list_update_beyond
% 0.29/0.51  thf(fact_737_list__update__beyond,axiom,
% 0.29/0.51      ! [Xs2: list_nat,I2: nat,X: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs2 ) @ I2 )
% 0.29/0.51       => ( ( list_update_nat @ Xs2 @ I2 @ X )
% 0.29/0.51          = Xs2 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % list_update_beyond
% 0.29/0.51  thf(fact_738_list__update__beyond,axiom,
% 0.29/0.51      ! [Xs2: list_int,I2: nat,X: int] :
% 0.29/0.51        ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs2 ) @ I2 )
% 0.29/0.51       => ( ( list_update_int @ Xs2 @ I2 @ X )
% 0.29/0.51          = Xs2 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % list_update_beyond
% 0.29/0.51  thf(fact_739_option_Ocollapse,axiom,
% 0.29/0.51      ! [Option: option4927543243414619207at_nat] :
% 0.29/0.51        ( ( Option != none_P5556105721700978146at_nat )
% 0.29/0.51       => ( ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) )
% 0.29/0.51          = Option ) ) ).
% 0.29/0.51  
% 0.29/0.51  % option.collapse
% 0.29/0.51  thf(fact_740_option_Ocollapse,axiom,
% 0.29/0.51      ! [Option: option_nat] :
% 0.29/0.51        ( ( Option != none_nat )
% 0.29/0.51       => ( ( some_nat @ ( the_nat @ Option ) )
% 0.29/0.51          = Option ) ) ).
% 0.29/0.51  
% 0.29/0.51  % option.collapse
% 0.29/0.51  thf(fact_741_option_Ocollapse,axiom,
% 0.29/0.51      ! [Option: option_num] :
% 0.29/0.51        ( ( Option != none_num )
% 0.29/0.51       => ( ( some_num @ ( the_num @ Option ) )
% 0.29/0.51          = Option ) ) ).
% 0.29/0.51  
% 0.29/0.51  % option.collapse
% 0.29/0.51  thf(fact_742_le__add__diff__inverse,axiom,
% 0.29/0.51      ! [B: real,A: real] :
% 0.29/0.51        ( ( ord_less_eq_real @ B @ A )
% 0.29/0.51       => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 0.29/0.51          = A ) ) ).
% 0.29/0.51  
% 0.29/0.51  % le_add_diff_inverse
% 0.29/0.51  thf(fact_743_le__add__diff__inverse,axiom,
% 0.29/0.51      ! [B: rat,A: rat] :
% 0.29/0.51        ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.51       => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 0.29/0.51          = A ) ) ).
% 0.29/0.51  
% 0.29/0.51  % le_add_diff_inverse
% 0.29/0.51  thf(fact_744_le__add__diff__inverse,axiom,
% 0.29/0.51      ! [B: nat,A: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.51       => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 0.29/0.51          = A ) ) ).
% 0.29/0.51  
% 0.29/0.51  % le_add_diff_inverse
% 0.29/0.51  thf(fact_745_le__add__diff__inverse,axiom,
% 0.29/0.51      ! [B: int,A: int] :
% 0.29/0.51        ( ( ord_less_eq_int @ B @ A )
% 0.29/0.51       => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 0.29/0.51          = A ) ) ).
% 0.29/0.51  
% 0.29/0.51  % le_add_diff_inverse
% 0.29/0.51  thf(fact_746_le__add__diff__inverse2,axiom,
% 0.29/0.51      ! [B: real,A: real] :
% 0.29/0.51        ( ( ord_less_eq_real @ B @ A )
% 0.29/0.51       => ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 0.29/0.51          = A ) ) ).
% 0.29/0.51  
% 0.29/0.51  % le_add_diff_inverse2
% 0.29/0.51  thf(fact_747_le__add__diff__inverse2,axiom,
% 0.29/0.51      ! [B: rat,A: rat] :
% 0.29/0.51        ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.51       => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 0.29/0.51          = A ) ) ).
% 0.29/0.51  
% 0.29/0.51  % le_add_diff_inverse2
% 0.29/0.51  thf(fact_748_le__add__diff__inverse2,axiom,
% 0.29/0.51      ! [B: nat,A: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.51       => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 0.29/0.51          = A ) ) ).
% 0.29/0.51  
% 0.29/0.51  % le_add_diff_inverse2
% 0.29/0.51  thf(fact_749_le__add__diff__inverse2,axiom,
% 0.29/0.51      ! [B: int,A: int] :
% 0.29/0.51        ( ( ord_less_eq_int @ B @ A )
% 0.29/0.51       => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 0.29/0.51          = A ) ) ).
% 0.29/0.51  
% 0.29/0.51  % le_add_diff_inverse2
% 0.29/0.51  thf(fact_750_minNullmin,axiom,
% 0.29/0.51      ! [T: vEBT_VEBT] :
% 0.29/0.51        ( ( vEBT_VEBT_minNull @ T )
% 0.29/0.51       => ( ( vEBT_vebt_mint @ T )
% 0.29/0.51          = none_nat ) ) ).
% 0.29/0.51  
% 0.29/0.51  % minNullmin
% 0.29/0.51  thf(fact_751_minminNull,axiom,
% 0.29/0.51      ! [T: vEBT_VEBT] :
% 0.29/0.51        ( ( ( vEBT_vebt_mint @ T )
% 0.29/0.51          = none_nat )
% 0.29/0.51       => ( vEBT_VEBT_minNull @ T ) ) ).
% 0.29/0.51  
% 0.29/0.51  % minminNull
% 0.29/0.51  thf(fact_752_option_Oinject,axiom,
% 0.29/0.51      ! [X23: product_prod_nat_nat,Y22: product_prod_nat_nat] :
% 0.29/0.51        ( ( ( some_P7363390416028606310at_nat @ X23 )
% 0.29/0.51          = ( some_P7363390416028606310at_nat @ Y22 ) )
% 0.29/0.51        = ( X23 = Y22 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % option.inject
% 0.29/0.51  thf(fact_753_option_Oinject,axiom,
% 0.29/0.51      ! [X23: nat,Y22: nat] :
% 0.29/0.51        ( ( ( some_nat @ X23 )
% 0.29/0.51          = ( some_nat @ Y22 ) )
% 0.29/0.51        = ( X23 = Y22 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % option.inject
% 0.29/0.51  thf(fact_754_option_Oinject,axiom,
% 0.29/0.51      ! [X23: num,Y22: num] :
% 0.29/0.51        ( ( ( some_num @ X23 )
% 0.29/0.51          = ( some_num @ Y22 ) )
% 0.29/0.51        = ( X23 = Y22 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % option.inject
% 0.29/0.51  thf(fact_755_list__update__overwrite,axiom,
% 0.29/0.51      ! [Xs2: list_VEBT_VEBT,I2: nat,X: vEBT_VEBT,Y2: vEBT_VEBT] :
% 0.29/0.51        ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ I2 @ Y2 )
% 0.29/0.51        = ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ Y2 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % list_update_overwrite
% 0.29/0.51  thf(fact_756_geqmaxNone,axiom,
% 0.29/0.51      ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.51        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 0.29/0.51       => ( ( ord_less_eq_nat @ Ma @ X )
% 0.29/0.51         => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.29/0.51            = none_nat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % geqmaxNone
% 0.29/0.51  thf(fact_757_div__by__1,axiom,
% 0.29/0.51      ! [A: complex] :
% 0.29/0.51        ( ( divide1717551699836669952omplex @ A @ one_one_complex )
% 0.29/0.51        = A ) ).
% 0.29/0.51  
% 0.29/0.51  % div_by_1
% 0.29/0.51  thf(fact_758_div__by__1,axiom,
% 0.29/0.51      ! [A: real] :
% 0.29/0.51        ( ( divide_divide_real @ A @ one_one_real )
% 0.29/0.51        = A ) ).
% 0.29/0.51  
% 0.29/0.51  % div_by_1
% 0.29/0.51  thf(fact_759_div__by__1,axiom,
% 0.29/0.51      ! [A: rat] :
% 0.29/0.51        ( ( divide_divide_rat @ A @ one_one_rat )
% 0.29/0.51        = A ) ).
% 0.29/0.51  
% 0.29/0.51  % div_by_1
% 0.29/0.51  thf(fact_760_div__by__1,axiom,
% 0.29/0.51      ! [A: nat] :
% 0.29/0.51        ( ( divide_divide_nat @ A @ one_one_nat )
% 0.29/0.51        = A ) ).
% 0.29/0.51  
% 0.29/0.51  % div_by_1
% 0.29/0.51  thf(fact_761_div__by__1,axiom,
% 0.29/0.51      ! [A: int] :
% 0.29/0.51        ( ( divide_divide_int @ A @ one_one_int )
% 0.29/0.51        = A ) ).
% 0.29/0.51  
% 0.29/0.51  % div_by_1
% 0.29/0.51  thf(fact_762_not__None__eq,axiom,
% 0.29/0.51      ! [X: option4927543243414619207at_nat] :
% 0.29/0.51        ( ( X != none_P5556105721700978146at_nat )
% 0.29/0.51        = ( ? [Y: product_prod_nat_nat] :
% 0.29/0.51              ( X
% 0.29/0.51              = ( some_P7363390416028606310at_nat @ Y ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % not_None_eq
% 0.29/0.51  thf(fact_763_not__None__eq,axiom,
% 0.29/0.51      ! [X: option_nat] :
% 0.29/0.51        ( ( X != none_nat )
% 0.29/0.51        = ( ? [Y: nat] :
% 0.29/0.51              ( X
% 0.29/0.51              = ( some_nat @ Y ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % not_None_eq
% 0.29/0.51  thf(fact_764_not__None__eq,axiom,
% 0.29/0.51      ! [X: option_num] :
% 0.29/0.51        ( ( X != none_num )
% 0.29/0.51        = ( ? [Y: num] :
% 0.29/0.51              ( X
% 0.29/0.51              = ( some_num @ Y ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % not_None_eq
% 0.29/0.51  thf(fact_765_not__Some__eq,axiom,
% 0.29/0.51      ! [X: option4927543243414619207at_nat] :
% 0.29/0.51        ( ( ! [Y: product_prod_nat_nat] :
% 0.29/0.51              ( X
% 0.29/0.51             != ( some_P7363390416028606310at_nat @ Y ) ) )
% 0.29/0.51        = ( X = none_P5556105721700978146at_nat ) ) ).
% 0.29/0.51  
% 0.29/0.51  % not_Some_eq
% 0.29/0.51  thf(fact_766_not__Some__eq,axiom,
% 0.29/0.51      ! [X: option_nat] :
% 0.29/0.51        ( ( ! [Y: nat] :
% 0.29/0.51              ( X
% 0.29/0.51             != ( some_nat @ Y ) ) )
% 0.29/0.51        = ( X = none_nat ) ) ).
% 0.29/0.51  
% 0.29/0.51  % not_Some_eq
% 0.29/0.51  thf(fact_767_not__Some__eq,axiom,
% 0.29/0.51      ! [X: option_num] :
% 0.29/0.51        ( ( ! [Y: num] :
% 0.29/0.51              ( X
% 0.29/0.51             != ( some_num @ Y ) ) )
% 0.29/0.51        = ( X = none_num ) ) ).
% 0.29/0.51  
% 0.29/0.51  % not_Some_eq
% 0.29/0.51  thf(fact_768_length__list__update,axiom,
% 0.29/0.51      ! [Xs2: list_VEBT_VEBT,I2: nat,X: vEBT_VEBT] :
% 0.29/0.51        ( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) )
% 0.29/0.51        = ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % length_list_update
% 0.29/0.51  thf(fact_769_length__list__update,axiom,
% 0.29/0.51      ! [Xs2: list_o,I2: nat,X: $o] :
% 0.29/0.51        ( ( size_size_list_o @ ( list_update_o @ Xs2 @ I2 @ X ) )
% 0.29/0.51        = ( size_size_list_o @ Xs2 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % length_list_update
% 0.29/0.51  thf(fact_770_length__list__update,axiom,
% 0.29/0.51      ! [Xs2: list_nat,I2: nat,X: nat] :
% 0.29/0.51        ( ( size_size_list_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) )
% 0.29/0.51        = ( size_size_list_nat @ Xs2 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % length_list_update
% 0.29/0.51  thf(fact_771_length__list__update,axiom,
% 0.29/0.51      ! [Xs2: list_int,I2: nat,X: int] :
% 0.29/0.51        ( ( size_size_list_int @ ( list_update_int @ Xs2 @ I2 @ X ) )
% 0.29/0.51        = ( size_size_list_int @ Xs2 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % length_list_update
% 0.29/0.51  thf(fact_772_list__update__id,axiom,
% 0.29/0.51      ! [Xs2: list_nat,I2: nat] :
% 0.29/0.51        ( ( list_update_nat @ Xs2 @ I2 @ ( nth_nat @ Xs2 @ I2 ) )
% 0.29/0.51        = Xs2 ) ).
% 0.29/0.51  
% 0.29/0.51  % list_update_id
% 0.29/0.51  thf(fact_773_list__update__id,axiom,
% 0.29/0.51      ! [Xs2: list_VEBT_VEBT,I2: nat] :
% 0.29/0.51        ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ ( nth_VEBT_VEBT @ Xs2 @ I2 ) )
% 0.29/0.51        = Xs2 ) ).
% 0.29/0.51  
% 0.29/0.51  % list_update_id
% 0.29/0.51  thf(fact_774_nth__list__update__neq,axiom,
% 0.29/0.51      ! [I2: nat,J: nat,Xs2: list_nat,X: nat] :
% 0.29/0.51        ( ( I2 != J )
% 0.29/0.51       => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) @ J )
% 0.29/0.51          = ( nth_nat @ Xs2 @ J ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nth_list_update_neq
% 0.29/0.51  thf(fact_775_nth__list__update__neq,axiom,
% 0.29/0.51      ! [I2: nat,J: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 0.29/0.51        ( ( I2 != J )
% 0.29/0.51       => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ J )
% 0.29/0.51          = ( nth_VEBT_VEBT @ Xs2 @ J ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nth_list_update_neq
% 0.29/0.51  thf(fact_776_max__Suc__Suc,axiom,
% 0.29/0.51      ! [M: nat,N: nat] :
% 0.29/0.51        ( ( ord_max_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.29/0.51        = ( suc @ ( ord_max_nat @ M @ N ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % max_Suc_Suc
% 0.29/0.51  thf(fact_777_max__number__of_I1_J,axiom,
% 0.29/0.51      ! [U: num,V: num] :
% 0.29/0.51        ( ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 0.29/0.51         => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 0.29/0.51            = ( numera1916890842035813515d_enat @ V ) ) )
% 0.29/0.51        & ( ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 0.29/0.51         => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 0.29/0.51            = ( numera1916890842035813515d_enat @ U ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % max_number_of(1)
% 0.29/0.51  thf(fact_778_max__number__of_I1_J,axiom,
% 0.29/0.51      ! [U: num,V: num] :
% 0.29/0.51        ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 0.29/0.51         => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 0.29/0.51            = ( numeral_numeral_real @ V ) ) )
% 0.29/0.51        & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 0.29/0.51         => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 0.29/0.51            = ( numeral_numeral_real @ U ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % max_number_of(1)
% 0.29/0.51  thf(fact_779_max__number__of_I1_J,axiom,
% 0.29/0.51      ! [U: num,V: num] :
% 0.29/0.51        ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 0.29/0.51         => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 0.29/0.51            = ( numeral_numeral_rat @ V ) ) )
% 0.29/0.51        & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 0.29/0.51         => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 0.29/0.51            = ( numeral_numeral_rat @ U ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % max_number_of(1)
% 0.29/0.51  thf(fact_780_max__number__of_I1_J,axiom,
% 0.29/0.51      ! [U: num,V: num] :
% 0.29/0.51        ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 0.29/0.51         => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 0.29/0.51            = ( numeral_numeral_nat @ V ) ) )
% 0.29/0.51        & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 0.29/0.51         => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 0.29/0.51            = ( numeral_numeral_nat @ U ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % max_number_of(1)
% 0.29/0.51  thf(fact_781_max__number__of_I1_J,axiom,
% 0.29/0.51      ! [U: num,V: num] :
% 0.29/0.51        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 0.29/0.51         => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 0.29/0.51            = ( numeral_numeral_int @ V ) ) )
% 0.29/0.51        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 0.29/0.51         => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 0.29/0.51            = ( numeral_numeral_int @ U ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % max_number_of(1)
% 0.29/0.51  thf(fact_782_max__0__1_I6_J,axiom,
% 0.29/0.51      ! [X: num] :
% 0.29/0.51        ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X ) @ one_on7984719198319812577d_enat )
% 0.29/0.51        = ( numera1916890842035813515d_enat @ X ) ) ).
% 0.29/0.51  
% 0.29/0.51  % max_0_1(6)
% 0.29/0.51  thf(fact_783_max__0__1_I6_J,axiom,
% 0.29/0.51      ! [X: num] :
% 0.29/0.51        ( ( ord_max_real @ ( numeral_numeral_real @ X ) @ one_one_real )
% 0.29/0.51        = ( numeral_numeral_real @ X ) ) ).
% 0.29/0.51  
% 0.29/0.51  % max_0_1(6)
% 0.29/0.51  thf(fact_784_max__0__1_I6_J,axiom,
% 0.29/0.51      ! [X: num] :
% 0.29/0.51        ( ( ord_max_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat )
% 0.29/0.51        = ( numeral_numeral_rat @ X ) ) ).
% 0.29/0.51  
% 0.29/0.51  % max_0_1(6)
% 0.29/0.51  thf(fact_785_max__0__1_I6_J,axiom,
% 0.29/0.51      ! [X: num] :
% 0.29/0.51        ( ( ord_max_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat )
% 0.29/0.51        = ( numeral_numeral_nat @ X ) ) ).
% 0.29/0.51  
% 0.29/0.51  % max_0_1(6)
% 0.29/0.51  thf(fact_786_max__0__1_I6_J,axiom,
% 0.29/0.51      ! [X: num] :
% 0.29/0.51        ( ( ord_max_int @ ( numeral_numeral_int @ X ) @ one_one_int )
% 0.29/0.51        = ( numeral_numeral_int @ X ) ) ).
% 0.29/0.51  
% 0.29/0.51  % max_0_1(6)
% 0.29/0.51  thf(fact_787_max__0__1_I5_J,axiom,
% 0.29/0.51      ! [X: num] :
% 0.29/0.51        ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 0.29/0.51        = ( numera1916890842035813515d_enat @ X ) ) ).
% 0.29/0.51  
% 0.29/0.51  % max_0_1(5)
% 0.29/0.51  thf(fact_788_max__0__1_I5_J,axiom,
% 0.29/0.51      ! [X: num] :
% 0.29/0.51        ( ( ord_max_real @ one_one_real @ ( numeral_numeral_real @ X ) )
% 0.29/0.51        = ( numeral_numeral_real @ X ) ) ).
% 0.29/0.51  
% 0.29/0.51  % max_0_1(5)
% 0.29/0.51  thf(fact_789_max__0__1_I5_J,axiom,
% 0.29/0.51      ! [X: num] :
% 0.29/0.51        ( ( ord_max_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 0.29/0.51        = ( numeral_numeral_rat @ X ) ) ).
% 0.29/0.51  
% 0.29/0.51  % max_0_1(5)
% 0.29/0.51  thf(fact_790_max__0__1_I5_J,axiom,
% 0.29/0.51      ! [X: num] :
% 0.29/0.51        ( ( ord_max_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 0.29/0.51        = ( numeral_numeral_nat @ X ) ) ).
% 0.29/0.51  
% 0.29/0.51  % max_0_1(5)
% 0.29/0.51  thf(fact_791_max__0__1_I5_J,axiom,
% 0.29/0.51      ! [X: num] :
% 0.29/0.51        ( ( ord_max_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 0.29/0.51        = ( numeral_numeral_int @ X ) ) ).
% 0.29/0.51  
% 0.29/0.51  % max_0_1(5)
% 0.29/0.51  thf(fact_792_nat__add__max__left,axiom,
% 0.29/0.51      ! [M: nat,N: nat,Q2: nat] :
% 0.29/0.51        ( ( plus_plus_nat @ ( ord_max_nat @ M @ N ) @ Q2 )
% 0.29/0.51        = ( ord_max_nat @ ( plus_plus_nat @ M @ Q2 ) @ ( plus_plus_nat @ N @ Q2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nat_add_max_left
% 0.29/0.51  thf(fact_793_nat__add__max__right,axiom,
% 0.29/0.51      ! [M: nat,N: nat,Q2: nat] :
% 0.29/0.51        ( ( plus_plus_nat @ M @ ( ord_max_nat @ N @ Q2 ) )
% 0.29/0.51        = ( ord_max_nat @ ( plus_plus_nat @ M @ N ) @ ( plus_plus_nat @ M @ Q2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nat_add_max_right
% 0.29/0.51  thf(fact_794_nat__mult__max__right,axiom,
% 0.29/0.51      ! [M: nat,N: nat,Q2: nat] :
% 0.29/0.51        ( ( times_times_nat @ M @ ( ord_max_nat @ N @ Q2 ) )
% 0.29/0.51        = ( ord_max_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nat_mult_max_right
% 0.29/0.51  thf(fact_795_nat__mult__max__left,axiom,
% 0.29/0.51      ! [M: nat,N: nat,Q2: nat] :
% 0.29/0.51        ( ( times_times_nat @ ( ord_max_nat @ M @ N ) @ Q2 )
% 0.29/0.51        = ( ord_max_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N @ Q2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nat_mult_max_left
% 0.29/0.51  thf(fact_796_add__diff__assoc__enat,axiom,
% 0.29/0.51      ! [Z: extended_enat,Y2: extended_enat,X: extended_enat] :
% 0.29/0.51        ( ( ord_le2932123472753598470d_enat @ Z @ Y2 )
% 0.29/0.51       => ( ( plus_p3455044024723400733d_enat @ X @ ( minus_3235023915231533773d_enat @ Y2 @ Z ) )
% 0.29/0.51          = ( minus_3235023915231533773d_enat @ ( plus_p3455044024723400733d_enat @ X @ Y2 ) @ Z ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % add_diff_assoc_enat
% 0.29/0.51  thf(fact_797_nat__minus__add__max,axiom,
% 0.29/0.51      ! [N: nat,M: nat] :
% 0.29/0.51        ( ( plus_plus_nat @ ( minus_minus_nat @ N @ M ) @ M )
% 0.29/0.51        = ( ord_max_nat @ N @ M ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nat_minus_add_max
% 0.29/0.51  thf(fact_798_xor__num_Ocases,axiom,
% 0.29/0.51      ! [X: product_prod_num_num] :
% 0.29/0.51        ( ( X
% 0.29/0.51         != ( product_Pair_num_num @ one @ one ) )
% 0.29/0.51       => ( ! [N3: num] :
% 0.29/0.51              ( X
% 0.29/0.51             != ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) )
% 0.29/0.51         => ( ! [N3: num] :
% 0.29/0.51                ( X
% 0.29/0.51               != ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) )
% 0.29/0.51           => ( ! [M4: num] :
% 0.29/0.51                  ( X
% 0.29/0.51                 != ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) )
% 0.29/0.51             => ( ! [M4: num,N3: num] :
% 0.29/0.51                    ( X
% 0.29/0.51                   != ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N3 ) ) )
% 0.29/0.51               => ( ! [M4: num,N3: num] :
% 0.29/0.51                      ( X
% 0.29/0.51                     != ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N3 ) ) )
% 0.29/0.51                 => ( ! [M4: num] :
% 0.29/0.51                        ( X
% 0.29/0.51                       != ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) )
% 0.29/0.51                   => ( ! [M4: num,N3: num] :
% 0.29/0.51                          ( X
% 0.29/0.51                         != ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N3 ) ) )
% 0.29/0.51                     => ~ ! [M4: num,N3: num] :
% 0.29/0.51                            ( X
% 0.29/0.51                           != ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % xor_num.cases
% 0.29/0.51  thf(fact_799_linorder__neqE__linordered__idom,axiom,
% 0.29/0.51      ! [X: real,Y2: real] :
% 0.29/0.51        ( ( X != Y2 )
% 0.29/0.51       => ( ~ ( ord_less_real @ X @ Y2 )
% 0.29/0.51         => ( ord_less_real @ Y2 @ X ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % linorder_neqE_linordered_idom
% 0.29/0.51  thf(fact_800_linorder__neqE__linordered__idom,axiom,
% 0.29/0.51      ! [X: rat,Y2: rat] :
% 0.29/0.51        ( ( X != Y2 )
% 0.29/0.51       => ( ~ ( ord_less_rat @ X @ Y2 )
% 0.29/0.51         => ( ord_less_rat @ Y2 @ X ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % linorder_neqE_linordered_idom
% 0.29/0.51  thf(fact_801_linorder__neqE__linordered__idom,axiom,
% 0.29/0.51      ! [X: int,Y2: int] :
% 0.29/0.51        ( ( X != Y2 )
% 0.29/0.51       => ( ~ ( ord_less_int @ X @ Y2 )
% 0.29/0.51         => ( ord_less_int @ Y2 @ X ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % linorder_neqE_linordered_idom
% 0.29/0.51  thf(fact_802_subset__code_I1_J,axiom,
% 0.29/0.51      ! [Xs2: list_P6011104703257516679at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.29/0.51        ( ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ Xs2 ) @ B2 )
% 0.29/0.51        = ( ! [X2: product_prod_nat_nat] :
% 0.29/0.51              ( ( member8440522571783428010at_nat @ X2 @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 0.29/0.51             => ( member8440522571783428010at_nat @ X2 @ B2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % subset_code(1)
% 0.29/0.51  thf(fact_803_subset__code_I1_J,axiom,
% 0.29/0.51      ! [Xs2: list_complex,B2: set_complex] :
% 0.29/0.51        ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ B2 )
% 0.29/0.51        = ( ! [X2: complex] :
% 0.29/0.51              ( ( member_complex @ X2 @ ( set_complex2 @ Xs2 ) )
% 0.29/0.51             => ( member_complex @ X2 @ B2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % subset_code(1)
% 0.29/0.51  thf(fact_804_subset__code_I1_J,axiom,
% 0.29/0.51      ! [Xs2: list_VEBT_VEBT,B2: set_VEBT_VEBT] :
% 0.29/0.51        ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ B2 )
% 0.29/0.51        = ( ! [X2: vEBT_VEBT] :
% 0.29/0.51              ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 0.29/0.51             => ( member_VEBT_VEBT @ X2 @ B2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % subset_code(1)
% 0.29/0.51  thf(fact_805_subset__code_I1_J,axiom,
% 0.29/0.51      ! [Xs2: list_int,B2: set_int] :
% 0.29/0.51        ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ B2 )
% 0.29/0.51        = ( ! [X2: int] :
% 0.29/0.51              ( ( member_int @ X2 @ ( set_int2 @ Xs2 ) )
% 0.29/0.51             => ( member_int @ X2 @ B2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % subset_code(1)
% 0.29/0.51  thf(fact_806_subset__code_I1_J,axiom,
% 0.29/0.51      ! [Xs2: list_real,B2: set_real] :
% 0.29/0.51        ( ( ord_less_eq_set_real @ ( set_real2 @ Xs2 ) @ B2 )
% 0.29/0.51        = ( ! [X2: real] :
% 0.29/0.51              ( ( member_real @ X2 @ ( set_real2 @ Xs2 ) )
% 0.29/0.51             => ( member_real @ X2 @ B2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % subset_code(1)
% 0.29/0.51  thf(fact_807_subset__code_I1_J,axiom,
% 0.29/0.51      ! [Xs2: list_nat,B2: set_nat] :
% 0.29/0.51        ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ B2 )
% 0.29/0.51        = ( ! [X2: nat] :
% 0.29/0.51              ( ( member_nat @ X2 @ ( set_nat2 @ Xs2 ) )
% 0.29/0.51             => ( member_nat @ X2 @ B2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % subset_code(1)
% 0.29/0.51  thf(fact_808_neq__if__length__neq,axiom,
% 0.29/0.51      ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 0.29/0.51        ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 0.29/0.51         != ( size_s6755466524823107622T_VEBT @ Ys ) )
% 0.29/0.51       => ( Xs2 != Ys ) ) ).
% 0.29/0.51  
% 0.29/0.51  % neq_if_length_neq
% 0.29/0.51  thf(fact_809_neq__if__length__neq,axiom,
% 0.29/0.51      ! [Xs2: list_o,Ys: list_o] :
% 0.29/0.51        ( ( ( size_size_list_o @ Xs2 )
% 0.29/0.51         != ( size_size_list_o @ Ys ) )
% 0.29/0.51       => ( Xs2 != Ys ) ) ).
% 0.29/0.51  
% 0.29/0.51  % neq_if_length_neq
% 0.29/0.51  thf(fact_810_neq__if__length__neq,axiom,
% 0.29/0.51      ! [Xs2: list_nat,Ys: list_nat] :
% 0.29/0.51        ( ( ( size_size_list_nat @ Xs2 )
% 0.29/0.51         != ( size_size_list_nat @ Ys ) )
% 0.29/0.51       => ( Xs2 != Ys ) ) ).
% 0.29/0.51  
% 0.29/0.51  % neq_if_length_neq
% 0.29/0.51  thf(fact_811_neq__if__length__neq,axiom,
% 0.29/0.51      ! [Xs2: list_int,Ys: list_int] :
% 0.29/0.51        ( ( ( size_size_list_int @ Xs2 )
% 0.29/0.51         != ( size_size_list_int @ Ys ) )
% 0.29/0.51       => ( Xs2 != Ys ) ) ).
% 0.29/0.51  
% 0.29/0.51  % neq_if_length_neq
% 0.29/0.51  thf(fact_812_Ex__list__of__length,axiom,
% 0.29/0.51      ! [N: nat] :
% 0.29/0.51      ? [Xs3: list_VEBT_VEBT] :
% 0.29/0.51        ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 0.29/0.51        = N ) ).
% 0.29/0.51  
% 0.29/0.51  % Ex_list_of_length
% 0.29/0.51  thf(fact_813_Ex__list__of__length,axiom,
% 0.29/0.51      ! [N: nat] :
% 0.29/0.51      ? [Xs3: list_o] :
% 0.29/0.51        ( ( size_size_list_o @ Xs3 )
% 0.29/0.51        = N ) ).
% 0.29/0.51  
% 0.29/0.51  % Ex_list_of_length
% 0.29/0.51  thf(fact_814_Ex__list__of__length,axiom,
% 0.29/0.51      ! [N: nat] :
% 0.29/0.51      ? [Xs3: list_nat] :
% 0.29/0.51        ( ( size_size_list_nat @ Xs3 )
% 0.29/0.51        = N ) ).
% 0.29/0.51  
% 0.29/0.51  % Ex_list_of_length
% 0.29/0.51  thf(fact_815_Ex__list__of__length,axiom,
% 0.29/0.51      ! [N: nat] :
% 0.29/0.51      ? [Xs3: list_int] :
% 0.29/0.51        ( ( size_size_list_int @ Xs3 )
% 0.29/0.51        = N ) ).
% 0.29/0.51  
% 0.29/0.51  % Ex_list_of_length
% 0.29/0.51  thf(fact_816_list__update__swap,axiom,
% 0.29/0.51      ! [I2: nat,I5: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT,X6: vEBT_VEBT] :
% 0.29/0.51        ( ( I2 != I5 )
% 0.29/0.51       => ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ I5 @ X6 )
% 0.29/0.51          = ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I5 @ X6 ) @ I2 @ X ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % list_update_swap
% 0.29/0.51  thf(fact_817_ring__class_Oring__distribs_I2_J,axiom,
% 0.29/0.51      ! [A: rat,B: rat,C: rat] :
% 0.29/0.51        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.29/0.51        = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % ring_class.ring_distribs(2)
% 0.29/0.51  thf(fact_818_ring__class_Oring__distribs_I2_J,axiom,
% 0.29/0.51      ! [A: complex,B: complex,C: complex] :
% 0.29/0.51        ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 0.29/0.51        = ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % ring_class.ring_distribs(2)
% 0.29/0.51  thf(fact_819_ring__class_Oring__distribs_I2_J,axiom,
% 0.29/0.51      ! [A: real,B: real,C: real] :
% 0.29/0.51        ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.29/0.51        = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % ring_class.ring_distribs(2)
% 0.29/0.51  thf(fact_820_ring__class_Oring__distribs_I2_J,axiom,
% 0.29/0.51      ! [A: int,B: int,C: int] :
% 0.29/0.51        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.29/0.51        = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % ring_class.ring_distribs(2)
% 0.29/0.51  thf(fact_821_ring__class_Oring__distribs_I1_J,axiom,
% 0.29/0.51      ! [A: rat,B: rat,C: rat] :
% 0.29/0.51        ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.29/0.51        = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % ring_class.ring_distribs(1)
% 0.29/0.51  thf(fact_822_ring__class_Oring__distribs_I1_J,axiom,
% 0.29/0.51      ! [A: complex,B: complex,C: complex] :
% 0.29/0.51        ( ( times_times_complex @ A @ ( plus_plus_complex @ B @ C ) )
% 0.29/0.51        = ( plus_plus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % ring_class.ring_distribs(1)
% 0.29/0.51  thf(fact_823_ring__class_Oring__distribs_I1_J,axiom,
% 0.29/0.51      ! [A: real,B: real,C: real] :
% 0.29/0.51        ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 0.29/0.51        = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % ring_class.ring_distribs(1)
% 0.29/0.51  thf(fact_824_ring__class_Oring__distribs_I1_J,axiom,
% 0.29/0.51      ! [A: int,B: int,C: int] :
% 0.29/0.51        ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.29/0.51        = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % ring_class.ring_distribs(1)
% 0.29/0.51  thf(fact_825_comm__semiring__class_Odistrib,axiom,
% 0.29/0.51      ! [A: rat,B: rat,C: rat] :
% 0.29/0.51        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.29/0.51        = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % comm_semiring_class.distrib
% 0.29/0.51  thf(fact_826_comm__semiring__class_Odistrib,axiom,
% 0.29/0.51      ! [A: complex,B: complex,C: complex] :
% 0.29/0.51        ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 0.29/0.51        = ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % comm_semiring_class.distrib
% 0.29/0.51  thf(fact_827_comm__semiring__class_Odistrib,axiom,
% 0.29/0.51      ! [A: real,B: real,C: real] :
% 0.29/0.51        ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.29/0.51        = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % comm_semiring_class.distrib
% 0.29/0.51  thf(fact_828_comm__semiring__class_Odistrib,axiom,
% 0.29/0.51      ! [A: nat,B: nat,C: nat] :
% 0.29/0.51        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.29/0.51        = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % comm_semiring_class.distrib
% 0.29/0.51  thf(fact_829_comm__semiring__class_Odistrib,axiom,
% 0.29/0.51      ! [A: int,B: int,C: int] :
% 0.29/0.51        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.29/0.51        = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % comm_semiring_class.distrib
% 0.29/0.51  thf(fact_830_distrib__left,axiom,
% 0.29/0.51      ! [A: rat,B: rat,C: rat] :
% 0.29/0.51        ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.29/0.51        = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % distrib_left
% 0.29/0.51  thf(fact_831_distrib__left,axiom,
% 0.29/0.51      ! [A: complex,B: complex,C: complex] :
% 0.29/0.51        ( ( times_times_complex @ A @ ( plus_plus_complex @ B @ C ) )
% 0.29/0.51        = ( plus_plus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % distrib_left
% 0.29/0.51  thf(fact_832_distrib__left,axiom,
% 0.29/0.51      ! [A: real,B: real,C: real] :
% 0.29/0.51        ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 0.29/0.51        = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % distrib_left
% 0.29/0.51  thf(fact_833_distrib__left,axiom,
% 0.29/0.51      ! [A: nat,B: nat,C: nat] :
% 0.29/0.51        ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 0.29/0.51        = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % distrib_left
% 0.29/0.51  thf(fact_834_distrib__left,axiom,
% 0.29/0.51      ! [A: int,B: int,C: int] :
% 0.29/0.51        ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.29/0.51        = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % distrib_left
% 0.29/0.51  thf(fact_835_distrib__right,axiom,
% 0.29/0.51      ! [A: rat,B: rat,C: rat] :
% 0.29/0.51        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.29/0.51        = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % distrib_right
% 0.29/0.51  thf(fact_836_distrib__right,axiom,
% 0.29/0.51      ! [A: complex,B: complex,C: complex] :
% 0.29/0.51        ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 0.29/0.51        = ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % distrib_right
% 0.29/0.51  thf(fact_837_distrib__right,axiom,
% 0.29/0.51      ! [A: real,B: real,C: real] :
% 0.29/0.51        ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.29/0.51        = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % distrib_right
% 0.29/0.51  thf(fact_838_distrib__right,axiom,
% 0.29/0.51      ! [A: nat,B: nat,C: nat] :
% 0.29/0.51        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.29/0.51        = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % distrib_right
% 0.29/0.51  thf(fact_839_distrib__right,axiom,
% 0.29/0.51      ! [A: int,B: int,C: int] :
% 0.29/0.51        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.29/0.51        = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % distrib_right
% 0.29/0.51  thf(fact_840_combine__common__factor,axiom,
% 0.29/0.51      ! [A: rat,E: rat,B: rat,C: rat] :
% 0.29/0.51        ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ C ) )
% 0.29/0.51        = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ E ) @ C ) ) ).
% 0.29/0.51  
% 0.29/0.51  % combine_common_factor
% 0.29/0.51  thf(fact_841_combine__common__factor,axiom,
% 0.29/0.51      ! [A: complex,E: complex,B: complex,C: complex] :
% 0.29/0.51        ( ( plus_plus_complex @ ( times_times_complex @ A @ E ) @ ( plus_plus_complex @ ( times_times_complex @ B @ E ) @ C ) )
% 0.29/0.51        = ( plus_plus_complex @ ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ E ) @ C ) ) ).
% 0.29/0.51  
% 0.29/0.51  % combine_common_factor
% 0.29/0.51  thf(fact_842_combine__common__factor,axiom,
% 0.29/0.51      ! [A: real,E: real,B: real,C: real] :
% 0.29/0.51        ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ C ) )
% 0.29/0.51        = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ E ) @ C ) ) ).
% 0.29/0.51  
% 0.29/0.51  % combine_common_factor
% 0.29/0.51  thf(fact_843_combine__common__factor,axiom,
% 0.29/0.51      ! [A: nat,E: nat,B: nat,C: nat] :
% 0.29/0.51        ( ( plus_plus_nat @ ( times_times_nat @ A @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E ) @ C ) )
% 0.29/0.51        = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E ) @ C ) ) ).
% 0.29/0.51  
% 0.29/0.51  % combine_common_factor
% 0.29/0.51  thf(fact_844_combine__common__factor,axiom,
% 0.29/0.51      ! [A: int,E: int,B: int,C: int] :
% 0.29/0.51        ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ C ) )
% 0.29/0.51        = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E ) @ C ) ) ).
% 0.29/0.51  
% 0.29/0.51  % combine_common_factor
% 0.29/0.51  thf(fact_845_right__diff__distrib_H,axiom,
% 0.29/0.51      ! [A: rat,B: rat,C: rat] :
% 0.29/0.51        ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 0.29/0.51        = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % right_diff_distrib'
% 0.29/0.51  thf(fact_846_right__diff__distrib_H,axiom,
% 0.29/0.51      ! [A: complex,B: complex,C: complex] :
% 0.29/0.51        ( ( times_times_complex @ A @ ( minus_minus_complex @ B @ C ) )
% 0.29/0.51        = ( minus_minus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % right_diff_distrib'
% 0.29/0.51  thf(fact_847_right__diff__distrib_H,axiom,
% 0.29/0.51      ! [A: real,B: real,C: real] :
% 0.29/0.51        ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 0.29/0.51        = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % right_diff_distrib'
% 0.29/0.51  thf(fact_848_right__diff__distrib_H,axiom,
% 0.29/0.51      ! [A: nat,B: nat,C: nat] :
% 0.29/0.51        ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
% 0.29/0.51        = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % right_diff_distrib'
% 0.29/0.51  thf(fact_849_right__diff__distrib_H,axiom,
% 0.29/0.51      ! [A: int,B: int,C: int] :
% 0.29/0.51        ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 0.29/0.51        = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % right_diff_distrib'
% 0.29/0.51  thf(fact_850_left__diff__distrib_H,axiom,
% 0.29/0.51      ! [B: rat,C: rat,A: rat] :
% 0.29/0.51        ( ( times_times_rat @ ( minus_minus_rat @ B @ C ) @ A )
% 0.29/0.51        = ( minus_minus_rat @ ( times_times_rat @ B @ A ) @ ( times_times_rat @ C @ A ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % left_diff_distrib'
% 0.29/0.51  thf(fact_851_left__diff__distrib_H,axiom,
% 0.29/0.51      ! [B: complex,C: complex,A: complex] :
% 0.29/0.51        ( ( times_times_complex @ ( minus_minus_complex @ B @ C ) @ A )
% 0.29/0.51        = ( minus_minus_complex @ ( times_times_complex @ B @ A ) @ ( times_times_complex @ C @ A ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % left_diff_distrib'
% 0.29/0.51  thf(fact_852_left__diff__distrib_H,axiom,
% 0.29/0.51      ! [B: real,C: real,A: real] :
% 0.29/0.51        ( ( times_times_real @ ( minus_minus_real @ B @ C ) @ A )
% 0.29/0.51        = ( minus_minus_real @ ( times_times_real @ B @ A ) @ ( times_times_real @ C @ A ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % left_diff_distrib'
% 0.29/0.51  thf(fact_853_left__diff__distrib_H,axiom,
% 0.29/0.51      ! [B: nat,C: nat,A: nat] :
% 0.29/0.51        ( ( times_times_nat @ ( minus_minus_nat @ B @ C ) @ A )
% 0.29/0.51        = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % left_diff_distrib'
% 0.29/0.51  thf(fact_854_left__diff__distrib_H,axiom,
% 0.29/0.51      ! [B: int,C: int,A: int] :
% 0.29/0.51        ( ( times_times_int @ ( minus_minus_int @ B @ C ) @ A )
% 0.29/0.51        = ( minus_minus_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % left_diff_distrib'
% 0.29/0.51  thf(fact_855_right__diff__distrib,axiom,
% 0.29/0.51      ! [A: rat,B: rat,C: rat] :
% 0.29/0.51        ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 0.29/0.51        = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % right_diff_distrib
% 0.29/0.51  thf(fact_856_right__diff__distrib,axiom,
% 0.29/0.51      ! [A: complex,B: complex,C: complex] :
% 0.29/0.51        ( ( times_times_complex @ A @ ( minus_minus_complex @ B @ C ) )
% 0.29/0.51        = ( minus_minus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % right_diff_distrib
% 0.29/0.51  thf(fact_857_right__diff__distrib,axiom,
% 0.29/0.51      ! [A: real,B: real,C: real] :
% 0.29/0.51        ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 0.29/0.51        = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % right_diff_distrib
% 0.29/0.51  thf(fact_858_right__diff__distrib,axiom,
% 0.29/0.51      ! [A: int,B: int,C: int] :
% 0.29/0.51        ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 0.29/0.51        = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % right_diff_distrib
% 0.29/0.51  thf(fact_859_left__diff__distrib,axiom,
% 0.29/0.51      ! [A: rat,B: rat,C: rat] :
% 0.29/0.51        ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.29/0.51        = ( minus_minus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % left_diff_distrib
% 0.29/0.51  thf(fact_860_left__diff__distrib,axiom,
% 0.29/0.51      ! [A: complex,B: complex,C: complex] :
% 0.29/0.51        ( ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ C )
% 0.29/0.51        = ( minus_minus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % left_diff_distrib
% 0.29/0.51  thf(fact_861_left__diff__distrib,axiom,
% 0.29/0.51      ! [A: real,B: real,C: real] :
% 0.29/0.51        ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.29/0.51        = ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % left_diff_distrib
% 0.29/0.51  thf(fact_862_left__diff__distrib,axiom,
% 0.29/0.51      ! [A: int,B: int,C: int] :
% 0.29/0.51        ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.29/0.51        = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % left_diff_distrib
% 0.29/0.51  thf(fact_863_length__induct,axiom,
% 0.29/0.51      ! [P: list_VEBT_VEBT > $o,Xs2: list_VEBT_VEBT] :
% 0.29/0.51        ( ! [Xs3: list_VEBT_VEBT] :
% 0.29/0.51            ( ! [Ys2: list_VEBT_VEBT] :
% 0.29/0.51                ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ys2 ) @ ( size_s6755466524823107622T_VEBT @ Xs3 ) )
% 0.29/0.51               => ( P @ Ys2 ) )
% 0.29/0.51           => ( P @ Xs3 ) )
% 0.29/0.51       => ( P @ Xs2 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % length_induct
% 0.29/0.51  thf(fact_864_length__induct,axiom,
% 0.29/0.51      ! [P: list_o > $o,Xs2: list_o] :
% 0.29/0.51        ( ! [Xs3: list_o] :
% 0.29/0.51            ( ! [Ys2: list_o] :
% 0.29/0.51                ( ( ord_less_nat @ ( size_size_list_o @ Ys2 ) @ ( size_size_list_o @ Xs3 ) )
% 0.29/0.51               => ( P @ Ys2 ) )
% 0.29/0.51           => ( P @ Xs3 ) )
% 0.29/0.51       => ( P @ Xs2 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % length_induct
% 0.29/0.51  thf(fact_865_length__induct,axiom,
% 0.29/0.51      ! [P: list_nat > $o,Xs2: list_nat] :
% 0.29/0.51        ( ! [Xs3: list_nat] :
% 0.29/0.51            ( ! [Ys2: list_nat] :
% 0.29/0.51                ( ( ord_less_nat @ ( size_size_list_nat @ Ys2 ) @ ( size_size_list_nat @ Xs3 ) )
% 0.29/0.51               => ( P @ Ys2 ) )
% 0.29/0.51           => ( P @ Xs3 ) )
% 0.29/0.51       => ( P @ Xs2 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % length_induct
% 0.29/0.51  thf(fact_866_length__induct,axiom,
% 0.29/0.51      ! [P: list_int > $o,Xs2: list_int] :
% 0.29/0.51        ( ! [Xs3: list_int] :
% 0.29/0.51            ( ! [Ys2: list_int] :
% 0.29/0.51                ( ( ord_less_nat @ ( size_size_list_int @ Ys2 ) @ ( size_size_list_int @ Xs3 ) )
% 0.29/0.51               => ( P @ Ys2 ) )
% 0.29/0.51           => ( P @ Xs3 ) )
% 0.29/0.51       => ( P @ Xs2 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % length_induct
% 0.29/0.51  thf(fact_867_option_Odistinct_I1_J,axiom,
% 0.29/0.51      ! [X23: product_prod_nat_nat] :
% 0.29/0.51        ( none_P5556105721700978146at_nat
% 0.29/0.51       != ( some_P7363390416028606310at_nat @ X23 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % option.distinct(1)
% 0.29/0.51  thf(fact_868_option_Odistinct_I1_J,axiom,
% 0.29/0.51      ! [X23: nat] :
% 0.29/0.51        ( none_nat
% 0.29/0.51       != ( some_nat @ X23 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % option.distinct(1)
% 0.29/0.51  thf(fact_869_option_Odistinct_I1_J,axiom,
% 0.29/0.51      ! [X23: num] :
% 0.29/0.51        ( none_num
% 0.29/0.51       != ( some_num @ X23 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % option.distinct(1)
% 0.29/0.51  thf(fact_870_option_OdiscI,axiom,
% 0.29/0.51      ! [Option: option4927543243414619207at_nat,X23: product_prod_nat_nat] :
% 0.29/0.51        ( ( Option
% 0.29/0.51          = ( some_P7363390416028606310at_nat @ X23 ) )
% 0.29/0.51       => ( Option != none_P5556105721700978146at_nat ) ) ).
% 0.29/0.51  
% 0.29/0.51  % option.discI
% 0.29/0.51  thf(fact_871_option_OdiscI,axiom,
% 0.29/0.51      ! [Option: option_nat,X23: nat] :
% 0.29/0.51        ( ( Option
% 0.29/0.51          = ( some_nat @ X23 ) )
% 0.29/0.51       => ( Option != none_nat ) ) ).
% 0.29/0.51  
% 0.29/0.51  % option.discI
% 0.29/0.51  thf(fact_872_option_OdiscI,axiom,
% 0.29/0.51      ! [Option: option_num,X23: num] :
% 0.29/0.51        ( ( Option
% 0.29/0.51          = ( some_num @ X23 ) )
% 0.29/0.51       => ( Option != none_num ) ) ).
% 0.29/0.51  
% 0.29/0.51  % option.discI
% 0.29/0.51  thf(fact_873_option_Oexhaust,axiom,
% 0.29/0.51      ! [Y2: option4927543243414619207at_nat] :
% 0.29/0.51        ( ( Y2 != none_P5556105721700978146at_nat )
% 0.29/0.51       => ~ ! [X22: product_prod_nat_nat] :
% 0.29/0.51              ( Y2
% 0.29/0.51             != ( some_P7363390416028606310at_nat @ X22 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % option.exhaust
% 0.29/0.51  thf(fact_874_option_Oexhaust,axiom,
% 0.29/0.51      ! [Y2: option_nat] :
% 0.29/0.51        ( ( Y2 != none_nat )
% 0.29/0.51       => ~ ! [X22: nat] :
% 0.29/0.51              ( Y2
% 0.29/0.51             != ( some_nat @ X22 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % option.exhaust
% 0.29/0.51  thf(fact_875_option_Oexhaust,axiom,
% 0.29/0.51      ! [Y2: option_num] :
% 0.29/0.51        ( ( Y2 != none_num )
% 0.29/0.51       => ~ ! [X22: num] :
% 0.29/0.51              ( Y2
% 0.29/0.51             != ( some_num @ X22 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % option.exhaust
% 0.29/0.51  thf(fact_876_split__option__ex,axiom,
% 0.29/0.51      ( ( ^ [P2: option4927543243414619207at_nat > $o] :
% 0.29/0.51          ? [X7: option4927543243414619207at_nat] : ( P2 @ X7 ) )
% 0.29/0.51      = ( ^ [P3: option4927543243414619207at_nat > $o] :
% 0.29/0.51            ( ( P3 @ none_P5556105721700978146at_nat )
% 0.29/0.51            | ? [X2: product_prod_nat_nat] : ( P3 @ ( some_P7363390416028606310at_nat @ X2 ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % split_option_ex
% 0.29/0.51  thf(fact_877_split__option__ex,axiom,
% 0.29/0.51      ( ( ^ [P2: option_nat > $o] :
% 0.29/0.51          ? [X7: option_nat] : ( P2 @ X7 ) )
% 0.29/0.51      = ( ^ [P3: option_nat > $o] :
% 0.29/0.51            ( ( P3 @ none_nat )
% 0.29/0.51            | ? [X2: nat] : ( P3 @ ( some_nat @ X2 ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % split_option_ex
% 0.29/0.51  thf(fact_878_split__option__ex,axiom,
% 0.29/0.51      ( ( ^ [P2: option_num > $o] :
% 0.29/0.51          ? [X7: option_num] : ( P2 @ X7 ) )
% 0.29/0.51      = ( ^ [P3: option_num > $o] :
% 0.29/0.51            ( ( P3 @ none_num )
% 0.29/0.51            | ? [X2: num] : ( P3 @ ( some_num @ X2 ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % split_option_ex
% 0.29/0.51  thf(fact_879_split__option__all,axiom,
% 0.29/0.51      ( ( ^ [P2: option4927543243414619207at_nat > $o] :
% 0.29/0.51          ! [X7: option4927543243414619207at_nat] : ( P2 @ X7 ) )
% 0.29/0.51      = ( ^ [P3: option4927543243414619207at_nat > $o] :
% 0.29/0.51            ( ( P3 @ none_P5556105721700978146at_nat )
% 0.29/0.51            & ! [X2: product_prod_nat_nat] : ( P3 @ ( some_P7363390416028606310at_nat @ X2 ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % split_option_all
% 0.29/0.51  thf(fact_880_split__option__all,axiom,
% 0.29/0.51      ( ( ^ [P2: option_nat > $o] :
% 0.29/0.51          ! [X7: option_nat] : ( P2 @ X7 ) )
% 0.29/0.51      = ( ^ [P3: option_nat > $o] :
% 0.29/0.51            ( ( P3 @ none_nat )
% 0.29/0.51            & ! [X2: nat] : ( P3 @ ( some_nat @ X2 ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % split_option_all
% 0.29/0.51  thf(fact_881_split__option__all,axiom,
% 0.29/0.51      ( ( ^ [P2: option_num > $o] :
% 0.29/0.51          ! [X7: option_num] : ( P2 @ X7 ) )
% 0.29/0.51      = ( ^ [P3: option_num > $o] :
% 0.29/0.51            ( ( P3 @ none_num )
% 0.29/0.51            & ! [X2: num] : ( P3 @ ( some_num @ X2 ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % split_option_all
% 0.29/0.51  thf(fact_882_combine__options__cases,axiom,
% 0.29/0.51      ! [X: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option4927543243414619207at_nat > $o,Y2: option4927543243414619207at_nat] :
% 0.29/0.51        ( ( ( X = none_P5556105721700978146at_nat )
% 0.29/0.51         => ( P @ X @ Y2 ) )
% 0.29/0.51       => ( ( ( Y2 = none_P5556105721700978146at_nat )
% 0.29/0.51           => ( P @ X @ Y2 ) )
% 0.29/0.51         => ( ! [A4: product_prod_nat_nat,B3: product_prod_nat_nat] :
% 0.29/0.51                ( ( X
% 0.29/0.51                  = ( some_P7363390416028606310at_nat @ A4 ) )
% 0.29/0.51               => ( ( Y2
% 0.29/0.51                    = ( some_P7363390416028606310at_nat @ B3 ) )
% 0.29/0.51                 => ( P @ X @ Y2 ) ) )
% 0.29/0.51           => ( P @ X @ Y2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % combine_options_cases
% 0.29/0.51  thf(fact_883_combine__options__cases,axiom,
% 0.29/0.51      ! [X: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_nat > $o,Y2: option_nat] :
% 0.29/0.51        ( ( ( X = none_P5556105721700978146at_nat )
% 0.29/0.51         => ( P @ X @ Y2 ) )
% 0.29/0.51       => ( ( ( Y2 = none_nat )
% 0.29/0.51           => ( P @ X @ Y2 ) )
% 0.29/0.51         => ( ! [A4: product_prod_nat_nat,B3: nat] :
% 0.29/0.51                ( ( X
% 0.29/0.51                  = ( some_P7363390416028606310at_nat @ A4 ) )
% 0.29/0.51               => ( ( Y2
% 0.29/0.51                    = ( some_nat @ B3 ) )
% 0.29/0.51                 => ( P @ X @ Y2 ) ) )
% 0.29/0.51           => ( P @ X @ Y2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % combine_options_cases
% 0.29/0.51  thf(fact_884_combine__options__cases,axiom,
% 0.29/0.51      ! [X: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_num > $o,Y2: option_num] :
% 0.29/0.51        ( ( ( X = none_P5556105721700978146at_nat )
% 0.29/0.51         => ( P @ X @ Y2 ) )
% 0.29/0.51       => ( ( ( Y2 = none_num )
% 0.29/0.51           => ( P @ X @ Y2 ) )
% 0.29/0.51         => ( ! [A4: product_prod_nat_nat,B3: num] :
% 0.29/0.51                ( ( X
% 0.29/0.51                  = ( some_P7363390416028606310at_nat @ A4 ) )
% 0.29/0.51               => ( ( Y2
% 0.29/0.51                    = ( some_num @ B3 ) )
% 0.29/0.51                 => ( P @ X @ Y2 ) ) )
% 0.29/0.51           => ( P @ X @ Y2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % combine_options_cases
% 0.29/0.51  thf(fact_885_combine__options__cases,axiom,
% 0.29/0.51      ! [X: option_nat,P: option_nat > option4927543243414619207at_nat > $o,Y2: option4927543243414619207at_nat] :
% 0.29/0.51        ( ( ( X = none_nat )
% 0.29/0.51         => ( P @ X @ Y2 ) )
% 0.29/0.51       => ( ( ( Y2 = none_P5556105721700978146at_nat )
% 0.29/0.51           => ( P @ X @ Y2 ) )
% 0.29/0.51         => ( ! [A4: nat,B3: product_prod_nat_nat] :
% 0.29/0.51                ( ( X
% 0.29/0.51                  = ( some_nat @ A4 ) )
% 0.29/0.51               => ( ( Y2
% 0.29/0.51                    = ( some_P7363390416028606310at_nat @ B3 ) )
% 0.29/0.51                 => ( P @ X @ Y2 ) ) )
% 0.29/0.51           => ( P @ X @ Y2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % combine_options_cases
% 0.29/0.51  thf(fact_886_combine__options__cases,axiom,
% 0.29/0.51      ! [X: option_nat,P: option_nat > option_nat > $o,Y2: option_nat] :
% 0.29/0.51        ( ( ( X = none_nat )
% 0.29/0.51         => ( P @ X @ Y2 ) )
% 0.29/0.51       => ( ( ( Y2 = none_nat )
% 0.29/0.51           => ( P @ X @ Y2 ) )
% 0.29/0.51         => ( ! [A4: nat,B3: nat] :
% 0.29/0.51                ( ( X
% 0.29/0.51                  = ( some_nat @ A4 ) )
% 0.29/0.51               => ( ( Y2
% 0.29/0.51                    = ( some_nat @ B3 ) )
% 0.29/0.51                 => ( P @ X @ Y2 ) ) )
% 0.29/0.51           => ( P @ X @ Y2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % combine_options_cases
% 0.29/0.51  thf(fact_887_combine__options__cases,axiom,
% 0.29/0.51      ! [X: option_nat,P: option_nat > option_num > $o,Y2: option_num] :
% 0.29/0.51        ( ( ( X = none_nat )
% 0.29/0.51         => ( P @ X @ Y2 ) )
% 0.29/0.51       => ( ( ( Y2 = none_num )
% 0.29/0.51           => ( P @ X @ Y2 ) )
% 0.29/0.51         => ( ! [A4: nat,B3: num] :
% 0.29/0.51                ( ( X
% 0.29/0.51                  = ( some_nat @ A4 ) )
% 0.29/0.51               => ( ( Y2
% 0.29/0.51                    = ( some_num @ B3 ) )
% 0.29/0.51                 => ( P @ X @ Y2 ) ) )
% 0.29/0.51           => ( P @ X @ Y2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % combine_options_cases
% 0.29/0.51  thf(fact_888_combine__options__cases,axiom,
% 0.29/0.51      ! [X: option_num,P: option_num > option4927543243414619207at_nat > $o,Y2: option4927543243414619207at_nat] :
% 0.29/0.51        ( ( ( X = none_num )
% 0.29/0.51         => ( P @ X @ Y2 ) )
% 0.29/0.51       => ( ( ( Y2 = none_P5556105721700978146at_nat )
% 0.29/0.51           => ( P @ X @ Y2 ) )
% 0.29/0.51         => ( ! [A4: num,B3: product_prod_nat_nat] :
% 0.29/0.51                ( ( X
% 0.29/0.51                  = ( some_num @ A4 ) )
% 0.29/0.51               => ( ( Y2
% 0.29/0.51                    = ( some_P7363390416028606310at_nat @ B3 ) )
% 0.29/0.51                 => ( P @ X @ Y2 ) ) )
% 0.29/0.51           => ( P @ X @ Y2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % combine_options_cases
% 0.29/0.51  thf(fact_889_combine__options__cases,axiom,
% 0.29/0.51      ! [X: option_num,P: option_num > option_nat > $o,Y2: option_nat] :
% 0.29/0.51        ( ( ( X = none_num )
% 0.29/0.51         => ( P @ X @ Y2 ) )
% 0.29/0.51       => ( ( ( Y2 = none_nat )
% 0.29/0.51           => ( P @ X @ Y2 ) )
% 0.29/0.51         => ( ! [A4: num,B3: nat] :
% 0.29/0.51                ( ( X
% 0.29/0.51                  = ( some_num @ A4 ) )
% 0.29/0.51               => ( ( Y2
% 0.29/0.51                    = ( some_nat @ B3 ) )
% 0.29/0.51                 => ( P @ X @ Y2 ) ) )
% 0.29/0.51           => ( P @ X @ Y2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % combine_options_cases
% 0.29/0.51  thf(fact_890_combine__options__cases,axiom,
% 0.29/0.51      ! [X: option_num,P: option_num > option_num > $o,Y2: option_num] :
% 0.29/0.51        ( ( ( X = none_num )
% 0.29/0.51         => ( P @ X @ Y2 ) )
% 0.29/0.51       => ( ( ( Y2 = none_num )
% 0.29/0.51           => ( P @ X @ Y2 ) )
% 0.29/0.51         => ( ! [A4: num,B3: num] :
% 0.29/0.51                ( ( X
% 0.29/0.51                  = ( some_num @ A4 ) )
% 0.29/0.51               => ( ( Y2
% 0.29/0.51                    = ( some_num @ B3 ) )
% 0.29/0.51                 => ( P @ X @ Y2 ) ) )
% 0.29/0.51           => ( P @ X @ Y2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % combine_options_cases
% 0.29/0.51  thf(fact_891_option_Osel,axiom,
% 0.29/0.51      ! [X23: product_prod_nat_nat] :
% 0.29/0.51        ( ( the_Pr8591224930841456533at_nat @ ( some_P7363390416028606310at_nat @ X23 ) )
% 0.29/0.51        = X23 ) ).
% 0.29/0.51  
% 0.29/0.51  % option.sel
% 0.29/0.51  thf(fact_892_option_Osel,axiom,
% 0.29/0.51      ! [X23: nat] :
% 0.29/0.51        ( ( the_nat @ ( some_nat @ X23 ) )
% 0.29/0.51        = X23 ) ).
% 0.29/0.51  
% 0.29/0.51  % option.sel
% 0.29/0.51  thf(fact_893_option_Osel,axiom,
% 0.29/0.51      ! [X23: num] :
% 0.29/0.51        ( ( the_num @ ( some_num @ X23 ) )
% 0.29/0.51        = X23 ) ).
% 0.29/0.51  
% 0.29/0.51  % option.sel
% 0.29/0.51  thf(fact_894_option_Oexpand,axiom,
% 0.29/0.51      ! [Option: option4927543243414619207at_nat,Option2: option4927543243414619207at_nat] :
% 0.29/0.51        ( ( ( Option = none_P5556105721700978146at_nat )
% 0.29/0.51          = ( Option2 = none_P5556105721700978146at_nat ) )
% 0.29/0.51       => ( ( ( Option != none_P5556105721700978146at_nat )
% 0.29/0.51           => ( ( Option2 != none_P5556105721700978146at_nat )
% 0.29/0.51             => ( ( the_Pr8591224930841456533at_nat @ Option )
% 0.29/0.51                = ( the_Pr8591224930841456533at_nat @ Option2 ) ) ) )
% 0.29/0.51         => ( Option = Option2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % option.expand
% 0.29/0.51  thf(fact_895_option_Oexpand,axiom,
% 0.29/0.51      ! [Option: option_nat,Option2: option_nat] :
% 0.29/0.51        ( ( ( Option = none_nat )
% 0.29/0.51          = ( Option2 = none_nat ) )
% 0.29/0.51       => ( ( ( Option != none_nat )
% 0.29/0.51           => ( ( Option2 != none_nat )
% 0.29/0.51             => ( ( the_nat @ Option )
% 0.29/0.51                = ( the_nat @ Option2 ) ) ) )
% 0.29/0.51         => ( Option = Option2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % option.expand
% 0.29/0.51  thf(fact_896_option_Oexpand,axiom,
% 0.29/0.51      ! [Option: option_num,Option2: option_num] :
% 0.29/0.51        ( ( ( Option = none_num )
% 0.29/0.51          = ( Option2 = none_num ) )
% 0.29/0.51       => ( ( ( Option != none_num )
% 0.29/0.51           => ( ( Option2 != none_num )
% 0.29/0.51             => ( ( the_num @ Option )
% 0.29/0.51                = ( the_num @ Option2 ) ) ) )
% 0.29/0.51         => ( Option = Option2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % option.expand
% 0.29/0.51  thf(fact_897_set__update__subsetI,axiom,
% 0.29/0.51      ! [Xs2: list_P6011104703257516679at_nat,A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,I2: nat] :
% 0.29/0.51        ( ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ Xs2 ) @ A2 )
% 0.29/0.51       => ( ( member8440522571783428010at_nat @ X @ A2 )
% 0.29/0.51         => ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ ( list_u6180841689913720943at_nat @ Xs2 @ I2 @ X ) ) @ A2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % set_update_subsetI
% 0.29/0.51  thf(fact_898_set__update__subsetI,axiom,
% 0.29/0.51      ! [Xs2: list_complex,A2: set_complex,X: complex,I2: nat] :
% 0.29/0.51        ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ A2 )
% 0.29/0.51       => ( ( member_complex @ X @ A2 )
% 0.29/0.51         => ( ord_le211207098394363844omplex @ ( set_complex2 @ ( list_update_complex @ Xs2 @ I2 @ X ) ) @ A2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % set_update_subsetI
% 0.29/0.51  thf(fact_899_set__update__subsetI,axiom,
% 0.29/0.51      ! [Xs2: list_int,A2: set_int,X: int,I2: nat] :
% 0.29/0.51        ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ A2 )
% 0.29/0.51       => ( ( member_int @ X @ A2 )
% 0.29/0.51         => ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs2 @ I2 @ X ) ) @ A2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % set_update_subsetI
% 0.29/0.51  thf(fact_900_set__update__subsetI,axiom,
% 0.29/0.51      ! [Xs2: list_VEBT_VEBT,A2: set_VEBT_VEBT,X: vEBT_VEBT,I2: nat] :
% 0.29/0.51        ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ A2 )
% 0.29/0.51       => ( ( member_VEBT_VEBT @ X @ A2 )
% 0.29/0.51         => ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) ) @ A2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % set_update_subsetI
% 0.29/0.51  thf(fact_901_set__update__subsetI,axiom,
% 0.29/0.51      ! [Xs2: list_real,A2: set_real,X: real,I2: nat] :
% 0.29/0.51        ( ( ord_less_eq_set_real @ ( set_real2 @ Xs2 ) @ A2 )
% 0.29/0.51       => ( ( member_real @ X @ A2 )
% 0.29/0.51         => ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs2 @ I2 @ X ) ) @ A2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % set_update_subsetI
% 0.29/0.51  thf(fact_902_set__update__subsetI,axiom,
% 0.29/0.51      ! [Xs2: list_nat,A2: set_nat,X: nat,I2: nat] :
% 0.29/0.51        ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ A2 )
% 0.29/0.51       => ( ( member_nat @ X @ A2 )
% 0.29/0.51         => ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs2 @ I2 @ X ) ) @ A2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % set_update_subsetI
% 0.29/0.51  thf(fact_903_less__1__mult,axiom,
% 0.29/0.51      ! [M: real,N: real] :
% 0.29/0.51        ( ( ord_less_real @ one_one_real @ M )
% 0.29/0.51       => ( ( ord_less_real @ one_one_real @ N )
% 0.29/0.51         => ( ord_less_real @ one_one_real @ ( times_times_real @ M @ N ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % less_1_mult
% 0.29/0.51  thf(fact_904_less__1__mult,axiom,
% 0.29/0.51      ! [M: rat,N: rat] :
% 0.29/0.51        ( ( ord_less_rat @ one_one_rat @ M )
% 0.29/0.51       => ( ( ord_less_rat @ one_one_rat @ N )
% 0.29/0.51         => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M @ N ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % less_1_mult
% 0.29/0.51  thf(fact_905_less__1__mult,axiom,
% 0.29/0.51      ! [M: nat,N: nat] :
% 0.29/0.51        ( ( ord_less_nat @ one_one_nat @ M )
% 0.29/0.51       => ( ( ord_less_nat @ one_one_nat @ N )
% 0.29/0.51         => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M @ N ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % less_1_mult
% 0.29/0.51  thf(fact_906_less__1__mult,axiom,
% 0.29/0.51      ! [M: int,N: int] :
% 0.29/0.51        ( ( ord_less_int @ one_one_int @ M )
% 0.29/0.51       => ( ( ord_less_int @ one_one_int @ N )
% 0.29/0.51         => ( ord_less_int @ one_one_int @ ( times_times_int @ M @ N ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % less_1_mult
% 0.29/0.51  thf(fact_907_less__add__one,axiom,
% 0.29/0.51      ! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ) ).
% 0.29/0.51  
% 0.29/0.51  % less_add_one
% 0.29/0.51  thf(fact_908_less__add__one,axiom,
% 0.29/0.51      ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 0.29/0.51  
% 0.29/0.51  % less_add_one
% 0.29/0.51  thf(fact_909_less__add__one,axiom,
% 0.29/0.51      ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 0.29/0.51  
% 0.29/0.51  % less_add_one
% 0.29/0.51  thf(fact_910_less__add__one,axiom,
% 0.29/0.51      ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 0.29/0.51  
% 0.29/0.51  % less_add_one
% 0.29/0.51  thf(fact_911_add__mono1,axiom,
% 0.29/0.51      ! [A: real,B: real] :
% 0.29/0.51        ( ( ord_less_real @ A @ B )
% 0.29/0.51       => ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B @ one_one_real ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % add_mono1
% 0.29/0.51  thf(fact_912_add__mono1,axiom,
% 0.29/0.51      ! [A: rat,B: rat] :
% 0.29/0.51        ( ( ord_less_rat @ A @ B )
% 0.29/0.51       => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % add_mono1
% 0.29/0.51  thf(fact_913_add__mono1,axiom,
% 0.29/0.51      ! [A: nat,B: nat] :
% 0.29/0.51        ( ( ord_less_nat @ A @ B )
% 0.29/0.51       => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % add_mono1
% 0.29/0.51  thf(fact_914_add__mono1,axiom,
% 0.29/0.51      ! [A: int,B: int] :
% 0.29/0.51        ( ( ord_less_int @ A @ B )
% 0.29/0.51       => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % add_mono1
% 0.29/0.51  thf(fact_915_add__le__add__imp__diff__le,axiom,
% 0.29/0.51      ! [I2: real,K: real,N: real,J: real] :
% 0.29/0.51        ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ N )
% 0.29/0.51       => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 0.29/0.51         => ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ N )
% 0.29/0.51           => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 0.29/0.51             => ( ord_less_eq_real @ ( minus_minus_real @ N @ K ) @ J ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % add_le_add_imp_diff_le
% 0.29/0.51  thf(fact_916_add__le__add__imp__diff__le,axiom,
% 0.29/0.51      ! [I2: rat,K: rat,N: rat,J: rat] :
% 0.29/0.51        ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ N )
% 0.29/0.51       => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 0.29/0.51         => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ N )
% 0.29/0.51           => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 0.29/0.51             => ( ord_less_eq_rat @ ( minus_minus_rat @ N @ K ) @ J ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % add_le_add_imp_diff_le
% 0.29/0.51  thf(fact_917_add__le__add__imp__diff__le,axiom,
% 0.29/0.51      ! [I2: nat,K: nat,N: nat,J: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ N )
% 0.29/0.51       => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 0.29/0.51         => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ N )
% 0.29/0.51           => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 0.29/0.51             => ( ord_less_eq_nat @ ( minus_minus_nat @ N @ K ) @ J ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % add_le_add_imp_diff_le
% 0.29/0.51  thf(fact_918_add__le__add__imp__diff__le,axiom,
% 0.29/0.51      ! [I2: int,K: int,N: int,J: int] :
% 0.29/0.51        ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ N )
% 0.29/0.51       => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 0.29/0.51         => ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ N )
% 0.29/0.51           => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 0.29/0.51             => ( ord_less_eq_int @ ( minus_minus_int @ N @ K ) @ J ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % add_le_add_imp_diff_le
% 0.29/0.51  thf(fact_919_add__le__imp__le__diff,axiom,
% 0.29/0.51      ! [I2: real,K: real,N: real] :
% 0.29/0.51        ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ N )
% 0.29/0.51       => ( ord_less_eq_real @ I2 @ ( minus_minus_real @ N @ K ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % add_le_imp_le_diff
% 0.29/0.51  thf(fact_920_add__le__imp__le__diff,axiom,
% 0.29/0.51      ! [I2: rat,K: rat,N: rat] :
% 0.29/0.51        ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ N )
% 0.29/0.51       => ( ord_less_eq_rat @ I2 @ ( minus_minus_rat @ N @ K ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % add_le_imp_le_diff
% 0.29/0.51  thf(fact_921_add__le__imp__le__diff,axiom,
% 0.29/0.51      ! [I2: nat,K: nat,N: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ N )
% 0.29/0.51       => ( ord_less_eq_nat @ I2 @ ( minus_minus_nat @ N @ K ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % add_le_imp_le_diff
% 0.29/0.51  thf(fact_922_add__le__imp__le__diff,axiom,
% 0.29/0.51      ! [I2: int,K: int,N: int] :
% 0.29/0.51        ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ N )
% 0.29/0.51       => ( ord_less_eq_int @ I2 @ ( minus_minus_int @ N @ K ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % add_le_imp_le_diff
% 0.29/0.51  thf(fact_923_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 0.29/0.51      ! [A: real,B: real] :
% 0.29/0.51        ( ~ ( ord_less_real @ A @ B )
% 0.29/0.51       => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 0.29/0.51          = A ) ) ).
% 0.29/0.51  
% 0.29/0.51  % linordered_semidom_class.add_diff_inverse
% 0.29/0.51  thf(fact_924_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 0.29/0.51      ! [A: rat,B: rat] :
% 0.29/0.51        ( ~ ( ord_less_rat @ A @ B )
% 0.29/0.51       => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 0.29/0.51          = A ) ) ).
% 0.29/0.51  
% 0.29/0.51  % linordered_semidom_class.add_diff_inverse
% 0.29/0.51  thf(fact_925_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 0.29/0.51      ! [A: nat,B: nat] :
% 0.29/0.51        ( ~ ( ord_less_nat @ A @ B )
% 0.29/0.51       => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 0.29/0.51          = A ) ) ).
% 0.29/0.51  
% 0.29/0.51  % linordered_semidom_class.add_diff_inverse
% 0.29/0.51  thf(fact_926_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 0.29/0.51      ! [A: int,B: int] :
% 0.29/0.51        ( ~ ( ord_less_int @ A @ B )
% 0.29/0.51       => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 0.29/0.51          = A ) ) ).
% 0.29/0.51  
% 0.29/0.51  % linordered_semidom_class.add_diff_inverse
% 0.29/0.51  thf(fact_927_eq__add__iff1,axiom,
% 0.29/0.51      ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 0.29/0.51        ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 0.29/0.51          = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 0.29/0.51        = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C )
% 0.29/0.51          = D2 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % eq_add_iff1
% 0.29/0.51  thf(fact_928_eq__add__iff1,axiom,
% 0.29/0.51      ! [A: complex,E: complex,C: complex,B: complex,D2: complex] :
% 0.29/0.51        ( ( ( plus_plus_complex @ ( times_times_complex @ A @ E ) @ C )
% 0.29/0.51          = ( plus_plus_complex @ ( times_times_complex @ B @ E ) @ D2 ) )
% 0.29/0.51        = ( ( plus_plus_complex @ ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ E ) @ C )
% 0.29/0.51          = D2 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % eq_add_iff1
% 0.29/0.51  thf(fact_929_eq__add__iff1,axiom,
% 0.29/0.51      ! [A: real,E: real,C: real,B: real,D2: real] :
% 0.29/0.51        ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 0.29/0.51          = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D2 ) )
% 0.29/0.51        = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C )
% 0.29/0.51          = D2 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % eq_add_iff1
% 0.29/0.51  thf(fact_930_eq__add__iff1,axiom,
% 0.29/0.51      ! [A: int,E: int,C: int,B: int,D2: int] :
% 0.29/0.51        ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 0.29/0.51          = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 0.29/0.51        = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C )
% 0.29/0.51          = D2 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % eq_add_iff1
% 0.29/0.51  thf(fact_931_eq__add__iff2,axiom,
% 0.29/0.51      ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 0.29/0.51        ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 0.29/0.51          = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 0.29/0.51        = ( C
% 0.29/0.51          = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % eq_add_iff2
% 0.29/0.51  thf(fact_932_eq__add__iff2,axiom,
% 0.29/0.51      ! [A: complex,E: complex,C: complex,B: complex,D2: complex] :
% 0.29/0.51        ( ( ( plus_plus_complex @ ( times_times_complex @ A @ E ) @ C )
% 0.29/0.51          = ( plus_plus_complex @ ( times_times_complex @ B @ E ) @ D2 ) )
% 0.29/0.51        = ( C
% 0.29/0.51          = ( plus_plus_complex @ ( times_times_complex @ ( minus_minus_complex @ B @ A ) @ E ) @ D2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % eq_add_iff2
% 0.29/0.51  thf(fact_933_eq__add__iff2,axiom,
% 0.29/0.51      ! [A: real,E: real,C: real,B: real,D2: real] :
% 0.29/0.51        ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 0.29/0.51          = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D2 ) )
% 0.29/0.51        = ( C
% 0.29/0.51          = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % eq_add_iff2
% 0.29/0.51  thf(fact_934_eq__add__iff2,axiom,
% 0.29/0.51      ! [A: int,E: int,C: int,B: int,D2: int] :
% 0.29/0.51        ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 0.29/0.51          = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 0.29/0.51        = ( C
% 0.29/0.51          = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % eq_add_iff2
% 0.29/0.51  thf(fact_935_square__diff__square__factored,axiom,
% 0.29/0.51      ! [X: rat,Y2: rat] :
% 0.29/0.51        ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y2 @ Y2 ) )
% 0.29/0.51        = ( times_times_rat @ ( plus_plus_rat @ X @ Y2 ) @ ( minus_minus_rat @ X @ Y2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % square_diff_square_factored
% 0.29/0.51  thf(fact_936_square__diff__square__factored,axiom,
% 0.29/0.51      ! [X: complex,Y2: complex] :
% 0.29/0.51        ( ( minus_minus_complex @ ( times_times_complex @ X @ X ) @ ( times_times_complex @ Y2 @ Y2 ) )
% 0.29/0.51        = ( times_times_complex @ ( plus_plus_complex @ X @ Y2 ) @ ( minus_minus_complex @ X @ Y2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % square_diff_square_factored
% 0.29/0.51  thf(fact_937_square__diff__square__factored,axiom,
% 0.29/0.51      ! [X: real,Y2: real] :
% 0.29/0.51        ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y2 @ Y2 ) )
% 0.29/0.51        = ( times_times_real @ ( plus_plus_real @ X @ Y2 ) @ ( minus_minus_real @ X @ Y2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % square_diff_square_factored
% 0.29/0.51  thf(fact_938_square__diff__square__factored,axiom,
% 0.29/0.51      ! [X: int,Y2: int] :
% 0.29/0.51        ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y2 @ Y2 ) )
% 0.29/0.51        = ( times_times_int @ ( plus_plus_int @ X @ Y2 ) @ ( minus_minus_int @ X @ Y2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % square_diff_square_factored
% 0.29/0.51  thf(fact_939_nth__equalityI,axiom,
% 0.29/0.51      ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 0.29/0.51        ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 0.29/0.51          = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 0.29/0.51       => ( ! [I4: nat] :
% 0.29/0.51              ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.29/0.51             => ( ( nth_VEBT_VEBT @ Xs2 @ I4 )
% 0.29/0.51                = ( nth_VEBT_VEBT @ Ys @ I4 ) ) )
% 0.29/0.51         => ( Xs2 = Ys ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nth_equalityI
% 0.29/0.51  thf(fact_940_nth__equalityI,axiom,
% 0.29/0.51      ! [Xs2: list_o,Ys: list_o] :
% 0.29/0.51        ( ( ( size_size_list_o @ Xs2 )
% 0.29/0.51          = ( size_size_list_o @ Ys ) )
% 0.29/0.51       => ( ! [I4: nat] :
% 0.29/0.51              ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs2 ) )
% 0.29/0.51             => ( ( nth_o @ Xs2 @ I4 )
% 0.29/0.51                = ( nth_o @ Ys @ I4 ) ) )
% 0.29/0.51         => ( Xs2 = Ys ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nth_equalityI
% 0.29/0.51  thf(fact_941_nth__equalityI,axiom,
% 0.29/0.51      ! [Xs2: list_nat,Ys: list_nat] :
% 0.29/0.51        ( ( ( size_size_list_nat @ Xs2 )
% 0.29/0.51          = ( size_size_list_nat @ Ys ) )
% 0.29/0.51       => ( ! [I4: nat] :
% 0.29/0.51              ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs2 ) )
% 0.29/0.51             => ( ( nth_nat @ Xs2 @ I4 )
% 0.29/0.51                = ( nth_nat @ Ys @ I4 ) ) )
% 0.29/0.51         => ( Xs2 = Ys ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nth_equalityI
% 0.29/0.51  thf(fact_942_nth__equalityI,axiom,
% 0.29/0.51      ! [Xs2: list_int,Ys: list_int] :
% 0.29/0.51        ( ( ( size_size_list_int @ Xs2 )
% 0.29/0.51          = ( size_size_list_int @ Ys ) )
% 0.29/0.51       => ( ! [I4: nat] :
% 0.29/0.51              ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs2 ) )
% 0.29/0.51             => ( ( nth_int @ Xs2 @ I4 )
% 0.29/0.51                = ( nth_int @ Ys @ I4 ) ) )
% 0.29/0.51         => ( Xs2 = Ys ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nth_equalityI
% 0.29/0.51  thf(fact_943_Skolem__list__nth,axiom,
% 0.29/0.51      ! [K: nat,P: nat > vEBT_VEBT > $o] :
% 0.29/0.51        ( ( ! [I3: nat] :
% 0.29/0.51              ( ( ord_less_nat @ I3 @ K )
% 0.29/0.51             => ? [X4: vEBT_VEBT] : ( P @ I3 @ X4 ) ) )
% 0.29/0.51        = ( ? [Xs: list_VEBT_VEBT] :
% 0.29/0.51              ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 0.29/0.51                = K )
% 0.29/0.51              & ! [I3: nat] :
% 0.29/0.51                  ( ( ord_less_nat @ I3 @ K )
% 0.29/0.51                 => ( P @ I3 @ ( nth_VEBT_VEBT @ Xs @ I3 ) ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Skolem_list_nth
% 0.29/0.51  thf(fact_944_Skolem__list__nth,axiom,
% 0.29/0.51      ! [K: nat,P: nat > $o > $o] :
% 0.29/0.51        ( ( ! [I3: nat] :
% 0.29/0.51              ( ( ord_less_nat @ I3 @ K )
% 0.29/0.51             => ? [X4: $o] : ( P @ I3 @ X4 ) ) )
% 0.29/0.51        = ( ? [Xs: list_o] :
% 0.29/0.51              ( ( ( size_size_list_o @ Xs )
% 0.29/0.51                = K )
% 0.29/0.51              & ! [I3: nat] :
% 0.29/0.51                  ( ( ord_less_nat @ I3 @ K )
% 0.29/0.51                 => ( P @ I3 @ ( nth_o @ Xs @ I3 ) ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Skolem_list_nth
% 0.29/0.51  thf(fact_945_Skolem__list__nth,axiom,
% 0.29/0.51      ! [K: nat,P: nat > nat > $o] :
% 0.29/0.51        ( ( ! [I3: nat] :
% 0.29/0.51              ( ( ord_less_nat @ I3 @ K )
% 0.29/0.51             => ? [X4: nat] : ( P @ I3 @ X4 ) ) )
% 0.29/0.51        = ( ? [Xs: list_nat] :
% 0.29/0.51              ( ( ( size_size_list_nat @ Xs )
% 0.29/0.51                = K )
% 0.29/0.51              & ! [I3: nat] :
% 0.29/0.51                  ( ( ord_less_nat @ I3 @ K )
% 0.29/0.51                 => ( P @ I3 @ ( nth_nat @ Xs @ I3 ) ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Skolem_list_nth
% 0.29/0.51  thf(fact_946_Skolem__list__nth,axiom,
% 0.29/0.51      ! [K: nat,P: nat > int > $o] :
% 0.29/0.51        ( ( ! [I3: nat] :
% 0.29/0.51              ( ( ord_less_nat @ I3 @ K )
% 0.29/0.51             => ? [X4: int] : ( P @ I3 @ X4 ) ) )
% 0.29/0.51        = ( ? [Xs: list_int] :
% 0.29/0.51              ( ( ( size_size_list_int @ Xs )
% 0.29/0.51                = K )
% 0.29/0.51              & ! [I3: nat] :
% 0.29/0.51                  ( ( ord_less_nat @ I3 @ K )
% 0.29/0.51                 => ( P @ I3 @ ( nth_int @ Xs @ I3 ) ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Skolem_list_nth
% 0.29/0.51  thf(fact_947_list__eq__iff__nth__eq,axiom,
% 0.29/0.51      ( ( ^ [Y5: list_VEBT_VEBT,Z5: list_VEBT_VEBT] : ( Y5 = Z5 ) )
% 0.29/0.51      = ( ^ [Xs: list_VEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 0.29/0.51            ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 0.29/0.51              = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 0.29/0.51            & ! [I3: nat] :
% 0.29/0.51                ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.29/0.51               => ( ( nth_VEBT_VEBT @ Xs @ I3 )
% 0.29/0.51                  = ( nth_VEBT_VEBT @ Ys3 @ I3 ) ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % list_eq_iff_nth_eq
% 0.29/0.51  thf(fact_948_list__eq__iff__nth__eq,axiom,
% 0.29/0.51      ( ( ^ [Y5: list_o,Z5: list_o] : ( Y5 = Z5 ) )
% 0.29/0.51      = ( ^ [Xs: list_o,Ys3: list_o] :
% 0.29/0.51            ( ( ( size_size_list_o @ Xs )
% 0.29/0.51              = ( size_size_list_o @ Ys3 ) )
% 0.29/0.51            & ! [I3: nat] :
% 0.29/0.51                ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs ) )
% 0.29/0.51               => ( ( nth_o @ Xs @ I3 )
% 0.29/0.51                  = ( nth_o @ Ys3 @ I3 ) ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % list_eq_iff_nth_eq
% 0.29/0.51  thf(fact_949_list__eq__iff__nth__eq,axiom,
% 0.29/0.51      ( ( ^ [Y5: list_nat,Z5: list_nat] : ( Y5 = Z5 ) )
% 0.29/0.51      = ( ^ [Xs: list_nat,Ys3: list_nat] :
% 0.29/0.51            ( ( ( size_size_list_nat @ Xs )
% 0.29/0.51              = ( size_size_list_nat @ Ys3 ) )
% 0.29/0.51            & ! [I3: nat] :
% 0.29/0.51                ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 0.29/0.51               => ( ( nth_nat @ Xs @ I3 )
% 0.29/0.51                  = ( nth_nat @ Ys3 @ I3 ) ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % list_eq_iff_nth_eq
% 0.29/0.51  thf(fact_950_list__eq__iff__nth__eq,axiom,
% 0.29/0.51      ( ( ^ [Y5: list_int,Z5: list_int] : ( Y5 = Z5 ) )
% 0.29/0.51      = ( ^ [Xs: list_int,Ys3: list_int] :
% 0.29/0.51            ( ( ( size_size_list_int @ Xs )
% 0.29/0.51              = ( size_size_list_int @ Ys3 ) )
% 0.29/0.51            & ! [I3: nat] :
% 0.29/0.51                ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) )
% 0.29/0.51               => ( ( nth_int @ Xs @ I3 )
% 0.29/0.51                  = ( nth_int @ Ys3 @ I3 ) ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % list_eq_iff_nth_eq
% 0.29/0.51  thf(fact_951_option_Oexhaust__sel,axiom,
% 0.29/0.51      ! [Option: option4927543243414619207at_nat] :
% 0.29/0.51        ( ( Option != none_P5556105721700978146at_nat )
% 0.29/0.51       => ( Option
% 0.29/0.51          = ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % option.exhaust_sel
% 0.29/0.51  thf(fact_952_option_Oexhaust__sel,axiom,
% 0.29/0.51      ! [Option: option_nat] :
% 0.29/0.51        ( ( Option != none_nat )
% 0.29/0.51       => ( Option
% 0.29/0.51          = ( some_nat @ ( the_nat @ Option ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % option.exhaust_sel
% 0.29/0.51  thf(fact_953_option_Oexhaust__sel,axiom,
% 0.29/0.51      ! [Option: option_num] :
% 0.29/0.51        ( ( Option != none_num )
% 0.29/0.51       => ( Option
% 0.29/0.51          = ( some_num @ ( the_num @ Option ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % option.exhaust_sel
% 0.29/0.51  thf(fact_954_ordered__ring__class_Ole__add__iff2,axiom,
% 0.29/0.51      ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 0.29/0.51        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 0.29/0.51        = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % ordered_ring_class.le_add_iff2
% 0.29/0.51  thf(fact_955_ordered__ring__class_Ole__add__iff2,axiom,
% 0.29/0.51      ! [A: real,E: real,C: real,B: real,D2: real] :
% 0.29/0.51        ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D2 ) )
% 0.29/0.51        = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % ordered_ring_class.le_add_iff2
% 0.29/0.51  thf(fact_956_ordered__ring__class_Ole__add__iff2,axiom,
% 0.29/0.51      ! [A: int,E: int,C: int,B: int,D2: int] :
% 0.29/0.51        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 0.29/0.51        = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % ordered_ring_class.le_add_iff2
% 0.29/0.51  thf(fact_957_ordered__ring__class_Ole__add__iff1,axiom,
% 0.29/0.51      ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 0.29/0.51        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 0.29/0.51        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % ordered_ring_class.le_add_iff1
% 0.29/0.51  thf(fact_958_ordered__ring__class_Ole__add__iff1,axiom,
% 0.29/0.51      ! [A: real,E: real,C: real,B: real,D2: real] :
% 0.29/0.51        ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D2 ) )
% 0.29/0.51        = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % ordered_ring_class.le_add_iff1
% 0.29/0.51  thf(fact_959_ordered__ring__class_Ole__add__iff1,axiom,
% 0.29/0.51      ! [A: int,E: int,C: int,B: int,D2: int] :
% 0.29/0.51        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 0.29/0.51        = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % ordered_ring_class.le_add_iff1
% 0.29/0.51  thf(fact_960_less__add__iff2,axiom,
% 0.29/0.51      ! [A: real,E: real,C: real,B: real,D2: real] :
% 0.29/0.51        ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D2 ) )
% 0.29/0.51        = ( ord_less_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % less_add_iff2
% 0.29/0.51  thf(fact_961_less__add__iff2,axiom,
% 0.29/0.51      ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 0.29/0.51        ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 0.29/0.51        = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % less_add_iff2
% 0.29/0.51  thf(fact_962_less__add__iff2,axiom,
% 0.29/0.51      ! [A: int,E: int,C: int,B: int,D2: int] :
% 0.29/0.51        ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 0.29/0.51        = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % less_add_iff2
% 0.29/0.51  thf(fact_963_less__add__iff1,axiom,
% 0.29/0.51      ! [A: real,E: real,C: real,B: real,D2: real] :
% 0.29/0.51        ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D2 ) )
% 0.29/0.51        = ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % less_add_iff1
% 0.29/0.51  thf(fact_964_less__add__iff1,axiom,
% 0.29/0.51      ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 0.29/0.51        ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 0.29/0.51        = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % less_add_iff1
% 0.29/0.51  thf(fact_965_less__add__iff1,axiom,
% 0.29/0.51      ! [A: int,E: int,C: int,B: int,D2: int] :
% 0.29/0.51        ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 0.29/0.51        = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % less_add_iff1
% 0.29/0.51  thf(fact_966_square__diff__one__factored,axiom,
% 0.29/0.51      ! [X: rat] :
% 0.29/0.51        ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ one_one_rat )
% 0.29/0.51        = ( times_times_rat @ ( plus_plus_rat @ X @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % square_diff_one_factored
% 0.29/0.51  thf(fact_967_square__diff__one__factored,axiom,
% 0.29/0.51      ! [X: complex] :
% 0.29/0.51        ( ( minus_minus_complex @ ( times_times_complex @ X @ X ) @ one_one_complex )
% 0.29/0.51        = ( times_times_complex @ ( plus_plus_complex @ X @ one_one_complex ) @ ( minus_minus_complex @ X @ one_one_complex ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % square_diff_one_factored
% 0.29/0.51  thf(fact_968_square__diff__one__factored,axiom,
% 0.29/0.51      ! [X: real] :
% 0.29/0.51        ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ one_one_real )
% 0.29/0.51        = ( times_times_real @ ( plus_plus_real @ X @ one_one_real ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % square_diff_one_factored
% 0.29/0.51  thf(fact_969_square__diff__one__factored,axiom,
% 0.29/0.51      ! [X: int] :
% 0.29/0.51        ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ one_one_int )
% 0.29/0.51        = ( times_times_int @ ( plus_plus_int @ X @ one_one_int ) @ ( minus_minus_int @ X @ one_one_int ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % square_diff_one_factored
% 0.29/0.51  thf(fact_970_all__set__conv__all__nth,axiom,
% 0.29/0.51      ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 0.29/0.51        ( ( ! [X2: vEBT_VEBT] :
% 0.29/0.51              ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 0.29/0.51             => ( P @ X2 ) ) )
% 0.29/0.51        = ( ! [I3: nat] :
% 0.29/0.51              ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.29/0.51             => ( P @ ( nth_VEBT_VEBT @ Xs2 @ I3 ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % all_set_conv_all_nth
% 0.29/0.51  thf(fact_971_all__set__conv__all__nth,axiom,
% 0.29/0.51      ! [Xs2: list_o,P: $o > $o] :
% 0.29/0.51        ( ( ! [X2: $o] :
% 0.29/0.51              ( ( member_o @ X2 @ ( set_o2 @ Xs2 ) )
% 0.29/0.51             => ( P @ X2 ) ) )
% 0.29/0.51        = ( ! [I3: nat] :
% 0.29/0.51              ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs2 ) )
% 0.29/0.51             => ( P @ ( nth_o @ Xs2 @ I3 ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % all_set_conv_all_nth
% 0.29/0.51  thf(fact_972_all__set__conv__all__nth,axiom,
% 0.29/0.51      ! [Xs2: list_nat,P: nat > $o] :
% 0.29/0.51        ( ( ! [X2: nat] :
% 0.29/0.51              ( ( member_nat @ X2 @ ( set_nat2 @ Xs2 ) )
% 0.29/0.51             => ( P @ X2 ) ) )
% 0.29/0.51        = ( ! [I3: nat] :
% 0.29/0.51              ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs2 ) )
% 0.29/0.51             => ( P @ ( nth_nat @ Xs2 @ I3 ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % all_set_conv_all_nth
% 0.29/0.51  thf(fact_973_all__set__conv__all__nth,axiom,
% 0.29/0.51      ! [Xs2: list_int,P: int > $o] :
% 0.29/0.51        ( ( ! [X2: int] :
% 0.29/0.51              ( ( member_int @ X2 @ ( set_int2 @ Xs2 ) )
% 0.29/0.51             => ( P @ X2 ) ) )
% 0.29/0.51        = ( ! [I3: nat] :
% 0.29/0.51              ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs2 ) )
% 0.29/0.51             => ( P @ ( nth_int @ Xs2 @ I3 ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % all_set_conv_all_nth
% 0.29/0.51  thf(fact_974_all__nth__imp__all__set,axiom,
% 0.29/0.51      ! [Xs2: list_P6011104703257516679at_nat,P: product_prod_nat_nat > $o,X: product_prod_nat_nat] :
% 0.29/0.51        ( ! [I4: nat] :
% 0.29/0.51            ( ( ord_less_nat @ I4 @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 0.29/0.51           => ( P @ ( nth_Pr7617993195940197384at_nat @ Xs2 @ I4 ) ) )
% 0.29/0.51       => ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 0.29/0.51         => ( P @ X ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % all_nth_imp_all_set
% 0.29/0.51  thf(fact_975_all__nth__imp__all__set,axiom,
% 0.29/0.51      ! [Xs2: list_complex,P: complex > $o,X: complex] :
% 0.29/0.51        ( ! [I4: nat] :
% 0.29/0.51            ( ( ord_less_nat @ I4 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 0.29/0.51           => ( P @ ( nth_complex @ Xs2 @ I4 ) ) )
% 0.29/0.51       => ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 0.29/0.51         => ( P @ X ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % all_nth_imp_all_set
% 0.29/0.51  thf(fact_976_all__nth__imp__all__set,axiom,
% 0.29/0.51      ! [Xs2: list_real,P: real > $o,X: real] :
% 0.29/0.51        ( ! [I4: nat] :
% 0.29/0.51            ( ( ord_less_nat @ I4 @ ( size_size_list_real @ Xs2 ) )
% 0.29/0.51           => ( P @ ( nth_real @ Xs2 @ I4 ) ) )
% 0.29/0.51       => ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 0.29/0.51         => ( P @ X ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % all_nth_imp_all_set
% 0.29/0.51  thf(fact_977_all__nth__imp__all__set,axiom,
% 0.29/0.51      ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o,X: vEBT_VEBT] :
% 0.29/0.51        ( ! [I4: nat] :
% 0.29/0.51            ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.29/0.51           => ( P @ ( nth_VEBT_VEBT @ Xs2 @ I4 ) ) )
% 0.29/0.51       => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 0.29/0.51         => ( P @ X ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % all_nth_imp_all_set
% 0.29/0.51  thf(fact_978_all__nth__imp__all__set,axiom,
% 0.29/0.51      ! [Xs2: list_o,P: $o > $o,X: $o] :
% 0.29/0.51        ( ! [I4: nat] :
% 0.29/0.51            ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs2 ) )
% 0.29/0.51           => ( P @ ( nth_o @ Xs2 @ I4 ) ) )
% 0.29/0.51       => ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 0.29/0.51         => ( P @ X ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % all_nth_imp_all_set
% 0.29/0.51  thf(fact_979_all__nth__imp__all__set,axiom,
% 0.29/0.51      ! [Xs2: list_nat,P: nat > $o,X: nat] :
% 0.29/0.51        ( ! [I4: nat] :
% 0.29/0.51            ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs2 ) )
% 0.29/0.51           => ( P @ ( nth_nat @ Xs2 @ I4 ) ) )
% 0.29/0.51       => ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 0.29/0.51         => ( P @ X ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % all_nth_imp_all_set
% 0.29/0.51  thf(fact_980_all__nth__imp__all__set,axiom,
% 0.29/0.51      ! [Xs2: list_int,P: int > $o,X: int] :
% 0.29/0.51        ( ! [I4: nat] :
% 0.29/0.51            ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs2 ) )
% 0.29/0.51           => ( P @ ( nth_int @ Xs2 @ I4 ) ) )
% 0.29/0.51       => ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 0.29/0.51         => ( P @ X ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % all_nth_imp_all_set
% 0.29/0.51  thf(fact_981_in__set__conv__nth,axiom,
% 0.29/0.51      ! [X: product_prod_nat_nat,Xs2: list_P6011104703257516679at_nat] :
% 0.29/0.51        ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 0.29/0.51        = ( ? [I3: nat] :
% 0.29/0.51              ( ( ord_less_nat @ I3 @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 0.29/0.51              & ( ( nth_Pr7617993195940197384at_nat @ Xs2 @ I3 )
% 0.29/0.51                = X ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % in_set_conv_nth
% 0.29/0.51  thf(fact_982_in__set__conv__nth,axiom,
% 0.29/0.51      ! [X: complex,Xs2: list_complex] :
% 0.29/0.51        ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 0.29/0.51        = ( ? [I3: nat] :
% 0.29/0.51              ( ( ord_less_nat @ I3 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 0.29/0.51              & ( ( nth_complex @ Xs2 @ I3 )
% 0.29/0.51                = X ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % in_set_conv_nth
% 0.29/0.51  thf(fact_983_in__set__conv__nth,axiom,
% 0.29/0.51      ! [X: real,Xs2: list_real] :
% 0.29/0.51        ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 0.29/0.51        = ( ? [I3: nat] :
% 0.29/0.51              ( ( ord_less_nat @ I3 @ ( size_size_list_real @ Xs2 ) )
% 0.29/0.51              & ( ( nth_real @ Xs2 @ I3 )
% 0.29/0.51                = X ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % in_set_conv_nth
% 0.29/0.51  thf(fact_984_in__set__conv__nth,axiom,
% 0.29/0.51      ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 0.29/0.51        ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 0.29/0.51        = ( ? [I3: nat] :
% 0.29/0.51              ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.29/0.51              & ( ( nth_VEBT_VEBT @ Xs2 @ I3 )
% 0.29/0.51                = X ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % in_set_conv_nth
% 0.29/0.51  thf(fact_985_in__set__conv__nth,axiom,
% 0.29/0.51      ! [X: $o,Xs2: list_o] :
% 0.29/0.51        ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 0.29/0.51        = ( ? [I3: nat] :
% 0.29/0.51              ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs2 ) )
% 0.29/0.51              & ( ( nth_o @ Xs2 @ I3 )
% 0.29/0.51                = X ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % in_set_conv_nth
% 0.29/0.51  thf(fact_986_in__set__conv__nth,axiom,
% 0.29/0.51      ! [X: nat,Xs2: list_nat] :
% 0.29/0.51        ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 0.29/0.51        = ( ? [I3: nat] :
% 0.29/0.51              ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs2 ) )
% 0.29/0.51              & ( ( nth_nat @ Xs2 @ I3 )
% 0.29/0.51                = X ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % in_set_conv_nth
% 0.29/0.51  thf(fact_987_in__set__conv__nth,axiom,
% 0.29/0.51      ! [X: int,Xs2: list_int] :
% 0.29/0.51        ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 0.29/0.51        = ( ? [I3: nat] :
% 0.29/0.51              ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs2 ) )
% 0.29/0.51              & ( ( nth_int @ Xs2 @ I3 )
% 0.29/0.51                = X ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % in_set_conv_nth
% 0.29/0.51  thf(fact_988_list__ball__nth,axiom,
% 0.29/0.51      ! [N: nat,Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 0.29/0.51        ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.29/0.51       => ( ! [X3: vEBT_VEBT] :
% 0.29/0.51              ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 0.29/0.51             => ( P @ X3 ) )
% 0.29/0.51         => ( P @ ( nth_VEBT_VEBT @ Xs2 @ N ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % list_ball_nth
% 0.29/0.51  thf(fact_989_list__ball__nth,axiom,
% 0.29/0.51      ! [N: nat,Xs2: list_o,P: $o > $o] :
% 0.29/0.51        ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 0.29/0.51       => ( ! [X3: $o] :
% 0.29/0.51              ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 0.29/0.51             => ( P @ X3 ) )
% 0.29/0.51         => ( P @ ( nth_o @ Xs2 @ N ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % list_ball_nth
% 0.29/0.51  thf(fact_990_list__ball__nth,axiom,
% 0.29/0.51      ! [N: nat,Xs2: list_nat,P: nat > $o] :
% 0.29/0.51        ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 0.29/0.51       => ( ! [X3: nat] :
% 0.29/0.51              ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 0.29/0.51             => ( P @ X3 ) )
% 0.29/0.51         => ( P @ ( nth_nat @ Xs2 @ N ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % list_ball_nth
% 0.29/0.51  thf(fact_991_list__ball__nth,axiom,
% 0.29/0.51      ! [N: nat,Xs2: list_int,P: int > $o] :
% 0.29/0.51        ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 0.29/0.51       => ( ! [X3: int] :
% 0.29/0.51              ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 0.29/0.51             => ( P @ X3 ) )
% 0.29/0.51         => ( P @ ( nth_int @ Xs2 @ N ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % list_ball_nth
% 0.29/0.51  thf(fact_992_nth__mem,axiom,
% 0.29/0.51      ! [N: nat,Xs2: list_P6011104703257516679at_nat] :
% 0.29/0.51        ( ( ord_less_nat @ N @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 0.29/0.51       => ( member8440522571783428010at_nat @ ( nth_Pr7617993195940197384at_nat @ Xs2 @ N ) @ ( set_Pr5648618587558075414at_nat @ Xs2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nth_mem
% 0.29/0.51  thf(fact_993_nth__mem,axiom,
% 0.29/0.51      ! [N: nat,Xs2: list_complex] :
% 0.29/0.51        ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 0.29/0.51       => ( member_complex @ ( nth_complex @ Xs2 @ N ) @ ( set_complex2 @ Xs2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nth_mem
% 0.29/0.51  thf(fact_994_nth__mem,axiom,
% 0.29/0.51      ! [N: nat,Xs2: list_real] :
% 0.29/0.51        ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 0.29/0.51       => ( member_real @ ( nth_real @ Xs2 @ N ) @ ( set_real2 @ Xs2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nth_mem
% 0.29/0.51  thf(fact_995_nth__mem,axiom,
% 0.29/0.51      ! [N: nat,Xs2: list_VEBT_VEBT] :
% 0.29/0.51        ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.29/0.51       => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ N ) @ ( set_VEBT_VEBT2 @ Xs2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nth_mem
% 0.29/0.51  thf(fact_996_nth__mem,axiom,
% 0.29/0.51      ! [N: nat,Xs2: list_o] :
% 0.29/0.51        ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 0.29/0.51       => ( member_o @ ( nth_o @ Xs2 @ N ) @ ( set_o2 @ Xs2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nth_mem
% 0.29/0.51  thf(fact_997_nth__mem,axiom,
% 0.29/0.51      ! [N: nat,Xs2: list_nat] :
% 0.29/0.51        ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 0.29/0.51       => ( member_nat @ ( nth_nat @ Xs2 @ N ) @ ( set_nat2 @ Xs2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nth_mem
% 0.29/0.51  thf(fact_998_nth__mem,axiom,
% 0.29/0.51      ! [N: nat,Xs2: list_int] :
% 0.29/0.51        ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 0.29/0.51       => ( member_int @ ( nth_int @ Xs2 @ N ) @ ( set_int2 @ Xs2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nth_mem
% 0.29/0.51  thf(fact_999_set__update__memI,axiom,
% 0.29/0.51      ! [N: nat,Xs2: list_P6011104703257516679at_nat,X: product_prod_nat_nat] :
% 0.29/0.51        ( ( ord_less_nat @ N @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 0.29/0.51       => ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ ( list_u6180841689913720943at_nat @ Xs2 @ N @ X ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % set_update_memI
% 0.29/0.51  thf(fact_1000_set__update__memI,axiom,
% 0.29/0.51      ! [N: nat,Xs2: list_complex,X: complex] :
% 0.29/0.51        ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 0.29/0.51       => ( member_complex @ X @ ( set_complex2 @ ( list_update_complex @ Xs2 @ N @ X ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % set_update_memI
% 0.29/0.51  thf(fact_1001_set__update__memI,axiom,
% 0.29/0.51      ! [N: nat,Xs2: list_real,X: real] :
% 0.29/0.51        ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 0.29/0.51       => ( member_real @ X @ ( set_real2 @ ( list_update_real @ Xs2 @ N @ X ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % set_update_memI
% 0.29/0.51  thf(fact_1002_set__update__memI,axiom,
% 0.29/0.51      ! [N: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 0.29/0.51        ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.29/0.51       => ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs2 @ N @ X ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % set_update_memI
% 0.29/0.51  thf(fact_1003_set__update__memI,axiom,
% 0.29/0.51      ! [N: nat,Xs2: list_o,X: $o] :
% 0.29/0.51        ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 0.29/0.51       => ( member_o @ X @ ( set_o2 @ ( list_update_o @ Xs2 @ N @ X ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % set_update_memI
% 0.29/0.51  thf(fact_1004_set__update__memI,axiom,
% 0.29/0.51      ! [N: nat,Xs2: list_nat,X: nat] :
% 0.29/0.51        ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 0.29/0.51       => ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ Xs2 @ N @ X ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % set_update_memI
% 0.29/0.51  thf(fact_1005_set__update__memI,axiom,
% 0.29/0.51      ! [N: nat,Xs2: list_int,X: int] :
% 0.29/0.51        ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 0.29/0.51       => ( member_int @ X @ ( set_int2 @ ( list_update_int @ Xs2 @ N @ X ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % set_update_memI
% 0.29/0.51  thf(fact_1006_nth__list__update,axiom,
% 0.29/0.51      ! [I2: nat,Xs2: list_VEBT_VEBT,J: nat,X: vEBT_VEBT] :
% 0.29/0.51        ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.29/0.51       => ( ( ( I2 = J )
% 0.29/0.51           => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ J )
% 0.29/0.51              = X ) )
% 0.29/0.51          & ( ( I2 != J )
% 0.29/0.51           => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ J )
% 0.29/0.51              = ( nth_VEBT_VEBT @ Xs2 @ J ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nth_list_update
% 0.29/0.51  thf(fact_1007_nth__list__update,axiom,
% 0.29/0.51      ! [I2: nat,Xs2: list_o,X: $o,J: nat] :
% 0.29/0.51        ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 0.29/0.51       => ( ( nth_o @ ( list_update_o @ Xs2 @ I2 @ X ) @ J )
% 0.29/0.51          = ( ( ( I2 = J )
% 0.29/0.51             => X )
% 0.29/0.51            & ( ( I2 != J )
% 0.29/0.51             => ( nth_o @ Xs2 @ J ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nth_list_update
% 0.29/0.51  thf(fact_1008_nth__list__update,axiom,
% 0.29/0.51      ! [I2: nat,Xs2: list_nat,J: nat,X: nat] :
% 0.29/0.51        ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 0.29/0.51       => ( ( ( I2 = J )
% 0.29/0.51           => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) @ J )
% 0.29/0.51              = X ) )
% 0.29/0.51          & ( ( I2 != J )
% 0.29/0.51           => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) @ J )
% 0.29/0.51              = ( nth_nat @ Xs2 @ J ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nth_list_update
% 0.29/0.51  thf(fact_1009_nth__list__update,axiom,
% 0.29/0.51      ! [I2: nat,Xs2: list_int,J: nat,X: int] :
% 0.29/0.51        ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 0.29/0.51       => ( ( ( I2 = J )
% 0.29/0.51           => ( ( nth_int @ ( list_update_int @ Xs2 @ I2 @ X ) @ J )
% 0.29/0.51              = X ) )
% 0.29/0.51          & ( ( I2 != J )
% 0.29/0.51           => ( ( nth_int @ ( list_update_int @ Xs2 @ I2 @ X ) @ J )
% 0.29/0.51              = ( nth_int @ Xs2 @ J ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nth_list_update
% 0.29/0.51  thf(fact_1010_list__update__same__conv,axiom,
% 0.29/0.51      ! [I2: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 0.29/0.51        ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.29/0.51       => ( ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X )
% 0.29/0.51            = Xs2 )
% 0.29/0.51          = ( ( nth_VEBT_VEBT @ Xs2 @ I2 )
% 0.29/0.51            = X ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % list_update_same_conv
% 0.29/0.51  thf(fact_1011_list__update__same__conv,axiom,
% 0.29/0.51      ! [I2: nat,Xs2: list_o,X: $o] :
% 0.29/0.51        ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 0.29/0.51       => ( ( ( list_update_o @ Xs2 @ I2 @ X )
% 0.29/0.51            = Xs2 )
% 0.29/0.51          = ( ( nth_o @ Xs2 @ I2 )
% 0.29/0.51            = X ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % list_update_same_conv
% 0.29/0.51  thf(fact_1012_list__update__same__conv,axiom,
% 0.29/0.51      ! [I2: nat,Xs2: list_nat,X: nat] :
% 0.29/0.51        ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 0.29/0.51       => ( ( ( list_update_nat @ Xs2 @ I2 @ X )
% 0.29/0.51            = Xs2 )
% 0.29/0.51          = ( ( nth_nat @ Xs2 @ I2 )
% 0.29/0.51            = X ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % list_update_same_conv
% 0.29/0.51  thf(fact_1013_list__update__same__conv,axiom,
% 0.29/0.51      ! [I2: nat,Xs2: list_int,X: int] :
% 0.29/0.51        ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 0.29/0.51       => ( ( ( list_update_int @ Xs2 @ I2 @ X )
% 0.29/0.51            = Xs2 )
% 0.29/0.51          = ( ( nth_int @ Xs2 @ I2 )
% 0.29/0.51            = X ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % list_update_same_conv
% 0.29/0.52  thf(fact_1014_real__average__minus__second,axiom,
% 0.29/0.52      ! [B: real,A: real] :
% 0.29/0.52        ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 0.29/0.52        = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % real_average_minus_second
% 0.29/0.52  thf(fact_1015_real__average__minus__first,axiom,
% 0.29/0.52      ! [A: real,B: real] :
% 0.29/0.52        ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 0.29/0.52        = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % real_average_minus_first
% 0.29/0.52  thf(fact_1016_vebt__insert_Osimps_I4_J,axiom,
% 0.29/0.52      ! [V: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.29/0.52        ( ( vEBT_vebt_insert @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) @ X )
% 0.29/0.52        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ X ) ) @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) ) ).
% 0.29/0.52  
% 0.29/0.52  % vebt_insert.simps(4)
% 0.29/0.52  thf(fact_1017_mul__def,axiom,
% 0.29/0.52      ( vEBT_VEBT_mul
% 0.29/0.52      = ( vEBT_V4262088993061758097ft_nat @ times_times_nat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mul_def
% 0.29/0.52  thf(fact_1018_add__def,axiom,
% 0.29/0.52      ( vEBT_VEBT_add
% 0.29/0.52      = ( vEBT_V4262088993061758097ft_nat @ plus_plus_nat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_def
% 0.29/0.52  thf(fact_1019_vebt__maxt_Osimps_I3_J,axiom,
% 0.29/0.52      ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 0.29/0.52        ( ( vEBT_vebt_maxt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 0.29/0.52        = ( some_nat @ Ma ) ) ).
% 0.29/0.52  
% 0.29/0.52  % vebt_maxt.simps(3)
% 0.29/0.52  thf(fact_1020_vebt__mint_Osimps_I3_J,axiom,
% 0.29/0.52      ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 0.29/0.52        ( ( vEBT_vebt_mint @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 0.29/0.52        = ( some_nat @ Mi ) ) ).
% 0.29/0.52  
% 0.29/0.52  % vebt_mint.simps(3)
% 0.29/0.52  thf(fact_1021_max__less__iff__conj,axiom,
% 0.29/0.52      ! [X: extended_enat,Y2: extended_enat,Z: extended_enat] :
% 0.29/0.52        ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ X @ Y2 ) @ Z )
% 0.29/0.52        = ( ( ord_le72135733267957522d_enat @ X @ Z )
% 0.29/0.52          & ( ord_le72135733267957522d_enat @ Y2 @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max_less_iff_conj
% 0.29/0.52  thf(fact_1022_max__less__iff__conj,axiom,
% 0.29/0.52      ! [X: real,Y2: real,Z: real] :
% 0.29/0.52        ( ( ord_less_real @ ( ord_max_real @ X @ Y2 ) @ Z )
% 0.29/0.52        = ( ( ord_less_real @ X @ Z )
% 0.29/0.52          & ( ord_less_real @ Y2 @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max_less_iff_conj
% 0.29/0.52  thf(fact_1023_max__less__iff__conj,axiom,
% 0.29/0.52      ! [X: rat,Y2: rat,Z: rat] :
% 0.29/0.52        ( ( ord_less_rat @ ( ord_max_rat @ X @ Y2 ) @ Z )
% 0.29/0.52        = ( ( ord_less_rat @ X @ Z )
% 0.29/0.52          & ( ord_less_rat @ Y2 @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max_less_iff_conj
% 0.29/0.52  thf(fact_1024_max__less__iff__conj,axiom,
% 0.29/0.52      ! [X: num,Y2: num,Z: num] :
% 0.29/0.52        ( ( ord_less_num @ ( ord_max_num @ X @ Y2 ) @ Z )
% 0.29/0.52        = ( ( ord_less_num @ X @ Z )
% 0.29/0.52          & ( ord_less_num @ Y2 @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max_less_iff_conj
% 0.29/0.52  thf(fact_1025_max__less__iff__conj,axiom,
% 0.29/0.52      ! [X: nat,Y2: nat,Z: nat] :
% 0.29/0.52        ( ( ord_less_nat @ ( ord_max_nat @ X @ Y2 ) @ Z )
% 0.29/0.52        = ( ( ord_less_nat @ X @ Z )
% 0.29/0.52          & ( ord_less_nat @ Y2 @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max_less_iff_conj
% 0.29/0.52  thf(fact_1026_max__less__iff__conj,axiom,
% 0.29/0.52      ! [X: int,Y2: int,Z: int] :
% 0.29/0.52        ( ( ord_less_int @ ( ord_max_int @ X @ Y2 ) @ Z )
% 0.29/0.52        = ( ( ord_less_int @ X @ Z )
% 0.29/0.52          & ( ord_less_int @ Y2 @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max_less_iff_conj
% 0.29/0.52  thf(fact_1027_max_Oabsorb4,axiom,
% 0.29/0.52      ! [A: extended_enat,B: extended_enat] :
% 0.29/0.52        ( ( ord_le72135733267957522d_enat @ A @ B )
% 0.29/0.52       => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 0.29/0.52          = B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.absorb4
% 0.29/0.52  thf(fact_1028_max_Oabsorb4,axiom,
% 0.29/0.52      ! [A: real,B: real] :
% 0.29/0.52        ( ( ord_less_real @ A @ B )
% 0.29/0.52       => ( ( ord_max_real @ A @ B )
% 0.29/0.52          = B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.absorb4
% 0.29/0.52  thf(fact_1029_max_Oabsorb4,axiom,
% 0.29/0.52      ! [A: rat,B: rat] :
% 0.29/0.52        ( ( ord_less_rat @ A @ B )
% 0.29/0.52       => ( ( ord_max_rat @ A @ B )
% 0.29/0.52          = B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.absorb4
% 0.29/0.52  thf(fact_1030_max_Oabsorb4,axiom,
% 0.29/0.52      ! [A: num,B: num] :
% 0.29/0.52        ( ( ord_less_num @ A @ B )
% 0.29/0.52       => ( ( ord_max_num @ A @ B )
% 0.29/0.52          = B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.absorb4
% 0.29/0.52  thf(fact_1031_max_Oabsorb4,axiom,
% 0.29/0.52      ! [A: nat,B: nat] :
% 0.29/0.52        ( ( ord_less_nat @ A @ B )
% 0.29/0.52       => ( ( ord_max_nat @ A @ B )
% 0.29/0.52          = B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.absorb4
% 0.29/0.52  thf(fact_1032_max_Oabsorb4,axiom,
% 0.29/0.52      ! [A: int,B: int] :
% 0.29/0.52        ( ( ord_less_int @ A @ B )
% 0.29/0.52       => ( ( ord_max_int @ A @ B )
% 0.29/0.52          = B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.absorb4
% 0.29/0.52  thf(fact_1033_max_Oabsorb3,axiom,
% 0.29/0.52      ! [B: extended_enat,A: extended_enat] :
% 0.29/0.52        ( ( ord_le72135733267957522d_enat @ B @ A )
% 0.29/0.52       => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 0.29/0.52          = A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.absorb3
% 0.29/0.52  thf(fact_1034_max_Oabsorb3,axiom,
% 0.29/0.52      ! [B: real,A: real] :
% 0.29/0.52        ( ( ord_less_real @ B @ A )
% 0.29/0.52       => ( ( ord_max_real @ A @ B )
% 0.29/0.52          = A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.absorb3
% 0.29/0.52  thf(fact_1035_max_Oabsorb3,axiom,
% 0.29/0.52      ! [B: rat,A: rat] :
% 0.29/0.52        ( ( ord_less_rat @ B @ A )
% 0.29/0.52       => ( ( ord_max_rat @ A @ B )
% 0.29/0.52          = A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.absorb3
% 0.29/0.52  thf(fact_1036_max_Oabsorb3,axiom,
% 0.29/0.52      ! [B: num,A: num] :
% 0.29/0.52        ( ( ord_less_num @ B @ A )
% 0.29/0.52       => ( ( ord_max_num @ A @ B )
% 0.29/0.52          = A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.absorb3
% 0.29/0.52  thf(fact_1037_max_Oabsorb3,axiom,
% 0.29/0.52      ! [B: nat,A: nat] :
% 0.29/0.52        ( ( ord_less_nat @ B @ A )
% 0.29/0.52       => ( ( ord_max_nat @ A @ B )
% 0.29/0.52          = A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.absorb3
% 0.29/0.52  thf(fact_1038_max_Oabsorb3,axiom,
% 0.29/0.52      ! [B: int,A: int] :
% 0.29/0.52        ( ( ord_less_int @ B @ A )
% 0.29/0.52       => ( ( ord_max_int @ A @ B )
% 0.29/0.52          = A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.absorb3
% 0.29/0.52  thf(fact_1039_max_Obounded__iff,axiom,
% 0.29/0.52      ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 0.29/0.52        ( ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 0.29/0.52        = ( ( ord_le2932123472753598470d_enat @ B @ A )
% 0.29/0.52          & ( ord_le2932123472753598470d_enat @ C @ A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.bounded_iff
% 0.29/0.52  thf(fact_1040_max_Obounded__iff,axiom,
% 0.29/0.52      ! [B: num,C: num,A: num] :
% 0.29/0.52        ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 0.29/0.52        = ( ( ord_less_eq_num @ B @ A )
% 0.29/0.52          & ( ord_less_eq_num @ C @ A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.bounded_iff
% 0.29/0.52  thf(fact_1041_max_Obounded__iff,axiom,
% 0.29/0.52      ! [B: nat,C: nat,A: nat] :
% 0.29/0.52        ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 0.29/0.52        = ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.52          & ( ord_less_eq_nat @ C @ A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.bounded_iff
% 0.29/0.52  thf(fact_1042_max_Obounded__iff,axiom,
% 0.29/0.52      ! [B: int,C: int,A: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 0.29/0.52        = ( ( ord_less_eq_int @ B @ A )
% 0.29/0.52          & ( ord_less_eq_int @ C @ A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.bounded_iff
% 0.29/0.52  thf(fact_1043_add__shift,axiom,
% 0.29/0.52      ! [X: nat,Y2: nat,Z: nat] :
% 0.29/0.52        ( ( ( plus_plus_nat @ X @ Y2 )
% 0.29/0.52          = Z )
% 0.29/0.52        = ( ( vEBT_VEBT_add @ ( some_nat @ X ) @ ( some_nat @ Y2 ) )
% 0.29/0.52          = ( some_nat @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_shift
% 0.29/0.52  thf(fact_1044_mul__shift,axiom,
% 0.29/0.52      ! [X: nat,Y2: nat,Z: nat] :
% 0.29/0.52        ( ( ( times_times_nat @ X @ Y2 )
% 0.29/0.52          = Z )
% 0.29/0.52        = ( ( vEBT_VEBT_mul @ ( some_nat @ X ) @ ( some_nat @ Y2 ) )
% 0.29/0.52          = ( some_nat @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mul_shift
% 0.29/0.52  thf(fact_1045_max_Oabsorb1,axiom,
% 0.29/0.52      ! [B: extended_enat,A: extended_enat] :
% 0.29/0.52        ( ( ord_le2932123472753598470d_enat @ B @ A )
% 0.29/0.52       => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 0.29/0.52          = A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.absorb1
% 0.29/0.52  thf(fact_1046_max_Oabsorb1,axiom,
% 0.29/0.52      ! [B: num,A: num] :
% 0.29/0.52        ( ( ord_less_eq_num @ B @ A )
% 0.29/0.52       => ( ( ord_max_num @ A @ B )
% 0.29/0.52          = A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.absorb1
% 0.29/0.52  thf(fact_1047_max_Oabsorb1,axiom,
% 0.29/0.52      ! [B: nat,A: nat] :
% 0.29/0.52        ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.52       => ( ( ord_max_nat @ A @ B )
% 0.29/0.52          = A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.absorb1
% 0.29/0.52  thf(fact_1048_max_Oabsorb1,axiom,
% 0.29/0.52      ! [B: int,A: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ B @ A )
% 0.29/0.52       => ( ( ord_max_int @ A @ B )
% 0.29/0.52          = A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.absorb1
% 0.29/0.52  thf(fact_1049_max_Oabsorb2,axiom,
% 0.29/0.52      ! [A: extended_enat,B: extended_enat] :
% 0.29/0.52        ( ( ord_le2932123472753598470d_enat @ A @ B )
% 0.29/0.52       => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 0.29/0.52          = B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.absorb2
% 0.29/0.52  thf(fact_1050_max_Oabsorb2,axiom,
% 0.29/0.52      ! [A: num,B: num] :
% 0.29/0.52        ( ( ord_less_eq_num @ A @ B )
% 0.29/0.52       => ( ( ord_max_num @ A @ B )
% 0.29/0.52          = B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.absorb2
% 0.29/0.52  thf(fact_1051_max_Oabsorb2,axiom,
% 0.29/0.52      ! [A: nat,B: nat] :
% 0.29/0.52        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.52       => ( ( ord_max_nat @ A @ B )
% 0.29/0.52          = B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.absorb2
% 0.29/0.52  thf(fact_1052_max_Oabsorb2,axiom,
% 0.29/0.52      ! [A: int,B: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.52       => ( ( ord_max_int @ A @ B )
% 0.29/0.52          = B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.absorb2
% 0.29/0.52  thf(fact_1053_max_Omono,axiom,
% 0.29/0.52      ! [C: extended_enat,A: extended_enat,D2: extended_enat,B: extended_enat] :
% 0.29/0.52        ( ( ord_le2932123472753598470d_enat @ C @ A )
% 0.29/0.52       => ( ( ord_le2932123472753598470d_enat @ D2 @ B )
% 0.29/0.52         => ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ C @ D2 ) @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.mono
% 0.29/0.52  thf(fact_1054_max_Omono,axiom,
% 0.29/0.52      ! [C: num,A: num,D2: num,B: num] :
% 0.29/0.52        ( ( ord_less_eq_num @ C @ A )
% 0.29/0.52       => ( ( ord_less_eq_num @ D2 @ B )
% 0.29/0.52         => ( ord_less_eq_num @ ( ord_max_num @ C @ D2 ) @ ( ord_max_num @ A @ B ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.mono
% 0.29/0.52  thf(fact_1055_max_Omono,axiom,
% 0.29/0.52      ! [C: nat,A: nat,D2: nat,B: nat] :
% 0.29/0.52        ( ( ord_less_eq_nat @ C @ A )
% 0.29/0.52       => ( ( ord_less_eq_nat @ D2 @ B )
% 0.29/0.52         => ( ord_less_eq_nat @ ( ord_max_nat @ C @ D2 ) @ ( ord_max_nat @ A @ B ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.mono
% 0.29/0.52  thf(fact_1056_max_Omono,axiom,
% 0.29/0.52      ! [C: int,A: int,D2: int,B: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ C @ A )
% 0.29/0.52       => ( ( ord_less_eq_int @ D2 @ B )
% 0.29/0.52         => ( ord_less_eq_int @ ( ord_max_int @ C @ D2 ) @ ( ord_max_int @ A @ B ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.mono
% 0.29/0.52  thf(fact_1057_max_OorderE,axiom,
% 0.29/0.52      ! [B: extended_enat,A: extended_enat] :
% 0.29/0.52        ( ( ord_le2932123472753598470d_enat @ B @ A )
% 0.29/0.52       => ( A
% 0.29/0.52          = ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.orderE
% 0.29/0.52  thf(fact_1058_max_OorderE,axiom,
% 0.29/0.52      ! [B: num,A: num] :
% 0.29/0.52        ( ( ord_less_eq_num @ B @ A )
% 0.29/0.52       => ( A
% 0.29/0.52          = ( ord_max_num @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.orderE
% 0.29/0.52  thf(fact_1059_max_OorderE,axiom,
% 0.29/0.52      ! [B: nat,A: nat] :
% 0.29/0.52        ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.52       => ( A
% 0.29/0.52          = ( ord_max_nat @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.orderE
% 0.29/0.52  thf(fact_1060_max_OorderE,axiom,
% 0.29/0.52      ! [B: int,A: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ B @ A )
% 0.29/0.52       => ( A
% 0.29/0.52          = ( ord_max_int @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.orderE
% 0.29/0.52  thf(fact_1061_max_OorderI,axiom,
% 0.29/0.52      ! [A: extended_enat,B: extended_enat] :
% 0.29/0.52        ( ( A
% 0.29/0.52          = ( ord_ma741700101516333627d_enat @ A @ B ) )
% 0.29/0.52       => ( ord_le2932123472753598470d_enat @ B @ A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.orderI
% 0.29/0.52  thf(fact_1062_max_OorderI,axiom,
% 0.29/0.52      ! [A: num,B: num] :
% 0.29/0.52        ( ( A
% 0.29/0.52          = ( ord_max_num @ A @ B ) )
% 0.29/0.52       => ( ord_less_eq_num @ B @ A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.orderI
% 0.29/0.52  thf(fact_1063_max_OorderI,axiom,
% 0.29/0.52      ! [A: nat,B: nat] :
% 0.29/0.52        ( ( A
% 0.29/0.52          = ( ord_max_nat @ A @ B ) )
% 0.29/0.52       => ( ord_less_eq_nat @ B @ A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.orderI
% 0.29/0.52  thf(fact_1064_max_OorderI,axiom,
% 0.29/0.52      ! [A: int,B: int] :
% 0.29/0.52        ( ( A
% 0.29/0.52          = ( ord_max_int @ A @ B ) )
% 0.29/0.52       => ( ord_less_eq_int @ B @ A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.orderI
% 0.29/0.52  thf(fact_1065_max_OboundedE,axiom,
% 0.29/0.52      ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 0.29/0.52        ( ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 0.29/0.52       => ~ ( ( ord_le2932123472753598470d_enat @ B @ A )
% 0.29/0.52           => ~ ( ord_le2932123472753598470d_enat @ C @ A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.boundedE
% 0.29/0.52  thf(fact_1066_max_OboundedE,axiom,
% 0.29/0.52      ! [B: num,C: num,A: num] :
% 0.29/0.52        ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 0.29/0.52       => ~ ( ( ord_less_eq_num @ B @ A )
% 0.29/0.52           => ~ ( ord_less_eq_num @ C @ A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.boundedE
% 0.29/0.52  thf(fact_1067_max_OboundedE,axiom,
% 0.29/0.52      ! [B: nat,C: nat,A: nat] :
% 0.29/0.52        ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 0.29/0.52       => ~ ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.52           => ~ ( ord_less_eq_nat @ C @ A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.boundedE
% 0.29/0.52  thf(fact_1068_max_OboundedE,axiom,
% 0.29/0.52      ! [B: int,C: int,A: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 0.29/0.52       => ~ ( ( ord_less_eq_int @ B @ A )
% 0.29/0.52           => ~ ( ord_less_eq_int @ C @ A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.boundedE
% 0.29/0.52  thf(fact_1069_max_OboundedI,axiom,
% 0.29/0.52      ! [B: extended_enat,A: extended_enat,C: extended_enat] :
% 0.29/0.52        ( ( ord_le2932123472753598470d_enat @ B @ A )
% 0.29/0.52       => ( ( ord_le2932123472753598470d_enat @ C @ A )
% 0.29/0.52         => ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.boundedI
% 0.29/0.52  thf(fact_1070_max_OboundedI,axiom,
% 0.29/0.52      ! [B: num,A: num,C: num] :
% 0.29/0.52        ( ( ord_less_eq_num @ B @ A )
% 0.29/0.52       => ( ( ord_less_eq_num @ C @ A )
% 0.29/0.52         => ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.boundedI
% 0.29/0.52  thf(fact_1071_max_OboundedI,axiom,
% 0.29/0.52      ! [B: nat,A: nat,C: nat] :
% 0.29/0.52        ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.52       => ( ( ord_less_eq_nat @ C @ A )
% 0.29/0.52         => ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.boundedI
% 0.29/0.52  thf(fact_1072_max_OboundedI,axiom,
% 0.29/0.52      ! [B: int,A: int,C: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ B @ A )
% 0.29/0.52       => ( ( ord_less_eq_int @ C @ A )
% 0.29/0.52         => ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.boundedI
% 0.29/0.52  thf(fact_1073_max_Oorder__iff,axiom,
% 0.29/0.52      ( ord_le2932123472753598470d_enat
% 0.29/0.52      = ( ^ [B4: extended_enat,A3: extended_enat] :
% 0.29/0.52            ( A3
% 0.29/0.52            = ( ord_ma741700101516333627d_enat @ A3 @ B4 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.order_iff
% 0.29/0.52  thf(fact_1074_max_Oorder__iff,axiom,
% 0.29/0.52      ( ord_less_eq_num
% 0.29/0.52      = ( ^ [B4: num,A3: num] :
% 0.29/0.52            ( A3
% 0.29/0.52            = ( ord_max_num @ A3 @ B4 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.order_iff
% 0.29/0.52  thf(fact_1075_max_Oorder__iff,axiom,
% 0.29/0.52      ( ord_less_eq_nat
% 0.29/0.52      = ( ^ [B4: nat,A3: nat] :
% 0.29/0.52            ( A3
% 0.29/0.52            = ( ord_max_nat @ A3 @ B4 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.order_iff
% 0.29/0.52  thf(fact_1076_max_Oorder__iff,axiom,
% 0.29/0.52      ( ord_less_eq_int
% 0.29/0.52      = ( ^ [B4: int,A3: int] :
% 0.29/0.52            ( A3
% 0.29/0.52            = ( ord_max_int @ A3 @ B4 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.order_iff
% 0.29/0.52  thf(fact_1077_max_Ocobounded1,axiom,
% 0.29/0.52      ! [A: extended_enat,B: extended_enat] : ( ord_le2932123472753598470d_enat @ A @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.cobounded1
% 0.29/0.52  thf(fact_1078_max_Ocobounded1,axiom,
% 0.29/0.52      ! [A: num,B: num] : ( ord_less_eq_num @ A @ ( ord_max_num @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.cobounded1
% 0.29/0.52  thf(fact_1079_max_Ocobounded1,axiom,
% 0.29/0.52      ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( ord_max_nat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.cobounded1
% 0.29/0.52  thf(fact_1080_max_Ocobounded1,axiom,
% 0.29/0.52      ! [A: int,B: int] : ( ord_less_eq_int @ A @ ( ord_max_int @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.cobounded1
% 0.29/0.52  thf(fact_1081_max_Ocobounded2,axiom,
% 0.29/0.52      ! [B: extended_enat,A: extended_enat] : ( ord_le2932123472753598470d_enat @ B @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.cobounded2
% 0.29/0.52  thf(fact_1082_max_Ocobounded2,axiom,
% 0.29/0.52      ! [B: num,A: num] : ( ord_less_eq_num @ B @ ( ord_max_num @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.cobounded2
% 0.29/0.52  thf(fact_1083_max_Ocobounded2,axiom,
% 0.29/0.52      ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( ord_max_nat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.cobounded2
% 0.29/0.52  thf(fact_1084_max_Ocobounded2,axiom,
% 0.29/0.52      ! [B: int,A: int] : ( ord_less_eq_int @ B @ ( ord_max_int @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.cobounded2
% 0.29/0.52  thf(fact_1085_le__max__iff__disj,axiom,
% 0.29/0.52      ! [Z: extended_enat,X: extended_enat,Y2: extended_enat] :
% 0.29/0.52        ( ( ord_le2932123472753598470d_enat @ Z @ ( ord_ma741700101516333627d_enat @ X @ Y2 ) )
% 0.29/0.52        = ( ( ord_le2932123472753598470d_enat @ Z @ X )
% 0.29/0.52          | ( ord_le2932123472753598470d_enat @ Z @ Y2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % le_max_iff_disj
% 0.29/0.52  thf(fact_1086_le__max__iff__disj,axiom,
% 0.29/0.52      ! [Z: num,X: num,Y2: num] :
% 0.29/0.52        ( ( ord_less_eq_num @ Z @ ( ord_max_num @ X @ Y2 ) )
% 0.29/0.52        = ( ( ord_less_eq_num @ Z @ X )
% 0.29/0.52          | ( ord_less_eq_num @ Z @ Y2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % le_max_iff_disj
% 0.29/0.52  thf(fact_1087_le__max__iff__disj,axiom,
% 0.29/0.52      ! [Z: nat,X: nat,Y2: nat] :
% 0.29/0.52        ( ( ord_less_eq_nat @ Z @ ( ord_max_nat @ X @ Y2 ) )
% 0.29/0.52        = ( ( ord_less_eq_nat @ Z @ X )
% 0.29/0.52          | ( ord_less_eq_nat @ Z @ Y2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % le_max_iff_disj
% 0.29/0.52  thf(fact_1088_le__max__iff__disj,axiom,
% 0.29/0.52      ! [Z: int,X: int,Y2: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ Z @ ( ord_max_int @ X @ Y2 ) )
% 0.29/0.52        = ( ( ord_less_eq_int @ Z @ X )
% 0.29/0.52          | ( ord_less_eq_int @ Z @ Y2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % le_max_iff_disj
% 0.29/0.52  thf(fact_1089_max_Oabsorb__iff1,axiom,
% 0.29/0.52      ( ord_le2932123472753598470d_enat
% 0.29/0.52      = ( ^ [B4: extended_enat,A3: extended_enat] :
% 0.29/0.52            ( ( ord_ma741700101516333627d_enat @ A3 @ B4 )
% 0.29/0.52            = A3 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.absorb_iff1
% 0.29/0.52  thf(fact_1090_max_Oabsorb__iff1,axiom,
% 0.29/0.52      ( ord_less_eq_num
% 0.29/0.52      = ( ^ [B4: num,A3: num] :
% 0.29/0.52            ( ( ord_max_num @ A3 @ B4 )
% 0.29/0.52            = A3 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.absorb_iff1
% 0.29/0.52  thf(fact_1091_max_Oabsorb__iff1,axiom,
% 0.29/0.52      ( ord_less_eq_nat
% 0.29/0.52      = ( ^ [B4: nat,A3: nat] :
% 0.29/0.52            ( ( ord_max_nat @ A3 @ B4 )
% 0.29/0.52            = A3 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.absorb_iff1
% 0.29/0.52  thf(fact_1092_max_Oabsorb__iff1,axiom,
% 0.29/0.52      ( ord_less_eq_int
% 0.29/0.52      = ( ^ [B4: int,A3: int] :
% 0.29/0.52            ( ( ord_max_int @ A3 @ B4 )
% 0.29/0.52            = A3 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.absorb_iff1
% 0.29/0.52  thf(fact_1093_max_Oabsorb__iff2,axiom,
% 0.29/0.52      ( ord_le2932123472753598470d_enat
% 0.29/0.52      = ( ^ [A3: extended_enat,B4: extended_enat] :
% 0.29/0.52            ( ( ord_ma741700101516333627d_enat @ A3 @ B4 )
% 0.29/0.52            = B4 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.absorb_iff2
% 0.29/0.52  thf(fact_1094_max_Oabsorb__iff2,axiom,
% 0.29/0.52      ( ord_less_eq_num
% 0.29/0.52      = ( ^ [A3: num,B4: num] :
% 0.29/0.52            ( ( ord_max_num @ A3 @ B4 )
% 0.29/0.52            = B4 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.absorb_iff2
% 0.29/0.52  thf(fact_1095_max_Oabsorb__iff2,axiom,
% 0.29/0.52      ( ord_less_eq_nat
% 0.29/0.52      = ( ^ [A3: nat,B4: nat] :
% 0.29/0.52            ( ( ord_max_nat @ A3 @ B4 )
% 0.29/0.52            = B4 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.absorb_iff2
% 0.29/0.52  thf(fact_1096_max_Oabsorb__iff2,axiom,
% 0.29/0.52      ( ord_less_eq_int
% 0.29/0.52      = ( ^ [A3: int,B4: int] :
% 0.29/0.52            ( ( ord_max_int @ A3 @ B4 )
% 0.29/0.52            = B4 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.absorb_iff2
% 0.29/0.52  thf(fact_1097_max_OcoboundedI1,axiom,
% 0.29/0.52      ! [C: extended_enat,A: extended_enat,B: extended_enat] :
% 0.29/0.52        ( ( ord_le2932123472753598470d_enat @ C @ A )
% 0.29/0.52       => ( ord_le2932123472753598470d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.coboundedI1
% 0.29/0.52  thf(fact_1098_max_OcoboundedI1,axiom,
% 0.29/0.52      ! [C: num,A: num,B: num] :
% 0.29/0.52        ( ( ord_less_eq_num @ C @ A )
% 0.29/0.52       => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.coboundedI1
% 0.29/0.52  thf(fact_1099_max_OcoboundedI1,axiom,
% 0.29/0.52      ! [C: nat,A: nat,B: nat] :
% 0.29/0.52        ( ( ord_less_eq_nat @ C @ A )
% 0.29/0.52       => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.coboundedI1
% 0.29/0.52  thf(fact_1100_max_OcoboundedI1,axiom,
% 0.29/0.52      ! [C: int,A: int,B: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ C @ A )
% 0.29/0.52       => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.coboundedI1
% 0.29/0.52  thf(fact_1101_max_OcoboundedI2,axiom,
% 0.29/0.52      ! [C: extended_enat,B: extended_enat,A: extended_enat] :
% 0.29/0.52        ( ( ord_le2932123472753598470d_enat @ C @ B )
% 0.29/0.52       => ( ord_le2932123472753598470d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.coboundedI2
% 0.29/0.52  thf(fact_1102_max_OcoboundedI2,axiom,
% 0.29/0.52      ! [C: num,B: num,A: num] :
% 0.29/0.52        ( ( ord_less_eq_num @ C @ B )
% 0.29/0.52       => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.coboundedI2
% 0.29/0.52  thf(fact_1103_max_OcoboundedI2,axiom,
% 0.29/0.52      ! [C: nat,B: nat,A: nat] :
% 0.29/0.52        ( ( ord_less_eq_nat @ C @ B )
% 0.29/0.52       => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.coboundedI2
% 0.29/0.52  thf(fact_1104_max_OcoboundedI2,axiom,
% 0.29/0.52      ! [C: int,B: int,A: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ C @ B )
% 0.29/0.52       => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.coboundedI2
% 0.29/0.52  thf(fact_1105_less__max__iff__disj,axiom,
% 0.29/0.52      ! [Z: extended_enat,X: extended_enat,Y2: extended_enat] :
% 0.29/0.52        ( ( ord_le72135733267957522d_enat @ Z @ ( ord_ma741700101516333627d_enat @ X @ Y2 ) )
% 0.29/0.52        = ( ( ord_le72135733267957522d_enat @ Z @ X )
% 0.29/0.52          | ( ord_le72135733267957522d_enat @ Z @ Y2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % less_max_iff_disj
% 0.29/0.52  thf(fact_1106_less__max__iff__disj,axiom,
% 0.29/0.52      ! [Z: real,X: real,Y2: real] :
% 0.29/0.52        ( ( ord_less_real @ Z @ ( ord_max_real @ X @ Y2 ) )
% 0.29/0.52        = ( ( ord_less_real @ Z @ X )
% 0.29/0.52          | ( ord_less_real @ Z @ Y2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % less_max_iff_disj
% 0.29/0.52  thf(fact_1107_less__max__iff__disj,axiom,
% 0.29/0.52      ! [Z: rat,X: rat,Y2: rat] :
% 0.29/0.52        ( ( ord_less_rat @ Z @ ( ord_max_rat @ X @ Y2 ) )
% 0.29/0.52        = ( ( ord_less_rat @ Z @ X )
% 0.29/0.52          | ( ord_less_rat @ Z @ Y2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % less_max_iff_disj
% 0.29/0.52  thf(fact_1108_less__max__iff__disj,axiom,
% 0.29/0.52      ! [Z: num,X: num,Y2: num] :
% 0.29/0.52        ( ( ord_less_num @ Z @ ( ord_max_num @ X @ Y2 ) )
% 0.29/0.52        = ( ( ord_less_num @ Z @ X )
% 0.29/0.52          | ( ord_less_num @ Z @ Y2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % less_max_iff_disj
% 0.29/0.52  thf(fact_1109_less__max__iff__disj,axiom,
% 0.29/0.52      ! [Z: nat,X: nat,Y2: nat] :
% 0.29/0.52        ( ( ord_less_nat @ Z @ ( ord_max_nat @ X @ Y2 ) )
% 0.29/0.52        = ( ( ord_less_nat @ Z @ X )
% 0.29/0.52          | ( ord_less_nat @ Z @ Y2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % less_max_iff_disj
% 0.29/0.52  thf(fact_1110_less__max__iff__disj,axiom,
% 0.29/0.52      ! [Z: int,X: int,Y2: int] :
% 0.29/0.52        ( ( ord_less_int @ Z @ ( ord_max_int @ X @ Y2 ) )
% 0.29/0.52        = ( ( ord_less_int @ Z @ X )
% 0.29/0.52          | ( ord_less_int @ Z @ Y2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % less_max_iff_disj
% 0.29/0.52  thf(fact_1111_max_Ostrict__boundedE,axiom,
% 0.29/0.52      ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 0.29/0.52        ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 0.29/0.52       => ~ ( ( ord_le72135733267957522d_enat @ B @ A )
% 0.29/0.52           => ~ ( ord_le72135733267957522d_enat @ C @ A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.strict_boundedE
% 0.29/0.52  thf(fact_1112_max_Ostrict__boundedE,axiom,
% 0.29/0.52      ! [B: real,C: real,A: real] :
% 0.29/0.52        ( ( ord_less_real @ ( ord_max_real @ B @ C ) @ A )
% 0.29/0.52       => ~ ( ( ord_less_real @ B @ A )
% 0.29/0.52           => ~ ( ord_less_real @ C @ A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.strict_boundedE
% 0.29/0.52  thf(fact_1113_max_Ostrict__boundedE,axiom,
% 0.29/0.52      ! [B: rat,C: rat,A: rat] :
% 0.29/0.52        ( ( ord_less_rat @ ( ord_max_rat @ B @ C ) @ A )
% 0.29/0.52       => ~ ( ( ord_less_rat @ B @ A )
% 0.29/0.52           => ~ ( ord_less_rat @ C @ A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.strict_boundedE
% 0.29/0.52  thf(fact_1114_max_Ostrict__boundedE,axiom,
% 0.29/0.52      ! [B: num,C: num,A: num] :
% 0.29/0.52        ( ( ord_less_num @ ( ord_max_num @ B @ C ) @ A )
% 0.29/0.52       => ~ ( ( ord_less_num @ B @ A )
% 0.29/0.52           => ~ ( ord_less_num @ C @ A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.strict_boundedE
% 0.29/0.52  thf(fact_1115_max_Ostrict__boundedE,axiom,
% 0.29/0.52      ! [B: nat,C: nat,A: nat] :
% 0.29/0.52        ( ( ord_less_nat @ ( ord_max_nat @ B @ C ) @ A )
% 0.29/0.52       => ~ ( ( ord_less_nat @ B @ A )
% 0.29/0.52           => ~ ( ord_less_nat @ C @ A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.strict_boundedE
% 0.29/0.52  thf(fact_1116_max_Ostrict__boundedE,axiom,
% 0.29/0.52      ! [B: int,C: int,A: int] :
% 0.29/0.52        ( ( ord_less_int @ ( ord_max_int @ B @ C ) @ A )
% 0.29/0.52       => ~ ( ( ord_less_int @ B @ A )
% 0.29/0.52           => ~ ( ord_less_int @ C @ A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.strict_boundedE
% 0.29/0.52  thf(fact_1117_max_Ostrict__order__iff,axiom,
% 0.29/0.52      ( ord_le72135733267957522d_enat
% 0.29/0.52      = ( ^ [B4: extended_enat,A3: extended_enat] :
% 0.29/0.52            ( ( A3
% 0.29/0.52              = ( ord_ma741700101516333627d_enat @ A3 @ B4 ) )
% 0.29/0.52            & ( A3 != B4 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.strict_order_iff
% 0.29/0.52  thf(fact_1118_max_Ostrict__order__iff,axiom,
% 0.29/0.52      ( ord_less_real
% 0.29/0.52      = ( ^ [B4: real,A3: real] :
% 0.29/0.52            ( ( A3
% 0.29/0.52              = ( ord_max_real @ A3 @ B4 ) )
% 0.29/0.52            & ( A3 != B4 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.strict_order_iff
% 0.29/0.52  thf(fact_1119_max_Ostrict__order__iff,axiom,
% 0.29/0.52      ( ord_less_rat
% 0.29/0.52      = ( ^ [B4: rat,A3: rat] :
% 0.29/0.52            ( ( A3
% 0.29/0.52              = ( ord_max_rat @ A3 @ B4 ) )
% 0.29/0.52            & ( A3 != B4 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.strict_order_iff
% 0.29/0.52  thf(fact_1120_max_Ostrict__order__iff,axiom,
% 0.29/0.52      ( ord_less_num
% 0.29/0.52      = ( ^ [B4: num,A3: num] :
% 0.29/0.52            ( ( A3
% 0.29/0.52              = ( ord_max_num @ A3 @ B4 ) )
% 0.29/0.52            & ( A3 != B4 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.strict_order_iff
% 0.29/0.52  thf(fact_1121_max_Ostrict__order__iff,axiom,
% 0.29/0.52      ( ord_less_nat
% 0.29/0.52      = ( ^ [B4: nat,A3: nat] :
% 0.29/0.52            ( ( A3
% 0.29/0.52              = ( ord_max_nat @ A3 @ B4 ) )
% 0.29/0.52            & ( A3 != B4 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.strict_order_iff
% 0.29/0.52  thf(fact_1122_max_Ostrict__order__iff,axiom,
% 0.29/0.52      ( ord_less_int
% 0.29/0.52      = ( ^ [B4: int,A3: int] :
% 0.29/0.52            ( ( A3
% 0.29/0.52              = ( ord_max_int @ A3 @ B4 ) )
% 0.29/0.52            & ( A3 != B4 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.strict_order_iff
% 0.29/0.52  thf(fact_1123_max_Ostrict__coboundedI1,axiom,
% 0.29/0.52      ! [C: extended_enat,A: extended_enat,B: extended_enat] :
% 0.29/0.52        ( ( ord_le72135733267957522d_enat @ C @ A )
% 0.29/0.52       => ( ord_le72135733267957522d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.strict_coboundedI1
% 0.29/0.52  thf(fact_1124_max_Ostrict__coboundedI1,axiom,
% 0.29/0.52      ! [C: real,A: real,B: real] :
% 0.29/0.52        ( ( ord_less_real @ C @ A )
% 0.29/0.52       => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.strict_coboundedI1
% 0.29/0.52  thf(fact_1125_max_Ostrict__coboundedI1,axiom,
% 0.29/0.52      ! [C: rat,A: rat,B: rat] :
% 0.29/0.52        ( ( ord_less_rat @ C @ A )
% 0.29/0.52       => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.strict_coboundedI1
% 0.29/0.52  thf(fact_1126_max_Ostrict__coboundedI1,axiom,
% 0.29/0.52      ! [C: num,A: num,B: num] :
% 0.29/0.52        ( ( ord_less_num @ C @ A )
% 0.29/0.52       => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.strict_coboundedI1
% 0.29/0.52  thf(fact_1127_max_Ostrict__coboundedI1,axiom,
% 0.29/0.52      ! [C: nat,A: nat,B: nat] :
% 0.29/0.52        ( ( ord_less_nat @ C @ A )
% 0.29/0.52       => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.strict_coboundedI1
% 0.29/0.52  thf(fact_1128_max_Ostrict__coboundedI1,axiom,
% 0.29/0.52      ! [C: int,A: int,B: int] :
% 0.29/0.52        ( ( ord_less_int @ C @ A )
% 0.29/0.52       => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.strict_coboundedI1
% 0.29/0.52  thf(fact_1129_max_Ostrict__coboundedI2,axiom,
% 0.29/0.52      ! [C: extended_enat,B: extended_enat,A: extended_enat] :
% 0.29/0.52        ( ( ord_le72135733267957522d_enat @ C @ B )
% 0.29/0.52       => ( ord_le72135733267957522d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.strict_coboundedI2
% 0.29/0.52  thf(fact_1130_max_Ostrict__coboundedI2,axiom,
% 0.29/0.52      ! [C: real,B: real,A: real] :
% 0.29/0.52        ( ( ord_less_real @ C @ B )
% 0.29/0.52       => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.strict_coboundedI2
% 0.29/0.52  thf(fact_1131_max_Ostrict__coboundedI2,axiom,
% 0.29/0.52      ! [C: rat,B: rat,A: rat] :
% 0.29/0.52        ( ( ord_less_rat @ C @ B )
% 0.29/0.52       => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.strict_coboundedI2
% 0.29/0.52  thf(fact_1132_max_Ostrict__coboundedI2,axiom,
% 0.29/0.52      ! [C: num,B: num,A: num] :
% 0.29/0.52        ( ( ord_less_num @ C @ B )
% 0.29/0.52       => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.strict_coboundedI2
% 0.29/0.52  thf(fact_1133_max_Ostrict__coboundedI2,axiom,
% 0.29/0.52      ! [C: nat,B: nat,A: nat] :
% 0.29/0.52        ( ( ord_less_nat @ C @ B )
% 0.29/0.52       => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.strict_coboundedI2
% 0.29/0.52  thf(fact_1134_max_Ostrict__coboundedI2,axiom,
% 0.29/0.52      ! [C: int,B: int,A: int] :
% 0.29/0.52        ( ( ord_less_int @ C @ B )
% 0.29/0.52       => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max.strict_coboundedI2
% 0.29/0.52  thf(fact_1135_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 0.29/0.52      ! [X: produc5491161045314408544at_nat] :
% 0.29/0.52        ( ! [Uu2: product_prod_nat_nat > product_prod_nat_nat > $o,Uv2: option4927543243414619207at_nat] :
% 0.29/0.52            ( X
% 0.29/0.52           != ( produc3994169339658061776at_nat @ Uu2 @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv2 ) ) )
% 0.29/0.52       => ( ! [Uw2: product_prod_nat_nat > product_prod_nat_nat > $o,V2: product_prod_nat_nat] :
% 0.29/0.52              ( X
% 0.29/0.52             != ( produc3994169339658061776at_nat @ Uw2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V2 ) @ none_P5556105721700978146at_nat ) ) )
% 0.29/0.52         => ~ ! [F2: product_prod_nat_nat > product_prod_nat_nat > $o,X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 0.29/0.52                ( X
% 0.29/0.52               != ( produc3994169339658061776at_nat @ F2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ X3 ) @ ( some_P7363390416028606310at_nat @ Y3 ) ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % VEBT_internal.option_comp_shift.cases
% 0.29/0.52  thf(fact_1136_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 0.29/0.52      ! [X: produc2233624965454879586on_nat] :
% 0.29/0.52        ( ! [Uu2: nat > nat > $o,Uv2: option_nat] :
% 0.29/0.52            ( X
% 0.29/0.52           != ( produc4035269172776083154on_nat @ Uu2 @ ( produc5098337634421038937on_nat @ none_nat @ Uv2 ) ) )
% 0.29/0.52       => ( ! [Uw2: nat > nat > $o,V2: nat] :
% 0.29/0.52              ( X
% 0.29/0.52             != ( produc4035269172776083154on_nat @ Uw2 @ ( produc5098337634421038937on_nat @ ( some_nat @ V2 ) @ none_nat ) ) )
% 0.29/0.52         => ~ ! [F2: nat > nat > $o,X3: nat,Y3: nat] :
% 0.29/0.52                ( X
% 0.29/0.52               != ( produc4035269172776083154on_nat @ F2 @ ( produc5098337634421038937on_nat @ ( some_nat @ X3 ) @ ( some_nat @ Y3 ) ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % VEBT_internal.option_comp_shift.cases
% 0.29/0.52  thf(fact_1137_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 0.29/0.52      ! [X: produc7036089656553540234on_num] :
% 0.29/0.52        ( ! [Uu2: num > num > $o,Uv2: option_num] :
% 0.29/0.52            ( X
% 0.29/0.52           != ( produc3576312749637752826on_num @ Uu2 @ ( produc8585076106096196333on_num @ none_num @ Uv2 ) ) )
% 0.29/0.52       => ( ! [Uw2: num > num > $o,V2: num] :
% 0.29/0.52              ( X
% 0.29/0.52             != ( produc3576312749637752826on_num @ Uw2 @ ( produc8585076106096196333on_num @ ( some_num @ V2 ) @ none_num ) ) )
% 0.29/0.52         => ~ ! [F2: num > num > $o,X3: num,Y3: num] :
% 0.29/0.52                ( X
% 0.29/0.52               != ( produc3576312749637752826on_num @ F2 @ ( produc8585076106096196333on_num @ ( some_num @ X3 ) @ ( some_num @ Y3 ) ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % VEBT_internal.option_comp_shift.cases
% 0.29/0.52  thf(fact_1138_VEBT__internal_Ooption__shift_Ocases,axiom,
% 0.29/0.52      ! [X: produc5542196010084753463at_nat] :
% 0.29/0.52        ( ! [Uu2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Uv2: option4927543243414619207at_nat] :
% 0.29/0.52            ( X
% 0.29/0.52           != ( produc2899441246263362727at_nat @ Uu2 @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv2 ) ) )
% 0.29/0.52       => ( ! [Uw2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V2: product_prod_nat_nat] :
% 0.29/0.52              ( X
% 0.29/0.52             != ( produc2899441246263362727at_nat @ Uw2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V2 ) @ none_P5556105721700978146at_nat ) ) )
% 0.29/0.52         => ~ ! [F2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A4: product_prod_nat_nat,B3: product_prod_nat_nat] :
% 0.29/0.52                ( X
% 0.29/0.52               != ( produc2899441246263362727at_nat @ F2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ A4 ) @ ( some_P7363390416028606310at_nat @ B3 ) ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % VEBT_internal.option_shift.cases
% 0.29/0.52  thf(fact_1139_VEBT__internal_Ooption__shift_Ocases,axiom,
% 0.29/0.52      ! [X: produc8306885398267862888on_nat] :
% 0.29/0.52        ( ! [Uu2: nat > nat > nat,Uv2: option_nat] :
% 0.29/0.52            ( X
% 0.29/0.52           != ( produc8929957630744042906on_nat @ Uu2 @ ( produc5098337634421038937on_nat @ none_nat @ Uv2 ) ) )
% 0.29/0.52       => ( ! [Uw2: nat > nat > nat,V2: nat] :
% 0.29/0.52              ( X
% 0.29/0.52             != ( produc8929957630744042906on_nat @ Uw2 @ ( produc5098337634421038937on_nat @ ( some_nat @ V2 ) @ none_nat ) ) )
% 0.29/0.52         => ~ ! [F2: nat > nat > nat,A4: nat,B3: nat] :
% 0.29/0.52                ( X
% 0.29/0.52               != ( produc8929957630744042906on_nat @ F2 @ ( produc5098337634421038937on_nat @ ( some_nat @ A4 ) @ ( some_nat @ B3 ) ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % VEBT_internal.option_shift.cases
% 0.29/0.52  thf(fact_1140_VEBT__internal_Ooption__shift_Ocases,axiom,
% 0.29/0.52      ! [X: produc1193250871479095198on_num] :
% 0.29/0.52        ( ! [Uu2: num > num > num,Uv2: option_num] :
% 0.29/0.52            ( X
% 0.29/0.52           != ( produc5778274026573060048on_num @ Uu2 @ ( produc8585076106096196333on_num @ none_num @ Uv2 ) ) )
% 0.29/0.52       => ( ! [Uw2: num > num > num,V2: num] :
% 0.29/0.52              ( X
% 0.29/0.52             != ( produc5778274026573060048on_num @ Uw2 @ ( produc8585076106096196333on_num @ ( some_num @ V2 ) @ none_num ) ) )
% 0.29/0.52         => ~ ! [F2: num > num > num,A4: num,B3: num] :
% 0.29/0.52                ( X
% 0.29/0.52               != ( produc5778274026573060048on_num @ F2 @ ( produc8585076106096196333on_num @ ( some_num @ A4 ) @ ( some_num @ B3 ) ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % VEBT_internal.option_shift.cases
% 0.29/0.52  thf(fact_1141_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 0.29/0.52      ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 0.29/0.52        ( ( vEBT_V1502963449132264192at_nat @ F @ ( some_P7363390416028606310at_nat @ A ) @ ( some_P7363390416028606310at_nat @ B ) )
% 0.29/0.52        = ( some_P7363390416028606310at_nat @ ( F @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % VEBT_internal.option_shift.simps(3)
% 0.29/0.52  thf(fact_1142_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 0.29/0.52      ! [F: num > num > num,A: num,B: num] :
% 0.29/0.52        ( ( vEBT_V819420779217536731ft_num @ F @ ( some_num @ A ) @ ( some_num @ B ) )
% 0.29/0.52        = ( some_num @ ( F @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % VEBT_internal.option_shift.simps(3)
% 0.29/0.52  thf(fact_1143_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 0.29/0.52      ! [F: nat > nat > nat,A: nat,B: nat] :
% 0.29/0.52        ( ( vEBT_V4262088993061758097ft_nat @ F @ ( some_nat @ A ) @ ( some_nat @ B ) )
% 0.29/0.52        = ( some_nat @ ( F @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % VEBT_internal.option_shift.simps(3)
% 0.29/0.52  thf(fact_1144_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 0.29/0.52      ! [Uu: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Uv: option4927543243414619207at_nat] :
% 0.29/0.52        ( ( vEBT_V1502963449132264192at_nat @ Uu @ none_P5556105721700978146at_nat @ Uv )
% 0.29/0.52        = none_P5556105721700978146at_nat ) ).
% 0.29/0.52  
% 0.29/0.52  % VEBT_internal.option_shift.simps(1)
% 0.29/0.52  thf(fact_1145_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 0.29/0.52      ! [Uu: num > num > num,Uv: option_num] :
% 0.29/0.52        ( ( vEBT_V819420779217536731ft_num @ Uu @ none_num @ Uv )
% 0.29/0.52        = none_num ) ).
% 0.29/0.52  
% 0.29/0.52  % VEBT_internal.option_shift.simps(1)
% 0.29/0.52  thf(fact_1146_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 0.29/0.52      ! [Uu: nat > nat > nat,Uv: option_nat] :
% 0.29/0.52        ( ( vEBT_V4262088993061758097ft_nat @ Uu @ none_nat @ Uv )
% 0.29/0.52        = none_nat ) ).
% 0.29/0.52  
% 0.29/0.52  % VEBT_internal.option_shift.simps(1)
% 0.29/0.52  thf(fact_1147_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 0.29/0.52      ! [Uw: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V: product_prod_nat_nat] :
% 0.29/0.52        ( ( vEBT_V1502963449132264192at_nat @ Uw @ ( some_P7363390416028606310at_nat @ V ) @ none_P5556105721700978146at_nat )
% 0.29/0.52        = none_P5556105721700978146at_nat ) ).
% 0.29/0.52  
% 0.29/0.52  % VEBT_internal.option_shift.simps(2)
% 0.29/0.52  thf(fact_1148_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 0.29/0.52      ! [Uw: num > num > num,V: num] :
% 0.29/0.52        ( ( vEBT_V819420779217536731ft_num @ Uw @ ( some_num @ V ) @ none_num )
% 0.29/0.52        = none_num ) ).
% 0.29/0.52  
% 0.29/0.52  % VEBT_internal.option_shift.simps(2)
% 0.29/0.52  thf(fact_1149_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 0.29/0.52      ! [Uw: nat > nat > nat,V: nat] :
% 0.29/0.52        ( ( vEBT_V4262088993061758097ft_nat @ Uw @ ( some_nat @ V ) @ none_nat )
% 0.29/0.52        = none_nat ) ).
% 0.29/0.52  
% 0.29/0.52  % VEBT_internal.option_shift.simps(2)
% 0.29/0.52  thf(fact_1150_VEBT__internal_Ooption__shift_Oelims,axiom,
% 0.29/0.52      ! [X: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Xa2: option4927543243414619207at_nat,Xb: option4927543243414619207at_nat,Y2: option4927543243414619207at_nat] :
% 0.29/0.52        ( ( ( vEBT_V1502963449132264192at_nat @ X @ Xa2 @ Xb )
% 0.29/0.52          = Y2 )
% 0.29/0.52       => ( ( ( Xa2 = none_P5556105721700978146at_nat )
% 0.29/0.52           => ( Y2 != none_P5556105721700978146at_nat ) )
% 0.29/0.52         => ( ( ? [V2: product_prod_nat_nat] :
% 0.29/0.52                  ( Xa2
% 0.29/0.52                  = ( some_P7363390416028606310at_nat @ V2 ) )
% 0.29/0.52             => ( ( Xb = none_P5556105721700978146at_nat )
% 0.29/0.52               => ( Y2 != none_P5556105721700978146at_nat ) ) )
% 0.29/0.52           => ~ ! [A4: product_prod_nat_nat] :
% 0.29/0.52                  ( ( Xa2
% 0.29/0.52                    = ( some_P7363390416028606310at_nat @ A4 ) )
% 0.29/0.52                 => ! [B3: product_prod_nat_nat] :
% 0.29/0.52                      ( ( Xb
% 0.29/0.52                        = ( some_P7363390416028606310at_nat @ B3 ) )
% 0.29/0.52                     => ( Y2
% 0.29/0.52                       != ( some_P7363390416028606310at_nat @ ( X @ A4 @ B3 ) ) ) ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % VEBT_internal.option_shift.elims
% 0.29/0.52  thf(fact_1151_VEBT__internal_Ooption__shift_Oelims,axiom,
% 0.29/0.52      ! [X: num > num > num,Xa2: option_num,Xb: option_num,Y2: option_num] :
% 0.29/0.52        ( ( ( vEBT_V819420779217536731ft_num @ X @ Xa2 @ Xb )
% 0.29/0.52          = Y2 )
% 0.29/0.52       => ( ( ( Xa2 = none_num )
% 0.29/0.52           => ( Y2 != none_num ) )
% 0.29/0.52         => ( ( ? [V2: num] :
% 0.29/0.52                  ( Xa2
% 0.29/0.52                  = ( some_num @ V2 ) )
% 0.29/0.52             => ( ( Xb = none_num )
% 0.29/0.52               => ( Y2 != none_num ) ) )
% 0.29/0.52           => ~ ! [A4: num] :
% 0.29/0.52                  ( ( Xa2
% 0.29/0.52                    = ( some_num @ A4 ) )
% 0.29/0.52                 => ! [B3: num] :
% 0.29/0.52                      ( ( Xb
% 0.29/0.52                        = ( some_num @ B3 ) )
% 0.29/0.52                     => ( Y2
% 0.29/0.52                       != ( some_num @ ( X @ A4 @ B3 ) ) ) ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % VEBT_internal.option_shift.elims
% 0.29/0.52  thf(fact_1152_VEBT__internal_Ooption__shift_Oelims,axiom,
% 0.29/0.52      ! [X: nat > nat > nat,Xa2: option_nat,Xb: option_nat,Y2: option_nat] :
% 0.29/0.52        ( ( ( vEBT_V4262088993061758097ft_nat @ X @ Xa2 @ Xb )
% 0.29/0.52          = Y2 )
% 0.29/0.52       => ( ( ( Xa2 = none_nat )
% 0.29/0.52           => ( Y2 != none_nat ) )
% 0.29/0.52         => ( ( ? [V2: nat] :
% 0.29/0.52                  ( Xa2
% 0.29/0.52                  = ( some_nat @ V2 ) )
% 0.29/0.52             => ( ( Xb = none_nat )
% 0.29/0.52               => ( Y2 != none_nat ) ) )
% 0.29/0.52           => ~ ! [A4: nat] :
% 0.29/0.52                  ( ( Xa2
% 0.29/0.52                    = ( some_nat @ A4 ) )
% 0.29/0.52                 => ! [B3: nat] :
% 0.29/0.52                      ( ( Xb
% 0.29/0.52                        = ( some_nat @ B3 ) )
% 0.29/0.52                     => ( Y2
% 0.29/0.52                       != ( some_nat @ ( X @ A4 @ B3 ) ) ) ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % VEBT_internal.option_shift.elims
% 0.29/0.52  thf(fact_1153_vebt__mint_Osimps_I2_J,axiom,
% 0.29/0.52      ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.29/0.52        ( ( vEBT_vebt_mint @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.29/0.52        = none_nat ) ).
% 0.29/0.52  
% 0.29/0.52  % vebt_mint.simps(2)
% 0.29/0.52  thf(fact_1154_vebt__maxt_Osimps_I2_J,axiom,
% 0.29/0.52      ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.29/0.52        ( ( vEBT_vebt_maxt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.29/0.52        = none_nat ) ).
% 0.29/0.52  
% 0.29/0.52  % vebt_maxt.simps(2)
% 0.29/0.52  thf(fact_1155_add__diff__cancel__right_H,axiom,
% 0.29/0.52      ! [A: real,B: real] :
% 0.29/0.52        ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % add_diff_cancel_right'
% 0.29/0.52  thf(fact_1156_add__diff__cancel__right_H,axiom,
% 0.29/0.52      ! [A: complex,B: complex] :
% 0.29/0.52        ( ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ B )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % add_diff_cancel_right'
% 0.29/0.52  thf(fact_1157_add__diff__cancel__right_H,axiom,
% 0.29/0.52      ! [A: rat,B: rat] :
% 0.29/0.52        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % add_diff_cancel_right'
% 0.29/0.52  thf(fact_1158_add__diff__cancel__right_H,axiom,
% 0.29/0.52      ! [A: nat,B: nat] :
% 0.29/0.52        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % add_diff_cancel_right'
% 0.29/0.52  thf(fact_1159_add__diff__cancel__right_H,axiom,
% 0.29/0.52      ! [A: int,B: int] :
% 0.29/0.52        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % add_diff_cancel_right'
% 0.29/0.52  thf(fact_1160_add__diff__cancel__right,axiom,
% 0.29/0.52      ! [A: real,C: real,B: real] :
% 0.29/0.52        ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 0.29/0.52        = ( minus_minus_real @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_diff_cancel_right
% 0.29/0.52  thf(fact_1161_add__diff__cancel__right,axiom,
% 0.29/0.52      ! [A: complex,C: complex,B: complex] :
% 0.29/0.52        ( ( minus_minus_complex @ ( plus_plus_complex @ A @ C ) @ ( plus_plus_complex @ B @ C ) )
% 0.29/0.52        = ( minus_minus_complex @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_diff_cancel_right
% 0.29/0.52  thf(fact_1162_add__diff__cancel__right,axiom,
% 0.29/0.52      ! [A: rat,C: rat,B: rat] :
% 0.29/0.52        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.29/0.52        = ( minus_minus_rat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_diff_cancel_right
% 0.29/0.52  thf(fact_1163_add__diff__cancel__right,axiom,
% 0.29/0.52      ! [A: nat,C: nat,B: nat] :
% 0.29/0.52        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.29/0.52        = ( minus_minus_nat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_diff_cancel_right
% 0.29/0.52  thf(fact_1164_add__diff__cancel__right,axiom,
% 0.29/0.52      ! [A: int,C: int,B: int] :
% 0.29/0.52        ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.29/0.52        = ( minus_minus_int @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_diff_cancel_right
% 0.29/0.52  thf(fact_1165_add__diff__cancel__left_H,axiom,
% 0.29/0.52      ! [A: real,B: real] :
% 0.29/0.52        ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 0.29/0.52        = B ) ).
% 0.29/0.52  
% 0.29/0.52  % add_diff_cancel_left'
% 0.29/0.52  thf(fact_1166_add__diff__cancel__left_H,axiom,
% 0.29/0.52      ! [A: complex,B: complex] :
% 0.29/0.52        ( ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ A )
% 0.29/0.52        = B ) ).
% 0.29/0.52  
% 0.29/0.52  % add_diff_cancel_left'
% 0.29/0.52  thf(fact_1167_add__diff__cancel__left_H,axiom,
% 0.29/0.52      ! [A: rat,B: rat] :
% 0.29/0.52        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 0.29/0.52        = B ) ).
% 0.29/0.52  
% 0.29/0.52  % add_diff_cancel_left'
% 0.29/0.52  thf(fact_1168_add__diff__cancel__left_H,axiom,
% 0.29/0.52      ! [A: nat,B: nat] :
% 0.29/0.52        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 0.29/0.52        = B ) ).
% 0.29/0.52  
% 0.29/0.52  % add_diff_cancel_left'
% 0.29/0.52  thf(fact_1169_add__diff__cancel__left_H,axiom,
% 0.29/0.52      ! [A: int,B: int] :
% 0.29/0.52        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 0.29/0.52        = B ) ).
% 0.29/0.52  
% 0.29/0.52  % add_diff_cancel_left'
% 0.29/0.52  thf(fact_1170_add__diff__cancel__left,axiom,
% 0.29/0.52      ! [C: real,A: real,B: real] :
% 0.29/0.52        ( ( minus_minus_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 0.29/0.52        = ( minus_minus_real @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_diff_cancel_left
% 0.29/0.52  thf(fact_1171_add__diff__cancel__left,axiom,
% 0.29/0.52      ! [C: complex,A: complex,B: complex] :
% 0.29/0.52        ( ( minus_minus_complex @ ( plus_plus_complex @ C @ A ) @ ( plus_plus_complex @ C @ B ) )
% 0.29/0.52        = ( minus_minus_complex @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_diff_cancel_left
% 0.29/0.52  thf(fact_1172_add__diff__cancel__left,axiom,
% 0.29/0.52      ! [C: rat,A: rat,B: rat] :
% 0.29/0.52        ( ( minus_minus_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.29/0.52        = ( minus_minus_rat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_diff_cancel_left
% 0.29/0.52  thf(fact_1173_add__diff__cancel__left,axiom,
% 0.29/0.52      ! [C: nat,A: nat,B: nat] :
% 0.29/0.52        ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.29/0.52        = ( minus_minus_nat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_diff_cancel_left
% 0.29/0.52  thf(fact_1174_add__diff__cancel__left,axiom,
% 0.29/0.52      ! [C: int,A: int,B: int] :
% 0.29/0.52        ( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.29/0.52        = ( minus_minus_int @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_diff_cancel_left
% 0.29/0.52  thf(fact_1175_diff__add__cancel,axiom,
% 0.29/0.52      ! [A: real,B: real] :
% 0.29/0.52        ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_add_cancel
% 0.29/0.52  thf(fact_1176_diff__add__cancel,axiom,
% 0.29/0.52      ! [A: complex,B: complex] :
% 0.29/0.52        ( ( plus_plus_complex @ ( minus_minus_complex @ A @ B ) @ B )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_add_cancel
% 0.29/0.52  thf(fact_1177_diff__add__cancel,axiom,
% 0.29/0.52      ! [A: rat,B: rat] :
% 0.29/0.52        ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_add_cancel
% 0.29/0.52  thf(fact_1178_diff__add__cancel,axiom,
% 0.29/0.52      ! [A: int,B: int] :
% 0.29/0.52        ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_add_cancel
% 0.29/0.52  thf(fact_1179_add__diff__cancel,axiom,
% 0.29/0.52      ! [A: real,B: real] :
% 0.29/0.52        ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % add_diff_cancel
% 0.29/0.52  thf(fact_1180_add__diff__cancel,axiom,
% 0.29/0.52      ! [A: complex,B: complex] :
% 0.29/0.52        ( ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ B )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % add_diff_cancel
% 0.29/0.52  thf(fact_1181_add__diff__cancel,axiom,
% 0.29/0.52      ! [A: rat,B: rat] :
% 0.29/0.52        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % add_diff_cancel
% 0.29/0.52  thf(fact_1182_add__diff__cancel,axiom,
% 0.29/0.52      ! [A: int,B: int] :
% 0.29/0.52        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % add_diff_cancel
% 0.29/0.52  thf(fact_1183_times__divide__eq__left,axiom,
% 0.29/0.52      ! [B: complex,C: complex,A: complex] :
% 0.29/0.52        ( ( times_times_complex @ ( divide1717551699836669952omplex @ B @ C ) @ A )
% 0.29/0.52        = ( divide1717551699836669952omplex @ ( times_times_complex @ B @ A ) @ C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % times_divide_eq_left
% 0.29/0.52  thf(fact_1184_times__divide__eq__left,axiom,
% 0.29/0.52      ! [B: real,C: real,A: real] :
% 0.29/0.52        ( ( times_times_real @ ( divide_divide_real @ B @ C ) @ A )
% 0.29/0.52        = ( divide_divide_real @ ( times_times_real @ B @ A ) @ C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % times_divide_eq_left
% 0.29/0.52  thf(fact_1185_times__divide__eq__left,axiom,
% 0.29/0.52      ! [B: rat,C: rat,A: rat] :
% 0.29/0.52        ( ( times_times_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.29/0.52        = ( divide_divide_rat @ ( times_times_rat @ B @ A ) @ C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % times_divide_eq_left
% 0.29/0.52  thf(fact_1186_divide__divide__eq__left,axiom,
% 0.29/0.52      ! [A: complex,B: complex,C: complex] :
% 0.29/0.52        ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 0.29/0.52        = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_divide_eq_left
% 0.29/0.52  thf(fact_1187_divide__divide__eq__left,axiom,
% 0.29/0.52      ! [A: real,B: real,C: real] :
% 0.29/0.52        ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 0.29/0.52        = ( divide_divide_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_divide_eq_left
% 0.29/0.52  thf(fact_1188_divide__divide__eq__left,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat] :
% 0.29/0.52        ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 0.29/0.52        = ( divide_divide_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_divide_eq_left
% 0.29/0.52  thf(fact_1189_divide__divide__eq__right,axiom,
% 0.29/0.52      ! [A: complex,B: complex,C: complex] :
% 0.29/0.52        ( ( divide1717551699836669952omplex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 0.29/0.52        = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_divide_eq_right
% 0.29/0.52  thf(fact_1190_divide__divide__eq__right,axiom,
% 0.29/0.52      ! [A: real,B: real,C: real] :
% 0.29/0.52        ( ( divide_divide_real @ A @ ( divide_divide_real @ B @ C ) )
% 0.29/0.52        = ( divide_divide_real @ ( times_times_real @ A @ C ) @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_divide_eq_right
% 0.29/0.52  thf(fact_1191_divide__divide__eq__right,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat] :
% 0.29/0.52        ( ( divide_divide_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.29/0.52        = ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_divide_eq_right
% 0.29/0.52  thf(fact_1192_times__divide__eq__right,axiom,
% 0.29/0.52      ! [A: complex,B: complex,C: complex] :
% 0.29/0.52        ( ( times_times_complex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 0.29/0.52        = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % times_divide_eq_right
% 0.29/0.52  thf(fact_1193_times__divide__eq__right,axiom,
% 0.29/0.52      ! [A: real,B: real,C: real] :
% 0.29/0.52        ( ( times_times_real @ A @ ( divide_divide_real @ B @ C ) )
% 0.29/0.52        = ( divide_divide_real @ ( times_times_real @ A @ B ) @ C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % times_divide_eq_right
% 0.29/0.52  thf(fact_1194_times__divide__eq__right,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat] :
% 0.29/0.52        ( ( times_times_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.29/0.52        = ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % times_divide_eq_right
% 0.29/0.52  thf(fact_1195_add__left__cancel,axiom,
% 0.29/0.52      ! [A: real,B: real,C: real] :
% 0.29/0.52        ( ( ( plus_plus_real @ A @ B )
% 0.29/0.52          = ( plus_plus_real @ A @ C ) )
% 0.29/0.52        = ( B = C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_left_cancel
% 0.29/0.52  thf(fact_1196_add__left__cancel,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat] :
% 0.29/0.52        ( ( ( plus_plus_rat @ A @ B )
% 0.29/0.52          = ( plus_plus_rat @ A @ C ) )
% 0.29/0.52        = ( B = C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_left_cancel
% 0.29/0.52  thf(fact_1197_add__left__cancel,axiom,
% 0.29/0.52      ! [A: nat,B: nat,C: nat] :
% 0.29/0.52        ( ( ( plus_plus_nat @ A @ B )
% 0.29/0.52          = ( plus_plus_nat @ A @ C ) )
% 0.29/0.52        = ( B = C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_left_cancel
% 0.29/0.52  thf(fact_1198_add__left__cancel,axiom,
% 0.29/0.52      ! [A: int,B: int,C: int] :
% 0.29/0.52        ( ( ( plus_plus_int @ A @ B )
% 0.29/0.52          = ( plus_plus_int @ A @ C ) )
% 0.29/0.52        = ( B = C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_left_cancel
% 0.29/0.52  thf(fact_1199_add__left__cancel,axiom,
% 0.29/0.52      ! [A: complex,B: complex,C: complex] :
% 0.29/0.52        ( ( ( plus_plus_complex @ A @ B )
% 0.29/0.52          = ( plus_plus_complex @ A @ C ) )
% 0.29/0.52        = ( B = C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_left_cancel
% 0.29/0.52  thf(fact_1200_add__right__cancel,axiom,
% 0.29/0.52      ! [B: real,A: real,C: real] :
% 0.29/0.52        ( ( ( plus_plus_real @ B @ A )
% 0.29/0.52          = ( plus_plus_real @ C @ A ) )
% 0.29/0.52        = ( B = C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_right_cancel
% 0.29/0.52  thf(fact_1201_add__right__cancel,axiom,
% 0.29/0.52      ! [B: rat,A: rat,C: rat] :
% 0.29/0.52        ( ( ( plus_plus_rat @ B @ A )
% 0.29/0.52          = ( plus_plus_rat @ C @ A ) )
% 0.29/0.52        = ( B = C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_right_cancel
% 0.29/0.52  thf(fact_1202_add__right__cancel,axiom,
% 0.29/0.52      ! [B: nat,A: nat,C: nat] :
% 0.29/0.52        ( ( ( plus_plus_nat @ B @ A )
% 0.29/0.52          = ( plus_plus_nat @ C @ A ) )
% 0.29/0.52        = ( B = C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_right_cancel
% 0.29/0.52  thf(fact_1203_add__right__cancel,axiom,
% 0.29/0.52      ! [B: int,A: int,C: int] :
% 0.29/0.52        ( ( ( plus_plus_int @ B @ A )
% 0.29/0.52          = ( plus_plus_int @ C @ A ) )
% 0.29/0.52        = ( B = C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_right_cancel
% 0.29/0.52  thf(fact_1204_add__right__cancel,axiom,
% 0.29/0.52      ! [B: complex,A: complex,C: complex] :
% 0.29/0.52        ( ( ( plus_plus_complex @ B @ A )
% 0.29/0.52          = ( plus_plus_complex @ C @ A ) )
% 0.29/0.52        = ( B = C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_right_cancel
% 0.29/0.52  thf(fact_1205_add__le__cancel__left,axiom,
% 0.29/0.52      ! [C: real,A: real,B: real] :
% 0.29/0.52        ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 0.29/0.52        = ( ord_less_eq_real @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_le_cancel_left
% 0.29/0.52  thf(fact_1206_add__le__cancel__left,axiom,
% 0.29/0.52      ! [C: rat,A: rat,B: rat] :
% 0.29/0.52        ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.29/0.52        = ( ord_less_eq_rat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_le_cancel_left
% 0.29/0.52  thf(fact_1207_add__le__cancel__left,axiom,
% 0.29/0.52      ! [C: nat,A: nat,B: nat] :
% 0.29/0.52        ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.29/0.52        = ( ord_less_eq_nat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_le_cancel_left
% 0.29/0.52  thf(fact_1208_add__le__cancel__left,axiom,
% 0.29/0.52      ! [C: int,A: int,B: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.29/0.52        = ( ord_less_eq_int @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_le_cancel_left
% 0.29/0.52  thf(fact_1209_add__le__cancel__right,axiom,
% 0.29/0.52      ! [A: real,C: real,B: real] :
% 0.29/0.52        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 0.29/0.52        = ( ord_less_eq_real @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_le_cancel_right
% 0.29/0.52  thf(fact_1210_add__le__cancel__right,axiom,
% 0.29/0.52      ! [A: rat,C: rat,B: rat] :
% 0.29/0.52        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.29/0.52        = ( ord_less_eq_rat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_le_cancel_right
% 0.29/0.52  thf(fact_1211_add__le__cancel__right,axiom,
% 0.29/0.52      ! [A: nat,C: nat,B: nat] :
% 0.29/0.52        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.29/0.52        = ( ord_less_eq_nat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_le_cancel_right
% 0.29/0.52  thf(fact_1212_add__le__cancel__right,axiom,
% 0.29/0.52      ! [A: int,C: int,B: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.29/0.52        = ( ord_less_eq_int @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_le_cancel_right
% 0.29/0.52  thf(fact_1213_add__less__cancel__left,axiom,
% 0.29/0.52      ! [C: real,A: real,B: real] :
% 0.29/0.52        ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 0.29/0.52        = ( ord_less_real @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_less_cancel_left
% 0.29/0.52  thf(fact_1214_add__less__cancel__left,axiom,
% 0.29/0.52      ! [C: rat,A: rat,B: rat] :
% 0.29/0.52        ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.29/0.52        = ( ord_less_rat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_less_cancel_left
% 0.29/0.52  thf(fact_1215_add__less__cancel__left,axiom,
% 0.29/0.52      ! [C: nat,A: nat,B: nat] :
% 0.29/0.52        ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.29/0.52        = ( ord_less_nat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_less_cancel_left
% 0.29/0.52  thf(fact_1216_add__less__cancel__left,axiom,
% 0.29/0.52      ! [C: int,A: int,B: int] :
% 0.29/0.52        ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.29/0.52        = ( ord_less_int @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_less_cancel_left
% 0.29/0.52  thf(fact_1217_add__less__cancel__right,axiom,
% 0.29/0.52      ! [A: real,C: real,B: real] :
% 0.29/0.52        ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 0.29/0.52        = ( ord_less_real @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_less_cancel_right
% 0.29/0.52  thf(fact_1218_add__less__cancel__right,axiom,
% 0.29/0.52      ! [A: rat,C: rat,B: rat] :
% 0.29/0.52        ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.29/0.52        = ( ord_less_rat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_less_cancel_right
% 0.29/0.52  thf(fact_1219_add__less__cancel__right,axiom,
% 0.29/0.52      ! [A: nat,C: nat,B: nat] :
% 0.29/0.52        ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.29/0.52        = ( ord_less_nat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_less_cancel_right
% 0.29/0.52  thf(fact_1220_add__less__cancel__right,axiom,
% 0.29/0.52      ! [A: int,C: int,B: int] :
% 0.29/0.52        ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.29/0.52        = ( ord_less_int @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_less_cancel_right
% 0.29/0.52  thf(fact_1221_mult_Oright__neutral,axiom,
% 0.29/0.52      ! [A: rat] :
% 0.29/0.52        ( ( times_times_rat @ A @ one_one_rat )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % mult.right_neutral
% 0.29/0.52  thf(fact_1222_mult_Oright__neutral,axiom,
% 0.29/0.52      ! [A: complex] :
% 0.29/0.52        ( ( times_times_complex @ A @ one_one_complex )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % mult.right_neutral
% 0.29/0.52  thf(fact_1223_mult_Oright__neutral,axiom,
% 0.29/0.52      ! [A: real] :
% 0.29/0.52        ( ( times_times_real @ A @ one_one_real )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % mult.right_neutral
% 0.29/0.52  thf(fact_1224_mult_Oright__neutral,axiom,
% 0.29/0.52      ! [A: nat] :
% 0.29/0.52        ( ( times_times_nat @ A @ one_one_nat )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % mult.right_neutral
% 0.29/0.52  thf(fact_1225_mult_Oright__neutral,axiom,
% 0.29/0.52      ! [A: int] :
% 0.29/0.52        ( ( times_times_int @ A @ one_one_int )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % mult.right_neutral
% 0.29/0.52  thf(fact_1226_mult__1,axiom,
% 0.29/0.52      ! [A: rat] :
% 0.29/0.52        ( ( times_times_rat @ one_one_rat @ A )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_1
% 0.29/0.52  thf(fact_1227_mult__1,axiom,
% 0.29/0.52      ! [A: complex] :
% 0.29/0.52        ( ( times_times_complex @ one_one_complex @ A )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_1
% 0.29/0.52  thf(fact_1228_mult__1,axiom,
% 0.29/0.52      ! [A: real] :
% 0.29/0.52        ( ( times_times_real @ one_one_real @ A )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_1
% 0.29/0.52  thf(fact_1229_mult__1,axiom,
% 0.29/0.52      ! [A: nat] :
% 0.29/0.52        ( ( times_times_nat @ one_one_nat @ A )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_1
% 0.29/0.52  thf(fact_1230_mult__1,axiom,
% 0.29/0.52      ! [A: int] :
% 0.29/0.52        ( ( times_times_int @ one_one_int @ A )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_1
% 0.29/0.52  thf(fact_1231_linordered__field__no__ub,axiom,
% 0.29/0.52      ! [X5: real] :
% 0.29/0.52      ? [X_12: real] : ( ord_less_real @ X5 @ X_12 ) ).
% 0.29/0.52  
% 0.29/0.52  % linordered_field_no_ub
% 0.29/0.52  thf(fact_1232_linordered__field__no__ub,axiom,
% 0.29/0.52      ! [X5: rat] :
% 0.29/0.52      ? [X_12: rat] : ( ord_less_rat @ X5 @ X_12 ) ).
% 0.29/0.52  
% 0.29/0.52  % linordered_field_no_ub
% 0.29/0.52  thf(fact_1233_linordered__field__no__lb,axiom,
% 0.29/0.52      ! [X5: real] :
% 0.29/0.52      ? [Y3: real] : ( ord_less_real @ Y3 @ X5 ) ).
% 0.29/0.52  
% 0.29/0.52  % linordered_field_no_lb
% 0.29/0.52  thf(fact_1234_linordered__field__no__lb,axiom,
% 0.29/0.52      ! [X5: rat] :
% 0.29/0.52      ? [Y3: rat] : ( ord_less_rat @ Y3 @ X5 ) ).
% 0.29/0.52  
% 0.29/0.52  % linordered_field_no_lb
% 0.29/0.52  thf(fact_1235_mult_Oleft__commute,axiom,
% 0.29/0.52      ! [B: complex,A: complex,C: complex] :
% 0.29/0.52        ( ( times_times_complex @ B @ ( times_times_complex @ A @ C ) )
% 0.29/0.52        = ( times_times_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult.left_commute
% 0.29/0.52  thf(fact_1236_mult_Oleft__commute,axiom,
% 0.29/0.52      ! [B: real,A: real,C: real] :
% 0.29/0.52        ( ( times_times_real @ B @ ( times_times_real @ A @ C ) )
% 0.29/0.52        = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult.left_commute
% 0.29/0.52  thf(fact_1237_mult_Oleft__commute,axiom,
% 0.29/0.52      ! [B: nat,A: nat,C: nat] :
% 0.29/0.52        ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 0.29/0.52        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult.left_commute
% 0.29/0.52  thf(fact_1238_mult_Oleft__commute,axiom,
% 0.29/0.52      ! [B: int,A: int,C: int] :
% 0.29/0.52        ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
% 0.29/0.52        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult.left_commute
% 0.29/0.52  thf(fact_1239_mult_Ocommute,axiom,
% 0.29/0.52      ( times_times_complex
% 0.29/0.52      = ( ^ [A3: complex,B4: complex] : ( times_times_complex @ B4 @ A3 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult.commute
% 0.29/0.52  thf(fact_1240_mult_Ocommute,axiom,
% 0.29/0.52      ( times_times_real
% 0.29/0.52      = ( ^ [A3: real,B4: real] : ( times_times_real @ B4 @ A3 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult.commute
% 0.29/0.52  thf(fact_1241_mult_Ocommute,axiom,
% 0.29/0.52      ( times_times_nat
% 0.29/0.52      = ( ^ [A3: nat,B4: nat] : ( times_times_nat @ B4 @ A3 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult.commute
% 0.29/0.52  thf(fact_1242_mult_Ocommute,axiom,
% 0.29/0.52      ( times_times_int
% 0.29/0.52      = ( ^ [A3: int,B4: int] : ( times_times_int @ B4 @ A3 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult.commute
% 0.29/0.52  thf(fact_1243_mult_Oassoc,axiom,
% 0.29/0.52      ! [A: complex,B: complex,C: complex] :
% 0.29/0.52        ( ( times_times_complex @ ( times_times_complex @ A @ B ) @ C )
% 0.29/0.52        = ( times_times_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult.assoc
% 0.29/0.52  thf(fact_1244_mult_Oassoc,axiom,
% 0.29/0.52      ! [A: real,B: real,C: real] :
% 0.29/0.52        ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 0.29/0.52        = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult.assoc
% 0.29/0.52  thf(fact_1245_mult_Oassoc,axiom,
% 0.29/0.52      ! [A: nat,B: nat,C: nat] :
% 0.29/0.52        ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.29/0.52        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult.assoc
% 0.29/0.52  thf(fact_1246_mult_Oassoc,axiom,
% 0.29/0.52      ! [A: int,B: int,C: int] :
% 0.29/0.52        ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 0.29/0.52        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult.assoc
% 0.29/0.52  thf(fact_1247_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.29/0.52      ! [A: complex,B: complex,C: complex] :
% 0.29/0.52        ( ( times_times_complex @ ( times_times_complex @ A @ B ) @ C )
% 0.29/0.52        = ( times_times_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % ab_semigroup_mult_class.mult_ac(1)
% 0.29/0.52  thf(fact_1248_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.29/0.52      ! [A: real,B: real,C: real] :
% 0.29/0.52        ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 0.29/0.52        = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % ab_semigroup_mult_class.mult_ac(1)
% 0.29/0.52  thf(fact_1249_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.29/0.52      ! [A: nat,B: nat,C: nat] :
% 0.29/0.52        ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.29/0.52        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % ab_semigroup_mult_class.mult_ac(1)
% 0.29/0.52  thf(fact_1250_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.29/0.52      ! [A: int,B: int,C: int] :
% 0.29/0.52        ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 0.29/0.52        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % ab_semigroup_mult_class.mult_ac(1)
% 0.29/0.52  thf(fact_1251_one__reorient,axiom,
% 0.29/0.52      ! [X: complex] :
% 0.29/0.52        ( ( one_one_complex = X )
% 0.29/0.52        = ( X = one_one_complex ) ) ).
% 0.29/0.52  
% 0.29/0.52  % one_reorient
% 0.29/0.52  thf(fact_1252_one__reorient,axiom,
% 0.29/0.52      ! [X: real] :
% 0.29/0.52        ( ( one_one_real = X )
% 0.29/0.52        = ( X = one_one_real ) ) ).
% 0.29/0.52  
% 0.29/0.52  % one_reorient
% 0.29/0.52  thf(fact_1253_one__reorient,axiom,
% 0.29/0.52      ! [X: rat] :
% 0.29/0.52        ( ( one_one_rat = X )
% 0.29/0.52        = ( X = one_one_rat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % one_reorient
% 0.29/0.52  thf(fact_1254_one__reorient,axiom,
% 0.29/0.52      ! [X: nat] :
% 0.29/0.52        ( ( one_one_nat = X )
% 0.29/0.52        = ( X = one_one_nat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % one_reorient
% 0.29/0.52  thf(fact_1255_one__reorient,axiom,
% 0.29/0.52      ! [X: int] :
% 0.29/0.52        ( ( one_one_int = X )
% 0.29/0.52        = ( X = one_one_int ) ) ).
% 0.29/0.52  
% 0.29/0.52  % one_reorient
% 0.29/0.52  thf(fact_1256_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.29/0.52      ! [A: real,B: real,C: real] :
% 0.29/0.52        ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.29/0.52        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % ab_semigroup_add_class.add_ac(1)
% 0.29/0.52  thf(fact_1257_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat] :
% 0.29/0.52        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.29/0.52        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % ab_semigroup_add_class.add_ac(1)
% 0.29/0.52  thf(fact_1258_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.29/0.52      ! [A: nat,B: nat,C: nat] :
% 0.29/0.52        ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.29/0.52        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % ab_semigroup_add_class.add_ac(1)
% 0.29/0.52  thf(fact_1259_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.29/0.52      ! [A: int,B: int,C: int] :
% 0.29/0.52        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.29/0.52        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % ab_semigroup_add_class.add_ac(1)
% 0.29/0.52  thf(fact_1260_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.29/0.52      ! [A: complex,B: complex,C: complex] :
% 0.29/0.52        ( ( plus_plus_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 0.29/0.52        = ( plus_plus_complex @ A @ ( plus_plus_complex @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % ab_semigroup_add_class.add_ac(1)
% 0.29/0.52  thf(fact_1261_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.29/0.52      ! [I2: real,J: real,K: real,L2: real] :
% 0.29/0.52        ( ( ( I2 = J )
% 0.29/0.52          & ( K = L2 ) )
% 0.29/0.52       => ( ( plus_plus_real @ I2 @ K )
% 0.29/0.52          = ( plus_plus_real @ J @ L2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_mono_thms_linordered_semiring(4)
% 0.29/0.52  thf(fact_1262_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.29/0.52      ! [I2: rat,J: rat,K: rat,L2: rat] :
% 0.29/0.52        ( ( ( I2 = J )
% 0.29/0.52          & ( K = L2 ) )
% 0.29/0.52       => ( ( plus_plus_rat @ I2 @ K )
% 0.29/0.52          = ( plus_plus_rat @ J @ L2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_mono_thms_linordered_semiring(4)
% 0.29/0.52  thf(fact_1263_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.29/0.52      ! [I2: nat,J: nat,K: nat,L2: nat] :
% 0.29/0.52        ( ( ( I2 = J )
% 0.29/0.52          & ( K = L2 ) )
% 0.29/0.52       => ( ( plus_plus_nat @ I2 @ K )
% 0.29/0.52          = ( plus_plus_nat @ J @ L2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_mono_thms_linordered_semiring(4)
% 0.29/0.52  thf(fact_1264_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.29/0.52      ! [I2: int,J: int,K: int,L2: int] :
% 0.29/0.52        ( ( ( I2 = J )
% 0.29/0.52          & ( K = L2 ) )
% 0.29/0.52       => ( ( plus_plus_int @ I2 @ K )
% 0.29/0.52          = ( plus_plus_int @ J @ L2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_mono_thms_linordered_semiring(4)
% 0.29/0.52  thf(fact_1265_group__cancel_Oadd1,axiom,
% 0.29/0.52      ! [A2: real,K: real,A: real,B: real] :
% 0.29/0.52        ( ( A2
% 0.29/0.52          = ( plus_plus_real @ K @ A ) )
% 0.29/0.52       => ( ( plus_plus_real @ A2 @ B )
% 0.29/0.52          = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % group_cancel.add1
% 0.29/0.52  thf(fact_1266_group__cancel_Oadd1,axiom,
% 0.29/0.52      ! [A2: rat,K: rat,A: rat,B: rat] :
% 0.29/0.52        ( ( A2
% 0.29/0.52          = ( plus_plus_rat @ K @ A ) )
% 0.29/0.52       => ( ( plus_plus_rat @ A2 @ B )
% 0.29/0.52          = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % group_cancel.add1
% 0.29/0.52  thf(fact_1267_group__cancel_Oadd1,axiom,
% 0.29/0.52      ! [A2: nat,K: nat,A: nat,B: nat] :
% 0.29/0.52        ( ( A2
% 0.29/0.52          = ( plus_plus_nat @ K @ A ) )
% 0.29/0.52       => ( ( plus_plus_nat @ A2 @ B )
% 0.29/0.52          = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % group_cancel.add1
% 0.29/0.52  thf(fact_1268_group__cancel_Oadd1,axiom,
% 0.29/0.52      ! [A2: int,K: int,A: int,B: int] :
% 0.29/0.52        ( ( A2
% 0.29/0.52          = ( plus_plus_int @ K @ A ) )
% 0.29/0.52       => ( ( plus_plus_int @ A2 @ B )
% 0.29/0.52          = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % group_cancel.add1
% 0.29/0.52  thf(fact_1269_group__cancel_Oadd1,axiom,
% 0.29/0.52      ! [A2: complex,K: complex,A: complex,B: complex] :
% 0.29/0.52        ( ( A2
% 0.29/0.52          = ( plus_plus_complex @ K @ A ) )
% 0.29/0.52       => ( ( plus_plus_complex @ A2 @ B )
% 0.29/0.52          = ( plus_plus_complex @ K @ ( plus_plus_complex @ A @ B ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % group_cancel.add1
% 0.29/0.52  thf(fact_1270_group__cancel_Oadd2,axiom,
% 0.29/0.52      ! [B2: real,K: real,B: real,A: real] :
% 0.29/0.52        ( ( B2
% 0.29/0.52          = ( plus_plus_real @ K @ B ) )
% 0.29/0.52       => ( ( plus_plus_real @ A @ B2 )
% 0.29/0.52          = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % group_cancel.add2
% 0.29/0.52  thf(fact_1271_group__cancel_Oadd2,axiom,
% 0.29/0.52      ! [B2: rat,K: rat,B: rat,A: rat] :
% 0.29/0.52        ( ( B2
% 0.29/0.52          = ( plus_plus_rat @ K @ B ) )
% 0.29/0.52       => ( ( plus_plus_rat @ A @ B2 )
% 0.29/0.52          = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % group_cancel.add2
% 0.29/0.52  thf(fact_1272_group__cancel_Oadd2,axiom,
% 0.29/0.52      ! [B2: nat,K: nat,B: nat,A: nat] :
% 0.29/0.52        ( ( B2
% 0.29/0.52          = ( plus_plus_nat @ K @ B ) )
% 0.29/0.52       => ( ( plus_plus_nat @ A @ B2 )
% 0.29/0.52          = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % group_cancel.add2
% 0.29/0.52  thf(fact_1273_group__cancel_Oadd2,axiom,
% 0.29/0.52      ! [B2: int,K: int,B: int,A: int] :
% 0.29/0.52        ( ( B2
% 0.29/0.52          = ( plus_plus_int @ K @ B ) )
% 0.29/0.52       => ( ( plus_plus_int @ A @ B2 )
% 0.29/0.52          = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % group_cancel.add2
% 0.29/0.52  thf(fact_1274_group__cancel_Oadd2,axiom,
% 0.29/0.52      ! [B2: complex,K: complex,B: complex,A: complex] :
% 0.29/0.52        ( ( B2
% 0.29/0.52          = ( plus_plus_complex @ K @ B ) )
% 0.29/0.52       => ( ( plus_plus_complex @ A @ B2 )
% 0.29/0.52          = ( plus_plus_complex @ K @ ( plus_plus_complex @ A @ B ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % group_cancel.add2
% 0.29/0.52  thf(fact_1275_add_Oassoc,axiom,
% 0.29/0.52      ! [A: real,B: real,C: real] :
% 0.29/0.52        ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.29/0.52        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add.assoc
% 0.29/0.52  thf(fact_1276_add_Oassoc,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat] :
% 0.29/0.52        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.29/0.52        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add.assoc
% 0.29/0.52  thf(fact_1277_add_Oassoc,axiom,
% 0.29/0.52      ! [A: nat,B: nat,C: nat] :
% 0.29/0.52        ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.29/0.52        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add.assoc
% 0.29/0.52  thf(fact_1278_add_Oassoc,axiom,
% 0.29/0.52      ! [A: int,B: int,C: int] :
% 0.29/0.52        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.29/0.52        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add.assoc
% 0.29/0.52  thf(fact_1279_add_Oassoc,axiom,
% 0.29/0.52      ! [A: complex,B: complex,C: complex] :
% 0.29/0.52        ( ( plus_plus_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 0.29/0.52        = ( plus_plus_complex @ A @ ( plus_plus_complex @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add.assoc
% 0.29/0.52  thf(fact_1280_add_Oleft__cancel,axiom,
% 0.29/0.52      ! [A: real,B: real,C: real] :
% 0.29/0.52        ( ( ( plus_plus_real @ A @ B )
% 0.29/0.52          = ( plus_plus_real @ A @ C ) )
% 0.29/0.52        = ( B = C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add.left_cancel
% 0.29/0.52  thf(fact_1281_add_Oleft__cancel,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat] :
% 0.29/0.52        ( ( ( plus_plus_rat @ A @ B )
% 0.29/0.52          = ( plus_plus_rat @ A @ C ) )
% 0.29/0.52        = ( B = C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add.left_cancel
% 0.29/0.52  thf(fact_1282_add_Oleft__cancel,axiom,
% 0.29/0.52      ! [A: int,B: int,C: int] :
% 0.29/0.52        ( ( ( plus_plus_int @ A @ B )
% 0.29/0.52          = ( plus_plus_int @ A @ C ) )
% 0.29/0.52        = ( B = C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add.left_cancel
% 0.29/0.52  thf(fact_1283_add_Oleft__cancel,axiom,
% 0.29/0.52      ! [A: complex,B: complex,C: complex] :
% 0.29/0.52        ( ( ( plus_plus_complex @ A @ B )
% 0.29/0.52          = ( plus_plus_complex @ A @ C ) )
% 0.29/0.52        = ( B = C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add.left_cancel
% 0.29/0.52  thf(fact_1284_add_Oright__cancel,axiom,
% 0.29/0.52      ! [B: real,A: real,C: real] :
% 0.29/0.52        ( ( ( plus_plus_real @ B @ A )
% 0.29/0.52          = ( plus_plus_real @ C @ A ) )
% 0.29/0.52        = ( B = C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add.right_cancel
% 0.29/0.52  thf(fact_1285_add_Oright__cancel,axiom,
% 0.29/0.52      ! [B: rat,A: rat,C: rat] :
% 0.29/0.52        ( ( ( plus_plus_rat @ B @ A )
% 0.29/0.52          = ( plus_plus_rat @ C @ A ) )
% 0.29/0.52        = ( B = C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add.right_cancel
% 0.29/0.52  thf(fact_1286_add_Oright__cancel,axiom,
% 0.29/0.52      ! [B: int,A: int,C: int] :
% 0.29/0.52        ( ( ( plus_plus_int @ B @ A )
% 0.29/0.52          = ( plus_plus_int @ C @ A ) )
% 0.29/0.52        = ( B = C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add.right_cancel
% 0.29/0.52  thf(fact_1287_add_Oright__cancel,axiom,
% 0.29/0.52      ! [B: complex,A: complex,C: complex] :
% 0.29/0.52        ( ( ( plus_plus_complex @ B @ A )
% 0.29/0.52          = ( plus_plus_complex @ C @ A ) )
% 0.29/0.52        = ( B = C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add.right_cancel
% 0.29/0.52  thf(fact_1288_add_Ocommute,axiom,
% 0.29/0.52      ( plus_plus_real
% 0.29/0.52      = ( ^ [A3: real,B4: real] : ( plus_plus_real @ B4 @ A3 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add.commute
% 0.29/0.52  thf(fact_1289_add_Ocommute,axiom,
% 0.29/0.52      ( plus_plus_rat
% 0.29/0.52      = ( ^ [A3: rat,B4: rat] : ( plus_plus_rat @ B4 @ A3 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add.commute
% 0.29/0.52  thf(fact_1290_add_Ocommute,axiom,
% 0.29/0.52      ( plus_plus_nat
% 0.29/0.52      = ( ^ [A3: nat,B4: nat] : ( plus_plus_nat @ B4 @ A3 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add.commute
% 0.29/0.52  thf(fact_1291_add_Ocommute,axiom,
% 0.29/0.52      ( plus_plus_int
% 0.29/0.52      = ( ^ [A3: int,B4: int] : ( plus_plus_int @ B4 @ A3 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add.commute
% 0.29/0.52  thf(fact_1292_add_Ocommute,axiom,
% 0.29/0.52      ( plus_plus_complex
% 0.29/0.52      = ( ^ [A3: complex,B4: complex] : ( plus_plus_complex @ B4 @ A3 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add.commute
% 0.29/0.52  thf(fact_1293_add_Oleft__commute,axiom,
% 0.29/0.52      ! [B: real,A: real,C: real] :
% 0.29/0.52        ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) )
% 0.29/0.52        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add.left_commute
% 0.29/0.52  thf(fact_1294_add_Oleft__commute,axiom,
% 0.29/0.52      ! [B: rat,A: rat,C: rat] :
% 0.29/0.52        ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C ) )
% 0.29/0.52        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add.left_commute
% 0.29/0.52  thf(fact_1295_add_Oleft__commute,axiom,
% 0.29/0.52      ! [B: nat,A: nat,C: nat] :
% 0.29/0.52        ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 0.29/0.52        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add.left_commute
% 0.29/0.52  thf(fact_1296_add_Oleft__commute,axiom,
% 0.29/0.52      ! [B: int,A: int,C: int] :
% 0.29/0.52        ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
% 0.29/0.52        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add.left_commute
% 0.29/0.52  thf(fact_1297_add_Oleft__commute,axiom,
% 0.29/0.52      ! [B: complex,A: complex,C: complex] :
% 0.29/0.52        ( ( plus_plus_complex @ B @ ( plus_plus_complex @ A @ C ) )
% 0.29/0.52        = ( plus_plus_complex @ A @ ( plus_plus_complex @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add.left_commute
% 0.29/0.52  thf(fact_1298_add__left__imp__eq,axiom,
% 0.29/0.52      ! [A: real,B: real,C: real] :
% 0.29/0.52        ( ( ( plus_plus_real @ A @ B )
% 0.29/0.52          = ( plus_plus_real @ A @ C ) )
% 0.29/0.52       => ( B = C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_left_imp_eq
% 0.29/0.52  thf(fact_1299_add__left__imp__eq,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat] :
% 0.29/0.52        ( ( ( plus_plus_rat @ A @ B )
% 0.29/0.52          = ( plus_plus_rat @ A @ C ) )
% 0.29/0.52       => ( B = C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_left_imp_eq
% 0.29/0.52  thf(fact_1300_add__left__imp__eq,axiom,
% 0.29/0.52      ! [A: nat,B: nat,C: nat] :
% 0.29/0.52        ( ( ( plus_plus_nat @ A @ B )
% 0.29/0.52          = ( plus_plus_nat @ A @ C ) )
% 0.29/0.52       => ( B = C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_left_imp_eq
% 0.29/0.52  thf(fact_1301_add__left__imp__eq,axiom,
% 0.29/0.52      ! [A: int,B: int,C: int] :
% 0.29/0.52        ( ( ( plus_plus_int @ A @ B )
% 0.29/0.52          = ( plus_plus_int @ A @ C ) )
% 0.29/0.52       => ( B = C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_left_imp_eq
% 0.29/0.52  thf(fact_1302_add__left__imp__eq,axiom,
% 0.29/0.52      ! [A: complex,B: complex,C: complex] :
% 0.29/0.52        ( ( ( plus_plus_complex @ A @ B )
% 0.29/0.52          = ( plus_plus_complex @ A @ C ) )
% 0.29/0.52       => ( B = C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_left_imp_eq
% 0.29/0.52  thf(fact_1303_add__right__imp__eq,axiom,
% 0.29/0.52      ! [B: real,A: real,C: real] :
% 0.29/0.52        ( ( ( plus_plus_real @ B @ A )
% 0.29/0.52          = ( plus_plus_real @ C @ A ) )
% 0.29/0.52       => ( B = C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_right_imp_eq
% 0.29/0.52  thf(fact_1304_add__right__imp__eq,axiom,
% 0.29/0.52      ! [B: rat,A: rat,C: rat] :
% 0.29/0.52        ( ( ( plus_plus_rat @ B @ A )
% 0.29/0.52          = ( plus_plus_rat @ C @ A ) )
% 0.29/0.52       => ( B = C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_right_imp_eq
% 0.29/0.52  thf(fact_1305_add__right__imp__eq,axiom,
% 0.29/0.52      ! [B: nat,A: nat,C: nat] :
% 0.29/0.52        ( ( ( plus_plus_nat @ B @ A )
% 0.29/0.52          = ( plus_plus_nat @ C @ A ) )
% 0.29/0.52       => ( B = C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_right_imp_eq
% 0.29/0.52  thf(fact_1306_add__right__imp__eq,axiom,
% 0.29/0.52      ! [B: int,A: int,C: int] :
% 0.29/0.52        ( ( ( plus_plus_int @ B @ A )
% 0.29/0.52          = ( plus_plus_int @ C @ A ) )
% 0.29/0.52       => ( B = C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_right_imp_eq
% 0.29/0.52  thf(fact_1307_add__right__imp__eq,axiom,
% 0.29/0.52      ! [B: complex,A: complex,C: complex] :
% 0.29/0.52        ( ( ( plus_plus_complex @ B @ A )
% 0.29/0.52          = ( plus_plus_complex @ C @ A ) )
% 0.29/0.52       => ( B = C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_right_imp_eq
% 0.29/0.52  thf(fact_1308_diff__right__commute,axiom,
% 0.29/0.52      ! [A: rat,C: rat,B: rat] :
% 0.29/0.52        ( ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B )
% 0.29/0.52        = ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_right_commute
% 0.29/0.52  thf(fact_1309_diff__right__commute,axiom,
% 0.29/0.52      ! [A: nat,C: nat,B: nat] :
% 0.29/0.52        ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 0.29/0.52        = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_right_commute
% 0.29/0.52  thf(fact_1310_diff__right__commute,axiom,
% 0.29/0.52      ! [A: int,C: int,B: int] :
% 0.29/0.52        ( ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B )
% 0.29/0.52        = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_right_commute
% 0.29/0.52  thf(fact_1311_diff__eq__diff__eq,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.29/0.52        ( ( ( minus_minus_rat @ A @ B )
% 0.29/0.52          = ( minus_minus_rat @ C @ D2 ) )
% 0.29/0.52       => ( ( A = B )
% 0.29/0.52          = ( C = D2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_eq_diff_eq
% 0.29/0.52  thf(fact_1312_diff__eq__diff__eq,axiom,
% 0.29/0.52      ! [A: int,B: int,C: int,D2: int] :
% 0.29/0.52        ( ( ( minus_minus_int @ A @ B )
% 0.29/0.52          = ( minus_minus_int @ C @ D2 ) )
% 0.29/0.52       => ( ( A = B )
% 0.29/0.52          = ( C = D2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_eq_diff_eq
% 0.29/0.52  thf(fact_1313_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.29/0.52      ! [I2: real,J: real,K: real,L2: real] :
% 0.29/0.52        ( ( ( ord_less_eq_real @ I2 @ J )
% 0.29/0.52          & ( K = L2 ) )
% 0.29/0.52       => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_mono_thms_linordered_semiring(3)
% 0.29/0.52  thf(fact_1314_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.29/0.52      ! [I2: rat,J: rat,K: rat,L2: rat] :
% 0.29/0.52        ( ( ( ord_less_eq_rat @ I2 @ J )
% 0.29/0.52          & ( K = L2 ) )
% 0.29/0.52       => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_mono_thms_linordered_semiring(3)
% 0.29/0.52  thf(fact_1315_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.29/0.52      ! [I2: nat,J: nat,K: nat,L2: nat] :
% 0.29/0.52        ( ( ( ord_less_eq_nat @ I2 @ J )
% 0.29/0.52          & ( K = L2 ) )
% 0.29/0.52       => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_mono_thms_linordered_semiring(3)
% 0.29/0.52  thf(fact_1316_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.29/0.52      ! [I2: int,J: int,K: int,L2: int] :
% 0.29/0.52        ( ( ( ord_less_eq_int @ I2 @ J )
% 0.29/0.52          & ( K = L2 ) )
% 0.29/0.52       => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_mono_thms_linordered_semiring(3)
% 0.29/0.52  thf(fact_1317_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.29/0.52      ! [I2: real,J: real,K: real,L2: real] :
% 0.29/0.52        ( ( ( I2 = J )
% 0.29/0.52          & ( ord_less_eq_real @ K @ L2 ) )
% 0.29/0.52       => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_mono_thms_linordered_semiring(2)
% 0.29/0.52  thf(fact_1318_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.29/0.52      ! [I2: rat,J: rat,K: rat,L2: rat] :
% 0.29/0.52        ( ( ( I2 = J )
% 0.29/0.52          & ( ord_less_eq_rat @ K @ L2 ) )
% 0.29/0.52       => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_mono_thms_linordered_semiring(2)
% 0.29/0.52  thf(fact_1319_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.29/0.52      ! [I2: nat,J: nat,K: nat,L2: nat] :
% 0.29/0.52        ( ( ( I2 = J )
% 0.29/0.52          & ( ord_less_eq_nat @ K @ L2 ) )
% 0.29/0.52       => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_mono_thms_linordered_semiring(2)
% 0.29/0.52  thf(fact_1320_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.29/0.52      ! [I2: int,J: int,K: int,L2: int] :
% 0.29/0.52        ( ( ( I2 = J )
% 0.29/0.52          & ( ord_less_eq_int @ K @ L2 ) )
% 0.29/0.52       => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_mono_thms_linordered_semiring(2)
% 0.29/0.52  thf(fact_1321_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.29/0.52      ! [I2: real,J: real,K: real,L2: real] :
% 0.29/0.52        ( ( ( ord_less_eq_real @ I2 @ J )
% 0.29/0.52          & ( ord_less_eq_real @ K @ L2 ) )
% 0.29/0.52       => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_mono_thms_linordered_semiring(1)
% 0.29/0.52  thf(fact_1322_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.29/0.52      ! [I2: rat,J: rat,K: rat,L2: rat] :
% 0.29/0.52        ( ( ( ord_less_eq_rat @ I2 @ J )
% 0.29/0.52          & ( ord_less_eq_rat @ K @ L2 ) )
% 0.29/0.52       => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_mono_thms_linordered_semiring(1)
% 0.29/0.52  thf(fact_1323_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.29/0.52      ! [I2: nat,J: nat,K: nat,L2: nat] :
% 0.29/0.52        ( ( ( ord_less_eq_nat @ I2 @ J )
% 0.29/0.52          & ( ord_less_eq_nat @ K @ L2 ) )
% 0.29/0.52       => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_mono_thms_linordered_semiring(1)
% 0.29/0.52  thf(fact_1324_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.29/0.52      ! [I2: int,J: int,K: int,L2: int] :
% 0.29/0.52        ( ( ( ord_less_eq_int @ I2 @ J )
% 0.29/0.52          & ( ord_less_eq_int @ K @ L2 ) )
% 0.29/0.52       => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_mono_thms_linordered_semiring(1)
% 0.29/0.52  thf(fact_1325_add__mono,axiom,
% 0.29/0.52      ! [A: real,B: real,C: real,D2: real] :
% 0.29/0.52        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.52       => ( ( ord_less_eq_real @ C @ D2 )
% 0.29/0.52         => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D2 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_mono
% 0.29/0.52  thf(fact_1326_add__mono,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.29/0.52        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.52       => ( ( ord_less_eq_rat @ C @ D2 )
% 0.29/0.52         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_mono
% 0.29/0.52  thf(fact_1327_add__mono,axiom,
% 0.29/0.52      ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.29/0.52        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.52       => ( ( ord_less_eq_nat @ C @ D2 )
% 0.29/0.52         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_mono
% 0.29/0.52  thf(fact_1328_add__mono,axiom,
% 0.29/0.52      ! [A: int,B: int,C: int,D2: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.52       => ( ( ord_less_eq_int @ C @ D2 )
% 0.29/0.52         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_mono
% 0.29/0.52  thf(fact_1329_add__left__mono,axiom,
% 0.29/0.52      ! [A: real,B: real,C: real] :
% 0.29/0.52        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.52       => ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_left_mono
% 0.29/0.52  thf(fact_1330_add__left__mono,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat] :
% 0.29/0.52        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.52       => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_left_mono
% 0.29/0.52  thf(fact_1331_add__left__mono,axiom,
% 0.29/0.52      ! [A: nat,B: nat,C: nat] :
% 0.29/0.52        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.52       => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_left_mono
% 0.29/0.52  thf(fact_1332_add__left__mono,axiom,
% 0.29/0.52      ! [A: int,B: int,C: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.52       => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_left_mono
% 0.29/0.52  thf(fact_1333_less__eqE,axiom,
% 0.29/0.52      ! [A: nat,B: nat] :
% 0.29/0.52        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.52       => ~ ! [C2: nat] :
% 0.29/0.52              ( B
% 0.29/0.52             != ( plus_plus_nat @ A @ C2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % less_eqE
% 0.29/0.52  thf(fact_1334_add__right__mono,axiom,
% 0.29/0.52      ! [A: real,B: real,C: real] :
% 0.29/0.52        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.52       => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_right_mono
% 0.29/0.52  thf(fact_1335_add__right__mono,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat] :
% 0.29/0.52        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.52       => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_right_mono
% 0.29/0.52  thf(fact_1336_add__right__mono,axiom,
% 0.29/0.52      ! [A: nat,B: nat,C: nat] :
% 0.29/0.52        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.52       => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_right_mono
% 0.29/0.52  thf(fact_1337_add__right__mono,axiom,
% 0.29/0.52      ! [A: int,B: int,C: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.52       => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_right_mono
% 0.29/0.52  thf(fact_1338_le__iff__add,axiom,
% 0.29/0.52      ( ord_less_eq_nat
% 0.29/0.52      = ( ^ [A3: nat,B4: nat] :
% 0.29/0.52          ? [C3: nat] :
% 0.29/0.52            ( B4
% 0.29/0.52            = ( plus_plus_nat @ A3 @ C3 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % le_iff_add
% 0.29/0.52  thf(fact_1339_add__le__imp__le__left,axiom,
% 0.29/0.52      ! [C: real,A: real,B: real] :
% 0.29/0.52        ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 0.29/0.52       => ( ord_less_eq_real @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_le_imp_le_left
% 0.29/0.52  thf(fact_1340_add__le__imp__le__left,axiom,
% 0.29/0.52      ! [C: rat,A: rat,B: rat] :
% 0.29/0.52        ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.29/0.52       => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_le_imp_le_left
% 0.29/0.52  thf(fact_1341_add__le__imp__le__left,axiom,
% 0.29/0.52      ! [C: nat,A: nat,B: nat] :
% 0.29/0.52        ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.29/0.52       => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_le_imp_le_left
% 0.29/0.52  thf(fact_1342_add__le__imp__le__left,axiom,
% 0.29/0.52      ! [C: int,A: int,B: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.29/0.52       => ( ord_less_eq_int @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_le_imp_le_left
% 0.29/0.52  thf(fact_1343_add__le__imp__le__right,axiom,
% 0.29/0.52      ! [A: real,C: real,B: real] :
% 0.29/0.52        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 0.29/0.52       => ( ord_less_eq_real @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_le_imp_le_right
% 0.29/0.52  thf(fact_1344_add__le__imp__le__right,axiom,
% 0.29/0.52      ! [A: rat,C: rat,B: rat] :
% 0.29/0.52        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.29/0.52       => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_le_imp_le_right
% 0.29/0.52  thf(fact_1345_add__le__imp__le__right,axiom,
% 0.29/0.52      ! [A: nat,C: nat,B: nat] :
% 0.29/0.52        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.29/0.52       => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_le_imp_le_right
% 0.29/0.52  thf(fact_1346_add__le__imp__le__right,axiom,
% 0.29/0.52      ! [A: int,C: int,B: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.29/0.52       => ( ord_less_eq_int @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_le_imp_le_right
% 0.29/0.52  thf(fact_1347_add__mono__thms__linordered__field_I5_J,axiom,
% 0.29/0.52      ! [I2: real,J: real,K: real,L2: real] :
% 0.29/0.52        ( ( ( ord_less_real @ I2 @ J )
% 0.29/0.52          & ( ord_less_real @ K @ L2 ) )
% 0.29/0.52       => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_mono_thms_linordered_field(5)
% 0.29/0.52  thf(fact_1348_add__mono__thms__linordered__field_I5_J,axiom,
% 0.29/0.52      ! [I2: rat,J: rat,K: rat,L2: rat] :
% 0.29/0.52        ( ( ( ord_less_rat @ I2 @ J )
% 0.29/0.52          & ( ord_less_rat @ K @ L2 ) )
% 0.29/0.52       => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_mono_thms_linordered_field(5)
% 0.29/0.52  thf(fact_1349_add__mono__thms__linordered__field_I5_J,axiom,
% 0.29/0.52      ! [I2: nat,J: nat,K: nat,L2: nat] :
% 0.29/0.52        ( ( ( ord_less_nat @ I2 @ J )
% 0.29/0.52          & ( ord_less_nat @ K @ L2 ) )
% 0.29/0.52       => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_mono_thms_linordered_field(5)
% 0.29/0.52  thf(fact_1350_add__mono__thms__linordered__field_I5_J,axiom,
% 0.29/0.52      ! [I2: int,J: int,K: int,L2: int] :
% 0.29/0.52        ( ( ( ord_less_int @ I2 @ J )
% 0.29/0.52          & ( ord_less_int @ K @ L2 ) )
% 0.29/0.52       => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_mono_thms_linordered_field(5)
% 0.29/0.52  thf(fact_1351_add__mono__thms__linordered__field_I2_J,axiom,
% 0.29/0.52      ! [I2: real,J: real,K: real,L2: real] :
% 0.29/0.52        ( ( ( I2 = J )
% 0.29/0.52          & ( ord_less_real @ K @ L2 ) )
% 0.29/0.52       => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_mono_thms_linordered_field(2)
% 0.29/0.52  thf(fact_1352_add__mono__thms__linordered__field_I2_J,axiom,
% 0.29/0.52      ! [I2: rat,J: rat,K: rat,L2: rat] :
% 0.29/0.52        ( ( ( I2 = J )
% 0.29/0.52          & ( ord_less_rat @ K @ L2 ) )
% 0.29/0.52       => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_mono_thms_linordered_field(2)
% 0.29/0.52  thf(fact_1353_add__mono__thms__linordered__field_I2_J,axiom,
% 0.29/0.52      ! [I2: nat,J: nat,K: nat,L2: nat] :
% 0.29/0.52        ( ( ( I2 = J )
% 0.29/0.52          & ( ord_less_nat @ K @ L2 ) )
% 0.29/0.52       => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_mono_thms_linordered_field(2)
% 0.29/0.52  thf(fact_1354_add__mono__thms__linordered__field_I2_J,axiom,
% 0.29/0.52      ! [I2: int,J: int,K: int,L2: int] :
% 0.29/0.52        ( ( ( I2 = J )
% 0.29/0.52          & ( ord_less_int @ K @ L2 ) )
% 0.29/0.52       => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_mono_thms_linordered_field(2)
% 0.29/0.52  thf(fact_1355_add__mono__thms__linordered__field_I1_J,axiom,
% 0.29/0.52      ! [I2: real,J: real,K: real,L2: real] :
% 0.29/0.52        ( ( ( ord_less_real @ I2 @ J )
% 0.29/0.52          & ( K = L2 ) )
% 0.29/0.52       => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_mono_thms_linordered_field(1)
% 0.29/0.52  thf(fact_1356_add__mono__thms__linordered__field_I1_J,axiom,
% 0.29/0.52      ! [I2: rat,J: rat,K: rat,L2: rat] :
% 0.29/0.52        ( ( ( ord_less_rat @ I2 @ J )
% 0.29/0.52          & ( K = L2 ) )
% 0.29/0.52       => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_mono_thms_linordered_field(1)
% 0.29/0.52  thf(fact_1357_add__mono__thms__linordered__field_I1_J,axiom,
% 0.29/0.52      ! [I2: nat,J: nat,K: nat,L2: nat] :
% 0.29/0.52        ( ( ( ord_less_nat @ I2 @ J )
% 0.29/0.52          & ( K = L2 ) )
% 0.29/0.52       => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_mono_thms_linordered_field(1)
% 0.29/0.52  thf(fact_1358_add__mono__thms__linordered__field_I1_J,axiom,
% 0.29/0.52      ! [I2: int,J: int,K: int,L2: int] :
% 0.29/0.52        ( ( ( ord_less_int @ I2 @ J )
% 0.29/0.52          & ( K = L2 ) )
% 0.29/0.52       => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_mono_thms_linordered_field(1)
% 0.29/0.52  thf(fact_1359_add__strict__mono,axiom,
% 0.29/0.52      ! [A: real,B: real,C: real,D2: real] :
% 0.29/0.52        ( ( ord_less_real @ A @ B )
% 0.29/0.52       => ( ( ord_less_real @ C @ D2 )
% 0.29/0.52         => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D2 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_strict_mono
% 0.29/0.52  thf(fact_1360_add__strict__mono,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.29/0.52        ( ( ord_less_rat @ A @ B )
% 0.29/0.52       => ( ( ord_less_rat @ C @ D2 )
% 0.29/0.52         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_strict_mono
% 0.29/0.52  thf(fact_1361_add__strict__mono,axiom,
% 0.29/0.52      ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.29/0.52        ( ( ord_less_nat @ A @ B )
% 0.29/0.52       => ( ( ord_less_nat @ C @ D2 )
% 0.29/0.52         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_strict_mono
% 0.29/0.52  thf(fact_1362_add__strict__mono,axiom,
% 0.29/0.52      ! [A: int,B: int,C: int,D2: int] :
% 0.29/0.52        ( ( ord_less_int @ A @ B )
% 0.29/0.52       => ( ( ord_less_int @ C @ D2 )
% 0.29/0.52         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_strict_mono
% 0.29/0.52  thf(fact_1363_add__strict__left__mono,axiom,
% 0.29/0.52      ! [A: real,B: real,C: real] :
% 0.29/0.52        ( ( ord_less_real @ A @ B )
% 0.29/0.52       => ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_strict_left_mono
% 0.29/0.52  thf(fact_1364_add__strict__left__mono,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat] :
% 0.29/0.52        ( ( ord_less_rat @ A @ B )
% 0.29/0.52       => ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_strict_left_mono
% 0.29/0.52  thf(fact_1365_add__strict__left__mono,axiom,
% 0.29/0.52      ! [A: nat,B: nat,C: nat] :
% 0.29/0.52        ( ( ord_less_nat @ A @ B )
% 0.29/0.52       => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_strict_left_mono
% 0.29/0.52  thf(fact_1366_add__strict__left__mono,axiom,
% 0.29/0.52      ! [A: int,B: int,C: int] :
% 0.29/0.52        ( ( ord_less_int @ A @ B )
% 0.29/0.52       => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_strict_left_mono
% 0.29/0.52  thf(fact_1367_add__strict__right__mono,axiom,
% 0.29/0.52      ! [A: real,B: real,C: real] :
% 0.29/0.52        ( ( ord_less_real @ A @ B )
% 0.29/0.52       => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_strict_right_mono
% 0.29/0.52  thf(fact_1368_add__strict__right__mono,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat] :
% 0.29/0.52        ( ( ord_less_rat @ A @ B )
% 0.29/0.52       => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_strict_right_mono
% 0.29/0.52  thf(fact_1369_add__strict__right__mono,axiom,
% 0.29/0.52      ! [A: nat,B: nat,C: nat] :
% 0.29/0.52        ( ( ord_less_nat @ A @ B )
% 0.29/0.52       => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_strict_right_mono
% 0.29/0.52  thf(fact_1370_add__strict__right__mono,axiom,
% 0.29/0.52      ! [A: int,B: int,C: int] :
% 0.29/0.52        ( ( ord_less_int @ A @ B )
% 0.29/0.52       => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_strict_right_mono
% 0.29/0.52  thf(fact_1371_add__less__imp__less__left,axiom,
% 0.29/0.52      ! [C: real,A: real,B: real] :
% 0.29/0.52        ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 0.29/0.52       => ( ord_less_real @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_less_imp_less_left
% 0.29/0.52  thf(fact_1372_add__less__imp__less__left,axiom,
% 0.29/0.52      ! [C: rat,A: rat,B: rat] :
% 0.29/0.52        ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.29/0.52       => ( ord_less_rat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_less_imp_less_left
% 0.29/0.52  thf(fact_1373_add__less__imp__less__left,axiom,
% 0.29/0.52      ! [C: nat,A: nat,B: nat] :
% 0.29/0.52        ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.29/0.52       => ( ord_less_nat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_less_imp_less_left
% 0.29/0.52  thf(fact_1374_add__less__imp__less__left,axiom,
% 0.29/0.52      ! [C: int,A: int,B: int] :
% 0.29/0.52        ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.29/0.52       => ( ord_less_int @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_less_imp_less_left
% 0.29/0.52  thf(fact_1375_add__less__imp__less__right,axiom,
% 0.29/0.52      ! [A: real,C: real,B: real] :
% 0.29/0.52        ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 0.29/0.52       => ( ord_less_real @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_less_imp_less_right
% 0.29/0.52  thf(fact_1376_add__less__imp__less__right,axiom,
% 0.29/0.52      ! [A: rat,C: rat,B: rat] :
% 0.29/0.52        ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.29/0.52       => ( ord_less_rat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_less_imp_less_right
% 0.29/0.52  thf(fact_1377_add__less__imp__less__right,axiom,
% 0.29/0.52      ! [A: nat,C: nat,B: nat] :
% 0.29/0.52        ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.29/0.52       => ( ord_less_nat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_less_imp_less_right
% 0.29/0.52  thf(fact_1378_add__less__imp__less__right,axiom,
% 0.29/0.52      ! [A: int,C: int,B: int] :
% 0.29/0.52        ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.29/0.52       => ( ord_less_int @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_less_imp_less_right
% 0.29/0.52  thf(fact_1379_diff__eq__diff__less__eq,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.29/0.52        ( ( ( minus_minus_rat @ A @ B )
% 0.29/0.52          = ( minus_minus_rat @ C @ D2 ) )
% 0.29/0.52       => ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.52          = ( ord_less_eq_rat @ C @ D2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_eq_diff_less_eq
% 0.29/0.52  thf(fact_1380_diff__eq__diff__less__eq,axiom,
% 0.29/0.52      ! [A: int,B: int,C: int,D2: int] :
% 0.29/0.52        ( ( ( minus_minus_int @ A @ B )
% 0.29/0.52          = ( minus_minus_int @ C @ D2 ) )
% 0.29/0.52       => ( ( ord_less_eq_int @ A @ B )
% 0.29/0.52          = ( ord_less_eq_int @ C @ D2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_eq_diff_less_eq
% 0.29/0.52  thf(fact_1381_diff__right__mono,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat] :
% 0.29/0.52        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.52       => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_right_mono
% 0.29/0.52  thf(fact_1382_diff__right__mono,axiom,
% 0.29/0.52      ! [A: int,B: int,C: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.52       => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_right_mono
% 0.29/0.52  thf(fact_1383_diff__left__mono,axiom,
% 0.29/0.52      ! [B: rat,A: rat,C: rat] :
% 0.29/0.52        ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.52       => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_left_mono
% 0.29/0.52  thf(fact_1384_diff__left__mono,axiom,
% 0.29/0.52      ! [B: int,A: int,C: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ B @ A )
% 0.29/0.52       => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_left_mono
% 0.29/0.52  thf(fact_1385_diff__mono,axiom,
% 0.29/0.52      ! [A: rat,B: rat,D2: rat,C: rat] :
% 0.29/0.52        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.52       => ( ( ord_less_eq_rat @ D2 @ C )
% 0.29/0.52         => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D2 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_mono
% 0.29/0.52  thf(fact_1386_diff__mono,axiom,
% 0.29/0.52      ! [A: int,B: int,D2: int,C: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.52       => ( ( ord_less_eq_int @ D2 @ C )
% 0.29/0.52         => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D2 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_mono
% 0.29/0.52  thf(fact_1387_diff__strict__right__mono,axiom,
% 0.29/0.52      ! [A: real,B: real,C: real] :
% 0.29/0.52        ( ( ord_less_real @ A @ B )
% 0.29/0.52       => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_strict_right_mono
% 0.29/0.52  thf(fact_1388_diff__strict__right__mono,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat] :
% 0.29/0.52        ( ( ord_less_rat @ A @ B )
% 0.29/0.52       => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_strict_right_mono
% 0.29/0.52  thf(fact_1389_diff__strict__right__mono,axiom,
% 0.29/0.52      ! [A: int,B: int,C: int] :
% 0.29/0.52        ( ( ord_less_int @ A @ B )
% 0.29/0.52       => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_strict_right_mono
% 0.29/0.52  thf(fact_1390_diff__strict__left__mono,axiom,
% 0.29/0.52      ! [B: real,A: real,C: real] :
% 0.29/0.52        ( ( ord_less_real @ B @ A )
% 0.29/0.52       => ( ord_less_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_strict_left_mono
% 0.29/0.52  thf(fact_1391_diff__strict__left__mono,axiom,
% 0.29/0.52      ! [B: rat,A: rat,C: rat] :
% 0.29/0.52        ( ( ord_less_rat @ B @ A )
% 0.29/0.52       => ( ord_less_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_strict_left_mono
% 0.29/0.52  thf(fact_1392_diff__strict__left__mono,axiom,
% 0.29/0.52      ! [B: int,A: int,C: int] :
% 0.29/0.52        ( ( ord_less_int @ B @ A )
% 0.29/0.52       => ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_strict_left_mono
% 0.29/0.52  thf(fact_1393_diff__eq__diff__less,axiom,
% 0.29/0.52      ! [A: real,B: real,C: real,D2: real] :
% 0.29/0.52        ( ( ( minus_minus_real @ A @ B )
% 0.29/0.52          = ( minus_minus_real @ C @ D2 ) )
% 0.29/0.52       => ( ( ord_less_real @ A @ B )
% 0.29/0.52          = ( ord_less_real @ C @ D2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_eq_diff_less
% 0.29/0.52  thf(fact_1394_diff__eq__diff__less,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.29/0.52        ( ( ( minus_minus_rat @ A @ B )
% 0.29/0.52          = ( minus_minus_rat @ C @ D2 ) )
% 0.29/0.52       => ( ( ord_less_rat @ A @ B )
% 0.29/0.52          = ( ord_less_rat @ C @ D2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_eq_diff_less
% 0.29/0.52  thf(fact_1395_diff__eq__diff__less,axiom,
% 0.29/0.52      ! [A: int,B: int,C: int,D2: int] :
% 0.29/0.52        ( ( ( minus_minus_int @ A @ B )
% 0.29/0.52          = ( minus_minus_int @ C @ D2 ) )
% 0.29/0.52       => ( ( ord_less_int @ A @ B )
% 0.29/0.52          = ( ord_less_int @ C @ D2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_eq_diff_less
% 0.29/0.52  thf(fact_1396_diff__strict__mono,axiom,
% 0.29/0.52      ! [A: real,B: real,D2: real,C: real] :
% 0.29/0.52        ( ( ord_less_real @ A @ B )
% 0.29/0.52       => ( ( ord_less_real @ D2 @ C )
% 0.29/0.52         => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D2 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_strict_mono
% 0.29/0.52  thf(fact_1397_diff__strict__mono,axiom,
% 0.29/0.52      ! [A: rat,B: rat,D2: rat,C: rat] :
% 0.29/0.52        ( ( ord_less_rat @ A @ B )
% 0.29/0.52       => ( ( ord_less_rat @ D2 @ C )
% 0.29/0.52         => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D2 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_strict_mono
% 0.29/0.52  thf(fact_1398_diff__strict__mono,axiom,
% 0.29/0.52      ! [A: int,B: int,D2: int,C: int] :
% 0.29/0.52        ( ( ord_less_int @ A @ B )
% 0.29/0.52       => ( ( ord_less_int @ D2 @ C )
% 0.29/0.52         => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D2 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_strict_mono
% 0.29/0.52  thf(fact_1399_comm__monoid__mult__class_Omult__1,axiom,
% 0.29/0.52      ! [A: rat] :
% 0.29/0.52        ( ( times_times_rat @ one_one_rat @ A )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % comm_monoid_mult_class.mult_1
% 0.29/0.52  thf(fact_1400_comm__monoid__mult__class_Omult__1,axiom,
% 0.29/0.52      ! [A: complex] :
% 0.29/0.52        ( ( times_times_complex @ one_one_complex @ A )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % comm_monoid_mult_class.mult_1
% 0.29/0.52  thf(fact_1401_comm__monoid__mult__class_Omult__1,axiom,
% 0.29/0.52      ! [A: real] :
% 0.29/0.52        ( ( times_times_real @ one_one_real @ A )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % comm_monoid_mult_class.mult_1
% 0.29/0.52  thf(fact_1402_comm__monoid__mult__class_Omult__1,axiom,
% 0.29/0.52      ! [A: nat] :
% 0.29/0.52        ( ( times_times_nat @ one_one_nat @ A )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % comm_monoid_mult_class.mult_1
% 0.29/0.52  thf(fact_1403_comm__monoid__mult__class_Omult__1,axiom,
% 0.29/0.52      ! [A: int] :
% 0.29/0.52        ( ( times_times_int @ one_one_int @ A )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % comm_monoid_mult_class.mult_1
% 0.29/0.52  thf(fact_1404_mult_Ocomm__neutral,axiom,
% 0.29/0.52      ! [A: rat] :
% 0.29/0.52        ( ( times_times_rat @ A @ one_one_rat )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % mult.comm_neutral
% 0.29/0.52  thf(fact_1405_mult_Ocomm__neutral,axiom,
% 0.29/0.52      ! [A: complex] :
% 0.29/0.52        ( ( times_times_complex @ A @ one_one_complex )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % mult.comm_neutral
% 0.29/0.52  thf(fact_1406_mult_Ocomm__neutral,axiom,
% 0.29/0.52      ! [A: real] :
% 0.29/0.52        ( ( times_times_real @ A @ one_one_real )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % mult.comm_neutral
% 0.29/0.52  thf(fact_1407_mult_Ocomm__neutral,axiom,
% 0.29/0.52      ! [A: nat] :
% 0.29/0.52        ( ( times_times_nat @ A @ one_one_nat )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % mult.comm_neutral
% 0.29/0.52  thf(fact_1408_mult_Ocomm__neutral,axiom,
% 0.29/0.52      ! [A: int] :
% 0.29/0.52        ( ( times_times_int @ A @ one_one_int )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % mult.comm_neutral
% 0.29/0.52  thf(fact_1409_divide__divide__eq__left_H,axiom,
% 0.29/0.52      ! [A: complex,B: complex,C: complex] :
% 0.29/0.52        ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 0.29/0.52        = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ C @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_divide_eq_left'
% 0.29/0.52  thf(fact_1410_divide__divide__eq__left_H,axiom,
% 0.29/0.52      ! [A: real,B: real,C: real] :
% 0.29/0.52        ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 0.29/0.52        = ( divide_divide_real @ A @ ( times_times_real @ C @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_divide_eq_left'
% 0.29/0.52  thf(fact_1411_divide__divide__eq__left_H,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat] :
% 0.29/0.52        ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 0.29/0.52        = ( divide_divide_rat @ A @ ( times_times_rat @ C @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_divide_eq_left'
% 0.29/0.52  thf(fact_1412_divide__divide__times__eq,axiom,
% 0.29/0.52      ! [X: complex,Y2: complex,Z: complex,W: complex] :
% 0.29/0.52        ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ X @ Y2 ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 0.29/0.52        = ( divide1717551699836669952omplex @ ( times_times_complex @ X @ W ) @ ( times_times_complex @ Y2 @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_divide_times_eq
% 0.29/0.52  thf(fact_1413_divide__divide__times__eq,axiom,
% 0.29/0.52      ! [X: real,Y2: real,Z: real,W: real] :
% 0.29/0.52        ( ( divide_divide_real @ ( divide_divide_real @ X @ Y2 ) @ ( divide_divide_real @ Z @ W ) )
% 0.29/0.52        = ( divide_divide_real @ ( times_times_real @ X @ W ) @ ( times_times_real @ Y2 @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_divide_times_eq
% 0.29/0.52  thf(fact_1414_divide__divide__times__eq,axiom,
% 0.29/0.52      ! [X: rat,Y2: rat,Z: rat,W: rat] :
% 0.29/0.52        ( ( divide_divide_rat @ ( divide_divide_rat @ X @ Y2 ) @ ( divide_divide_rat @ Z @ W ) )
% 0.29/0.52        = ( divide_divide_rat @ ( times_times_rat @ X @ W ) @ ( times_times_rat @ Y2 @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_divide_times_eq
% 0.29/0.52  thf(fact_1415_times__divide__times__eq,axiom,
% 0.29/0.52      ! [X: complex,Y2: complex,Z: complex,W: complex] :
% 0.29/0.52        ( ( times_times_complex @ ( divide1717551699836669952omplex @ X @ Y2 ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 0.29/0.52        = ( divide1717551699836669952omplex @ ( times_times_complex @ X @ Z ) @ ( times_times_complex @ Y2 @ W ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % times_divide_times_eq
% 0.29/0.52  thf(fact_1416_times__divide__times__eq,axiom,
% 0.29/0.52      ! [X: real,Y2: real,Z: real,W: real] :
% 0.29/0.52        ( ( times_times_real @ ( divide_divide_real @ X @ Y2 ) @ ( divide_divide_real @ Z @ W ) )
% 0.29/0.52        = ( divide_divide_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y2 @ W ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % times_divide_times_eq
% 0.29/0.52  thf(fact_1417_times__divide__times__eq,axiom,
% 0.29/0.52      ! [X: rat,Y2: rat,Z: rat,W: rat] :
% 0.29/0.52        ( ( times_times_rat @ ( divide_divide_rat @ X @ Y2 ) @ ( divide_divide_rat @ Z @ W ) )
% 0.29/0.52        = ( divide_divide_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y2 @ W ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % times_divide_times_eq
% 0.29/0.52  thf(fact_1418_group__cancel_Osub1,axiom,
% 0.29/0.52      ! [A2: real,K: real,A: real,B: real] :
% 0.29/0.52        ( ( A2
% 0.29/0.52          = ( plus_plus_real @ K @ A ) )
% 0.29/0.52       => ( ( minus_minus_real @ A2 @ B )
% 0.29/0.52          = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % group_cancel.sub1
% 0.29/0.52  thf(fact_1419_group__cancel_Osub1,axiom,
% 0.29/0.52      ! [A2: complex,K: complex,A: complex,B: complex] :
% 0.29/0.52        ( ( A2
% 0.29/0.52          = ( plus_plus_complex @ K @ A ) )
% 0.29/0.52       => ( ( minus_minus_complex @ A2 @ B )
% 0.29/0.52          = ( plus_plus_complex @ K @ ( minus_minus_complex @ A @ B ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % group_cancel.sub1
% 0.29/0.52  thf(fact_1420_group__cancel_Osub1,axiom,
% 0.29/0.52      ! [A2: rat,K: rat,A: rat,B: rat] :
% 0.29/0.52        ( ( A2
% 0.29/0.52          = ( plus_plus_rat @ K @ A ) )
% 0.29/0.52       => ( ( minus_minus_rat @ A2 @ B )
% 0.29/0.52          = ( plus_plus_rat @ K @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % group_cancel.sub1
% 0.29/0.52  thf(fact_1421_group__cancel_Osub1,axiom,
% 0.29/0.52      ! [A2: int,K: int,A: int,B: int] :
% 0.29/0.52        ( ( A2
% 0.29/0.52          = ( plus_plus_int @ K @ A ) )
% 0.29/0.52       => ( ( minus_minus_int @ A2 @ B )
% 0.29/0.52          = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % group_cancel.sub1
% 0.29/0.52  thf(fact_1422_diff__eq__eq,axiom,
% 0.29/0.52      ! [A: real,B: real,C: real] :
% 0.29/0.52        ( ( ( minus_minus_real @ A @ B )
% 0.29/0.52          = C )
% 0.29/0.52        = ( A
% 0.29/0.52          = ( plus_plus_real @ C @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_eq_eq
% 0.29/0.52  thf(fact_1423_diff__eq__eq,axiom,
% 0.29/0.52      ! [A: complex,B: complex,C: complex] :
% 0.29/0.52        ( ( ( minus_minus_complex @ A @ B )
% 0.29/0.52          = C )
% 0.29/0.52        = ( A
% 0.29/0.52          = ( plus_plus_complex @ C @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_eq_eq
% 0.29/0.52  thf(fact_1424_diff__eq__eq,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat] :
% 0.29/0.52        ( ( ( minus_minus_rat @ A @ B )
% 0.29/0.52          = C )
% 0.29/0.52        = ( A
% 0.29/0.52          = ( plus_plus_rat @ C @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_eq_eq
% 0.29/0.52  thf(fact_1425_diff__eq__eq,axiom,
% 0.29/0.52      ! [A: int,B: int,C: int] :
% 0.29/0.52        ( ( ( minus_minus_int @ A @ B )
% 0.29/0.52          = C )
% 0.29/0.52        = ( A
% 0.29/0.52          = ( plus_plus_int @ C @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_eq_eq
% 0.29/0.52  thf(fact_1426_eq__diff__eq,axiom,
% 0.29/0.52      ! [A: real,C: real,B: real] :
% 0.29/0.52        ( ( A
% 0.29/0.52          = ( minus_minus_real @ C @ B ) )
% 0.29/0.52        = ( ( plus_plus_real @ A @ B )
% 0.29/0.52          = C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % eq_diff_eq
% 0.29/0.52  thf(fact_1427_eq__diff__eq,axiom,
% 0.29/0.52      ! [A: complex,C: complex,B: complex] :
% 0.29/0.52        ( ( A
% 0.29/0.52          = ( minus_minus_complex @ C @ B ) )
% 0.29/0.52        = ( ( plus_plus_complex @ A @ B )
% 0.29/0.52          = C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % eq_diff_eq
% 0.29/0.52  thf(fact_1428_eq__diff__eq,axiom,
% 0.29/0.52      ! [A: rat,C: rat,B: rat] :
% 0.29/0.52        ( ( A
% 0.29/0.52          = ( minus_minus_rat @ C @ B ) )
% 0.29/0.52        = ( ( plus_plus_rat @ A @ B )
% 0.29/0.52          = C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % eq_diff_eq
% 0.29/0.52  thf(fact_1429_eq__diff__eq,axiom,
% 0.29/0.52      ! [A: int,C: int,B: int] :
% 0.29/0.52        ( ( A
% 0.29/0.52          = ( minus_minus_int @ C @ B ) )
% 0.29/0.52        = ( ( plus_plus_int @ A @ B )
% 0.29/0.52          = C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % eq_diff_eq
% 0.29/0.52  thf(fact_1430_add__diff__eq,axiom,
% 0.29/0.52      ! [A: real,B: real,C: real] :
% 0.29/0.52        ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
% 0.29/0.52        = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_diff_eq
% 0.29/0.52  thf(fact_1431_add__diff__eq,axiom,
% 0.29/0.52      ! [A: complex,B: complex,C: complex] :
% 0.29/0.52        ( ( plus_plus_complex @ A @ ( minus_minus_complex @ B @ C ) )
% 0.29/0.52        = ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_diff_eq
% 0.29/0.52  thf(fact_1432_add__diff__eq,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat] :
% 0.29/0.52        ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 0.29/0.52        = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_diff_eq
% 0.29/0.52  thf(fact_1433_add__diff__eq,axiom,
% 0.29/0.52      ! [A: int,B: int,C: int] :
% 0.29/0.52        ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
% 0.29/0.52        = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_diff_eq
% 0.29/0.52  thf(fact_1434_diff__diff__eq2,axiom,
% 0.29/0.52      ! [A: real,B: real,C: real] :
% 0.29/0.52        ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
% 0.29/0.52        = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_diff_eq2
% 0.29/0.52  thf(fact_1435_diff__diff__eq2,axiom,
% 0.29/0.52      ! [A: complex,B: complex,C: complex] :
% 0.29/0.52        ( ( minus_minus_complex @ A @ ( minus_minus_complex @ B @ C ) )
% 0.29/0.52        = ( minus_minus_complex @ ( plus_plus_complex @ A @ C ) @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_diff_eq2
% 0.29/0.52  thf(fact_1436_diff__diff__eq2,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat] :
% 0.29/0.52        ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 0.29/0.52        = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_diff_eq2
% 0.29/0.52  thf(fact_1437_diff__diff__eq2,axiom,
% 0.29/0.52      ! [A: int,B: int,C: int] :
% 0.29/0.52        ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
% 0.29/0.52        = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_diff_eq2
% 0.29/0.52  thf(fact_1438_diff__add__eq,axiom,
% 0.29/0.52      ! [A: real,B: real,C: real] :
% 0.29/0.52        ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.29/0.52        = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_add_eq
% 0.29/0.52  thf(fact_1439_diff__add__eq,axiom,
% 0.29/0.52      ! [A: complex,B: complex,C: complex] :
% 0.29/0.52        ( ( plus_plus_complex @ ( minus_minus_complex @ A @ B ) @ C )
% 0.29/0.52        = ( minus_minus_complex @ ( plus_plus_complex @ A @ C ) @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_add_eq
% 0.29/0.52  thf(fact_1440_diff__add__eq,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat] :
% 0.29/0.52        ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.29/0.52        = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_add_eq
% 0.29/0.52  thf(fact_1441_diff__add__eq,axiom,
% 0.29/0.52      ! [A: int,B: int,C: int] :
% 0.29/0.52        ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.29/0.52        = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_add_eq
% 0.29/0.52  thf(fact_1442_diff__add__eq__diff__diff__swap,axiom,
% 0.29/0.52      ! [A: real,B: real,C: real] :
% 0.29/0.52        ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
% 0.29/0.52        = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_add_eq_diff_diff_swap
% 0.29/0.52  thf(fact_1443_diff__add__eq__diff__diff__swap,axiom,
% 0.29/0.52      ! [A: complex,B: complex,C: complex] :
% 0.29/0.52        ( ( minus_minus_complex @ A @ ( plus_plus_complex @ B @ C ) )
% 0.29/0.52        = ( minus_minus_complex @ ( minus_minus_complex @ A @ C ) @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_add_eq_diff_diff_swap
% 0.29/0.52  thf(fact_1444_diff__add__eq__diff__diff__swap,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat] :
% 0.29/0.52        ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.29/0.52        = ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_add_eq_diff_diff_swap
% 0.29/0.52  thf(fact_1445_diff__add__eq__diff__diff__swap,axiom,
% 0.29/0.52      ! [A: int,B: int,C: int] :
% 0.29/0.52        ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.29/0.52        = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_add_eq_diff_diff_swap
% 0.29/0.52  thf(fact_1446_add__implies__diff,axiom,
% 0.29/0.52      ! [C: real,B: real,A: real] :
% 0.29/0.52        ( ( ( plus_plus_real @ C @ B )
% 0.29/0.52          = A )
% 0.29/0.52       => ( C
% 0.29/0.52          = ( minus_minus_real @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_implies_diff
% 0.29/0.52  thf(fact_1447_add__implies__diff,axiom,
% 0.29/0.52      ! [C: complex,B: complex,A: complex] :
% 0.29/0.52        ( ( ( plus_plus_complex @ C @ B )
% 0.29/0.52          = A )
% 0.29/0.52       => ( C
% 0.29/0.52          = ( minus_minus_complex @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_implies_diff
% 0.29/0.52  thf(fact_1448_add__implies__diff,axiom,
% 0.29/0.52      ! [C: rat,B: rat,A: rat] :
% 0.29/0.52        ( ( ( plus_plus_rat @ C @ B )
% 0.29/0.52          = A )
% 0.29/0.52       => ( C
% 0.29/0.52          = ( minus_minus_rat @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_implies_diff
% 0.29/0.52  thf(fact_1449_add__implies__diff,axiom,
% 0.29/0.52      ! [C: nat,B: nat,A: nat] :
% 0.29/0.52        ( ( ( plus_plus_nat @ C @ B )
% 0.29/0.52          = A )
% 0.29/0.52       => ( C
% 0.29/0.52          = ( minus_minus_nat @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_implies_diff
% 0.29/0.52  thf(fact_1450_add__implies__diff,axiom,
% 0.29/0.52      ! [C: int,B: int,A: int] :
% 0.29/0.52        ( ( ( plus_plus_int @ C @ B )
% 0.29/0.52          = A )
% 0.29/0.52       => ( C
% 0.29/0.52          = ( minus_minus_int @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_implies_diff
% 0.29/0.52  thf(fact_1451_diff__diff__eq,axiom,
% 0.29/0.52      ! [A: real,B: real,C: real] :
% 0.29/0.52        ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.29/0.52        = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_diff_eq
% 0.29/0.52  thf(fact_1452_diff__diff__eq,axiom,
% 0.29/0.52      ! [A: complex,B: complex,C: complex] :
% 0.29/0.52        ( ( minus_minus_complex @ ( minus_minus_complex @ A @ B ) @ C )
% 0.29/0.52        = ( minus_minus_complex @ A @ ( plus_plus_complex @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_diff_eq
% 0.29/0.52  thf(fact_1453_diff__diff__eq,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat] :
% 0.29/0.52        ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.29/0.52        = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_diff_eq
% 0.29/0.52  thf(fact_1454_diff__diff__eq,axiom,
% 0.29/0.52      ! [A: nat,B: nat,C: nat] :
% 0.29/0.52        ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
% 0.29/0.52        = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_diff_eq
% 0.29/0.52  thf(fact_1455_diff__diff__eq,axiom,
% 0.29/0.52      ! [A: int,B: int,C: int] :
% 0.29/0.52        ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.29/0.52        = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_diff_eq
% 0.29/0.52  thf(fact_1456_add__divide__distrib,axiom,
% 0.29/0.52      ! [A: complex,B: complex,C: complex] :
% 0.29/0.52        ( ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ B ) @ C )
% 0.29/0.52        = ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_divide_distrib
% 0.29/0.52  thf(fact_1457_add__divide__distrib,axiom,
% 0.29/0.52      ! [A: real,B: real,C: real] :
% 0.29/0.52        ( ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.29/0.52        = ( plus_plus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_divide_distrib
% 0.29/0.52  thf(fact_1458_add__divide__distrib,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat] :
% 0.29/0.52        ( ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.29/0.52        = ( plus_plus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_divide_distrib
% 0.29/0.52  thf(fact_1459_diff__divide__distrib,axiom,
% 0.29/0.52      ! [A: complex,B: complex,C: complex] :
% 0.29/0.52        ( ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ B ) @ C )
% 0.29/0.52        = ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_divide_distrib
% 0.29/0.52  thf(fact_1460_diff__divide__distrib,axiom,
% 0.29/0.52      ! [A: real,B: real,C: real] :
% 0.29/0.52        ( ( divide_divide_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.29/0.52        = ( minus_minus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_divide_distrib
% 0.29/0.52  thf(fact_1461_diff__divide__distrib,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat] :
% 0.29/0.52        ( ( divide_divide_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.29/0.52        = ( minus_minus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_divide_distrib
% 0.29/0.52  thf(fact_1462_max__add__distrib__left,axiom,
% 0.29/0.52      ! [X: real,Y2: real,Z: real] :
% 0.29/0.52        ( ( plus_plus_real @ ( ord_max_real @ X @ Y2 ) @ Z )
% 0.29/0.52        = ( ord_max_real @ ( plus_plus_real @ X @ Z ) @ ( plus_plus_real @ Y2 @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max_add_distrib_left
% 0.29/0.52  thf(fact_1463_max__add__distrib__left,axiom,
% 0.29/0.52      ! [X: rat,Y2: rat,Z: rat] :
% 0.29/0.52        ( ( plus_plus_rat @ ( ord_max_rat @ X @ Y2 ) @ Z )
% 0.29/0.52        = ( ord_max_rat @ ( plus_plus_rat @ X @ Z ) @ ( plus_plus_rat @ Y2 @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max_add_distrib_left
% 0.29/0.52  thf(fact_1464_max__add__distrib__left,axiom,
% 0.29/0.52      ! [X: nat,Y2: nat,Z: nat] :
% 0.29/0.52        ( ( plus_plus_nat @ ( ord_max_nat @ X @ Y2 ) @ Z )
% 0.29/0.52        = ( ord_max_nat @ ( plus_plus_nat @ X @ Z ) @ ( plus_plus_nat @ Y2 @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max_add_distrib_left
% 0.29/0.52  thf(fact_1465_max__add__distrib__left,axiom,
% 0.29/0.52      ! [X: int,Y2: int,Z: int] :
% 0.29/0.52        ( ( plus_plus_int @ ( ord_max_int @ X @ Y2 ) @ Z )
% 0.29/0.52        = ( ord_max_int @ ( plus_plus_int @ X @ Z ) @ ( plus_plus_int @ Y2 @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max_add_distrib_left
% 0.29/0.52  thf(fact_1466_max__add__distrib__right,axiom,
% 0.29/0.52      ! [X: real,Y2: real,Z: real] :
% 0.29/0.52        ( ( plus_plus_real @ X @ ( ord_max_real @ Y2 @ Z ) )
% 0.29/0.52        = ( ord_max_real @ ( plus_plus_real @ X @ Y2 ) @ ( plus_plus_real @ X @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max_add_distrib_right
% 0.29/0.52  thf(fact_1467_max__add__distrib__right,axiom,
% 0.29/0.52      ! [X: rat,Y2: rat,Z: rat] :
% 0.29/0.52        ( ( plus_plus_rat @ X @ ( ord_max_rat @ Y2 @ Z ) )
% 0.29/0.52        = ( ord_max_rat @ ( plus_plus_rat @ X @ Y2 ) @ ( plus_plus_rat @ X @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max_add_distrib_right
% 0.29/0.52  thf(fact_1468_max__add__distrib__right,axiom,
% 0.29/0.52      ! [X: nat,Y2: nat,Z: nat] :
% 0.29/0.52        ( ( plus_plus_nat @ X @ ( ord_max_nat @ Y2 @ Z ) )
% 0.29/0.52        = ( ord_max_nat @ ( plus_plus_nat @ X @ Y2 ) @ ( plus_plus_nat @ X @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max_add_distrib_right
% 0.29/0.52  thf(fact_1469_max__add__distrib__right,axiom,
% 0.29/0.52      ! [X: int,Y2: int,Z: int] :
% 0.29/0.52        ( ( plus_plus_int @ X @ ( ord_max_int @ Y2 @ Z ) )
% 0.29/0.52        = ( ord_max_int @ ( plus_plus_int @ X @ Y2 ) @ ( plus_plus_int @ X @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max_add_distrib_right
% 0.29/0.52  thf(fact_1470_max__diff__distrib__left,axiom,
% 0.29/0.52      ! [X: rat,Y2: rat,Z: rat] :
% 0.29/0.52        ( ( minus_minus_rat @ ( ord_max_rat @ X @ Y2 ) @ Z )
% 0.29/0.52        = ( ord_max_rat @ ( minus_minus_rat @ X @ Z ) @ ( minus_minus_rat @ Y2 @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max_diff_distrib_left
% 0.29/0.52  thf(fact_1471_max__diff__distrib__left,axiom,
% 0.29/0.52      ! [X: int,Y2: int,Z: int] :
% 0.29/0.52        ( ( minus_minus_int @ ( ord_max_int @ X @ Y2 ) @ Z )
% 0.29/0.52        = ( ord_max_int @ ( minus_minus_int @ X @ Z ) @ ( minus_minus_int @ Y2 @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % max_diff_distrib_left
% 0.29/0.52  thf(fact_1472_add__mono__thms__linordered__field_I4_J,axiom,
% 0.29/0.52      ! [I2: real,J: real,K: real,L2: real] :
% 0.29/0.52        ( ( ( ord_less_eq_real @ I2 @ J )
% 0.29/0.52          & ( ord_less_real @ K @ L2 ) )
% 0.29/0.52       => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_mono_thms_linordered_field(4)
% 0.29/0.52  thf(fact_1473_add__mono__thms__linordered__field_I4_J,axiom,
% 0.29/0.52      ! [I2: rat,J: rat,K: rat,L2: rat] :
% 0.29/0.52        ( ( ( ord_less_eq_rat @ I2 @ J )
% 0.29/0.52          & ( ord_less_rat @ K @ L2 ) )
% 0.29/0.52       => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_mono_thms_linordered_field(4)
% 0.29/0.52  thf(fact_1474_add__mono__thms__linordered__field_I4_J,axiom,
% 0.29/0.52      ! [I2: nat,J: nat,K: nat,L2: nat] :
% 0.29/0.52        ( ( ( ord_less_eq_nat @ I2 @ J )
% 0.29/0.52          & ( ord_less_nat @ K @ L2 ) )
% 0.29/0.52       => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_mono_thms_linordered_field(4)
% 0.29/0.52  thf(fact_1475_add__mono__thms__linordered__field_I4_J,axiom,
% 0.29/0.52      ! [I2: int,J: int,K: int,L2: int] :
% 0.29/0.52        ( ( ( ord_less_eq_int @ I2 @ J )
% 0.29/0.52          & ( ord_less_int @ K @ L2 ) )
% 0.29/0.52       => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_mono_thms_linordered_field(4)
% 0.29/0.52  thf(fact_1476_add__mono__thms__linordered__field_I3_J,axiom,
% 0.29/0.52      ! [I2: real,J: real,K: real,L2: real] :
% 0.29/0.52        ( ( ( ord_less_real @ I2 @ J )
% 0.29/0.53          & ( ord_less_eq_real @ K @ L2 ) )
% 0.29/0.53       => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_mono_thms_linordered_field(3)
% 0.29/0.53  thf(fact_1477_add__mono__thms__linordered__field_I3_J,axiom,
% 0.29/0.53      ! [I2: rat,J: rat,K: rat,L2: rat] :
% 0.29/0.53        ( ( ( ord_less_rat @ I2 @ J )
% 0.29/0.53          & ( ord_less_eq_rat @ K @ L2 ) )
% 0.29/0.53       => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_mono_thms_linordered_field(3)
% 0.29/0.53  thf(fact_1478_add__mono__thms__linordered__field_I3_J,axiom,
% 0.29/0.53      ! [I2: nat,J: nat,K: nat,L2: nat] :
% 0.29/0.53        ( ( ( ord_less_nat @ I2 @ J )
% 0.29/0.53          & ( ord_less_eq_nat @ K @ L2 ) )
% 0.29/0.53       => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_mono_thms_linordered_field(3)
% 0.29/0.53  thf(fact_1479_add__mono__thms__linordered__field_I3_J,axiom,
% 0.29/0.53      ! [I2: int,J: int,K: int,L2: int] :
% 0.29/0.53        ( ( ( ord_less_int @ I2 @ J )
% 0.29/0.53          & ( ord_less_eq_int @ K @ L2 ) )
% 0.29/0.53       => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_mono_thms_linordered_field(3)
% 0.29/0.53  thf(fact_1480_add__le__less__mono,axiom,
% 0.29/0.53      ! [A: real,B: real,C: real,D2: real] :
% 0.29/0.53        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.53       => ( ( ord_less_real @ C @ D2 )
% 0.29/0.53         => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D2 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_le_less_mono
% 0.29/0.53  thf(fact_1481_add__le__less__mono,axiom,
% 0.29/0.53      ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.29/0.53        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.53       => ( ( ord_less_rat @ C @ D2 )
% 0.29/0.53         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_le_less_mono
% 0.29/0.53  thf(fact_1482_add__le__less__mono,axiom,
% 0.29/0.53      ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.29/0.53        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.53       => ( ( ord_less_nat @ C @ D2 )
% 0.29/0.53         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_le_less_mono
% 0.29/0.53  thf(fact_1483_add__le__less__mono,axiom,
% 0.29/0.53      ! [A: int,B: int,C: int,D2: int] :
% 0.29/0.53        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.53       => ( ( ord_less_int @ C @ D2 )
% 0.29/0.53         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_le_less_mono
% 0.29/0.53  thf(fact_1484_add__less__le__mono,axiom,
% 0.29/0.53      ! [A: real,B: real,C: real,D2: real] :
% 0.29/0.53        ( ( ord_less_real @ A @ B )
% 0.29/0.53       => ( ( ord_less_eq_real @ C @ D2 )
% 0.29/0.53         => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D2 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_less_le_mono
% 0.29/0.53  thf(fact_1485_add__less__le__mono,axiom,
% 0.29/0.53      ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.29/0.53        ( ( ord_less_rat @ A @ B )
% 0.29/0.53       => ( ( ord_less_eq_rat @ C @ D2 )
% 0.29/0.53         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_less_le_mono
% 0.29/0.53  thf(fact_1486_add__less__le__mono,axiom,
% 0.29/0.53      ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.29/0.53        ( ( ord_less_nat @ A @ B )
% 0.29/0.53       => ( ( ord_less_eq_nat @ C @ D2 )
% 0.29/0.53         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_less_le_mono
% 0.29/0.53  thf(fact_1487_add__less__le__mono,axiom,
% 0.29/0.53      ! [A: int,B: int,C: int,D2: int] :
% 0.29/0.53        ( ( ord_less_int @ A @ B )
% 0.29/0.53       => ( ( ord_less_eq_int @ C @ D2 )
% 0.29/0.53         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_less_le_mono
% 0.29/0.53  thf(fact_1488_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 0.29/0.53      ! [A: nat,B: nat,C: nat] :
% 0.29/0.53        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.53       => ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.53         => ( ( ( minus_minus_nat @ B @ A )
% 0.29/0.53              = C )
% 0.29/0.53            = ( B
% 0.29/0.53              = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 0.29/0.53  thf(fact_1489_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 0.29/0.53      ! [A: nat,B: nat] :
% 0.29/0.53        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.53       => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 0.29/0.53          = B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 0.29/0.53  thf(fact_1490_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 0.29/0.53      ! [A: nat,B: nat,C: nat] :
% 0.29/0.53        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.53       => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 0.29/0.53          = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 0.29/0.53  thf(fact_1491_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 0.29/0.53      ! [A: nat,B: nat,C: nat] :
% 0.29/0.53        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.53       => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
% 0.29/0.53          = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 0.29/0.53  thf(fact_1492_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 0.29/0.53      ! [A: nat,B: nat,C: nat] :
% 0.29/0.53        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.53       => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
% 0.29/0.53          = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 0.29/0.53  thf(fact_1493_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 0.29/0.53      ! [A: nat,B: nat,C: nat] :
% 0.29/0.53        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.53       => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
% 0.29/0.53          = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 0.29/0.53  thf(fact_1494_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 0.29/0.53      ! [A: nat,B: nat,C: nat] :
% 0.29/0.53        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.53       => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 0.29/0.53          = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 0.29/0.53  thf(fact_1495_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 0.29/0.53      ! [A: nat,B: nat,C: nat] :
% 0.29/0.53        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.53       => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 0.29/0.53          = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 0.29/0.53  thf(fact_1496_le__add__diff,axiom,
% 0.29/0.53      ! [A: nat,B: nat,C: nat] :
% 0.29/0.53        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.53       => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % le_add_diff
% 0.29/0.53  thf(fact_1497_diff__add,axiom,
% 0.29/0.53      ! [A: nat,B: nat] :
% 0.29/0.53        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.53       => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 0.29/0.53          = B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % diff_add
% 0.29/0.53  thf(fact_1498_le__diff__eq,axiom,
% 0.29/0.53      ! [A: real,C: real,B: real] :
% 0.29/0.53        ( ( ord_less_eq_real @ A @ ( minus_minus_real @ C @ B ) )
% 0.29/0.53        = ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 0.29/0.53  
% 0.29/0.53  % le_diff_eq
% 0.29/0.53  thf(fact_1499_le__diff__eq,axiom,
% 0.29/0.53      ! [A: rat,C: rat,B: rat] :
% 0.29/0.53        ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 0.29/0.53        = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 0.29/0.53  
% 0.29/0.53  % le_diff_eq
% 0.29/0.53  thf(fact_1500_le__diff__eq,axiom,
% 0.29/0.53      ! [A: int,C: int,B: int] :
% 0.29/0.53        ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
% 0.29/0.53        = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.29/0.53  
% 0.29/0.53  % le_diff_eq
% 0.29/0.53  thf(fact_1501_diff__le__eq,axiom,
% 0.29/0.53      ! [A: real,B: real,C: real] :
% 0.29/0.53        ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.29/0.53        = ( ord_less_eq_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % diff_le_eq
% 0.29/0.53  thf(fact_1502_diff__le__eq,axiom,
% 0.29/0.53      ! [A: rat,B: rat,C: rat] :
% 0.29/0.53        ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.29/0.53        = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % diff_le_eq
% 0.29/0.53  thf(fact_1503_diff__le__eq,axiom,
% 0.29/0.53      ! [A: int,B: int,C: int] :
% 0.29/0.53        ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.29/0.53        = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % diff_le_eq
% 0.29/0.53  thf(fact_1504_diff__less__eq,axiom,
% 0.29/0.53      ! [A: real,B: real,C: real] :
% 0.29/0.53        ( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.29/0.53        = ( ord_less_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % diff_less_eq
% 0.29/0.53  thf(fact_1505_diff__less__eq,axiom,
% 0.29/0.53      ! [A: rat,B: rat,C: rat] :
% 0.29/0.53        ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.29/0.53        = ( ord_less_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % diff_less_eq
% 0.29/0.53  thf(fact_1506_diff__less__eq,axiom,
% 0.29/0.53      ! [A: int,B: int,C: int] :
% 0.29/0.53        ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.29/0.53        = ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % diff_less_eq
% 0.29/0.53  thf(fact_1507_less__diff__eq,axiom,
% 0.29/0.53      ! [A: real,C: real,B: real] :
% 0.29/0.53        ( ( ord_less_real @ A @ ( minus_minus_real @ C @ B ) )
% 0.29/0.53        = ( ord_less_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 0.29/0.53  
% 0.29/0.53  % less_diff_eq
% 0.29/0.53  thf(fact_1508_less__diff__eq,axiom,
% 0.29/0.53      ! [A: rat,C: rat,B: rat] :
% 0.29/0.53        ( ( ord_less_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 0.29/0.53        = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 0.29/0.53  
% 0.29/0.53  % less_diff_eq
% 0.29/0.53  thf(fact_1509_less__diff__eq,axiom,
% 0.29/0.53      ! [A: int,C: int,B: int] :
% 0.29/0.53        ( ( ord_less_int @ A @ ( minus_minus_int @ C @ B ) )
% 0.29/0.53        = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.29/0.53  
% 0.29/0.53  % less_diff_eq
% 0.29/0.53  thf(fact_1510_gt__half__sum,axiom,
% 0.29/0.53      ! [A: real,B: real] :
% 0.29/0.53        ( ( ord_less_real @ A @ B )
% 0.29/0.53       => ( ord_less_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % gt_half_sum
% 0.29/0.53  thf(fact_1511_gt__half__sum,axiom,
% 0.29/0.53      ! [A: rat,B: rat] :
% 0.29/0.53        ( ( ord_less_rat @ A @ B )
% 0.29/0.53       => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % gt_half_sum
% 0.29/0.53  thf(fact_1512_less__half__sum,axiom,
% 0.29/0.53      ! [A: real,B: real] :
% 0.29/0.53        ( ( ord_less_real @ A @ B )
% 0.29/0.53       => ( ord_less_real @ A @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % less_half_sum
% 0.29/0.53  thf(fact_1513_less__half__sum,axiom,
% 0.29/0.53      ! [A: rat,B: rat] :
% 0.29/0.53        ( ( ord_less_rat @ A @ B )
% 0.29/0.53       => ( ord_less_rat @ A @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % less_half_sum
% 0.29/0.53  thf(fact_1514_less__shift,axiom,
% 0.29/0.53      ( ord_less_nat
% 0.29/0.53      = ( ^ [X2: nat,Y: nat] : ( vEBT_VEBT_less @ ( some_nat @ X2 ) @ ( some_nat @ Y ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % less_shift
% 0.29/0.53  thf(fact_1515_greater__shift,axiom,
% 0.29/0.53      ( ord_less_nat
% 0.29/0.53      = ( ^ [Y: nat,X2: nat] : ( vEBT_VEBT_greater @ ( some_nat @ X2 ) @ ( some_nat @ Y ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % greater_shift
% 0.29/0.53  thf(fact_1516_vebt__succ_Osimps_I3_J,axiom,
% 0.29/0.53      ! [Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,Va: nat] :
% 0.29/0.53        ( ( vEBT_vebt_succ @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz ) @ Va )
% 0.29/0.53        = none_nat ) ).
% 0.29/0.53  
% 0.29/0.53  % vebt_succ.simps(3)
% 0.29/0.53  thf(fact_1517_vebt__pred_Osimps_I4_J,axiom,
% 0.29/0.53      ! [Uy: nat,Uz: list_VEBT_VEBT,Va: vEBT_VEBT,Vb: nat] :
% 0.29/0.53        ( ( vEBT_vebt_pred @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz @ Va ) @ Vb )
% 0.29/0.53        = none_nat ) ).
% 0.29/0.53  
% 0.29/0.53  % vebt_pred.simps(4)
% 0.29/0.53  thf(fact_1518_member__bound__height,axiom,
% 0.29/0.53      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.53        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.53       => ( ord_less_eq_nat @ ( vEBT_T_m_e_m_b_e_r @ T @ X ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % member_bound_height
% 0.29/0.53  thf(fact_1519_succ__bound__height,axiom,
% 0.29/0.53      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.53        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.53       => ( ord_less_eq_nat @ ( vEBT_T_s_u_c_c @ T @ X ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % succ_bound_height
% 0.29/0.53  thf(fact_1520_del__in__range,axiom,
% 0.29/0.53      ! [Mi: nat,X: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.29/0.53        ( ( ( ord_less_eq_nat @ Mi @ X )
% 0.29/0.53          & ( ord_less_eq_nat @ X @ Ma ) )
% 0.29/0.53       => ( ( Mi != Ma )
% 0.29/0.53         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.29/0.53           => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.29/0.53              = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.29/0.53                @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                  @ ( vEBT_Node
% 0.29/0.53                    @ ( some_P7363390416028606310at_nat
% 0.29/0.53                      @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 0.29/0.53                        @ ( if_nat
% 0.29/0.53                          @ ( ( ( X = Mi )
% 0.29/0.53                             => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.29/0.53                                = Ma ) )
% 0.29/0.53                            & ( ( X != Mi )
% 0.29/0.53                             => ( X = Ma ) ) )
% 0.29/0.53                          @ ( if_nat
% 0.29/0.53                            @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                              = none_nat )
% 0.29/0.53                            @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 0.29/0.53                            @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 0.29/0.53                          @ Ma ) ) )
% 0.29/0.53                    @ Deg
% 0.29/0.53                    @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                    @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                  @ ( vEBT_Node
% 0.29/0.53                    @ ( some_P7363390416028606310at_nat
% 0.29/0.53                      @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 0.29/0.53                        @ ( if_nat
% 0.29/0.53                          @ ( ( ( X = Mi )
% 0.29/0.53                             => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.29/0.53                                = Ma ) )
% 0.29/0.53                            & ( ( X != Mi )
% 0.29/0.53                             => ( X = Ma ) ) )
% 0.29/0.53                          @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.29/0.53                          @ Ma ) ) )
% 0.29/0.53                    @ Deg
% 0.29/0.53                    @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                    @ Summary ) )
% 0.29/0.53                @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % del_in_range
% 0.29/0.53  thf(fact_1521_del__x__mi,axiom,
% 0.29/0.53      ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList: list_VEBT_VEBT,L2: nat] :
% 0.29/0.53        ( ( ( X = Mi )
% 0.29/0.53          & ( ord_less_nat @ X @ Ma ) )
% 0.29/0.53       => ( ( Mi != Ma )
% 0.29/0.53         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.29/0.53           => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.53                = H2 )
% 0.29/0.53             => ( ( Xn
% 0.29/0.53                  = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 0.29/0.53               => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.53                    = L2 )
% 0.29/0.53                 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.29/0.53                   => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.29/0.53                      = ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) )
% 0.29/0.53                        @ ( vEBT_Node
% 0.29/0.53                          @ ( some_P7363390416028606310at_nat
% 0.29/0.53                            @ ( product_Pair_nat_nat @ Xn
% 0.29/0.53                              @ ( if_nat @ ( Xn = Ma )
% 0.29/0.53                                @ ( if_nat
% 0.29/0.53                                  @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 0.29/0.53                                    = none_nat )
% 0.29/0.53                                  @ Xn
% 0.29/0.53                                  @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 0.29/0.53                                @ Ma ) ) )
% 0.29/0.53                          @ Deg
% 0.29/0.53                          @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) )
% 0.29/0.53                          @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 0.29/0.53                        @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) ) @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) ) @ Summary ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % del_x_mi
% 0.29/0.53  thf(fact_1522_del__x__mi__lets__in,axiom,
% 0.29/0.53      ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList: list_VEBT_VEBT,L2: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 0.29/0.53        ( ( ( X = Mi )
% 0.29/0.53          & ( ord_less_nat @ X @ Ma ) )
% 0.29/0.53       => ( ( Mi != Ma )
% 0.29/0.53         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.29/0.53           => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.53                = H2 )
% 0.29/0.53             => ( ( Xn
% 0.29/0.53                  = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 0.29/0.53               => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.53                    = L2 )
% 0.29/0.53                 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.29/0.53                   => ( ( Newnode
% 0.29/0.53                        = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) )
% 0.29/0.53                     => ( ( Newlist
% 0.29/0.53                          = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 0.29/0.53                       => ( ( ( vEBT_VEBT_minNull @ Newnode )
% 0.29/0.53                           => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.29/0.53                              = ( vEBT_Node
% 0.29/0.53                                @ ( some_P7363390416028606310at_nat
% 0.29/0.53                                  @ ( product_Pair_nat_nat @ Xn
% 0.29/0.53                                    @ ( if_nat @ ( Xn = Ma )
% 0.29/0.53                                      @ ( if_nat
% 0.29/0.53                                        @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 0.29/0.53                                          = none_nat )
% 0.29/0.53                                        @ Xn
% 0.29/0.53                                        @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 0.29/0.53                                      @ Ma ) ) )
% 0.29/0.53                                @ Deg
% 0.29/0.53                                @ Newlist
% 0.29/0.53                                @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) )
% 0.29/0.53                          & ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 0.29/0.53                           => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.29/0.53                              = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % del_x_mi_lets_in
% 0.29/0.53  thf(fact_1523_del__x__mi__lets__in__minNull,axiom,
% 0.29/0.53      ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList: list_VEBT_VEBT,L2: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT,Sn: vEBT_VEBT] :
% 0.29/0.53        ( ( ( X = Mi )
% 0.29/0.53          & ( ord_less_nat @ X @ Ma ) )
% 0.29/0.53       => ( ( Mi != Ma )
% 0.29/0.53         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.29/0.53           => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.53                = H2 )
% 0.29/0.53             => ( ( Xn
% 0.29/0.53                  = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 0.29/0.53               => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.53                    = L2 )
% 0.29/0.53                 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.29/0.53                   => ( ( Newnode
% 0.29/0.53                        = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) )
% 0.29/0.53                     => ( ( Newlist
% 0.29/0.53                          = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 0.29/0.53                       => ( ( vEBT_VEBT_minNull @ Newnode )
% 0.29/0.53                         => ( ( Sn
% 0.29/0.53                              = ( vEBT_vebt_delete @ Summary @ H2 ) )
% 0.29/0.53                           => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.29/0.53                              = ( vEBT_Node
% 0.29/0.53                                @ ( some_P7363390416028606310at_nat
% 0.29/0.53                                  @ ( product_Pair_nat_nat @ Xn
% 0.29/0.53                                    @ ( if_nat @ ( Xn = Ma )
% 0.29/0.53                                      @ ( if_nat
% 0.29/0.53                                        @ ( ( vEBT_vebt_maxt @ Sn )
% 0.29/0.53                                          = none_nat )
% 0.29/0.53                                        @ Xn
% 0.29/0.53                                        @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) ) ) ) )
% 0.29/0.53                                      @ Ma ) ) )
% 0.29/0.53                                @ Deg
% 0.29/0.53                                @ Newlist
% 0.29/0.53                                @ Sn ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % del_x_mi_lets_in_minNull
% 0.29/0.53  thf(fact_1524_set__vebt_H__def,axiom,
% 0.29/0.53      ( vEBT_VEBT_set_vebt
% 0.29/0.53      = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_vebt_member @ T2 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % set_vebt'_def
% 0.29/0.53  thf(fact_1525_del__x__not__mia,axiom,
% 0.29/0.53      ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.29/0.53        ( ( ( ord_less_nat @ Mi @ X )
% 0.29/0.53          & ( ord_less_eq_nat @ X @ Ma ) )
% 0.29/0.53       => ( ( Mi != Ma )
% 0.29/0.53         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.29/0.53           => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.53                = H2 )
% 0.29/0.53             => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.53                  = L2 )
% 0.29/0.53               => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.29/0.53                 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.29/0.53                    = ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) )
% 0.29/0.53                      @ ( vEBT_Node
% 0.29/0.53                        @ ( some_P7363390416028606310at_nat
% 0.29/0.53                          @ ( product_Pair_nat_nat @ Mi
% 0.29/0.53                            @ ( if_nat @ ( X = Ma )
% 0.29/0.53                              @ ( if_nat
% 0.29/0.53                                @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 0.29/0.53                                  = none_nat )
% 0.29/0.53                                @ Mi
% 0.29/0.53                                @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 0.29/0.53                              @ Ma ) ) )
% 0.29/0.53                        @ Deg
% 0.29/0.53                        @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) )
% 0.29/0.53                        @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 0.29/0.53                      @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) ) @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) ) @ Summary ) ) ) ) ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % del_x_not_mia
% 0.29/0.53  thf(fact_1526_del__x__not__mi__new__node__nil,axiom,
% 0.29/0.53      ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L2: nat,Newnode: vEBT_VEBT,TreeList: list_VEBT_VEBT,Sn: vEBT_VEBT,Summary: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 0.29/0.53        ( ( ( ord_less_nat @ Mi @ X )
% 0.29/0.53          & ( ord_less_eq_nat @ X @ Ma ) )
% 0.29/0.53       => ( ( Mi != Ma )
% 0.29/0.53         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.29/0.53           => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.53                = H2 )
% 0.29/0.53             => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.53                  = L2 )
% 0.29/0.53               => ( ( Newnode
% 0.29/0.53                    = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) )
% 0.29/0.53                 => ( ( vEBT_VEBT_minNull @ Newnode )
% 0.29/0.53                   => ( ( Sn
% 0.29/0.53                        = ( vEBT_vebt_delete @ Summary @ H2 ) )
% 0.29/0.53                     => ( ( Newlist
% 0.29/0.53                          = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 0.29/0.53                       => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.29/0.53                         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.29/0.53                            = ( vEBT_Node
% 0.29/0.53                              @ ( some_P7363390416028606310at_nat
% 0.29/0.53                                @ ( product_Pair_nat_nat @ Mi
% 0.29/0.53                                  @ ( if_nat @ ( X = Ma )
% 0.29/0.53                                    @ ( if_nat
% 0.29/0.53                                      @ ( ( vEBT_vebt_maxt @ Sn )
% 0.29/0.53                                        = none_nat )
% 0.29/0.53                                      @ Mi
% 0.29/0.53                                      @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) ) ) ) )
% 0.29/0.53                                    @ Ma ) ) )
% 0.29/0.53                              @ Deg
% 0.29/0.53                              @ Newlist
% 0.29/0.53                              @ Sn ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % del_x_not_mi_new_node_nil
% 0.29/0.53  thf(fact_1527_del__x__not__mi,axiom,
% 0.29/0.53      ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L2: nat,Newnode: vEBT_VEBT,TreeList: list_VEBT_VEBT,Newlist: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.29/0.53        ( ( ( ord_less_nat @ Mi @ X )
% 0.29/0.53          & ( ord_less_eq_nat @ X @ Ma ) )
% 0.29/0.53       => ( ( Mi != Ma )
% 0.29/0.53         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.29/0.53           => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.53                = H2 )
% 0.29/0.53             => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.53                  = L2 )
% 0.29/0.53               => ( ( Newnode
% 0.29/0.53                    = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) )
% 0.29/0.53                 => ( ( Newlist
% 0.29/0.53                      = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 0.29/0.53                   => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.29/0.53                     => ( ( ( vEBT_VEBT_minNull @ Newnode )
% 0.29/0.53                         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.29/0.53                            = ( vEBT_Node
% 0.29/0.53                              @ ( some_P7363390416028606310at_nat
% 0.29/0.53                                @ ( product_Pair_nat_nat @ Mi
% 0.29/0.53                                  @ ( if_nat @ ( X = Ma )
% 0.29/0.53                                    @ ( if_nat
% 0.29/0.53                                      @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 0.29/0.53                                        = none_nat )
% 0.29/0.53                                      @ Mi
% 0.29/0.53                                      @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 0.29/0.53                                    @ Ma ) ) )
% 0.29/0.53                              @ Deg
% 0.29/0.53                              @ Newlist
% 0.29/0.53                              @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) )
% 0.29/0.53                        & ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 0.29/0.53                         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.29/0.53                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % del_x_not_mi
% 0.29/0.53  thf(fact_1528_del__x__mia,axiom,
% 0.29/0.53      ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.29/0.53        ( ( ( X = Mi )
% 0.29/0.53          & ( ord_less_nat @ X @ Ma ) )
% 0.29/0.53       => ( ( Mi != Ma )
% 0.29/0.53         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.29/0.53           => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.29/0.53              = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.29/0.53                @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                  @ ( vEBT_Node
% 0.29/0.53                    @ ( some_P7363390416028606310at_nat
% 0.29/0.53                      @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.29/0.53                        @ ( if_nat
% 0.29/0.53                          @ ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.29/0.53                            = Ma )
% 0.29/0.53                          @ ( if_nat
% 0.29/0.53                            @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                              = none_nat )
% 0.29/0.53                            @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.29/0.53                            @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 0.29/0.53                          @ Ma ) ) )
% 0.29/0.53                    @ Deg
% 0.29/0.53                    @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                    @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                  @ ( vEBT_Node
% 0.29/0.53                    @ ( some_P7363390416028606310at_nat
% 0.29/0.53                      @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.29/0.53                        @ ( if_nat
% 0.29/0.53                          @ ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.29/0.53                            = Ma )
% 0.29/0.53                          @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.29/0.53                          @ Ma ) ) )
% 0.29/0.53                    @ Deg
% 0.29/0.53                    @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                    @ Summary ) )
% 0.29/0.53                @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % del_x_mia
% 0.29/0.53  thf(fact_1529_succ__less__length__list,axiom,
% 0.29/0.53      ! [Deg: nat,Mi: nat,X: nat,TreeList: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 0.29/0.53        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.29/0.53       => ( ( ord_less_eq_nat @ Mi @ X )
% 0.29/0.53         => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.29/0.53           => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.29/0.53              = ( if_option_nat
% 0.29/0.53                @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                   != none_nat )
% 0.29/0.53                  & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.29/0.53                @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                @ ( if_option_nat
% 0.29/0.53                  @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.53                    = none_nat )
% 0.29/0.53                  @ none_nat
% 0.29/0.53                  @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % succ_less_length_list
% 0.29/0.53  thf(fact_1530_succ__greatereq__min,axiom,
% 0.29/0.53      ! [Deg: nat,Mi: nat,X: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.29/0.53        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.29/0.53       => ( ( ord_less_eq_nat @ Mi @ X )
% 0.29/0.53         => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.29/0.53            = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.29/0.53              @ ( if_option_nat
% 0.29/0.53                @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                   != none_nat )
% 0.29/0.53                  & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.29/0.53                @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                @ ( if_option_nat
% 0.29/0.53                  @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.53                    = none_nat )
% 0.29/0.53                  @ none_nat
% 0.29/0.53                  @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.29/0.53              @ none_nat ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % succ_greatereq_min
% 0.29/0.53  thf(fact_1531_pred__lesseq__max,axiom,
% 0.29/0.53      ! [Deg: nat,X: nat,Ma: nat,Mi: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.29/0.53        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.29/0.53       => ( ( ord_less_eq_nat @ X @ Ma )
% 0.29/0.53         => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.29/0.53            = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.29/0.53              @ ( if_option_nat
% 0.29/0.53                @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                   != none_nat )
% 0.29/0.53                  & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.29/0.53                @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                @ ( if_option_nat
% 0.29/0.53                  @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.53                    = none_nat )
% 0.29/0.53                  @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 0.29/0.53                  @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.29/0.53              @ none_nat ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % pred_lesseq_max
% 0.29/0.53  thf(fact_1532_pred__less__length__list,axiom,
% 0.29/0.53      ! [Deg: nat,X: nat,Ma: nat,TreeList: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 0.29/0.53        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.29/0.53       => ( ( ord_less_eq_nat @ X @ Ma )
% 0.29/0.53         => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.29/0.53           => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.29/0.53              = ( if_option_nat
% 0.29/0.53                @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                   != none_nat )
% 0.29/0.53                  & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.29/0.53                @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                @ ( if_option_nat
% 0.29/0.53                  @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.53                    = none_nat )
% 0.29/0.53                  @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 0.29/0.53                  @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % pred_less_length_list
% 0.29/0.53  thf(fact_1533_mult__commute__abs,axiom,
% 0.29/0.53      ! [C: complex] :
% 0.29/0.53        ( ( ^ [X2: complex] : ( times_times_complex @ X2 @ C ) )
% 0.29/0.53        = ( times_times_complex @ C ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_commute_abs
% 0.29/0.53  thf(fact_1534_mult__commute__abs,axiom,
% 0.29/0.53      ! [C: real] :
% 0.29/0.53        ( ( ^ [X2: real] : ( times_times_real @ X2 @ C ) )
% 0.29/0.53        = ( times_times_real @ C ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_commute_abs
% 0.29/0.53  thf(fact_1535_mult__commute__abs,axiom,
% 0.29/0.53      ! [C: nat] :
% 0.29/0.53        ( ( ^ [X2: nat] : ( times_times_nat @ X2 @ C ) )
% 0.29/0.53        = ( times_times_nat @ C ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_commute_abs
% 0.29/0.53  thf(fact_1536_mult__commute__abs,axiom,
% 0.29/0.53      ! [C: int] :
% 0.29/0.53        ( ( ^ [X2: int] : ( times_times_int @ X2 @ C ) )
% 0.29/0.53        = ( times_times_int @ C ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_commute_abs
% 0.29/0.53  thf(fact_1537_lambda__one,axiom,
% 0.29/0.53      ( ( ^ [X2: rat] : X2 )
% 0.29/0.53      = ( times_times_rat @ one_one_rat ) ) ).
% 0.29/0.53  
% 0.29/0.53  % lambda_one
% 0.29/0.53  thf(fact_1538_lambda__one,axiom,
% 0.29/0.53      ( ( ^ [X2: complex] : X2 )
% 0.29/0.53      = ( times_times_complex @ one_one_complex ) ) ).
% 0.29/0.53  
% 0.29/0.53  % lambda_one
% 0.29/0.53  thf(fact_1539_lambda__one,axiom,
% 0.29/0.53      ( ( ^ [X2: real] : X2 )
% 0.29/0.53      = ( times_times_real @ one_one_real ) ) ).
% 0.29/0.53  
% 0.29/0.53  % lambda_one
% 0.29/0.53  thf(fact_1540_lambda__one,axiom,
% 0.29/0.53      ( ( ^ [X2: nat] : X2 )
% 0.29/0.53      = ( times_times_nat @ one_one_nat ) ) ).
% 0.29/0.53  
% 0.29/0.53  % lambda_one
% 0.29/0.53  thf(fact_1541_lambda__one,axiom,
% 0.29/0.53      ( ( ^ [X2: int] : X2 )
% 0.29/0.53      = ( times_times_int @ one_one_int ) ) ).
% 0.29/0.53  
% 0.29/0.53  % lambda_one
% 0.29/0.53  thf(fact_1542_set__vebt__def,axiom,
% 0.29/0.53      ( vEBT_set_vebt
% 0.29/0.53      = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ T2 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % set_vebt_def
% 0.29/0.53  thf(fact_1543_numeral__code_I2_J,axiom,
% 0.29/0.53      ! [N: num] :
% 0.29/0.53        ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 0.29/0.53        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % numeral_code(2)
% 0.29/0.53  thf(fact_1544_numeral__code_I2_J,axiom,
% 0.29/0.53      ! [N: num] :
% 0.29/0.53        ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 0.29/0.53        = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % numeral_code(2)
% 0.29/0.53  thf(fact_1545_numeral__code_I2_J,axiom,
% 0.29/0.53      ! [N: num] :
% 0.29/0.53        ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 0.29/0.53        = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % numeral_code(2)
% 0.29/0.53  thf(fact_1546_numeral__code_I2_J,axiom,
% 0.29/0.53      ! [N: num] :
% 0.29/0.53        ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 0.29/0.53        = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % numeral_code(2)
% 0.29/0.53  thf(fact_1547_numeral__code_I2_J,axiom,
% 0.29/0.53      ! [N: num] :
% 0.29/0.53        ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 0.29/0.53        = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % numeral_code(2)
% 0.29/0.53  thf(fact_1548_numeral__code_I3_J,axiom,
% 0.29/0.53      ! [N: num] :
% 0.29/0.53        ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 0.29/0.53        = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 0.29/0.53  
% 0.29/0.53  % numeral_code(3)
% 0.29/0.53  thf(fact_1549_numeral__code_I3_J,axiom,
% 0.29/0.53      ! [N: num] :
% 0.29/0.53        ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 0.29/0.53        = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 0.29/0.53  
% 0.29/0.53  % numeral_code(3)
% 0.29/0.53  thf(fact_1550_numeral__code_I3_J,axiom,
% 0.29/0.53      ! [N: num] :
% 0.29/0.53        ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 0.29/0.53        = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 0.29/0.53  
% 0.29/0.53  % numeral_code(3)
% 0.29/0.53  thf(fact_1551_numeral__code_I3_J,axiom,
% 0.29/0.53      ! [N: num] :
% 0.29/0.53        ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 0.29/0.53        = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 0.29/0.53  
% 0.29/0.53  % numeral_code(3)
% 0.29/0.53  thf(fact_1552_numeral__code_I3_J,axiom,
% 0.29/0.53      ! [N: num] :
% 0.29/0.53        ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 0.29/0.53        = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 0.29/0.53  
% 0.29/0.53  % numeral_code(3)
% 0.29/0.53  thf(fact_1553_power__numeral__even,axiom,
% 0.29/0.53      ! [Z: complex,W: num] :
% 0.29/0.53        ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 0.29/0.53        = ( times_times_complex @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % power_numeral_even
% 0.29/0.53  thf(fact_1554_power__numeral__even,axiom,
% 0.29/0.53      ! [Z: real,W: num] :
% 0.29/0.53        ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 0.29/0.53        = ( times_times_real @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % power_numeral_even
% 0.29/0.53  thf(fact_1555_power__numeral__even,axiom,
% 0.29/0.53      ! [Z: nat,W: num] :
% 0.29/0.53        ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 0.29/0.53        = ( times_times_nat @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % power_numeral_even
% 0.29/0.53  thf(fact_1556_power__numeral__even,axiom,
% 0.29/0.53      ! [Z: int,W: num] :
% 0.29/0.53        ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 0.29/0.53        = ( times_times_int @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % power_numeral_even
% 0.29/0.53  thf(fact_1557_power__numeral__odd,axiom,
% 0.29/0.53      ! [Z: complex,W: num] :
% 0.29/0.53        ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 0.29/0.53        = ( times_times_complex @ ( times_times_complex @ Z @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % power_numeral_odd
% 0.29/0.53  thf(fact_1558_power__numeral__odd,axiom,
% 0.29/0.53      ! [Z: real,W: num] :
% 0.29/0.53        ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 0.29/0.53        = ( times_times_real @ ( times_times_real @ Z @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % power_numeral_odd
% 0.29/0.53  thf(fact_1559_power__numeral__odd,axiom,
% 0.29/0.53      ! [Z: nat,W: num] :
% 0.29/0.53        ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 0.29/0.53        = ( times_times_nat @ ( times_times_nat @ Z @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % power_numeral_odd
% 0.29/0.53  thf(fact_1560_power__numeral__odd,axiom,
% 0.29/0.53      ! [Z: int,W: num] :
% 0.29/0.53        ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 0.29/0.53        = ( times_times_int @ ( times_times_int @ Z @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % power_numeral_odd
% 0.29/0.53  thf(fact_1561_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I3_J,axiom,
% 0.29/0.53      ! [Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,Va: nat] :
% 0.29/0.53        ( ( vEBT_T_s_u_c_c @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz ) @ Va )
% 0.29/0.53        = one_one_nat ) ).
% 0.29/0.53  
% 0.29/0.53  % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.simps(3)
% 0.29/0.53  thf(fact_1562_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I5_J,axiom,
% 0.29/0.53      ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.29/0.53        ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 0.29/0.53        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( X = Mi ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( X = Ma ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Ma @ X ) @ one_one_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_e_m_b_e_r @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(5)
% 0.29/0.53  thf(fact_1563_vebt__succ_Osimps_I6_J,axiom,
% 0.29/0.53      ! [X: nat,Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.29/0.53        ( ( ( ord_less_nat @ X @ Mi )
% 0.29/0.53         => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 0.29/0.53            = ( some_nat @ Mi ) ) )
% 0.29/0.53        & ( ~ ( ord_less_nat @ X @ Mi )
% 0.29/0.53         => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 0.29/0.53            = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.29/0.53              @ ( if_option_nat
% 0.29/0.53                @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                   != none_nat )
% 0.29/0.53                  & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.29/0.53                @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                @ ( if_option_nat
% 0.29/0.53                  @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.53                    = none_nat )
% 0.29/0.53                  @ none_nat
% 0.29/0.53                  @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.29/0.53              @ none_nat ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % vebt_succ.simps(6)
% 0.29/0.53  thf(fact_1564_vebt__pred_Osimps_I7_J,axiom,
% 0.29/0.53      ! [Ma: nat,X: nat,Mi: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.29/0.53        ( ( ( ord_less_nat @ Ma @ X )
% 0.29/0.53         => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 0.29/0.53            = ( some_nat @ Ma ) ) )
% 0.29/0.53        & ( ~ ( ord_less_nat @ Ma @ X )
% 0.29/0.53         => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 0.29/0.53            = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.29/0.53              @ ( if_option_nat
% 0.29/0.53                @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                   != none_nat )
% 0.29/0.53                  & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.29/0.53                @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                @ ( if_option_nat
% 0.29/0.53                  @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.53                    = none_nat )
% 0.29/0.53                  @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 0.29/0.53                  @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.29/0.53              @ none_nat ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % vebt_pred.simps(7)
% 0.29/0.53  thf(fact_1565_vebt__insert_Osimps_I5_J,axiom,
% 0.29/0.53      ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.29/0.53        ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 0.29/0.53        = ( if_VEBT_VEBT
% 0.29/0.53          @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.29/0.53            & ~ ( ( X = Mi )
% 0.29/0.53                | ( X = Ma ) ) )
% 0.29/0.53          @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ X @ Mi ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ Ma ) ) ) @ ( suc @ ( suc @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) )
% 0.29/0.53          @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % vebt_insert.simps(5)
% 0.29/0.53  thf(fact_1566_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I2_J,axiom,
% 0.29/0.53      ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X: nat] :
% 0.29/0.53        ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X )
% 0.29/0.53        = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(2)
% 0.29/0.53  thf(fact_1567_is__pred__in__set__def,axiom,
% 0.29/0.53      ( vEBT_is_pred_in_set
% 0.29/0.53      = ( ^ [Xs: set_nat,X2: nat,Y: nat] :
% 0.29/0.53            ( ( member_nat @ Y @ Xs )
% 0.29/0.53            & ( ord_less_nat @ Y @ X2 )
% 0.29/0.53            & ! [Z4: nat] :
% 0.29/0.53                ( ( member_nat @ Z4 @ Xs )
% 0.29/0.53               => ( ( ord_less_nat @ Z4 @ X2 )
% 0.29/0.53                 => ( ord_less_eq_nat @ Z4 @ Y ) ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % is_pred_in_set_def
% 0.29/0.53  thf(fact_1568_is__succ__in__set__def,axiom,
% 0.29/0.53      ( vEBT_is_succ_in_set
% 0.29/0.53      = ( ^ [Xs: set_nat,X2: nat,Y: nat] :
% 0.29/0.53            ( ( member_nat @ Y @ Xs )
% 0.29/0.53            & ( ord_less_nat @ X2 @ Y )
% 0.29/0.53            & ! [Z4: nat] :
% 0.29/0.53                ( ( member_nat @ Z4 @ Xs )
% 0.29/0.53               => ( ( ord_less_nat @ X2 @ Z4 )
% 0.29/0.53                 => ( ord_less_eq_nat @ Y @ Z4 ) ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % is_succ_in_set_def
% 0.29/0.53  thf(fact_1569_vebt__delete_Osimps_I7_J,axiom,
% 0.29/0.53      ! [X: nat,Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.29/0.53        ( ( ( ( ord_less_nat @ X @ Mi )
% 0.29/0.53            | ( ord_less_nat @ Ma @ X ) )
% 0.29/0.53         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 0.29/0.53            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) ) )
% 0.29/0.53        & ( ~ ( ( ord_less_nat @ X @ Mi )
% 0.29/0.53              | ( ord_less_nat @ Ma @ X ) )
% 0.29/0.53         => ( ( ( ( X = Mi )
% 0.29/0.53                & ( X = Ma ) )
% 0.29/0.53             => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 0.29/0.53                = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) ) )
% 0.29/0.53            & ( ~ ( ( X = Mi )
% 0.29/0.53                  & ( X = Ma ) )
% 0.29/0.53             => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 0.29/0.53                = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.29/0.53                  @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                    @ ( vEBT_Node
% 0.29/0.53                      @ ( some_P7363390416028606310at_nat
% 0.29/0.53                        @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 0.29/0.53                          @ ( if_nat
% 0.29/0.53                            @ ( ( ( X = Mi )
% 0.29/0.53                               => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.29/0.53                                  = Ma ) )
% 0.29/0.53                              & ( ( X != Mi )
% 0.29/0.53                               => ( X = Ma ) ) )
% 0.29/0.53                            @ ( if_nat
% 0.29/0.53                              @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                                = none_nat )
% 0.29/0.53                              @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 0.29/0.53                              @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 0.29/0.53                            @ Ma ) ) )
% 0.29/0.53                      @ ( suc @ ( suc @ Va ) )
% 0.29/0.53                      @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                      @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                    @ ( vEBT_Node
% 0.29/0.53                      @ ( some_P7363390416028606310at_nat
% 0.29/0.53                        @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 0.29/0.53                          @ ( if_nat
% 0.29/0.53                            @ ( ( ( X = Mi )
% 0.29/0.53                               => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.29/0.53                                  = Ma ) )
% 0.29/0.53                              & ( ( X != Mi )
% 0.29/0.53                               => ( X = Ma ) ) )
% 0.29/0.53                            @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.29/0.53                            @ Ma ) ) )
% 0.29/0.53                      @ ( suc @ ( suc @ Va ) )
% 0.29/0.53                      @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                      @ Summary ) )
% 0.29/0.53                  @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) ) ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % vebt_delete.simps(7)
% 0.29/0.53  thf(fact_1570_vebt__member_Osimps_I5_J,axiom,
% 0.29/0.53      ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.29/0.53        ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 0.29/0.53        = ( ( X != Mi )
% 0.29/0.53         => ( ( X != Ma )
% 0.29/0.53           => ( ~ ( ord_less_nat @ X @ Mi )
% 0.29/0.53              & ( ~ ( ord_less_nat @ X @ Mi )
% 0.29/0.53               => ( ~ ( ord_less_nat @ Ma @ X )
% 0.29/0.53                  & ( ~ ( ord_less_nat @ Ma @ X )
% 0.29/0.53                   => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.29/0.53                       => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                      & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % vebt_member.simps(5)
% 0.29/0.53  thf(fact_1571__C3_C,axiom,
% 0.29/0.53      ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 0.29/0.53      = ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_t @ summary ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat )
% 0.29/0.53        @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) )
% 0.29/0.53          @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53            @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.29/0.53              @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_d_e_l_e_t_e @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                  @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.29/0.53                    @ ( if_nat
% 0.29/0.53                      @ ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) )
% 0.29/0.53                        = ma )
% 0.29/0.53                      @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.29/0.53                        @ ( plus_plus_nat @ one_one_nat
% 0.29/0.53                          @ ( if_nat
% 0.29/0.53                            @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                              = none_nat )
% 0.29/0.53                            @ one_one_nat
% 0.29/0.53                            @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.29/0.53                      @ one_one_nat ) ) )
% 0.29/0.53                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.29/0.53                  @ ( if_nat
% 0.29/0.53                    @ ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) )
% 0.29/0.53                      = ma )
% 0.29/0.53                    @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.29/0.53                    @ one_one_nat ) ) ) ) )
% 0.29/0.53          @ one_one_nat ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % "3"
% 0.29/0.53  thf(fact_1572__C2_C,axiom,
% 0.29/0.53      ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 0.29/0.53      = ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_t @ summary ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat )
% 0.29/0.53        @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) )
% 0.29/0.53          @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53            @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.29/0.53              @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_d_e_l_e_t_e @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                  @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.29/0.53                    @ ( if_nat
% 0.29/0.53                      @ ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) )
% 0.29/0.53                        = ma )
% 0.29/0.53                      @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.29/0.53                        @ ( plus_plus_nat @ one_one_nat
% 0.29/0.53                          @ ( if_nat
% 0.29/0.53                            @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                              = none_nat )
% 0.29/0.53                            @ one_one_nat
% 0.29/0.53                            @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.29/0.53                      @ one_one_nat ) ) )
% 0.29/0.53                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.29/0.53                  @ ( if_nat
% 0.29/0.53                    @ ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) )
% 0.29/0.53                      = ma )
% 0.29/0.53                    @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.29/0.53                    @ one_one_nat ) ) ) ) )
% 0.29/0.53          @ one_one_nat ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % "2"
% 0.29/0.53  thf(fact_1573__C1_C,axiom,
% 0.29/0.53      ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 0.29/0.53      = ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ summary ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat ) ) @ one_one_nat )
% 0.29/0.53        @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) )
% 0.29/0.53          @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53            @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.29/0.53              @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_d_e_l_e_t_e @ summary @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                  @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.29/0.53                    @ ( if_nat
% 0.29/0.53                      @ ( ( ( xa = mi )
% 0.29/0.53                         => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) )
% 0.29/0.53                            = ma ) )
% 0.29/0.53                        & ( ( xa != mi )
% 0.29/0.53                         => ( xa = ma ) ) )
% 0.29/0.53                      @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.29/0.53                        @ ( plus_plus_nat @ one_one_nat
% 0.29/0.53                          @ ( if_nat
% 0.29/0.53                            @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                              = none_nat )
% 0.29/0.53                            @ one_one_nat
% 0.29/0.53                            @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.29/0.53                      @ one_one_nat ) ) )
% 0.29/0.53                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.29/0.53                  @ ( if_nat
% 0.29/0.53                    @ ( ( ( xa = mi )
% 0.29/0.53                       => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) )
% 0.29/0.53                          = ma ) )
% 0.29/0.53                      & ( ( xa != mi )
% 0.29/0.53                       => ( xa = ma ) ) )
% 0.29/0.53                    @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.29/0.53                    @ one_one_nat ) ) ) ) )
% 0.29/0.53          @ one_one_nat ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % "1"
% 0.29/0.53  thf(fact_1574__C0_C,axiom,
% 0.29/0.53      ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 0.29/0.53      = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.29/0.53        @ ( if_nat
% 0.29/0.53          @ ( ( xa = mi )
% 0.29/0.53            & ( xa = ma ) )
% 0.29/0.53          @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.29/0.53          @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ summary ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat ) ) @ one_one_nat )
% 0.29/0.53            @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) )
% 0.29/0.53              @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.29/0.53                  @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                    @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_d_e_l_e_t_e @ summary @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                      @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.29/0.53                        @ ( if_nat
% 0.29/0.53                          @ ( ( ( xa = mi )
% 0.29/0.53                             => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) )
% 0.29/0.53                                = ma ) )
% 0.29/0.53                            & ( ( xa != mi )
% 0.29/0.53                             => ( xa = ma ) ) )
% 0.29/0.53                          @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.29/0.53                            @ ( plus_plus_nat @ one_one_nat
% 0.29/0.53                              @ ( if_nat
% 0.29/0.53                                @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                                  = none_nat )
% 0.29/0.53                                @ one_one_nat
% 0.29/0.53                                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.29/0.53                          @ one_one_nat ) ) )
% 0.29/0.53                    @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.29/0.53                      @ ( if_nat
% 0.29/0.53                        @ ( ( ( xa = mi )
% 0.29/0.53                           => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) )
% 0.29/0.53                              = ma ) )
% 0.29/0.53                          & ( ( xa != mi )
% 0.29/0.53                           => ( xa = ma ) ) )
% 0.29/0.53                        @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.29/0.53                        @ one_one_nat ) ) ) ) )
% 0.29/0.53              @ one_one_nat ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % "0"
% 0.29/0.53  thf(fact_1575_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I6_J,axiom,
% 0.29/0.53      ! [X: nat,Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.29/0.53        ( ( ( ord_less_nat @ X @ Mi )
% 0.29/0.53         => ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 0.29/0.53            = one_one_nat ) )
% 0.29/0.53        & ( ~ ( ord_less_nat @ X @ Mi )
% 0.29/0.53         => ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 0.29/0.53            = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.29/0.53              @ ( if_nat
% 0.29/0.53                @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                   != none_nat )
% 0.29/0.53                  & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.29/0.53                @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c2 @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                @ ( plus_plus_nat @ ( vEBT_T_s_u_c_c2 @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 0.29/0.53              @ one_one_nat ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.simps(6)
% 0.29/0.53  thf(fact_1576_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I7_J,axiom,
% 0.29/0.53      ! [Ma: nat,X: nat,Mi: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.29/0.53        ( ( ( ord_less_nat @ Ma @ X )
% 0.29/0.53         => ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 0.29/0.53            = one_one_nat ) )
% 0.29/0.53        & ( ~ ( ord_less_nat @ Ma @ X )
% 0.29/0.53         => ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 0.29/0.53            = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.29/0.53              @ ( if_nat
% 0.29/0.53                @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                   != none_nat )
% 0.29/0.53                  & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.29/0.53                @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d2 @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                @ ( plus_plus_nat @ ( vEBT_T_p_r_e_d2 @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 0.29/0.53              @ one_one_nat ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.simps(7)
% 0.29/0.53  thf(fact_1577_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I6_J,axiom,
% 0.29/0.53      ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.29/0.53        ( ( vEBT_T_s_u_c_c @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 0.29/0.53        = ( plus_plus_nat @ one_one_nat
% 0.29/0.53          @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ one_one_nat
% 0.29/0.53            @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) )
% 0.29/0.53              @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.29/0.53                @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.29/0.53                  @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.29/0.53                    @ ( if_nat
% 0.29/0.53                      @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                         != none_nat )
% 0.29/0.53                        & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.29/0.53                      @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_s_u_c_c @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                      @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 0.29/0.53                        @ ( if_nat
% 0.29/0.53                          @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.53                            = none_nat )
% 0.29/0.53                          @ one_one_nat
% 0.29/0.53                          @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.29/0.53                @ one_one_nat ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.simps(6)
% 0.29/0.53  thf(fact_1578_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I5_J,axiom,
% 0.29/0.53      ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.29/0.53        ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 0.29/0.53        = ( if_nat
% 0.29/0.53          @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.29/0.53            & ~ ( ( X = Mi )
% 0.29/0.53                | ( X = Ma ) ) )
% 0.29/0.53          @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t2 @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t2 @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 0.29/0.53          @ one_one_nat ) ) ).
% 0.29/0.53  
% 0.29/0.53  % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(5)
% 0.29/0.53  thf(fact_1579_minNull__bound,axiom,
% 0.29/0.53      ! [T: vEBT_VEBT] : ( ord_less_eq_nat @ ( vEBT_T_m_i_n_N_u_l_l @ T ) @ one_one_nat ) ).
% 0.29/0.53  
% 0.29/0.53  % minNull_bound
% 0.29/0.53  thf(fact_1580_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Osimps_I2_J,axiom,
% 0.29/0.53      ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.29/0.53        ( ( vEBT_T_m_a_x_t @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.29/0.53        = one_one_nat ) ).
% 0.29/0.53  
% 0.29/0.53  % T\<^sub>m\<^sub>a\<^sub>x\<^sub>t.simps(2)
% 0.29/0.53  thf(fact_1581_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I5_J,axiom,
% 0.29/0.53      ! [Uz: product_prod_nat_nat,Va: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 0.29/0.53        ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz ) @ Va @ Vb @ Vc ) )
% 0.29/0.53        = one_one_nat ) ).
% 0.29/0.53  
% 0.29/0.53  % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.simps(5)
% 0.29/0.53  thf(fact_1582_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I4_J,axiom,
% 0.29/0.53      ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 0.29/0.53        ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) )
% 0.29/0.53        = one_one_nat ) ).
% 0.29/0.53  
% 0.29/0.53  % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.simps(4)
% 0.29/0.53  thf(fact_1583_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I4_J,axiom,
% 0.29/0.53      ! [Uy: nat,Uz: list_VEBT_VEBT,Va: vEBT_VEBT,Vb: nat] :
% 0.29/0.53        ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz @ Va ) @ Vb )
% 0.29/0.53        = one_one_nat ) ).
% 0.29/0.53  
% 0.29/0.53  % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.simps(4)
% 0.29/0.53  thf(fact_1584_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I3_J,axiom,
% 0.29/0.53      ! [Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,Va: nat] :
% 0.29/0.53        ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz ) @ Va )
% 0.29/0.53        = one_one_nat ) ).
% 0.29/0.53  
% 0.29/0.53  % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.simps(3)
% 0.29/0.53  thf(fact_1585_maxt__bound,axiom,
% 0.29/0.53      ! [T: vEBT_VEBT] : ( ord_less_eq_nat @ ( vEBT_T_m_a_x_t @ T ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % maxt_bound
% 0.29/0.53  thf(fact_1586_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Osimps_I3_J,axiom,
% 0.29/0.53      ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 0.29/0.53        ( ( vEBT_T_m_a_x_t @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 0.29/0.53        = one_one_nat ) ).
% 0.29/0.53  
% 0.29/0.53  % T\<^sub>m\<^sub>a\<^sub>x\<^sub>t.simps(3)
% 0.29/0.53  thf(fact_1587_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I4_J,axiom,
% 0.29/0.53      ! [V: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.29/0.53        ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) @ X )
% 0.29/0.53        = one_one_nat ) ).
% 0.29/0.53  
% 0.29/0.53  % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(4)
% 0.29/0.53  thf(fact_1588_insersimp_H,axiom,
% 0.29/0.53      ! [T: vEBT_VEBT,N: nat,Y2: nat] :
% 0.29/0.53        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.53       => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_12 )
% 0.29/0.53         => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t2 @ T @ Y2 ) @ one_one_nat ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % insersimp'
% 0.29/0.53  thf(fact_1589_insertsimp_H,axiom,
% 0.29/0.53      ! [T: vEBT_VEBT,N: nat,L2: nat] :
% 0.29/0.53        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.53       => ( ( vEBT_VEBT_minNull @ T )
% 0.29/0.53         => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t2 @ T @ L2 ) @ one_one_nat ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % insertsimp'
% 0.29/0.53  thf(fact_1590_pred__bound__height_H,axiom,
% 0.29/0.53      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.53        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.53       => ( ord_less_eq_nat @ ( vEBT_T_p_r_e_d2 @ T @ X ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % pred_bound_height'
% 0.29/0.53  thf(fact_1591_insert_H__bound__height,axiom,
% 0.29/0.53      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.53        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.53       => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t2 @ T @ X ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % insert'_bound_height
% 0.29/0.53  thf(fact_1592_succ_H__bound__height,axiom,
% 0.29/0.53      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.53        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.53       => ( ord_less_eq_nat @ ( vEBT_T_s_u_c_c2 @ T @ X ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % succ'_bound_height
% 0.29/0.53  thf(fact_1593_VEBT__internal_OminNull_Osimps_I5_J,axiom,
% 0.29/0.53      ! [Uz: product_prod_nat_nat,Va: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 0.29/0.53        ~ ( vEBT_VEBT_minNull @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz ) @ Va @ Vb @ Vc ) ) ).
% 0.29/0.53  
% 0.29/0.53  % VEBT_internal.minNull.simps(5)
% 0.29/0.53  thf(fact_1594_vebt__delete_Osimps_I4_J,axiom,
% 0.29/0.53      ! [Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Uu: nat] :
% 0.29/0.53        ( ( vEBT_vebt_delete @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Uu )
% 0.29/0.53        = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) ) ).
% 0.29/0.53  
% 0.29/0.53  % vebt_delete.simps(4)
% 0.29/0.53  thf(fact_1595_VEBT__internal_OminNull_Osimps_I4_J,axiom,
% 0.29/0.53      ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] : ( vEBT_VEBT_minNull @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) ) ).
% 0.29/0.53  
% 0.29/0.53  % VEBT_internal.minNull.simps(4)
% 0.29/0.53  thf(fact_1596_vebt__member_Osimps_I2_J,axiom,
% 0.29/0.53      ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X: nat] :
% 0.29/0.53        ~ ( vEBT_vebt_member @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X ) ).
% 0.29/0.53  
% 0.29/0.53  % vebt_member.simps(2)
% 0.29/0.53  thf(fact_1597_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I7_J,axiom,
% 0.29/0.53      ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.29/0.53        ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 0.29/0.53        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.29/0.53          @ ( if_nat
% 0.29/0.53            @ ( ( ord_less_nat @ X @ Mi )
% 0.29/0.53              | ( ord_less_nat @ Ma @ X ) )
% 0.29/0.53            @ one_one_nat
% 0.29/0.53            @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.29/0.53              @ ( if_nat
% 0.29/0.53                @ ( ( X = Mi )
% 0.29/0.53                  & ( X = Ma ) )
% 0.29/0.53                @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.29/0.53                @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ Summary ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat ) ) @ one_one_nat )
% 0.29/0.53                  @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.29/0.53                    @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                      @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.29/0.53                        @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                          @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_d_e_l_e_t_e @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                            @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.29/0.53                              @ ( if_nat
% 0.29/0.53                                @ ( ( ( X = Mi )
% 0.29/0.53                                   => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.29/0.53                                      = Ma ) )
% 0.29/0.53                                  & ( ( X != Mi )
% 0.29/0.53                                   => ( X = Ma ) ) )
% 0.29/0.53                                @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.29/0.53                                  @ ( plus_plus_nat @ one_one_nat
% 0.29/0.53                                    @ ( if_nat
% 0.29/0.53                                      @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                                        = none_nat )
% 0.29/0.53                                      @ one_one_nat
% 0.29/0.53                                      @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.29/0.53                                @ one_one_nat ) ) )
% 0.29/0.53                          @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.29/0.53                            @ ( if_nat
% 0.29/0.53                              @ ( ( ( X = Mi )
% 0.29/0.53                                 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.29/0.53                                    = Ma ) )
% 0.29/0.53                                & ( ( X != Mi )
% 0.29/0.53                                 => ( X = Ma ) ) )
% 0.29/0.53                              @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.29/0.53                              @ one_one_nat ) ) ) ) )
% 0.29/0.53                    @ one_one_nat ) ) ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.simps(7)
% 0.29/0.53  thf(fact_1598_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I7_J,axiom,
% 0.29/0.53      ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.29/0.53        ( ( vEBT_T_p_r_e_d @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 0.29/0.53        = ( plus_plus_nat @ one_one_nat
% 0.29/0.53          @ ( if_nat @ ( ord_less_nat @ Ma @ X ) @ one_one_nat
% 0.29/0.53            @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 0.29/0.53              @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.29/0.53                @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.29/0.53                  @ ( if_nat
% 0.29/0.53                    @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                       != none_nat )
% 0.29/0.53                      & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.29/0.53                    @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_p_r_e_d @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                    @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 0.29/0.53                      @ ( if_nat
% 0.29/0.53                        @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.53                          = none_nat )
% 0.29/0.53                        @ ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 0.29/0.53                        @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.29/0.53                @ one_one_nat ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.simps(7)
% 0.29/0.53  thf(fact_1599_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I5_J,axiom,
% 0.29/0.53      ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.29/0.53        ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 0.29/0.53        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 0.29/0.53          @ ( if_nat
% 0.29/0.53            @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.29/0.53              & ~ ( ( X = Mi )
% 0.29/0.53                  | ( X = Ma ) ) )
% 0.29/0.53            @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 0.29/0.53            @ one_one_nat ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(5)
% 0.29/0.53  thf(fact_1600_succ__empty,axiom,
% 0.29/0.53      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.53        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.53       => ( ( ( vEBT_vebt_succ @ T @ X )
% 0.29/0.53            = none_nat )
% 0.29/0.53          = ( ( collect_nat
% 0.29/0.53              @ ^ [Y: nat] :
% 0.29/0.53                  ( ( vEBT_vebt_member @ T @ Y )
% 0.29/0.53                  & ( ord_less_nat @ X @ Y ) ) )
% 0.29/0.53            = bot_bot_set_nat ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % succ_empty
% 0.29/0.53  thf(fact_1601_pred__empty,axiom,
% 0.29/0.53      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.53        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.53       => ( ( ( vEBT_vebt_pred @ T @ X )
% 0.29/0.53            = none_nat )
% 0.29/0.53          = ( ( collect_nat
% 0.29/0.53              @ ^ [Y: nat] :
% 0.29/0.53                  ( ( vEBT_vebt_member @ T @ Y )
% 0.29/0.53                  & ( ord_less_nat @ Y @ X ) ) )
% 0.29/0.53            = bot_bot_set_nat ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % pred_empty
% 0.29/0.53  thf(fact_1602_VEBT__internal_Omembermima_Osimps_I4_J,axiom,
% 0.29/0.53      ! [Mi: nat,Ma: nat,V: nat,TreeList: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 0.29/0.53        ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ V ) @ TreeList @ Vc ) @ X )
% 0.29/0.53        = ( ( X = Mi )
% 0.29/0.53          | ( X = Ma )
% 0.29/0.53          | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.29/0.53             => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53            & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % VEBT_internal.membermima.simps(4)
% 0.29/0.53  thf(fact_1603_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Oelims,axiom,
% 0.29/0.53      ! [X: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 0.29/0.53        ( ( ( vEBT_T_d_e_l_e_t_e @ X @ Xa2 )
% 0.29/0.53          = Y2 )
% 0.29/0.53       => ( ( ? [A4: $o,B3: $o] :
% 0.29/0.53                ( X
% 0.29/0.53                = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.29/0.53           => ( ( Xa2 = zero_zero_nat )
% 0.29/0.53             => ( Y2 != one_one_nat ) ) )
% 0.29/0.53         => ( ( ? [A4: $o,B3: $o] :
% 0.29/0.53                  ( X
% 0.29/0.53                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.29/0.53             => ( ( Xa2
% 0.29/0.53                  = ( suc @ zero_zero_nat ) )
% 0.29/0.53               => ( Y2 != one_one_nat ) ) )
% 0.29/0.53           => ( ( ? [A4: $o,B3: $o] :
% 0.29/0.53                    ( X
% 0.29/0.53                    = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.29/0.53               => ( ? [N3: nat] :
% 0.29/0.53                      ( Xa2
% 0.29/0.53                      = ( suc @ ( suc @ N3 ) ) )
% 0.29/0.53                 => ( Y2 != one_one_nat ) ) )
% 0.29/0.53             => ( ( ? [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.29/0.53                      ( X
% 0.29/0.53                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.29/0.53                 => ( Y2 != one_one_nat ) )
% 0.29/0.53               => ( ( ? [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.29/0.53                        ( X
% 0.29/0.53                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TreeList2 @ Summary2 ) )
% 0.29/0.53                   => ( Y2 != one_one_nat ) )
% 0.29/0.53                 => ( ( ? [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.29/0.53                          ( X
% 0.29/0.53                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary2 ) )
% 0.29/0.53                     => ( Y2 != one_one_nat ) )
% 0.29/0.53                   => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.29/0.53                          ( ( X
% 0.29/0.53                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 0.29/0.53                         => ( Y2
% 0.29/0.53                           != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.29/0.53                              @ ( if_nat
% 0.29/0.53                                @ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 0.29/0.53                                  | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 0.29/0.53                                @ one_one_nat
% 0.29/0.53                                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.29/0.53                                  @ ( if_nat
% 0.29/0.53                                    @ ( ( Xa2 = Mi2 )
% 0.29/0.53                                      & ( Xa2 = Ma2 ) )
% 0.29/0.53                                    @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.29/0.53                                    @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ Summary2 ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat ) ) @ one_one_nat )
% 0.29/0.53                                      @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.29/0.53                                        @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                                          @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.29/0.53                                            @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                                              @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_d_e_l_e_t_e @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                                                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.29/0.53                                                  @ ( if_nat
% 0.29/0.53                                                    @ ( ( ( Xa2 = Mi2 )
% 0.29/0.53                                                       => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 0.29/0.53                                                          = Ma2 ) )
% 0.29/0.53                                                      & ( ( Xa2 != Mi2 )
% 0.29/0.53                                                       => ( Xa2 = Ma2 ) ) )
% 0.29/0.53                                                    @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.29/0.53                                                      @ ( plus_plus_nat @ one_one_nat
% 0.29/0.53                                                        @ ( if_nat
% 0.29/0.53                                                          @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53                                                            = none_nat )
% 0.29/0.53                                                          @ one_one_nat
% 0.29/0.53                                                          @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.29/0.53                                                    @ one_one_nat ) ) )
% 0.29/0.53                                              @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.29/0.53                                                @ ( if_nat
% 0.29/0.53                                                  @ ( ( ( Xa2 = Mi2 )
% 0.29/0.53                                                     => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 0.29/0.53                                                        = Ma2 ) )
% 0.29/0.53                                                    & ( ( Xa2 != Mi2 )
% 0.29/0.53                                                     => ( Xa2 = Ma2 ) ) )
% 0.29/0.53                                                  @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.29/0.53                                                  @ one_one_nat ) ) ) ) )
% 0.29/0.53                                        @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.elims
% 0.29/0.53  thf(fact_1604_VEBT__internal_Onaive__member_Osimps_I3_J,axiom,
% 0.29/0.53      ! [Uy: option4927543243414619207at_nat,V: nat,TreeList: list_VEBT_VEBT,S3: vEBT_VEBT,X: nat] :
% 0.29/0.53        ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S3 ) @ X )
% 0.29/0.53        = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.29/0.53           => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53          & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % VEBT_internal.naive_member.simps(3)
% 0.29/0.53  thf(fact_1605_VEBT__internal_Omembermima_Osimps_I5_J,axiom,
% 0.29/0.53      ! [V: nat,TreeList: list_VEBT_VEBT,Vd: vEBT_VEBT,X: nat] :
% 0.29/0.53        ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) @ X )
% 0.29/0.53        = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.29/0.53           => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.53          & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % VEBT_internal.membermima.simps(5)
% 0.29/0.53  thf(fact_1606_pred__bound__height,axiom,
% 0.29/0.53      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.53        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.53       => ( ord_less_eq_nat @ ( vEBT_T_p_r_e_d @ T @ X ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % pred_bound_height
% 0.29/0.53  thf(fact_1607_insert__bound__height,axiom,
% 0.29/0.53      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.53        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.53       => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ T @ X ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % insert_bound_height
% 0.29/0.53  thf(fact_1608_valid__0__not,axiom,
% 0.29/0.53      ! [T: vEBT_VEBT] :
% 0.29/0.53        ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 0.29/0.53  
% 0.29/0.53  % valid_0_not
% 0.29/0.53  thf(fact_1609_valid__tree__deg__neq__0,axiom,
% 0.29/0.53      ! [T: vEBT_VEBT] :
% 0.29/0.53        ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 0.29/0.53  
% 0.29/0.53  % valid_tree_deg_neq_0
% 0.29/0.53  thf(fact_1610_deg__not__0,axiom,
% 0.29/0.53      ! [T: vEBT_VEBT,N: nat] :
% 0.29/0.53        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.53       => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.29/0.53  
% 0.29/0.53  % deg_not_0
% 0.29/0.53  thf(fact_1611_Leaf__0__not,axiom,
% 0.29/0.53      ! [A: $o,B: $o] :
% 0.29/0.53        ~ ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat ) ).
% 0.29/0.53  
% 0.29/0.53  % Leaf_0_not
% 0.29/0.53  thf(fact_1612_deg__1__Leafy,axiom,
% 0.29/0.53      ! [T: vEBT_VEBT,N: nat] :
% 0.29/0.53        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.53       => ( ( N = one_one_nat )
% 0.29/0.53         => ? [A4: $o,B3: $o] :
% 0.29/0.53              ( T
% 0.29/0.53              = ( vEBT_Leaf @ A4 @ B3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % deg_1_Leafy
% 0.29/0.53  thf(fact_1613_deg__1__Leaf,axiom,
% 0.29/0.53      ! [T: vEBT_VEBT] :
% 0.29/0.53        ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 0.29/0.53       => ? [A4: $o,B3: $o] :
% 0.29/0.53            ( T
% 0.29/0.53            = ( vEBT_Leaf @ A4 @ B3 ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % deg_1_Leaf
% 0.29/0.53  thf(fact_1614_deg1Leaf,axiom,
% 0.29/0.53      ! [T: vEBT_VEBT] :
% 0.29/0.53        ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 0.29/0.53        = ( ? [A3: $o,B4: $o] :
% 0.29/0.53              ( T
% 0.29/0.53              = ( vEBT_Leaf @ A3 @ B4 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % deg1Leaf
% 0.29/0.53  thf(fact_1615_both__member__options__def,axiom,
% 0.29/0.53      ( vEBT_V8194947554948674370ptions
% 0.29/0.53      = ( ^ [T2: vEBT_VEBT,X2: nat] :
% 0.29/0.53            ( ( vEBT_V5719532721284313246member @ T2 @ X2 )
% 0.29/0.53            | ( vEBT_VEBT_membermima @ T2 @ X2 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % both_member_options_def
% 0.29/0.53  thf(fact_1616_member__valid__both__member__options,axiom,
% 0.29/0.53      ! [Tree: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.53        ( ( vEBT_invar_vebt @ Tree @ N )
% 0.29/0.53       => ( ( vEBT_vebt_member @ Tree @ X )
% 0.29/0.53         => ( ( vEBT_V5719532721284313246member @ Tree @ X )
% 0.29/0.53            | ( vEBT_VEBT_membermima @ Tree @ X ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % member_valid_both_member_options
% 0.29/0.53  thf(fact_1617_VEBT_Oinject_I2_J,axiom,
% 0.29/0.53      ! [X21: $o,X222: $o,Y21: $o,Y222: $o] :
% 0.29/0.53        ( ( ( vEBT_Leaf @ X21 @ X222 )
% 0.29/0.53          = ( vEBT_Leaf @ Y21 @ Y222 ) )
% 0.29/0.53        = ( ( X21 = Y21 )
% 0.29/0.53          & ( X222 = Y222 ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % VEBT.inject(2)
% 0.29/0.53  thf(fact_1618_mint__corr__help__empty,axiom,
% 0.29/0.53      ! [T: vEBT_VEBT,N: nat] :
% 0.29/0.53        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.53       => ( ( ( vEBT_vebt_mint @ T )
% 0.29/0.53            = none_nat )
% 0.29/0.53         => ( ( vEBT_VEBT_set_vebt @ T )
% 0.29/0.53            = bot_bot_set_nat ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mint_corr_help_empty
% 0.29/0.53  thf(fact_1619_maxt__corr__help__empty,axiom,
% 0.29/0.53      ! [T: vEBT_VEBT,N: nat] :
% 0.29/0.53        ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.53       => ( ( ( vEBT_vebt_maxt @ T )
% 0.29/0.53            = none_nat )
% 0.29/0.53         => ( ( vEBT_VEBT_set_vebt @ T )
% 0.29/0.53            = bot_bot_set_nat ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % maxt_corr_help_empty
% 0.29/0.53  thf(fact_1620_le__zero__eq,axiom,
% 0.29/0.53      ! [N: nat] :
% 0.29/0.53        ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.29/0.53        = ( N = zero_zero_nat ) ) ).
% 0.29/0.53  
% 0.29/0.53  % le_zero_eq
% 0.29/0.53  thf(fact_1621_not__gr__zero,axiom,
% 0.29/0.53      ! [N: nat] :
% 0.29/0.53        ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 0.29/0.53        = ( N = zero_zero_nat ) ) ).
% 0.29/0.53  
% 0.29/0.53  % not_gr_zero
% 0.29/0.53  thf(fact_1622_mult__zero__left,axiom,
% 0.29/0.53      ! [A: rat] :
% 0.29/0.53        ( ( times_times_rat @ zero_zero_rat @ A )
% 0.29/0.53        = zero_zero_rat ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_zero_left
% 0.29/0.53  thf(fact_1623_mult__zero__left,axiom,
% 0.29/0.53      ! [A: complex] :
% 0.29/0.53        ( ( times_times_complex @ zero_zero_complex @ A )
% 0.29/0.53        = zero_zero_complex ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_zero_left
% 0.29/0.53  thf(fact_1624_mult__zero__left,axiom,
% 0.29/0.53      ! [A: real] :
% 0.29/0.53        ( ( times_times_real @ zero_zero_real @ A )
% 0.29/0.53        = zero_zero_real ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_zero_left
% 0.29/0.53  thf(fact_1625_mult__zero__left,axiom,
% 0.29/0.53      ! [A: nat] :
% 0.29/0.53        ( ( times_times_nat @ zero_zero_nat @ A )
% 0.29/0.53        = zero_zero_nat ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_zero_left
% 0.29/0.53  thf(fact_1626_mult__zero__left,axiom,
% 0.29/0.53      ! [A: int] :
% 0.29/0.53        ( ( times_times_int @ zero_zero_int @ A )
% 0.29/0.53        = zero_zero_int ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_zero_left
% 0.29/0.53  thf(fact_1627_mult__zero__right,axiom,
% 0.29/0.53      ! [A: rat] :
% 0.29/0.53        ( ( times_times_rat @ A @ zero_zero_rat )
% 0.29/0.53        = zero_zero_rat ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_zero_right
% 0.29/0.53  thf(fact_1628_mult__zero__right,axiom,
% 0.29/0.53      ! [A: complex] :
% 0.29/0.53        ( ( times_times_complex @ A @ zero_zero_complex )
% 0.29/0.53        = zero_zero_complex ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_zero_right
% 0.29/0.53  thf(fact_1629_mult__zero__right,axiom,
% 0.29/0.53      ! [A: real] :
% 0.29/0.53        ( ( times_times_real @ A @ zero_zero_real )
% 0.29/0.53        = zero_zero_real ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_zero_right
% 0.29/0.53  thf(fact_1630_mult__zero__right,axiom,
% 0.29/0.53      ! [A: nat] :
% 0.29/0.53        ( ( times_times_nat @ A @ zero_zero_nat )
% 0.29/0.53        = zero_zero_nat ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_zero_right
% 0.29/0.53  thf(fact_1631_mult__zero__right,axiom,
% 0.29/0.53      ! [A: int] :
% 0.29/0.53        ( ( times_times_int @ A @ zero_zero_int )
% 0.29/0.53        = zero_zero_int ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_zero_right
% 0.29/0.53  thf(fact_1632_mult__eq__0__iff,axiom,
% 0.29/0.53      ! [A: rat,B: rat] :
% 0.29/0.53        ( ( ( times_times_rat @ A @ B )
% 0.29/0.53          = zero_zero_rat )
% 0.29/0.53        = ( ( A = zero_zero_rat )
% 0.29/0.53          | ( B = zero_zero_rat ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_eq_0_iff
% 0.29/0.53  thf(fact_1633_mult__eq__0__iff,axiom,
% 0.29/0.53      ! [A: complex,B: complex] :
% 0.29/0.53        ( ( ( times_times_complex @ A @ B )
% 0.29/0.53          = zero_zero_complex )
% 0.29/0.53        = ( ( A = zero_zero_complex )
% 0.29/0.53          | ( B = zero_zero_complex ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_eq_0_iff
% 0.29/0.53  thf(fact_1634_mult__eq__0__iff,axiom,
% 0.29/0.53      ! [A: real,B: real] :
% 0.29/0.53        ( ( ( times_times_real @ A @ B )
% 0.29/0.53          = zero_zero_real )
% 0.29/0.53        = ( ( A = zero_zero_real )
% 0.29/0.53          | ( B = zero_zero_real ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_eq_0_iff
% 0.29/0.53  thf(fact_1635_mult__eq__0__iff,axiom,
% 0.29/0.53      ! [A: nat,B: nat] :
% 0.29/0.53        ( ( ( times_times_nat @ A @ B )
% 0.29/0.53          = zero_zero_nat )
% 0.29/0.53        = ( ( A = zero_zero_nat )
% 0.29/0.53          | ( B = zero_zero_nat ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_eq_0_iff
% 0.29/0.53  thf(fact_1636_mult__eq__0__iff,axiom,
% 0.29/0.53      ! [A: int,B: int] :
% 0.29/0.53        ( ( ( times_times_int @ A @ B )
% 0.29/0.53          = zero_zero_int )
% 0.29/0.53        = ( ( A = zero_zero_int )
% 0.29/0.53          | ( B = zero_zero_int ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_eq_0_iff
% 0.29/0.53  thf(fact_1637_mult__cancel__left,axiom,
% 0.29/0.53      ! [C: rat,A: rat,B: rat] :
% 0.29/0.53        ( ( ( times_times_rat @ C @ A )
% 0.29/0.53          = ( times_times_rat @ C @ B ) )
% 0.29/0.53        = ( ( C = zero_zero_rat )
% 0.29/0.53          | ( A = B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_cancel_left
% 0.29/0.53  thf(fact_1638_mult__cancel__left,axiom,
% 0.29/0.53      ! [C: complex,A: complex,B: complex] :
% 0.29/0.53        ( ( ( times_times_complex @ C @ A )
% 0.29/0.53          = ( times_times_complex @ C @ B ) )
% 0.29/0.53        = ( ( C = zero_zero_complex )
% 0.29/0.53          | ( A = B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_cancel_left
% 0.29/0.53  thf(fact_1639_mult__cancel__left,axiom,
% 0.29/0.53      ! [C: real,A: real,B: real] :
% 0.29/0.53        ( ( ( times_times_real @ C @ A )
% 0.29/0.53          = ( times_times_real @ C @ B ) )
% 0.29/0.53        = ( ( C = zero_zero_real )
% 0.29/0.53          | ( A = B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_cancel_left
% 0.29/0.53  thf(fact_1640_mult__cancel__left,axiom,
% 0.29/0.53      ! [C: nat,A: nat,B: nat] :
% 0.29/0.53        ( ( ( times_times_nat @ C @ A )
% 0.29/0.53          = ( times_times_nat @ C @ B ) )
% 0.29/0.53        = ( ( C = zero_zero_nat )
% 0.29/0.53          | ( A = B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_cancel_left
% 0.29/0.53  thf(fact_1641_mult__cancel__left,axiom,
% 0.29/0.53      ! [C: int,A: int,B: int] :
% 0.29/0.53        ( ( ( times_times_int @ C @ A )
% 0.29/0.53          = ( times_times_int @ C @ B ) )
% 0.29/0.53        = ( ( C = zero_zero_int )
% 0.29/0.53          | ( A = B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_cancel_left
% 0.29/0.53  thf(fact_1642_mult__cancel__right,axiom,
% 0.29/0.53      ! [A: rat,C: rat,B: rat] :
% 0.29/0.53        ( ( ( times_times_rat @ A @ C )
% 0.29/0.53          = ( times_times_rat @ B @ C ) )
% 0.29/0.53        = ( ( C = zero_zero_rat )
% 0.29/0.53          | ( A = B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_cancel_right
% 0.29/0.53  thf(fact_1643_mult__cancel__right,axiom,
% 0.29/0.53      ! [A: complex,C: complex,B: complex] :
% 0.29/0.53        ( ( ( times_times_complex @ A @ C )
% 0.29/0.53          = ( times_times_complex @ B @ C ) )
% 0.29/0.53        = ( ( C = zero_zero_complex )
% 0.29/0.53          | ( A = B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_cancel_right
% 0.29/0.53  thf(fact_1644_mult__cancel__right,axiom,
% 0.29/0.53      ! [A: real,C: real,B: real] :
% 0.29/0.53        ( ( ( times_times_real @ A @ C )
% 0.29/0.53          = ( times_times_real @ B @ C ) )
% 0.29/0.53        = ( ( C = zero_zero_real )
% 0.29/0.53          | ( A = B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_cancel_right
% 0.29/0.53  thf(fact_1645_mult__cancel__right,axiom,
% 0.29/0.53      ! [A: nat,C: nat,B: nat] :
% 0.29/0.53        ( ( ( times_times_nat @ A @ C )
% 0.29/0.53          = ( times_times_nat @ B @ C ) )
% 0.29/0.53        = ( ( C = zero_zero_nat )
% 0.29/0.53          | ( A = B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_cancel_right
% 0.29/0.53  thf(fact_1646_mult__cancel__right,axiom,
% 0.29/0.53      ! [A: int,C: int,B: int] :
% 0.29/0.53        ( ( ( times_times_int @ A @ C )
% 0.29/0.53          = ( times_times_int @ B @ C ) )
% 0.29/0.53        = ( ( C = zero_zero_int )
% 0.29/0.53          | ( A = B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_cancel_right
% 0.29/0.53  thf(fact_1647_add__0,axiom,
% 0.29/0.53      ! [A: complex] :
% 0.29/0.53        ( ( plus_plus_complex @ zero_zero_complex @ A )
% 0.29/0.53        = A ) ).
% 0.29/0.53  
% 0.29/0.53  % add_0
% 0.29/0.53  thf(fact_1648_add__0,axiom,
% 0.29/0.53      ! [A: real] :
% 0.29/0.53        ( ( plus_plus_real @ zero_zero_real @ A )
% 0.29/0.53        = A ) ).
% 0.29/0.53  
% 0.29/0.53  % add_0
% 0.29/0.53  thf(fact_1649_add__0,axiom,
% 0.29/0.53      ! [A: rat] :
% 0.29/0.53        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 0.29/0.53        = A ) ).
% 0.29/0.53  
% 0.29/0.53  % add_0
% 0.29/0.53  thf(fact_1650_add__0,axiom,
% 0.29/0.53      ! [A: nat] :
% 0.29/0.53        ( ( plus_plus_nat @ zero_zero_nat @ A )
% 0.29/0.53        = A ) ).
% 0.29/0.53  
% 0.29/0.53  % add_0
% 0.29/0.53  thf(fact_1651_add__0,axiom,
% 0.29/0.53      ! [A: int] :
% 0.29/0.53        ( ( plus_plus_int @ zero_zero_int @ A )
% 0.29/0.53        = A ) ).
% 0.29/0.53  
% 0.29/0.53  % add_0
% 0.29/0.53  thf(fact_1652_zero__eq__add__iff__both__eq__0,axiom,
% 0.29/0.53      ! [X: nat,Y2: nat] :
% 0.29/0.53        ( ( zero_zero_nat
% 0.29/0.53          = ( plus_plus_nat @ X @ Y2 ) )
% 0.29/0.53        = ( ( X = zero_zero_nat )
% 0.29/0.53          & ( Y2 = zero_zero_nat ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % zero_eq_add_iff_both_eq_0
% 0.29/0.53  thf(fact_1653_add__eq__0__iff__both__eq__0,axiom,
% 0.29/0.53      ! [X: nat,Y2: nat] :
% 0.29/0.53        ( ( ( plus_plus_nat @ X @ Y2 )
% 0.29/0.53          = zero_zero_nat )
% 0.29/0.53        = ( ( X = zero_zero_nat )
% 0.29/0.53          & ( Y2 = zero_zero_nat ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_eq_0_iff_both_eq_0
% 0.29/0.53  thf(fact_1654_add__cancel__right__right,axiom,
% 0.29/0.53      ! [A: complex,B: complex] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( plus_plus_complex @ A @ B ) )
% 0.29/0.53        = ( B = zero_zero_complex ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_cancel_right_right
% 0.29/0.53  thf(fact_1655_add__cancel__right__right,axiom,
% 0.29/0.53      ! [A: real,B: real] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( plus_plus_real @ A @ B ) )
% 0.29/0.53        = ( B = zero_zero_real ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_cancel_right_right
% 0.29/0.53  thf(fact_1656_add__cancel__right__right,axiom,
% 0.29/0.53      ! [A: rat,B: rat] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( plus_plus_rat @ A @ B ) )
% 0.29/0.53        = ( B = zero_zero_rat ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_cancel_right_right
% 0.29/0.53  thf(fact_1657_add__cancel__right__right,axiom,
% 0.29/0.53      ! [A: nat,B: nat] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( plus_plus_nat @ A @ B ) )
% 0.29/0.53        = ( B = zero_zero_nat ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_cancel_right_right
% 0.29/0.53  thf(fact_1658_add__cancel__right__right,axiom,
% 0.29/0.53      ! [A: int,B: int] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( plus_plus_int @ A @ B ) )
% 0.29/0.53        = ( B = zero_zero_int ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_cancel_right_right
% 0.29/0.53  thf(fact_1659_add__cancel__right__left,axiom,
% 0.29/0.53      ! [A: complex,B: complex] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( plus_plus_complex @ B @ A ) )
% 0.29/0.53        = ( B = zero_zero_complex ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_cancel_right_left
% 0.29/0.53  thf(fact_1660_add__cancel__right__left,axiom,
% 0.29/0.53      ! [A: real,B: real] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( plus_plus_real @ B @ A ) )
% 0.29/0.53        = ( B = zero_zero_real ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_cancel_right_left
% 0.29/0.53  thf(fact_1661_add__cancel__right__left,axiom,
% 0.29/0.53      ! [A: rat,B: rat] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( plus_plus_rat @ B @ A ) )
% 0.29/0.53        = ( B = zero_zero_rat ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_cancel_right_left
% 0.29/0.53  thf(fact_1662_add__cancel__right__left,axiom,
% 0.29/0.53      ! [A: nat,B: nat] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( plus_plus_nat @ B @ A ) )
% 0.29/0.53        = ( B = zero_zero_nat ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_cancel_right_left
% 0.29/0.53  thf(fact_1663_add__cancel__right__left,axiom,
% 0.29/0.53      ! [A: int,B: int] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( plus_plus_int @ B @ A ) )
% 0.29/0.53        = ( B = zero_zero_int ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_cancel_right_left
% 0.29/0.53  thf(fact_1664_add__cancel__left__right,axiom,
% 0.29/0.53      ! [A: complex,B: complex] :
% 0.29/0.53        ( ( ( plus_plus_complex @ A @ B )
% 0.29/0.53          = A )
% 0.29/0.53        = ( B = zero_zero_complex ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_cancel_left_right
% 0.29/0.53  thf(fact_1665_add__cancel__left__right,axiom,
% 0.29/0.53      ! [A: real,B: real] :
% 0.29/0.53        ( ( ( plus_plus_real @ A @ B )
% 0.29/0.53          = A )
% 0.29/0.53        = ( B = zero_zero_real ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_cancel_left_right
% 0.29/0.53  thf(fact_1666_add__cancel__left__right,axiom,
% 0.29/0.53      ! [A: rat,B: rat] :
% 0.29/0.53        ( ( ( plus_plus_rat @ A @ B )
% 0.29/0.53          = A )
% 0.29/0.53        = ( B = zero_zero_rat ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_cancel_left_right
% 0.29/0.53  thf(fact_1667_add__cancel__left__right,axiom,
% 0.29/0.53      ! [A: nat,B: nat] :
% 0.29/0.53        ( ( ( plus_plus_nat @ A @ B )
% 0.29/0.53          = A )
% 0.29/0.53        = ( B = zero_zero_nat ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_cancel_left_right
% 0.29/0.53  thf(fact_1668_add__cancel__left__right,axiom,
% 0.29/0.53      ! [A: int,B: int] :
% 0.29/0.53        ( ( ( plus_plus_int @ A @ B )
% 0.29/0.53          = A )
% 0.29/0.53        = ( B = zero_zero_int ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_cancel_left_right
% 0.29/0.53  thf(fact_1669_add__cancel__left__left,axiom,
% 0.29/0.53      ! [B: complex,A: complex] :
% 0.29/0.53        ( ( ( plus_plus_complex @ B @ A )
% 0.29/0.53          = A )
% 0.29/0.53        = ( B = zero_zero_complex ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_cancel_left_left
% 0.29/0.53  thf(fact_1670_add__cancel__left__left,axiom,
% 0.29/0.53      ! [B: real,A: real] :
% 0.29/0.53        ( ( ( plus_plus_real @ B @ A )
% 0.29/0.53          = A )
% 0.29/0.53        = ( B = zero_zero_real ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_cancel_left_left
% 0.29/0.53  thf(fact_1671_add__cancel__left__left,axiom,
% 0.29/0.53      ! [B: rat,A: rat] :
% 0.29/0.53        ( ( ( plus_plus_rat @ B @ A )
% 0.29/0.53          = A )
% 0.29/0.53        = ( B = zero_zero_rat ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_cancel_left_left
% 0.29/0.53  thf(fact_1672_add__cancel__left__left,axiom,
% 0.29/0.53      ! [B: nat,A: nat] :
% 0.29/0.53        ( ( ( plus_plus_nat @ B @ A )
% 0.29/0.53          = A )
% 0.29/0.53        = ( B = zero_zero_nat ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_cancel_left_left
% 0.29/0.53  thf(fact_1673_add__cancel__left__left,axiom,
% 0.29/0.53      ! [B: int,A: int] :
% 0.29/0.53        ( ( ( plus_plus_int @ B @ A )
% 0.29/0.53          = A )
% 0.29/0.53        = ( B = zero_zero_int ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_cancel_left_left
% 0.29/0.53  thf(fact_1674_double__zero__sym,axiom,
% 0.29/0.53      ! [A: real] :
% 0.29/0.53        ( ( zero_zero_real
% 0.29/0.53          = ( plus_plus_real @ A @ A ) )
% 0.29/0.53        = ( A = zero_zero_real ) ) ).
% 0.29/0.53  
% 0.29/0.53  % double_zero_sym
% 0.29/0.53  thf(fact_1675_double__zero__sym,axiom,
% 0.29/0.53      ! [A: rat] :
% 0.29/0.53        ( ( zero_zero_rat
% 0.29/0.53          = ( plus_plus_rat @ A @ A ) )
% 0.29/0.53        = ( A = zero_zero_rat ) ) ).
% 0.29/0.53  
% 0.29/0.53  % double_zero_sym
% 0.29/0.53  thf(fact_1676_double__zero__sym,axiom,
% 0.29/0.53      ! [A: int] :
% 0.29/0.53        ( ( zero_zero_int
% 0.29/0.53          = ( plus_plus_int @ A @ A ) )
% 0.29/0.53        = ( A = zero_zero_int ) ) ).
% 0.29/0.53  
% 0.29/0.53  % double_zero_sym
% 0.29/0.53  thf(fact_1677_add_Oright__neutral,axiom,
% 0.29/0.53      ! [A: complex] :
% 0.29/0.53        ( ( plus_plus_complex @ A @ zero_zero_complex )
% 0.29/0.53        = A ) ).
% 0.29/0.53  
% 0.29/0.53  % add.right_neutral
% 0.29/0.53  thf(fact_1678_add_Oright__neutral,axiom,
% 0.29/0.53      ! [A: real] :
% 0.29/0.53        ( ( plus_plus_real @ A @ zero_zero_real )
% 0.29/0.53        = A ) ).
% 0.29/0.53  
% 0.29/0.53  % add.right_neutral
% 0.29/0.53  thf(fact_1679_add_Oright__neutral,axiom,
% 0.29/0.53      ! [A: rat] :
% 0.29/0.53        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 0.29/0.53        = A ) ).
% 0.29/0.53  
% 0.29/0.53  % add.right_neutral
% 0.29/0.53  thf(fact_1680_add_Oright__neutral,axiom,
% 0.29/0.53      ! [A: nat] :
% 0.29/0.53        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.29/0.53        = A ) ).
% 0.29/0.53  
% 0.29/0.53  % add.right_neutral
% 0.29/0.53  thf(fact_1681_add_Oright__neutral,axiom,
% 0.29/0.53      ! [A: int] :
% 0.29/0.53        ( ( plus_plus_int @ A @ zero_zero_int )
% 0.29/0.53        = A ) ).
% 0.29/0.53  
% 0.29/0.53  % add.right_neutral
% 0.29/0.53  thf(fact_1682_diff__self,axiom,
% 0.29/0.53      ! [A: complex] :
% 0.29/0.53        ( ( minus_minus_complex @ A @ A )
% 0.29/0.53        = zero_zero_complex ) ).
% 0.29/0.53  
% 0.29/0.53  % diff_self
% 0.29/0.53  thf(fact_1683_diff__self,axiom,
% 0.29/0.53      ! [A: real] :
% 0.29/0.53        ( ( minus_minus_real @ A @ A )
% 0.29/0.53        = zero_zero_real ) ).
% 0.29/0.53  
% 0.29/0.53  % diff_self
% 0.29/0.53  thf(fact_1684_diff__self,axiom,
% 0.29/0.53      ! [A: rat] :
% 0.29/0.53        ( ( minus_minus_rat @ A @ A )
% 0.29/0.53        = zero_zero_rat ) ).
% 0.29/0.53  
% 0.29/0.53  % diff_self
% 0.29/0.53  thf(fact_1685_diff__self,axiom,
% 0.29/0.53      ! [A: int] :
% 0.29/0.53        ( ( minus_minus_int @ A @ A )
% 0.29/0.53        = zero_zero_int ) ).
% 0.29/0.53  
% 0.29/0.53  % diff_self
% 0.29/0.53  thf(fact_1686_diff__0__right,axiom,
% 0.29/0.53      ! [A: complex] :
% 0.29/0.53        ( ( minus_minus_complex @ A @ zero_zero_complex )
% 0.29/0.53        = A ) ).
% 0.29/0.53  
% 0.29/0.53  % diff_0_right
% 0.29/0.53  thf(fact_1687_diff__0__right,axiom,
% 0.29/0.53      ! [A: real] :
% 0.29/0.53        ( ( minus_minus_real @ A @ zero_zero_real )
% 0.29/0.53        = A ) ).
% 0.29/0.53  
% 0.29/0.53  % diff_0_right
% 0.29/0.53  thf(fact_1688_diff__0__right,axiom,
% 0.29/0.53      ! [A: rat] :
% 0.29/0.53        ( ( minus_minus_rat @ A @ zero_zero_rat )
% 0.29/0.53        = A ) ).
% 0.29/0.53  
% 0.29/0.53  % diff_0_right
% 0.29/0.53  thf(fact_1689_diff__0__right,axiom,
% 0.29/0.53      ! [A: int] :
% 0.29/0.53        ( ( minus_minus_int @ A @ zero_zero_int )
% 0.29/0.53        = A ) ).
% 0.29/0.53  
% 0.29/0.53  % diff_0_right
% 0.29/0.53  thf(fact_1690_zero__diff,axiom,
% 0.29/0.53      ! [A: nat] :
% 0.29/0.53        ( ( minus_minus_nat @ zero_zero_nat @ A )
% 0.29/0.53        = zero_zero_nat ) ).
% 0.29/0.53  
% 0.29/0.53  % zero_diff
% 0.29/0.53  thf(fact_1691_diff__zero,axiom,
% 0.29/0.53      ! [A: complex] :
% 0.29/0.53        ( ( minus_minus_complex @ A @ zero_zero_complex )
% 0.29/0.53        = A ) ).
% 0.29/0.53  
% 0.29/0.53  % diff_zero
% 0.29/0.53  thf(fact_1692_diff__zero,axiom,
% 0.29/0.53      ! [A: real] :
% 0.29/0.53        ( ( minus_minus_real @ A @ zero_zero_real )
% 0.29/0.53        = A ) ).
% 0.29/0.53  
% 0.29/0.53  % diff_zero
% 0.29/0.53  thf(fact_1693_diff__zero,axiom,
% 0.29/0.53      ! [A: rat] :
% 0.29/0.53        ( ( minus_minus_rat @ A @ zero_zero_rat )
% 0.29/0.53        = A ) ).
% 0.29/0.53  
% 0.29/0.53  % diff_zero
% 0.29/0.53  thf(fact_1694_diff__zero,axiom,
% 0.29/0.53      ! [A: nat] :
% 0.29/0.53        ( ( minus_minus_nat @ A @ zero_zero_nat )
% 0.29/0.53        = A ) ).
% 0.29/0.53  
% 0.29/0.53  % diff_zero
% 0.29/0.53  thf(fact_1695_diff__zero,axiom,
% 0.29/0.53      ! [A: int] :
% 0.29/0.53        ( ( minus_minus_int @ A @ zero_zero_int )
% 0.29/0.53        = A ) ).
% 0.29/0.53  
% 0.29/0.53  % diff_zero
% 0.29/0.53  thf(fact_1696_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.29/0.53      ! [A: complex] :
% 0.29/0.53        ( ( minus_minus_complex @ A @ A )
% 0.29/0.53        = zero_zero_complex ) ).
% 0.29/0.53  
% 0.29/0.53  % cancel_comm_monoid_add_class.diff_cancel
% 0.29/0.53  thf(fact_1697_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.29/0.53      ! [A: real] :
% 0.29/0.53        ( ( minus_minus_real @ A @ A )
% 0.29/0.53        = zero_zero_real ) ).
% 0.29/0.53  
% 0.29/0.53  % cancel_comm_monoid_add_class.diff_cancel
% 0.29/0.53  thf(fact_1698_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.29/0.53      ! [A: rat] :
% 0.29/0.53        ( ( minus_minus_rat @ A @ A )
% 0.29/0.53        = zero_zero_rat ) ).
% 0.29/0.53  
% 0.29/0.53  % cancel_comm_monoid_add_class.diff_cancel
% 0.29/0.53  thf(fact_1699_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.29/0.53      ! [A: nat] :
% 0.29/0.53        ( ( minus_minus_nat @ A @ A )
% 0.29/0.53        = zero_zero_nat ) ).
% 0.29/0.53  
% 0.29/0.53  % cancel_comm_monoid_add_class.diff_cancel
% 0.29/0.53  thf(fact_1700_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.29/0.53      ! [A: int] :
% 0.29/0.53        ( ( minus_minus_int @ A @ A )
% 0.29/0.53        = zero_zero_int ) ).
% 0.29/0.53  
% 0.29/0.53  % cancel_comm_monoid_add_class.diff_cancel
% 0.29/0.53  thf(fact_1701_bits__div__0,axiom,
% 0.29/0.53      ! [A: nat] :
% 0.29/0.53        ( ( divide_divide_nat @ zero_zero_nat @ A )
% 0.29/0.53        = zero_zero_nat ) ).
% 0.29/0.53  
% 0.29/0.53  % bits_div_0
% 0.29/0.53  thf(fact_1702_bits__div__0,axiom,
% 0.29/0.53      ! [A: int] :
% 0.29/0.53        ( ( divide_divide_int @ zero_zero_int @ A )
% 0.29/0.53        = zero_zero_int ) ).
% 0.29/0.53  
% 0.29/0.53  % bits_div_0
% 0.29/0.53  thf(fact_1703_bits__div__by__0,axiom,
% 0.29/0.53      ! [A: nat] :
% 0.29/0.53        ( ( divide_divide_nat @ A @ zero_zero_nat )
% 0.29/0.53        = zero_zero_nat ) ).
% 0.29/0.53  
% 0.29/0.53  % bits_div_by_0
% 0.29/0.53  thf(fact_1704_bits__div__by__0,axiom,
% 0.29/0.53      ! [A: int] :
% 0.29/0.53        ( ( divide_divide_int @ A @ zero_zero_int )
% 0.29/0.53        = zero_zero_int ) ).
% 0.29/0.53  
% 0.29/0.53  % bits_div_by_0
% 0.29/0.53  thf(fact_1705_div__0,axiom,
% 0.29/0.53      ! [A: complex] :
% 0.29/0.53        ( ( divide1717551699836669952omplex @ zero_zero_complex @ A )
% 0.29/0.53        = zero_zero_complex ) ).
% 0.29/0.53  
% 0.29/0.53  % div_0
% 0.29/0.53  thf(fact_1706_div__0,axiom,
% 0.29/0.53      ! [A: real] :
% 0.29/0.53        ( ( divide_divide_real @ zero_zero_real @ A )
% 0.29/0.53        = zero_zero_real ) ).
% 0.29/0.53  
% 0.29/0.53  % div_0
% 0.29/0.53  thf(fact_1707_div__0,axiom,
% 0.29/0.53      ! [A: rat] :
% 0.29/0.53        ( ( divide_divide_rat @ zero_zero_rat @ A )
% 0.29/0.53        = zero_zero_rat ) ).
% 0.29/0.53  
% 0.29/0.53  % div_0
% 0.29/0.53  thf(fact_1708_div__0,axiom,
% 0.29/0.53      ! [A: nat] :
% 0.29/0.53        ( ( divide_divide_nat @ zero_zero_nat @ A )
% 0.29/0.53        = zero_zero_nat ) ).
% 0.29/0.53  
% 0.29/0.53  % div_0
% 0.29/0.53  thf(fact_1709_div__0,axiom,
% 0.29/0.53      ! [A: int] :
% 0.29/0.53        ( ( divide_divide_int @ zero_zero_int @ A )
% 0.29/0.53        = zero_zero_int ) ).
% 0.29/0.53  
% 0.29/0.53  % div_0
% 0.29/0.53  thf(fact_1710_div__by__0,axiom,
% 0.29/0.53      ! [A: complex] :
% 0.29/0.53        ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 0.29/0.53        = zero_zero_complex ) ).
% 0.29/0.53  
% 0.29/0.53  % div_by_0
% 0.29/0.53  thf(fact_1711_div__by__0,axiom,
% 0.29/0.53      ! [A: real] :
% 0.29/0.53        ( ( divide_divide_real @ A @ zero_zero_real )
% 0.29/0.53        = zero_zero_real ) ).
% 0.29/0.53  
% 0.29/0.53  % div_by_0
% 0.29/0.53  thf(fact_1712_div__by__0,axiom,
% 0.29/0.53      ! [A: rat] :
% 0.29/0.53        ( ( divide_divide_rat @ A @ zero_zero_rat )
% 0.29/0.53        = zero_zero_rat ) ).
% 0.29/0.53  
% 0.29/0.53  % div_by_0
% 0.29/0.53  thf(fact_1713_div__by__0,axiom,
% 0.29/0.53      ! [A: nat] :
% 0.29/0.53        ( ( divide_divide_nat @ A @ zero_zero_nat )
% 0.29/0.53        = zero_zero_nat ) ).
% 0.29/0.53  
% 0.29/0.53  % div_by_0
% 0.29/0.53  thf(fact_1714_div__by__0,axiom,
% 0.29/0.53      ! [A: int] :
% 0.29/0.53        ( ( divide_divide_int @ A @ zero_zero_int )
% 0.29/0.53        = zero_zero_int ) ).
% 0.29/0.53  
% 0.29/0.53  % div_by_0
% 0.29/0.53  thf(fact_1715_divide__eq__0__iff,axiom,
% 0.29/0.53      ! [A: complex,B: complex] :
% 0.29/0.53        ( ( ( divide1717551699836669952omplex @ A @ B )
% 0.29/0.53          = zero_zero_complex )
% 0.29/0.53        = ( ( A = zero_zero_complex )
% 0.29/0.53          | ( B = zero_zero_complex ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % divide_eq_0_iff
% 0.29/0.53  thf(fact_1716_divide__eq__0__iff,axiom,
% 0.29/0.53      ! [A: real,B: real] :
% 0.29/0.53        ( ( ( divide_divide_real @ A @ B )
% 0.29/0.53          = zero_zero_real )
% 0.29/0.53        = ( ( A = zero_zero_real )
% 0.29/0.53          | ( B = zero_zero_real ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % divide_eq_0_iff
% 0.29/0.53  thf(fact_1717_divide__eq__0__iff,axiom,
% 0.29/0.53      ! [A: rat,B: rat] :
% 0.29/0.53        ( ( ( divide_divide_rat @ A @ B )
% 0.29/0.53          = zero_zero_rat )
% 0.29/0.53        = ( ( A = zero_zero_rat )
% 0.29/0.53          | ( B = zero_zero_rat ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % divide_eq_0_iff
% 0.29/0.53  thf(fact_1718_divide__cancel__left,axiom,
% 0.29/0.53      ! [C: complex,A: complex,B: complex] :
% 0.29/0.53        ( ( ( divide1717551699836669952omplex @ C @ A )
% 0.29/0.53          = ( divide1717551699836669952omplex @ C @ B ) )
% 0.29/0.53        = ( ( C = zero_zero_complex )
% 0.29/0.53          | ( A = B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % divide_cancel_left
% 0.29/0.53  thf(fact_1719_divide__cancel__left,axiom,
% 0.29/0.53      ! [C: real,A: real,B: real] :
% 0.29/0.53        ( ( ( divide_divide_real @ C @ A )
% 0.29/0.53          = ( divide_divide_real @ C @ B ) )
% 0.29/0.53        = ( ( C = zero_zero_real )
% 0.29/0.53          | ( A = B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % divide_cancel_left
% 0.29/0.53  thf(fact_1720_divide__cancel__left,axiom,
% 0.29/0.53      ! [C: rat,A: rat,B: rat] :
% 0.29/0.53        ( ( ( divide_divide_rat @ C @ A )
% 0.29/0.53          = ( divide_divide_rat @ C @ B ) )
% 0.29/0.53        = ( ( C = zero_zero_rat )
% 0.29/0.53          | ( A = B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % divide_cancel_left
% 0.29/0.53  thf(fact_1721_divide__cancel__right,axiom,
% 0.29/0.53      ! [A: complex,C: complex,B: complex] :
% 0.29/0.53        ( ( ( divide1717551699836669952omplex @ A @ C )
% 0.29/0.53          = ( divide1717551699836669952omplex @ B @ C ) )
% 0.29/0.53        = ( ( C = zero_zero_complex )
% 0.29/0.53          | ( A = B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % divide_cancel_right
% 0.29/0.53  thf(fact_1722_divide__cancel__right,axiom,
% 0.29/0.53      ! [A: real,C: real,B: real] :
% 0.29/0.53        ( ( ( divide_divide_real @ A @ C )
% 0.29/0.53          = ( divide_divide_real @ B @ C ) )
% 0.29/0.53        = ( ( C = zero_zero_real )
% 0.29/0.53          | ( A = B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % divide_cancel_right
% 0.29/0.53  thf(fact_1723_divide__cancel__right,axiom,
% 0.29/0.53      ! [A: rat,C: rat,B: rat] :
% 0.29/0.53        ( ( ( divide_divide_rat @ A @ C )
% 0.29/0.53          = ( divide_divide_rat @ B @ C ) )
% 0.29/0.53        = ( ( C = zero_zero_rat )
% 0.29/0.53          | ( A = B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % divide_cancel_right
% 0.29/0.53  thf(fact_1724_division__ring__divide__zero,axiom,
% 0.29/0.53      ! [A: complex] :
% 0.29/0.53        ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 0.29/0.53        = zero_zero_complex ) ).
% 0.29/0.53  
% 0.29/0.53  % division_ring_divide_zero
% 0.29/0.53  thf(fact_1725_division__ring__divide__zero,axiom,
% 0.29/0.53      ! [A: real] :
% 0.29/0.53        ( ( divide_divide_real @ A @ zero_zero_real )
% 0.29/0.53        = zero_zero_real ) ).
% 0.29/0.53  
% 0.29/0.53  % division_ring_divide_zero
% 0.29/0.53  thf(fact_1726_division__ring__divide__zero,axiom,
% 0.29/0.53      ! [A: rat] :
% 0.29/0.53        ( ( divide_divide_rat @ A @ zero_zero_rat )
% 0.29/0.53        = zero_zero_rat ) ).
% 0.29/0.53  
% 0.29/0.53  % division_ring_divide_zero
% 0.29/0.53  thf(fact_1727_bot__nat__0_Onot__eq__extremum,axiom,
% 0.29/0.53      ! [A: nat] :
% 0.29/0.53        ( ( A != zero_zero_nat )
% 0.29/0.53        = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % bot_nat_0.not_eq_extremum
% 0.29/0.53  thf(fact_1728_neq0__conv,axiom,
% 0.29/0.53      ! [N: nat] :
% 0.29/0.53        ( ( N != zero_zero_nat )
% 0.29/0.53        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.29/0.53  
% 0.29/0.53  % neq0_conv
% 0.29/0.53  thf(fact_1729_less__nat__zero__code,axiom,
% 0.29/0.53      ! [N: nat] :
% 0.29/0.53        ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.29/0.53  
% 0.29/0.53  % less_nat_zero_code
% 0.29/0.53  thf(fact_1730_Nat_Oadd__0__right,axiom,
% 0.29/0.53      ! [M: nat] :
% 0.29/0.53        ( ( plus_plus_nat @ M @ zero_zero_nat )
% 0.29/0.53        = M ) ).
% 0.29/0.53  
% 0.29/0.53  % Nat.add_0_right
% 0.29/0.53  thf(fact_1731_add__is__0,axiom,
% 0.29/0.53      ! [M: nat,N: nat] :
% 0.29/0.53        ( ( ( plus_plus_nat @ M @ N )
% 0.29/0.53          = zero_zero_nat )
% 0.29/0.53        = ( ( M = zero_zero_nat )
% 0.29/0.53          & ( N = zero_zero_nat ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_is_0
% 0.29/0.53  thf(fact_1732_bot__nat__0_Oextremum,axiom,
% 0.29/0.53      ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 0.29/0.53  
% 0.29/0.53  % bot_nat_0.extremum
% 0.29/0.53  thf(fact_1733_le0,axiom,
% 0.29/0.53      ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.29/0.53  
% 0.29/0.53  % le0
% 0.29/0.53  thf(fact_1734_mult__is__0,axiom,
% 0.29/0.53      ! [M: nat,N: nat] :
% 0.29/0.53        ( ( ( times_times_nat @ M @ N )
% 0.29/0.53          = zero_zero_nat )
% 0.29/0.53        = ( ( M = zero_zero_nat )
% 0.29/0.53          | ( N = zero_zero_nat ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_is_0
% 0.29/0.53  thf(fact_1735_mult__0__right,axiom,
% 0.29/0.53      ! [M: nat] :
% 0.29/0.53        ( ( times_times_nat @ M @ zero_zero_nat )
% 0.29/0.53        = zero_zero_nat ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_0_right
% 0.29/0.53  thf(fact_1736_mult__cancel1,axiom,
% 0.29/0.53      ! [K: nat,M: nat,N: nat] :
% 0.29/0.53        ( ( ( times_times_nat @ K @ M )
% 0.29/0.53          = ( times_times_nat @ K @ N ) )
% 0.29/0.53        = ( ( M = N )
% 0.29/0.53          | ( K = zero_zero_nat ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_cancel1
% 0.29/0.53  thf(fact_1737_mult__cancel2,axiom,
% 0.29/0.53      ! [M: nat,K: nat,N: nat] :
% 0.29/0.53        ( ( ( times_times_nat @ M @ K )
% 0.29/0.53          = ( times_times_nat @ N @ K ) )
% 0.29/0.53        = ( ( M = N )
% 0.29/0.53          | ( K = zero_zero_nat ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_cancel2
% 0.29/0.53  thf(fact_1738_diff__self__eq__0,axiom,
% 0.29/0.53      ! [M: nat] :
% 0.29/0.53        ( ( minus_minus_nat @ M @ M )
% 0.29/0.53        = zero_zero_nat ) ).
% 0.29/0.53  
% 0.29/0.53  % diff_self_eq_0
% 0.29/0.53  thf(fact_1739_diff__0__eq__0,axiom,
% 0.29/0.53      ! [N: nat] :
% 0.29/0.53        ( ( minus_minus_nat @ zero_zero_nat @ N )
% 0.29/0.53        = zero_zero_nat ) ).
% 0.29/0.53  
% 0.29/0.53  % diff_0_eq_0
% 0.29/0.53  thf(fact_1740_max__0R,axiom,
% 0.29/0.53      ! [N: nat] :
% 0.29/0.53        ( ( ord_max_nat @ N @ zero_zero_nat )
% 0.29/0.53        = N ) ).
% 0.29/0.53  
% 0.29/0.53  % max_0R
% 0.29/0.53  thf(fact_1741_max__0L,axiom,
% 0.29/0.53      ! [N: nat] :
% 0.29/0.53        ( ( ord_max_nat @ zero_zero_nat @ N )
% 0.29/0.53        = N ) ).
% 0.29/0.53  
% 0.29/0.53  % max_0L
% 0.29/0.53  thf(fact_1742_max__nat_Oright__neutral,axiom,
% 0.29/0.53      ! [A: nat] :
% 0.29/0.53        ( ( ord_max_nat @ A @ zero_zero_nat )
% 0.29/0.53        = A ) ).
% 0.29/0.53  
% 0.29/0.53  % max_nat.right_neutral
% 0.29/0.53  thf(fact_1743_max__nat_Oneutr__eq__iff,axiom,
% 0.29/0.53      ! [A: nat,B: nat] :
% 0.29/0.53        ( ( zero_zero_nat
% 0.29/0.53          = ( ord_max_nat @ A @ B ) )
% 0.29/0.53        = ( ( A = zero_zero_nat )
% 0.29/0.53          & ( B = zero_zero_nat ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % max_nat.neutr_eq_iff
% 0.29/0.53  thf(fact_1744_max__nat_Oleft__neutral,axiom,
% 0.29/0.53      ! [A: nat] :
% 0.29/0.53        ( ( ord_max_nat @ zero_zero_nat @ A )
% 0.29/0.53        = A ) ).
% 0.29/0.53  
% 0.29/0.53  % max_nat.left_neutral
% 0.29/0.53  thf(fact_1745_max__nat_Oeq__neutr__iff,axiom,
% 0.29/0.53      ! [A: nat,B: nat] :
% 0.29/0.53        ( ( ( ord_max_nat @ A @ B )
% 0.29/0.53          = zero_zero_nat )
% 0.29/0.53        = ( ( A = zero_zero_nat )
% 0.29/0.53          & ( B = zero_zero_nat ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % max_nat.eq_neutr_iff
% 0.29/0.53  thf(fact_1746_add__le__same__cancel1,axiom,
% 0.29/0.53      ! [B: real,A: real] :
% 0.29/0.53        ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B )
% 0.29/0.53        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_le_same_cancel1
% 0.29/0.53  thf(fact_1747_add__le__same__cancel1,axiom,
% 0.29/0.53      ! [B: rat,A: rat] :
% 0.29/0.53        ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 0.29/0.53        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_le_same_cancel1
% 0.29/0.53  thf(fact_1748_add__le__same__cancel1,axiom,
% 0.29/0.53      ! [B: nat,A: nat] :
% 0.29/0.53        ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.29/0.53        = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_le_same_cancel1
% 0.29/0.53  thf(fact_1749_add__le__same__cancel1,axiom,
% 0.29/0.53      ! [B: int,A: int] :
% 0.29/0.53        ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 0.29/0.53        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_le_same_cancel1
% 0.29/0.53  thf(fact_1750_add__le__same__cancel2,axiom,
% 0.29/0.53      ! [A: real,B: real] :
% 0.29/0.53        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.29/0.53        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_le_same_cancel2
% 0.29/0.53  thf(fact_1751_add__le__same__cancel2,axiom,
% 0.29/0.53      ! [A: rat,B: rat] :
% 0.29/0.53        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.29/0.53        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_le_same_cancel2
% 0.29/0.53  thf(fact_1752_add__le__same__cancel2,axiom,
% 0.29/0.53      ! [A: nat,B: nat] :
% 0.29/0.53        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.29/0.53        = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_le_same_cancel2
% 0.29/0.53  thf(fact_1753_add__le__same__cancel2,axiom,
% 0.29/0.53      ! [A: int,B: int] :
% 0.29/0.53        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.29/0.53        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_le_same_cancel2
% 0.29/0.53  thf(fact_1754_le__add__same__cancel1,axiom,
% 0.29/0.53      ! [A: real,B: real] :
% 0.29/0.53        ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
% 0.29/0.53        = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % le_add_same_cancel1
% 0.29/0.53  thf(fact_1755_le__add__same__cancel1,axiom,
% 0.29/0.53      ! [A: rat,B: rat] :
% 0.29/0.53        ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 0.29/0.53        = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % le_add_same_cancel1
% 0.29/0.53  thf(fact_1756_le__add__same__cancel1,axiom,
% 0.29/0.53      ! [A: nat,B: nat] :
% 0.29/0.53        ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.29/0.53        = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % le_add_same_cancel1
% 0.29/0.53  thf(fact_1757_le__add__same__cancel1,axiom,
% 0.29/0.53      ! [A: int,B: int] :
% 0.29/0.53        ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 0.29/0.53        = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % le_add_same_cancel1
% 0.29/0.53  thf(fact_1758_le__add__same__cancel2,axiom,
% 0.29/0.53      ! [A: real,B: real] :
% 0.29/0.53        ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
% 0.29/0.53        = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % le_add_same_cancel2
% 0.29/0.53  thf(fact_1759_le__add__same__cancel2,axiom,
% 0.29/0.53      ! [A: rat,B: rat] :
% 0.29/0.53        ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 0.29/0.53        = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % le_add_same_cancel2
% 0.29/0.53  thf(fact_1760_le__add__same__cancel2,axiom,
% 0.29/0.53      ! [A: nat,B: nat] :
% 0.29/0.53        ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 0.29/0.53        = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % le_add_same_cancel2
% 0.29/0.53  thf(fact_1761_le__add__same__cancel2,axiom,
% 0.29/0.53      ! [A: int,B: int] :
% 0.29/0.53        ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 0.29/0.53        = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % le_add_same_cancel2
% 0.29/0.53  thf(fact_1762_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.29/0.53      ! [A: real] :
% 0.29/0.53        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 0.29/0.53        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.29/0.53  
% 0.29/0.53  % double_add_le_zero_iff_single_add_le_zero
% 0.29/0.53  thf(fact_1763_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.29/0.53      ! [A: rat] :
% 0.29/0.53        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 0.29/0.53        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.29/0.53  
% 0.29/0.53  % double_add_le_zero_iff_single_add_le_zero
% 0.29/0.53  thf(fact_1764_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.29/0.53      ! [A: int] :
% 0.29/0.53        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 0.29/0.53        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.29/0.53  
% 0.29/0.53  % double_add_le_zero_iff_single_add_le_zero
% 0.29/0.53  thf(fact_1765_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.29/0.53      ! [A: real] :
% 0.29/0.53        ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 0.29/0.53        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % zero_le_double_add_iff_zero_le_single_add
% 0.29/0.53  thf(fact_1766_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.29/0.53      ! [A: rat] :
% 0.29/0.53        ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 0.29/0.53        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % zero_le_double_add_iff_zero_le_single_add
% 0.29/0.53  thf(fact_1767_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.29/0.53      ! [A: int] :
% 0.29/0.53        ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 0.29/0.53        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % zero_le_double_add_iff_zero_le_single_add
% 0.29/0.53  thf(fact_1768_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.29/0.53      ! [A: real] :
% 0.29/0.53        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 0.29/0.53        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % zero_less_double_add_iff_zero_less_single_add
% 0.29/0.53  thf(fact_1769_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.29/0.53      ! [A: rat] :
% 0.29/0.53        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 0.29/0.53        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % zero_less_double_add_iff_zero_less_single_add
% 0.29/0.53  thf(fact_1770_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.29/0.53      ! [A: int] :
% 0.29/0.53        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 0.29/0.53        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % zero_less_double_add_iff_zero_less_single_add
% 0.29/0.53  thf(fact_1771_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.29/0.53      ! [A: real] :
% 0.29/0.53        ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 0.29/0.53        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.29/0.53  
% 0.29/0.53  % double_add_less_zero_iff_single_add_less_zero
% 0.29/0.53  thf(fact_1772_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.29/0.53      ! [A: rat] :
% 0.29/0.53        ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 0.29/0.53        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.29/0.53  
% 0.29/0.53  % double_add_less_zero_iff_single_add_less_zero
% 0.29/0.53  thf(fact_1773_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.29/0.53      ! [A: int] :
% 0.29/0.53        ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 0.29/0.53        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.29/0.53  
% 0.29/0.53  % double_add_less_zero_iff_single_add_less_zero
% 0.29/0.53  thf(fact_1774_less__add__same__cancel2,axiom,
% 0.29/0.53      ! [A: real,B: real] :
% 0.29/0.53        ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 0.29/0.53        = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % less_add_same_cancel2
% 0.29/0.53  thf(fact_1775_less__add__same__cancel2,axiom,
% 0.29/0.53      ! [A: rat,B: rat] :
% 0.29/0.53        ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 0.29/0.53        = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % less_add_same_cancel2
% 0.29/0.53  thf(fact_1776_less__add__same__cancel2,axiom,
% 0.29/0.53      ! [A: nat,B: nat] :
% 0.29/0.53        ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 0.29/0.53        = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % less_add_same_cancel2
% 0.29/0.53  thf(fact_1777_less__add__same__cancel2,axiom,
% 0.29/0.53      ! [A: int,B: int] :
% 0.29/0.53        ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 0.29/0.53        = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % less_add_same_cancel2
% 0.29/0.53  thf(fact_1778_less__add__same__cancel1,axiom,
% 0.29/0.53      ! [A: real,B: real] :
% 0.29/0.53        ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 0.29/0.53        = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % less_add_same_cancel1
% 0.29/0.53  thf(fact_1779_less__add__same__cancel1,axiom,
% 0.29/0.53      ! [A: rat,B: rat] :
% 0.29/0.53        ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 0.29/0.53        = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % less_add_same_cancel1
% 0.29/0.53  thf(fact_1780_less__add__same__cancel1,axiom,
% 0.29/0.53      ! [A: nat,B: nat] :
% 0.29/0.53        ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.29/0.53        = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % less_add_same_cancel1
% 0.29/0.53  thf(fact_1781_less__add__same__cancel1,axiom,
% 0.29/0.53      ! [A: int,B: int] :
% 0.29/0.53        ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 0.29/0.53        = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % less_add_same_cancel1
% 0.29/0.53  thf(fact_1782_add__less__same__cancel2,axiom,
% 0.29/0.53      ! [A: real,B: real] :
% 0.29/0.53        ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.29/0.53        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_less_same_cancel2
% 0.29/0.53  thf(fact_1783_add__less__same__cancel2,axiom,
% 0.29/0.53      ! [A: rat,B: rat] :
% 0.29/0.53        ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.29/0.53        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_less_same_cancel2
% 0.29/0.53  thf(fact_1784_add__less__same__cancel2,axiom,
% 0.29/0.53      ! [A: nat,B: nat] :
% 0.29/0.53        ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.29/0.53        = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_less_same_cancel2
% 0.29/0.53  thf(fact_1785_add__less__same__cancel2,axiom,
% 0.29/0.53      ! [A: int,B: int] :
% 0.29/0.53        ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.29/0.53        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_less_same_cancel2
% 0.29/0.53  thf(fact_1786_add__less__same__cancel1,axiom,
% 0.29/0.53      ! [B: real,A: real] :
% 0.29/0.53        ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 0.29/0.53        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_less_same_cancel1
% 0.29/0.53  thf(fact_1787_add__less__same__cancel1,axiom,
% 0.29/0.53      ! [B: rat,A: rat] :
% 0.29/0.53        ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 0.29/0.53        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_less_same_cancel1
% 0.29/0.53  thf(fact_1788_add__less__same__cancel1,axiom,
% 0.29/0.53      ! [B: nat,A: nat] :
% 0.29/0.53        ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.29/0.53        = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_less_same_cancel1
% 0.29/0.53  thf(fact_1789_add__less__same__cancel1,axiom,
% 0.29/0.53      ! [B: int,A: int] :
% 0.29/0.53        ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 0.29/0.53        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add_less_same_cancel1
% 0.29/0.53  thf(fact_1790_diff__ge__0__iff__ge,axiom,
% 0.29/0.53      ! [A: real,B: real] :
% 0.29/0.53        ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 0.29/0.53        = ( ord_less_eq_real @ B @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % diff_ge_0_iff_ge
% 0.29/0.53  thf(fact_1791_diff__ge__0__iff__ge,axiom,
% 0.29/0.53      ! [A: rat,B: rat] :
% 0.29/0.53        ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 0.29/0.53        = ( ord_less_eq_rat @ B @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % diff_ge_0_iff_ge
% 0.29/0.53  thf(fact_1792_diff__ge__0__iff__ge,axiom,
% 0.29/0.53      ! [A: int,B: int] :
% 0.29/0.53        ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 0.29/0.53        = ( ord_less_eq_int @ B @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % diff_ge_0_iff_ge
% 0.29/0.53  thf(fact_1793_diff__gt__0__iff__gt,axiom,
% 0.29/0.53      ! [A: real,B: real] :
% 0.29/0.53        ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 0.29/0.53        = ( ord_less_real @ B @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % diff_gt_0_iff_gt
% 0.29/0.53  thf(fact_1794_diff__gt__0__iff__gt,axiom,
% 0.29/0.53      ! [A: rat,B: rat] :
% 0.29/0.53        ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 0.29/0.53        = ( ord_less_rat @ B @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % diff_gt_0_iff_gt
% 0.29/0.53  thf(fact_1795_diff__gt__0__iff__gt,axiom,
% 0.29/0.53      ! [A: int,B: int] :
% 0.29/0.53        ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 0.29/0.53        = ( ord_less_int @ B @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % diff_gt_0_iff_gt
% 0.29/0.53  thf(fact_1796_mult__cancel__right2,axiom,
% 0.29/0.54      ! [A: rat,C: rat] :
% 0.29/0.54        ( ( ( times_times_rat @ A @ C )
% 0.29/0.54          = C )
% 0.29/0.54        = ( ( C = zero_zero_rat )
% 0.29/0.54          | ( A = one_one_rat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_cancel_right2
% 0.29/0.54  thf(fact_1797_mult__cancel__right2,axiom,
% 0.29/0.54      ! [A: complex,C: complex] :
% 0.29/0.54        ( ( ( times_times_complex @ A @ C )
% 0.29/0.54          = C )
% 0.29/0.54        = ( ( C = zero_zero_complex )
% 0.29/0.54          | ( A = one_one_complex ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_cancel_right2
% 0.29/0.54  thf(fact_1798_mult__cancel__right2,axiom,
% 0.29/0.54      ! [A: real,C: real] :
% 0.29/0.54        ( ( ( times_times_real @ A @ C )
% 0.29/0.54          = C )
% 0.29/0.54        = ( ( C = zero_zero_real )
% 0.29/0.54          | ( A = one_one_real ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_cancel_right2
% 0.29/0.54  thf(fact_1799_mult__cancel__right2,axiom,
% 0.29/0.54      ! [A: int,C: int] :
% 0.29/0.54        ( ( ( times_times_int @ A @ C )
% 0.29/0.54          = C )
% 0.29/0.54        = ( ( C = zero_zero_int )
% 0.29/0.54          | ( A = one_one_int ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_cancel_right2
% 0.29/0.54  thf(fact_1800_mult__cancel__right1,axiom,
% 0.29/0.54      ! [C: rat,B: rat] :
% 0.29/0.54        ( ( C
% 0.29/0.54          = ( times_times_rat @ B @ C ) )
% 0.29/0.54        = ( ( C = zero_zero_rat )
% 0.29/0.54          | ( B = one_one_rat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_cancel_right1
% 0.29/0.54  thf(fact_1801_mult__cancel__right1,axiom,
% 0.29/0.54      ! [C: complex,B: complex] :
% 0.29/0.54        ( ( C
% 0.29/0.54          = ( times_times_complex @ B @ C ) )
% 0.29/0.54        = ( ( C = zero_zero_complex )
% 0.29/0.54          | ( B = one_one_complex ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_cancel_right1
% 0.29/0.54  thf(fact_1802_mult__cancel__right1,axiom,
% 0.29/0.54      ! [C: real,B: real] :
% 0.29/0.54        ( ( C
% 0.29/0.54          = ( times_times_real @ B @ C ) )
% 0.29/0.54        = ( ( C = zero_zero_real )
% 0.29/0.54          | ( B = one_one_real ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_cancel_right1
% 0.29/0.54  thf(fact_1803_mult__cancel__right1,axiom,
% 0.29/0.54      ! [C: int,B: int] :
% 0.29/0.54        ( ( C
% 0.29/0.54          = ( times_times_int @ B @ C ) )
% 0.29/0.54        = ( ( C = zero_zero_int )
% 0.29/0.54          | ( B = one_one_int ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_cancel_right1
% 0.29/0.54  thf(fact_1804_mult__cancel__left2,axiom,
% 0.29/0.54      ! [C: rat,A: rat] :
% 0.29/0.54        ( ( ( times_times_rat @ C @ A )
% 0.29/0.54          = C )
% 0.29/0.54        = ( ( C = zero_zero_rat )
% 0.29/0.54          | ( A = one_one_rat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_cancel_left2
% 0.29/0.54  thf(fact_1805_mult__cancel__left2,axiom,
% 0.29/0.54      ! [C: complex,A: complex] :
% 0.29/0.54        ( ( ( times_times_complex @ C @ A )
% 0.29/0.54          = C )
% 0.29/0.54        = ( ( C = zero_zero_complex )
% 0.29/0.54          | ( A = one_one_complex ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_cancel_left2
% 0.29/0.54  thf(fact_1806_mult__cancel__left2,axiom,
% 0.29/0.54      ! [C: real,A: real] :
% 0.29/0.54        ( ( ( times_times_real @ C @ A )
% 0.29/0.54          = C )
% 0.29/0.54        = ( ( C = zero_zero_real )
% 0.29/0.54          | ( A = one_one_real ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_cancel_left2
% 0.29/0.54  thf(fact_1807_mult__cancel__left2,axiom,
% 0.29/0.54      ! [C: int,A: int] :
% 0.29/0.54        ( ( ( times_times_int @ C @ A )
% 0.29/0.54          = C )
% 0.29/0.54        = ( ( C = zero_zero_int )
% 0.29/0.54          | ( A = one_one_int ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_cancel_left2
% 0.29/0.54  thf(fact_1808_mult__cancel__left1,axiom,
% 0.29/0.54      ! [C: rat,B: rat] :
% 0.29/0.54        ( ( C
% 0.29/0.54          = ( times_times_rat @ C @ B ) )
% 0.29/0.54        = ( ( C = zero_zero_rat )
% 0.29/0.54          | ( B = one_one_rat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_cancel_left1
% 0.29/0.54  thf(fact_1809_mult__cancel__left1,axiom,
% 0.29/0.54      ! [C: complex,B: complex] :
% 0.29/0.54        ( ( C
% 0.29/0.54          = ( times_times_complex @ C @ B ) )
% 0.29/0.54        = ( ( C = zero_zero_complex )
% 0.29/0.54          | ( B = one_one_complex ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_cancel_left1
% 0.29/0.54  thf(fact_1810_mult__cancel__left1,axiom,
% 0.29/0.54      ! [C: real,B: real] :
% 0.29/0.54        ( ( C
% 0.29/0.54          = ( times_times_real @ C @ B ) )
% 0.29/0.54        = ( ( C = zero_zero_real )
% 0.29/0.54          | ( B = one_one_real ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_cancel_left1
% 0.29/0.54  thf(fact_1811_mult__cancel__left1,axiom,
% 0.29/0.54      ! [C: int,B: int] :
% 0.29/0.54        ( ( C
% 0.29/0.54          = ( times_times_int @ C @ B ) )
% 0.29/0.54        = ( ( C = zero_zero_int )
% 0.29/0.54          | ( B = one_one_int ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_cancel_left1
% 0.29/0.54  thf(fact_1812_sum__squares__eq__zero__iff,axiom,
% 0.29/0.54      ! [X: rat,Y2: rat] :
% 0.29/0.54        ( ( ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y2 @ Y2 ) )
% 0.29/0.54          = zero_zero_rat )
% 0.29/0.54        = ( ( X = zero_zero_rat )
% 0.29/0.54          & ( Y2 = zero_zero_rat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sum_squares_eq_zero_iff
% 0.29/0.54  thf(fact_1813_sum__squares__eq__zero__iff,axiom,
% 0.29/0.54      ! [X: real,Y2: real] :
% 0.29/0.54        ( ( ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y2 @ Y2 ) )
% 0.29/0.54          = zero_zero_real )
% 0.29/0.54        = ( ( X = zero_zero_real )
% 0.29/0.54          & ( Y2 = zero_zero_real ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sum_squares_eq_zero_iff
% 0.29/0.54  thf(fact_1814_sum__squares__eq__zero__iff,axiom,
% 0.29/0.54      ! [X: int,Y2: int] :
% 0.29/0.54        ( ( ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y2 @ Y2 ) )
% 0.29/0.54          = zero_zero_int )
% 0.29/0.54        = ( ( X = zero_zero_int )
% 0.29/0.54          & ( Y2 = zero_zero_int ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sum_squares_eq_zero_iff
% 0.29/0.54  thf(fact_1815_diff__numeral__special_I9_J,axiom,
% 0.29/0.54      ( ( minus_minus_complex @ one_one_complex @ one_one_complex )
% 0.29/0.54      = zero_zero_complex ) ).
% 0.29/0.54  
% 0.29/0.54  % diff_numeral_special(9)
% 0.29/0.54  thf(fact_1816_diff__numeral__special_I9_J,axiom,
% 0.29/0.54      ( ( minus_minus_real @ one_one_real @ one_one_real )
% 0.29/0.54      = zero_zero_real ) ).
% 0.29/0.54  
% 0.29/0.54  % diff_numeral_special(9)
% 0.29/0.54  thf(fact_1817_diff__numeral__special_I9_J,axiom,
% 0.29/0.54      ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 0.29/0.54      = zero_zero_rat ) ).
% 0.29/0.54  
% 0.29/0.54  % diff_numeral_special(9)
% 0.29/0.54  thf(fact_1818_diff__numeral__special_I9_J,axiom,
% 0.29/0.54      ( ( minus_minus_int @ one_one_int @ one_one_int )
% 0.29/0.54      = zero_zero_int ) ).
% 0.29/0.54  
% 0.29/0.54  % diff_numeral_special(9)
% 0.29/0.54  thf(fact_1819_div__mult__mult1,axiom,
% 0.29/0.54      ! [C: nat,A: nat,B: nat] :
% 0.29/0.54        ( ( C != zero_zero_nat )
% 0.29/0.54       => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 0.29/0.54          = ( divide_divide_nat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_mult_mult1
% 0.29/0.54  thf(fact_1820_div__mult__mult1,axiom,
% 0.29/0.54      ! [C: int,A: int,B: int] :
% 0.29/0.54        ( ( C != zero_zero_int )
% 0.29/0.54       => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.29/0.54          = ( divide_divide_int @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_mult_mult1
% 0.29/0.54  thf(fact_1821_div__mult__mult2,axiom,
% 0.29/0.54      ! [C: nat,A: nat,B: nat] :
% 0.29/0.54        ( ( C != zero_zero_nat )
% 0.29/0.54       => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 0.29/0.54          = ( divide_divide_nat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_mult_mult2
% 0.29/0.54  thf(fact_1822_div__mult__mult2,axiom,
% 0.29/0.54      ! [C: int,A: int,B: int] :
% 0.29/0.54        ( ( C != zero_zero_int )
% 0.29/0.54       => ( ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.29/0.54          = ( divide_divide_int @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_mult_mult2
% 0.29/0.54  thf(fact_1823_div__mult__mult1__if,axiom,
% 0.29/0.54      ! [C: nat,A: nat,B: nat] :
% 0.29/0.54        ( ( ( C = zero_zero_nat )
% 0.29/0.54         => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 0.29/0.54            = zero_zero_nat ) )
% 0.29/0.54        & ( ( C != zero_zero_nat )
% 0.29/0.54         => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 0.29/0.54            = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_mult_mult1_if
% 0.29/0.54  thf(fact_1824_div__mult__mult1__if,axiom,
% 0.29/0.54      ! [C: int,A: int,B: int] :
% 0.29/0.54        ( ( ( C = zero_zero_int )
% 0.29/0.54         => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.29/0.54            = zero_zero_int ) )
% 0.29/0.54        & ( ( C != zero_zero_int )
% 0.29/0.54         => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.29/0.54            = ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_mult_mult1_if
% 0.29/0.54  thf(fact_1825_nonzero__mult__div__cancel__left,axiom,
% 0.29/0.54      ! [A: complex,B: complex] :
% 0.29/0.54        ( ( A != zero_zero_complex )
% 0.29/0.54       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ A )
% 0.29/0.54          = B ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nonzero_mult_div_cancel_left
% 0.29/0.54  thf(fact_1826_nonzero__mult__div__cancel__left,axiom,
% 0.29/0.54      ! [A: real,B: real] :
% 0.29/0.54        ( ( A != zero_zero_real )
% 0.29/0.54       => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ A )
% 0.29/0.54          = B ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nonzero_mult_div_cancel_left
% 0.29/0.54  thf(fact_1827_nonzero__mult__div__cancel__left,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 0.29/0.54        ( ( A != zero_zero_rat )
% 0.29/0.54       => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ A )
% 0.29/0.54          = B ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nonzero_mult_div_cancel_left
% 0.29/0.54  thf(fact_1828_nonzero__mult__div__cancel__left,axiom,
% 0.29/0.54      ! [A: nat,B: nat] :
% 0.29/0.54        ( ( A != zero_zero_nat )
% 0.29/0.54       => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 0.29/0.54          = B ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nonzero_mult_div_cancel_left
% 0.29/0.54  thf(fact_1829_nonzero__mult__div__cancel__left,axiom,
% 0.29/0.54      ! [A: int,B: int] :
% 0.29/0.54        ( ( A != zero_zero_int )
% 0.29/0.54       => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 0.29/0.54          = B ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nonzero_mult_div_cancel_left
% 0.29/0.54  thf(fact_1830_nonzero__mult__div__cancel__right,axiom,
% 0.29/0.54      ! [B: complex,A: complex] :
% 0.29/0.54        ( ( B != zero_zero_complex )
% 0.29/0.54       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ B )
% 0.29/0.54          = A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nonzero_mult_div_cancel_right
% 0.29/0.54  thf(fact_1831_nonzero__mult__div__cancel__right,axiom,
% 0.29/0.54      ! [B: real,A: real] :
% 0.29/0.54        ( ( B != zero_zero_real )
% 0.29/0.54       => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ B )
% 0.29/0.54          = A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nonzero_mult_div_cancel_right
% 0.29/0.54  thf(fact_1832_nonzero__mult__div__cancel__right,axiom,
% 0.29/0.54      ! [B: rat,A: rat] :
% 0.29/0.54        ( ( B != zero_zero_rat )
% 0.29/0.54       => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ B )
% 0.29/0.54          = A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nonzero_mult_div_cancel_right
% 0.29/0.54  thf(fact_1833_nonzero__mult__div__cancel__right,axiom,
% 0.29/0.54      ! [B: nat,A: nat] :
% 0.29/0.54        ( ( B != zero_zero_nat )
% 0.29/0.54       => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 0.29/0.54          = A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nonzero_mult_div_cancel_right
% 0.29/0.54  thf(fact_1834_nonzero__mult__div__cancel__right,axiom,
% 0.29/0.54      ! [B: int,A: int] :
% 0.29/0.54        ( ( B != zero_zero_int )
% 0.29/0.54       => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 0.29/0.54          = A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nonzero_mult_div_cancel_right
% 0.29/0.54  thf(fact_1835_mult__divide__mult__cancel__left__if,axiom,
% 0.29/0.54      ! [C: complex,A: complex,B: complex] :
% 0.29/0.54        ( ( ( C = zero_zero_complex )
% 0.29/0.54         => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 0.29/0.54            = zero_zero_complex ) )
% 0.29/0.54        & ( ( C != zero_zero_complex )
% 0.29/0.54         => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 0.29/0.54            = ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_divide_mult_cancel_left_if
% 0.29/0.54  thf(fact_1836_mult__divide__mult__cancel__left__if,axiom,
% 0.29/0.54      ! [C: real,A: real,B: real] :
% 0.29/0.54        ( ( ( C = zero_zero_real )
% 0.29/0.54         => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.29/0.54            = zero_zero_real ) )
% 0.29/0.54        & ( ( C != zero_zero_real )
% 0.29/0.54         => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.29/0.54            = ( divide_divide_real @ A @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_divide_mult_cancel_left_if
% 0.29/0.54  thf(fact_1837_mult__divide__mult__cancel__left__if,axiom,
% 0.29/0.54      ! [C: rat,A: rat,B: rat] :
% 0.29/0.54        ( ( ( C = zero_zero_rat )
% 0.29/0.54         => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.29/0.54            = zero_zero_rat ) )
% 0.29/0.54        & ( ( C != zero_zero_rat )
% 0.29/0.54         => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.29/0.54            = ( divide_divide_rat @ A @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_divide_mult_cancel_left_if
% 0.29/0.54  thf(fact_1838_nonzero__mult__divide__mult__cancel__left,axiom,
% 0.29/0.54      ! [C: complex,A: complex,B: complex] :
% 0.29/0.54        ( ( C != zero_zero_complex )
% 0.29/0.54       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 0.29/0.54          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nonzero_mult_divide_mult_cancel_left
% 0.29/0.54  thf(fact_1839_nonzero__mult__divide__mult__cancel__left,axiom,
% 0.29/0.54      ! [C: real,A: real,B: real] :
% 0.29/0.54        ( ( C != zero_zero_real )
% 0.29/0.54       => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.29/0.54          = ( divide_divide_real @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nonzero_mult_divide_mult_cancel_left
% 0.29/0.54  thf(fact_1840_nonzero__mult__divide__mult__cancel__left,axiom,
% 0.29/0.54      ! [C: rat,A: rat,B: rat] :
% 0.29/0.54        ( ( C != zero_zero_rat )
% 0.29/0.54       => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.29/0.54          = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nonzero_mult_divide_mult_cancel_left
% 0.29/0.54  thf(fact_1841_nonzero__mult__divide__mult__cancel__left2,axiom,
% 0.29/0.54      ! [C: complex,A: complex,B: complex] :
% 0.29/0.54        ( ( C != zero_zero_complex )
% 0.29/0.54       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ B @ C ) )
% 0.29/0.54          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nonzero_mult_divide_mult_cancel_left2
% 0.29/0.54  thf(fact_1842_nonzero__mult__divide__mult__cancel__left2,axiom,
% 0.29/0.54      ! [C: real,A: real,B: real] :
% 0.29/0.54        ( ( C != zero_zero_real )
% 0.29/0.54       => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ B @ C ) )
% 0.29/0.54          = ( divide_divide_real @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nonzero_mult_divide_mult_cancel_left2
% 0.29/0.54  thf(fact_1843_nonzero__mult__divide__mult__cancel__left2,axiom,
% 0.29/0.54      ! [C: rat,A: rat,B: rat] :
% 0.29/0.54        ( ( C != zero_zero_rat )
% 0.29/0.54       => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ B @ C ) )
% 0.29/0.54          = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nonzero_mult_divide_mult_cancel_left2
% 0.29/0.54  thf(fact_1844_nonzero__mult__divide__mult__cancel__right,axiom,
% 0.29/0.54      ! [C: complex,A: complex,B: complex] :
% 0.29/0.54        ( ( C != zero_zero_complex )
% 0.29/0.54       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 0.29/0.54          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nonzero_mult_divide_mult_cancel_right
% 0.29/0.54  thf(fact_1845_nonzero__mult__divide__mult__cancel__right,axiom,
% 0.29/0.54      ! [C: real,A: real,B: real] :
% 0.29/0.54        ( ( C != zero_zero_real )
% 0.29/0.54       => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 0.29/0.54          = ( divide_divide_real @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nonzero_mult_divide_mult_cancel_right
% 0.29/0.54  thf(fact_1846_nonzero__mult__divide__mult__cancel__right,axiom,
% 0.29/0.54      ! [C: rat,A: rat,B: rat] :
% 0.29/0.54        ( ( C != zero_zero_rat )
% 0.29/0.54       => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.29/0.54          = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nonzero_mult_divide_mult_cancel_right
% 0.29/0.54  thf(fact_1847_nonzero__mult__divide__mult__cancel__right2,axiom,
% 0.29/0.54      ! [C: complex,A: complex,B: complex] :
% 0.29/0.54        ( ( C != zero_zero_complex )
% 0.29/0.54       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ C @ B ) )
% 0.29/0.54          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nonzero_mult_divide_mult_cancel_right2
% 0.29/0.54  thf(fact_1848_nonzero__mult__divide__mult__cancel__right2,axiom,
% 0.29/0.54      ! [C: real,A: real,B: real] :
% 0.29/0.54        ( ( C != zero_zero_real )
% 0.29/0.54       => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ C @ B ) )
% 0.29/0.54          = ( divide_divide_real @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nonzero_mult_divide_mult_cancel_right2
% 0.29/0.54  thf(fact_1849_nonzero__mult__divide__mult__cancel__right2,axiom,
% 0.29/0.54      ! [C: rat,A: rat,B: rat] :
% 0.29/0.54        ( ( C != zero_zero_rat )
% 0.29/0.54       => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ C @ B ) )
% 0.29/0.54          = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nonzero_mult_divide_mult_cancel_right2
% 0.29/0.54  thf(fact_1850_diff__add__zero,axiom,
% 0.29/0.54      ! [A: nat,B: nat] :
% 0.29/0.54        ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.29/0.54        = zero_zero_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % diff_add_zero
% 0.29/0.54  thf(fact_1851_div__self,axiom,
% 0.29/0.54      ! [A: complex] :
% 0.29/0.54        ( ( A != zero_zero_complex )
% 0.29/0.54       => ( ( divide1717551699836669952omplex @ A @ A )
% 0.29/0.54          = one_one_complex ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_self
% 0.29/0.54  thf(fact_1852_div__self,axiom,
% 0.29/0.54      ! [A: real] :
% 0.29/0.54        ( ( A != zero_zero_real )
% 0.29/0.54       => ( ( divide_divide_real @ A @ A )
% 0.29/0.54          = one_one_real ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_self
% 0.29/0.54  thf(fact_1853_div__self,axiom,
% 0.29/0.54      ! [A: rat] :
% 0.29/0.54        ( ( A != zero_zero_rat )
% 0.29/0.54       => ( ( divide_divide_rat @ A @ A )
% 0.29/0.54          = one_one_rat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_self
% 0.29/0.54  thf(fact_1854_div__self,axiom,
% 0.29/0.54      ! [A: nat] :
% 0.29/0.54        ( ( A != zero_zero_nat )
% 0.29/0.54       => ( ( divide_divide_nat @ A @ A )
% 0.29/0.54          = one_one_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_self
% 0.29/0.54  thf(fact_1855_div__self,axiom,
% 0.29/0.54      ! [A: int] :
% 0.29/0.54        ( ( A != zero_zero_int )
% 0.29/0.54       => ( ( divide_divide_int @ A @ A )
% 0.29/0.54          = one_one_int ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_self
% 0.29/0.54  thf(fact_1856_zero__eq__1__divide__iff,axiom,
% 0.29/0.54      ! [A: real] :
% 0.29/0.54        ( ( zero_zero_real
% 0.29/0.54          = ( divide_divide_real @ one_one_real @ A ) )
% 0.29/0.54        = ( A = zero_zero_real ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_eq_1_divide_iff
% 0.29/0.54  thf(fact_1857_zero__eq__1__divide__iff,axiom,
% 0.29/0.54      ! [A: rat] :
% 0.29/0.54        ( ( zero_zero_rat
% 0.29/0.54          = ( divide_divide_rat @ one_one_rat @ A ) )
% 0.29/0.54        = ( A = zero_zero_rat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_eq_1_divide_iff
% 0.29/0.54  thf(fact_1858_one__divide__eq__0__iff,axiom,
% 0.29/0.54      ! [A: real] :
% 0.29/0.54        ( ( ( divide_divide_real @ one_one_real @ A )
% 0.29/0.54          = zero_zero_real )
% 0.29/0.54        = ( A = zero_zero_real ) ) ).
% 0.29/0.54  
% 0.29/0.54  % one_divide_eq_0_iff
% 0.29/0.54  thf(fact_1859_one__divide__eq__0__iff,axiom,
% 0.29/0.54      ! [A: rat] :
% 0.29/0.54        ( ( ( divide_divide_rat @ one_one_rat @ A )
% 0.29/0.54          = zero_zero_rat )
% 0.29/0.54        = ( A = zero_zero_rat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % one_divide_eq_0_iff
% 0.29/0.54  thf(fact_1860_eq__divide__eq__1,axiom,
% 0.29/0.54      ! [B: real,A: real] :
% 0.29/0.54        ( ( one_one_real
% 0.29/0.54          = ( divide_divide_real @ B @ A ) )
% 0.29/0.54        = ( ( A != zero_zero_real )
% 0.29/0.54          & ( A = B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % eq_divide_eq_1
% 0.29/0.54  thf(fact_1861_eq__divide__eq__1,axiom,
% 0.29/0.54      ! [B: rat,A: rat] :
% 0.29/0.54        ( ( one_one_rat
% 0.29/0.54          = ( divide_divide_rat @ B @ A ) )
% 0.29/0.54        = ( ( A != zero_zero_rat )
% 0.29/0.54          & ( A = B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % eq_divide_eq_1
% 0.29/0.54  thf(fact_1862_divide__eq__eq__1,axiom,
% 0.29/0.54      ! [B: real,A: real] :
% 0.29/0.54        ( ( ( divide_divide_real @ B @ A )
% 0.29/0.54          = one_one_real )
% 0.29/0.54        = ( ( A != zero_zero_real )
% 0.29/0.54          & ( A = B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divide_eq_eq_1
% 0.29/0.54  thf(fact_1863_divide__eq__eq__1,axiom,
% 0.29/0.54      ! [B: rat,A: rat] :
% 0.29/0.54        ( ( ( divide_divide_rat @ B @ A )
% 0.29/0.54          = one_one_rat )
% 0.29/0.54        = ( ( A != zero_zero_rat )
% 0.29/0.54          & ( A = B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divide_eq_eq_1
% 0.29/0.54  thf(fact_1864_divide__self__if,axiom,
% 0.29/0.54      ! [A: complex] :
% 0.29/0.54        ( ( ( A = zero_zero_complex )
% 0.29/0.54         => ( ( divide1717551699836669952omplex @ A @ A )
% 0.29/0.54            = zero_zero_complex ) )
% 0.29/0.54        & ( ( A != zero_zero_complex )
% 0.29/0.54         => ( ( divide1717551699836669952omplex @ A @ A )
% 0.29/0.54            = one_one_complex ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divide_self_if
% 0.29/0.54  thf(fact_1865_divide__self__if,axiom,
% 0.29/0.54      ! [A: real] :
% 0.29/0.54        ( ( ( A = zero_zero_real )
% 0.29/0.54         => ( ( divide_divide_real @ A @ A )
% 0.29/0.54            = zero_zero_real ) )
% 0.29/0.54        & ( ( A != zero_zero_real )
% 0.29/0.54         => ( ( divide_divide_real @ A @ A )
% 0.29/0.54            = one_one_real ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divide_self_if
% 0.29/0.54  thf(fact_1866_divide__self__if,axiom,
% 0.29/0.54      ! [A: rat] :
% 0.29/0.54        ( ( ( A = zero_zero_rat )
% 0.29/0.54         => ( ( divide_divide_rat @ A @ A )
% 0.29/0.54            = zero_zero_rat ) )
% 0.29/0.54        & ( ( A != zero_zero_rat )
% 0.29/0.54         => ( ( divide_divide_rat @ A @ A )
% 0.29/0.54            = one_one_rat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divide_self_if
% 0.29/0.54  thf(fact_1867_divide__self,axiom,
% 0.29/0.54      ! [A: complex] :
% 0.29/0.54        ( ( A != zero_zero_complex )
% 0.29/0.54       => ( ( divide1717551699836669952omplex @ A @ A )
% 0.29/0.54          = one_one_complex ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divide_self
% 0.29/0.54  thf(fact_1868_divide__self,axiom,
% 0.29/0.54      ! [A: real] :
% 0.29/0.54        ( ( A != zero_zero_real )
% 0.29/0.54       => ( ( divide_divide_real @ A @ A )
% 0.29/0.54          = one_one_real ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divide_self
% 0.29/0.54  thf(fact_1869_divide__self,axiom,
% 0.29/0.54      ! [A: rat] :
% 0.29/0.54        ( ( A != zero_zero_rat )
% 0.29/0.54       => ( ( divide_divide_rat @ A @ A )
% 0.29/0.54          = one_one_rat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divide_self
% 0.29/0.54  thf(fact_1870_one__eq__divide__iff,axiom,
% 0.29/0.54      ! [A: complex,B: complex] :
% 0.29/0.54        ( ( one_one_complex
% 0.29/0.54          = ( divide1717551699836669952omplex @ A @ B ) )
% 0.29/0.54        = ( ( B != zero_zero_complex )
% 0.29/0.54          & ( A = B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % one_eq_divide_iff
% 0.29/0.54  thf(fact_1871_one__eq__divide__iff,axiom,
% 0.29/0.54      ! [A: real,B: real] :
% 0.29/0.54        ( ( one_one_real
% 0.29/0.54          = ( divide_divide_real @ A @ B ) )
% 0.29/0.54        = ( ( B != zero_zero_real )
% 0.29/0.54          & ( A = B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % one_eq_divide_iff
% 0.29/0.54  thf(fact_1872_one__eq__divide__iff,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 0.29/0.54        ( ( one_one_rat
% 0.29/0.54          = ( divide_divide_rat @ A @ B ) )
% 0.29/0.54        = ( ( B != zero_zero_rat )
% 0.29/0.54          & ( A = B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % one_eq_divide_iff
% 0.29/0.54  thf(fact_1873_divide__eq__1__iff,axiom,
% 0.29/0.54      ! [A: complex,B: complex] :
% 0.29/0.54        ( ( ( divide1717551699836669952omplex @ A @ B )
% 0.29/0.54          = one_one_complex )
% 0.29/0.54        = ( ( B != zero_zero_complex )
% 0.29/0.54          & ( A = B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divide_eq_1_iff
% 0.29/0.54  thf(fact_1874_divide__eq__1__iff,axiom,
% 0.29/0.54      ! [A: real,B: real] :
% 0.29/0.54        ( ( ( divide_divide_real @ A @ B )
% 0.29/0.54          = one_one_real )
% 0.29/0.54        = ( ( B != zero_zero_real )
% 0.29/0.54          & ( A = B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divide_eq_1_iff
% 0.29/0.54  thf(fact_1875_divide__eq__1__iff,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 0.29/0.54        ( ( ( divide_divide_rat @ A @ B )
% 0.29/0.54          = one_one_rat )
% 0.29/0.54        = ( ( B != zero_zero_rat )
% 0.29/0.54          & ( A = B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divide_eq_1_iff
% 0.29/0.54  thf(fact_1876_power__0__Suc,axiom,
% 0.29/0.54      ! [N: nat] :
% 0.29/0.54        ( ( power_power_rat @ zero_zero_rat @ ( suc @ N ) )
% 0.29/0.54        = zero_zero_rat ) ).
% 0.29/0.54  
% 0.29/0.54  % power_0_Suc
% 0.29/0.54  thf(fact_1877_power__0__Suc,axiom,
% 0.29/0.54      ! [N: nat] :
% 0.29/0.54        ( ( power_power_nat @ zero_zero_nat @ ( suc @ N ) )
% 0.29/0.54        = zero_zero_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % power_0_Suc
% 0.29/0.54  thf(fact_1878_power__0__Suc,axiom,
% 0.29/0.54      ! [N: nat] :
% 0.29/0.54        ( ( power_power_real @ zero_zero_real @ ( suc @ N ) )
% 0.29/0.54        = zero_zero_real ) ).
% 0.29/0.54  
% 0.29/0.54  % power_0_Suc
% 0.29/0.54  thf(fact_1879_power__0__Suc,axiom,
% 0.29/0.54      ! [N: nat] :
% 0.29/0.54        ( ( power_power_int @ zero_zero_int @ ( suc @ N ) )
% 0.29/0.54        = zero_zero_int ) ).
% 0.29/0.54  
% 0.29/0.54  % power_0_Suc
% 0.29/0.54  thf(fact_1880_power__0__Suc,axiom,
% 0.29/0.54      ! [N: nat] :
% 0.29/0.54        ( ( power_power_complex @ zero_zero_complex @ ( suc @ N ) )
% 0.29/0.54        = zero_zero_complex ) ).
% 0.29/0.54  
% 0.29/0.54  % power_0_Suc
% 0.29/0.54  thf(fact_1881_power__zero__numeral,axiom,
% 0.29/0.54      ! [K: num] :
% 0.29/0.54        ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ K ) )
% 0.29/0.54        = zero_zero_rat ) ).
% 0.29/0.54  
% 0.29/0.54  % power_zero_numeral
% 0.29/0.54  thf(fact_1882_power__zero__numeral,axiom,
% 0.29/0.54      ! [K: num] :
% 0.29/0.54        ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K ) )
% 0.29/0.54        = zero_zero_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % power_zero_numeral
% 0.29/0.54  thf(fact_1883_power__zero__numeral,axiom,
% 0.29/0.54      ! [K: num] :
% 0.29/0.54        ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ K ) )
% 0.29/0.54        = zero_zero_real ) ).
% 0.29/0.54  
% 0.29/0.54  % power_zero_numeral
% 0.29/0.54  thf(fact_1884_power__zero__numeral,axiom,
% 0.29/0.54      ! [K: num] :
% 0.29/0.54        ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ K ) )
% 0.29/0.54        = zero_zero_int ) ).
% 0.29/0.54  
% 0.29/0.54  % power_zero_numeral
% 0.29/0.54  thf(fact_1885_power__zero__numeral,axiom,
% 0.29/0.54      ! [K: num] :
% 0.29/0.54        ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ K ) )
% 0.29/0.54        = zero_zero_complex ) ).
% 0.29/0.54  
% 0.29/0.54  % power_zero_numeral
% 0.29/0.54  thf(fact_1886_power__Suc0__right,axiom,
% 0.29/0.54      ! [A: nat] :
% 0.29/0.54        ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 0.29/0.54        = A ) ).
% 0.29/0.54  
% 0.29/0.54  % power_Suc0_right
% 0.29/0.54  thf(fact_1887_power__Suc0__right,axiom,
% 0.29/0.54      ! [A: real] :
% 0.29/0.54        ( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
% 0.29/0.54        = A ) ).
% 0.29/0.54  
% 0.29/0.54  % power_Suc0_right
% 0.29/0.54  thf(fact_1888_power__Suc0__right,axiom,
% 0.29/0.54      ! [A: int] :
% 0.29/0.54        ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 0.29/0.54        = A ) ).
% 0.29/0.54  
% 0.29/0.54  % power_Suc0_right
% 0.29/0.54  thf(fact_1889_power__Suc0__right,axiom,
% 0.29/0.54      ! [A: complex] :
% 0.29/0.54        ( ( power_power_complex @ A @ ( suc @ zero_zero_nat ) )
% 0.29/0.54        = A ) ).
% 0.29/0.54  
% 0.29/0.54  % power_Suc0_right
% 0.29/0.54  thf(fact_1890_less__Suc0,axiom,
% 0.29/0.54      ! [N: nat] :
% 0.29/0.54        ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.29/0.54        = ( N = zero_zero_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_Suc0
% 0.29/0.54  thf(fact_1891_zero__less__Suc,axiom,
% 0.29/0.54      ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_less_Suc
% 0.29/0.54  thf(fact_1892_add__gr__0,axiom,
% 0.29/0.54      ! [M: nat,N: nat] :
% 0.29/0.54        ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
% 0.29/0.54        = ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.29/0.54          | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % add_gr_0
% 0.29/0.54  thf(fact_1893_max__0__1_I4_J,axiom,
% 0.29/0.54      ! [X: num] :
% 0.29/0.54        ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X ) @ zero_z5237406670263579293d_enat )
% 0.29/0.54        = ( numera1916890842035813515d_enat @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % max_0_1(4)
% 0.29/0.54  thf(fact_1894_max__0__1_I4_J,axiom,
% 0.29/0.54      ! [X: num] :
% 0.29/0.54        ( ( ord_max_real @ ( numeral_numeral_real @ X ) @ zero_zero_real )
% 0.29/0.54        = ( numeral_numeral_real @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % max_0_1(4)
% 0.29/0.54  thf(fact_1895_max__0__1_I4_J,axiom,
% 0.29/0.54      ! [X: num] :
% 0.29/0.54        ( ( ord_max_rat @ ( numeral_numeral_rat @ X ) @ zero_zero_rat )
% 0.29/0.54        = ( numeral_numeral_rat @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % max_0_1(4)
% 0.29/0.54  thf(fact_1896_max__0__1_I4_J,axiom,
% 0.29/0.54      ! [X: num] :
% 0.29/0.54        ( ( ord_max_nat @ ( numeral_numeral_nat @ X ) @ zero_zero_nat )
% 0.29/0.54        = ( numeral_numeral_nat @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % max_0_1(4)
% 0.29/0.54  thf(fact_1897_max__0__1_I4_J,axiom,
% 0.29/0.54      ! [X: num] :
% 0.29/0.54        ( ( ord_max_int @ ( numeral_numeral_int @ X ) @ zero_zero_int )
% 0.29/0.54        = ( numeral_numeral_int @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % max_0_1(4)
% 0.29/0.54  thf(fact_1898_max__0__1_I3_J,axiom,
% 0.29/0.54      ! [X: num] :
% 0.29/0.54        ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 0.29/0.54        = ( numera1916890842035813515d_enat @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % max_0_1(3)
% 0.29/0.54  thf(fact_1899_max__0__1_I3_J,axiom,
% 0.29/0.54      ! [X: num] :
% 0.29/0.54        ( ( ord_max_real @ zero_zero_real @ ( numeral_numeral_real @ X ) )
% 0.29/0.54        = ( numeral_numeral_real @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % max_0_1(3)
% 0.29/0.54  thf(fact_1900_max__0__1_I3_J,axiom,
% 0.29/0.54      ! [X: num] :
% 0.29/0.54        ( ( ord_max_rat @ zero_zero_rat @ ( numeral_numeral_rat @ X ) )
% 0.29/0.54        = ( numeral_numeral_rat @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % max_0_1(3)
% 0.29/0.54  thf(fact_1901_max__0__1_I3_J,axiom,
% 0.29/0.54      ! [X: num] :
% 0.29/0.54        ( ( ord_max_nat @ zero_zero_nat @ ( numeral_numeral_nat @ X ) )
% 0.29/0.54        = ( numeral_numeral_nat @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % max_0_1(3)
% 0.29/0.54  thf(fact_1902_max__0__1_I3_J,axiom,
% 0.29/0.54      ! [X: num] :
% 0.29/0.54        ( ( ord_max_int @ zero_zero_int @ ( numeral_numeral_int @ X ) )
% 0.29/0.54        = ( numeral_numeral_int @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % max_0_1(3)
% 0.29/0.54  thf(fact_1903_less__one,axiom,
% 0.29/0.54      ! [N: nat] :
% 0.29/0.54        ( ( ord_less_nat @ N @ one_one_nat )
% 0.29/0.54        = ( N = zero_zero_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_one
% 0.29/0.54  thf(fact_1904_div__by__Suc__0,axiom,
% 0.29/0.54      ! [M: nat] :
% 0.29/0.54        ( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
% 0.29/0.54        = M ) ).
% 0.29/0.54  
% 0.29/0.54  % div_by_Suc_0
% 0.29/0.54  thf(fact_1905_mult__eq__1__iff,axiom,
% 0.29/0.54      ! [M: nat,N: nat] :
% 0.29/0.54        ( ( ( times_times_nat @ M @ N )
% 0.29/0.54          = ( suc @ zero_zero_nat ) )
% 0.29/0.54        = ( ( M
% 0.29/0.54            = ( suc @ zero_zero_nat ) )
% 0.29/0.54          & ( N
% 0.29/0.54            = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_eq_1_iff
% 0.29/0.54  thf(fact_1906_one__eq__mult__iff,axiom,
% 0.29/0.54      ! [M: nat,N: nat] :
% 0.29/0.54        ( ( ( suc @ zero_zero_nat )
% 0.29/0.54          = ( times_times_nat @ M @ N ) )
% 0.29/0.54        = ( ( M
% 0.29/0.54            = ( suc @ zero_zero_nat ) )
% 0.29/0.54          & ( N
% 0.29/0.54            = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % one_eq_mult_iff
% 0.29/0.54  thf(fact_1907_max__0__1_I2_J,axiom,
% 0.29/0.54      ( ( ord_max_real @ one_one_real @ zero_zero_real )
% 0.29/0.54      = one_one_real ) ).
% 0.29/0.54  
% 0.29/0.54  % max_0_1(2)
% 0.29/0.54  thf(fact_1908_max__0__1_I2_J,axiom,
% 0.29/0.54      ( ( ord_max_rat @ one_one_rat @ zero_zero_rat )
% 0.29/0.54      = one_one_rat ) ).
% 0.29/0.54  
% 0.29/0.54  % max_0_1(2)
% 0.29/0.54  thf(fact_1909_max__0__1_I2_J,axiom,
% 0.29/0.54      ( ( ord_max_nat @ one_one_nat @ zero_zero_nat )
% 0.29/0.54      = one_one_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % max_0_1(2)
% 0.29/0.54  thf(fact_1910_max__0__1_I2_J,axiom,
% 0.29/0.54      ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ zero_z5237406670263579293d_enat )
% 0.29/0.54      = one_on7984719198319812577d_enat ) ).
% 0.29/0.54  
% 0.29/0.54  % max_0_1(2)
% 0.29/0.54  thf(fact_1911_max__0__1_I2_J,axiom,
% 0.29/0.54      ( ( ord_max_int @ one_one_int @ zero_zero_int )
% 0.29/0.54      = one_one_int ) ).
% 0.29/0.54  
% 0.29/0.54  % max_0_1(2)
% 0.29/0.54  thf(fact_1912_max__0__1_I1_J,axiom,
% 0.29/0.54      ( ( ord_max_real @ zero_zero_real @ one_one_real )
% 0.29/0.54      = one_one_real ) ).
% 0.29/0.54  
% 0.29/0.54  % max_0_1(1)
% 0.29/0.54  thf(fact_1913_max__0__1_I1_J,axiom,
% 0.29/0.54      ( ( ord_max_rat @ zero_zero_rat @ one_one_rat )
% 0.29/0.54      = one_one_rat ) ).
% 0.29/0.54  
% 0.29/0.54  % max_0_1(1)
% 0.29/0.54  thf(fact_1914_max__0__1_I1_J,axiom,
% 0.29/0.54      ( ( ord_max_nat @ zero_zero_nat @ one_one_nat )
% 0.29/0.54      = one_one_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % max_0_1(1)
% 0.29/0.54  thf(fact_1915_max__0__1_I1_J,axiom,
% 0.29/0.54      ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ one_on7984719198319812577d_enat )
% 0.29/0.54      = one_on7984719198319812577d_enat ) ).
% 0.29/0.54  
% 0.29/0.54  % max_0_1(1)
% 0.29/0.54  thf(fact_1916_max__0__1_I1_J,axiom,
% 0.29/0.54      ( ( ord_max_int @ zero_zero_int @ one_one_int )
% 0.29/0.54      = one_one_int ) ).
% 0.29/0.54  
% 0.29/0.54  % max_0_1(1)
% 0.29/0.54  thf(fact_1917_div__less,axiom,
% 0.29/0.54      ! [M: nat,N: nat] :
% 0.29/0.54        ( ( ord_less_nat @ M @ N )
% 0.29/0.54       => ( ( divide_divide_nat @ M @ N )
% 0.29/0.54          = zero_zero_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_less
% 0.29/0.54  thf(fact_1918_mult__less__cancel2,axiom,
% 0.29/0.54      ! [M: nat,K: nat,N: nat] :
% 0.29/0.54        ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 0.29/0.54        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.29/0.54          & ( ord_less_nat @ M @ N ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_less_cancel2
% 0.29/0.54  thf(fact_1919_nat__0__less__mult__iff,axiom,
% 0.29/0.54      ! [M: nat,N: nat] :
% 0.29/0.54        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N ) )
% 0.29/0.54        = ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.29/0.54          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nat_0_less_mult_iff
% 0.29/0.54  thf(fact_1920_nat__mult__less__cancel__disj,axiom,
% 0.29/0.54      ! [K: nat,M: nat,N: nat] :
% 0.29/0.54        ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.29/0.54        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.29/0.54          & ( ord_less_nat @ M @ N ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nat_mult_less_cancel_disj
% 0.29/0.54  thf(fact_1921_zero__less__diff,axiom,
% 0.29/0.54      ! [N: nat,M: nat] :
% 0.29/0.54        ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
% 0.29/0.54        = ( ord_less_nat @ M @ N ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_less_diff
% 0.29/0.54  thf(fact_1922_nat__power__eq__Suc__0__iff,axiom,
% 0.29/0.54      ! [X: nat,M: nat] :
% 0.29/0.54        ( ( ( power_power_nat @ X @ M )
% 0.29/0.54          = ( suc @ zero_zero_nat ) )
% 0.29/0.54        = ( ( M = zero_zero_nat )
% 0.29/0.54          | ( X
% 0.29/0.54            = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nat_power_eq_Suc_0_iff
% 0.29/0.54  thf(fact_1923_power__Suc__0,axiom,
% 0.29/0.54      ! [N: nat] :
% 0.29/0.54        ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.29/0.54        = ( suc @ zero_zero_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_Suc_0
% 0.29/0.54  thf(fact_1924_diff__is__0__eq,axiom,
% 0.29/0.54      ! [M: nat,N: nat] :
% 0.29/0.54        ( ( ( minus_minus_nat @ M @ N )
% 0.29/0.54          = zero_zero_nat )
% 0.29/0.54        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.29/0.54  
% 0.29/0.54  % diff_is_0_eq
% 0.29/0.54  thf(fact_1925_diff__is__0__eq_H,axiom,
% 0.29/0.54      ! [M: nat,N: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.54       => ( ( minus_minus_nat @ M @ N )
% 0.29/0.54          = zero_zero_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % diff_is_0_eq'
% 0.29/0.54  thf(fact_1926_nat__zero__less__power__iff,axiom,
% 0.29/0.54      ! [X: nat,N: nat] :
% 0.29/0.54        ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
% 0.29/0.54        = ( ( ord_less_nat @ zero_zero_nat @ X )
% 0.29/0.54          | ( N = zero_zero_nat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nat_zero_less_power_iff
% 0.29/0.54  thf(fact_1927_nat__mult__div__cancel__disj,axiom,
% 0.29/0.54      ! [K: nat,M: nat,N: nat] :
% 0.29/0.54        ( ( ( K = zero_zero_nat )
% 0.29/0.54         => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.29/0.54            = zero_zero_nat ) )
% 0.29/0.54        & ( ( K != zero_zero_nat )
% 0.29/0.54         => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.29/0.54            = ( divide_divide_nat @ M @ N ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nat_mult_div_cancel_disj
% 0.29/0.54  thf(fact_1928_divide__le__0__1__iff,axiom,
% 0.29/0.54      ! [A: real] :
% 0.29/0.54        ( ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 0.29/0.54        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divide_le_0_1_iff
% 0.29/0.54  thf(fact_1929_divide__le__0__1__iff,axiom,
% 0.29/0.54      ! [A: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 0.29/0.54        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divide_le_0_1_iff
% 0.29/0.54  thf(fact_1930_zero__le__divide__1__iff,axiom,
% 0.29/0.54      ! [A: real] :
% 0.29/0.54        ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 0.29/0.54        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_le_divide_1_iff
% 0.29/0.54  thf(fact_1931_zero__le__divide__1__iff,axiom,
% 0.29/0.54      ! [A: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 0.29/0.54        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_le_divide_1_iff
% 0.29/0.54  thf(fact_1932_zero__less__divide__1__iff,axiom,
% 0.29/0.54      ! [A: real] :
% 0.29/0.54        ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 0.29/0.54        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_less_divide_1_iff
% 0.29/0.54  thf(fact_1933_zero__less__divide__1__iff,axiom,
% 0.29/0.54      ! [A: rat] :
% 0.29/0.54        ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 0.29/0.54        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_less_divide_1_iff
% 0.29/0.54  thf(fact_1934_less__divide__eq__1__pos,axiom,
% 0.29/0.54      ! [A: real,B: real] :
% 0.29/0.54        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.54       => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 0.29/0.54          = ( ord_less_real @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_divide_eq_1_pos
% 0.29/0.54  thf(fact_1935_less__divide__eq__1__pos,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.54       => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.29/0.54          = ( ord_less_rat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_divide_eq_1_pos
% 0.29/0.54  thf(fact_1936_less__divide__eq__1__neg,axiom,
% 0.29/0.54      ! [A: real,B: real] :
% 0.29/0.54        ( ( ord_less_real @ A @ zero_zero_real )
% 0.29/0.54       => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 0.29/0.54          = ( ord_less_real @ B @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_divide_eq_1_neg
% 0.29/0.54  thf(fact_1937_less__divide__eq__1__neg,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.54       => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.29/0.54          = ( ord_less_rat @ B @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_divide_eq_1_neg
% 0.29/0.54  thf(fact_1938_divide__less__eq__1__pos,axiom,
% 0.29/0.54      ! [A: real,B: real] :
% 0.29/0.54        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.54       => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 0.29/0.54          = ( ord_less_real @ B @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divide_less_eq_1_pos
% 0.29/0.54  thf(fact_1939_divide__less__eq__1__pos,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.54       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.29/0.54          = ( ord_less_rat @ B @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divide_less_eq_1_pos
% 0.29/0.54  thf(fact_1940_divide__less__eq__1__neg,axiom,
% 0.29/0.54      ! [A: real,B: real] :
% 0.29/0.54        ( ( ord_less_real @ A @ zero_zero_real )
% 0.29/0.54       => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 0.29/0.54          = ( ord_less_real @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divide_less_eq_1_neg
% 0.29/0.54  thf(fact_1941_divide__less__eq__1__neg,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.54       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.29/0.54          = ( ord_less_rat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divide_less_eq_1_neg
% 0.29/0.54  thf(fact_1942_divide__less__0__1__iff,axiom,
% 0.29/0.54      ! [A: real] :
% 0.29/0.54        ( ( ord_less_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 0.29/0.54        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divide_less_0_1_iff
% 0.29/0.54  thf(fact_1943_divide__less__0__1__iff,axiom,
% 0.29/0.54      ! [A: rat] :
% 0.29/0.54        ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 0.29/0.54        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divide_less_0_1_iff
% 0.29/0.54  thf(fact_1944_eq__divide__eq__numeral1_I1_J,axiom,
% 0.29/0.54      ! [A: complex,B: complex,W: num] :
% 0.29/0.54        ( ( A
% 0.29/0.54          = ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) ) )
% 0.29/0.54        = ( ( ( ( numera6690914467698888265omplex @ W )
% 0.29/0.54             != zero_zero_complex )
% 0.29/0.54           => ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) )
% 0.29/0.54              = B ) )
% 0.29/0.54          & ( ( ( numera6690914467698888265omplex @ W )
% 0.29/0.54              = zero_zero_complex )
% 0.29/0.54           => ( A = zero_zero_complex ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % eq_divide_eq_numeral1(1)
% 0.29/0.54  thf(fact_1945_eq__divide__eq__numeral1_I1_J,axiom,
% 0.29/0.54      ! [A: real,B: real,W: num] :
% 0.29/0.54        ( ( A
% 0.29/0.54          = ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 0.29/0.54        = ( ( ( ( numeral_numeral_real @ W )
% 0.29/0.54             != zero_zero_real )
% 0.29/0.54           => ( ( times_times_real @ A @ ( numeral_numeral_real @ W ) )
% 0.29/0.54              = B ) )
% 0.29/0.54          & ( ( ( numeral_numeral_real @ W )
% 0.29/0.54              = zero_zero_real )
% 0.29/0.54           => ( A = zero_zero_real ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % eq_divide_eq_numeral1(1)
% 0.29/0.54  thf(fact_1946_eq__divide__eq__numeral1_I1_J,axiom,
% 0.29/0.54      ! [A: rat,B: rat,W: num] :
% 0.29/0.54        ( ( A
% 0.29/0.54          = ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 0.29/0.54        = ( ( ( ( numeral_numeral_rat @ W )
% 0.29/0.54             != zero_zero_rat )
% 0.29/0.54           => ( ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) )
% 0.29/0.54              = B ) )
% 0.29/0.54          & ( ( ( numeral_numeral_rat @ W )
% 0.29/0.54              = zero_zero_rat )
% 0.29/0.54           => ( A = zero_zero_rat ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % eq_divide_eq_numeral1(1)
% 0.29/0.54  thf(fact_1947_divide__eq__eq__numeral1_I1_J,axiom,
% 0.29/0.54      ! [B: complex,W: num,A: complex] :
% 0.29/0.54        ( ( ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) )
% 0.29/0.54          = A )
% 0.29/0.54        = ( ( ( ( numera6690914467698888265omplex @ W )
% 0.29/0.54             != zero_zero_complex )
% 0.29/0.54           => ( B
% 0.29/0.54              = ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) ) )
% 0.29/0.54          & ( ( ( numera6690914467698888265omplex @ W )
% 0.29/0.54              = zero_zero_complex )
% 0.29/0.54           => ( A = zero_zero_complex ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divide_eq_eq_numeral1(1)
% 0.29/0.54  thf(fact_1948_divide__eq__eq__numeral1_I1_J,axiom,
% 0.29/0.54      ! [B: real,W: num,A: real] :
% 0.29/0.54        ( ( ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) )
% 0.29/0.54          = A )
% 0.29/0.54        = ( ( ( ( numeral_numeral_real @ W )
% 0.29/0.54             != zero_zero_real )
% 0.29/0.54           => ( B
% 0.29/0.54              = ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) )
% 0.29/0.54          & ( ( ( numeral_numeral_real @ W )
% 0.29/0.54              = zero_zero_real )
% 0.29/0.54           => ( A = zero_zero_real ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divide_eq_eq_numeral1(1)
% 0.29/0.54  thf(fact_1949_divide__eq__eq__numeral1_I1_J,axiom,
% 0.29/0.54      ! [B: rat,W: num,A: rat] :
% 0.29/0.54        ( ( ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) )
% 0.29/0.54          = A )
% 0.29/0.54        = ( ( ( ( numeral_numeral_rat @ W )
% 0.29/0.54             != zero_zero_rat )
% 0.29/0.54           => ( B
% 0.29/0.54              = ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) )
% 0.29/0.54          & ( ( ( numeral_numeral_rat @ W )
% 0.29/0.54              = zero_zero_rat )
% 0.29/0.54           => ( A = zero_zero_rat ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divide_eq_eq_numeral1(1)
% 0.29/0.54  thf(fact_1950_nonzero__divide__mult__cancel__right,axiom,
% 0.29/0.54      ! [B: complex,A: complex] :
% 0.29/0.54        ( ( B != zero_zero_complex )
% 0.29/0.54       => ( ( divide1717551699836669952omplex @ B @ ( times_times_complex @ A @ B ) )
% 0.29/0.54          = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nonzero_divide_mult_cancel_right
% 0.29/0.54  thf(fact_1951_nonzero__divide__mult__cancel__right,axiom,
% 0.29/0.54      ! [B: real,A: real] :
% 0.29/0.54        ( ( B != zero_zero_real )
% 0.29/0.54       => ( ( divide_divide_real @ B @ ( times_times_real @ A @ B ) )
% 0.29/0.54          = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nonzero_divide_mult_cancel_right
% 0.29/0.54  thf(fact_1952_nonzero__divide__mult__cancel__right,axiom,
% 0.29/0.54      ! [B: rat,A: rat] :
% 0.29/0.54        ( ( B != zero_zero_rat )
% 0.29/0.54       => ( ( divide_divide_rat @ B @ ( times_times_rat @ A @ B ) )
% 0.29/0.54          = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nonzero_divide_mult_cancel_right
% 0.29/0.54  thf(fact_1953_nonzero__divide__mult__cancel__left,axiom,
% 0.29/0.54      ! [A: complex,B: complex] :
% 0.29/0.54        ( ( A != zero_zero_complex )
% 0.29/0.54       => ( ( divide1717551699836669952omplex @ A @ ( times_times_complex @ A @ B ) )
% 0.29/0.54          = ( divide1717551699836669952omplex @ one_one_complex @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nonzero_divide_mult_cancel_left
% 0.29/0.54  thf(fact_1954_nonzero__divide__mult__cancel__left,axiom,
% 0.29/0.54      ! [A: real,B: real] :
% 0.29/0.54        ( ( A != zero_zero_real )
% 0.29/0.54       => ( ( divide_divide_real @ A @ ( times_times_real @ A @ B ) )
% 0.29/0.54          = ( divide_divide_real @ one_one_real @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nonzero_divide_mult_cancel_left
% 0.29/0.54  thf(fact_1955_nonzero__divide__mult__cancel__left,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 0.29/0.54        ( ( A != zero_zero_rat )
% 0.29/0.54       => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B ) )
% 0.29/0.54          = ( divide_divide_rat @ one_one_rat @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nonzero_divide_mult_cancel_left
% 0.29/0.54  thf(fact_1956_div__mult__self4,axiom,
% 0.29/0.54      ! [B: nat,C: nat,A: nat] :
% 0.29/0.54        ( ( B != zero_zero_nat )
% 0.29/0.54       => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 0.29/0.54          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_mult_self4
% 0.29/0.54  thf(fact_1957_div__mult__self4,axiom,
% 0.29/0.54      ! [B: int,C: int,A: int] :
% 0.29/0.54        ( ( B != zero_zero_int )
% 0.29/0.54       => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 0.29/0.54          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_mult_self4
% 0.29/0.54  thf(fact_1958_div__mult__self3,axiom,
% 0.29/0.54      ! [B: nat,C: nat,A: nat] :
% 0.29/0.54        ( ( B != zero_zero_nat )
% 0.29/0.54       => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 0.29/0.54          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_mult_self3
% 0.29/0.54  thf(fact_1959_div__mult__self3,axiom,
% 0.29/0.54      ! [B: int,C: int,A: int] :
% 0.29/0.54        ( ( B != zero_zero_int )
% 0.29/0.54       => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 0.29/0.54          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_mult_self3
% 0.29/0.54  thf(fact_1960_div__mult__self2,axiom,
% 0.29/0.54      ! [B: nat,A: nat,C: nat] :
% 0.29/0.54        ( ( B != zero_zero_nat )
% 0.29/0.54       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 0.29/0.54          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_mult_self2
% 0.29/0.54  thf(fact_1961_div__mult__self2,axiom,
% 0.29/0.54      ! [B: int,A: int,C: int] :
% 0.29/0.54        ( ( B != zero_zero_int )
% 0.29/0.54       => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 0.29/0.54          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_mult_self2
% 0.29/0.54  thf(fact_1962_div__mult__self1,axiom,
% 0.29/0.54      ! [B: nat,A: nat,C: nat] :
% 0.29/0.54        ( ( B != zero_zero_nat )
% 0.29/0.54       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 0.29/0.54          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_mult_self1
% 0.29/0.54  thf(fact_1963_div__mult__self1,axiom,
% 0.29/0.54      ! [B: int,A: int,C: int] :
% 0.29/0.54        ( ( B != zero_zero_int )
% 0.29/0.54       => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 0.29/0.54          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_mult_self1
% 0.29/0.54  thf(fact_1964_power__eq__0__iff,axiom,
% 0.29/0.54      ! [A: rat,N: nat] :
% 0.29/0.54        ( ( ( power_power_rat @ A @ N )
% 0.29/0.54          = zero_zero_rat )
% 0.29/0.54        = ( ( A = zero_zero_rat )
% 0.29/0.54          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_eq_0_iff
% 0.29/0.54  thf(fact_1965_power__eq__0__iff,axiom,
% 0.29/0.54      ! [A: nat,N: nat] :
% 0.29/0.54        ( ( ( power_power_nat @ A @ N )
% 0.29/0.54          = zero_zero_nat )
% 0.29/0.54        = ( ( A = zero_zero_nat )
% 0.29/0.54          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_eq_0_iff
% 0.29/0.54  thf(fact_1966_power__eq__0__iff,axiom,
% 0.29/0.54      ! [A: real,N: nat] :
% 0.29/0.54        ( ( ( power_power_real @ A @ N )
% 0.29/0.54          = zero_zero_real )
% 0.29/0.54        = ( ( A = zero_zero_real )
% 0.29/0.54          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_eq_0_iff
% 0.29/0.54  thf(fact_1967_power__eq__0__iff,axiom,
% 0.29/0.54      ! [A: int,N: nat] :
% 0.29/0.54        ( ( ( power_power_int @ A @ N )
% 0.29/0.54          = zero_zero_int )
% 0.29/0.54        = ( ( A = zero_zero_int )
% 0.29/0.54          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_eq_0_iff
% 0.29/0.54  thf(fact_1968_power__eq__0__iff,axiom,
% 0.29/0.54      ! [A: complex,N: nat] :
% 0.29/0.54        ( ( ( power_power_complex @ A @ N )
% 0.29/0.54          = zero_zero_complex )
% 0.29/0.54        = ( ( A = zero_zero_complex )
% 0.29/0.54          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_eq_0_iff
% 0.29/0.54  thf(fact_1969_Suc__pred,axiom,
% 0.29/0.54      ! [N: nat] :
% 0.29/0.54        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.54       => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 0.29/0.54          = N ) ) ).
% 0.29/0.54  
% 0.29/0.54  % Suc_pred
% 0.29/0.54  thf(fact_1970_one__le__mult__iff,axiom,
% 0.29/0.54      ! [M: nat,N: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) )
% 0.29/0.54        = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.29/0.54          & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % one_le_mult_iff
% 0.29/0.54  thf(fact_1971_mult__le__cancel2,axiom,
% 0.29/0.54      ! [M: nat,K: nat,N: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 0.29/0.54        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.29/0.54         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_le_cancel2
% 0.29/0.54  thf(fact_1972_nat__mult__le__cancel__disj,axiom,
% 0.29/0.54      ! [K: nat,M: nat,N: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.29/0.54        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.29/0.54         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nat_mult_le_cancel_disj
% 0.29/0.54  thf(fact_1973_div__mult__self__is__m,axiom,
% 0.29/0.54      ! [N: nat,M: nat] :
% 0.29/0.54        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.54       => ( ( divide_divide_nat @ ( times_times_nat @ M @ N ) @ N )
% 0.29/0.54          = M ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_mult_self_is_m
% 0.29/0.54  thf(fact_1974_div__mult__self1__is__m,axiom,
% 0.29/0.54      ! [N: nat,M: nat] :
% 0.29/0.54        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.54       => ( ( divide_divide_nat @ ( times_times_nat @ N @ M ) @ N )
% 0.29/0.54          = M ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_mult_self1_is_m
% 0.29/0.54  thf(fact_1975_divide__le__eq__1__neg,axiom,
% 0.29/0.54      ! [A: real,B: real] :
% 0.29/0.54        ( ( ord_less_real @ A @ zero_zero_real )
% 0.29/0.54       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 0.29/0.54          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divide_le_eq_1_neg
% 0.29/0.54  thf(fact_1976_divide__le__eq__1__neg,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.54       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.29/0.54          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divide_le_eq_1_neg
% 0.29/0.54  thf(fact_1977_divide__le__eq__1__pos,axiom,
% 0.29/0.54      ! [A: real,B: real] :
% 0.29/0.54        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.54       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 0.29/0.54          = ( ord_less_eq_real @ B @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divide_le_eq_1_pos
% 0.29/0.54  thf(fact_1978_divide__le__eq__1__pos,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.54       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.29/0.54          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divide_le_eq_1_pos
% 0.29/0.54  thf(fact_1979_le__divide__eq__1__neg,axiom,
% 0.29/0.54      ! [A: real,B: real] :
% 0.29/0.54        ( ( ord_less_real @ A @ zero_zero_real )
% 0.29/0.54       => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 0.29/0.54          = ( ord_less_eq_real @ B @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_divide_eq_1_neg
% 0.29/0.54  thf(fact_1980_le__divide__eq__1__neg,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.54       => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.29/0.54          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_divide_eq_1_neg
% 0.29/0.54  thf(fact_1981_le__divide__eq__1__pos,axiom,
% 0.29/0.54      ! [A: real,B: real] :
% 0.29/0.54        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.54       => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 0.29/0.54          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_divide_eq_1_pos
% 0.29/0.54  thf(fact_1982_le__divide__eq__1__pos,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.54       => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.29/0.54          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_divide_eq_1_pos
% 0.29/0.54  thf(fact_1983_power__strict__decreasing__iff,axiom,
% 0.29/0.54      ! [B: real,M: nat,N: nat] :
% 0.29/0.54        ( ( ord_less_real @ zero_zero_real @ B )
% 0.29/0.54       => ( ( ord_less_real @ B @ one_one_real )
% 0.29/0.54         => ( ( ord_less_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N ) )
% 0.29/0.54            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_strict_decreasing_iff
% 0.29/0.54  thf(fact_1984_power__strict__decreasing__iff,axiom,
% 0.29/0.54      ! [B: rat,M: nat,N: nat] :
% 0.29/0.54        ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.29/0.54       => ( ( ord_less_rat @ B @ one_one_rat )
% 0.29/0.54         => ( ( ord_less_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 0.29/0.54            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_strict_decreasing_iff
% 0.29/0.54  thf(fact_1985_power__strict__decreasing__iff,axiom,
% 0.29/0.54      ! [B: nat,M: nat,N: nat] :
% 0.29/0.54        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.29/0.54       => ( ( ord_less_nat @ B @ one_one_nat )
% 0.29/0.54         => ( ( ord_less_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 0.29/0.54            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_strict_decreasing_iff
% 0.29/0.54  thf(fact_1986_power__strict__decreasing__iff,axiom,
% 0.29/0.54      ! [B: int,M: nat,N: nat] :
% 0.29/0.54        ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.54       => ( ( ord_less_int @ B @ one_one_int )
% 0.29/0.54         => ( ( ord_less_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 0.29/0.54            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_strict_decreasing_iff
% 0.29/0.54  thf(fact_1987_zero__eq__power2,axiom,
% 0.29/0.54      ! [A: rat] :
% 0.29/0.54        ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.54          = zero_zero_rat )
% 0.29/0.54        = ( A = zero_zero_rat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_eq_power2
% 0.29/0.54  thf(fact_1988_zero__eq__power2,axiom,
% 0.29/0.54      ! [A: nat] :
% 0.29/0.54        ( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.54          = zero_zero_nat )
% 0.29/0.54        = ( A = zero_zero_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_eq_power2
% 0.29/0.54  thf(fact_1989_zero__eq__power2,axiom,
% 0.29/0.54      ! [A: real] :
% 0.29/0.54        ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.54          = zero_zero_real )
% 0.29/0.54        = ( A = zero_zero_real ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_eq_power2
% 0.29/0.54  thf(fact_1990_zero__eq__power2,axiom,
% 0.29/0.54      ! [A: int] :
% 0.29/0.54        ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.54          = zero_zero_int )
% 0.29/0.54        = ( A = zero_zero_int ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_eq_power2
% 0.29/0.54  thf(fact_1991_zero__eq__power2,axiom,
% 0.29/0.54      ! [A: complex] :
% 0.29/0.54        ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.54          = zero_zero_complex )
% 0.29/0.54        = ( A = zero_zero_complex ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_eq_power2
% 0.29/0.54  thf(fact_1992_power__mono__iff,axiom,
% 0.29/0.54      ! [A: rat,B: rat,N: nat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.54       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.29/0.54         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.54           => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 0.29/0.54              = ( ord_less_eq_rat @ A @ B ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_mono_iff
% 0.29/0.54  thf(fact_1993_power__mono__iff,axiom,
% 0.29/0.54      ! [A: real,B: real,N: nat] :
% 0.29/0.54        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.54       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.29/0.54         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.54           => ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 0.29/0.54              = ( ord_less_eq_real @ A @ B ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_mono_iff
% 0.29/0.54  thf(fact_1994_power__mono__iff,axiom,
% 0.29/0.54      ! [A: nat,B: nat,N: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.54       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.29/0.54         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.54           => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 0.29/0.54              = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_mono_iff
% 0.29/0.54  thf(fact_1995_power__mono__iff,axiom,
% 0.29/0.54      ! [A: int,B: int,N: nat] :
% 0.29/0.54        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.54       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.29/0.54         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.54           => ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 0.29/0.54              = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_mono_iff
% 0.29/0.54  thf(fact_1996_Suc__diff__1,axiom,
% 0.29/0.54      ! [N: nat] :
% 0.29/0.54        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.54       => ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
% 0.29/0.54          = N ) ) ).
% 0.29/0.54  
% 0.29/0.54  % Suc_diff_1
% 0.29/0.54  thf(fact_1997_bits__1__div__2,axiom,
% 0.29/0.54      ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.54      = zero_zero_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % bits_1_div_2
% 0.29/0.54  thf(fact_1998_bits__1__div__2,axiom,
% 0.29/0.54      ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.54      = zero_zero_int ) ).
% 0.29/0.54  
% 0.29/0.54  % bits_1_div_2
% 0.29/0.54  thf(fact_1999_one__div__two__eq__zero,axiom,
% 0.29/0.54      ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.54      = zero_zero_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % one_div_two_eq_zero
% 0.29/0.54  thf(fact_2000_one__div__two__eq__zero,axiom,
% 0.29/0.54      ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.54      = zero_zero_int ) ).
% 0.29/0.54  
% 0.29/0.54  % one_div_two_eq_zero
% 0.29/0.54  thf(fact_2001_power2__eq__iff__nonneg,axiom,
% 0.29/0.54      ! [X: rat,Y2: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.29/0.54       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 0.29/0.54         => ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.54              = ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.54            = ( X = Y2 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power2_eq_iff_nonneg
% 0.29/0.54  thf(fact_2002_power2__eq__iff__nonneg,axiom,
% 0.29/0.54      ! [X: real,Y2: real] :
% 0.29/0.54        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.29/0.54       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 0.29/0.54         => ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.54              = ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.54            = ( X = Y2 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power2_eq_iff_nonneg
% 0.29/0.54  thf(fact_2003_power2__eq__iff__nonneg,axiom,
% 0.29/0.54      ! [X: nat,Y2: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 0.29/0.54       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y2 )
% 0.29/0.54         => ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.54              = ( power_power_nat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.54            = ( X = Y2 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power2_eq_iff_nonneg
% 0.29/0.54  thf(fact_2004_power2__eq__iff__nonneg,axiom,
% 0.29/0.54      ! [X: int,Y2: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.29/0.54       => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 0.29/0.54         => ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.54              = ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.54            = ( X = Y2 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power2_eq_iff_nonneg
% 0.29/0.54  thf(fact_2005_power2__less__eq__zero__iff,axiom,
% 0.29/0.54      ! [A: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat )
% 0.29/0.54        = ( A = zero_zero_rat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power2_less_eq_zero_iff
% 0.29/0.54  thf(fact_2006_power2__less__eq__zero__iff,axiom,
% 0.29/0.54      ! [A: real] :
% 0.29/0.54        ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real )
% 0.29/0.54        = ( A = zero_zero_real ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power2_less_eq_zero_iff
% 0.29/0.54  thf(fact_2007_power2__less__eq__zero__iff,axiom,
% 0.29/0.54      ! [A: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 0.29/0.54        = ( A = zero_zero_int ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power2_less_eq_zero_iff
% 0.29/0.54  thf(fact_2008_zero__less__power2,axiom,
% 0.29/0.54      ! [A: real] :
% 0.29/0.54        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.54        = ( A != zero_zero_real ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_less_power2
% 0.29/0.54  thf(fact_2009_zero__less__power2,axiom,
% 0.29/0.54      ! [A: rat] :
% 0.29/0.54        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.54        = ( A != zero_zero_rat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_less_power2
% 0.29/0.54  thf(fact_2010_zero__less__power2,axiom,
% 0.29/0.54      ! [A: int] :
% 0.29/0.54        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.54        = ( A != zero_zero_int ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_less_power2
% 0.29/0.54  thf(fact_2011_power__decreasing__iff,axiom,
% 0.29/0.54      ! [B: real,M: nat,N: nat] :
% 0.29/0.54        ( ( ord_less_real @ zero_zero_real @ B )
% 0.29/0.54       => ( ( ord_less_real @ B @ one_one_real )
% 0.29/0.54         => ( ( ord_less_eq_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N ) )
% 0.29/0.54            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_decreasing_iff
% 0.29/0.54  thf(fact_2012_power__decreasing__iff,axiom,
% 0.29/0.54      ! [B: rat,M: nat,N: nat] :
% 0.29/0.54        ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.29/0.54       => ( ( ord_less_rat @ B @ one_one_rat )
% 0.29/0.54         => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 0.29/0.54            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_decreasing_iff
% 0.29/0.54  thf(fact_2013_power__decreasing__iff,axiom,
% 0.29/0.54      ! [B: nat,M: nat,N: nat] :
% 0.29/0.54        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.29/0.54       => ( ( ord_less_nat @ B @ one_one_nat )
% 0.29/0.54         => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 0.29/0.54            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_decreasing_iff
% 0.29/0.54  thf(fact_2014_power__decreasing__iff,axiom,
% 0.29/0.54      ! [B: int,M: nat,N: nat] :
% 0.29/0.54        ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.54       => ( ( ord_less_int @ B @ one_one_int )
% 0.29/0.54         => ( ( ord_less_eq_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 0.29/0.54            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_decreasing_iff
% 0.29/0.54  thf(fact_2015_sum__power2__eq__zero__iff,axiom,
% 0.29/0.54      ! [X: rat,Y2: rat] :
% 0.29/0.54        ( ( ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.54          = zero_zero_rat )
% 0.29/0.54        = ( ( X = zero_zero_rat )
% 0.29/0.54          & ( Y2 = zero_zero_rat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sum_power2_eq_zero_iff
% 0.29/0.54  thf(fact_2016_sum__power2__eq__zero__iff,axiom,
% 0.29/0.54      ! [X: real,Y2: real] :
% 0.29/0.54        ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.54          = zero_zero_real )
% 0.29/0.54        = ( ( X = zero_zero_real )
% 0.29/0.54          & ( Y2 = zero_zero_real ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sum_power2_eq_zero_iff
% 0.29/0.54  thf(fact_2017_sum__power2__eq__zero__iff,axiom,
% 0.29/0.54      ! [X: int,Y2: int] :
% 0.29/0.54        ( ( ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.54          = zero_zero_int )
% 0.29/0.54        = ( ( X = zero_zero_int )
% 0.29/0.54          & ( Y2 = zero_zero_int ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sum_power2_eq_zero_iff
% 0.29/0.54  thf(fact_2018_VEBT_Osize_I4_J,axiom,
% 0.29/0.54      ! [X21: $o,X222: $o] :
% 0.29/0.54        ( ( size_size_VEBT_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 0.29/0.54        = zero_zero_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % VEBT.size(4)
% 0.29/0.54  thf(fact_2019_VEBT__internal_Onaive__member_Osimps_I1_J,axiom,
% 0.29/0.54      ! [A: $o,B: $o,X: nat] :
% 0.29/0.54        ( ( vEBT_V5719532721284313246member @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.29/0.54        = ( ( ( X = zero_zero_nat )
% 0.29/0.54           => A )
% 0.29/0.54          & ( ( X != zero_zero_nat )
% 0.29/0.54           => ( ( ( X = one_one_nat )
% 0.29/0.54               => B )
% 0.29/0.54              & ( X = one_one_nat ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % VEBT_internal.naive_member.simps(1)
% 0.29/0.54  thf(fact_2020_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I1_J,axiom,
% 0.29/0.54      ! [Uu: $o,Uv: $o] :
% 0.29/0.54        ( ( vEBT_T_p_r_e_d @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat )
% 0.29/0.54        = one_one_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.simps(1)
% 0.29/0.54  thf(fact_2021_VEBT__internal_Omembermima_Osimps_I1_J,axiom,
% 0.29/0.54      ! [Uu: $o,Uv: $o,Uw: nat] :
% 0.29/0.54        ~ ( vEBT_VEBT_membermima @ ( vEBT_Leaf @ Uu @ Uv ) @ Uw ) ).
% 0.29/0.54  
% 0.29/0.54  % VEBT_internal.membermima.simps(1)
% 0.29/0.54  thf(fact_2022_vebt__delete_Osimps_I1_J,axiom,
% 0.29/0.54      ! [A: $o,B: $o] :
% 0.29/0.54        ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat )
% 0.29/0.54        = ( vEBT_Leaf @ $false @ B ) ) ).
% 0.29/0.54  
% 0.29/0.54  % vebt_delete.simps(1)
% 0.29/0.54  thf(fact_2023_VEBT__internal_Onaive__member_Osimps_I2_J,axiom,
% 0.29/0.54      ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,Ux: nat] :
% 0.29/0.54        ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Ux ) ).
% 0.29/0.54  
% 0.29/0.54  % VEBT_internal.naive_member.simps(2)
% 0.29/0.54  thf(fact_2024_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I1_J,axiom,
% 0.29/0.54      ! [A: $o,B: $o,X: nat] :
% 0.29/0.54        ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.29/0.54        = ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( X = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(1)
% 0.29/0.54  thf(fact_2025_VEBT__internal_Onaive__member_Ocases,axiom,
% 0.29/0.54      ! [X: produc9072475918466114483BT_nat] :
% 0.29/0.54        ( ! [A4: $o,B3: $o,X3: nat] :
% 0.29/0.54            ( X
% 0.29/0.54           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ X3 ) )
% 0.29/0.54       => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,Ux2: nat] :
% 0.29/0.54              ( X
% 0.29/0.54             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Ux2 ) )
% 0.29/0.54         => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 0.29/0.54                ( X
% 0.29/0.54               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) @ X3 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % VEBT_internal.naive_member.cases
% 0.29/0.54  thf(fact_2026_invar__vebt_Ointros_I1_J,axiom,
% 0.29/0.54      ! [A: $o,B: $o] : ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % invar_vebt.intros(1)
% 0.29/0.54  thf(fact_2027_power__0__left,axiom,
% 0.29/0.54      ! [N: nat] :
% 0.29/0.54        ( ( ( N = zero_zero_nat )
% 0.29/0.54         => ( ( power_power_rat @ zero_zero_rat @ N )
% 0.29/0.54            = one_one_rat ) )
% 0.29/0.54        & ( ( N != zero_zero_nat )
% 0.29/0.54         => ( ( power_power_rat @ zero_zero_rat @ N )
% 0.29/0.54            = zero_zero_rat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_0_left
% 0.29/0.54  thf(fact_2028_power__0__left,axiom,
% 0.29/0.54      ! [N: nat] :
% 0.29/0.54        ( ( ( N = zero_zero_nat )
% 0.29/0.54         => ( ( power_power_nat @ zero_zero_nat @ N )
% 0.29/0.54            = one_one_nat ) )
% 0.29/0.54        & ( ( N != zero_zero_nat )
% 0.29/0.54         => ( ( power_power_nat @ zero_zero_nat @ N )
% 0.29/0.54            = zero_zero_nat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_0_left
% 0.29/0.54  thf(fact_2029_power__0__left,axiom,
% 0.29/0.54      ! [N: nat] :
% 0.29/0.54        ( ( ( N = zero_zero_nat )
% 0.29/0.54         => ( ( power_power_real @ zero_zero_real @ N )
% 0.29/0.54            = one_one_real ) )
% 0.29/0.54        & ( ( N != zero_zero_nat )
% 0.29/0.54         => ( ( power_power_real @ zero_zero_real @ N )
% 0.29/0.54            = zero_zero_real ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_0_left
% 0.29/0.54  thf(fact_2030_power__0__left,axiom,
% 0.29/0.54      ! [N: nat] :
% 0.29/0.54        ( ( ( N = zero_zero_nat )
% 0.29/0.54         => ( ( power_power_int @ zero_zero_int @ N )
% 0.29/0.54            = one_one_int ) )
% 0.29/0.54        & ( ( N != zero_zero_nat )
% 0.29/0.54         => ( ( power_power_int @ zero_zero_int @ N )
% 0.29/0.54            = zero_zero_int ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_0_left
% 0.29/0.54  thf(fact_2031_power__0__left,axiom,
% 0.29/0.54      ! [N: nat] :
% 0.29/0.54        ( ( ( N = zero_zero_nat )
% 0.29/0.54         => ( ( power_power_complex @ zero_zero_complex @ N )
% 0.29/0.54            = one_one_complex ) )
% 0.29/0.54        & ( ( N != zero_zero_nat )
% 0.29/0.54         => ( ( power_power_complex @ zero_zero_complex @ N )
% 0.29/0.54            = zero_zero_complex ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_0_left
% 0.29/0.54  thf(fact_2032_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I2_J,axiom,
% 0.29/0.54      ! [A: $o,Uw: $o] :
% 0.29/0.54        ( ( vEBT_T_p_r_e_d @ ( vEBT_Leaf @ A @ Uw ) @ ( suc @ zero_zero_nat ) )
% 0.29/0.54        = ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.simps(2)
% 0.29/0.54  thf(fact_2033_vebt__delete_Osimps_I2_J,axiom,
% 0.29/0.54      ! [A: $o,B: $o] :
% 0.29/0.54        ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) )
% 0.29/0.54        = ( vEBT_Leaf @ A @ $false ) ) ).
% 0.29/0.54  
% 0.29/0.54  % vebt_delete.simps(2)
% 0.29/0.54  thf(fact_2034_zero__power,axiom,
% 0.29/0.54      ! [N: nat] :
% 0.29/0.54        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.54       => ( ( power_power_rat @ zero_zero_rat @ N )
% 0.29/0.54          = zero_zero_rat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_power
% 0.29/0.54  thf(fact_2035_zero__power,axiom,
% 0.29/0.54      ! [N: nat] :
% 0.29/0.54        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.54       => ( ( power_power_nat @ zero_zero_nat @ N )
% 0.29/0.54          = zero_zero_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_power
% 0.29/0.54  thf(fact_2036_zero__power,axiom,
% 0.29/0.54      ! [N: nat] :
% 0.29/0.54        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.54       => ( ( power_power_real @ zero_zero_real @ N )
% 0.29/0.54          = zero_zero_real ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_power
% 0.29/0.54  thf(fact_2037_zero__power,axiom,
% 0.29/0.54      ! [N: nat] :
% 0.29/0.54        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.54       => ( ( power_power_int @ zero_zero_int @ N )
% 0.29/0.54          = zero_zero_int ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_power
% 0.29/0.54  thf(fact_2038_zero__power,axiom,
% 0.29/0.54      ! [N: nat] :
% 0.29/0.54        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.54       => ( ( power_power_complex @ zero_zero_complex @ N )
% 0.29/0.54          = zero_zero_complex ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_power
% 0.29/0.54  thf(fact_2039_vebt__member_Osimps_I1_J,axiom,
% 0.29/0.54      ! [A: $o,B: $o,X: nat] :
% 0.29/0.54        ( ( vEBT_vebt_member @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.29/0.54        = ( ( ( X = zero_zero_nat )
% 0.29/0.54           => A )
% 0.29/0.54          & ( ( X != zero_zero_nat )
% 0.29/0.54           => ( ( ( X = one_one_nat )
% 0.29/0.54               => B )
% 0.29/0.54              & ( X = one_one_nat ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % vebt_member.simps(1)
% 0.29/0.54  thf(fact_2040_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I1_J,axiom,
% 0.29/0.54      ! [A: $o,B: $o] :
% 0.29/0.54        ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat )
% 0.29/0.54        = one_one_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.simps(1)
% 0.29/0.54  thf(fact_2041_VEBT_Oexhaust,axiom,
% 0.29/0.54      ! [Y2: vEBT_VEBT] :
% 0.29/0.54        ( ! [X112: option4927543243414619207at_nat,X122: nat,X132: list_VEBT_VEBT,X142: vEBT_VEBT] :
% 0.29/0.54            ( Y2
% 0.29/0.54           != ( vEBT_Node @ X112 @ X122 @ X132 @ X142 ) )
% 0.29/0.54       => ~ ! [X212: $o,X223: $o] :
% 0.29/0.54              ( Y2
% 0.29/0.54             != ( vEBT_Leaf @ X212 @ X223 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % VEBT.exhaust
% 0.29/0.54  thf(fact_2042_VEBT_Odistinct_I1_J,axiom,
% 0.29/0.54      ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,X21: $o,X222: $o] :
% 0.29/0.54        ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 0.29/0.54       != ( vEBT_Leaf @ X21 @ X222 ) ) ).
% 0.29/0.54  
% 0.29/0.54  % VEBT.distinct(1)
% 0.29/0.54  thf(fact_2043_VEBT__internal_Ovalid_H_Ocases,axiom,
% 0.29/0.54      ! [X: produc9072475918466114483BT_nat] :
% 0.29/0.54        ( ! [Uu2: $o,Uv2: $o,D3: nat] :
% 0.29/0.54            ( X
% 0.29/0.54           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ D3 ) )
% 0.29/0.54       => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,Deg3: nat] :
% 0.29/0.54              ( X
% 0.29/0.54             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Deg3 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % VEBT_internal.valid'.cases
% 0.29/0.54  thf(fact_2044_vebt__insert_Osimps_I1_J,axiom,
% 0.29/0.54      ! [X: nat,A: $o,B: $o] :
% 0.29/0.54        ( ( ( X = zero_zero_nat )
% 0.29/0.54         => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.29/0.54            = ( vEBT_Leaf @ $true @ B ) ) )
% 0.29/0.54        & ( ( X != zero_zero_nat )
% 0.29/0.54         => ( ( ( X = one_one_nat )
% 0.29/0.54             => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.29/0.54                = ( vEBT_Leaf @ A @ $true ) ) )
% 0.29/0.54            & ( ( X != one_one_nat )
% 0.29/0.54             => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.29/0.54                = ( vEBT_Leaf @ A @ B ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % vebt_insert.simps(1)
% 0.29/0.54  thf(fact_2045_vebt__pred_Osimps_I1_J,axiom,
% 0.29/0.54      ! [Uu: $o,Uv: $o] :
% 0.29/0.54        ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat )
% 0.29/0.54        = none_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % vebt_pred.simps(1)
% 0.29/0.54  thf(fact_2046_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I1_J,axiom,
% 0.29/0.54      ! [Uu: $o,Uv: $o] :
% 0.29/0.54        ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat )
% 0.29/0.54        = one_one_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.simps(1)
% 0.29/0.54  thf(fact_2047_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I1_J,axiom,
% 0.29/0.54      ! [Uu: $o,B: $o] :
% 0.29/0.54        ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 0.29/0.54        = one_one_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.simps(1)
% 0.29/0.54  thf(fact_2048_VEBT__internal_Omembermima_Osimps_I2_J,axiom,
% 0.29/0.54      ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT,Uz: nat] :
% 0.29/0.54        ~ ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Uz ) ).
% 0.29/0.54  
% 0.29/0.54  % VEBT_internal.membermima.simps(2)
% 0.29/0.54  thf(fact_2049_le__numeral__extra_I3_J,axiom,
% 0.29/0.54      ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 0.29/0.54  
% 0.29/0.54  % le_numeral_extra(3)
% 0.29/0.54  thf(fact_2050_le__numeral__extra_I3_J,axiom,
% 0.29/0.54      ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 0.29/0.54  
% 0.29/0.54  % le_numeral_extra(3)
% 0.29/0.54  thf(fact_2051_le__numeral__extra_I3_J,axiom,
% 0.29/0.54      ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 0.29/0.54  
% 0.29/0.54  % le_numeral_extra(3)
% 0.29/0.54  thf(fact_2052_le__numeral__extra_I3_J,axiom,
% 0.29/0.54      ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 0.29/0.54  
% 0.29/0.54  % le_numeral_extra(3)
% 0.29/0.54  thf(fact_2053_zero__le,axiom,
% 0.29/0.54      ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_le
% 0.29/0.54  thf(fact_2054_field__lbound__gt__zero,axiom,
% 0.29/0.54      ! [D1: real,D22: real] :
% 0.29/0.54        ( ( ord_less_real @ zero_zero_real @ D1 )
% 0.29/0.54       => ( ( ord_less_real @ zero_zero_real @ D22 )
% 0.29/0.54         => ? [E2: real] :
% 0.29/0.54              ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.29/0.54              & ( ord_less_real @ E2 @ D1 )
% 0.29/0.54              & ( ord_less_real @ E2 @ D22 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % field_lbound_gt_zero
% 0.29/0.54  thf(fact_2055_field__lbound__gt__zero,axiom,
% 0.29/0.54      ! [D1: rat,D22: rat] :
% 0.29/0.54        ( ( ord_less_rat @ zero_zero_rat @ D1 )
% 0.29/0.54       => ( ( ord_less_rat @ zero_zero_rat @ D22 )
% 0.29/0.54         => ? [E2: rat] :
% 0.29/0.54              ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 0.29/0.54              & ( ord_less_rat @ E2 @ D1 )
% 0.29/0.54              & ( ord_less_rat @ E2 @ D22 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % field_lbound_gt_zero
% 0.29/0.54  thf(fact_2056_less__numeral__extra_I3_J,axiom,
% 0.29/0.54      ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 0.29/0.54  
% 0.29/0.54  % less_numeral_extra(3)
% 0.29/0.54  thf(fact_2057_less__numeral__extra_I3_J,axiom,
% 0.29/0.54      ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 0.29/0.54  
% 0.29/0.54  % less_numeral_extra(3)
% 0.29/0.54  thf(fact_2058_less__numeral__extra_I3_J,axiom,
% 0.29/0.54      ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % less_numeral_extra(3)
% 0.29/0.54  thf(fact_2059_less__numeral__extra_I3_J,axiom,
% 0.29/0.54      ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 0.29/0.54  
% 0.29/0.54  % less_numeral_extra(3)
% 0.29/0.54  thf(fact_2060_gr__zeroI,axiom,
% 0.29/0.54      ! [N: nat] :
% 0.29/0.54        ( ( N != zero_zero_nat )
% 0.29/0.54       => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.29/0.54  
% 0.29/0.54  % gr_zeroI
% 0.29/0.54  thf(fact_2061_not__less__zero,axiom,
% 0.29/0.54      ! [N: nat] :
% 0.29/0.54        ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % not_less_zero
% 0.29/0.54  thf(fact_2062_gr__implies__not__zero,axiom,
% 0.29/0.54      ! [M: nat,N: nat] :
% 0.29/0.54        ( ( ord_less_nat @ M @ N )
% 0.29/0.54       => ( N != zero_zero_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % gr_implies_not_zero
% 0.29/0.54  thf(fact_2063_zero__less__iff__neq__zero,axiom,
% 0.29/0.54      ! [N: nat] :
% 0.29/0.54        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.54        = ( N != zero_zero_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_less_iff_neq_zero
% 0.29/0.54  thf(fact_2064_zero__neq__numeral,axiom,
% 0.29/0.54      ! [N: num] :
% 0.29/0.54        ( zero_zero_complex
% 0.29/0.54       != ( numera6690914467698888265omplex @ N ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_neq_numeral
% 0.29/0.54  thf(fact_2065_zero__neq__numeral,axiom,
% 0.29/0.54      ! [N: num] :
% 0.29/0.54        ( zero_zero_real
% 0.29/0.54       != ( numeral_numeral_real @ N ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_neq_numeral
% 0.29/0.54  thf(fact_2066_zero__neq__numeral,axiom,
% 0.29/0.54      ! [N: num] :
% 0.29/0.54        ( zero_zero_rat
% 0.29/0.54       != ( numeral_numeral_rat @ N ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_neq_numeral
% 0.29/0.54  thf(fact_2067_zero__neq__numeral,axiom,
% 0.29/0.54      ! [N: num] :
% 0.29/0.54        ( zero_zero_nat
% 0.29/0.54       != ( numeral_numeral_nat @ N ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_neq_numeral
% 0.29/0.54  thf(fact_2068_zero__neq__numeral,axiom,
% 0.29/0.54      ! [N: num] :
% 0.29/0.54        ( zero_zero_int
% 0.29/0.54       != ( numeral_numeral_int @ N ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_neq_numeral
% 0.29/0.54  thf(fact_2069_mult__not__zero,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 0.29/0.54        ( ( ( times_times_rat @ A @ B )
% 0.29/0.54         != zero_zero_rat )
% 0.29/0.54       => ( ( A != zero_zero_rat )
% 0.29/0.54          & ( B != zero_zero_rat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_not_zero
% 0.29/0.54  thf(fact_2070_mult__not__zero,axiom,
% 0.29/0.54      ! [A: complex,B: complex] :
% 0.29/0.54        ( ( ( times_times_complex @ A @ B )
% 0.29/0.54         != zero_zero_complex )
% 0.29/0.54       => ( ( A != zero_zero_complex )
% 0.29/0.54          & ( B != zero_zero_complex ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_not_zero
% 0.29/0.54  thf(fact_2071_mult__not__zero,axiom,
% 0.29/0.54      ! [A: real,B: real] :
% 0.29/0.54        ( ( ( times_times_real @ A @ B )
% 0.29/0.54         != zero_zero_real )
% 0.29/0.54       => ( ( A != zero_zero_real )
% 0.29/0.54          & ( B != zero_zero_real ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_not_zero
% 0.29/0.54  thf(fact_2072_mult__not__zero,axiom,
% 0.29/0.54      ! [A: nat,B: nat] :
% 0.29/0.54        ( ( ( times_times_nat @ A @ B )
% 0.29/0.54         != zero_zero_nat )
% 0.29/0.54       => ( ( A != zero_zero_nat )
% 0.29/0.54          & ( B != zero_zero_nat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_not_zero
% 0.29/0.54  thf(fact_2073_mult__not__zero,axiom,
% 0.29/0.54      ! [A: int,B: int] :
% 0.29/0.54        ( ( ( times_times_int @ A @ B )
% 0.29/0.54         != zero_zero_int )
% 0.29/0.54       => ( ( A != zero_zero_int )
% 0.29/0.54          & ( B != zero_zero_int ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_not_zero
% 0.29/0.54  thf(fact_2074_divisors__zero,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 0.29/0.54        ( ( ( times_times_rat @ A @ B )
% 0.29/0.54          = zero_zero_rat )
% 0.29/0.54       => ( ( A = zero_zero_rat )
% 0.29/0.54          | ( B = zero_zero_rat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divisors_zero
% 0.29/0.54  thf(fact_2075_divisors__zero,axiom,
% 0.29/0.54      ! [A: complex,B: complex] :
% 0.29/0.54        ( ( ( times_times_complex @ A @ B )
% 0.29/0.54          = zero_zero_complex )
% 0.29/0.54       => ( ( A = zero_zero_complex )
% 0.29/0.54          | ( B = zero_zero_complex ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divisors_zero
% 0.29/0.54  thf(fact_2076_divisors__zero,axiom,
% 0.29/0.54      ! [A: real,B: real] :
% 0.29/0.54        ( ( ( times_times_real @ A @ B )
% 0.29/0.54          = zero_zero_real )
% 0.29/0.54       => ( ( A = zero_zero_real )
% 0.29/0.54          | ( B = zero_zero_real ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divisors_zero
% 0.29/0.54  thf(fact_2077_divisors__zero,axiom,
% 0.29/0.54      ! [A: nat,B: nat] :
% 0.29/0.54        ( ( ( times_times_nat @ A @ B )
% 0.29/0.54          = zero_zero_nat )
% 0.29/0.54       => ( ( A = zero_zero_nat )
% 0.29/0.54          | ( B = zero_zero_nat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divisors_zero
% 0.29/0.54  thf(fact_2078_divisors__zero,axiom,
% 0.29/0.54      ! [A: int,B: int] :
% 0.29/0.54        ( ( ( times_times_int @ A @ B )
% 0.29/0.54          = zero_zero_int )
% 0.29/0.54       => ( ( A = zero_zero_int )
% 0.29/0.54          | ( B = zero_zero_int ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divisors_zero
% 0.29/0.54  thf(fact_2079_no__zero__divisors,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 0.29/0.54        ( ( A != zero_zero_rat )
% 0.29/0.54       => ( ( B != zero_zero_rat )
% 0.29/0.54         => ( ( times_times_rat @ A @ B )
% 0.29/0.54           != zero_zero_rat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % no_zero_divisors
% 0.29/0.54  thf(fact_2080_no__zero__divisors,axiom,
% 0.29/0.54      ! [A: complex,B: complex] :
% 0.29/0.54        ( ( A != zero_zero_complex )
% 0.29/0.54       => ( ( B != zero_zero_complex )
% 0.29/0.54         => ( ( times_times_complex @ A @ B )
% 0.29/0.54           != zero_zero_complex ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % no_zero_divisors
% 0.29/0.54  thf(fact_2081_no__zero__divisors,axiom,
% 0.29/0.54      ! [A: real,B: real] :
% 0.29/0.54        ( ( A != zero_zero_real )
% 0.29/0.54       => ( ( B != zero_zero_real )
% 0.29/0.54         => ( ( times_times_real @ A @ B )
% 0.29/0.54           != zero_zero_real ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % no_zero_divisors
% 0.29/0.54  thf(fact_2082_no__zero__divisors,axiom,
% 0.29/0.54      ! [A: nat,B: nat] :
% 0.29/0.54        ( ( A != zero_zero_nat )
% 0.29/0.54       => ( ( B != zero_zero_nat )
% 0.29/0.54         => ( ( times_times_nat @ A @ B )
% 0.29/0.54           != zero_zero_nat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % no_zero_divisors
% 0.29/0.54  thf(fact_2083_no__zero__divisors,axiom,
% 0.29/0.54      ! [A: int,B: int] :
% 0.29/0.54        ( ( A != zero_zero_int )
% 0.29/0.54       => ( ( B != zero_zero_int )
% 0.29/0.54         => ( ( times_times_int @ A @ B )
% 0.29/0.54           != zero_zero_int ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % no_zero_divisors
% 0.29/0.54  thf(fact_2084_mult__left__cancel,axiom,
% 0.29/0.54      ! [C: rat,A: rat,B: rat] :
% 0.29/0.54        ( ( C != zero_zero_rat )
% 0.29/0.54       => ( ( ( times_times_rat @ C @ A )
% 0.29/0.54            = ( times_times_rat @ C @ B ) )
% 0.29/0.54          = ( A = B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_left_cancel
% 0.29/0.54  thf(fact_2085_mult__left__cancel,axiom,
% 0.29/0.54      ! [C: complex,A: complex,B: complex] :
% 0.29/0.54        ( ( C != zero_zero_complex )
% 0.29/0.54       => ( ( ( times_times_complex @ C @ A )
% 0.29/0.54            = ( times_times_complex @ C @ B ) )
% 0.29/0.54          = ( A = B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_left_cancel
% 0.29/0.54  thf(fact_2086_mult__left__cancel,axiom,
% 0.29/0.54      ! [C: real,A: real,B: real] :
% 0.29/0.54        ( ( C != zero_zero_real )
% 0.29/0.54       => ( ( ( times_times_real @ C @ A )
% 0.29/0.54            = ( times_times_real @ C @ B ) )
% 0.29/0.54          = ( A = B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_left_cancel
% 0.29/0.54  thf(fact_2087_mult__left__cancel,axiom,
% 0.29/0.54      ! [C: nat,A: nat,B: nat] :
% 0.29/0.54        ( ( C != zero_zero_nat )
% 0.29/0.54       => ( ( ( times_times_nat @ C @ A )
% 0.29/0.54            = ( times_times_nat @ C @ B ) )
% 0.29/0.54          = ( A = B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_left_cancel
% 0.29/0.54  thf(fact_2088_mult__left__cancel,axiom,
% 0.29/0.54      ! [C: int,A: int,B: int] :
% 0.29/0.54        ( ( C != zero_zero_int )
% 0.29/0.54       => ( ( ( times_times_int @ C @ A )
% 0.29/0.54            = ( times_times_int @ C @ B ) )
% 0.29/0.54          = ( A = B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_left_cancel
% 0.29/0.54  thf(fact_2089_mult__right__cancel,axiom,
% 0.29/0.54      ! [C: rat,A: rat,B: rat] :
% 0.29/0.54        ( ( C != zero_zero_rat )
% 0.29/0.54       => ( ( ( times_times_rat @ A @ C )
% 0.29/0.54            = ( times_times_rat @ B @ C ) )
% 0.29/0.54          = ( A = B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_right_cancel
% 0.29/0.54  thf(fact_2090_mult__right__cancel,axiom,
% 0.29/0.54      ! [C: complex,A: complex,B: complex] :
% 0.29/0.54        ( ( C != zero_zero_complex )
% 0.29/0.54       => ( ( ( times_times_complex @ A @ C )
% 0.29/0.54            = ( times_times_complex @ B @ C ) )
% 0.29/0.54          = ( A = B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_right_cancel
% 0.29/0.54  thf(fact_2091_mult__right__cancel,axiom,
% 0.29/0.54      ! [C: real,A: real,B: real] :
% 0.29/0.54        ( ( C != zero_zero_real )
% 0.29/0.54       => ( ( ( times_times_real @ A @ C )
% 0.29/0.54            = ( times_times_real @ B @ C ) )
% 0.29/0.54          = ( A = B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_right_cancel
% 0.29/0.54  thf(fact_2092_mult__right__cancel,axiom,
% 0.29/0.54      ! [C: nat,A: nat,B: nat] :
% 0.29/0.54        ( ( C != zero_zero_nat )
% 0.29/0.54       => ( ( ( times_times_nat @ A @ C )
% 0.29/0.54            = ( times_times_nat @ B @ C ) )
% 0.29/0.54          = ( A = B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_right_cancel
% 0.29/0.54  thf(fact_2093_mult__right__cancel,axiom,
% 0.29/0.54      ! [C: int,A: int,B: int] :
% 0.29/0.54        ( ( C != zero_zero_int )
% 0.29/0.54       => ( ( ( times_times_int @ A @ C )
% 0.29/0.54            = ( times_times_int @ B @ C ) )
% 0.29/0.54          = ( A = B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_right_cancel
% 0.29/0.54  thf(fact_2094_zero__neq__one,axiom,
% 0.29/0.54      zero_zero_complex != one_one_complex ).
% 0.29/0.54  
% 0.29/0.54  % zero_neq_one
% 0.29/0.54  thf(fact_2095_zero__neq__one,axiom,
% 0.29/0.54      zero_zero_real != one_one_real ).
% 0.29/0.54  
% 0.29/0.54  % zero_neq_one
% 0.29/0.54  thf(fact_2096_zero__neq__one,axiom,
% 0.29/0.54      zero_zero_rat != one_one_rat ).
% 0.29/0.54  
% 0.29/0.54  % zero_neq_one
% 0.29/0.54  thf(fact_2097_zero__neq__one,axiom,
% 0.29/0.54      zero_zero_nat != one_one_nat ).
% 0.29/0.54  
% 0.29/0.54  % zero_neq_one
% 0.29/0.54  thf(fact_2098_zero__neq__one,axiom,
% 0.29/0.54      zero_zero_int != one_one_int ).
% 0.29/0.54  
% 0.29/0.54  % zero_neq_one
% 0.29/0.54  thf(fact_2099_add_Ogroup__left__neutral,axiom,
% 0.29/0.54      ! [A: complex] :
% 0.29/0.54        ( ( plus_plus_complex @ zero_zero_complex @ A )
% 0.29/0.54        = A ) ).
% 0.29/0.54  
% 0.29/0.54  % add.group_left_neutral
% 0.29/0.54  thf(fact_2100_add_Ogroup__left__neutral,axiom,
% 0.29/0.54      ! [A: real] :
% 0.29/0.54        ( ( plus_plus_real @ zero_zero_real @ A )
% 0.29/0.54        = A ) ).
% 0.29/0.54  
% 0.29/0.54  % add.group_left_neutral
% 0.29/0.54  thf(fact_2101_add_Ogroup__left__neutral,axiom,
% 0.29/0.54      ! [A: rat] :
% 0.29/0.54        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 0.29/0.54        = A ) ).
% 0.29/0.54  
% 0.29/0.54  % add.group_left_neutral
% 0.29/0.54  thf(fact_2102_add_Ogroup__left__neutral,axiom,
% 0.29/0.54      ! [A: int] :
% 0.29/0.54        ( ( plus_plus_int @ zero_zero_int @ A )
% 0.29/0.54        = A ) ).
% 0.29/0.54  
% 0.29/0.54  % add.group_left_neutral
% 0.29/0.54  thf(fact_2103_add_Ocomm__neutral,axiom,
% 0.29/0.54      ! [A: complex] :
% 0.29/0.54        ( ( plus_plus_complex @ A @ zero_zero_complex )
% 0.29/0.54        = A ) ).
% 0.29/0.54  
% 0.29/0.54  % add.comm_neutral
% 0.29/0.54  thf(fact_2104_add_Ocomm__neutral,axiom,
% 0.29/0.54      ! [A: real] :
% 0.29/0.54        ( ( plus_plus_real @ A @ zero_zero_real )
% 0.29/0.54        = A ) ).
% 0.29/0.54  
% 0.29/0.54  % add.comm_neutral
% 0.29/0.54  thf(fact_2105_add_Ocomm__neutral,axiom,
% 0.29/0.54      ! [A: rat] :
% 0.29/0.54        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 0.29/0.54        = A ) ).
% 0.29/0.54  
% 0.29/0.54  % add.comm_neutral
% 0.29/0.54  thf(fact_2106_add_Ocomm__neutral,axiom,
% 0.29/0.54      ! [A: nat] :
% 0.29/0.54        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.29/0.54        = A ) ).
% 0.29/0.54  
% 0.29/0.54  % add.comm_neutral
% 0.29/0.54  thf(fact_2107_add_Ocomm__neutral,axiom,
% 0.29/0.54      ! [A: int] :
% 0.29/0.54        ( ( plus_plus_int @ A @ zero_zero_int )
% 0.29/0.54        = A ) ).
% 0.29/0.54  
% 0.29/0.54  % add.comm_neutral
% 0.29/0.54  thf(fact_2108_comm__monoid__add__class_Oadd__0,axiom,
% 0.29/0.54      ! [A: complex] :
% 0.29/0.54        ( ( plus_plus_complex @ zero_zero_complex @ A )
% 0.29/0.54        = A ) ).
% 0.29/0.54  
% 0.29/0.54  % comm_monoid_add_class.add_0
% 0.29/0.54  thf(fact_2109_comm__monoid__add__class_Oadd__0,axiom,
% 0.29/0.54      ! [A: real] :
% 0.29/0.54        ( ( plus_plus_real @ zero_zero_real @ A )
% 0.29/0.54        = A ) ).
% 0.29/0.54  
% 0.29/0.54  % comm_monoid_add_class.add_0
% 0.29/0.54  thf(fact_2110_comm__monoid__add__class_Oadd__0,axiom,
% 0.29/0.54      ! [A: rat] :
% 0.29/0.54        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 0.29/0.54        = A ) ).
% 0.29/0.54  
% 0.29/0.54  % comm_monoid_add_class.add_0
% 0.29/0.54  thf(fact_2111_comm__monoid__add__class_Oadd__0,axiom,
% 0.29/0.54      ! [A: nat] :
% 0.29/0.54        ( ( plus_plus_nat @ zero_zero_nat @ A )
% 0.29/0.54        = A ) ).
% 0.29/0.54  
% 0.29/0.54  % comm_monoid_add_class.add_0
% 0.29/0.54  thf(fact_2112_comm__monoid__add__class_Oadd__0,axiom,
% 0.29/0.54      ! [A: int] :
% 0.29/0.54        ( ( plus_plus_int @ zero_zero_int @ A )
% 0.29/0.54        = A ) ).
% 0.29/0.54  
% 0.29/0.54  % comm_monoid_add_class.add_0
% 0.29/0.54  thf(fact_2113_eq__iff__diff__eq__0,axiom,
% 0.29/0.54      ( ( ^ [Y5: complex,Z5: complex] : ( Y5 = Z5 ) )
% 0.29/0.54      = ( ^ [A3: complex,B4: complex] :
% 0.29/0.54            ( ( minus_minus_complex @ A3 @ B4 )
% 0.29/0.54            = zero_zero_complex ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % eq_iff_diff_eq_0
% 0.29/0.54  thf(fact_2114_eq__iff__diff__eq__0,axiom,
% 0.29/0.54      ( ( ^ [Y5: real,Z5: real] : ( Y5 = Z5 ) )
% 0.29/0.54      = ( ^ [A3: real,B4: real] :
% 0.29/0.54            ( ( minus_minus_real @ A3 @ B4 )
% 0.29/0.54            = zero_zero_real ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % eq_iff_diff_eq_0
% 0.29/0.54  thf(fact_2115_eq__iff__diff__eq__0,axiom,
% 0.29/0.54      ( ( ^ [Y5: rat,Z5: rat] : ( Y5 = Z5 ) )
% 0.29/0.54      = ( ^ [A3: rat,B4: rat] :
% 0.29/0.54            ( ( minus_minus_rat @ A3 @ B4 )
% 0.29/0.54            = zero_zero_rat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % eq_iff_diff_eq_0
% 0.29/0.54  thf(fact_2116_eq__iff__diff__eq__0,axiom,
% 0.29/0.54      ( ( ^ [Y5: int,Z5: int] : ( Y5 = Z5 ) )
% 0.29/0.54      = ( ^ [A3: int,B4: int] :
% 0.29/0.54            ( ( minus_minus_int @ A3 @ B4 )
% 0.29/0.54            = zero_zero_int ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % eq_iff_diff_eq_0
% 0.29/0.54  thf(fact_2117_power__not__zero,axiom,
% 0.29/0.54      ! [A: rat,N: nat] :
% 0.29/0.54        ( ( A != zero_zero_rat )
% 0.29/0.54       => ( ( power_power_rat @ A @ N )
% 0.29/0.54         != zero_zero_rat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_not_zero
% 0.29/0.54  thf(fact_2118_power__not__zero,axiom,
% 0.29/0.54      ! [A: nat,N: nat] :
% 0.29/0.54        ( ( A != zero_zero_nat )
% 0.29/0.54       => ( ( power_power_nat @ A @ N )
% 0.29/0.54         != zero_zero_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_not_zero
% 0.29/0.54  thf(fact_2119_power__not__zero,axiom,
% 0.29/0.54      ! [A: real,N: nat] :
% 0.29/0.54        ( ( A != zero_zero_real )
% 0.29/0.54       => ( ( power_power_real @ A @ N )
% 0.29/0.54         != zero_zero_real ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_not_zero
% 0.29/0.54  thf(fact_2120_power__not__zero,axiom,
% 0.29/0.54      ! [A: int,N: nat] :
% 0.29/0.54        ( ( A != zero_zero_int )
% 0.29/0.54       => ( ( power_power_int @ A @ N )
% 0.29/0.54         != zero_zero_int ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_not_zero
% 0.29/0.54  thf(fact_2121_power__not__zero,axiom,
% 0.29/0.54      ! [A: complex,N: nat] :
% 0.29/0.54        ( ( A != zero_zero_complex )
% 0.29/0.54       => ( ( power_power_complex @ A @ N )
% 0.29/0.54         != zero_zero_complex ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_not_zero
% 0.29/0.54  thf(fact_2122_num_Osize_I4_J,axiom,
% 0.29/0.54      ( ( size_size_num @ one )
% 0.29/0.54      = zero_zero_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % num.size(4)
% 0.29/0.54  thf(fact_2123_VEBT__internal_OminNull_Osimps_I3_J,axiom,
% 0.29/0.54      ! [Uu: $o] :
% 0.29/0.54        ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ Uu @ $true ) ) ).
% 0.29/0.54  
% 0.29/0.54  % VEBT_internal.minNull.simps(3)
% 0.29/0.54  thf(fact_2124_VEBT__internal_OminNull_Osimps_I2_J,axiom,
% 0.29/0.54      ! [Uv: $o] :
% 0.29/0.54        ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ $true @ Uv ) ) ).
% 0.29/0.54  
% 0.29/0.54  % VEBT_internal.minNull.simps(2)
% 0.29/0.54  thf(fact_2125_VEBT__internal_OminNull_Osimps_I1_J,axiom,
% 0.29/0.54      vEBT_VEBT_minNull @ ( vEBT_Leaf @ $false @ $false ) ).
% 0.29/0.54  
% 0.29/0.54  % VEBT_internal.minNull.simps(1)
% 0.29/0.54  thf(fact_2126_nat_Odistinct_I1_J,axiom,
% 0.29/0.54      ! [X23: nat] :
% 0.29/0.54        ( zero_zero_nat
% 0.29/0.54       != ( suc @ X23 ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nat.distinct(1)
% 0.29/0.54  thf(fact_2127_old_Onat_Odistinct_I2_J,axiom,
% 0.29/0.54      ! [Nat2: nat] :
% 0.29/0.54        ( ( suc @ Nat2 )
% 0.29/0.54       != zero_zero_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % old.nat.distinct(2)
% 0.29/0.54  thf(fact_2128_old_Onat_Odistinct_I1_J,axiom,
% 0.29/0.54      ! [Nat2: nat] :
% 0.29/0.54        ( zero_zero_nat
% 0.29/0.54       != ( suc @ Nat2 ) ) ).
% 0.29/0.54  
% 0.29/0.54  % old.nat.distinct(1)
% 0.29/0.54  thf(fact_2129_nat_OdiscI,axiom,
% 0.29/0.54      ! [Nat: nat,X23: nat] :
% 0.29/0.54        ( ( Nat
% 0.29/0.54          = ( suc @ X23 ) )
% 0.29/0.54       => ( Nat != zero_zero_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nat.discI
% 0.29/0.54  thf(fact_2130_old_Onat_Oexhaust,axiom,
% 0.29/0.54      ! [Y2: nat] :
% 0.29/0.54        ( ( Y2 != zero_zero_nat )
% 0.29/0.54       => ~ ! [Nat3: nat] :
% 0.29/0.54              ( Y2
% 0.29/0.54             != ( suc @ Nat3 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % old.nat.exhaust
% 0.29/0.54  thf(fact_2131_nat__induct,axiom,
% 0.29/0.54      ! [P: nat > $o,N: nat] :
% 0.29/0.54        ( ( P @ zero_zero_nat )
% 0.29/0.54       => ( ! [N3: nat] :
% 0.29/0.54              ( ( P @ N3 )
% 0.29/0.54             => ( P @ ( suc @ N3 ) ) )
% 0.29/0.54         => ( P @ N ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nat_induct
% 0.29/0.54  thf(fact_2132_diff__induct,axiom,
% 0.29/0.54      ! [P: nat > nat > $o,M: nat,N: nat] :
% 0.29/0.54        ( ! [X3: nat] : ( P @ X3 @ zero_zero_nat )
% 0.29/0.54       => ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
% 0.29/0.54         => ( ! [X3: nat,Y3: nat] :
% 0.29/0.54                ( ( P @ X3 @ Y3 )
% 0.29/0.54               => ( P @ ( suc @ X3 ) @ ( suc @ Y3 ) ) )
% 0.29/0.54           => ( P @ M @ N ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % diff_induct
% 0.29/0.54  thf(fact_2133_zero__induct,axiom,
% 0.29/0.54      ! [P: nat > $o,K: nat] :
% 0.29/0.54        ( ( P @ K )
% 0.29/0.54       => ( ! [N3: nat] :
% 0.29/0.54              ( ( P @ ( suc @ N3 ) )
% 0.29/0.54             => ( P @ N3 ) )
% 0.29/0.54         => ( P @ zero_zero_nat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_induct
% 0.29/0.54  thf(fact_2134_Suc__neq__Zero,axiom,
% 0.29/0.54      ! [M: nat] :
% 0.29/0.54        ( ( suc @ M )
% 0.29/0.54       != zero_zero_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % Suc_neq_Zero
% 0.29/0.54  thf(fact_2135_Zero__neq__Suc,axiom,
% 0.29/0.54      ! [M: nat] :
% 0.29/0.54        ( zero_zero_nat
% 0.29/0.54       != ( suc @ M ) ) ).
% 0.29/0.54  
% 0.29/0.54  % Zero_neq_Suc
% 0.29/0.54  thf(fact_2136_Zero__not__Suc,axiom,
% 0.29/0.54      ! [M: nat] :
% 0.29/0.54        ( zero_zero_nat
% 0.29/0.54       != ( suc @ M ) ) ).
% 0.29/0.54  
% 0.29/0.54  % Zero_not_Suc
% 0.29/0.54  thf(fact_2137_not0__implies__Suc,axiom,
% 0.29/0.54      ! [N: nat] :
% 0.29/0.54        ( ( N != zero_zero_nat )
% 0.29/0.54       => ? [M4: nat] :
% 0.29/0.54            ( N
% 0.29/0.54            = ( suc @ M4 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % not0_implies_Suc
% 0.29/0.54  thf(fact_2138_vebt__buildup_Ocases,axiom,
% 0.29/0.54      ! [X: nat] :
% 0.29/0.54        ( ( X != zero_zero_nat )
% 0.29/0.54       => ( ( X
% 0.29/0.54           != ( suc @ zero_zero_nat ) )
% 0.29/0.54         => ~ ! [Va2: nat] :
% 0.29/0.54                ( X
% 0.29/0.54               != ( suc @ ( suc @ Va2 ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % vebt_buildup.cases
% 0.29/0.54  thf(fact_2139_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I2_J,axiom,
% 0.29/0.54      ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT,X: nat] :
% 0.29/0.54        ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S3 ) @ X )
% 0.29/0.54        = one_one_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(2)
% 0.29/0.54  thf(fact_2140_bot__nat__0_Oextremum__strict,axiom,
% 0.29/0.54      ! [A: nat] :
% 0.29/0.54        ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % bot_nat_0.extremum_strict
% 0.29/0.54  thf(fact_2141_gr0I,axiom,
% 0.29/0.54      ! [N: nat] :
% 0.29/0.54        ( ( N != zero_zero_nat )
% 0.29/0.54       => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.29/0.54  
% 0.29/0.54  % gr0I
% 0.29/0.54  thf(fact_2142_not__gr0,axiom,
% 0.29/0.54      ! [N: nat] :
% 0.29/0.54        ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 0.29/0.54        = ( N = zero_zero_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % not_gr0
% 0.29/0.54  thf(fact_2143_not__less0,axiom,
% 0.29/0.54      ! [N: nat] :
% 0.29/0.54        ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % not_less0
% 0.29/0.54  thf(fact_2144_less__zeroE,axiom,
% 0.29/0.54      ! [N: nat] :
% 0.29/0.54        ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % less_zeroE
% 0.29/0.54  thf(fact_2145_gr__implies__not0,axiom,
% 0.29/0.54      ! [M: nat,N: nat] :
% 0.29/0.54        ( ( ord_less_nat @ M @ N )
% 0.29/0.54       => ( N != zero_zero_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % gr_implies_not0
% 0.29/0.54  thf(fact_2146_infinite__descent0,axiom,
% 0.29/0.54      ! [P: nat > $o,N: nat] :
% 0.29/0.54        ( ( P @ zero_zero_nat )
% 0.29/0.54       => ( ! [N3: nat] :
% 0.29/0.54              ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.29/0.54             => ( ~ ( P @ N3 )
% 0.29/0.54               => ? [M5: nat] :
% 0.29/0.54                    ( ( ord_less_nat @ M5 @ N3 )
% 0.29/0.54                    & ~ ( P @ M5 ) ) ) )
% 0.29/0.54         => ( P @ N ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % infinite_descent0
% 0.29/0.54  thf(fact_2147_add__eq__self__zero,axiom,
% 0.29/0.54      ! [M: nat,N: nat] :
% 0.29/0.54        ( ( ( plus_plus_nat @ M @ N )
% 0.29/0.54          = M )
% 0.29/0.54       => ( N = zero_zero_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % add_eq_self_zero
% 0.29/0.54  thf(fact_2148_plus__nat_Oadd__0,axiom,
% 0.29/0.54      ! [N: nat] :
% 0.29/0.54        ( ( plus_plus_nat @ zero_zero_nat @ N )
% 0.29/0.54        = N ) ).
% 0.29/0.54  
% 0.29/0.54  % plus_nat.add_0
% 0.29/0.54  thf(fact_2149_less__eq__nat_Osimps_I1_J,axiom,
% 0.29/0.54      ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.29/0.54  
% 0.29/0.54  % less_eq_nat.simps(1)
% 0.29/0.54  thf(fact_2150_bot__nat__0_Oextremum__unique,axiom,
% 0.29/0.54      ! [A: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.29/0.54        = ( A = zero_zero_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % bot_nat_0.extremum_unique
% 0.29/0.54  thf(fact_2151_bot__nat__0_Oextremum__uniqueI,axiom,
% 0.29/0.54      ! [A: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.29/0.54       => ( A = zero_zero_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % bot_nat_0.extremum_uniqueI
% 0.29/0.54  thf(fact_2152_le__0__eq,axiom,
% 0.29/0.54      ! [N: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.29/0.54        = ( N = zero_zero_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_0_eq
% 0.29/0.54  thf(fact_2153_mult__0,axiom,
% 0.29/0.54      ! [N: nat] :
% 0.29/0.54        ( ( times_times_nat @ zero_zero_nat @ N )
% 0.29/0.54        = zero_zero_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_0
% 0.29/0.54  thf(fact_2154_nat__mult__eq__cancel__disj,axiom,
% 0.29/0.54      ! [K: nat,M: nat,N: nat] :
% 0.29/0.54        ( ( ( times_times_nat @ K @ M )
% 0.29/0.54          = ( times_times_nat @ K @ N ) )
% 0.29/0.54        = ( ( K = zero_zero_nat )
% 0.29/0.54          | ( M = N ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nat_mult_eq_cancel_disj
% 0.29/0.54  thf(fact_2155_diffs0__imp__equal,axiom,
% 0.29/0.54      ! [M: nat,N: nat] :
% 0.29/0.54        ( ( ( minus_minus_nat @ M @ N )
% 0.29/0.54          = zero_zero_nat )
% 0.29/0.54       => ( ( ( minus_minus_nat @ N @ M )
% 0.29/0.54            = zero_zero_nat )
% 0.29/0.54         => ( M = N ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % diffs0_imp_equal
% 0.29/0.54  thf(fact_2156_minus__nat_Odiff__0,axiom,
% 0.29/0.54      ! [M: nat] :
% 0.29/0.54        ( ( minus_minus_nat @ M @ zero_zero_nat )
% 0.29/0.54        = M ) ).
% 0.29/0.54  
% 0.29/0.54  % minus_nat.diff_0
% 0.29/0.54  thf(fact_2157_power__eq__iff__eq__base,axiom,
% 0.29/0.54      ! [N: nat,A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.54       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.54         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.29/0.54           => ( ( ( power_power_rat @ A @ N )
% 0.29/0.54                = ( power_power_rat @ B @ N ) )
% 0.29/0.54              = ( A = B ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_eq_iff_eq_base
% 0.29/0.54  thf(fact_2158_power__eq__iff__eq__base,axiom,
% 0.29/0.54      ! [N: nat,A: real,B: real] :
% 0.29/0.54        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.54       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.54         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.29/0.54           => ( ( ( power_power_real @ A @ N )
% 0.29/0.54                = ( power_power_real @ B @ N ) )
% 0.29/0.54              = ( A = B ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_eq_iff_eq_base
% 0.29/0.54  thf(fact_2159_power__eq__iff__eq__base,axiom,
% 0.29/0.54      ! [N: nat,A: nat,B: nat] :
% 0.29/0.54        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.54       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.54         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.29/0.54           => ( ( ( power_power_nat @ A @ N )
% 0.29/0.54                = ( power_power_nat @ B @ N ) )
% 0.29/0.54              = ( A = B ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_eq_iff_eq_base
% 0.29/0.54  thf(fact_2160_power__eq__iff__eq__base,axiom,
% 0.29/0.54      ! [N: nat,A: int,B: int] :
% 0.29/0.54        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.54       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.54         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.29/0.54           => ( ( ( power_power_int @ A @ N )
% 0.29/0.54                = ( power_power_int @ B @ N ) )
% 0.29/0.54              = ( A = B ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_eq_iff_eq_base
% 0.29/0.54  thf(fact_2161_power__eq__imp__eq__base,axiom,
% 0.29/0.54      ! [A: rat,N: nat,B: rat] :
% 0.29/0.54        ( ( ( power_power_rat @ A @ N )
% 0.29/0.54          = ( power_power_rat @ B @ N ) )
% 0.29/0.54       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.54         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.29/0.54           => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.54             => ( A = B ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_eq_imp_eq_base
% 0.29/0.54  thf(fact_2162_power__eq__imp__eq__base,axiom,
% 0.29/0.54      ! [A: real,N: nat,B: real] :
% 0.29/0.54        ( ( ( power_power_real @ A @ N )
% 0.29/0.54          = ( power_power_real @ B @ N ) )
% 0.29/0.54       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.54         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.29/0.54           => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.54             => ( A = B ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_eq_imp_eq_base
% 0.29/0.54  thf(fact_2163_power__eq__imp__eq__base,axiom,
% 0.29/0.54      ! [A: nat,N: nat,B: nat] :
% 0.29/0.54        ( ( ( power_power_nat @ A @ N )
% 0.29/0.54          = ( power_power_nat @ B @ N ) )
% 0.29/0.54       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.54         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.29/0.54           => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.54             => ( A = B ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_eq_imp_eq_base
% 0.29/0.54  thf(fact_2164_power__eq__imp__eq__base,axiom,
% 0.29/0.54      ! [A: int,N: nat,B: int] :
% 0.29/0.54        ( ( ( power_power_int @ A @ N )
% 0.29/0.54          = ( power_power_int @ B @ N ) )
% 0.29/0.54       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.54         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.29/0.54           => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.54             => ( A = B ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_eq_imp_eq_base
% 0.29/0.54  thf(fact_2165_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I2_J,axiom,
% 0.29/0.54      ! [A: $o,B: $o] :
% 0.29/0.54        ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) )
% 0.29/0.54        = one_one_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.simps(2)
% 0.29/0.54  thf(fact_2166_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Osimps_I1_J,axiom,
% 0.29/0.54      ! [A: $o,B: $o] :
% 0.29/0.54        ( ( vEBT_T_m_i_n_t @ ( vEBT_Leaf @ A @ B ) )
% 0.29/0.54        = ( plus_plus_nat @ one_one_nat @ ( if_nat @ A @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.simps(1)
% 0.29/0.54  thf(fact_2167_lambda__zero,axiom,
% 0.29/0.54      ( ( ^ [H: rat] : zero_zero_rat )
% 0.29/0.54      = ( times_times_rat @ zero_zero_rat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % lambda_zero
% 0.29/0.54  thf(fact_2168_lambda__zero,axiom,
% 0.29/0.54      ( ( ^ [H: complex] : zero_zero_complex )
% 0.29/0.54      = ( times_times_complex @ zero_zero_complex ) ) ).
% 0.29/0.54  
% 0.29/0.54  % lambda_zero
% 0.29/0.54  thf(fact_2169_lambda__zero,axiom,
% 0.29/0.54      ( ( ^ [H: real] : zero_zero_real )
% 0.29/0.54      = ( times_times_real @ zero_zero_real ) ) ).
% 0.29/0.54  
% 0.29/0.54  % lambda_zero
% 0.29/0.54  thf(fact_2170_lambda__zero,axiom,
% 0.29/0.54      ( ( ^ [H: nat] : zero_zero_nat )
% 0.29/0.54      = ( times_times_nat @ zero_zero_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % lambda_zero
% 0.29/0.54  thf(fact_2171_lambda__zero,axiom,
% 0.29/0.54      ( ( ^ [H: int] : zero_zero_int )
% 0.29/0.54      = ( times_times_int @ zero_zero_int ) ) ).
% 0.29/0.54  
% 0.29/0.54  % lambda_zero
% 0.29/0.54  thf(fact_2172_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I2_J,axiom,
% 0.29/0.54      ! [A: $o,Uw: $o] :
% 0.29/0.54        ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Leaf @ A @ Uw ) @ ( suc @ zero_zero_nat ) )
% 0.29/0.54        = one_one_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.simps(2)
% 0.29/0.54  thf(fact_2173_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I1_J,axiom,
% 0.29/0.54      ! [Uu: $o,B: $o] :
% 0.29/0.54        ( ( vEBT_T_s_u_c_c @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 0.29/0.54        = ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.simps(1)
% 0.29/0.54  thf(fact_2174_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I3_J,axiom,
% 0.29/0.54      ! [A: $o,B: $o,Va: nat] :
% 0.29/0.54        ( ( vEBT_T_p_r_e_d @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 0.29/0.54        = ( plus_plus_nat @ one_one_nat @ ( if_nat @ B @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.simps(3)
% 0.29/0.54  thf(fact_2175_VEBT__internal_Omembermima_Osimps_I3_J,axiom,
% 0.29/0.54      ! [Mi: nat,Ma: nat,Va: list_VEBT_VEBT,Vb: vEBT_VEBT,X: nat] :
% 0.29/0.54        ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ Va @ Vb ) @ X )
% 0.29/0.54        = ( ( X = Mi )
% 0.29/0.54          | ( X = Ma ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % VEBT_internal.membermima.simps(3)
% 0.29/0.54  thf(fact_2176_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I3_J,axiom,
% 0.29/0.54      ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT,X: nat] :
% 0.29/0.54        ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) @ X )
% 0.29/0.54        = one_one_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(3)
% 0.29/0.54  thf(fact_2177_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I5_J,axiom,
% 0.29/0.54      ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT,Vf: nat] :
% 0.29/0.54        ( ( vEBT_T_p_r_e_d @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) @ Vf )
% 0.29/0.54        = one_one_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.simps(5)
% 0.29/0.54  thf(fact_2178_power__strict__mono,axiom,
% 0.29/0.54      ! [A: real,B: real,N: nat] :
% 0.29/0.54        ( ( ord_less_real @ A @ B )
% 0.29/0.54       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.54         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.54           => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_strict_mono
% 0.29/0.54  thf(fact_2179_power__strict__mono,axiom,
% 0.29/0.54      ! [A: rat,B: rat,N: nat] :
% 0.29/0.54        ( ( ord_less_rat @ A @ B )
% 0.29/0.54       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.54         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.54           => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_strict_mono
% 0.29/0.54  thf(fact_2180_power__strict__mono,axiom,
% 0.29/0.54      ! [A: nat,B: nat,N: nat] :
% 0.29/0.54        ( ( ord_less_nat @ A @ B )
% 0.29/0.54       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.54         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.54           => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_strict_mono
% 0.29/0.54  thf(fact_2181_power__strict__mono,axiom,
% 0.29/0.54      ! [A: int,B: int,N: nat] :
% 0.29/0.54        ( ( ord_less_int @ A @ B )
% 0.29/0.54       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.54         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.54           => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_strict_mono
% 0.29/0.54  thf(fact_2182_vebt__mint_Osimps_I1_J,axiom,
% 0.29/0.54      ! [A: $o,B: $o] :
% 0.29/0.54        ( ( A
% 0.29/0.54         => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 0.29/0.54            = ( some_nat @ zero_zero_nat ) ) )
% 0.29/0.54        & ( ~ A
% 0.29/0.54         => ( ( B
% 0.29/0.54             => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 0.29/0.54                = ( some_nat @ one_one_nat ) ) )
% 0.29/0.54            & ( ~ B
% 0.29/0.54             => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 0.29/0.54                = none_nat ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % vebt_mint.simps(1)
% 0.29/0.54  thf(fact_2183_vebt__maxt_Osimps_I1_J,axiom,
% 0.29/0.54      ! [B: $o,A: $o] :
% 0.29/0.54        ( ( B
% 0.29/0.54         => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 0.29/0.54            = ( some_nat @ one_one_nat ) ) )
% 0.29/0.54        & ( ~ B
% 0.29/0.54         => ( ( A
% 0.29/0.54             => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 0.29/0.54                = ( some_nat @ zero_zero_nat ) ) )
% 0.29/0.54            & ( ~ A
% 0.29/0.54             => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 0.29/0.54                = none_nat ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % vebt_maxt.simps(1)
% 0.29/0.54  thf(fact_2184_vebt__delete_Osimps_I3_J,axiom,
% 0.29/0.54      ! [A: $o,B: $o,N: nat] :
% 0.29/0.54        ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ N ) ) )
% 0.29/0.54        = ( vEBT_Leaf @ A @ B ) ) ).
% 0.29/0.54  
% 0.29/0.54  % vebt_delete.simps(3)
% 0.29/0.54  thf(fact_2185_vebt__pred_Osimps_I2_J,axiom,
% 0.29/0.54      ! [A: $o,Uw: $o] :
% 0.29/0.54        ( ( A
% 0.29/0.54         => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw ) @ ( suc @ zero_zero_nat ) )
% 0.29/0.54            = ( some_nat @ zero_zero_nat ) ) )
% 0.29/0.54        & ( ~ A
% 0.29/0.54         => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw ) @ ( suc @ zero_zero_nat ) )
% 0.29/0.54            = none_nat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % vebt_pred.simps(2)
% 0.29/0.54  thf(fact_2186_vebt__succ_Osimps_I1_J,axiom,
% 0.29/0.54      ! [B: $o,Uu: $o] :
% 0.29/0.54        ( ( B
% 0.29/0.54         => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 0.29/0.54            = ( some_nat @ one_one_nat ) ) )
% 0.29/0.54        & ( ~ B
% 0.29/0.54         => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 0.29/0.54            = none_nat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % vebt_succ.simps(1)
% 0.29/0.54  thf(fact_2187_zero__le__numeral,axiom,
% 0.29/0.54      ! [N: num] : ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_le_numeral
% 0.29/0.54  thf(fact_2188_zero__le__numeral,axiom,
% 0.29/0.54      ! [N: num] : ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_le_numeral
% 0.29/0.54  thf(fact_2189_zero__le__numeral,axiom,
% 0.29/0.54      ! [N: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_le_numeral
% 0.29/0.54  thf(fact_2190_zero__le__numeral,axiom,
% 0.29/0.54      ! [N: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_le_numeral
% 0.29/0.54  thf(fact_2191_not__numeral__le__zero,axiom,
% 0.29/0.54      ! [N: num] :
% 0.29/0.54        ~ ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 0.29/0.54  
% 0.29/0.54  % not_numeral_le_zero
% 0.29/0.54  thf(fact_2192_not__numeral__le__zero,axiom,
% 0.29/0.54      ! [N: num] :
% 0.29/0.54        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 0.29/0.54  
% 0.29/0.54  % not_numeral_le_zero
% 0.29/0.54  thf(fact_2193_not__numeral__le__zero,axiom,
% 0.29/0.54      ! [N: num] :
% 0.29/0.54        ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % not_numeral_le_zero
% 0.29/0.54  thf(fact_2194_not__numeral__le__zero,axiom,
% 0.29/0.54      ! [N: num] :
% 0.29/0.54        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 0.29/0.54  
% 0.29/0.54  % not_numeral_le_zero
% 0.29/0.54  thf(fact_2195_not__numeral__less__zero,axiom,
% 0.29/0.54      ! [N: num] :
% 0.29/0.54        ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 0.29/0.54  
% 0.29/0.54  % not_numeral_less_zero
% 0.29/0.54  thf(fact_2196_not__numeral__less__zero,axiom,
% 0.29/0.54      ! [N: num] :
% 0.29/0.54        ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 0.29/0.54  
% 0.29/0.54  % not_numeral_less_zero
% 0.29/0.54  thf(fact_2197_not__numeral__less__zero,axiom,
% 0.29/0.54      ! [N: num] :
% 0.29/0.54        ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % not_numeral_less_zero
% 0.29/0.54  thf(fact_2198_not__numeral__less__zero,axiom,
% 0.29/0.54      ! [N: num] :
% 0.29/0.54        ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 0.29/0.54  
% 0.29/0.54  % not_numeral_less_zero
% 0.29/0.54  thf(fact_2199_zero__less__numeral,axiom,
% 0.29/0.54      ! [N: num] : ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_less_numeral
% 0.29/0.54  thf(fact_2200_zero__less__numeral,axiom,
% 0.29/0.54      ! [N: num] : ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_less_numeral
% 0.29/0.54  thf(fact_2201_zero__less__numeral,axiom,
% 0.29/0.54      ! [N: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_less_numeral
% 0.29/0.54  thf(fact_2202_zero__less__numeral,axiom,
% 0.29/0.54      ! [N: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_less_numeral
% 0.29/0.54  thf(fact_2203_mult__mono,axiom,
% 0.29/0.54      ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54       => ( ( ord_less_eq_rat @ C @ D2 )
% 0.29/0.54         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.29/0.54           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.29/0.54             => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_mono
% 0.29/0.54  thf(fact_2204_mult__mono,axiom,
% 0.29/0.54      ! [A: real,B: real,C: real,D2: real] :
% 0.29/0.54        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.54       => ( ( ord_less_eq_real @ C @ D2 )
% 0.29/0.54         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.29/0.54           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.29/0.54             => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_mono
% 0.29/0.54  thf(fact_2205_mult__mono,axiom,
% 0.29/0.54      ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.54       => ( ( ord_less_eq_nat @ C @ D2 )
% 0.29/0.54         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.29/0.54           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.29/0.54             => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_mono
% 0.29/0.54  thf(fact_2206_mult__mono,axiom,
% 0.29/0.54      ! [A: int,B: int,C: int,D2: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.54       => ( ( ord_less_eq_int @ C @ D2 )
% 0.29/0.54         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.29/0.54           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.54             => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_mono
% 0.29/0.54  thf(fact_2207_mult__mono_H,axiom,
% 0.29/0.54      ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54       => ( ( ord_less_eq_rat @ C @ D2 )
% 0.29/0.54         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.54           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.29/0.54             => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_mono'
% 0.29/0.54  thf(fact_2208_mult__mono_H,axiom,
% 0.29/0.54      ! [A: real,B: real,C: real,D2: real] :
% 0.29/0.54        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.54       => ( ( ord_less_eq_real @ C @ D2 )
% 0.29/0.54         => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.54           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.29/0.55             => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_mono'
% 0.29/0.55  thf(fact_2209_mult__mono_H,axiom,
% 0.29/0.55      ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.55       => ( ( ord_less_eq_nat @ C @ D2 )
% 0.29/0.55         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.55           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.29/0.55             => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_mono'
% 0.29/0.55  thf(fact_2210_mult__mono_H,axiom,
% 0.29/0.55      ! [A: int,B: int,C: int,D2: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.55       => ( ( ord_less_eq_int @ C @ D2 )
% 0.29/0.55         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.55           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.55             => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_mono'
% 0.29/0.55  thf(fact_2211_zero__le__square,axiom,
% 0.29/0.55      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_le_square
% 0.29/0.55  thf(fact_2212_zero__le__square,axiom,
% 0.29/0.55      ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_le_square
% 0.29/0.55  thf(fact_2213_zero__le__square,axiom,
% 0.29/0.55      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_le_square
% 0.29/0.55  thf(fact_2214_split__mult__pos__le,axiom,
% 0.29/0.55      ! [A: rat,B: rat] :
% 0.29/0.55        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.55            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 0.29/0.55          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.29/0.55            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 0.29/0.55       => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % split_mult_pos_le
% 0.29/0.55  thf(fact_2215_split__mult__pos__le,axiom,
% 0.29/0.55      ! [A: real,B: real] :
% 0.29/0.55        ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.55            & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 0.29/0.55          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.29/0.55            & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 0.29/0.55       => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % split_mult_pos_le
% 0.29/0.55  thf(fact_2216_split__mult__pos__le,axiom,
% 0.29/0.55      ! [A: int,B: int] :
% 0.29/0.55        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.55            & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 0.29/0.55          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.29/0.55            & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 0.29/0.55       => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % split_mult_pos_le
% 0.29/0.55  thf(fact_2217_mult__left__mono__neg,axiom,
% 0.29/0.55      ! [B: rat,A: rat,C: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.55       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.29/0.55         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_left_mono_neg
% 0.29/0.55  thf(fact_2218_mult__left__mono__neg,axiom,
% 0.29/0.55      ! [B: real,A: real,C: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ B @ A )
% 0.29/0.55       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.29/0.55         => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_left_mono_neg
% 0.29/0.55  thf(fact_2219_mult__left__mono__neg,axiom,
% 0.29/0.55      ! [B: int,A: int,C: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ B @ A )
% 0.29/0.55       => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.29/0.55         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_left_mono_neg
% 0.29/0.55  thf(fact_2220_mult__nonpos__nonpos,axiom,
% 0.29/0.55      ! [A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.29/0.55       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.29/0.55         => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_nonpos_nonpos
% 0.29/0.55  thf(fact_2221_mult__nonpos__nonpos,axiom,
% 0.29/0.55      ! [A: real,B: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.29/0.55       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.29/0.55         => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_nonpos_nonpos
% 0.29/0.55  thf(fact_2222_mult__nonpos__nonpos,axiom,
% 0.29/0.55      ! [A: int,B: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.29/0.55       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.29/0.55         => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_nonpos_nonpos
% 0.29/0.55  thf(fact_2223_mult__left__mono,axiom,
% 0.29/0.55      ! [A: rat,B: rat,C: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.29/0.55         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_left_mono
% 0.29/0.55  thf(fact_2224_mult__left__mono,axiom,
% 0.29/0.55      ! [A: real,B: real,C: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.55       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.29/0.55         => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_left_mono
% 0.29/0.55  thf(fact_2225_mult__left__mono,axiom,
% 0.29/0.55      ! [A: nat,B: nat,C: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.55       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.29/0.55         => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_left_mono
% 0.29/0.55  thf(fact_2226_mult__left__mono,axiom,
% 0.29/0.55      ! [A: int,B: int,C: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.55       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.55         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_left_mono
% 0.29/0.55  thf(fact_2227_mult__right__mono__neg,axiom,
% 0.29/0.55      ! [B: rat,A: rat,C: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.55       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.29/0.55         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_right_mono_neg
% 0.29/0.55  thf(fact_2228_mult__right__mono__neg,axiom,
% 0.29/0.55      ! [B: real,A: real,C: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ B @ A )
% 0.29/0.55       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.29/0.55         => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_right_mono_neg
% 0.29/0.55  thf(fact_2229_mult__right__mono__neg,axiom,
% 0.29/0.55      ! [B: int,A: int,C: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ B @ A )
% 0.29/0.55       => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.29/0.55         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_right_mono_neg
% 0.29/0.55  thf(fact_2230_mult__right__mono,axiom,
% 0.29/0.55      ! [A: rat,B: rat,C: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.29/0.55         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_right_mono
% 0.29/0.55  thf(fact_2231_mult__right__mono,axiom,
% 0.29/0.55      ! [A: real,B: real,C: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.55       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.29/0.55         => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_right_mono
% 0.29/0.55  thf(fact_2232_mult__right__mono,axiom,
% 0.29/0.55      ! [A: nat,B: nat,C: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.55       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.29/0.55         => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_right_mono
% 0.29/0.55  thf(fact_2233_mult__right__mono,axiom,
% 0.29/0.55      ! [A: int,B: int,C: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.55       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.55         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_right_mono
% 0.29/0.55  thf(fact_2234_mult__le__0__iff,axiom,
% 0.29/0.55      ! [A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 0.29/0.55        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.55            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 0.29/0.55          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.29/0.55            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_0_iff
% 0.29/0.55  thf(fact_2235_mult__le__0__iff,axiom,
% 0.29/0.55      ! [A: real,B: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 0.29/0.55        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.55            & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 0.29/0.55          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.29/0.55            & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_0_iff
% 0.29/0.55  thf(fact_2236_mult__le__0__iff,axiom,
% 0.29/0.55      ! [A: int,B: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 0.29/0.55        = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.55            & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 0.29/0.55          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.29/0.55            & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_0_iff
% 0.29/0.55  thf(fact_2237_split__mult__neg__le,axiom,
% 0.29/0.55      ! [A: rat,B: rat] :
% 0.29/0.55        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.55            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 0.29/0.55          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.29/0.55            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 0.29/0.55       => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 0.29/0.55  
% 0.29/0.55  % split_mult_neg_le
% 0.29/0.55  thf(fact_2238_split__mult__neg__le,axiom,
% 0.29/0.55      ! [A: real,B: real] :
% 0.29/0.55        ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.55            & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 0.29/0.55          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.29/0.55            & ( ord_less_eq_real @ zero_zero_real @ B ) ) )
% 0.29/0.55       => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ).
% 0.29/0.55  
% 0.29/0.55  % split_mult_neg_le
% 0.29/0.55  thf(fact_2239_split__mult__neg__le,axiom,
% 0.29/0.55      ! [A: nat,B: nat] :
% 0.29/0.55        ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.55            & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 0.29/0.55          | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.29/0.55            & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 0.29/0.55       => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 0.29/0.55  
% 0.29/0.55  % split_mult_neg_le
% 0.29/0.55  thf(fact_2240_split__mult__neg__le,axiom,
% 0.29/0.55      ! [A: int,B: int] :
% 0.29/0.55        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.55            & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 0.29/0.55          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.29/0.55            & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 0.29/0.55       => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 0.29/0.55  
% 0.29/0.55  % split_mult_neg_le
% 0.29/0.55  thf(fact_2241_mult__nonneg__nonneg,axiom,
% 0.29/0.55      ! [A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.29/0.55         => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_nonneg_nonneg
% 0.29/0.55  thf(fact_2242_mult__nonneg__nonneg,axiom,
% 0.29/0.55      ! [A: real,B: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.55       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.29/0.55         => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_nonneg_nonneg
% 0.29/0.55  thf(fact_2243_mult__nonneg__nonneg,axiom,
% 0.29/0.55      ! [A: nat,B: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.55       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.29/0.55         => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_nonneg_nonneg
% 0.29/0.55  thf(fact_2244_mult__nonneg__nonneg,axiom,
% 0.29/0.55      ! [A: int,B: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.55       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.29/0.55         => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_nonneg_nonneg
% 0.29/0.55  thf(fact_2245_mult__nonneg__nonpos,axiom,
% 0.29/0.55      ! [A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.55       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.29/0.55         => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_nonneg_nonpos
% 0.29/0.55  thf(fact_2246_mult__nonneg__nonpos,axiom,
% 0.29/0.55      ! [A: real,B: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.55       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.29/0.55         => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_nonneg_nonpos
% 0.29/0.55  thf(fact_2247_mult__nonneg__nonpos,axiom,
% 0.29/0.55      ! [A: nat,B: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.55       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.29/0.55         => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_nonneg_nonpos
% 0.29/0.55  thf(fact_2248_mult__nonneg__nonpos,axiom,
% 0.29/0.55      ! [A: int,B: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.55       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.29/0.55         => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_nonneg_nonpos
% 0.29/0.55  thf(fact_2249_mult__nonpos__nonneg,axiom,
% 0.29/0.55      ! [A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.29/0.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.29/0.55         => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_nonpos_nonneg
% 0.29/0.55  thf(fact_2250_mult__nonpos__nonneg,axiom,
% 0.29/0.55      ! [A: real,B: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.29/0.55       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.29/0.55         => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_nonpos_nonneg
% 0.29/0.55  thf(fact_2251_mult__nonpos__nonneg,axiom,
% 0.29/0.55      ! [A: nat,B: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.29/0.55       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.29/0.55         => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_nonpos_nonneg
% 0.29/0.55  thf(fact_2252_mult__nonpos__nonneg,axiom,
% 0.29/0.55      ! [A: int,B: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.29/0.55       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.29/0.55         => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_nonpos_nonneg
% 0.29/0.55  thf(fact_2253_mult__nonneg__nonpos2,axiom,
% 0.29/0.55      ! [A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.55       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.29/0.55         => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_nonneg_nonpos2
% 0.29/0.55  thf(fact_2254_mult__nonneg__nonpos2,axiom,
% 0.29/0.55      ! [A: real,B: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.55       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.29/0.55         => ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_nonneg_nonpos2
% 0.29/0.55  thf(fact_2255_mult__nonneg__nonpos2,axiom,
% 0.29/0.55      ! [A: nat,B: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.55       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.29/0.55         => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_nonneg_nonpos2
% 0.29/0.55  thf(fact_2256_mult__nonneg__nonpos2,axiom,
% 0.29/0.55      ! [A: int,B: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.55       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.29/0.55         => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_nonneg_nonpos2
% 0.29/0.55  thf(fact_2257_zero__le__mult__iff,axiom,
% 0.29/0.55      ! [A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.29/0.55        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.55            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 0.29/0.55          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.29/0.55            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_le_mult_iff
% 0.29/0.55  thf(fact_2258_zero__le__mult__iff,axiom,
% 0.29/0.55      ! [A: real,B: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.29/0.55        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.55            & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 0.29/0.55          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.29/0.55            & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_le_mult_iff
% 0.29/0.55  thf(fact_2259_zero__le__mult__iff,axiom,
% 0.29/0.55      ! [A: int,B: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 0.29/0.55        = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.55            & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 0.29/0.55          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.29/0.55            & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_le_mult_iff
% 0.29/0.55  thf(fact_2260_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.29/0.55      ! [A: rat,B: rat,C: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.29/0.55         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % ordered_comm_semiring_class.comm_mult_left_mono
% 0.29/0.55  thf(fact_2261_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.29/0.55      ! [A: real,B: real,C: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.55       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.29/0.55         => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % ordered_comm_semiring_class.comm_mult_left_mono
% 0.29/0.55  thf(fact_2262_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.29/0.55      ! [A: nat,B: nat,C: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.55       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.29/0.55         => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % ordered_comm_semiring_class.comm_mult_left_mono
% 0.29/0.55  thf(fact_2263_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.29/0.55      ! [A: int,B: int,C: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.55       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.55         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % ordered_comm_semiring_class.comm_mult_left_mono
% 0.29/0.55  thf(fact_2264_zero__less__one__class_Ozero__le__one,axiom,
% 0.29/0.55      ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 0.29/0.55  
% 0.29/0.55  % zero_less_one_class.zero_le_one
% 0.29/0.55  thf(fact_2265_zero__less__one__class_Ozero__le__one,axiom,
% 0.29/0.55      ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 0.29/0.55  
% 0.29/0.55  % zero_less_one_class.zero_le_one
% 0.29/0.55  thf(fact_2266_zero__less__one__class_Ozero__le__one,axiom,
% 0.29/0.55      ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 0.29/0.55  
% 0.29/0.55  % zero_less_one_class.zero_le_one
% 0.29/0.55  thf(fact_2267_zero__less__one__class_Ozero__le__one,axiom,
% 0.29/0.55      ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 0.29/0.55  
% 0.29/0.55  % zero_less_one_class.zero_le_one
% 0.29/0.55  thf(fact_2268_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.29/0.55      ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 0.29/0.55  
% 0.29/0.55  % linordered_nonzero_semiring_class.zero_le_one
% 0.29/0.55  thf(fact_2269_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.29/0.55      ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 0.29/0.55  
% 0.29/0.55  % linordered_nonzero_semiring_class.zero_le_one
% 0.29/0.55  thf(fact_2270_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.29/0.55      ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 0.29/0.55  
% 0.29/0.55  % linordered_nonzero_semiring_class.zero_le_one
% 0.29/0.55  thf(fact_2271_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.29/0.55      ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 0.29/0.55  
% 0.29/0.55  % linordered_nonzero_semiring_class.zero_le_one
% 0.29/0.55  thf(fact_2272_not__one__le__zero,axiom,
% 0.29/0.55      ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).
% 0.29/0.55  
% 0.29/0.55  % not_one_le_zero
% 0.29/0.55  thf(fact_2273_not__one__le__zero,axiom,
% 0.29/0.55      ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 0.29/0.55  
% 0.29/0.55  % not_one_le_zero
% 0.29/0.55  thf(fact_2274_not__one__le__zero,axiom,
% 0.29/0.55      ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 0.29/0.55  
% 0.29/0.55  % not_one_le_zero
% 0.29/0.55  thf(fact_2275_not__one__le__zero,axiom,
% 0.29/0.55      ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 0.29/0.55  
% 0.29/0.55  % not_one_le_zero
% 0.29/0.55  thf(fact_2276_add__decreasing,axiom,
% 0.29/0.55      ! [A: real,C: real,B: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.29/0.55       => ( ( ord_less_eq_real @ C @ B )
% 0.29/0.55         => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_decreasing
% 0.29/0.55  thf(fact_2277_add__decreasing,axiom,
% 0.29/0.55      ! [A: rat,C: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.29/0.55       => ( ( ord_less_eq_rat @ C @ B )
% 0.29/0.55         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_decreasing
% 0.29/0.55  thf(fact_2278_add__decreasing,axiom,
% 0.29/0.55      ! [A: nat,C: nat,B: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.29/0.55       => ( ( ord_less_eq_nat @ C @ B )
% 0.29/0.55         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_decreasing
% 0.29/0.55  thf(fact_2279_add__decreasing,axiom,
% 0.29/0.55      ! [A: int,C: int,B: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.29/0.55       => ( ( ord_less_eq_int @ C @ B )
% 0.29/0.55         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_decreasing
% 0.29/0.55  thf(fact_2280_add__increasing,axiom,
% 0.29/0.55      ! [A: real,B: real,C: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.55       => ( ( ord_less_eq_real @ B @ C )
% 0.29/0.55         => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_increasing
% 0.29/0.55  thf(fact_2281_add__increasing,axiom,
% 0.29/0.55      ! [A: rat,B: rat,C: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.55       => ( ( ord_less_eq_rat @ B @ C )
% 0.29/0.55         => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_increasing
% 0.29/0.55  thf(fact_2282_add__increasing,axiom,
% 0.29/0.55      ! [A: nat,B: nat,C: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.55       => ( ( ord_less_eq_nat @ B @ C )
% 0.29/0.55         => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_increasing
% 0.29/0.55  thf(fact_2283_add__increasing,axiom,
% 0.29/0.55      ! [A: int,B: int,C: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.55       => ( ( ord_less_eq_int @ B @ C )
% 0.29/0.55         => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_increasing
% 0.29/0.55  thf(fact_2284_add__decreasing2,axiom,
% 0.29/0.55      ! [C: real,A: real,B: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.29/0.55       => ( ( ord_less_eq_real @ A @ B )
% 0.29/0.55         => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_decreasing2
% 0.29/0.55  thf(fact_2285_add__decreasing2,axiom,
% 0.29/0.55      ! [C: rat,A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.29/0.55       => ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.55         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_decreasing2
% 0.29/0.55  thf(fact_2286_add__decreasing2,axiom,
% 0.29/0.55      ! [C: nat,A: nat,B: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 0.29/0.55       => ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.55         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_decreasing2
% 0.29/0.55  thf(fact_2287_add__decreasing2,axiom,
% 0.29/0.55      ! [C: int,A: int,B: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.29/0.55       => ( ( ord_less_eq_int @ A @ B )
% 0.29/0.55         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_decreasing2
% 0.29/0.55  thf(fact_2288_add__increasing2,axiom,
% 0.29/0.55      ! [C: real,B: real,A: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.29/0.55       => ( ( ord_less_eq_real @ B @ A )
% 0.29/0.55         => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_increasing2
% 0.29/0.55  thf(fact_2289_add__increasing2,axiom,
% 0.29/0.55      ! [C: rat,B: rat,A: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.29/0.55       => ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.55         => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_increasing2
% 0.29/0.55  thf(fact_2290_add__increasing2,axiom,
% 0.29/0.55      ! [C: nat,B: nat,A: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.29/0.55       => ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.55         => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_increasing2
% 0.29/0.55  thf(fact_2291_add__increasing2,axiom,
% 0.29/0.55      ! [C: int,B: int,A: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.55       => ( ( ord_less_eq_int @ B @ A )
% 0.29/0.55         => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_increasing2
% 0.29/0.55  thf(fact_2292_add__nonneg__nonneg,axiom,
% 0.29/0.55      ! [A: real,B: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.55       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.29/0.55         => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_nonneg_nonneg
% 0.29/0.55  thf(fact_2293_add__nonneg__nonneg,axiom,
% 0.29/0.55      ! [A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.29/0.55         => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_nonneg_nonneg
% 0.29/0.55  thf(fact_2294_add__nonneg__nonneg,axiom,
% 0.29/0.55      ! [A: nat,B: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.55       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.29/0.55         => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_nonneg_nonneg
% 0.29/0.55  thf(fact_2295_add__nonneg__nonneg,axiom,
% 0.29/0.55      ! [A: int,B: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.55       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.29/0.55         => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_nonneg_nonneg
% 0.29/0.55  thf(fact_2296_add__nonpos__nonpos,axiom,
% 0.29/0.55      ! [A: real,B: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.29/0.55       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.29/0.55         => ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_nonpos_nonpos
% 0.29/0.55  thf(fact_2297_add__nonpos__nonpos,axiom,
% 0.29/0.55      ! [A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.29/0.55       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.29/0.55         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_nonpos_nonpos
% 0.29/0.55  thf(fact_2298_add__nonpos__nonpos,axiom,
% 0.29/0.55      ! [A: nat,B: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.29/0.55       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.29/0.55         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_nonpos_nonpos
% 0.29/0.55  thf(fact_2299_add__nonpos__nonpos,axiom,
% 0.29/0.55      ! [A: int,B: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.29/0.55       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.29/0.55         => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_nonpos_nonpos
% 0.29/0.55  thf(fact_2300_add__nonneg__eq__0__iff,axiom,
% 0.29/0.55      ! [X: real,Y2: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.29/0.55       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 0.29/0.55         => ( ( ( plus_plus_real @ X @ Y2 )
% 0.29/0.55              = zero_zero_real )
% 0.29/0.55            = ( ( X = zero_zero_real )
% 0.29/0.55              & ( Y2 = zero_zero_real ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_nonneg_eq_0_iff
% 0.29/0.55  thf(fact_2301_add__nonneg__eq__0__iff,axiom,
% 0.29/0.55      ! [X: rat,Y2: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.29/0.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 0.29/0.55         => ( ( ( plus_plus_rat @ X @ Y2 )
% 0.29/0.55              = zero_zero_rat )
% 0.29/0.55            = ( ( X = zero_zero_rat )
% 0.29/0.55              & ( Y2 = zero_zero_rat ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_nonneg_eq_0_iff
% 0.29/0.55  thf(fact_2302_add__nonneg__eq__0__iff,axiom,
% 0.29/0.55      ! [X: nat,Y2: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 0.29/0.55       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y2 )
% 0.29/0.55         => ( ( ( plus_plus_nat @ X @ Y2 )
% 0.29/0.55              = zero_zero_nat )
% 0.29/0.55            = ( ( X = zero_zero_nat )
% 0.29/0.55              & ( Y2 = zero_zero_nat ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_nonneg_eq_0_iff
% 0.29/0.55  thf(fact_2303_add__nonneg__eq__0__iff,axiom,
% 0.29/0.55      ! [X: int,Y2: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.29/0.55       => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 0.29/0.55         => ( ( ( plus_plus_int @ X @ Y2 )
% 0.29/0.55              = zero_zero_int )
% 0.29/0.55            = ( ( X = zero_zero_int )
% 0.29/0.55              & ( Y2 = zero_zero_int ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_nonneg_eq_0_iff
% 0.29/0.55  thf(fact_2304_add__nonpos__eq__0__iff,axiom,
% 0.29/0.55      ! [X: real,Y2: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.29/0.55       => ( ( ord_less_eq_real @ Y2 @ zero_zero_real )
% 0.29/0.55         => ( ( ( plus_plus_real @ X @ Y2 )
% 0.29/0.55              = zero_zero_real )
% 0.29/0.55            = ( ( X = zero_zero_real )
% 0.29/0.55              & ( Y2 = zero_zero_real ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_nonpos_eq_0_iff
% 0.29/0.55  thf(fact_2305_add__nonpos__eq__0__iff,axiom,
% 0.29/0.55      ! [X: rat,Y2: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 0.29/0.55       => ( ( ord_less_eq_rat @ Y2 @ zero_zero_rat )
% 0.29/0.55         => ( ( ( plus_plus_rat @ X @ Y2 )
% 0.29/0.55              = zero_zero_rat )
% 0.29/0.55            = ( ( X = zero_zero_rat )
% 0.29/0.55              & ( Y2 = zero_zero_rat ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_nonpos_eq_0_iff
% 0.29/0.55  thf(fact_2306_add__nonpos__eq__0__iff,axiom,
% 0.29/0.55      ! [X: nat,Y2: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ X @ zero_zero_nat )
% 0.29/0.55       => ( ( ord_less_eq_nat @ Y2 @ zero_zero_nat )
% 0.29/0.55         => ( ( ( plus_plus_nat @ X @ Y2 )
% 0.29/0.55              = zero_zero_nat )
% 0.29/0.55            = ( ( X = zero_zero_nat )
% 0.29/0.55              & ( Y2 = zero_zero_nat ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_nonpos_eq_0_iff
% 0.29/0.55  thf(fact_2307_add__nonpos__eq__0__iff,axiom,
% 0.29/0.55      ! [X: int,Y2: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ X @ zero_zero_int )
% 0.29/0.55       => ( ( ord_less_eq_int @ Y2 @ zero_zero_int )
% 0.29/0.55         => ( ( ( plus_plus_int @ X @ Y2 )
% 0.29/0.55              = zero_zero_int )
% 0.29/0.55            = ( ( X = zero_zero_int )
% 0.29/0.55              & ( Y2 = zero_zero_int ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_nonpos_eq_0_iff
% 0.29/0.55  thf(fact_2308_mult__neg__neg,axiom,
% 0.29/0.55      ! [A: real,B: real] :
% 0.29/0.55        ( ( ord_less_real @ A @ zero_zero_real )
% 0.29/0.55       => ( ( ord_less_real @ B @ zero_zero_real )
% 0.29/0.55         => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_neg_neg
% 0.29/0.55  thf(fact_2309_mult__neg__neg,axiom,
% 0.29/0.55      ! [A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.55       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.29/0.55         => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_neg_neg
% 0.29/0.55  thf(fact_2310_mult__neg__neg,axiom,
% 0.29/0.55      ! [A: int,B: int] :
% 0.29/0.55        ( ( ord_less_int @ A @ zero_zero_int )
% 0.29/0.55       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.29/0.55         => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_neg_neg
% 0.29/0.55  thf(fact_2311_not__square__less__zero,axiom,
% 0.29/0.55      ! [A: real] :
% 0.29/0.55        ~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ) ).
% 0.29/0.55  
% 0.29/0.55  % not_square_less_zero
% 0.29/0.55  thf(fact_2312_not__square__less__zero,axiom,
% 0.29/0.55      ! [A: rat] :
% 0.29/0.55        ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 0.29/0.55  
% 0.29/0.55  % not_square_less_zero
% 0.29/0.55  thf(fact_2313_not__square__less__zero,axiom,
% 0.29/0.55      ! [A: int] :
% 0.29/0.55        ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 0.29/0.55  
% 0.29/0.55  % not_square_less_zero
% 0.29/0.55  thf(fact_2314_mult__less__0__iff,axiom,
% 0.29/0.55      ! [A: real,B: real] :
% 0.29/0.55        ( ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 0.29/0.55        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.55            & ( ord_less_real @ B @ zero_zero_real ) )
% 0.29/0.55          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.29/0.55            & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_0_iff
% 0.29/0.55  thf(fact_2315_mult__less__0__iff,axiom,
% 0.29/0.55      ! [A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 0.29/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.55            & ( ord_less_rat @ B @ zero_zero_rat ) )
% 0.29/0.55          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.55            & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_0_iff
% 0.29/0.55  thf(fact_2316_mult__less__0__iff,axiom,
% 0.29/0.55      ! [A: int,B: int] :
% 0.29/0.55        ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 0.29/0.55        = ( ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.55            & ( ord_less_int @ B @ zero_zero_int ) )
% 0.29/0.55          | ( ( ord_less_int @ A @ zero_zero_int )
% 0.29/0.55            & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_0_iff
% 0.29/0.55  thf(fact_2317_mult__neg__pos,axiom,
% 0.29/0.55      ! [A: real,B: real] :
% 0.29/0.55        ( ( ord_less_real @ A @ zero_zero_real )
% 0.29/0.55       => ( ( ord_less_real @ zero_zero_real @ B )
% 0.29/0.55         => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_neg_pos
% 0.29/0.55  thf(fact_2318_mult__neg__pos,axiom,
% 0.29/0.55      ! [A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.55       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.29/0.55         => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_neg_pos
% 0.29/0.55  thf(fact_2319_mult__neg__pos,axiom,
% 0.29/0.55      ! [A: nat,B: nat] :
% 0.29/0.55        ( ( ord_less_nat @ A @ zero_zero_nat )
% 0.29/0.55       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.29/0.55         => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_neg_pos
% 0.29/0.55  thf(fact_2320_mult__neg__pos,axiom,
% 0.29/0.55      ! [A: int,B: int] :
% 0.29/0.55        ( ( ord_less_int @ A @ zero_zero_int )
% 0.29/0.55       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.55         => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_neg_pos
% 0.29/0.55  thf(fact_2321_mult__pos__neg,axiom,
% 0.29/0.55      ! [A: real,B: real] :
% 0.29/0.55        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.55       => ( ( ord_less_real @ B @ zero_zero_real )
% 0.29/0.55         => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_pos_neg
% 0.29/0.55  thf(fact_2322_mult__pos__neg,axiom,
% 0.29/0.55      ! [A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.55       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.29/0.55         => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_pos_neg
% 0.29/0.55  thf(fact_2323_mult__pos__neg,axiom,
% 0.29/0.55      ! [A: nat,B: nat] :
% 0.29/0.55        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.29/0.55       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.29/0.55         => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_pos_neg
% 0.29/0.55  thf(fact_2324_mult__pos__neg,axiom,
% 0.29/0.55      ! [A: int,B: int] :
% 0.29/0.55        ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.55       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.29/0.55         => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_pos_neg
% 0.29/0.55  thf(fact_2325_mult__pos__pos,axiom,
% 0.29/0.55      ! [A: real,B: real] :
% 0.29/0.55        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.55       => ( ( ord_less_real @ zero_zero_real @ B )
% 0.29/0.55         => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_pos_pos
% 0.29/0.55  thf(fact_2326_mult__pos__pos,axiom,
% 0.29/0.55      ! [A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.55       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.29/0.55         => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_pos_pos
% 0.29/0.55  thf(fact_2327_mult__pos__pos,axiom,
% 0.29/0.55      ! [A: nat,B: nat] :
% 0.29/0.55        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.29/0.55       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.29/0.55         => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_pos_pos
% 0.29/0.55  thf(fact_2328_mult__pos__pos,axiom,
% 0.29/0.55      ! [A: int,B: int] :
% 0.29/0.55        ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.55       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.55         => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_pos_pos
% 0.29/0.55  thf(fact_2329_mult__pos__neg2,axiom,
% 0.29/0.55      ! [A: real,B: real] :
% 0.29/0.55        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.55       => ( ( ord_less_real @ B @ zero_zero_real )
% 0.29/0.55         => ( ord_less_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_pos_neg2
% 0.29/0.55  thf(fact_2330_mult__pos__neg2,axiom,
% 0.29/0.55      ! [A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.55       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.29/0.55         => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_pos_neg2
% 0.29/0.55  thf(fact_2331_mult__pos__neg2,axiom,
% 0.29/0.55      ! [A: nat,B: nat] :
% 0.29/0.55        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.29/0.55       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.29/0.55         => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_pos_neg2
% 0.29/0.55  thf(fact_2332_mult__pos__neg2,axiom,
% 0.29/0.55      ! [A: int,B: int] :
% 0.29/0.55        ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.55       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.29/0.55         => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_pos_neg2
% 0.29/0.55  thf(fact_2333_zero__less__mult__iff,axiom,
% 0.29/0.55      ! [A: real,B: real] :
% 0.29/0.55        ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.29/0.55        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.55            & ( ord_less_real @ zero_zero_real @ B ) )
% 0.29/0.55          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.29/0.55            & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_less_mult_iff
% 0.29/0.55  thf(fact_2334_zero__less__mult__iff,axiom,
% 0.29/0.55      ! [A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.29/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.55            & ( ord_less_rat @ zero_zero_rat @ B ) )
% 0.29/0.55          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.55            & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_less_mult_iff
% 0.29/0.55  thf(fact_2335_zero__less__mult__iff,axiom,
% 0.29/0.55      ! [A: int,B: int] :
% 0.29/0.55        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 0.29/0.55        = ( ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.55            & ( ord_less_int @ zero_zero_int @ B ) )
% 0.29/0.55          | ( ( ord_less_int @ A @ zero_zero_int )
% 0.29/0.55            & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_less_mult_iff
% 0.29/0.55  thf(fact_2336_zero__less__mult__pos,axiom,
% 0.29/0.55      ! [A: real,B: real] :
% 0.29/0.55        ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.29/0.55       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.55         => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_less_mult_pos
% 0.29/0.55  thf(fact_2337_zero__less__mult__pos,axiom,
% 0.29/0.55      ! [A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.29/0.55       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.55         => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_less_mult_pos
% 0.29/0.55  thf(fact_2338_zero__less__mult__pos,axiom,
% 0.29/0.55      ! [A: nat,B: nat] :
% 0.29/0.55        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 0.29/0.55       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.29/0.55         => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_less_mult_pos
% 0.29/0.55  thf(fact_2339_zero__less__mult__pos,axiom,
% 0.29/0.55      ! [A: int,B: int] :
% 0.29/0.55        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 0.29/0.55       => ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.55         => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_less_mult_pos
% 0.29/0.55  thf(fact_2340_zero__less__mult__pos2,axiom,
% 0.29/0.55      ! [B: real,A: real] :
% 0.29/0.55        ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) )
% 0.29/0.55       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.55         => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_less_mult_pos2
% 0.29/0.55  thf(fact_2341_zero__less__mult__pos2,axiom,
% 0.29/0.55      ! [B: rat,A: rat] :
% 0.29/0.55        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 0.29/0.55       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.55         => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_less_mult_pos2
% 0.29/0.55  thf(fact_2342_zero__less__mult__pos2,axiom,
% 0.29/0.55      ! [B: nat,A: nat] :
% 0.29/0.55        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 0.29/0.55       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.29/0.55         => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_less_mult_pos2
% 0.29/0.55  thf(fact_2343_zero__less__mult__pos2,axiom,
% 0.29/0.55      ! [B: int,A: int] :
% 0.29/0.55        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 0.29/0.55       => ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.55         => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_less_mult_pos2
% 0.29/0.55  thf(fact_2344_mult__less__cancel__left__neg,axiom,
% 0.29/0.55      ! [C: real,A: real,B: real] :
% 0.29/0.55        ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.55       => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.29/0.55          = ( ord_less_real @ B @ A ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_cancel_left_neg
% 0.29/0.55  thf(fact_2345_mult__less__cancel__left__neg,axiom,
% 0.29/0.55      ! [C: rat,A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.55       => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.29/0.55          = ( ord_less_rat @ B @ A ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_cancel_left_neg
% 0.29/0.55  thf(fact_2346_mult__less__cancel__left__neg,axiom,
% 0.29/0.55      ! [C: int,A: int,B: int] :
% 0.29/0.55        ( ( ord_less_int @ C @ zero_zero_int )
% 0.29/0.55       => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.29/0.55          = ( ord_less_int @ B @ A ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_cancel_left_neg
% 0.29/0.55  thf(fact_2347_mult__less__cancel__left__pos,axiom,
% 0.29/0.55      ! [C: real,A: real,B: real] :
% 0.29/0.55        ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.55       => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.29/0.55          = ( ord_less_real @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_cancel_left_pos
% 0.29/0.55  thf(fact_2348_mult__less__cancel__left__pos,axiom,
% 0.29/0.55      ! [C: rat,A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.55       => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.29/0.55          = ( ord_less_rat @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_cancel_left_pos
% 0.29/0.55  thf(fact_2349_mult__less__cancel__left__pos,axiom,
% 0.29/0.55      ! [C: int,A: int,B: int] :
% 0.29/0.55        ( ( ord_less_int @ zero_zero_int @ C )
% 0.29/0.55       => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.29/0.55          = ( ord_less_int @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_cancel_left_pos
% 0.29/0.55  thf(fact_2350_mult__strict__left__mono__neg,axiom,
% 0.29/0.55      ! [B: real,A: real,C: real] :
% 0.29/0.55        ( ( ord_less_real @ B @ A )
% 0.29/0.55       => ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.55         => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_strict_left_mono_neg
% 0.29/0.55  thf(fact_2351_mult__strict__left__mono__neg,axiom,
% 0.29/0.55      ! [B: rat,A: rat,C: rat] :
% 0.29/0.55        ( ( ord_less_rat @ B @ A )
% 0.29/0.55       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.55         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_strict_left_mono_neg
% 0.29/0.55  thf(fact_2352_mult__strict__left__mono__neg,axiom,
% 0.29/0.55      ! [B: int,A: int,C: int] :
% 0.29/0.55        ( ( ord_less_int @ B @ A )
% 0.29/0.55       => ( ( ord_less_int @ C @ zero_zero_int )
% 0.29/0.55         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_strict_left_mono_neg
% 0.29/0.55  thf(fact_2353_mult__strict__left__mono,axiom,
% 0.29/0.55      ! [A: real,B: real,C: real] :
% 0.29/0.55        ( ( ord_less_real @ A @ B )
% 0.29/0.55       => ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.55         => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_strict_left_mono
% 0.29/0.55  thf(fact_2354_mult__strict__left__mono,axiom,
% 0.29/0.55      ! [A: rat,B: rat,C: rat] :
% 0.29/0.55        ( ( ord_less_rat @ A @ B )
% 0.29/0.55       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.55         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_strict_left_mono
% 0.29/0.55  thf(fact_2355_mult__strict__left__mono,axiom,
% 0.29/0.55      ! [A: nat,B: nat,C: nat] :
% 0.29/0.55        ( ( ord_less_nat @ A @ B )
% 0.29/0.55       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.29/0.55         => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_strict_left_mono
% 0.29/0.55  thf(fact_2356_mult__strict__left__mono,axiom,
% 0.29/0.55      ! [A: int,B: int,C: int] :
% 0.29/0.55        ( ( ord_less_int @ A @ B )
% 0.29/0.55       => ( ( ord_less_int @ zero_zero_int @ C )
% 0.29/0.55         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_strict_left_mono
% 0.29/0.55  thf(fact_2357_mult__less__cancel__left__disj,axiom,
% 0.29/0.55      ! [C: real,A: real,B: real] :
% 0.29/0.55        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.29/0.55        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.55            & ( ord_less_real @ A @ B ) )
% 0.29/0.55          | ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.55            & ( ord_less_real @ B @ A ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_cancel_left_disj
% 0.29/0.55  thf(fact_2358_mult__less__cancel__left__disj,axiom,
% 0.29/0.55      ! [C: rat,A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.29/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.55            & ( ord_less_rat @ A @ B ) )
% 0.29/0.55          | ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.55            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_cancel_left_disj
% 0.29/0.55  thf(fact_2359_mult__less__cancel__left__disj,axiom,
% 0.29/0.55      ! [C: int,A: int,B: int] :
% 0.29/0.55        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.29/0.55        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.29/0.55            & ( ord_less_int @ A @ B ) )
% 0.29/0.55          | ( ( ord_less_int @ C @ zero_zero_int )
% 0.29/0.55            & ( ord_less_int @ B @ A ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_cancel_left_disj
% 0.29/0.55  thf(fact_2360_mult__strict__right__mono__neg,axiom,
% 0.29/0.55      ! [B: real,A: real,C: real] :
% 0.29/0.55        ( ( ord_less_real @ B @ A )
% 0.29/0.55       => ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.55         => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_strict_right_mono_neg
% 0.29/0.55  thf(fact_2361_mult__strict__right__mono__neg,axiom,
% 0.29/0.55      ! [B: rat,A: rat,C: rat] :
% 0.29/0.55        ( ( ord_less_rat @ B @ A )
% 0.29/0.55       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.55         => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_strict_right_mono_neg
% 0.29/0.55  thf(fact_2362_mult__strict__right__mono__neg,axiom,
% 0.29/0.55      ! [B: int,A: int,C: int] :
% 0.29/0.55        ( ( ord_less_int @ B @ A )
% 0.29/0.55       => ( ( ord_less_int @ C @ zero_zero_int )
% 0.29/0.55         => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_strict_right_mono_neg
% 0.29/0.55  thf(fact_2363_mult__strict__right__mono,axiom,
% 0.29/0.55      ! [A: real,B: real,C: real] :
% 0.29/0.55        ( ( ord_less_real @ A @ B )
% 0.29/0.55       => ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.55         => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_strict_right_mono
% 0.29/0.55  thf(fact_2364_mult__strict__right__mono,axiom,
% 0.29/0.55      ! [A: rat,B: rat,C: rat] :
% 0.29/0.55        ( ( ord_less_rat @ A @ B )
% 0.29/0.55       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.55         => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_strict_right_mono
% 0.29/0.55  thf(fact_2365_mult__strict__right__mono,axiom,
% 0.29/0.55      ! [A: nat,B: nat,C: nat] :
% 0.29/0.55        ( ( ord_less_nat @ A @ B )
% 0.29/0.55       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.29/0.55         => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_strict_right_mono
% 0.29/0.55  thf(fact_2366_mult__strict__right__mono,axiom,
% 0.29/0.55      ! [A: int,B: int,C: int] :
% 0.29/0.55        ( ( ord_less_int @ A @ B )
% 0.29/0.55       => ( ( ord_less_int @ zero_zero_int @ C )
% 0.29/0.55         => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_strict_right_mono
% 0.29/0.55  thf(fact_2367_mult__less__cancel__right__disj,axiom,
% 0.29/0.55      ! [A: real,C: real,B: real] :
% 0.29/0.55        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 0.29/0.55        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.55            & ( ord_less_real @ A @ B ) )
% 0.29/0.55          | ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.55            & ( ord_less_real @ B @ A ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_cancel_right_disj
% 0.29/0.55  thf(fact_2368_mult__less__cancel__right__disj,axiom,
% 0.29/0.55      ! [A: rat,C: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.29/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.55            & ( ord_less_rat @ A @ B ) )
% 0.29/0.55          | ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.55            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_cancel_right_disj
% 0.29/0.55  thf(fact_2369_mult__less__cancel__right__disj,axiom,
% 0.29/0.55      ! [A: int,C: int,B: int] :
% 0.29/0.55        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.29/0.55        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.29/0.55            & ( ord_less_int @ A @ B ) )
% 0.29/0.55          | ( ( ord_less_int @ C @ zero_zero_int )
% 0.29/0.55            & ( ord_less_int @ B @ A ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_cancel_right_disj
% 0.29/0.55  thf(fact_2370_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.29/0.55      ! [A: real,B: real,C: real] :
% 0.29/0.55        ( ( ord_less_real @ A @ B )
% 0.29/0.55       => ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.55         => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.29/0.55  thf(fact_2371_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.29/0.55      ! [A: rat,B: rat,C: rat] :
% 0.29/0.55        ( ( ord_less_rat @ A @ B )
% 0.29/0.55       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.55         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.29/0.55  thf(fact_2372_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.29/0.55      ! [A: nat,B: nat,C: nat] :
% 0.29/0.55        ( ( ord_less_nat @ A @ B )
% 0.29/0.55       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.29/0.55         => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.29/0.55  thf(fact_2373_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.29/0.55      ! [A: int,B: int,C: int] :
% 0.29/0.55        ( ( ord_less_int @ A @ B )
% 0.29/0.55       => ( ( ord_less_int @ zero_zero_int @ C )
% 0.29/0.55         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.29/0.55  thf(fact_2374_less__numeral__extra_I1_J,axiom,
% 0.29/0.55      ord_less_real @ zero_zero_real @ one_one_real ).
% 0.29/0.55  
% 0.29/0.55  % less_numeral_extra(1)
% 0.29/0.55  thf(fact_2375_less__numeral__extra_I1_J,axiom,
% 0.29/0.55      ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 0.29/0.55  
% 0.29/0.55  % less_numeral_extra(1)
% 0.29/0.55  thf(fact_2376_less__numeral__extra_I1_J,axiom,
% 0.29/0.55      ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 0.29/0.55  
% 0.29/0.55  % less_numeral_extra(1)
% 0.29/0.55  thf(fact_2377_less__numeral__extra_I1_J,axiom,
% 0.29/0.55      ord_less_int @ zero_zero_int @ one_one_int ).
% 0.29/0.55  
% 0.29/0.55  % less_numeral_extra(1)
% 0.29/0.55  thf(fact_2378_not__one__less__zero,axiom,
% 0.29/0.55      ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 0.29/0.55  
% 0.29/0.55  % not_one_less_zero
% 0.29/0.55  thf(fact_2379_not__one__less__zero,axiom,
% 0.29/0.55      ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 0.29/0.55  
% 0.29/0.55  % not_one_less_zero
% 0.29/0.55  thf(fact_2380_not__one__less__zero,axiom,
% 0.29/0.55      ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 0.29/0.55  
% 0.29/0.55  % not_one_less_zero
% 0.29/0.55  thf(fact_2381_not__one__less__zero,axiom,
% 0.29/0.55      ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 0.29/0.55  
% 0.29/0.55  % not_one_less_zero
% 0.29/0.55  thf(fact_2382_zero__less__one,axiom,
% 0.29/0.55      ord_less_real @ zero_zero_real @ one_one_real ).
% 0.29/0.55  
% 0.29/0.55  % zero_less_one
% 0.29/0.55  thf(fact_2383_zero__less__one,axiom,
% 0.29/0.55      ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 0.29/0.55  
% 0.29/0.55  % zero_less_one
% 0.29/0.55  thf(fact_2384_zero__less__one,axiom,
% 0.29/0.55      ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 0.29/0.55  
% 0.29/0.55  % zero_less_one
% 0.29/0.55  thf(fact_2385_zero__less__one,axiom,
% 0.29/0.55      ord_less_int @ zero_zero_int @ one_one_int ).
% 0.29/0.55  
% 0.29/0.55  % zero_less_one
% 0.29/0.55  thf(fact_2386_add__less__zeroD,axiom,
% 0.29/0.55      ! [X: real,Y2: real] :
% 0.29/0.55        ( ( ord_less_real @ ( plus_plus_real @ X @ Y2 ) @ zero_zero_real )
% 0.29/0.55       => ( ( ord_less_real @ X @ zero_zero_real )
% 0.29/0.55          | ( ord_less_real @ Y2 @ zero_zero_real ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_less_zeroD
% 0.29/0.55  thf(fact_2387_add__less__zeroD,axiom,
% 0.29/0.55      ! [X: rat,Y2: rat] :
% 0.29/0.55        ( ( ord_less_rat @ ( plus_plus_rat @ X @ Y2 ) @ zero_zero_rat )
% 0.29/0.55       => ( ( ord_less_rat @ X @ zero_zero_rat )
% 0.29/0.55          | ( ord_less_rat @ Y2 @ zero_zero_rat ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_less_zeroD
% 0.29/0.55  thf(fact_2388_add__less__zeroD,axiom,
% 0.29/0.55      ! [X: int,Y2: int] :
% 0.29/0.55        ( ( ord_less_int @ ( plus_plus_int @ X @ Y2 ) @ zero_zero_int )
% 0.29/0.55       => ( ( ord_less_int @ X @ zero_zero_int )
% 0.29/0.55          | ( ord_less_int @ Y2 @ zero_zero_int ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_less_zeroD
% 0.29/0.55  thf(fact_2389_pos__add__strict,axiom,
% 0.29/0.55      ! [A: real,B: real,C: real] :
% 0.29/0.55        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.55       => ( ( ord_less_real @ B @ C )
% 0.29/0.55         => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % pos_add_strict
% 0.29/0.55  thf(fact_2390_pos__add__strict,axiom,
% 0.29/0.55      ! [A: rat,B: rat,C: rat] :
% 0.29/0.55        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.55       => ( ( ord_less_rat @ B @ C )
% 0.29/0.55         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % pos_add_strict
% 0.29/0.55  thf(fact_2391_pos__add__strict,axiom,
% 0.29/0.55      ! [A: nat,B: nat,C: nat] :
% 0.29/0.55        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.29/0.55       => ( ( ord_less_nat @ B @ C )
% 0.29/0.55         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % pos_add_strict
% 0.29/0.55  thf(fact_2392_pos__add__strict,axiom,
% 0.29/0.55      ! [A: int,B: int,C: int] :
% 0.29/0.55        ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.55       => ( ( ord_less_int @ B @ C )
% 0.29/0.55         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % pos_add_strict
% 0.29/0.55  thf(fact_2393_canonically__ordered__monoid__add__class_OlessE,axiom,
% 0.29/0.55      ! [A: nat,B: nat] :
% 0.29/0.55        ( ( ord_less_nat @ A @ B )
% 0.29/0.55       => ~ ! [C2: nat] :
% 0.29/0.55              ( ( B
% 0.29/0.55                = ( plus_plus_nat @ A @ C2 ) )
% 0.29/0.55             => ( C2 = zero_zero_nat ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % canonically_ordered_monoid_add_class.lessE
% 0.29/0.55  thf(fact_2394_add__pos__pos,axiom,
% 0.29/0.55      ! [A: real,B: real] :
% 0.29/0.55        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.55       => ( ( ord_less_real @ zero_zero_real @ B )
% 0.29/0.55         => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_pos_pos
% 0.29/0.55  thf(fact_2395_add__pos__pos,axiom,
% 0.29/0.55      ! [A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.55       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.29/0.55         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_pos_pos
% 0.29/0.55  thf(fact_2396_add__pos__pos,axiom,
% 0.29/0.55      ! [A: nat,B: nat] :
% 0.29/0.55        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.29/0.55       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.29/0.55         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_pos_pos
% 0.29/0.55  thf(fact_2397_add__pos__pos,axiom,
% 0.29/0.55      ! [A: int,B: int] :
% 0.29/0.55        ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.55       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.55         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_pos_pos
% 0.29/0.55  thf(fact_2398_add__neg__neg,axiom,
% 0.29/0.55      ! [A: real,B: real] :
% 0.29/0.55        ( ( ord_less_real @ A @ zero_zero_real )
% 0.29/0.55       => ( ( ord_less_real @ B @ zero_zero_real )
% 0.29/0.55         => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_neg_neg
% 0.29/0.55  thf(fact_2399_add__neg__neg,axiom,
% 0.29/0.55      ! [A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.55       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.29/0.55         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_neg_neg
% 0.29/0.55  thf(fact_2400_add__neg__neg,axiom,
% 0.29/0.55      ! [A: nat,B: nat] :
% 0.29/0.55        ( ( ord_less_nat @ A @ zero_zero_nat )
% 0.29/0.55       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.29/0.55         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_neg_neg
% 0.29/0.55  thf(fact_2401_add__neg__neg,axiom,
% 0.29/0.55      ! [A: int,B: int] :
% 0.29/0.55        ( ( ord_less_int @ A @ zero_zero_int )
% 0.29/0.55       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.29/0.55         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_neg_neg
% 0.29/0.55  thf(fact_2402_le__iff__diff__le__0,axiom,
% 0.29/0.55      ( ord_less_eq_real
% 0.29/0.55      = ( ^ [A3: real,B4: real] : ( ord_less_eq_real @ ( minus_minus_real @ A3 @ B4 ) @ zero_zero_real ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_iff_diff_le_0
% 0.29/0.55  thf(fact_2403_le__iff__diff__le__0,axiom,
% 0.29/0.55      ( ord_less_eq_rat
% 0.29/0.55      = ( ^ [A3: rat,B4: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A3 @ B4 ) @ zero_zero_rat ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_iff_diff_le_0
% 0.29/0.55  thf(fact_2404_le__iff__diff__le__0,axiom,
% 0.29/0.55      ( ord_less_eq_int
% 0.29/0.55      = ( ^ [A3: int,B4: int] : ( ord_less_eq_int @ ( minus_minus_int @ A3 @ B4 ) @ zero_zero_int ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_iff_diff_le_0
% 0.29/0.55  thf(fact_2405_divide__le__0__iff,axiom,
% 0.29/0.55      ! [A: real,B: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 0.29/0.55        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.55            & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 0.29/0.55          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.29/0.55            & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_le_0_iff
% 0.29/0.55  thf(fact_2406_divide__le__0__iff,axiom,
% 0.29/0.55      ! [A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 0.29/0.55        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.55            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 0.29/0.55          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.29/0.55            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_le_0_iff
% 0.29/0.55  thf(fact_2407_divide__right__mono,axiom,
% 0.29/0.55      ! [A: real,B: real,C: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.55       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.29/0.55         => ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_right_mono
% 0.29/0.55  thf(fact_2408_divide__right__mono,axiom,
% 0.29/0.55      ! [A: rat,B: rat,C: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.29/0.55         => ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_right_mono
% 0.29/0.55  thf(fact_2409_zero__le__divide__iff,axiom,
% 0.29/0.55      ! [A: real,B: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 0.29/0.55        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.55            & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 0.29/0.55          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.29/0.55            & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_le_divide_iff
% 0.29/0.55  thf(fact_2410_zero__le__divide__iff,axiom,
% 0.29/0.55      ! [A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 0.29/0.55        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.55            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 0.29/0.55          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.29/0.55            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_le_divide_iff
% 0.29/0.55  thf(fact_2411_divide__nonneg__nonneg,axiom,
% 0.29/0.55      ! [X: real,Y2: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.29/0.55       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 0.29/0.55         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_nonneg_nonneg
% 0.29/0.55  thf(fact_2412_divide__nonneg__nonneg,axiom,
% 0.29/0.55      ! [X: rat,Y2: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.29/0.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 0.29/0.55         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_nonneg_nonneg
% 0.29/0.55  thf(fact_2413_divide__nonneg__nonpos,axiom,
% 0.29/0.55      ! [X: real,Y2: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.29/0.55       => ( ( ord_less_eq_real @ Y2 @ zero_zero_real )
% 0.29/0.55         => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y2 ) @ zero_zero_real ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_nonneg_nonpos
% 0.29/0.55  thf(fact_2414_divide__nonneg__nonpos,axiom,
% 0.29/0.55      ! [X: rat,Y2: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.29/0.55       => ( ( ord_less_eq_rat @ Y2 @ zero_zero_rat )
% 0.29/0.55         => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y2 ) @ zero_zero_rat ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_nonneg_nonpos
% 0.29/0.55  thf(fact_2415_divide__nonpos__nonneg,axiom,
% 0.29/0.55      ! [X: real,Y2: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.29/0.55       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 0.29/0.55         => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y2 ) @ zero_zero_real ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_nonpos_nonneg
% 0.29/0.55  thf(fact_2416_divide__nonpos__nonneg,axiom,
% 0.29/0.55      ! [X: rat,Y2: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 0.29/0.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 0.29/0.55         => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y2 ) @ zero_zero_rat ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_nonpos_nonneg
% 0.29/0.55  thf(fact_2417_divide__nonpos__nonpos,axiom,
% 0.29/0.55      ! [X: real,Y2: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.29/0.55       => ( ( ord_less_eq_real @ Y2 @ zero_zero_real )
% 0.29/0.55         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_nonpos_nonpos
% 0.29/0.55  thf(fact_2418_divide__nonpos__nonpos,axiom,
% 0.29/0.55      ! [X: rat,Y2: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 0.29/0.55       => ( ( ord_less_eq_rat @ Y2 @ zero_zero_rat )
% 0.29/0.55         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_nonpos_nonpos
% 0.29/0.55  thf(fact_2419_divide__right__mono__neg,axiom,
% 0.29/0.55      ! [A: real,B: real,C: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.55       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.29/0.55         => ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_right_mono_neg
% 0.29/0.55  thf(fact_2420_divide__right__mono__neg,axiom,
% 0.29/0.55      ! [A: rat,B: rat,C: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.55       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.29/0.55         => ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( divide_divide_rat @ A @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_right_mono_neg
% 0.29/0.55  thf(fact_2421_less__iff__diff__less__0,axiom,
% 0.29/0.55      ( ord_less_real
% 0.29/0.55      = ( ^ [A3: real,B4: real] : ( ord_less_real @ ( minus_minus_real @ A3 @ B4 ) @ zero_zero_real ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % less_iff_diff_less_0
% 0.29/0.55  thf(fact_2422_less__iff__diff__less__0,axiom,
% 0.29/0.55      ( ord_less_rat
% 0.29/0.55      = ( ^ [A3: rat,B4: rat] : ( ord_less_rat @ ( minus_minus_rat @ A3 @ B4 ) @ zero_zero_rat ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % less_iff_diff_less_0
% 0.29/0.55  thf(fact_2423_less__iff__diff__less__0,axiom,
% 0.29/0.55      ( ord_less_int
% 0.29/0.55      = ( ^ [A3: int,B4: int] : ( ord_less_int @ ( minus_minus_int @ A3 @ B4 ) @ zero_zero_int ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % less_iff_diff_less_0
% 0.29/0.55  thf(fact_2424_divide__neg__neg,axiom,
% 0.29/0.55      ! [X: real,Y2: real] :
% 0.29/0.55        ( ( ord_less_real @ X @ zero_zero_real )
% 0.29/0.55       => ( ( ord_less_real @ Y2 @ zero_zero_real )
% 0.29/0.55         => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_neg_neg
% 0.29/0.55  thf(fact_2425_divide__neg__neg,axiom,
% 0.29/0.55      ! [X: rat,Y2: rat] :
% 0.29/0.55        ( ( ord_less_rat @ X @ zero_zero_rat )
% 0.29/0.55       => ( ( ord_less_rat @ Y2 @ zero_zero_rat )
% 0.29/0.55         => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_neg_neg
% 0.29/0.55  thf(fact_2426_divide__neg__pos,axiom,
% 0.29/0.55      ! [X: real,Y2: real] :
% 0.29/0.55        ( ( ord_less_real @ X @ zero_zero_real )
% 0.29/0.55       => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 0.29/0.55         => ( ord_less_real @ ( divide_divide_real @ X @ Y2 ) @ zero_zero_real ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_neg_pos
% 0.29/0.55  thf(fact_2427_divide__neg__pos,axiom,
% 0.29/0.55      ! [X: rat,Y2: rat] :
% 0.29/0.55        ( ( ord_less_rat @ X @ zero_zero_rat )
% 0.29/0.55       => ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 0.29/0.55         => ( ord_less_rat @ ( divide_divide_rat @ X @ Y2 ) @ zero_zero_rat ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_neg_pos
% 0.29/0.55  thf(fact_2428_divide__pos__neg,axiom,
% 0.29/0.55      ! [X: real,Y2: real] :
% 0.29/0.55        ( ( ord_less_real @ zero_zero_real @ X )
% 0.29/0.55       => ( ( ord_less_real @ Y2 @ zero_zero_real )
% 0.29/0.55         => ( ord_less_real @ ( divide_divide_real @ X @ Y2 ) @ zero_zero_real ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_pos_neg
% 0.29/0.55  thf(fact_2429_divide__pos__neg,axiom,
% 0.29/0.55      ! [X: rat,Y2: rat] :
% 0.29/0.55        ( ( ord_less_rat @ zero_zero_rat @ X )
% 0.29/0.55       => ( ( ord_less_rat @ Y2 @ zero_zero_rat )
% 0.29/0.55         => ( ord_less_rat @ ( divide_divide_rat @ X @ Y2 ) @ zero_zero_rat ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_pos_neg
% 0.29/0.55  thf(fact_2430_divide__pos__pos,axiom,
% 0.29/0.55      ! [X: real,Y2: real] :
% 0.29/0.55        ( ( ord_less_real @ zero_zero_real @ X )
% 0.29/0.55       => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 0.29/0.55         => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_pos_pos
% 0.29/0.55  thf(fact_2431_divide__pos__pos,axiom,
% 0.29/0.55      ! [X: rat,Y2: rat] :
% 0.29/0.55        ( ( ord_less_rat @ zero_zero_rat @ X )
% 0.29/0.55       => ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 0.29/0.55         => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_pos_pos
% 0.29/0.55  thf(fact_2432_divide__less__0__iff,axiom,
% 0.29/0.55      ! [A: real,B: real] :
% 0.29/0.55        ( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 0.29/0.55        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.55            & ( ord_less_real @ B @ zero_zero_real ) )
% 0.29/0.55          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.29/0.55            & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_less_0_iff
% 0.29/0.55  thf(fact_2433_divide__less__0__iff,axiom,
% 0.29/0.55      ! [A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 0.29/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.55            & ( ord_less_rat @ B @ zero_zero_rat ) )
% 0.29/0.55          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.55            & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_less_0_iff
% 0.29/0.55  thf(fact_2434_divide__less__cancel,axiom,
% 0.29/0.55      ! [A: real,C: real,B: real] :
% 0.29/0.55        ( ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 0.29/0.55        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.55           => ( ord_less_real @ A @ B ) )
% 0.29/0.55          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.55           => ( ord_less_real @ B @ A ) )
% 0.29/0.55          & ( C != zero_zero_real ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_less_cancel
% 0.29/0.55  thf(fact_2435_divide__less__cancel,axiom,
% 0.29/0.55      ! [A: rat,C: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 0.29/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.55           => ( ord_less_rat @ A @ B ) )
% 0.29/0.55          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.55           => ( ord_less_rat @ B @ A ) )
% 0.29/0.55          & ( C != zero_zero_rat ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_less_cancel
% 0.29/0.55  thf(fact_2436_zero__less__divide__iff,axiom,
% 0.29/0.55      ! [A: real,B: real] :
% 0.29/0.55        ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 0.29/0.55        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.55            & ( ord_less_real @ zero_zero_real @ B ) )
% 0.29/0.55          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.29/0.55            & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_less_divide_iff
% 0.29/0.55  thf(fact_2437_zero__less__divide__iff,axiom,
% 0.29/0.55      ! [A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 0.29/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.55            & ( ord_less_rat @ zero_zero_rat @ B ) )
% 0.29/0.55          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.55            & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_less_divide_iff
% 0.29/0.55  thf(fact_2438_divide__strict__right__mono,axiom,
% 0.29/0.55      ! [A: real,B: real,C: real] :
% 0.29/0.55        ( ( ord_less_real @ A @ B )
% 0.29/0.55       => ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.55         => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_strict_right_mono
% 0.29/0.55  thf(fact_2439_divide__strict__right__mono,axiom,
% 0.29/0.55      ! [A: rat,B: rat,C: rat] :
% 0.29/0.55        ( ( ord_less_rat @ A @ B )
% 0.29/0.55       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.55         => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_strict_right_mono
% 0.29/0.55  thf(fact_2440_divide__strict__right__mono__neg,axiom,
% 0.29/0.55      ! [B: real,A: real,C: real] :
% 0.29/0.55        ( ( ord_less_real @ B @ A )
% 0.29/0.55       => ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.55         => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_strict_right_mono_neg
% 0.29/0.55  thf(fact_2441_divide__strict__right__mono__neg,axiom,
% 0.29/0.55      ! [B: rat,A: rat,C: rat] :
% 0.29/0.55        ( ( ord_less_rat @ B @ A )
% 0.29/0.55       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.55         => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_strict_right_mono_neg
% 0.29/0.55  thf(fact_2442_power__mono,axiom,
% 0.29/0.55      ! [A: rat,B: rat,N: nat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.55         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power_mono
% 0.29/0.55  thf(fact_2443_power__mono,axiom,
% 0.29/0.55      ! [A: real,B: real,N: nat] :
% 0.29/0.55        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.55       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.55         => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power_mono
% 0.29/0.55  thf(fact_2444_power__mono,axiom,
% 0.29/0.55      ! [A: nat,B: nat,N: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.55       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.55         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power_mono
% 0.29/0.55  thf(fact_2445_power__mono,axiom,
% 0.29/0.55      ! [A: int,B: int,N: nat] :
% 0.29/0.55        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.55       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.55         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power_mono
% 0.29/0.55  thf(fact_2446_zero__le__power,axiom,
% 0.29/0.55      ! [A: rat,N: nat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.55       => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_le_power
% 0.29/0.55  thf(fact_2447_zero__le__power,axiom,
% 0.29/0.55      ! [A: real,N: nat] :
% 0.29/0.55        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.55       => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_le_power
% 0.29/0.55  thf(fact_2448_zero__le__power,axiom,
% 0.29/0.55      ! [A: nat,N: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.55       => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_le_power
% 0.29/0.55  thf(fact_2449_zero__le__power,axiom,
% 0.29/0.55      ! [A: int,N: nat] :
% 0.29/0.55        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.55       => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_le_power
% 0.29/0.55  thf(fact_2450_zero__less__power,axiom,
% 0.29/0.55      ! [A: real,N: nat] :
% 0.29/0.55        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.55       => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_less_power
% 0.29/0.55  thf(fact_2451_zero__less__power,axiom,
% 0.29/0.55      ! [A: rat,N: nat] :
% 0.29/0.55        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.55       => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_less_power
% 0.29/0.55  thf(fact_2452_zero__less__power,axiom,
% 0.29/0.55      ! [A: nat,N: nat] :
% 0.29/0.55        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.29/0.55       => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_less_power
% 0.29/0.55  thf(fact_2453_zero__less__power,axiom,
% 0.29/0.55      ! [A: int,N: nat] :
% 0.29/0.55        ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.55       => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_less_power
% 0.29/0.55  thf(fact_2454_frac__eq__eq,axiom,
% 0.29/0.55      ! [Y2: complex,Z: complex,X: complex,W: complex] :
% 0.29/0.55        ( ( Y2 != zero_zero_complex )
% 0.29/0.55       => ( ( Z != zero_zero_complex )
% 0.29/0.55         => ( ( ( divide1717551699836669952omplex @ X @ Y2 )
% 0.29/0.55              = ( divide1717551699836669952omplex @ W @ Z ) )
% 0.29/0.55            = ( ( times_times_complex @ X @ Z )
% 0.29/0.55              = ( times_times_complex @ W @ Y2 ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % frac_eq_eq
% 0.29/0.55  thf(fact_2455_frac__eq__eq,axiom,
% 0.29/0.55      ! [Y2: real,Z: real,X: real,W: real] :
% 0.29/0.55        ( ( Y2 != zero_zero_real )
% 0.29/0.55       => ( ( Z != zero_zero_real )
% 0.29/0.55         => ( ( ( divide_divide_real @ X @ Y2 )
% 0.29/0.55              = ( divide_divide_real @ W @ Z ) )
% 0.29/0.55            = ( ( times_times_real @ X @ Z )
% 0.29/0.55              = ( times_times_real @ W @ Y2 ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % frac_eq_eq
% 0.29/0.55  thf(fact_2456_frac__eq__eq,axiom,
% 0.29/0.55      ! [Y2: rat,Z: rat,X: rat,W: rat] :
% 0.29/0.55        ( ( Y2 != zero_zero_rat )
% 0.29/0.55       => ( ( Z != zero_zero_rat )
% 0.29/0.55         => ( ( ( divide_divide_rat @ X @ Y2 )
% 0.29/0.55              = ( divide_divide_rat @ W @ Z ) )
% 0.29/0.55            = ( ( times_times_rat @ X @ Z )
% 0.29/0.55              = ( times_times_rat @ W @ Y2 ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % frac_eq_eq
% 0.29/0.55  thf(fact_2457_divide__eq__eq,axiom,
% 0.29/0.55      ! [B: complex,C: complex,A: complex] :
% 0.29/0.55        ( ( ( divide1717551699836669952omplex @ B @ C )
% 0.29/0.55          = A )
% 0.29/0.55        = ( ( ( C != zero_zero_complex )
% 0.29/0.55           => ( B
% 0.29/0.55              = ( times_times_complex @ A @ C ) ) )
% 0.29/0.55          & ( ( C = zero_zero_complex )
% 0.29/0.55           => ( A = zero_zero_complex ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_eq_eq
% 0.29/0.55  thf(fact_2458_divide__eq__eq,axiom,
% 0.29/0.55      ! [B: real,C: real,A: real] :
% 0.29/0.55        ( ( ( divide_divide_real @ B @ C )
% 0.29/0.55          = A )
% 0.29/0.55        = ( ( ( C != zero_zero_real )
% 0.29/0.55           => ( B
% 0.29/0.55              = ( times_times_real @ A @ C ) ) )
% 0.29/0.55          & ( ( C = zero_zero_real )
% 0.29/0.55           => ( A = zero_zero_real ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_eq_eq
% 0.29/0.55  thf(fact_2459_divide__eq__eq,axiom,
% 0.29/0.55      ! [B: rat,C: rat,A: rat] :
% 0.29/0.55        ( ( ( divide_divide_rat @ B @ C )
% 0.29/0.55          = A )
% 0.29/0.55        = ( ( ( C != zero_zero_rat )
% 0.29/0.55           => ( B
% 0.29/0.55              = ( times_times_rat @ A @ C ) ) )
% 0.29/0.55          & ( ( C = zero_zero_rat )
% 0.29/0.55           => ( A = zero_zero_rat ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_eq_eq
% 0.29/0.55  thf(fact_2460_eq__divide__eq,axiom,
% 0.29/0.55      ! [A: complex,B: complex,C: complex] :
% 0.29/0.55        ( ( A
% 0.29/0.55          = ( divide1717551699836669952omplex @ B @ C ) )
% 0.29/0.55        = ( ( ( C != zero_zero_complex )
% 0.29/0.55           => ( ( times_times_complex @ A @ C )
% 0.29/0.55              = B ) )
% 0.29/0.55          & ( ( C = zero_zero_complex )
% 0.29/0.55           => ( A = zero_zero_complex ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % eq_divide_eq
% 0.29/0.55  thf(fact_2461_eq__divide__eq,axiom,
% 0.29/0.55      ! [A: real,B: real,C: real] :
% 0.29/0.55        ( ( A
% 0.29/0.55          = ( divide_divide_real @ B @ C ) )
% 0.29/0.55        = ( ( ( C != zero_zero_real )
% 0.29/0.55           => ( ( times_times_real @ A @ C )
% 0.29/0.55              = B ) )
% 0.29/0.55          & ( ( C = zero_zero_real )
% 0.29/0.55           => ( A = zero_zero_real ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % eq_divide_eq
% 0.29/0.55  thf(fact_2462_eq__divide__eq,axiom,
% 0.29/0.55      ! [A: rat,B: rat,C: rat] :
% 0.29/0.55        ( ( A
% 0.29/0.55          = ( divide_divide_rat @ B @ C ) )
% 0.29/0.55        = ( ( ( C != zero_zero_rat )
% 0.29/0.55           => ( ( times_times_rat @ A @ C )
% 0.29/0.55              = B ) )
% 0.29/0.55          & ( ( C = zero_zero_rat )
% 0.29/0.55           => ( A = zero_zero_rat ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % eq_divide_eq
% 0.29/0.55  thf(fact_2463_divide__eq__imp,axiom,
% 0.29/0.55      ! [C: complex,B: complex,A: complex] :
% 0.29/0.55        ( ( C != zero_zero_complex )
% 0.29/0.55       => ( ( B
% 0.29/0.55            = ( times_times_complex @ A @ C ) )
% 0.29/0.55         => ( ( divide1717551699836669952omplex @ B @ C )
% 0.29/0.55            = A ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_eq_imp
% 0.29/0.55  thf(fact_2464_divide__eq__imp,axiom,
% 0.29/0.55      ! [C: real,B: real,A: real] :
% 0.29/0.55        ( ( C != zero_zero_real )
% 0.29/0.55       => ( ( B
% 0.29/0.55            = ( times_times_real @ A @ C ) )
% 0.29/0.55         => ( ( divide_divide_real @ B @ C )
% 0.29/0.55            = A ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_eq_imp
% 0.29/0.55  thf(fact_2465_divide__eq__imp,axiom,
% 0.29/0.55      ! [C: rat,B: rat,A: rat] :
% 0.29/0.55        ( ( C != zero_zero_rat )
% 0.29/0.55       => ( ( B
% 0.29/0.55            = ( times_times_rat @ A @ C ) )
% 0.29/0.55         => ( ( divide_divide_rat @ B @ C )
% 0.29/0.55            = A ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_eq_imp
% 0.29/0.55  thf(fact_2466_eq__divide__imp,axiom,
% 0.29/0.55      ! [C: complex,A: complex,B: complex] :
% 0.29/0.55        ( ( C != zero_zero_complex )
% 0.29/0.55       => ( ( ( times_times_complex @ A @ C )
% 0.29/0.55            = B )
% 0.29/0.55         => ( A
% 0.29/0.55            = ( divide1717551699836669952omplex @ B @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % eq_divide_imp
% 0.29/0.55  thf(fact_2467_eq__divide__imp,axiom,
% 0.29/0.55      ! [C: real,A: real,B: real] :
% 0.29/0.55        ( ( C != zero_zero_real )
% 0.29/0.55       => ( ( ( times_times_real @ A @ C )
% 0.29/0.55            = B )
% 0.29/0.55         => ( A
% 0.29/0.55            = ( divide_divide_real @ B @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % eq_divide_imp
% 0.29/0.55  thf(fact_2468_eq__divide__imp,axiom,
% 0.29/0.55      ! [C: rat,A: rat,B: rat] :
% 0.29/0.55        ( ( C != zero_zero_rat )
% 0.29/0.55       => ( ( ( times_times_rat @ A @ C )
% 0.29/0.55            = B )
% 0.29/0.55         => ( A
% 0.29/0.55            = ( divide_divide_rat @ B @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % eq_divide_imp
% 0.29/0.55  thf(fact_2469_nonzero__divide__eq__eq,axiom,
% 0.29/0.55      ! [C: complex,B: complex,A: complex] :
% 0.29/0.55        ( ( C != zero_zero_complex )
% 0.29/0.55       => ( ( ( divide1717551699836669952omplex @ B @ C )
% 0.29/0.55            = A )
% 0.29/0.55          = ( B
% 0.29/0.55            = ( times_times_complex @ A @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % nonzero_divide_eq_eq
% 0.29/0.55  thf(fact_2470_nonzero__divide__eq__eq,axiom,
% 0.29/0.55      ! [C: real,B: real,A: real] :
% 0.29/0.55        ( ( C != zero_zero_real )
% 0.29/0.55       => ( ( ( divide_divide_real @ B @ C )
% 0.29/0.55            = A )
% 0.29/0.55          = ( B
% 0.29/0.55            = ( times_times_real @ A @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % nonzero_divide_eq_eq
% 0.29/0.55  thf(fact_2471_nonzero__divide__eq__eq,axiom,
% 0.29/0.55      ! [C: rat,B: rat,A: rat] :
% 0.29/0.55        ( ( C != zero_zero_rat )
% 0.29/0.55       => ( ( ( divide_divide_rat @ B @ C )
% 0.29/0.55            = A )
% 0.29/0.55          = ( B
% 0.29/0.55            = ( times_times_rat @ A @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % nonzero_divide_eq_eq
% 0.29/0.55  thf(fact_2472_nonzero__eq__divide__eq,axiom,
% 0.29/0.55      ! [C: complex,A: complex,B: complex] :
% 0.29/0.55        ( ( C != zero_zero_complex )
% 0.29/0.55       => ( ( A
% 0.29/0.55            = ( divide1717551699836669952omplex @ B @ C ) )
% 0.29/0.55          = ( ( times_times_complex @ A @ C )
% 0.29/0.55            = B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % nonzero_eq_divide_eq
% 0.29/0.55  thf(fact_2473_nonzero__eq__divide__eq,axiom,
% 0.29/0.55      ! [C: real,A: real,B: real] :
% 0.29/0.55        ( ( C != zero_zero_real )
% 0.29/0.55       => ( ( A
% 0.29/0.55            = ( divide_divide_real @ B @ C ) )
% 0.29/0.55          = ( ( times_times_real @ A @ C )
% 0.29/0.55            = B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % nonzero_eq_divide_eq
% 0.29/0.55  thf(fact_2474_nonzero__eq__divide__eq,axiom,
% 0.29/0.55      ! [C: rat,A: rat,B: rat] :
% 0.29/0.55        ( ( C != zero_zero_rat )
% 0.29/0.55       => ( ( A
% 0.29/0.55            = ( divide_divide_rat @ B @ C ) )
% 0.29/0.55          = ( ( times_times_rat @ A @ C )
% 0.29/0.55            = B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % nonzero_eq_divide_eq
% 0.29/0.55  thf(fact_2475_right__inverse__eq,axiom,
% 0.29/0.55      ! [B: complex,A: complex] :
% 0.29/0.55        ( ( B != zero_zero_complex )
% 0.29/0.55       => ( ( ( divide1717551699836669952omplex @ A @ B )
% 0.29/0.55            = one_one_complex )
% 0.29/0.55          = ( A = B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % right_inverse_eq
% 0.29/0.55  thf(fact_2476_right__inverse__eq,axiom,
% 0.29/0.55      ! [B: real,A: real] :
% 0.29/0.55        ( ( B != zero_zero_real )
% 0.29/0.55       => ( ( ( divide_divide_real @ A @ B )
% 0.29/0.55            = one_one_real )
% 0.29/0.55          = ( A = B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % right_inverse_eq
% 0.29/0.55  thf(fact_2477_right__inverse__eq,axiom,
% 0.29/0.55      ! [B: rat,A: rat] :
% 0.29/0.55        ( ( B != zero_zero_rat )
% 0.29/0.55       => ( ( ( divide_divide_rat @ A @ B )
% 0.29/0.55            = one_one_rat )
% 0.29/0.55          = ( A = B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % right_inverse_eq
% 0.29/0.55  thf(fact_2478_power__0,axiom,
% 0.29/0.55      ! [A: rat] :
% 0.29/0.55        ( ( power_power_rat @ A @ zero_zero_nat )
% 0.29/0.55        = one_one_rat ) ).
% 0.29/0.55  
% 0.29/0.55  % power_0
% 0.29/0.55  thf(fact_2479_power__0,axiom,
% 0.29/0.55      ! [A: nat] :
% 0.29/0.55        ( ( power_power_nat @ A @ zero_zero_nat )
% 0.29/0.55        = one_one_nat ) ).
% 0.29/0.55  
% 0.29/0.55  % power_0
% 0.29/0.55  thf(fact_2480_power__0,axiom,
% 0.29/0.55      ! [A: real] :
% 0.29/0.55        ( ( power_power_real @ A @ zero_zero_nat )
% 0.29/0.55        = one_one_real ) ).
% 0.29/0.55  
% 0.29/0.55  % power_0
% 0.29/0.55  thf(fact_2481_power__0,axiom,
% 0.29/0.55      ! [A: int] :
% 0.29/0.55        ( ( power_power_int @ A @ zero_zero_nat )
% 0.29/0.55        = one_one_int ) ).
% 0.29/0.55  
% 0.29/0.55  % power_0
% 0.29/0.55  thf(fact_2482_power__0,axiom,
% 0.29/0.55      ! [A: complex] :
% 0.29/0.55        ( ( power_power_complex @ A @ zero_zero_nat )
% 0.29/0.55        = one_one_complex ) ).
% 0.29/0.55  
% 0.29/0.55  % power_0
% 0.29/0.55  thf(fact_2483_Ex__less__Suc2,axiom,
% 0.29/0.55      ! [N: nat,P: nat > $o] :
% 0.29/0.55        ( ( ? [I3: nat] :
% 0.29/0.55              ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 0.29/0.55              & ( P @ I3 ) ) )
% 0.29/0.55        = ( ( P @ zero_zero_nat )
% 0.29/0.55          | ? [I3: nat] :
% 0.29/0.55              ( ( ord_less_nat @ I3 @ N )
% 0.29/0.55              & ( P @ ( suc @ I3 ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % Ex_less_Suc2
% 0.29/0.55  thf(fact_2484_gr0__conv__Suc,axiom,
% 0.29/0.55      ! [N: nat] :
% 0.29/0.55        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.55        = ( ? [M6: nat] :
% 0.29/0.55              ( N
% 0.29/0.55              = ( suc @ M6 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % gr0_conv_Suc
% 0.29/0.55  thf(fact_2485_All__less__Suc2,axiom,
% 0.29/0.55      ! [N: nat,P: nat > $o] :
% 0.29/0.55        ( ( ! [I3: nat] :
% 0.29/0.55              ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 0.29/0.55             => ( P @ I3 ) ) )
% 0.29/0.55        = ( ( P @ zero_zero_nat )
% 0.29/0.55          & ! [I3: nat] :
% 0.29/0.55              ( ( ord_less_nat @ I3 @ N )
% 0.29/0.55             => ( P @ ( suc @ I3 ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % All_less_Suc2
% 0.29/0.55  thf(fact_2486_gr0__implies__Suc,axiom,
% 0.29/0.55      ! [N: nat] :
% 0.29/0.55        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.55       => ? [M4: nat] :
% 0.29/0.55            ( N
% 0.29/0.55            = ( suc @ M4 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % gr0_implies_Suc
% 0.29/0.55  thf(fact_2487_less__Suc__eq__0__disj,axiom,
% 0.29/0.55      ! [M: nat,N: nat] :
% 0.29/0.55        ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.29/0.55        = ( ( M = zero_zero_nat )
% 0.29/0.55          | ? [J3: nat] :
% 0.29/0.55              ( ( M
% 0.29/0.55                = ( suc @ J3 ) )
% 0.29/0.55              & ( ord_less_nat @ J3 @ N ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % less_Suc_eq_0_disj
% 0.29/0.55  thf(fact_2488_one__is__add,axiom,
% 0.29/0.55      ! [M: nat,N: nat] :
% 0.29/0.55        ( ( ( suc @ zero_zero_nat )
% 0.29/0.55          = ( plus_plus_nat @ M @ N ) )
% 0.29/0.55        = ( ( ( M
% 0.29/0.55              = ( suc @ zero_zero_nat ) )
% 0.29/0.55            & ( N = zero_zero_nat ) )
% 0.29/0.55          | ( ( M = zero_zero_nat )
% 0.29/0.55            & ( N
% 0.29/0.55              = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % one_is_add
% 0.29/0.55  thf(fact_2489_add__is__1,axiom,
% 0.29/0.55      ! [M: nat,N: nat] :
% 0.29/0.55        ( ( ( plus_plus_nat @ M @ N )
% 0.29/0.55          = ( suc @ zero_zero_nat ) )
% 0.29/0.55        = ( ( ( M
% 0.29/0.55              = ( suc @ zero_zero_nat ) )
% 0.29/0.55            & ( N = zero_zero_nat ) )
% 0.29/0.55          | ( ( M = zero_zero_nat )
% 0.29/0.55            & ( N
% 0.29/0.55              = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_is_1
% 0.29/0.55  thf(fact_2490_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I3_J,axiom,
% 0.29/0.55      ! [Uu: $o] :
% 0.29/0.55        ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Leaf @ Uu @ $true ) )
% 0.29/0.55        = one_one_nat ) ).
% 0.29/0.55  
% 0.29/0.55  % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.simps(3)
% 0.29/0.55  thf(fact_2491_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I2_J,axiom,
% 0.29/0.55      ! [Uv: $o] :
% 0.29/0.55        ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Leaf @ $true @ Uv ) )
% 0.29/0.55        = one_one_nat ) ).
% 0.29/0.55  
% 0.29/0.55  % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.simps(2)
% 0.29/0.55  thf(fact_2492_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I1_J,axiom,
% 0.29/0.55      ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Leaf @ $false @ $false ) )
% 0.29/0.55      = one_one_nat ) ).
% 0.29/0.55  
% 0.29/0.55  % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.simps(1)
% 0.29/0.55  thf(fact_2493_option_Osize_I4_J,axiom,
% 0.29/0.55      ! [X23: product_prod_nat_nat] :
% 0.29/0.55        ( ( size_s170228958280169651at_nat @ ( some_P7363390416028606310at_nat @ X23 ) )
% 0.29/0.55        = ( suc @ zero_zero_nat ) ) ).
% 0.29/0.55  
% 0.29/0.55  % option.size(4)
% 0.29/0.55  thf(fact_2494_option_Osize_I4_J,axiom,
% 0.29/0.55      ! [X23: nat] :
% 0.29/0.55        ( ( size_size_option_nat @ ( some_nat @ X23 ) )
% 0.29/0.55        = ( suc @ zero_zero_nat ) ) ).
% 0.29/0.55  
% 0.29/0.55  % option.size(4)
% 0.29/0.55  thf(fact_2495_option_Osize_I4_J,axiom,
% 0.29/0.55      ! [X23: num] :
% 0.29/0.55        ( ( size_size_option_num @ ( some_num @ X23 ) )
% 0.29/0.55        = ( suc @ zero_zero_nat ) ) ).
% 0.29/0.55  
% 0.29/0.55  % option.size(4)
% 0.29/0.55  thf(fact_2496_One__nat__def,axiom,
% 0.29/0.55      ( one_one_nat
% 0.29/0.55      = ( suc @ zero_zero_nat ) ) ).
% 0.29/0.55  
% 0.29/0.55  % One_nat_def
% 0.29/0.55  thf(fact_2497_less__imp__add__positive,axiom,
% 0.29/0.55      ! [I2: nat,J: nat] :
% 0.29/0.55        ( ( ord_less_nat @ I2 @ J )
% 0.29/0.55       => ? [K2: nat] :
% 0.29/0.55            ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 0.29/0.55            & ( ( plus_plus_nat @ I2 @ K2 )
% 0.29/0.55              = J ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % less_imp_add_positive
% 0.29/0.55  thf(fact_2498_ex__least__nat__le,axiom,
% 0.29/0.55      ! [P: nat > $o,N: nat] :
% 0.29/0.55        ( ( P @ N )
% 0.29/0.55       => ( ~ ( P @ zero_zero_nat )
% 0.29/0.55         => ? [K2: nat] :
% 0.29/0.55              ( ( ord_less_eq_nat @ K2 @ N )
% 0.29/0.55              & ! [I: nat] :
% 0.29/0.55                  ( ( ord_less_nat @ I @ K2 )
% 0.29/0.55                 => ~ ( P @ I ) )
% 0.29/0.55              & ( P @ K2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % ex_least_nat_le
% 0.29/0.55  thf(fact_2499_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I1_J,axiom,
% 0.29/0.55      ! [A: $o,B: $o,X: nat] :
% 0.29/0.55        ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.29/0.55        = one_one_nat ) ).
% 0.29/0.55  
% 0.29/0.55  % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(1)
% 0.29/0.55  thf(fact_2500_option_Osize_I3_J,axiom,
% 0.29/0.55      ( ( size_s170228958280169651at_nat @ none_P5556105721700978146at_nat )
% 0.29/0.55      = ( suc @ zero_zero_nat ) ) ).
% 0.29/0.55  
% 0.29/0.55  % option.size(3)
% 0.29/0.55  thf(fact_2501_option_Osize_I3_J,axiom,
% 0.29/0.55      ( ( size_size_option_nat @ none_nat )
% 0.29/0.55      = ( suc @ zero_zero_nat ) ) ).
% 0.29/0.55  
% 0.29/0.55  % option.size(3)
% 0.29/0.55  thf(fact_2502_option_Osize_I3_J,axiom,
% 0.29/0.55      ( ( size_size_option_num @ none_num )
% 0.29/0.55      = ( suc @ zero_zero_nat ) ) ).
% 0.29/0.55  
% 0.29/0.55  % option.size(3)
% 0.29/0.55  thf(fact_2503_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 0.29/0.55      ! [M: nat,N: nat] :
% 0.29/0.55        ( ( ( divide_divide_nat @ M @ N )
% 0.29/0.55          = zero_zero_nat )
% 0.29/0.55        = ( ( ord_less_nat @ M @ N )
% 0.29/0.55          | ( N = zero_zero_nat ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % Euclidean_Division.div_eq_0_iff
% 0.29/0.55  thf(fact_2504_mult__less__mono1,axiom,
% 0.29/0.55      ! [I2: nat,J: nat,K: nat] :
% 0.29/0.55        ( ( ord_less_nat @ I2 @ J )
% 0.29/0.55       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.29/0.55         => ( ord_less_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_mono1
% 0.29/0.55  thf(fact_2505_mult__less__mono2,axiom,
% 0.29/0.55      ! [I2: nat,J: nat,K: nat] :
% 0.29/0.55        ( ( ord_less_nat @ I2 @ J )
% 0.29/0.55       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.29/0.55         => ( ord_less_nat @ ( times_times_nat @ K @ I2 ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_mono2
% 0.29/0.55  thf(fact_2506_nat__mult__eq__cancel1,axiom,
% 0.29/0.55      ! [K: nat,M: nat,N: nat] :
% 0.29/0.55        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.29/0.55       => ( ( ( times_times_nat @ K @ M )
% 0.29/0.55            = ( times_times_nat @ K @ N ) )
% 0.29/0.55          = ( M = N ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % nat_mult_eq_cancel1
% 0.29/0.55  thf(fact_2507_nat__mult__less__cancel1,axiom,
% 0.29/0.55      ! [K: nat,M: nat,N: nat] :
% 0.29/0.55        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.29/0.55       => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.29/0.55          = ( ord_less_nat @ M @ N ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % nat_mult_less_cancel1
% 0.29/0.55  thf(fact_2508_diff__less,axiom,
% 0.29/0.55      ! [N: nat,M: nat] :
% 0.29/0.55        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.55       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.29/0.55         => ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ M ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % diff_less
% 0.29/0.55  thf(fact_2509_diff__add__0,axiom,
% 0.29/0.55      ! [N: nat,M: nat] :
% 0.29/0.55        ( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M ) )
% 0.29/0.55        = zero_zero_nat ) ).
% 0.29/0.55  
% 0.29/0.55  % diff_add_0
% 0.29/0.55  thf(fact_2510_mult__eq__self__implies__10,axiom,
% 0.29/0.55      ! [M: nat,N: nat] :
% 0.29/0.55        ( ( M
% 0.29/0.55          = ( times_times_nat @ M @ N ) )
% 0.29/0.55       => ( ( N = one_one_nat )
% 0.29/0.55          | ( M = zero_zero_nat ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_eq_self_implies_10
% 0.29/0.55  thf(fact_2511_nat__power__less__imp__less,axiom,
% 0.29/0.55      ! [I2: nat,M: nat,N: nat] :
% 0.29/0.55        ( ( ord_less_nat @ zero_zero_nat @ I2 )
% 0.29/0.55       => ( ( ord_less_nat @ ( power_power_nat @ I2 @ M ) @ ( power_power_nat @ I2 @ N ) )
% 0.29/0.55         => ( ord_less_nat @ M @ N ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % nat_power_less_imp_less
% 0.29/0.55  thf(fact_2512_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I6_J,axiom,
% 0.29/0.55      ! [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT,Vj: nat] :
% 0.29/0.55        ( ( vEBT_T_p_r_e_d @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Vj )
% 0.29/0.55        = one_one_nat ) ).
% 0.29/0.55  
% 0.29/0.55  % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.simps(6)
% 0.29/0.55  thf(fact_2513_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Ocases,axiom,
% 0.29/0.55      ! [X: produc9072475918466114483BT_nat] :
% 0.29/0.55        ( ! [A4: $o,B3: $o,X3: nat] :
% 0.29/0.55            ( X
% 0.29/0.55           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ X3 ) )
% 0.29/0.55       => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,X3: nat] :
% 0.29/0.55              ( X
% 0.29/0.55             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ X3 ) )
% 0.29/0.55         => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,X3: nat] :
% 0.29/0.55                ( X
% 0.29/0.55               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ X3 ) )
% 0.29/0.55           => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X3: nat] :
% 0.29/0.55                  ( X
% 0.29/0.55                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ X3 ) )
% 0.29/0.55             => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 0.29/0.55                    ( X
% 0.29/0.55                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ X3 ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.cases
% 0.29/0.55  thf(fact_2514_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Ocases,axiom,
% 0.29/0.55      ! [X: produc9072475918466114483BT_nat] :
% 0.29/0.55        ( ! [A4: $o,B3: $o,X3: nat] :
% 0.29/0.55            ( X
% 0.29/0.55           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ X3 ) )
% 0.29/0.55       => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 0.29/0.55              ( X
% 0.29/0.55             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S ) @ X3 ) )
% 0.29/0.55         => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 0.29/0.55                ( X
% 0.29/0.55               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) @ X3 ) )
% 0.29/0.55           => ( ! [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 0.29/0.55                  ( X
% 0.29/0.55                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) @ X3 ) )
% 0.29/0.55             => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 0.29/0.55                    ( X
% 0.29/0.55                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ X3 ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.cases
% 0.29/0.55  thf(fact_2515_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Ocases,axiom,
% 0.29/0.55      ! [X: produc9072475918466114483BT_nat] :
% 0.29/0.55        ( ! [Uu2: $o,B3: $o] :
% 0.29/0.55            ( X
% 0.29/0.55           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B3 ) @ zero_zero_nat ) )
% 0.29/0.55       => ( ! [Uv2: $o,Uw2: $o,N3: nat] :
% 0.29/0.55              ( X
% 0.29/0.55             != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N3 ) ) )
% 0.29/0.55         => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,Va3: nat] :
% 0.29/0.55                ( X
% 0.29/0.55               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Va3 ) )
% 0.29/0.55           => ( ! [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT,Ve2: nat] :
% 0.29/0.55                  ( X
% 0.29/0.55                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Ve2 ) )
% 0.29/0.55             => ( ! [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh2: vEBT_VEBT,Vi2: nat] :
% 0.29/0.55                    ( X
% 0.29/0.55                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh2 ) @ Vi2 ) )
% 0.29/0.55               => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 0.29/0.55                      ( X
% 0.29/0.55                     != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ X3 ) ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.cases
% 0.29/0.55  thf(fact_2516_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Ocases,axiom,
% 0.29/0.55      ! [X: produc9072475918466114483BT_nat] :
% 0.29/0.55        ( ! [Uu2: $o,Uv2: $o] :
% 0.29/0.55            ( X
% 0.29/0.55           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) )
% 0.29/0.55       => ( ! [A4: $o,Uw2: $o] :
% 0.29/0.55              ( X
% 0.29/0.55             != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) )
% 0.29/0.55         => ( ! [A4: $o,B3: $o,Va2: nat] :
% 0.29/0.55                ( X
% 0.29/0.55               != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ ( suc @ ( suc @ Va2 ) ) ) )
% 0.29/0.55           => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT,Vb2: nat] :
% 0.29/0.55                  ( X
% 0.29/0.55                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) @ Vb2 ) )
% 0.29/0.55             => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT,Vf2: nat] :
% 0.29/0.55                    ( X
% 0.29/0.55                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Vf2 ) )
% 0.29/0.55               => ( ! [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT,Vj2: nat] :
% 0.29/0.55                      ( X
% 0.29/0.55                     != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Vj2 ) )
% 0.29/0.55                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 0.29/0.55                        ( X
% 0.29/0.55                       != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ X3 ) ) ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.cases
% 0.29/0.55  thf(fact_2517_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Ocases,axiom,
% 0.29/0.55      ! [X: produc9072475918466114483BT_nat] :
% 0.29/0.55        ( ! [A4: $o,B3: $o] :
% 0.29/0.55            ( X
% 0.29/0.55           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ zero_zero_nat ) )
% 0.29/0.55       => ( ! [A4: $o,B3: $o] :
% 0.29/0.55              ( X
% 0.29/0.55             != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ ( suc @ zero_zero_nat ) ) )
% 0.29/0.55         => ( ! [A4: $o,B3: $o,N3: nat] :
% 0.29/0.55                ( X
% 0.29/0.55               != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ ( suc @ ( suc @ N3 ) ) ) )
% 0.29/0.55           => ( ! [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,Uu2: nat] :
% 0.29/0.55                  ( X
% 0.29/0.55                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) @ Uu2 ) )
% 0.29/0.55             => ( ! [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 0.29/0.55                    ( X
% 0.29/0.55                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TreeList2 @ Summary2 ) @ X3 ) )
% 0.29/0.55               => ( ! [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 0.29/0.55                      ( X
% 0.29/0.55                     != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary2 ) @ X3 ) )
% 0.29/0.55                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 0.29/0.55                        ( X
% 0.29/0.55                       != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ X3 ) ) ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.cases
% 0.29/0.55  thf(fact_2518_VEBT__internal_Omembermima_Ocases,axiom,
% 0.29/0.55      ! [X: produc9072475918466114483BT_nat] :
% 0.29/0.55        ( ! [Uu2: $o,Uv2: $o,Uw2: nat] :
% 0.29/0.55            ( X
% 0.29/0.55           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Uw2 ) )
% 0.29/0.55       => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT,Uz2: nat] :
% 0.29/0.55              ( X
% 0.29/0.55             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Uz2 ) )
% 0.29/0.55         => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT,X3: nat] :
% 0.29/0.55                ( X
% 0.29/0.55               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ X3 ) )
% 0.29/0.55           => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X3: nat] :
% 0.29/0.55                  ( X
% 0.29/0.55                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) @ X3 ) )
% 0.29/0.55             => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT,X3: nat] :
% 0.29/0.55                    ( X
% 0.29/0.55                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) @ X3 ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % VEBT_internal.membermima.cases
% 0.29/0.55  thf(fact_2519_vebt__insert_Osimps_I2_J,axiom,
% 0.29/0.55      ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT,X: nat] :
% 0.29/0.55        ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S3 ) @ X )
% 0.29/0.55        = ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S3 ) ) ).
% 0.29/0.55  
% 0.29/0.55  % vebt_insert.simps(2)
% 0.29/0.55  thf(fact_2520_vebt__pred_Osimps_I3_J,axiom,
% 0.29/0.55      ! [B: $o,A: $o,Va: nat] :
% 0.29/0.55        ( ( B
% 0.29/0.55         => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 0.29/0.55            = ( some_nat @ one_one_nat ) ) )
% 0.29/0.55        & ( ~ B
% 0.29/0.55         => ( ( A
% 0.29/0.55             => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 0.29/0.55                = ( some_nat @ zero_zero_nat ) ) )
% 0.29/0.55            & ( ~ A
% 0.29/0.55             => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 0.29/0.55                = none_nat ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % vebt_pred.simps(3)
% 0.29/0.55  thf(fact_2521_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Ocases,axiom,
% 0.29/0.55      ! [X: vEBT_VEBT] :
% 0.29/0.55        ( ( X
% 0.29/0.55         != ( vEBT_Leaf @ $false @ $false ) )
% 0.29/0.55       => ( ! [Uv2: $o] :
% 0.29/0.55              ( X
% 0.29/0.55             != ( vEBT_Leaf @ $true @ Uv2 ) )
% 0.29/0.55         => ( ! [Uu2: $o] :
% 0.29/0.55                ( X
% 0.29/0.55               != ( vEBT_Leaf @ Uu2 @ $true ) )
% 0.29/0.55           => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 0.29/0.55                  ( X
% 0.29/0.55                 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 0.29/0.55             => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.29/0.55                    ( X
% 0.29/0.55                   != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.cases
% 0.29/0.55  thf(fact_2522_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I1_J,axiom,
% 0.29/0.55      ! [A: $o,B: $o,X: nat] :
% 0.29/0.55        ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.29/0.55        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( X = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(1)
% 0.29/0.55  thf(fact_2523_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I3_J,axiom,
% 0.29/0.55      ! [A: $o,B: $o,N: nat] :
% 0.29/0.55        ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ N ) ) )
% 0.29/0.55        = one_one_nat ) ).
% 0.29/0.55  
% 0.29/0.55  % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.simps(3)
% 0.29/0.55  thf(fact_2524_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Osimps_I1_J,axiom,
% 0.29/0.55      ! [A: $o,B: $o] :
% 0.29/0.55        ( ( vEBT_T_m_a_x_t @ ( vEBT_Leaf @ A @ B ) )
% 0.29/0.55        = ( plus_plus_nat @ one_one_nat @ ( if_nat @ B @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % T\<^sub>m\<^sub>a\<^sub>x\<^sub>t.simps(1)
% 0.29/0.55  thf(fact_2525_VEBT__internal_OminNull_Oelims_I3_J,axiom,
% 0.29/0.55      ! [X: vEBT_VEBT] :
% 0.29/0.55        ( ~ ( vEBT_VEBT_minNull @ X )
% 0.29/0.55       => ( ! [Uv2: $o] :
% 0.29/0.55              ( X
% 0.29/0.55             != ( vEBT_Leaf @ $true @ Uv2 ) )
% 0.29/0.55         => ( ! [Uu2: $o] :
% 0.29/0.55                ( X
% 0.29/0.55               != ( vEBT_Leaf @ Uu2 @ $true ) )
% 0.29/0.55           => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.29/0.55                  ( X
% 0.29/0.55                 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % VEBT_internal.minNull.elims(3)
% 0.29/0.55  thf(fact_2526_VEBT__internal_OminNull_Oelims_I2_J,axiom,
% 0.29/0.55      ! [X: vEBT_VEBT] :
% 0.29/0.55        ( ( vEBT_VEBT_minNull @ X )
% 0.29/0.55       => ( ( X
% 0.29/0.55           != ( vEBT_Leaf @ $false @ $false ) )
% 0.29/0.55         => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 0.29/0.55                ( X
% 0.29/0.55               != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % VEBT_internal.minNull.elims(2)
% 0.29/0.55  thf(fact_2527_vebt__succ_Osimps_I2_J,axiom,
% 0.29/0.55      ! [Uv: $o,Uw: $o,N: nat] :
% 0.29/0.55        ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N ) )
% 0.29/0.55        = none_nat ) ).
% 0.29/0.55  
% 0.29/0.55  % vebt_succ.simps(2)
% 0.29/0.55  thf(fact_2528_mult__le__cancel__left,axiom,
% 0.29/0.55      ! [C: real,A: real,B: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.29/0.55        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.55           => ( ord_less_eq_real @ A @ B ) )
% 0.29/0.55          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.55           => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_cancel_left
% 0.29/0.55  thf(fact_2529_mult__le__cancel__left,axiom,
% 0.29/0.55      ! [C: rat,A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.29/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.55           => ( ord_less_eq_rat @ A @ B ) )
% 0.29/0.55          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.55           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_cancel_left
% 0.29/0.55  thf(fact_2530_mult__le__cancel__left,axiom,
% 0.29/0.55      ! [C: int,A: int,B: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.29/0.55        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.29/0.55           => ( ord_less_eq_int @ A @ B ) )
% 0.29/0.55          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.29/0.55           => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_cancel_left
% 0.29/0.55  thf(fact_2531_mult__le__cancel__right,axiom,
% 0.29/0.55      ! [A: real,C: real,B: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 0.29/0.55        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.55           => ( ord_less_eq_real @ A @ B ) )
% 0.29/0.55          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.55           => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_cancel_right
% 0.29/0.55  thf(fact_2532_mult__le__cancel__right,axiom,
% 0.29/0.55      ! [A: rat,C: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.29/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.55           => ( ord_less_eq_rat @ A @ B ) )
% 0.29/0.55          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.55           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_cancel_right
% 0.29/0.55  thf(fact_2533_mult__le__cancel__right,axiom,
% 0.29/0.55      ! [A: int,C: int,B: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.29/0.55        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.29/0.55           => ( ord_less_eq_int @ A @ B ) )
% 0.29/0.55          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.29/0.55           => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_cancel_right
% 0.29/0.55  thf(fact_2534_mult__left__less__imp__less,axiom,
% 0.29/0.55      ! [C: real,A: real,B: real] :
% 0.29/0.55        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.29/0.55       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.29/0.55         => ( ord_less_real @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_left_less_imp_less
% 0.29/0.55  thf(fact_2535_mult__left__less__imp__less,axiom,
% 0.29/0.55      ! [C: rat,A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.29/0.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.29/0.55         => ( ord_less_rat @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_left_less_imp_less
% 0.29/0.55  thf(fact_2536_mult__left__less__imp__less,axiom,
% 0.29/0.55      ! [C: nat,A: nat,B: nat] :
% 0.29/0.55        ( ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 0.29/0.55       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.29/0.55         => ( ord_less_nat @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_left_less_imp_less
% 0.29/0.55  thf(fact_2537_mult__left__less__imp__less,axiom,
% 0.29/0.55      ! [C: int,A: int,B: int] :
% 0.29/0.55        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.29/0.55       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.55         => ( ord_less_int @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_left_less_imp_less
% 0.29/0.55  thf(fact_2538_mult__strict__mono,axiom,
% 0.29/0.55      ! [A: real,B: real,C: real,D2: real] :
% 0.29/0.55        ( ( ord_less_real @ A @ B )
% 0.29/0.55       => ( ( ord_less_real @ C @ D2 )
% 0.29/0.55         => ( ( ord_less_real @ zero_zero_real @ B )
% 0.29/0.55           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.29/0.55             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_strict_mono
% 0.29/0.55  thf(fact_2539_mult__strict__mono,axiom,
% 0.29/0.55      ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.29/0.55        ( ( ord_less_rat @ A @ B )
% 0.29/0.55       => ( ( ord_less_rat @ C @ D2 )
% 0.29/0.55         => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.29/0.55           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.29/0.55             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_strict_mono
% 0.29/0.55  thf(fact_2540_mult__strict__mono,axiom,
% 0.29/0.55      ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.29/0.55        ( ( ord_less_nat @ A @ B )
% 0.29/0.55       => ( ( ord_less_nat @ C @ D2 )
% 0.29/0.55         => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.29/0.55           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.29/0.55             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_strict_mono
% 0.29/0.55  thf(fact_2541_mult__strict__mono,axiom,
% 0.29/0.55      ! [A: int,B: int,C: int,D2: int] :
% 0.29/0.55        ( ( ord_less_int @ A @ B )
% 0.29/0.55       => ( ( ord_less_int @ C @ D2 )
% 0.29/0.55         => ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.55           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.55             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_strict_mono
% 0.29/0.55  thf(fact_2542_mult__less__cancel__left,axiom,
% 0.29/0.55      ! [C: real,A: real,B: real] :
% 0.29/0.55        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.29/0.55        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.29/0.55           => ( ord_less_real @ A @ B ) )
% 0.29/0.55          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.29/0.55           => ( ord_less_real @ B @ A ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_cancel_left
% 0.29/0.55  thf(fact_2543_mult__less__cancel__left,axiom,
% 0.29/0.55      ! [C: rat,A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.29/0.55        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.29/0.55           => ( ord_less_rat @ A @ B ) )
% 0.29/0.55          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.29/0.55           => ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_cancel_left
% 0.29/0.55  thf(fact_2544_mult__less__cancel__left,axiom,
% 0.29/0.55      ! [C: int,A: int,B: int] :
% 0.29/0.55        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.29/0.55        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.55           => ( ord_less_int @ A @ B ) )
% 0.29/0.55          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.29/0.55           => ( ord_less_int @ B @ A ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_cancel_left
% 0.29/0.55  thf(fact_2545_mult__right__less__imp__less,axiom,
% 0.29/0.55      ! [A: real,C: real,B: real] :
% 0.29/0.55        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 0.29/0.55       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.29/0.55         => ( ord_less_real @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_right_less_imp_less
% 0.29/0.55  thf(fact_2546_mult__right__less__imp__less,axiom,
% 0.29/0.55      ! [A: rat,C: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.29/0.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.29/0.55         => ( ord_less_rat @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_right_less_imp_less
% 0.29/0.55  thf(fact_2547_mult__right__less__imp__less,axiom,
% 0.29/0.55      ! [A: nat,C: nat,B: nat] :
% 0.29/0.55        ( ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 0.29/0.55       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.29/0.55         => ( ord_less_nat @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_right_less_imp_less
% 0.29/0.55  thf(fact_2548_mult__right__less__imp__less,axiom,
% 0.29/0.55      ! [A: int,C: int,B: int] :
% 0.29/0.55        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.29/0.55       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.55         => ( ord_less_int @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_right_less_imp_less
% 0.29/0.55  thf(fact_2549_mult__strict__mono_H,axiom,
% 0.29/0.55      ! [A: real,B: real,C: real,D2: real] :
% 0.29/0.55        ( ( ord_less_real @ A @ B )
% 0.29/0.55       => ( ( ord_less_real @ C @ D2 )
% 0.29/0.55         => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.55           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.29/0.55             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_strict_mono'
% 0.29/0.55  thf(fact_2550_mult__strict__mono_H,axiom,
% 0.29/0.55      ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.29/0.55        ( ( ord_less_rat @ A @ B )
% 0.29/0.55       => ( ( ord_less_rat @ C @ D2 )
% 0.29/0.55         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.55           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.29/0.55             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_strict_mono'
% 0.29/0.55  thf(fact_2551_mult__strict__mono_H,axiom,
% 0.29/0.55      ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.29/0.55        ( ( ord_less_nat @ A @ B )
% 0.29/0.55       => ( ( ord_less_nat @ C @ D2 )
% 0.29/0.55         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.55           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.29/0.55             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_strict_mono'
% 0.29/0.55  thf(fact_2552_mult__strict__mono_H,axiom,
% 0.29/0.55      ! [A: int,B: int,C: int,D2: int] :
% 0.29/0.55        ( ( ord_less_int @ A @ B )
% 0.29/0.55       => ( ( ord_less_int @ C @ D2 )
% 0.29/0.55         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.55           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.55             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_strict_mono'
% 0.29/0.55  thf(fact_2553_mult__less__cancel__right,axiom,
% 0.29/0.55      ! [A: real,C: real,B: real] :
% 0.29/0.55        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 0.29/0.55        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.29/0.55           => ( ord_less_real @ A @ B ) )
% 0.29/0.55          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.29/0.55           => ( ord_less_real @ B @ A ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_cancel_right
% 0.29/0.55  thf(fact_2554_mult__less__cancel__right,axiom,
% 0.29/0.55      ! [A: rat,C: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.29/0.55        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.29/0.55           => ( ord_less_rat @ A @ B ) )
% 0.29/0.55          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.29/0.55           => ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_cancel_right
% 0.29/0.55  thf(fact_2555_mult__less__cancel__right,axiom,
% 0.29/0.55      ! [A: int,C: int,B: int] :
% 0.29/0.55        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.29/0.55        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.55           => ( ord_less_int @ A @ B ) )
% 0.29/0.55          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.29/0.55           => ( ord_less_int @ B @ A ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_cancel_right
% 0.29/0.55  thf(fact_2556_mult__le__cancel__left__neg,axiom,
% 0.29/0.55      ! [C: real,A: real,B: real] :
% 0.29/0.55        ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.55       => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.29/0.55          = ( ord_less_eq_real @ B @ A ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_cancel_left_neg
% 0.29/0.55  thf(fact_2557_mult__le__cancel__left__neg,axiom,
% 0.29/0.55      ! [C: rat,A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.55       => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.29/0.55          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_cancel_left_neg
% 0.29/0.55  thf(fact_2558_mult__le__cancel__left__neg,axiom,
% 0.29/0.55      ! [C: int,A: int,B: int] :
% 0.29/0.55        ( ( ord_less_int @ C @ zero_zero_int )
% 0.29/0.55       => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.29/0.55          = ( ord_less_eq_int @ B @ A ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_cancel_left_neg
% 0.29/0.55  thf(fact_2559_mult__le__cancel__left__pos,axiom,
% 0.29/0.55      ! [C: real,A: real,B: real] :
% 0.29/0.55        ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.55       => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.29/0.55          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_cancel_left_pos
% 0.29/0.55  thf(fact_2560_mult__le__cancel__left__pos,axiom,
% 0.29/0.55      ! [C: rat,A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.55       => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.29/0.55          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_cancel_left_pos
% 0.29/0.55  thf(fact_2561_mult__le__cancel__left__pos,axiom,
% 0.29/0.55      ! [C: int,A: int,B: int] :
% 0.29/0.55        ( ( ord_less_int @ zero_zero_int @ C )
% 0.29/0.55       => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.29/0.55          = ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_cancel_left_pos
% 0.29/0.55  thf(fact_2562_mult__left__le__imp__le,axiom,
% 0.29/0.55      ! [C: real,A: real,B: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.29/0.55       => ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.55         => ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_left_le_imp_le
% 0.29/0.55  thf(fact_2563_mult__left__le__imp__le,axiom,
% 0.29/0.55      ! [C: rat,A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.29/0.55       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.55         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_left_le_imp_le
% 0.29/0.55  thf(fact_2564_mult__left__le__imp__le,axiom,
% 0.29/0.55      ! [C: nat,A: nat,B: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 0.29/0.55       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.29/0.55         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_left_le_imp_le
% 0.29/0.55  thf(fact_2565_mult__left__le__imp__le,axiom,
% 0.29/0.55      ! [C: int,A: int,B: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.29/0.55       => ( ( ord_less_int @ zero_zero_int @ C )
% 0.29/0.55         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_left_le_imp_le
% 0.29/0.55  thf(fact_2566_mult__right__le__imp__le,axiom,
% 0.29/0.55      ! [A: real,C: real,B: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 0.29/0.55       => ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.55         => ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_right_le_imp_le
% 0.29/0.55  thf(fact_2567_mult__right__le__imp__le,axiom,
% 0.29/0.55      ! [A: rat,C: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.29/0.55       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.55         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_right_le_imp_le
% 0.29/0.55  thf(fact_2568_mult__right__le__imp__le,axiom,
% 0.29/0.55      ! [A: nat,C: nat,B: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 0.29/0.55       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.29/0.55         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_right_le_imp_le
% 0.29/0.55  thf(fact_2569_mult__right__le__imp__le,axiom,
% 0.29/0.55      ! [A: int,C: int,B: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.29/0.55       => ( ( ord_less_int @ zero_zero_int @ C )
% 0.29/0.55         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_right_le_imp_le
% 0.29/0.55  thf(fact_2570_mult__le__less__imp__less,axiom,
% 0.29/0.55      ! [A: real,B: real,C: real,D2: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.55       => ( ( ord_less_real @ C @ D2 )
% 0.29/0.55         => ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.55           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.29/0.55             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_less_imp_less
% 0.29/0.55  thf(fact_2571_mult__le__less__imp__less,axiom,
% 0.29/0.55      ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.55       => ( ( ord_less_rat @ C @ D2 )
% 0.29/0.55         => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.55           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.29/0.55             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_less_imp_less
% 0.29/0.55  thf(fact_2572_mult__le__less__imp__less,axiom,
% 0.29/0.55      ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.55       => ( ( ord_less_nat @ C @ D2 )
% 0.29/0.55         => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.29/0.55           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.29/0.55             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_less_imp_less
% 0.29/0.55  thf(fact_2573_mult__le__less__imp__less,axiom,
% 0.29/0.55      ! [A: int,B: int,C: int,D2: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.55       => ( ( ord_less_int @ C @ D2 )
% 0.29/0.55         => ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.55           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.55             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_less_imp_less
% 0.29/0.55  thf(fact_2574_mult__less__le__imp__less,axiom,
% 0.29/0.55      ! [A: real,B: real,C: real,D2: real] :
% 0.29/0.55        ( ( ord_less_real @ A @ B )
% 0.29/0.55       => ( ( ord_less_eq_real @ C @ D2 )
% 0.29/0.55         => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.55           => ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.55             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_le_imp_less
% 0.29/0.55  thf(fact_2575_mult__less__le__imp__less,axiom,
% 0.29/0.55      ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.29/0.55        ( ( ord_less_rat @ A @ B )
% 0.29/0.55       => ( ( ord_less_eq_rat @ C @ D2 )
% 0.29/0.55         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.55           => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.55             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_le_imp_less
% 0.29/0.55  thf(fact_2576_mult__less__le__imp__less,axiom,
% 0.29/0.55      ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.29/0.55        ( ( ord_less_nat @ A @ B )
% 0.29/0.55       => ( ( ord_less_eq_nat @ C @ D2 )
% 0.29/0.55         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.55           => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.29/0.55             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_le_imp_less
% 0.29/0.55  thf(fact_2577_mult__less__le__imp__less,axiom,
% 0.29/0.55      ! [A: int,B: int,C: int,D2: int] :
% 0.29/0.55        ( ( ord_less_int @ A @ B )
% 0.29/0.55       => ( ( ord_less_eq_int @ C @ D2 )
% 0.29/0.55         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.55           => ( ( ord_less_int @ zero_zero_int @ C )
% 0.29/0.55             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_le_imp_less
% 0.29/0.55  thf(fact_2578_field__le__epsilon,axiom,
% 0.29/0.55      ! [X: real,Y2: real] :
% 0.29/0.55        ( ! [E2: real] :
% 0.29/0.55            ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.29/0.55           => ( ord_less_eq_real @ X @ ( plus_plus_real @ Y2 @ E2 ) ) )
% 0.29/0.55       => ( ord_less_eq_real @ X @ Y2 ) ) ).
% 0.29/0.55  
% 0.29/0.55  % field_le_epsilon
% 0.29/0.55  thf(fact_2579_field__le__epsilon,axiom,
% 0.29/0.55      ! [X: rat,Y2: rat] :
% 0.29/0.55        ( ! [E2: rat] :
% 0.29/0.55            ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 0.29/0.55           => ( ord_less_eq_rat @ X @ ( plus_plus_rat @ Y2 @ E2 ) ) )
% 0.29/0.55       => ( ord_less_eq_rat @ X @ Y2 ) ) ).
% 0.29/0.55  
% 0.29/0.55  % field_le_epsilon
% 0.29/0.55  thf(fact_2580_add__neg__nonpos,axiom,
% 0.29/0.55      ! [A: real,B: real] :
% 0.29/0.55        ( ( ord_less_real @ A @ zero_zero_real )
% 0.29/0.55       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.29/0.55         => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_neg_nonpos
% 0.29/0.55  thf(fact_2581_add__neg__nonpos,axiom,
% 0.29/0.55      ! [A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.55       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.29/0.55         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_neg_nonpos
% 0.29/0.55  thf(fact_2582_add__neg__nonpos,axiom,
% 0.29/0.55      ! [A: nat,B: nat] :
% 0.29/0.55        ( ( ord_less_nat @ A @ zero_zero_nat )
% 0.29/0.55       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.29/0.55         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_neg_nonpos
% 0.29/0.55  thf(fact_2583_add__neg__nonpos,axiom,
% 0.29/0.55      ! [A: int,B: int] :
% 0.29/0.55        ( ( ord_less_int @ A @ zero_zero_int )
% 0.29/0.55       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.29/0.55         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_neg_nonpos
% 0.29/0.55  thf(fact_2584_add__nonneg__pos,axiom,
% 0.29/0.55      ! [A: real,B: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.55       => ( ( ord_less_real @ zero_zero_real @ B )
% 0.29/0.55         => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_nonneg_pos
% 0.29/0.55  thf(fact_2585_add__nonneg__pos,axiom,
% 0.29/0.55      ! [A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.55       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.29/0.55         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_nonneg_pos
% 0.29/0.55  thf(fact_2586_add__nonneg__pos,axiom,
% 0.29/0.55      ! [A: nat,B: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.55       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.29/0.55         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_nonneg_pos
% 0.29/0.55  thf(fact_2587_add__nonneg__pos,axiom,
% 0.29/0.55      ! [A: int,B: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.55       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.55         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_nonneg_pos
% 0.29/0.55  thf(fact_2588_add__nonpos__neg,axiom,
% 0.29/0.55      ! [A: real,B: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.29/0.55       => ( ( ord_less_real @ B @ zero_zero_real )
% 0.29/0.55         => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_nonpos_neg
% 0.29/0.55  thf(fact_2589_add__nonpos__neg,axiom,
% 0.29/0.55      ! [A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.29/0.55       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.29/0.55         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_nonpos_neg
% 0.29/0.55  thf(fact_2590_add__nonpos__neg,axiom,
% 0.29/0.55      ! [A: nat,B: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.29/0.55       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.29/0.55         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_nonpos_neg
% 0.29/0.55  thf(fact_2591_add__nonpos__neg,axiom,
% 0.29/0.55      ! [A: int,B: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.29/0.55       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.29/0.55         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_nonpos_neg
% 0.29/0.55  thf(fact_2592_add__pos__nonneg,axiom,
% 0.29/0.55      ! [A: real,B: real] :
% 0.29/0.55        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.55       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.29/0.55         => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_pos_nonneg
% 0.29/0.55  thf(fact_2593_add__pos__nonneg,axiom,
% 0.29/0.55      ! [A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.29/0.55         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_pos_nonneg
% 0.29/0.55  thf(fact_2594_add__pos__nonneg,axiom,
% 0.29/0.55      ! [A: nat,B: nat] :
% 0.29/0.55        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.29/0.55       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.29/0.55         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_pos_nonneg
% 0.29/0.55  thf(fact_2595_add__pos__nonneg,axiom,
% 0.29/0.55      ! [A: int,B: int] :
% 0.29/0.55        ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.55       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.29/0.55         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_pos_nonneg
% 0.29/0.55  thf(fact_2596_add__strict__increasing,axiom,
% 0.29/0.55      ! [A: real,B: real,C: real] :
% 0.29/0.55        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.55       => ( ( ord_less_eq_real @ B @ C )
% 0.29/0.55         => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_strict_increasing
% 0.29/0.55  thf(fact_2597_add__strict__increasing,axiom,
% 0.29/0.55      ! [A: rat,B: rat,C: rat] :
% 0.29/0.56        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.56       => ( ( ord_less_eq_rat @ B @ C )
% 0.29/0.56         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_strict_increasing
% 0.29/0.56  thf(fact_2598_add__strict__increasing,axiom,
% 0.29/0.56      ! [A: nat,B: nat,C: nat] :
% 0.29/0.56        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.29/0.56       => ( ( ord_less_eq_nat @ B @ C )
% 0.29/0.56         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_strict_increasing
% 0.29/0.56  thf(fact_2599_add__strict__increasing,axiom,
% 0.29/0.56      ! [A: int,B: int,C: int] :
% 0.29/0.56        ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.56       => ( ( ord_less_eq_int @ B @ C )
% 0.29/0.56         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_strict_increasing
% 0.29/0.56  thf(fact_2600_add__strict__increasing2,axiom,
% 0.29/0.56      ! [A: real,B: real,C: real] :
% 0.29/0.56        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.56       => ( ( ord_less_real @ B @ C )
% 0.29/0.56         => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_strict_increasing2
% 0.29/0.56  thf(fact_2601_add__strict__increasing2,axiom,
% 0.29/0.56      ! [A: rat,B: rat,C: rat] :
% 0.29/0.56        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.56       => ( ( ord_less_rat @ B @ C )
% 0.29/0.56         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_strict_increasing2
% 0.29/0.56  thf(fact_2602_add__strict__increasing2,axiom,
% 0.29/0.56      ! [A: nat,B: nat,C: nat] :
% 0.29/0.56        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.56       => ( ( ord_less_nat @ B @ C )
% 0.29/0.56         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_strict_increasing2
% 0.29/0.56  thf(fact_2603_add__strict__increasing2,axiom,
% 0.29/0.56      ! [A: int,B: int,C: int] :
% 0.29/0.56        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.56       => ( ( ord_less_int @ B @ C )
% 0.29/0.56         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_strict_increasing2
% 0.29/0.56  thf(fact_2604_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I3_J,axiom,
% 0.29/0.56      ! [A: $o,B: $o,Va: nat] :
% 0.29/0.56        ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 0.29/0.56        = one_one_nat ) ).
% 0.29/0.56  
% 0.29/0.56  % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.simps(3)
% 0.29/0.56  thf(fact_2605_mult__left__le__one__le,axiom,
% 0.29/0.56      ! [X: rat,Y2: rat] :
% 0.29/0.56        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.29/0.56       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 0.29/0.56         => ( ( ord_less_eq_rat @ Y2 @ one_one_rat )
% 0.29/0.56           => ( ord_less_eq_rat @ ( times_times_rat @ Y2 @ X ) @ X ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % mult_left_le_one_le
% 0.29/0.56  thf(fact_2606_mult__left__le__one__le,axiom,
% 0.29/0.56      ! [X: real,Y2: real] :
% 0.29/0.56        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.29/0.56       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 0.29/0.56         => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 0.29/0.56           => ( ord_less_eq_real @ ( times_times_real @ Y2 @ X ) @ X ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % mult_left_le_one_le
% 0.29/0.56  thf(fact_2607_mult__left__le__one__le,axiom,
% 0.29/0.56      ! [X: int,Y2: int] :
% 0.29/0.56        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.29/0.56       => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 0.29/0.56         => ( ( ord_less_eq_int @ Y2 @ one_one_int )
% 0.29/0.56           => ( ord_less_eq_int @ ( times_times_int @ Y2 @ X ) @ X ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % mult_left_le_one_le
% 0.29/0.56  thf(fact_2608_mult__right__le__one__le,axiom,
% 0.29/0.56      ! [X: rat,Y2: rat] :
% 0.29/0.56        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.29/0.56       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 0.29/0.56         => ( ( ord_less_eq_rat @ Y2 @ one_one_rat )
% 0.29/0.56           => ( ord_less_eq_rat @ ( times_times_rat @ X @ Y2 ) @ X ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % mult_right_le_one_le
% 0.29/0.56  thf(fact_2609_mult__right__le__one__le,axiom,
% 0.29/0.56      ! [X: real,Y2: real] :
% 0.29/0.56        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.29/0.56       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 0.29/0.56         => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 0.29/0.56           => ( ord_less_eq_real @ ( times_times_real @ X @ Y2 ) @ X ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % mult_right_le_one_le
% 0.29/0.56  thf(fact_2610_mult__right__le__one__le,axiom,
% 0.29/0.56      ! [X: int,Y2: int] :
% 0.29/0.56        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.29/0.56       => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 0.29/0.56         => ( ( ord_less_eq_int @ Y2 @ one_one_int )
% 0.29/0.56           => ( ord_less_eq_int @ ( times_times_int @ X @ Y2 ) @ X ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % mult_right_le_one_le
% 0.29/0.56  thf(fact_2611_mult__le__one,axiom,
% 0.29/0.56      ! [A: rat,B: rat] :
% 0.29/0.56        ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.29/0.56       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.29/0.56         => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 0.29/0.56           => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % mult_le_one
% 0.29/0.56  thf(fact_2612_mult__le__one,axiom,
% 0.29/0.56      ! [A: real,B: real] :
% 0.29/0.56        ( ( ord_less_eq_real @ A @ one_one_real )
% 0.29/0.56       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.29/0.56         => ( ( ord_less_eq_real @ B @ one_one_real )
% 0.29/0.56           => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ one_one_real ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % mult_le_one
% 0.29/0.56  thf(fact_2613_mult__le__one,axiom,
% 0.29/0.56      ! [A: nat,B: nat] :
% 0.29/0.56        ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.29/0.56       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.29/0.56         => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 0.29/0.56           => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % mult_le_one
% 0.29/0.56  thf(fact_2614_mult__le__one,axiom,
% 0.29/0.56      ! [A: int,B: int] :
% 0.29/0.56        ( ( ord_less_eq_int @ A @ one_one_int )
% 0.29/0.56       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.29/0.56         => ( ( ord_less_eq_int @ B @ one_one_int )
% 0.29/0.56           => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % mult_le_one
% 0.29/0.56  thf(fact_2615_mult__left__le,axiom,
% 0.29/0.56      ! [C: rat,A: rat] :
% 0.29/0.56        ( ( ord_less_eq_rat @ C @ one_one_rat )
% 0.29/0.56       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.56         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ A ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % mult_left_le
% 0.29/0.56  thf(fact_2616_mult__left__le,axiom,
% 0.29/0.56      ! [C: real,A: real] :
% 0.29/0.56        ( ( ord_less_eq_real @ C @ one_one_real )
% 0.29/0.56       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.56         => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ A ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % mult_left_le
% 0.29/0.56  thf(fact_2617_mult__left__le,axiom,
% 0.29/0.56      ! [C: nat,A: nat] :
% 0.29/0.56        ( ( ord_less_eq_nat @ C @ one_one_nat )
% 0.29/0.56       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.56         => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % mult_left_le
% 0.29/0.56  thf(fact_2618_mult__left__le,axiom,
% 0.29/0.56      ! [C: int,A: int] :
% 0.29/0.56        ( ( ord_less_eq_int @ C @ one_one_int )
% 0.29/0.56       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.56         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % mult_left_le
% 0.29/0.56  thf(fact_2619_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 0.29/0.56      ! [A: nat,B: nat] :
% 0.29/0.56        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.56       => ( ( ord_less_nat @ A @ B )
% 0.29/0.56         => ( ( divide_divide_nat @ A @ B )
% 0.29/0.56            = zero_zero_nat ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % unique_euclidean_semiring_numeral_class.div_less
% 0.29/0.56  thf(fact_2620_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 0.29/0.56      ! [A: int,B: int] :
% 0.29/0.56        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.56       => ( ( ord_less_int @ A @ B )
% 0.29/0.56         => ( ( divide_divide_int @ A @ B )
% 0.29/0.56            = zero_zero_int ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % unique_euclidean_semiring_numeral_class.div_less
% 0.29/0.56  thf(fact_2621_div__positive,axiom,
% 0.29/0.56      ! [B: nat,A: nat] :
% 0.29/0.56        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.29/0.56       => ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.56         => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % div_positive
% 0.29/0.56  thf(fact_2622_div__positive,axiom,
% 0.29/0.56      ! [B: int,A: int] :
% 0.29/0.56        ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.56       => ( ( ord_less_eq_int @ B @ A )
% 0.29/0.56         => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % div_positive
% 0.29/0.56  thf(fact_2623_frac__le,axiom,
% 0.29/0.56      ! [Y2: real,X: real,W: real,Z: real] :
% 0.29/0.56        ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 0.29/0.56       => ( ( ord_less_eq_real @ X @ Y2 )
% 0.29/0.56         => ( ( ord_less_real @ zero_zero_real @ W )
% 0.29/0.56           => ( ( ord_less_eq_real @ W @ Z )
% 0.29/0.56             => ( ord_less_eq_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y2 @ W ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % frac_le
% 0.29/0.56  thf(fact_2624_frac__le,axiom,
% 0.29/0.56      ! [Y2: rat,X: rat,W: rat,Z: rat] :
% 0.29/0.56        ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 0.29/0.56       => ( ( ord_less_eq_rat @ X @ Y2 )
% 0.29/0.56         => ( ( ord_less_rat @ zero_zero_rat @ W )
% 0.29/0.56           => ( ( ord_less_eq_rat @ W @ Z )
% 0.29/0.56             => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Z ) @ ( divide_divide_rat @ Y2 @ W ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % frac_le
% 0.29/0.56  thf(fact_2625_frac__less,axiom,
% 0.29/0.56      ! [X: real,Y2: real,W: real,Z: real] :
% 0.29/0.56        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.29/0.56       => ( ( ord_less_real @ X @ Y2 )
% 0.29/0.56         => ( ( ord_less_real @ zero_zero_real @ W )
% 0.29/0.56           => ( ( ord_less_eq_real @ W @ Z )
% 0.29/0.56             => ( ord_less_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y2 @ W ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % frac_less
% 0.29/0.56  thf(fact_2626_frac__less,axiom,
% 0.29/0.56      ! [X: rat,Y2: rat,W: rat,Z: rat] :
% 0.29/0.56        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.29/0.56       => ( ( ord_less_rat @ X @ Y2 )
% 0.29/0.56         => ( ( ord_less_rat @ zero_zero_rat @ W )
% 0.29/0.56           => ( ( ord_less_eq_rat @ W @ Z )
% 0.29/0.56             => ( ord_less_rat @ ( divide_divide_rat @ X @ Z ) @ ( divide_divide_rat @ Y2 @ W ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % frac_less
% 0.29/0.56  thf(fact_2627_frac__less2,axiom,
% 0.29/0.56      ! [X: real,Y2: real,W: real,Z: real] :
% 0.29/0.56        ( ( ord_less_real @ zero_zero_real @ X )
% 0.29/0.56       => ( ( ord_less_eq_real @ X @ Y2 )
% 0.29/0.56         => ( ( ord_less_real @ zero_zero_real @ W )
% 0.29/0.56           => ( ( ord_less_real @ W @ Z )
% 0.29/0.56             => ( ord_less_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y2 @ W ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % frac_less2
% 0.29/0.56  thf(fact_2628_frac__less2,axiom,
% 0.29/0.56      ! [X: rat,Y2: rat,W: rat,Z: rat] :
% 0.29/0.56        ( ( ord_less_rat @ zero_zero_rat @ X )
% 0.29/0.56       => ( ( ord_less_eq_rat @ X @ Y2 )
% 0.29/0.56         => ( ( ord_less_rat @ zero_zero_rat @ W )
% 0.29/0.56           => ( ( ord_less_rat @ W @ Z )
% 0.29/0.56             => ( ord_less_rat @ ( divide_divide_rat @ X @ Z ) @ ( divide_divide_rat @ Y2 @ W ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % frac_less2
% 0.29/0.56  thf(fact_2629_divide__le__cancel,axiom,
% 0.29/0.56      ! [A: real,C: real,B: real] :
% 0.29/0.56        ( ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 0.29/0.56        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.56           => ( ord_less_eq_real @ A @ B ) )
% 0.29/0.56          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.56           => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % divide_le_cancel
% 0.29/0.56  thf(fact_2630_divide__le__cancel,axiom,
% 0.29/0.56      ! [A: rat,C: rat,B: rat] :
% 0.29/0.56        ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 0.29/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.56           => ( ord_less_eq_rat @ A @ B ) )
% 0.29/0.56          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.56           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % divide_le_cancel
% 0.29/0.56  thf(fact_2631_divide__nonneg__neg,axiom,
% 0.29/0.56      ! [X: real,Y2: real] :
% 0.29/0.56        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.29/0.56       => ( ( ord_less_real @ Y2 @ zero_zero_real )
% 0.29/0.56         => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y2 ) @ zero_zero_real ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % divide_nonneg_neg
% 0.29/0.56  thf(fact_2632_divide__nonneg__neg,axiom,
% 0.29/0.56      ! [X: rat,Y2: rat] :
% 0.29/0.56        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.29/0.56       => ( ( ord_less_rat @ Y2 @ zero_zero_rat )
% 0.29/0.56         => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y2 ) @ zero_zero_rat ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % divide_nonneg_neg
% 0.29/0.56  thf(fact_2633_divide__nonneg__pos,axiom,
% 0.29/0.56      ! [X: real,Y2: real] :
% 0.29/0.56        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.29/0.56       => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 0.29/0.56         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y2 ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % divide_nonneg_pos
% 0.29/0.56  thf(fact_2634_divide__nonneg__pos,axiom,
% 0.29/0.56      ! [X: rat,Y2: rat] :
% 0.29/0.56        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.29/0.56       => ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 0.29/0.56         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y2 ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % divide_nonneg_pos
% 0.29/0.56  thf(fact_2635_divide__nonpos__neg,axiom,
% 0.29/0.56      ! [X: real,Y2: real] :
% 0.29/0.56        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.29/0.56       => ( ( ord_less_real @ Y2 @ zero_zero_real )
% 0.29/0.56         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y2 ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % divide_nonpos_neg
% 0.29/0.56  thf(fact_2636_divide__nonpos__neg,axiom,
% 0.29/0.56      ! [X: rat,Y2: rat] :
% 0.29/0.56        ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 0.29/0.56       => ( ( ord_less_rat @ Y2 @ zero_zero_rat )
% 0.29/0.56         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y2 ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % divide_nonpos_neg
% 0.29/0.56  thf(fact_2637_divide__nonpos__pos,axiom,
% 0.29/0.56      ! [X: real,Y2: real] :
% 0.29/0.56        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.29/0.56       => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 0.29/0.56         => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y2 ) @ zero_zero_real ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % divide_nonpos_pos
% 0.29/0.56  thf(fact_2638_divide__nonpos__pos,axiom,
% 0.29/0.56      ! [X: rat,Y2: rat] :
% 0.29/0.56        ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 0.29/0.56       => ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 0.29/0.56         => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y2 ) @ zero_zero_rat ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % divide_nonpos_pos
% 0.29/0.56  thf(fact_2639_sum__squares__le__zero__iff,axiom,
% 0.29/0.56      ! [X: rat,Y2: rat] :
% 0.29/0.56        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y2 @ Y2 ) ) @ zero_zero_rat )
% 0.29/0.56        = ( ( X = zero_zero_rat )
% 0.29/0.56          & ( Y2 = zero_zero_rat ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % sum_squares_le_zero_iff
% 0.29/0.56  thf(fact_2640_sum__squares__le__zero__iff,axiom,
% 0.29/0.56      ! [X: real,Y2: real] :
% 0.29/0.56        ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y2 @ Y2 ) ) @ zero_zero_real )
% 0.29/0.56        = ( ( X = zero_zero_real )
% 0.29/0.56          & ( Y2 = zero_zero_real ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % sum_squares_le_zero_iff
% 0.29/0.56  thf(fact_2641_sum__squares__le__zero__iff,axiom,
% 0.29/0.56      ! [X: int,Y2: int] :
% 0.29/0.56        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y2 @ Y2 ) ) @ zero_zero_int )
% 0.29/0.56        = ( ( X = zero_zero_int )
% 0.29/0.56          & ( Y2 = zero_zero_int ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % sum_squares_le_zero_iff
% 0.29/0.56  thf(fact_2642_sum__squares__ge__zero,axiom,
% 0.29/0.56      ! [X: rat,Y2: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y2 @ Y2 ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % sum_squares_ge_zero
% 0.29/0.56  thf(fact_2643_sum__squares__ge__zero,axiom,
% 0.29/0.56      ! [X: real,Y2: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y2 @ Y2 ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % sum_squares_ge_zero
% 0.29/0.56  thf(fact_2644_sum__squares__ge__zero,axiom,
% 0.29/0.56      ! [X: int,Y2: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y2 @ Y2 ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % sum_squares_ge_zero
% 0.29/0.56  thf(fact_2645_sum__squares__gt__zero__iff,axiom,
% 0.29/0.56      ! [X: real,Y2: real] :
% 0.29/0.56        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y2 @ Y2 ) ) )
% 0.29/0.56        = ( ( X != zero_zero_real )
% 0.29/0.56          | ( Y2 != zero_zero_real ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % sum_squares_gt_zero_iff
% 0.29/0.56  thf(fact_2646_sum__squares__gt__zero__iff,axiom,
% 0.29/0.56      ! [X: rat,Y2: rat] :
% 0.29/0.56        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y2 @ Y2 ) ) )
% 0.29/0.56        = ( ( X != zero_zero_rat )
% 0.29/0.56          | ( Y2 != zero_zero_rat ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % sum_squares_gt_zero_iff
% 0.29/0.56  thf(fact_2647_sum__squares__gt__zero__iff,axiom,
% 0.29/0.56      ! [X: int,Y2: int] :
% 0.29/0.56        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y2 @ Y2 ) ) )
% 0.29/0.56        = ( ( X != zero_zero_int )
% 0.29/0.56          | ( Y2 != zero_zero_int ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % sum_squares_gt_zero_iff
% 0.29/0.56  thf(fact_2648_not__sum__squares__lt__zero,axiom,
% 0.29/0.56      ! [X: real,Y2: real] :
% 0.29/0.56        ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y2 @ Y2 ) ) @ zero_zero_real ) ).
% 0.29/0.56  
% 0.29/0.56  % not_sum_squares_lt_zero
% 0.29/0.56  thf(fact_2649_not__sum__squares__lt__zero,axiom,
% 0.29/0.56      ! [X: rat,Y2: rat] :
% 0.29/0.56        ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y2 @ Y2 ) ) @ zero_zero_rat ) ).
% 0.29/0.56  
% 0.29/0.56  % not_sum_squares_lt_zero
% 0.29/0.56  thf(fact_2650_not__sum__squares__lt__zero,axiom,
% 0.29/0.56      ! [X: int,Y2: int] :
% 0.29/0.56        ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y2 @ Y2 ) ) @ zero_zero_int ) ).
% 0.29/0.56  
% 0.29/0.56  % not_sum_squares_lt_zero
% 0.29/0.56  thf(fact_2651_zero__less__two,axiom,
% 0.29/0.56      ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 0.29/0.56  
% 0.29/0.56  % zero_less_two
% 0.29/0.56  thf(fact_2652_zero__less__two,axiom,
% 0.29/0.56      ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 0.29/0.56  
% 0.29/0.56  % zero_less_two
% 0.29/0.56  thf(fact_2653_zero__less__two,axiom,
% 0.29/0.56      ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 0.29/0.56  
% 0.29/0.56  % zero_less_two
% 0.29/0.56  thf(fact_2654_zero__less__two,axiom,
% 0.29/0.56      ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 0.29/0.56  
% 0.29/0.56  % zero_less_two
% 0.29/0.56  thf(fact_2655_power__less__imp__less__base,axiom,
% 0.29/0.56      ! [A: real,N: nat,B: real] :
% 0.29/0.56        ( ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 0.29/0.56       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.29/0.56         => ( ord_less_real @ A @ B ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % power_less_imp_less_base
% 0.29/0.56  thf(fact_2656_power__less__imp__less__base,axiom,
% 0.29/0.56      ! [A: rat,N: nat,B: rat] :
% 0.29/0.56        ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 0.29/0.56       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.29/0.56         => ( ord_less_rat @ A @ B ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % power_less_imp_less_base
% 0.29/0.56  thf(fact_2657_power__less__imp__less__base,axiom,
% 0.29/0.56      ! [A: nat,N: nat,B: nat] :
% 0.29/0.56        ( ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 0.29/0.56       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.29/0.56         => ( ord_less_nat @ A @ B ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % power_less_imp_less_base
% 0.29/0.56  thf(fact_2658_power__less__imp__less__base,axiom,
% 0.29/0.56      ! [A: int,N: nat,B: int] :
% 0.29/0.56        ( ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 0.29/0.56       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.29/0.56         => ( ord_less_int @ A @ B ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % power_less_imp_less_base
% 0.29/0.56  thf(fact_2659_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I2_J,axiom,
% 0.29/0.56      ! [Uv: $o,Uw: $o,N: nat] :
% 0.29/0.56        ( ( vEBT_T_s_u_c_c @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N ) )
% 0.29/0.56        = one_one_nat ) ).
% 0.29/0.56  
% 0.29/0.56  % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.simps(2)
% 0.29/0.56  thf(fact_2660_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I2_J,axiom,
% 0.29/0.56      ! [Uv: $o,Uw: $o,N: nat] :
% 0.29/0.56        ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N ) )
% 0.29/0.56        = one_one_nat ) ).
% 0.29/0.56  
% 0.29/0.56  % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.simps(2)
% 0.29/0.56  thf(fact_2661_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 0.29/0.56      ! [C: nat,A: nat,B: nat] :
% 0.29/0.56        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.29/0.56       => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.29/0.56          = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 0.29/0.56  thf(fact_2662_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 0.29/0.56      ! [C: int,A: int,B: int] :
% 0.29/0.56        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.56       => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 0.29/0.56          = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 0.29/0.56  thf(fact_2663_divide__less__eq,axiom,
% 0.29/0.56      ! [B: real,C: real,A: real] :
% 0.29/0.56        ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 0.29/0.56        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.56           => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 0.29/0.56          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.56           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.56               => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 0.29/0.56              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.56               => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % divide_less_eq
% 0.29/0.56  thf(fact_2664_divide__less__eq,axiom,
% 0.29/0.56      ! [B: rat,C: rat,A: rat] :
% 0.29/0.56        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.29/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.56           => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 0.29/0.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.56               => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 0.29/0.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.56               => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % divide_less_eq
% 0.29/0.56  thf(fact_2665_less__divide__eq,axiom,
% 0.29/0.56      ! [A: real,B: real,C: real] :
% 0.29/0.56        ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 0.29/0.56        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.56           => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 0.29/0.56          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.56           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.56               => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 0.29/0.56              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.56               => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % less_divide_eq
% 0.29/0.56  thf(fact_2666_less__divide__eq,axiom,
% 0.29/0.56      ! [A: rat,B: rat,C: rat] :
% 0.29/0.56        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.29/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.56           => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 0.29/0.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.56               => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 0.29/0.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.56               => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % less_divide_eq
% 0.29/0.56  thf(fact_2667_neg__divide__less__eq,axiom,
% 0.29/0.56      ! [C: real,B: real,A: real] :
% 0.29/0.56        ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.56       => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 0.29/0.56          = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % neg_divide_less_eq
% 0.29/0.56  thf(fact_2668_neg__divide__less__eq,axiom,
% 0.29/0.56      ! [C: rat,B: rat,A: rat] :
% 0.29/0.56        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.56       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.29/0.56          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % neg_divide_less_eq
% 0.29/0.56  thf(fact_2669_neg__less__divide__eq,axiom,
% 0.29/0.56      ! [C: real,A: real,B: real] :
% 0.29/0.56        ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.56       => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 0.29/0.56          = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % neg_less_divide_eq
% 0.29/0.56  thf(fact_2670_neg__less__divide__eq,axiom,
% 0.29/0.56      ! [C: rat,A: rat,B: rat] :
% 0.29/0.56        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.56       => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.29/0.56          = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % neg_less_divide_eq
% 0.29/0.56  thf(fact_2671_pos__divide__less__eq,axiom,
% 0.29/0.56      ! [C: real,B: real,A: real] :
% 0.29/0.56        ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.56       => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 0.29/0.56          = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pos_divide_less_eq
% 0.29/0.56  thf(fact_2672_pos__divide__less__eq,axiom,
% 0.29/0.56      ! [C: rat,B: rat,A: rat] :
% 0.29/0.56        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.56       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.29/0.56          = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pos_divide_less_eq
% 0.29/0.56  thf(fact_2673_pos__less__divide__eq,axiom,
% 0.29/0.56      ! [C: real,A: real,B: real] :
% 0.29/0.56        ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.56       => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 0.29/0.56          = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pos_less_divide_eq
% 0.29/0.56  thf(fact_2674_pos__less__divide__eq,axiom,
% 0.29/0.56      ! [C: rat,A: rat,B: rat] :
% 0.29/0.56        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.56       => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.29/0.56          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pos_less_divide_eq
% 0.29/0.56  thf(fact_2675_mult__imp__div__pos__less,axiom,
% 0.29/0.56      ! [Y2: real,X: real,Z: real] :
% 0.29/0.56        ( ( ord_less_real @ zero_zero_real @ Y2 )
% 0.29/0.56       => ( ( ord_less_real @ X @ ( times_times_real @ Z @ Y2 ) )
% 0.29/0.56         => ( ord_less_real @ ( divide_divide_real @ X @ Y2 ) @ Z ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % mult_imp_div_pos_less
% 0.29/0.56  thf(fact_2676_mult__imp__div__pos__less,axiom,
% 0.29/0.56      ! [Y2: rat,X: rat,Z: rat] :
% 0.29/0.56        ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 0.29/0.56       => ( ( ord_less_rat @ X @ ( times_times_rat @ Z @ Y2 ) )
% 0.29/0.56         => ( ord_less_rat @ ( divide_divide_rat @ X @ Y2 ) @ Z ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % mult_imp_div_pos_less
% 0.29/0.56  thf(fact_2677_mult__imp__less__div__pos,axiom,
% 0.29/0.56      ! [Y2: real,Z: real,X: real] :
% 0.29/0.56        ( ( ord_less_real @ zero_zero_real @ Y2 )
% 0.29/0.56       => ( ( ord_less_real @ ( times_times_real @ Z @ Y2 ) @ X )
% 0.29/0.56         => ( ord_less_real @ Z @ ( divide_divide_real @ X @ Y2 ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % mult_imp_less_div_pos
% 0.29/0.56  thf(fact_2678_mult__imp__less__div__pos,axiom,
% 0.29/0.56      ! [Y2: rat,Z: rat,X: rat] :
% 0.29/0.56        ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 0.29/0.56       => ( ( ord_less_rat @ ( times_times_rat @ Z @ Y2 ) @ X )
% 0.29/0.56         => ( ord_less_rat @ Z @ ( divide_divide_rat @ X @ Y2 ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % mult_imp_less_div_pos
% 0.29/0.56  thf(fact_2679_divide__strict__left__mono,axiom,
% 0.29/0.56      ! [B: real,A: real,C: real] :
% 0.29/0.56        ( ( ord_less_real @ B @ A )
% 0.29/0.56       => ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.56         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.29/0.56           => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % divide_strict_left_mono
% 0.29/0.56  thf(fact_2680_divide__strict__left__mono,axiom,
% 0.29/0.56      ! [B: rat,A: rat,C: rat] :
% 0.29/0.56        ( ( ord_less_rat @ B @ A )
% 0.29/0.56       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.56         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.29/0.56           => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % divide_strict_left_mono
% 0.29/0.56  thf(fact_2681_divide__strict__left__mono__neg,axiom,
% 0.29/0.56      ! [A: real,B: real,C: real] :
% 0.29/0.56        ( ( ord_less_real @ A @ B )
% 0.29/0.56       => ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.56         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.29/0.56           => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % divide_strict_left_mono_neg
% 0.29/0.56  thf(fact_2682_divide__strict__left__mono__neg,axiom,
% 0.29/0.56      ! [A: rat,B: rat,C: rat] :
% 0.29/0.56        ( ( ord_less_rat @ A @ B )
% 0.29/0.56       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.56         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.29/0.56           => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % divide_strict_left_mono_neg
% 0.29/0.56  thf(fact_2683_divide__less__eq__1,axiom,
% 0.29/0.56      ! [B: real,A: real] :
% 0.29/0.56        ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 0.29/0.56        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.56            & ( ord_less_real @ B @ A ) )
% 0.29/0.56          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.29/0.56            & ( ord_less_real @ A @ B ) )
% 0.29/0.56          | ( A = zero_zero_real ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % divide_less_eq_1
% 0.29/0.56  thf(fact_2684_divide__less__eq__1,axiom,
% 0.29/0.56      ! [B: rat,A: rat] :
% 0.29/0.56        ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.29/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.56            & ( ord_less_rat @ B @ A ) )
% 0.29/0.56          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.56            & ( ord_less_rat @ A @ B ) )
% 0.29/0.56          | ( A = zero_zero_rat ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % divide_less_eq_1
% 0.29/0.56  thf(fact_2685_less__divide__eq__1,axiom,
% 0.29/0.56      ! [B: real,A: real] :
% 0.29/0.56        ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 0.29/0.56        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.56            & ( ord_less_real @ A @ B ) )
% 0.29/0.56          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.29/0.56            & ( ord_less_real @ B @ A ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % less_divide_eq_1
% 0.29/0.56  thf(fact_2686_less__divide__eq__1,axiom,
% 0.29/0.56      ! [B: rat,A: rat] :
% 0.29/0.56        ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.29/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.56            & ( ord_less_rat @ A @ B ) )
% 0.29/0.56          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.56            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % less_divide_eq_1
% 0.29/0.56  thf(fact_2687_power__le__one,axiom,
% 0.29/0.56      ! [A: rat,N: nat] :
% 0.29/0.56        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.56       => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.29/0.56         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ one_one_rat ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % power_le_one
% 0.29/0.56  thf(fact_2688_power__le__one,axiom,
% 0.29/0.56      ! [A: real,N: nat] :
% 0.29/0.56        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.56       => ( ( ord_less_eq_real @ A @ one_one_real )
% 0.29/0.56         => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ one_one_real ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % power_le_one
% 0.29/0.56  thf(fact_2689_power__le__one,axiom,
% 0.29/0.56      ! [A: nat,N: nat] :
% 0.29/0.56        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.56       => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.29/0.56         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ one_one_nat ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % power_le_one
% 0.29/0.56  thf(fact_2690_power__le__one,axiom,
% 0.29/0.56      ! [A: int,N: nat] :
% 0.29/0.56        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.56       => ( ( ord_less_eq_int @ A @ one_one_int )
% 0.29/0.56         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ one_one_int ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % power_le_one
% 0.29/0.56  thf(fact_2691_divide__eq__eq__numeral_I1_J,axiom,
% 0.29/0.56      ! [B: complex,C: complex,W: num] :
% 0.29/0.56        ( ( ( divide1717551699836669952omplex @ B @ C )
% 0.29/0.56          = ( numera6690914467698888265omplex @ W ) )
% 0.29/0.56        = ( ( ( C != zero_zero_complex )
% 0.29/0.56           => ( B
% 0.29/0.56              = ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C ) ) )
% 0.29/0.56          & ( ( C = zero_zero_complex )
% 0.29/0.56           => ( ( numera6690914467698888265omplex @ W )
% 0.29/0.56              = zero_zero_complex ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % divide_eq_eq_numeral(1)
% 0.29/0.56  thf(fact_2692_divide__eq__eq__numeral_I1_J,axiom,
% 0.29/0.56      ! [B: real,C: real,W: num] :
% 0.29/0.56        ( ( ( divide_divide_real @ B @ C )
% 0.29/0.56          = ( numeral_numeral_real @ W ) )
% 0.29/0.56        = ( ( ( C != zero_zero_real )
% 0.29/0.56           => ( B
% 0.29/0.56              = ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 0.29/0.56          & ( ( C = zero_zero_real )
% 0.29/0.56           => ( ( numeral_numeral_real @ W )
% 0.29/0.56              = zero_zero_real ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % divide_eq_eq_numeral(1)
% 0.29/0.56  thf(fact_2693_divide__eq__eq__numeral_I1_J,axiom,
% 0.29/0.56      ! [B: rat,C: rat,W: num] :
% 0.29/0.56        ( ( ( divide_divide_rat @ B @ C )
% 0.29/0.56          = ( numeral_numeral_rat @ W ) )
% 0.29/0.56        = ( ( ( C != zero_zero_rat )
% 0.29/0.56           => ( B
% 0.29/0.56              = ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 0.29/0.56          & ( ( C = zero_zero_rat )
% 0.29/0.56           => ( ( numeral_numeral_rat @ W )
% 0.29/0.56              = zero_zero_rat ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % divide_eq_eq_numeral(1)
% 0.29/0.56  thf(fact_2694_eq__divide__eq__numeral_I1_J,axiom,
% 0.29/0.56      ! [W: num,B: complex,C: complex] :
% 0.29/0.56        ( ( ( numera6690914467698888265omplex @ W )
% 0.29/0.56          = ( divide1717551699836669952omplex @ B @ C ) )
% 0.29/0.56        = ( ( ( C != zero_zero_complex )
% 0.29/0.56           => ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C )
% 0.29/0.56              = B ) )
% 0.29/0.56          & ( ( C = zero_zero_complex )
% 0.29/0.56           => ( ( numera6690914467698888265omplex @ W )
% 0.29/0.56              = zero_zero_complex ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % eq_divide_eq_numeral(1)
% 0.29/0.56  thf(fact_2695_eq__divide__eq__numeral_I1_J,axiom,
% 0.29/0.56      ! [W: num,B: real,C: real] :
% 0.29/0.56        ( ( ( numeral_numeral_real @ W )
% 0.29/0.56          = ( divide_divide_real @ B @ C ) )
% 0.29/0.56        = ( ( ( C != zero_zero_real )
% 0.29/0.56           => ( ( times_times_real @ ( numeral_numeral_real @ W ) @ C )
% 0.29/0.56              = B ) )
% 0.29/0.56          & ( ( C = zero_zero_real )
% 0.29/0.56           => ( ( numeral_numeral_real @ W )
% 0.29/0.56              = zero_zero_real ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % eq_divide_eq_numeral(1)
% 0.29/0.56  thf(fact_2696_eq__divide__eq__numeral_I1_J,axiom,
% 0.29/0.56      ! [W: num,B: rat,C: rat] :
% 0.29/0.56        ( ( ( numeral_numeral_rat @ W )
% 0.29/0.56          = ( divide_divide_rat @ B @ C ) )
% 0.29/0.56        = ( ( ( C != zero_zero_rat )
% 0.29/0.56           => ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C )
% 0.29/0.56              = B ) )
% 0.29/0.56          & ( ( C = zero_zero_rat )
% 0.29/0.56           => ( ( numeral_numeral_rat @ W )
% 0.29/0.56              = zero_zero_rat ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % eq_divide_eq_numeral(1)
% 0.29/0.56  thf(fact_2697_add__divide__eq__if__simps_I2_J,axiom,
% 0.29/0.56      ! [Z: complex,A: complex,B: complex] :
% 0.29/0.56        ( ( ( Z = zero_zero_complex )
% 0.29/0.56         => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 0.29/0.56            = B ) )
% 0.29/0.56        & ( ( Z != zero_zero_complex )
% 0.29/0.56         => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 0.29/0.56            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_divide_eq_if_simps(2)
% 0.29/0.56  thf(fact_2698_add__divide__eq__if__simps_I2_J,axiom,
% 0.29/0.56      ! [Z: real,A: real,B: real] :
% 0.29/0.56        ( ( ( Z = zero_zero_real )
% 0.29/0.56         => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 0.29/0.56            = B ) )
% 0.29/0.56        & ( ( Z != zero_zero_real )
% 0.29/0.56         => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 0.29/0.56            = ( divide_divide_real @ ( plus_plus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_divide_eq_if_simps(2)
% 0.29/0.56  thf(fact_2699_add__divide__eq__if__simps_I2_J,axiom,
% 0.29/0.56      ! [Z: rat,A: rat,B: rat] :
% 0.29/0.56        ( ( ( Z = zero_zero_rat )
% 0.29/0.56         => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 0.29/0.56            = B ) )
% 0.29/0.56        & ( ( Z != zero_zero_rat )
% 0.29/0.56         => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 0.29/0.56            = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_divide_eq_if_simps(2)
% 0.29/0.56  thf(fact_2700_add__divide__eq__if__simps_I1_J,axiom,
% 0.29/0.56      ! [Z: complex,A: complex,B: complex] :
% 0.29/0.56        ( ( ( Z = zero_zero_complex )
% 0.29/0.56         => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 0.29/0.56            = A ) )
% 0.29/0.56        & ( ( Z != zero_zero_complex )
% 0.29/0.56         => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 0.29/0.56            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_divide_eq_if_simps(1)
% 0.29/0.56  thf(fact_2701_add__divide__eq__if__simps_I1_J,axiom,
% 0.29/0.56      ! [Z: real,A: real,B: real] :
% 0.29/0.56        ( ( ( Z = zero_zero_real )
% 0.29/0.56         => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 0.29/0.56            = A ) )
% 0.29/0.56        & ( ( Z != zero_zero_real )
% 0.29/0.56         => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 0.29/0.56            = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_divide_eq_if_simps(1)
% 0.29/0.56  thf(fact_2702_add__divide__eq__if__simps_I1_J,axiom,
% 0.29/0.56      ! [Z: rat,A: rat,B: rat] :
% 0.29/0.56        ( ( ( Z = zero_zero_rat )
% 0.29/0.56         => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 0.29/0.56            = A ) )
% 0.29/0.56        & ( ( Z != zero_zero_rat )
% 0.29/0.56         => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 0.29/0.56            = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_divide_eq_if_simps(1)
% 0.29/0.56  thf(fact_2703_add__frac__eq,axiom,
% 0.29/0.56      ! [Y2: complex,Z: complex,X: complex,W: complex] :
% 0.29/0.56        ( ( Y2 != zero_zero_complex )
% 0.29/0.56       => ( ( Z != zero_zero_complex )
% 0.29/0.56         => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Y2 ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 0.29/0.56            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X @ Z ) @ ( times_times_complex @ W @ Y2 ) ) @ ( times_times_complex @ Y2 @ Z ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_frac_eq
% 0.29/0.56  thf(fact_2704_add__frac__eq,axiom,
% 0.29/0.56      ! [Y2: real,Z: real,X: real,W: real] :
% 0.29/0.56        ( ( Y2 != zero_zero_real )
% 0.29/0.56       => ( ( Z != zero_zero_real )
% 0.29/0.56         => ( ( plus_plus_real @ ( divide_divide_real @ X @ Y2 ) @ ( divide_divide_real @ W @ Z ) )
% 0.29/0.56            = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y2 ) ) @ ( times_times_real @ Y2 @ Z ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_frac_eq
% 0.29/0.56  thf(fact_2705_add__frac__eq,axiom,
% 0.29/0.56      ! [Y2: rat,Z: rat,X: rat,W: rat] :
% 0.29/0.56        ( ( Y2 != zero_zero_rat )
% 0.29/0.56       => ( ( Z != zero_zero_rat )
% 0.29/0.56         => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y2 ) @ ( divide_divide_rat @ W @ Z ) )
% 0.29/0.56            = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y2 ) ) @ ( times_times_rat @ Y2 @ Z ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_frac_eq
% 0.29/0.56  thf(fact_2706_add__frac__num,axiom,
% 0.29/0.56      ! [Y2: complex,X: complex,Z: complex] :
% 0.29/0.56        ( ( Y2 != zero_zero_complex )
% 0.29/0.56       => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Y2 ) @ Z )
% 0.29/0.56          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Z @ Y2 ) ) @ Y2 ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_frac_num
% 0.29/0.56  thf(fact_2707_add__frac__num,axiom,
% 0.29/0.56      ! [Y2: real,X: real,Z: real] :
% 0.29/0.56        ( ( Y2 != zero_zero_real )
% 0.29/0.56       => ( ( plus_plus_real @ ( divide_divide_real @ X @ Y2 ) @ Z )
% 0.29/0.56          = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Z @ Y2 ) ) @ Y2 ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_frac_num
% 0.29/0.56  thf(fact_2708_add__frac__num,axiom,
% 0.29/0.56      ! [Y2: rat,X: rat,Z: rat] :
% 0.29/0.56        ( ( Y2 != zero_zero_rat )
% 0.29/0.56       => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y2 ) @ Z )
% 0.29/0.56          = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z @ Y2 ) ) @ Y2 ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_frac_num
% 0.29/0.56  thf(fact_2709_add__num__frac,axiom,
% 0.29/0.56      ! [Y2: complex,Z: complex,X: complex] :
% 0.29/0.56        ( ( Y2 != zero_zero_complex )
% 0.29/0.56       => ( ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ X @ Y2 ) )
% 0.29/0.56          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Z @ Y2 ) ) @ Y2 ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_num_frac
% 0.29/0.56  thf(fact_2710_add__num__frac,axiom,
% 0.29/0.56      ! [Y2: real,Z: real,X: real] :
% 0.29/0.56        ( ( Y2 != zero_zero_real )
% 0.29/0.56       => ( ( plus_plus_real @ Z @ ( divide_divide_real @ X @ Y2 ) )
% 0.29/0.56          = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Z @ Y2 ) ) @ Y2 ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_num_frac
% 0.29/0.56  thf(fact_2711_add__num__frac,axiom,
% 0.29/0.56      ! [Y2: rat,Z: rat,X: rat] :
% 0.29/0.56        ( ( Y2 != zero_zero_rat )
% 0.29/0.56       => ( ( plus_plus_rat @ Z @ ( divide_divide_rat @ X @ Y2 ) )
% 0.29/0.56          = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z @ Y2 ) ) @ Y2 ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_num_frac
% 0.29/0.56  thf(fact_2712_add__divide__eq__iff,axiom,
% 0.29/0.56      ! [Z: complex,X: complex,Y2: complex] :
% 0.29/0.56        ( ( Z != zero_zero_complex )
% 0.29/0.56       => ( ( plus_plus_complex @ X @ ( divide1717551699836669952omplex @ Y2 @ Z ) )
% 0.29/0.56          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X @ Z ) @ Y2 ) @ Z ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_divide_eq_iff
% 0.29/0.56  thf(fact_2713_add__divide__eq__iff,axiom,
% 0.29/0.56      ! [Z: real,X: real,Y2: real] :
% 0.29/0.56        ( ( Z != zero_zero_real )
% 0.29/0.56       => ( ( plus_plus_real @ X @ ( divide_divide_real @ Y2 @ Z ) )
% 0.29/0.56          = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X @ Z ) @ Y2 ) @ Z ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_divide_eq_iff
% 0.29/0.56  thf(fact_2714_add__divide__eq__iff,axiom,
% 0.29/0.56      ! [Z: rat,X: rat,Y2: rat] :
% 0.29/0.56        ( ( Z != zero_zero_rat )
% 0.29/0.56       => ( ( plus_plus_rat @ X @ ( divide_divide_rat @ Y2 @ Z ) )
% 0.29/0.56          = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z ) @ Y2 ) @ Z ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_divide_eq_iff
% 0.29/0.56  thf(fact_2715_divide__add__eq__iff,axiom,
% 0.29/0.56      ! [Z: complex,X: complex,Y2: complex] :
% 0.29/0.56        ( ( Z != zero_zero_complex )
% 0.29/0.56       => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Z ) @ Y2 )
% 0.29/0.56          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Y2 @ Z ) ) @ Z ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % divide_add_eq_iff
% 0.29/0.56  thf(fact_2716_divide__add__eq__iff,axiom,
% 0.29/0.56      ! [Z: real,X: real,Y2: real] :
% 0.29/0.56        ( ( Z != zero_zero_real )
% 0.29/0.56       => ( ( plus_plus_real @ ( divide_divide_real @ X @ Z ) @ Y2 )
% 0.29/0.56          = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Y2 @ Z ) ) @ Z ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % divide_add_eq_iff
% 0.29/0.56  thf(fact_2717_divide__add__eq__iff,axiom,
% 0.29/0.56      ! [Z: rat,X: rat,Y2: rat] :
% 0.29/0.56        ( ( Z != zero_zero_rat )
% 0.29/0.56       => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Z ) @ Y2 )
% 0.29/0.56          = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Y2 @ Z ) ) @ Z ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % divide_add_eq_iff
% 0.29/0.56  thf(fact_2718_div__add__self2,axiom,
% 0.29/0.56      ! [B: nat,A: nat] :
% 0.29/0.56        ( ( B != zero_zero_nat )
% 0.29/0.56       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.29/0.56          = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % div_add_self2
% 0.29/0.56  thf(fact_2719_div__add__self2,axiom,
% 0.29/0.56      ! [B: int,A: int] :
% 0.29/0.56        ( ( B != zero_zero_int )
% 0.29/0.56       => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.29/0.56          = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % div_add_self2
% 0.29/0.56  thf(fact_2720_div__add__self1,axiom,
% 0.29/0.56      ! [B: nat,A: nat] :
% 0.29/0.56        ( ( B != zero_zero_nat )
% 0.29/0.56       => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.29/0.56          = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % div_add_self1
% 0.29/0.56  thf(fact_2721_div__add__self1,axiom,
% 0.29/0.56      ! [B: int,A: int] :
% 0.29/0.56        ( ( B != zero_zero_int )
% 0.29/0.56       => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 0.29/0.56          = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % div_add_self1
% 0.29/0.56  thf(fact_2722_power__inject__base,axiom,
% 0.29/0.56      ! [A: rat,N: nat,B: rat] :
% 0.29/0.56        ( ( ( power_power_rat @ A @ ( suc @ N ) )
% 0.29/0.56          = ( power_power_rat @ B @ ( suc @ N ) ) )
% 0.29/0.56       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.56         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.29/0.56           => ( A = B ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % power_inject_base
% 0.29/0.56  thf(fact_2723_power__inject__base,axiom,
% 0.29/0.56      ! [A: real,N: nat,B: real] :
% 0.29/0.56        ( ( ( power_power_real @ A @ ( suc @ N ) )
% 0.29/0.56          = ( power_power_real @ B @ ( suc @ N ) ) )
% 0.29/0.56       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.56         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.29/0.56           => ( A = B ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % power_inject_base
% 0.29/0.56  thf(fact_2724_power__inject__base,axiom,
% 0.29/0.56      ! [A: nat,N: nat,B: nat] :
% 0.29/0.56        ( ( ( power_power_nat @ A @ ( suc @ N ) )
% 0.29/0.56          = ( power_power_nat @ B @ ( suc @ N ) ) )
% 0.29/0.56       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.56         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.29/0.56           => ( A = B ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % power_inject_base
% 0.29/0.56  thf(fact_2725_power__inject__base,axiom,
% 0.29/0.56      ! [A: int,N: nat,B: int] :
% 0.29/0.56        ( ( ( power_power_int @ A @ ( suc @ N ) )
% 0.29/0.56          = ( power_power_int @ B @ ( suc @ N ) ) )
% 0.29/0.56       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.56         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.29/0.56           => ( A = B ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % power_inject_base
% 0.29/0.56  thf(fact_2726_power__le__imp__le__base,axiom,
% 0.29/0.56      ! [A: rat,N: nat,B: rat] :
% 0.29/0.56        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ ( power_power_rat @ B @ ( suc @ N ) ) )
% 0.29/0.56       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.29/0.56         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % power_le_imp_le_base
% 0.29/0.56  thf(fact_2727_power__le__imp__le__base,axiom,
% 0.29/0.56      ! [A: real,N: nat,B: real] :
% 0.29/0.56        ( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ ( power_power_real @ B @ ( suc @ N ) ) )
% 0.29/0.56       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.29/0.56         => ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % power_le_imp_le_base
% 0.29/0.56  thf(fact_2728_power__le__imp__le__base,axiom,
% 0.29/0.56      ! [A: nat,N: nat,B: nat] :
% 0.29/0.56        ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ ( power_power_nat @ B @ ( suc @ N ) ) )
% 0.29/0.56       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.29/0.56         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % power_le_imp_le_base
% 0.29/0.56  thf(fact_2729_power__le__imp__le__base,axiom,
% 0.29/0.56      ! [A: int,N: nat,B: int] :
% 0.29/0.56        ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ ( power_power_int @ B @ ( suc @ N ) ) )
% 0.29/0.56       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.29/0.56         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % power_le_imp_le_base
% 0.29/0.56  thf(fact_2730_add__divide__eq__if__simps_I4_J,axiom,
% 0.29/0.56      ! [Z: complex,A: complex,B: complex] :
% 0.29/0.56        ( ( ( Z = zero_zero_complex )
% 0.29/0.56         => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 0.29/0.56            = A ) )
% 0.29/0.56        & ( ( Z != zero_zero_complex )
% 0.29/0.56         => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 0.29/0.56            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_divide_eq_if_simps(4)
% 0.29/0.56  thf(fact_2731_add__divide__eq__if__simps_I4_J,axiom,
% 0.29/0.56      ! [Z: real,A: real,B: real] :
% 0.29/0.56        ( ( ( Z = zero_zero_real )
% 0.29/0.56         => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 0.29/0.56            = A ) )
% 0.29/0.56        & ( ( Z != zero_zero_real )
% 0.29/0.56         => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 0.29/0.56            = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_divide_eq_if_simps(4)
% 0.29/0.56  thf(fact_2732_add__divide__eq__if__simps_I4_J,axiom,
% 0.29/0.56      ! [Z: rat,A: rat,B: rat] :
% 0.29/0.56        ( ( ( Z = zero_zero_rat )
% 0.29/0.56         => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 0.29/0.56            = A ) )
% 0.29/0.56        & ( ( Z != zero_zero_rat )
% 0.29/0.56         => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 0.29/0.56            = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_divide_eq_if_simps(4)
% 0.29/0.56  thf(fact_2733_diff__frac__eq,axiom,
% 0.29/0.56      ! [Y2: complex,Z: complex,X: complex,W: complex] :
% 0.29/0.56        ( ( Y2 != zero_zero_complex )
% 0.29/0.56       => ( ( Z != zero_zero_complex )
% 0.29/0.56         => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X @ Y2 ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 0.29/0.56            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X @ Z ) @ ( times_times_complex @ W @ Y2 ) ) @ ( times_times_complex @ Y2 @ Z ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_frac_eq
% 0.29/0.56  thf(fact_2734_diff__frac__eq,axiom,
% 0.29/0.56      ! [Y2: real,Z: real,X: real,W: real] :
% 0.29/0.56        ( ( Y2 != zero_zero_real )
% 0.29/0.56       => ( ( Z != zero_zero_real )
% 0.29/0.56         => ( ( minus_minus_real @ ( divide_divide_real @ X @ Y2 ) @ ( divide_divide_real @ W @ Z ) )
% 0.29/0.56            = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y2 ) ) @ ( times_times_real @ Y2 @ Z ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_frac_eq
% 0.29/0.56  thf(fact_2735_diff__frac__eq,axiom,
% 0.29/0.56      ! [Y2: rat,Z: rat,X: rat,W: rat] :
% 0.29/0.56        ( ( Y2 != zero_zero_rat )
% 0.29/0.56       => ( ( Z != zero_zero_rat )
% 0.29/0.56         => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Y2 ) @ ( divide_divide_rat @ W @ Z ) )
% 0.29/0.56            = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y2 ) ) @ ( times_times_rat @ Y2 @ Z ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_frac_eq
% 0.29/0.56  thf(fact_2736_diff__divide__eq__iff,axiom,
% 0.29/0.56      ! [Z: complex,X: complex,Y2: complex] :
% 0.29/0.56        ( ( Z != zero_zero_complex )
% 0.29/0.56       => ( ( minus_minus_complex @ X @ ( divide1717551699836669952omplex @ Y2 @ Z ) )
% 0.29/0.56          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X @ Z ) @ Y2 ) @ Z ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_divide_eq_iff
% 0.29/0.56  thf(fact_2737_diff__divide__eq__iff,axiom,
% 0.29/0.56      ! [Z: real,X: real,Y2: real] :
% 0.29/0.56        ( ( Z != zero_zero_real )
% 0.29/0.56       => ( ( minus_minus_real @ X @ ( divide_divide_real @ Y2 @ Z ) )
% 0.29/0.56          = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ Y2 ) @ Z ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_divide_eq_iff
% 0.29/0.56  thf(fact_2738_diff__divide__eq__iff,axiom,
% 0.29/0.56      ! [Z: rat,X: rat,Y2: rat] :
% 0.29/0.56        ( ( Z != zero_zero_rat )
% 0.29/0.56       => ( ( minus_minus_rat @ X @ ( divide_divide_rat @ Y2 @ Z ) )
% 0.29/0.56          = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ Y2 ) @ Z ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_divide_eq_iff
% 0.29/0.56  thf(fact_2739_divide__diff__eq__iff,axiom,
% 0.29/0.56      ! [Z: complex,X: complex,Y2: complex] :
% 0.29/0.56        ( ( Z != zero_zero_complex )
% 0.29/0.56       => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X @ Z ) @ Y2 )
% 0.29/0.56          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ X @ ( times_times_complex @ Y2 @ Z ) ) @ Z ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % divide_diff_eq_iff
% 0.29/0.56  thf(fact_2740_divide__diff__eq__iff,axiom,
% 0.29/0.56      ! [Z: real,X: real,Y2: real] :
% 0.29/0.56        ( ( Z != zero_zero_real )
% 0.29/0.56       => ( ( minus_minus_real @ ( divide_divide_real @ X @ Z ) @ Y2 )
% 0.29/0.56          = ( divide_divide_real @ ( minus_minus_real @ X @ ( times_times_real @ Y2 @ Z ) ) @ Z ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % divide_diff_eq_iff
% 0.29/0.56  thf(fact_2741_divide__diff__eq__iff,axiom,
% 0.29/0.56      ! [Z: rat,X: rat,Y2: rat] :
% 0.29/0.56        ( ( Z != zero_zero_rat )
% 0.29/0.56       => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Z ) @ Y2 )
% 0.29/0.56          = ( divide_divide_rat @ ( minus_minus_rat @ X @ ( times_times_rat @ Y2 @ Z ) ) @ Z ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % divide_diff_eq_iff
% 0.29/0.56  thf(fact_2742_numeral__1__eq__Suc__0,axiom,
% 0.29/0.56      ( ( numeral_numeral_nat @ one )
% 0.29/0.56      = ( suc @ zero_zero_nat ) ) ).
% 0.29/0.56  
% 0.29/0.56  % numeral_1_eq_Suc_0
% 0.29/0.56  thf(fact_2743_num_Osize_I5_J,axiom,
% 0.29/0.56      ! [X23: num] :
% 0.29/0.56        ( ( size_size_num @ ( bit0 @ X23 ) )
% 0.29/0.56        = ( plus_plus_nat @ ( size_size_num @ X23 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % num.size(5)
% 0.29/0.56  thf(fact_2744_ex__least__nat__less,axiom,
% 0.29/0.56      ! [P: nat > $o,N: nat] :
% 0.29/0.56        ( ( P @ N )
% 0.29/0.56       => ( ~ ( P @ zero_zero_nat )
% 0.29/0.56         => ? [K2: nat] :
% 0.29/0.56              ( ( ord_less_nat @ K2 @ N )
% 0.29/0.56              & ! [I: nat] :
% 0.29/0.56                  ( ( ord_less_eq_nat @ I @ K2 )
% 0.29/0.56                 => ~ ( P @ I ) )
% 0.29/0.56              & ( P @ ( suc @ K2 ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % ex_least_nat_less
% 0.29/0.56  thf(fact_2745_nat__induct__non__zero,axiom,
% 0.29/0.56      ! [N: nat,P: nat > $o] :
% 0.29/0.56        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.56       => ( ( P @ one_one_nat )
% 0.29/0.56         => ( ! [N3: nat] :
% 0.29/0.56                ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.29/0.56               => ( ( P @ N3 )
% 0.29/0.56                 => ( P @ ( suc @ N3 ) ) ) )
% 0.29/0.56           => ( P @ N ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % nat_induct_non_zero
% 0.29/0.56  thf(fact_2746_num_Osize_I6_J,axiom,
% 0.29/0.56      ! [X33: num] :
% 0.29/0.56        ( ( size_size_num @ ( bit1 @ X33 ) )
% 0.29/0.56        = ( plus_plus_nat @ ( size_size_num @ X33 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % num.size(6)
% 0.29/0.56  thf(fact_2747_one__less__mult,axiom,
% 0.29/0.56      ! [N: nat,M: nat] :
% 0.29/0.56        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.29/0.56       => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.29/0.56         => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % one_less_mult
% 0.29/0.56  thf(fact_2748_n__less__m__mult__n,axiom,
% 0.29/0.56      ! [N: nat,M: nat] :
% 0.29/0.56        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.56       => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.29/0.56         => ( ord_less_nat @ N @ ( times_times_nat @ M @ N ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % n_less_m_mult_n
% 0.29/0.56  thf(fact_2749_n__less__n__mult__m,axiom,
% 0.29/0.56      ! [N: nat,M: nat] :
% 0.29/0.56        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.56       => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.29/0.56         => ( ord_less_nat @ N @ ( times_times_nat @ N @ M ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % n_less_n_mult_m
% 0.29/0.56  thf(fact_2750_diff__Suc__less,axiom,
% 0.29/0.56      ! [N: nat,I2: nat] :
% 0.29/0.56        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.56       => ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I2 ) ) @ N ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_Suc_less
% 0.29/0.56  thf(fact_2751_length__pos__if__in__set,axiom,
% 0.29/0.56      ! [X: product_prod_nat_nat,Xs2: list_P6011104703257516679at_nat] :
% 0.29/0.56        ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 0.35/0.56       => ( ord_less_nat @ zero_zero_nat @ ( size_s5460976970255530739at_nat @ Xs2 ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % length_pos_if_in_set
% 0.35/0.56  thf(fact_2752_length__pos__if__in__set,axiom,
% 0.35/0.56      ! [X: complex,Xs2: list_complex] :
% 0.35/0.56        ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 0.35/0.56       => ( ord_less_nat @ zero_zero_nat @ ( size_s3451745648224563538omplex @ Xs2 ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % length_pos_if_in_set
% 0.35/0.56  thf(fact_2753_length__pos__if__in__set,axiom,
% 0.35/0.56      ! [X: real,Xs2: list_real] :
% 0.35/0.56        ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 0.35/0.56       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_real @ Xs2 ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % length_pos_if_in_set
% 0.35/0.56  thf(fact_2754_length__pos__if__in__set,axiom,
% 0.35/0.56      ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 0.35/0.56        ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 0.35/0.56       => ( ord_less_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % length_pos_if_in_set
% 0.35/0.56  thf(fact_2755_length__pos__if__in__set,axiom,
% 0.35/0.56      ! [X: $o,Xs2: list_o] :
% 0.35/0.56        ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 0.35/0.56       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_o @ Xs2 ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % length_pos_if_in_set
% 0.35/0.56  thf(fact_2756_length__pos__if__in__set,axiom,
% 0.35/0.56      ! [X: nat,Xs2: list_nat] :
% 0.35/0.56        ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 0.35/0.56       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs2 ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % length_pos_if_in_set
% 0.35/0.56  thf(fact_2757_length__pos__if__in__set,axiom,
% 0.35/0.56      ! [X: int,Xs2: list_int] :
% 0.35/0.56        ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 0.35/0.56       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs2 ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % length_pos_if_in_set
% 0.35/0.56  thf(fact_2758_power__gt__expt,axiom,
% 0.35/0.56      ! [N: nat,K: nat] :
% 0.35/0.56        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.35/0.56       => ( ord_less_nat @ K @ ( power_power_nat @ N @ K ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power_gt_expt
% 0.35/0.56  thf(fact_2759_div__le__mono2,axiom,
% 0.35/0.56      ! [M: nat,N: nat,K: nat] :
% 0.35/0.56        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.35/0.56       => ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.56         => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N ) @ ( divide_divide_nat @ K @ M ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % div_le_mono2
% 0.35/0.56  thf(fact_2760_div__greater__zero__iff,axiom,
% 0.35/0.56      ! [M: nat,N: nat] :
% 0.35/0.56        ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M @ N ) )
% 0.35/0.56        = ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.56          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % div_greater_zero_iff
% 0.35/0.56  thf(fact_2761_nat__diff__split,axiom,
% 0.35/0.56      ! [P: nat > $o,A: nat,B: nat] :
% 0.35/0.56        ( ( P @ ( minus_minus_nat @ A @ B ) )
% 0.35/0.56        = ( ( ( ord_less_nat @ A @ B )
% 0.35/0.56           => ( P @ zero_zero_nat ) )
% 0.35/0.56          & ! [D: nat] :
% 0.35/0.56              ( ( A
% 0.35/0.56                = ( plus_plus_nat @ B @ D ) )
% 0.35/0.56             => ( P @ D ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % nat_diff_split
% 0.35/0.56  thf(fact_2762_nat__diff__split__asm,axiom,
% 0.35/0.56      ! [P: nat > $o,A: nat,B: nat] :
% 0.35/0.56        ( ( P @ ( minus_minus_nat @ A @ B ) )
% 0.35/0.56        = ( ~ ( ( ( ord_less_nat @ A @ B )
% 0.35/0.56                & ~ ( P @ zero_zero_nat ) )
% 0.35/0.56              | ? [D: nat] :
% 0.35/0.56                  ( ( A
% 0.35/0.56                    = ( plus_plus_nat @ B @ D ) )
% 0.35/0.56                  & ~ ( P @ D ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % nat_diff_split_asm
% 0.35/0.56  thf(fact_2763_nat__mult__le__cancel1,axiom,
% 0.35/0.56      ! [K: nat,M: nat,N: nat] :
% 0.35/0.56        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.35/0.56       => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.35/0.56          = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % nat_mult_le_cancel1
% 0.35/0.56  thf(fact_2764_div__eq__dividend__iff,axiom,
% 0.35/0.56      ! [M: nat,N: nat] :
% 0.35/0.56        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.35/0.56       => ( ( ( divide_divide_nat @ M @ N )
% 0.35/0.56            = M )
% 0.35/0.56          = ( N = one_one_nat ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % div_eq_dividend_iff
% 0.35/0.56  thf(fact_2765_div__less__dividend,axiom,
% 0.35/0.56      ! [N: nat,M: nat] :
% 0.35/0.56        ( ( ord_less_nat @ one_one_nat @ N )
% 0.35/0.56       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.35/0.56         => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ M ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % div_less_dividend
% 0.35/0.56  thf(fact_2766_nat__one__le__power,axiom,
% 0.35/0.56      ! [I2: nat,N: nat] :
% 0.35/0.56        ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I2 )
% 0.35/0.56       => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I2 @ N ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % nat_one_le_power
% 0.35/0.56  thf(fact_2767_nat__mult__div__cancel1,axiom,
% 0.35/0.56      ! [K: nat,M: nat,N: nat] :
% 0.35/0.56        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.35/0.56       => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.35/0.56          = ( divide_divide_nat @ M @ N ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % nat_mult_div_cancel1
% 0.35/0.56  thf(fact_2768_div__less__iff__less__mult,axiom,
% 0.35/0.56      ! [Q2: nat,M: nat,N: nat] :
% 0.35/0.56        ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 0.35/0.56       => ( ( ord_less_nat @ ( divide_divide_nat @ M @ Q2 ) @ N )
% 0.35/0.56          = ( ord_less_nat @ M @ ( times_times_nat @ N @ Q2 ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % div_less_iff_less_mult
% 0.35/0.56  thf(fact_2769_vebt__member_Osimps_I3_J,axiom,
% 0.35/0.56      ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X: nat] :
% 0.35/0.56        ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X ) ).
% 0.35/0.56  
% 0.35/0.56  % vebt_member.simps(3)
% 0.35/0.56  thf(fact_2770_vebt__insert_Osimps_I3_J,axiom,
% 0.35/0.56      ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT,X: nat] :
% 0.35/0.56        ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) @ X )
% 0.35/0.56        = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) ) ).
% 0.35/0.56  
% 0.35/0.56  % vebt_insert.simps(3)
% 0.35/0.56  thf(fact_2771_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Oelims,axiom,
% 0.35/0.56      ! [X: vEBT_VEBT,Y2: nat] :
% 0.35/0.56        ( ( ( vEBT_T_m_i_n_t @ X )
% 0.35/0.56          = Y2 )
% 0.35/0.56       => ( ! [A4: $o] :
% 0.35/0.56              ( ? [B3: $o] :
% 0.35/0.56                  ( X
% 0.35/0.56                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.56             => ( Y2
% 0.35/0.56               != ( plus_plus_nat @ one_one_nat @ ( if_nat @ A4 @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 0.35/0.56         => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.35/0.56                  ( X
% 0.35/0.56                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.35/0.56             => ( Y2 != one_one_nat ) )
% 0.35/0.56           => ~ ( ? [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.35/0.56                    ( X
% 0.35/0.56                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 0.35/0.56               => ( Y2 != one_one_nat ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.elims
% 0.35/0.56  thf(fact_2772_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I2_J,axiom,
% 0.35/0.56      ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT,X: nat] :
% 0.35/0.56        ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S3 ) @ X )
% 0.35/0.56        = one_one_nat ) ).
% 0.35/0.56  
% 0.35/0.56  % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(2)
% 0.35/0.56  thf(fact_2773_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Ocases,axiom,
% 0.35/0.56      ! [X: vEBT_VEBT] :
% 0.35/0.56        ( ! [A4: $o,B3: $o] :
% 0.35/0.56            ( X
% 0.35/0.56           != ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.56       => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.35/0.56              ( X
% 0.35/0.56             != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.35/0.56         => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.35/0.56                ( X
% 0.35/0.56               != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.cases
% 0.35/0.56  thf(fact_2774_VEBT__internal_OminNull_Oelims_I1_J,axiom,
% 0.35/0.56      ! [X: vEBT_VEBT,Y2: $o] :
% 0.35/0.56        ( ( ( vEBT_VEBT_minNull @ X )
% 0.35/0.56          = Y2 )
% 0.35/0.56       => ( ( ( X
% 0.35/0.56              = ( vEBT_Leaf @ $false @ $false ) )
% 0.35/0.56           => ~ Y2 )
% 0.35/0.56         => ( ( ? [Uv2: $o] :
% 0.35/0.56                  ( X
% 0.35/0.56                  = ( vEBT_Leaf @ $true @ Uv2 ) )
% 0.35/0.56             => Y2 )
% 0.35/0.56           => ( ( ? [Uu2: $o] :
% 0.35/0.56                    ( X
% 0.35/0.56                    = ( vEBT_Leaf @ Uu2 @ $true ) )
% 0.35/0.56               => Y2 )
% 0.35/0.56             => ( ( ? [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 0.35/0.56                      ( X
% 0.35/0.56                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 0.35/0.56                 => ~ Y2 )
% 0.35/0.56               => ~ ( ? [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.35/0.56                        ( X
% 0.35/0.56                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 0.35/0.56                   => Y2 ) ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % VEBT_internal.minNull.elims(1)
% 0.35/0.56  thf(fact_2775_vebt__mint_Oelims,axiom,
% 0.35/0.56      ! [X: vEBT_VEBT,Y2: option_nat] :
% 0.35/0.56        ( ( ( vEBT_vebt_mint @ X )
% 0.35/0.56          = Y2 )
% 0.35/0.56       => ( ! [A4: $o,B3: $o] :
% 0.35/0.56              ( ( X
% 0.35/0.56                = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.56             => ~ ( ( A4
% 0.35/0.56                   => ( Y2
% 0.35/0.56                      = ( some_nat @ zero_zero_nat ) ) )
% 0.35/0.56                  & ( ~ A4
% 0.35/0.56                   => ( ( B3
% 0.35/0.56                       => ( Y2
% 0.35/0.56                          = ( some_nat @ one_one_nat ) ) )
% 0.35/0.56                      & ( ~ B3
% 0.35/0.56                       => ( Y2 = none_nat ) ) ) ) ) )
% 0.35/0.56         => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.35/0.56                  ( X
% 0.35/0.56                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.35/0.56             => ( Y2 != none_nat ) )
% 0.35/0.56           => ~ ! [Mi2: nat] :
% 0.35/0.56                  ( ? [Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.35/0.56                      ( X
% 0.35/0.56                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 0.35/0.56                 => ( Y2
% 0.35/0.56                   != ( some_nat @ Mi2 ) ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % vebt_mint.elims
% 0.35/0.56  thf(fact_2776_vebt__maxt_Oelims,axiom,
% 0.35/0.56      ! [X: vEBT_VEBT,Y2: option_nat] :
% 0.35/0.56        ( ( ( vEBT_vebt_maxt @ X )
% 0.35/0.56          = Y2 )
% 0.35/0.56       => ( ! [A4: $o,B3: $o] :
% 0.35/0.56              ( ( X
% 0.35/0.56                = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.56             => ~ ( ( B3
% 0.35/0.56                   => ( Y2
% 0.35/0.56                      = ( some_nat @ one_one_nat ) ) )
% 0.35/0.56                  & ( ~ B3
% 0.35/0.56                   => ( ( A4
% 0.35/0.56                       => ( Y2
% 0.35/0.56                          = ( some_nat @ zero_zero_nat ) ) )
% 0.35/0.56                      & ( ~ A4
% 0.35/0.56                       => ( Y2 = none_nat ) ) ) ) ) )
% 0.35/0.56         => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.35/0.56                  ( X
% 0.35/0.56                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.35/0.56             => ( Y2 != none_nat ) )
% 0.35/0.56           => ~ ! [Mi2: nat,Ma2: nat] :
% 0.35/0.56                  ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.35/0.56                      ( X
% 0.35/0.56                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 0.35/0.56                 => ( Y2
% 0.35/0.56                   != ( some_nat @ Ma2 ) ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % vebt_maxt.elims
% 0.35/0.56  thf(fact_2777_mult__le__cancel__left1,axiom,
% 0.35/0.56      ! [C: real,B: real] :
% 0.35/0.56        ( ( ord_less_eq_real @ C @ ( times_times_real @ C @ B ) )
% 0.35/0.56        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.56           => ( ord_less_eq_real @ one_one_real @ B ) )
% 0.35/0.56          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.56           => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % mult_le_cancel_left1
% 0.35/0.56  thf(fact_2778_mult__le__cancel__left1,axiom,
% 0.35/0.56      ! [C: rat,B: rat] :
% 0.35/0.56        ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B ) )
% 0.35/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.56           => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 0.35/0.56          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.56           => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % mult_le_cancel_left1
% 0.35/0.56  thf(fact_2779_mult__le__cancel__left1,axiom,
% 0.35/0.56      ! [C: int,B: int] :
% 0.35/0.56        ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B ) )
% 0.35/0.56        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.35/0.56           => ( ord_less_eq_int @ one_one_int @ B ) )
% 0.35/0.56          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.35/0.56           => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % mult_le_cancel_left1
% 0.35/0.56  thf(fact_2780_mult__le__cancel__left2,axiom,
% 0.35/0.56      ! [C: real,A: real] :
% 0.35/0.56        ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ C )
% 0.35/0.56        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.56           => ( ord_less_eq_real @ A @ one_one_real ) )
% 0.35/0.56          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.56           => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % mult_le_cancel_left2
% 0.35/0.56  thf(fact_2781_mult__le__cancel__left2,axiom,
% 0.35/0.56      ! [C: rat,A: rat] :
% 0.35/0.56        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ C )
% 0.35/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.56           => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 0.35/0.56          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.56           => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % mult_le_cancel_left2
% 0.35/0.56  thf(fact_2782_mult__le__cancel__left2,axiom,
% 0.35/0.56      ! [C: int,A: int] :
% 0.35/0.56        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ C )
% 0.35/0.56        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.35/0.56           => ( ord_less_eq_int @ A @ one_one_int ) )
% 0.35/0.56          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.35/0.56           => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % mult_le_cancel_left2
% 0.35/0.56  thf(fact_2783_mult__le__cancel__right1,axiom,
% 0.35/0.56      ! [C: real,B: real] :
% 0.35/0.56        ( ( ord_less_eq_real @ C @ ( times_times_real @ B @ C ) )
% 0.35/0.56        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.56           => ( ord_less_eq_real @ one_one_real @ B ) )
% 0.35/0.56          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.56           => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % mult_le_cancel_right1
% 0.35/0.56  thf(fact_2784_mult__le__cancel__right1,axiom,
% 0.35/0.56      ! [C: rat,B: rat] :
% 0.35/0.56        ( ( ord_less_eq_rat @ C @ ( times_times_rat @ B @ C ) )
% 0.35/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.56           => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 0.35/0.56          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.56           => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % mult_le_cancel_right1
% 0.35/0.56  thf(fact_2785_mult__le__cancel__right1,axiom,
% 0.35/0.56      ! [C: int,B: int] :
% 0.35/0.56        ( ( ord_less_eq_int @ C @ ( times_times_int @ B @ C ) )
% 0.35/0.56        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.35/0.56           => ( ord_less_eq_int @ one_one_int @ B ) )
% 0.35/0.56          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.35/0.56           => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % mult_le_cancel_right1
% 0.35/0.56  thf(fact_2786_mult__le__cancel__right2,axiom,
% 0.35/0.56      ! [A: real,C: real] :
% 0.35/0.56        ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ C )
% 0.35/0.56        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.56           => ( ord_less_eq_real @ A @ one_one_real ) )
% 0.35/0.56          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.56           => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % mult_le_cancel_right2
% 0.35/0.56  thf(fact_2787_mult__le__cancel__right2,axiom,
% 0.35/0.56      ! [A: rat,C: rat] :
% 0.35/0.56        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ C )
% 0.35/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.56           => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 0.35/0.56          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.56           => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % mult_le_cancel_right2
% 0.35/0.56  thf(fact_2788_mult__le__cancel__right2,axiom,
% 0.35/0.56      ! [A: int,C: int] :
% 0.35/0.56        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ C )
% 0.35/0.56        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.35/0.56           => ( ord_less_eq_int @ A @ one_one_int ) )
% 0.35/0.56          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.35/0.56           => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % mult_le_cancel_right2
% 0.35/0.56  thf(fact_2789_mult__less__cancel__left1,axiom,
% 0.35/0.56      ! [C: real,B: real] :
% 0.35/0.56        ( ( ord_less_real @ C @ ( times_times_real @ C @ B ) )
% 0.35/0.56        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.35/0.56           => ( ord_less_real @ one_one_real @ B ) )
% 0.35/0.56          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.35/0.56           => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % mult_less_cancel_left1
% 0.35/0.56  thf(fact_2790_mult__less__cancel__left1,axiom,
% 0.35/0.56      ! [C: rat,B: rat] :
% 0.35/0.56        ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B ) )
% 0.35/0.56        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.35/0.56           => ( ord_less_rat @ one_one_rat @ B ) )
% 0.35/0.56          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.35/0.56           => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % mult_less_cancel_left1
% 0.35/0.56  thf(fact_2791_mult__less__cancel__left1,axiom,
% 0.35/0.56      ! [C: int,B: int] :
% 0.35/0.56        ( ( ord_less_int @ C @ ( times_times_int @ C @ B ) )
% 0.35/0.56        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.35/0.56           => ( ord_less_int @ one_one_int @ B ) )
% 0.35/0.56          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.35/0.56           => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % mult_less_cancel_left1
% 0.35/0.56  thf(fact_2792_mult__less__cancel__left2,axiom,
% 0.35/0.56      ! [C: real,A: real] :
% 0.35/0.56        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ C )
% 0.35/0.56        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.35/0.56           => ( ord_less_real @ A @ one_one_real ) )
% 0.35/0.56          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.35/0.56           => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % mult_less_cancel_left2
% 0.35/0.56  thf(fact_2793_mult__less__cancel__left2,axiom,
% 0.35/0.56      ! [C: rat,A: rat] :
% 0.35/0.56        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ C )
% 0.35/0.56        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.35/0.56           => ( ord_less_rat @ A @ one_one_rat ) )
% 0.35/0.56          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.35/0.56           => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % mult_less_cancel_left2
% 0.35/0.56  thf(fact_2794_mult__less__cancel__left2,axiom,
% 0.35/0.56      ! [C: int,A: int] :
% 0.35/0.56        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ C )
% 0.35/0.56        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.35/0.56           => ( ord_less_int @ A @ one_one_int ) )
% 0.35/0.56          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.35/0.56           => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % mult_less_cancel_left2
% 0.35/0.56  thf(fact_2795_mult__less__cancel__right1,axiom,
% 0.35/0.56      ! [C: real,B: real] :
% 0.35/0.56        ( ( ord_less_real @ C @ ( times_times_real @ B @ C ) )
% 0.35/0.56        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.35/0.56           => ( ord_less_real @ one_one_real @ B ) )
% 0.35/0.56          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.35/0.56           => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % mult_less_cancel_right1
% 0.35/0.56  thf(fact_2796_mult__less__cancel__right1,axiom,
% 0.35/0.56      ! [C: rat,B: rat] :
% 0.35/0.56        ( ( ord_less_rat @ C @ ( times_times_rat @ B @ C ) )
% 0.35/0.56        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.35/0.56           => ( ord_less_rat @ one_one_rat @ B ) )
% 0.35/0.56          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.35/0.56           => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % mult_less_cancel_right1
% 0.35/0.56  thf(fact_2797_mult__less__cancel__right1,axiom,
% 0.35/0.56      ! [C: int,B: int] :
% 0.35/0.56        ( ( ord_less_int @ C @ ( times_times_int @ B @ C ) )
% 0.35/0.56        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.35/0.56           => ( ord_less_int @ one_one_int @ B ) )
% 0.35/0.56          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.35/0.56           => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % mult_less_cancel_right1
% 0.35/0.56  thf(fact_2798_mult__less__cancel__right2,axiom,
% 0.35/0.56      ! [A: real,C: real] :
% 0.35/0.56        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ C )
% 0.35/0.56        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.35/0.56           => ( ord_less_real @ A @ one_one_real ) )
% 0.35/0.56          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.35/0.56           => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % mult_less_cancel_right2
% 0.35/0.56  thf(fact_2799_mult__less__cancel__right2,axiom,
% 0.35/0.56      ! [A: rat,C: rat] :
% 0.35/0.56        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ C )
% 0.35/0.56        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.35/0.56           => ( ord_less_rat @ A @ one_one_rat ) )
% 0.35/0.56          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.35/0.56           => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % mult_less_cancel_right2
% 0.35/0.56  thf(fact_2800_mult__less__cancel__right2,axiom,
% 0.35/0.56      ! [A: int,C: int] :
% 0.35/0.56        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ C )
% 0.35/0.56        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.35/0.56           => ( ord_less_int @ A @ one_one_int ) )
% 0.35/0.56          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.35/0.56           => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % mult_less_cancel_right2
% 0.35/0.56  thf(fact_2801_field__le__mult__one__interval,axiom,
% 0.35/0.56      ! [X: real,Y2: real] :
% 0.35/0.56        ( ! [Z3: real] :
% 0.35/0.56            ( ( ord_less_real @ zero_zero_real @ Z3 )
% 0.35/0.56           => ( ( ord_less_real @ Z3 @ one_one_real )
% 0.35/0.56             => ( ord_less_eq_real @ ( times_times_real @ Z3 @ X ) @ Y2 ) ) )
% 0.35/0.56       => ( ord_less_eq_real @ X @ Y2 ) ) ).
% 0.35/0.56  
% 0.35/0.56  % field_le_mult_one_interval
% 0.35/0.56  thf(fact_2802_field__le__mult__one__interval,axiom,
% 0.35/0.56      ! [X: rat,Y2: rat] :
% 0.35/0.56        ( ! [Z3: rat] :
% 0.35/0.56            ( ( ord_less_rat @ zero_zero_rat @ Z3 )
% 0.35/0.56           => ( ( ord_less_rat @ Z3 @ one_one_rat )
% 0.35/0.56             => ( ord_less_eq_rat @ ( times_times_rat @ Z3 @ X ) @ Y2 ) ) )
% 0.35/0.56       => ( ord_less_eq_rat @ X @ Y2 ) ) ).
% 0.35/0.56  
% 0.35/0.56  % field_le_mult_one_interval
% 0.35/0.56  thf(fact_2803_divide__le__eq,axiom,
% 0.35/0.56      ! [B: real,C: real,A: real] :
% 0.35/0.56        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 0.35/0.56        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.56           => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 0.35/0.56          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.56           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.56               => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 0.35/0.56              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.56               => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % divide_le_eq
% 0.35/0.56  thf(fact_2804_divide__le__eq,axiom,
% 0.35/0.56      ! [B: rat,C: rat,A: rat] :
% 0.35/0.56        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.35/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.56           => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 0.35/0.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.56               => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 0.35/0.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.56               => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % divide_le_eq
% 0.35/0.56  thf(fact_2805_le__divide__eq,axiom,
% 0.35/0.56      ! [A: real,B: real,C: real] :
% 0.35/0.56        ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 0.35/0.56        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.56           => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 0.35/0.56          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.56           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.56               => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 0.35/0.56              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.56               => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % le_divide_eq
% 0.35/0.56  thf(fact_2806_le__divide__eq,axiom,
% 0.35/0.56      ! [A: rat,B: rat,C: rat] :
% 0.35/0.56        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.35/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.56           => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 0.35/0.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.56               => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 0.35/0.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.56               => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % le_divide_eq
% 0.35/0.56  thf(fact_2807_divide__left__mono,axiom,
% 0.35/0.56      ! [B: real,A: real,C: real] :
% 0.35/0.56        ( ( ord_less_eq_real @ B @ A )
% 0.35/0.56       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.35/0.56         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.35/0.56           => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % divide_left_mono
% 0.35/0.56  thf(fact_2808_divide__left__mono,axiom,
% 0.35/0.56      ! [B: rat,A: rat,C: rat] :
% 0.35/0.56        ( ( ord_less_eq_rat @ B @ A )
% 0.35/0.56       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.35/0.56         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.35/0.56           => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % divide_left_mono
% 0.35/0.56  thf(fact_2809_neg__divide__le__eq,axiom,
% 0.35/0.56      ! [C: real,B: real,A: real] :
% 0.35/0.56        ( ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.56       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 0.35/0.56          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % neg_divide_le_eq
% 0.35/0.56  thf(fact_2810_neg__divide__le__eq,axiom,
% 0.35/0.56      ! [C: rat,B: rat,A: rat] :
% 0.35/0.56        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.56       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.35/0.56          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % neg_divide_le_eq
% 0.35/0.56  thf(fact_2811_neg__le__divide__eq,axiom,
% 0.35/0.56      ! [C: real,A: real,B: real] :
% 0.35/0.56        ( ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.56       => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 0.35/0.56          = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % neg_le_divide_eq
% 0.35/0.56  thf(fact_2812_neg__le__divide__eq,axiom,
% 0.35/0.56      ! [C: rat,A: rat,B: rat] :
% 0.35/0.56        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.56       => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.35/0.56          = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % neg_le_divide_eq
% 0.35/0.56  thf(fact_2813_pos__divide__le__eq,axiom,
% 0.35/0.56      ! [C: real,B: real,A: real] :
% 0.35/0.56        ( ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.56       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 0.35/0.56          = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % pos_divide_le_eq
% 0.35/0.56  thf(fact_2814_pos__divide__le__eq,axiom,
% 0.35/0.56      ! [C: rat,B: rat,A: rat] :
% 0.35/0.56        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.56       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.35/0.56          = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % pos_divide_le_eq
% 0.35/0.56  thf(fact_2815_pos__le__divide__eq,axiom,
% 0.35/0.56      ! [C: real,A: real,B: real] :
% 0.35/0.56        ( ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.56       => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 0.35/0.56          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % pos_le_divide_eq
% 0.35/0.56  thf(fact_2816_pos__le__divide__eq,axiom,
% 0.35/0.56      ! [C: rat,A: rat,B: rat] :
% 0.35/0.56        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.56       => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.35/0.56          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % pos_le_divide_eq
% 0.35/0.56  thf(fact_2817_mult__imp__div__pos__le,axiom,
% 0.35/0.56      ! [Y2: real,X: real,Z: real] :
% 0.35/0.56        ( ( ord_less_real @ zero_zero_real @ Y2 )
% 0.35/0.56       => ( ( ord_less_eq_real @ X @ ( times_times_real @ Z @ Y2 ) )
% 0.35/0.56         => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y2 ) @ Z ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % mult_imp_div_pos_le
% 0.35/0.56  thf(fact_2818_mult__imp__div__pos__le,axiom,
% 0.35/0.56      ! [Y2: rat,X: rat,Z: rat] :
% 0.35/0.56        ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 0.35/0.56       => ( ( ord_less_eq_rat @ X @ ( times_times_rat @ Z @ Y2 ) )
% 0.35/0.56         => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y2 ) @ Z ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % mult_imp_div_pos_le
% 0.35/0.56  thf(fact_2819_mult__imp__le__div__pos,axiom,
% 0.35/0.56      ! [Y2: real,Z: real,X: real] :
% 0.35/0.56        ( ( ord_less_real @ zero_zero_real @ Y2 )
% 0.35/0.56       => ( ( ord_less_eq_real @ ( times_times_real @ Z @ Y2 ) @ X )
% 0.35/0.56         => ( ord_less_eq_real @ Z @ ( divide_divide_real @ X @ Y2 ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % mult_imp_le_div_pos
% 0.35/0.56  thf(fact_2820_mult__imp__le__div__pos,axiom,
% 0.35/0.56      ! [Y2: rat,Z: rat,X: rat] :
% 0.35/0.56        ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 0.35/0.56       => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ Y2 ) @ X )
% 0.35/0.56         => ( ord_less_eq_rat @ Z @ ( divide_divide_rat @ X @ Y2 ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % mult_imp_le_div_pos
% 0.35/0.56  thf(fact_2821_divide__left__mono__neg,axiom,
% 0.35/0.56      ! [A: real,B: real,C: real] :
% 0.35/0.56        ( ( ord_less_eq_real @ A @ B )
% 0.35/0.56       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.35/0.56         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.35/0.56           => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % divide_left_mono_neg
% 0.35/0.56  thf(fact_2822_divide__left__mono__neg,axiom,
% 0.35/0.56      ! [A: rat,B: rat,C: rat] :
% 0.35/0.56        ( ( ord_less_eq_rat @ A @ B )
% 0.35/0.56       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.35/0.56         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.35/0.56           => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % divide_left_mono_neg
% 0.35/0.56  thf(fact_2823_divide__le__eq__1,axiom,
% 0.35/0.56      ! [B: real,A: real] :
% 0.35/0.56        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 0.35/0.56        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.56            & ( ord_less_eq_real @ B @ A ) )
% 0.35/0.56          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.35/0.56            & ( ord_less_eq_real @ A @ B ) )
% 0.35/0.56          | ( A = zero_zero_real ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % divide_le_eq_1
% 0.35/0.56  thf(fact_2824_divide__le__eq__1,axiom,
% 0.35/0.56      ! [B: rat,A: rat] :
% 0.35/0.56        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.35/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.35/0.56            & ( ord_less_eq_rat @ B @ A ) )
% 0.35/0.56          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.35/0.56            & ( ord_less_eq_rat @ A @ B ) )
% 0.35/0.56          | ( A = zero_zero_rat ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % divide_le_eq_1
% 0.35/0.56  thf(fact_2825_le__divide__eq__1,axiom,
% 0.35/0.56      ! [B: real,A: real] :
% 0.35/0.56        ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 0.35/0.56        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.56            & ( ord_less_eq_real @ A @ B ) )
% 0.35/0.56          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.35/0.56            & ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % le_divide_eq_1
% 0.35/0.56  thf(fact_2826_le__divide__eq__1,axiom,
% 0.35/0.56      ! [B: rat,A: rat] :
% 0.35/0.56        ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.35/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.35/0.56            & ( ord_less_eq_rat @ A @ B ) )
% 0.35/0.56          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.35/0.56            & ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % le_divide_eq_1
% 0.35/0.56  thf(fact_2827_convex__bound__le,axiom,
% 0.35/0.56      ! [X: rat,A: rat,Y2: rat,U: rat,V: rat] :
% 0.35/0.56        ( ( ord_less_eq_rat @ X @ A )
% 0.35/0.56       => ( ( ord_less_eq_rat @ Y2 @ A )
% 0.35/0.56         => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 0.35/0.56           => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 0.35/0.56             => ( ( ( plus_plus_rat @ U @ V )
% 0.35/0.56                  = one_one_rat )
% 0.35/0.56               => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y2 ) ) @ A ) ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % convex_bound_le
% 0.35/0.56  thf(fact_2828_convex__bound__le,axiom,
% 0.35/0.56      ! [X: real,A: real,Y2: real,U: real,V: real] :
% 0.35/0.56        ( ( ord_less_eq_real @ X @ A )
% 0.35/0.56       => ( ( ord_less_eq_real @ Y2 @ A )
% 0.35/0.56         => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 0.35/0.56           => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 0.35/0.56             => ( ( ( plus_plus_real @ U @ V )
% 0.35/0.56                  = one_one_real )
% 0.35/0.56               => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V @ Y2 ) ) @ A ) ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % convex_bound_le
% 0.35/0.56  thf(fact_2829_convex__bound__le,axiom,
% 0.35/0.56      ! [X: int,A: int,Y2: int,U: int,V: int] :
% 0.35/0.56        ( ( ord_less_eq_int @ X @ A )
% 0.35/0.56       => ( ( ord_less_eq_int @ Y2 @ A )
% 0.35/0.56         => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 0.35/0.56           => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 0.35/0.56             => ( ( ( plus_plus_int @ U @ V )
% 0.35/0.56                  = one_one_int )
% 0.35/0.56               => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y2 ) ) @ A ) ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % convex_bound_le
% 0.35/0.56  thf(fact_2830_divide__less__eq__numeral_I1_J,axiom,
% 0.35/0.56      ! [B: real,C: real,W: num] :
% 0.35/0.56        ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 0.35/0.56        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.56           => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 0.35/0.56          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.56           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.56               => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 0.35/0.56              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.56               => ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % divide_less_eq_numeral(1)
% 0.35/0.56  thf(fact_2831_divide__less__eq__numeral_I1_J,axiom,
% 0.35/0.56      ! [B: rat,C: rat,W: num] :
% 0.35/0.56        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 0.35/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.56           => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 0.35/0.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.56               => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 0.35/0.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.56               => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % divide_less_eq_numeral(1)
% 0.35/0.56  thf(fact_2832_less__divide__eq__numeral_I1_J,axiom,
% 0.35/0.56      ! [W: num,B: real,C: real] :
% 0.35/0.56        ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 0.35/0.56        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.56           => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 0.35/0.56          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.56           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.56               => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 0.35/0.56              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.56               => ( ord_less_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % less_divide_eq_numeral(1)
% 0.35/0.56  thf(fact_2833_less__divide__eq__numeral_I1_J,axiom,
% 0.35/0.56      ! [W: num,B: rat,C: rat] :
% 0.35/0.56        ( ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 0.35/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.56           => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 0.35/0.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.56               => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 0.35/0.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.56               => ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % less_divide_eq_numeral(1)
% 0.35/0.56  thf(fact_2834_frac__le__eq,axiom,
% 0.35/0.56      ! [Y2: real,Z: real,X: real,W: real] :
% 0.35/0.56        ( ( Y2 != zero_zero_real )
% 0.35/0.56       => ( ( Z != zero_zero_real )
% 0.35/0.56         => ( ( ord_less_eq_real @ ( divide_divide_real @ X @ Y2 ) @ ( divide_divide_real @ W @ Z ) )
% 0.35/0.56            = ( ord_less_eq_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y2 ) ) @ ( times_times_real @ Y2 @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % frac_le_eq
% 0.35/0.56  thf(fact_2835_frac__le__eq,axiom,
% 0.35/0.56      ! [Y2: rat,Z: rat,X: rat,W: rat] :
% 0.35/0.56        ( ( Y2 != zero_zero_rat )
% 0.35/0.56       => ( ( Z != zero_zero_rat )
% 0.35/0.56         => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y2 ) @ ( divide_divide_rat @ W @ Z ) )
% 0.35/0.56            = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y2 ) ) @ ( times_times_rat @ Y2 @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % frac_le_eq
% 0.35/0.56  thf(fact_2836_power__Suc__less,axiom,
% 0.35/0.56      ! [A: real,N: nat] :
% 0.35/0.56        ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.56       => ( ( ord_less_real @ A @ one_one_real )
% 0.35/0.56         => ( ord_less_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) @ ( power_power_real @ A @ N ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power_Suc_less
% 0.35/0.56  thf(fact_2837_power__Suc__less,axiom,
% 0.35/0.56      ! [A: rat,N: nat] :
% 0.35/0.56        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.35/0.56       => ( ( ord_less_rat @ A @ one_one_rat )
% 0.35/0.56         => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power_Suc_less
% 0.35/0.56  thf(fact_2838_power__Suc__less,axiom,
% 0.35/0.56      ! [A: nat,N: nat] :
% 0.35/0.56        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.35/0.56       => ( ( ord_less_nat @ A @ one_one_nat )
% 0.35/0.56         => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) @ ( power_power_nat @ A @ N ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power_Suc_less
% 0.35/0.56  thf(fact_2839_power__Suc__less,axiom,
% 0.35/0.56      ! [A: int,N: nat] :
% 0.35/0.56        ( ( ord_less_int @ zero_zero_int @ A )
% 0.35/0.56       => ( ( ord_less_int @ A @ one_one_int )
% 0.35/0.56         => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power_Suc_less
% 0.35/0.56  thf(fact_2840_frac__less__eq,axiom,
% 0.35/0.56      ! [Y2: real,Z: real,X: real,W: real] :
% 0.35/0.56        ( ( Y2 != zero_zero_real )
% 0.35/0.56       => ( ( Z != zero_zero_real )
% 0.35/0.56         => ( ( ord_less_real @ ( divide_divide_real @ X @ Y2 ) @ ( divide_divide_real @ W @ Z ) )
% 0.35/0.56            = ( ord_less_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y2 ) ) @ ( times_times_real @ Y2 @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % frac_less_eq
% 0.35/0.56  thf(fact_2841_frac__less__eq,axiom,
% 0.35/0.56      ! [Y2: rat,Z: rat,X: rat,W: rat] :
% 0.35/0.56        ( ( Y2 != zero_zero_rat )
% 0.35/0.56       => ( ( Z != zero_zero_rat )
% 0.35/0.56         => ( ( ord_less_rat @ ( divide_divide_rat @ X @ Y2 ) @ ( divide_divide_rat @ W @ Z ) )
% 0.35/0.56            = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y2 ) ) @ ( times_times_rat @ Y2 @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % frac_less_eq
% 0.35/0.56  thf(fact_2842_power__Suc__le__self,axiom,
% 0.35/0.56      ! [A: rat,N: nat] :
% 0.35/0.56        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.35/0.56       => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.35/0.56         => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power_Suc_le_self
% 0.35/0.56  thf(fact_2843_power__Suc__le__self,axiom,
% 0.35/0.56      ! [A: real,N: nat] :
% 0.35/0.56        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.35/0.56       => ( ( ord_less_eq_real @ A @ one_one_real )
% 0.35/0.56         => ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power_Suc_le_self
% 0.35/0.56  thf(fact_2844_power__Suc__le__self,axiom,
% 0.35/0.56      ! [A: nat,N: nat] :
% 0.35/0.56        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.35/0.56       => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.35/0.56         => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power_Suc_le_self
% 0.35/0.56  thf(fact_2845_power__Suc__le__self,axiom,
% 0.35/0.56      ! [A: int,N: nat] :
% 0.35/0.56        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.35/0.56       => ( ( ord_less_eq_int @ A @ one_one_int )
% 0.35/0.56         => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power_Suc_le_self
% 0.35/0.56  thf(fact_2846_power__Suc__less__one,axiom,
% 0.35/0.56      ! [A: real,N: nat] :
% 0.35/0.56        ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.56       => ( ( ord_less_real @ A @ one_one_real )
% 0.35/0.56         => ( ord_less_real @ ( power_power_real @ A @ ( suc @ N ) ) @ one_one_real ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power_Suc_less_one
% 0.35/0.56  thf(fact_2847_power__Suc__less__one,axiom,
% 0.35/0.56      ! [A: rat,N: nat] :
% 0.35/0.56        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.35/0.56       => ( ( ord_less_rat @ A @ one_one_rat )
% 0.35/0.56         => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ one_one_rat ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power_Suc_less_one
% 0.35/0.56  thf(fact_2848_power__Suc__less__one,axiom,
% 0.35/0.56      ! [A: nat,N: nat] :
% 0.35/0.56        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.35/0.56       => ( ( ord_less_nat @ A @ one_one_nat )
% 0.35/0.56         => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ one_one_nat ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power_Suc_less_one
% 0.35/0.56  thf(fact_2849_power__Suc__less__one,axiom,
% 0.35/0.56      ! [A: int,N: nat] :
% 0.35/0.56        ( ( ord_less_int @ zero_zero_int @ A )
% 0.35/0.56       => ( ( ord_less_int @ A @ one_one_int )
% 0.35/0.56         => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N ) ) @ one_one_int ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power_Suc_less_one
% 0.35/0.56  thf(fact_2850_power__strict__decreasing,axiom,
% 0.35/0.56      ! [N: nat,N4: nat,A: real] :
% 0.35/0.56        ( ( ord_less_nat @ N @ N4 )
% 0.35/0.56       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.56         => ( ( ord_less_real @ A @ one_one_real )
% 0.35/0.56           => ( ord_less_real @ ( power_power_real @ A @ N4 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power_strict_decreasing
% 0.35/0.56  thf(fact_2851_power__strict__decreasing,axiom,
% 0.35/0.56      ! [N: nat,N4: nat,A: rat] :
% 0.35/0.56        ( ( ord_less_nat @ N @ N4 )
% 0.35/0.56       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.35/0.56         => ( ( ord_less_rat @ A @ one_one_rat )
% 0.35/0.56           => ( ord_less_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power_strict_decreasing
% 0.35/0.56  thf(fact_2852_power__strict__decreasing,axiom,
% 0.35/0.56      ! [N: nat,N4: nat,A: nat] :
% 0.35/0.56        ( ( ord_less_nat @ N @ N4 )
% 0.35/0.56       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.35/0.56         => ( ( ord_less_nat @ A @ one_one_nat )
% 0.35/0.56           => ( ord_less_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power_strict_decreasing
% 0.35/0.56  thf(fact_2853_power__strict__decreasing,axiom,
% 0.35/0.56      ! [N: nat,N4: nat,A: int] :
% 0.35/0.56        ( ( ord_less_nat @ N @ N4 )
% 0.35/0.56       => ( ( ord_less_int @ zero_zero_int @ A )
% 0.35/0.56         => ( ( ord_less_int @ A @ one_one_int )
% 0.35/0.56           => ( ord_less_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power_strict_decreasing
% 0.35/0.56  thf(fact_2854_zero__power2,axiom,
% 0.35/0.56      ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.56      = zero_zero_rat ) ).
% 0.35/0.56  
% 0.35/0.56  % zero_power2
% 0.35/0.56  thf(fact_2855_zero__power2,axiom,
% 0.35/0.56      ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.56      = zero_zero_nat ) ).
% 0.35/0.56  
% 0.35/0.56  % zero_power2
% 0.35/0.56  thf(fact_2856_zero__power2,axiom,
% 0.35/0.56      ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.56      = zero_zero_real ) ).
% 0.35/0.56  
% 0.35/0.56  % zero_power2
% 0.35/0.56  thf(fact_2857_zero__power2,axiom,
% 0.35/0.56      ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.56      = zero_zero_int ) ).
% 0.35/0.56  
% 0.35/0.56  % zero_power2
% 0.35/0.56  thf(fact_2858_zero__power2,axiom,
% 0.35/0.56      ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.56      = zero_zero_complex ) ).
% 0.35/0.56  
% 0.35/0.56  % zero_power2
% 0.35/0.56  thf(fact_2859_power__decreasing,axiom,
% 0.35/0.56      ! [N: nat,N4: nat,A: rat] :
% 0.35/0.56        ( ( ord_less_eq_nat @ N @ N4 )
% 0.35/0.56       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.35/0.56         => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.35/0.56           => ( ord_less_eq_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power_decreasing
% 0.35/0.56  thf(fact_2860_power__decreasing,axiom,
% 0.35/0.56      ! [N: nat,N4: nat,A: real] :
% 0.35/0.56        ( ( ord_less_eq_nat @ N @ N4 )
% 0.35/0.56       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.35/0.56         => ( ( ord_less_eq_real @ A @ one_one_real )
% 0.35/0.56           => ( ord_less_eq_real @ ( power_power_real @ A @ N4 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power_decreasing
% 0.35/0.56  thf(fact_2861_power__decreasing,axiom,
% 0.35/0.56      ! [N: nat,N4: nat,A: nat] :
% 0.35/0.56        ( ( ord_less_eq_nat @ N @ N4 )
% 0.35/0.56       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.35/0.56         => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.35/0.56           => ( ord_less_eq_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power_decreasing
% 0.35/0.56  thf(fact_2862_power__decreasing,axiom,
% 0.35/0.56      ! [N: nat,N4: nat,A: int] :
% 0.35/0.56        ( ( ord_less_eq_nat @ N @ N4 )
% 0.35/0.56       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.35/0.56         => ( ( ord_less_eq_int @ A @ one_one_int )
% 0.35/0.56           => ( ord_less_eq_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power_decreasing
% 0.35/0.56  thf(fact_2863_numeral__2__eq__2,axiom,
% 0.35/0.56      ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.35/0.56      = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % numeral_2_eq_2
% 0.35/0.56  thf(fact_2864_self__le__power,axiom,
% 0.35/0.56      ! [A: rat,N: nat] :
% 0.35/0.56        ( ( ord_less_eq_rat @ one_one_rat @ A )
% 0.35/0.56       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.56         => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % self_le_power
% 0.35/0.56  thf(fact_2865_self__le__power,axiom,
% 0.35/0.56      ! [A: real,N: nat] :
% 0.35/0.56        ( ( ord_less_eq_real @ one_one_real @ A )
% 0.35/0.56       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.56         => ( ord_less_eq_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % self_le_power
% 0.35/0.56  thf(fact_2866_self__le__power,axiom,
% 0.35/0.56      ! [A: nat,N: nat] :
% 0.35/0.56        ( ( ord_less_eq_nat @ one_one_nat @ A )
% 0.35/0.56       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.56         => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % self_le_power
% 0.35/0.56  thf(fact_2867_self__le__power,axiom,
% 0.35/0.56      ! [A: int,N: nat] :
% 0.35/0.56        ( ( ord_less_eq_int @ one_one_int @ A )
% 0.35/0.56       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.56         => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % self_le_power
% 0.35/0.56  thf(fact_2868_one__less__power,axiom,
% 0.35/0.56      ! [A: real,N: nat] :
% 0.35/0.56        ( ( ord_less_real @ one_one_real @ A )
% 0.35/0.56       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.56         => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % one_less_power
% 0.35/0.56  thf(fact_2869_one__less__power,axiom,
% 0.35/0.56      ! [A: rat,N: nat] :
% 0.35/0.56        ( ( ord_less_rat @ one_one_rat @ A )
% 0.35/0.56       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.56         => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % one_less_power
% 0.35/0.56  thf(fact_2870_one__less__power,axiom,
% 0.35/0.56      ! [A: nat,N: nat] :
% 0.35/0.56        ( ( ord_less_nat @ one_one_nat @ A )
% 0.35/0.56       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.56         => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % one_less_power
% 0.35/0.56  thf(fact_2871_one__less__power,axiom,
% 0.35/0.56      ! [A: int,N: nat] :
% 0.35/0.56        ( ( ord_less_int @ one_one_int @ A )
% 0.35/0.56       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.56         => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % one_less_power
% 0.35/0.56  thf(fact_2872_pos2,axiom,
% 0.35/0.56      ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ).
% 0.35/0.56  
% 0.35/0.56  % pos2
% 0.35/0.56  thf(fact_2873_power__diff,axiom,
% 0.35/0.56      ! [A: complex,N: nat,M: nat] :
% 0.35/0.56        ( ( A != zero_zero_complex )
% 0.35/0.56       => ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.56         => ( ( power_power_complex @ A @ ( minus_minus_nat @ M @ N ) )
% 0.35/0.56            = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power_diff
% 0.35/0.56  thf(fact_2874_power__diff,axiom,
% 0.35/0.56      ! [A: real,N: nat,M: nat] :
% 0.35/0.56        ( ( A != zero_zero_real )
% 0.35/0.56       => ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.56         => ( ( power_power_real @ A @ ( minus_minus_nat @ M @ N ) )
% 0.35/0.56            = ( divide_divide_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power_diff
% 0.35/0.56  thf(fact_2875_power__diff,axiom,
% 0.35/0.56      ! [A: rat,N: nat,M: nat] :
% 0.35/0.56        ( ( A != zero_zero_rat )
% 0.35/0.56       => ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.56         => ( ( power_power_rat @ A @ ( minus_minus_nat @ M @ N ) )
% 0.35/0.56            = ( divide_divide_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power_diff
% 0.35/0.56  thf(fact_2876_power__diff,axiom,
% 0.35/0.56      ! [A: nat,N: nat,M: nat] :
% 0.35/0.56        ( ( A != zero_zero_nat )
% 0.35/0.56       => ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.56         => ( ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) )
% 0.35/0.56            = ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power_diff
% 0.35/0.56  thf(fact_2877_power__diff,axiom,
% 0.35/0.56      ! [A: int,N: nat,M: nat] :
% 0.35/0.56        ( ( A != zero_zero_int )
% 0.35/0.56       => ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.56         => ( ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) )
% 0.35/0.56            = ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power_diff
% 0.35/0.56  thf(fact_2878_numeral__3__eq__3,axiom,
% 0.35/0.56      ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.35/0.56      = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % numeral_3_eq_3
% 0.35/0.56  thf(fact_2879_Suc__pred_H,axiom,
% 0.35/0.56      ! [N: nat] :
% 0.35/0.56        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.56       => ( N
% 0.35/0.56          = ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % Suc_pred'
% 0.35/0.56  thf(fact_2880_Suc__diff__eq__diff__pred,axiom,
% 0.35/0.56      ! [N: nat,M: nat] :
% 0.35/0.56        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.56       => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 0.35/0.56          = ( minus_minus_nat @ M @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % Suc_diff_eq_diff_pred
% 0.35/0.56  thf(fact_2881_add__eq__if,axiom,
% 0.35/0.56      ( plus_plus_nat
% 0.35/0.56      = ( ^ [M6: nat,N2: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N2 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) @ N2 ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % add_eq_if
% 0.35/0.56  thf(fact_2882_div__if,axiom,
% 0.35/0.56      ( divide_divide_nat
% 0.35/0.56      = ( ^ [M6: nat,N2: nat] :
% 0.35/0.56            ( if_nat
% 0.35/0.56            @ ( ( ord_less_nat @ M6 @ N2 )
% 0.35/0.56              | ( N2 = zero_zero_nat ) )
% 0.35/0.56            @ zero_zero_nat
% 0.35/0.56            @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M6 @ N2 ) @ N2 ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % div_if
% 0.35/0.56  thf(fact_2883_div__geq,axiom,
% 0.35/0.56      ! [N: nat,M: nat] :
% 0.35/0.56        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.56       => ( ~ ( ord_less_nat @ M @ N )
% 0.35/0.56         => ( ( divide_divide_nat @ M @ N )
% 0.35/0.56            = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % div_geq
% 0.35/0.56  thf(fact_2884_split__div,axiom,
% 0.35/0.56      ! [P: nat > $o,M: nat,N: nat] :
% 0.35/0.56        ( ( P @ ( divide_divide_nat @ M @ N ) )
% 0.35/0.56        = ( ( ( N = zero_zero_nat )
% 0.35/0.56           => ( P @ zero_zero_nat ) )
% 0.35/0.56          & ( ( N != zero_zero_nat )
% 0.35/0.56           => ! [I3: nat,J3: nat] :
% 0.35/0.56                ( ( ord_less_nat @ J3 @ N )
% 0.35/0.56               => ( ( M
% 0.35/0.56                    = ( plus_plus_nat @ ( times_times_nat @ N @ I3 ) @ J3 ) )
% 0.35/0.56                 => ( P @ I3 ) ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % split_div
% 0.35/0.56  thf(fact_2885_dividend__less__div__times,axiom,
% 0.35/0.56      ! [N: nat,M: nat] :
% 0.35/0.56        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.56       => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % dividend_less_div_times
% 0.35/0.56  thf(fact_2886_dividend__less__times__div,axiom,
% 0.35/0.56      ! [N: nat,M: nat] :
% 0.35/0.56        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.56       => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % dividend_less_times_div
% 0.35/0.56  thf(fact_2887_less__eq__div__iff__mult__less__eq,axiom,
% 0.35/0.56      ! [Q2: nat,M: nat,N: nat] :
% 0.35/0.56        ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 0.35/0.56       => ( ( ord_less_eq_nat @ M @ ( divide_divide_nat @ N @ Q2 ) )
% 0.35/0.56          = ( ord_less_eq_nat @ ( times_times_nat @ M @ Q2 ) @ N ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % less_eq_div_iff_mult_less_eq
% 0.35/0.56  thf(fact_2888_mult__eq__if,axiom,
% 0.35/0.56      ( times_times_nat
% 0.35/0.56      = ( ^ [M6: nat,N2: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N2 @ ( times_times_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) @ N2 ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % mult_eq_if
% 0.35/0.56  thf(fact_2889_VEBT__internal_Onaive__member_Oelims_I1_J,axiom,
% 0.35/0.56      ! [X: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 0.35/0.56        ( ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 0.35/0.56          = Y2 )
% 0.35/0.56       => ( ! [A4: $o,B3: $o] :
% 0.35/0.56              ( ( X
% 0.35/0.56                = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.56             => ( Y2
% 0.35/0.56                = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 0.35/0.56                       => A4 )
% 0.35/0.56                      & ( ( Xa2 != zero_zero_nat )
% 0.35/0.56                       => ( ( ( Xa2 = one_one_nat )
% 0.35/0.56                           => B3 )
% 0.35/0.56                          & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 0.35/0.56         => ( ( ? [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.35/0.56                  ( X
% 0.35/0.56                  = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 0.35/0.56             => Y2 )
% 0.35/0.56           => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 0.35/0.56                  ( ? [S: vEBT_VEBT] :
% 0.35/0.56                      ( X
% 0.35/0.56                      = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) )
% 0.35/0.56                 => ( Y2
% 0.35/0.56                    = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.56                           => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.56                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % VEBT_internal.naive_member.elims(1)
% 0.35/0.56  thf(fact_2890_VEBT__internal_Onaive__member_Oelims_I2_J,axiom,
% 0.35/0.56      ! [X: vEBT_VEBT,Xa2: nat] :
% 0.35/0.56        ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 0.35/0.56       => ( ! [A4: $o,B3: $o] :
% 0.35/0.56              ( ( X
% 0.35/0.56                = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.56             => ~ ( ( ( Xa2 = zero_zero_nat )
% 0.35/0.56                   => A4 )
% 0.35/0.56                  & ( ( Xa2 != zero_zero_nat )
% 0.35/0.56                   => ( ( ( Xa2 = one_one_nat )
% 0.35/0.56                       => B3 )
% 0.35/0.56                      & ( Xa2 = one_one_nat ) ) ) ) )
% 0.35/0.56         => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 0.35/0.56                ( ? [S: vEBT_VEBT] :
% 0.35/0.56                    ( X
% 0.35/0.56                    = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) )
% 0.35/0.56               => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.56                     => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.56                    & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % VEBT_internal.naive_member.elims(2)
% 0.35/0.56  thf(fact_2891_VEBT__internal_Onaive__member_Oelims_I3_J,axiom,
% 0.35/0.56      ! [X: vEBT_VEBT,Xa2: nat] :
% 0.35/0.56        ( ~ ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 0.35/0.56       => ( ! [A4: $o,B3: $o] :
% 0.35/0.56              ( ( X
% 0.35/0.56                = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.56             => ( ( ( Xa2 = zero_zero_nat )
% 0.35/0.56                 => A4 )
% 0.35/0.56                & ( ( Xa2 != zero_zero_nat )
% 0.35/0.56                 => ( ( ( Xa2 = one_one_nat )
% 0.35/0.56                     => B3 )
% 0.35/0.56                    & ( Xa2 = one_one_nat ) ) ) ) )
% 0.35/0.56         => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.35/0.56                ( X
% 0.35/0.56               != ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 0.35/0.56           => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 0.35/0.56                  ( ? [S: vEBT_VEBT] :
% 0.35/0.56                      ( X
% 0.35/0.56                      = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) )
% 0.35/0.56                 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.56                     => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.56                    & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % VEBT_internal.naive_member.elims(3)
% 0.35/0.56  thf(fact_2892_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I4_J,axiom,
% 0.35/0.56      ! [Uy: nat,Uz: list_VEBT_VEBT,Va: vEBT_VEBT,Vb: nat] :
% 0.35/0.56        ( ( vEBT_T_p_r_e_d @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz @ Va ) @ Vb )
% 0.35/0.56        = one_one_nat ) ).
% 0.35/0.56  
% 0.35/0.56  % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.simps(4)
% 0.35/0.56  thf(fact_2893_vebt__member_Osimps_I4_J,axiom,
% 0.35/0.56      ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 0.35/0.56        ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X ) ).
% 0.35/0.56  
% 0.35/0.56  % vebt_member.simps(4)
% 0.35/0.56  thf(fact_2894_vebt__delete_Osimps_I5_J,axiom,
% 0.35/0.56      ! [Mi: nat,Ma: nat,TrLst: list_VEBT_VEBT,Smry: vEBT_VEBT,X: nat] :
% 0.35/0.56        ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TrLst @ Smry ) @ X )
% 0.35/0.56        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TrLst @ Smry ) ) ).
% 0.35/0.56  
% 0.35/0.56  % vebt_delete.simps(5)
% 0.35/0.56  thf(fact_2895_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I3_J,axiom,
% 0.35/0.56      ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT,X: nat] :
% 0.35/0.56        ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) @ X )
% 0.35/0.56        = one_one_nat ) ).
% 0.35/0.56  
% 0.35/0.56  % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(3)
% 0.35/0.56  thf(fact_2896_vebt__succ_Osimps_I4_J,axiom,
% 0.35/0.56      ! [V: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd: vEBT_VEBT,Ve: nat] :
% 0.35/0.56        ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc @ Vd ) @ Ve )
% 0.35/0.56        = none_nat ) ).
% 0.35/0.56  
% 0.35/0.56  % vebt_succ.simps(4)
% 0.35/0.56  thf(fact_2897_vebt__pred_Osimps_I5_J,axiom,
% 0.35/0.56      ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT,Vf: nat] :
% 0.35/0.56        ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) @ Vf )
% 0.35/0.56        = none_nat ) ).
% 0.35/0.56  
% 0.35/0.56  % vebt_pred.simps(5)
% 0.35/0.56  thf(fact_2898_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I5_J,axiom,
% 0.35/0.56      ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT,Vf: nat] :
% 0.35/0.56        ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) @ Vf )
% 0.35/0.56        = one_one_nat ) ).
% 0.35/0.56  
% 0.35/0.56  % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.simps(5)
% 0.35/0.56  thf(fact_2899_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I4_J,axiom,
% 0.35/0.56      ! [V: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd: vEBT_VEBT,Ve: nat] :
% 0.35/0.56        ( ( vEBT_T_s_u_c_c @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc @ Vd ) @ Ve )
% 0.35/0.56        = one_one_nat ) ).
% 0.35/0.56  
% 0.35/0.56  % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.simps(4)
% 0.35/0.56  thf(fact_2900_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I4_J,axiom,
% 0.35/0.56      ! [V: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd: vEBT_VEBT,Ve: nat] :
% 0.35/0.56        ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc @ Vd ) @ Ve )
% 0.35/0.56        = one_one_nat ) ).
% 0.35/0.56  
% 0.35/0.56  % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.simps(4)
% 0.35/0.56  thf(fact_2901_VEBT__internal_Omembermima_Oelims_I1_J,axiom,
% 0.35/0.56      ! [X: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 0.35/0.56        ( ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 0.35/0.56          = Y2 )
% 0.35/0.56       => ( ( ? [Uu2: $o,Uv2: $o] :
% 0.35/0.56                ( X
% 0.35/0.56                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.35/0.56           => Y2 )
% 0.35/0.56         => ( ( ? [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 0.35/0.56                  ( X
% 0.35/0.56                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 0.35/0.56             => Y2 )
% 0.35/0.56           => ( ! [Mi2: nat,Ma2: nat] :
% 0.35/0.56                  ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 0.35/0.56                      ( X
% 0.35/0.56                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 0.35/0.56                 => ( Y2
% 0.35/0.56                    = ( ~ ( ( Xa2 = Mi2 )
% 0.35/0.56                          | ( Xa2 = Ma2 ) ) ) ) )
% 0.35/0.56             => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 0.35/0.56                    ( ? [Vc2: vEBT_VEBT] :
% 0.35/0.56                        ( X
% 0.35/0.56                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 0.35/0.56                   => ( Y2
% 0.35/0.56                      = ( ~ ( ( Xa2 = Mi2 )
% 0.35/0.56                            | ( Xa2 = Ma2 )
% 0.35/0.56                            | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.56                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.56                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) )
% 0.35/0.56               => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT] :
% 0.35/0.56                      ( ? [Vd2: vEBT_VEBT] :
% 0.35/0.56                          ( X
% 0.35/0.56                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 0.35/0.56                     => ( Y2
% 0.35/0.56                        = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.56                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.56                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % VEBT_internal.membermima.elims(1)
% 0.35/0.56  thf(fact_2902_VEBT__internal_Omembermima_Oelims_I3_J,axiom,
% 0.35/0.56      ! [X: vEBT_VEBT,Xa2: nat] :
% 0.35/0.56        ( ~ ( vEBT_VEBT_membermima @ X @ Xa2 )
% 0.35/0.56       => ( ! [Uu2: $o,Uv2: $o] :
% 0.35/0.56              ( X
% 0.35/0.56             != ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.35/0.56         => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 0.35/0.56                ( X
% 0.35/0.56               != ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 0.35/0.56           => ( ! [Mi2: nat,Ma2: nat] :
% 0.35/0.56                  ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 0.35/0.56                      ( X
% 0.35/0.56                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 0.35/0.56                 => ( ( Xa2 = Mi2 )
% 0.35/0.56                    | ( Xa2 = Ma2 ) ) )
% 0.35/0.56             => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 0.35/0.56                    ( ? [Vc2: vEBT_VEBT] :
% 0.35/0.56                        ( X
% 0.35/0.56                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 0.35/0.56                   => ( ( Xa2 = Mi2 )
% 0.35/0.56                      | ( Xa2 = Ma2 )
% 0.35/0.56                      | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.56                         => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.56                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 0.35/0.56               => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT] :
% 0.35/0.56                      ( ? [Vd2: vEBT_VEBT] :
% 0.35/0.56                          ( X
% 0.35/0.56                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 0.35/0.56                     => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.56                         => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.56                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % VEBT_internal.membermima.elims(3)
% 0.35/0.56  thf(fact_2903_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Oelims,axiom,
% 0.35/0.56      ! [X: vEBT_VEBT,Y2: nat] :
% 0.35/0.56        ( ( ( vEBT_T_m_i_n_N_u_l_l @ X )
% 0.35/0.56          = Y2 )
% 0.35/0.56       => ( ( ( X
% 0.35/0.56              = ( vEBT_Leaf @ $false @ $false ) )
% 0.35/0.56           => ( Y2 != one_one_nat ) )
% 0.35/0.56         => ( ( ? [Uv2: $o] :
% 0.35/0.56                  ( X
% 0.35/0.56                  = ( vEBT_Leaf @ $true @ Uv2 ) )
% 0.35/0.56             => ( Y2 != one_one_nat ) )
% 0.35/0.56           => ( ( ? [Uu2: $o] :
% 0.35/0.56                    ( X
% 0.35/0.56                    = ( vEBT_Leaf @ Uu2 @ $true ) )
% 0.35/0.56               => ( Y2 != one_one_nat ) )
% 0.35/0.56             => ( ( ? [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 0.35/0.56                      ( X
% 0.35/0.56                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 0.35/0.56                 => ( Y2 != one_one_nat ) )
% 0.35/0.56               => ~ ( ? [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.35/0.56                        ( X
% 0.35/0.56                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 0.35/0.56                   => ( Y2 != one_one_nat ) ) ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.elims
% 0.35/0.56  thf(fact_2904_convex__bound__lt,axiom,
% 0.35/0.56      ! [X: real,A: real,Y2: real,U: real,V: real] :
% 0.35/0.56        ( ( ord_less_real @ X @ A )
% 0.35/0.56       => ( ( ord_less_real @ Y2 @ A )
% 0.35/0.56         => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 0.35/0.56           => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 0.35/0.56             => ( ( ( plus_plus_real @ U @ V )
% 0.35/0.56                  = one_one_real )
% 0.35/0.56               => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V @ Y2 ) ) @ A ) ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % convex_bound_lt
% 0.35/0.56  thf(fact_2905_convex__bound__lt,axiom,
% 0.35/0.56      ! [X: rat,A: rat,Y2: rat,U: rat,V: rat] :
% 0.35/0.56        ( ( ord_less_rat @ X @ A )
% 0.35/0.56       => ( ( ord_less_rat @ Y2 @ A )
% 0.35/0.56         => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 0.35/0.56           => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 0.35/0.56             => ( ( ( plus_plus_rat @ U @ V )
% 0.35/0.56                  = one_one_rat )
% 0.35/0.56               => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y2 ) ) @ A ) ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % convex_bound_lt
% 0.35/0.56  thf(fact_2906_convex__bound__lt,axiom,
% 0.35/0.56      ! [X: int,A: int,Y2: int,U: int,V: int] :
% 0.35/0.56        ( ( ord_less_int @ X @ A )
% 0.35/0.56       => ( ( ord_less_int @ Y2 @ A )
% 0.35/0.56         => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 0.35/0.56           => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 0.35/0.56             => ( ( ( plus_plus_int @ U @ V )
% 0.35/0.56                  = one_one_int )
% 0.35/0.56               => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y2 ) ) @ A ) ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % convex_bound_lt
% 0.35/0.56  thf(fact_2907_divide__le__eq__numeral_I1_J,axiom,
% 0.35/0.56      ! [B: real,C: real,W: num] :
% 0.35/0.56        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 0.35/0.56        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.56           => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 0.35/0.56          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.56           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.56               => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 0.35/0.56              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.56               => ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % divide_le_eq_numeral(1)
% 0.35/0.56  thf(fact_2908_divide__le__eq__numeral_I1_J,axiom,
% 0.35/0.56      ! [B: rat,C: rat,W: num] :
% 0.35/0.56        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 0.35/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.56           => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 0.35/0.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.56               => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 0.35/0.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.56               => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % divide_le_eq_numeral(1)
% 0.35/0.56  thf(fact_2909_le__divide__eq__numeral_I1_J,axiom,
% 0.35/0.56      ! [W: num,B: real,C: real] :
% 0.35/0.56        ( ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 0.35/0.56        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.56           => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 0.35/0.56          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.56           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.56               => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 0.35/0.56              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.56               => ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % le_divide_eq_numeral(1)
% 0.35/0.56  thf(fact_2910_le__divide__eq__numeral_I1_J,axiom,
% 0.35/0.56      ! [W: num,B: rat,C: rat] :
% 0.35/0.56        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 0.35/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.56           => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 0.35/0.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.56               => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 0.35/0.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.56               => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % le_divide_eq_numeral(1)
% 0.35/0.56  thf(fact_2911_half__gt__zero__iff,axiom,
% 0.35/0.56      ! [A: real] :
% 0.35/0.56        ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.56        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.35/0.56  
% 0.35/0.56  % half_gt_zero_iff
% 0.35/0.56  thf(fact_2912_half__gt__zero__iff,axiom,
% 0.35/0.56      ! [A: rat] :
% 0.35/0.56        ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 0.35/0.56        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.35/0.56  
% 0.35/0.56  % half_gt_zero_iff
% 0.35/0.56  thf(fact_2913_half__gt__zero,axiom,
% 0.35/0.56      ! [A: real] :
% 0.35/0.56        ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.56       => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % half_gt_zero
% 0.35/0.56  thf(fact_2914_half__gt__zero,axiom,
% 0.35/0.56      ! [A: rat] :
% 0.35/0.56        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.35/0.56       => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % half_gt_zero
% 0.35/0.56  thf(fact_2915_scaling__mono,axiom,
% 0.35/0.56      ! [U: real,V: real,R: real,S3: real] :
% 0.35/0.56        ( ( ord_less_eq_real @ U @ V )
% 0.35/0.56       => ( ( ord_less_eq_real @ zero_zero_real @ R )
% 0.35/0.56         => ( ( ord_less_eq_real @ R @ S3 )
% 0.35/0.56           => ( ord_less_eq_real @ ( plus_plus_real @ U @ ( divide_divide_real @ ( times_times_real @ R @ ( minus_minus_real @ V @ U ) ) @ S3 ) ) @ V ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % scaling_mono
% 0.35/0.56  thf(fact_2916_scaling__mono,axiom,
% 0.35/0.56      ! [U: rat,V: rat,R: rat,S3: rat] :
% 0.35/0.56        ( ( ord_less_eq_rat @ U @ V )
% 0.35/0.56       => ( ( ord_less_eq_rat @ zero_zero_rat @ R )
% 0.35/0.56         => ( ( ord_less_eq_rat @ R @ S3 )
% 0.35/0.56           => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R @ ( minus_minus_rat @ V @ U ) ) @ S3 ) ) @ V ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % scaling_mono
% 0.35/0.56  thf(fact_2917_power2__le__imp__le,axiom,
% 0.35/0.56      ! [X: rat,Y2: rat] :
% 0.35/0.56        ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.56       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 0.35/0.56         => ( ord_less_eq_rat @ X @ Y2 ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power2_le_imp_le
% 0.35/0.56  thf(fact_2918_power2__le__imp__le,axiom,
% 0.35/0.56      ! [X: real,Y2: real] :
% 0.35/0.56        ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.56       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 0.35/0.56         => ( ord_less_eq_real @ X @ Y2 ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power2_le_imp_le
% 0.35/0.56  thf(fact_2919_power2__le__imp__le,axiom,
% 0.35/0.56      ! [X: nat,Y2: nat] :
% 0.35/0.56        ( ( ord_less_eq_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.56       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y2 )
% 0.35/0.56         => ( ord_less_eq_nat @ X @ Y2 ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power2_le_imp_le
% 0.35/0.56  thf(fact_2920_power2__le__imp__le,axiom,
% 0.35/0.56      ! [X: int,Y2: int] :
% 0.35/0.56        ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.56       => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 0.35/0.56         => ( ord_less_eq_int @ X @ Y2 ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power2_le_imp_le
% 0.35/0.56  thf(fact_2921_power2__eq__imp__eq,axiom,
% 0.35/0.56      ! [X: rat,Y2: rat] :
% 0.35/0.56        ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.56          = ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.56       => ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.35/0.56         => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 0.35/0.56           => ( X = Y2 ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power2_eq_imp_eq
% 0.35/0.56  thf(fact_2922_power2__eq__imp__eq,axiom,
% 0.35/0.56      ! [X: real,Y2: real] :
% 0.35/0.56        ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.56          = ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.56       => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.56         => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 0.35/0.56           => ( X = Y2 ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power2_eq_imp_eq
% 0.35/0.56  thf(fact_2923_power2__eq__imp__eq,axiom,
% 0.35/0.56      ! [X: nat,Y2: nat] :
% 0.35/0.56        ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.56          = ( power_power_nat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.56       => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 0.35/0.56         => ( ( ord_less_eq_nat @ zero_zero_nat @ Y2 )
% 0.35/0.56           => ( X = Y2 ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power2_eq_imp_eq
% 0.35/0.56  thf(fact_2924_power2__eq__imp__eq,axiom,
% 0.35/0.56      ! [X: int,Y2: int] :
% 0.35/0.56        ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.56          = ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.56       => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.35/0.56         => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 0.35/0.56           => ( X = Y2 ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power2_eq_imp_eq
% 0.35/0.56  thf(fact_2925_zero__le__power2,axiom,
% 0.35/0.56      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % zero_le_power2
% 0.35/0.56  thf(fact_2926_zero__le__power2,axiom,
% 0.35/0.56      ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % zero_le_power2
% 0.35/0.56  thf(fact_2927_zero__le__power2,axiom,
% 0.35/0.56      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % zero_le_power2
% 0.35/0.56  thf(fact_2928_power2__less__0,axiom,
% 0.35/0.56      ! [A: real] :
% 0.35/0.56        ~ ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real ) ).
% 0.35/0.56  
% 0.35/0.56  % power2_less_0
% 0.35/0.56  thf(fact_2929_power2__less__0,axiom,
% 0.35/0.56      ! [A: rat] :
% 0.35/0.56        ~ ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat ) ).
% 0.35/0.56  
% 0.35/0.56  % power2_less_0
% 0.35/0.56  thf(fact_2930_power2__less__0,axiom,
% 0.35/0.56      ! [A: int] :
% 0.35/0.56        ~ ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int ) ).
% 0.35/0.56  
% 0.35/0.56  % power2_less_0
% 0.35/0.56  thf(fact_2931_exp__add__not__zero__imp__right,axiom,
% 0.35/0.56      ! [M: nat,N: nat] :
% 0.35/0.56        ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 0.35/0.56         != zero_zero_nat )
% 0.35/0.56       => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.56         != zero_zero_nat ) ) ).
% 0.35/0.56  
% 0.35/0.56  % exp_add_not_zero_imp_right
% 0.35/0.56  thf(fact_2932_exp__add__not__zero__imp__right,axiom,
% 0.35/0.56      ! [M: nat,N: nat] :
% 0.35/0.56        ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 0.35/0.56         != zero_zero_int )
% 0.35/0.56       => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 0.35/0.56         != zero_zero_int ) ) ).
% 0.35/0.56  
% 0.35/0.56  % exp_add_not_zero_imp_right
% 0.35/0.56  thf(fact_2933_exp__add__not__zero__imp__left,axiom,
% 0.35/0.56      ! [M: nat,N: nat] :
% 0.35/0.56        ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 0.35/0.56         != zero_zero_nat )
% 0.35/0.56       => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 0.35/0.56         != zero_zero_nat ) ) ).
% 0.35/0.56  
% 0.35/0.56  % exp_add_not_zero_imp_left
% 0.35/0.56  thf(fact_2934_exp__add__not__zero__imp__left,axiom,
% 0.35/0.56      ! [M: nat,N: nat] :
% 0.35/0.56        ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 0.35/0.56         != zero_zero_int )
% 0.35/0.56       => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 0.35/0.56         != zero_zero_int ) ) ).
% 0.35/0.56  
% 0.35/0.56  % exp_add_not_zero_imp_left
% 0.35/0.56  thf(fact_2935_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 0.35/0.56      ! [N: nat,M: nat] :
% 0.35/0.56        ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.56         != zero_zero_nat )
% 0.35/0.56       => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 0.35/0.56         != zero_zero_nat ) ) ).
% 0.35/0.56  
% 0.35/0.56  % exp_not_zero_imp_exp_diff_not_zero
% 0.35/0.56  thf(fact_2936_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 0.35/0.56      ! [N: nat,M: nat] :
% 0.35/0.56        ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 0.35/0.56         != zero_zero_int )
% 0.35/0.56       => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 0.35/0.56         != zero_zero_int ) ) ).
% 0.35/0.56  
% 0.35/0.56  % exp_not_zero_imp_exp_diff_not_zero
% 0.35/0.56  thf(fact_2937_power__diff__power__eq,axiom,
% 0.35/0.56      ! [A: nat,N: nat,M: nat] :
% 0.35/0.56        ( ( A != zero_zero_nat )
% 0.35/0.56       => ( ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.56           => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 0.35/0.56              = ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 0.35/0.56          & ( ~ ( ord_less_eq_nat @ N @ M )
% 0.35/0.56           => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 0.35/0.56              = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power_diff_power_eq
% 0.35/0.56  thf(fact_2938_power__diff__power__eq,axiom,
% 0.35/0.56      ! [A: int,N: nat,M: nat] :
% 0.35/0.56        ( ( A != zero_zero_int )
% 0.35/0.56       => ( ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.56           => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 0.35/0.56              = ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 0.35/0.56          & ( ~ ( ord_less_eq_nat @ N @ M )
% 0.35/0.56           => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 0.35/0.56              = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power_diff_power_eq
% 0.35/0.56  thf(fact_2939_less__2__cases__iff,axiom,
% 0.35/0.56      ! [N: nat] :
% 0.35/0.56        ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.56        = ( ( N = zero_zero_nat )
% 0.35/0.56          | ( N
% 0.35/0.56            = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % less_2_cases_iff
% 0.35/0.56  thf(fact_2940_less__2__cases,axiom,
% 0.35/0.56      ! [N: nat] :
% 0.35/0.56        ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.56       => ( ( N = zero_zero_nat )
% 0.35/0.56          | ( N
% 0.35/0.56            = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % less_2_cases
% 0.35/0.56  thf(fact_2941_nat__induct2,axiom,
% 0.35/0.56      ! [P: nat > $o,N: nat] :
% 0.35/0.56        ( ( P @ zero_zero_nat )
% 0.35/0.56       => ( ( P @ one_one_nat )
% 0.35/0.56         => ( ! [N3: nat] :
% 0.35/0.56                ( ( P @ N3 )
% 0.35/0.56               => ( P @ ( plus_plus_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.56           => ( P @ N ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % nat_induct2
% 0.35/0.56  thf(fact_2942_power__eq__if,axiom,
% 0.35/0.56      ( power_power_rat
% 0.35/0.56      = ( ^ [P4: rat,M6: nat] : ( if_rat @ ( M6 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P4 @ ( power_power_rat @ P4 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power_eq_if
% 0.35/0.56  thf(fact_2943_power__eq__if,axiom,
% 0.35/0.56      ( power_power_complex
% 0.35/0.56      = ( ^ [P4: complex,M6: nat] : ( if_complex @ ( M6 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ P4 @ ( power_power_complex @ P4 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power_eq_if
% 0.35/0.56  thf(fact_2944_power__eq__if,axiom,
% 0.35/0.56      ( power_power_real
% 0.35/0.56      = ( ^ [P4: real,M6: nat] : ( if_real @ ( M6 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ P4 @ ( power_power_real @ P4 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power_eq_if
% 0.35/0.56  thf(fact_2945_power__eq__if,axiom,
% 0.35/0.56      ( power_power_nat
% 0.35/0.56      = ( ^ [P4: nat,M6: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P4 @ ( power_power_nat @ P4 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power_eq_if
% 0.35/0.56  thf(fact_2946_power__eq__if,axiom,
% 0.35/0.56      ( power_power_int
% 0.35/0.56      = ( ^ [P4: int,M6: nat] : ( if_int @ ( M6 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P4 @ ( power_power_int @ P4 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power_eq_if
% 0.35/0.56  thf(fact_2947_power__minus__mult,axiom,
% 0.35/0.56      ! [N: nat,A: complex] :
% 0.35/0.56        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.56       => ( ( times_times_complex @ ( power_power_complex @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 0.35/0.56          = ( power_power_complex @ A @ N ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power_minus_mult
% 0.35/0.56  thf(fact_2948_power__minus__mult,axiom,
% 0.35/0.56      ! [N: nat,A: real] :
% 0.35/0.56        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.56       => ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 0.35/0.56          = ( power_power_real @ A @ N ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power_minus_mult
% 0.35/0.56  thf(fact_2949_power__minus__mult,axiom,
% 0.35/0.56      ! [N: nat,A: nat] :
% 0.35/0.56        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.56       => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 0.35/0.56          = ( power_power_nat @ A @ N ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power_minus_mult
% 0.35/0.56  thf(fact_2950_power__minus__mult,axiom,
% 0.35/0.56      ! [N: nat,A: int] :
% 0.35/0.56        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.56       => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 0.35/0.56          = ( power_power_int @ A @ N ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % power_minus_mult
% 0.35/0.56  thf(fact_2951_split__div_H,axiom,
% 0.35/0.56      ! [P: nat > $o,M: nat,N: nat] :
% 0.35/0.56        ( ( P @ ( divide_divide_nat @ M @ N ) )
% 0.35/0.56        = ( ( ( N = zero_zero_nat )
% 0.35/0.56            & ( P @ zero_zero_nat ) )
% 0.35/0.56          | ? [Q4: nat] :
% 0.35/0.56              ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q4 ) @ M )
% 0.35/0.56              & ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q4 ) ) )
% 0.35/0.56              & ( P @ Q4 ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % split_div'
% 0.35/0.56  thf(fact_2952_le__div__geq,axiom,
% 0.35/0.56      ! [N: nat,M: nat] :
% 0.35/0.56        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.56       => ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.56         => ( ( divide_divide_nat @ M @ N )
% 0.35/0.56            = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 0.35/0.56  
% 0.35/0.56  % le_div_geq
% 0.35/0.56  thf(fact_2953_vebt__delete_Osimps_I6_J,axiom,
% 0.35/0.56      ! [Mi: nat,Ma: nat,Tr: list_VEBT_VEBT,Sm: vEBT_VEBT,X: nat] :
% 0.35/0.56        ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) @ X )
% 0.35/0.56        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) ) ).
% 0.35/0.56  
% 0.35/0.56  % vebt_delete.simps(6)
% 0.35/0.56  thf(fact_2954_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I5_J,axiom,
% 0.35/0.56      ! [Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.35/0.56        ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TreeList @ Summary ) @ X )
% 0.35/0.56        = one_one_nat ) ).
% 0.35/0.56  
% 0.35/0.56  % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.simps(5)
% 0.35/0.56  thf(fact_2955_vebt__pred_Osimps_I6_J,axiom,
% 0.35/0.56      ! [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT,Vj: nat] :
% 0.35/0.56        ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Vj )
% 0.35/0.56        = none_nat ) ).
% 0.35/0.56  
% 0.35/0.56  % vebt_pred.simps(6)
% 0.35/0.56  thf(fact_2956_vebt__succ_Osimps_I5_J,axiom,
% 0.35/0.56      ! [V: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh: vEBT_VEBT,Vi: nat] :
% 0.35/0.56        ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh ) @ Vi )
% 0.35/0.57        = none_nat ) ).
% 0.35/0.57  
% 0.35/0.57  % vebt_succ.simps(5)
% 0.35/0.57  thf(fact_2957_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I6_J,axiom,
% 0.35/0.57      ! [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT,Vj: nat] :
% 0.35/0.57        ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Vj )
% 0.35/0.57        = one_one_nat ) ).
% 0.35/0.57  
% 0.35/0.57  % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.simps(6)
% 0.35/0.57  thf(fact_2958_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I5_J,axiom,
% 0.35/0.57      ! [V: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh: vEBT_VEBT,Vi: nat] :
% 0.35/0.57        ( ( vEBT_T_s_u_c_c @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh ) @ Vi )
% 0.35/0.57        = one_one_nat ) ).
% 0.35/0.57  
% 0.35/0.57  % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.simps(5)
% 0.35/0.57  thf(fact_2959_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I5_J,axiom,
% 0.35/0.57      ! [V: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh: vEBT_VEBT,Vi: nat] :
% 0.35/0.57        ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh ) @ Vi )
% 0.35/0.57        = one_one_nat ) ).
% 0.35/0.57  
% 0.35/0.57  % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.simps(5)
% 0.35/0.57  thf(fact_2960_power2__less__imp__less,axiom,
% 0.35/0.57      ! [X: real,Y2: real] :
% 0.35/0.57        ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.57       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 0.35/0.57         => ( ord_less_real @ X @ Y2 ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % power2_less_imp_less
% 0.35/0.57  thf(fact_2961_power2__less__imp__less,axiom,
% 0.35/0.57      ! [X: rat,Y2: rat] :
% 0.35/0.57        ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.57       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 0.35/0.57         => ( ord_less_rat @ X @ Y2 ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % power2_less_imp_less
% 0.35/0.57  thf(fact_2962_power2__less__imp__less,axiom,
% 0.35/0.57      ! [X: nat,Y2: nat] :
% 0.35/0.57        ( ( ord_less_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.57       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y2 )
% 0.35/0.57         => ( ord_less_nat @ X @ Y2 ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % power2_less_imp_less
% 0.35/0.57  thf(fact_2963_power2__less__imp__less,axiom,
% 0.35/0.57      ! [X: int,Y2: int] :
% 0.35/0.57        ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.57       => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 0.35/0.57         => ( ord_less_int @ X @ Y2 ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % power2_less_imp_less
% 0.35/0.57  thf(fact_2964_sum__power2__le__zero__iff,axiom,
% 0.35/0.57      ! [X: rat,Y2: rat] :
% 0.35/0.57        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat )
% 0.35/0.57        = ( ( X = zero_zero_rat )
% 0.35/0.57          & ( Y2 = zero_zero_rat ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % sum_power2_le_zero_iff
% 0.35/0.57  thf(fact_2965_sum__power2__le__zero__iff,axiom,
% 0.35/0.57      ! [X: real,Y2: real] :
% 0.35/0.57        ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real )
% 0.35/0.57        = ( ( X = zero_zero_real )
% 0.35/0.57          & ( Y2 = zero_zero_real ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % sum_power2_le_zero_iff
% 0.35/0.57  thf(fact_2966_sum__power2__le__zero__iff,axiom,
% 0.35/0.57      ! [X: int,Y2: int] :
% 0.35/0.57        ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int )
% 0.35/0.57        = ( ( X = zero_zero_int )
% 0.35/0.57          & ( Y2 = zero_zero_int ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % sum_power2_le_zero_iff
% 0.35/0.57  thf(fact_2967_sum__power2__ge__zero,axiom,
% 0.35/0.57      ! [X: rat,Y2: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % sum_power2_ge_zero
% 0.35/0.57  thf(fact_2968_sum__power2__ge__zero,axiom,
% 0.35/0.57      ! [X: real,Y2: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % sum_power2_ge_zero
% 0.35/0.57  thf(fact_2969_sum__power2__ge__zero,axiom,
% 0.35/0.57      ! [X: int,Y2: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % sum_power2_ge_zero
% 0.35/0.57  thf(fact_2970_sum__power2__gt__zero__iff,axiom,
% 0.35/0.57      ! [X: real,Y2: real] :
% 0.35/0.57        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.57        = ( ( X != zero_zero_real )
% 0.35/0.57          | ( Y2 != zero_zero_real ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % sum_power2_gt_zero_iff
% 0.35/0.57  thf(fact_2971_sum__power2__gt__zero__iff,axiom,
% 0.35/0.57      ! [X: rat,Y2: rat] :
% 0.35/0.57        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.57        = ( ( X != zero_zero_rat )
% 0.35/0.57          | ( Y2 != zero_zero_rat ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % sum_power2_gt_zero_iff
% 0.35/0.57  thf(fact_2972_sum__power2__gt__zero__iff,axiom,
% 0.35/0.57      ! [X: int,Y2: int] :
% 0.35/0.57        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.57        = ( ( X != zero_zero_int )
% 0.35/0.57          | ( Y2 != zero_zero_int ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % sum_power2_gt_zero_iff
% 0.35/0.57  thf(fact_2973_not__sum__power2__lt__zero,axiom,
% 0.35/0.57      ! [X: real,Y2: real] :
% 0.35/0.57        ~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real ) ).
% 0.35/0.57  
% 0.35/0.57  % not_sum_power2_lt_zero
% 0.35/0.57  thf(fact_2974_not__sum__power2__lt__zero,axiom,
% 0.35/0.57      ! [X: rat,Y2: rat] :
% 0.35/0.57        ~ ( ord_less_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat ) ).
% 0.35/0.57  
% 0.35/0.57  % not_sum_power2_lt_zero
% 0.35/0.57  thf(fact_2975_not__sum__power2__lt__zero,axiom,
% 0.35/0.57      ! [X: int,Y2: int] :
% 0.35/0.57        ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int ) ).
% 0.35/0.57  
% 0.35/0.57  % not_sum_power2_lt_zero
% 0.35/0.57  thf(fact_2976_zero__le__even__power_H,axiom,
% 0.35/0.57      ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % zero_le_even_power'
% 0.35/0.57  thf(fact_2977_zero__le__even__power_H,axiom,
% 0.35/0.57      ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % zero_le_even_power'
% 0.35/0.57  thf(fact_2978_zero__le__even__power_H,axiom,
% 0.35/0.57      ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % zero_le_even_power'
% 0.35/0.57  thf(fact_2979_Suc__n__div__2__gt__zero,axiom,
% 0.35/0.57      ! [N: nat] :
% 0.35/0.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.57       => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % Suc_n_div_2_gt_zero
% 0.35/0.57  thf(fact_2980_div__2__gt__zero,axiom,
% 0.35/0.57      ! [N: nat] :
% 0.35/0.57        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.35/0.57       => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % div_2_gt_zero
% 0.35/0.57  thf(fact_2981_nat__bit__induct,axiom,
% 0.35/0.57      ! [P: nat > $o,N: nat] :
% 0.35/0.57        ( ( P @ zero_zero_nat )
% 0.35/0.57       => ( ! [N3: nat] :
% 0.35/0.57              ( ( P @ N3 )
% 0.35/0.57             => ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.35/0.57               => ( P @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 0.35/0.57         => ( ! [N3: nat] :
% 0.35/0.57                ( ( P @ N3 )
% 0.35/0.57               => ( P @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 0.35/0.57           => ( P @ N ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % nat_bit_induct
% 0.35/0.57  thf(fact_2982_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I6_J,axiom,
% 0.35/0.57      ! [Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.35/0.57        ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ TreeList @ Summary ) @ X )
% 0.35/0.57        = one_one_nat ) ).
% 0.35/0.57  
% 0.35/0.57  % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.simps(6)
% 0.35/0.57  thf(fact_2983_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I3_J,axiom,
% 0.35/0.57      ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X: nat] :
% 0.35/0.57        ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X )
% 0.35/0.57        = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(3)
% 0.35/0.57  thf(fact_2984_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Oelims,axiom,
% 0.35/0.57      ! [X: vEBT_VEBT,Y2: nat] :
% 0.35/0.57        ( ( ( vEBT_T_m_a_x_t @ X )
% 0.35/0.57          = Y2 )
% 0.35/0.57       => ( ! [A4: $o,B3: $o] :
% 0.35/0.57              ( ( X
% 0.35/0.57                = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.57             => ( Y2
% 0.35/0.57               != ( plus_plus_nat @ one_one_nat @ ( if_nat @ B3 @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 0.35/0.57         => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.35/0.57                  ( X
% 0.35/0.57                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.35/0.57             => ( Y2 != one_one_nat ) )
% 0.35/0.57           => ~ ( ? [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.35/0.57                    ( X
% 0.35/0.57                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 0.35/0.57               => ( Y2 != one_one_nat ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % T\<^sub>m\<^sub>a\<^sub>x\<^sub>t.elims
% 0.35/0.57  thf(fact_2985_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Oelims,axiom,
% 0.35/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 0.35/0.57        ( ( ( vEBT_T_i_n_s_e_r_t @ X @ Xa2 )
% 0.35/0.57          = Y2 )
% 0.35/0.57       => ( ( ? [A4: $o,B3: $o] :
% 0.35/0.57                ( X
% 0.35/0.57                = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.57           => ( Y2
% 0.35/0.57             != ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa2 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 0.35/0.57         => ( ( ? [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 0.35/0.57                  ( X
% 0.35/0.57                  = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S ) )
% 0.35/0.57             => ( Y2 != one_one_nat ) )
% 0.35/0.57           => ( ( ? [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 0.35/0.57                    ( X
% 0.35/0.57                    = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) )
% 0.35/0.57               => ( Y2 != one_one_nat ) )
% 0.35/0.57             => ( ( ? [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.57                      ( X
% 0.35/0.57                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                 => ( Y2
% 0.35/0.57                   != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.57               => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.57                      ( ( X
% 0.35/0.57                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                     => ( Y2
% 0.35/0.57                       != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 0.35/0.57                          @ ( if_nat
% 0.35/0.57                            @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.57                              & ~ ( ( Xa2 = Mi2 )
% 0.35/0.57                                  | ( Xa2 = Ma2 ) ) )
% 0.35/0.57                            @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 0.35/0.57                            @ one_one_nat ) ) ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.elims
% 0.35/0.57  thf(fact_2986_odd__0__le__power__imp__0__le,axiom,
% 0.35/0.57      ! [A: rat,N: nat] :
% 0.35/0.57        ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.35/0.57       => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.35/0.57  
% 0.35/0.57  % odd_0_le_power_imp_0_le
% 0.35/0.57  thf(fact_2987_odd__0__le__power__imp__0__le,axiom,
% 0.35/0.57      ! [A: real,N: nat] :
% 0.35/0.57        ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.35/0.57       => ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.35/0.57  
% 0.35/0.57  % odd_0_le_power_imp_0_le
% 0.35/0.57  thf(fact_2988_odd__0__le__power__imp__0__le,axiom,
% 0.35/0.57      ! [A: int,N: nat] :
% 0.35/0.57        ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.35/0.57       => ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.35/0.57  
% 0.35/0.57  % odd_0_le_power_imp_0_le
% 0.35/0.57  thf(fact_2989_odd__power__less__zero,axiom,
% 0.35/0.57      ! [A: real,N: nat] :
% 0.35/0.57        ( ( ord_less_real @ A @ zero_zero_real )
% 0.35/0.57       => ( ord_less_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_real ) ) ).
% 0.35/0.57  
% 0.35/0.57  % odd_power_less_zero
% 0.35/0.57  thf(fact_2990_odd__power__less__zero,axiom,
% 0.35/0.57      ! [A: rat,N: nat] :
% 0.35/0.57        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.35/0.57       => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_rat ) ) ).
% 0.35/0.57  
% 0.35/0.57  % odd_power_less_zero
% 0.35/0.57  thf(fact_2991_odd__power__less__zero,axiom,
% 0.35/0.57      ! [A: int,N: nat] :
% 0.35/0.57        ( ( ord_less_int @ A @ zero_zero_int )
% 0.35/0.57       => ( ord_less_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_int ) ) ).
% 0.35/0.57  
% 0.35/0.57  % odd_power_less_zero
% 0.35/0.57  thf(fact_2992_VEBT__internal_Oexp__split__high__low_I1_J,axiom,
% 0.35/0.57      ! [X: nat,N: nat,M: nat] :
% 0.35/0.57        ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 0.35/0.57       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.57         => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.35/0.57           => ( ord_less_nat @ ( vEBT_VEBT_high @ X @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % VEBT_internal.exp_split_high_low(1)
% 0.35/0.57  thf(fact_2993_VEBT__internal_Oexp__split__high__low_I2_J,axiom,
% 0.35/0.57      ! [X: nat,N: nat,M: nat] :
% 0.35/0.57        ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 0.35/0.57       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.57         => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.35/0.57           => ( ord_less_nat @ ( vEBT_VEBT_low @ X @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % VEBT_internal.exp_split_high_low(2)
% 0.35/0.57  thf(fact_2994_vebt__member_Oelims_I2_J,axiom,
% 0.35/0.57      ! [X: vEBT_VEBT,Xa2: nat] :
% 0.35/0.57        ( ( vEBT_vebt_member @ X @ Xa2 )
% 0.35/0.57       => ( ! [A4: $o,B3: $o] :
% 0.35/0.57              ( ( X
% 0.35/0.57                = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.57             => ~ ( ( ( Xa2 = zero_zero_nat )
% 0.35/0.57                   => A4 )
% 0.35/0.57                  & ( ( Xa2 != zero_zero_nat )
% 0.35/0.57                   => ( ( ( Xa2 = one_one_nat )
% 0.35/0.57                       => B3 )
% 0.35/0.57                      & ( Xa2 = one_one_nat ) ) ) ) )
% 0.35/0.57         => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT] :
% 0.35/0.57                ( ? [Summary2: vEBT_VEBT] :
% 0.35/0.57                    ( X
% 0.35/0.57                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57               => ~ ( ( Xa2 != Mi2 )
% 0.35/0.57                   => ( ( Xa2 != Ma2 )
% 0.35/0.57                     => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.57                        & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.57                         => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.35/0.57                            & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.35/0.57                             => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.57                                 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % vebt_member.elims(2)
% 0.35/0.57  thf(fact_2995_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I4_J,axiom,
% 0.35/0.57      ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 0.35/0.57        ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X )
% 0.35/0.57        = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(4)
% 0.35/0.57  thf(fact_2996_VEBT__internal_Omembermima_Oelims_I2_J,axiom,
% 0.35/0.57      ! [X: vEBT_VEBT,Xa2: nat] :
% 0.35/0.57        ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 0.35/0.57       => ( ! [Mi2: nat,Ma2: nat] :
% 0.35/0.57              ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 0.35/0.57                  ( X
% 0.35/0.57                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 0.35/0.57             => ~ ( ( Xa2 = Mi2 )
% 0.35/0.57                  | ( Xa2 = Ma2 ) ) )
% 0.35/0.57         => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 0.35/0.57                ( ? [Vc2: vEBT_VEBT] :
% 0.35/0.57                    ( X
% 0.35/0.57                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 0.35/0.57               => ~ ( ( Xa2 = Mi2 )
% 0.35/0.57                    | ( Xa2 = Ma2 )
% 0.35/0.57                    | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.57                       => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                      & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 0.35/0.57           => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT] :
% 0.35/0.57                  ( ? [Vd2: vEBT_VEBT] :
% 0.35/0.57                      ( X
% 0.35/0.57                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 0.35/0.57                 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.57                       => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                      & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % VEBT_internal.membermima.elims(2)
% 0.35/0.57  thf(fact_2997_vebt__member_Oelims_I1_J,axiom,
% 0.35/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 0.35/0.57        ( ( ( vEBT_vebt_member @ X @ Xa2 )
% 0.35/0.57          = Y2 )
% 0.35/0.57       => ( ! [A4: $o,B3: $o] :
% 0.35/0.57              ( ( X
% 0.35/0.57                = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.57             => ( Y2
% 0.35/0.57                = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 0.35/0.57                       => A4 )
% 0.35/0.57                      & ( ( Xa2 != zero_zero_nat )
% 0.35/0.57                       => ( ( ( Xa2 = one_one_nat )
% 0.35/0.57                           => B3 )
% 0.35/0.57                          & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 0.35/0.57         => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.35/0.57                  ( X
% 0.35/0.57                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.35/0.57             => Y2 )
% 0.35/0.57           => ( ( ? [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.35/0.57                    ( X
% 0.35/0.57                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 0.35/0.57               => Y2 )
% 0.35/0.57             => ( ( ? [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.35/0.57                      ( X
% 0.35/0.57                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 0.35/0.57                 => Y2 )
% 0.35/0.57               => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT] :
% 0.35/0.57                      ( ? [Summary2: vEBT_VEBT] :
% 0.35/0.57                          ( X
% 0.35/0.57                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                     => ( Y2
% 0.35/0.57                        = ( ~ ( ( Xa2 != Mi2 )
% 0.35/0.57                             => ( ( Xa2 != Ma2 )
% 0.35/0.57                               => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.57                                  & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.57                                   => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.35/0.57                                      & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.35/0.57                                       => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.57                                           => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % vebt_member.elims(1)
% 0.35/0.57  thf(fact_2998_vebt__member_Oelims_I3_J,axiom,
% 0.35/0.57      ! [X: vEBT_VEBT,Xa2: nat] :
% 0.35/0.57        ( ~ ( vEBT_vebt_member @ X @ Xa2 )
% 0.35/0.57       => ( ! [A4: $o,B3: $o] :
% 0.35/0.57              ( ( X
% 0.35/0.57                = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.57             => ( ( ( Xa2 = zero_zero_nat )
% 0.35/0.57                 => A4 )
% 0.35/0.57                & ( ( Xa2 != zero_zero_nat )
% 0.35/0.57                 => ( ( ( Xa2 = one_one_nat )
% 0.35/0.57                     => B3 )
% 0.35/0.57                    & ( Xa2 = one_one_nat ) ) ) ) )
% 0.35/0.57         => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.35/0.57                ( X
% 0.35/0.57               != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.35/0.57           => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.35/0.57                  ( X
% 0.35/0.57                 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 0.35/0.57             => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.35/0.57                    ( X
% 0.35/0.57                   != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 0.35/0.57               => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT] :
% 0.35/0.57                      ( ? [Summary2: vEBT_VEBT] :
% 0.35/0.57                          ( X
% 0.35/0.57                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                     => ( ( Xa2 != Mi2 )
% 0.35/0.57                       => ( ( Xa2 != Ma2 )
% 0.35/0.57                         => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.57                            & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.57                             => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.35/0.57                                & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.35/0.57                                 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.57                                     => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                    & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % vebt_member.elims(3)
% 0.35/0.57  thf(fact_2999_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I4_J,axiom,
% 0.35/0.57      ! [V: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.35/0.57        ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) @ X )
% 0.35/0.57        = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(4)
% 0.35/0.57  thf(fact_3000_insersimp,axiom,
% 0.35/0.57      ! [T: vEBT_VEBT,N: nat,Y2: nat] :
% 0.35/0.57        ( ( vEBT_invar_vebt @ T @ N )
% 0.35/0.57       => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_12 )
% 0.35/0.57         => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ T @ Y2 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % insersimp
% 0.35/0.57  thf(fact_3001_insertsimp,axiom,
% 0.35/0.57      ! [T: vEBT_VEBT,N: nat,L2: nat] :
% 0.35/0.57        ( ( vEBT_invar_vebt @ T @ N )
% 0.35/0.57       => ( ( vEBT_VEBT_minNull @ T )
% 0.35/0.57         => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ T @ L2 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % insertsimp
% 0.35/0.57  thf(fact_3002_arith__geo__mean,axiom,
% 0.35/0.57      ! [U: real,X: real,Y2: real] :
% 0.35/0.57        ( ( ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.57          = ( times_times_real @ X @ Y2 ) )
% 0.35/0.57       => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.57         => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 0.35/0.57           => ( ord_less_eq_real @ U @ ( divide_divide_real @ ( plus_plus_real @ X @ Y2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % arith_geo_mean
% 0.35/0.57  thf(fact_3003_arith__geo__mean,axiom,
% 0.35/0.57      ! [U: rat,X: rat,Y2: rat] :
% 0.35/0.57        ( ( ( power_power_rat @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.57          = ( times_times_rat @ X @ Y2 ) )
% 0.35/0.57       => ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.35/0.57         => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 0.35/0.57           => ( ord_less_eq_rat @ U @ ( divide_divide_rat @ ( plus_plus_rat @ X @ Y2 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % arith_geo_mean
% 0.35/0.57  thf(fact_3004_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Oelims,axiom,
% 0.35/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 0.35/0.57        ( ( ( vEBT_T_m_e_m_b_e_r @ X @ Xa2 )
% 0.35/0.57          = Y2 )
% 0.35/0.57       => ( ( ? [A4: $o,B3: $o] :
% 0.35/0.57                ( X
% 0.35/0.57                = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.57           => ( Y2
% 0.35/0.57             != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa2 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 0.35/0.57         => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.35/0.57                  ( X
% 0.35/0.57                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.35/0.57             => ( Y2
% 0.35/0.57               != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.57           => ( ( ? [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.35/0.57                    ( X
% 0.35/0.57                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 0.35/0.57               => ( Y2
% 0.35/0.57                 != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.57             => ( ( ? [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.35/0.57                      ( X
% 0.35/0.57                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 0.35/0.57                 => ( Y2
% 0.35/0.57                   != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.57               => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT] :
% 0.35/0.57                      ( ? [Summary2: vEBT_VEBT] :
% 0.35/0.57                          ( X
% 0.35/0.57                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                     => ( Y2
% 0.35/0.57                       != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa2 = Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa2 = Ma2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ one_one_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_e_m_b_e_r @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.elims
% 0.35/0.57  thf(fact_3005_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Oelims,axiom,
% 0.35/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 0.35/0.57        ( ( ( vEBT_T_i_n_s_e_r_t2 @ X @ Xa2 )
% 0.35/0.57          = Y2 )
% 0.35/0.57       => ( ( ? [A4: $o,B3: $o] :
% 0.35/0.57                ( X
% 0.35/0.57                = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.57           => ( Y2 != one_one_nat ) )
% 0.35/0.57         => ( ( ? [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 0.35/0.57                  ( X
% 0.35/0.57                  = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S ) )
% 0.35/0.57             => ( Y2 != one_one_nat ) )
% 0.35/0.57           => ( ( ? [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 0.35/0.57                    ( X
% 0.35/0.57                    = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) )
% 0.35/0.57               => ( Y2 != one_one_nat ) )
% 0.35/0.57             => ( ( ? [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.57                      ( X
% 0.35/0.57                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                 => ( Y2 != one_one_nat ) )
% 0.35/0.57               => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.57                      ( ( X
% 0.35/0.57                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                     => ( Y2
% 0.35/0.57                       != ( if_nat
% 0.35/0.57                          @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.57                            & ~ ( ( Xa2 = Mi2 )
% 0.35/0.57                                | ( Xa2 = Ma2 ) ) )
% 0.35/0.57                          @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t2 @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 0.35/0.57                          @ one_one_nat ) ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.elims
% 0.35/0.57  thf(fact_3006_invar__vebt_Osimps,axiom,
% 0.35/0.57      ( vEBT_invar_vebt
% 0.35/0.57      = ( ^ [A1: vEBT_VEBT,A22: nat] :
% 0.35/0.57            ( ( ? [A3: $o,B4: $o] :
% 0.35/0.57                  ( A1
% 0.35/0.57                  = ( vEBT_Leaf @ A3 @ B4 ) )
% 0.35/0.57              & ( A22
% 0.35/0.57                = ( suc @ zero_zero_nat ) ) )
% 0.35/0.57            | ? [TreeList3: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT] :
% 0.35/0.57                ( ( A1
% 0.35/0.57                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ A22 @ TreeList3 @ Summary3 ) )
% 0.35/0.57                & ! [X2: vEBT_VEBT] :
% 0.35/0.57                    ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.35/0.57                   => ( vEBT_invar_vebt @ X2 @ N2 ) )
% 0.35/0.57                & ( vEBT_invar_vebt @ Summary3 @ N2 )
% 0.35/0.57                & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.35/0.57                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.35/0.57                & ( A22
% 0.35/0.57                  = ( plus_plus_nat @ N2 @ N2 ) )
% 0.35/0.57                & ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X4 )
% 0.35/0.57                & ! [X2: vEBT_VEBT] :
% 0.35/0.57                    ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.35/0.57                   => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 0.35/0.57            | ? [TreeList3: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT] :
% 0.35/0.57                ( ( A1
% 0.35/0.57                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ A22 @ TreeList3 @ Summary3 ) )
% 0.35/0.57                & ! [X2: vEBT_VEBT] :
% 0.35/0.57                    ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.35/0.57                   => ( vEBT_invar_vebt @ X2 @ N2 ) )
% 0.35/0.57                & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N2 ) )
% 0.35/0.57                & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.35/0.57                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 0.35/0.57                & ( A22
% 0.35/0.57                  = ( plus_plus_nat @ N2 @ ( suc @ N2 ) ) )
% 0.35/0.57                & ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X4 )
% 0.35/0.57                & ! [X2: vEBT_VEBT] :
% 0.35/0.57                    ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.35/0.57                   => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 0.35/0.57            | ? [TreeList3: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 0.35/0.57                ( ( A1
% 0.35/0.57                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A22 @ TreeList3 @ Summary3 ) )
% 0.35/0.57                & ! [X2: vEBT_VEBT] :
% 0.35/0.57                    ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.35/0.57                   => ( vEBT_invar_vebt @ X2 @ N2 ) )
% 0.35/0.57                & ( vEBT_invar_vebt @ Summary3 @ N2 )
% 0.35/0.57                & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.35/0.57                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.35/0.57                & ( A22
% 0.35/0.57                  = ( plus_plus_nat @ N2 @ N2 ) )
% 0.35/0.57                & ! [I3: nat] :
% 0.35/0.57                    ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.35/0.57                   => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X4 ) )
% 0.35/0.57                      = ( vEBT_V8194947554948674370ptions @ Summary3 @ I3 ) ) )
% 0.35/0.57                & ( ( Mi3 = Ma3 )
% 0.35/0.57                 => ! [X2: vEBT_VEBT] :
% 0.35/0.57                      ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.35/0.57                     => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 0.35/0.57                & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.35/0.57                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A22 ) )
% 0.35/0.57                & ( ( Mi3 != Ma3 )
% 0.35/0.57                 => ! [I3: nat] :
% 0.35/0.57                      ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.35/0.57                     => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N2 )
% 0.35/0.57                            = I3 )
% 0.35/0.57                         => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ ( vEBT_VEBT_low @ Ma3 @ N2 ) ) )
% 0.35/0.57                        & ! [X2: nat] :
% 0.35/0.57                            ( ( ( ( vEBT_VEBT_high @ X2 @ N2 )
% 0.35/0.57                                = I3 )
% 0.35/0.57                              & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ ( vEBT_VEBT_low @ X2 @ N2 ) ) )
% 0.35/0.57                           => ( ( ord_less_nat @ Mi3 @ X2 )
% 0.35/0.57                              & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) )
% 0.35/0.57            | ? [TreeList3: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 0.35/0.57                ( ( A1
% 0.35/0.57                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A22 @ TreeList3 @ Summary3 ) )
% 0.35/0.57                & ! [X2: vEBT_VEBT] :
% 0.35/0.57                    ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.35/0.57                   => ( vEBT_invar_vebt @ X2 @ N2 ) )
% 0.35/0.57                & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N2 ) )
% 0.35/0.57                & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.35/0.57                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 0.35/0.57                & ( A22
% 0.35/0.57                  = ( plus_plus_nat @ N2 @ ( suc @ N2 ) ) )
% 0.35/0.57                & ! [I3: nat] :
% 0.35/0.57                    ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 0.35/0.57                   => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X4 ) )
% 0.35/0.57                      = ( vEBT_V8194947554948674370ptions @ Summary3 @ I3 ) ) )
% 0.35/0.57                & ( ( Mi3 = Ma3 )
% 0.35/0.57                 => ! [X2: vEBT_VEBT] :
% 0.35/0.57                      ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.35/0.57                     => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 0.35/0.57                & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.35/0.57                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A22 ) )
% 0.35/0.57                & ( ( Mi3 != Ma3 )
% 0.35/0.57                 => ! [I3: nat] :
% 0.35/0.57                      ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 0.35/0.57                     => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N2 )
% 0.35/0.57                            = I3 )
% 0.35/0.57                         => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ ( vEBT_VEBT_low @ Ma3 @ N2 ) ) )
% 0.35/0.57                        & ! [X2: nat] :
% 0.35/0.57                            ( ( ( ( vEBT_VEBT_high @ X2 @ N2 )
% 0.35/0.57                                = I3 )
% 0.35/0.57                              & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ ( vEBT_VEBT_low @ X2 @ N2 ) ) )
% 0.35/0.57                           => ( ( ord_less_nat @ Mi3 @ X2 )
% 0.35/0.57                              & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % invar_vebt.simps
% 0.35/0.57  thf(fact_3007_invar__vebt_Ocases,axiom,
% 0.35/0.57      ! [A12: vEBT_VEBT,A23: nat] :
% 0.35/0.57        ( ( vEBT_invar_vebt @ A12 @ A23 )
% 0.35/0.57       => ( ( ? [A4: $o,B3: $o] :
% 0.35/0.57                ( A12
% 0.35/0.57                = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.57           => ( A23
% 0.35/0.57             != ( suc @ zero_zero_nat ) ) )
% 0.35/0.57         => ( ! [TreeList2: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat] :
% 0.35/0.57                ( ( A12
% 0.35/0.57                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.35/0.57               => ( ( A23 = Deg2 )
% 0.35/0.57                 => ( ! [X5: vEBT_VEBT] :
% 0.35/0.57                        ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.35/0.57                       => ( vEBT_invar_vebt @ X5 @ N3 ) )
% 0.35/0.57                   => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 0.35/0.57                     => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.35/0.57                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 0.35/0.57                       => ( ( M4 = N3 )
% 0.35/0.57                         => ( ( Deg2
% 0.35/0.57                              = ( plus_plus_nat @ N3 @ M4 ) )
% 0.35/0.57                           => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_1 )
% 0.35/0.57                             => ~ ! [X5: vEBT_VEBT] :
% 0.35/0.57                                    ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.35/0.57                                   => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) ) ) ) ) ) ) ) ) )
% 0.35/0.57           => ( ! [TreeList2: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat] :
% 0.35/0.57                  ( ( A12
% 0.35/0.57                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.35/0.57                 => ( ( A23 = Deg2 )
% 0.35/0.57                   => ( ! [X5: vEBT_VEBT] :
% 0.35/0.57                          ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.35/0.57                         => ( vEBT_invar_vebt @ X5 @ N3 ) )
% 0.35/0.57                     => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 0.35/0.57                       => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.35/0.57                            = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 0.35/0.57                         => ( ( M4
% 0.35/0.57                              = ( suc @ N3 ) )
% 0.35/0.57                           => ( ( Deg2
% 0.35/0.57                                = ( plus_plus_nat @ N3 @ M4 ) )
% 0.35/0.57                             => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_1 )
% 0.35/0.57                               => ~ ! [X5: vEBT_VEBT] :
% 0.35/0.57                                      ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.35/0.57                                     => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) ) ) ) ) ) ) ) ) )
% 0.35/0.57             => ( ! [TreeList2: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 0.35/0.57                    ( ( A12
% 0.35/0.57                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.35/0.57                   => ( ( A23 = Deg2 )
% 0.35/0.57                     => ( ! [X5: vEBT_VEBT] :
% 0.35/0.57                            ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.35/0.57                           => ( vEBT_invar_vebt @ X5 @ N3 ) )
% 0.35/0.57                       => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 0.35/0.57                         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.35/0.57                              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 0.35/0.57                           => ( ( M4 = N3 )
% 0.35/0.57                             => ( ( Deg2
% 0.35/0.57                                  = ( plus_plus_nat @ N3 @ M4 ) )
% 0.35/0.57                               => ( ! [I: nat] :
% 0.35/0.57                                      ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 0.35/0.57                                     => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I ) @ X4 ) )
% 0.35/0.57                                        = ( vEBT_V8194947554948674370ptions @ Summary2 @ I ) ) )
% 0.35/0.57                                 => ( ( ( Mi2 = Ma2 )
% 0.35/0.57                                     => ! [X5: vEBT_VEBT] :
% 0.35/0.57                                          ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.35/0.57                                         => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) ) )
% 0.35/0.57                                   => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 0.35/0.57                                     => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.35/0.57                                       => ~ ( ( Mi2 != Ma2 )
% 0.35/0.57                                           => ! [I: nat] :
% 0.35/0.57                                                ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 0.35/0.57                                               => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 0.35/0.57                                                      = I )
% 0.35/0.57                                                   => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 0.35/0.57                                                  & ! [X5: nat] :
% 0.35/0.57                                                      ( ( ( ( vEBT_VEBT_high @ X5 @ N3 )
% 0.35/0.57                                                          = I )
% 0.35/0.57                                                        & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I ) @ ( vEBT_VEBT_low @ X5 @ N3 ) ) )
% 0.35/0.57                                                     => ( ( ord_less_nat @ Mi2 @ X5 )
% 0.35/0.57                                                        & ( ord_less_eq_nat @ X5 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.35/0.57               => ~ ! [TreeList2: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 0.35/0.57                      ( ( A12
% 0.35/0.57                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.35/0.57                     => ( ( A23 = Deg2 )
% 0.35/0.57                       => ( ! [X5: vEBT_VEBT] :
% 0.35/0.57                              ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.35/0.57                             => ( vEBT_invar_vebt @ X5 @ N3 ) )
% 0.35/0.57                         => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 0.35/0.57                           => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.35/0.57                                = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 0.35/0.57                             => ( ( M4
% 0.35/0.57                                  = ( suc @ N3 ) )
% 0.35/0.57                               => ( ( Deg2
% 0.35/0.57                                    = ( plus_plus_nat @ N3 @ M4 ) )
% 0.35/0.57                                 => ( ! [I: nat] :
% 0.35/0.57                                        ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 0.35/0.57                                       => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I ) @ X4 ) )
% 0.35/0.57                                          = ( vEBT_V8194947554948674370ptions @ Summary2 @ I ) ) )
% 0.35/0.57                                   => ( ( ( Mi2 = Ma2 )
% 0.35/0.57                                       => ! [X5: vEBT_VEBT] :
% 0.35/0.57                                            ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.35/0.57                                           => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) ) )
% 0.35/0.57                                     => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 0.35/0.57                                       => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.35/0.57                                         => ~ ( ( Mi2 != Ma2 )
% 0.35/0.57                                             => ! [I: nat] :
% 0.35/0.57                                                  ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 0.35/0.57                                                 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 0.35/0.57                                                        = I )
% 0.35/0.57                                                     => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 0.35/0.57                                                    & ! [X5: nat] :
% 0.35/0.57                                                        ( ( ( ( vEBT_VEBT_high @ X5 @ N3 )
% 0.35/0.57                                                            = I )
% 0.35/0.57                                                          & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I ) @ ( vEBT_VEBT_low @ X5 @ N3 ) ) )
% 0.35/0.57                                                       => ( ( ord_less_nat @ Mi2 @ X5 )
% 0.35/0.57                                                          & ( ord_less_eq_nat @ X5 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % invar_vebt.cases
% 0.35/0.57  thf(fact_3008_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Oelims,axiom,
% 0.35/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 0.35/0.57        ( ( ( vEBT_T_p_r_e_d @ X @ Xa2 )
% 0.35/0.57          = Y2 )
% 0.35/0.57       => ( ( ? [Uu2: $o,Uv2: $o] :
% 0.35/0.57                ( X
% 0.35/0.57                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.35/0.57           => ( ( Xa2 = zero_zero_nat )
% 0.35/0.57             => ( Y2 != one_one_nat ) ) )
% 0.35/0.57         => ( ( ? [A4: $o,Uw2: $o] :
% 0.35/0.57                  ( X
% 0.35/0.57                  = ( vEBT_Leaf @ A4 @ Uw2 ) )
% 0.35/0.57             => ( ( Xa2
% 0.35/0.57                  = ( suc @ zero_zero_nat ) )
% 0.35/0.57               => ( Y2
% 0.35/0.57                 != ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 0.35/0.57           => ( ! [A4: $o,B3: $o] :
% 0.35/0.57                  ( ( X
% 0.35/0.57                    = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.57                 => ( ? [Va2: nat] :
% 0.35/0.57                        ( Xa2
% 0.35/0.57                        = ( suc @ ( suc @ Va2 ) ) )
% 0.35/0.57                   => ( Y2
% 0.35/0.57                     != ( plus_plus_nat @ one_one_nat @ ( if_nat @ B3 @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ) )
% 0.35/0.57             => ( ( ? [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 0.35/0.57                      ( X
% 0.35/0.57                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 0.35/0.57                 => ( Y2 != one_one_nat ) )
% 0.35/0.57               => ( ( ? [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 0.35/0.57                        ( X
% 0.35/0.57                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 0.35/0.57                   => ( Y2 != one_one_nat ) )
% 0.35/0.57                 => ( ( ? [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 0.35/0.57                          ( X
% 0.35/0.57                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 0.35/0.57                     => ( Y2 != one_one_nat ) )
% 0.35/0.57                   => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.57                          ( ( X
% 0.35/0.57                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                         => ( Y2
% 0.35/0.57                           != ( plus_plus_nat @ one_one_nat
% 0.35/0.57                              @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ one_one_nat
% 0.35/0.57                                @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 0.35/0.57                                  @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.57                                    @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.35/0.57                                      @ ( if_nat
% 0.35/0.57                                        @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                           != none_nat )
% 0.35/0.57                                          & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.35/0.57                                        @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_p_r_e_d @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                        @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 0.35/0.57                                          @ ( if_nat
% 0.35/0.57                                            @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.57                                              = none_nat )
% 0.35/0.57                                            @ ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 0.35/0.57                                            @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.35/0.57                                    @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.elims
% 0.35/0.57  thf(fact_3009_vebt__insert_Oelims,axiom,
% 0.35/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y2: vEBT_VEBT] :
% 0.35/0.57        ( ( ( vEBT_vebt_insert @ X @ Xa2 )
% 0.35/0.57          = Y2 )
% 0.35/0.57       => ( ! [A4: $o,B3: $o] :
% 0.35/0.57              ( ( X
% 0.35/0.57                = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.57             => ~ ( ( ( Xa2 = zero_zero_nat )
% 0.35/0.57                   => ( Y2
% 0.35/0.57                      = ( vEBT_Leaf @ $true @ B3 ) ) )
% 0.35/0.57                  & ( ( Xa2 != zero_zero_nat )
% 0.35/0.57                   => ( ( ( Xa2 = one_one_nat )
% 0.35/0.57                       => ( Y2
% 0.35/0.57                          = ( vEBT_Leaf @ A4 @ $true ) ) )
% 0.35/0.57                      & ( ( Xa2 != one_one_nat )
% 0.35/0.57                       => ( Y2
% 0.35/0.57                          = ( vEBT_Leaf @ A4 @ B3 ) ) ) ) ) ) )
% 0.35/0.57         => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 0.35/0.57                ( ( X
% 0.35/0.57                  = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S ) )
% 0.35/0.57               => ( Y2
% 0.35/0.57                 != ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S ) ) )
% 0.35/0.57           => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 0.35/0.57                  ( ( X
% 0.35/0.57                    = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) )
% 0.35/0.57                 => ( Y2
% 0.35/0.57                   != ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) ) )
% 0.35/0.57             => ( ! [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.57                    ( ( X
% 0.35/0.57                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                   => ( Y2
% 0.35/0.57                     != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) ) )
% 0.35/0.57               => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.57                      ( ( X
% 0.35/0.57                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                     => ( Y2
% 0.35/0.57                       != ( if_VEBT_VEBT
% 0.35/0.57                          @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.57                            & ~ ( ( Xa2 = Mi2 )
% 0.35/0.57                                | ( Xa2 = Ma2 ) ) )
% 0.35/0.57                          @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va2 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 0.35/0.57                          @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % vebt_insert.elims
% 0.35/0.57  thf(fact_3010_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Oelims,axiom,
% 0.35/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 0.35/0.57        ( ( ( vEBT_T_p_r_e_d2 @ X @ Xa2 )
% 0.35/0.57          = Y2 )
% 0.35/0.57       => ( ( ? [Uu2: $o,Uv2: $o] :
% 0.35/0.57                ( X
% 0.35/0.57                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.35/0.57           => ( ( Xa2 = zero_zero_nat )
% 0.35/0.57             => ( Y2 != one_one_nat ) ) )
% 0.35/0.57         => ( ( ? [A4: $o,Uw2: $o] :
% 0.35/0.57                  ( X
% 0.35/0.57                  = ( vEBT_Leaf @ A4 @ Uw2 ) )
% 0.35/0.57             => ( ( Xa2
% 0.35/0.57                  = ( suc @ zero_zero_nat ) )
% 0.35/0.57               => ( Y2 != one_one_nat ) ) )
% 0.35/0.57           => ( ( ? [A4: $o,B3: $o] :
% 0.35/0.57                    ( X
% 0.35/0.57                    = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.57               => ( ? [Va2: nat] :
% 0.35/0.57                      ( Xa2
% 0.35/0.57                      = ( suc @ ( suc @ Va2 ) ) )
% 0.35/0.57                 => ( Y2 != one_one_nat ) ) )
% 0.35/0.57             => ( ( ? [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 0.35/0.57                      ( X
% 0.35/0.57                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 0.35/0.57                 => ( Y2 != one_one_nat ) )
% 0.35/0.57               => ( ( ? [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 0.35/0.57                        ( X
% 0.35/0.57                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 0.35/0.57                   => ( Y2 != one_one_nat ) )
% 0.35/0.57                 => ( ( ? [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 0.35/0.57                          ( X
% 0.35/0.57                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 0.35/0.57                     => ( Y2 != one_one_nat ) )
% 0.35/0.57                   => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.57                          ( ( X
% 0.35/0.57                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                         => ~ ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 0.35/0.57                               => ( Y2 = one_one_nat ) )
% 0.35/0.57                              & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.35/0.57                               => ( Y2
% 0.35/0.57                                  = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.57                                    @ ( if_nat
% 0.35/0.57                                      @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                         != none_nat )
% 0.35/0.57                                        & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.35/0.57                                      @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                      @ ( plus_plus_nat @ ( vEBT_T_p_r_e_d2 @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 0.35/0.57                                    @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.elims
% 0.35/0.57  thf(fact_3011_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Oelims,axiom,
% 0.35/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 0.35/0.57        ( ( ( vEBT_T_s_u_c_c2 @ X @ Xa2 )
% 0.35/0.57          = Y2 )
% 0.35/0.57       => ( ( ? [Uu2: $o,B3: $o] :
% 0.35/0.57                ( X
% 0.35/0.57                = ( vEBT_Leaf @ Uu2 @ B3 ) )
% 0.35/0.57           => ( ( Xa2 = zero_zero_nat )
% 0.35/0.57             => ( Y2 != one_one_nat ) ) )
% 0.35/0.57         => ( ( ? [Uv2: $o,Uw2: $o] :
% 0.35/0.57                  ( X
% 0.35/0.57                  = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 0.35/0.57             => ( ? [N3: nat] :
% 0.35/0.57                    ( Xa2
% 0.35/0.57                    = ( suc @ N3 ) )
% 0.35/0.57               => ( Y2 != one_one_nat ) ) )
% 0.35/0.57           => ( ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.35/0.57                    ( X
% 0.35/0.57                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 0.35/0.57               => ( Y2 != one_one_nat ) )
% 0.35/0.57             => ( ( ? [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 0.35/0.57                      ( X
% 0.35/0.57                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 0.35/0.57                 => ( Y2 != one_one_nat ) )
% 0.35/0.57               => ( ( ? [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 0.35/0.57                        ( X
% 0.35/0.57                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh2 ) )
% 0.35/0.57                   => ( Y2 != one_one_nat ) )
% 0.35/0.57                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.57                        ( ( X
% 0.35/0.57                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                       => ~ ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.57                             => ( Y2 = one_one_nat ) )
% 0.35/0.57                            & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.57                             => ( Y2
% 0.35/0.57                                = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.57                                  @ ( if_nat
% 0.35/0.57                                    @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                       != none_nat )
% 0.35/0.57                                      & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.35/0.57                                    @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                    @ ( plus_plus_nat @ ( vEBT_T_s_u_c_c2 @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 0.35/0.57                                  @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.elims
% 0.35/0.57  thf(fact_3012_vebt__delete_Oelims,axiom,
% 0.35/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y2: vEBT_VEBT] :
% 0.35/0.57        ( ( ( vEBT_vebt_delete @ X @ Xa2 )
% 0.35/0.57          = Y2 )
% 0.35/0.57       => ( ! [A4: $o,B3: $o] :
% 0.35/0.57              ( ( X
% 0.35/0.57                = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.57             => ( ( Xa2 = zero_zero_nat )
% 0.35/0.57               => ( Y2
% 0.35/0.57                 != ( vEBT_Leaf @ $false @ B3 ) ) ) )
% 0.35/0.57         => ( ! [A4: $o] :
% 0.35/0.57                ( ? [B3: $o] :
% 0.35/0.57                    ( X
% 0.35/0.57                    = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.57               => ( ( Xa2
% 0.35/0.57                    = ( suc @ zero_zero_nat ) )
% 0.35/0.57                 => ( Y2
% 0.35/0.57                   != ( vEBT_Leaf @ A4 @ $false ) ) ) )
% 0.35/0.57           => ( ! [A4: $o,B3: $o] :
% 0.35/0.57                  ( ( X
% 0.35/0.57                    = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.57                 => ( ? [N3: nat] :
% 0.35/0.57                        ( Xa2
% 0.35/0.57                        = ( suc @ ( suc @ N3 ) ) )
% 0.35/0.57                   => ( Y2
% 0.35/0.57                     != ( vEBT_Leaf @ A4 @ B3 ) ) ) )
% 0.35/0.57             => ( ! [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.57                    ( ( X
% 0.35/0.57                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.35/0.57                   => ( Y2
% 0.35/0.57                     != ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) ) )
% 0.35/0.57               => ( ! [Mi2: nat,Ma2: nat,TrLst2: list_VEBT_VEBT,Smry2: vEBT_VEBT] :
% 0.35/0.57                      ( ( X
% 0.35/0.57                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 0.35/0.57                     => ( Y2
% 0.35/0.57                       != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) ) )
% 0.35/0.57                 => ( ! [Mi2: nat,Ma2: nat,Tr2: list_VEBT_VEBT,Sm2: vEBT_VEBT] :
% 0.35/0.57                        ( ( X
% 0.35/0.57                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 0.35/0.57                       => ( Y2
% 0.35/0.57                         != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) ) )
% 0.35/0.57                   => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.57                          ( ( X
% 0.35/0.57                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                         => ~ ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.57                                  | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 0.35/0.57                               => ( Y2
% 0.35/0.57                                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) ) )
% 0.35/0.57                              & ( ~ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.57                                    | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 0.35/0.57                               => ( ( ( ( Xa2 = Mi2 )
% 0.35/0.57                                      & ( Xa2 = Ma2 ) )
% 0.35/0.57                                   => ( Y2
% 0.35/0.57                                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) ) )
% 0.35/0.57                                  & ( ~ ( ( Xa2 = Mi2 )
% 0.35/0.57                                        & ( Xa2 = Ma2 ) )
% 0.35/0.57                                   => ( Y2
% 0.35/0.57                                      = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.57                                        @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                          @ ( vEBT_Node
% 0.35/0.57                                            @ ( some_P7363390416028606310at_nat
% 0.35/0.57                                              @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 0.35/0.57                                                @ ( if_nat
% 0.35/0.57                                                  @ ( ( ( Xa2 = Mi2 )
% 0.35/0.57                                                     => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 0.35/0.57                                                        = Ma2 ) )
% 0.35/0.57                                                    & ( ( Xa2 != Mi2 )
% 0.35/0.57                                                     => ( Xa2 = Ma2 ) ) )
% 0.35/0.57                                                  @ ( if_nat
% 0.35/0.57                                                    @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                                      = none_nat )
% 0.35/0.57                                                    @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 0.35/0.57                                                    @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 0.35/0.57                                                  @ Ma2 ) ) )
% 0.35/0.57                                            @ ( suc @ ( suc @ Va2 ) )
% 0.35/0.57                                            @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                            @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                          @ ( vEBT_Node
% 0.35/0.57                                            @ ( some_P7363390416028606310at_nat
% 0.35/0.57                                              @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 0.35/0.57                                                @ ( if_nat
% 0.35/0.57                                                  @ ( ( ( Xa2 = Mi2 )
% 0.35/0.57                                                     => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 0.35/0.57                                                        = Ma2 ) )
% 0.35/0.57                                                    & ( ( Xa2 != Mi2 )
% 0.35/0.57                                                     => ( Xa2 = Ma2 ) ) )
% 0.35/0.57                                                  @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.35/0.57                                                  @ Ma2 ) ) )
% 0.35/0.57                                            @ ( suc @ ( suc @ Va2 ) )
% 0.35/0.57                                            @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                            @ Summary2 ) )
% 0.35/0.57                                        @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % vebt_delete.elims
% 0.35/0.57  thf(fact_3013_vebt__succ_Oelims,axiom,
% 0.35/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y2: option_nat] :
% 0.35/0.57        ( ( ( vEBT_vebt_succ @ X @ Xa2 )
% 0.35/0.57          = Y2 )
% 0.35/0.57       => ( ! [Uu2: $o,B3: $o] :
% 0.35/0.57              ( ( X
% 0.35/0.57                = ( vEBT_Leaf @ Uu2 @ B3 ) )
% 0.35/0.57             => ( ( Xa2 = zero_zero_nat )
% 0.35/0.57               => ~ ( ( B3
% 0.35/0.57                     => ( Y2
% 0.35/0.57                        = ( some_nat @ one_one_nat ) ) )
% 0.35/0.57                    & ( ~ B3
% 0.35/0.57                     => ( Y2 = none_nat ) ) ) ) )
% 0.35/0.57         => ( ( ? [Uv2: $o,Uw2: $o] :
% 0.35/0.57                  ( X
% 0.35/0.57                  = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 0.35/0.57             => ( ? [N3: nat] :
% 0.35/0.57                    ( Xa2
% 0.35/0.57                    = ( suc @ N3 ) )
% 0.35/0.57               => ( Y2 != none_nat ) ) )
% 0.35/0.57           => ( ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.35/0.57                    ( X
% 0.35/0.57                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 0.35/0.57               => ( Y2 != none_nat ) )
% 0.35/0.57             => ( ( ? [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 0.35/0.57                      ( X
% 0.35/0.57                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 0.35/0.57                 => ( Y2 != none_nat ) )
% 0.35/0.57               => ( ( ? [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 0.35/0.57                        ( X
% 0.35/0.57                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh2 ) )
% 0.35/0.57                   => ( Y2 != none_nat ) )
% 0.35/0.57                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.57                        ( ( X
% 0.35/0.57                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                       => ~ ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.57                             => ( Y2
% 0.35/0.57                                = ( some_nat @ Mi2 ) ) )
% 0.35/0.57                            & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.57                             => ( Y2
% 0.35/0.57                                = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.57                                  @ ( if_option_nat
% 0.35/0.57                                    @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                       != none_nat )
% 0.35/0.57                                      & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.35/0.57                                    @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                    @ ( if_option_nat
% 0.35/0.57                                      @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.57                                        = none_nat )
% 0.35/0.57                                      @ none_nat
% 0.35/0.57                                      @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.35/0.57                                  @ none_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % vebt_succ.elims
% 0.35/0.57  thf(fact_3014_vebt__pred_Oelims,axiom,
% 0.35/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y2: option_nat] :
% 0.35/0.57        ( ( ( vEBT_vebt_pred @ X @ Xa2 )
% 0.35/0.57          = Y2 )
% 0.35/0.57       => ( ( ? [Uu2: $o,Uv2: $o] :
% 0.35/0.57                ( X
% 0.35/0.57                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.35/0.57           => ( ( Xa2 = zero_zero_nat )
% 0.35/0.57             => ( Y2 != none_nat ) ) )
% 0.35/0.57         => ( ! [A4: $o] :
% 0.35/0.57                ( ? [Uw2: $o] :
% 0.35/0.57                    ( X
% 0.35/0.57                    = ( vEBT_Leaf @ A4 @ Uw2 ) )
% 0.35/0.57               => ( ( Xa2
% 0.35/0.57                    = ( suc @ zero_zero_nat ) )
% 0.35/0.57                 => ~ ( ( A4
% 0.35/0.57                       => ( Y2
% 0.35/0.57                          = ( some_nat @ zero_zero_nat ) ) )
% 0.35/0.57                      & ( ~ A4
% 0.35/0.57                       => ( Y2 = none_nat ) ) ) ) )
% 0.35/0.57           => ( ! [A4: $o,B3: $o] :
% 0.35/0.57                  ( ( X
% 0.35/0.57                    = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.57                 => ( ? [Va2: nat] :
% 0.35/0.57                        ( Xa2
% 0.35/0.57                        = ( suc @ ( suc @ Va2 ) ) )
% 0.35/0.57                   => ~ ( ( B3
% 0.35/0.57                         => ( Y2
% 0.35/0.57                            = ( some_nat @ one_one_nat ) ) )
% 0.35/0.57                        & ( ~ B3
% 0.35/0.57                         => ( ( A4
% 0.35/0.57                             => ( Y2
% 0.35/0.57                                = ( some_nat @ zero_zero_nat ) ) )
% 0.35/0.57                            & ( ~ A4
% 0.35/0.57                             => ( Y2 = none_nat ) ) ) ) ) ) )
% 0.35/0.57             => ( ( ? [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 0.35/0.57                      ( X
% 0.35/0.57                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 0.35/0.57                 => ( Y2 != none_nat ) )
% 0.35/0.57               => ( ( ? [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 0.35/0.57                        ( X
% 0.35/0.57                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 0.35/0.57                   => ( Y2 != none_nat ) )
% 0.35/0.57                 => ( ( ? [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 0.35/0.57                          ( X
% 0.35/0.57                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 0.35/0.57                     => ( Y2 != none_nat ) )
% 0.35/0.57                   => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.57                          ( ( X
% 0.35/0.57                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                         => ~ ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 0.35/0.57                               => ( Y2
% 0.35/0.57                                  = ( some_nat @ Ma2 ) ) )
% 0.35/0.57                              & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.35/0.57                               => ( Y2
% 0.35/0.57                                  = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.57                                    @ ( if_option_nat
% 0.35/0.57                                      @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                         != none_nat )
% 0.35/0.57                                        & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.35/0.57                                      @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                      @ ( if_option_nat
% 0.35/0.57                                        @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.57                                          = none_nat )
% 0.35/0.57                                        @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 0.35/0.57                                        @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.35/0.57                                    @ none_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % vebt_pred.elims
% 0.35/0.57  thf(fact_3015_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Oelims,axiom,
% 0.35/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 0.35/0.57        ( ( ( vEBT_T_s_u_c_c @ X @ Xa2 )
% 0.35/0.57          = Y2 )
% 0.35/0.57       => ( ( ? [Uu2: $o,B3: $o] :
% 0.35/0.57                ( X
% 0.35/0.57                = ( vEBT_Leaf @ Uu2 @ B3 ) )
% 0.35/0.57           => ( ( Xa2 = zero_zero_nat )
% 0.35/0.57             => ( Y2
% 0.35/0.57               != ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 0.35/0.57         => ( ( ? [Uv2: $o,Uw2: $o] :
% 0.35/0.57                  ( X
% 0.35/0.57                  = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 0.35/0.57             => ( ? [N3: nat] :
% 0.35/0.57                    ( Xa2
% 0.35/0.57                    = ( suc @ N3 ) )
% 0.35/0.57               => ( Y2 != one_one_nat ) ) )
% 0.35/0.57           => ( ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.35/0.57                    ( X
% 0.35/0.57                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 0.35/0.57               => ( Y2 != one_one_nat ) )
% 0.35/0.57             => ( ( ? [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 0.35/0.57                      ( X
% 0.35/0.57                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 0.35/0.57                 => ( Y2 != one_one_nat ) )
% 0.35/0.57               => ( ( ? [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 0.35/0.57                        ( X
% 0.35/0.57                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh2 ) )
% 0.35/0.57                   => ( Y2 != one_one_nat ) )
% 0.35/0.57                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.57                        ( ( X
% 0.35/0.57                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                       => ( Y2
% 0.35/0.57                         != ( plus_plus_nat @ one_one_nat
% 0.35/0.57                            @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ one_one_nat
% 0.35/0.57                              @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) )
% 0.35/0.57                                @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.57                                  @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.35/0.57                                    @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.35/0.57                                      @ ( if_nat
% 0.35/0.57                                        @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                           != none_nat )
% 0.35/0.57                                          & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.35/0.57                                        @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_s_u_c_c @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                        @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 0.35/0.57                                          @ ( if_nat
% 0.35/0.57                                            @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.57                                              = none_nat )
% 0.35/0.57                                            @ one_one_nat
% 0.35/0.57                                            @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.35/0.57                                  @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.elims
% 0.35/0.57  thf(fact_3016_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Oelims,axiom,
% 0.35/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 0.35/0.57        ( ( ( vEBT_T_m_e_m_b_e_r2 @ X @ Xa2 )
% 0.35/0.57          = Y2 )
% 0.35/0.57       => ( ( ? [A4: $o,B3: $o] :
% 0.35/0.57                ( X
% 0.35/0.57                = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.57           => ( Y2 != one_one_nat ) )
% 0.35/0.57         => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.35/0.57                  ( X
% 0.35/0.57                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.35/0.57             => ( Y2 != one_one_nat ) )
% 0.35/0.57           => ( ( ? [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.35/0.57                    ( X
% 0.35/0.57                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 0.35/0.57               => ( Y2 != one_one_nat ) )
% 0.35/0.57             => ( ( ? [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.35/0.57                      ( X
% 0.35/0.57                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 0.35/0.57                 => ( Y2 != one_one_nat ) )
% 0.35/0.57               => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT] :
% 0.35/0.57                      ( ? [Summary2: vEBT_VEBT] :
% 0.35/0.57                          ( X
% 0.35/0.57                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                     => ( Y2
% 0.35/0.57                       != ( plus_plus_nat @ one_one_nat
% 0.35/0.57                          @ ( if_nat @ ( Xa2 = Mi2 ) @ zero_zero_nat
% 0.35/0.57                            @ ( if_nat @ ( Xa2 = Ma2 ) @ zero_zero_nat
% 0.35/0.57                              @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ zero_zero_nat
% 0.35/0.57                                @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ zero_zero_nat
% 0.35/0.57                                  @ ( if_nat
% 0.35/0.57                                    @ ( ( ord_less_nat @ Mi2 @ Xa2 )
% 0.35/0.57                                      & ( ord_less_nat @ Xa2 @ Ma2 ) )
% 0.35/0.57                                    @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( vEBT_T_m_e_m_b_e_r2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ zero_zero_nat )
% 0.35/0.57                                    @ zero_zero_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.elims
% 0.35/0.57  thf(fact_3017_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I5_J,axiom,
% 0.35/0.57      ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.35/0.57        ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 0.35/0.57        = ( plus_plus_nat @ one_one_nat
% 0.35/0.57          @ ( if_nat @ ( X = Mi ) @ zero_zero_nat
% 0.35/0.57            @ ( if_nat @ ( X = Ma ) @ zero_zero_nat
% 0.35/0.57              @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ zero_zero_nat
% 0.35/0.57                @ ( if_nat @ ( ord_less_nat @ Ma @ X ) @ zero_zero_nat
% 0.35/0.57                  @ ( if_nat
% 0.35/0.57                    @ ( ( ord_less_nat @ Mi @ X )
% 0.35/0.57                      & ( ord_less_nat @ X @ Ma ) )
% 0.35/0.57                    @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( vEBT_T_m_e_m_b_e_r2 @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ zero_zero_nat )
% 0.35/0.57                    @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(5)
% 0.35/0.57  thf(fact_3018_buildup__gives__valid,axiom,
% 0.35/0.57      ! [N: nat] :
% 0.35/0.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.57       => ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N ) @ N ) ) ).
% 0.35/0.57  
% 0.35/0.57  % buildup_gives_valid
% 0.35/0.57  thf(fact_3019_inrange,axiom,
% 0.35/0.57      ! [T: vEBT_VEBT,N: nat] :
% 0.35/0.57        ( ( vEBT_invar_vebt @ T @ N )
% 0.35/0.57       => ( ord_less_eq_set_nat @ ( vEBT_VEBT_set_vebt @ T ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % inrange
% 0.35/0.57  thf(fact_3020_buildup__gives__empty,axiom,
% 0.35/0.57      ! [N: nat] :
% 0.35/0.57        ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_buildup @ N ) )
% 0.35/0.57        = bot_bot_set_nat ) ).
% 0.35/0.57  
% 0.35/0.57  % buildup_gives_empty
% 0.35/0.57  thf(fact_3021_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Opelims,axiom,
% 0.35/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 0.35/0.57        ( ( ( vEBT_T_d_e_l_e_t_e @ X @ Xa2 )
% 0.35/0.57          = Y2 )
% 0.35/0.57       => ( ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.57         => ( ! [A4: $o,B3: $o] :
% 0.35/0.57                ( ( X
% 0.35/0.57                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.57               => ( ( Xa2 = zero_zero_nat )
% 0.35/0.57                 => ( ( Y2 = one_one_nat )
% 0.35/0.57                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ zero_zero_nat ) ) ) ) )
% 0.35/0.57           => ( ! [A4: $o,B3: $o] :
% 0.35/0.57                  ( ( X
% 0.35/0.57                    = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.57                 => ( ( Xa2
% 0.35/0.57                      = ( suc @ zero_zero_nat ) )
% 0.35/0.57                   => ( ( Y2 = one_one_nat )
% 0.35/0.57                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 0.35/0.57             => ( ! [A4: $o,B3: $o] :
% 0.35/0.57                    ( ( X
% 0.35/0.57                      = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.57                   => ! [N3: nat] :
% 0.35/0.57                        ( ( Xa2
% 0.35/0.57                          = ( suc @ ( suc @ N3 ) ) )
% 0.35/0.57                       => ( ( Y2 = one_one_nat )
% 0.35/0.57                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ ( suc @ ( suc @ N3 ) ) ) ) ) ) )
% 0.35/0.57               => ( ! [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.57                      ( ( X
% 0.35/0.57                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.35/0.57                     => ( ( Y2 = one_one_nat )
% 0.35/0.57                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 0.35/0.57                 => ( ! [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.57                        ( ( X
% 0.35/0.57                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TreeList2 @ Summary2 ) )
% 0.35/0.57                       => ( ( Y2 = one_one_nat )
% 0.35/0.57                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 0.35/0.57                   => ( ! [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.57                          ( ( X
% 0.35/0.57                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                         => ( ( Y2 = one_one_nat )
% 0.35/0.57                           => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 0.35/0.57                     => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.57                            ( ( X
% 0.35/0.57                              = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                           => ( ( Y2
% 0.35/0.57                                = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.35/0.57                                  @ ( if_nat
% 0.35/0.57                                    @ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.57                                      | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 0.35/0.57                                    @ one_one_nat
% 0.35/0.57                                    @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.35/0.57                                      @ ( if_nat
% 0.35/0.57                                        @ ( ( Xa2 = Mi2 )
% 0.35/0.57                                          & ( Xa2 = Ma2 ) )
% 0.35/0.57                                        @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.35/0.57                                        @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ Summary2 ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat ) ) @ one_one_nat )
% 0.35/0.57                                          @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.57                                            @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                              @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.35/0.57                                                @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                                  @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_d_e_l_e_t_e @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                                    @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.35/0.57                                                      @ ( if_nat
% 0.35/0.57                                                        @ ( ( ( Xa2 = Mi2 )
% 0.35/0.57                                                           => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 0.35/0.57                                                              = Ma2 ) )
% 0.35/0.57                                                          & ( ( Xa2 != Mi2 )
% 0.35/0.57                                                           => ( Xa2 = Ma2 ) ) )
% 0.35/0.57                                                        @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.35/0.57                                                          @ ( plus_plus_nat @ one_one_nat
% 0.35/0.57                                                            @ ( if_nat
% 0.35/0.57                                                              @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                                                = none_nat )
% 0.35/0.57                                                              @ one_one_nat
% 0.35/0.57                                                              @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.35/0.57                                                        @ one_one_nat ) ) )
% 0.35/0.57                                                  @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.35/0.57                                                    @ ( if_nat
% 0.35/0.57                                                      @ ( ( ( Xa2 = Mi2 )
% 0.35/0.57                                                         => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 0.35/0.57                                                            = Ma2 ) )
% 0.35/0.57                                                        & ( ( Xa2 != Mi2 )
% 0.35/0.57                                                         => ( Xa2 = Ma2 ) ) )
% 0.35/0.57                                                      @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.35/0.57                                                      @ one_one_nat ) ) ) ) )
% 0.35/0.57                                            @ one_one_nat ) ) ) ) ) ) )
% 0.35/0.57                             => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.pelims
% 0.35/0.57  thf(fact_3022_set__bit__0,axiom,
% 0.35/0.57      ! [A: int] :
% 0.35/0.57        ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 0.35/0.57        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % set_bit_0
% 0.35/0.57  thf(fact_3023_set__bit__0,axiom,
% 0.35/0.57      ! [A: nat] :
% 0.35/0.57        ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 0.35/0.57        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % set_bit_0
% 0.35/0.57  thf(fact_3024_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Opelims,axiom,
% 0.35/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 0.35/0.57        ( ( ( vEBT_T_s_u_c_c @ X @ Xa2 )
% 0.35/0.57          = Y2 )
% 0.35/0.57       => ( ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.57         => ( ! [Uu2: $o,B3: $o] :
% 0.35/0.57                ( ( X
% 0.35/0.57                  = ( vEBT_Leaf @ Uu2 @ B3 ) )
% 0.35/0.57               => ( ( Xa2 = zero_zero_nat )
% 0.35/0.57                 => ( ( Y2
% 0.35/0.57                      = ( plus_plus_nat @ one_one_nat @ one_one_nat ) )
% 0.35/0.57                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B3 ) @ zero_zero_nat ) ) ) ) )
% 0.35/0.57           => ( ! [Uv2: $o,Uw2: $o] :
% 0.35/0.57                  ( ( X
% 0.35/0.57                    = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 0.35/0.57                 => ! [N3: nat] :
% 0.35/0.57                      ( ( Xa2
% 0.35/0.57                        = ( suc @ N3 ) )
% 0.35/0.57                     => ( ( Y2 = one_one_nat )
% 0.35/0.57                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N3 ) ) ) ) ) )
% 0.35/0.57             => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.35/0.57                    ( ( X
% 0.35/0.57                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 0.35/0.57                   => ( ( Y2 = one_one_nat )
% 0.35/0.57                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 0.35/0.57               => ( ! [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 0.35/0.57                      ( ( X
% 0.35/0.57                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 0.35/0.57                     => ( ( Y2 = one_one_nat )
% 0.35/0.57                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Xa2 ) ) ) )
% 0.35/0.57                 => ( ! [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 0.35/0.57                        ( ( X
% 0.35/0.57                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh2 ) )
% 0.35/0.57                       => ( ( Y2 = one_one_nat )
% 0.35/0.57                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh2 ) @ Xa2 ) ) ) )
% 0.35/0.57                   => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.57                          ( ( X
% 0.35/0.57                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                         => ( ( Y2
% 0.35/0.57                              = ( plus_plus_nat @ one_one_nat
% 0.35/0.57                                @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ one_one_nat
% 0.35/0.57                                  @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) )
% 0.35/0.57                                    @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.57                                      @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.35/0.57                                        @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.35/0.57                                          @ ( if_nat
% 0.35/0.57                                            @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                               != none_nat )
% 0.35/0.57                                              & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.35/0.57                                            @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_s_u_c_c @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                            @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 0.35/0.57                                              @ ( if_nat
% 0.35/0.57                                                @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.57                                                  = none_nat )
% 0.35/0.57                                                @ one_one_nat
% 0.35/0.57                                                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.35/0.57                                      @ one_one_nat ) ) ) ) )
% 0.35/0.57                           => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.pelims
% 0.35/0.57  thf(fact_3025_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Opelims,axiom,
% 0.35/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 0.35/0.57        ( ( ( vEBT_T_p_r_e_d @ X @ Xa2 )
% 0.35/0.57          = Y2 )
% 0.35/0.57       => ( ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.57         => ( ! [Uu2: $o,Uv2: $o] :
% 0.35/0.57                ( ( X
% 0.35/0.57                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.35/0.57               => ( ( Xa2 = zero_zero_nat )
% 0.35/0.57                 => ( ( Y2 = one_one_nat )
% 0.35/0.57                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) ) ) ) )
% 0.35/0.57           => ( ! [A4: $o,Uw2: $o] :
% 0.35/0.57                  ( ( X
% 0.35/0.57                    = ( vEBT_Leaf @ A4 @ Uw2 ) )
% 0.35/0.57                 => ( ( Xa2
% 0.35/0.57                      = ( suc @ zero_zero_nat ) )
% 0.35/0.57                   => ( ( Y2
% 0.35/0.57                        = ( plus_plus_nat @ one_one_nat @ one_one_nat ) )
% 0.35/0.57                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 0.35/0.57             => ( ! [A4: $o,B3: $o] :
% 0.35/0.57                    ( ( X
% 0.35/0.57                      = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.57                   => ! [Va2: nat] :
% 0.35/0.57                        ( ( Xa2
% 0.35/0.57                          = ( suc @ ( suc @ Va2 ) ) )
% 0.35/0.57                       => ( ( Y2
% 0.35/0.57                            = ( plus_plus_nat @ one_one_nat @ ( if_nat @ B3 @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 0.35/0.57                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ ( suc @ ( suc @ Va2 ) ) ) ) ) ) )
% 0.35/0.57               => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 0.35/0.57                      ( ( X
% 0.35/0.57                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 0.35/0.57                     => ( ( Y2 = one_one_nat )
% 0.35/0.57                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) @ Xa2 ) ) ) )
% 0.35/0.57                 => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 0.35/0.57                        ( ( X
% 0.35/0.57                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 0.35/0.57                       => ( ( Y2 = one_one_nat )
% 0.35/0.57                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Xa2 ) ) ) )
% 0.35/0.57                   => ( ! [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 0.35/0.57                          ( ( X
% 0.35/0.57                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 0.35/0.57                         => ( ( Y2 = one_one_nat )
% 0.35/0.57                           => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Xa2 ) ) ) )
% 0.35/0.57                     => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.57                            ( ( X
% 0.35/0.57                              = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                           => ( ( Y2
% 0.35/0.57                                = ( plus_plus_nat @ one_one_nat
% 0.35/0.57                                  @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ one_one_nat
% 0.35/0.57                                    @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 0.35/0.57                                      @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.57                                        @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.35/0.57                                          @ ( if_nat
% 0.35/0.57                                            @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                               != none_nat )
% 0.35/0.57                                              & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.35/0.57                                            @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_p_r_e_d @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                            @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 0.35/0.57                                              @ ( if_nat
% 0.35/0.57                                                @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.57                                                  = none_nat )
% 0.35/0.57                                                @ ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 0.35/0.57                                                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.35/0.57                                        @ one_one_nat ) ) ) ) )
% 0.35/0.57                             => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.pelims
% 0.35/0.57  thf(fact_3026_vebt__succ_Opelims,axiom,
% 0.35/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y2: option_nat] :
% 0.35/0.57        ( ( ( vEBT_vebt_succ @ X @ Xa2 )
% 0.35/0.57          = Y2 )
% 0.35/0.57       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.57         => ( ! [Uu2: $o,B3: $o] :
% 0.35/0.57                ( ( X
% 0.35/0.57                  = ( vEBT_Leaf @ Uu2 @ B3 ) )
% 0.35/0.57               => ( ( Xa2 = zero_zero_nat )
% 0.35/0.57                 => ( ( ( B3
% 0.35/0.57                       => ( Y2
% 0.35/0.57                          = ( some_nat @ one_one_nat ) ) )
% 0.35/0.57                      & ( ~ B3
% 0.35/0.57                       => ( Y2 = none_nat ) ) )
% 0.35/0.57                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B3 ) @ zero_zero_nat ) ) ) ) )
% 0.35/0.57           => ( ! [Uv2: $o,Uw2: $o] :
% 0.35/0.57                  ( ( X
% 0.35/0.57                    = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 0.35/0.57                 => ! [N3: nat] :
% 0.35/0.57                      ( ( Xa2
% 0.35/0.57                        = ( suc @ N3 ) )
% 0.35/0.57                     => ( ( Y2 = none_nat )
% 0.35/0.57                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N3 ) ) ) ) ) )
% 0.35/0.57             => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.35/0.57                    ( ( X
% 0.35/0.57                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 0.35/0.57                   => ( ( Y2 = none_nat )
% 0.35/0.57                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 0.35/0.57               => ( ! [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 0.35/0.57                      ( ( X
% 0.35/0.57                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 0.35/0.57                     => ( ( Y2 = none_nat )
% 0.35/0.57                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Xa2 ) ) ) )
% 0.35/0.57                 => ( ! [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 0.35/0.57                        ( ( X
% 0.35/0.57                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh2 ) )
% 0.35/0.57                       => ( ( Y2 = none_nat )
% 0.35/0.57                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh2 ) @ Xa2 ) ) ) )
% 0.35/0.57                   => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.57                          ( ( X
% 0.35/0.57                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                         => ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.57                               => ( Y2
% 0.35/0.57                                  = ( some_nat @ Mi2 ) ) )
% 0.35/0.57                              & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.57                               => ( Y2
% 0.35/0.57                                  = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.57                                    @ ( if_option_nat
% 0.35/0.57                                      @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                         != none_nat )
% 0.35/0.57                                        & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.35/0.57                                      @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                      @ ( if_option_nat
% 0.35/0.57                                        @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.57                                          = none_nat )
% 0.35/0.57                                        @ none_nat
% 0.35/0.57                                        @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.35/0.57                                    @ none_nat ) ) ) )
% 0.35/0.57                           => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % vebt_succ.pelims
% 0.35/0.57  thf(fact_3027_buildup__nothing__in__min__max,axiom,
% 0.35/0.57      ! [N: nat,X: nat] :
% 0.35/0.57        ~ ( vEBT_VEBT_membermima @ ( vEBT_vebt_buildup @ N ) @ X ) ).
% 0.35/0.57  
% 0.35/0.57  % buildup_nothing_in_min_max
% 0.35/0.57  thf(fact_3028_buildup__nothing__in__leaf,axiom,
% 0.35/0.57      ! [N: nat,X: nat] :
% 0.35/0.57        ~ ( vEBT_V5719532721284313246member @ ( vEBT_vebt_buildup @ N ) @ X ) ).
% 0.35/0.57  
% 0.35/0.57  % buildup_nothing_in_leaf
% 0.35/0.57  thf(fact_3029_div__neg__neg__trivial,axiom,
% 0.35/0.57      ! [K: int,L2: int] :
% 0.35/0.57        ( ( ord_less_eq_int @ K @ zero_zero_int )
% 0.35/0.57       => ( ( ord_less_int @ L2 @ K )
% 0.35/0.57         => ( ( divide_divide_int @ K @ L2 )
% 0.35/0.57            = zero_zero_int ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % div_neg_neg_trivial
% 0.35/0.57  thf(fact_3030_div__pos__pos__trivial,axiom,
% 0.35/0.57      ! [K: int,L2: int] :
% 0.35/0.57        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.35/0.57       => ( ( ord_less_int @ K @ L2 )
% 0.35/0.57         => ( ( divide_divide_int @ K @ L2 )
% 0.35/0.57            = zero_zero_int ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % div_pos_pos_trivial
% 0.35/0.57  thf(fact_3031_i0__less,axiom,
% 0.35/0.57      ! [N: extended_enat] :
% 0.35/0.57        ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 0.35/0.57        = ( N != zero_z5237406670263579293d_enat ) ) ).
% 0.35/0.57  
% 0.35/0.57  % i0_less
% 0.35/0.57  thf(fact_3032_idiff__0,axiom,
% 0.35/0.57      ! [N: extended_enat] :
% 0.35/0.57        ( ( minus_3235023915231533773d_enat @ zero_z5237406670263579293d_enat @ N )
% 0.35/0.57        = zero_z5237406670263579293d_enat ) ).
% 0.35/0.57  
% 0.35/0.57  % idiff_0
% 0.35/0.57  thf(fact_3033_idiff__0__right,axiom,
% 0.35/0.57      ! [N: extended_enat] :
% 0.35/0.57        ( ( minus_3235023915231533773d_enat @ N @ zero_z5237406670263579293d_enat )
% 0.35/0.57        = N ) ).
% 0.35/0.57  
% 0.35/0.57  % idiff_0_right
% 0.35/0.57  thf(fact_3034_not__real__square__gt__zero,axiom,
% 0.35/0.57      ! [X: real] :
% 0.35/0.57        ( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X @ X ) ) )
% 0.35/0.57        = ( X = zero_zero_real ) ) ).
% 0.35/0.57  
% 0.35/0.57  % not_real_square_gt_zero
% 0.35/0.57  thf(fact_3035_half__negative__int__iff,axiom,
% 0.35/0.57      ! [K: int] :
% 0.35/0.57        ( ( ord_less_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 0.35/0.57        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.35/0.57  
% 0.35/0.57  % half_negative_int_iff
% 0.35/0.57  thf(fact_3036_half__nonnegative__int__iff,axiom,
% 0.35/0.57      ! [K: int] :
% 0.35/0.57        ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 0.35/0.57        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.35/0.57  
% 0.35/0.57  % half_nonnegative_int_iff
% 0.35/0.57  thf(fact_3037_div__pos__geq,axiom,
% 0.35/0.57      ! [L2: int,K: int] :
% 0.35/0.57        ( ( ord_less_int @ zero_zero_int @ L2 )
% 0.35/0.57       => ( ( ord_less_eq_int @ L2 @ K )
% 0.35/0.57         => ( ( divide_divide_int @ K @ L2 )
% 0.35/0.57            = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L2 ) @ L2 ) @ one_one_int ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % div_pos_geq
% 0.35/0.57  thf(fact_3038_split__zdiv,axiom,
% 0.35/0.57      ! [P: int > $o,N: int,K: int] :
% 0.35/0.57        ( ( P @ ( divide_divide_int @ N @ K ) )
% 0.35/0.57        = ( ( ( K = zero_zero_int )
% 0.35/0.57           => ( P @ zero_zero_int ) )
% 0.35/0.57          & ( ( ord_less_int @ zero_zero_int @ K )
% 0.35/0.57           => ! [I3: int,J3: int] :
% 0.35/0.57                ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 0.35/0.57                  & ( ord_less_int @ J3 @ K )
% 0.35/0.57                  & ( N
% 0.35/0.57                    = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 0.35/0.57               => ( P @ I3 ) ) )
% 0.35/0.57          & ( ( ord_less_int @ K @ zero_zero_int )
% 0.35/0.57           => ! [I3: int,J3: int] :
% 0.35/0.57                ( ( ( ord_less_int @ K @ J3 )
% 0.35/0.57                  & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 0.35/0.57                  & ( N
% 0.35/0.57                    = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 0.35/0.57               => ( P @ I3 ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % split_zdiv
% 0.35/0.57  thf(fact_3039_zdiv__mono1,axiom,
% 0.35/0.57      ! [A: int,A5: int,B: int] :
% 0.35/0.57        ( ( ord_less_eq_int @ A @ A5 )
% 0.35/0.57       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.35/0.57         => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A5 @ B ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % zdiv_mono1
% 0.35/0.57  thf(fact_3040_zdiv__mono2,axiom,
% 0.35/0.57      ! [A: int,B5: int,B: int] :
% 0.35/0.57        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.35/0.57       => ( ( ord_less_int @ zero_zero_int @ B5 )
% 0.35/0.57         => ( ( ord_less_eq_int @ B5 @ B )
% 0.35/0.57           => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B5 ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % zdiv_mono2
% 0.35/0.57  thf(fact_3041_zdiv__eq__0__iff,axiom,
% 0.35/0.57      ! [I2: int,K: int] :
% 0.35/0.57        ( ( ( divide_divide_int @ I2 @ K )
% 0.35/0.57          = zero_zero_int )
% 0.35/0.57        = ( ( K = zero_zero_int )
% 0.35/0.57          | ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 0.35/0.57            & ( ord_less_int @ I2 @ K ) )
% 0.35/0.57          | ( ( ord_less_eq_int @ I2 @ zero_zero_int )
% 0.35/0.57            & ( ord_less_int @ K @ I2 ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % zdiv_eq_0_iff
% 0.35/0.57  thf(fact_3042_int__div__neg__eq,axiom,
% 0.35/0.57      ! [A: int,B: int,Q2: int,R: int] :
% 0.35/0.57        ( ( A
% 0.35/0.57          = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 0.35/0.57       => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 0.35/0.57         => ( ( ord_less_int @ B @ R )
% 0.35/0.57           => ( ( divide_divide_int @ A @ B )
% 0.35/0.57              = Q2 ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % int_div_neg_eq
% 0.35/0.57  thf(fact_3043_int__div__pos__eq,axiom,
% 0.35/0.57      ! [A: int,B: int,Q2: int,R: int] :
% 0.35/0.57        ( ( A
% 0.35/0.57          = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 0.35/0.57       => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 0.35/0.57         => ( ( ord_less_int @ R @ B )
% 0.35/0.57           => ( ( divide_divide_int @ A @ B )
% 0.35/0.57              = Q2 ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % int_div_pos_eq
% 0.35/0.57  thf(fact_3044_zdiv__mono1__neg,axiom,
% 0.35/0.57      ! [A: int,A5: int,B: int] :
% 0.35/0.57        ( ( ord_less_eq_int @ A @ A5 )
% 0.35/0.57       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.35/0.57         => ( ord_less_eq_int @ ( divide_divide_int @ A5 @ B ) @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % zdiv_mono1_neg
% 0.35/0.57  thf(fact_3045_zdiv__mono2__neg,axiom,
% 0.35/0.57      ! [A: int,B5: int,B: int] :
% 0.35/0.57        ( ( ord_less_int @ A @ zero_zero_int )
% 0.35/0.57       => ( ( ord_less_int @ zero_zero_int @ B5 )
% 0.35/0.57         => ( ( ord_less_eq_int @ B5 @ B )
% 0.35/0.57           => ( ord_less_eq_int @ ( divide_divide_int @ A @ B5 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % zdiv_mono2_neg
% 0.35/0.57  thf(fact_3046_div__int__pos__iff,axiom,
% 0.35/0.57      ! [K: int,L2: int] :
% 0.35/0.57        ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ L2 ) )
% 0.35/0.57        = ( ( K = zero_zero_int )
% 0.35/0.57          | ( L2 = zero_zero_int )
% 0.35/0.57          | ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.35/0.57            & ( ord_less_eq_int @ zero_zero_int @ L2 ) )
% 0.35/0.57          | ( ( ord_less_int @ K @ zero_zero_int )
% 0.35/0.57            & ( ord_less_int @ L2 @ zero_zero_int ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % div_int_pos_iff
% 0.35/0.57  thf(fact_3047_div__positive__int,axiom,
% 0.35/0.57      ! [L2: int,K: int] :
% 0.35/0.57        ( ( ord_less_eq_int @ L2 @ K )
% 0.35/0.57       => ( ( ord_less_int @ zero_zero_int @ L2 )
% 0.35/0.57         => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K @ L2 ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % div_positive_int
% 0.35/0.57  thf(fact_3048_div__nonneg__neg__le0,axiom,
% 0.35/0.57      ! [A: int,B: int] :
% 0.35/0.57        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.35/0.57       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.35/0.57         => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % div_nonneg_neg_le0
% 0.35/0.57  thf(fact_3049_div__nonpos__pos__le0,axiom,
% 0.35/0.57      ! [A: int,B: int] :
% 0.35/0.57        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.35/0.57       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.35/0.57         => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % div_nonpos_pos_le0
% 0.35/0.57  thf(fact_3050_pos__imp__zdiv__pos__iff,axiom,
% 0.35/0.57      ! [K: int,I2: int] :
% 0.35/0.57        ( ( ord_less_int @ zero_zero_int @ K )
% 0.35/0.57       => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I2 @ K ) )
% 0.35/0.57          = ( ord_less_eq_int @ K @ I2 ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % pos_imp_zdiv_pos_iff
% 0.35/0.57  thf(fact_3051_neg__imp__zdiv__nonneg__iff,axiom,
% 0.35/0.57      ! [B: int,A: int] :
% 0.35/0.57        ( ( ord_less_int @ B @ zero_zero_int )
% 0.35/0.57       => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 0.35/0.57          = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % neg_imp_zdiv_nonneg_iff
% 0.35/0.57  thf(fact_3052_pos__imp__zdiv__nonneg__iff,axiom,
% 0.35/0.57      ! [B: int,A: int] :
% 0.35/0.57        ( ( ord_less_int @ zero_zero_int @ B )
% 0.35/0.57       => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 0.35/0.57          = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % pos_imp_zdiv_nonneg_iff
% 0.35/0.57  thf(fact_3053_nonneg1__imp__zdiv__pos__iff,axiom,
% 0.35/0.57      ! [A: int,B: int] :
% 0.35/0.57        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.35/0.57       => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 0.35/0.57          = ( ( ord_less_eq_int @ B @ A )
% 0.35/0.57            & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % nonneg1_imp_zdiv_pos_iff
% 0.35/0.57  thf(fact_3054_zdiv__zmult2__eq,axiom,
% 0.35/0.57      ! [C: int,A: int,B: int] :
% 0.35/0.57        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.35/0.57       => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 0.35/0.57          = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % zdiv_zmult2_eq
% 0.35/0.57  thf(fact_3055_pos__imp__zdiv__neg__iff,axiom,
% 0.35/0.57      ! [B: int,A: int] :
% 0.35/0.57        ( ( ord_less_int @ zero_zero_int @ B )
% 0.35/0.57       => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 0.35/0.57          = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % pos_imp_zdiv_neg_iff
% 0.35/0.57  thf(fact_3056_neg__imp__zdiv__neg__iff,axiom,
% 0.35/0.57      ! [B: int,A: int] :
% 0.35/0.57        ( ( ord_less_int @ B @ zero_zero_int )
% 0.35/0.57       => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 0.35/0.57          = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % neg_imp_zdiv_neg_iff
% 0.35/0.57  thf(fact_3057_int__div__less__self,axiom,
% 0.35/0.57      ! [X: int,K: int] :
% 0.35/0.57        ( ( ord_less_int @ zero_zero_int @ X )
% 0.35/0.57       => ( ( ord_less_int @ one_one_int @ K )
% 0.35/0.57         => ( ord_less_int @ ( divide_divide_int @ X @ K ) @ X ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % int_div_less_self
% 0.35/0.57  thf(fact_3058_div__neg__pos__less0,axiom,
% 0.35/0.57      ! [A: int,B: int] :
% 0.35/0.57        ( ( ord_less_int @ A @ zero_zero_int )
% 0.35/0.57       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.35/0.57         => ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % div_neg_pos_less0
% 0.35/0.57  thf(fact_3059_enat__0__less__mult__iff,axiom,
% 0.35/0.57      ! [M: extended_enat,N: extended_enat] :
% 0.35/0.57        ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( times_7803423173614009249d_enat @ M @ N ) )
% 0.35/0.57        = ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ M )
% 0.35/0.57          & ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % enat_0_less_mult_iff
% 0.35/0.57  thf(fact_3060_not__iless0,axiom,
% 0.35/0.57      ! [N: extended_enat] :
% 0.35/0.57        ~ ( ord_le72135733267957522d_enat @ N @ zero_z5237406670263579293d_enat ) ).
% 0.35/0.57  
% 0.35/0.57  % not_iless0
% 0.35/0.57  thf(fact_3061_iadd__is__0,axiom,
% 0.35/0.57      ! [M: extended_enat,N: extended_enat] :
% 0.35/0.57        ( ( ( plus_p3455044024723400733d_enat @ M @ N )
% 0.35/0.57          = zero_z5237406670263579293d_enat )
% 0.35/0.57        = ( ( M = zero_z5237406670263579293d_enat )
% 0.35/0.57          & ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % iadd_is_0
% 0.35/0.57  thf(fact_3062_i0__lb,axiom,
% 0.35/0.57      ! [N: extended_enat] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ N ) ).
% 0.35/0.57  
% 0.35/0.57  % i0_lb
% 0.35/0.57  thf(fact_3063_ile0__eq,axiom,
% 0.35/0.57      ! [N: extended_enat] :
% 0.35/0.57        ( ( ord_le2932123472753598470d_enat @ N @ zero_z5237406670263579293d_enat )
% 0.35/0.57        = ( N = zero_z5237406670263579293d_enat ) ) ).
% 0.35/0.57  
% 0.35/0.57  % ile0_eq
% 0.35/0.57  thf(fact_3064_ex__nat__less,axiom,
% 0.35/0.57      ! [N: nat,P: nat > $o] :
% 0.35/0.57        ( ( ? [M6: nat] :
% 0.35/0.57              ( ( ord_less_eq_nat @ M6 @ N )
% 0.35/0.57              & ( P @ M6 ) ) )
% 0.35/0.57        = ( ? [X2: nat] :
% 0.35/0.57              ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.35/0.57              & ( P @ X2 ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % ex_nat_less
% 0.35/0.57  thf(fact_3065_all__nat__less,axiom,
% 0.35/0.57      ! [N: nat,P: nat > $o] :
% 0.35/0.57        ( ( ! [M6: nat] :
% 0.35/0.57              ( ( ord_less_eq_nat @ M6 @ N )
% 0.35/0.57             => ( P @ M6 ) ) )
% 0.35/0.57        = ( ! [X2: nat] :
% 0.35/0.57              ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.35/0.57             => ( P @ X2 ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % all_nat_less
% 0.35/0.57  thf(fact_3066_vebt__buildup_Osimps_I1_J,axiom,
% 0.35/0.57      ( ( vEBT_vebt_buildup @ zero_zero_nat )
% 0.35/0.57      = ( vEBT_Leaf @ $false @ $false ) ) ).
% 0.35/0.57  
% 0.35/0.57  % vebt_buildup.simps(1)
% 0.35/0.57  thf(fact_3067_not__exp__less__eq__0__int,axiom,
% 0.35/0.57      ! [N: nat] :
% 0.35/0.57        ~ ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ zero_zero_int ) ).
% 0.35/0.57  
% 0.35/0.57  % not_exp_less_eq_0_int
% 0.35/0.57  thf(fact_3068_realpow__pos__nth2,axiom,
% 0.35/0.57      ! [A: real,N: nat] :
% 0.35/0.57        ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.57       => ? [R3: real] :
% 0.35/0.57            ( ( ord_less_real @ zero_zero_real @ R3 )
% 0.35/0.57            & ( ( power_power_real @ R3 @ ( suc @ N ) )
% 0.35/0.57              = A ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % realpow_pos_nth2
% 0.35/0.57  thf(fact_3069_real__arch__pow__inv,axiom,
% 0.35/0.57      ! [Y2: real,X: real] :
% 0.35/0.57        ( ( ord_less_real @ zero_zero_real @ Y2 )
% 0.35/0.57       => ( ( ord_less_real @ X @ one_one_real )
% 0.35/0.57         => ? [N3: nat] : ( ord_less_real @ ( power_power_real @ X @ N3 ) @ Y2 ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % real_arch_pow_inv
% 0.35/0.57  thf(fact_3070_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I1_J,axiom,
% 0.35/0.57      ! [A: $o,B: $o,X: nat] :
% 0.35/0.57        ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.35/0.57        = one_one_nat ) ).
% 0.35/0.57  
% 0.35/0.57  % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(1)
% 0.35/0.57  thf(fact_3071_vebt__buildup_Osimps_I2_J,axiom,
% 0.35/0.57      ( ( vEBT_vebt_buildup @ ( suc @ zero_zero_nat ) )
% 0.35/0.57      = ( vEBT_Leaf @ $false @ $false ) ) ).
% 0.35/0.57  
% 0.35/0.57  % vebt_buildup.simps(2)
% 0.35/0.57  thf(fact_3072_realpow__pos__nth,axiom,
% 0.35/0.57      ! [N: nat,A: real] :
% 0.35/0.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.57       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.57         => ? [R3: real] :
% 0.35/0.57              ( ( ord_less_real @ zero_zero_real @ R3 )
% 0.35/0.57              & ( ( power_power_real @ R3 @ N )
% 0.35/0.57                = A ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % realpow_pos_nth
% 0.35/0.57  thf(fact_3073_realpow__pos__nth__unique,axiom,
% 0.35/0.57      ! [N: nat,A: real] :
% 0.35/0.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.57       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.57         => ? [X3: real] :
% 0.35/0.57              ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.35/0.57              & ( ( power_power_real @ X3 @ N )
% 0.35/0.57                = A )
% 0.35/0.57              & ! [Y4: real] :
% 0.35/0.57                  ( ( ( ord_less_real @ zero_zero_real @ Y4 )
% 0.35/0.57                    & ( ( power_power_real @ Y4 @ N )
% 0.35/0.57                      = A ) )
% 0.35/0.57                 => ( Y4 = X3 ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % realpow_pos_nth_unique
% 0.35/0.57  thf(fact_3074_neg__zdiv__mult__2,axiom,
% 0.35/0.57      ! [A: int,B: int] :
% 0.35/0.57        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.35/0.57       => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 0.35/0.57          = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % neg_zdiv_mult_2
% 0.35/0.57  thf(fact_3075_pos__zdiv__mult__2,axiom,
% 0.35/0.57      ! [A: int,B: int] :
% 0.35/0.57        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.35/0.57       => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 0.35/0.57          = ( divide_divide_int @ B @ A ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % pos_zdiv_mult_2
% 0.35/0.57  thf(fact_3076_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I2_J,axiom,
% 0.35/0.57      ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X: nat] :
% 0.35/0.57        ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X )
% 0.35/0.57        = one_one_nat ) ).
% 0.35/0.57  
% 0.35/0.57  % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(2)
% 0.35/0.57  thf(fact_3077_int__power__div__base,axiom,
% 0.35/0.57      ! [M: nat,K: int] :
% 0.35/0.57        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.35/0.57       => ( ( ord_less_int @ zero_zero_int @ K )
% 0.35/0.57         => ( ( divide_divide_int @ ( power_power_int @ K @ M ) @ K )
% 0.35/0.57            = ( power_power_int @ K @ ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % int_power_div_base
% 0.35/0.57  thf(fact_3078_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I3_J,axiom,
% 0.35/0.57      ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X: nat] :
% 0.35/0.57        ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X )
% 0.35/0.57        = one_one_nat ) ).
% 0.35/0.57  
% 0.35/0.57  % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(3)
% 0.35/0.57  thf(fact_3079_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I4_J,axiom,
% 0.35/0.57      ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 0.35/0.57        ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X )
% 0.35/0.57        = one_one_nat ) ).
% 0.35/0.57  
% 0.35/0.57  % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(4)
% 0.35/0.57  thf(fact_3080_member__bound__height_H,axiom,
% 0.35/0.57      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.35/0.57        ( ( vEBT_invar_vebt @ T @ N )
% 0.35/0.57       => ( ord_less_eq_nat @ ( vEBT_T_m_e_m_b_e_r2 @ T @ X ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % member_bound_height'
% 0.35/0.57  thf(fact_3081_vebt__pred_Opelims,axiom,
% 0.35/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y2: option_nat] :
% 0.35/0.57        ( ( ( vEBT_vebt_pred @ X @ Xa2 )
% 0.35/0.57          = Y2 )
% 0.35/0.57       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.57         => ( ! [Uu2: $o,Uv2: $o] :
% 0.35/0.57                ( ( X
% 0.35/0.57                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.35/0.57               => ( ( Xa2 = zero_zero_nat )
% 0.35/0.57                 => ( ( Y2 = none_nat )
% 0.35/0.57                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) ) ) ) )
% 0.35/0.57           => ( ! [A4: $o,Uw2: $o] :
% 0.35/0.57                  ( ( X
% 0.35/0.57                    = ( vEBT_Leaf @ A4 @ Uw2 ) )
% 0.35/0.57                 => ( ( Xa2
% 0.35/0.57                      = ( suc @ zero_zero_nat ) )
% 0.35/0.57                   => ( ( ( A4
% 0.35/0.57                         => ( Y2
% 0.35/0.57                            = ( some_nat @ zero_zero_nat ) ) )
% 0.35/0.57                        & ( ~ A4
% 0.35/0.57                         => ( Y2 = none_nat ) ) )
% 0.35/0.57                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 0.35/0.57             => ( ! [A4: $o,B3: $o] :
% 0.35/0.57                    ( ( X
% 0.35/0.57                      = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.57                   => ! [Va2: nat] :
% 0.35/0.57                        ( ( Xa2
% 0.35/0.57                          = ( suc @ ( suc @ Va2 ) ) )
% 0.35/0.57                       => ( ( ( B3
% 0.35/0.57                             => ( Y2
% 0.35/0.57                                = ( some_nat @ one_one_nat ) ) )
% 0.35/0.57                            & ( ~ B3
% 0.35/0.57                             => ( ( A4
% 0.35/0.57                                 => ( Y2
% 0.35/0.57                                    = ( some_nat @ zero_zero_nat ) ) )
% 0.35/0.57                                & ( ~ A4
% 0.35/0.57                                 => ( Y2 = none_nat ) ) ) ) )
% 0.35/0.57                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ ( suc @ ( suc @ Va2 ) ) ) ) ) ) )
% 0.35/0.57               => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 0.35/0.57                      ( ( X
% 0.35/0.57                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 0.35/0.57                     => ( ( Y2 = none_nat )
% 0.35/0.57                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) @ Xa2 ) ) ) )
% 0.35/0.57                 => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 0.35/0.57                        ( ( X
% 0.35/0.57                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 0.35/0.57                       => ( ( Y2 = none_nat )
% 0.35/0.57                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Xa2 ) ) ) )
% 0.35/0.57                   => ( ! [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 0.35/0.57                          ( ( X
% 0.35/0.57                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 0.35/0.57                         => ( ( Y2 = none_nat )
% 0.35/0.57                           => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Xa2 ) ) ) )
% 0.35/0.57                     => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.57                            ( ( X
% 0.35/0.57                              = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                           => ( ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 0.35/0.57                                 => ( Y2
% 0.35/0.57                                    = ( some_nat @ Ma2 ) ) )
% 0.35/0.57                                & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.35/0.57                                 => ( Y2
% 0.35/0.57                                    = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.57                                      @ ( if_option_nat
% 0.35/0.57                                        @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                           != none_nat )
% 0.35/0.57                                          & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.35/0.57                                        @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                        @ ( if_option_nat
% 0.35/0.57                                          @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.57                                            = none_nat )
% 0.35/0.57                                          @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 0.35/0.57                                          @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.35/0.57                                      @ none_nat ) ) ) )
% 0.35/0.57                             => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % vebt_pred.pelims
% 0.35/0.57  thf(fact_3082_vebt__delete_Opelims,axiom,
% 0.35/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y2: vEBT_VEBT] :
% 0.35/0.57        ( ( ( vEBT_vebt_delete @ X @ Xa2 )
% 0.35/0.57          = Y2 )
% 0.35/0.57       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.57         => ( ! [A4: $o,B3: $o] :
% 0.35/0.57                ( ( X
% 0.35/0.57                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.57               => ( ( Xa2 = zero_zero_nat )
% 0.35/0.57                 => ( ( Y2
% 0.35/0.57                      = ( vEBT_Leaf @ $false @ B3 ) )
% 0.35/0.57                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ zero_zero_nat ) ) ) ) )
% 0.35/0.57           => ( ! [A4: $o,B3: $o] :
% 0.35/0.57                  ( ( X
% 0.35/0.57                    = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.57                 => ( ( Xa2
% 0.35/0.57                      = ( suc @ zero_zero_nat ) )
% 0.35/0.57                   => ( ( Y2
% 0.35/0.57                        = ( vEBT_Leaf @ A4 @ $false ) )
% 0.35/0.57                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 0.35/0.57             => ( ! [A4: $o,B3: $o] :
% 0.35/0.57                    ( ( X
% 0.35/0.57                      = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.57                   => ! [N3: nat] :
% 0.35/0.57                        ( ( Xa2
% 0.35/0.57                          = ( suc @ ( suc @ N3 ) ) )
% 0.35/0.57                       => ( ( Y2
% 0.35/0.57                            = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.57                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ ( suc @ ( suc @ N3 ) ) ) ) ) ) )
% 0.35/0.57               => ( ! [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.57                      ( ( X
% 0.35/0.57                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.35/0.57                     => ( ( Y2
% 0.35/0.57                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.35/0.57                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 0.35/0.57                 => ( ! [Mi2: nat,Ma2: nat,TrLst2: list_VEBT_VEBT,Smry2: vEBT_VEBT] :
% 0.35/0.57                        ( ( X
% 0.35/0.57                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 0.35/0.57                       => ( ( Y2
% 0.35/0.57                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 0.35/0.57                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) @ Xa2 ) ) ) )
% 0.35/0.57                   => ( ! [Mi2: nat,Ma2: nat,Tr2: list_VEBT_VEBT,Sm2: vEBT_VEBT] :
% 0.35/0.57                          ( ( X
% 0.35/0.57                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 0.35/0.57                         => ( ( Y2
% 0.35/0.57                              = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 0.35/0.57                           => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) @ Xa2 ) ) ) )
% 0.35/0.57                     => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.57                            ( ( X
% 0.35/0.57                              = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                           => ( ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.57                                    | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 0.35/0.57                                 => ( Y2
% 0.35/0.57                                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) ) )
% 0.35/0.57                                & ( ~ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.57                                      | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 0.35/0.57                                 => ( ( ( ( Xa2 = Mi2 )
% 0.35/0.57                                        & ( Xa2 = Ma2 ) )
% 0.35/0.57                                     => ( Y2
% 0.35/0.57                                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) ) )
% 0.35/0.57                                    & ( ~ ( ( Xa2 = Mi2 )
% 0.35/0.57                                          & ( Xa2 = Ma2 ) )
% 0.35/0.57                                     => ( Y2
% 0.35/0.57                                        = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.57                                          @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                            @ ( vEBT_Node
% 0.35/0.57                                              @ ( some_P7363390416028606310at_nat
% 0.35/0.57                                                @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 0.35/0.57                                                  @ ( if_nat
% 0.35/0.57                                                    @ ( ( ( Xa2 = Mi2 )
% 0.35/0.57                                                       => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 0.35/0.57                                                          = Ma2 ) )
% 0.35/0.57                                                      & ( ( Xa2 != Mi2 )
% 0.35/0.57                                                       => ( Xa2 = Ma2 ) ) )
% 0.35/0.57                                                    @ ( if_nat
% 0.35/0.57                                                      @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                                        = none_nat )
% 0.35/0.57                                                      @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 0.35/0.57                                                      @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 0.35/0.57                                                    @ Ma2 ) ) )
% 0.35/0.57                                              @ ( suc @ ( suc @ Va2 ) )
% 0.35/0.57                                              @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                              @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                            @ ( vEBT_Node
% 0.35/0.57                                              @ ( some_P7363390416028606310at_nat
% 0.35/0.57                                                @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 0.35/0.57                                                  @ ( if_nat
% 0.35/0.57                                                    @ ( ( ( Xa2 = Mi2 )
% 0.35/0.57                                                       => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 0.35/0.57                                                          = Ma2 ) )
% 0.35/0.57                                                      & ( ( Xa2 != Mi2 )
% 0.35/0.57                                                       => ( Xa2 = Ma2 ) ) )
% 0.35/0.57                                                    @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.35/0.57                                                    @ Ma2 ) ) )
% 0.35/0.57                                              @ ( suc @ ( suc @ Va2 ) )
% 0.35/0.57                                              @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                              @ Summary2 ) )
% 0.35/0.57                                          @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) ) ) ) ) ) )
% 0.35/0.57                             => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % vebt_delete.pelims
% 0.35/0.57  thf(fact_3083_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Opelims,axiom,
% 0.35/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 0.35/0.57        ( ( ( vEBT_T_s_u_c_c2 @ X @ Xa2 )
% 0.35/0.57          = Y2 )
% 0.35/0.57       => ( ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.57         => ( ! [Uu2: $o,B3: $o] :
% 0.35/0.57                ( ( X
% 0.35/0.57                  = ( vEBT_Leaf @ Uu2 @ B3 ) )
% 0.35/0.57               => ( ( Xa2 = zero_zero_nat )
% 0.35/0.57                 => ( ( Y2 = one_one_nat )
% 0.35/0.57                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B3 ) @ zero_zero_nat ) ) ) ) )
% 0.35/0.57           => ( ! [Uv2: $o,Uw2: $o] :
% 0.35/0.57                  ( ( X
% 0.35/0.57                    = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 0.35/0.57                 => ! [N3: nat] :
% 0.35/0.57                      ( ( Xa2
% 0.35/0.57                        = ( suc @ N3 ) )
% 0.35/0.57                     => ( ( Y2 = one_one_nat )
% 0.35/0.57                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N3 ) ) ) ) ) )
% 0.35/0.57             => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.35/0.57                    ( ( X
% 0.35/0.57                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 0.35/0.57                   => ( ( Y2 = one_one_nat )
% 0.35/0.57                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 0.35/0.57               => ( ! [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 0.35/0.57                      ( ( X
% 0.35/0.57                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 0.35/0.57                     => ( ( Y2 = one_one_nat )
% 0.35/0.57                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Xa2 ) ) ) )
% 0.35/0.57                 => ( ! [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 0.35/0.57                        ( ( X
% 0.35/0.57                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh2 ) )
% 0.35/0.57                       => ( ( Y2 = one_one_nat )
% 0.35/0.57                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh2 ) @ Xa2 ) ) ) )
% 0.35/0.57                   => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.57                          ( ( X
% 0.35/0.57                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                         => ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.57                               => ( Y2 = one_one_nat ) )
% 0.35/0.57                              & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.57                               => ( Y2
% 0.35/0.57                                  = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.57                                    @ ( if_nat
% 0.35/0.57                                      @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                         != none_nat )
% 0.35/0.57                                        & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.35/0.57                                      @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                      @ ( plus_plus_nat @ ( vEBT_T_s_u_c_c2 @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 0.35/0.57                                    @ one_one_nat ) ) ) )
% 0.35/0.57                           => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.pelims
% 0.35/0.57  thf(fact_3084_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Opelims,axiom,
% 0.35/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 0.35/0.57        ( ( ( vEBT_T_i_n_s_e_r_t @ X @ Xa2 )
% 0.35/0.57          = Y2 )
% 0.35/0.57       => ( ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.57         => ( ! [A4: $o,B3: $o] :
% 0.35/0.57                ( ( X
% 0.35/0.57                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.57               => ( ( Y2
% 0.35/0.57                    = ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa2 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 0.35/0.57                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa2 ) ) ) )
% 0.35/0.57           => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 0.35/0.57                  ( ( X
% 0.35/0.57                    = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S ) )
% 0.35/0.57                 => ( ( Y2 = one_one_nat )
% 0.35/0.57                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S ) @ Xa2 ) ) ) )
% 0.35/0.57             => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 0.35/0.57                    ( ( X
% 0.35/0.57                      = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) )
% 0.35/0.57                   => ( ( Y2 = one_one_nat )
% 0.35/0.57                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) @ Xa2 ) ) ) )
% 0.35/0.57               => ( ! [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.57                      ( ( X
% 0.35/0.57                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                     => ( ( Y2
% 0.35/0.57                          = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.57                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 0.35/0.57                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.57                        ( ( X
% 0.35/0.57                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                       => ( ( Y2
% 0.35/0.57                            = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 0.35/0.57                              @ ( if_nat
% 0.35/0.57                                @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.57                                  & ~ ( ( Xa2 = Mi2 )
% 0.35/0.57                                      | ( Xa2 = Ma2 ) ) )
% 0.35/0.57                                @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 0.35/0.57                                @ one_one_nat ) ) )
% 0.35/0.57                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.pelims
% 0.35/0.57  thf(fact_3085_vebt__insert_Opelims,axiom,
% 0.35/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y2: vEBT_VEBT] :
% 0.35/0.57        ( ( ( vEBT_vebt_insert @ X @ Xa2 )
% 0.35/0.57          = Y2 )
% 0.35/0.57       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.57         => ( ! [A4: $o,B3: $o] :
% 0.35/0.57                ( ( X
% 0.35/0.57                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.57               => ( ( ( ( Xa2 = zero_zero_nat )
% 0.35/0.57                     => ( Y2
% 0.35/0.57                        = ( vEBT_Leaf @ $true @ B3 ) ) )
% 0.35/0.57                    & ( ( Xa2 != zero_zero_nat )
% 0.35/0.57                     => ( ( ( Xa2 = one_one_nat )
% 0.35/0.57                         => ( Y2
% 0.35/0.57                            = ( vEBT_Leaf @ A4 @ $true ) ) )
% 0.35/0.57                        & ( ( Xa2 != one_one_nat )
% 0.35/0.57                         => ( Y2
% 0.35/0.57                            = ( vEBT_Leaf @ A4 @ B3 ) ) ) ) ) )
% 0.35/0.57                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa2 ) ) ) )
% 0.35/0.57           => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 0.35/0.57                  ( ( X
% 0.35/0.57                    = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S ) )
% 0.35/0.57                 => ( ( Y2
% 0.35/0.57                      = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S ) )
% 0.35/0.57                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S ) @ Xa2 ) ) ) )
% 0.35/0.57             => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 0.35/0.57                    ( ( X
% 0.35/0.57                      = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) )
% 0.35/0.57                   => ( ( Y2
% 0.35/0.57                        = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) )
% 0.35/0.57                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) @ Xa2 ) ) ) )
% 0.35/0.57               => ( ! [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.57                      ( ( X
% 0.35/0.57                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                     => ( ( Y2
% 0.35/0.57                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 0.35/0.57                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.57                        ( ( X
% 0.35/0.57                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                       => ( ( Y2
% 0.35/0.57                            = ( if_VEBT_VEBT
% 0.35/0.57                              @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.57                                & ~ ( ( Xa2 = Mi2 )
% 0.35/0.57                                    | ( Xa2 = Ma2 ) ) )
% 0.35/0.57                              @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va2 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 0.35/0.57                              @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) ) )
% 0.35/0.57                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % vebt_insert.pelims
% 0.35/0.57  thf(fact_3086_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Opelims,axiom,
% 0.35/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 0.35/0.57        ( ( ( vEBT_T_p_r_e_d2 @ X @ Xa2 )
% 0.35/0.57          = Y2 )
% 0.35/0.57       => ( ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.57         => ( ! [Uu2: $o,Uv2: $o] :
% 0.35/0.57                ( ( X
% 0.35/0.57                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.35/0.57               => ( ( Xa2 = zero_zero_nat )
% 0.35/0.57                 => ( ( Y2 = one_one_nat )
% 0.35/0.57                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) ) ) ) )
% 0.35/0.57           => ( ! [A4: $o,Uw2: $o] :
% 0.35/0.57                  ( ( X
% 0.35/0.57                    = ( vEBT_Leaf @ A4 @ Uw2 ) )
% 0.35/0.57                 => ( ( Xa2
% 0.35/0.57                      = ( suc @ zero_zero_nat ) )
% 0.35/0.57                   => ( ( Y2 = one_one_nat )
% 0.35/0.57                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 0.35/0.57             => ( ! [A4: $o,B3: $o] :
% 0.35/0.57                    ( ( X
% 0.35/0.57                      = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.57                   => ! [Va2: nat] :
% 0.35/0.57                        ( ( Xa2
% 0.35/0.57                          = ( suc @ ( suc @ Va2 ) ) )
% 0.35/0.57                       => ( ( Y2 = one_one_nat )
% 0.35/0.57                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ ( suc @ ( suc @ Va2 ) ) ) ) ) ) )
% 0.35/0.57               => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 0.35/0.57                      ( ( X
% 0.35/0.57                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 0.35/0.57                     => ( ( Y2 = one_one_nat )
% 0.35/0.57                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) @ Xa2 ) ) ) )
% 0.35/0.57                 => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 0.35/0.57                        ( ( X
% 0.35/0.57                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 0.35/0.57                       => ( ( Y2 = one_one_nat )
% 0.35/0.57                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Xa2 ) ) ) )
% 0.35/0.57                   => ( ! [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 0.35/0.57                          ( ( X
% 0.35/0.57                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 0.35/0.57                         => ( ( Y2 = one_one_nat )
% 0.35/0.57                           => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Xa2 ) ) ) )
% 0.35/0.57                     => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.57                            ( ( X
% 0.35/0.57                              = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                           => ( ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 0.35/0.57                                 => ( Y2 = one_one_nat ) )
% 0.35/0.57                                & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.35/0.57                                 => ( Y2
% 0.35/0.57                                    = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.57                                      @ ( if_nat
% 0.35/0.57                                        @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                           != none_nat )
% 0.35/0.57                                          & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.35/0.57                                        @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                        @ ( plus_plus_nat @ ( vEBT_T_p_r_e_d2 @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 0.35/0.57                                      @ one_one_nat ) ) ) )
% 0.35/0.57                             => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.pelims
% 0.35/0.57  thf(fact_3087_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Opelims,axiom,
% 0.35/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 0.35/0.57        ( ( ( vEBT_T_i_n_s_e_r_t2 @ X @ Xa2 )
% 0.35/0.57          = Y2 )
% 0.35/0.57       => ( ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.57         => ( ! [A4: $o,B3: $o] :
% 0.35/0.57                ( ( X
% 0.35/0.57                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.57               => ( ( Y2 = one_one_nat )
% 0.35/0.57                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa2 ) ) ) )
% 0.35/0.57           => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 0.35/0.57                  ( ( X
% 0.35/0.57                    = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S ) )
% 0.35/0.57                 => ( ( Y2 = one_one_nat )
% 0.35/0.57                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S ) @ Xa2 ) ) ) )
% 0.35/0.57             => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 0.35/0.57                    ( ( X
% 0.35/0.57                      = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) )
% 0.35/0.57                   => ( ( Y2 = one_one_nat )
% 0.35/0.57                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) @ Xa2 ) ) ) )
% 0.35/0.57               => ( ! [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.57                      ( ( X
% 0.35/0.57                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                     => ( ( Y2 = one_one_nat )
% 0.35/0.57                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 0.35/0.57                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.57                        ( ( X
% 0.35/0.57                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                       => ( ( Y2
% 0.35/0.57                            = ( if_nat
% 0.35/0.57                              @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.57                                & ~ ( ( Xa2 = Mi2 )
% 0.35/0.57                                    | ( Xa2 = Ma2 ) ) )
% 0.35/0.57                              @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t2 @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 0.35/0.57                              @ one_one_nat ) )
% 0.35/0.57                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.pelims
% 0.35/0.57  thf(fact_3088_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Opelims,axiom,
% 0.35/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 0.35/0.57        ( ( ( vEBT_T_m_e_m_b_e_r @ X @ Xa2 )
% 0.35/0.57          = Y2 )
% 0.35/0.57       => ( ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.57         => ( ! [A4: $o,B3: $o] :
% 0.35/0.57                ( ( X
% 0.35/0.57                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.57               => ( ( Y2
% 0.35/0.57                    = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa2 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 0.35/0.57                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa2 ) ) ) )
% 0.35/0.57           => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.35/0.57                  ( ( X
% 0.35/0.57                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.35/0.57                 => ( ( Y2
% 0.35/0.57                      = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.57                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 0.35/0.57             => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.35/0.57                    ( ( X
% 0.35/0.57                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 0.35/0.57                   => ( ( Y2
% 0.35/0.57                        = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.57                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 0.35/0.57               => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.35/0.57                      ( ( X
% 0.35/0.57                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 0.35/0.57                     => ( ( Y2
% 0.35/0.57                          = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.57                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 0.35/0.57                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.57                        ( ( X
% 0.35/0.57                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                       => ( ( Y2
% 0.35/0.57                            = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa2 = Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa2 = Ma2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ one_one_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_e_m_b_e_r @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) )
% 0.35/0.57                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.pelims
% 0.35/0.57  thf(fact_3089_max__enat__simps_I2_J,axiom,
% 0.35/0.57      ! [Q2: extended_enat] :
% 0.35/0.57        ( ( ord_ma741700101516333627d_enat @ Q2 @ zero_z5237406670263579293d_enat )
% 0.35/0.57        = Q2 ) ).
% 0.35/0.57  
% 0.35/0.57  % max_enat_simps(2)
% 0.35/0.57  thf(fact_3090_max__enat__simps_I3_J,axiom,
% 0.35/0.57      ! [Q2: extended_enat] :
% 0.35/0.57        ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ Q2 )
% 0.35/0.57        = Q2 ) ).
% 0.35/0.57  
% 0.35/0.57  % max_enat_simps(3)
% 0.35/0.57  thf(fact_3091_set__bit__nonnegative__int__iff,axiom,
% 0.35/0.57      ! [N: nat,K: int] :
% 0.35/0.57        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se7879613467334960850it_int @ N @ K ) )
% 0.35/0.57        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.35/0.57  
% 0.35/0.57  % set_bit_nonnegative_int_iff
% 0.35/0.57  thf(fact_3092_set__bit__negative__int__iff,axiom,
% 0.35/0.57      ! [N: nat,K: int] :
% 0.35/0.57        ( ( ord_less_int @ ( bit_se7879613467334960850it_int @ N @ K ) @ zero_zero_int )
% 0.35/0.57        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.35/0.57  
% 0.35/0.57  % set_bit_negative_int_iff
% 0.35/0.57  thf(fact_3093_imult__is__0,axiom,
% 0.35/0.57      ! [M: extended_enat,N: extended_enat] :
% 0.35/0.57        ( ( ( times_7803423173614009249d_enat @ M @ N )
% 0.35/0.57          = zero_z5237406670263579293d_enat )
% 0.35/0.57        = ( ( M = zero_z5237406670263579293d_enat )
% 0.35/0.57          | ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % imult_is_0
% 0.35/0.57  thf(fact_3094_zero__one__enat__neq_I1_J,axiom,
% 0.35/0.57      zero_z5237406670263579293d_enat != one_on7984719198319812577d_enat ).
% 0.35/0.57  
% 0.35/0.57  % zero_one_enat_neq(1)
% 0.35/0.57  thf(fact_3095_unique__quotient__lemma__neg,axiom,
% 0.35/0.57      ! [B: int,Q5: int,R4: int,Q2: int,R: int] :
% 0.35/0.57        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 0.35/0.57       => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 0.35/0.57         => ( ( ord_less_int @ B @ R )
% 0.35/0.57           => ( ( ord_less_int @ B @ R4 )
% 0.35/0.57             => ( ord_less_eq_int @ Q2 @ Q5 ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % unique_quotient_lemma_neg
% 0.35/0.57  thf(fact_3096_unique__quotient__lemma,axiom,
% 0.35/0.57      ! [B: int,Q5: int,R4: int,Q2: int,R: int] :
% 0.35/0.57        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 0.35/0.57       => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 0.35/0.57         => ( ( ord_less_int @ R4 @ B )
% 0.35/0.57           => ( ( ord_less_int @ R @ B )
% 0.35/0.57             => ( ord_less_eq_int @ Q5 @ Q2 ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % unique_quotient_lemma
% 0.35/0.57  thf(fact_3097_zdiv__mono2__neg__lemma,axiom,
% 0.35/0.57      ! [B: int,Q2: int,R: int,B5: int,Q5: int,R4: int] :
% 0.35/0.57        ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R )
% 0.35/0.57          = ( plus_plus_int @ ( times_times_int @ B5 @ Q5 ) @ R4 ) )
% 0.35/0.57       => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B5 @ Q5 ) @ R4 ) @ zero_zero_int )
% 0.35/0.57         => ( ( ord_less_int @ R @ B )
% 0.35/0.57           => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 0.35/0.57             => ( ( ord_less_int @ zero_zero_int @ B5 )
% 0.35/0.57               => ( ( ord_less_eq_int @ B5 @ B )
% 0.35/0.57                 => ( ord_less_eq_int @ Q5 @ Q2 ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % zdiv_mono2_neg_lemma
% 0.35/0.57  thf(fact_3098_zdiv__mono2__lemma,axiom,
% 0.35/0.57      ! [B: int,Q2: int,R: int,B5: int,Q5: int,R4: int] :
% 0.35/0.57        ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R )
% 0.35/0.57          = ( plus_plus_int @ ( times_times_int @ B5 @ Q5 ) @ R4 ) )
% 0.35/0.57       => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B5 @ Q5 ) @ R4 ) )
% 0.35/0.57         => ( ( ord_less_int @ R4 @ B5 )
% 0.35/0.57           => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 0.35/0.57             => ( ( ord_less_int @ zero_zero_int @ B5 )
% 0.35/0.57               => ( ( ord_less_eq_int @ B5 @ B )
% 0.35/0.57                 => ( ord_less_eq_int @ Q2 @ Q5 ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % zdiv_mono2_lemma
% 0.35/0.57  thf(fact_3099_q__pos__lemma,axiom,
% 0.35/0.57      ! [B5: int,Q5: int,R4: int] :
% 0.35/0.57        ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B5 @ Q5 ) @ R4 ) )
% 0.35/0.57       => ( ( ord_less_int @ R4 @ B5 )
% 0.35/0.57         => ( ( ord_less_int @ zero_zero_int @ B5 )
% 0.35/0.57           => ( ord_less_eq_int @ zero_zero_int @ Q5 ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % q_pos_lemma
% 0.35/0.57  thf(fact_3100_set__bit__greater__eq,axiom,
% 0.35/0.57      ! [K: int,N: nat] : ( ord_less_eq_int @ K @ ( bit_se7879613467334960850it_int @ N @ K ) ) ).
% 0.35/0.57  
% 0.35/0.57  % set_bit_greater_eq
% 0.35/0.57  thf(fact_3101_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Opelims,axiom,
% 0.35/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 0.35/0.57        ( ( ( vEBT_T_m_e_m_b_e_r2 @ X @ Xa2 )
% 0.35/0.57          = Y2 )
% 0.35/0.57       => ( ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.57         => ( ! [A4: $o,B3: $o] :
% 0.35/0.57                ( ( X
% 0.35/0.57                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.57               => ( ( Y2 = one_one_nat )
% 0.35/0.57                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa2 ) ) ) )
% 0.35/0.57           => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.35/0.57                  ( ( X
% 0.35/0.57                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.35/0.57                 => ( ( Y2 = one_one_nat )
% 0.35/0.57                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 0.35/0.57             => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.35/0.57                    ( ( X
% 0.35/0.57                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 0.35/0.57                   => ( ( Y2 = one_one_nat )
% 0.35/0.57                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 0.35/0.57               => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.35/0.57                      ( ( X
% 0.35/0.57                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 0.35/0.57                     => ( ( Y2 = one_one_nat )
% 0.35/0.57                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 0.35/0.57                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.57                        ( ( X
% 0.35/0.57                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                       => ( ( Y2
% 0.35/0.57                            = ( plus_plus_nat @ one_one_nat
% 0.35/0.57                              @ ( if_nat @ ( Xa2 = Mi2 ) @ zero_zero_nat
% 0.35/0.57                                @ ( if_nat @ ( Xa2 = Ma2 ) @ zero_zero_nat
% 0.35/0.57                                  @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ zero_zero_nat
% 0.35/0.57                                    @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ zero_zero_nat
% 0.35/0.57                                      @ ( if_nat
% 0.35/0.57                                        @ ( ( ord_less_nat @ Mi2 @ Xa2 )
% 0.35/0.57                                          & ( ord_less_nat @ Xa2 @ Ma2 ) )
% 0.35/0.57                                        @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( vEBT_T_m_e_m_b_e_r2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ zero_zero_nat )
% 0.35/0.57                                        @ zero_zero_nat ) ) ) ) ) ) )
% 0.35/0.57                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.pelims
% 0.35/0.57  thf(fact_3102_zle__diff1__eq,axiom,
% 0.35/0.57      ! [W: int,Z: int] :
% 0.35/0.57        ( ( ord_less_eq_int @ W @ ( minus_minus_int @ Z @ one_one_int ) )
% 0.35/0.57        = ( ord_less_int @ W @ Z ) ) ).
% 0.35/0.57  
% 0.35/0.57  % zle_diff1_eq
% 0.35/0.57  thf(fact_3103_vebt__member_Opelims_I1_J,axiom,
% 0.35/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 0.35/0.57        ( ( ( vEBT_vebt_member @ X @ Xa2 )
% 0.35/0.57          = Y2 )
% 0.35/0.57       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.57         => ( ! [A4: $o,B3: $o] :
% 0.35/0.57                ( ( X
% 0.35/0.57                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.57               => ( ( Y2
% 0.35/0.57                    = ( ( ( Xa2 = zero_zero_nat )
% 0.35/0.57                       => A4 )
% 0.35/0.57                      & ( ( Xa2 != zero_zero_nat )
% 0.35/0.57                       => ( ( ( Xa2 = one_one_nat )
% 0.35/0.57                           => B3 )
% 0.35/0.57                          & ( Xa2 = one_one_nat ) ) ) ) )
% 0.35/0.57                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa2 ) ) ) )
% 0.35/0.57           => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.35/0.57                  ( ( X
% 0.35/0.57                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.35/0.57                 => ( ~ Y2
% 0.35/0.57                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 0.35/0.57             => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.35/0.57                    ( ( X
% 0.35/0.57                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 0.35/0.57                   => ( ~ Y2
% 0.35/0.57                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 0.35/0.57               => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.35/0.57                      ( ( X
% 0.35/0.57                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 0.35/0.57                     => ( ~ Y2
% 0.35/0.57                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 0.35/0.57                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.57                        ( ( X
% 0.35/0.57                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                       => ( ( Y2
% 0.35/0.57                            = ( ( Xa2 != Mi2 )
% 0.35/0.57                             => ( ( Xa2 != Ma2 )
% 0.35/0.57                               => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.57                                  & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.57                                   => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.35/0.57                                      & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.35/0.57                                       => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.57                                           => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) )
% 0.35/0.57                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % vebt_member.pelims(1)
% 0.35/0.57  thf(fact_3104_vebt__member_Opelims_I3_J,axiom,
% 0.35/0.57      ! [X: vEBT_VEBT,Xa2: nat] :
% 0.35/0.57        ( ~ ( vEBT_vebt_member @ X @ Xa2 )
% 0.35/0.57       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.57         => ( ! [A4: $o,B3: $o] :
% 0.35/0.57                ( ( X
% 0.35/0.57                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.57               => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa2 ) )
% 0.35/0.57                 => ( ( ( Xa2 = zero_zero_nat )
% 0.35/0.57                     => A4 )
% 0.35/0.57                    & ( ( Xa2 != zero_zero_nat )
% 0.35/0.57                     => ( ( ( Xa2 = one_one_nat )
% 0.35/0.57                         => B3 )
% 0.35/0.57                        & ( Xa2 = one_one_nat ) ) ) ) ) )
% 0.35/0.57           => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.35/0.57                  ( ( X
% 0.35/0.57                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.35/0.57                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) )
% 0.35/0.57             => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.35/0.57                    ( ( X
% 0.35/0.57                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 0.35/0.57                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) )
% 0.35/0.57               => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.35/0.57                      ( ( X
% 0.35/0.57                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 0.35/0.57                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) )
% 0.35/0.57                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.57                        ( ( X
% 0.35/0.57                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) )
% 0.35/0.57                         => ( ( Xa2 != Mi2 )
% 0.35/0.57                           => ( ( Xa2 != Ma2 )
% 0.35/0.57                             => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.57                                & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.57                                 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.35/0.57                                    & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.35/0.57                                     => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.57                                         => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % vebt_member.pelims(3)
% 0.35/0.57  thf(fact_3105_VEBT__internal_Onaive__member_Opelims_I3_J,axiom,
% 0.35/0.57      ! [X: vEBT_VEBT,Xa2: nat] :
% 0.35/0.57        ( ~ ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 0.35/0.57       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.57         => ( ! [A4: $o,B3: $o] :
% 0.35/0.57                ( ( X
% 0.35/0.57                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.57               => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa2 ) )
% 0.35/0.57                 => ( ( ( Xa2 = zero_zero_nat )
% 0.35/0.57                     => A4 )
% 0.35/0.57                    & ( ( Xa2 != zero_zero_nat )
% 0.35/0.57                     => ( ( ( Xa2 = one_one_nat )
% 0.35/0.57                         => B3 )
% 0.35/0.57                        & ( Xa2 = one_one_nat ) ) ) ) ) )
% 0.35/0.57           => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.35/0.57                  ( ( X
% 0.35/0.57                    = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 0.35/0.57                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa2 ) ) )
% 0.35/0.57             => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 0.35/0.57                    ( ( X
% 0.35/0.57                      = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) )
% 0.35/0.57                   => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) @ Xa2 ) )
% 0.35/0.57                     => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.57                         => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % VEBT_internal.naive_member.pelims(3)
% 0.35/0.57  thf(fact_3106_VEBT__internal_Onaive__member_Opelims_I2_J,axiom,
% 0.35/0.57      ! [X: vEBT_VEBT,Xa2: nat] :
% 0.35/0.57        ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 0.35/0.57       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.57         => ( ! [A4: $o,B3: $o] :
% 0.35/0.57                ( ( X
% 0.35/0.57                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.57               => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa2 ) )
% 0.35/0.57                 => ~ ( ( ( Xa2 = zero_zero_nat )
% 0.35/0.57                       => A4 )
% 0.35/0.57                      & ( ( Xa2 != zero_zero_nat )
% 0.35/0.57                       => ( ( ( Xa2 = one_one_nat )
% 0.35/0.57                           => B3 )
% 0.35/0.57                          & ( Xa2 = one_one_nat ) ) ) ) ) )
% 0.35/0.57           => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 0.35/0.57                  ( ( X
% 0.35/0.57                    = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) )
% 0.35/0.57                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) @ Xa2 ) )
% 0.35/0.57                   => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.57                         => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % VEBT_internal.naive_member.pelims(2)
% 0.35/0.57  thf(fact_3107_VEBT__internal_Onaive__member_Opelims_I1_J,axiom,
% 0.35/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 0.35/0.57        ( ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 0.35/0.57          = Y2 )
% 0.35/0.57       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.57         => ( ! [A4: $o,B3: $o] :
% 0.35/0.57                ( ( X
% 0.35/0.57                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.57               => ( ( Y2
% 0.35/0.57                    = ( ( ( Xa2 = zero_zero_nat )
% 0.35/0.57                       => A4 )
% 0.35/0.57                      & ( ( Xa2 != zero_zero_nat )
% 0.35/0.57                       => ( ( ( Xa2 = one_one_nat )
% 0.35/0.57                           => B3 )
% 0.35/0.57                          & ( Xa2 = one_one_nat ) ) ) ) )
% 0.35/0.57                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa2 ) ) ) )
% 0.35/0.57           => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.35/0.57                  ( ( X
% 0.35/0.57                    = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 0.35/0.57                 => ( ~ Y2
% 0.35/0.57                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 0.35/0.57             => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 0.35/0.57                    ( ( X
% 0.35/0.57                      = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) )
% 0.35/0.57                   => ( ( Y2
% 0.35/0.57                        = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.57                           => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) )
% 0.35/0.57                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) @ Xa2 ) ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % VEBT_internal.naive_member.pelims(1)
% 0.35/0.57  thf(fact_3108_vebt__member_Opelims_I2_J,axiom,
% 0.35/0.57      ! [X: vEBT_VEBT,Xa2: nat] :
% 0.35/0.57        ( ( vEBT_vebt_member @ X @ Xa2 )
% 0.35/0.57       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.57         => ( ! [A4: $o,B3: $o] :
% 0.35/0.57                ( ( X
% 0.35/0.57                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.57               => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa2 ) )
% 0.35/0.57                 => ~ ( ( ( Xa2 = zero_zero_nat )
% 0.35/0.57                       => A4 )
% 0.35/0.57                      & ( ( Xa2 != zero_zero_nat )
% 0.35/0.57                       => ( ( ( Xa2 = one_one_nat )
% 0.35/0.57                           => B3 )
% 0.35/0.57                          & ( Xa2 = one_one_nat ) ) ) ) ) )
% 0.35/0.57           => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.57                  ( ( X
% 0.35/0.57                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 0.35/0.57                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) )
% 0.35/0.57                   => ~ ( ( Xa2 != Mi2 )
% 0.35/0.57                       => ( ( Xa2 != Ma2 )
% 0.35/0.57                         => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.57                            & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.57                             => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.35/0.57                                & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.35/0.57                                 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.57                                     => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.57                                    & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % vebt_member.pelims(2)
% 0.35/0.57  thf(fact_3109_double__eq__0__iff,axiom,
% 0.35/0.57      ! [A: real] :
% 0.35/0.57        ( ( ( plus_plus_real @ A @ A )
% 0.35/0.57          = zero_zero_real )
% 0.35/0.57        = ( A = zero_zero_real ) ) ).
% 0.35/0.57  
% 0.35/0.57  % double_eq_0_iff
% 0.35/0.57  thf(fact_3110_double__eq__0__iff,axiom,
% 0.35/0.57      ! [A: rat] :
% 0.35/0.57        ( ( ( plus_plus_rat @ A @ A )
% 0.35/0.57          = zero_zero_rat )
% 0.35/0.57        = ( A = zero_zero_rat ) ) ).
% 0.35/0.57  
% 0.35/0.57  % double_eq_0_iff
% 0.35/0.57  thf(fact_3111_double__eq__0__iff,axiom,
% 0.35/0.57      ! [A: int] :
% 0.35/0.57        ( ( ( plus_plus_int @ A @ A )
% 0.35/0.57          = zero_zero_int )
% 0.35/0.57        = ( A = zero_zero_int ) ) ).
% 0.35/0.57  
% 0.35/0.57  % double_eq_0_iff
% 0.35/0.57  thf(fact_3112_minus__int__code_I1_J,axiom,
% 0.35/0.57      ! [K: int] :
% 0.35/0.57        ( ( minus_minus_int @ K @ zero_zero_int )
% 0.35/0.57        = K ) ).
% 0.35/0.57  
% 0.35/0.57  % minus_int_code(1)
% 0.35/0.57  thf(fact_3113_int__distrib_I4_J,axiom,
% 0.35/0.57      ! [W: int,Z1: int,Z22: int] :
% 0.35/0.57        ( ( times_times_int @ W @ ( minus_minus_int @ Z1 @ Z22 ) )
% 0.35/0.57        = ( minus_minus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % int_distrib(4)
% 0.35/0.57  thf(fact_3114_int__distrib_I3_J,axiom,
% 0.35/0.57      ! [Z1: int,Z22: int,W: int] :
% 0.35/0.57        ( ( times_times_int @ ( minus_minus_int @ Z1 @ Z22 ) @ W )
% 0.35/0.57        = ( minus_minus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % int_distrib(3)
% 0.35/0.57  thf(fact_3115_int__le__induct,axiom,
% 0.35/0.57      ! [I2: int,K: int,P: int > $o] :
% 0.35/0.57        ( ( ord_less_eq_int @ I2 @ K )
% 0.35/0.57       => ( ( P @ K )
% 0.35/0.57         => ( ! [I4: int] :
% 0.35/0.57                ( ( ord_less_eq_int @ I4 @ K )
% 0.35/0.57               => ( ( P @ I4 )
% 0.35/0.57                 => ( P @ ( minus_minus_int @ I4 @ one_one_int ) ) ) )
% 0.35/0.57           => ( P @ I2 ) ) ) ) ).
% 0.35/0.57  
% 0.35/0.57  % int_le_induct
% 0.35/0.57  thf(fact_3116_int__less__induct,axiom,
% 0.35/0.57      ! [I2: int,K: int,P: int > $o] :
% 0.35/0.57        ( ( ord_less_int @ I2 @ K )
% 0.35/0.57       => ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
% 0.35/0.57         => ( ! [I4: int] :
% 0.35/0.57                ( ( ord_less_int @ I4 @ K )
% 0.35/0.58               => ( ( P @ I4 )
% 0.35/0.58                 => ( P @ ( minus_minus_int @ I4 @ one_one_int ) ) ) )
% 0.35/0.58           => ( P @ I2 ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % int_less_induct
% 0.35/0.58  thf(fact_3117_int__induct,axiom,
% 0.35/0.58      ! [P: int > $o,K: int,I2: int] :
% 0.35/0.58        ( ( P @ K )
% 0.35/0.58       => ( ! [I4: int] :
% 0.35/0.58              ( ( ord_less_eq_int @ K @ I4 )
% 0.35/0.58             => ( ( P @ I4 )
% 0.35/0.58               => ( P @ ( plus_plus_int @ I4 @ one_one_int ) ) ) )
% 0.35/0.58         => ( ! [I4: int] :
% 0.35/0.58                ( ( ord_less_eq_int @ I4 @ K )
% 0.35/0.58               => ( ( P @ I4 )
% 0.35/0.58                 => ( P @ ( minus_minus_int @ I4 @ one_one_int ) ) ) )
% 0.35/0.58           => ( P @ I2 ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % int_induct
% 0.35/0.58  thf(fact_3118_VEBT__internal_Omembermima_Opelims_I3_J,axiom,
% 0.35/0.58      ! [X: vEBT_VEBT,Xa2: nat] :
% 0.35/0.58        ( ~ ( vEBT_VEBT_membermima @ X @ Xa2 )
% 0.35/0.58       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.58         => ( ! [Uu2: $o,Uv2: $o] :
% 0.35/0.58                ( ( X
% 0.35/0.58                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.35/0.58               => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) )
% 0.35/0.58           => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 0.35/0.58                  ( ( X
% 0.35/0.58                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 0.35/0.58                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) )
% 0.35/0.58             => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 0.35/0.58                    ( ( X
% 0.35/0.58                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 0.35/0.58                   => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) )
% 0.35/0.58                     => ( ( Xa2 = Mi2 )
% 0.35/0.58                        | ( Xa2 = Ma2 ) ) ) )
% 0.35/0.58               => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.35/0.58                      ( ( X
% 0.35/0.58                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 0.35/0.58                     => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) @ Xa2 ) )
% 0.35/0.58                       => ( ( Xa2 = Mi2 )
% 0.35/0.58                          | ( Xa2 = Ma2 )
% 0.35/0.58                          | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.58                             => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.58                            & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) )
% 0.35/0.58                 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 0.35/0.58                        ( ( X
% 0.35/0.58                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 0.35/0.58                       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) @ Xa2 ) )
% 0.35/0.58                         => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.58                             => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.58                            & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % VEBT_internal.membermima.pelims(3)
% 0.35/0.58  thf(fact_3119_VEBT__internal_Omembermima_Opelims_I1_J,axiom,
% 0.35/0.58      ! [X: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 0.35/0.58        ( ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 0.35/0.58          = Y2 )
% 0.35/0.58       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.58         => ( ! [Uu2: $o,Uv2: $o] :
% 0.35/0.58                ( ( X
% 0.35/0.58                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.35/0.58               => ( ~ Y2
% 0.35/0.58                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 0.35/0.58           => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 0.35/0.58                  ( ( X
% 0.35/0.58                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 0.35/0.58                 => ( ~ Y2
% 0.35/0.58                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) ) )
% 0.35/0.58             => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 0.35/0.58                    ( ( X
% 0.35/0.58                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 0.35/0.58                   => ( ( Y2
% 0.35/0.58                        = ( ( Xa2 = Mi2 )
% 0.35/0.58                          | ( Xa2 = Ma2 ) ) )
% 0.35/0.58                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) ) ) )
% 0.35/0.58               => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.35/0.58                      ( ( X
% 0.35/0.58                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 0.35/0.58                     => ( ( Y2
% 0.35/0.58                          = ( ( Xa2 = Mi2 )
% 0.35/0.58                            | ( Xa2 = Ma2 )
% 0.35/0.58                            | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.58                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.58                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 0.35/0.58                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) @ Xa2 ) ) ) )
% 0.35/0.58                 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 0.35/0.58                        ( ( X
% 0.35/0.58                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 0.35/0.58                       => ( ( Y2
% 0.35/0.58                            = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.58                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.58                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) )
% 0.35/0.58                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % VEBT_internal.membermima.pelims(1)
% 0.35/0.58  thf(fact_3120_VEBT__internal_Omembermima_Opelims_I2_J,axiom,
% 0.35/0.58      ! [X: vEBT_VEBT,Xa2: nat] :
% 0.35/0.58        ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 0.35/0.58       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.58         => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 0.35/0.58                ( ( X
% 0.35/0.58                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 0.35/0.58               => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) )
% 0.35/0.58                 => ~ ( ( Xa2 = Mi2 )
% 0.35/0.58                      | ( Xa2 = Ma2 ) ) ) )
% 0.35/0.58           => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.35/0.58                  ( ( X
% 0.35/0.58                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 0.35/0.58                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) @ Xa2 ) )
% 0.35/0.58                   => ~ ( ( Xa2 = Mi2 )
% 0.35/0.58                        | ( Xa2 = Ma2 )
% 0.35/0.58                        | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.58                           => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.58                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) )
% 0.35/0.58             => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 0.35/0.58                    ( ( X
% 0.35/0.58                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 0.35/0.58                   => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) @ Xa2 ) )
% 0.35/0.58                     => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.58                           => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.58                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % VEBT_internal.membermima.pelims(2)
% 0.35/0.58  thf(fact_3121_atLeastatMost__empty,axiom,
% 0.35/0.58      ! [B: rat,A: rat] :
% 0.35/0.58        ( ( ord_less_rat @ B @ A )
% 0.35/0.58       => ( ( set_or633870826150836451st_rat @ A @ B )
% 0.35/0.58          = bot_bot_set_rat ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastatMost_empty
% 0.35/0.58  thf(fact_3122_atLeastatMost__empty,axiom,
% 0.35/0.58      ! [B: num,A: num] :
% 0.35/0.58        ( ( ord_less_num @ B @ A )
% 0.35/0.58       => ( ( set_or7049704709247886629st_num @ A @ B )
% 0.35/0.58          = bot_bot_set_num ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastatMost_empty
% 0.35/0.58  thf(fact_3123_atLeastatMost__empty,axiom,
% 0.35/0.58      ! [B: nat,A: nat] :
% 0.35/0.58        ( ( ord_less_nat @ B @ A )
% 0.35/0.58       => ( ( set_or1269000886237332187st_nat @ A @ B )
% 0.35/0.58          = bot_bot_set_nat ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastatMost_empty
% 0.35/0.58  thf(fact_3124_atLeastatMost__empty,axiom,
% 0.35/0.58      ! [B: int,A: int] :
% 0.35/0.58        ( ( ord_less_int @ B @ A )
% 0.35/0.58       => ( ( set_or1266510415728281911st_int @ A @ B )
% 0.35/0.58          = bot_bot_set_int ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastatMost_empty
% 0.35/0.58  thf(fact_3125_atLeastatMost__empty,axiom,
% 0.35/0.58      ! [B: real,A: real] :
% 0.35/0.58        ( ( ord_less_real @ B @ A )
% 0.35/0.58       => ( ( set_or1222579329274155063t_real @ A @ B )
% 0.35/0.58          = bot_bot_set_real ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastatMost_empty
% 0.35/0.58  thf(fact_3126_atLeastatMost__subset__iff,axiom,
% 0.35/0.58      ! [A: set_real,B: set_real,C: set_real,D2: set_real] :
% 0.35/0.58        ( ( ord_le3558479182127378552t_real @ ( set_or7743017856606604397t_real @ A @ B ) @ ( set_or7743017856606604397t_real @ C @ D2 ) )
% 0.35/0.58        = ( ~ ( ord_less_eq_set_real @ A @ B )
% 0.35/0.58          | ( ( ord_less_eq_set_real @ C @ A )
% 0.35/0.58            & ( ord_less_eq_set_real @ B @ D2 ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastatMost_subset_iff
% 0.35/0.58  thf(fact_3127_atLeastatMost__subset__iff,axiom,
% 0.35/0.58      ! [A: set_nat,B: set_nat,C: set_nat,D2: set_nat] :
% 0.35/0.58        ( ( ord_le6893508408891458716et_nat @ ( set_or4548717258645045905et_nat @ A @ B ) @ ( set_or4548717258645045905et_nat @ C @ D2 ) )
% 0.35/0.58        = ( ~ ( ord_less_eq_set_nat @ A @ B )
% 0.35/0.58          | ( ( ord_less_eq_set_nat @ C @ A )
% 0.35/0.58            & ( ord_less_eq_set_nat @ B @ D2 ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastatMost_subset_iff
% 0.35/0.58  thf(fact_3128_atLeastatMost__subset__iff,axiom,
% 0.35/0.58      ! [A: num,B: num,C: num,D2: num] :
% 0.35/0.58        ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D2 ) )
% 0.35/0.58        = ( ~ ( ord_less_eq_num @ A @ B )
% 0.35/0.58          | ( ( ord_less_eq_num @ C @ A )
% 0.35/0.58            & ( ord_less_eq_num @ B @ D2 ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastatMost_subset_iff
% 0.35/0.58  thf(fact_3129_atLeastatMost__subset__iff,axiom,
% 0.35/0.58      ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.35/0.58        ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D2 ) )
% 0.35/0.58        = ( ~ ( ord_less_eq_nat @ A @ B )
% 0.35/0.58          | ( ( ord_less_eq_nat @ C @ A )
% 0.35/0.58            & ( ord_less_eq_nat @ B @ D2 ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastatMost_subset_iff
% 0.35/0.58  thf(fact_3130_atLeastatMost__subset__iff,axiom,
% 0.35/0.58      ! [A: int,B: int,C: int,D2: int] :
% 0.35/0.58        ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D2 ) )
% 0.35/0.58        = ( ~ ( ord_less_eq_int @ A @ B )
% 0.35/0.58          | ( ( ord_less_eq_int @ C @ A )
% 0.35/0.58            & ( ord_less_eq_int @ B @ D2 ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastatMost_subset_iff
% 0.35/0.58  thf(fact_3131_atLeastatMost__subset__iff,axiom,
% 0.35/0.58      ! [A: real,B: real,C: real,D2: real] :
% 0.35/0.58        ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D2 ) )
% 0.35/0.58        = ( ~ ( ord_less_eq_real @ A @ B )
% 0.35/0.58          | ( ( ord_less_eq_real @ C @ A )
% 0.35/0.58            & ( ord_less_eq_real @ B @ D2 ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastatMost_subset_iff
% 0.35/0.58  thf(fact_3132_atLeastatMost__empty__iff,axiom,
% 0.35/0.58      ! [A: set_real,B: set_real] :
% 0.35/0.58        ( ( ( set_or7743017856606604397t_real @ A @ B )
% 0.35/0.58          = bot_bot_set_set_real )
% 0.35/0.58        = ( ~ ( ord_less_eq_set_real @ A @ B ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastatMost_empty_iff
% 0.35/0.58  thf(fact_3133_atLeastatMost__empty__iff,axiom,
% 0.35/0.58      ! [A: set_nat,B: set_nat] :
% 0.35/0.58        ( ( ( set_or4548717258645045905et_nat @ A @ B )
% 0.35/0.58          = bot_bot_set_set_nat )
% 0.35/0.58        = ( ~ ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastatMost_empty_iff
% 0.35/0.58  thf(fact_3134_atLeastatMost__empty__iff,axiom,
% 0.35/0.58      ! [A: num,B: num] :
% 0.35/0.58        ( ( ( set_or7049704709247886629st_num @ A @ B )
% 0.35/0.58          = bot_bot_set_num )
% 0.35/0.58        = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastatMost_empty_iff
% 0.35/0.58  thf(fact_3135_atLeastatMost__empty__iff,axiom,
% 0.35/0.58      ! [A: nat,B: nat] :
% 0.35/0.58        ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 0.35/0.58          = bot_bot_set_nat )
% 0.35/0.58        = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastatMost_empty_iff
% 0.35/0.58  thf(fact_3136_atLeastatMost__empty__iff,axiom,
% 0.35/0.58      ! [A: int,B: int] :
% 0.35/0.58        ( ( ( set_or1266510415728281911st_int @ A @ B )
% 0.35/0.58          = bot_bot_set_int )
% 0.35/0.58        = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastatMost_empty_iff
% 0.35/0.58  thf(fact_3137_atLeastatMost__empty__iff,axiom,
% 0.35/0.58      ! [A: real,B: real] :
% 0.35/0.58        ( ( ( set_or1222579329274155063t_real @ A @ B )
% 0.35/0.58          = bot_bot_set_real )
% 0.35/0.58        = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastatMost_empty_iff
% 0.35/0.58  thf(fact_3138_atLeastatMost__empty__iff2,axiom,
% 0.35/0.58      ! [A: set_real,B: set_real] :
% 0.35/0.58        ( ( bot_bot_set_set_real
% 0.35/0.58          = ( set_or7743017856606604397t_real @ A @ B ) )
% 0.35/0.58        = ( ~ ( ord_less_eq_set_real @ A @ B ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastatMost_empty_iff2
% 0.35/0.58  thf(fact_3139_atLeastatMost__empty__iff2,axiom,
% 0.35/0.58      ! [A: set_nat,B: set_nat] :
% 0.35/0.58        ( ( bot_bot_set_set_nat
% 0.35/0.58          = ( set_or4548717258645045905et_nat @ A @ B ) )
% 0.35/0.58        = ( ~ ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastatMost_empty_iff2
% 0.35/0.58  thf(fact_3140_atLeastatMost__empty__iff2,axiom,
% 0.35/0.58      ! [A: num,B: num] :
% 0.35/0.58        ( ( bot_bot_set_num
% 0.35/0.58          = ( set_or7049704709247886629st_num @ A @ B ) )
% 0.35/0.58        = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastatMost_empty_iff2
% 0.35/0.58  thf(fact_3141_atLeastatMost__empty__iff2,axiom,
% 0.35/0.58      ! [A: nat,B: nat] :
% 0.35/0.58        ( ( bot_bot_set_nat
% 0.35/0.58          = ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.35/0.58        = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastatMost_empty_iff2
% 0.35/0.58  thf(fact_3142_atLeastatMost__empty__iff2,axiom,
% 0.35/0.58      ! [A: int,B: int] :
% 0.35/0.58        ( ( bot_bot_set_int
% 0.35/0.58          = ( set_or1266510415728281911st_int @ A @ B ) )
% 0.35/0.58        = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastatMost_empty_iff2
% 0.35/0.58  thf(fact_3143_atLeastatMost__empty__iff2,axiom,
% 0.35/0.58      ! [A: real,B: real] :
% 0.35/0.58        ( ( bot_bot_set_real
% 0.35/0.58          = ( set_or1222579329274155063t_real @ A @ B ) )
% 0.35/0.58        = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastatMost_empty_iff2
% 0.35/0.58  thf(fact_3144_decr__mult__lemma,axiom,
% 0.35/0.58      ! [D2: int,P: int > $o,K: int] :
% 0.35/0.58        ( ( ord_less_int @ zero_zero_int @ D2 )
% 0.35/0.58       => ( ! [X3: int] :
% 0.35/0.58              ( ( P @ X3 )
% 0.35/0.58             => ( P @ ( minus_minus_int @ X3 @ D2 ) ) )
% 0.35/0.58         => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.35/0.58           => ! [X5: int] :
% 0.35/0.58                ( ( P @ X5 )
% 0.35/0.58               => ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K @ D2 ) ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % decr_mult_lemma
% 0.35/0.58  thf(fact_3145_Icc__eq__Icc,axiom,
% 0.35/0.58      ! [L2: set_real,H2: set_real,L3: set_real,H3: set_real] :
% 0.35/0.58        ( ( ( set_or7743017856606604397t_real @ L2 @ H2 )
% 0.35/0.58          = ( set_or7743017856606604397t_real @ L3 @ H3 ) )
% 0.35/0.58        = ( ( ( L2 = L3 )
% 0.35/0.58            & ( H2 = H3 ) )
% 0.35/0.58          | ( ~ ( ord_less_eq_set_real @ L2 @ H2 )
% 0.35/0.58            & ~ ( ord_less_eq_set_real @ L3 @ H3 ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Icc_eq_Icc
% 0.35/0.58  thf(fact_3146_Icc__eq__Icc,axiom,
% 0.35/0.58      ! [L2: set_nat,H2: set_nat,L3: set_nat,H3: set_nat] :
% 0.35/0.58        ( ( ( set_or4548717258645045905et_nat @ L2 @ H2 )
% 0.35/0.58          = ( set_or4548717258645045905et_nat @ L3 @ H3 ) )
% 0.35/0.58        = ( ( ( L2 = L3 )
% 0.35/0.58            & ( H2 = H3 ) )
% 0.35/0.58          | ( ~ ( ord_less_eq_set_nat @ L2 @ H2 )
% 0.35/0.58            & ~ ( ord_less_eq_set_nat @ L3 @ H3 ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Icc_eq_Icc
% 0.35/0.58  thf(fact_3147_Icc__eq__Icc,axiom,
% 0.35/0.58      ! [L2: num,H2: num,L3: num,H3: num] :
% 0.35/0.58        ( ( ( set_or7049704709247886629st_num @ L2 @ H2 )
% 0.35/0.58          = ( set_or7049704709247886629st_num @ L3 @ H3 ) )
% 0.35/0.58        = ( ( ( L2 = L3 )
% 0.35/0.58            & ( H2 = H3 ) )
% 0.35/0.58          | ( ~ ( ord_less_eq_num @ L2 @ H2 )
% 0.35/0.58            & ~ ( ord_less_eq_num @ L3 @ H3 ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Icc_eq_Icc
% 0.35/0.58  thf(fact_3148_Icc__eq__Icc,axiom,
% 0.35/0.58      ! [L2: nat,H2: nat,L3: nat,H3: nat] :
% 0.35/0.58        ( ( ( set_or1269000886237332187st_nat @ L2 @ H2 )
% 0.35/0.58          = ( set_or1269000886237332187st_nat @ L3 @ H3 ) )
% 0.35/0.58        = ( ( ( L2 = L3 )
% 0.35/0.58            & ( H2 = H3 ) )
% 0.35/0.58          | ( ~ ( ord_less_eq_nat @ L2 @ H2 )
% 0.35/0.58            & ~ ( ord_less_eq_nat @ L3 @ H3 ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Icc_eq_Icc
% 0.35/0.58  thf(fact_3149_Icc__eq__Icc,axiom,
% 0.35/0.58      ! [L2: int,H2: int,L3: int,H3: int] :
% 0.35/0.58        ( ( ( set_or1266510415728281911st_int @ L2 @ H2 )
% 0.35/0.58          = ( set_or1266510415728281911st_int @ L3 @ H3 ) )
% 0.35/0.58        = ( ( ( L2 = L3 )
% 0.35/0.58            & ( H2 = H3 ) )
% 0.35/0.58          | ( ~ ( ord_less_eq_int @ L2 @ H2 )
% 0.35/0.58            & ~ ( ord_less_eq_int @ L3 @ H3 ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Icc_eq_Icc
% 0.35/0.58  thf(fact_3150_Icc__eq__Icc,axiom,
% 0.35/0.58      ! [L2: real,H2: real,L3: real,H3: real] :
% 0.35/0.58        ( ( ( set_or1222579329274155063t_real @ L2 @ H2 )
% 0.35/0.58          = ( set_or1222579329274155063t_real @ L3 @ H3 ) )
% 0.35/0.58        = ( ( ( L2 = L3 )
% 0.35/0.58            & ( H2 = H3 ) )
% 0.35/0.58          | ( ~ ( ord_less_eq_real @ L2 @ H2 )
% 0.35/0.58            & ~ ( ord_less_eq_real @ L3 @ H3 ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Icc_eq_Icc
% 0.35/0.58  thf(fact_3151_atLeastAtMost__iff,axiom,
% 0.35/0.58      ! [I2: set_real,L2: set_real,U: set_real] :
% 0.35/0.58        ( ( member_set_real @ I2 @ ( set_or7743017856606604397t_real @ L2 @ U ) )
% 0.35/0.58        = ( ( ord_less_eq_set_real @ L2 @ I2 )
% 0.35/0.58          & ( ord_less_eq_set_real @ I2 @ U ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastAtMost_iff
% 0.35/0.58  thf(fact_3152_atLeastAtMost__iff,axiom,
% 0.35/0.58      ! [I2: set_nat,L2: set_nat,U: set_nat] :
% 0.35/0.58        ( ( member_set_nat @ I2 @ ( set_or4548717258645045905et_nat @ L2 @ U ) )
% 0.35/0.58        = ( ( ord_less_eq_set_nat @ L2 @ I2 )
% 0.35/0.58          & ( ord_less_eq_set_nat @ I2 @ U ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastAtMost_iff
% 0.35/0.58  thf(fact_3153_atLeastAtMost__iff,axiom,
% 0.35/0.58      ! [I2: num,L2: num,U: num] :
% 0.35/0.58        ( ( member_num @ I2 @ ( set_or7049704709247886629st_num @ L2 @ U ) )
% 0.35/0.58        = ( ( ord_less_eq_num @ L2 @ I2 )
% 0.35/0.58          & ( ord_less_eq_num @ I2 @ U ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastAtMost_iff
% 0.35/0.58  thf(fact_3154_atLeastAtMost__iff,axiom,
% 0.35/0.58      ! [I2: nat,L2: nat,U: nat] :
% 0.35/0.58        ( ( member_nat @ I2 @ ( set_or1269000886237332187st_nat @ L2 @ U ) )
% 0.35/0.58        = ( ( ord_less_eq_nat @ L2 @ I2 )
% 0.35/0.58          & ( ord_less_eq_nat @ I2 @ U ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastAtMost_iff
% 0.35/0.58  thf(fact_3155_atLeastAtMost__iff,axiom,
% 0.35/0.58      ! [I2: int,L2: int,U: int] :
% 0.35/0.58        ( ( member_int @ I2 @ ( set_or1266510415728281911st_int @ L2 @ U ) )
% 0.35/0.58        = ( ( ord_less_eq_int @ L2 @ I2 )
% 0.35/0.58          & ( ord_less_eq_int @ I2 @ U ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastAtMost_iff
% 0.35/0.58  thf(fact_3156_atLeastAtMost__iff,axiom,
% 0.35/0.58      ! [I2: real,L2: real,U: real] :
% 0.35/0.58        ( ( member_real @ I2 @ ( set_or1222579329274155063t_real @ L2 @ U ) )
% 0.35/0.58        = ( ( ord_less_eq_real @ L2 @ I2 )
% 0.35/0.58          & ( ord_less_eq_real @ I2 @ U ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastAtMost_iff
% 0.35/0.58  thf(fact_3157_aset_I2_J,axiom,
% 0.35/0.58      ! [D4: int,A2: set_int,P: int > $o,Q: int > $o] :
% 0.35/0.58        ( ! [X3: int] :
% 0.35/0.58            ( ! [Xa: int] :
% 0.35/0.58                ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.35/0.58               => ! [Xb2: int] :
% 0.35/0.58                    ( ( member_int @ Xb2 @ A2 )
% 0.35/0.58                   => ( X3
% 0.35/0.58                     != ( minus_minus_int @ Xb2 @ Xa ) ) ) )
% 0.35/0.58           => ( ( P @ X3 )
% 0.35/0.58             => ( P @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 0.35/0.58       => ( ! [X3: int] :
% 0.35/0.58              ( ! [Xa: int] :
% 0.35/0.58                  ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.35/0.58                 => ! [Xb2: int] :
% 0.35/0.58                      ( ( member_int @ Xb2 @ A2 )
% 0.35/0.58                     => ( X3
% 0.35/0.58                       != ( minus_minus_int @ Xb2 @ Xa ) ) ) )
% 0.35/0.58             => ( ( Q @ X3 )
% 0.35/0.58               => ( Q @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 0.35/0.58         => ! [X5: int] :
% 0.35/0.58              ( ! [Xa3: int] :
% 0.35/0.58                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.35/0.58                 => ! [Xb3: int] :
% 0.35/0.58                      ( ( member_int @ Xb3 @ A2 )
% 0.35/0.58                     => ( X5
% 0.35/0.58                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.35/0.58             => ( ( ( P @ X5 )
% 0.35/0.58                  | ( Q @ X5 ) )
% 0.35/0.58               => ( ( P @ ( plus_plus_int @ X5 @ D4 ) )
% 0.35/0.58                  | ( Q @ ( plus_plus_int @ X5 @ D4 ) ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % aset(2)
% 0.35/0.58  thf(fact_3158_aset_I1_J,axiom,
% 0.35/0.58      ! [D4: int,A2: set_int,P: int > $o,Q: int > $o] :
% 0.35/0.58        ( ! [X3: int] :
% 0.35/0.58            ( ! [Xa: int] :
% 0.35/0.58                ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.35/0.58               => ! [Xb2: int] :
% 0.35/0.58                    ( ( member_int @ Xb2 @ A2 )
% 0.35/0.58                   => ( X3
% 0.35/0.58                     != ( minus_minus_int @ Xb2 @ Xa ) ) ) )
% 0.35/0.58           => ( ( P @ X3 )
% 0.35/0.58             => ( P @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 0.35/0.58       => ( ! [X3: int] :
% 0.35/0.58              ( ! [Xa: int] :
% 0.35/0.58                  ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.35/0.58                 => ! [Xb2: int] :
% 0.35/0.58                      ( ( member_int @ Xb2 @ A2 )
% 0.35/0.58                     => ( X3
% 0.35/0.58                       != ( minus_minus_int @ Xb2 @ Xa ) ) ) )
% 0.35/0.58             => ( ( Q @ X3 )
% 0.35/0.58               => ( Q @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 0.35/0.58         => ! [X5: int] :
% 0.35/0.58              ( ! [Xa3: int] :
% 0.35/0.58                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.35/0.58                 => ! [Xb3: int] :
% 0.35/0.58                      ( ( member_int @ Xb3 @ A2 )
% 0.35/0.58                     => ( X5
% 0.35/0.58                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.35/0.58             => ( ( ( P @ X5 )
% 0.35/0.58                  & ( Q @ X5 ) )
% 0.35/0.58               => ( ( P @ ( plus_plus_int @ X5 @ D4 ) )
% 0.35/0.58                  & ( Q @ ( plus_plus_int @ X5 @ D4 ) ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % aset(1)
% 0.35/0.58  thf(fact_3159_bset_I2_J,axiom,
% 0.35/0.58      ! [D4: int,B2: set_int,P: int > $o,Q: int > $o] :
% 0.35/0.58        ( ! [X3: int] :
% 0.35/0.58            ( ! [Xa: int] :
% 0.35/0.58                ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.35/0.58               => ! [Xb2: int] :
% 0.35/0.58                    ( ( member_int @ Xb2 @ B2 )
% 0.35/0.58                   => ( X3
% 0.35/0.58                     != ( plus_plus_int @ Xb2 @ Xa ) ) ) )
% 0.35/0.58           => ( ( P @ X3 )
% 0.35/0.58             => ( P @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 0.35/0.58       => ( ! [X3: int] :
% 0.35/0.58              ( ! [Xa: int] :
% 0.35/0.58                  ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.35/0.58                 => ! [Xb2: int] :
% 0.35/0.58                      ( ( member_int @ Xb2 @ B2 )
% 0.35/0.58                     => ( X3
% 0.35/0.58                       != ( plus_plus_int @ Xb2 @ Xa ) ) ) )
% 0.35/0.58             => ( ( Q @ X3 )
% 0.35/0.58               => ( Q @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 0.35/0.58         => ! [X5: int] :
% 0.35/0.58              ( ! [Xa3: int] :
% 0.35/0.58                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.35/0.58                 => ! [Xb3: int] :
% 0.35/0.58                      ( ( member_int @ Xb3 @ B2 )
% 0.35/0.58                     => ( X5
% 0.35/0.58                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.35/0.58             => ( ( ( P @ X5 )
% 0.35/0.58                  | ( Q @ X5 ) )
% 0.35/0.58               => ( ( P @ ( minus_minus_int @ X5 @ D4 ) )
% 0.35/0.58                  | ( Q @ ( minus_minus_int @ X5 @ D4 ) ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % bset(2)
% 0.35/0.58  thf(fact_3160_bset_I1_J,axiom,
% 0.35/0.58      ! [D4: int,B2: set_int,P: int > $o,Q: int > $o] :
% 0.35/0.58        ( ! [X3: int] :
% 0.35/0.58            ( ! [Xa: int] :
% 0.35/0.58                ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.35/0.58               => ! [Xb2: int] :
% 0.35/0.58                    ( ( member_int @ Xb2 @ B2 )
% 0.35/0.58                   => ( X3
% 0.35/0.58                     != ( plus_plus_int @ Xb2 @ Xa ) ) ) )
% 0.35/0.58           => ( ( P @ X3 )
% 0.35/0.58             => ( P @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 0.35/0.58       => ( ! [X3: int] :
% 0.35/0.58              ( ! [Xa: int] :
% 0.35/0.58                  ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.35/0.58                 => ! [Xb2: int] :
% 0.35/0.58                      ( ( member_int @ Xb2 @ B2 )
% 0.35/0.58                     => ( X3
% 0.35/0.58                       != ( plus_plus_int @ Xb2 @ Xa ) ) ) )
% 0.35/0.58             => ( ( Q @ X3 )
% 0.35/0.58               => ( Q @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 0.35/0.58         => ! [X5: int] :
% 0.35/0.58              ( ! [Xa3: int] :
% 0.35/0.58                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.35/0.58                 => ! [Xb3: int] :
% 0.35/0.58                      ( ( member_int @ Xb3 @ B2 )
% 0.35/0.58                     => ( X5
% 0.35/0.58                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.35/0.58             => ( ( ( P @ X5 )
% 0.35/0.58                  & ( Q @ X5 ) )
% 0.35/0.58               => ( ( P @ ( minus_minus_int @ X5 @ D4 ) )
% 0.35/0.58                  & ( Q @ ( minus_minus_int @ X5 @ D4 ) ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % bset(1)
% 0.35/0.58  thf(fact_3161_minf_I7_J,axiom,
% 0.35/0.58      ! [T: real] :
% 0.35/0.58      ? [Z3: real] :
% 0.35/0.58      ! [X5: real] :
% 0.35/0.58        ( ( ord_less_real @ X5 @ Z3 )
% 0.35/0.58       => ~ ( ord_less_real @ T @ X5 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(7)
% 0.35/0.58  thf(fact_3162_minf_I7_J,axiom,
% 0.35/0.58      ! [T: rat] :
% 0.35/0.58      ? [Z3: rat] :
% 0.35/0.58      ! [X5: rat] :
% 0.35/0.58        ( ( ord_less_rat @ X5 @ Z3 )
% 0.35/0.58       => ~ ( ord_less_rat @ T @ X5 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(7)
% 0.35/0.58  thf(fact_3163_minf_I7_J,axiom,
% 0.35/0.58      ! [T: num] :
% 0.35/0.58      ? [Z3: num] :
% 0.35/0.58      ! [X5: num] :
% 0.35/0.58        ( ( ord_less_num @ X5 @ Z3 )
% 0.35/0.58       => ~ ( ord_less_num @ T @ X5 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(7)
% 0.35/0.58  thf(fact_3164_minf_I7_J,axiom,
% 0.35/0.58      ! [T: nat] :
% 0.35/0.58      ? [Z3: nat] :
% 0.35/0.58      ! [X5: nat] :
% 0.35/0.58        ( ( ord_less_nat @ X5 @ Z3 )
% 0.35/0.58       => ~ ( ord_less_nat @ T @ X5 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(7)
% 0.35/0.58  thf(fact_3165_minf_I7_J,axiom,
% 0.35/0.58      ! [T: int] :
% 0.35/0.58      ? [Z3: int] :
% 0.35/0.58      ! [X5: int] :
% 0.35/0.58        ( ( ord_less_int @ X5 @ Z3 )
% 0.35/0.58       => ~ ( ord_less_int @ T @ X5 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(7)
% 0.35/0.58  thf(fact_3166_minf_I5_J,axiom,
% 0.35/0.58      ! [T: real] :
% 0.35/0.58      ? [Z3: real] :
% 0.35/0.58      ! [X5: real] :
% 0.35/0.58        ( ( ord_less_real @ X5 @ Z3 )
% 0.35/0.58       => ( ord_less_real @ X5 @ T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(5)
% 0.35/0.58  thf(fact_3167_minf_I5_J,axiom,
% 0.35/0.58      ! [T: rat] :
% 0.35/0.58      ? [Z3: rat] :
% 0.35/0.58      ! [X5: rat] :
% 0.35/0.58        ( ( ord_less_rat @ X5 @ Z3 )
% 0.35/0.58       => ( ord_less_rat @ X5 @ T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(5)
% 0.35/0.58  thf(fact_3168_minf_I5_J,axiom,
% 0.35/0.58      ! [T: num] :
% 0.35/0.58      ? [Z3: num] :
% 0.35/0.58      ! [X5: num] :
% 0.35/0.58        ( ( ord_less_num @ X5 @ Z3 )
% 0.35/0.58       => ( ord_less_num @ X5 @ T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(5)
% 0.35/0.58  thf(fact_3169_minf_I5_J,axiom,
% 0.35/0.58      ! [T: nat] :
% 0.35/0.58      ? [Z3: nat] :
% 0.35/0.58      ! [X5: nat] :
% 0.35/0.58        ( ( ord_less_nat @ X5 @ Z3 )
% 0.35/0.58       => ( ord_less_nat @ X5 @ T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(5)
% 0.35/0.58  thf(fact_3170_minf_I5_J,axiom,
% 0.35/0.58      ! [T: int] :
% 0.35/0.58      ? [Z3: int] :
% 0.35/0.58      ! [X5: int] :
% 0.35/0.58        ( ( ord_less_int @ X5 @ Z3 )
% 0.35/0.58       => ( ord_less_int @ X5 @ T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(5)
% 0.35/0.58  thf(fact_3171_minf_I4_J,axiom,
% 0.35/0.58      ! [T: real] :
% 0.35/0.58      ? [Z3: real] :
% 0.35/0.58      ! [X5: real] :
% 0.35/0.58        ( ( ord_less_real @ X5 @ Z3 )
% 0.35/0.58       => ( X5 != T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(4)
% 0.35/0.58  thf(fact_3172_minf_I4_J,axiom,
% 0.35/0.58      ! [T: rat] :
% 0.35/0.58      ? [Z3: rat] :
% 0.35/0.58      ! [X5: rat] :
% 0.35/0.58        ( ( ord_less_rat @ X5 @ Z3 )
% 0.35/0.58       => ( X5 != T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(4)
% 0.35/0.58  thf(fact_3173_minf_I4_J,axiom,
% 0.35/0.58      ! [T: num] :
% 0.35/0.58      ? [Z3: num] :
% 0.35/0.58      ! [X5: num] :
% 0.35/0.58        ( ( ord_less_num @ X5 @ Z3 )
% 0.35/0.58       => ( X5 != T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(4)
% 0.35/0.58  thf(fact_3174_minf_I4_J,axiom,
% 0.35/0.58      ! [T: nat] :
% 0.35/0.58      ? [Z3: nat] :
% 0.35/0.58      ! [X5: nat] :
% 0.35/0.58        ( ( ord_less_nat @ X5 @ Z3 )
% 0.35/0.58       => ( X5 != T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(4)
% 0.35/0.58  thf(fact_3175_minf_I4_J,axiom,
% 0.35/0.58      ! [T: int] :
% 0.35/0.58      ? [Z3: int] :
% 0.35/0.58      ! [X5: int] :
% 0.35/0.58        ( ( ord_less_int @ X5 @ Z3 )
% 0.35/0.58       => ( X5 != T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(4)
% 0.35/0.58  thf(fact_3176_minf_I3_J,axiom,
% 0.35/0.58      ! [T: real] :
% 0.35/0.58      ? [Z3: real] :
% 0.35/0.58      ! [X5: real] :
% 0.35/0.58        ( ( ord_less_real @ X5 @ Z3 )
% 0.35/0.58       => ( X5 != T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(3)
% 0.35/0.58  thf(fact_3177_minf_I3_J,axiom,
% 0.35/0.58      ! [T: rat] :
% 0.35/0.58      ? [Z3: rat] :
% 0.35/0.58      ! [X5: rat] :
% 0.35/0.58        ( ( ord_less_rat @ X5 @ Z3 )
% 0.35/0.58       => ( X5 != T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(3)
% 0.35/0.58  thf(fact_3178_minf_I3_J,axiom,
% 0.35/0.58      ! [T: num] :
% 0.35/0.58      ? [Z3: num] :
% 0.35/0.58      ! [X5: num] :
% 0.35/0.58        ( ( ord_less_num @ X5 @ Z3 )
% 0.35/0.58       => ( X5 != T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(3)
% 0.35/0.58  thf(fact_3179_minf_I3_J,axiom,
% 0.35/0.58      ! [T: nat] :
% 0.35/0.58      ? [Z3: nat] :
% 0.35/0.58      ! [X5: nat] :
% 0.35/0.58        ( ( ord_less_nat @ X5 @ Z3 )
% 0.35/0.58       => ( X5 != T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(3)
% 0.35/0.58  thf(fact_3180_minf_I3_J,axiom,
% 0.35/0.58      ! [T: int] :
% 0.35/0.58      ? [Z3: int] :
% 0.35/0.58      ! [X5: int] :
% 0.35/0.58        ( ( ord_less_int @ X5 @ Z3 )
% 0.35/0.58       => ( X5 != T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(3)
% 0.35/0.58  thf(fact_3181_minf_I2_J,axiom,
% 0.35/0.58      ! [P: real > $o,P5: real > $o,Q: real > $o,Q6: real > $o] :
% 0.35/0.58        ( ? [Z2: real] :
% 0.35/0.58          ! [X3: real] :
% 0.35/0.58            ( ( ord_less_real @ X3 @ Z2 )
% 0.35/0.58           => ( ( P @ X3 )
% 0.35/0.58              = ( P5 @ X3 ) ) )
% 0.35/0.58       => ( ? [Z2: real] :
% 0.35/0.58            ! [X3: real] :
% 0.35/0.58              ( ( ord_less_real @ X3 @ Z2 )
% 0.35/0.58             => ( ( Q @ X3 )
% 0.35/0.58                = ( Q6 @ X3 ) ) )
% 0.35/0.58         => ? [Z3: real] :
% 0.35/0.58            ! [X5: real] :
% 0.35/0.58              ( ( ord_less_real @ X5 @ Z3 )
% 0.35/0.58             => ( ( ( P @ X5 )
% 0.35/0.58                  | ( Q @ X5 ) )
% 0.35/0.58                = ( ( P5 @ X5 )
% 0.35/0.58                  | ( Q6 @ X5 ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(2)
% 0.35/0.58  thf(fact_3182_minf_I2_J,axiom,
% 0.35/0.58      ! [P: rat > $o,P5: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 0.35/0.58        ( ? [Z2: rat] :
% 0.35/0.58          ! [X3: rat] :
% 0.35/0.58            ( ( ord_less_rat @ X3 @ Z2 )
% 0.35/0.58           => ( ( P @ X3 )
% 0.35/0.58              = ( P5 @ X3 ) ) )
% 0.35/0.58       => ( ? [Z2: rat] :
% 0.35/0.58            ! [X3: rat] :
% 0.35/0.58              ( ( ord_less_rat @ X3 @ Z2 )
% 0.35/0.58             => ( ( Q @ X3 )
% 0.35/0.58                = ( Q6 @ X3 ) ) )
% 0.35/0.58         => ? [Z3: rat] :
% 0.35/0.58            ! [X5: rat] :
% 0.35/0.58              ( ( ord_less_rat @ X5 @ Z3 )
% 0.35/0.58             => ( ( ( P @ X5 )
% 0.35/0.58                  | ( Q @ X5 ) )
% 0.35/0.58                = ( ( P5 @ X5 )
% 0.35/0.58                  | ( Q6 @ X5 ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(2)
% 0.35/0.58  thf(fact_3183_minf_I2_J,axiom,
% 0.35/0.58      ! [P: num > $o,P5: num > $o,Q: num > $o,Q6: num > $o] :
% 0.35/0.58        ( ? [Z2: num] :
% 0.35/0.58          ! [X3: num] :
% 0.35/0.58            ( ( ord_less_num @ X3 @ Z2 )
% 0.35/0.58           => ( ( P @ X3 )
% 0.35/0.58              = ( P5 @ X3 ) ) )
% 0.35/0.58       => ( ? [Z2: num] :
% 0.35/0.58            ! [X3: num] :
% 0.35/0.58              ( ( ord_less_num @ X3 @ Z2 )
% 0.35/0.58             => ( ( Q @ X3 )
% 0.35/0.58                = ( Q6 @ X3 ) ) )
% 0.35/0.58         => ? [Z3: num] :
% 0.35/0.58            ! [X5: num] :
% 0.35/0.58              ( ( ord_less_num @ X5 @ Z3 )
% 0.35/0.58             => ( ( ( P @ X5 )
% 0.35/0.58                  | ( Q @ X5 ) )
% 0.35/0.58                = ( ( P5 @ X5 )
% 0.35/0.58                  | ( Q6 @ X5 ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(2)
% 0.35/0.58  thf(fact_3184_minf_I2_J,axiom,
% 0.35/0.58      ! [P: nat > $o,P5: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 0.35/0.58        ( ? [Z2: nat] :
% 0.35/0.58          ! [X3: nat] :
% 0.35/0.58            ( ( ord_less_nat @ X3 @ Z2 )
% 0.35/0.58           => ( ( P @ X3 )
% 0.35/0.58              = ( P5 @ X3 ) ) )
% 0.35/0.58       => ( ? [Z2: nat] :
% 0.35/0.58            ! [X3: nat] :
% 0.35/0.58              ( ( ord_less_nat @ X3 @ Z2 )
% 0.35/0.58             => ( ( Q @ X3 )
% 0.35/0.58                = ( Q6 @ X3 ) ) )
% 0.35/0.58         => ? [Z3: nat] :
% 0.35/0.58            ! [X5: nat] :
% 0.35/0.58              ( ( ord_less_nat @ X5 @ Z3 )
% 0.35/0.58             => ( ( ( P @ X5 )
% 0.35/0.58                  | ( Q @ X5 ) )
% 0.35/0.58                = ( ( P5 @ X5 )
% 0.35/0.58                  | ( Q6 @ X5 ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(2)
% 0.35/0.58  thf(fact_3185_minf_I2_J,axiom,
% 0.35/0.58      ! [P: int > $o,P5: int > $o,Q: int > $o,Q6: int > $o] :
% 0.35/0.58        ( ? [Z2: int] :
% 0.35/0.58          ! [X3: int] :
% 0.35/0.58            ( ( ord_less_int @ X3 @ Z2 )
% 0.35/0.58           => ( ( P @ X3 )
% 0.35/0.58              = ( P5 @ X3 ) ) )
% 0.35/0.58       => ( ? [Z2: int] :
% 0.35/0.58            ! [X3: int] :
% 0.35/0.58              ( ( ord_less_int @ X3 @ Z2 )
% 0.35/0.58             => ( ( Q @ X3 )
% 0.35/0.58                = ( Q6 @ X3 ) ) )
% 0.35/0.58         => ? [Z3: int] :
% 0.35/0.58            ! [X5: int] :
% 0.35/0.58              ( ( ord_less_int @ X5 @ Z3 )
% 0.35/0.58             => ( ( ( P @ X5 )
% 0.35/0.58                  | ( Q @ X5 ) )
% 0.35/0.58                = ( ( P5 @ X5 )
% 0.35/0.58                  | ( Q6 @ X5 ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(2)
% 0.35/0.58  thf(fact_3186_minf_I1_J,axiom,
% 0.35/0.58      ! [P: real > $o,P5: real > $o,Q: real > $o,Q6: real > $o] :
% 0.35/0.58        ( ? [Z2: real] :
% 0.35/0.58          ! [X3: real] :
% 0.35/0.58            ( ( ord_less_real @ X3 @ Z2 )
% 0.35/0.58           => ( ( P @ X3 )
% 0.35/0.58              = ( P5 @ X3 ) ) )
% 0.35/0.58       => ( ? [Z2: real] :
% 0.35/0.58            ! [X3: real] :
% 0.35/0.58              ( ( ord_less_real @ X3 @ Z2 )
% 0.35/0.58             => ( ( Q @ X3 )
% 0.35/0.58                = ( Q6 @ X3 ) ) )
% 0.35/0.58         => ? [Z3: real] :
% 0.35/0.58            ! [X5: real] :
% 0.35/0.58              ( ( ord_less_real @ X5 @ Z3 )
% 0.35/0.58             => ( ( ( P @ X5 )
% 0.35/0.58                  & ( Q @ X5 ) )
% 0.35/0.58                = ( ( P5 @ X5 )
% 0.35/0.58                  & ( Q6 @ X5 ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(1)
% 0.35/0.58  thf(fact_3187_minf_I1_J,axiom,
% 0.35/0.58      ! [P: rat > $o,P5: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 0.35/0.58        ( ? [Z2: rat] :
% 0.35/0.58          ! [X3: rat] :
% 0.35/0.58            ( ( ord_less_rat @ X3 @ Z2 )
% 0.35/0.58           => ( ( P @ X3 )
% 0.35/0.58              = ( P5 @ X3 ) ) )
% 0.35/0.58       => ( ? [Z2: rat] :
% 0.35/0.58            ! [X3: rat] :
% 0.35/0.58              ( ( ord_less_rat @ X3 @ Z2 )
% 0.35/0.58             => ( ( Q @ X3 )
% 0.35/0.58                = ( Q6 @ X3 ) ) )
% 0.35/0.58         => ? [Z3: rat] :
% 0.35/0.58            ! [X5: rat] :
% 0.35/0.58              ( ( ord_less_rat @ X5 @ Z3 )
% 0.35/0.58             => ( ( ( P @ X5 )
% 0.35/0.58                  & ( Q @ X5 ) )
% 0.35/0.58                = ( ( P5 @ X5 )
% 0.35/0.58                  & ( Q6 @ X5 ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(1)
% 0.35/0.58  thf(fact_3188_minf_I1_J,axiom,
% 0.35/0.58      ! [P: num > $o,P5: num > $o,Q: num > $o,Q6: num > $o] :
% 0.35/0.58        ( ? [Z2: num] :
% 0.35/0.58          ! [X3: num] :
% 0.35/0.58            ( ( ord_less_num @ X3 @ Z2 )
% 0.35/0.58           => ( ( P @ X3 )
% 0.35/0.58              = ( P5 @ X3 ) ) )
% 0.35/0.58       => ( ? [Z2: num] :
% 0.35/0.58            ! [X3: num] :
% 0.35/0.58              ( ( ord_less_num @ X3 @ Z2 )
% 0.35/0.58             => ( ( Q @ X3 )
% 0.35/0.58                = ( Q6 @ X3 ) ) )
% 0.35/0.58         => ? [Z3: num] :
% 0.35/0.58            ! [X5: num] :
% 0.35/0.58              ( ( ord_less_num @ X5 @ Z3 )
% 0.35/0.58             => ( ( ( P @ X5 )
% 0.35/0.58                  & ( Q @ X5 ) )
% 0.35/0.58                = ( ( P5 @ X5 )
% 0.35/0.58                  & ( Q6 @ X5 ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(1)
% 0.35/0.58  thf(fact_3189_minf_I1_J,axiom,
% 0.35/0.58      ! [P: nat > $o,P5: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 0.35/0.58        ( ? [Z2: nat] :
% 0.35/0.58          ! [X3: nat] :
% 0.35/0.58            ( ( ord_less_nat @ X3 @ Z2 )
% 0.35/0.58           => ( ( P @ X3 )
% 0.35/0.58              = ( P5 @ X3 ) ) )
% 0.35/0.58       => ( ? [Z2: nat] :
% 0.35/0.58            ! [X3: nat] :
% 0.35/0.58              ( ( ord_less_nat @ X3 @ Z2 )
% 0.35/0.58             => ( ( Q @ X3 )
% 0.35/0.58                = ( Q6 @ X3 ) ) )
% 0.35/0.58         => ? [Z3: nat] :
% 0.35/0.58            ! [X5: nat] :
% 0.35/0.58              ( ( ord_less_nat @ X5 @ Z3 )
% 0.35/0.58             => ( ( ( P @ X5 )
% 0.35/0.58                  & ( Q @ X5 ) )
% 0.35/0.58                = ( ( P5 @ X5 )
% 0.35/0.58                  & ( Q6 @ X5 ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(1)
% 0.35/0.58  thf(fact_3190_minf_I1_J,axiom,
% 0.35/0.58      ! [P: int > $o,P5: int > $o,Q: int > $o,Q6: int > $o] :
% 0.35/0.58        ( ? [Z2: int] :
% 0.35/0.58          ! [X3: int] :
% 0.35/0.58            ( ( ord_less_int @ X3 @ Z2 )
% 0.35/0.58           => ( ( P @ X3 )
% 0.35/0.58              = ( P5 @ X3 ) ) )
% 0.35/0.58       => ( ? [Z2: int] :
% 0.35/0.58            ! [X3: int] :
% 0.35/0.58              ( ( ord_less_int @ X3 @ Z2 )
% 0.35/0.58             => ( ( Q @ X3 )
% 0.35/0.58                = ( Q6 @ X3 ) ) )
% 0.35/0.58         => ? [Z3: int] :
% 0.35/0.58            ! [X5: int] :
% 0.35/0.58              ( ( ord_less_int @ X5 @ Z3 )
% 0.35/0.58             => ( ( ( P @ X5 )
% 0.35/0.58                  & ( Q @ X5 ) )
% 0.35/0.58                = ( ( P5 @ X5 )
% 0.35/0.58                  & ( Q6 @ X5 ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(1)
% 0.35/0.58  thf(fact_3191_pinf_I7_J,axiom,
% 0.35/0.58      ! [T: real] :
% 0.35/0.58      ? [Z3: real] :
% 0.35/0.58      ! [X5: real] :
% 0.35/0.58        ( ( ord_less_real @ Z3 @ X5 )
% 0.35/0.58       => ( ord_less_real @ T @ X5 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(7)
% 0.35/0.58  thf(fact_3192_pinf_I7_J,axiom,
% 0.35/0.58      ! [T: rat] :
% 0.35/0.58      ? [Z3: rat] :
% 0.35/0.58      ! [X5: rat] :
% 0.35/0.58        ( ( ord_less_rat @ Z3 @ X5 )
% 0.35/0.58       => ( ord_less_rat @ T @ X5 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(7)
% 0.35/0.58  thf(fact_3193_pinf_I7_J,axiom,
% 0.35/0.58      ! [T: num] :
% 0.35/0.58      ? [Z3: num] :
% 0.35/0.58      ! [X5: num] :
% 0.35/0.58        ( ( ord_less_num @ Z3 @ X5 )
% 0.35/0.58       => ( ord_less_num @ T @ X5 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(7)
% 0.35/0.58  thf(fact_3194_pinf_I7_J,axiom,
% 0.35/0.58      ! [T: nat] :
% 0.35/0.58      ? [Z3: nat] :
% 0.35/0.58      ! [X5: nat] :
% 0.35/0.58        ( ( ord_less_nat @ Z3 @ X5 )
% 0.35/0.58       => ( ord_less_nat @ T @ X5 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(7)
% 0.35/0.58  thf(fact_3195_pinf_I7_J,axiom,
% 0.35/0.58      ! [T: int] :
% 0.35/0.58      ? [Z3: int] :
% 0.35/0.58      ! [X5: int] :
% 0.35/0.58        ( ( ord_less_int @ Z3 @ X5 )
% 0.35/0.58       => ( ord_less_int @ T @ X5 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(7)
% 0.35/0.58  thf(fact_3196_pinf_I5_J,axiom,
% 0.35/0.58      ! [T: real] :
% 0.35/0.58      ? [Z3: real] :
% 0.35/0.58      ! [X5: real] :
% 0.35/0.58        ( ( ord_less_real @ Z3 @ X5 )
% 0.35/0.58       => ~ ( ord_less_real @ X5 @ T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(5)
% 0.35/0.58  thf(fact_3197_pinf_I5_J,axiom,
% 0.35/0.58      ! [T: rat] :
% 0.35/0.58      ? [Z3: rat] :
% 0.35/0.58      ! [X5: rat] :
% 0.35/0.58        ( ( ord_less_rat @ Z3 @ X5 )
% 0.35/0.58       => ~ ( ord_less_rat @ X5 @ T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(5)
% 0.35/0.58  thf(fact_3198_pinf_I5_J,axiom,
% 0.35/0.58      ! [T: num] :
% 0.35/0.58      ? [Z3: num] :
% 0.35/0.58      ! [X5: num] :
% 0.35/0.58        ( ( ord_less_num @ Z3 @ X5 )
% 0.35/0.58       => ~ ( ord_less_num @ X5 @ T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(5)
% 0.35/0.58  thf(fact_3199_pinf_I5_J,axiom,
% 0.35/0.58      ! [T: nat] :
% 0.35/0.58      ? [Z3: nat] :
% 0.35/0.58      ! [X5: nat] :
% 0.35/0.58        ( ( ord_less_nat @ Z3 @ X5 )
% 0.35/0.58       => ~ ( ord_less_nat @ X5 @ T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(5)
% 0.35/0.58  thf(fact_3200_pinf_I5_J,axiom,
% 0.35/0.58      ! [T: int] :
% 0.35/0.58      ? [Z3: int] :
% 0.35/0.58      ! [X5: int] :
% 0.35/0.58        ( ( ord_less_int @ Z3 @ X5 )
% 0.35/0.58       => ~ ( ord_less_int @ X5 @ T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(5)
% 0.35/0.58  thf(fact_3201_pinf_I4_J,axiom,
% 0.35/0.58      ! [T: real] :
% 0.35/0.58      ? [Z3: real] :
% 0.35/0.58      ! [X5: real] :
% 0.35/0.58        ( ( ord_less_real @ Z3 @ X5 )
% 0.35/0.58       => ( X5 != T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(4)
% 0.35/0.58  thf(fact_3202_pinf_I4_J,axiom,
% 0.35/0.58      ! [T: rat] :
% 0.35/0.58      ? [Z3: rat] :
% 0.35/0.58      ! [X5: rat] :
% 0.35/0.58        ( ( ord_less_rat @ Z3 @ X5 )
% 0.35/0.58       => ( X5 != T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(4)
% 0.35/0.58  thf(fact_3203_pinf_I4_J,axiom,
% 0.35/0.58      ! [T: num] :
% 0.35/0.58      ? [Z3: num] :
% 0.35/0.58      ! [X5: num] :
% 0.35/0.58        ( ( ord_less_num @ Z3 @ X5 )
% 0.35/0.58       => ( X5 != T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(4)
% 0.35/0.58  thf(fact_3204_pinf_I4_J,axiom,
% 0.35/0.58      ! [T: nat] :
% 0.35/0.58      ? [Z3: nat] :
% 0.35/0.58      ! [X5: nat] :
% 0.35/0.58        ( ( ord_less_nat @ Z3 @ X5 )
% 0.35/0.58       => ( X5 != T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(4)
% 0.35/0.58  thf(fact_3205_pinf_I4_J,axiom,
% 0.35/0.58      ! [T: int] :
% 0.35/0.58      ? [Z3: int] :
% 0.35/0.58      ! [X5: int] :
% 0.35/0.58        ( ( ord_less_int @ Z3 @ X5 )
% 0.35/0.58       => ( X5 != T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(4)
% 0.35/0.58  thf(fact_3206_pinf_I3_J,axiom,
% 0.35/0.58      ! [T: real] :
% 0.35/0.58      ? [Z3: real] :
% 0.35/0.58      ! [X5: real] :
% 0.35/0.58        ( ( ord_less_real @ Z3 @ X5 )
% 0.35/0.58       => ( X5 != T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(3)
% 0.35/0.58  thf(fact_3207_pinf_I3_J,axiom,
% 0.35/0.58      ! [T: rat] :
% 0.35/0.58      ? [Z3: rat] :
% 0.35/0.58      ! [X5: rat] :
% 0.35/0.58        ( ( ord_less_rat @ Z3 @ X5 )
% 0.35/0.58       => ( X5 != T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(3)
% 0.35/0.58  thf(fact_3208_pinf_I3_J,axiom,
% 0.35/0.58      ! [T: num] :
% 0.35/0.58      ? [Z3: num] :
% 0.35/0.58      ! [X5: num] :
% 0.35/0.58        ( ( ord_less_num @ Z3 @ X5 )
% 0.35/0.58       => ( X5 != T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(3)
% 0.35/0.58  thf(fact_3209_pinf_I3_J,axiom,
% 0.35/0.58      ! [T: nat] :
% 0.35/0.58      ? [Z3: nat] :
% 0.35/0.58      ! [X5: nat] :
% 0.35/0.58        ( ( ord_less_nat @ Z3 @ X5 )
% 0.35/0.58       => ( X5 != T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(3)
% 0.35/0.58  thf(fact_3210_pinf_I3_J,axiom,
% 0.35/0.58      ! [T: int] :
% 0.35/0.58      ? [Z3: int] :
% 0.35/0.58      ! [X5: int] :
% 0.35/0.58        ( ( ord_less_int @ Z3 @ X5 )
% 0.35/0.58       => ( X5 != T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(3)
% 0.35/0.58  thf(fact_3211_pinf_I2_J,axiom,
% 0.35/0.58      ! [P: real > $o,P5: real > $o,Q: real > $o,Q6: real > $o] :
% 0.35/0.58        ( ? [Z2: real] :
% 0.35/0.58          ! [X3: real] :
% 0.35/0.58            ( ( ord_less_real @ Z2 @ X3 )
% 0.35/0.58           => ( ( P @ X3 )
% 0.35/0.58              = ( P5 @ X3 ) ) )
% 0.35/0.58       => ( ? [Z2: real] :
% 0.35/0.58            ! [X3: real] :
% 0.35/0.58              ( ( ord_less_real @ Z2 @ X3 )
% 0.35/0.58             => ( ( Q @ X3 )
% 0.35/0.58                = ( Q6 @ X3 ) ) )
% 0.35/0.58         => ? [Z3: real] :
% 0.35/0.58            ! [X5: real] :
% 0.35/0.58              ( ( ord_less_real @ Z3 @ X5 )
% 0.35/0.58             => ( ( ( P @ X5 )
% 0.35/0.58                  | ( Q @ X5 ) )
% 0.35/0.58                = ( ( P5 @ X5 )
% 0.35/0.58                  | ( Q6 @ X5 ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(2)
% 0.35/0.58  thf(fact_3212_pinf_I2_J,axiom,
% 0.35/0.58      ! [P: rat > $o,P5: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 0.35/0.58        ( ? [Z2: rat] :
% 0.35/0.58          ! [X3: rat] :
% 0.35/0.58            ( ( ord_less_rat @ Z2 @ X3 )
% 0.35/0.58           => ( ( P @ X3 )
% 0.35/0.58              = ( P5 @ X3 ) ) )
% 0.35/0.58       => ( ? [Z2: rat] :
% 0.35/0.58            ! [X3: rat] :
% 0.35/0.58              ( ( ord_less_rat @ Z2 @ X3 )
% 0.35/0.58             => ( ( Q @ X3 )
% 0.35/0.58                = ( Q6 @ X3 ) ) )
% 0.35/0.58         => ? [Z3: rat] :
% 0.35/0.58            ! [X5: rat] :
% 0.35/0.58              ( ( ord_less_rat @ Z3 @ X5 )
% 0.35/0.58             => ( ( ( P @ X5 )
% 0.35/0.58                  | ( Q @ X5 ) )
% 0.35/0.58                = ( ( P5 @ X5 )
% 0.35/0.58                  | ( Q6 @ X5 ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(2)
% 0.35/0.58  thf(fact_3213_pinf_I2_J,axiom,
% 0.35/0.58      ! [P: num > $o,P5: num > $o,Q: num > $o,Q6: num > $o] :
% 0.35/0.58        ( ? [Z2: num] :
% 0.35/0.58          ! [X3: num] :
% 0.35/0.58            ( ( ord_less_num @ Z2 @ X3 )
% 0.35/0.58           => ( ( P @ X3 )
% 0.35/0.58              = ( P5 @ X3 ) ) )
% 0.35/0.58       => ( ? [Z2: num] :
% 0.35/0.58            ! [X3: num] :
% 0.35/0.58              ( ( ord_less_num @ Z2 @ X3 )
% 0.35/0.58             => ( ( Q @ X3 )
% 0.35/0.58                = ( Q6 @ X3 ) ) )
% 0.35/0.58         => ? [Z3: num] :
% 0.35/0.58            ! [X5: num] :
% 0.35/0.58              ( ( ord_less_num @ Z3 @ X5 )
% 0.35/0.58             => ( ( ( P @ X5 )
% 0.35/0.58                  | ( Q @ X5 ) )
% 0.35/0.58                = ( ( P5 @ X5 )
% 0.35/0.58                  | ( Q6 @ X5 ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(2)
% 0.35/0.58  thf(fact_3214_pinf_I2_J,axiom,
% 0.35/0.58      ! [P: nat > $o,P5: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 0.35/0.58        ( ? [Z2: nat] :
% 0.35/0.58          ! [X3: nat] :
% 0.35/0.58            ( ( ord_less_nat @ Z2 @ X3 )
% 0.35/0.58           => ( ( P @ X3 )
% 0.35/0.58              = ( P5 @ X3 ) ) )
% 0.35/0.58       => ( ? [Z2: nat] :
% 0.35/0.58            ! [X3: nat] :
% 0.35/0.58              ( ( ord_less_nat @ Z2 @ X3 )
% 0.35/0.58             => ( ( Q @ X3 )
% 0.35/0.58                = ( Q6 @ X3 ) ) )
% 0.35/0.58         => ? [Z3: nat] :
% 0.35/0.58            ! [X5: nat] :
% 0.35/0.58              ( ( ord_less_nat @ Z3 @ X5 )
% 0.35/0.58             => ( ( ( P @ X5 )
% 0.35/0.58                  | ( Q @ X5 ) )
% 0.35/0.58                = ( ( P5 @ X5 )
% 0.35/0.58                  | ( Q6 @ X5 ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(2)
% 0.35/0.58  thf(fact_3215_pinf_I2_J,axiom,
% 0.35/0.58      ! [P: int > $o,P5: int > $o,Q: int > $o,Q6: int > $o] :
% 0.35/0.58        ( ? [Z2: int] :
% 0.35/0.58          ! [X3: int] :
% 0.35/0.58            ( ( ord_less_int @ Z2 @ X3 )
% 0.35/0.58           => ( ( P @ X3 )
% 0.35/0.58              = ( P5 @ X3 ) ) )
% 0.35/0.58       => ( ? [Z2: int] :
% 0.35/0.58            ! [X3: int] :
% 0.35/0.58              ( ( ord_less_int @ Z2 @ X3 )
% 0.35/0.58             => ( ( Q @ X3 )
% 0.35/0.58                = ( Q6 @ X3 ) ) )
% 0.35/0.58         => ? [Z3: int] :
% 0.35/0.58            ! [X5: int] :
% 0.35/0.58              ( ( ord_less_int @ Z3 @ X5 )
% 0.35/0.58             => ( ( ( P @ X5 )
% 0.35/0.58                  | ( Q @ X5 ) )
% 0.35/0.58                = ( ( P5 @ X5 )
% 0.35/0.58                  | ( Q6 @ X5 ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(2)
% 0.35/0.58  thf(fact_3216_pinf_I1_J,axiom,
% 0.35/0.58      ! [P: real > $o,P5: real > $o,Q: real > $o,Q6: real > $o] :
% 0.35/0.58        ( ? [Z2: real] :
% 0.35/0.58          ! [X3: real] :
% 0.35/0.58            ( ( ord_less_real @ Z2 @ X3 )
% 0.35/0.58           => ( ( P @ X3 )
% 0.35/0.58              = ( P5 @ X3 ) ) )
% 0.35/0.58       => ( ? [Z2: real] :
% 0.35/0.58            ! [X3: real] :
% 0.35/0.58              ( ( ord_less_real @ Z2 @ X3 )
% 0.35/0.58             => ( ( Q @ X3 )
% 0.35/0.58                = ( Q6 @ X3 ) ) )
% 0.35/0.58         => ? [Z3: real] :
% 0.35/0.58            ! [X5: real] :
% 0.35/0.58              ( ( ord_less_real @ Z3 @ X5 )
% 0.35/0.58             => ( ( ( P @ X5 )
% 0.35/0.58                  & ( Q @ X5 ) )
% 0.35/0.58                = ( ( P5 @ X5 )
% 0.35/0.58                  & ( Q6 @ X5 ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(1)
% 0.35/0.58  thf(fact_3217_pinf_I1_J,axiom,
% 0.35/0.58      ! [P: rat > $o,P5: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 0.35/0.58        ( ? [Z2: rat] :
% 0.35/0.58          ! [X3: rat] :
% 0.35/0.58            ( ( ord_less_rat @ Z2 @ X3 )
% 0.35/0.58           => ( ( P @ X3 )
% 0.35/0.58              = ( P5 @ X3 ) ) )
% 0.35/0.58       => ( ? [Z2: rat] :
% 0.35/0.58            ! [X3: rat] :
% 0.35/0.58              ( ( ord_less_rat @ Z2 @ X3 )
% 0.35/0.58             => ( ( Q @ X3 )
% 0.35/0.58                = ( Q6 @ X3 ) ) )
% 0.35/0.58         => ? [Z3: rat] :
% 0.35/0.58            ! [X5: rat] :
% 0.35/0.58              ( ( ord_less_rat @ Z3 @ X5 )
% 0.35/0.58             => ( ( ( P @ X5 )
% 0.35/0.58                  & ( Q @ X5 ) )
% 0.35/0.58                = ( ( P5 @ X5 )
% 0.35/0.58                  & ( Q6 @ X5 ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(1)
% 0.35/0.58  thf(fact_3218_pinf_I1_J,axiom,
% 0.35/0.58      ! [P: num > $o,P5: num > $o,Q: num > $o,Q6: num > $o] :
% 0.35/0.58        ( ? [Z2: num] :
% 0.35/0.58          ! [X3: num] :
% 0.35/0.58            ( ( ord_less_num @ Z2 @ X3 )
% 0.35/0.58           => ( ( P @ X3 )
% 0.35/0.58              = ( P5 @ X3 ) ) )
% 0.35/0.58       => ( ? [Z2: num] :
% 0.35/0.58            ! [X3: num] :
% 0.35/0.58              ( ( ord_less_num @ Z2 @ X3 )
% 0.35/0.58             => ( ( Q @ X3 )
% 0.35/0.58                = ( Q6 @ X3 ) ) )
% 0.35/0.58         => ? [Z3: num] :
% 0.35/0.58            ! [X5: num] :
% 0.35/0.58              ( ( ord_less_num @ Z3 @ X5 )
% 0.35/0.58             => ( ( ( P @ X5 )
% 0.35/0.58                  & ( Q @ X5 ) )
% 0.35/0.58                = ( ( P5 @ X5 )
% 0.35/0.58                  & ( Q6 @ X5 ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(1)
% 0.35/0.58  thf(fact_3219_pinf_I1_J,axiom,
% 0.35/0.58      ! [P: nat > $o,P5: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 0.35/0.58        ( ? [Z2: nat] :
% 0.35/0.58          ! [X3: nat] :
% 0.35/0.58            ( ( ord_less_nat @ Z2 @ X3 )
% 0.35/0.58           => ( ( P @ X3 )
% 0.35/0.58              = ( P5 @ X3 ) ) )
% 0.35/0.58       => ( ? [Z2: nat] :
% 0.35/0.58            ! [X3: nat] :
% 0.35/0.58              ( ( ord_less_nat @ Z2 @ X3 )
% 0.35/0.58             => ( ( Q @ X3 )
% 0.35/0.58                = ( Q6 @ X3 ) ) )
% 0.35/0.58         => ? [Z3: nat] :
% 0.35/0.58            ! [X5: nat] :
% 0.35/0.58              ( ( ord_less_nat @ Z3 @ X5 )
% 0.35/0.58             => ( ( ( P @ X5 )
% 0.35/0.58                  & ( Q @ X5 ) )
% 0.35/0.58                = ( ( P5 @ X5 )
% 0.35/0.58                  & ( Q6 @ X5 ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(1)
% 0.35/0.58  thf(fact_3220_pinf_I1_J,axiom,
% 0.35/0.58      ! [P: int > $o,P5: int > $o,Q: int > $o,Q6: int > $o] :
% 0.35/0.58        ( ? [Z2: int] :
% 0.35/0.58          ! [X3: int] :
% 0.35/0.58            ( ( ord_less_int @ Z2 @ X3 )
% 0.35/0.58           => ( ( P @ X3 )
% 0.35/0.58              = ( P5 @ X3 ) ) )
% 0.35/0.58       => ( ? [Z2: int] :
% 0.35/0.58            ! [X3: int] :
% 0.35/0.58              ( ( ord_less_int @ Z2 @ X3 )
% 0.35/0.58             => ( ( Q @ X3 )
% 0.35/0.58                = ( Q6 @ X3 ) ) )
% 0.35/0.58         => ? [Z3: int] :
% 0.35/0.58            ! [X5: int] :
% 0.35/0.58              ( ( ord_less_int @ Z3 @ X5 )
% 0.35/0.58             => ( ( ( P @ X5 )
% 0.35/0.58                  & ( Q @ X5 ) )
% 0.35/0.58                = ( ( P5 @ X5 )
% 0.35/0.58                  & ( Q6 @ X5 ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(1)
% 0.35/0.58  thf(fact_3221_bounded__Max__nat,axiom,
% 0.35/0.58      ! [P: nat > $o,X: nat,M7: nat] :
% 0.35/0.58        ( ( P @ X )
% 0.35/0.58       => ( ! [X3: nat] :
% 0.35/0.58              ( ( P @ X3 )
% 0.35/0.58             => ( ord_less_eq_nat @ X3 @ M7 ) )
% 0.35/0.58         => ~ ! [M4: nat] :
% 0.35/0.58                ( ( P @ M4 )
% 0.35/0.58               => ~ ! [X5: nat] :
% 0.35/0.58                      ( ( P @ X5 )
% 0.35/0.58                     => ( ord_less_eq_nat @ X5 @ M4 ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % bounded_Max_nat
% 0.35/0.58  thf(fact_3222_fold__atLeastAtMost__nat_Ocases,axiom,
% 0.35/0.58      ! [X: produc3368934014287244435at_num] :
% 0.35/0.58        ~ ! [F2: nat > num > num,A4: nat,B3: nat,Acc: num] :
% 0.35/0.58            ( X
% 0.35/0.58           != ( produc851828971589881931at_num @ F2 @ ( produc1195630363706982562at_num @ A4 @ ( product_Pair_nat_num @ B3 @ Acc ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % fold_atLeastAtMost_nat.cases
% 0.35/0.58  thf(fact_3223_fold__atLeastAtMost__nat_Ocases,axiom,
% 0.35/0.58      ! [X: produc4471711990508489141at_nat] :
% 0.35/0.58        ~ ! [F2: nat > nat > nat,A4: nat,B3: nat,Acc: nat] :
% 0.35/0.58            ( X
% 0.35/0.58           != ( produc3209952032786966637at_nat @ F2 @ ( produc487386426758144856at_nat @ A4 @ ( product_Pair_nat_nat @ B3 @ Acc ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % fold_atLeastAtMost_nat.cases
% 0.35/0.58  thf(fact_3224_periodic__finite__ex,axiom,
% 0.35/0.58      ! [D2: int,P: int > $o] :
% 0.35/0.58        ( ( ord_less_int @ zero_zero_int @ D2 )
% 0.35/0.58       => ( ! [X3: int,K2: int] :
% 0.35/0.58              ( ( P @ X3 )
% 0.35/0.58              = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D2 ) ) ) )
% 0.35/0.58         => ( ( ? [X4: int] : ( P @ X4 ) )
% 0.35/0.58            = ( ? [X2: int] :
% 0.35/0.58                  ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D2 ) )
% 0.35/0.58                  & ( P @ X2 ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % periodic_finite_ex
% 0.35/0.58  thf(fact_3225_aset_I7_J,axiom,
% 0.35/0.58      ! [D4: int,A2: set_int,T: int] :
% 0.35/0.58        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.35/0.58       => ! [X5: int] :
% 0.35/0.58            ( ! [Xa3: int] :
% 0.35/0.58                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.35/0.58               => ! [Xb3: int] :
% 0.35/0.58                    ( ( member_int @ Xb3 @ A2 )
% 0.35/0.58                   => ( X5
% 0.35/0.58                     != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.35/0.58           => ( ( ord_less_int @ T @ X5 )
% 0.35/0.58             => ( ord_less_int @ T @ ( plus_plus_int @ X5 @ D4 ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % aset(7)
% 0.35/0.58  thf(fact_3226_aset_I5_J,axiom,
% 0.35/0.58      ! [D4: int,T: int,A2: set_int] :
% 0.35/0.58        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.35/0.58       => ( ( member_int @ T @ A2 )
% 0.35/0.58         => ! [X5: int] :
% 0.35/0.58              ( ! [Xa3: int] :
% 0.35/0.58                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.35/0.58                 => ! [Xb3: int] :
% 0.35/0.58                      ( ( member_int @ Xb3 @ A2 )
% 0.35/0.58                     => ( X5
% 0.35/0.58                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.35/0.58             => ( ( ord_less_int @ X5 @ T )
% 0.35/0.58               => ( ord_less_int @ ( plus_plus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % aset(5)
% 0.35/0.58  thf(fact_3227_aset_I4_J,axiom,
% 0.35/0.58      ! [D4: int,T: int,A2: set_int] :
% 0.35/0.58        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.35/0.58       => ( ( member_int @ T @ A2 )
% 0.35/0.58         => ! [X5: int] :
% 0.35/0.58              ( ! [Xa3: int] :
% 0.35/0.58                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.35/0.58                 => ! [Xb3: int] :
% 0.35/0.58                      ( ( member_int @ Xb3 @ A2 )
% 0.35/0.58                     => ( X5
% 0.35/0.58                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.35/0.58             => ( ( X5 != T )
% 0.35/0.58               => ( ( plus_plus_int @ X5 @ D4 )
% 0.35/0.58                 != T ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % aset(4)
% 0.35/0.58  thf(fact_3228_aset_I3_J,axiom,
% 0.35/0.58      ! [D4: int,T: int,A2: set_int] :
% 0.35/0.58        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.35/0.58       => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 0.35/0.58         => ! [X5: int] :
% 0.35/0.58              ( ! [Xa3: int] :
% 0.35/0.58                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.35/0.58                 => ! [Xb3: int] :
% 0.35/0.58                      ( ( member_int @ Xb3 @ A2 )
% 0.35/0.58                     => ( X5
% 0.35/0.58                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.35/0.58             => ( ( X5 = T )
% 0.35/0.58               => ( ( plus_plus_int @ X5 @ D4 )
% 0.35/0.58                  = T ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % aset(3)
% 0.35/0.58  thf(fact_3229_bset_I7_J,axiom,
% 0.35/0.58      ! [D4: int,T: int,B2: set_int] :
% 0.35/0.58        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.35/0.58       => ( ( member_int @ T @ B2 )
% 0.35/0.58         => ! [X5: int] :
% 0.35/0.58              ( ! [Xa3: int] :
% 0.35/0.58                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.35/0.58                 => ! [Xb3: int] :
% 0.35/0.58                      ( ( member_int @ Xb3 @ B2 )
% 0.35/0.58                     => ( X5
% 0.35/0.58                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.35/0.58             => ( ( ord_less_int @ T @ X5 )
% 0.35/0.58               => ( ord_less_int @ T @ ( minus_minus_int @ X5 @ D4 ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % bset(7)
% 0.35/0.58  thf(fact_3230_bset_I5_J,axiom,
% 0.35/0.58      ! [D4: int,B2: set_int,T: int] :
% 0.35/0.58        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.35/0.58       => ! [X5: int] :
% 0.35/0.58            ( ! [Xa3: int] :
% 0.35/0.58                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.35/0.58               => ! [Xb3: int] :
% 0.35/0.58                    ( ( member_int @ Xb3 @ B2 )
% 0.35/0.58                   => ( X5
% 0.35/0.58                     != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.35/0.58           => ( ( ord_less_int @ X5 @ T )
% 0.35/0.58             => ( ord_less_int @ ( minus_minus_int @ X5 @ D4 ) @ T ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % bset(5)
% 0.35/0.58  thf(fact_3231_bset_I4_J,axiom,
% 0.35/0.58      ! [D4: int,T: int,B2: set_int] :
% 0.35/0.58        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.35/0.58       => ( ( member_int @ T @ B2 )
% 0.35/0.58         => ! [X5: int] :
% 0.35/0.58              ( ! [Xa3: int] :
% 0.35/0.58                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.35/0.58                 => ! [Xb3: int] :
% 0.35/0.58                      ( ( member_int @ Xb3 @ B2 )
% 0.35/0.58                     => ( X5
% 0.35/0.58                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.35/0.58             => ( ( X5 != T )
% 0.35/0.58               => ( ( minus_minus_int @ X5 @ D4 )
% 0.35/0.58                 != T ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % bset(4)
% 0.35/0.58  thf(fact_3232_bset_I3_J,axiom,
% 0.35/0.58      ! [D4: int,T: int,B2: set_int] :
% 0.35/0.58        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.35/0.58       => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B2 )
% 0.35/0.58         => ! [X5: int] :
% 0.35/0.58              ( ! [Xa3: int] :
% 0.35/0.58                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.35/0.58                 => ! [Xb3: int] :
% 0.35/0.58                      ( ( member_int @ Xb3 @ B2 )
% 0.35/0.58                     => ( X5
% 0.35/0.58                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.35/0.58             => ( ( X5 = T )
% 0.35/0.58               => ( ( minus_minus_int @ X5 @ D4 )
% 0.35/0.58                  = T ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % bset(3)
% 0.35/0.58  thf(fact_3233_aset_I8_J,axiom,
% 0.35/0.58      ! [D4: int,A2: set_int,T: int] :
% 0.35/0.58        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.35/0.58       => ! [X5: int] :
% 0.35/0.58            ( ! [Xa3: int] :
% 0.35/0.58                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.35/0.58               => ! [Xb3: int] :
% 0.35/0.58                    ( ( member_int @ Xb3 @ A2 )
% 0.35/0.58                   => ( X5
% 0.35/0.58                     != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.35/0.58           => ( ( ord_less_eq_int @ T @ X5 )
% 0.35/0.58             => ( ord_less_eq_int @ T @ ( plus_plus_int @ X5 @ D4 ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % aset(8)
% 0.35/0.58  thf(fact_3234_aset_I6_J,axiom,
% 0.35/0.58      ! [D4: int,T: int,A2: set_int] :
% 0.35/0.58        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.35/0.58       => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 0.35/0.58         => ! [X5: int] :
% 0.35/0.58              ( ! [Xa3: int] :
% 0.35/0.58                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.35/0.58                 => ! [Xb3: int] :
% 0.35/0.58                      ( ( member_int @ Xb3 @ A2 )
% 0.35/0.58                     => ( X5
% 0.35/0.58                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.35/0.58             => ( ( ord_less_eq_int @ X5 @ T )
% 0.35/0.58               => ( ord_less_eq_int @ ( plus_plus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % aset(6)
% 0.35/0.58  thf(fact_3235_bset_I8_J,axiom,
% 0.35/0.58      ! [D4: int,T: int,B2: set_int] :
% 0.35/0.58        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.35/0.58       => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B2 )
% 0.35/0.58         => ! [X5: int] :
% 0.35/0.58              ( ! [Xa3: int] :
% 0.35/0.58                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.35/0.58                 => ! [Xb3: int] :
% 0.35/0.58                      ( ( member_int @ Xb3 @ B2 )
% 0.35/0.58                     => ( X5
% 0.35/0.58                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.35/0.58             => ( ( ord_less_eq_int @ T @ X5 )
% 0.35/0.58               => ( ord_less_eq_int @ T @ ( minus_minus_int @ X5 @ D4 ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % bset(8)
% 0.35/0.58  thf(fact_3236_bset_I6_J,axiom,
% 0.35/0.58      ! [D4: int,B2: set_int,T: int] :
% 0.35/0.58        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.35/0.58       => ! [X5: int] :
% 0.35/0.58            ( ! [Xa3: int] :
% 0.35/0.58                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.35/0.58               => ! [Xb3: int] :
% 0.35/0.58                    ( ( member_int @ Xb3 @ B2 )
% 0.35/0.58                   => ( X5
% 0.35/0.58                     != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.35/0.58           => ( ( ord_less_eq_int @ X5 @ T )
% 0.35/0.58             => ( ord_less_eq_int @ ( minus_minus_int @ X5 @ D4 ) @ T ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % bset(6)
% 0.35/0.58  thf(fact_3237_cpmi,axiom,
% 0.35/0.58      ! [D4: int,P: int > $o,P5: int > $o,B2: set_int] :
% 0.35/0.58        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.35/0.58       => ( ? [Z2: int] :
% 0.35/0.58            ! [X3: int] :
% 0.35/0.58              ( ( ord_less_int @ X3 @ Z2 )
% 0.35/0.58             => ( ( P @ X3 )
% 0.35/0.58                = ( P5 @ X3 ) ) )
% 0.35/0.58         => ( ! [X3: int] :
% 0.35/0.58                ( ! [Xa: int] :
% 0.35/0.58                    ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.35/0.58                   => ! [Xb2: int] :
% 0.35/0.58                        ( ( member_int @ Xb2 @ B2 )
% 0.35/0.58                       => ( X3
% 0.35/0.58                         != ( plus_plus_int @ Xb2 @ Xa ) ) ) )
% 0.35/0.58               => ( ( P @ X3 )
% 0.35/0.58                 => ( P @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 0.35/0.58           => ( ! [X3: int,K2: int] :
% 0.35/0.58                  ( ( P5 @ X3 )
% 0.35/0.58                  = ( P5 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 0.35/0.58             => ( ( ? [X4: int] : ( P @ X4 ) )
% 0.35/0.58                = ( ? [X2: int] :
% 0.35/0.58                      ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.35/0.58                      & ( P5 @ X2 ) )
% 0.35/0.58                  | ? [X2: int] :
% 0.35/0.58                      ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.35/0.58                      & ? [Y: int] :
% 0.35/0.58                          ( ( member_int @ Y @ B2 )
% 0.35/0.58                          & ( P @ ( plus_plus_int @ Y @ X2 ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % cpmi
% 0.35/0.58  thf(fact_3238_cppi,axiom,
% 0.35/0.58      ! [D4: int,P: int > $o,P5: int > $o,A2: set_int] :
% 0.35/0.58        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.35/0.58       => ( ? [Z2: int] :
% 0.35/0.58            ! [X3: int] :
% 0.35/0.58              ( ( ord_less_int @ Z2 @ X3 )
% 0.35/0.58             => ( ( P @ X3 )
% 0.35/0.58                = ( P5 @ X3 ) ) )
% 0.35/0.58         => ( ! [X3: int] :
% 0.35/0.58                ( ! [Xa: int] :
% 0.35/0.58                    ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.35/0.58                   => ! [Xb2: int] :
% 0.35/0.58                        ( ( member_int @ Xb2 @ A2 )
% 0.35/0.58                       => ( X3
% 0.35/0.58                         != ( minus_minus_int @ Xb2 @ Xa ) ) ) )
% 0.35/0.58               => ( ( P @ X3 )
% 0.35/0.58                 => ( P @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 0.35/0.58           => ( ! [X3: int,K2: int] :
% 0.35/0.58                  ( ( P5 @ X3 )
% 0.35/0.58                  = ( P5 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 0.35/0.58             => ( ( ? [X4: int] : ( P @ X4 ) )
% 0.35/0.58                = ( ? [X2: int] :
% 0.35/0.58                      ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.35/0.58                      & ( P5 @ X2 ) )
% 0.35/0.58                  | ? [X2: int] :
% 0.35/0.58                      ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.35/0.58                      & ? [Y: int] :
% 0.35/0.58                          ( ( member_int @ Y @ A2 )
% 0.35/0.58                          & ( P @ ( minus_minus_int @ Y @ X2 ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % cppi
% 0.35/0.58  thf(fact_3239_minf_I8_J,axiom,
% 0.35/0.58      ! [T: real] :
% 0.35/0.58      ? [Z3: real] :
% 0.35/0.58      ! [X5: real] :
% 0.35/0.58        ( ( ord_less_real @ X5 @ Z3 )
% 0.35/0.58       => ~ ( ord_less_eq_real @ T @ X5 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(8)
% 0.35/0.58  thf(fact_3240_minf_I8_J,axiom,
% 0.35/0.58      ! [T: rat] :
% 0.35/0.58      ? [Z3: rat] :
% 0.35/0.58      ! [X5: rat] :
% 0.35/0.58        ( ( ord_less_rat @ X5 @ Z3 )
% 0.35/0.58       => ~ ( ord_less_eq_rat @ T @ X5 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(8)
% 0.35/0.58  thf(fact_3241_minf_I8_J,axiom,
% 0.35/0.58      ! [T: num] :
% 0.35/0.58      ? [Z3: num] :
% 0.35/0.58      ! [X5: num] :
% 0.35/0.58        ( ( ord_less_num @ X5 @ Z3 )
% 0.35/0.58       => ~ ( ord_less_eq_num @ T @ X5 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(8)
% 0.35/0.58  thf(fact_3242_minf_I8_J,axiom,
% 0.35/0.58      ! [T: nat] :
% 0.35/0.58      ? [Z3: nat] :
% 0.35/0.58      ! [X5: nat] :
% 0.35/0.58        ( ( ord_less_nat @ X5 @ Z3 )
% 0.35/0.58       => ~ ( ord_less_eq_nat @ T @ X5 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(8)
% 0.35/0.58  thf(fact_3243_minf_I8_J,axiom,
% 0.35/0.58      ! [T: int] :
% 0.35/0.58      ? [Z3: int] :
% 0.35/0.58      ! [X5: int] :
% 0.35/0.58        ( ( ord_less_int @ X5 @ Z3 )
% 0.35/0.58       => ~ ( ord_less_eq_int @ T @ X5 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(8)
% 0.35/0.58  thf(fact_3244_minf_I6_J,axiom,
% 0.35/0.58      ! [T: real] :
% 0.35/0.58      ? [Z3: real] :
% 0.35/0.58      ! [X5: real] :
% 0.35/0.58        ( ( ord_less_real @ X5 @ Z3 )
% 0.35/0.58       => ( ord_less_eq_real @ X5 @ T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(6)
% 0.35/0.58  thf(fact_3245_minf_I6_J,axiom,
% 0.35/0.58      ! [T: rat] :
% 0.35/0.58      ? [Z3: rat] :
% 0.35/0.58      ! [X5: rat] :
% 0.35/0.58        ( ( ord_less_rat @ X5 @ Z3 )
% 0.35/0.58       => ( ord_less_eq_rat @ X5 @ T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(6)
% 0.35/0.58  thf(fact_3246_minf_I6_J,axiom,
% 0.35/0.58      ! [T: num] :
% 0.35/0.58      ? [Z3: num] :
% 0.35/0.58      ! [X5: num] :
% 0.35/0.58        ( ( ord_less_num @ X5 @ Z3 )
% 0.35/0.58       => ( ord_less_eq_num @ X5 @ T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(6)
% 0.35/0.58  thf(fact_3247_minf_I6_J,axiom,
% 0.35/0.58      ! [T: nat] :
% 0.35/0.58      ? [Z3: nat] :
% 0.35/0.58      ! [X5: nat] :
% 0.35/0.58        ( ( ord_less_nat @ X5 @ Z3 )
% 0.35/0.58       => ( ord_less_eq_nat @ X5 @ T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(6)
% 0.35/0.58  thf(fact_3248_minf_I6_J,axiom,
% 0.35/0.58      ! [T: int] :
% 0.35/0.58      ? [Z3: int] :
% 0.35/0.58      ! [X5: int] :
% 0.35/0.58        ( ( ord_less_int @ X5 @ Z3 )
% 0.35/0.58       => ( ord_less_eq_int @ X5 @ T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minf(6)
% 0.35/0.58  thf(fact_3249_pinf_I8_J,axiom,
% 0.35/0.58      ! [T: real] :
% 0.35/0.58      ? [Z3: real] :
% 0.35/0.58      ! [X5: real] :
% 0.35/0.58        ( ( ord_less_real @ Z3 @ X5 )
% 0.35/0.58       => ( ord_less_eq_real @ T @ X5 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(8)
% 0.35/0.58  thf(fact_3250_pinf_I8_J,axiom,
% 0.35/0.58      ! [T: rat] :
% 0.35/0.58      ? [Z3: rat] :
% 0.35/0.58      ! [X5: rat] :
% 0.35/0.58        ( ( ord_less_rat @ Z3 @ X5 )
% 0.35/0.58       => ( ord_less_eq_rat @ T @ X5 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(8)
% 0.35/0.58  thf(fact_3251_pinf_I8_J,axiom,
% 0.35/0.58      ! [T: num] :
% 0.35/0.58      ? [Z3: num] :
% 0.35/0.58      ! [X5: num] :
% 0.35/0.58        ( ( ord_less_num @ Z3 @ X5 )
% 0.35/0.58       => ( ord_less_eq_num @ T @ X5 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(8)
% 0.35/0.58  thf(fact_3252_pinf_I8_J,axiom,
% 0.35/0.58      ! [T: nat] :
% 0.35/0.58      ? [Z3: nat] :
% 0.35/0.58      ! [X5: nat] :
% 0.35/0.58        ( ( ord_less_nat @ Z3 @ X5 )
% 0.35/0.58       => ( ord_less_eq_nat @ T @ X5 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(8)
% 0.35/0.58  thf(fact_3253_pinf_I8_J,axiom,
% 0.35/0.58      ! [T: int] :
% 0.35/0.58      ? [Z3: int] :
% 0.35/0.58      ! [X5: int] :
% 0.35/0.58        ( ( ord_less_int @ Z3 @ X5 )
% 0.35/0.58       => ( ord_less_eq_int @ T @ X5 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(8)
% 0.35/0.58  thf(fact_3254_pinf_I6_J,axiom,
% 0.35/0.58      ! [T: real] :
% 0.35/0.58      ? [Z3: real] :
% 0.35/0.58      ! [X5: real] :
% 0.35/0.58        ( ( ord_less_real @ Z3 @ X5 )
% 0.35/0.58       => ~ ( ord_less_eq_real @ X5 @ T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(6)
% 0.35/0.58  thf(fact_3255_pinf_I6_J,axiom,
% 0.35/0.58      ! [T: rat] :
% 0.35/0.58      ? [Z3: rat] :
% 0.35/0.58      ! [X5: rat] :
% 0.35/0.58        ( ( ord_less_rat @ Z3 @ X5 )
% 0.35/0.58       => ~ ( ord_less_eq_rat @ X5 @ T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(6)
% 0.35/0.58  thf(fact_3256_pinf_I6_J,axiom,
% 0.35/0.58      ! [T: num] :
% 0.35/0.58      ? [Z3: num] :
% 0.35/0.58      ! [X5: num] :
% 0.35/0.58        ( ( ord_less_num @ Z3 @ X5 )
% 0.35/0.58       => ~ ( ord_less_eq_num @ X5 @ T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(6)
% 0.35/0.58  thf(fact_3257_pinf_I6_J,axiom,
% 0.35/0.58      ! [T: nat] :
% 0.35/0.58      ? [Z3: nat] :
% 0.35/0.58      ! [X5: nat] :
% 0.35/0.58        ( ( ord_less_nat @ Z3 @ X5 )
% 0.35/0.58       => ~ ( ord_less_eq_nat @ X5 @ T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(6)
% 0.35/0.58  thf(fact_3258_pinf_I6_J,axiom,
% 0.35/0.58      ! [T: int] :
% 0.35/0.58      ? [Z3: int] :
% 0.35/0.58      ! [X5: int] :
% 0.35/0.58        ( ( ord_less_int @ Z3 @ X5 )
% 0.35/0.58       => ~ ( ord_less_eq_int @ X5 @ T ) ) ).
% 0.35/0.58  
% 0.35/0.58  % pinf(6)
% 0.35/0.58  thf(fact_3259_inf__period_I2_J,axiom,
% 0.35/0.58      ! [P: rat > $o,D4: rat,Q: rat > $o] :
% 0.35/0.58        ( ! [X3: rat,K2: rat] :
% 0.35/0.58            ( ( P @ X3 )
% 0.35/0.58            = ( P @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K2 @ D4 ) ) ) )
% 0.35/0.58       => ( ! [X3: rat,K2: rat] :
% 0.35/0.58              ( ( Q @ X3 )
% 0.35/0.58              = ( Q @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K2 @ D4 ) ) ) )
% 0.35/0.58         => ! [X5: rat,K4: rat] :
% 0.35/0.58              ( ( ( P @ X5 )
% 0.35/0.58                | ( Q @ X5 ) )
% 0.35/0.58              = ( ( P @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D4 ) ) )
% 0.35/0.58                | ( Q @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D4 ) ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % inf_period(2)
% 0.35/0.58  thf(fact_3260_inf__period_I2_J,axiom,
% 0.35/0.58      ! [P: complex > $o,D4: complex,Q: complex > $o] :
% 0.35/0.58        ( ! [X3: complex,K2: complex] :
% 0.35/0.58            ( ( P @ X3 )
% 0.35/0.58            = ( P @ ( minus_minus_complex @ X3 @ ( times_times_complex @ K2 @ D4 ) ) ) )
% 0.35/0.58       => ( ! [X3: complex,K2: complex] :
% 0.35/0.58              ( ( Q @ X3 )
% 0.35/0.58              = ( Q @ ( minus_minus_complex @ X3 @ ( times_times_complex @ K2 @ D4 ) ) ) )
% 0.35/0.58         => ! [X5: complex,K4: complex] :
% 0.35/0.58              ( ( ( P @ X5 )
% 0.35/0.58                | ( Q @ X5 ) )
% 0.35/0.58              = ( ( P @ ( minus_minus_complex @ X5 @ ( times_times_complex @ K4 @ D4 ) ) )
% 0.35/0.58                | ( Q @ ( minus_minus_complex @ X5 @ ( times_times_complex @ K4 @ D4 ) ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % inf_period(2)
% 0.35/0.58  thf(fact_3261_inf__period_I2_J,axiom,
% 0.35/0.58      ! [P: real > $o,D4: real,Q: real > $o] :
% 0.35/0.58        ( ! [X3: real,K2: real] :
% 0.35/0.58            ( ( P @ X3 )
% 0.35/0.58            = ( P @ ( minus_minus_real @ X3 @ ( times_times_real @ K2 @ D4 ) ) ) )
% 0.35/0.58       => ( ! [X3: real,K2: real] :
% 0.35/0.58              ( ( Q @ X3 )
% 0.35/0.58              = ( Q @ ( minus_minus_real @ X3 @ ( times_times_real @ K2 @ D4 ) ) ) )
% 0.35/0.58         => ! [X5: real,K4: real] :
% 0.35/0.58              ( ( ( P @ X5 )
% 0.35/0.58                | ( Q @ X5 ) )
% 0.35/0.58              = ( ( P @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D4 ) ) )
% 0.35/0.58                | ( Q @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D4 ) ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % inf_period(2)
% 0.35/0.58  thf(fact_3262_inf__period_I2_J,axiom,
% 0.35/0.58      ! [P: int > $o,D4: int,Q: int > $o] :
% 0.35/0.58        ( ! [X3: int,K2: int] :
% 0.35/0.58            ( ( P @ X3 )
% 0.35/0.58            = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 0.35/0.58       => ( ! [X3: int,K2: int] :
% 0.35/0.58              ( ( Q @ X3 )
% 0.35/0.58              = ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 0.35/0.58         => ! [X5: int,K4: int] :
% 0.35/0.58              ( ( ( P @ X5 )
% 0.35/0.58                | ( Q @ X5 ) )
% 0.35/0.58              = ( ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D4 ) ) )
% 0.35/0.58                | ( Q @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D4 ) ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % inf_period(2)
% 0.35/0.58  thf(fact_3263_inf__period_I1_J,axiom,
% 0.35/0.58      ! [P: rat > $o,D4: rat,Q: rat > $o] :
% 0.35/0.58        ( ! [X3: rat,K2: rat] :
% 0.35/0.58            ( ( P @ X3 )
% 0.35/0.58            = ( P @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K2 @ D4 ) ) ) )
% 0.35/0.58       => ( ! [X3: rat,K2: rat] :
% 0.35/0.58              ( ( Q @ X3 )
% 0.35/0.58              = ( Q @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K2 @ D4 ) ) ) )
% 0.35/0.58         => ! [X5: rat,K4: rat] :
% 0.35/0.58              ( ( ( P @ X5 )
% 0.35/0.58                & ( Q @ X5 ) )
% 0.35/0.58              = ( ( P @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D4 ) ) )
% 0.35/0.58                & ( Q @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D4 ) ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % inf_period(1)
% 0.35/0.58  thf(fact_3264_inf__period_I1_J,axiom,
% 0.35/0.58      ! [P: complex > $o,D4: complex,Q: complex > $o] :
% 0.35/0.58        ( ! [X3: complex,K2: complex] :
% 0.35/0.58            ( ( P @ X3 )
% 0.35/0.58            = ( P @ ( minus_minus_complex @ X3 @ ( times_times_complex @ K2 @ D4 ) ) ) )
% 0.35/0.58       => ( ! [X3: complex,K2: complex] :
% 0.35/0.58              ( ( Q @ X3 )
% 0.35/0.58              = ( Q @ ( minus_minus_complex @ X3 @ ( times_times_complex @ K2 @ D4 ) ) ) )
% 0.35/0.58         => ! [X5: complex,K4: complex] :
% 0.35/0.58              ( ( ( P @ X5 )
% 0.35/0.58                & ( Q @ X5 ) )
% 0.35/0.58              = ( ( P @ ( minus_minus_complex @ X5 @ ( times_times_complex @ K4 @ D4 ) ) )
% 0.35/0.58                & ( Q @ ( minus_minus_complex @ X5 @ ( times_times_complex @ K4 @ D4 ) ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % inf_period(1)
% 0.35/0.58  thf(fact_3265_inf__period_I1_J,axiom,
% 0.35/0.58      ! [P: real > $o,D4: real,Q: real > $o] :
% 0.35/0.58        ( ! [X3: real,K2: real] :
% 0.35/0.58            ( ( P @ X3 )
% 0.35/0.58            = ( P @ ( minus_minus_real @ X3 @ ( times_times_real @ K2 @ D4 ) ) ) )
% 0.35/0.58       => ( ! [X3: real,K2: real] :
% 0.35/0.58              ( ( Q @ X3 )
% 0.35/0.58              = ( Q @ ( minus_minus_real @ X3 @ ( times_times_real @ K2 @ D4 ) ) ) )
% 0.35/0.58         => ! [X5: real,K4: real] :
% 0.35/0.58              ( ( ( P @ X5 )
% 0.35/0.58                & ( Q @ X5 ) )
% 0.35/0.58              = ( ( P @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D4 ) ) )
% 0.35/0.58                & ( Q @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D4 ) ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % inf_period(1)
% 0.35/0.58  thf(fact_3266_inf__period_I1_J,axiom,
% 0.35/0.58      ! [P: int > $o,D4: int,Q: int > $o] :
% 0.35/0.58        ( ! [X3: int,K2: int] :
% 0.35/0.58            ( ( P @ X3 )
% 0.35/0.58            = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 0.35/0.58       => ( ! [X3: int,K2: int] :
% 0.35/0.58              ( ( Q @ X3 )
% 0.35/0.58              = ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 0.35/0.58         => ! [X5: int,K4: int] :
% 0.35/0.58              ( ( ( P @ X5 )
% 0.35/0.58                & ( Q @ X5 ) )
% 0.35/0.58              = ( ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D4 ) ) )
% 0.35/0.58                & ( Q @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D4 ) ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % inf_period(1)
% 0.35/0.58  thf(fact_3267_atLeastatMost__psubset__iff,axiom,
% 0.35/0.58      ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.35/0.58        ( ( ord_less_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D2 ) )
% 0.35/0.58        = ( ( ~ ( ord_less_eq_rat @ A @ B )
% 0.35/0.58            | ( ( ord_less_eq_rat @ C @ A )
% 0.35/0.58              & ( ord_less_eq_rat @ B @ D2 )
% 0.35/0.58              & ( ( ord_less_rat @ C @ A )
% 0.35/0.58                | ( ord_less_rat @ B @ D2 ) ) ) )
% 0.35/0.58          & ( ord_less_eq_rat @ C @ D2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastatMost_psubset_iff
% 0.35/0.58  thf(fact_3268_atLeastatMost__psubset__iff,axiom,
% 0.35/0.58      ! [A: set_real,B: set_real,C: set_real,D2: set_real] :
% 0.35/0.58        ( ( ord_le7926960851185191020t_real @ ( set_or7743017856606604397t_real @ A @ B ) @ ( set_or7743017856606604397t_real @ C @ D2 ) )
% 0.35/0.58        = ( ( ~ ( ord_less_eq_set_real @ A @ B )
% 0.35/0.58            | ( ( ord_less_eq_set_real @ C @ A )
% 0.35/0.58              & ( ord_less_eq_set_real @ B @ D2 )
% 0.35/0.58              & ( ( ord_less_set_real @ C @ A )
% 0.35/0.58                | ( ord_less_set_real @ B @ D2 ) ) ) )
% 0.35/0.58          & ( ord_less_eq_set_real @ C @ D2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastatMost_psubset_iff
% 0.35/0.58  thf(fact_3269_atLeastatMost__psubset__iff,axiom,
% 0.35/0.58      ! [A: set_nat,B: set_nat,C: set_nat,D2: set_nat] :
% 0.35/0.58        ( ( ord_less_set_set_nat @ ( set_or4548717258645045905et_nat @ A @ B ) @ ( set_or4548717258645045905et_nat @ C @ D2 ) )
% 0.35/0.58        = ( ( ~ ( ord_less_eq_set_nat @ A @ B )
% 0.35/0.58            | ( ( ord_less_eq_set_nat @ C @ A )
% 0.35/0.58              & ( ord_less_eq_set_nat @ B @ D2 )
% 0.35/0.58              & ( ( ord_less_set_nat @ C @ A )
% 0.35/0.58                | ( ord_less_set_nat @ B @ D2 ) ) ) )
% 0.35/0.58          & ( ord_less_eq_set_nat @ C @ D2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastatMost_psubset_iff
% 0.35/0.58  thf(fact_3270_atLeastatMost__psubset__iff,axiom,
% 0.35/0.58      ! [A: num,B: num,C: num,D2: num] :
% 0.35/0.58        ( ( ord_less_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D2 ) )
% 0.35/0.58        = ( ( ~ ( ord_less_eq_num @ A @ B )
% 0.35/0.58            | ( ( ord_less_eq_num @ C @ A )
% 0.35/0.58              & ( ord_less_eq_num @ B @ D2 )
% 0.35/0.58              & ( ( ord_less_num @ C @ A )
% 0.35/0.58                | ( ord_less_num @ B @ D2 ) ) ) )
% 0.35/0.58          & ( ord_less_eq_num @ C @ D2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastatMost_psubset_iff
% 0.35/0.58  thf(fact_3271_atLeastatMost__psubset__iff,axiom,
% 0.35/0.58      ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.35/0.58        ( ( ord_less_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D2 ) )
% 0.35/0.58        = ( ( ~ ( ord_less_eq_nat @ A @ B )
% 0.35/0.58            | ( ( ord_less_eq_nat @ C @ A )
% 0.35/0.58              & ( ord_less_eq_nat @ B @ D2 )
% 0.35/0.58              & ( ( ord_less_nat @ C @ A )
% 0.35/0.58                | ( ord_less_nat @ B @ D2 ) ) ) )
% 0.35/0.58          & ( ord_less_eq_nat @ C @ D2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastatMost_psubset_iff
% 0.35/0.58  thf(fact_3272_atLeastatMost__psubset__iff,axiom,
% 0.35/0.58      ! [A: int,B: int,C: int,D2: int] :
% 0.35/0.58        ( ( ord_less_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D2 ) )
% 0.35/0.58        = ( ( ~ ( ord_less_eq_int @ A @ B )
% 0.35/0.58            | ( ( ord_less_eq_int @ C @ A )
% 0.35/0.58              & ( ord_less_eq_int @ B @ D2 )
% 0.35/0.58              & ( ( ord_less_int @ C @ A )
% 0.35/0.58                | ( ord_less_int @ B @ D2 ) ) ) )
% 0.35/0.58          & ( ord_less_eq_int @ C @ D2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastatMost_psubset_iff
% 0.35/0.58  thf(fact_3273_atLeastatMost__psubset__iff,axiom,
% 0.35/0.58      ! [A: real,B: real,C: real,D2: real] :
% 0.35/0.58        ( ( ord_less_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D2 ) )
% 0.35/0.58        = ( ( ~ ( ord_less_eq_real @ A @ B )
% 0.35/0.58            | ( ( ord_less_eq_real @ C @ A )
% 0.35/0.58              & ( ord_less_eq_real @ B @ D2 )
% 0.35/0.58              & ( ( ord_less_real @ C @ A )
% 0.35/0.58                | ( ord_less_real @ B @ D2 ) ) ) )
% 0.35/0.58          & ( ord_less_eq_real @ C @ D2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastatMost_psubset_iff
% 0.35/0.58  thf(fact_3274_plusinfinity,axiom,
% 0.35/0.58      ! [D2: int,P5: int > $o,P: int > $o] :
% 0.35/0.58        ( ( ord_less_int @ zero_zero_int @ D2 )
% 0.35/0.58       => ( ! [X3: int,K2: int] :
% 0.35/0.58              ( ( P5 @ X3 )
% 0.35/0.58              = ( P5 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D2 ) ) ) )
% 0.35/0.58         => ( ? [Z2: int] :
% 0.35/0.58              ! [X3: int] :
% 0.35/0.58                ( ( ord_less_int @ Z2 @ X3 )
% 0.35/0.58               => ( ( P @ X3 )
% 0.35/0.58                  = ( P5 @ X3 ) ) )
% 0.35/0.58           => ( ? [X_1: int] : ( P5 @ X_1 )
% 0.35/0.58             => ? [X_12: int] : ( P @ X_12 ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % plusinfinity
% 0.35/0.58  thf(fact_3275_minusinfinity,axiom,
% 0.35/0.58      ! [D2: int,P1: int > $o,P: int > $o] :
% 0.35/0.58        ( ( ord_less_int @ zero_zero_int @ D2 )
% 0.35/0.58       => ( ! [X3: int,K2: int] :
% 0.35/0.58              ( ( P1 @ X3 )
% 0.35/0.58              = ( P1 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D2 ) ) ) )
% 0.35/0.58         => ( ? [Z2: int] :
% 0.35/0.58              ! [X3: int] :
% 0.35/0.58                ( ( ord_less_int @ X3 @ Z2 )
% 0.35/0.58               => ( ( P @ X3 )
% 0.35/0.58                  = ( P1 @ X3 ) ) )
% 0.35/0.58           => ( ? [X_1: int] : ( P1 @ X_1 )
% 0.35/0.58             => ? [X_12: int] : ( P @ X_12 ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minusinfinity
% 0.35/0.58  thf(fact_3276_Diff__eq__empty__iff,axiom,
% 0.35/0.58      ! [A2: set_int,B2: set_int] :
% 0.35/0.58        ( ( ( minus_minus_set_int @ A2 @ B2 )
% 0.35/0.58          = bot_bot_set_int )
% 0.35/0.58        = ( ord_less_eq_set_int @ A2 @ B2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_eq_empty_iff
% 0.35/0.58  thf(fact_3277_Diff__eq__empty__iff,axiom,
% 0.35/0.58      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.35/0.58        ( ( ( minus_1356011639430497352at_nat @ A2 @ B2 )
% 0.35/0.58          = bot_bo2099793752762293965at_nat )
% 0.35/0.58        = ( ord_le3146513528884898305at_nat @ A2 @ B2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_eq_empty_iff
% 0.35/0.58  thf(fact_3278_Diff__eq__empty__iff,axiom,
% 0.35/0.58      ! [A2: set_real,B2: set_real] :
% 0.35/0.58        ( ( ( minus_minus_set_real @ A2 @ B2 )
% 0.35/0.58          = bot_bot_set_real )
% 0.35/0.58        = ( ord_less_eq_set_real @ A2 @ B2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_eq_empty_iff
% 0.35/0.58  thf(fact_3279_Diff__eq__empty__iff,axiom,
% 0.35/0.58      ! [A2: set_nat,B2: set_nat] :
% 0.35/0.58        ( ( ( minus_minus_set_nat @ A2 @ B2 )
% 0.35/0.58          = bot_bot_set_nat )
% 0.35/0.58        = ( ord_less_eq_set_nat @ A2 @ B2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_eq_empty_iff
% 0.35/0.58  thf(fact_3280_delete__correct,axiom,
% 0.35/0.58      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.35/0.58        ( ( vEBT_invar_vebt @ T @ N )
% 0.35/0.58       => ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_delete @ T @ X ) )
% 0.35/0.58          = ( minus_minus_set_nat @ ( vEBT_set_vebt @ T ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % delete_correct
% 0.35/0.58  thf(fact_3281_unset__bit__0,axiom,
% 0.35/0.58      ! [A: int] :
% 0.35/0.58        ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A )
% 0.35/0.58        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % unset_bit_0
% 0.35/0.58  thf(fact_3282_unset__bit__0,axiom,
% 0.35/0.58      ! [A: nat] :
% 0.35/0.58        ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A )
% 0.35/0.58        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % unset_bit_0
% 0.35/0.58  thf(fact_3283_Bolzano,axiom,
% 0.35/0.58      ! [A: real,B: real,P: real > real > $o] :
% 0.35/0.58        ( ( ord_less_eq_real @ A @ B )
% 0.35/0.58       => ( ! [A4: real,B3: real,C2: real] :
% 0.35/0.58              ( ( P @ A4 @ B3 )
% 0.35/0.58             => ( ( P @ B3 @ C2 )
% 0.35/0.58               => ( ( ord_less_eq_real @ A4 @ B3 )
% 0.35/0.58                 => ( ( ord_less_eq_real @ B3 @ C2 )
% 0.35/0.58                   => ( P @ A4 @ C2 ) ) ) ) )
% 0.35/0.58         => ( ! [X3: real] :
% 0.35/0.58                ( ( ord_less_eq_real @ A @ X3 )
% 0.35/0.58               => ( ( ord_less_eq_real @ X3 @ B )
% 0.35/0.58                 => ? [D5: real] :
% 0.35/0.58                      ( ( ord_less_real @ zero_zero_real @ D5 )
% 0.35/0.58                      & ! [A4: real,B3: real] :
% 0.35/0.58                          ( ( ( ord_less_eq_real @ A4 @ X3 )
% 0.35/0.58                            & ( ord_less_eq_real @ X3 @ B3 )
% 0.35/0.58                            & ( ord_less_real @ ( minus_minus_real @ B3 @ A4 ) @ D5 ) )
% 0.35/0.58                         => ( P @ A4 @ B3 ) ) ) ) )
% 0.35/0.58           => ( P @ A @ B ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Bolzano
% 0.35/0.58  thf(fact_3284_mult__le__cancel__iff1,axiom,
% 0.35/0.58      ! [Z: real,X: real,Y2: real] :
% 0.35/0.58        ( ( ord_less_real @ zero_zero_real @ Z )
% 0.35/0.58       => ( ( ord_less_eq_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y2 @ Z ) )
% 0.35/0.58          = ( ord_less_eq_real @ X @ Y2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % mult_le_cancel_iff1
% 0.35/0.58  thf(fact_3285_mult__le__cancel__iff1,axiom,
% 0.35/0.58      ! [Z: rat,X: rat,Y2: rat] :
% 0.35/0.58        ( ( ord_less_rat @ zero_zero_rat @ Z )
% 0.35/0.58       => ( ( ord_less_eq_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y2 @ Z ) )
% 0.35/0.58          = ( ord_less_eq_rat @ X @ Y2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % mult_le_cancel_iff1
% 0.35/0.58  thf(fact_3286_mult__le__cancel__iff1,axiom,
% 0.35/0.58      ! [Z: int,X: int,Y2: int] :
% 0.35/0.58        ( ( ord_less_int @ zero_zero_int @ Z )
% 0.35/0.58       => ( ( ord_less_eq_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y2 @ Z ) )
% 0.35/0.58          = ( ord_less_eq_int @ X @ Y2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % mult_le_cancel_iff1
% 0.35/0.58  thf(fact_3287_mult__le__cancel__iff2,axiom,
% 0.35/0.58      ! [Z: real,X: real,Y2: real] :
% 0.35/0.58        ( ( ord_less_real @ zero_zero_real @ Z )
% 0.35/0.58       => ( ( ord_less_eq_real @ ( times_times_real @ Z @ X ) @ ( times_times_real @ Z @ Y2 ) )
% 0.35/0.58          = ( ord_less_eq_real @ X @ Y2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % mult_le_cancel_iff2
% 0.35/0.58  thf(fact_3288_mult__le__cancel__iff2,axiom,
% 0.35/0.58      ! [Z: rat,X: rat,Y2: rat] :
% 0.35/0.58        ( ( ord_less_rat @ zero_zero_rat @ Z )
% 0.35/0.58       => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ X ) @ ( times_times_rat @ Z @ Y2 ) )
% 0.35/0.58          = ( ord_less_eq_rat @ X @ Y2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % mult_le_cancel_iff2
% 0.35/0.58  thf(fact_3289_mult__le__cancel__iff2,axiom,
% 0.35/0.58      ! [Z: int,X: int,Y2: int] :
% 0.35/0.58        ( ( ord_less_int @ zero_zero_int @ Z )
% 0.35/0.58       => ( ( ord_less_eq_int @ ( times_times_int @ Z @ X ) @ ( times_times_int @ Z @ Y2 ) )
% 0.35/0.58          = ( ord_less_eq_int @ X @ Y2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % mult_le_cancel_iff2
% 0.35/0.58  thf(fact_3290_DiffI,axiom,
% 0.35/0.58      ! [C: complex,A2: set_complex,B2: set_complex] :
% 0.35/0.58        ( ( member_complex @ C @ A2 )
% 0.35/0.58       => ( ~ ( member_complex @ C @ B2 )
% 0.35/0.58         => ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % DiffI
% 0.35/0.58  thf(fact_3291_DiffI,axiom,
% 0.35/0.58      ! [C: real,A2: set_real,B2: set_real] :
% 0.35/0.58        ( ( member_real @ C @ A2 )
% 0.35/0.58       => ( ~ ( member_real @ C @ B2 )
% 0.35/0.58         => ( member_real @ C @ ( minus_minus_set_real @ A2 @ B2 ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % DiffI
% 0.35/0.58  thf(fact_3292_DiffI,axiom,
% 0.35/0.58      ! [C: int,A2: set_int,B2: set_int] :
% 0.35/0.58        ( ( member_int @ C @ A2 )
% 0.35/0.58       => ( ~ ( member_int @ C @ B2 )
% 0.35/0.58         => ( member_int @ C @ ( minus_minus_set_int @ A2 @ B2 ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % DiffI
% 0.35/0.58  thf(fact_3293_DiffI,axiom,
% 0.35/0.58      ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.35/0.58        ( ( member8440522571783428010at_nat @ C @ A2 )
% 0.35/0.58       => ( ~ ( member8440522571783428010at_nat @ C @ B2 )
% 0.35/0.58         => ( member8440522571783428010at_nat @ C @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % DiffI
% 0.35/0.58  thf(fact_3294_DiffI,axiom,
% 0.35/0.58      ! [C: nat,A2: set_nat,B2: set_nat] :
% 0.35/0.58        ( ( member_nat @ C @ A2 )
% 0.35/0.58       => ( ~ ( member_nat @ C @ B2 )
% 0.35/0.58         => ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % DiffI
% 0.35/0.58  thf(fact_3295_Diff__iff,axiom,
% 0.35/0.58      ! [C: complex,A2: set_complex,B2: set_complex] :
% 0.35/0.58        ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B2 ) )
% 0.35/0.58        = ( ( member_complex @ C @ A2 )
% 0.35/0.58          & ~ ( member_complex @ C @ B2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_iff
% 0.35/0.58  thf(fact_3296_Diff__iff,axiom,
% 0.35/0.58      ! [C: real,A2: set_real,B2: set_real] :
% 0.35/0.58        ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B2 ) )
% 0.35/0.58        = ( ( member_real @ C @ A2 )
% 0.35/0.58          & ~ ( member_real @ C @ B2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_iff
% 0.35/0.58  thf(fact_3297_Diff__iff,axiom,
% 0.35/0.58      ! [C: int,A2: set_int,B2: set_int] :
% 0.35/0.58        ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B2 ) )
% 0.35/0.58        = ( ( member_int @ C @ A2 )
% 0.35/0.58          & ~ ( member_int @ C @ B2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_iff
% 0.35/0.58  thf(fact_3298_Diff__iff,axiom,
% 0.35/0.58      ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.35/0.58        ( ( member8440522571783428010at_nat @ C @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) )
% 0.35/0.58        = ( ( member8440522571783428010at_nat @ C @ A2 )
% 0.35/0.58          & ~ ( member8440522571783428010at_nat @ C @ B2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_iff
% 0.35/0.58  thf(fact_3299_Diff__iff,axiom,
% 0.35/0.58      ! [C: nat,A2: set_nat,B2: set_nat] :
% 0.35/0.58        ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 0.35/0.58        = ( ( member_nat @ C @ A2 )
% 0.35/0.58          & ~ ( member_nat @ C @ B2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_iff
% 0.35/0.58  thf(fact_3300_Diff__idemp,axiom,
% 0.35/0.58      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.35/0.58        ( ( minus_1356011639430497352at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) @ B2 )
% 0.35/0.58        = ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_idemp
% 0.35/0.58  thf(fact_3301_Diff__idemp,axiom,
% 0.35/0.58      ! [A2: set_nat,B2: set_nat] :
% 0.35/0.58        ( ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ B2 )
% 0.35/0.58        = ( minus_minus_set_nat @ A2 @ B2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_idemp
% 0.35/0.58  thf(fact_3302_delete__correct_H,axiom,
% 0.35/0.58      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.35/0.58        ( ( vEBT_invar_vebt @ T @ N )
% 0.35/0.58       => ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_delete @ T @ X ) )
% 0.35/0.58          = ( minus_minus_set_nat @ ( vEBT_VEBT_set_vebt @ T ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % delete_correct'
% 0.35/0.58  thf(fact_3303_Diff__cancel,axiom,
% 0.35/0.58      ! [A2: set_int] :
% 0.35/0.58        ( ( minus_minus_set_int @ A2 @ A2 )
% 0.35/0.58        = bot_bot_set_int ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_cancel
% 0.35/0.58  thf(fact_3304_Diff__cancel,axiom,
% 0.35/0.58      ! [A2: set_real] :
% 0.35/0.58        ( ( minus_minus_set_real @ A2 @ A2 )
% 0.35/0.58        = bot_bot_set_real ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_cancel
% 0.35/0.58  thf(fact_3305_Diff__cancel,axiom,
% 0.35/0.58      ! [A2: set_Pr1261947904930325089at_nat] :
% 0.35/0.58        ( ( minus_1356011639430497352at_nat @ A2 @ A2 )
% 0.35/0.58        = bot_bo2099793752762293965at_nat ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_cancel
% 0.35/0.58  thf(fact_3306_Diff__cancel,axiom,
% 0.35/0.58      ! [A2: set_nat] :
% 0.35/0.58        ( ( minus_minus_set_nat @ A2 @ A2 )
% 0.35/0.58        = bot_bot_set_nat ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_cancel
% 0.35/0.58  thf(fact_3307_empty__Diff,axiom,
% 0.35/0.58      ! [A2: set_int] :
% 0.35/0.58        ( ( minus_minus_set_int @ bot_bot_set_int @ A2 )
% 0.35/0.58        = bot_bot_set_int ) ).
% 0.35/0.58  
% 0.35/0.58  % empty_Diff
% 0.35/0.58  thf(fact_3308_empty__Diff,axiom,
% 0.35/0.58      ! [A2: set_real] :
% 0.35/0.58        ( ( minus_minus_set_real @ bot_bot_set_real @ A2 )
% 0.35/0.58        = bot_bot_set_real ) ).
% 0.35/0.58  
% 0.35/0.58  % empty_Diff
% 0.35/0.58  thf(fact_3309_empty__Diff,axiom,
% 0.35/0.58      ! [A2: set_Pr1261947904930325089at_nat] :
% 0.35/0.58        ( ( minus_1356011639430497352at_nat @ bot_bo2099793752762293965at_nat @ A2 )
% 0.35/0.58        = bot_bo2099793752762293965at_nat ) ).
% 0.35/0.58  
% 0.35/0.58  % empty_Diff
% 0.35/0.58  thf(fact_3310_empty__Diff,axiom,
% 0.35/0.58      ! [A2: set_nat] :
% 0.35/0.58        ( ( minus_minus_set_nat @ bot_bot_set_nat @ A2 )
% 0.35/0.58        = bot_bot_set_nat ) ).
% 0.35/0.58  
% 0.35/0.58  % empty_Diff
% 0.35/0.58  thf(fact_3311_Diff__empty,axiom,
% 0.35/0.58      ! [A2: set_int] :
% 0.35/0.58        ( ( minus_minus_set_int @ A2 @ bot_bot_set_int )
% 0.35/0.58        = A2 ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_empty
% 0.35/0.58  thf(fact_3312_Diff__empty,axiom,
% 0.35/0.58      ! [A2: set_real] :
% 0.35/0.58        ( ( minus_minus_set_real @ A2 @ bot_bot_set_real )
% 0.35/0.58        = A2 ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_empty
% 0.35/0.58  thf(fact_3313_Diff__empty,axiom,
% 0.35/0.58      ! [A2: set_Pr1261947904930325089at_nat] :
% 0.35/0.58        ( ( minus_1356011639430497352at_nat @ A2 @ bot_bo2099793752762293965at_nat )
% 0.35/0.58        = A2 ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_empty
% 0.35/0.58  thf(fact_3314_Diff__empty,axiom,
% 0.35/0.58      ! [A2: set_nat] :
% 0.35/0.58        ( ( minus_minus_set_nat @ A2 @ bot_bot_set_nat )
% 0.35/0.58        = A2 ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_empty
% 0.35/0.58  thf(fact_3315_Diff__insert0,axiom,
% 0.35/0.58      ! [X: vEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT] :
% 0.35/0.58        ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 0.35/0.58       => ( ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ B2 ) )
% 0.35/0.58          = ( minus_5127226145743854075T_VEBT @ A2 @ B2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_insert0
% 0.35/0.58  thf(fact_3316_Diff__insert0,axiom,
% 0.35/0.58      ! [X: complex,A2: set_complex,B2: set_complex] :
% 0.35/0.58        ( ~ ( member_complex @ X @ A2 )
% 0.35/0.58       => ( ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ B2 ) )
% 0.35/0.58          = ( minus_811609699411566653omplex @ A2 @ B2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_insert0
% 0.35/0.58  thf(fact_3317_Diff__insert0,axiom,
% 0.35/0.58      ! [X: real,A2: set_real,B2: set_real] :
% 0.35/0.58        ( ~ ( member_real @ X @ A2 )
% 0.35/0.58       => ( ( minus_minus_set_real @ A2 @ ( insert_real @ X @ B2 ) )
% 0.35/0.58          = ( minus_minus_set_real @ A2 @ B2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_insert0
% 0.35/0.58  thf(fact_3318_Diff__insert0,axiom,
% 0.35/0.58      ! [X: int,A2: set_int,B2: set_int] :
% 0.35/0.58        ( ~ ( member_int @ X @ A2 )
% 0.35/0.58       => ( ( minus_minus_set_int @ A2 @ ( insert_int @ X @ B2 ) )
% 0.35/0.58          = ( minus_minus_set_int @ A2 @ B2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_insert0
% 0.35/0.58  thf(fact_3319_Diff__insert0,axiom,
% 0.35/0.58      ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.35/0.58        ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 0.35/0.58       => ( ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ B2 ) )
% 0.35/0.58          = ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_insert0
% 0.35/0.58  thf(fact_3320_Diff__insert0,axiom,
% 0.35/0.58      ! [X: nat,A2: set_nat,B2: set_nat] :
% 0.35/0.58        ( ~ ( member_nat @ X @ A2 )
% 0.35/0.58       => ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ B2 ) )
% 0.35/0.58          = ( minus_minus_set_nat @ A2 @ B2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_insert0
% 0.35/0.58  thf(fact_3321_insert__Diff1,axiom,
% 0.35/0.58      ! [X: vEBT_VEBT,B2: set_VEBT_VEBT,A2: set_VEBT_VEBT] :
% 0.35/0.58        ( ( member_VEBT_VEBT @ X @ B2 )
% 0.35/0.58       => ( ( minus_5127226145743854075T_VEBT @ ( insert_VEBT_VEBT @ X @ A2 ) @ B2 )
% 0.35/0.58          = ( minus_5127226145743854075T_VEBT @ A2 @ B2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % insert_Diff1
% 0.35/0.58  thf(fact_3322_insert__Diff1,axiom,
% 0.35/0.58      ! [X: complex,B2: set_complex,A2: set_complex] :
% 0.35/0.58        ( ( member_complex @ X @ B2 )
% 0.35/0.58       => ( ( minus_811609699411566653omplex @ ( insert_complex @ X @ A2 ) @ B2 )
% 0.35/0.58          = ( minus_811609699411566653omplex @ A2 @ B2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % insert_Diff1
% 0.35/0.58  thf(fact_3323_insert__Diff1,axiom,
% 0.35/0.58      ! [X: real,B2: set_real,A2: set_real] :
% 0.35/0.58        ( ( member_real @ X @ B2 )
% 0.35/0.58       => ( ( minus_minus_set_real @ ( insert_real @ X @ A2 ) @ B2 )
% 0.35/0.58          = ( minus_minus_set_real @ A2 @ B2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % insert_Diff1
% 0.35/0.58  thf(fact_3324_insert__Diff1,axiom,
% 0.35/0.58      ! [X: int,B2: set_int,A2: set_int] :
% 0.35/0.58        ( ( member_int @ X @ B2 )
% 0.35/0.58       => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ B2 )
% 0.35/0.58          = ( minus_minus_set_int @ A2 @ B2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % insert_Diff1
% 0.35/0.58  thf(fact_3325_insert__Diff1,axiom,
% 0.35/0.58      ! [X: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 0.35/0.58        ( ( member8440522571783428010at_nat @ X @ B2 )
% 0.35/0.58       => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X @ A2 ) @ B2 )
% 0.35/0.58          = ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % insert_Diff1
% 0.35/0.58  thf(fact_3326_insert__Diff1,axiom,
% 0.35/0.58      ! [X: nat,B2: set_nat,A2: set_nat] :
% 0.35/0.58        ( ( member_nat @ X @ B2 )
% 0.35/0.58       => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ B2 )
% 0.35/0.58          = ( minus_minus_set_nat @ A2 @ B2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % insert_Diff1
% 0.35/0.58  thf(fact_3327_unset__bit__nonnegative__int__iff,axiom,
% 0.35/0.58      ! [N: nat,K: int] :
% 0.35/0.58        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se4203085406695923979it_int @ N @ K ) )
% 0.35/0.58        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.35/0.58  
% 0.35/0.58  % unset_bit_nonnegative_int_iff
% 0.35/0.58  thf(fact_3328_unset__bit__negative__int__iff,axiom,
% 0.35/0.58      ! [N: nat,K: int] :
% 0.35/0.58        ( ( ord_less_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ zero_zero_int )
% 0.35/0.58        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.35/0.58  
% 0.35/0.58  % unset_bit_negative_int_iff
% 0.35/0.58  thf(fact_3329_insert__Diff__single,axiom,
% 0.35/0.58      ! [A: vEBT_VEBT,A2: set_VEBT_VEBT] :
% 0.35/0.58        ( ( insert_VEBT_VEBT @ A @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.35/0.58        = ( insert_VEBT_VEBT @ A @ A2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % insert_Diff_single
% 0.35/0.58  thf(fact_3330_insert__Diff__single,axiom,
% 0.35/0.58      ! [A: int,A2: set_int] :
% 0.35/0.58        ( ( insert_int @ A @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.35/0.58        = ( insert_int @ A @ A2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % insert_Diff_single
% 0.35/0.58  thf(fact_3331_insert__Diff__single,axiom,
% 0.35/0.58      ! [A: real,A2: set_real] :
% 0.35/0.58        ( ( insert_real @ A @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.35/0.58        = ( insert_real @ A @ A2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % insert_Diff_single
% 0.35/0.58  thf(fact_3332_insert__Diff__single,axiom,
% 0.35/0.58      ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 0.35/0.58        ( ( insert8211810215607154385at_nat @ A @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 0.35/0.58        = ( insert8211810215607154385at_nat @ A @ A2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % insert_Diff_single
% 0.35/0.58  thf(fact_3333_insert__Diff__single,axiom,
% 0.35/0.58      ! [A: nat,A2: set_nat] :
% 0.35/0.58        ( ( insert_nat @ A @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.35/0.58        = ( insert_nat @ A @ A2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % insert_Diff_single
% 0.35/0.58  thf(fact_3334_Diff__insert,axiom,
% 0.35/0.58      ! [A2: set_VEBT_VEBT,A: vEBT_VEBT,B2: set_VEBT_VEBT] :
% 0.35/0.58        ( ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ B2 ) )
% 0.35/0.58        = ( minus_5127226145743854075T_VEBT @ ( minus_5127226145743854075T_VEBT @ A2 @ B2 ) @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_insert
% 0.35/0.58  thf(fact_3335_Diff__insert,axiom,
% 0.35/0.58      ! [A2: set_int,A: int,B2: set_int] :
% 0.35/0.58        ( ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B2 ) )
% 0.35/0.58        = ( minus_minus_set_int @ ( minus_minus_set_int @ A2 @ B2 ) @ ( insert_int @ A @ bot_bot_set_int ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_insert
% 0.35/0.58  thf(fact_3336_Diff__insert,axiom,
% 0.35/0.58      ! [A2: set_real,A: real,B2: set_real] :
% 0.35/0.58        ( ( minus_minus_set_real @ A2 @ ( insert_real @ A @ B2 ) )
% 0.35/0.58        = ( minus_minus_set_real @ ( minus_minus_set_real @ A2 @ B2 ) @ ( insert_real @ A @ bot_bot_set_real ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_insert
% 0.35/0.58  thf(fact_3337_Diff__insert,axiom,
% 0.35/0.58      ! [A2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.35/0.58        ( ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ B2 ) )
% 0.35/0.58        = ( minus_1356011639430497352at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_insert
% 0.35/0.58  thf(fact_3338_Diff__insert,axiom,
% 0.35/0.58      ! [A2: set_nat,A: nat,B2: set_nat] :
% 0.35/0.58        ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B2 ) )
% 0.35/0.58        = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_insert
% 0.35/0.58  thf(fact_3339_insert__Diff,axiom,
% 0.35/0.58      ! [A: vEBT_VEBT,A2: set_VEBT_VEBT] :
% 0.35/0.58        ( ( member_VEBT_VEBT @ A @ A2 )
% 0.35/0.58       => ( ( insert_VEBT_VEBT @ A @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.35/0.58          = A2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % insert_Diff
% 0.35/0.58  thf(fact_3340_insert__Diff,axiom,
% 0.35/0.58      ! [A: complex,A2: set_complex] :
% 0.35/0.58        ( ( member_complex @ A @ A2 )
% 0.35/0.58       => ( ( insert_complex @ A @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.35/0.58          = A2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % insert_Diff
% 0.35/0.58  thf(fact_3341_insert__Diff,axiom,
% 0.35/0.58      ! [A: int,A2: set_int] :
% 0.35/0.58        ( ( member_int @ A @ A2 )
% 0.35/0.58       => ( ( insert_int @ A @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.35/0.58          = A2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % insert_Diff
% 0.35/0.58  thf(fact_3342_insert__Diff,axiom,
% 0.35/0.58      ! [A: real,A2: set_real] :
% 0.35/0.58        ( ( member_real @ A @ A2 )
% 0.35/0.58       => ( ( insert_real @ A @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.35/0.58          = A2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % insert_Diff
% 0.35/0.58  thf(fact_3343_insert__Diff,axiom,
% 0.35/0.58      ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 0.35/0.58        ( ( member8440522571783428010at_nat @ A @ A2 )
% 0.35/0.58       => ( ( insert8211810215607154385at_nat @ A @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 0.35/0.58          = A2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % insert_Diff
% 0.35/0.58  thf(fact_3344_insert__Diff,axiom,
% 0.35/0.58      ! [A: nat,A2: set_nat] :
% 0.35/0.58        ( ( member_nat @ A @ A2 )
% 0.35/0.58       => ( ( insert_nat @ A @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.35/0.58          = A2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % insert_Diff
% 0.35/0.58  thf(fact_3345_Diff__insert2,axiom,
% 0.35/0.58      ! [A2: set_VEBT_VEBT,A: vEBT_VEBT,B2: set_VEBT_VEBT] :
% 0.35/0.58        ( ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ B2 ) )
% 0.35/0.58        = ( minus_5127226145743854075T_VEBT @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) @ B2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_insert2
% 0.35/0.58  thf(fact_3346_Diff__insert2,axiom,
% 0.35/0.58      ! [A2: set_int,A: int,B2: set_int] :
% 0.35/0.58        ( ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B2 ) )
% 0.35/0.58        = ( minus_minus_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) @ B2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_insert2
% 0.35/0.58  thf(fact_3347_Diff__insert2,axiom,
% 0.35/0.58      ! [A2: set_real,A: real,B2: set_real] :
% 0.35/0.58        ( ( minus_minus_set_real @ A2 @ ( insert_real @ A @ B2 ) )
% 0.35/0.58        = ( minus_minus_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) @ B2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_insert2
% 0.35/0.58  thf(fact_3348_Diff__insert2,axiom,
% 0.35/0.58      ! [A2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.35/0.58        ( ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ B2 ) )
% 0.35/0.58        = ( minus_1356011639430497352at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) @ B2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_insert2
% 0.35/0.58  thf(fact_3349_Diff__insert2,axiom,
% 0.35/0.58      ! [A2: set_nat,A: nat,B2: set_nat] :
% 0.35/0.58        ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B2 ) )
% 0.35/0.58        = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) @ B2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_insert2
% 0.35/0.58  thf(fact_3350_Diff__insert__absorb,axiom,
% 0.35/0.58      ! [X: vEBT_VEBT,A2: set_VEBT_VEBT] :
% 0.35/0.58        ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 0.35/0.58       => ( ( minus_5127226145743854075T_VEBT @ ( insert_VEBT_VEBT @ X @ A2 ) @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) )
% 0.35/0.58          = A2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_insert_absorb
% 0.35/0.58  thf(fact_3351_Diff__insert__absorb,axiom,
% 0.35/0.58      ! [X: complex,A2: set_complex] :
% 0.35/0.58        ( ~ ( member_complex @ X @ A2 )
% 0.35/0.58       => ( ( minus_811609699411566653omplex @ ( insert_complex @ X @ A2 ) @ ( insert_complex @ X @ bot_bot_set_complex ) )
% 0.35/0.58          = A2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_insert_absorb
% 0.35/0.58  thf(fact_3352_Diff__insert__absorb,axiom,
% 0.35/0.58      ! [X: int,A2: set_int] :
% 0.35/0.58        ( ~ ( member_int @ X @ A2 )
% 0.35/0.58       => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ ( insert_int @ X @ bot_bot_set_int ) )
% 0.35/0.58          = A2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_insert_absorb
% 0.35/0.58  thf(fact_3353_Diff__insert__absorb,axiom,
% 0.35/0.58      ! [X: real,A2: set_real] :
% 0.35/0.58        ( ~ ( member_real @ X @ A2 )
% 0.35/0.58       => ( ( minus_minus_set_real @ ( insert_real @ X @ A2 ) @ ( insert_real @ X @ bot_bot_set_real ) )
% 0.35/0.58          = A2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_insert_absorb
% 0.35/0.58  thf(fact_3354_Diff__insert__absorb,axiom,
% 0.35/0.58      ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 0.35/0.58        ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 0.35/0.58       => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X @ A2 ) @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 0.35/0.58          = A2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_insert_absorb
% 0.35/0.58  thf(fact_3355_Diff__insert__absorb,axiom,
% 0.35/0.58      ! [X: nat,A2: set_nat] :
% 0.35/0.58        ( ~ ( member_nat @ X @ A2 )
% 0.35/0.58       => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 0.35/0.58          = A2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_insert_absorb
% 0.35/0.58  thf(fact_3356_subset__Diff__insert,axiom,
% 0.35/0.58      ! [A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,X: vEBT_VEBT,C4: set_VEBT_VEBT] :
% 0.35/0.58        ( ( ord_le4337996190870823476T_VEBT @ A2 @ ( minus_5127226145743854075T_VEBT @ B2 @ ( insert_VEBT_VEBT @ X @ C4 ) ) )
% 0.35/0.58        = ( ( ord_le4337996190870823476T_VEBT @ A2 @ ( minus_5127226145743854075T_VEBT @ B2 @ C4 ) )
% 0.35/0.58          & ~ ( member_VEBT_VEBT @ X @ A2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % subset_Diff_insert
% 0.35/0.58  thf(fact_3357_subset__Diff__insert,axiom,
% 0.35/0.58      ! [A2: set_complex,B2: set_complex,X: complex,C4: set_complex] :
% 0.35/0.58        ( ( ord_le211207098394363844omplex @ A2 @ ( minus_811609699411566653omplex @ B2 @ ( insert_complex @ X @ C4 ) ) )
% 0.35/0.58        = ( ( ord_le211207098394363844omplex @ A2 @ ( minus_811609699411566653omplex @ B2 @ C4 ) )
% 0.35/0.58          & ~ ( member_complex @ X @ A2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % subset_Diff_insert
% 0.35/0.58  thf(fact_3358_subset__Diff__insert,axiom,
% 0.35/0.58      ! [A2: set_int,B2: set_int,X: int,C4: set_int] :
% 0.35/0.58        ( ( ord_less_eq_set_int @ A2 @ ( minus_minus_set_int @ B2 @ ( insert_int @ X @ C4 ) ) )
% 0.35/0.58        = ( ( ord_less_eq_set_int @ A2 @ ( minus_minus_set_int @ B2 @ C4 ) )
% 0.35/0.58          & ~ ( member_int @ X @ A2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % subset_Diff_insert
% 0.35/0.58  thf(fact_3359_subset__Diff__insert,axiom,
% 0.35/0.58      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,C4: set_Pr1261947904930325089at_nat] :
% 0.35/0.58        ( ( ord_le3146513528884898305at_nat @ A2 @ ( minus_1356011639430497352at_nat @ B2 @ ( insert8211810215607154385at_nat @ X @ C4 ) ) )
% 0.35/0.58        = ( ( ord_le3146513528884898305at_nat @ A2 @ ( minus_1356011639430497352at_nat @ B2 @ C4 ) )
% 0.35/0.58          & ~ ( member8440522571783428010at_nat @ X @ A2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % subset_Diff_insert
% 0.35/0.58  thf(fact_3360_subset__Diff__insert,axiom,
% 0.35/0.58      ! [A2: set_real,B2: set_real,X: real,C4: set_real] :
% 0.35/0.58        ( ( ord_less_eq_set_real @ A2 @ ( minus_minus_set_real @ B2 @ ( insert_real @ X @ C4 ) ) )
% 0.35/0.58        = ( ( ord_less_eq_set_real @ A2 @ ( minus_minus_set_real @ B2 @ C4 ) )
% 0.35/0.58          & ~ ( member_real @ X @ A2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % subset_Diff_insert
% 0.35/0.58  thf(fact_3361_subset__Diff__insert,axiom,
% 0.35/0.58      ! [A2: set_nat,B2: set_nat,X: nat,C4: set_nat] :
% 0.35/0.58        ( ( ord_less_eq_set_nat @ A2 @ ( minus_minus_set_nat @ B2 @ ( insert_nat @ X @ C4 ) ) )
% 0.35/0.58        = ( ( ord_less_eq_set_nat @ A2 @ ( minus_minus_set_nat @ B2 @ C4 ) )
% 0.35/0.58          & ~ ( member_nat @ X @ A2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % subset_Diff_insert
% 0.35/0.58  thf(fact_3362_psubset__imp__ex__mem,axiom,
% 0.35/0.58      ! [A2: set_complex,B2: set_complex] :
% 0.35/0.58        ( ( ord_less_set_complex @ A2 @ B2 )
% 0.35/0.58       => ? [B3: complex] : ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B2 @ A2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % psubset_imp_ex_mem
% 0.35/0.58  thf(fact_3363_psubset__imp__ex__mem,axiom,
% 0.35/0.58      ! [A2: set_real,B2: set_real] :
% 0.35/0.58        ( ( ord_less_set_real @ A2 @ B2 )
% 0.35/0.58       => ? [B3: real] : ( member_real @ B3 @ ( minus_minus_set_real @ B2 @ A2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % psubset_imp_ex_mem
% 0.35/0.58  thf(fact_3364_psubset__imp__ex__mem,axiom,
% 0.35/0.58      ! [A2: set_int,B2: set_int] :
% 0.35/0.58        ( ( ord_less_set_int @ A2 @ B2 )
% 0.35/0.58       => ? [B3: int] : ( member_int @ B3 @ ( minus_minus_set_int @ B2 @ A2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % psubset_imp_ex_mem
% 0.35/0.58  thf(fact_3365_psubset__imp__ex__mem,axiom,
% 0.35/0.58      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.35/0.58        ( ( ord_le7866589430770878221at_nat @ A2 @ B2 )
% 0.35/0.58       => ? [B3: product_prod_nat_nat] : ( member8440522571783428010at_nat @ B3 @ ( minus_1356011639430497352at_nat @ B2 @ A2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % psubset_imp_ex_mem
% 0.35/0.58  thf(fact_3366_psubset__imp__ex__mem,axiom,
% 0.35/0.58      ! [A2: set_nat,B2: set_nat] :
% 0.35/0.58        ( ( ord_less_set_nat @ A2 @ B2 )
% 0.35/0.58       => ? [B3: nat] : ( member_nat @ B3 @ ( minus_minus_set_nat @ B2 @ A2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % psubset_imp_ex_mem
% 0.35/0.58  thf(fact_3367_DiffE,axiom,
% 0.35/0.58      ! [C: complex,A2: set_complex,B2: set_complex] :
% 0.35/0.58        ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B2 ) )
% 0.35/0.58       => ~ ( ( member_complex @ C @ A2 )
% 0.35/0.58           => ( member_complex @ C @ B2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % DiffE
% 0.35/0.58  thf(fact_3368_DiffE,axiom,
% 0.35/0.58      ! [C: real,A2: set_real,B2: set_real] :
% 0.35/0.58        ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B2 ) )
% 0.35/0.58       => ~ ( ( member_real @ C @ A2 )
% 0.35/0.58           => ( member_real @ C @ B2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % DiffE
% 0.35/0.58  thf(fact_3369_DiffE,axiom,
% 0.35/0.58      ! [C: int,A2: set_int,B2: set_int] :
% 0.35/0.58        ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B2 ) )
% 0.35/0.58       => ~ ( ( member_int @ C @ A2 )
% 0.35/0.58           => ( member_int @ C @ B2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % DiffE
% 0.35/0.58  thf(fact_3370_DiffE,axiom,
% 0.35/0.58      ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.35/0.58        ( ( member8440522571783428010at_nat @ C @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) )
% 0.35/0.58       => ~ ( ( member8440522571783428010at_nat @ C @ A2 )
% 0.35/0.58           => ( member8440522571783428010at_nat @ C @ B2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % DiffE
% 0.35/0.58  thf(fact_3371_DiffE,axiom,
% 0.35/0.58      ! [C: nat,A2: set_nat,B2: set_nat] :
% 0.35/0.58        ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 0.35/0.58       => ~ ( ( member_nat @ C @ A2 )
% 0.35/0.58           => ( member_nat @ C @ B2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % DiffE
% 0.35/0.58  thf(fact_3372_DiffD1,axiom,
% 0.35/0.58      ! [C: complex,A2: set_complex,B2: set_complex] :
% 0.35/0.58        ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B2 ) )
% 0.35/0.58       => ( member_complex @ C @ A2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % DiffD1
% 0.35/0.58  thf(fact_3373_DiffD1,axiom,
% 0.35/0.58      ! [C: real,A2: set_real,B2: set_real] :
% 0.35/0.58        ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B2 ) )
% 0.35/0.58       => ( member_real @ C @ A2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % DiffD1
% 0.35/0.58  thf(fact_3374_DiffD1,axiom,
% 0.35/0.58      ! [C: int,A2: set_int,B2: set_int] :
% 0.35/0.58        ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B2 ) )
% 0.35/0.58       => ( member_int @ C @ A2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % DiffD1
% 0.35/0.58  thf(fact_3375_DiffD1,axiom,
% 0.35/0.58      ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.35/0.58        ( ( member8440522571783428010at_nat @ C @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) )
% 0.35/0.58       => ( member8440522571783428010at_nat @ C @ A2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % DiffD1
% 0.35/0.58  thf(fact_3376_DiffD1,axiom,
% 0.35/0.58      ! [C: nat,A2: set_nat,B2: set_nat] :
% 0.35/0.58        ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 0.35/0.58       => ( member_nat @ C @ A2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % DiffD1
% 0.35/0.58  thf(fact_3377_DiffD2,axiom,
% 0.35/0.58      ! [C: complex,A2: set_complex,B2: set_complex] :
% 0.35/0.58        ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B2 ) )
% 0.35/0.58       => ~ ( member_complex @ C @ B2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % DiffD2
% 0.35/0.58  thf(fact_3378_DiffD2,axiom,
% 0.35/0.58      ! [C: real,A2: set_real,B2: set_real] :
% 0.35/0.58        ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B2 ) )
% 0.35/0.58       => ~ ( member_real @ C @ B2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % DiffD2
% 0.35/0.58  thf(fact_3379_DiffD2,axiom,
% 0.35/0.58      ! [C: int,A2: set_int,B2: set_int] :
% 0.35/0.58        ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B2 ) )
% 0.35/0.58       => ~ ( member_int @ C @ B2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % DiffD2
% 0.35/0.58  thf(fact_3380_DiffD2,axiom,
% 0.35/0.58      ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.35/0.58        ( ( member8440522571783428010at_nat @ C @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) )
% 0.35/0.58       => ~ ( member8440522571783428010at_nat @ C @ B2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % DiffD2
% 0.35/0.58  thf(fact_3381_DiffD2,axiom,
% 0.35/0.58      ! [C: nat,A2: set_nat,B2: set_nat] :
% 0.35/0.58        ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 0.35/0.58       => ~ ( member_nat @ C @ B2 ) ) ).
% 0.35/0.58  
% 0.35/0.58  % DiffD2
% 0.35/0.58  thf(fact_3382_insert__Diff__if,axiom,
% 0.35/0.58      ! [X: vEBT_VEBT,B2: set_VEBT_VEBT,A2: set_VEBT_VEBT] :
% 0.35/0.58        ( ( ( member_VEBT_VEBT @ X @ B2 )
% 0.35/0.58         => ( ( minus_5127226145743854075T_VEBT @ ( insert_VEBT_VEBT @ X @ A2 ) @ B2 )
% 0.35/0.58            = ( minus_5127226145743854075T_VEBT @ A2 @ B2 ) ) )
% 0.35/0.58        & ( ~ ( member_VEBT_VEBT @ X @ B2 )
% 0.35/0.58         => ( ( minus_5127226145743854075T_VEBT @ ( insert_VEBT_VEBT @ X @ A2 ) @ B2 )
% 0.35/0.58            = ( insert_VEBT_VEBT @ X @ ( minus_5127226145743854075T_VEBT @ A2 @ B2 ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % insert_Diff_if
% 0.35/0.58  thf(fact_3383_insert__Diff__if,axiom,
% 0.35/0.58      ! [X: complex,B2: set_complex,A2: set_complex] :
% 0.35/0.58        ( ( ( member_complex @ X @ B2 )
% 0.35/0.58         => ( ( minus_811609699411566653omplex @ ( insert_complex @ X @ A2 ) @ B2 )
% 0.35/0.58            = ( minus_811609699411566653omplex @ A2 @ B2 ) ) )
% 0.35/0.58        & ( ~ ( member_complex @ X @ B2 )
% 0.35/0.58         => ( ( minus_811609699411566653omplex @ ( insert_complex @ X @ A2 ) @ B2 )
% 0.35/0.58            = ( insert_complex @ X @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % insert_Diff_if
% 0.35/0.58  thf(fact_3384_insert__Diff__if,axiom,
% 0.35/0.58      ! [X: real,B2: set_real,A2: set_real] :
% 0.35/0.58        ( ( ( member_real @ X @ B2 )
% 0.35/0.58         => ( ( minus_minus_set_real @ ( insert_real @ X @ A2 ) @ B2 )
% 0.35/0.58            = ( minus_minus_set_real @ A2 @ B2 ) ) )
% 0.35/0.58        & ( ~ ( member_real @ X @ B2 )
% 0.35/0.58         => ( ( minus_minus_set_real @ ( insert_real @ X @ A2 ) @ B2 )
% 0.35/0.58            = ( insert_real @ X @ ( minus_minus_set_real @ A2 @ B2 ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % insert_Diff_if
% 0.35/0.58  thf(fact_3385_insert__Diff__if,axiom,
% 0.35/0.58      ! [X: int,B2: set_int,A2: set_int] :
% 0.35/0.58        ( ( ( member_int @ X @ B2 )
% 0.35/0.58         => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ B2 )
% 0.35/0.58            = ( minus_minus_set_int @ A2 @ B2 ) ) )
% 0.35/0.58        & ( ~ ( member_int @ X @ B2 )
% 0.35/0.58         => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ B2 )
% 0.35/0.58            = ( insert_int @ X @ ( minus_minus_set_int @ A2 @ B2 ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % insert_Diff_if
% 0.35/0.58  thf(fact_3386_insert__Diff__if,axiom,
% 0.35/0.58      ! [X: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 0.35/0.58        ( ( ( member8440522571783428010at_nat @ X @ B2 )
% 0.35/0.58         => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X @ A2 ) @ B2 )
% 0.35/0.58            = ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) )
% 0.35/0.58        & ( ~ ( member8440522571783428010at_nat @ X @ B2 )
% 0.35/0.58         => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X @ A2 ) @ B2 )
% 0.35/0.58            = ( insert8211810215607154385at_nat @ X @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % insert_Diff_if
% 0.35/0.58  thf(fact_3387_insert__Diff__if,axiom,
% 0.35/0.58      ! [X: nat,B2: set_nat,A2: set_nat] :
% 0.35/0.58        ( ( ( member_nat @ X @ B2 )
% 0.35/0.58         => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ B2 )
% 0.35/0.58            = ( minus_minus_set_nat @ A2 @ B2 ) ) )
% 0.35/0.58        & ( ~ ( member_nat @ X @ B2 )
% 0.35/0.58         => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ B2 )
% 0.35/0.58            = ( insert_nat @ X @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % insert_Diff_if
% 0.35/0.58  thf(fact_3388_minus__set__def,axiom,
% 0.35/0.58      ( minus_minus_set_int
% 0.35/0.58      = ( ^ [A6: set_int,B6: set_int] :
% 0.35/0.58            ( collect_int
% 0.35/0.58            @ ( minus_minus_int_o
% 0.35/0.58              @ ^ [X2: int] : ( member_int @ X2 @ A6 )
% 0.35/0.58              @ ^ [X2: int] : ( member_int @ X2 @ B6 ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minus_set_def
% 0.35/0.58  thf(fact_3389_minus__set__def,axiom,
% 0.35/0.58      ( minus_811609699411566653omplex
% 0.35/0.58      = ( ^ [A6: set_complex,B6: set_complex] :
% 0.35/0.58            ( collect_complex
% 0.35/0.58            @ ( minus_8727706125548526216plex_o
% 0.35/0.58              @ ^ [X2: complex] : ( member_complex @ X2 @ A6 )
% 0.35/0.58              @ ^ [X2: complex] : ( member_complex @ X2 @ B6 ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minus_set_def
% 0.35/0.58  thf(fact_3390_minus__set__def,axiom,
% 0.35/0.58      ( minus_minus_set_real
% 0.35/0.58      = ( ^ [A6: set_real,B6: set_real] :
% 0.35/0.58            ( collect_real
% 0.35/0.58            @ ( minus_minus_real_o
% 0.35/0.58              @ ^ [X2: real] : ( member_real @ X2 @ A6 )
% 0.35/0.58              @ ^ [X2: real] : ( member_real @ X2 @ B6 ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minus_set_def
% 0.35/0.58  thf(fact_3391_minus__set__def,axiom,
% 0.35/0.58      ( minus_7954133019191499631st_nat
% 0.35/0.58      = ( ^ [A6: set_list_nat,B6: set_list_nat] :
% 0.35/0.58            ( collect_list_nat
% 0.35/0.58            @ ( minus_1139252259498527702_nat_o
% 0.35/0.58              @ ^ [X2: list_nat] : ( member_list_nat @ X2 @ A6 )
% 0.35/0.58              @ ^ [X2: list_nat] : ( member_list_nat @ X2 @ B6 ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minus_set_def
% 0.35/0.58  thf(fact_3392_minus__set__def,axiom,
% 0.35/0.58      ( minus_1356011639430497352at_nat
% 0.35/0.58      = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 0.35/0.58            ( collec3392354462482085612at_nat
% 0.35/0.58            @ ( minus_2270307095948843157_nat_o
% 0.35/0.58              @ ^ [X2: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X2 @ A6 )
% 0.35/0.58              @ ^ [X2: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X2 @ B6 ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minus_set_def
% 0.35/0.58  thf(fact_3393_minus__set__def,axiom,
% 0.35/0.58      ( minus_minus_set_nat
% 0.35/0.58      = ( ^ [A6: set_nat,B6: set_nat] :
% 0.35/0.58            ( collect_nat
% 0.35/0.58            @ ( minus_minus_nat_o
% 0.35/0.58              @ ^ [X2: nat] : ( member_nat @ X2 @ A6 )
% 0.35/0.58              @ ^ [X2: nat] : ( member_nat @ X2 @ B6 ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % minus_set_def
% 0.35/0.58  thf(fact_3394_set__diff__eq,axiom,
% 0.35/0.58      ( minus_minus_set_int
% 0.35/0.58      = ( ^ [A6: set_int,B6: set_int] :
% 0.35/0.58            ( collect_int
% 0.35/0.58            @ ^ [X2: int] :
% 0.35/0.58                ( ( member_int @ X2 @ A6 )
% 0.35/0.58                & ~ ( member_int @ X2 @ B6 ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % set_diff_eq
% 0.35/0.58  thf(fact_3395_set__diff__eq,axiom,
% 0.35/0.58      ( minus_811609699411566653omplex
% 0.35/0.58      = ( ^ [A6: set_complex,B6: set_complex] :
% 0.35/0.58            ( collect_complex
% 0.35/0.58            @ ^ [X2: complex] :
% 0.35/0.58                ( ( member_complex @ X2 @ A6 )
% 0.35/0.58                & ~ ( member_complex @ X2 @ B6 ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % set_diff_eq
% 0.35/0.58  thf(fact_3396_set__diff__eq,axiom,
% 0.35/0.58      ( minus_minus_set_real
% 0.35/0.58      = ( ^ [A6: set_real,B6: set_real] :
% 0.35/0.58            ( collect_real
% 0.35/0.58            @ ^ [X2: real] :
% 0.35/0.58                ( ( member_real @ X2 @ A6 )
% 0.35/0.58                & ~ ( member_real @ X2 @ B6 ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % set_diff_eq
% 0.35/0.58  thf(fact_3397_set__diff__eq,axiom,
% 0.35/0.58      ( minus_7954133019191499631st_nat
% 0.35/0.58      = ( ^ [A6: set_list_nat,B6: set_list_nat] :
% 0.35/0.58            ( collect_list_nat
% 0.35/0.58            @ ^ [X2: list_nat] :
% 0.35/0.58                ( ( member_list_nat @ X2 @ A6 )
% 0.35/0.58                & ~ ( member_list_nat @ X2 @ B6 ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % set_diff_eq
% 0.35/0.58  thf(fact_3398_set__diff__eq,axiom,
% 0.35/0.58      ( minus_1356011639430497352at_nat
% 0.35/0.58      = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 0.35/0.58            ( collec3392354462482085612at_nat
% 0.35/0.58            @ ^ [X2: product_prod_nat_nat] :
% 0.35/0.58                ( ( member8440522571783428010at_nat @ X2 @ A6 )
% 0.35/0.58                & ~ ( member8440522571783428010at_nat @ X2 @ B6 ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % set_diff_eq
% 0.35/0.58  thf(fact_3399_set__diff__eq,axiom,
% 0.35/0.58      ( minus_minus_set_nat
% 0.35/0.58      = ( ^ [A6: set_nat,B6: set_nat] :
% 0.35/0.58            ( collect_nat
% 0.35/0.58            @ ^ [X2: nat] :
% 0.35/0.58                ( ( member_nat @ X2 @ A6 )
% 0.35/0.58                & ~ ( member_nat @ X2 @ B6 ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % set_diff_eq
% 0.35/0.58  thf(fact_3400_psubset__insert__iff,axiom,
% 0.35/0.58      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,B2: set_VEBT_VEBT] :
% 0.35/0.58        ( ( ord_le3480810397992357184T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ B2 ) )
% 0.35/0.58        = ( ( ( member_VEBT_VEBT @ X @ B2 )
% 0.35/0.58           => ( ord_le3480810397992357184T_VEBT @ A2 @ B2 ) )
% 0.35/0.58          & ( ~ ( member_VEBT_VEBT @ X @ B2 )
% 0.35/0.58           => ( ( ( member_VEBT_VEBT @ X @ A2 )
% 0.35/0.58               => ( ord_le3480810397992357184T_VEBT @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) @ B2 ) )
% 0.35/0.58              & ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 0.35/0.58               => ( ord_le4337996190870823476T_VEBT @ A2 @ B2 ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % psubset_insert_iff
% 0.35/0.58  thf(fact_3401_psubset__insert__iff,axiom,
% 0.35/0.58      ! [A2: set_complex,X: complex,B2: set_complex] :
% 0.35/0.58        ( ( ord_less_set_complex @ A2 @ ( insert_complex @ X @ B2 ) )
% 0.35/0.58        = ( ( ( member_complex @ X @ B2 )
% 0.35/0.58           => ( ord_less_set_complex @ A2 @ B2 ) )
% 0.35/0.58          & ( ~ ( member_complex @ X @ B2 )
% 0.35/0.58           => ( ( ( member_complex @ X @ A2 )
% 0.35/0.58               => ( ord_less_set_complex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) @ B2 ) )
% 0.35/0.58              & ( ~ ( member_complex @ X @ A2 )
% 0.35/0.58               => ( ord_le211207098394363844omplex @ A2 @ B2 ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % psubset_insert_iff
% 0.35/0.58  thf(fact_3402_psubset__insert__iff,axiom,
% 0.35/0.58      ! [A2: set_int,X: int,B2: set_int] :
% 0.35/0.58        ( ( ord_less_set_int @ A2 @ ( insert_int @ X @ B2 ) )
% 0.35/0.58        = ( ( ( member_int @ X @ B2 )
% 0.35/0.58           => ( ord_less_set_int @ A2 @ B2 ) )
% 0.35/0.58          & ( ~ ( member_int @ X @ B2 )
% 0.35/0.58           => ( ( ( member_int @ X @ A2 )
% 0.35/0.58               => ( ord_less_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B2 ) )
% 0.35/0.58              & ( ~ ( member_int @ X @ A2 )
% 0.35/0.58               => ( ord_less_eq_set_int @ A2 @ B2 ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % psubset_insert_iff
% 0.35/0.58  thf(fact_3403_psubset__insert__iff,axiom,
% 0.35/0.58      ! [A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.35/0.58        ( ( ord_le7866589430770878221at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ B2 ) )
% 0.35/0.58        = ( ( ( member8440522571783428010at_nat @ X @ B2 )
% 0.35/0.58           => ( ord_le7866589430770878221at_nat @ A2 @ B2 ) )
% 0.35/0.58          & ( ~ ( member8440522571783428010at_nat @ X @ B2 )
% 0.35/0.58           => ( ( ( member8440522571783428010at_nat @ X @ A2 )
% 0.35/0.58               => ( ord_le7866589430770878221at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) @ B2 ) )
% 0.35/0.58              & ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 0.35/0.58               => ( ord_le3146513528884898305at_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % psubset_insert_iff
% 0.35/0.58  thf(fact_3404_psubset__insert__iff,axiom,
% 0.35/0.58      ! [A2: set_real,X: real,B2: set_real] :
% 0.35/0.58        ( ( ord_less_set_real @ A2 @ ( insert_real @ X @ B2 ) )
% 0.35/0.58        = ( ( ( member_real @ X @ B2 )
% 0.35/0.58           => ( ord_less_set_real @ A2 @ B2 ) )
% 0.35/0.58          & ( ~ ( member_real @ X @ B2 )
% 0.35/0.58           => ( ( ( member_real @ X @ A2 )
% 0.35/0.58               => ( ord_less_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) @ B2 ) )
% 0.35/0.58              & ( ~ ( member_real @ X @ A2 )
% 0.35/0.58               => ( ord_less_eq_set_real @ A2 @ B2 ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % psubset_insert_iff
% 0.35/0.58  thf(fact_3405_psubset__insert__iff,axiom,
% 0.35/0.58      ! [A2: set_nat,X: nat,B2: set_nat] :
% 0.35/0.58        ( ( ord_less_set_nat @ A2 @ ( insert_nat @ X @ B2 ) )
% 0.35/0.58        = ( ( ( member_nat @ X @ B2 )
% 0.35/0.58           => ( ord_less_set_nat @ A2 @ B2 ) )
% 0.35/0.58          & ( ~ ( member_nat @ X @ B2 )
% 0.35/0.58           => ( ( ( member_nat @ X @ A2 )
% 0.35/0.58               => ( ord_less_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B2 ) )
% 0.35/0.58              & ( ~ ( member_nat @ X @ A2 )
% 0.35/0.58               => ( ord_less_eq_set_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % psubset_insert_iff
% 0.35/0.58  thf(fact_3406_Diff__single__insert,axiom,
% 0.35/0.58      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,B2: set_VEBT_VEBT] :
% 0.35/0.58        ( ( ord_le4337996190870823476T_VEBT @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) @ B2 )
% 0.35/0.58       => ( ord_le4337996190870823476T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ B2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_single_insert
% 0.35/0.58  thf(fact_3407_Diff__single__insert,axiom,
% 0.35/0.58      ! [A2: set_int,X: int,B2: set_int] :
% 0.35/0.58        ( ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B2 )
% 0.35/0.58       => ( ord_less_eq_set_int @ A2 @ ( insert_int @ X @ B2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_single_insert
% 0.35/0.58  thf(fact_3408_Diff__single__insert,axiom,
% 0.35/0.58      ! [A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.35/0.58        ( ( ord_le3146513528884898305at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) @ B2 )
% 0.35/0.58       => ( ord_le3146513528884898305at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ B2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_single_insert
% 0.35/0.58  thf(fact_3409_Diff__single__insert,axiom,
% 0.35/0.58      ! [A2: set_real,X: real,B2: set_real] :
% 0.35/0.58        ( ( ord_less_eq_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) @ B2 )
% 0.35/0.58       => ( ord_less_eq_set_real @ A2 @ ( insert_real @ X @ B2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_single_insert
% 0.35/0.58  thf(fact_3410_Diff__single__insert,axiom,
% 0.35/0.58      ! [A2: set_nat,X: nat,B2: set_nat] :
% 0.35/0.58        ( ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B2 )
% 0.35/0.58       => ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X @ B2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_single_insert
% 0.35/0.58  thf(fact_3411_subset__insert__iff,axiom,
% 0.35/0.58      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,B2: set_VEBT_VEBT] :
% 0.35/0.58        ( ( ord_le4337996190870823476T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ B2 ) )
% 0.35/0.58        = ( ( ( member_VEBT_VEBT @ X @ A2 )
% 0.35/0.58           => ( ord_le4337996190870823476T_VEBT @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) @ B2 ) )
% 0.35/0.58          & ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 0.35/0.58           => ( ord_le4337996190870823476T_VEBT @ A2 @ B2 ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % subset_insert_iff
% 0.35/0.58  thf(fact_3412_subset__insert__iff,axiom,
% 0.35/0.58      ! [A2: set_complex,X: complex,B2: set_complex] :
% 0.35/0.58        ( ( ord_le211207098394363844omplex @ A2 @ ( insert_complex @ X @ B2 ) )
% 0.35/0.58        = ( ( ( member_complex @ X @ A2 )
% 0.35/0.58           => ( ord_le211207098394363844omplex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) @ B2 ) )
% 0.35/0.58          & ( ~ ( member_complex @ X @ A2 )
% 0.35/0.58           => ( ord_le211207098394363844omplex @ A2 @ B2 ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % subset_insert_iff
% 0.35/0.58  thf(fact_3413_subset__insert__iff,axiom,
% 0.35/0.58      ! [A2: set_int,X: int,B2: set_int] :
% 0.35/0.58        ( ( ord_less_eq_set_int @ A2 @ ( insert_int @ X @ B2 ) )
% 0.35/0.58        = ( ( ( member_int @ X @ A2 )
% 0.35/0.58           => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B2 ) )
% 0.35/0.58          & ( ~ ( member_int @ X @ A2 )
% 0.35/0.58           => ( ord_less_eq_set_int @ A2 @ B2 ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % subset_insert_iff
% 0.35/0.58  thf(fact_3414_subset__insert__iff,axiom,
% 0.35/0.58      ! [A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.35/0.58        ( ( ord_le3146513528884898305at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ B2 ) )
% 0.35/0.58        = ( ( ( member8440522571783428010at_nat @ X @ A2 )
% 0.35/0.58           => ( ord_le3146513528884898305at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) @ B2 ) )
% 0.35/0.58          & ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 0.35/0.58           => ( ord_le3146513528884898305at_nat @ A2 @ B2 ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % subset_insert_iff
% 0.35/0.58  thf(fact_3415_subset__insert__iff,axiom,
% 0.35/0.58      ! [A2: set_real,X: real,B2: set_real] :
% 0.35/0.58        ( ( ord_less_eq_set_real @ A2 @ ( insert_real @ X @ B2 ) )
% 0.35/0.58        = ( ( ( member_real @ X @ A2 )
% 0.35/0.58           => ( ord_less_eq_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) @ B2 ) )
% 0.35/0.58          & ( ~ ( member_real @ X @ A2 )
% 0.35/0.58           => ( ord_less_eq_set_real @ A2 @ B2 ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % subset_insert_iff
% 0.35/0.58  thf(fact_3416_subset__insert__iff,axiom,
% 0.35/0.58      ! [A2: set_nat,X: nat,B2: set_nat] :
% 0.35/0.58        ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X @ B2 ) )
% 0.35/0.58        = ( ( ( member_nat @ X @ A2 )
% 0.35/0.58           => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B2 ) )
% 0.35/0.58          & ( ~ ( member_nat @ X @ A2 )
% 0.35/0.58           => ( ord_less_eq_set_nat @ A2 @ B2 ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % subset_insert_iff
% 0.35/0.58  thf(fact_3417_unset__bit__less__eq,axiom,
% 0.35/0.58      ! [N: nat,K: int] : ( ord_less_eq_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ K ) ).
% 0.35/0.58  
% 0.35/0.58  % unset_bit_less_eq
% 0.35/0.58  thf(fact_3418_atLeast0__atMost__Suc,axiom,
% 0.35/0.58      ! [N: nat] :
% 0.35/0.58        ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 0.35/0.58        = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeast0_atMost_Suc
% 0.35/0.58  thf(fact_3419_atLeastAtMost__insertL,axiom,
% 0.35/0.58      ! [M: nat,N: nat] :
% 0.35/0.58        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.58       => ( ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 0.35/0.58          = ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastAtMost_insertL
% 0.35/0.58  thf(fact_3420_atLeastAtMostSuc__conv,axiom,
% 0.35/0.58      ! [M: nat,N: nat] :
% 0.35/0.58        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.35/0.58       => ( ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) )
% 0.35/0.58          = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % atLeastAtMostSuc_conv
% 0.35/0.58  thf(fact_3421_Icc__eq__insert__lb__nat,axiom,
% 0.35/0.58      ! [M: nat,N: nat] :
% 0.35/0.58        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.58       => ( ( set_or1269000886237332187st_nat @ M @ N )
% 0.35/0.58          = ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % Icc_eq_insert_lb_nat
% 0.35/0.58  thf(fact_3422_set__update__subset__insert,axiom,
% 0.35/0.58      ! [Xs2: list_int,I2: nat,X: int] : ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs2 @ I2 @ X ) ) @ ( insert_int @ X @ ( set_int2 @ Xs2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % set_update_subset_insert
% 0.35/0.58  thf(fact_3423_set__update__subset__insert,axiom,
% 0.35/0.58      ! [Xs2: list_VEBT_VEBT,I2: nat,X: vEBT_VEBT] : ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) ) @ ( insert_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % set_update_subset_insert
% 0.35/0.58  thf(fact_3424_set__update__subset__insert,axiom,
% 0.35/0.58      ! [Xs2: list_real,I2: nat,X: real] : ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs2 @ I2 @ X ) ) @ ( insert_real @ X @ ( set_real2 @ Xs2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % set_update_subset_insert
% 0.35/0.58  thf(fact_3425_set__update__subset__insert,axiom,
% 0.35/0.58      ! [Xs2: list_nat,I2: nat,X: nat] : ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs2 @ I2 @ X ) ) @ ( insert_nat @ X @ ( set_nat2 @ Xs2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % set_update_subset_insert
% 0.35/0.58  thf(fact_3426_double__diff,axiom,
% 0.35/0.58      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C4: set_Pr1261947904930325089at_nat] :
% 0.35/0.58        ( ( ord_le3146513528884898305at_nat @ A2 @ B2 )
% 0.35/0.58       => ( ( ord_le3146513528884898305at_nat @ B2 @ C4 )
% 0.35/0.58         => ( ( minus_1356011639430497352at_nat @ B2 @ ( minus_1356011639430497352at_nat @ C4 @ A2 ) )
% 0.35/0.58            = A2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % double_diff
% 0.35/0.58  thf(fact_3427_double__diff,axiom,
% 0.35/0.58      ! [A2: set_real,B2: set_real,C4: set_real] :
% 0.35/0.58        ( ( ord_less_eq_set_real @ A2 @ B2 )
% 0.35/0.58       => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 0.35/0.58         => ( ( minus_minus_set_real @ B2 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 0.35/0.58            = A2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % double_diff
% 0.35/0.58  thf(fact_3428_double__diff,axiom,
% 0.35/0.58      ! [A2: set_nat,B2: set_nat,C4: set_nat] :
% 0.35/0.58        ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.35/0.58       => ( ( ord_less_eq_set_nat @ B2 @ C4 )
% 0.35/0.58         => ( ( minus_minus_set_nat @ B2 @ ( minus_minus_set_nat @ C4 @ A2 ) )
% 0.35/0.58            = A2 ) ) ) ).
% 0.35/0.58  
% 0.35/0.58  % double_diff
% 0.35/0.58  thf(fact_3429_Diff__subset,axiom,
% 0.35/0.58      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) @ A2 ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_subset
% 0.35/0.58  thf(fact_3430_Diff__subset,axiom,
% 0.35/0.58      ! [A2: set_real,B2: set_real] : ( ord_less_eq_set_real @ ( minus_minus_set_real @ A2 @ B2 ) @ A2 ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_subset
% 0.35/0.58  thf(fact_3431_Diff__subset,axiom,
% 0.35/0.58      ! [A2: set_nat,B2: set_nat] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ A2 ) ).
% 0.35/0.58  
% 0.35/0.58  % Diff_subset
% 0.35/0.58  thf(fact_3432_Diff__mono,axiom,
% 0.35/0.59      ! [A2: set_Pr1261947904930325089at_nat,C4: set_Pr1261947904930325089at_nat,D4: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.35/0.59        ( ( ord_le3146513528884898305at_nat @ A2 @ C4 )
% 0.35/0.59       => ( ( ord_le3146513528884898305at_nat @ D4 @ B2 )
% 0.35/0.59         => ( ord_le3146513528884898305at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) @ ( minus_1356011639430497352at_nat @ C4 @ D4 ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % Diff_mono
% 0.35/0.59  thf(fact_3433_Diff__mono,axiom,
% 0.35/0.59      ! [A2: set_real,C4: set_real,D4: set_real,B2: set_real] :
% 0.35/0.59        ( ( ord_less_eq_set_real @ A2 @ C4 )
% 0.35/0.59       => ( ( ord_less_eq_set_real @ D4 @ B2 )
% 0.35/0.59         => ( ord_less_eq_set_real @ ( minus_minus_set_real @ A2 @ B2 ) @ ( minus_minus_set_real @ C4 @ D4 ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % Diff_mono
% 0.35/0.59  thf(fact_3434_Diff__mono,axiom,
% 0.35/0.59      ! [A2: set_nat,C4: set_nat,D4: set_nat,B2: set_nat] :
% 0.35/0.59        ( ( ord_less_eq_set_nat @ A2 @ C4 )
% 0.35/0.59       => ( ( ord_less_eq_set_nat @ D4 @ B2 )
% 0.35/0.59         => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ ( minus_minus_set_nat @ C4 @ D4 ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % Diff_mono
% 0.35/0.59  thf(fact_3435_mult__less__iff1,axiom,
% 0.35/0.59      ! [Z: real,X: real,Y2: real] :
% 0.35/0.59        ( ( ord_less_real @ zero_zero_real @ Z )
% 0.35/0.59       => ( ( ord_less_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y2 @ Z ) )
% 0.35/0.59          = ( ord_less_real @ X @ Y2 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mult_less_iff1
% 0.35/0.59  thf(fact_3436_mult__less__iff1,axiom,
% 0.35/0.59      ! [Z: rat,X: rat,Y2: rat] :
% 0.35/0.59        ( ( ord_less_rat @ zero_zero_rat @ Z )
% 0.35/0.59       => ( ( ord_less_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y2 @ Z ) )
% 0.35/0.59          = ( ord_less_rat @ X @ Y2 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mult_less_iff1
% 0.35/0.59  thf(fact_3437_mult__less__iff1,axiom,
% 0.35/0.59      ! [Z: int,X: int,Y2: int] :
% 0.35/0.59        ( ( ord_less_int @ zero_zero_int @ Z )
% 0.35/0.59       => ( ( ord_less_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y2 @ Z ) )
% 0.35/0.59          = ( ord_less_int @ X @ Y2 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mult_less_iff1
% 0.35/0.59  thf(fact_3438_divmod__algorithm__code_I8_J,axiom,
% 0.35/0.59      ! [M: num,N: num] :
% 0.35/0.59        ( ( ( ord_less_num @ M @ N )
% 0.35/0.59         => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.35/0.59            = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) ) ) )
% 0.35/0.59        & ( ~ ( ord_less_num @ M @ N )
% 0.35/0.59         => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.35/0.59            = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % divmod_algorithm_code(8)
% 0.35/0.59  thf(fact_3439_divmod__algorithm__code_I8_J,axiom,
% 0.35/0.59      ! [M: num,N: num] :
% 0.35/0.59        ( ( ( ord_less_num @ M @ N )
% 0.35/0.59         => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.35/0.59            = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) ) ) )
% 0.35/0.59        & ( ~ ( ord_less_num @ M @ N )
% 0.35/0.59         => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.35/0.59            = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % divmod_algorithm_code(8)
% 0.35/0.59  thf(fact_3440_divmod__algorithm__code_I8_J,axiom,
% 0.35/0.59      ! [M: num,N: num] :
% 0.35/0.59        ( ( ( ord_less_num @ M @ N )
% 0.35/0.59         => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.35/0.59            = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) ) ) )
% 0.35/0.59        & ( ~ ( ord_less_num @ M @ N )
% 0.35/0.59         => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.35/0.59            = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % divmod_algorithm_code(8)
% 0.35/0.59  thf(fact_3441_divmod__algorithm__code_I7_J,axiom,
% 0.35/0.59      ! [M: num,N: num] :
% 0.35/0.59        ( ( ( ord_less_eq_num @ M @ N )
% 0.35/0.59         => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.35/0.59            = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) ) ) )
% 0.35/0.59        & ( ~ ( ord_less_eq_num @ M @ N )
% 0.35/0.59         => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.35/0.59            = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % divmod_algorithm_code(7)
% 0.35/0.59  thf(fact_3442_divmod__algorithm__code_I7_J,axiom,
% 0.35/0.59      ! [M: num,N: num] :
% 0.35/0.59        ( ( ( ord_less_eq_num @ M @ N )
% 0.35/0.59         => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.35/0.59            = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) ) ) )
% 0.35/0.59        & ( ~ ( ord_less_eq_num @ M @ N )
% 0.35/0.59         => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.35/0.59            = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % divmod_algorithm_code(7)
% 0.35/0.59  thf(fact_3443_divmod__algorithm__code_I7_J,axiom,
% 0.35/0.59      ! [M: num,N: num] :
% 0.35/0.59        ( ( ( ord_less_eq_num @ M @ N )
% 0.35/0.59         => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.35/0.59            = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) ) ) )
% 0.35/0.59        & ( ~ ( ord_less_eq_num @ M @ N )
% 0.35/0.59         => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.35/0.59            = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % divmod_algorithm_code(7)
% 0.35/0.59  thf(fact_3444_divides__aux__eq,axiom,
% 0.35/0.59      ! [Q2: nat,R: nat] :
% 0.35/0.59        ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q2 @ R ) )
% 0.35/0.59        = ( R = zero_zero_nat ) ) ).
% 0.35/0.59  
% 0.35/0.59  % divides_aux_eq
% 0.35/0.59  thf(fact_3445_divides__aux__eq,axiom,
% 0.35/0.59      ! [Q2: int,R: int] :
% 0.35/0.59        ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q2 @ R ) )
% 0.35/0.59        = ( R = zero_zero_int ) ) ).
% 0.35/0.59  
% 0.35/0.59  % divides_aux_eq
% 0.35/0.59  thf(fact_3446_neg__eucl__rel__int__mult__2,axiom,
% 0.35/0.59      ! [B: int,A: int,Q2: int,R: int] :
% 0.35/0.59        ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.35/0.59       => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 0.35/0.59         => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q2 @ ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R ) @ one_one_int ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % neg_eucl_rel_int_mult_2
% 0.35/0.59  thf(fact_3447_low__def,axiom,
% 0.35/0.59      ( vEBT_VEBT_low
% 0.35/0.59      = ( ^ [X2: nat,N2: nat] : ( modulo_modulo_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % low_def
% 0.35/0.59  thf(fact_3448_obtain__set__succ,axiom,
% 0.35/0.59      ! [X: nat,Z: nat,A2: set_nat,B2: set_nat] :
% 0.35/0.59        ( ( ord_less_nat @ X @ Z )
% 0.35/0.59       => ( ( vEBT_VEBT_max_in_set @ A2 @ Z )
% 0.35/0.59         => ( ( finite_finite_nat @ B2 )
% 0.35/0.59           => ( ( A2 = B2 )
% 0.35/0.59             => ? [X_12: nat] : ( vEBT_is_succ_in_set @ A2 @ X @ X_12 ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % obtain_set_succ
% 0.35/0.59  thf(fact_3449_obtain__set__pred,axiom,
% 0.35/0.59      ! [Z: nat,X: nat,A2: set_nat] :
% 0.35/0.59        ( ( ord_less_nat @ Z @ X )
% 0.35/0.59       => ( ( vEBT_VEBT_min_in_set @ A2 @ Z )
% 0.35/0.59         => ( ( finite_finite_nat @ A2 )
% 0.35/0.59           => ? [X_12: nat] : ( vEBT_is_pred_in_set @ A2 @ X @ X_12 ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % obtain_set_pred
% 0.35/0.59  thf(fact_3450_set__vebt__finite,axiom,
% 0.35/0.59      ! [T: vEBT_VEBT,N: nat] :
% 0.35/0.59        ( ( vEBT_invar_vebt @ T @ N )
% 0.35/0.59       => ( finite_finite_nat @ ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % set_vebt_finite
% 0.35/0.59  thf(fact_3451_pred__none__empty,axiom,
% 0.35/0.59      ! [Xs2: set_nat,A: nat] :
% 0.35/0.59        ( ~ ? [X_12: nat] : ( vEBT_is_pred_in_set @ Xs2 @ A @ X_12 )
% 0.35/0.59       => ( ( finite_finite_nat @ Xs2 )
% 0.35/0.59         => ~ ? [X5: nat] :
% 0.35/0.59                ( ( member_nat @ X5 @ Xs2 )
% 0.35/0.59                & ( ord_less_nat @ X5 @ A ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % pred_none_empty
% 0.35/0.59  thf(fact_3452_succ__none__empty,axiom,
% 0.35/0.59      ! [Xs2: set_nat,A: nat] :
% 0.35/0.59        ( ~ ? [X_12: nat] : ( vEBT_is_succ_in_set @ Xs2 @ A @ X_12 )
% 0.35/0.59       => ( ( finite_finite_nat @ Xs2 )
% 0.35/0.59         => ~ ? [X5: nat] :
% 0.35/0.59                ( ( member_nat @ X5 @ Xs2 )
% 0.35/0.59                & ( ord_less_nat @ A @ X5 ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % succ_none_empty
% 0.35/0.59  thf(fact_3453_old_Oprod_Oinject,axiom,
% 0.35/0.59      ! [A: product_prod_nat_nat,B: product_prod_nat_nat,A5: product_prod_nat_nat,B5: product_prod_nat_nat] :
% 0.35/0.59        ( ( ( produc6161850002892822231at_nat @ A @ B )
% 0.35/0.59          = ( produc6161850002892822231at_nat @ A5 @ B5 ) )
% 0.35/0.59        = ( ( A = A5 )
% 0.35/0.59          & ( B = B5 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % old.prod.inject
% 0.35/0.59  thf(fact_3454_old_Oprod_Oinject,axiom,
% 0.35/0.59      ! [A: num,B: num,A5: num,B5: num] :
% 0.35/0.59        ( ( ( product_Pair_num_num @ A @ B )
% 0.35/0.59          = ( product_Pair_num_num @ A5 @ B5 ) )
% 0.35/0.59        = ( ( A = A5 )
% 0.35/0.59          & ( B = B5 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % old.prod.inject
% 0.35/0.59  thf(fact_3455_old_Oprod_Oinject,axiom,
% 0.35/0.59      ! [A: nat,B: num,A5: nat,B5: num] :
% 0.35/0.59        ( ( ( product_Pair_nat_num @ A @ B )
% 0.35/0.59          = ( product_Pair_nat_num @ A5 @ B5 ) )
% 0.35/0.59        = ( ( A = A5 )
% 0.35/0.59          & ( B = B5 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % old.prod.inject
% 0.35/0.59  thf(fact_3456_old_Oprod_Oinject,axiom,
% 0.35/0.59      ! [A: nat,B: nat,A5: nat,B5: nat] :
% 0.35/0.59        ( ( ( product_Pair_nat_nat @ A @ B )
% 0.35/0.59          = ( product_Pair_nat_nat @ A5 @ B5 ) )
% 0.35/0.59        = ( ( A = A5 )
% 0.35/0.59          & ( B = B5 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % old.prod.inject
% 0.35/0.59  thf(fact_3457_old_Oprod_Oinject,axiom,
% 0.35/0.59      ! [A: int,B: int,A5: int,B5: int] :
% 0.35/0.59        ( ( ( product_Pair_int_int @ A @ B )
% 0.35/0.59          = ( product_Pair_int_int @ A5 @ B5 ) )
% 0.35/0.59        = ( ( A = A5 )
% 0.35/0.59          & ( B = B5 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % old.prod.inject
% 0.35/0.59  thf(fact_3458_prod_Oinject,axiom,
% 0.35/0.59      ! [X1: product_prod_nat_nat,X23: product_prod_nat_nat,Y1: product_prod_nat_nat,Y22: product_prod_nat_nat] :
% 0.35/0.59        ( ( ( produc6161850002892822231at_nat @ X1 @ X23 )
% 0.35/0.59          = ( produc6161850002892822231at_nat @ Y1 @ Y22 ) )
% 0.35/0.59        = ( ( X1 = Y1 )
% 0.35/0.59          & ( X23 = Y22 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % prod.inject
% 0.35/0.59  thf(fact_3459_prod_Oinject,axiom,
% 0.35/0.59      ! [X1: num,X23: num,Y1: num,Y22: num] :
% 0.35/0.59        ( ( ( product_Pair_num_num @ X1 @ X23 )
% 0.35/0.59          = ( product_Pair_num_num @ Y1 @ Y22 ) )
% 0.35/0.59        = ( ( X1 = Y1 )
% 0.35/0.59          & ( X23 = Y22 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % prod.inject
% 0.35/0.59  thf(fact_3460_prod_Oinject,axiom,
% 0.35/0.59      ! [X1: nat,X23: num,Y1: nat,Y22: num] :
% 0.35/0.59        ( ( ( product_Pair_nat_num @ X1 @ X23 )
% 0.35/0.59          = ( product_Pair_nat_num @ Y1 @ Y22 ) )
% 0.35/0.59        = ( ( X1 = Y1 )
% 0.35/0.59          & ( X23 = Y22 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % prod.inject
% 0.35/0.59  thf(fact_3461_prod_Oinject,axiom,
% 0.35/0.59      ! [X1: nat,X23: nat,Y1: nat,Y22: nat] :
% 0.35/0.59        ( ( ( product_Pair_nat_nat @ X1 @ X23 )
% 0.35/0.59          = ( product_Pair_nat_nat @ Y1 @ Y22 ) )
% 0.35/0.59        = ( ( X1 = Y1 )
% 0.35/0.59          & ( X23 = Y22 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % prod.inject
% 0.35/0.59  thf(fact_3462_prod_Oinject,axiom,
% 0.35/0.59      ! [X1: int,X23: int,Y1: int,Y22: int] :
% 0.35/0.59        ( ( ( product_Pair_int_int @ X1 @ X23 )
% 0.35/0.59          = ( product_Pair_int_int @ Y1 @ Y22 ) )
% 0.35/0.59        = ( ( X1 = Y1 )
% 0.35/0.59          & ( X23 = Y22 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % prod.inject
% 0.35/0.59  thf(fact_3463_mod__mod__trivial,axiom,
% 0.35/0.59      ! [A: nat,B: nat] :
% 0.35/0.59        ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 0.35/0.59        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_mod_trivial
% 0.35/0.59  thf(fact_3464_mod__mod__trivial,axiom,
% 0.35/0.59      ! [A: int,B: int] :
% 0.35/0.59        ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 0.35/0.59        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_mod_trivial
% 0.35/0.59  thf(fact_3465_bits__mod__0,axiom,
% 0.35/0.59      ! [A: nat] :
% 0.35/0.59        ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 0.35/0.59        = zero_zero_nat ) ).
% 0.35/0.59  
% 0.35/0.59  % bits_mod_0
% 0.35/0.59  thf(fact_3466_bits__mod__0,axiom,
% 0.35/0.59      ! [A: int] :
% 0.35/0.59        ( ( modulo_modulo_int @ zero_zero_int @ A )
% 0.35/0.59        = zero_zero_int ) ).
% 0.35/0.59  
% 0.35/0.59  % bits_mod_0
% 0.35/0.59  thf(fact_3467_mod__add__self2,axiom,
% 0.35/0.59      ! [A: nat,B: nat] :
% 0.35/0.59        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.35/0.59        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_add_self2
% 0.35/0.59  thf(fact_3468_mod__add__self2,axiom,
% 0.35/0.59      ! [A: int,B: int] :
% 0.35/0.59        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.35/0.59        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_add_self2
% 0.35/0.59  thf(fact_3469_mod__add__self1,axiom,
% 0.35/0.59      ! [B: nat,A: nat] :
% 0.35/0.59        ( ( modulo_modulo_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.35/0.59        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_add_self1
% 0.35/0.59  thf(fact_3470_mod__add__self1,axiom,
% 0.35/0.59      ! [B: int,A: int] :
% 0.35/0.59        ( ( modulo_modulo_int @ ( plus_plus_int @ B @ A ) @ B )
% 0.35/0.59        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_add_self1
% 0.35/0.59  thf(fact_3471_List_Ofinite__set,axiom,
% 0.35/0.59      ! [Xs2: list_VEBT_VEBT] : ( finite5795047828879050333T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) ) ).
% 0.35/0.59  
% 0.35/0.59  % List.finite_set
% 0.35/0.59  thf(fact_3472_List_Ofinite__set,axiom,
% 0.35/0.59      ! [Xs2: list_int] : ( finite_finite_int @ ( set_int2 @ Xs2 ) ) ).
% 0.35/0.59  
% 0.35/0.59  % List.finite_set
% 0.35/0.59  thf(fact_3473_List_Ofinite__set,axiom,
% 0.35/0.59      ! [Xs2: list_nat] : ( finite_finite_nat @ ( set_nat2 @ Xs2 ) ) ).
% 0.35/0.59  
% 0.35/0.59  % List.finite_set
% 0.35/0.59  thf(fact_3474_List_Ofinite__set,axiom,
% 0.35/0.59      ! [Xs2: list_complex] : ( finite3207457112153483333omplex @ ( set_complex2 @ Xs2 ) ) ).
% 0.35/0.59  
% 0.35/0.59  % List.finite_set
% 0.35/0.59  thf(fact_3475_minus__mod__self2,axiom,
% 0.35/0.59      ! [A: int,B: int] :
% 0.35/0.59        ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ B )
% 0.35/0.59        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.35/0.59  
% 0.35/0.59  % minus_mod_self2
% 0.35/0.59  thf(fact_3476_mod__less,axiom,
% 0.35/0.59      ! [M: nat,N: nat] :
% 0.35/0.59        ( ( ord_less_nat @ M @ N )
% 0.35/0.59       => ( ( modulo_modulo_nat @ M @ N )
% 0.35/0.59          = M ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_less
% 0.35/0.59  thf(fact_3477_mod__mult__self2__is__0,axiom,
% 0.35/0.59      ! [A: nat,B: nat] :
% 0.35/0.59        ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ B )
% 0.35/0.59        = zero_zero_nat ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_mult_self2_is_0
% 0.35/0.59  thf(fact_3478_mod__mult__self2__is__0,axiom,
% 0.35/0.59      ! [A: int,B: int] :
% 0.35/0.59        ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ B )
% 0.35/0.59        = zero_zero_int ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_mult_self2_is_0
% 0.35/0.59  thf(fact_3479_mod__mult__self1__is__0,axiom,
% 0.35/0.59      ! [B: nat,A: nat] :
% 0.35/0.59        ( ( modulo_modulo_nat @ ( times_times_nat @ B @ A ) @ B )
% 0.35/0.59        = zero_zero_nat ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_mult_self1_is_0
% 0.35/0.59  thf(fact_3480_mod__mult__self1__is__0,axiom,
% 0.35/0.59      ! [B: int,A: int] :
% 0.35/0.59        ( ( modulo_modulo_int @ ( times_times_int @ B @ A ) @ B )
% 0.35/0.59        = zero_zero_int ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_mult_self1_is_0
% 0.35/0.59  thf(fact_3481_bits__mod__by__1,axiom,
% 0.35/0.59      ! [A: nat] :
% 0.35/0.59        ( ( modulo_modulo_nat @ A @ one_one_nat )
% 0.35/0.59        = zero_zero_nat ) ).
% 0.35/0.59  
% 0.35/0.59  % bits_mod_by_1
% 0.35/0.59  thf(fact_3482_bits__mod__by__1,axiom,
% 0.35/0.59      ! [A: int] :
% 0.35/0.59        ( ( modulo_modulo_int @ A @ one_one_int )
% 0.35/0.59        = zero_zero_int ) ).
% 0.35/0.59  
% 0.35/0.59  % bits_mod_by_1
% 0.35/0.59  thf(fact_3483_mod__by__1,axiom,
% 0.35/0.59      ! [A: nat] :
% 0.35/0.59        ( ( modulo_modulo_nat @ A @ one_one_nat )
% 0.35/0.59        = zero_zero_nat ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_by_1
% 0.35/0.59  thf(fact_3484_mod__by__1,axiom,
% 0.35/0.59      ! [A: int] :
% 0.35/0.59        ( ( modulo_modulo_int @ A @ one_one_int )
% 0.35/0.59        = zero_zero_int ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_by_1
% 0.35/0.59  thf(fact_3485_bits__mod__div__trivial,axiom,
% 0.35/0.59      ! [A: nat,B: nat] :
% 0.35/0.59        ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 0.35/0.59        = zero_zero_nat ) ).
% 0.35/0.59  
% 0.35/0.59  % bits_mod_div_trivial
% 0.35/0.59  thf(fact_3486_bits__mod__div__trivial,axiom,
% 0.35/0.59      ! [A: int,B: int] :
% 0.35/0.59        ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 0.35/0.59        = zero_zero_int ) ).
% 0.35/0.59  
% 0.35/0.59  % bits_mod_div_trivial
% 0.35/0.59  thf(fact_3487_mod__div__trivial,axiom,
% 0.35/0.59      ! [A: nat,B: nat] :
% 0.35/0.59        ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 0.35/0.59        = zero_zero_nat ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_div_trivial
% 0.35/0.59  thf(fact_3488_mod__div__trivial,axiom,
% 0.35/0.59      ! [A: int,B: int] :
% 0.35/0.59        ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 0.35/0.59        = zero_zero_int ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_div_trivial
% 0.35/0.59  thf(fact_3489_mod__mult__self4,axiom,
% 0.35/0.59      ! [B: nat,C: nat,A: nat] :
% 0.35/0.59        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 0.35/0.59        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_mult_self4
% 0.35/0.59  thf(fact_3490_mod__mult__self4,axiom,
% 0.35/0.59      ! [B: int,C: int,A: int] :
% 0.35/0.59        ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 0.35/0.59        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_mult_self4
% 0.35/0.59  thf(fact_3491_mod__mult__self3,axiom,
% 0.35/0.59      ! [C: nat,B: nat,A: nat] :
% 0.35/0.59        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 0.35/0.59        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_mult_self3
% 0.35/0.59  thf(fact_3492_mod__mult__self3,axiom,
% 0.35/0.59      ! [C: int,B: int,A: int] :
% 0.35/0.59        ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 0.35/0.59        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_mult_self3
% 0.35/0.59  thf(fact_3493_mod__mult__self2,axiom,
% 0.35/0.59      ! [A: nat,B: nat,C: nat] :
% 0.35/0.59        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 0.35/0.59        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_mult_self2
% 0.35/0.59  thf(fact_3494_mod__mult__self2,axiom,
% 0.35/0.59      ! [A: int,B: int,C: int] :
% 0.35/0.59        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 0.35/0.59        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_mult_self2
% 0.35/0.59  thf(fact_3495_mod__mult__self1,axiom,
% 0.35/0.59      ! [A: nat,C: nat,B: nat] :
% 0.35/0.59        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 0.35/0.59        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_mult_self1
% 0.35/0.59  thf(fact_3496_mod__mult__self1,axiom,
% 0.35/0.59      ! [A: int,C: int,B: int] :
% 0.35/0.59        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 0.35/0.59        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_mult_self1
% 0.35/0.59  thf(fact_3497_infinite__Icc__iff,axiom,
% 0.35/0.59      ! [A: rat,B: rat] :
% 0.35/0.59        ( ( ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) )
% 0.35/0.59        = ( ord_less_rat @ A @ B ) ) ).
% 0.35/0.59  
% 0.35/0.59  % infinite_Icc_iff
% 0.35/0.59  thf(fact_3498_infinite__Icc__iff,axiom,
% 0.35/0.59      ! [A: real,B: real] :
% 0.35/0.59        ( ( ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) )
% 0.35/0.59        = ( ord_less_real @ A @ B ) ) ).
% 0.35/0.59  
% 0.35/0.59  % infinite_Icc_iff
% 0.35/0.59  thf(fact_3499_mod__by__Suc__0,axiom,
% 0.35/0.59      ! [M: nat] :
% 0.35/0.59        ( ( modulo_modulo_nat @ M @ ( suc @ zero_zero_nat ) )
% 0.35/0.59        = zero_zero_nat ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_by_Suc_0
% 0.35/0.59  thf(fact_3500_Suc__mod__mult__self1,axiom,
% 0.35/0.59      ! [M: nat,K: nat,N: nat] :
% 0.35/0.59        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ K @ N ) ) ) @ N )
% 0.35/0.59        = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 0.35/0.59  
% 0.35/0.59  % Suc_mod_mult_self1
% 0.35/0.59  thf(fact_3501_Suc__mod__mult__self2,axiom,
% 0.35/0.59      ! [M: nat,N: nat,K: nat] :
% 0.35/0.59        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ N @ K ) ) ) @ N )
% 0.35/0.59        = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 0.35/0.59  
% 0.35/0.59  % Suc_mod_mult_self2
% 0.35/0.59  thf(fact_3502_Suc__mod__mult__self3,axiom,
% 0.35/0.59      ! [K: nat,N: nat,M: nat] :
% 0.35/0.59        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K @ N ) @ M ) ) @ N )
% 0.35/0.59        = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 0.35/0.59  
% 0.35/0.59  % Suc_mod_mult_self3
% 0.35/0.59  thf(fact_3503_Suc__mod__mult__self4,axiom,
% 0.35/0.59      ! [N: nat,K: nat,M: nat] :
% 0.35/0.59        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N @ K ) @ M ) ) @ N )
% 0.35/0.59        = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 0.35/0.59  
% 0.35/0.59  % Suc_mod_mult_self4
% 0.35/0.59  thf(fact_3504_bits__one__mod__two__eq__one,axiom,
% 0.35/0.59      ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.59      = one_one_nat ) ).
% 0.35/0.59  
% 0.35/0.59  % bits_one_mod_two_eq_one
% 0.35/0.59  thf(fact_3505_bits__one__mod__two__eq__one,axiom,
% 0.35/0.59      ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.59      = one_one_int ) ).
% 0.35/0.59  
% 0.35/0.59  % bits_one_mod_two_eq_one
% 0.35/0.59  thf(fact_3506_one__mod__two__eq__one,axiom,
% 0.35/0.59      ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.59      = one_one_nat ) ).
% 0.35/0.59  
% 0.35/0.59  % one_mod_two_eq_one
% 0.35/0.59  thf(fact_3507_one__mod__two__eq__one,axiom,
% 0.35/0.59      ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.59      = one_one_int ) ).
% 0.35/0.59  
% 0.35/0.59  % one_mod_two_eq_one
% 0.35/0.59  thf(fact_3508_mod2__Suc__Suc,axiom,
% 0.35/0.59      ! [M: nat] :
% 0.35/0.59        ( ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.59        = ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod2_Suc_Suc
% 0.35/0.59  thf(fact_3509_divmod__algorithm__code_I2_J,axiom,
% 0.35/0.59      ! [M: num] :
% 0.35/0.59        ( ( unique5055182867167087721od_nat @ M @ one )
% 0.35/0.59        = ( product_Pair_nat_nat @ ( numeral_numeral_nat @ M ) @ zero_zero_nat ) ) ).
% 0.35/0.59  
% 0.35/0.59  % divmod_algorithm_code(2)
% 0.35/0.59  thf(fact_3510_divmod__algorithm__code_I2_J,axiom,
% 0.35/0.59      ! [M: num] :
% 0.35/0.59        ( ( unique5052692396658037445od_int @ M @ one )
% 0.35/0.59        = ( product_Pair_int_int @ ( numeral_numeral_int @ M ) @ zero_zero_int ) ) ).
% 0.35/0.59  
% 0.35/0.59  % divmod_algorithm_code(2)
% 0.35/0.59  thf(fact_3511_Suc__times__numeral__mod__eq,axiom,
% 0.35/0.59      ! [K: num,N: nat] :
% 0.35/0.59        ( ( ( numeral_numeral_nat @ K )
% 0.35/0.59         != one_one_nat )
% 0.35/0.59       => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N ) ) @ ( numeral_numeral_nat @ K ) )
% 0.35/0.59          = one_one_nat ) ) ).
% 0.35/0.59  
% 0.35/0.59  % Suc_times_numeral_mod_eq
% 0.35/0.59  thf(fact_3512_not__mod__2__eq__1__eq__0,axiom,
% 0.35/0.59      ! [A: nat] :
% 0.35/0.59        ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.59         != one_one_nat )
% 0.35/0.59        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.59          = zero_zero_nat ) ) ).
% 0.35/0.59  
% 0.35/0.59  % not_mod_2_eq_1_eq_0
% 0.35/0.59  thf(fact_3513_not__mod__2__eq__1__eq__0,axiom,
% 0.35/0.59      ! [A: int] :
% 0.35/0.59        ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.59         != one_one_int )
% 0.35/0.59        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.59          = zero_zero_int ) ) ).
% 0.35/0.59  
% 0.35/0.59  % not_mod_2_eq_1_eq_0
% 0.35/0.59  thf(fact_3514_not__mod__2__eq__0__eq__1,axiom,
% 0.35/0.59      ! [A: nat] :
% 0.35/0.59        ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.59         != zero_zero_nat )
% 0.35/0.59        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.59          = one_one_nat ) ) ).
% 0.35/0.59  
% 0.35/0.59  % not_mod_2_eq_0_eq_1
% 0.35/0.59  thf(fact_3515_not__mod__2__eq__0__eq__1,axiom,
% 0.35/0.59      ! [A: int] :
% 0.35/0.59        ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.59         != zero_zero_int )
% 0.35/0.59        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.59          = one_one_int ) ) ).
% 0.35/0.59  
% 0.35/0.59  % not_mod_2_eq_0_eq_1
% 0.35/0.59  thf(fact_3516_not__mod2__eq__Suc__0__eq__0,axiom,
% 0.35/0.59      ! [N: nat] :
% 0.35/0.59        ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.59         != ( suc @ zero_zero_nat ) )
% 0.35/0.59        = ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.59          = zero_zero_nat ) ) ).
% 0.35/0.59  
% 0.35/0.59  % not_mod2_eq_Suc_0_eq_0
% 0.35/0.59  thf(fact_3517_add__self__mod__2,axiom,
% 0.35/0.59      ! [M: nat] :
% 0.35/0.59        ( ( modulo_modulo_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.59        = zero_zero_nat ) ).
% 0.35/0.59  
% 0.35/0.59  % add_self_mod_2
% 0.35/0.59  thf(fact_3518_divmod__algorithm__code_I3_J,axiom,
% 0.35/0.59      ! [N: num] :
% 0.35/0.59        ( ( unique5055182867167087721od_nat @ one @ ( bit0 @ N ) )
% 0.35/0.59        = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % divmod_algorithm_code(3)
% 0.35/0.59  thf(fact_3519_divmod__algorithm__code_I3_J,axiom,
% 0.35/0.59      ! [N: num] :
% 0.35/0.59        ( ( unique5052692396658037445od_int @ one @ ( bit0 @ N ) )
% 0.35/0.59        = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % divmod_algorithm_code(3)
% 0.35/0.59  thf(fact_3520_Suc__mod__eq__add3__mod__numeral,axiom,
% 0.35/0.59      ! [M: nat,V: num] :
% 0.35/0.59        ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 0.35/0.59        = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % Suc_mod_eq_add3_mod_numeral
% 0.35/0.59  thf(fact_3521_mod__Suc__eq__mod__add3,axiom,
% 0.35/0.59      ! [M: nat,N: nat] :
% 0.35/0.59        ( ( modulo_modulo_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 0.35/0.59        = ( modulo_modulo_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_Suc_eq_mod_add3
% 0.35/0.59  thf(fact_3522_divmod__algorithm__code_I4_J,axiom,
% 0.35/0.59      ! [N: num] :
% 0.35/0.59        ( ( unique5055182867167087721od_nat @ one @ ( bit1 @ N ) )
% 0.35/0.59        = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % divmod_algorithm_code(4)
% 0.35/0.59  thf(fact_3523_divmod__algorithm__code_I4_J,axiom,
% 0.35/0.59      ! [N: num] :
% 0.35/0.59        ( ( unique5052692396658037445od_int @ one @ ( bit1 @ N ) )
% 0.35/0.59        = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % divmod_algorithm_code(4)
% 0.35/0.59  thf(fact_3524_mod2__gr__0,axiom,
% 0.35/0.59      ! [M: nat] :
% 0.35/0.59        ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.59        = ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.59          = one_one_nat ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod2_gr_0
% 0.35/0.59  thf(fact_3525_unique__quotient,axiom,
% 0.35/0.59      ! [A: int,B: int,Q2: int,R: int,Q5: int,R4: int] :
% 0.35/0.59        ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 0.35/0.59       => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q5 @ R4 ) )
% 0.35/0.59         => ( Q2 = Q5 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % unique_quotient
% 0.35/0.59  thf(fact_3526_unique__remainder,axiom,
% 0.35/0.59      ! [A: int,B: int,Q2: int,R: int,Q5: int,R4: int] :
% 0.35/0.59        ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 0.35/0.59       => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q5 @ R4 ) )
% 0.35/0.59         => ( R = R4 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % unique_remainder
% 0.35/0.59  thf(fact_3527_mod__mult__eq,axiom,
% 0.35/0.59      ! [A: nat,C: nat,B: nat] :
% 0.35/0.59        ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 0.35/0.59        = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_mult_eq
% 0.35/0.59  thf(fact_3528_mod__mult__eq,axiom,
% 0.35/0.59      ! [A: int,C: int,B: int] :
% 0.35/0.59        ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 0.35/0.59        = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_mult_eq
% 0.35/0.59  thf(fact_3529_mod__mult__cong,axiom,
% 0.35/0.59      ! [A: nat,C: nat,A5: nat,B: nat,B5: nat] :
% 0.35/0.59        ( ( ( modulo_modulo_nat @ A @ C )
% 0.35/0.59          = ( modulo_modulo_nat @ A5 @ C ) )
% 0.35/0.59       => ( ( ( modulo_modulo_nat @ B @ C )
% 0.35/0.59            = ( modulo_modulo_nat @ B5 @ C ) )
% 0.35/0.59         => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.35/0.59            = ( modulo_modulo_nat @ ( times_times_nat @ A5 @ B5 ) @ C ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_mult_cong
% 0.35/0.59  thf(fact_3530_mod__mult__cong,axiom,
% 0.35/0.59      ! [A: int,C: int,A5: int,B: int,B5: int] :
% 0.35/0.59        ( ( ( modulo_modulo_int @ A @ C )
% 0.35/0.59          = ( modulo_modulo_int @ A5 @ C ) )
% 0.35/0.59       => ( ( ( modulo_modulo_int @ B @ C )
% 0.35/0.59            = ( modulo_modulo_int @ B5 @ C ) )
% 0.35/0.59         => ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C )
% 0.35/0.59            = ( modulo_modulo_int @ ( times_times_int @ A5 @ B5 ) @ C ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_mult_cong
% 0.35/0.59  thf(fact_3531_mod__mult__mult2,axiom,
% 0.35/0.59      ! [A: nat,C: nat,B: nat] :
% 0.35/0.59        ( ( modulo_modulo_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 0.35/0.59        = ( times_times_nat @ ( modulo_modulo_nat @ A @ B ) @ C ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_mult_mult2
% 0.35/0.59  thf(fact_3532_mod__mult__mult2,axiom,
% 0.35/0.59      ! [A: int,C: int,B: int] :
% 0.35/0.59        ( ( modulo_modulo_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.35/0.59        = ( times_times_int @ ( modulo_modulo_int @ A @ B ) @ C ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_mult_mult2
% 0.35/0.59  thf(fact_3533_mult__mod__right,axiom,
% 0.35/0.59      ! [C: nat,A: nat,B: nat] :
% 0.35/0.59        ( ( times_times_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 0.35/0.59        = ( modulo_modulo_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mult_mod_right
% 0.35/0.59  thf(fact_3534_mult__mod__right,axiom,
% 0.35/0.59      ! [C: int,A: int,B: int] :
% 0.35/0.59        ( ( times_times_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 0.35/0.59        = ( modulo_modulo_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mult_mod_right
% 0.35/0.59  thf(fact_3535_mod__mult__left__eq,axiom,
% 0.35/0.59      ! [A: nat,C: nat,B: nat] :
% 0.35/0.59        ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 0.35/0.59        = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_mult_left_eq
% 0.35/0.59  thf(fact_3536_mod__mult__left__eq,axiom,
% 0.35/0.59      ! [A: int,C: int,B: int] :
% 0.35/0.59        ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 0.35/0.59        = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_mult_left_eq
% 0.35/0.59  thf(fact_3537_mod__mult__right__eq,axiom,
% 0.35/0.59      ! [A: nat,B: nat,C: nat] :
% 0.35/0.59        ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 0.35/0.59        = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_mult_right_eq
% 0.35/0.59  thf(fact_3538_mod__mult__right__eq,axiom,
% 0.35/0.59      ! [A: int,B: int,C: int] :
% 0.35/0.59        ( ( modulo_modulo_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 0.35/0.59        = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_mult_right_eq
% 0.35/0.59  thf(fact_3539_mod__add__right__eq,axiom,
% 0.35/0.59      ! [A: nat,B: nat,C: nat] :
% 0.35/0.59        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 0.35/0.59        = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_add_right_eq
% 0.35/0.59  thf(fact_3540_mod__add__right__eq,axiom,
% 0.35/0.59      ! [A: int,B: int,C: int] :
% 0.35/0.59        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 0.35/0.59        = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_add_right_eq
% 0.35/0.59  thf(fact_3541_mod__add__left__eq,axiom,
% 0.35/0.59      ! [A: nat,C: nat,B: nat] :
% 0.35/0.59        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 0.35/0.59        = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_add_left_eq
% 0.35/0.59  thf(fact_3542_mod__add__left__eq,axiom,
% 0.35/0.59      ! [A: int,C: int,B: int] :
% 0.35/0.59        ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 0.35/0.59        = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_add_left_eq
% 0.35/0.59  thf(fact_3543_mod__add__cong,axiom,
% 0.35/0.59      ! [A: nat,C: nat,A5: nat,B: nat,B5: nat] :
% 0.35/0.59        ( ( ( modulo_modulo_nat @ A @ C )
% 0.35/0.59          = ( modulo_modulo_nat @ A5 @ C ) )
% 0.35/0.59       => ( ( ( modulo_modulo_nat @ B @ C )
% 0.35/0.59            = ( modulo_modulo_nat @ B5 @ C ) )
% 0.35/0.59         => ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.35/0.59            = ( modulo_modulo_nat @ ( plus_plus_nat @ A5 @ B5 ) @ C ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_add_cong
% 0.35/0.59  thf(fact_3544_mod__add__cong,axiom,
% 0.35/0.59      ! [A: int,C: int,A5: int,B: int,B5: int] :
% 0.35/0.59        ( ( ( modulo_modulo_int @ A @ C )
% 0.35/0.59          = ( modulo_modulo_int @ A5 @ C ) )
% 0.35/0.59       => ( ( ( modulo_modulo_int @ B @ C )
% 0.35/0.59            = ( modulo_modulo_int @ B5 @ C ) )
% 0.35/0.59         => ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.35/0.59            = ( modulo_modulo_int @ ( plus_plus_int @ A5 @ B5 ) @ C ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_add_cong
% 0.35/0.59  thf(fact_3545_mod__add__eq,axiom,
% 0.35/0.59      ! [A: nat,C: nat,B: nat] :
% 0.35/0.59        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 0.35/0.59        = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_add_eq
% 0.35/0.59  thf(fact_3546_mod__add__eq,axiom,
% 0.35/0.59      ! [A: int,C: int,B: int] :
% 0.35/0.59        ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 0.35/0.59        = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_add_eq
% 0.35/0.59  thf(fact_3547_mod__diff__right__eq,axiom,
% 0.35/0.59      ! [A: int,B: int,C: int] :
% 0.35/0.59        ( ( modulo_modulo_int @ ( minus_minus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 0.35/0.59        = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_diff_right_eq
% 0.35/0.59  thf(fact_3548_mod__diff__left__eq,axiom,
% 0.35/0.59      ! [A: int,C: int,B: int] :
% 0.35/0.59        ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 0.35/0.59        = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_diff_left_eq
% 0.35/0.59  thf(fact_3549_mod__diff__cong,axiom,
% 0.35/0.59      ! [A: int,C: int,A5: int,B: int,B5: int] :
% 0.35/0.59        ( ( ( modulo_modulo_int @ A @ C )
% 0.35/0.59          = ( modulo_modulo_int @ A5 @ C ) )
% 0.35/0.59       => ( ( ( modulo_modulo_int @ B @ C )
% 0.35/0.59            = ( modulo_modulo_int @ B5 @ C ) )
% 0.35/0.59         => ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.35/0.59            = ( modulo_modulo_int @ ( minus_minus_int @ A5 @ B5 ) @ C ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_diff_cong
% 0.35/0.59  thf(fact_3550_mod__diff__eq,axiom,
% 0.35/0.59      ! [A: int,C: int,B: int] :
% 0.35/0.59        ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 0.35/0.59        = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_diff_eq
% 0.35/0.59  thf(fact_3551_power__mod,axiom,
% 0.35/0.59      ! [A: nat,B: nat,N: nat] :
% 0.35/0.59        ( ( modulo_modulo_nat @ ( power_power_nat @ ( modulo_modulo_nat @ A @ B ) @ N ) @ B )
% 0.35/0.59        = ( modulo_modulo_nat @ ( power_power_nat @ A @ N ) @ B ) ) ).
% 0.35/0.59  
% 0.35/0.59  % power_mod
% 0.35/0.59  thf(fact_3552_power__mod,axiom,
% 0.35/0.59      ! [A: int,B: int,N: nat] :
% 0.35/0.59        ( ( modulo_modulo_int @ ( power_power_int @ ( modulo_modulo_int @ A @ B ) @ N ) @ B )
% 0.35/0.59        = ( modulo_modulo_int @ ( power_power_int @ A @ N ) @ B ) ) ).
% 0.35/0.59  
% 0.35/0.59  % power_mod
% 0.35/0.59  thf(fact_3553_mod__Suc__Suc__eq,axiom,
% 0.35/0.59      ! [M: nat,N: nat] :
% 0.35/0.59        ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) @ N )
% 0.35/0.59        = ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ N ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_Suc_Suc_eq
% 0.35/0.59  thf(fact_3554_mod__Suc__eq,axiom,
% 0.35/0.59      ! [M: nat,N: nat] :
% 0.35/0.59        ( ( modulo_modulo_nat @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) @ N )
% 0.35/0.59        = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_Suc_eq
% 0.35/0.59  thf(fact_3555_mod__less__eq__dividend,axiom,
% 0.35/0.59      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ M ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_less_eq_dividend
% 0.35/0.59  thf(fact_3556_bounded__nat__set__is__finite,axiom,
% 0.35/0.59      ! [N4: set_nat,N: nat] :
% 0.35/0.59        ( ! [X3: nat] :
% 0.35/0.59            ( ( member_nat @ X3 @ N4 )
% 0.35/0.59           => ( ord_less_nat @ X3 @ N ) )
% 0.35/0.59       => ( finite_finite_nat @ N4 ) ) ).
% 0.35/0.59  
% 0.35/0.59  % bounded_nat_set_is_finite
% 0.35/0.59  thf(fact_3557_finite__nat__set__iff__bounded,axiom,
% 0.35/0.59      ( finite_finite_nat
% 0.35/0.59      = ( ^ [N6: set_nat] :
% 0.35/0.59          ? [M6: nat] :
% 0.35/0.59          ! [X2: nat] :
% 0.35/0.59            ( ( member_nat @ X2 @ N6 )
% 0.35/0.59           => ( ord_less_nat @ X2 @ M6 ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_nat_set_iff_bounded
% 0.35/0.59  thf(fact_3558_finite__nat__set__iff__bounded__le,axiom,
% 0.35/0.59      ( finite_finite_nat
% 0.35/0.59      = ( ^ [N6: set_nat] :
% 0.35/0.59          ? [M6: nat] :
% 0.35/0.59          ! [X2: nat] :
% 0.35/0.59            ( ( member_nat @ X2 @ N6 )
% 0.35/0.59           => ( ord_less_eq_nat @ X2 @ M6 ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_nat_set_iff_bounded_le
% 0.35/0.59  thf(fact_3559_finite__list,axiom,
% 0.35/0.59      ! [A2: set_VEBT_VEBT] :
% 0.35/0.59        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.35/0.59       => ? [Xs3: list_VEBT_VEBT] :
% 0.35/0.59            ( ( set_VEBT_VEBT2 @ Xs3 )
% 0.35/0.59            = A2 ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_list
% 0.35/0.59  thf(fact_3560_finite__list,axiom,
% 0.35/0.59      ! [A2: set_int] :
% 0.35/0.59        ( ( finite_finite_int @ A2 )
% 0.35/0.59       => ? [Xs3: list_int] :
% 0.35/0.59            ( ( set_int2 @ Xs3 )
% 0.35/0.59            = A2 ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_list
% 0.35/0.59  thf(fact_3561_finite__list,axiom,
% 0.35/0.59      ! [A2: set_nat] :
% 0.35/0.59        ( ( finite_finite_nat @ A2 )
% 0.35/0.59       => ? [Xs3: list_nat] :
% 0.35/0.59            ( ( set_nat2 @ Xs3 )
% 0.35/0.59            = A2 ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_list
% 0.35/0.59  thf(fact_3562_finite__list,axiom,
% 0.35/0.59      ! [A2: set_complex] :
% 0.35/0.59        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.59       => ? [Xs3: list_complex] :
% 0.35/0.59            ( ( set_complex2 @ Xs3 )
% 0.35/0.59            = A2 ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_list
% 0.35/0.59  thf(fact_3563_finite__M__bounded__by__nat,axiom,
% 0.35/0.59      ! [P: nat > $o,I2: nat] :
% 0.35/0.59        ( finite_finite_nat
% 0.35/0.59        @ ( collect_nat
% 0.35/0.59          @ ^ [K3: nat] :
% 0.35/0.59              ( ( P @ K3 )
% 0.35/0.59              & ( ord_less_nat @ K3 @ I2 ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_M_bounded_by_nat
% 0.35/0.59  thf(fact_3564_finite__less__ub,axiom,
% 0.35/0.59      ! [F: nat > nat,U: nat] :
% 0.35/0.59        ( ! [N3: nat] : ( ord_less_eq_nat @ N3 @ ( F @ N3 ) )
% 0.35/0.59       => ( finite_finite_nat
% 0.35/0.59          @ ( collect_nat
% 0.35/0.59            @ ^ [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ U ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_less_ub
% 0.35/0.59  thf(fact_3565_divmod__def,axiom,
% 0.35/0.59      ( unique5055182867167087721od_nat
% 0.35/0.59      = ( ^ [M6: num,N2: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N2 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % divmod_def
% 0.35/0.59  thf(fact_3566_divmod__def,axiom,
% 0.35/0.59      ( unique5052692396658037445od_int
% 0.35/0.59      = ( ^ [M6: num,N2: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N2 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % divmod_def
% 0.35/0.59  thf(fact_3567_divmod_H__nat__def,axiom,
% 0.35/0.59      ( unique5055182867167087721od_nat
% 0.35/0.59      = ( ^ [M6: num,N2: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N2 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % divmod'_nat_def
% 0.35/0.59  thf(fact_3568_finite__lists__length__eq,axiom,
% 0.35/0.59      ! [A2: set_complex,N: nat] :
% 0.35/0.59        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.59       => ( finite8712137658972009173omplex
% 0.35/0.59          @ ( collect_list_complex
% 0.35/0.59            @ ^ [Xs: list_complex] :
% 0.35/0.59                ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A2 )
% 0.35/0.59                & ( ( size_s3451745648224563538omplex @ Xs )
% 0.35/0.59                  = N ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_lists_length_eq
% 0.35/0.59  thf(fact_3569_finite__lists__length__eq,axiom,
% 0.35/0.59      ! [A2: set_VEBT_VEBT,N: nat] :
% 0.35/0.59        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.35/0.59       => ( finite3004134309566078307T_VEBT
% 0.35/0.59          @ ( collec5608196760682091941T_VEBT
% 0.35/0.59            @ ^ [Xs: list_VEBT_VEBT] :
% 0.35/0.59                ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A2 )
% 0.35/0.59                & ( ( size_s6755466524823107622T_VEBT @ Xs )
% 0.35/0.59                  = N ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_lists_length_eq
% 0.35/0.59  thf(fact_3570_finite__lists__length__eq,axiom,
% 0.35/0.59      ! [A2: set_o,N: nat] :
% 0.35/0.59        ( ( finite_finite_o @ A2 )
% 0.35/0.59       => ( finite_finite_list_o
% 0.35/0.59          @ ( collect_list_o
% 0.35/0.59            @ ^ [Xs: list_o] :
% 0.35/0.59                ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A2 )
% 0.35/0.59                & ( ( size_size_list_o @ Xs )
% 0.35/0.59                  = N ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_lists_length_eq
% 0.35/0.59  thf(fact_3571_finite__lists__length__eq,axiom,
% 0.35/0.59      ! [A2: set_int,N: nat] :
% 0.35/0.59        ( ( finite_finite_int @ A2 )
% 0.35/0.59       => ( finite3922522038869484883st_int
% 0.35/0.59          @ ( collect_list_int
% 0.35/0.59            @ ^ [Xs: list_int] :
% 0.35/0.59                ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A2 )
% 0.35/0.59                & ( ( size_size_list_int @ Xs )
% 0.35/0.59                  = N ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_lists_length_eq
% 0.35/0.59  thf(fact_3572_finite__lists__length__eq,axiom,
% 0.35/0.59      ! [A2: set_real,N: nat] :
% 0.35/0.59        ( ( finite_finite_real @ A2 )
% 0.35/0.59       => ( finite306553202115118035t_real
% 0.35/0.59          @ ( collect_list_real
% 0.35/0.59            @ ^ [Xs: list_real] :
% 0.35/0.59                ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ A2 )
% 0.35/0.59                & ( ( size_size_list_real @ Xs )
% 0.35/0.59                  = N ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_lists_length_eq
% 0.35/0.59  thf(fact_3573_finite__lists__length__eq,axiom,
% 0.35/0.59      ! [A2: set_nat,N: nat] :
% 0.35/0.59        ( ( finite_finite_nat @ A2 )
% 0.35/0.59       => ( finite8100373058378681591st_nat
% 0.35/0.59          @ ( collect_list_nat
% 0.35/0.59            @ ^ [Xs: list_nat] :
% 0.35/0.59                ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A2 )
% 0.35/0.59                & ( ( size_size_list_nat @ Xs )
% 0.35/0.59                  = N ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_lists_length_eq
% 0.35/0.59  thf(fact_3574_eucl__rel__int__by0,axiom,
% 0.35/0.59      ! [K: int] : ( eucl_rel_int @ K @ zero_zero_int @ ( product_Pair_int_int @ zero_zero_int @ K ) ) ).
% 0.35/0.59  
% 0.35/0.59  % eucl_rel_int_by0
% 0.35/0.59  thf(fact_3575_div__int__unique,axiom,
% 0.35/0.59      ! [K: int,L2: int,Q2: int,R: int] :
% 0.35/0.59        ( ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R ) )
% 0.35/0.59       => ( ( divide_divide_int @ K @ L2 )
% 0.35/0.59          = Q2 ) ) ).
% 0.35/0.59  
% 0.35/0.59  % div_int_unique
% 0.35/0.59  thf(fact_3576_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 0.35/0.59      ! [A: nat,B: nat] :
% 0.35/0.59        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.35/0.59       => ( ord_less_eq_nat @ ( modulo_modulo_nat @ A @ B ) @ A ) ) ).
% 0.35/0.59  
% 0.35/0.59  % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 0.35/0.59  thf(fact_3577_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 0.35/0.59      ! [A: int,B: int] :
% 0.35/0.59        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.35/0.59       => ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ A ) ) ).
% 0.35/0.59  
% 0.35/0.59  % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 0.35/0.59  thf(fact_3578_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 0.35/0.59      ! [B: nat,A: nat] :
% 0.35/0.59        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.35/0.59       => ( ord_less_nat @ ( modulo_modulo_nat @ A @ B ) @ B ) ) ).
% 0.35/0.59  
% 0.35/0.59  % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 0.35/0.59  thf(fact_3579_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 0.35/0.59      ! [B: int,A: int] :
% 0.35/0.59        ( ( ord_less_int @ zero_zero_int @ B )
% 0.35/0.59       => ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ).
% 0.35/0.59  
% 0.35/0.59  % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 0.35/0.59  thf(fact_3580_cong__exp__iff__simps_I9_J,axiom,
% 0.35/0.59      ! [M: num,Q2: num,N: num] :
% 0.35/0.59        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 0.35/0.59          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 0.35/0.59        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 0.35/0.59          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % cong_exp_iff_simps(9)
% 0.35/0.59  thf(fact_3581_cong__exp__iff__simps_I9_J,axiom,
% 0.35/0.59      ! [M: num,Q2: num,N: num] :
% 0.35/0.59        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 0.35/0.59          = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 0.35/0.59        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 0.35/0.59          = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % cong_exp_iff_simps(9)
% 0.35/0.59  thf(fact_3582_cong__exp__iff__simps_I4_J,axiom,
% 0.35/0.59      ! [M: num,N: num] :
% 0.35/0.59        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ one ) )
% 0.35/0.59        = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % cong_exp_iff_simps(4)
% 0.35/0.59  thf(fact_3583_cong__exp__iff__simps_I4_J,axiom,
% 0.35/0.59      ! [M: num,N: num] :
% 0.35/0.59        ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ one ) )
% 0.35/0.59        = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % cong_exp_iff_simps(4)
% 0.35/0.59  thf(fact_3584_mod__eq__self__iff__div__eq__0,axiom,
% 0.35/0.59      ! [A: nat,B: nat] :
% 0.35/0.59        ( ( ( modulo_modulo_nat @ A @ B )
% 0.35/0.59          = A )
% 0.35/0.59        = ( ( divide_divide_nat @ A @ B )
% 0.35/0.59          = zero_zero_nat ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_eq_self_iff_div_eq_0
% 0.35/0.59  thf(fact_3585_mod__eq__self__iff__div__eq__0,axiom,
% 0.35/0.59      ! [A: int,B: int] :
% 0.35/0.59        ( ( ( modulo_modulo_int @ A @ B )
% 0.35/0.59          = A )
% 0.35/0.59        = ( ( divide_divide_int @ A @ B )
% 0.35/0.59          = zero_zero_int ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_eq_self_iff_div_eq_0
% 0.35/0.59  thf(fact_3586_mod__eqE,axiom,
% 0.35/0.59      ! [A: int,C: int,B: int] :
% 0.35/0.59        ( ( ( modulo_modulo_int @ A @ C )
% 0.35/0.59          = ( modulo_modulo_int @ B @ C ) )
% 0.35/0.59       => ~ ! [D3: int] :
% 0.35/0.59              ( B
% 0.35/0.59             != ( plus_plus_int @ A @ ( times_times_int @ C @ D3 ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_eqE
% 0.35/0.59  thf(fact_3587_div__add1__eq,axiom,
% 0.35/0.59      ! [A: nat,B: nat,C: nat] :
% 0.35/0.59        ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.35/0.59        = ( plus_plus_nat @ ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % div_add1_eq
% 0.35/0.59  thf(fact_3588_div__add1__eq,axiom,
% 0.35/0.59      ! [A: int,B: int,C: int] :
% 0.35/0.59        ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.35/0.59        = ( plus_plus_int @ ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) @ ( divide_divide_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % div_add1_eq
% 0.35/0.59  thf(fact_3589_mod__Suc,axiom,
% 0.35/0.59      ! [M: nat,N: nat] :
% 0.35/0.59        ( ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 0.35/0.59            = N )
% 0.35/0.59         => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 0.35/0.59            = zero_zero_nat ) )
% 0.35/0.59        & ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 0.35/0.59           != N )
% 0.35/0.59         => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 0.35/0.59            = ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_Suc
% 0.35/0.59  thf(fact_3590_mod__induct,axiom,
% 0.35/0.59      ! [P: nat > $o,N: nat,P6: nat,M: nat] :
% 0.35/0.59        ( ( P @ N )
% 0.35/0.59       => ( ( ord_less_nat @ N @ P6 )
% 0.35/0.59         => ( ( ord_less_nat @ M @ P6 )
% 0.35/0.59           => ( ! [N3: nat] :
% 0.35/0.59                  ( ( ord_less_nat @ N3 @ P6 )
% 0.35/0.59                 => ( ( P @ N3 )
% 0.35/0.59                   => ( P @ ( modulo_modulo_nat @ ( suc @ N3 ) @ P6 ) ) ) )
% 0.35/0.59             => ( P @ M ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_induct
% 0.35/0.59  thf(fact_3591_mod__less__divisor,axiom,
% 0.35/0.59      ! [N: nat,M: nat] :
% 0.35/0.59        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.59       => ( ord_less_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_less_divisor
% 0.35/0.59  thf(fact_3592_mod__Suc__le__divisor,axiom,
% 0.35/0.59      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ ( suc @ N ) ) @ N ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_Suc_le_divisor
% 0.35/0.59  thf(fact_3593_mod__eq__0D,axiom,
% 0.35/0.59      ! [M: nat,D2: nat] :
% 0.35/0.59        ( ( ( modulo_modulo_nat @ M @ D2 )
% 0.35/0.59          = zero_zero_nat )
% 0.35/0.59       => ? [Q3: nat] :
% 0.35/0.59            ( M
% 0.35/0.59            = ( times_times_nat @ D2 @ Q3 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_eq_0D
% 0.35/0.59  thf(fact_3594_mod__if,axiom,
% 0.35/0.59      ( modulo_modulo_nat
% 0.35/0.59      = ( ^ [M6: nat,N2: nat] : ( if_nat @ ( ord_less_nat @ M6 @ N2 ) @ M6 @ ( modulo_modulo_nat @ ( minus_minus_nat @ M6 @ N2 ) @ N2 ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_if
% 0.35/0.59  thf(fact_3595_mod__geq,axiom,
% 0.35/0.59      ! [M: nat,N: nat] :
% 0.35/0.59        ( ~ ( ord_less_nat @ M @ N )
% 0.35/0.59       => ( ( modulo_modulo_nat @ M @ N )
% 0.35/0.59          = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_geq
% 0.35/0.59  thf(fact_3596_nat__mod__eq__iff,axiom,
% 0.35/0.59      ! [X: nat,N: nat,Y2: nat] :
% 0.35/0.59        ( ( ( modulo_modulo_nat @ X @ N )
% 0.35/0.59          = ( modulo_modulo_nat @ Y2 @ N ) )
% 0.35/0.59        = ( ? [Q1: nat,Q22: nat] :
% 0.35/0.59              ( ( plus_plus_nat @ X @ ( times_times_nat @ N @ Q1 ) )
% 0.35/0.59              = ( plus_plus_nat @ Y2 @ ( times_times_nat @ N @ Q22 ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % nat_mod_eq_iff
% 0.35/0.59  thf(fact_3597_le__mod__geq,axiom,
% 0.35/0.59      ! [N: nat,M: nat] :
% 0.35/0.59        ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.59       => ( ( modulo_modulo_nat @ M @ N )
% 0.35/0.59          = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % le_mod_geq
% 0.35/0.59  thf(fact_3598_infinite__Icc,axiom,
% 0.35/0.59      ! [A: rat,B: rat] :
% 0.35/0.59        ( ( ord_less_rat @ A @ B )
% 0.35/0.59       => ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % infinite_Icc
% 0.35/0.59  thf(fact_3599_infinite__Icc,axiom,
% 0.35/0.59      ! [A: real,B: real] :
% 0.35/0.59        ( ( ord_less_real @ A @ B )
% 0.35/0.59       => ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % infinite_Icc
% 0.35/0.59  thf(fact_3600_finite__lists__length__le,axiom,
% 0.35/0.59      ! [A2: set_complex,N: nat] :
% 0.35/0.59        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.59       => ( finite8712137658972009173omplex
% 0.35/0.59          @ ( collect_list_complex
% 0.35/0.59            @ ^ [Xs: list_complex] :
% 0.35/0.59                ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A2 )
% 0.35/0.59                & ( ord_less_eq_nat @ ( size_s3451745648224563538omplex @ Xs ) @ N ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_lists_length_le
% 0.35/0.59  thf(fact_3601_finite__lists__length__le,axiom,
% 0.35/0.59      ! [A2: set_VEBT_VEBT,N: nat] :
% 0.35/0.59        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.35/0.59       => ( finite3004134309566078307T_VEBT
% 0.35/0.59          @ ( collec5608196760682091941T_VEBT
% 0.35/0.59            @ ^ [Xs: list_VEBT_VEBT] :
% 0.35/0.59                ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A2 )
% 0.35/0.59                & ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ N ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_lists_length_le
% 0.35/0.59  thf(fact_3602_finite__lists__length__le,axiom,
% 0.35/0.59      ! [A2: set_o,N: nat] :
% 0.35/0.59        ( ( finite_finite_o @ A2 )
% 0.35/0.59       => ( finite_finite_list_o
% 0.35/0.59          @ ( collect_list_o
% 0.35/0.59            @ ^ [Xs: list_o] :
% 0.35/0.59                ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A2 )
% 0.35/0.59                & ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ N ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_lists_length_le
% 0.35/0.59  thf(fact_3603_finite__lists__length__le,axiom,
% 0.35/0.59      ! [A2: set_int,N: nat] :
% 0.35/0.59        ( ( finite_finite_int @ A2 )
% 0.35/0.59       => ( finite3922522038869484883st_int
% 0.35/0.59          @ ( collect_list_int
% 0.35/0.59            @ ^ [Xs: list_int] :
% 0.35/0.59                ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A2 )
% 0.35/0.59                & ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ N ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_lists_length_le
% 0.35/0.59  thf(fact_3604_finite__lists__length__le,axiom,
% 0.35/0.59      ! [A2: set_real,N: nat] :
% 0.35/0.59        ( ( finite_finite_real @ A2 )
% 0.35/0.59       => ( finite306553202115118035t_real
% 0.35/0.59          @ ( collect_list_real
% 0.35/0.59            @ ^ [Xs: list_real] :
% 0.35/0.59                ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ A2 )
% 0.35/0.59                & ( ord_less_eq_nat @ ( size_size_list_real @ Xs ) @ N ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_lists_length_le
% 0.35/0.59  thf(fact_3605_finite__lists__length__le,axiom,
% 0.35/0.59      ! [A2: set_nat,N: nat] :
% 0.35/0.59        ( ( finite_finite_nat @ A2 )
% 0.35/0.59       => ( finite8100373058378681591st_nat
% 0.35/0.59          @ ( collect_list_nat
% 0.35/0.59            @ ^ [Xs: list_nat] :
% 0.35/0.59                ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A2 )
% 0.35/0.59                & ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ N ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_lists_length_le
% 0.35/0.59  thf(fact_3606_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 0.35/0.59      ! [A: nat,B: nat] :
% 0.35/0.59        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.35/0.59       => ( ( ord_less_nat @ A @ B )
% 0.35/0.59         => ( ( modulo_modulo_nat @ A @ B )
% 0.35/0.59            = A ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % unique_euclidean_semiring_numeral_class.mod_less
% 0.35/0.59  thf(fact_3607_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 0.35/0.59      ! [A: int,B: int] :
% 0.35/0.59        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.35/0.59       => ( ( ord_less_int @ A @ B )
% 0.35/0.59         => ( ( modulo_modulo_int @ A @ B )
% 0.35/0.59            = A ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % unique_euclidean_semiring_numeral_class.mod_less
% 0.35/0.59  thf(fact_3608_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 0.35/0.59      ! [B: nat,A: nat] :
% 0.35/0.59        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.35/0.59       => ( ord_less_eq_nat @ zero_zero_nat @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 0.35/0.59  thf(fact_3609_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 0.35/0.59      ! [B: int,A: int] :
% 0.35/0.59        ( ( ord_less_int @ zero_zero_int @ B )
% 0.35/0.59       => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 0.35/0.59  thf(fact_3610_cong__exp__iff__simps_I2_J,axiom,
% 0.35/0.59      ! [N: num,Q2: num] :
% 0.35/0.59        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 0.35/0.59          = zero_zero_nat )
% 0.35/0.59        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) )
% 0.35/0.59          = zero_zero_nat ) ) ).
% 0.35/0.59  
% 0.35/0.59  % cong_exp_iff_simps(2)
% 0.35/0.59  thf(fact_3611_cong__exp__iff__simps_I2_J,axiom,
% 0.35/0.59      ! [N: num,Q2: num] :
% 0.35/0.59        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 0.35/0.59          = zero_zero_int )
% 0.35/0.59        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) )
% 0.35/0.59          = zero_zero_int ) ) ).
% 0.35/0.59  
% 0.35/0.59  % cong_exp_iff_simps(2)
% 0.35/0.59  thf(fact_3612_cong__exp__iff__simps_I1_J,axiom,
% 0.35/0.59      ! [N: num] :
% 0.35/0.59        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) )
% 0.35/0.59        = zero_zero_nat ) ).
% 0.35/0.59  
% 0.35/0.59  % cong_exp_iff_simps(1)
% 0.35/0.59  thf(fact_3613_cong__exp__iff__simps_I1_J,axiom,
% 0.35/0.59      ! [N: num] :
% 0.35/0.59        ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) )
% 0.35/0.59        = zero_zero_int ) ).
% 0.35/0.59  
% 0.35/0.59  % cong_exp_iff_simps(1)
% 0.35/0.59  thf(fact_3614_cong__exp__iff__simps_I6_J,axiom,
% 0.35/0.59      ! [Q2: num,N: num] :
% 0.35/0.59        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 0.35/0.59       != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % cong_exp_iff_simps(6)
% 0.35/0.59  thf(fact_3615_cong__exp__iff__simps_I6_J,axiom,
% 0.35/0.59      ! [Q2: num,N: num] :
% 0.35/0.59        ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 0.35/0.59       != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % cong_exp_iff_simps(6)
% 0.35/0.59  thf(fact_3616_cong__exp__iff__simps_I8_J,axiom,
% 0.35/0.59      ! [M: num,Q2: num] :
% 0.35/0.59        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 0.35/0.59       != ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % cong_exp_iff_simps(8)
% 0.35/0.59  thf(fact_3617_cong__exp__iff__simps_I8_J,axiom,
% 0.35/0.59      ! [M: num,Q2: num] :
% 0.35/0.59        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 0.35/0.59       != ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % cong_exp_iff_simps(8)
% 0.35/0.59  thf(fact_3618_div__mult1__eq,axiom,
% 0.35/0.59      ! [A: nat,B: nat,C: nat] :
% 0.35/0.59        ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.35/0.59        = ( plus_plus_nat @ ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % div_mult1_eq
% 0.35/0.59  thf(fact_3619_div__mult1__eq,axiom,
% 0.35/0.59      ! [A: int,B: int,C: int] :
% 0.35/0.59        ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ C )
% 0.35/0.59        = ( plus_plus_int @ ( times_times_int @ A @ ( divide_divide_int @ B @ C ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % div_mult1_eq
% 0.35/0.59  thf(fact_3620_cancel__div__mod__rules_I2_J,axiom,
% 0.35/0.59      ! [B: nat,A: nat,C: nat] :
% 0.35/0.59        ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 0.35/0.59        = ( plus_plus_nat @ A @ C ) ) ).
% 0.35/0.59  
% 0.35/0.59  % cancel_div_mod_rules(2)
% 0.35/0.59  thf(fact_3621_cancel__div__mod__rules_I2_J,axiom,
% 0.35/0.59      ! [B: int,A: int,C: int] :
% 0.35/0.59        ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 0.35/0.59        = ( plus_plus_int @ A @ C ) ) ).
% 0.35/0.59  
% 0.35/0.59  % cancel_div_mod_rules(2)
% 0.35/0.59  thf(fact_3622_cancel__div__mod__rules_I1_J,axiom,
% 0.35/0.59      ! [A: nat,B: nat,C: nat] :
% 0.35/0.59        ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 0.35/0.59        = ( plus_plus_nat @ A @ C ) ) ).
% 0.35/0.59  
% 0.35/0.59  % cancel_div_mod_rules(1)
% 0.35/0.59  thf(fact_3623_cancel__div__mod__rules_I1_J,axiom,
% 0.35/0.59      ! [A: int,B: int,C: int] :
% 0.35/0.59        ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 0.35/0.59        = ( plus_plus_int @ A @ C ) ) ).
% 0.35/0.59  
% 0.35/0.59  % cancel_div_mod_rules(1)
% 0.35/0.59  thf(fact_3624_mod__div__decomp,axiom,
% 0.35/0.59      ! [A: nat,B: nat] :
% 0.35/0.59        ( A
% 0.35/0.59        = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_div_decomp
% 0.35/0.59  thf(fact_3625_mod__div__decomp,axiom,
% 0.35/0.59      ! [A: int,B: int] :
% 0.35/0.59        ( A
% 0.35/0.59        = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_div_decomp
% 0.35/0.59  thf(fact_3626_div__mult__mod__eq,axiom,
% 0.35/0.59      ! [A: nat,B: nat] :
% 0.35/0.59        ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
% 0.35/0.59        = A ) ).
% 0.35/0.59  
% 0.35/0.59  % div_mult_mod_eq
% 0.35/0.59  thf(fact_3627_div__mult__mod__eq,axiom,
% 0.35/0.59      ! [A: int,B: int] :
% 0.35/0.59        ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) )
% 0.35/0.59        = A ) ).
% 0.35/0.59  
% 0.35/0.59  % div_mult_mod_eq
% 0.35/0.59  thf(fact_3628_mod__div__mult__eq,axiom,
% 0.35/0.59      ! [A: nat,B: nat] :
% 0.35/0.59        ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 0.35/0.59        = A ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_div_mult_eq
% 0.35/0.59  thf(fact_3629_mod__div__mult__eq,axiom,
% 0.35/0.59      ! [A: int,B: int] :
% 0.35/0.59        ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 0.35/0.59        = A ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_div_mult_eq
% 0.35/0.59  thf(fact_3630_mod__mult__div__eq,axiom,
% 0.35/0.59      ! [A: nat,B: nat] :
% 0.35/0.59        ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 0.35/0.59        = A ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_mult_div_eq
% 0.35/0.59  thf(fact_3631_mod__mult__div__eq,axiom,
% 0.35/0.59      ! [A: int,B: int] :
% 0.35/0.59        ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 0.35/0.59        = A ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_mult_div_eq
% 0.35/0.59  thf(fact_3632_mult__div__mod__eq,axiom,
% 0.35/0.59      ! [B: nat,A: nat] :
% 0.35/0.59        ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
% 0.35/0.59        = A ) ).
% 0.35/0.59  
% 0.35/0.59  % mult_div_mod_eq
% 0.35/0.59  thf(fact_3633_mult__div__mod__eq,axiom,
% 0.35/0.59      ! [B: int,A: int] :
% 0.35/0.59        ( ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) )
% 0.35/0.59        = A ) ).
% 0.35/0.59  
% 0.35/0.59  % mult_div_mod_eq
% 0.35/0.59  thf(fact_3634_minus__div__mult__eq__mod,axiom,
% 0.35/0.59      ! [A: nat,B: nat] :
% 0.35/0.59        ( ( minus_minus_nat @ A @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 0.35/0.59        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.35/0.59  
% 0.35/0.59  % minus_div_mult_eq_mod
% 0.35/0.59  thf(fact_3635_minus__div__mult__eq__mod,axiom,
% 0.35/0.59      ! [A: int,B: int] :
% 0.35/0.59        ( ( minus_minus_int @ A @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 0.35/0.59        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.35/0.59  
% 0.35/0.59  % minus_div_mult_eq_mod
% 0.35/0.59  thf(fact_3636_minus__mod__eq__div__mult,axiom,
% 0.35/0.59      ! [A: nat,B: nat] :
% 0.35/0.59        ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 0.35/0.59        = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) ) ).
% 0.35/0.59  
% 0.35/0.59  % minus_mod_eq_div_mult
% 0.35/0.59  thf(fact_3637_minus__mod__eq__div__mult,axiom,
% 0.35/0.59      ! [A: int,B: int] :
% 0.35/0.59        ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 0.35/0.59        = ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) ) ).
% 0.35/0.59  
% 0.35/0.59  % minus_mod_eq_div_mult
% 0.35/0.59  thf(fact_3638_minus__mod__eq__mult__div,axiom,
% 0.35/0.59      ! [A: nat,B: nat] :
% 0.35/0.59        ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 0.35/0.59        = ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % minus_mod_eq_mult_div
% 0.35/0.59  thf(fact_3639_minus__mod__eq__mult__div,axiom,
% 0.35/0.59      ! [A: int,B: int] :
% 0.35/0.59        ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 0.35/0.59        = ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % minus_mod_eq_mult_div
% 0.35/0.59  thf(fact_3640_minus__mult__div__eq__mod,axiom,
% 0.35/0.59      ! [A: nat,B: nat] :
% 0.35/0.59        ( ( minus_minus_nat @ A @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 0.35/0.59        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.35/0.59  
% 0.35/0.59  % minus_mult_div_eq_mod
% 0.35/0.59  thf(fact_3641_minus__mult__div__eq__mod,axiom,
% 0.35/0.59      ! [A: int,B: int] :
% 0.35/0.59        ( ( minus_minus_int @ A @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 0.35/0.59        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.35/0.59  
% 0.35/0.59  % minus_mult_div_eq_mod
% 0.35/0.59  thf(fact_3642_cong__exp__iff__simps_I10_J,axiom,
% 0.35/0.59      ! [M: num,Q2: num,N: num] :
% 0.35/0.59        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 0.35/0.59       != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % cong_exp_iff_simps(10)
% 0.35/0.59  thf(fact_3643_cong__exp__iff__simps_I10_J,axiom,
% 0.35/0.59      ! [M: num,Q2: num,N: num] :
% 0.35/0.59        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 0.35/0.59       != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % cong_exp_iff_simps(10)
% 0.35/0.59  thf(fact_3644_cong__exp__iff__simps_I12_J,axiom,
% 0.35/0.59      ! [M: num,Q2: num,N: num] :
% 0.35/0.59        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 0.35/0.59       != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % cong_exp_iff_simps(12)
% 0.35/0.59  thf(fact_3645_cong__exp__iff__simps_I12_J,axiom,
% 0.35/0.59      ! [M: num,Q2: num,N: num] :
% 0.35/0.59        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 0.35/0.59       != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % cong_exp_iff_simps(12)
% 0.35/0.59  thf(fact_3646_cong__exp__iff__simps_I13_J,axiom,
% 0.35/0.59      ! [M: num,Q2: num,N: num] :
% 0.35/0.59        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 0.35/0.59          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 0.35/0.59        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 0.35/0.59          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % cong_exp_iff_simps(13)
% 0.35/0.59  thf(fact_3647_cong__exp__iff__simps_I13_J,axiom,
% 0.35/0.59      ! [M: num,Q2: num,N: num] :
% 0.35/0.59        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 0.35/0.59          = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 0.35/0.59        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 0.35/0.59          = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % cong_exp_iff_simps(13)
% 0.35/0.59  thf(fact_3648_mod__le__divisor,axiom,
% 0.35/0.59      ! [N: nat,M: nat] :
% 0.35/0.59        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.59       => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_le_divisor
% 0.35/0.59  thf(fact_3649_mod__eq__nat1E,axiom,
% 0.35/0.59      ! [M: nat,Q2: nat,N: nat] :
% 0.35/0.59        ( ( ( modulo_modulo_nat @ M @ Q2 )
% 0.35/0.59          = ( modulo_modulo_nat @ N @ Q2 ) )
% 0.35/0.59       => ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.59         => ~ ! [S: nat] :
% 0.35/0.59                ( M
% 0.35/0.59               != ( plus_plus_nat @ N @ ( times_times_nat @ Q2 @ S ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_eq_nat1E
% 0.35/0.59  thf(fact_3650_mod__eq__nat2E,axiom,
% 0.35/0.59      ! [M: nat,Q2: nat,N: nat] :
% 0.35/0.59        ( ( ( modulo_modulo_nat @ M @ Q2 )
% 0.35/0.59          = ( modulo_modulo_nat @ N @ Q2 ) )
% 0.35/0.59       => ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.59         => ~ ! [S: nat] :
% 0.35/0.59                ( N
% 0.35/0.59               != ( plus_plus_nat @ M @ ( times_times_nat @ Q2 @ S ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_eq_nat2E
% 0.35/0.59  thf(fact_3651_nat__mod__eq__lemma,axiom,
% 0.35/0.59      ! [X: nat,N: nat,Y2: nat] :
% 0.35/0.59        ( ( ( modulo_modulo_nat @ X @ N )
% 0.35/0.59          = ( modulo_modulo_nat @ Y2 @ N ) )
% 0.35/0.59       => ( ( ord_less_eq_nat @ Y2 @ X )
% 0.35/0.59         => ? [Q3: nat] :
% 0.35/0.59              ( X
% 0.35/0.59              = ( plus_plus_nat @ Y2 @ ( times_times_nat @ N @ Q3 ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % nat_mod_eq_lemma
% 0.35/0.59  thf(fact_3652_mod__mult2__eq,axiom,
% 0.35/0.59      ! [M: nat,N: nat,Q2: nat] :
% 0.35/0.59        ( ( modulo_modulo_nat @ M @ ( times_times_nat @ N @ Q2 ) )
% 0.35/0.59        = ( plus_plus_nat @ ( times_times_nat @ N @ ( modulo_modulo_nat @ ( divide_divide_nat @ M @ N ) @ Q2 ) ) @ ( modulo_modulo_nat @ M @ N ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_mult2_eq
% 0.35/0.59  thf(fact_3653_eucl__rel__int__dividesI,axiom,
% 0.35/0.59      ! [L2: int,K: int,Q2: int] :
% 0.35/0.59        ( ( L2 != zero_zero_int )
% 0.35/0.59       => ( ( K
% 0.35/0.59            = ( times_times_int @ Q2 @ L2 ) )
% 0.35/0.59         => ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ zero_zero_int ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % eucl_rel_int_dividesI
% 0.35/0.59  thf(fact_3654_modulo__nat__def,axiom,
% 0.35/0.59      ( modulo_modulo_nat
% 0.35/0.59      = ( ^ [M6: nat,N2: nat] : ( minus_minus_nat @ M6 @ ( times_times_nat @ ( divide_divide_nat @ M6 @ N2 ) @ N2 ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % modulo_nat_def
% 0.35/0.59  thf(fact_3655_Pair__inject,axiom,
% 0.35/0.59      ! [A: product_prod_nat_nat,B: product_prod_nat_nat,A5: product_prod_nat_nat,B5: product_prod_nat_nat] :
% 0.35/0.59        ( ( ( produc6161850002892822231at_nat @ A @ B )
% 0.35/0.59          = ( produc6161850002892822231at_nat @ A5 @ B5 ) )
% 0.35/0.59       => ~ ( ( A = A5 )
% 0.35/0.59           => ( B != B5 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % Pair_inject
% 0.35/0.59  thf(fact_3656_Pair__inject,axiom,
% 0.35/0.59      ! [A: num,B: num,A5: num,B5: num] :
% 0.35/0.59        ( ( ( product_Pair_num_num @ A @ B )
% 0.35/0.59          = ( product_Pair_num_num @ A5 @ B5 ) )
% 0.35/0.59       => ~ ( ( A = A5 )
% 0.35/0.59           => ( B != B5 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % Pair_inject
% 0.35/0.59  thf(fact_3657_Pair__inject,axiom,
% 0.35/0.59      ! [A: nat,B: num,A5: nat,B5: num] :
% 0.35/0.59        ( ( ( product_Pair_nat_num @ A @ B )
% 0.35/0.59          = ( product_Pair_nat_num @ A5 @ B5 ) )
% 0.35/0.59       => ~ ( ( A = A5 )
% 0.35/0.59           => ( B != B5 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % Pair_inject
% 0.35/0.59  thf(fact_3658_Pair__inject,axiom,
% 0.35/0.59      ! [A: nat,B: nat,A5: nat,B5: nat] :
% 0.35/0.59        ( ( ( product_Pair_nat_nat @ A @ B )
% 0.35/0.59          = ( product_Pair_nat_nat @ A5 @ B5 ) )
% 0.35/0.59       => ~ ( ( A = A5 )
% 0.35/0.59           => ( B != B5 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % Pair_inject
% 0.35/0.59  thf(fact_3659_Pair__inject,axiom,
% 0.35/0.59      ! [A: int,B: int,A5: int,B5: int] :
% 0.35/0.59        ( ( ( product_Pair_int_int @ A @ B )
% 0.35/0.59          = ( product_Pair_int_int @ A5 @ B5 ) )
% 0.35/0.59       => ~ ( ( A = A5 )
% 0.35/0.59           => ( B != B5 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % Pair_inject
% 0.35/0.59  thf(fact_3660_prod__cases,axiom,
% 0.35/0.59      ! [P: produc859450856879609959at_nat > $o,P6: produc859450856879609959at_nat] :
% 0.35/0.59        ( ! [A4: product_prod_nat_nat,B3: product_prod_nat_nat] : ( P @ ( produc6161850002892822231at_nat @ A4 @ B3 ) )
% 0.35/0.59       => ( P @ P6 ) ) ).
% 0.35/0.59  
% 0.35/0.59  % prod_cases
% 0.35/0.59  thf(fact_3661_prod__cases,axiom,
% 0.35/0.59      ! [P: product_prod_num_num > $o,P6: product_prod_num_num] :
% 0.35/0.59        ( ! [A4: num,B3: num] : ( P @ ( product_Pair_num_num @ A4 @ B3 ) )
% 0.35/0.59       => ( P @ P6 ) ) ).
% 0.35/0.59  
% 0.35/0.59  % prod_cases
% 0.35/0.59  thf(fact_3662_prod__cases,axiom,
% 0.35/0.59      ! [P: product_prod_nat_num > $o,P6: product_prod_nat_num] :
% 0.35/0.59        ( ! [A4: nat,B3: num] : ( P @ ( product_Pair_nat_num @ A4 @ B3 ) )
% 0.35/0.59       => ( P @ P6 ) ) ).
% 0.35/0.59  
% 0.35/0.59  % prod_cases
% 0.35/0.59  thf(fact_3663_prod__cases,axiom,
% 0.35/0.59      ! [P: product_prod_nat_nat > $o,P6: product_prod_nat_nat] :
% 0.35/0.59        ( ! [A4: nat,B3: nat] : ( P @ ( product_Pair_nat_nat @ A4 @ B3 ) )
% 0.35/0.59       => ( P @ P6 ) ) ).
% 0.35/0.59  
% 0.35/0.59  % prod_cases
% 0.35/0.59  thf(fact_3664_prod__cases,axiom,
% 0.35/0.59      ! [P: product_prod_int_int > $o,P6: product_prod_int_int] :
% 0.35/0.59        ( ! [A4: int,B3: int] : ( P @ ( product_Pair_int_int @ A4 @ B3 ) )
% 0.35/0.59       => ( P @ P6 ) ) ).
% 0.35/0.59  
% 0.35/0.59  % prod_cases
% 0.35/0.59  thf(fact_3665_surj__pair,axiom,
% 0.35/0.59      ! [P6: produc859450856879609959at_nat] :
% 0.35/0.59      ? [X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 0.35/0.59        ( P6
% 0.35/0.59        = ( produc6161850002892822231at_nat @ X3 @ Y3 ) ) ).
% 0.35/0.59  
% 0.35/0.59  % surj_pair
% 0.35/0.59  thf(fact_3666_surj__pair,axiom,
% 0.35/0.59      ! [P6: product_prod_num_num] :
% 0.35/0.59      ? [X3: num,Y3: num] :
% 0.35/0.59        ( P6
% 0.35/0.59        = ( product_Pair_num_num @ X3 @ Y3 ) ) ).
% 0.35/0.59  
% 0.35/0.59  % surj_pair
% 0.35/0.59  thf(fact_3667_surj__pair,axiom,
% 0.35/0.59      ! [P6: product_prod_nat_num] :
% 0.35/0.59      ? [X3: nat,Y3: num] :
% 0.35/0.59        ( P6
% 0.35/0.59        = ( product_Pair_nat_num @ X3 @ Y3 ) ) ).
% 0.35/0.59  
% 0.35/0.59  % surj_pair
% 0.35/0.59  thf(fact_3668_surj__pair,axiom,
% 0.35/0.59      ! [P6: product_prod_nat_nat] :
% 0.35/0.59      ? [X3: nat,Y3: nat] :
% 0.35/0.59        ( P6
% 0.35/0.59        = ( product_Pair_nat_nat @ X3 @ Y3 ) ) ).
% 0.35/0.59  
% 0.35/0.59  % surj_pair
% 0.35/0.59  thf(fact_3669_surj__pair,axiom,
% 0.35/0.59      ! [P6: product_prod_int_int] :
% 0.35/0.59      ? [X3: int,Y3: int] :
% 0.35/0.59        ( P6
% 0.35/0.59        = ( product_Pair_int_int @ X3 @ Y3 ) ) ).
% 0.35/0.59  
% 0.35/0.59  % surj_pair
% 0.35/0.59  thf(fact_3670_old_Oprod_Oexhaust,axiom,
% 0.35/0.59      ! [Y2: produc859450856879609959at_nat] :
% 0.35/0.59        ~ ! [A4: product_prod_nat_nat,B3: product_prod_nat_nat] :
% 0.35/0.59            ( Y2
% 0.35/0.59           != ( produc6161850002892822231at_nat @ A4 @ B3 ) ) ).
% 0.35/0.59  
% 0.35/0.59  % old.prod.exhaust
% 0.35/0.59  thf(fact_3671_old_Oprod_Oexhaust,axiom,
% 0.35/0.59      ! [Y2: product_prod_num_num] :
% 0.35/0.59        ~ ! [A4: num,B3: num] :
% 0.35/0.59            ( Y2
% 0.35/0.59           != ( product_Pair_num_num @ A4 @ B3 ) ) ).
% 0.35/0.59  
% 0.35/0.59  % old.prod.exhaust
% 0.35/0.59  thf(fact_3672_old_Oprod_Oexhaust,axiom,
% 0.35/0.59      ! [Y2: product_prod_nat_num] :
% 0.35/0.59        ~ ! [A4: nat,B3: num] :
% 0.35/0.59            ( Y2
% 0.35/0.59           != ( product_Pair_nat_num @ A4 @ B3 ) ) ).
% 0.35/0.59  
% 0.35/0.59  % old.prod.exhaust
% 0.35/0.59  thf(fact_3673_old_Oprod_Oexhaust,axiom,
% 0.35/0.59      ! [Y2: product_prod_nat_nat] :
% 0.35/0.59        ~ ! [A4: nat,B3: nat] :
% 0.35/0.59            ( Y2
% 0.35/0.59           != ( product_Pair_nat_nat @ A4 @ B3 ) ) ).
% 0.35/0.59  
% 0.35/0.59  % old.prod.exhaust
% 0.35/0.59  thf(fact_3674_old_Oprod_Oexhaust,axiom,
% 0.35/0.59      ! [Y2: product_prod_int_int] :
% 0.35/0.59        ~ ! [A4: int,B3: int] :
% 0.35/0.59            ( Y2
% 0.35/0.59           != ( product_Pair_int_int @ A4 @ B3 ) ) ).
% 0.35/0.59  
% 0.35/0.59  % old.prod.exhaust
% 0.35/0.59  thf(fact_3675_cong__exp__iff__simps_I3_J,axiom,
% 0.35/0.59      ! [N: num,Q2: num] :
% 0.35/0.59        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 0.35/0.59       != zero_zero_nat ) ).
% 0.35/0.59  
% 0.35/0.59  % cong_exp_iff_simps(3)
% 0.35/0.59  thf(fact_3676_cong__exp__iff__simps_I3_J,axiom,
% 0.35/0.59      ! [N: num,Q2: num] :
% 0.35/0.59        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 0.35/0.59       != zero_zero_int ) ).
% 0.35/0.59  
% 0.35/0.59  % cong_exp_iff_simps(3)
% 0.35/0.59  thf(fact_3677_split__mod,axiom,
% 0.35/0.59      ! [P: nat > $o,M: nat,N: nat] :
% 0.35/0.59        ( ( P @ ( modulo_modulo_nat @ M @ N ) )
% 0.35/0.59        = ( ( ( N = zero_zero_nat )
% 0.35/0.59           => ( P @ M ) )
% 0.35/0.59          & ( ( N != zero_zero_nat )
% 0.35/0.59           => ! [I3: nat,J3: nat] :
% 0.35/0.59                ( ( ord_less_nat @ J3 @ N )
% 0.35/0.59               => ( ( M
% 0.35/0.59                    = ( plus_plus_nat @ ( times_times_nat @ N @ I3 ) @ J3 ) )
% 0.35/0.59                 => ( P @ J3 ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % split_mod
% 0.35/0.59  thf(fact_3678_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 0.35/0.59      ! [C: nat,A: nat,B: nat] :
% 0.35/0.59        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.35/0.59       => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.35/0.59          = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 0.35/0.59  thf(fact_3679_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 0.35/0.59      ! [C: int,A: int,B: int] :
% 0.35/0.59        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.35/0.59       => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 0.35/0.59          = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 0.35/0.59  thf(fact_3680_cong__exp__iff__simps_I7_J,axiom,
% 0.35/0.59      ! [Q2: num,N: num] :
% 0.35/0.59        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 0.35/0.59          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 0.35/0.59        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) )
% 0.35/0.59          = zero_zero_nat ) ) ).
% 0.35/0.59  
% 0.35/0.59  % cong_exp_iff_simps(7)
% 0.35/0.59  thf(fact_3681_cong__exp__iff__simps_I7_J,axiom,
% 0.35/0.59      ! [Q2: num,N: num] :
% 0.35/0.59        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 0.35/0.59          = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 0.35/0.59        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) )
% 0.35/0.59          = zero_zero_int ) ) ).
% 0.35/0.59  
% 0.35/0.59  % cong_exp_iff_simps(7)
% 0.35/0.59  thf(fact_3682_cong__exp__iff__simps_I11_J,axiom,
% 0.35/0.59      ! [M: num,Q2: num] :
% 0.35/0.59        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 0.35/0.59          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 0.35/0.59        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 0.35/0.59          = zero_zero_nat ) ) ).
% 0.35/0.59  
% 0.35/0.59  % cong_exp_iff_simps(11)
% 0.35/0.59  thf(fact_3683_cong__exp__iff__simps_I11_J,axiom,
% 0.35/0.59      ! [M: num,Q2: num] :
% 0.35/0.59        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 0.35/0.59          = ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 0.35/0.59        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 0.35/0.59          = zero_zero_int ) ) ).
% 0.35/0.59  
% 0.35/0.59  % cong_exp_iff_simps(11)
% 0.35/0.59  thf(fact_3684_Suc__mod__eq__add3__mod,axiom,
% 0.35/0.59      ! [M: nat,N: nat] :
% 0.35/0.59        ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 0.35/0.59        = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 0.35/0.59  
% 0.35/0.59  % Suc_mod_eq_add3_mod
% 0.35/0.59  thf(fact_3685_Suc__times__mod__eq,axiom,
% 0.35/0.59      ! [M: nat,N: nat] :
% 0.35/0.59        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.35/0.59       => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M @ N ) ) @ M )
% 0.35/0.59          = one_one_nat ) ) ).
% 0.35/0.59  
% 0.35/0.59  % Suc_times_mod_eq
% 0.35/0.59  thf(fact_3686_divmod__digit__0_I2_J,axiom,
% 0.35/0.59      ! [B: nat,A: nat] :
% 0.35/0.59        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.35/0.59       => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.35/0.59         => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) )
% 0.35/0.59            = ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % divmod_digit_0(2)
% 0.35/0.59  thf(fact_3687_divmod__digit__0_I2_J,axiom,
% 0.35/0.59      ! [B: int,A: int] :
% 0.35/0.59        ( ( ord_less_int @ zero_zero_int @ B )
% 0.35/0.59       => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.35/0.59         => ( ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) )
% 0.35/0.59            = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % divmod_digit_0(2)
% 0.35/0.59  thf(fact_3688_bits__stable__imp__add__self,axiom,
% 0.35/0.59      ! [A: nat] :
% 0.35/0.59        ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.59          = A )
% 0.35/0.59       => ( ( plus_plus_nat @ A @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.59          = zero_zero_nat ) ) ).
% 0.35/0.59  
% 0.35/0.59  % bits_stable_imp_add_self
% 0.35/0.59  thf(fact_3689_bits__stable__imp__add__self,axiom,
% 0.35/0.59      ! [A: int] :
% 0.35/0.59        ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.59          = A )
% 0.35/0.59       => ( ( plus_plus_int @ A @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 0.35/0.59          = zero_zero_int ) ) ).
% 0.35/0.59  
% 0.35/0.59  % bits_stable_imp_add_self
% 0.35/0.59  thf(fact_3690_div__exp__mod__exp__eq,axiom,
% 0.35/0.59      ! [A: nat,N: nat,M: nat] :
% 0.35/0.59        ( ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.35/0.59        = ( divide_divide_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % div_exp_mod_exp_eq
% 0.35/0.59  thf(fact_3691_div__exp__mod__exp__eq,axiom,
% 0.35/0.59      ! [A: int,N: nat,M: nat] :
% 0.35/0.59        ( ( modulo_modulo_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 0.35/0.59        = ( divide_divide_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % div_exp_mod_exp_eq
% 0.35/0.59  thf(fact_3692_divmod__digit__0_I1_J,axiom,
% 0.35/0.59      ! [B: nat,A: nat] :
% 0.35/0.59        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.35/0.59       => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.35/0.59         => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 0.35/0.59            = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % divmod_digit_0(1)
% 0.35/0.59  thf(fact_3693_divmod__digit__0_I1_J,axiom,
% 0.35/0.59      ! [B: int,A: int] :
% 0.35/0.59        ( ( ord_less_int @ zero_zero_int @ B )
% 0.35/0.59       => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.35/0.59         => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 0.35/0.59            = ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % divmod_digit_0(1)
% 0.35/0.59  thf(fact_3694_mult__exp__mod__exp__eq,axiom,
% 0.35/0.59      ! [M: nat,N: nat,A: nat] :
% 0.35/0.59        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.59       => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.59          = ( times_times_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mult_exp_mod_exp_eq
% 0.35/0.59  thf(fact_3695_mult__exp__mod__exp__eq,axiom,
% 0.35/0.59      ! [M: nat,N: nat,A: int] :
% 0.35/0.59        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.59       => ( ( modulo_modulo_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.59          = ( times_times_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mult_exp_mod_exp_eq
% 0.35/0.59  thf(fact_3696_prod__induct3,axiom,
% 0.35/0.59      ! [P: produc859450856879609959at_nat > $o,X: produc859450856879609959at_nat] :
% 0.35/0.59        ( ! [A4: product_prod_nat_nat,B3: nat,C2: nat] : ( P @ ( produc6161850002892822231at_nat @ A4 @ ( product_Pair_nat_nat @ B3 @ C2 ) ) )
% 0.35/0.59       => ( P @ X ) ) ).
% 0.35/0.59  
% 0.35/0.59  % prod_induct3
% 0.35/0.59  thf(fact_3697_prod__cases3,axiom,
% 0.35/0.59      ! [Y2: produc859450856879609959at_nat] :
% 0.35/0.59        ~ ! [A4: product_prod_nat_nat,B3: nat,C2: nat] :
% 0.35/0.59            ( Y2
% 0.35/0.59           != ( produc6161850002892822231at_nat @ A4 @ ( product_Pair_nat_nat @ B3 @ C2 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % prod_cases3
% 0.35/0.59  thf(fact_3698_eucl__rel__int__iff,axiom,
% 0.35/0.59      ! [K: int,L2: int,Q2: int,R: int] :
% 0.35/0.59        ( ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R ) )
% 0.35/0.59        = ( ( K
% 0.35/0.59            = ( plus_plus_int @ ( times_times_int @ L2 @ Q2 ) @ R ) )
% 0.35/0.59          & ( ( ord_less_int @ zero_zero_int @ L2 )
% 0.35/0.59           => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 0.35/0.59              & ( ord_less_int @ R @ L2 ) ) )
% 0.35/0.59          & ( ~ ( ord_less_int @ zero_zero_int @ L2 )
% 0.35/0.59           => ( ( ( ord_less_int @ L2 @ zero_zero_int )
% 0.35/0.59               => ( ( ord_less_int @ L2 @ R )
% 0.35/0.59                  & ( ord_less_eq_int @ R @ zero_zero_int ) ) )
% 0.35/0.59              & ( ~ ( ord_less_int @ L2 @ zero_zero_int )
% 0.35/0.59               => ( Q2 = zero_zero_int ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % eucl_rel_int_iff
% 0.35/0.59  thf(fact_3699_mod__double__modulus,axiom,
% 0.35/0.59      ! [M: nat,X: nat] :
% 0.35/0.59        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.35/0.59       => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 0.35/0.59         => ( ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.35/0.59              = ( modulo_modulo_nat @ X @ M ) )
% 0.35/0.59            | ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.35/0.59              = ( plus_plus_nat @ ( modulo_modulo_nat @ X @ M ) @ M ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_double_modulus
% 0.35/0.59  thf(fact_3700_mod__double__modulus,axiom,
% 0.35/0.59      ! [M: int,X: int] :
% 0.35/0.59        ( ( ord_less_int @ zero_zero_int @ M )
% 0.35/0.59       => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.35/0.59         => ( ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 0.35/0.59              = ( modulo_modulo_int @ X @ M ) )
% 0.35/0.59            | ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 0.35/0.59              = ( plus_plus_int @ ( modulo_modulo_int @ X @ M ) @ M ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_double_modulus
% 0.35/0.59  thf(fact_3701_divmod__digit__1_I2_J,axiom,
% 0.35/0.59      ! [A: nat,B: nat] :
% 0.35/0.59        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.35/0.59       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.35/0.59         => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 0.35/0.59           => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.35/0.59              = ( modulo_modulo_nat @ A @ B ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % divmod_digit_1(2)
% 0.35/0.59  thf(fact_3702_divmod__digit__1_I2_J,axiom,
% 0.35/0.59      ! [A: int,B: int] :
% 0.35/0.59        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.35/0.59       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.35/0.59         => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 0.35/0.59           => ( ( minus_minus_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.35/0.59              = ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % divmod_digit_1(2)
% 0.35/0.59  thf(fact_3703_unset__bit__Suc,axiom,
% 0.35/0.59      ! [N: nat,A: int] :
% 0.35/0.59        ( ( bit_se4203085406695923979it_int @ ( suc @ N ) @ A )
% 0.35/0.59        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % unset_bit_Suc
% 0.35/0.59  thf(fact_3704_unset__bit__Suc,axiom,
% 0.35/0.59      ! [N: nat,A: nat] :
% 0.35/0.59        ( ( bit_se4205575877204974255it_nat @ ( suc @ N ) @ A )
% 0.35/0.59        = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % unset_bit_Suc
% 0.35/0.59  thf(fact_3705_set__bit__Suc,axiom,
% 0.35/0.59      ! [N: nat,A: int] :
% 0.35/0.59        ( ( bit_se7879613467334960850it_int @ ( suc @ N ) @ A )
% 0.35/0.59        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % set_bit_Suc
% 0.35/0.59  thf(fact_3706_set__bit__Suc,axiom,
% 0.35/0.59      ! [N: nat,A: nat] :
% 0.35/0.59        ( ( bit_se7882103937844011126it_nat @ ( suc @ N ) @ A )
% 0.35/0.59        = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % set_bit_Suc
% 0.35/0.59  thf(fact_3707_divmod__divmod__step,axiom,
% 0.35/0.59      ( unique5055182867167087721od_nat
% 0.35/0.59      = ( ^ [M6: num,N2: num] : ( if_Pro6206227464963214023at_nat @ ( ord_less_num @ M6 @ N2 ) @ ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ M6 ) ) @ ( unique5026877609467782581ep_nat @ N2 @ ( unique5055182867167087721od_nat @ M6 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % divmod_divmod_step
% 0.35/0.59  thf(fact_3708_divmod__divmod__step,axiom,
% 0.35/0.59      ( unique5052692396658037445od_int
% 0.35/0.59      = ( ^ [M6: num,N2: num] : ( if_Pro3027730157355071871nt_int @ ( ord_less_num @ M6 @ N2 ) @ ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ M6 ) ) @ ( unique5024387138958732305ep_int @ N2 @ ( unique5052692396658037445od_int @ M6 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % divmod_divmod_step
% 0.35/0.59  thf(fact_3709_divmod__divmod__step,axiom,
% 0.35/0.59      ( unique3479559517661332726nteger
% 0.35/0.59      = ( ^ [M6: num,N2: num] : ( if_Pro6119634080678213985nteger @ ( ord_less_num @ M6 @ N2 ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ M6 ) ) @ ( unique4921790084139445826nteger @ N2 @ ( unique3479559517661332726nteger @ M6 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % divmod_divmod_step
% 0.35/0.59  thf(fact_3710_divmod__digit__1_I1_J,axiom,
% 0.35/0.59      ! [A: nat,B: nat] :
% 0.35/0.59        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.35/0.59       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.35/0.59         => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 0.35/0.59           => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_nat )
% 0.35/0.59              = ( divide_divide_nat @ A @ B ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % divmod_digit_1(1)
% 0.35/0.59  thf(fact_3711_divmod__digit__1_I1_J,axiom,
% 0.35/0.59      ! [A: int,B: int] :
% 0.35/0.59        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.35/0.59       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.35/0.59         => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 0.35/0.59           => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_int )
% 0.35/0.59              = ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % divmod_digit_1(1)
% 0.35/0.59  thf(fact_3712_pos__eucl__rel__int__mult__2,axiom,
% 0.35/0.59      ! [B: int,A: int,Q2: int,R: int] :
% 0.35/0.59        ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.35/0.59       => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 0.35/0.59         => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q2 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % pos_eucl_rel_int_mult_2
% 0.35/0.59  thf(fact_3713_finite__Diff__insert,axiom,
% 0.35/0.59      ! [A2: set_int,A: int,B2: set_int] :
% 0.35/0.59        ( ( finite_finite_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B2 ) ) )
% 0.35/0.59        = ( finite_finite_int @ ( minus_minus_set_int @ A2 @ B2 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_Diff_insert
% 0.35/0.59  thf(fact_3714_finite__Diff__insert,axiom,
% 0.35/0.59      ! [A2: set_VEBT_VEBT,A: vEBT_VEBT,B2: set_VEBT_VEBT] :
% 0.35/0.59        ( ( finite5795047828879050333T_VEBT @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ B2 ) ) )
% 0.35/0.59        = ( finite5795047828879050333T_VEBT @ ( minus_5127226145743854075T_VEBT @ A2 @ B2 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_Diff_insert
% 0.35/0.59  thf(fact_3715_finite__Diff__insert,axiom,
% 0.35/0.59      ! [A2: set_real,A: real,B2: set_real] :
% 0.35/0.59        ( ( finite_finite_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ B2 ) ) )
% 0.35/0.59        = ( finite_finite_real @ ( minus_minus_set_real @ A2 @ B2 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_Diff_insert
% 0.35/0.59  thf(fact_3716_finite__Diff__insert,axiom,
% 0.35/0.59      ! [A2: set_complex,A: complex,B2: set_complex] :
% 0.35/0.59        ( ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ B2 ) ) )
% 0.35/0.59        = ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_Diff_insert
% 0.35/0.59  thf(fact_3717_finite__Diff__insert,axiom,
% 0.35/0.59      ! [A2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.35/0.59        ( ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ B2 ) ) )
% 0.35/0.59        = ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_Diff_insert
% 0.35/0.59  thf(fact_3718_finite__Diff__insert,axiom,
% 0.35/0.59      ! [A2: set_nat,A: nat,B2: set_nat] :
% 0.35/0.59        ( ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B2 ) ) )
% 0.35/0.59        = ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_Diff_insert
% 0.35/0.59  thf(fact_3719_verit__le__mono__div,axiom,
% 0.35/0.59      ! [A2: nat,B2: nat,N: nat] :
% 0.35/0.59        ( ( ord_less_nat @ A2 @ B2 )
% 0.35/0.59       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.59         => ( ord_less_eq_nat
% 0.35/0.59            @ ( plus_plus_nat @ ( divide_divide_nat @ A2 @ N )
% 0.35/0.59              @ ( if_nat
% 0.35/0.59                @ ( ( modulo_modulo_nat @ B2 @ N )
% 0.35/0.59                  = zero_zero_nat )
% 0.35/0.59                @ one_one_nat
% 0.35/0.59                @ zero_zero_nat ) )
% 0.35/0.59            @ ( divide_divide_nat @ B2 @ N ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % verit_le_mono_div
% 0.35/0.59  thf(fact_3720_mod__exhaust__less__4,axiom,
% 0.35/0.59      ! [M: nat] :
% 0.35/0.59        ( ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.35/0.59          = zero_zero_nat )
% 0.35/0.59        | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.35/0.59          = one_one_nat )
% 0.35/0.59        | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.35/0.59          = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.59        | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.35/0.59          = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_exhaust_less_4
% 0.35/0.59  thf(fact_3721_finite__Collect__le__nat,axiom,
% 0.35/0.59      ! [K: nat] :
% 0.35/0.59        ( finite_finite_nat
% 0.35/0.59        @ ( collect_nat
% 0.35/0.59          @ ^ [N2: nat] : ( ord_less_eq_nat @ N2 @ K ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_Collect_le_nat
% 0.35/0.59  thf(fact_3722_finite__Collect__less__nat,axiom,
% 0.35/0.59      ! [K: nat] :
% 0.35/0.59        ( finite_finite_nat
% 0.35/0.59        @ ( collect_nat
% 0.35/0.59          @ ^ [N2: nat] : ( ord_less_nat @ N2 @ K ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_Collect_less_nat
% 0.35/0.59  thf(fact_3723_finite__roots__unity,axiom,
% 0.35/0.59      ! [N: nat] :
% 0.35/0.59        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 0.35/0.59       => ( finite_finite_real
% 0.35/0.59          @ ( collect_real
% 0.35/0.59            @ ^ [Z4: real] :
% 0.35/0.59                ( ( power_power_real @ Z4 @ N )
% 0.35/0.59                = one_one_real ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_roots_unity
% 0.35/0.59  thf(fact_3724_finite__roots__unity,axiom,
% 0.35/0.59      ! [N: nat] :
% 0.35/0.59        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 0.35/0.59       => ( finite3207457112153483333omplex
% 0.35/0.59          @ ( collect_complex
% 0.35/0.59            @ ^ [Z4: complex] :
% 0.35/0.59                ( ( power_power_complex @ Z4 @ N )
% 0.35/0.59                = one_one_complex ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_roots_unity
% 0.35/0.59  thf(fact_3725_finite__induct__select,axiom,
% 0.35/0.59      ! [S2: set_VEBT_VEBT,P: set_VEBT_VEBT > $o] :
% 0.35/0.59        ( ( finite5795047828879050333T_VEBT @ S2 )
% 0.35/0.59       => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 0.35/0.59         => ( ! [T3: set_VEBT_VEBT] :
% 0.35/0.59                ( ( ord_le3480810397992357184T_VEBT @ T3 @ S2 )
% 0.35/0.59               => ( ( P @ T3 )
% 0.35/0.59                 => ? [X5: vEBT_VEBT] :
% 0.35/0.59                      ( ( member_VEBT_VEBT @ X5 @ ( minus_5127226145743854075T_VEBT @ S2 @ T3 ) )
% 0.35/0.59                      & ( P @ ( insert_VEBT_VEBT @ X5 @ T3 ) ) ) ) )
% 0.35/0.59           => ( P @ S2 ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_induct_select
% 0.35/0.59  thf(fact_3726_finite__induct__select,axiom,
% 0.35/0.59      ! [S2: set_complex,P: set_complex > $o] :
% 0.35/0.59        ( ( finite3207457112153483333omplex @ S2 )
% 0.35/0.59       => ( ( P @ bot_bot_set_complex )
% 0.35/0.59         => ( ! [T3: set_complex] :
% 0.35/0.59                ( ( ord_less_set_complex @ T3 @ S2 )
% 0.35/0.59               => ( ( P @ T3 )
% 0.35/0.59                 => ? [X5: complex] :
% 0.35/0.59                      ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ S2 @ T3 ) )
% 0.35/0.59                      & ( P @ ( insert_complex @ X5 @ T3 ) ) ) ) )
% 0.35/0.59           => ( P @ S2 ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_induct_select
% 0.35/0.59  thf(fact_3727_finite__induct__select,axiom,
% 0.35/0.59      ! [S2: set_int,P: set_int > $o] :
% 0.35/0.59        ( ( finite_finite_int @ S2 )
% 0.35/0.59       => ( ( P @ bot_bot_set_int )
% 0.35/0.59         => ( ! [T3: set_int] :
% 0.35/0.59                ( ( ord_less_set_int @ T3 @ S2 )
% 0.35/0.59               => ( ( P @ T3 )
% 0.35/0.59                 => ? [X5: int] :
% 0.35/0.59                      ( ( member_int @ X5 @ ( minus_minus_set_int @ S2 @ T3 ) )
% 0.35/0.59                      & ( P @ ( insert_int @ X5 @ T3 ) ) ) ) )
% 0.35/0.59           => ( P @ S2 ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_induct_select
% 0.35/0.59  thf(fact_3728_finite__induct__select,axiom,
% 0.35/0.59      ! [S2: set_real,P: set_real > $o] :
% 0.35/0.59        ( ( finite_finite_real @ S2 )
% 0.35/0.59       => ( ( P @ bot_bot_set_real )
% 0.35/0.59         => ( ! [T3: set_real] :
% 0.35/0.59                ( ( ord_less_set_real @ T3 @ S2 )
% 0.35/0.59               => ( ( P @ T3 )
% 0.35/0.59                 => ? [X5: real] :
% 0.35/0.59                      ( ( member_real @ X5 @ ( minus_minus_set_real @ S2 @ T3 ) )
% 0.35/0.59                      & ( P @ ( insert_real @ X5 @ T3 ) ) ) ) )
% 0.35/0.59           => ( P @ S2 ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_induct_select
% 0.35/0.59  thf(fact_3729_finite__induct__select,axiom,
% 0.35/0.59      ! [S2: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 0.35/0.59        ( ( finite6177210948735845034at_nat @ S2 )
% 0.35/0.59       => ( ( P @ bot_bo2099793752762293965at_nat )
% 0.35/0.59         => ( ! [T3: set_Pr1261947904930325089at_nat] :
% 0.35/0.59                ( ( ord_le7866589430770878221at_nat @ T3 @ S2 )
% 0.35/0.59               => ( ( P @ T3 )
% 0.35/0.59                 => ? [X5: product_prod_nat_nat] :
% 0.35/0.59                      ( ( member8440522571783428010at_nat @ X5 @ ( minus_1356011639430497352at_nat @ S2 @ T3 ) )
% 0.35/0.59                      & ( P @ ( insert8211810215607154385at_nat @ X5 @ T3 ) ) ) ) )
% 0.35/0.59           => ( P @ S2 ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_induct_select
% 0.35/0.59  thf(fact_3730_finite__induct__select,axiom,
% 0.35/0.59      ! [S2: set_nat,P: set_nat > $o] :
% 0.35/0.59        ( ( finite_finite_nat @ S2 )
% 0.35/0.59       => ( ( P @ bot_bot_set_nat )
% 0.35/0.59         => ( ! [T3: set_nat] :
% 0.35/0.59                ( ( ord_less_set_nat @ T3 @ S2 )
% 0.35/0.59               => ( ( P @ T3 )
% 0.35/0.59                 => ? [X5: nat] :
% 0.35/0.59                      ( ( member_nat @ X5 @ ( minus_minus_set_nat @ S2 @ T3 ) )
% 0.35/0.59                      & ( P @ ( insert_nat @ X5 @ T3 ) ) ) ) )
% 0.35/0.59           => ( P @ S2 ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_induct_select
% 0.35/0.59  thf(fact_3731_finite__Diff2,axiom,
% 0.35/0.59      ! [B2: set_complex,A2: set_complex] :
% 0.35/0.59        ( ( finite3207457112153483333omplex @ B2 )
% 0.35/0.59       => ( ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ B2 ) )
% 0.35/0.59          = ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_Diff2
% 0.35/0.59  thf(fact_3732_finite__Diff2,axiom,
% 0.35/0.59      ! [B2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 0.35/0.59        ( ( finite6177210948735845034at_nat @ B2 )
% 0.35/0.59       => ( ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) )
% 0.35/0.59          = ( finite6177210948735845034at_nat @ A2 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_Diff2
% 0.35/0.59  thf(fact_3733_finite__Diff2,axiom,
% 0.35/0.59      ! [B2: set_nat,A2: set_nat] :
% 0.35/0.59        ( ( finite_finite_nat @ B2 )
% 0.35/0.59       => ( ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 0.35/0.59          = ( finite_finite_nat @ A2 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_Diff2
% 0.35/0.59  thf(fact_3734_verit__eq__simplify_I8_J,axiom,
% 0.35/0.59      ! [X23: num,Y22: num] :
% 0.35/0.59        ( ( ( bit0 @ X23 )
% 0.35/0.59          = ( bit0 @ Y22 ) )
% 0.35/0.59        = ( X23 = Y22 ) ) ).
% 0.35/0.59  
% 0.35/0.59  % verit_eq_simplify(8)
% 0.35/0.59  thf(fact_3735_verit__eq__simplify_I9_J,axiom,
% 0.35/0.59      ! [X33: num,Y32: num] :
% 0.35/0.59        ( ( ( bit1 @ X33 )
% 0.35/0.59          = ( bit1 @ Y32 ) )
% 0.35/0.59        = ( X33 = Y32 ) ) ).
% 0.35/0.59  
% 0.35/0.59  % verit_eq_simplify(9)
% 0.35/0.59  thf(fact_3736_finite__Diff,axiom,
% 0.35/0.59      ! [A2: set_complex,B2: set_complex] :
% 0.35/0.59        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.59       => ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_Diff
% 0.35/0.59  thf(fact_3737_finite__Diff,axiom,
% 0.35/0.59      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.35/0.59        ( ( finite6177210948735845034at_nat @ A2 )
% 0.35/0.59       => ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_Diff
% 0.35/0.59  thf(fact_3738_finite__Diff,axiom,
% 0.35/0.59      ! [A2: set_nat,B2: set_nat] :
% 0.35/0.59        ( ( finite_finite_nat @ A2 )
% 0.35/0.59       => ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_Diff
% 0.35/0.59  thf(fact_3739_mod__neg__neg__trivial,axiom,
% 0.35/0.59      ! [K: int,L2: int] :
% 0.35/0.59        ( ( ord_less_eq_int @ K @ zero_zero_int )
% 0.35/0.59       => ( ( ord_less_int @ L2 @ K )
% 0.35/0.59         => ( ( modulo_modulo_int @ K @ L2 )
% 0.35/0.59            = K ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_neg_neg_trivial
% 0.35/0.59  thf(fact_3740_mod__pos__pos__trivial,axiom,
% 0.35/0.59      ! [K: int,L2: int] :
% 0.35/0.59        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.35/0.59       => ( ( ord_less_int @ K @ L2 )
% 0.35/0.59         => ( ( modulo_modulo_int @ K @ L2 )
% 0.35/0.59            = K ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_pos_pos_trivial
% 0.35/0.59  thf(fact_3741_zmod__numeral__Bit0,axiom,
% 0.35/0.59      ! [V: num,W: num] :
% 0.35/0.59        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 0.35/0.59        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % zmod_numeral_Bit0
% 0.35/0.59  thf(fact_3742_zmod__numeral__Bit1,axiom,
% 0.35/0.59      ! [V: num,W: num] :
% 0.35/0.59        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 0.35/0.59        = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) @ one_one_int ) ) ).
% 0.35/0.59  
% 0.35/0.59  % zmod_numeral_Bit1
% 0.35/0.59  thf(fact_3743_zmod__le__nonneg__dividend,axiom,
% 0.35/0.59      ! [M: int,K: int] :
% 0.35/0.59        ( ( ord_less_eq_int @ zero_zero_int @ M )
% 0.35/0.59       => ( ord_less_eq_int @ ( modulo_modulo_int @ M @ K ) @ M ) ) ).
% 0.35/0.59  
% 0.35/0.59  % zmod_le_nonneg_dividend
% 0.35/0.59  thf(fact_3744_neg__mod__bound,axiom,
% 0.35/0.59      ! [L2: int,K: int] :
% 0.35/0.59        ( ( ord_less_int @ L2 @ zero_zero_int )
% 0.35/0.59       => ( ord_less_int @ L2 @ ( modulo_modulo_int @ K @ L2 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % neg_mod_bound
% 0.35/0.59  thf(fact_3745_Euclidean__Division_Opos__mod__bound,axiom,
% 0.35/0.59      ! [L2: int,K: int] :
% 0.35/0.59        ( ( ord_less_int @ zero_zero_int @ L2 )
% 0.35/0.59       => ( ord_less_int @ ( modulo_modulo_int @ K @ L2 ) @ L2 ) ) ).
% 0.35/0.59  
% 0.35/0.59  % Euclidean_Division.pos_mod_bound
% 0.35/0.59  thf(fact_3746_zmod__eq__0__iff,axiom,
% 0.35/0.59      ! [M: int,D2: int] :
% 0.35/0.59        ( ( ( modulo_modulo_int @ M @ D2 )
% 0.35/0.59          = zero_zero_int )
% 0.35/0.59        = ( ? [Q4: int] :
% 0.35/0.59              ( M
% 0.35/0.59              = ( times_times_int @ D2 @ Q4 ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % zmod_eq_0_iff
% 0.35/0.59  thf(fact_3747_zmod__eq__0D,axiom,
% 0.35/0.59      ! [M: int,D2: int] :
% 0.35/0.59        ( ( ( modulo_modulo_int @ M @ D2 )
% 0.35/0.59          = zero_zero_int )
% 0.35/0.59       => ? [Q3: int] :
% 0.35/0.59            ( M
% 0.35/0.59            = ( times_times_int @ D2 @ Q3 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % zmod_eq_0D
% 0.35/0.59  thf(fact_3748_zdiv__mono__strict,axiom,
% 0.35/0.59      ! [A2: int,B2: int,N: int] :
% 0.35/0.59        ( ( ord_less_int @ A2 @ B2 )
% 0.35/0.59       => ( ( ord_less_int @ zero_zero_int @ N )
% 0.35/0.59         => ( ( ( modulo_modulo_int @ A2 @ N )
% 0.35/0.59              = zero_zero_int )
% 0.35/0.59           => ( ( ( modulo_modulo_int @ B2 @ N )
% 0.35/0.59                = zero_zero_int )
% 0.35/0.59             => ( ord_less_int @ ( divide_divide_int @ A2 @ N ) @ ( divide_divide_int @ B2 @ N ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % zdiv_mono_strict
% 0.35/0.59  thf(fact_3749_finite__maxlen,axiom,
% 0.35/0.59      ! [M7: set_list_VEBT_VEBT] :
% 0.35/0.59        ( ( finite3004134309566078307T_VEBT @ M7 )
% 0.35/0.59       => ? [N3: nat] :
% 0.35/0.59          ! [X5: list_VEBT_VEBT] :
% 0.35/0.59            ( ( member2936631157270082147T_VEBT @ X5 @ M7 )
% 0.35/0.59           => ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ X5 ) @ N3 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_maxlen
% 0.35/0.59  thf(fact_3750_finite__maxlen,axiom,
% 0.35/0.59      ! [M7: set_list_o] :
% 0.35/0.59        ( ( finite_finite_list_o @ M7 )
% 0.35/0.59       => ? [N3: nat] :
% 0.35/0.59          ! [X5: list_o] :
% 0.35/0.59            ( ( member_list_o @ X5 @ M7 )
% 0.35/0.59           => ( ord_less_nat @ ( size_size_list_o @ X5 ) @ N3 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_maxlen
% 0.35/0.59  thf(fact_3751_finite__maxlen,axiom,
% 0.35/0.59      ! [M7: set_list_nat] :
% 0.35/0.59        ( ( finite8100373058378681591st_nat @ M7 )
% 0.35/0.59       => ? [N3: nat] :
% 0.35/0.59          ! [X5: list_nat] :
% 0.35/0.59            ( ( member_list_nat @ X5 @ M7 )
% 0.35/0.59           => ( ord_less_nat @ ( size_size_list_nat @ X5 ) @ N3 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_maxlen
% 0.35/0.59  thf(fact_3752_finite__maxlen,axiom,
% 0.35/0.59      ! [M7: set_list_int] :
% 0.35/0.59        ( ( finite3922522038869484883st_int @ M7 )
% 0.35/0.59       => ? [N3: nat] :
% 0.35/0.59          ! [X5: list_int] :
% 0.35/0.59            ( ( member_list_int @ X5 @ M7 )
% 0.35/0.59           => ( ord_less_nat @ ( size_size_list_int @ X5 ) @ N3 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_maxlen
% 0.35/0.59  thf(fact_3753_div__mod__decomp__int,axiom,
% 0.35/0.59      ! [A2: int,N: int] :
% 0.35/0.59        ( A2
% 0.35/0.59        = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A2 @ N ) @ N ) @ ( modulo_modulo_int @ A2 @ N ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % div_mod_decomp_int
% 0.35/0.59  thf(fact_3754_mod__int__unique,axiom,
% 0.35/0.59      ! [K: int,L2: int,Q2: int,R: int] :
% 0.35/0.59        ( ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R ) )
% 0.35/0.59       => ( ( modulo_modulo_int @ K @ L2 )
% 0.35/0.59          = R ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_int_unique
% 0.35/0.59  thf(fact_3755_neg__mod__conj,axiom,
% 0.35/0.59      ! [B: int,A: int] :
% 0.35/0.59        ( ( ord_less_int @ B @ zero_zero_int )
% 0.35/0.59       => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ zero_zero_int )
% 0.35/0.59          & ( ord_less_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % neg_mod_conj
% 0.35/0.59  thf(fact_3756_pos__mod__conj,axiom,
% 0.35/0.59      ! [B: int,A: int] :
% 0.35/0.59        ( ( ord_less_int @ zero_zero_int @ B )
% 0.35/0.59       => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 0.35/0.59          & ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % pos_mod_conj
% 0.35/0.59  thf(fact_3757_zmod__trivial__iff,axiom,
% 0.35/0.59      ! [I2: int,K: int] :
% 0.35/0.59        ( ( ( modulo_modulo_int @ I2 @ K )
% 0.35/0.59          = I2 )
% 0.35/0.59        = ( ( K = zero_zero_int )
% 0.35/0.59          | ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 0.35/0.59            & ( ord_less_int @ I2 @ K ) )
% 0.35/0.59          | ( ( ord_less_eq_int @ I2 @ zero_zero_int )
% 0.35/0.59            & ( ord_less_int @ K @ I2 ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % zmod_trivial_iff
% 0.35/0.59  thf(fact_3758_neg__mod__sign,axiom,
% 0.35/0.59      ! [L2: int,K: int] :
% 0.35/0.59        ( ( ord_less_int @ L2 @ zero_zero_int )
% 0.35/0.59       => ( ord_less_eq_int @ ( modulo_modulo_int @ K @ L2 ) @ zero_zero_int ) ) ).
% 0.35/0.59  
% 0.35/0.59  % neg_mod_sign
% 0.35/0.59  thf(fact_3759_Euclidean__Division_Opos__mod__sign,axiom,
% 0.35/0.59      ! [L2: int,K: int] :
% 0.35/0.59        ( ( ord_less_int @ zero_zero_int @ L2 )
% 0.35/0.59       => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L2 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % Euclidean_Division.pos_mod_sign
% 0.35/0.59  thf(fact_3760_verit__la__disequality,axiom,
% 0.35/0.59      ! [A: num,B: num] :
% 0.35/0.59        ( ( A = B )
% 0.35/0.59        | ~ ( ord_less_eq_num @ A @ B )
% 0.35/0.59        | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 0.35/0.59  
% 0.35/0.59  % verit_la_disequality
% 0.35/0.59  thf(fact_3761_verit__la__disequality,axiom,
% 0.35/0.59      ! [A: nat,B: nat] :
% 0.35/0.59        ( ( A = B )
% 0.35/0.59        | ~ ( ord_less_eq_nat @ A @ B )
% 0.35/0.59        | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 0.35/0.59  
% 0.35/0.59  % verit_la_disequality
% 0.35/0.59  thf(fact_3762_verit__la__disequality,axiom,
% 0.35/0.59      ! [A: int,B: int] :
% 0.35/0.59        ( ( A = B )
% 0.35/0.59        | ~ ( ord_less_eq_int @ A @ B )
% 0.35/0.59        | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 0.35/0.59  
% 0.35/0.59  % verit_la_disequality
% 0.35/0.59  thf(fact_3763_verit__comp__simplify1_I2_J,axiom,
% 0.35/0.59      ! [A: set_real] : ( ord_less_eq_set_real @ A @ A ) ).
% 0.35/0.59  
% 0.35/0.59  % verit_comp_simplify1(2)
% 0.35/0.59  thf(fact_3764_verit__comp__simplify1_I2_J,axiom,
% 0.35/0.59      ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 0.35/0.59  
% 0.35/0.59  % verit_comp_simplify1(2)
% 0.35/0.59  thf(fact_3765_verit__comp__simplify1_I2_J,axiom,
% 0.35/0.59      ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 0.35/0.59  
% 0.35/0.59  % verit_comp_simplify1(2)
% 0.35/0.59  thf(fact_3766_verit__comp__simplify1_I2_J,axiom,
% 0.35/0.59      ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 0.35/0.59  
% 0.35/0.59  % verit_comp_simplify1(2)
% 0.35/0.59  thf(fact_3767_verit__comp__simplify1_I2_J,axiom,
% 0.35/0.59      ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 0.35/0.59  
% 0.35/0.59  % verit_comp_simplify1(2)
% 0.35/0.59  thf(fact_3768_divmod__int__def,axiom,
% 0.35/0.59      ( unique5052692396658037445od_int
% 0.35/0.59      = ( ^ [M6: num,N2: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N2 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % divmod_int_def
% 0.35/0.59  thf(fact_3769_verit__comp__simplify1_I1_J,axiom,
% 0.35/0.59      ! [A: real] :
% 0.35/0.59        ~ ( ord_less_real @ A @ A ) ).
% 0.35/0.59  
% 0.35/0.59  % verit_comp_simplify1(1)
% 0.35/0.59  thf(fact_3770_verit__comp__simplify1_I1_J,axiom,
% 0.35/0.59      ! [A: rat] :
% 0.35/0.59        ~ ( ord_less_rat @ A @ A ) ).
% 0.35/0.59  
% 0.35/0.59  % verit_comp_simplify1(1)
% 0.35/0.59  thf(fact_3771_verit__comp__simplify1_I1_J,axiom,
% 0.35/0.59      ! [A: num] :
% 0.35/0.59        ~ ( ord_less_num @ A @ A ) ).
% 0.35/0.59  
% 0.35/0.59  % verit_comp_simplify1(1)
% 0.35/0.59  thf(fact_3772_verit__comp__simplify1_I1_J,axiom,
% 0.35/0.59      ! [A: nat] :
% 0.35/0.59        ~ ( ord_less_nat @ A @ A ) ).
% 0.35/0.59  
% 0.35/0.59  % verit_comp_simplify1(1)
% 0.35/0.59  thf(fact_3773_verit__comp__simplify1_I1_J,axiom,
% 0.35/0.59      ! [A: int] :
% 0.35/0.59        ~ ( ord_less_int @ A @ A ) ).
% 0.35/0.59  
% 0.35/0.59  % verit_comp_simplify1(1)
% 0.35/0.59  thf(fact_3774_eucl__rel__int,axiom,
% 0.35/0.59      ! [K: int,L2: int] : ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ ( divide_divide_int @ K @ L2 ) @ ( modulo_modulo_int @ K @ L2 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % eucl_rel_int
% 0.35/0.59  thf(fact_3775_mod__pos__neg__trivial,axiom,
% 0.35/0.59      ! [K: int,L2: int] :
% 0.35/0.59        ( ( ord_less_int @ zero_zero_int @ K )
% 0.35/0.59       => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L2 ) @ zero_zero_int )
% 0.35/0.59         => ( ( modulo_modulo_int @ K @ L2 )
% 0.35/0.59            = ( plus_plus_int @ K @ L2 ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_pos_neg_trivial
% 0.35/0.59  thf(fact_3776_mod__pos__geq,axiom,
% 0.35/0.59      ! [L2: int,K: int] :
% 0.35/0.59        ( ( ord_less_int @ zero_zero_int @ L2 )
% 0.35/0.59       => ( ( ord_less_eq_int @ L2 @ K )
% 0.35/0.59         => ( ( modulo_modulo_int @ K @ L2 )
% 0.35/0.59            = ( modulo_modulo_int @ ( minus_minus_int @ K @ L2 ) @ L2 ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % mod_pos_geq
% 0.35/0.59  thf(fact_3777_verit__le__mono__div__int,axiom,
% 0.35/0.59      ! [A2: int,B2: int,N: int] :
% 0.35/0.59        ( ( ord_less_int @ A2 @ B2 )
% 0.35/0.59       => ( ( ord_less_int @ zero_zero_int @ N )
% 0.35/0.59         => ( ord_less_eq_int
% 0.35/0.59            @ ( plus_plus_int @ ( divide_divide_int @ A2 @ N )
% 0.35/0.59              @ ( if_int
% 0.35/0.59                @ ( ( modulo_modulo_int @ B2 @ N )
% 0.35/0.59                  = zero_zero_int )
% 0.35/0.59                @ one_one_int
% 0.35/0.59                @ zero_zero_int ) )
% 0.35/0.59            @ ( divide_divide_int @ B2 @ N ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % verit_le_mono_div_int
% 0.35/0.59  thf(fact_3778_split__zmod,axiom,
% 0.35/0.59      ! [P: int > $o,N: int,K: int] :
% 0.35/0.59        ( ( P @ ( modulo_modulo_int @ N @ K ) )
% 0.35/0.59        = ( ( ( K = zero_zero_int )
% 0.35/0.59           => ( P @ N ) )
% 0.35/0.59          & ( ( ord_less_int @ zero_zero_int @ K )
% 0.35/0.59           => ! [I3: int,J3: int] :
% 0.35/0.59                ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 0.35/0.59                  & ( ord_less_int @ J3 @ K )
% 0.35/0.59                  & ( N
% 0.35/0.59                    = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 0.35/0.59               => ( P @ J3 ) ) )
% 0.35/0.59          & ( ( ord_less_int @ K @ zero_zero_int )
% 0.35/0.59           => ! [I3: int,J3: int] :
% 0.35/0.59                ( ( ( ord_less_int @ K @ J3 )
% 0.35/0.59                  & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 0.35/0.59                  & ( N
% 0.35/0.59                    = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 0.35/0.59               => ( P @ J3 ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % split_zmod
% 0.35/0.59  thf(fact_3779_int__mod__neg__eq,axiom,
% 0.35/0.59      ! [A: int,B: int,Q2: int,R: int] :
% 0.35/0.59        ( ( A
% 0.35/0.59          = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 0.35/0.59       => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 0.35/0.59         => ( ( ord_less_int @ B @ R )
% 0.35/0.59           => ( ( modulo_modulo_int @ A @ B )
% 0.35/0.59              = R ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % int_mod_neg_eq
% 0.35/0.59  thf(fact_3780_int__mod__pos__eq,axiom,
% 0.35/0.59      ! [A: int,B: int,Q2: int,R: int] :
% 0.35/0.59        ( ( A
% 0.35/0.59          = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 0.35/0.59       => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 0.35/0.59         => ( ( ord_less_int @ R @ B )
% 0.35/0.59           => ( ( modulo_modulo_int @ A @ B )
% 0.35/0.59              = R ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % int_mod_pos_eq
% 0.35/0.59  thf(fact_3781_zmod__zmult2__eq,axiom,
% 0.35/0.59      ! [C: int,A: int,B: int] :
% 0.35/0.59        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.35/0.59       => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 0.35/0.59          = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % zmod_zmult2_eq
% 0.35/0.59  thf(fact_3782_split__neg__lemma,axiom,
% 0.35/0.59      ! [K: int,P: int > int > $o,N: int] :
% 0.35/0.59        ( ( ord_less_int @ K @ zero_zero_int )
% 0.35/0.59       => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 0.35/0.59          = ( ! [I3: int,J3: int] :
% 0.35/0.59                ( ( ( ord_less_int @ K @ J3 )
% 0.35/0.59                  & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 0.35/0.59                  & ( N
% 0.35/0.59                    = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 0.35/0.59               => ( P @ I3 @ J3 ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % split_neg_lemma
% 0.35/0.59  thf(fact_3783_split__pos__lemma,axiom,
% 0.35/0.59      ! [K: int,P: int > int > $o,N: int] :
% 0.35/0.59        ( ( ord_less_int @ zero_zero_int @ K )
% 0.35/0.59       => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 0.35/0.59          = ( ! [I3: int,J3: int] :
% 0.35/0.59                ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 0.35/0.59                  & ( ord_less_int @ J3 @ K )
% 0.35/0.59                  & ( N
% 0.35/0.59                    = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 0.35/0.59               => ( P @ I3 @ J3 ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % split_pos_lemma
% 0.35/0.59  thf(fact_3784_verit__comp__simplify1_I3_J,axiom,
% 0.35/0.59      ! [B5: real,A5: real] :
% 0.35/0.59        ( ( ~ ( ord_less_eq_real @ B5 @ A5 ) )
% 0.35/0.59        = ( ord_less_real @ A5 @ B5 ) ) ).
% 0.35/0.59  
% 0.35/0.59  % verit_comp_simplify1(3)
% 0.35/0.59  thf(fact_3785_verit__comp__simplify1_I3_J,axiom,
% 0.35/0.59      ! [B5: rat,A5: rat] :
% 0.35/0.59        ( ( ~ ( ord_less_eq_rat @ B5 @ A5 ) )
% 0.35/0.59        = ( ord_less_rat @ A5 @ B5 ) ) ).
% 0.35/0.59  
% 0.35/0.59  % verit_comp_simplify1(3)
% 0.35/0.59  thf(fact_3786_verit__comp__simplify1_I3_J,axiom,
% 0.35/0.59      ! [B5: num,A5: num] :
% 0.35/0.59        ( ( ~ ( ord_less_eq_num @ B5 @ A5 ) )
% 0.35/0.59        = ( ord_less_num @ A5 @ B5 ) ) ).
% 0.35/0.59  
% 0.35/0.59  % verit_comp_simplify1(3)
% 0.35/0.59  thf(fact_3787_verit__comp__simplify1_I3_J,axiom,
% 0.35/0.59      ! [B5: nat,A5: nat] :
% 0.35/0.59        ( ( ~ ( ord_less_eq_nat @ B5 @ A5 ) )
% 0.35/0.59        = ( ord_less_nat @ A5 @ B5 ) ) ).
% 0.35/0.59  
% 0.35/0.59  % verit_comp_simplify1(3)
% 0.35/0.59  thf(fact_3788_verit__comp__simplify1_I3_J,axiom,
% 0.35/0.59      ! [B5: int,A5: int] :
% 0.35/0.59        ( ( ~ ( ord_less_eq_int @ B5 @ A5 ) )
% 0.35/0.59        = ( ord_less_int @ A5 @ B5 ) ) ).
% 0.35/0.59  
% 0.35/0.59  % verit_comp_simplify1(3)
% 0.35/0.59  thf(fact_3789_verit__sum__simplify,axiom,
% 0.35/0.59      ! [A: complex] :
% 0.35/0.59        ( ( plus_plus_complex @ A @ zero_zero_complex )
% 0.35/0.59        = A ) ).
% 0.35/0.59  
% 0.35/0.59  % verit_sum_simplify
% 0.35/0.59  thf(fact_3790_verit__sum__simplify,axiom,
% 0.35/0.59      ! [A: real] :
% 0.35/0.59        ( ( plus_plus_real @ A @ zero_zero_real )
% 0.35/0.59        = A ) ).
% 0.35/0.59  
% 0.35/0.59  % verit_sum_simplify
% 0.35/0.59  thf(fact_3791_verit__sum__simplify,axiom,
% 0.35/0.59      ! [A: rat] :
% 0.35/0.59        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 0.35/0.59        = A ) ).
% 0.35/0.59  
% 0.35/0.59  % verit_sum_simplify
% 0.35/0.59  thf(fact_3792_verit__sum__simplify,axiom,
% 0.35/0.59      ! [A: nat] :
% 0.35/0.59        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.35/0.59        = A ) ).
% 0.35/0.59  
% 0.35/0.59  % verit_sum_simplify
% 0.35/0.59  thf(fact_3793_verit__sum__simplify,axiom,
% 0.35/0.59      ! [A: int] :
% 0.35/0.59        ( ( plus_plus_int @ A @ zero_zero_int )
% 0.35/0.59        = A ) ).
% 0.35/0.59  
% 0.35/0.59  % verit_sum_simplify
% 0.35/0.59  thf(fact_3794_verit__eq__simplify_I10_J,axiom,
% 0.35/0.59      ! [X23: num] :
% 0.35/0.59        ( one
% 0.35/0.59       != ( bit0 @ X23 ) ) ).
% 0.35/0.59  
% 0.35/0.59  % verit_eq_simplify(10)
% 0.35/0.59  thf(fact_3795_finite__has__minimal2,axiom,
% 0.35/0.59      ! [A2: set_real,A: real] :
% 0.35/0.59        ( ( finite_finite_real @ A2 )
% 0.35/0.59       => ( ( member_real @ A @ A2 )
% 0.35/0.59         => ? [X3: real] :
% 0.35/0.59              ( ( member_real @ X3 @ A2 )
% 0.35/0.59              & ( ord_less_eq_real @ X3 @ A )
% 0.35/0.59              & ! [Xa: real] :
% 0.35/0.59                  ( ( member_real @ Xa @ A2 )
% 0.35/0.59                 => ( ( ord_less_eq_real @ Xa @ X3 )
% 0.35/0.59                   => ( X3 = Xa ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_has_minimal2
% 0.35/0.59  thf(fact_3796_finite__has__minimal2,axiom,
% 0.35/0.59      ! [A2: set_set_real,A: set_real] :
% 0.35/0.59        ( ( finite9007344921179782393t_real @ A2 )
% 0.35/0.59       => ( ( member_set_real @ A @ A2 )
% 0.35/0.59         => ? [X3: set_real] :
% 0.35/0.59              ( ( member_set_real @ X3 @ A2 )
% 0.35/0.59              & ( ord_less_eq_set_real @ X3 @ A )
% 0.35/0.59              & ! [Xa: set_real] :
% 0.35/0.59                  ( ( member_set_real @ Xa @ A2 )
% 0.35/0.59                 => ( ( ord_less_eq_set_real @ Xa @ X3 )
% 0.35/0.59                   => ( X3 = Xa ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_has_minimal2
% 0.35/0.59  thf(fact_3797_finite__has__minimal2,axiom,
% 0.35/0.59      ! [A2: set_set_nat,A: set_nat] :
% 0.35/0.59        ( ( finite1152437895449049373et_nat @ A2 )
% 0.35/0.59       => ( ( member_set_nat @ A @ A2 )
% 0.35/0.59         => ? [X3: set_nat] :
% 0.35/0.59              ( ( member_set_nat @ X3 @ A2 )
% 0.35/0.59              & ( ord_less_eq_set_nat @ X3 @ A )
% 0.35/0.59              & ! [Xa: set_nat] :
% 0.35/0.59                  ( ( member_set_nat @ Xa @ A2 )
% 0.35/0.59                 => ( ( ord_less_eq_set_nat @ Xa @ X3 )
% 0.35/0.59                   => ( X3 = Xa ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_has_minimal2
% 0.35/0.59  thf(fact_3798_finite__has__minimal2,axiom,
% 0.35/0.59      ! [A2: set_num,A: num] :
% 0.35/0.59        ( ( finite_finite_num @ A2 )
% 0.35/0.59       => ( ( member_num @ A @ A2 )
% 0.35/0.59         => ? [X3: num] :
% 0.35/0.59              ( ( member_num @ X3 @ A2 )
% 0.35/0.59              & ( ord_less_eq_num @ X3 @ A )
% 0.35/0.59              & ! [Xa: num] :
% 0.35/0.59                  ( ( member_num @ Xa @ A2 )
% 0.35/0.59                 => ( ( ord_less_eq_num @ Xa @ X3 )
% 0.35/0.59                   => ( X3 = Xa ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_has_minimal2
% 0.35/0.59  thf(fact_3799_finite__has__minimal2,axiom,
% 0.35/0.59      ! [A2: set_nat,A: nat] :
% 0.35/0.59        ( ( finite_finite_nat @ A2 )
% 0.35/0.59       => ( ( member_nat @ A @ A2 )
% 0.35/0.59         => ? [X3: nat] :
% 0.35/0.59              ( ( member_nat @ X3 @ A2 )
% 0.35/0.59              & ( ord_less_eq_nat @ X3 @ A )
% 0.35/0.59              & ! [Xa: nat] :
% 0.35/0.59                  ( ( member_nat @ Xa @ A2 )
% 0.35/0.59                 => ( ( ord_less_eq_nat @ Xa @ X3 )
% 0.35/0.59                   => ( X3 = Xa ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_has_minimal2
% 0.35/0.59  thf(fact_3800_finite__has__minimal2,axiom,
% 0.35/0.59      ! [A2: set_int,A: int] :
% 0.35/0.59        ( ( finite_finite_int @ A2 )
% 0.35/0.59       => ( ( member_int @ A @ A2 )
% 0.35/0.59         => ? [X3: int] :
% 0.35/0.59              ( ( member_int @ X3 @ A2 )
% 0.35/0.59              & ( ord_less_eq_int @ X3 @ A )
% 0.35/0.59              & ! [Xa: int] :
% 0.35/0.59                  ( ( member_int @ Xa @ A2 )
% 0.35/0.59                 => ( ( ord_less_eq_int @ Xa @ X3 )
% 0.35/0.59                   => ( X3 = Xa ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_has_minimal2
% 0.35/0.59  thf(fact_3801_finite__has__maximal2,axiom,
% 0.35/0.59      ! [A2: set_real,A: real] :
% 0.35/0.59        ( ( finite_finite_real @ A2 )
% 0.35/0.59       => ( ( member_real @ A @ A2 )
% 0.35/0.59         => ? [X3: real] :
% 0.35/0.59              ( ( member_real @ X3 @ A2 )
% 0.35/0.59              & ( ord_less_eq_real @ A @ X3 )
% 0.35/0.59              & ! [Xa: real] :
% 0.35/0.59                  ( ( member_real @ Xa @ A2 )
% 0.35/0.59                 => ( ( ord_less_eq_real @ X3 @ Xa )
% 0.35/0.59                   => ( X3 = Xa ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_has_maximal2
% 0.35/0.59  thf(fact_3802_finite__has__maximal2,axiom,
% 0.35/0.59      ! [A2: set_set_real,A: set_real] :
% 0.35/0.59        ( ( finite9007344921179782393t_real @ A2 )
% 0.35/0.59       => ( ( member_set_real @ A @ A2 )
% 0.35/0.59         => ? [X3: set_real] :
% 0.35/0.59              ( ( member_set_real @ X3 @ A2 )
% 0.35/0.59              & ( ord_less_eq_set_real @ A @ X3 )
% 0.35/0.59              & ! [Xa: set_real] :
% 0.35/0.59                  ( ( member_set_real @ Xa @ A2 )
% 0.35/0.59                 => ( ( ord_less_eq_set_real @ X3 @ Xa )
% 0.35/0.59                   => ( X3 = Xa ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_has_maximal2
% 0.35/0.59  thf(fact_3803_finite__has__maximal2,axiom,
% 0.35/0.59      ! [A2: set_set_nat,A: set_nat] :
% 0.35/0.59        ( ( finite1152437895449049373et_nat @ A2 )
% 0.35/0.59       => ( ( member_set_nat @ A @ A2 )
% 0.35/0.59         => ? [X3: set_nat] :
% 0.35/0.59              ( ( member_set_nat @ X3 @ A2 )
% 0.35/0.59              & ( ord_less_eq_set_nat @ A @ X3 )
% 0.35/0.59              & ! [Xa: set_nat] :
% 0.35/0.59                  ( ( member_set_nat @ Xa @ A2 )
% 0.35/0.59                 => ( ( ord_less_eq_set_nat @ X3 @ Xa )
% 0.35/0.59                   => ( X3 = Xa ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_has_maximal2
% 0.35/0.59  thf(fact_3804_finite__has__maximal2,axiom,
% 0.35/0.59      ! [A2: set_num,A: num] :
% 0.35/0.59        ( ( finite_finite_num @ A2 )
% 0.35/0.59       => ( ( member_num @ A @ A2 )
% 0.35/0.59         => ? [X3: num] :
% 0.35/0.59              ( ( member_num @ X3 @ A2 )
% 0.35/0.59              & ( ord_less_eq_num @ A @ X3 )
% 0.35/0.59              & ! [Xa: num] :
% 0.35/0.59                  ( ( member_num @ Xa @ A2 )
% 0.35/0.59                 => ( ( ord_less_eq_num @ X3 @ Xa )
% 0.35/0.59                   => ( X3 = Xa ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_has_maximal2
% 0.35/0.59  thf(fact_3805_finite__has__maximal2,axiom,
% 0.35/0.59      ! [A2: set_nat,A: nat] :
% 0.35/0.59        ( ( finite_finite_nat @ A2 )
% 0.35/0.59       => ( ( member_nat @ A @ A2 )
% 0.35/0.59         => ? [X3: nat] :
% 0.35/0.59              ( ( member_nat @ X3 @ A2 )
% 0.35/0.59              & ( ord_less_eq_nat @ A @ X3 )
% 0.35/0.59              & ! [Xa: nat] :
% 0.35/0.59                  ( ( member_nat @ Xa @ A2 )
% 0.35/0.59                 => ( ( ord_less_eq_nat @ X3 @ Xa )
% 0.35/0.59                   => ( X3 = Xa ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_has_maximal2
% 0.35/0.59  thf(fact_3806_finite__has__maximal2,axiom,
% 0.35/0.59      ! [A2: set_int,A: int] :
% 0.35/0.59        ( ( finite_finite_int @ A2 )
% 0.35/0.59       => ( ( member_int @ A @ A2 )
% 0.35/0.59         => ? [X3: int] :
% 0.35/0.59              ( ( member_int @ X3 @ A2 )
% 0.35/0.59              & ( ord_less_eq_int @ A @ X3 )
% 0.35/0.59              & ! [Xa: int] :
% 0.35/0.59                  ( ( member_int @ Xa @ A2 )
% 0.35/0.59                 => ( ( ord_less_eq_int @ X3 @ Xa )
% 0.35/0.59                   => ( X3 = Xa ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_has_maximal2
% 0.35/0.59  thf(fact_3807_verit__eq__simplify_I14_J,axiom,
% 0.35/0.59      ! [X23: num,X33: num] :
% 0.35/0.59        ( ( bit0 @ X23 )
% 0.35/0.59       != ( bit1 @ X33 ) ) ).
% 0.35/0.59  
% 0.35/0.59  % verit_eq_simplify(14)
% 0.35/0.59  thf(fact_3808_verit__eq__simplify_I12_J,axiom,
% 0.35/0.59      ! [X33: num] :
% 0.35/0.59        ( one
% 0.35/0.59       != ( bit1 @ X33 ) ) ).
% 0.35/0.59  
% 0.35/0.59  % verit_eq_simplify(12)
% 0.35/0.59  thf(fact_3809_Diff__infinite__finite,axiom,
% 0.35/0.59      ! [T4: set_complex,S2: set_complex] :
% 0.35/0.59        ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.59       => ( ~ ( finite3207457112153483333omplex @ S2 )
% 0.35/0.59         => ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ S2 @ T4 ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % Diff_infinite_finite
% 0.35/0.59  thf(fact_3810_Diff__infinite__finite,axiom,
% 0.35/0.59      ! [T4: set_Pr1261947904930325089at_nat,S2: set_Pr1261947904930325089at_nat] :
% 0.35/0.59        ( ( finite6177210948735845034at_nat @ T4 )
% 0.35/0.59       => ( ~ ( finite6177210948735845034at_nat @ S2 )
% 0.35/0.59         => ~ ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ S2 @ T4 ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % Diff_infinite_finite
% 0.35/0.59  thf(fact_3811_Diff__infinite__finite,axiom,
% 0.35/0.59      ! [T4: set_nat,S2: set_nat] :
% 0.35/0.59        ( ( finite_finite_nat @ T4 )
% 0.35/0.59       => ( ~ ( finite_finite_nat @ S2 )
% 0.35/0.59         => ~ ( finite_finite_nat @ ( minus_minus_set_nat @ S2 @ T4 ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % Diff_infinite_finite
% 0.35/0.59  thf(fact_3812_eq__diff__eq_H,axiom,
% 0.35/0.59      ! [X: real,Y2: real,Z: real] :
% 0.35/0.59        ( ( X
% 0.35/0.59          = ( minus_minus_real @ Y2 @ Z ) )
% 0.35/0.59        = ( Y2
% 0.35/0.59          = ( plus_plus_real @ X @ Z ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % eq_diff_eq'
% 0.35/0.59  thf(fact_3813_pos__zmod__mult__2,axiom,
% 0.35/0.59      ! [A: int,B: int] :
% 0.35/0.59        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.35/0.59       => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 0.35/0.59          = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % pos_zmod_mult_2
% 0.35/0.59  thf(fact_3814_max__def__raw,axiom,
% 0.35/0.59      ( ord_ma741700101516333627d_enat
% 0.35/0.59      = ( ^ [A3: extended_enat,B4: extended_enat] : ( if_Extended_enat @ ( ord_le2932123472753598470d_enat @ A3 @ B4 ) @ B4 @ A3 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % max_def_raw
% 0.35/0.59  thf(fact_3815_max__def__raw,axiom,
% 0.35/0.59      ( ord_max_set_real
% 0.35/0.59      = ( ^ [A3: set_real,B4: set_real] : ( if_set_real @ ( ord_less_eq_set_real @ A3 @ B4 ) @ B4 @ A3 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % max_def_raw
% 0.35/0.59  thf(fact_3816_max__def__raw,axiom,
% 0.35/0.59      ( ord_max_set_nat
% 0.35/0.59      = ( ^ [A3: set_nat,B4: set_nat] : ( if_set_nat @ ( ord_less_eq_set_nat @ A3 @ B4 ) @ B4 @ A3 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % max_def_raw
% 0.35/0.59  thf(fact_3817_max__def__raw,axiom,
% 0.35/0.59      ( ord_max_num
% 0.35/0.59      = ( ^ [A3: num,B4: num] : ( if_num @ ( ord_less_eq_num @ A3 @ B4 ) @ B4 @ A3 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % max_def_raw
% 0.35/0.59  thf(fact_3818_max__def__raw,axiom,
% 0.35/0.59      ( ord_max_nat
% 0.35/0.59      = ( ^ [A3: nat,B4: nat] : ( if_nat @ ( ord_less_eq_nat @ A3 @ B4 ) @ B4 @ A3 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % max_def_raw
% 0.35/0.59  thf(fact_3819_max__def__raw,axiom,
% 0.35/0.59      ( ord_max_int
% 0.35/0.59      = ( ^ [A3: int,B4: int] : ( if_int @ ( ord_less_eq_int @ A3 @ B4 ) @ B4 @ A3 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % max_def_raw
% 0.35/0.59  thf(fact_3820_neg__zmod__mult__2,axiom,
% 0.35/0.59      ! [A: int,B: int] :
% 0.35/0.59        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.35/0.59       => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 0.35/0.59          = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) @ one_one_int ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % neg_zmod_mult_2
% 0.35/0.59  thf(fact_3821_finite__has__maximal,axiom,
% 0.35/0.59      ! [A2: set_real] :
% 0.35/0.59        ( ( finite_finite_real @ A2 )
% 0.35/0.59       => ( ( A2 != bot_bot_set_real )
% 0.35/0.59         => ? [X3: real] :
% 0.35/0.59              ( ( member_real @ X3 @ A2 )
% 0.35/0.59              & ! [Xa: real] :
% 0.35/0.59                  ( ( member_real @ Xa @ A2 )
% 0.35/0.59                 => ( ( ord_less_eq_real @ X3 @ Xa )
% 0.35/0.59                   => ( X3 = Xa ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_has_maximal
% 0.35/0.59  thf(fact_3822_finite__has__maximal,axiom,
% 0.35/0.59      ! [A2: set_set_real] :
% 0.35/0.59        ( ( finite9007344921179782393t_real @ A2 )
% 0.35/0.59       => ( ( A2 != bot_bot_set_set_real )
% 0.35/0.59         => ? [X3: set_real] :
% 0.35/0.59              ( ( member_set_real @ X3 @ A2 )
% 0.35/0.59              & ! [Xa: set_real] :
% 0.35/0.59                  ( ( member_set_real @ Xa @ A2 )
% 0.35/0.59                 => ( ( ord_less_eq_set_real @ X3 @ Xa )
% 0.35/0.59                   => ( X3 = Xa ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_has_maximal
% 0.35/0.59  thf(fact_3823_finite__has__maximal,axiom,
% 0.35/0.59      ! [A2: set_set_nat] :
% 0.35/0.59        ( ( finite1152437895449049373et_nat @ A2 )
% 0.35/0.59       => ( ( A2 != bot_bot_set_set_nat )
% 0.35/0.59         => ? [X3: set_nat] :
% 0.35/0.59              ( ( member_set_nat @ X3 @ A2 )
% 0.35/0.59              & ! [Xa: set_nat] :
% 0.35/0.59                  ( ( member_set_nat @ Xa @ A2 )
% 0.35/0.59                 => ( ( ord_less_eq_set_nat @ X3 @ Xa )
% 0.35/0.59                   => ( X3 = Xa ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_has_maximal
% 0.35/0.59  thf(fact_3824_finite__has__maximal,axiom,
% 0.35/0.59      ! [A2: set_num] :
% 0.35/0.59        ( ( finite_finite_num @ A2 )
% 0.35/0.59       => ( ( A2 != bot_bot_set_num )
% 0.35/0.59         => ? [X3: num] :
% 0.35/0.59              ( ( member_num @ X3 @ A2 )
% 0.35/0.59              & ! [Xa: num] :
% 0.35/0.59                  ( ( member_num @ Xa @ A2 )
% 0.35/0.59                 => ( ( ord_less_eq_num @ X3 @ Xa )
% 0.35/0.59                   => ( X3 = Xa ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_has_maximal
% 0.35/0.59  thf(fact_3825_finite__has__maximal,axiom,
% 0.35/0.59      ! [A2: set_nat] :
% 0.35/0.59        ( ( finite_finite_nat @ A2 )
% 0.35/0.59       => ( ( A2 != bot_bot_set_nat )
% 0.35/0.59         => ? [X3: nat] :
% 0.35/0.59              ( ( member_nat @ X3 @ A2 )
% 0.35/0.59              & ! [Xa: nat] :
% 0.35/0.59                  ( ( member_nat @ Xa @ A2 )
% 0.35/0.59                 => ( ( ord_less_eq_nat @ X3 @ Xa )
% 0.35/0.59                   => ( X3 = Xa ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_has_maximal
% 0.35/0.59  thf(fact_3826_finite__has__maximal,axiom,
% 0.35/0.59      ! [A2: set_int] :
% 0.35/0.59        ( ( finite_finite_int @ A2 )
% 0.35/0.59       => ( ( A2 != bot_bot_set_int )
% 0.35/0.59         => ? [X3: int] :
% 0.35/0.59              ( ( member_int @ X3 @ A2 )
% 0.35/0.59              & ! [Xa: int] :
% 0.35/0.59                  ( ( member_int @ Xa @ A2 )
% 0.35/0.59                 => ( ( ord_less_eq_int @ X3 @ Xa )
% 0.35/0.59                   => ( X3 = Xa ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_has_maximal
% 0.35/0.59  thf(fact_3827_finite__has__minimal,axiom,
% 0.35/0.59      ! [A2: set_real] :
% 0.35/0.59        ( ( finite_finite_real @ A2 )
% 0.35/0.59       => ( ( A2 != bot_bot_set_real )
% 0.35/0.59         => ? [X3: real] :
% 0.35/0.59              ( ( member_real @ X3 @ A2 )
% 0.35/0.59              & ! [Xa: real] :
% 0.35/0.59                  ( ( member_real @ Xa @ A2 )
% 0.35/0.59                 => ( ( ord_less_eq_real @ Xa @ X3 )
% 0.35/0.59                   => ( X3 = Xa ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_has_minimal
% 0.35/0.59  thf(fact_3828_finite__has__minimal,axiom,
% 0.35/0.59      ! [A2: set_set_real] :
% 0.35/0.59        ( ( finite9007344921179782393t_real @ A2 )
% 0.35/0.59       => ( ( A2 != bot_bot_set_set_real )
% 0.35/0.59         => ? [X3: set_real] :
% 0.35/0.59              ( ( member_set_real @ X3 @ A2 )
% 0.35/0.59              & ! [Xa: set_real] :
% 0.35/0.59                  ( ( member_set_real @ Xa @ A2 )
% 0.35/0.59                 => ( ( ord_less_eq_set_real @ Xa @ X3 )
% 0.35/0.59                   => ( X3 = Xa ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_has_minimal
% 0.35/0.59  thf(fact_3829_finite__has__minimal,axiom,
% 0.35/0.59      ! [A2: set_set_nat] :
% 0.35/0.59        ( ( finite1152437895449049373et_nat @ A2 )
% 0.35/0.59       => ( ( A2 != bot_bot_set_set_nat )
% 0.35/0.59         => ? [X3: set_nat] :
% 0.35/0.59              ( ( member_set_nat @ X3 @ A2 )
% 0.35/0.59              & ! [Xa: set_nat] :
% 0.35/0.59                  ( ( member_set_nat @ Xa @ A2 )
% 0.35/0.59                 => ( ( ord_less_eq_set_nat @ Xa @ X3 )
% 0.35/0.59                   => ( X3 = Xa ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_has_minimal
% 0.35/0.59  thf(fact_3830_finite__has__minimal,axiom,
% 0.35/0.59      ! [A2: set_num] :
% 0.35/0.59        ( ( finite_finite_num @ A2 )
% 0.35/0.59       => ( ( A2 != bot_bot_set_num )
% 0.35/0.59         => ? [X3: num] :
% 0.35/0.59              ( ( member_num @ X3 @ A2 )
% 0.35/0.59              & ! [Xa: num] :
% 0.35/0.59                  ( ( member_num @ Xa @ A2 )
% 0.35/0.59                 => ( ( ord_less_eq_num @ Xa @ X3 )
% 0.35/0.59                   => ( X3 = Xa ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_has_minimal
% 0.35/0.59  thf(fact_3831_finite__has__minimal,axiom,
% 0.35/0.59      ! [A2: set_nat] :
% 0.35/0.59        ( ( finite_finite_nat @ A2 )
% 0.35/0.59       => ( ( A2 != bot_bot_set_nat )
% 0.35/0.59         => ? [X3: nat] :
% 0.35/0.59              ( ( member_nat @ X3 @ A2 )
% 0.35/0.59              & ! [Xa: nat] :
% 0.35/0.59                  ( ( member_nat @ Xa @ A2 )
% 0.35/0.59                 => ( ( ord_less_eq_nat @ Xa @ X3 )
% 0.35/0.59                   => ( X3 = Xa ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_has_minimal
% 0.35/0.59  thf(fact_3832_finite__has__minimal,axiom,
% 0.35/0.59      ! [A2: set_int] :
% 0.35/0.59        ( ( finite_finite_int @ A2 )
% 0.35/0.59       => ( ( A2 != bot_bot_set_int )
% 0.35/0.59         => ? [X3: int] :
% 0.35/0.59              ( ( member_int @ X3 @ A2 )
% 0.35/0.59              & ! [Xa: int] :
% 0.35/0.59                  ( ( member_int @ Xa @ A2 )
% 0.35/0.59                 => ( ( ord_less_eq_int @ Xa @ X3 )
% 0.35/0.59                   => ( X3 = Xa ) ) ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_has_minimal
% 0.35/0.59  thf(fact_3833_infinite__remove,axiom,
% 0.35/0.59      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT] :
% 0.35/0.59        ( ~ ( finite5795047828879050333T_VEBT @ S2 )
% 0.35/0.59       => ~ ( finite5795047828879050333T_VEBT @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % infinite_remove
% 0.35/0.59  thf(fact_3834_infinite__remove,axiom,
% 0.35/0.59      ! [S2: set_complex,A: complex] :
% 0.35/0.59        ( ~ ( finite3207457112153483333omplex @ S2 )
% 0.35/0.59       => ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % infinite_remove
% 0.35/0.59  thf(fact_3835_infinite__remove,axiom,
% 0.35/0.59      ! [S2: set_int,A: int] :
% 0.35/0.59        ( ~ ( finite_finite_int @ S2 )
% 0.35/0.59       => ~ ( finite_finite_int @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % infinite_remove
% 0.35/0.59  thf(fact_3836_infinite__remove,axiom,
% 0.35/0.59      ! [S2: set_real,A: real] :
% 0.35/0.59        ( ~ ( finite_finite_real @ S2 )
% 0.35/0.59       => ~ ( finite_finite_real @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % infinite_remove
% 0.35/0.59  thf(fact_3837_infinite__remove,axiom,
% 0.35/0.59      ! [S2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat] :
% 0.35/0.59        ( ~ ( finite6177210948735845034at_nat @ S2 )
% 0.35/0.59       => ~ ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ S2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % infinite_remove
% 0.35/0.59  thf(fact_3838_infinite__remove,axiom,
% 0.35/0.59      ! [S2: set_nat,A: nat] :
% 0.35/0.59        ( ~ ( finite_finite_nat @ S2 )
% 0.35/0.59       => ~ ( finite_finite_nat @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % infinite_remove
% 0.35/0.59  thf(fact_3839_infinite__coinduct,axiom,
% 0.35/0.59      ! [X8: set_VEBT_VEBT > $o,A2: set_VEBT_VEBT] :
% 0.35/0.59        ( ( X8 @ A2 )
% 0.35/0.59       => ( ! [A7: set_VEBT_VEBT] :
% 0.35/0.59              ( ( X8 @ A7 )
% 0.35/0.59             => ? [X5: vEBT_VEBT] :
% 0.35/0.59                  ( ( member_VEBT_VEBT @ X5 @ A7 )
% 0.35/0.59                  & ( ( X8 @ ( minus_5127226145743854075T_VEBT @ A7 @ ( insert_VEBT_VEBT @ X5 @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.35/0.59                    | ~ ( finite5795047828879050333T_VEBT @ ( minus_5127226145743854075T_VEBT @ A7 @ ( insert_VEBT_VEBT @ X5 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 0.35/0.59         => ~ ( finite5795047828879050333T_VEBT @ A2 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % infinite_coinduct
% 0.35/0.59  thf(fact_3840_infinite__coinduct,axiom,
% 0.35/0.59      ! [X8: set_complex > $o,A2: set_complex] :
% 0.35/0.59        ( ( X8 @ A2 )
% 0.35/0.59       => ( ! [A7: set_complex] :
% 0.35/0.59              ( ( X8 @ A7 )
% 0.35/0.59             => ? [X5: complex] :
% 0.35/0.59                  ( ( member_complex @ X5 @ A7 )
% 0.35/0.59                  & ( ( X8 @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ X5 @ bot_bot_set_complex ) ) )
% 0.35/0.59                    | ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ X5 @ bot_bot_set_complex ) ) ) ) ) )
% 0.35/0.59         => ~ ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % infinite_coinduct
% 0.35/0.59  thf(fact_3841_infinite__coinduct,axiom,
% 0.35/0.59      ! [X8: set_int > $o,A2: set_int] :
% 0.35/0.59        ( ( X8 @ A2 )
% 0.35/0.59       => ( ! [A7: set_int] :
% 0.35/0.59              ( ( X8 @ A7 )
% 0.35/0.59             => ? [X5: int] :
% 0.35/0.59                  ( ( member_int @ X5 @ A7 )
% 0.35/0.59                  & ( ( X8 @ ( minus_minus_set_int @ A7 @ ( insert_int @ X5 @ bot_bot_set_int ) ) )
% 0.35/0.59                    | ~ ( finite_finite_int @ ( minus_minus_set_int @ A7 @ ( insert_int @ X5 @ bot_bot_set_int ) ) ) ) ) )
% 0.35/0.59         => ~ ( finite_finite_int @ A2 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % infinite_coinduct
% 0.35/0.59  thf(fact_3842_infinite__coinduct,axiom,
% 0.35/0.59      ! [X8: set_real > $o,A2: set_real] :
% 0.35/0.59        ( ( X8 @ A2 )
% 0.35/0.59       => ( ! [A7: set_real] :
% 0.35/0.59              ( ( X8 @ A7 )
% 0.35/0.59             => ? [X5: real] :
% 0.35/0.59                  ( ( member_real @ X5 @ A7 )
% 0.35/0.59                  & ( ( X8 @ ( minus_minus_set_real @ A7 @ ( insert_real @ X5 @ bot_bot_set_real ) ) )
% 0.35/0.59                    | ~ ( finite_finite_real @ ( minus_minus_set_real @ A7 @ ( insert_real @ X5 @ bot_bot_set_real ) ) ) ) ) )
% 0.35/0.59         => ~ ( finite_finite_real @ A2 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % infinite_coinduct
% 0.35/0.59  thf(fact_3843_infinite__coinduct,axiom,
% 0.35/0.59      ! [X8: set_Pr1261947904930325089at_nat > $o,A2: set_Pr1261947904930325089at_nat] :
% 0.35/0.59        ( ( X8 @ A2 )
% 0.35/0.59       => ( ! [A7: set_Pr1261947904930325089at_nat] :
% 0.35/0.59              ( ( X8 @ A7 )
% 0.35/0.59             => ? [X5: product_prod_nat_nat] :
% 0.35/0.59                  ( ( member8440522571783428010at_nat @ X5 @ A7 )
% 0.35/0.59                  & ( ( X8 @ ( minus_1356011639430497352at_nat @ A7 @ ( insert8211810215607154385at_nat @ X5 @ bot_bo2099793752762293965at_nat ) ) )
% 0.35/0.59                    | ~ ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ A7 @ ( insert8211810215607154385at_nat @ X5 @ bot_bo2099793752762293965at_nat ) ) ) ) ) )
% 0.35/0.59         => ~ ( finite6177210948735845034at_nat @ A2 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % infinite_coinduct
% 0.35/0.59  thf(fact_3844_infinite__coinduct,axiom,
% 0.35/0.59      ! [X8: set_nat > $o,A2: set_nat] :
% 0.35/0.59        ( ( X8 @ A2 )
% 0.35/0.59       => ( ! [A7: set_nat] :
% 0.35/0.59              ( ( X8 @ A7 )
% 0.35/0.59             => ? [X5: nat] :
% 0.35/0.59                  ( ( member_nat @ X5 @ A7 )
% 0.35/0.59                  & ( ( X8 @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ X5 @ bot_bot_set_nat ) ) )
% 0.35/0.59                    | ~ ( finite_finite_nat @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ X5 @ bot_bot_set_nat ) ) ) ) ) )
% 0.35/0.59         => ~ ( finite_finite_nat @ A2 ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % infinite_coinduct
% 0.35/0.59  thf(fact_3845_finite__empty__induct,axiom,
% 0.35/0.59      ! [A2: set_VEBT_VEBT,P: set_VEBT_VEBT > $o] :
% 0.35/0.59        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.35/0.59       => ( ( P @ A2 )
% 0.35/0.59         => ( ! [A4: vEBT_VEBT,A7: set_VEBT_VEBT] :
% 0.35/0.59                ( ( finite5795047828879050333T_VEBT @ A7 )
% 0.35/0.59               => ( ( member_VEBT_VEBT @ A4 @ A7 )
% 0.35/0.59                 => ( ( P @ A7 )
% 0.35/0.59                   => ( P @ ( minus_5127226145743854075T_VEBT @ A7 @ ( insert_VEBT_VEBT @ A4 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 0.35/0.59           => ( P @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_empty_induct
% 0.35/0.59  thf(fact_3846_finite__empty__induct,axiom,
% 0.35/0.59      ! [A2: set_complex,P: set_complex > $o] :
% 0.35/0.59        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.59       => ( ( P @ A2 )
% 0.35/0.59         => ( ! [A4: complex,A7: set_complex] :
% 0.35/0.59                ( ( finite3207457112153483333omplex @ A7 )
% 0.35/0.59               => ( ( member_complex @ A4 @ A7 )
% 0.35/0.59                 => ( ( P @ A7 )
% 0.35/0.59                   => ( P @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ A4 @ bot_bot_set_complex ) ) ) ) ) )
% 0.35/0.59           => ( P @ bot_bot_set_complex ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_empty_induct
% 0.35/0.59  thf(fact_3847_finite__empty__induct,axiom,
% 0.35/0.59      ! [A2: set_int,P: set_int > $o] :
% 0.35/0.59        ( ( finite_finite_int @ A2 )
% 0.35/0.59       => ( ( P @ A2 )
% 0.35/0.59         => ( ! [A4: int,A7: set_int] :
% 0.35/0.59                ( ( finite_finite_int @ A7 )
% 0.35/0.59               => ( ( member_int @ A4 @ A7 )
% 0.35/0.59                 => ( ( P @ A7 )
% 0.35/0.59                   => ( P @ ( minus_minus_set_int @ A7 @ ( insert_int @ A4 @ bot_bot_set_int ) ) ) ) ) )
% 0.35/0.59           => ( P @ bot_bot_set_int ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_empty_induct
% 0.35/0.59  thf(fact_3848_finite__empty__induct,axiom,
% 0.35/0.59      ! [A2: set_real,P: set_real > $o] :
% 0.35/0.59        ( ( finite_finite_real @ A2 )
% 0.35/0.59       => ( ( P @ A2 )
% 0.35/0.59         => ( ! [A4: real,A7: set_real] :
% 0.35/0.59                ( ( finite_finite_real @ A7 )
% 0.35/0.59               => ( ( member_real @ A4 @ A7 )
% 0.35/0.59                 => ( ( P @ A7 )
% 0.35/0.59                   => ( P @ ( minus_minus_set_real @ A7 @ ( insert_real @ A4 @ bot_bot_set_real ) ) ) ) ) )
% 0.35/0.59           => ( P @ bot_bot_set_real ) ) ) ) ).
% 0.35/0.59  
% 0.35/0.59  % finite_empty_induct
% 0.35/0.60  thf(fact_3849_finite__empty__induct,axiom,
% 0.35/0.60      ! [A2: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 0.35/0.60        ( ( finite6177210948735845034at_nat @ A2 )
% 0.35/0.60       => ( ( P @ A2 )
% 0.35/0.60         => ( ! [A4: product_prod_nat_nat,A7: set_Pr1261947904930325089at_nat] :
% 0.35/0.60                ( ( finite6177210948735845034at_nat @ A7 )
% 0.35/0.60               => ( ( member8440522571783428010at_nat @ A4 @ A7 )
% 0.35/0.60                 => ( ( P @ A7 )
% 0.35/0.60                   => ( P @ ( minus_1356011639430497352at_nat @ A7 @ ( insert8211810215607154385at_nat @ A4 @ bot_bo2099793752762293965at_nat ) ) ) ) ) )
% 0.35/0.60           => ( P @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % finite_empty_induct
% 0.35/0.60  thf(fact_3850_finite__empty__induct,axiom,
% 0.35/0.60      ! [A2: set_nat,P: set_nat > $o] :
% 0.35/0.60        ( ( finite_finite_nat @ A2 )
% 0.35/0.60       => ( ( P @ A2 )
% 0.35/0.60         => ( ! [A4: nat,A7: set_nat] :
% 0.35/0.60                ( ( finite_finite_nat @ A7 )
% 0.35/0.60               => ( ( member_nat @ A4 @ A7 )
% 0.35/0.60                 => ( ( P @ A7 )
% 0.35/0.60                   => ( P @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ A4 @ bot_bot_set_nat ) ) ) ) ) )
% 0.35/0.60           => ( P @ bot_bot_set_nat ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % finite_empty_induct
% 0.35/0.60  thf(fact_3851_div__less__mono,axiom,
% 0.35/0.60      ! [A2: nat,B2: nat,N: nat] :
% 0.35/0.60        ( ( ord_less_nat @ A2 @ B2 )
% 0.35/0.60       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.60         => ( ( ( modulo_modulo_nat @ A2 @ N )
% 0.35/0.60              = zero_zero_nat )
% 0.35/0.60           => ( ( ( modulo_modulo_nat @ B2 @ N )
% 0.35/0.60                = zero_zero_nat )
% 0.35/0.60             => ( ord_less_nat @ ( divide_divide_nat @ A2 @ N ) @ ( divide_divide_nat @ B2 @ N ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_less_mono
% 0.35/0.60  thf(fact_3852_div__mod__decomp,axiom,
% 0.35/0.60      ! [A2: nat,N: nat] :
% 0.35/0.60        ( A2
% 0.35/0.60        = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A2 @ N ) @ N ) @ ( modulo_modulo_nat @ A2 @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_mod_decomp
% 0.35/0.60  thf(fact_3853_remove__induct,axiom,
% 0.35/0.60      ! [P: set_VEBT_VEBT > $o,B2: set_VEBT_VEBT] :
% 0.35/0.60        ( ( P @ bot_bo8194388402131092736T_VEBT )
% 0.35/0.60       => ( ( ~ ( finite5795047828879050333T_VEBT @ B2 )
% 0.35/0.60           => ( P @ B2 ) )
% 0.35/0.60         => ( ! [A7: set_VEBT_VEBT] :
% 0.35/0.60                ( ( finite5795047828879050333T_VEBT @ A7 )
% 0.35/0.60               => ( ( A7 != bot_bo8194388402131092736T_VEBT )
% 0.35/0.60                 => ( ( ord_le4337996190870823476T_VEBT @ A7 @ B2 )
% 0.35/0.60                   => ( ! [X5: vEBT_VEBT] :
% 0.35/0.60                          ( ( member_VEBT_VEBT @ X5 @ A7 )
% 0.35/0.60                         => ( P @ ( minus_5127226145743854075T_VEBT @ A7 @ ( insert_VEBT_VEBT @ X5 @ bot_bo8194388402131092736T_VEBT ) ) ) )
% 0.35/0.60                     => ( P @ A7 ) ) ) ) )
% 0.35/0.60           => ( P @ B2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % remove_induct
% 0.35/0.60  thf(fact_3854_remove__induct,axiom,
% 0.35/0.60      ! [P: set_complex > $o,B2: set_complex] :
% 0.35/0.60        ( ( P @ bot_bot_set_complex )
% 0.35/0.60       => ( ( ~ ( finite3207457112153483333omplex @ B2 )
% 0.35/0.60           => ( P @ B2 ) )
% 0.35/0.60         => ( ! [A7: set_complex] :
% 0.35/0.60                ( ( finite3207457112153483333omplex @ A7 )
% 0.35/0.60               => ( ( A7 != bot_bot_set_complex )
% 0.35/0.60                 => ( ( ord_le211207098394363844omplex @ A7 @ B2 )
% 0.35/0.60                   => ( ! [X5: complex] :
% 0.35/0.60                          ( ( member_complex @ X5 @ A7 )
% 0.35/0.60                         => ( P @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ X5 @ bot_bot_set_complex ) ) ) )
% 0.35/0.60                     => ( P @ A7 ) ) ) ) )
% 0.35/0.60           => ( P @ B2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % remove_induct
% 0.35/0.60  thf(fact_3855_remove__induct,axiom,
% 0.35/0.60      ! [P: set_int > $o,B2: set_int] :
% 0.35/0.60        ( ( P @ bot_bot_set_int )
% 0.35/0.60       => ( ( ~ ( finite_finite_int @ B2 )
% 0.35/0.60           => ( P @ B2 ) )
% 0.35/0.60         => ( ! [A7: set_int] :
% 0.35/0.60                ( ( finite_finite_int @ A7 )
% 0.35/0.60               => ( ( A7 != bot_bot_set_int )
% 0.35/0.60                 => ( ( ord_less_eq_set_int @ A7 @ B2 )
% 0.35/0.60                   => ( ! [X5: int] :
% 0.35/0.60                          ( ( member_int @ X5 @ A7 )
% 0.35/0.60                         => ( P @ ( minus_minus_set_int @ A7 @ ( insert_int @ X5 @ bot_bot_set_int ) ) ) )
% 0.35/0.60                     => ( P @ A7 ) ) ) ) )
% 0.35/0.60           => ( P @ B2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % remove_induct
% 0.35/0.60  thf(fact_3856_remove__induct,axiom,
% 0.35/0.60      ! [P: set_Pr1261947904930325089at_nat > $o,B2: set_Pr1261947904930325089at_nat] :
% 0.35/0.60        ( ( P @ bot_bo2099793752762293965at_nat )
% 0.35/0.60       => ( ( ~ ( finite6177210948735845034at_nat @ B2 )
% 0.35/0.60           => ( P @ B2 ) )
% 0.35/0.60         => ( ! [A7: set_Pr1261947904930325089at_nat] :
% 0.35/0.60                ( ( finite6177210948735845034at_nat @ A7 )
% 0.35/0.60               => ( ( A7 != bot_bo2099793752762293965at_nat )
% 0.35/0.60                 => ( ( ord_le3146513528884898305at_nat @ A7 @ B2 )
% 0.35/0.60                   => ( ! [X5: product_prod_nat_nat] :
% 0.35/0.60                          ( ( member8440522571783428010at_nat @ X5 @ A7 )
% 0.35/0.60                         => ( P @ ( minus_1356011639430497352at_nat @ A7 @ ( insert8211810215607154385at_nat @ X5 @ bot_bo2099793752762293965at_nat ) ) ) )
% 0.35/0.60                     => ( P @ A7 ) ) ) ) )
% 0.35/0.60           => ( P @ B2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % remove_induct
% 0.35/0.60  thf(fact_3857_remove__induct,axiom,
% 0.35/0.60      ! [P: set_real > $o,B2: set_real] :
% 0.35/0.60        ( ( P @ bot_bot_set_real )
% 0.35/0.60       => ( ( ~ ( finite_finite_real @ B2 )
% 0.35/0.60           => ( P @ B2 ) )
% 0.35/0.60         => ( ! [A7: set_real] :
% 0.35/0.60                ( ( finite_finite_real @ A7 )
% 0.35/0.60               => ( ( A7 != bot_bot_set_real )
% 0.35/0.60                 => ( ( ord_less_eq_set_real @ A7 @ B2 )
% 0.35/0.60                   => ( ! [X5: real] :
% 0.35/0.60                          ( ( member_real @ X5 @ A7 )
% 0.35/0.60                         => ( P @ ( minus_minus_set_real @ A7 @ ( insert_real @ X5 @ bot_bot_set_real ) ) ) )
% 0.35/0.60                     => ( P @ A7 ) ) ) ) )
% 0.35/0.60           => ( P @ B2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % remove_induct
% 0.35/0.60  thf(fact_3858_remove__induct,axiom,
% 0.35/0.60      ! [P: set_nat > $o,B2: set_nat] :
% 0.35/0.60        ( ( P @ bot_bot_set_nat )
% 0.35/0.60       => ( ( ~ ( finite_finite_nat @ B2 )
% 0.35/0.60           => ( P @ B2 ) )
% 0.35/0.60         => ( ! [A7: set_nat] :
% 0.35/0.60                ( ( finite_finite_nat @ A7 )
% 0.35/0.60               => ( ( A7 != bot_bot_set_nat )
% 0.35/0.60                 => ( ( ord_less_eq_set_nat @ A7 @ B2 )
% 0.35/0.60                   => ( ! [X5: nat] :
% 0.35/0.60                          ( ( member_nat @ X5 @ A7 )
% 0.35/0.60                         => ( P @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ X5 @ bot_bot_set_nat ) ) ) )
% 0.35/0.60                     => ( P @ A7 ) ) ) ) )
% 0.35/0.60           => ( P @ B2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % remove_induct
% 0.35/0.60  thf(fact_3859_finite__remove__induct,axiom,
% 0.35/0.60      ! [B2: set_VEBT_VEBT,P: set_VEBT_VEBT > $o] :
% 0.35/0.60        ( ( finite5795047828879050333T_VEBT @ B2 )
% 0.35/0.60       => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 0.35/0.60         => ( ! [A7: set_VEBT_VEBT] :
% 0.35/0.60                ( ( finite5795047828879050333T_VEBT @ A7 )
% 0.35/0.60               => ( ( A7 != bot_bo8194388402131092736T_VEBT )
% 0.35/0.60                 => ( ( ord_le4337996190870823476T_VEBT @ A7 @ B2 )
% 0.35/0.60                   => ( ! [X5: vEBT_VEBT] :
% 0.35/0.60                          ( ( member_VEBT_VEBT @ X5 @ A7 )
% 0.35/0.60                         => ( P @ ( minus_5127226145743854075T_VEBT @ A7 @ ( insert_VEBT_VEBT @ X5 @ bot_bo8194388402131092736T_VEBT ) ) ) )
% 0.35/0.60                     => ( P @ A7 ) ) ) ) )
% 0.35/0.60           => ( P @ B2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % finite_remove_induct
% 0.35/0.60  thf(fact_3860_finite__remove__induct,axiom,
% 0.35/0.60      ! [B2: set_complex,P: set_complex > $o] :
% 0.35/0.60        ( ( finite3207457112153483333omplex @ B2 )
% 0.35/0.60       => ( ( P @ bot_bot_set_complex )
% 0.35/0.60         => ( ! [A7: set_complex] :
% 0.35/0.60                ( ( finite3207457112153483333omplex @ A7 )
% 0.35/0.60               => ( ( A7 != bot_bot_set_complex )
% 0.35/0.60                 => ( ( ord_le211207098394363844omplex @ A7 @ B2 )
% 0.35/0.60                   => ( ! [X5: complex] :
% 0.35/0.60                          ( ( member_complex @ X5 @ A7 )
% 0.35/0.60                         => ( P @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ X5 @ bot_bot_set_complex ) ) ) )
% 0.35/0.60                     => ( P @ A7 ) ) ) ) )
% 0.35/0.60           => ( P @ B2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % finite_remove_induct
% 0.35/0.60  thf(fact_3861_finite__remove__induct,axiom,
% 0.35/0.60      ! [B2: set_int,P: set_int > $o] :
% 0.35/0.60        ( ( finite_finite_int @ B2 )
% 0.35/0.60       => ( ( P @ bot_bot_set_int )
% 0.35/0.60         => ( ! [A7: set_int] :
% 0.35/0.60                ( ( finite_finite_int @ A7 )
% 0.35/0.60               => ( ( A7 != bot_bot_set_int )
% 0.35/0.60                 => ( ( ord_less_eq_set_int @ A7 @ B2 )
% 0.35/0.60                   => ( ! [X5: int] :
% 0.35/0.60                          ( ( member_int @ X5 @ A7 )
% 0.35/0.60                         => ( P @ ( minus_minus_set_int @ A7 @ ( insert_int @ X5 @ bot_bot_set_int ) ) ) )
% 0.35/0.60                     => ( P @ A7 ) ) ) ) )
% 0.35/0.60           => ( P @ B2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % finite_remove_induct
% 0.35/0.60  thf(fact_3862_finite__remove__induct,axiom,
% 0.35/0.60      ! [B2: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 0.35/0.60        ( ( finite6177210948735845034at_nat @ B2 )
% 0.35/0.60       => ( ( P @ bot_bo2099793752762293965at_nat )
% 0.35/0.60         => ( ! [A7: set_Pr1261947904930325089at_nat] :
% 0.35/0.60                ( ( finite6177210948735845034at_nat @ A7 )
% 0.35/0.60               => ( ( A7 != bot_bo2099793752762293965at_nat )
% 0.35/0.60                 => ( ( ord_le3146513528884898305at_nat @ A7 @ B2 )
% 0.35/0.60                   => ( ! [X5: product_prod_nat_nat] :
% 0.35/0.60                          ( ( member8440522571783428010at_nat @ X5 @ A7 )
% 0.35/0.60                         => ( P @ ( minus_1356011639430497352at_nat @ A7 @ ( insert8211810215607154385at_nat @ X5 @ bot_bo2099793752762293965at_nat ) ) ) )
% 0.35/0.60                     => ( P @ A7 ) ) ) ) )
% 0.35/0.60           => ( P @ B2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % finite_remove_induct
% 0.35/0.60  thf(fact_3863_finite__remove__induct,axiom,
% 0.35/0.60      ! [B2: set_real,P: set_real > $o] :
% 0.35/0.60        ( ( finite_finite_real @ B2 )
% 0.35/0.60       => ( ( P @ bot_bot_set_real )
% 0.35/0.60         => ( ! [A7: set_real] :
% 0.35/0.60                ( ( finite_finite_real @ A7 )
% 0.35/0.60               => ( ( A7 != bot_bot_set_real )
% 0.35/0.60                 => ( ( ord_less_eq_set_real @ A7 @ B2 )
% 0.35/0.60                   => ( ! [X5: real] :
% 0.35/0.60                          ( ( member_real @ X5 @ A7 )
% 0.35/0.60                         => ( P @ ( minus_minus_set_real @ A7 @ ( insert_real @ X5 @ bot_bot_set_real ) ) ) )
% 0.35/0.60                     => ( P @ A7 ) ) ) ) )
% 0.35/0.60           => ( P @ B2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % finite_remove_induct
% 0.35/0.60  thf(fact_3864_finite__remove__induct,axiom,
% 0.35/0.60      ! [B2: set_nat,P: set_nat > $o] :
% 0.35/0.60        ( ( finite_finite_nat @ B2 )
% 0.35/0.60       => ( ( P @ bot_bot_set_nat )
% 0.35/0.60         => ( ! [A7: set_nat] :
% 0.35/0.60                ( ( finite_finite_nat @ A7 )
% 0.35/0.60               => ( ( A7 != bot_bot_set_nat )
% 0.35/0.60                 => ( ( ord_less_eq_set_nat @ A7 @ B2 )
% 0.35/0.60                   => ( ! [X5: nat] :
% 0.35/0.60                          ( ( member_nat @ X5 @ A7 )
% 0.35/0.60                         => ( P @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ X5 @ bot_bot_set_nat ) ) ) )
% 0.35/0.60                     => ( P @ A7 ) ) ) ) )
% 0.35/0.60           => ( P @ B2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % finite_remove_induct
% 0.35/0.60  thf(fact_3865_arcosh__1,axiom,
% 0.35/0.60      ( ( arcosh_real @ one_one_real )
% 0.35/0.60      = zero_zero_real ) ).
% 0.35/0.60  
% 0.35/0.60  % arcosh_1
% 0.35/0.60  thf(fact_3866_finite__nth__roots,axiom,
% 0.35/0.60      ! [N: nat,C: complex] :
% 0.35/0.60        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.60       => ( finite3207457112153483333omplex
% 0.35/0.60          @ ( collect_complex
% 0.35/0.60            @ ^ [Z4: complex] :
% 0.35/0.60                ( ( power_power_complex @ Z4 @ N )
% 0.35/0.60                = C ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % finite_nth_roots
% 0.35/0.60  thf(fact_3867_flip__bit__Suc,axiom,
% 0.35/0.60      ! [N: nat,A: int] :
% 0.35/0.60        ( ( bit_se2159334234014336723it_int @ ( suc @ N ) @ A )
% 0.35/0.60        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % flip_bit_Suc
% 0.35/0.60  thf(fact_3868_flip__bit__Suc,axiom,
% 0.35/0.60      ! [N: nat,A: nat] :
% 0.35/0.60        ( ( bit_se2161824704523386999it_nat @ ( suc @ N ) @ A )
% 0.35/0.60        = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % flip_bit_Suc
% 0.35/0.60  thf(fact_3869_finite__linorder__min__induct,axiom,
% 0.35/0.60      ! [A2: set_real,P: set_real > $o] :
% 0.35/0.60        ( ( finite_finite_real @ A2 )
% 0.35/0.60       => ( ( P @ bot_bot_set_real )
% 0.35/0.60         => ( ! [B3: real,A7: set_real] :
% 0.35/0.60                ( ( finite_finite_real @ A7 )
% 0.35/0.60               => ( ! [X5: real] :
% 0.35/0.60                      ( ( member_real @ X5 @ A7 )
% 0.35/0.60                     => ( ord_less_real @ B3 @ X5 ) )
% 0.35/0.60                 => ( ( P @ A7 )
% 0.35/0.60                   => ( P @ ( insert_real @ B3 @ A7 ) ) ) ) )
% 0.35/0.60           => ( P @ A2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % finite_linorder_min_induct
% 0.35/0.60  thf(fact_3870_finite__linorder__min__induct,axiom,
% 0.35/0.60      ! [A2: set_rat,P: set_rat > $o] :
% 0.35/0.60        ( ( finite_finite_rat @ A2 )
% 0.35/0.60       => ( ( P @ bot_bot_set_rat )
% 0.35/0.60         => ( ! [B3: rat,A7: set_rat] :
% 0.35/0.60                ( ( finite_finite_rat @ A7 )
% 0.35/0.60               => ( ! [X5: rat] :
% 0.35/0.60                      ( ( member_rat @ X5 @ A7 )
% 0.35/0.60                     => ( ord_less_rat @ B3 @ X5 ) )
% 0.35/0.60                 => ( ( P @ A7 )
% 0.35/0.60                   => ( P @ ( insert_rat @ B3 @ A7 ) ) ) ) )
% 0.35/0.60           => ( P @ A2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % finite_linorder_min_induct
% 0.35/0.60  thf(fact_3871_finite__linorder__min__induct,axiom,
% 0.35/0.60      ! [A2: set_num,P: set_num > $o] :
% 0.35/0.60        ( ( finite_finite_num @ A2 )
% 0.35/0.60       => ( ( P @ bot_bot_set_num )
% 0.35/0.60         => ( ! [B3: num,A7: set_num] :
% 0.35/0.60                ( ( finite_finite_num @ A7 )
% 0.35/0.60               => ( ! [X5: num] :
% 0.35/0.60                      ( ( member_num @ X5 @ A7 )
% 0.35/0.60                     => ( ord_less_num @ B3 @ X5 ) )
% 0.35/0.60                 => ( ( P @ A7 )
% 0.35/0.60                   => ( P @ ( insert_num @ B3 @ A7 ) ) ) ) )
% 0.35/0.60           => ( P @ A2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % finite_linorder_min_induct
% 0.35/0.60  thf(fact_3872_finite__linorder__min__induct,axiom,
% 0.35/0.60      ! [A2: set_nat,P: set_nat > $o] :
% 0.35/0.60        ( ( finite_finite_nat @ A2 )
% 0.35/0.60       => ( ( P @ bot_bot_set_nat )
% 0.35/0.60         => ( ! [B3: nat,A7: set_nat] :
% 0.35/0.60                ( ( finite_finite_nat @ A7 )
% 0.35/0.60               => ( ! [X5: nat] :
% 0.35/0.60                      ( ( member_nat @ X5 @ A7 )
% 0.35/0.60                     => ( ord_less_nat @ B3 @ X5 ) )
% 0.35/0.60                 => ( ( P @ A7 )
% 0.35/0.60                   => ( P @ ( insert_nat @ B3 @ A7 ) ) ) ) )
% 0.35/0.60           => ( P @ A2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % finite_linorder_min_induct
% 0.35/0.60  thf(fact_3873_finite__linorder__min__induct,axiom,
% 0.35/0.60      ! [A2: set_int,P: set_int > $o] :
% 0.35/0.60        ( ( finite_finite_int @ A2 )
% 0.35/0.60       => ( ( P @ bot_bot_set_int )
% 0.35/0.60         => ( ! [B3: int,A7: set_int] :
% 0.35/0.60                ( ( finite_finite_int @ A7 )
% 0.35/0.60               => ( ! [X5: int] :
% 0.35/0.60                      ( ( member_int @ X5 @ A7 )
% 0.35/0.60                     => ( ord_less_int @ B3 @ X5 ) )
% 0.35/0.60                 => ( ( P @ A7 )
% 0.35/0.60                   => ( P @ ( insert_int @ B3 @ A7 ) ) ) ) )
% 0.35/0.60           => ( P @ A2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % finite_linorder_min_induct
% 0.35/0.60  thf(fact_3874_finite__linorder__max__induct,axiom,
% 0.35/0.60      ! [A2: set_real,P: set_real > $o] :
% 0.35/0.60        ( ( finite_finite_real @ A2 )
% 0.35/0.60       => ( ( P @ bot_bot_set_real )
% 0.35/0.60         => ( ! [B3: real,A7: set_real] :
% 0.35/0.60                ( ( finite_finite_real @ A7 )
% 0.35/0.60               => ( ! [X5: real] :
% 0.35/0.60                      ( ( member_real @ X5 @ A7 )
% 0.35/0.60                     => ( ord_less_real @ X5 @ B3 ) )
% 0.35/0.60                 => ( ( P @ A7 )
% 0.35/0.60                   => ( P @ ( insert_real @ B3 @ A7 ) ) ) ) )
% 0.35/0.60           => ( P @ A2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % finite_linorder_max_induct
% 0.35/0.60  thf(fact_3875_finite__linorder__max__induct,axiom,
% 0.35/0.60      ! [A2: set_rat,P: set_rat > $o] :
% 0.35/0.60        ( ( finite_finite_rat @ A2 )
% 0.35/0.60       => ( ( P @ bot_bot_set_rat )
% 0.35/0.60         => ( ! [B3: rat,A7: set_rat] :
% 0.35/0.60                ( ( finite_finite_rat @ A7 )
% 0.35/0.60               => ( ! [X5: rat] :
% 0.35/0.60                      ( ( member_rat @ X5 @ A7 )
% 0.35/0.60                     => ( ord_less_rat @ X5 @ B3 ) )
% 0.35/0.60                 => ( ( P @ A7 )
% 0.35/0.60                   => ( P @ ( insert_rat @ B3 @ A7 ) ) ) ) )
% 0.35/0.60           => ( P @ A2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % finite_linorder_max_induct
% 0.35/0.60  thf(fact_3876_finite__linorder__max__induct,axiom,
% 0.35/0.60      ! [A2: set_num,P: set_num > $o] :
% 0.35/0.60        ( ( finite_finite_num @ A2 )
% 0.35/0.60       => ( ( P @ bot_bot_set_num )
% 0.35/0.60         => ( ! [B3: num,A7: set_num] :
% 0.35/0.60                ( ( finite_finite_num @ A7 )
% 0.35/0.60               => ( ! [X5: num] :
% 0.35/0.60                      ( ( member_num @ X5 @ A7 )
% 0.35/0.60                     => ( ord_less_num @ X5 @ B3 ) )
% 0.35/0.60                 => ( ( P @ A7 )
% 0.35/0.60                   => ( P @ ( insert_num @ B3 @ A7 ) ) ) ) )
% 0.35/0.60           => ( P @ A2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % finite_linorder_max_induct
% 0.35/0.60  thf(fact_3877_finite__linorder__max__induct,axiom,
% 0.35/0.60      ! [A2: set_nat,P: set_nat > $o] :
% 0.35/0.60        ( ( finite_finite_nat @ A2 )
% 0.35/0.60       => ( ( P @ bot_bot_set_nat )
% 0.35/0.60         => ( ! [B3: nat,A7: set_nat] :
% 0.35/0.60                ( ( finite_finite_nat @ A7 )
% 0.35/0.60               => ( ! [X5: nat] :
% 0.35/0.60                      ( ( member_nat @ X5 @ A7 )
% 0.35/0.60                     => ( ord_less_nat @ X5 @ B3 ) )
% 0.35/0.60                 => ( ( P @ A7 )
% 0.35/0.60                   => ( P @ ( insert_nat @ B3 @ A7 ) ) ) ) )
% 0.35/0.60           => ( P @ A2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % finite_linorder_max_induct
% 0.35/0.60  thf(fact_3878_finite__linorder__max__induct,axiom,
% 0.35/0.60      ! [A2: set_int,P: set_int > $o] :
% 0.35/0.60        ( ( finite_finite_int @ A2 )
% 0.35/0.60       => ( ( P @ bot_bot_set_int )
% 0.35/0.60         => ( ! [B3: int,A7: set_int] :
% 0.35/0.60                ( ( finite_finite_int @ A7 )
% 0.35/0.60               => ( ! [X5: int] :
% 0.35/0.60                      ( ( member_int @ X5 @ A7 )
% 0.35/0.60                     => ( ord_less_int @ X5 @ B3 ) )
% 0.35/0.60                 => ( ( P @ A7 )
% 0.35/0.60                   => ( P @ ( insert_int @ B3 @ A7 ) ) ) ) )
% 0.35/0.60           => ( P @ A2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % finite_linorder_max_induct
% 0.35/0.60  thf(fact_3879_finite__ranking__induct,axiom,
% 0.35/0.60      ! [S2: set_VEBT_VEBT,P: set_VEBT_VEBT > $o,F: vEBT_VEBT > num] :
% 0.35/0.60        ( ( finite5795047828879050333T_VEBT @ S2 )
% 0.35/0.60       => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 0.35/0.60         => ( ! [X3: vEBT_VEBT,S4: set_VEBT_VEBT] :
% 0.35/0.60                ( ( finite5795047828879050333T_VEBT @ S4 )
% 0.35/0.60               => ( ! [Y4: vEBT_VEBT] :
% 0.35/0.60                      ( ( member_VEBT_VEBT @ Y4 @ S4 )
% 0.35/0.60                     => ( ord_less_eq_num @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 0.35/0.60                 => ( ( P @ S4 )
% 0.35/0.60                   => ( P @ ( insert_VEBT_VEBT @ X3 @ S4 ) ) ) ) )
% 0.35/0.60           => ( P @ S2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % finite_ranking_induct
% 0.35/0.60  thf(fact_3880_finite__ranking__induct,axiom,
% 0.35/0.60      ! [S2: set_complex,P: set_complex > $o,F: complex > num] :
% 0.35/0.60        ( ( finite3207457112153483333omplex @ S2 )
% 0.35/0.60       => ( ( P @ bot_bot_set_complex )
% 0.35/0.60         => ( ! [X3: complex,S4: set_complex] :
% 0.35/0.60                ( ( finite3207457112153483333omplex @ S4 )
% 0.35/0.60               => ( ! [Y4: complex] :
% 0.35/0.60                      ( ( member_complex @ Y4 @ S4 )
% 0.35/0.60                     => ( ord_less_eq_num @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 0.35/0.60                 => ( ( P @ S4 )
% 0.35/0.60                   => ( P @ ( insert_complex @ X3 @ S4 ) ) ) ) )
% 0.35/0.60           => ( P @ S2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % finite_ranking_induct
% 0.35/0.60  thf(fact_3881_finite__ranking__induct,axiom,
% 0.35/0.60      ! [S2: set_nat,P: set_nat > $o,F: nat > num] :
% 0.35/0.60        ( ( finite_finite_nat @ S2 )
% 0.35/0.60       => ( ( P @ bot_bot_set_nat )
% 0.35/0.60         => ( ! [X3: nat,S4: set_nat] :
% 0.35/0.60                ( ( finite_finite_nat @ S4 )
% 0.35/0.60               => ( ! [Y4: nat] :
% 0.35/0.60                      ( ( member_nat @ Y4 @ S4 )
% 0.35/0.60                     => ( ord_less_eq_num @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 0.35/0.60                 => ( ( P @ S4 )
% 0.35/0.60                   => ( P @ ( insert_nat @ X3 @ S4 ) ) ) ) )
% 0.35/0.60           => ( P @ S2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % finite_ranking_induct
% 0.35/0.60  thf(fact_3882_finite__ranking__induct,axiom,
% 0.35/0.60      ! [S2: set_int,P: set_int > $o,F: int > num] :
% 0.35/0.60        ( ( finite_finite_int @ S2 )
% 0.35/0.60       => ( ( P @ bot_bot_set_int )
% 0.35/0.60         => ( ! [X3: int,S4: set_int] :
% 0.35/0.60                ( ( finite_finite_int @ S4 )
% 0.35/0.60               => ( ! [Y4: int] :
% 0.35/0.60                      ( ( member_int @ Y4 @ S4 )
% 0.35/0.60                     => ( ord_less_eq_num @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 0.35/0.60                 => ( ( P @ S4 )
% 0.35/0.60                   => ( P @ ( insert_int @ X3 @ S4 ) ) ) ) )
% 0.35/0.60           => ( P @ S2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % finite_ranking_induct
% 0.35/0.60  thf(fact_3883_finite__ranking__induct,axiom,
% 0.35/0.60      ! [S2: set_real,P: set_real > $o,F: real > num] :
% 0.35/0.60        ( ( finite_finite_real @ S2 )
% 0.35/0.60       => ( ( P @ bot_bot_set_real )
% 0.35/0.60         => ( ! [X3: real,S4: set_real] :
% 0.35/0.60                ( ( finite_finite_real @ S4 )
% 0.35/0.60               => ( ! [Y4: real] :
% 0.35/0.60                      ( ( member_real @ Y4 @ S4 )
% 0.35/0.60                     => ( ord_less_eq_num @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 0.35/0.60                 => ( ( P @ S4 )
% 0.35/0.60                   => ( P @ ( insert_real @ X3 @ S4 ) ) ) ) )
% 0.35/0.60           => ( P @ S2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % finite_ranking_induct
% 0.35/0.60  thf(fact_3884_finite__ranking__induct,axiom,
% 0.35/0.60      ! [S2: set_VEBT_VEBT,P: set_VEBT_VEBT > $o,F: vEBT_VEBT > nat] :
% 0.35/0.60        ( ( finite5795047828879050333T_VEBT @ S2 )
% 0.35/0.60       => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 0.35/0.60         => ( ! [X3: vEBT_VEBT,S4: set_VEBT_VEBT] :
% 0.35/0.60                ( ( finite5795047828879050333T_VEBT @ S4 )
% 0.35/0.60               => ( ! [Y4: vEBT_VEBT] :
% 0.35/0.60                      ( ( member_VEBT_VEBT @ Y4 @ S4 )
% 0.35/0.60                     => ( ord_less_eq_nat @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 0.35/0.60                 => ( ( P @ S4 )
% 0.35/0.60                   => ( P @ ( insert_VEBT_VEBT @ X3 @ S4 ) ) ) ) )
% 0.35/0.60           => ( P @ S2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % finite_ranking_induct
% 0.35/0.60  thf(fact_3885_finite__ranking__induct,axiom,
% 0.35/0.60      ! [S2: set_complex,P: set_complex > $o,F: complex > nat] :
% 0.35/0.60        ( ( finite3207457112153483333omplex @ S2 )
% 0.35/0.60       => ( ( P @ bot_bot_set_complex )
% 0.35/0.60         => ( ! [X3: complex,S4: set_complex] :
% 0.35/0.60                ( ( finite3207457112153483333omplex @ S4 )
% 0.35/0.60               => ( ! [Y4: complex] :
% 0.35/0.60                      ( ( member_complex @ Y4 @ S4 )
% 0.35/0.60                     => ( ord_less_eq_nat @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 0.35/0.60                 => ( ( P @ S4 )
% 0.35/0.60                   => ( P @ ( insert_complex @ X3 @ S4 ) ) ) ) )
% 0.35/0.60           => ( P @ S2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % finite_ranking_induct
% 0.35/0.60  thf(fact_3886_finite__ranking__induct,axiom,
% 0.35/0.60      ! [S2: set_nat,P: set_nat > $o,F: nat > nat] :
% 0.35/0.60        ( ( finite_finite_nat @ S2 )
% 0.35/0.60       => ( ( P @ bot_bot_set_nat )
% 0.35/0.60         => ( ! [X3: nat,S4: set_nat] :
% 0.35/0.60                ( ( finite_finite_nat @ S4 )
% 0.35/0.60               => ( ! [Y4: nat] :
% 0.35/0.60                      ( ( member_nat @ Y4 @ S4 )
% 0.35/0.60                     => ( ord_less_eq_nat @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 0.35/0.60                 => ( ( P @ S4 )
% 0.35/0.60                   => ( P @ ( insert_nat @ X3 @ S4 ) ) ) ) )
% 0.35/0.60           => ( P @ S2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % finite_ranking_induct
% 0.35/0.60  thf(fact_3887_finite__ranking__induct,axiom,
% 0.35/0.60      ! [S2: set_int,P: set_int > $o,F: int > nat] :
% 0.35/0.60        ( ( finite_finite_int @ S2 )
% 0.35/0.60       => ( ( P @ bot_bot_set_int )
% 0.35/0.60         => ( ! [X3: int,S4: set_int] :
% 0.35/0.60                ( ( finite_finite_int @ S4 )
% 0.35/0.60               => ( ! [Y4: int] :
% 0.35/0.60                      ( ( member_int @ Y4 @ S4 )
% 0.35/0.60                     => ( ord_less_eq_nat @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 0.35/0.60                 => ( ( P @ S4 )
% 0.35/0.60                   => ( P @ ( insert_int @ X3 @ S4 ) ) ) ) )
% 0.35/0.60           => ( P @ S2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % finite_ranking_induct
% 0.35/0.60  thf(fact_3888_finite__ranking__induct,axiom,
% 0.35/0.60      ! [S2: set_real,P: set_real > $o,F: real > nat] :
% 0.35/0.60        ( ( finite_finite_real @ S2 )
% 0.35/0.60       => ( ( P @ bot_bot_set_real )
% 0.35/0.60         => ( ! [X3: real,S4: set_real] :
% 0.35/0.60                ( ( finite_finite_real @ S4 )
% 0.35/0.60               => ( ! [Y4: real] :
% 0.35/0.60                      ( ( member_real @ Y4 @ S4 )
% 0.35/0.60                     => ( ord_less_eq_nat @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 0.35/0.60                 => ( ( P @ S4 )
% 0.35/0.60                   => ( P @ ( insert_real @ X3 @ S4 ) ) ) ) )
% 0.35/0.60           => ( P @ S2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % finite_ranking_induct
% 0.35/0.60  thf(fact_3889_product__nth,axiom,
% 0.35/0.60      ! [N: nat,Xs2: list_num,Ys: list_num] :
% 0.35/0.60        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_num @ Xs2 ) @ ( size_size_list_num @ Ys ) ) )
% 0.35/0.60       => ( ( nth_Pr6456567536196504476um_num @ ( product_num_num @ Xs2 @ Ys ) @ N )
% 0.35/0.60          = ( product_Pair_num_num @ ( nth_num @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_num @ Ys ) ) ) @ ( nth_num @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_num @ Ys ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % product_nth
% 0.35/0.60  thf(fact_3890_product__nth,axiom,
% 0.35/0.60      ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 0.35/0.60        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 0.35/0.60       => ( ( nth_Pr4953567300277697838T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs2 @ Ys ) @ N )
% 0.35/0.60          = ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % product_nth
% 0.35/0.60  thf(fact_3891_product__nth,axiom,
% 0.35/0.60      ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_o] :
% 0.35/0.60        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_o @ Ys ) ) )
% 0.35/0.60       => ( ( nth_Pr4606735188037164562VEBT_o @ ( product_VEBT_VEBT_o @ Xs2 @ Ys ) @ N )
% 0.35/0.60          = ( produc8721562602347293563VEBT_o @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % product_nth
% 0.35/0.60  thf(fact_3892_product__nth,axiom,
% 0.35/0.60      ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_nat] :
% 0.35/0.60        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) )
% 0.35/0.60       => ( ( nth_Pr1791586995822124652BT_nat @ ( produc7295137177222721919BT_nat @ Xs2 @ Ys ) @ N )
% 0.35/0.60          = ( produc738532404422230701BT_nat @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % product_nth
% 0.35/0.60  thf(fact_3893_product__nth,axiom,
% 0.35/0.60      ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_int] :
% 0.35/0.60        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_int @ Ys ) ) )
% 0.35/0.60       => ( ( nth_Pr6837108013167703752BT_int @ ( produc7292646706713671643BT_int @ Xs2 @ Ys ) @ N )
% 0.35/0.60          = ( produc736041933913180425BT_int @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % product_nth
% 0.35/0.60  thf(fact_3894_product__nth,axiom,
% 0.35/0.60      ! [N: nat,Xs2: list_o,Ys: list_VEBT_VEBT] :
% 0.35/0.60        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 0.35/0.60       => ( ( nth_Pr6777367263587873994T_VEBT @ ( product_o_VEBT_VEBT @ Xs2 @ Ys ) @ N )
% 0.35/0.60          = ( produc2982872950893828659T_VEBT @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % product_nth
% 0.35/0.60  thf(fact_3895_product__nth,axiom,
% 0.35/0.60      ! [N: nat,Xs2: list_o,Ys: list_o] :
% 0.35/0.60        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_o @ Ys ) ) )
% 0.35/0.60       => ( ( nth_Product_prod_o_o @ ( product_o_o @ Xs2 @ Ys ) @ N )
% 0.35/0.60          = ( product_Pair_o_o @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % product_nth
% 0.35/0.60  thf(fact_3896_product__nth,axiom,
% 0.35/0.60      ! [N: nat,Xs2: list_o,Ys: list_nat] :
% 0.35/0.60        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) )
% 0.35/0.60       => ( ( nth_Pr5826913651314560976_o_nat @ ( product_o_nat @ Xs2 @ Ys ) @ N )
% 0.35/0.60          = ( product_Pair_o_nat @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % product_nth
% 0.35/0.60  thf(fact_3897_product__nth,axiom,
% 0.35/0.60      ! [N: nat,Xs2: list_o,Ys: list_int] :
% 0.35/0.60        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_int @ Ys ) ) )
% 0.35/0.60       => ( ( nth_Pr1649062631805364268_o_int @ ( product_o_int @ Xs2 @ Ys ) @ N )
% 0.35/0.60          = ( product_Pair_o_int @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % product_nth
% 0.35/0.60  thf(fact_3898_product__nth,axiom,
% 0.35/0.60      ! [N: nat,Xs2: list_nat,Ys: list_num] :
% 0.35/0.60        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_size_list_num @ Ys ) ) )
% 0.35/0.60       => ( ( nth_Pr8326237132889035090at_num @ ( product_nat_num @ Xs2 @ Ys ) @ N )
% 0.35/0.60          = ( product_Pair_nat_num @ ( nth_nat @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_num @ Ys ) ) ) @ ( nth_num @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_num @ Ys ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % product_nth
% 0.35/0.60  thf(fact_3899_flip__bit__nonnegative__int__iff,axiom,
% 0.35/0.60      ! [N: nat,K: int] :
% 0.35/0.60        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se2159334234014336723it_int @ N @ K ) )
% 0.35/0.60        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.35/0.60  
% 0.35/0.60  % flip_bit_nonnegative_int_iff
% 0.35/0.60  thf(fact_3900_flip__bit__negative__int__iff,axiom,
% 0.35/0.60      ! [N: nat,K: int] :
% 0.35/0.60        ( ( ord_less_int @ ( bit_se2159334234014336723it_int @ N @ K ) @ zero_zero_int )
% 0.35/0.60        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.35/0.60  
% 0.35/0.60  % flip_bit_negative_int_iff
% 0.35/0.60  thf(fact_3901_length__product,axiom,
% 0.35/0.60      ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 0.35/0.60        ( ( size_s7466405169056248089T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs2 @ Ys ) )
% 0.35/0.60        = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % length_product
% 0.35/0.60  thf(fact_3902_length__product,axiom,
% 0.35/0.60      ! [Xs2: list_VEBT_VEBT,Ys: list_o] :
% 0.35/0.60        ( ( size_s9168528473962070013VEBT_o @ ( product_VEBT_VEBT_o @ Xs2 @ Ys ) )
% 0.35/0.60        = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % length_product
% 0.35/0.60  thf(fact_3903_length__product,axiom,
% 0.35/0.60      ! [Xs2: list_VEBT_VEBT,Ys: list_nat] :
% 0.35/0.60        ( ( size_s6152045936467909847BT_nat @ ( produc7295137177222721919BT_nat @ Xs2 @ Ys ) )
% 0.35/0.60        = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % length_product
% 0.35/0.60  thf(fact_3904_length__product,axiom,
% 0.35/0.60      ! [Xs2: list_VEBT_VEBT,Ys: list_int] :
% 0.35/0.60        ( ( size_s3661962791536183091BT_int @ ( produc7292646706713671643BT_int @ Xs2 @ Ys ) )
% 0.35/0.60        = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_int @ Ys ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % length_product
% 0.35/0.60  thf(fact_3905_length__product,axiom,
% 0.35/0.60      ! [Xs2: list_o,Ys: list_VEBT_VEBT] :
% 0.35/0.60        ( ( size_s4313452262239582901T_VEBT @ ( product_o_VEBT_VEBT @ Xs2 @ Ys ) )
% 0.35/0.60        = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % length_product
% 0.35/0.60  thf(fact_3906_length__product,axiom,
% 0.35/0.60      ! [Xs2: list_o,Ys: list_o] :
% 0.35/0.60        ( ( size_s1515746228057227161od_o_o @ ( product_o_o @ Xs2 @ Ys ) )
% 0.35/0.60        = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % length_product
% 0.35/0.60  thf(fact_3907_length__product,axiom,
% 0.35/0.60      ! [Xs2: list_o,Ys: list_nat] :
% 0.35/0.60        ( ( size_s5443766701097040955_o_nat @ ( product_o_nat @ Xs2 @ Ys ) )
% 0.35/0.60        = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % length_product
% 0.35/0.60  thf(fact_3908_length__product,axiom,
% 0.35/0.60      ! [Xs2: list_o,Ys: list_int] :
% 0.35/0.60        ( ( size_s2953683556165314199_o_int @ ( product_o_int @ Xs2 @ Ys ) )
% 0.35/0.60        = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_int @ Ys ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % length_product
% 0.35/0.60  thf(fact_3909_length__product,axiom,
% 0.35/0.60      ! [Xs2: list_nat,Ys: list_VEBT_VEBT] :
% 0.35/0.60        ( ( size_s4762443039079500285T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs2 @ Ys ) )
% 0.35/0.60        = ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % length_product
% 0.35/0.60  thf(fact_3910_length__product,axiom,
% 0.35/0.60      ! [Xs2: list_nat,Ys: list_o] :
% 0.35/0.60        ( ( size_s6491369823275344609_nat_o @ ( product_nat_o @ Xs2 @ Ys ) )
% 0.35/0.60        = ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % length_product
% 0.35/0.60  thf(fact_3911_ex__min__if__finite,axiom,
% 0.35/0.60      ! [S2: set_real] :
% 0.35/0.60        ( ( finite_finite_real @ S2 )
% 0.35/0.60       => ( ( S2 != bot_bot_set_real )
% 0.35/0.60         => ? [X3: real] :
% 0.35/0.60              ( ( member_real @ X3 @ S2 )
% 0.35/0.60              & ~ ? [Xa: real] :
% 0.35/0.60                    ( ( member_real @ Xa @ S2 )
% 0.35/0.60                    & ( ord_less_real @ Xa @ X3 ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % ex_min_if_finite
% 0.35/0.60  thf(fact_3912_ex__min__if__finite,axiom,
% 0.35/0.60      ! [S2: set_rat] :
% 0.35/0.60        ( ( finite_finite_rat @ S2 )
% 0.35/0.60       => ( ( S2 != bot_bot_set_rat )
% 0.35/0.60         => ? [X3: rat] :
% 0.35/0.60              ( ( member_rat @ X3 @ S2 )
% 0.35/0.60              & ~ ? [Xa: rat] :
% 0.35/0.60                    ( ( member_rat @ Xa @ S2 )
% 0.35/0.60                    & ( ord_less_rat @ Xa @ X3 ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % ex_min_if_finite
% 0.35/0.60  thf(fact_3913_ex__min__if__finite,axiom,
% 0.35/0.60      ! [S2: set_num] :
% 0.35/0.60        ( ( finite_finite_num @ S2 )
% 0.35/0.60       => ( ( S2 != bot_bot_set_num )
% 0.35/0.60         => ? [X3: num] :
% 0.35/0.60              ( ( member_num @ X3 @ S2 )
% 0.35/0.60              & ~ ? [Xa: num] :
% 0.35/0.60                    ( ( member_num @ Xa @ S2 )
% 0.35/0.60                    & ( ord_less_num @ Xa @ X3 ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % ex_min_if_finite
% 0.35/0.60  thf(fact_3914_ex__min__if__finite,axiom,
% 0.35/0.60      ! [S2: set_nat] :
% 0.35/0.60        ( ( finite_finite_nat @ S2 )
% 0.35/0.60       => ( ( S2 != bot_bot_set_nat )
% 0.35/0.60         => ? [X3: nat] :
% 0.35/0.60              ( ( member_nat @ X3 @ S2 )
% 0.35/0.60              & ~ ? [Xa: nat] :
% 0.35/0.60                    ( ( member_nat @ Xa @ S2 )
% 0.35/0.60                    & ( ord_less_nat @ Xa @ X3 ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % ex_min_if_finite
% 0.35/0.60  thf(fact_3915_ex__min__if__finite,axiom,
% 0.35/0.60      ! [S2: set_int] :
% 0.35/0.60        ( ( finite_finite_int @ S2 )
% 0.35/0.60       => ( ( S2 != bot_bot_set_int )
% 0.35/0.60         => ? [X3: int] :
% 0.35/0.60              ( ( member_int @ X3 @ S2 )
% 0.35/0.60              & ~ ? [Xa: int] :
% 0.35/0.60                    ( ( member_int @ Xa @ S2 )
% 0.35/0.60                    & ( ord_less_int @ Xa @ X3 ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % ex_min_if_finite
% 0.35/0.60  thf(fact_3916_infinite__growing,axiom,
% 0.35/0.60      ! [X8: set_real] :
% 0.35/0.60        ( ( X8 != bot_bot_set_real )
% 0.35/0.60       => ( ! [X3: real] :
% 0.35/0.60              ( ( member_real @ X3 @ X8 )
% 0.35/0.60             => ? [Xa: real] :
% 0.35/0.60                  ( ( member_real @ Xa @ X8 )
% 0.35/0.60                  & ( ord_less_real @ X3 @ Xa ) ) )
% 0.35/0.60         => ~ ( finite_finite_real @ X8 ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % infinite_growing
% 0.35/0.60  thf(fact_3917_infinite__growing,axiom,
% 0.35/0.60      ! [X8: set_rat] :
% 0.35/0.60        ( ( X8 != bot_bot_set_rat )
% 0.35/0.60       => ( ! [X3: rat] :
% 0.35/0.60              ( ( member_rat @ X3 @ X8 )
% 0.35/0.60             => ? [Xa: rat] :
% 0.35/0.60                  ( ( member_rat @ Xa @ X8 )
% 0.35/0.60                  & ( ord_less_rat @ X3 @ Xa ) ) )
% 0.35/0.60         => ~ ( finite_finite_rat @ X8 ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % infinite_growing
% 0.35/0.60  thf(fact_3918_infinite__growing,axiom,
% 0.35/0.60      ! [X8: set_num] :
% 0.35/0.60        ( ( X8 != bot_bot_set_num )
% 0.35/0.60       => ( ! [X3: num] :
% 0.35/0.60              ( ( member_num @ X3 @ X8 )
% 0.35/0.60             => ? [Xa: num] :
% 0.35/0.60                  ( ( member_num @ Xa @ X8 )
% 0.35/0.60                  & ( ord_less_num @ X3 @ Xa ) ) )
% 0.35/0.60         => ~ ( finite_finite_num @ X8 ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % infinite_growing
% 0.35/0.60  thf(fact_3919_infinite__growing,axiom,
% 0.35/0.60      ! [X8: set_nat] :
% 0.35/0.60        ( ( X8 != bot_bot_set_nat )
% 0.35/0.60       => ( ! [X3: nat] :
% 0.35/0.60              ( ( member_nat @ X3 @ X8 )
% 0.35/0.60             => ? [Xa: nat] :
% 0.35/0.60                  ( ( member_nat @ Xa @ X8 )
% 0.35/0.60                  & ( ord_less_nat @ X3 @ Xa ) ) )
% 0.35/0.60         => ~ ( finite_finite_nat @ X8 ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % infinite_growing
% 0.35/0.60  thf(fact_3920_infinite__growing,axiom,
% 0.35/0.60      ! [X8: set_int] :
% 0.35/0.60        ( ( X8 != bot_bot_set_int )
% 0.35/0.60       => ( ! [X3: int] :
% 0.35/0.60              ( ( member_int @ X3 @ X8 )
% 0.35/0.60             => ? [Xa: int] :
% 0.35/0.60                  ( ( member_int @ Xa @ X8 )
% 0.35/0.60                  & ( ord_less_int @ X3 @ Xa ) ) )
% 0.35/0.60         => ~ ( finite_finite_int @ X8 ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % infinite_growing
% 0.35/0.60  thf(fact_3921_prod_Ofinite__Collect__op,axiom,
% 0.35/0.60      ! [I6: set_int,X: int > rat,Y2: int > rat] :
% 0.35/0.60        ( ( finite_finite_int
% 0.35/0.60          @ ( collect_int
% 0.35/0.60            @ ^ [I3: int] :
% 0.35/0.60                ( ( member_int @ I3 @ I6 )
% 0.35/0.60                & ( ( X @ I3 )
% 0.35/0.60                 != one_one_rat ) ) ) )
% 0.35/0.60       => ( ( finite_finite_int
% 0.35/0.60            @ ( collect_int
% 0.35/0.60              @ ^ [I3: int] :
% 0.35/0.60                  ( ( member_int @ I3 @ I6 )
% 0.35/0.60                  & ( ( Y2 @ I3 )
% 0.35/0.60                   != one_one_rat ) ) ) )
% 0.35/0.60         => ( finite_finite_int
% 0.35/0.60            @ ( collect_int
% 0.35/0.60              @ ^ [I3: int] :
% 0.35/0.60                  ( ( member_int @ I3 @ I6 )
% 0.35/0.60                  & ( ( times_times_rat @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 0.35/0.60                   != one_one_rat ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % prod.finite_Collect_op
% 0.35/0.60  thf(fact_3922_prod_Ofinite__Collect__op,axiom,
% 0.35/0.60      ! [I6: set_real,X: real > rat,Y2: real > rat] :
% 0.35/0.60        ( ( finite_finite_real
% 0.35/0.60          @ ( collect_real
% 0.35/0.60            @ ^ [I3: real] :
% 0.35/0.60                ( ( member_real @ I3 @ I6 )
% 0.35/0.60                & ( ( X @ I3 )
% 0.35/0.60                 != one_one_rat ) ) ) )
% 0.35/0.60       => ( ( finite_finite_real
% 0.35/0.60            @ ( collect_real
% 0.35/0.60              @ ^ [I3: real] :
% 0.35/0.60                  ( ( member_real @ I3 @ I6 )
% 0.35/0.60                  & ( ( Y2 @ I3 )
% 0.35/0.60                   != one_one_rat ) ) ) )
% 0.35/0.60         => ( finite_finite_real
% 0.35/0.60            @ ( collect_real
% 0.35/0.60              @ ^ [I3: real] :
% 0.35/0.60                  ( ( member_real @ I3 @ I6 )
% 0.35/0.60                  & ( ( times_times_rat @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 0.35/0.60                   != one_one_rat ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % prod.finite_Collect_op
% 0.35/0.60  thf(fact_3923_prod_Ofinite__Collect__op,axiom,
% 0.35/0.60      ! [I6: set_nat,X: nat > rat,Y2: nat > rat] :
% 0.35/0.60        ( ( finite_finite_nat
% 0.35/0.60          @ ( collect_nat
% 0.35/0.60            @ ^ [I3: nat] :
% 0.35/0.60                ( ( member_nat @ I3 @ I6 )
% 0.35/0.60                & ( ( X @ I3 )
% 0.35/0.60                 != one_one_rat ) ) ) )
% 0.35/0.60       => ( ( finite_finite_nat
% 0.35/0.60            @ ( collect_nat
% 0.35/0.60              @ ^ [I3: nat] :
% 0.35/0.60                  ( ( member_nat @ I3 @ I6 )
% 0.35/0.60                  & ( ( Y2 @ I3 )
% 0.35/0.60                   != one_one_rat ) ) ) )
% 0.35/0.60         => ( finite_finite_nat
% 0.35/0.60            @ ( collect_nat
% 0.35/0.60              @ ^ [I3: nat] :
% 0.35/0.60                  ( ( member_nat @ I3 @ I6 )
% 0.35/0.60                  & ( ( times_times_rat @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 0.35/0.60                   != one_one_rat ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % prod.finite_Collect_op
% 0.35/0.60  thf(fact_3924_prod_Ofinite__Collect__op,axiom,
% 0.35/0.60      ! [I6: set_complex,X: complex > rat,Y2: complex > rat] :
% 0.35/0.60        ( ( finite3207457112153483333omplex
% 0.35/0.60          @ ( collect_complex
% 0.35/0.60            @ ^ [I3: complex] :
% 0.35/0.60                ( ( member_complex @ I3 @ I6 )
% 0.35/0.60                & ( ( X @ I3 )
% 0.35/0.60                 != one_one_rat ) ) ) )
% 0.35/0.60       => ( ( finite3207457112153483333omplex
% 0.35/0.60            @ ( collect_complex
% 0.35/0.60              @ ^ [I3: complex] :
% 0.35/0.60                  ( ( member_complex @ I3 @ I6 )
% 0.35/0.60                  & ( ( Y2 @ I3 )
% 0.35/0.60                   != one_one_rat ) ) ) )
% 0.35/0.60         => ( finite3207457112153483333omplex
% 0.35/0.60            @ ( collect_complex
% 0.35/0.60              @ ^ [I3: complex] :
% 0.35/0.60                  ( ( member_complex @ I3 @ I6 )
% 0.35/0.60                  & ( ( times_times_rat @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 0.35/0.60                   != one_one_rat ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % prod.finite_Collect_op
% 0.35/0.60  thf(fact_3925_prod_Ofinite__Collect__op,axiom,
% 0.35/0.60      ! [I6: set_int,X: int > complex,Y2: int > complex] :
% 0.35/0.60        ( ( finite_finite_int
% 0.35/0.60          @ ( collect_int
% 0.35/0.60            @ ^ [I3: int] :
% 0.35/0.60                ( ( member_int @ I3 @ I6 )
% 0.35/0.60                & ( ( X @ I3 )
% 0.35/0.60                 != one_one_complex ) ) ) )
% 0.35/0.60       => ( ( finite_finite_int
% 0.35/0.60            @ ( collect_int
% 0.35/0.60              @ ^ [I3: int] :
% 0.35/0.60                  ( ( member_int @ I3 @ I6 )
% 0.35/0.60                  & ( ( Y2 @ I3 )
% 0.35/0.60                   != one_one_complex ) ) ) )
% 0.35/0.60         => ( finite_finite_int
% 0.35/0.60            @ ( collect_int
% 0.35/0.60              @ ^ [I3: int] :
% 0.35/0.60                  ( ( member_int @ I3 @ I6 )
% 0.35/0.60                  & ( ( times_times_complex @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 0.35/0.60                   != one_one_complex ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % prod.finite_Collect_op
% 0.35/0.60  thf(fact_3926_prod_Ofinite__Collect__op,axiom,
% 0.35/0.60      ! [I6: set_real,X: real > complex,Y2: real > complex] :
% 0.35/0.60        ( ( finite_finite_real
% 0.35/0.60          @ ( collect_real
% 0.35/0.60            @ ^ [I3: real] :
% 0.35/0.60                ( ( member_real @ I3 @ I6 )
% 0.35/0.60                & ( ( X @ I3 )
% 0.35/0.60                 != one_one_complex ) ) ) )
% 0.35/0.60       => ( ( finite_finite_real
% 0.35/0.60            @ ( collect_real
% 0.35/0.60              @ ^ [I3: real] :
% 0.35/0.60                  ( ( member_real @ I3 @ I6 )
% 0.35/0.60                  & ( ( Y2 @ I3 )
% 0.35/0.60                   != one_one_complex ) ) ) )
% 0.35/0.60         => ( finite_finite_real
% 0.35/0.60            @ ( collect_real
% 0.35/0.60              @ ^ [I3: real] :
% 0.35/0.60                  ( ( member_real @ I3 @ I6 )
% 0.35/0.60                  & ( ( times_times_complex @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 0.35/0.60                   != one_one_complex ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % prod.finite_Collect_op
% 0.35/0.60  thf(fact_3927_prod_Ofinite__Collect__op,axiom,
% 0.35/0.60      ! [I6: set_nat,X: nat > complex,Y2: nat > complex] :
% 0.35/0.60        ( ( finite_finite_nat
% 0.35/0.60          @ ( collect_nat
% 0.35/0.60            @ ^ [I3: nat] :
% 0.35/0.60                ( ( member_nat @ I3 @ I6 )
% 0.35/0.60                & ( ( X @ I3 )
% 0.35/0.60                 != one_one_complex ) ) ) )
% 0.35/0.60       => ( ( finite_finite_nat
% 0.35/0.60            @ ( collect_nat
% 0.35/0.60              @ ^ [I3: nat] :
% 0.35/0.60                  ( ( member_nat @ I3 @ I6 )
% 0.35/0.60                  & ( ( Y2 @ I3 )
% 0.35/0.60                   != one_one_complex ) ) ) )
% 0.35/0.60         => ( finite_finite_nat
% 0.35/0.60            @ ( collect_nat
% 0.35/0.60              @ ^ [I3: nat] :
% 0.35/0.60                  ( ( member_nat @ I3 @ I6 )
% 0.35/0.60                  & ( ( times_times_complex @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 0.35/0.60                   != one_one_complex ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % prod.finite_Collect_op
% 0.35/0.60  thf(fact_3928_prod_Ofinite__Collect__op,axiom,
% 0.35/0.60      ! [I6: set_complex,X: complex > complex,Y2: complex > complex] :
% 0.35/0.60        ( ( finite3207457112153483333omplex
% 0.35/0.60          @ ( collect_complex
% 0.35/0.60            @ ^ [I3: complex] :
% 0.35/0.60                ( ( member_complex @ I3 @ I6 )
% 0.35/0.60                & ( ( X @ I3 )
% 0.35/0.60                 != one_one_complex ) ) ) )
% 0.35/0.60       => ( ( finite3207457112153483333omplex
% 0.35/0.60            @ ( collect_complex
% 0.35/0.60              @ ^ [I3: complex] :
% 0.35/0.60                  ( ( member_complex @ I3 @ I6 )
% 0.35/0.60                  & ( ( Y2 @ I3 )
% 0.35/0.60                   != one_one_complex ) ) ) )
% 0.35/0.60         => ( finite3207457112153483333omplex
% 0.35/0.60            @ ( collect_complex
% 0.35/0.60              @ ^ [I3: complex] :
% 0.35/0.60                  ( ( member_complex @ I3 @ I6 )
% 0.35/0.60                  & ( ( times_times_complex @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 0.35/0.60                   != one_one_complex ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % prod.finite_Collect_op
% 0.35/0.60  thf(fact_3929_prod_Ofinite__Collect__op,axiom,
% 0.35/0.60      ! [I6: set_int,X: int > real,Y2: int > real] :
% 0.35/0.60        ( ( finite_finite_int
% 0.35/0.60          @ ( collect_int
% 0.35/0.60            @ ^ [I3: int] :
% 0.35/0.60                ( ( member_int @ I3 @ I6 )
% 0.35/0.60                & ( ( X @ I3 )
% 0.35/0.60                 != one_one_real ) ) ) )
% 0.35/0.60       => ( ( finite_finite_int
% 0.35/0.60            @ ( collect_int
% 0.35/0.60              @ ^ [I3: int] :
% 0.35/0.60                  ( ( member_int @ I3 @ I6 )
% 0.35/0.60                  & ( ( Y2 @ I3 )
% 0.35/0.60                   != one_one_real ) ) ) )
% 0.35/0.60         => ( finite_finite_int
% 0.35/0.60            @ ( collect_int
% 0.35/0.60              @ ^ [I3: int] :
% 0.35/0.60                  ( ( member_int @ I3 @ I6 )
% 0.35/0.60                  & ( ( times_times_real @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 0.35/0.60                   != one_one_real ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % prod.finite_Collect_op
% 0.35/0.60  thf(fact_3930_prod_Ofinite__Collect__op,axiom,
% 0.35/0.60      ! [I6: set_real,X: real > real,Y2: real > real] :
% 0.35/0.60        ( ( finite_finite_real
% 0.35/0.60          @ ( collect_real
% 0.35/0.60            @ ^ [I3: real] :
% 0.35/0.60                ( ( member_real @ I3 @ I6 )
% 0.35/0.60                & ( ( X @ I3 )
% 0.35/0.60                 != one_one_real ) ) ) )
% 0.35/0.60       => ( ( finite_finite_real
% 0.35/0.60            @ ( collect_real
% 0.35/0.60              @ ^ [I3: real] :
% 0.35/0.60                  ( ( member_real @ I3 @ I6 )
% 0.35/0.60                  & ( ( Y2 @ I3 )
% 0.35/0.60                   != one_one_real ) ) ) )
% 0.35/0.60         => ( finite_finite_real
% 0.35/0.60            @ ( collect_real
% 0.35/0.60              @ ^ [I3: real] :
% 0.35/0.60                  ( ( member_real @ I3 @ I6 )
% 0.35/0.60                  & ( ( times_times_real @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 0.35/0.60                   != one_one_real ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % prod.finite_Collect_op
% 0.35/0.60  thf(fact_3931_sum_Ofinite__Collect__op,axiom,
% 0.35/0.60      ! [I6: set_int,X: int > complex,Y2: int > complex] :
% 0.35/0.60        ( ( finite_finite_int
% 0.35/0.60          @ ( collect_int
% 0.35/0.60            @ ^ [I3: int] :
% 0.35/0.60                ( ( member_int @ I3 @ I6 )
% 0.35/0.60                & ( ( X @ I3 )
% 0.35/0.60                 != zero_zero_complex ) ) ) )
% 0.35/0.60       => ( ( finite_finite_int
% 0.35/0.60            @ ( collect_int
% 0.35/0.60              @ ^ [I3: int] :
% 0.35/0.60                  ( ( member_int @ I3 @ I6 )
% 0.35/0.60                  & ( ( Y2 @ I3 )
% 0.35/0.60                   != zero_zero_complex ) ) ) )
% 0.35/0.60         => ( finite_finite_int
% 0.35/0.60            @ ( collect_int
% 0.35/0.60              @ ^ [I3: int] :
% 0.35/0.60                  ( ( member_int @ I3 @ I6 )
% 0.35/0.60                  & ( ( plus_plus_complex @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 0.35/0.60                   != zero_zero_complex ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % sum.finite_Collect_op
% 0.35/0.60  thf(fact_3932_sum_Ofinite__Collect__op,axiom,
% 0.35/0.60      ! [I6: set_real,X: real > complex,Y2: real > complex] :
% 0.35/0.60        ( ( finite_finite_real
% 0.35/0.60          @ ( collect_real
% 0.35/0.60            @ ^ [I3: real] :
% 0.35/0.60                ( ( member_real @ I3 @ I6 )
% 0.35/0.60                & ( ( X @ I3 )
% 0.35/0.60                 != zero_zero_complex ) ) ) )
% 0.35/0.60       => ( ( finite_finite_real
% 0.35/0.60            @ ( collect_real
% 0.35/0.60              @ ^ [I3: real] :
% 0.35/0.60                  ( ( member_real @ I3 @ I6 )
% 0.35/0.60                  & ( ( Y2 @ I3 )
% 0.35/0.60                   != zero_zero_complex ) ) ) )
% 0.35/0.60         => ( finite_finite_real
% 0.35/0.60            @ ( collect_real
% 0.35/0.60              @ ^ [I3: real] :
% 0.35/0.60                  ( ( member_real @ I3 @ I6 )
% 0.35/0.60                  & ( ( plus_plus_complex @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 0.35/0.60                   != zero_zero_complex ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % sum.finite_Collect_op
% 0.35/0.60  thf(fact_3933_sum_Ofinite__Collect__op,axiom,
% 0.35/0.60      ! [I6: set_nat,X: nat > complex,Y2: nat > complex] :
% 0.35/0.60        ( ( finite_finite_nat
% 0.35/0.60          @ ( collect_nat
% 0.35/0.60            @ ^ [I3: nat] :
% 0.35/0.60                ( ( member_nat @ I3 @ I6 )
% 0.35/0.60                & ( ( X @ I3 )
% 0.35/0.60                 != zero_zero_complex ) ) ) )
% 0.35/0.60       => ( ( finite_finite_nat
% 0.35/0.60            @ ( collect_nat
% 0.35/0.60              @ ^ [I3: nat] :
% 0.35/0.60                  ( ( member_nat @ I3 @ I6 )
% 0.35/0.60                  & ( ( Y2 @ I3 )
% 0.35/0.60                   != zero_zero_complex ) ) ) )
% 0.35/0.60         => ( finite_finite_nat
% 0.35/0.60            @ ( collect_nat
% 0.35/0.60              @ ^ [I3: nat] :
% 0.35/0.60                  ( ( member_nat @ I3 @ I6 )
% 0.35/0.60                  & ( ( plus_plus_complex @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 0.35/0.60                   != zero_zero_complex ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % sum.finite_Collect_op
% 0.35/0.60  thf(fact_3934_sum_Ofinite__Collect__op,axiom,
% 0.35/0.60      ! [I6: set_complex,X: complex > complex,Y2: complex > complex] :
% 0.35/0.60        ( ( finite3207457112153483333omplex
% 0.35/0.60          @ ( collect_complex
% 0.35/0.60            @ ^ [I3: complex] :
% 0.35/0.60                ( ( member_complex @ I3 @ I6 )
% 0.35/0.60                & ( ( X @ I3 )
% 0.35/0.60                 != zero_zero_complex ) ) ) )
% 0.35/0.60       => ( ( finite3207457112153483333omplex
% 0.35/0.60            @ ( collect_complex
% 0.35/0.60              @ ^ [I3: complex] :
% 0.35/0.60                  ( ( member_complex @ I3 @ I6 )
% 0.35/0.60                  & ( ( Y2 @ I3 )
% 0.35/0.60                   != zero_zero_complex ) ) ) )
% 0.35/0.60         => ( finite3207457112153483333omplex
% 0.35/0.60            @ ( collect_complex
% 0.35/0.60              @ ^ [I3: complex] :
% 0.35/0.60                  ( ( member_complex @ I3 @ I6 )
% 0.35/0.60                  & ( ( plus_plus_complex @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 0.35/0.60                   != zero_zero_complex ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % sum.finite_Collect_op
% 0.35/0.60  thf(fact_3935_sum_Ofinite__Collect__op,axiom,
% 0.35/0.60      ! [I6: set_int,X: int > real,Y2: int > real] :
% 0.35/0.60        ( ( finite_finite_int
% 0.35/0.60          @ ( collect_int
% 0.35/0.60            @ ^ [I3: int] :
% 0.35/0.60                ( ( member_int @ I3 @ I6 )
% 0.35/0.60                & ( ( X @ I3 )
% 0.35/0.60                 != zero_zero_real ) ) ) )
% 0.35/0.60       => ( ( finite_finite_int
% 0.35/0.60            @ ( collect_int
% 0.35/0.60              @ ^ [I3: int] :
% 0.35/0.60                  ( ( member_int @ I3 @ I6 )
% 0.35/0.60                  & ( ( Y2 @ I3 )
% 0.35/0.60                   != zero_zero_real ) ) ) )
% 0.35/0.60         => ( finite_finite_int
% 0.35/0.60            @ ( collect_int
% 0.35/0.60              @ ^ [I3: int] :
% 0.35/0.60                  ( ( member_int @ I3 @ I6 )
% 0.35/0.60                  & ( ( plus_plus_real @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 0.35/0.60                   != zero_zero_real ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % sum.finite_Collect_op
% 0.35/0.60  thf(fact_3936_sum_Ofinite__Collect__op,axiom,
% 0.35/0.60      ! [I6: set_real,X: real > real,Y2: real > real] :
% 0.35/0.60        ( ( finite_finite_real
% 0.35/0.60          @ ( collect_real
% 0.35/0.60            @ ^ [I3: real] :
% 0.35/0.60                ( ( member_real @ I3 @ I6 )
% 0.35/0.60                & ( ( X @ I3 )
% 0.35/0.60                 != zero_zero_real ) ) ) )
% 0.35/0.60       => ( ( finite_finite_real
% 0.35/0.60            @ ( collect_real
% 0.35/0.60              @ ^ [I3: real] :
% 0.35/0.60                  ( ( member_real @ I3 @ I6 )
% 0.35/0.60                  & ( ( Y2 @ I3 )
% 0.35/0.60                   != zero_zero_real ) ) ) )
% 0.35/0.60         => ( finite_finite_real
% 0.35/0.60            @ ( collect_real
% 0.35/0.60              @ ^ [I3: real] :
% 0.35/0.60                  ( ( member_real @ I3 @ I6 )
% 0.35/0.60                  & ( ( plus_plus_real @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 0.35/0.60                   != zero_zero_real ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % sum.finite_Collect_op
% 0.35/0.60  thf(fact_3937_sum_Ofinite__Collect__op,axiom,
% 0.35/0.60      ! [I6: set_nat,X: nat > real,Y2: nat > real] :
% 0.35/0.60        ( ( finite_finite_nat
% 0.35/0.60          @ ( collect_nat
% 0.35/0.60            @ ^ [I3: nat] :
% 0.35/0.60                ( ( member_nat @ I3 @ I6 )
% 0.35/0.60                & ( ( X @ I3 )
% 0.35/0.60                 != zero_zero_real ) ) ) )
% 0.35/0.60       => ( ( finite_finite_nat
% 0.35/0.60            @ ( collect_nat
% 0.35/0.60              @ ^ [I3: nat] :
% 0.35/0.60                  ( ( member_nat @ I3 @ I6 )
% 0.35/0.60                  & ( ( Y2 @ I3 )
% 0.35/0.60                   != zero_zero_real ) ) ) )
% 0.35/0.60         => ( finite_finite_nat
% 0.35/0.60            @ ( collect_nat
% 0.35/0.60              @ ^ [I3: nat] :
% 0.35/0.60                  ( ( member_nat @ I3 @ I6 )
% 0.35/0.60                  & ( ( plus_plus_real @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 0.35/0.60                   != zero_zero_real ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % sum.finite_Collect_op
% 0.35/0.60  thf(fact_3938_sum_Ofinite__Collect__op,axiom,
% 0.35/0.60      ! [I6: set_complex,X: complex > real,Y2: complex > real] :
% 0.35/0.60        ( ( finite3207457112153483333omplex
% 0.35/0.60          @ ( collect_complex
% 0.35/0.60            @ ^ [I3: complex] :
% 0.35/0.60                ( ( member_complex @ I3 @ I6 )
% 0.35/0.60                & ( ( X @ I3 )
% 0.35/0.60                 != zero_zero_real ) ) ) )
% 0.35/0.60       => ( ( finite3207457112153483333omplex
% 0.35/0.60            @ ( collect_complex
% 0.35/0.60              @ ^ [I3: complex] :
% 0.35/0.60                  ( ( member_complex @ I3 @ I6 )
% 0.35/0.60                  & ( ( Y2 @ I3 )
% 0.35/0.60                   != zero_zero_real ) ) ) )
% 0.35/0.60         => ( finite3207457112153483333omplex
% 0.35/0.60            @ ( collect_complex
% 0.35/0.60              @ ^ [I3: complex] :
% 0.35/0.60                  ( ( member_complex @ I3 @ I6 )
% 0.35/0.60                  & ( ( plus_plus_real @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 0.35/0.60                   != zero_zero_real ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % sum.finite_Collect_op
% 0.35/0.60  thf(fact_3939_sum_Ofinite__Collect__op,axiom,
% 0.35/0.60      ! [I6: set_int,X: int > rat,Y2: int > rat] :
% 0.35/0.60        ( ( finite_finite_int
% 0.35/0.60          @ ( collect_int
% 0.35/0.60            @ ^ [I3: int] :
% 0.35/0.60                ( ( member_int @ I3 @ I6 )
% 0.35/0.60                & ( ( X @ I3 )
% 0.35/0.60                 != zero_zero_rat ) ) ) )
% 0.35/0.60       => ( ( finite_finite_int
% 0.35/0.60            @ ( collect_int
% 0.35/0.60              @ ^ [I3: int] :
% 0.35/0.60                  ( ( member_int @ I3 @ I6 )
% 0.35/0.60                  & ( ( Y2 @ I3 )
% 0.35/0.60                   != zero_zero_rat ) ) ) )
% 0.35/0.60         => ( finite_finite_int
% 0.35/0.60            @ ( collect_int
% 0.35/0.60              @ ^ [I3: int] :
% 0.35/0.60                  ( ( member_int @ I3 @ I6 )
% 0.35/0.60                  & ( ( plus_plus_rat @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 0.35/0.60                   != zero_zero_rat ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % sum.finite_Collect_op
% 0.35/0.60  thf(fact_3940_sum_Ofinite__Collect__op,axiom,
% 0.35/0.60      ! [I6: set_real,X: real > rat,Y2: real > rat] :
% 0.35/0.60        ( ( finite_finite_real
% 0.35/0.60          @ ( collect_real
% 0.35/0.60            @ ^ [I3: real] :
% 0.35/0.60                ( ( member_real @ I3 @ I6 )
% 0.35/0.60                & ( ( X @ I3 )
% 0.35/0.60                 != zero_zero_rat ) ) ) )
% 0.35/0.60       => ( ( finite_finite_real
% 0.35/0.60            @ ( collect_real
% 0.35/0.60              @ ^ [I3: real] :
% 0.35/0.60                  ( ( member_real @ I3 @ I6 )
% 0.35/0.60                  & ( ( Y2 @ I3 )
% 0.35/0.60                   != zero_zero_rat ) ) ) )
% 0.35/0.60         => ( finite_finite_real
% 0.35/0.60            @ ( collect_real
% 0.35/0.60              @ ^ [I3: real] :
% 0.35/0.60                  ( ( member_real @ I3 @ I6 )
% 0.35/0.60                  & ( ( plus_plus_rat @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 0.35/0.60                   != zero_zero_rat ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % sum.finite_Collect_op
% 0.35/0.60  thf(fact_3941_dbl__inc__simps_I3_J,axiom,
% 0.35/0.60      ( ( neg_nu8557863876264182079omplex @ one_one_complex )
% 0.35/0.60      = ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dbl_inc_simps(3)
% 0.35/0.60  thf(fact_3942_dbl__inc__simps_I3_J,axiom,
% 0.35/0.60      ( ( neg_nu8295874005876285629c_real @ one_one_real )
% 0.35/0.60      = ( numeral_numeral_real @ ( bit1 @ one ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dbl_inc_simps(3)
% 0.35/0.60  thf(fact_3943_dbl__inc__simps_I3_J,axiom,
% 0.35/0.60      ( ( neg_nu5219082963157363817nc_rat @ one_one_rat )
% 0.35/0.60      = ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dbl_inc_simps(3)
% 0.35/0.60  thf(fact_3944_dbl__inc__simps_I3_J,axiom,
% 0.35/0.60      ( ( neg_nu5851722552734809277nc_int @ one_one_int )
% 0.35/0.60      = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dbl_inc_simps(3)
% 0.35/0.60  thf(fact_3945_VEBT__internal_Oheight_Osimps_I1_J,axiom,
% 0.35/0.60      ! [A: $o,B: $o] :
% 0.35/0.60        ( ( vEBT_VEBT_height @ ( vEBT_Leaf @ A @ B ) )
% 0.35/0.60        = zero_zero_nat ) ).
% 0.35/0.60  
% 0.35/0.60  % VEBT_internal.height.simps(1)
% 0.35/0.60  thf(fact_3946_divmod__BitM__2__eq,axiom,
% 0.35/0.60      ! [M: num] :
% 0.35/0.60        ( ( unique5052692396658037445od_int @ ( bitM @ M ) @ ( bit0 @ one ) )
% 0.35/0.60        = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ one_one_int ) ) ).
% 0.35/0.60  
% 0.35/0.60  % divmod_BitM_2_eq
% 0.35/0.60  thf(fact_3947_dbl__inc__simps_I2_J,axiom,
% 0.35/0.60      ( ( neg_nu8557863876264182079omplex @ zero_zero_complex )
% 0.35/0.60      = one_one_complex ) ).
% 0.35/0.60  
% 0.35/0.60  % dbl_inc_simps(2)
% 0.35/0.60  thf(fact_3948_dbl__inc__simps_I2_J,axiom,
% 0.35/0.60      ( ( neg_nu8295874005876285629c_real @ zero_zero_real )
% 0.35/0.60      = one_one_real ) ).
% 0.35/0.60  
% 0.35/0.60  % dbl_inc_simps(2)
% 0.35/0.60  thf(fact_3949_dbl__inc__simps_I2_J,axiom,
% 0.35/0.60      ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 0.35/0.60      = one_one_rat ) ).
% 0.35/0.60  
% 0.35/0.60  % dbl_inc_simps(2)
% 0.35/0.60  thf(fact_3950_dbl__inc__simps_I2_J,axiom,
% 0.35/0.60      ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 0.35/0.60      = one_one_int ) ).
% 0.35/0.60  
% 0.35/0.60  % dbl_inc_simps(2)
% 0.35/0.60  thf(fact_3951_dbl__inc__simps_I5_J,axiom,
% 0.35/0.60      ! [K: num] :
% 0.35/0.60        ( ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) )
% 0.35/0.60        = ( numera6690914467698888265omplex @ ( bit1 @ K ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dbl_inc_simps(5)
% 0.35/0.60  thf(fact_3952_dbl__inc__simps_I5_J,axiom,
% 0.35/0.60      ! [K: num] :
% 0.35/0.60        ( ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) )
% 0.35/0.60        = ( numeral_numeral_real @ ( bit1 @ K ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dbl_inc_simps(5)
% 0.35/0.60  thf(fact_3953_dbl__inc__simps_I5_J,axiom,
% 0.35/0.60      ! [K: num] :
% 0.35/0.60        ( ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) )
% 0.35/0.60        = ( numeral_numeral_rat @ ( bit1 @ K ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dbl_inc_simps(5)
% 0.35/0.60  thf(fact_3954_dbl__inc__simps_I5_J,axiom,
% 0.35/0.60      ! [K: num] :
% 0.35/0.60        ( ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) )
% 0.35/0.60        = ( numeral_numeral_int @ ( bit1 @ K ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dbl_inc_simps(5)
% 0.35/0.60  thf(fact_3955_semiring__norm_I26_J,axiom,
% 0.35/0.60      ( ( bitM @ one )
% 0.35/0.60      = one ) ).
% 0.35/0.60  
% 0.35/0.60  % semiring_norm(26)
% 0.35/0.60  thf(fact_3956_semiring__norm_I28_J,axiom,
% 0.35/0.60      ! [N: num] :
% 0.35/0.60        ( ( bitM @ ( bit1 @ N ) )
% 0.35/0.60        = ( bit1 @ ( bit0 @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % semiring_norm(28)
% 0.35/0.60  thf(fact_3957_semiring__norm_I27_J,axiom,
% 0.35/0.60      ! [N: num] :
% 0.35/0.60        ( ( bitM @ ( bit0 @ N ) )
% 0.35/0.60        = ( bit1 @ ( bitM @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % semiring_norm(27)
% 0.35/0.60  thf(fact_3958_eval__nat__numeral_I2_J,axiom,
% 0.35/0.60      ! [N: num] :
% 0.35/0.60        ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 0.35/0.60        = ( suc @ ( numeral_numeral_nat @ ( bitM @ N ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % eval_nat_numeral(2)
% 0.35/0.60  thf(fact_3959_BitM__plus__one,axiom,
% 0.35/0.60      ! [N: num] :
% 0.35/0.60        ( ( plus_plus_num @ ( bitM @ N ) @ one )
% 0.35/0.60        = ( bit0 @ N ) ) ).
% 0.35/0.60  
% 0.35/0.60  % BitM_plus_one
% 0.35/0.60  thf(fact_3960_one__plus__BitM,axiom,
% 0.35/0.60      ! [N: num] :
% 0.35/0.60        ( ( plus_plus_num @ one @ ( bitM @ N ) )
% 0.35/0.60        = ( bit0 @ N ) ) ).
% 0.35/0.60  
% 0.35/0.60  % one_plus_BitM
% 0.35/0.60  thf(fact_3961_dbl__inc__def,axiom,
% 0.35/0.60      ( neg_nu8295874005876285629c_real
% 0.35/0.60      = ( ^ [X2: real] : ( plus_plus_real @ ( plus_plus_real @ X2 @ X2 ) @ one_one_real ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dbl_inc_def
% 0.35/0.60  thf(fact_3962_dbl__inc__def,axiom,
% 0.35/0.60      ( neg_nu5219082963157363817nc_rat
% 0.35/0.60      = ( ^ [X2: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X2 @ X2 ) @ one_one_rat ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dbl_inc_def
% 0.35/0.60  thf(fact_3963_dbl__inc__def,axiom,
% 0.35/0.60      ( neg_nu5851722552734809277nc_int
% 0.35/0.60      = ( ^ [X2: int] : ( plus_plus_int @ ( plus_plus_int @ X2 @ X2 ) @ one_one_int ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dbl_inc_def
% 0.35/0.60  thf(fact_3964_dbl__inc__def,axiom,
% 0.35/0.60      ( neg_nu8557863876264182079omplex
% 0.35/0.60      = ( ^ [X2: complex] : ( plus_plus_complex @ ( plus_plus_complex @ X2 @ X2 ) @ one_one_complex ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dbl_inc_def
% 0.35/0.60  thf(fact_3965_numeral__BitM,axiom,
% 0.35/0.60      ! [N: num] :
% 0.35/0.60        ( ( numera6690914467698888265omplex @ ( bitM @ N ) )
% 0.35/0.60        = ( minus_minus_complex @ ( numera6690914467698888265omplex @ ( bit0 @ N ) ) @ one_one_complex ) ) ).
% 0.35/0.60  
% 0.35/0.60  % numeral_BitM
% 0.35/0.60  thf(fact_3966_numeral__BitM,axiom,
% 0.35/0.60      ! [N: num] :
% 0.35/0.60        ( ( numeral_numeral_real @ ( bitM @ N ) )
% 0.35/0.60        = ( minus_minus_real @ ( numeral_numeral_real @ ( bit0 @ N ) ) @ one_one_real ) ) ).
% 0.35/0.60  
% 0.35/0.60  % numeral_BitM
% 0.35/0.60  thf(fact_3967_numeral__BitM,axiom,
% 0.35/0.60      ! [N: num] :
% 0.35/0.60        ( ( numeral_numeral_rat @ ( bitM @ N ) )
% 0.35/0.60        = ( minus_minus_rat @ ( numeral_numeral_rat @ ( bit0 @ N ) ) @ one_one_rat ) ) ).
% 0.35/0.60  
% 0.35/0.60  % numeral_BitM
% 0.35/0.60  thf(fact_3968_numeral__BitM,axiom,
% 0.35/0.60      ! [N: num] :
% 0.35/0.60        ( ( numeral_numeral_int @ ( bitM @ N ) )
% 0.35/0.60        = ( minus_minus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ one_one_int ) ) ).
% 0.35/0.60  
% 0.35/0.60  % numeral_BitM
% 0.35/0.60  thf(fact_3969_VEBT__internal_Oheight_Ocases,axiom,
% 0.35/0.60      ! [X: vEBT_VEBT] :
% 0.35/0.60        ( ! [A4: $o,B3: $o] :
% 0.35/0.60            ( X
% 0.35/0.60           != ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.60       => ~ ! [Uu2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.60              ( X
% 0.35/0.60             != ( vEBT_Node @ Uu2 @ Deg2 @ TreeList2 @ Summary2 ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % VEBT_internal.height.cases
% 0.35/0.60  thf(fact_3970_gcd__nat__induct,axiom,
% 0.35/0.60      ! [P: nat > nat > $o,M: nat,N: nat] :
% 0.35/0.60        ( ! [M4: nat] : ( P @ M4 @ zero_zero_nat )
% 0.35/0.60       => ( ! [M4: nat,N3: nat] :
% 0.35/0.60              ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.35/0.60             => ( ( P @ N3 @ ( modulo_modulo_nat @ M4 @ N3 ) )
% 0.35/0.60               => ( P @ M4 @ N3 ) ) )
% 0.35/0.60         => ( P @ M @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % gcd_nat_induct
% 0.35/0.60  thf(fact_3971_concat__bit__Suc,axiom,
% 0.35/0.60      ! [N: nat,K: int,L2: int] :
% 0.35/0.60        ( ( bit_concat_bit @ ( suc @ N ) @ K @ L2 )
% 0.35/0.60        = ( plus_plus_int @ ( modulo_modulo_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_concat_bit @ N @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ L2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % concat_bit_Suc
% 0.35/0.60  thf(fact_3972_dbl__simps_I3_J,axiom,
% 0.35/0.60      ( ( neg_nu7009210354673126013omplex @ one_one_complex )
% 0.35/0.60      = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dbl_simps(3)
% 0.35/0.60  thf(fact_3973_dbl__simps_I3_J,axiom,
% 0.35/0.60      ( ( neg_numeral_dbl_real @ one_one_real )
% 0.35/0.60      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dbl_simps(3)
% 0.35/0.60  thf(fact_3974_dbl__simps_I3_J,axiom,
% 0.35/0.60      ( ( neg_numeral_dbl_rat @ one_one_rat )
% 0.35/0.60      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dbl_simps(3)
% 0.35/0.60  thf(fact_3975_dbl__simps_I3_J,axiom,
% 0.35/0.60      ( ( neg_numeral_dbl_int @ one_one_int )
% 0.35/0.60      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dbl_simps(3)
% 0.35/0.60  thf(fact_3976_even__succ__mod__exp,axiom,
% 0.35/0.60      ! [A: code_integer,N: nat] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.35/0.60       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.60         => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.60            = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % even_succ_mod_exp
% 0.35/0.60  thf(fact_3977_even__succ__mod__exp,axiom,
% 0.35/0.60      ! [A: nat,N: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.60       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.60         => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.60            = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % even_succ_mod_exp
% 0.35/0.60  thf(fact_3978_even__succ__mod__exp,axiom,
% 0.35/0.60      ! [A: int,N: nat] :
% 0.35/0.60        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.60       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.60         => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.60            = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % even_succ_mod_exp
% 0.35/0.60  thf(fact_3979_divmod__algorithm__code_I6_J,axiom,
% 0.35/0.60      ! [M: num,N: num] :
% 0.35/0.60        ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.35/0.60        = ( produc2626176000494625587at_nat
% 0.35/0.60          @ ^ [Q4: nat,R5: nat] : ( product_Pair_nat_nat @ Q4 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) @ one_one_nat ) )
% 0.35/0.60          @ ( unique5055182867167087721od_nat @ M @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % divmod_algorithm_code(6)
% 0.35/0.60  thf(fact_3980_divmod__algorithm__code_I6_J,axiom,
% 0.35/0.60      ! [M: num,N: num] :
% 0.35/0.60        ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.35/0.60        = ( produc4245557441103728435nt_int
% 0.35/0.60          @ ^ [Q4: int,R5: int] : ( product_Pair_int_int @ Q4 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) @ one_one_int ) )
% 0.35/0.60          @ ( unique5052692396658037445od_int @ M @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % divmod_algorithm_code(6)
% 0.35/0.60  thf(fact_3981_even__succ__div__exp,axiom,
% 0.35/0.60      ! [A: code_integer,N: nat] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.35/0.60       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.60         => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.60            = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % even_succ_div_exp
% 0.35/0.60  thf(fact_3982_even__succ__div__exp,axiom,
% 0.35/0.60      ! [A: nat,N: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.60       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.60         => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.60            = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % even_succ_div_exp
% 0.35/0.60  thf(fact_3983_even__succ__div__exp,axiom,
% 0.35/0.60      ! [A: int,N: nat] :
% 0.35/0.60        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.60       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.60         => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.60            = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % even_succ_div_exp
% 0.35/0.60  thf(fact_3984_nat__dvd__1__iff__1,axiom,
% 0.35/0.60      ! [M: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ M @ one_one_nat )
% 0.35/0.60        = ( M = one_one_nat ) ) ).
% 0.35/0.60  
% 0.35/0.60  % nat_dvd_1_iff_1
% 0.35/0.60  thf(fact_3985_dvd__1__left,axiom,
% 0.35/0.60      ! [K: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_1_left
% 0.35/0.60  thf(fact_3986_dvd__1__iff__1,axiom,
% 0.35/0.60      ! [M: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ M @ ( suc @ zero_zero_nat ) )
% 0.35/0.60        = ( M
% 0.35/0.60          = ( suc @ zero_zero_nat ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_1_iff_1
% 0.35/0.60  thf(fact_3987_dvd__add__triv__right__iff,axiom,
% 0.35/0.60      ! [A: code_integer,B: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 0.35/0.60        = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add_triv_right_iff
% 0.35/0.60  thf(fact_3988_dvd__add__triv__right__iff,axiom,
% 0.35/0.60      ! [A: real,B: real] :
% 0.35/0.60        ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ A ) )
% 0.35/0.60        = ( dvd_dvd_real @ A @ B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add_triv_right_iff
% 0.35/0.60  thf(fact_3989_dvd__add__triv__right__iff,axiom,
% 0.35/0.60      ! [A: rat,B: rat] :
% 0.35/0.60        ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 0.35/0.60        = ( dvd_dvd_rat @ A @ B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add_triv_right_iff
% 0.35/0.60  thf(fact_3990_dvd__add__triv__right__iff,axiom,
% 0.35/0.60      ! [A: nat,B: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 0.35/0.60        = ( dvd_dvd_nat @ A @ B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add_triv_right_iff
% 0.35/0.60  thf(fact_3991_dvd__add__triv__right__iff,axiom,
% 0.35/0.60      ! [A: int,B: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ A ) )
% 0.35/0.60        = ( dvd_dvd_int @ A @ B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add_triv_right_iff
% 0.35/0.60  thf(fact_3992_dvd__add__triv__right__iff,axiom,
% 0.35/0.60      ! [A: complex,B: complex] :
% 0.35/0.60        ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ B @ A ) )
% 0.35/0.60        = ( dvd_dvd_complex @ A @ B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add_triv_right_iff
% 0.35/0.60  thf(fact_3993_dvd__add__triv__left__iff,axiom,
% 0.35/0.60      ! [A: code_integer,B: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.35/0.60        = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add_triv_left_iff
% 0.35/0.60  thf(fact_3994_dvd__add__triv__left__iff,axiom,
% 0.35/0.60      ! [A: real,B: real] :
% 0.35/0.60        ( ( dvd_dvd_real @ A @ ( plus_plus_real @ A @ B ) )
% 0.35/0.60        = ( dvd_dvd_real @ A @ B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add_triv_left_iff
% 0.35/0.60  thf(fact_3995_dvd__add__triv__left__iff,axiom,
% 0.35/0.60      ! [A: rat,B: rat] :
% 0.35/0.60        ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 0.35/0.60        = ( dvd_dvd_rat @ A @ B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add_triv_left_iff
% 0.35/0.60  thf(fact_3996_dvd__add__triv__left__iff,axiom,
% 0.35/0.60      ! [A: nat,B: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.35/0.60        = ( dvd_dvd_nat @ A @ B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add_triv_left_iff
% 0.35/0.60  thf(fact_3997_dvd__add__triv__left__iff,axiom,
% 0.35/0.60      ! [A: int,B: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ A @ ( plus_plus_int @ A @ B ) )
% 0.35/0.60        = ( dvd_dvd_int @ A @ B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add_triv_left_iff
% 0.35/0.60  thf(fact_3998_dvd__add__triv__left__iff,axiom,
% 0.35/0.60      ! [A: complex,B: complex] :
% 0.35/0.60        ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ A @ B ) )
% 0.35/0.60        = ( dvd_dvd_complex @ A @ B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add_triv_left_iff
% 0.35/0.60  thf(fact_3999_div__dvd__div,axiom,
% 0.35/0.60      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ A @ B )
% 0.35/0.60       => ( ( dvd_dvd_Code_integer @ A @ C )
% 0.35/0.60         => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ B @ A ) @ ( divide6298287555418463151nteger @ C @ A ) )
% 0.35/0.60            = ( dvd_dvd_Code_integer @ B @ C ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_dvd_div
% 0.35/0.60  thf(fact_4000_div__dvd__div,axiom,
% 0.35/0.60      ! [A: nat,B: nat,C: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ A @ B )
% 0.35/0.60       => ( ( dvd_dvd_nat @ A @ C )
% 0.35/0.60         => ( ( dvd_dvd_nat @ ( divide_divide_nat @ B @ A ) @ ( divide_divide_nat @ C @ A ) )
% 0.35/0.60            = ( dvd_dvd_nat @ B @ C ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_dvd_div
% 0.35/0.60  thf(fact_4001_div__dvd__div,axiom,
% 0.35/0.60      ! [A: int,B: int,C: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ A @ B )
% 0.35/0.60       => ( ( dvd_dvd_int @ A @ C )
% 0.35/0.60         => ( ( dvd_dvd_int @ ( divide_divide_int @ B @ A ) @ ( divide_divide_int @ C @ A ) )
% 0.35/0.60            = ( dvd_dvd_int @ B @ C ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_dvd_div
% 0.35/0.60  thf(fact_4002_nat__mult__dvd__cancel__disj,axiom,
% 0.35/0.60      ! [K: nat,M: nat,N: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.35/0.60        = ( ( K = zero_zero_nat )
% 0.35/0.60          | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % nat_mult_dvd_cancel_disj
% 0.35/0.60  thf(fact_4003_concat__bit__0,axiom,
% 0.35/0.60      ! [K: int,L2: int] :
% 0.35/0.60        ( ( bit_concat_bit @ zero_zero_nat @ K @ L2 )
% 0.35/0.60        = L2 ) ).
% 0.35/0.60  
% 0.35/0.60  % concat_bit_0
% 0.35/0.60  thf(fact_4004_case__prod__conv,axiom,
% 0.35/0.60      ! [F: nat > nat > nat,A: nat,B: nat] :
% 0.35/0.60        ( ( produc6842872674320459806at_nat @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 0.35/0.60        = ( F @ A @ B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % case_prod_conv
% 0.35/0.60  thf(fact_4005_case__prod__conv,axiom,
% 0.35/0.60      ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,A: nat,B: nat] :
% 0.35/0.60        ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 0.35/0.60        = ( F @ A @ B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % case_prod_conv
% 0.35/0.60  thf(fact_4006_case__prod__conv,axiom,
% 0.35/0.60      ! [F: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat] :
% 0.35/0.60        ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 0.35/0.60        = ( F @ A @ B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % case_prod_conv
% 0.35/0.60  thf(fact_4007_case__prod__conv,axiom,
% 0.35/0.60      ! [F: int > int > product_prod_int_int,A: int,B: int] :
% 0.35/0.60        ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 0.35/0.60        = ( F @ A @ B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % case_prod_conv
% 0.35/0.60  thf(fact_4008_case__prod__conv,axiom,
% 0.35/0.60      ! [F: int > int > int,A: int,B: int] :
% 0.35/0.60        ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 0.35/0.60        = ( F @ A @ B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % case_prod_conv
% 0.35/0.60  thf(fact_4009_dbl__simps_I2_J,axiom,
% 0.35/0.60      ( ( neg_nu7009210354673126013omplex @ zero_zero_complex )
% 0.35/0.60      = zero_zero_complex ) ).
% 0.35/0.60  
% 0.35/0.60  % dbl_simps(2)
% 0.35/0.60  thf(fact_4010_dbl__simps_I2_J,axiom,
% 0.35/0.60      ( ( neg_numeral_dbl_real @ zero_zero_real )
% 0.35/0.60      = zero_zero_real ) ).
% 0.35/0.60  
% 0.35/0.60  % dbl_simps(2)
% 0.35/0.60  thf(fact_4011_dbl__simps_I2_J,axiom,
% 0.35/0.60      ( ( neg_numeral_dbl_rat @ zero_zero_rat )
% 0.35/0.60      = zero_zero_rat ) ).
% 0.35/0.60  
% 0.35/0.60  % dbl_simps(2)
% 0.35/0.60  thf(fact_4012_dbl__simps_I2_J,axiom,
% 0.35/0.60      ( ( neg_numeral_dbl_int @ zero_zero_int )
% 0.35/0.60      = zero_zero_int ) ).
% 0.35/0.60  
% 0.35/0.60  % dbl_simps(2)
% 0.35/0.60  thf(fact_4013_dvd__times__right__cancel__iff,axiom,
% 0.35/0.60      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.35/0.60        ( ( A != zero_z3403309356797280102nteger )
% 0.35/0.60       => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ A ) @ ( times_3573771949741848930nteger @ C @ A ) )
% 0.35/0.60          = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_times_right_cancel_iff
% 0.35/0.60  thf(fact_4014_dvd__times__right__cancel__iff,axiom,
% 0.35/0.60      ! [A: nat,B: nat,C: nat] :
% 0.35/0.60        ( ( A != zero_zero_nat )
% 0.35/0.60       => ( ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) )
% 0.35/0.60          = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_times_right_cancel_iff
% 0.35/0.60  thf(fact_4015_dvd__times__right__cancel__iff,axiom,
% 0.35/0.60      ! [A: int,B: int,C: int] :
% 0.35/0.60        ( ( A != zero_zero_int )
% 0.35/0.60       => ( ( dvd_dvd_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) )
% 0.35/0.60          = ( dvd_dvd_int @ B @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_times_right_cancel_iff
% 0.35/0.60  thf(fact_4016_dvd__times__left__cancel__iff,axiom,
% 0.35/0.60      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.35/0.60        ( ( A != zero_z3403309356797280102nteger )
% 0.35/0.60       => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) )
% 0.35/0.60          = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_times_left_cancel_iff
% 0.35/0.60  thf(fact_4017_dvd__times__left__cancel__iff,axiom,
% 0.35/0.60      ! [A: nat,B: nat,C: nat] :
% 0.35/0.60        ( ( A != zero_zero_nat )
% 0.35/0.60       => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
% 0.35/0.60          = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_times_left_cancel_iff
% 0.35/0.60  thf(fact_4018_dvd__times__left__cancel__iff,axiom,
% 0.35/0.60      ! [A: int,B: int,C: int] :
% 0.35/0.60        ( ( A != zero_zero_int )
% 0.35/0.60       => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
% 0.35/0.60          = ( dvd_dvd_int @ B @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_times_left_cancel_iff
% 0.35/0.60  thf(fact_4019_dvd__mult__cancel__right,axiom,
% 0.35/0.60      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.35/0.60        = ( ( C = zero_z3403309356797280102nteger )
% 0.35/0.60          | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult_cancel_right
% 0.35/0.60  thf(fact_4020_dvd__mult__cancel__right,axiom,
% 0.35/0.60      ! [A: rat,C: rat,B: rat] :
% 0.35/0.60        ( ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.35/0.60        = ( ( C = zero_zero_rat )
% 0.35/0.60          | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult_cancel_right
% 0.35/0.60  thf(fact_4021_dvd__mult__cancel__right,axiom,
% 0.35/0.60      ! [A: complex,C: complex,B: complex] :
% 0.35/0.60        ( ( dvd_dvd_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 0.35/0.60        = ( ( C = zero_zero_complex )
% 0.35/0.60          | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult_cancel_right
% 0.35/0.60  thf(fact_4022_dvd__mult__cancel__right,axiom,
% 0.35/0.60      ! [A: real,C: real,B: real] :
% 0.35/0.60        ( ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 0.35/0.60        = ( ( C = zero_zero_real )
% 0.35/0.60          | ( dvd_dvd_real @ A @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult_cancel_right
% 0.35/0.60  thf(fact_4023_dvd__mult__cancel__right,axiom,
% 0.35/0.60      ! [A: int,C: int,B: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.35/0.60        = ( ( C = zero_zero_int )
% 0.35/0.60          | ( dvd_dvd_int @ A @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult_cancel_right
% 0.35/0.60  thf(fact_4024_dvd__mult__cancel__left,axiom,
% 0.35/0.60      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.35/0.60        = ( ( C = zero_z3403309356797280102nteger )
% 0.35/0.60          | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult_cancel_left
% 0.35/0.60  thf(fact_4025_dvd__mult__cancel__left,axiom,
% 0.35/0.60      ! [C: rat,A: rat,B: rat] :
% 0.35/0.60        ( ( dvd_dvd_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.35/0.60        = ( ( C = zero_zero_rat )
% 0.35/0.60          | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult_cancel_left
% 0.35/0.60  thf(fact_4026_dvd__mult__cancel__left,axiom,
% 0.35/0.60      ! [C: complex,A: complex,B: complex] :
% 0.35/0.60        ( ( dvd_dvd_complex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 0.35/0.60        = ( ( C = zero_zero_complex )
% 0.35/0.60          | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult_cancel_left
% 0.35/0.60  thf(fact_4027_dvd__mult__cancel__left,axiom,
% 0.35/0.60      ! [C: real,A: real,B: real] :
% 0.35/0.60        ( ( dvd_dvd_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.35/0.60        = ( ( C = zero_zero_real )
% 0.35/0.60          | ( dvd_dvd_real @ A @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult_cancel_left
% 0.35/0.60  thf(fact_4028_dvd__mult__cancel__left,axiom,
% 0.35/0.60      ! [C: int,A: int,B: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.35/0.60        = ( ( C = zero_zero_int )
% 0.35/0.60          | ( dvd_dvd_int @ A @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult_cancel_left
% 0.35/0.60  thf(fact_4029_unit__prod,axiom,
% 0.35/0.60      ! [A: code_integer,B: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.35/0.60       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.35/0.60         => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_prod
% 0.35/0.60  thf(fact_4030_unit__prod,axiom,
% 0.35/0.60      ! [A: nat,B: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.35/0.60       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.35/0.60         => ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_prod
% 0.35/0.60  thf(fact_4031_unit__prod,axiom,
% 0.35/0.60      ! [A: int,B: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.35/0.60       => ( ( dvd_dvd_int @ B @ one_one_int )
% 0.35/0.60         => ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_prod
% 0.35/0.60  thf(fact_4032_dvd__add__times__triv__right__iff,axiom,
% 0.35/0.60      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ C @ A ) ) )
% 0.35/0.60        = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add_times_triv_right_iff
% 0.35/0.60  thf(fact_4033_dvd__add__times__triv__right__iff,axiom,
% 0.35/0.60      ! [A: rat,B: rat,C: rat] :
% 0.35/0.60        ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ ( times_times_rat @ C @ A ) ) )
% 0.35/0.60        = ( dvd_dvd_rat @ A @ B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add_times_triv_right_iff
% 0.35/0.60  thf(fact_4034_dvd__add__times__triv__right__iff,axiom,
% 0.35/0.60      ! [A: complex,B: complex,C: complex] :
% 0.35/0.60        ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ B @ ( times_times_complex @ C @ A ) ) )
% 0.35/0.60        = ( dvd_dvd_complex @ A @ B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add_times_triv_right_iff
% 0.35/0.60  thf(fact_4035_dvd__add__times__triv__right__iff,axiom,
% 0.35/0.60      ! [A: real,B: real,C: real] :
% 0.35/0.60        ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ ( times_times_real @ C @ A ) ) )
% 0.35/0.60        = ( dvd_dvd_real @ A @ B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add_times_triv_right_iff
% 0.35/0.60  thf(fact_4036_dvd__add__times__triv__right__iff,axiom,
% 0.35/0.60      ! [A: nat,B: nat,C: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ ( times_times_nat @ C @ A ) ) )
% 0.35/0.60        = ( dvd_dvd_nat @ A @ B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add_times_triv_right_iff
% 0.35/0.60  thf(fact_4037_dvd__add__times__triv__right__iff,axiom,
% 0.35/0.60      ! [A: int,B: int,C: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ C @ A ) ) )
% 0.35/0.60        = ( dvd_dvd_int @ A @ B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add_times_triv_right_iff
% 0.35/0.60  thf(fact_4038_dvd__add__times__triv__left__iff,axiom,
% 0.35/0.60      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ A ) @ B ) )
% 0.35/0.60        = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add_times_triv_left_iff
% 0.35/0.60  thf(fact_4039_dvd__add__times__triv__left__iff,axiom,
% 0.35/0.60      ! [A: rat,C: rat,B: rat] :
% 0.35/0.60        ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ ( times_times_rat @ C @ A ) @ B ) )
% 0.35/0.60        = ( dvd_dvd_rat @ A @ B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add_times_triv_left_iff
% 0.35/0.60  thf(fact_4040_dvd__add__times__triv__left__iff,axiom,
% 0.35/0.60      ! [A: complex,C: complex,B: complex] :
% 0.35/0.60        ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ ( times_times_complex @ C @ A ) @ B ) )
% 0.35/0.60        = ( dvd_dvd_complex @ A @ B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add_times_triv_left_iff
% 0.35/0.60  thf(fact_4041_dvd__add__times__triv__left__iff,axiom,
% 0.35/0.60      ! [A: real,C: real,B: real] :
% 0.35/0.60        ( ( dvd_dvd_real @ A @ ( plus_plus_real @ ( times_times_real @ C @ A ) @ B ) )
% 0.35/0.60        = ( dvd_dvd_real @ A @ B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add_times_triv_left_iff
% 0.35/0.60  thf(fact_4042_dvd__add__times__triv__left__iff,axiom,
% 0.35/0.60      ! [A: nat,C: nat,B: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ B ) )
% 0.35/0.60        = ( dvd_dvd_nat @ A @ B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add_times_triv_left_iff
% 0.35/0.60  thf(fact_4043_dvd__add__times__triv__left__iff,axiom,
% 0.35/0.60      ! [A: int,C: int,B: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ A @ ( plus_plus_int @ ( times_times_int @ C @ A ) @ B ) )
% 0.35/0.60        = ( dvd_dvd_int @ A @ B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add_times_triv_left_iff
% 0.35/0.60  thf(fact_4044_dvd__div__mult__self,axiom,
% 0.35/0.60      ! [A: code_integer,B: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ A @ B )
% 0.35/0.60       => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 0.35/0.60          = B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_mult_self
% 0.35/0.60  thf(fact_4045_dvd__div__mult__self,axiom,
% 0.35/0.60      ! [A: nat,B: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ A @ B )
% 0.35/0.60       => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 0.35/0.60          = B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_mult_self
% 0.35/0.60  thf(fact_4046_dvd__div__mult__self,axiom,
% 0.35/0.60      ! [A: int,B: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ A @ B )
% 0.35/0.60       => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 0.35/0.60          = B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_mult_self
% 0.35/0.60  thf(fact_4047_dvd__mult__div__cancel,axiom,
% 0.35/0.60      ! [A: code_integer,B: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ A @ B )
% 0.35/0.60       => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ A ) )
% 0.35/0.60          = B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult_div_cancel
% 0.35/0.60  thf(fact_4048_dvd__mult__div__cancel,axiom,
% 0.35/0.60      ! [A: nat,B: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ A @ B )
% 0.35/0.60       => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ A ) )
% 0.35/0.60          = B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult_div_cancel
% 0.35/0.60  thf(fact_4049_dvd__mult__div__cancel,axiom,
% 0.35/0.60      ! [A: int,B: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ A @ B )
% 0.35/0.60       => ( ( times_times_int @ A @ ( divide_divide_int @ B @ A ) )
% 0.35/0.60          = B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult_div_cancel
% 0.35/0.60  thf(fact_4050_unit__div__1__div__1,axiom,
% 0.35/0.60      ! [A: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.35/0.60       => ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 0.35/0.60          = A ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_div_1_div_1
% 0.35/0.60  thf(fact_4051_unit__div__1__div__1,axiom,
% 0.35/0.60      ! [A: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.35/0.60       => ( ( divide_divide_nat @ one_one_nat @ ( divide_divide_nat @ one_one_nat @ A ) )
% 0.35/0.60          = A ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_div_1_div_1
% 0.35/0.60  thf(fact_4052_unit__div__1__div__1,axiom,
% 0.35/0.60      ! [A: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.35/0.60       => ( ( divide_divide_int @ one_one_int @ ( divide_divide_int @ one_one_int @ A ) )
% 0.35/0.60          = A ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_div_1_div_1
% 0.35/0.60  thf(fact_4053_unit__div__1__unit,axiom,
% 0.35/0.60      ! [A: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.35/0.60       => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) @ one_one_Code_integer ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_div_1_unit
% 0.35/0.60  thf(fact_4054_unit__div__1__unit,axiom,
% 0.35/0.60      ! [A: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.35/0.60       => ( dvd_dvd_nat @ ( divide_divide_nat @ one_one_nat @ A ) @ one_one_nat ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_div_1_unit
% 0.35/0.60  thf(fact_4055_unit__div__1__unit,axiom,
% 0.35/0.60      ! [A: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.35/0.60       => ( dvd_dvd_int @ ( divide_divide_int @ one_one_int @ A ) @ one_one_int ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_div_1_unit
% 0.35/0.60  thf(fact_4056_unit__div,axiom,
% 0.35/0.60      ! [A: code_integer,B: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.35/0.60       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.35/0.60         => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_div
% 0.35/0.60  thf(fact_4057_unit__div,axiom,
% 0.35/0.60      ! [A: nat,B: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.35/0.60       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.35/0.60         => ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_div
% 0.35/0.60  thf(fact_4058_unit__div,axiom,
% 0.35/0.60      ! [A: int,B: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.35/0.60       => ( ( dvd_dvd_int @ B @ one_one_int )
% 0.35/0.60         => ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_div
% 0.35/0.60  thf(fact_4059_div__add,axiom,
% 0.35/0.60      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ C @ A )
% 0.35/0.60       => ( ( dvd_dvd_Code_integer @ C @ B )
% 0.35/0.60         => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 0.35/0.60            = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_add
% 0.35/0.60  thf(fact_4060_div__add,axiom,
% 0.35/0.60      ! [C: nat,A: nat,B: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ C @ A )
% 0.35/0.60       => ( ( dvd_dvd_nat @ C @ B )
% 0.35/0.60         => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.35/0.60            = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_add
% 0.35/0.60  thf(fact_4061_div__add,axiom,
% 0.35/0.60      ! [C: int,A: int,B: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ C @ A )
% 0.35/0.60       => ( ( dvd_dvd_int @ C @ B )
% 0.35/0.60         => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.35/0.60            = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_add
% 0.35/0.60  thf(fact_4062_div__diff,axiom,
% 0.35/0.60      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ C @ A )
% 0.35/0.60       => ( ( dvd_dvd_Code_integer @ C @ B )
% 0.35/0.60         => ( ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 0.35/0.60            = ( minus_8373710615458151222nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_diff
% 0.35/0.60  thf(fact_4063_div__diff,axiom,
% 0.35/0.60      ! [C: int,A: int,B: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ C @ A )
% 0.35/0.60       => ( ( dvd_dvd_int @ C @ B )
% 0.35/0.60         => ( ( divide_divide_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.35/0.60            = ( minus_minus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_diff
% 0.35/0.60  thf(fact_4064_concat__bit__nonnegative__iff,axiom,
% 0.35/0.60      ! [N: nat,K: int,L2: int] :
% 0.35/0.60        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_concat_bit @ N @ K @ L2 ) )
% 0.35/0.60        = ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ).
% 0.35/0.60  
% 0.35/0.60  % concat_bit_nonnegative_iff
% 0.35/0.60  thf(fact_4065_concat__bit__negative__iff,axiom,
% 0.35/0.60      ! [N: nat,K: int,L2: int] :
% 0.35/0.60        ( ( ord_less_int @ ( bit_concat_bit @ N @ K @ L2 ) @ zero_zero_int )
% 0.35/0.60        = ( ord_less_int @ L2 @ zero_zero_int ) ) ).
% 0.35/0.60  
% 0.35/0.60  % concat_bit_negative_iff
% 0.35/0.60  thf(fact_4066_dbl__simps_I5_J,axiom,
% 0.35/0.60      ! [K: num] :
% 0.35/0.60        ( ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) )
% 0.35/0.60        = ( numera6690914467698888265omplex @ ( bit0 @ K ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dbl_simps(5)
% 0.35/0.60  thf(fact_4067_dbl__simps_I5_J,axiom,
% 0.35/0.60      ! [K: num] :
% 0.35/0.60        ( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) )
% 0.35/0.60        = ( numeral_numeral_real @ ( bit0 @ K ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dbl_simps(5)
% 0.35/0.60  thf(fact_4068_dbl__simps_I5_J,axiom,
% 0.35/0.60      ! [K: num] :
% 0.35/0.60        ( ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) )
% 0.35/0.60        = ( numeral_numeral_rat @ ( bit0 @ K ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dbl_simps(5)
% 0.35/0.60  thf(fact_4069_dbl__simps_I5_J,axiom,
% 0.35/0.60      ! [K: num] :
% 0.35/0.60        ( ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) )
% 0.35/0.60        = ( numeral_numeral_int @ ( bit0 @ K ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dbl_simps(5)
% 0.35/0.60  thf(fact_4070_even__Suc__Suc__iff,axiom,
% 0.35/0.60      ! [N: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ N ) ) )
% 0.35/0.60        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.35/0.60  
% 0.35/0.60  % even_Suc_Suc_iff
% 0.35/0.60  thf(fact_4071_even__Suc,axiom,
% 0.35/0.60      ! [N: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) )
% 0.35/0.60        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % even_Suc
% 0.35/0.60  thf(fact_4072_unit__div__mult__self,axiom,
% 0.35/0.60      ! [A: code_integer,B: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.35/0.60       => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 0.35/0.60          = B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_div_mult_self
% 0.35/0.60  thf(fact_4073_unit__div__mult__self,axiom,
% 0.35/0.60      ! [A: nat,B: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.35/0.60       => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 0.35/0.60          = B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_div_mult_self
% 0.35/0.60  thf(fact_4074_unit__div__mult__self,axiom,
% 0.35/0.60      ! [A: int,B: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.35/0.60       => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 0.35/0.60          = B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_div_mult_self
% 0.35/0.60  thf(fact_4075_unit__mult__div__div,axiom,
% 0.35/0.60      ! [A: code_integer,B: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.35/0.60       => ( ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 0.35/0.60          = ( divide6298287555418463151nteger @ B @ A ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_mult_div_div
% 0.35/0.60  thf(fact_4076_unit__mult__div__div,axiom,
% 0.35/0.60      ! [A: nat,B: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.35/0.60       => ( ( times_times_nat @ B @ ( divide_divide_nat @ one_one_nat @ A ) )
% 0.35/0.60          = ( divide_divide_nat @ B @ A ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_mult_div_div
% 0.35/0.60  thf(fact_4077_unit__mult__div__div,axiom,
% 0.35/0.60      ! [A: int,B: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.35/0.60       => ( ( times_times_int @ B @ ( divide_divide_int @ one_one_int @ A ) )
% 0.35/0.60          = ( divide_divide_int @ B @ A ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_mult_div_div
% 0.35/0.60  thf(fact_4078_pow__divides__pow__iff,axiom,
% 0.35/0.60      ! [N: nat,A: nat,B: nat] :
% 0.35/0.60        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.60       => ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 0.35/0.60          = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % pow_divides_pow_iff
% 0.35/0.60  thf(fact_4079_pow__divides__pow__iff,axiom,
% 0.35/0.60      ! [N: nat,A: int,B: int] :
% 0.35/0.60        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.60       => ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 0.35/0.60          = ( dvd_dvd_int @ A @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % pow_divides_pow_iff
% 0.35/0.60  thf(fact_4080_even__mult__iff,axiom,
% 0.35/0.60      ! [A: code_integer,B: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( times_3573771949741848930nteger @ A @ B ) )
% 0.35/0.60        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.35/0.60          | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % even_mult_iff
% 0.35/0.60  thf(fact_4081_even__mult__iff,axiom,
% 0.35/0.60      ! [A: nat,B: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ A @ B ) )
% 0.35/0.60        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.60          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % even_mult_iff
% 0.35/0.60  thf(fact_4082_even__mult__iff,axiom,
% 0.35/0.60      ! [A: int,B: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ A @ B ) )
% 0.35/0.60        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.60          | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % even_mult_iff
% 0.35/0.60  thf(fact_4083_even__add,axiom,
% 0.35/0.60      ! [A: code_integer,B: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.35/0.60        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.35/0.60          = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % even_add
% 0.35/0.60  thf(fact_4084_even__add,axiom,
% 0.35/0.60      ! [A: nat,B: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) )
% 0.35/0.60        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.60          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % even_add
% 0.35/0.60  thf(fact_4085_even__add,axiom,
% 0.35/0.60      ! [A: int,B: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) )
% 0.35/0.60        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.60          = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % even_add
% 0.35/0.60  thf(fact_4086_odd__add,axiom,
% 0.35/0.60      ! [A: code_integer,B: code_integer] :
% 0.35/0.60        ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) )
% 0.35/0.60        = ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 0.35/0.60         != ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % odd_add
% 0.35/0.60  thf(fact_4087_odd__add,axiom,
% 0.35/0.60      ! [A: nat,B: nat] :
% 0.35/0.60        ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) )
% 0.35/0.60        = ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 0.35/0.60         != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % odd_add
% 0.35/0.60  thf(fact_4088_odd__add,axiom,
% 0.35/0.60      ! [A: int,B: int] :
% 0.35/0.60        ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) )
% 0.35/0.60        = ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 0.35/0.60         != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % odd_add
% 0.35/0.60  thf(fact_4089_even__Suc__div__two,axiom,
% 0.35/0.60      ! [N: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.60       => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.60          = ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % even_Suc_div_two
% 0.35/0.60  thf(fact_4090_odd__Suc__div__two,axiom,
% 0.35/0.60      ! [N: nat] :
% 0.35/0.60        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.60       => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.60          = ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % odd_Suc_div_two
% 0.35/0.60  thf(fact_4091_even__mod__2__iff,axiom,
% 0.35/0.60      ! [A: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 0.35/0.60        = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 0.35/0.60  
% 0.35/0.60  % even_mod_2_iff
% 0.35/0.60  thf(fact_4092_even__mod__2__iff,axiom,
% 0.35/0.60      ! [A: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.60        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ).
% 0.35/0.60  
% 0.35/0.60  % even_mod_2_iff
% 0.35/0.60  thf(fact_4093_even__mod__2__iff,axiom,
% 0.35/0.60      ! [A: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 0.35/0.60        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 0.35/0.60  
% 0.35/0.60  % even_mod_2_iff
% 0.35/0.60  thf(fact_4094_dvd__numeral__simp,axiom,
% 0.35/0.60      ! [M: num,N: num] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) )
% 0.35/0.60        = ( unique5706413561485394159nteger @ ( unique3479559517661332726nteger @ N @ M ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_numeral_simp
% 0.35/0.60  thf(fact_4095_dvd__numeral__simp,axiom,
% 0.35/0.60      ! [M: num,N: num] :
% 0.35/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.35/0.60        = ( unique6322359934112328802ux_nat @ ( unique5055182867167087721od_nat @ N @ M ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_numeral_simp
% 0.35/0.60  thf(fact_4096_dvd__numeral__simp,axiom,
% 0.35/0.60      ! [M: num,N: num] :
% 0.35/0.60        ( ( dvd_dvd_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.35/0.60        = ( unique6319869463603278526ux_int @ ( unique5052692396658037445od_int @ N @ M ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_numeral_simp
% 0.35/0.60  thf(fact_4097_zero__le__power__eq__numeral,axiom,
% 0.35/0.60      ! [A: rat,W: num] :
% 0.35/0.60        ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 0.35/0.60        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.35/0.60          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.35/0.60            & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % zero_le_power_eq_numeral
% 0.35/0.60  thf(fact_4098_zero__le__power__eq__numeral,axiom,
% 0.35/0.60      ! [A: real,W: num] :
% 0.35/0.60        ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 0.35/0.60        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.35/0.60          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.35/0.60            & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % zero_le_power_eq_numeral
% 0.35/0.60  thf(fact_4099_zero__le__power__eq__numeral,axiom,
% 0.35/0.60      ! [A: int,W: num] :
% 0.35/0.60        ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 0.35/0.60        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.35/0.60          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.35/0.60            & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % zero_le_power_eq_numeral
% 0.35/0.60  thf(fact_4100_power__less__zero__eq__numeral,axiom,
% 0.35/0.60      ! [A: real,W: num] :
% 0.35/0.60        ( ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 0.35/0.60        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.35/0.60          & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % power_less_zero_eq_numeral
% 0.35/0.60  thf(fact_4101_power__less__zero__eq__numeral,axiom,
% 0.35/0.60      ! [A: rat,W: num] :
% 0.35/0.60        ( ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 0.35/0.60        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.35/0.60          & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % power_less_zero_eq_numeral
% 0.35/0.60  thf(fact_4102_power__less__zero__eq__numeral,axiom,
% 0.35/0.60      ! [A: int,W: num] :
% 0.35/0.60        ( ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 0.35/0.60        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.35/0.60          & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % power_less_zero_eq_numeral
% 0.35/0.60  thf(fact_4103_power__less__zero__eq,axiom,
% 0.35/0.60      ! [A: real,N: nat] :
% 0.35/0.60        ( ( ord_less_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 0.35/0.60        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.60          & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % power_less_zero_eq
% 0.35/0.60  thf(fact_4104_power__less__zero__eq,axiom,
% 0.35/0.60      ! [A: rat,N: nat] :
% 0.35/0.60        ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 0.35/0.60        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.60          & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % power_less_zero_eq
% 0.35/0.60  thf(fact_4105_power__less__zero__eq,axiom,
% 0.35/0.60      ! [A: int,N: nat] :
% 0.35/0.60        ( ( ord_less_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 0.35/0.60        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.60          & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % power_less_zero_eq
% 0.35/0.60  thf(fact_4106_even__plus__one__iff,axiom,
% 0.35/0.60      ! [A: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) )
% 0.35/0.60        = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % even_plus_one_iff
% 0.35/0.60  thf(fact_4107_even__plus__one__iff,axiom,
% 0.35/0.60      ! [A: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ one_one_nat ) )
% 0.35/0.60        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % even_plus_one_iff
% 0.35/0.60  thf(fact_4108_even__plus__one__iff,axiom,
% 0.35/0.60      ! [A: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ one_one_int ) )
% 0.35/0.60        = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % even_plus_one_iff
% 0.35/0.60  thf(fact_4109_even__diff,axiom,
% 0.35/0.60      ! [A: code_integer,B: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.35/0.60        = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % even_diff
% 0.35/0.60  thf(fact_4110_even__diff,axiom,
% 0.35/0.60      ! [A: int,B: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ A @ B ) )
% 0.35/0.60        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % even_diff
% 0.35/0.60  thf(fact_4111_odd__Suc__minus__one,axiom,
% 0.35/0.60      ! [N: nat] :
% 0.35/0.60        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.60       => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 0.35/0.60          = N ) ) ).
% 0.35/0.60  
% 0.35/0.60  % odd_Suc_minus_one
% 0.35/0.60  thf(fact_4112_even__diff__nat,axiom,
% 0.35/0.60      ! [M: nat,N: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) )
% 0.35/0.60        = ( ( ord_less_nat @ M @ N )
% 0.35/0.60          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % even_diff_nat
% 0.35/0.60  thf(fact_4113_zero__less__power__eq__numeral,axiom,
% 0.35/0.60      ! [A: real,W: num] :
% 0.35/0.60        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 0.35/0.60        = ( ( ( numeral_numeral_nat @ W )
% 0.35/0.60            = zero_zero_nat )
% 0.35/0.60          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.35/0.60            & ( A != zero_zero_real ) )
% 0.35/0.60          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.35/0.60            & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % zero_less_power_eq_numeral
% 0.35/0.60  thf(fact_4114_zero__less__power__eq__numeral,axiom,
% 0.35/0.60      ! [A: rat,W: num] :
% 0.35/0.60        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 0.35/0.60        = ( ( ( numeral_numeral_nat @ W )
% 0.35/0.60            = zero_zero_nat )
% 0.35/0.60          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.35/0.60            & ( A != zero_zero_rat ) )
% 0.35/0.60          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.35/0.60            & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % zero_less_power_eq_numeral
% 0.35/0.60  thf(fact_4115_zero__less__power__eq__numeral,axiom,
% 0.35/0.60      ! [A: int,W: num] :
% 0.35/0.60        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 0.35/0.60        = ( ( ( numeral_numeral_nat @ W )
% 0.35/0.60            = zero_zero_nat )
% 0.35/0.60          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.35/0.60            & ( A != zero_zero_int ) )
% 0.35/0.60          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.35/0.60            & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % zero_less_power_eq_numeral
% 0.35/0.60  thf(fact_4116_even__succ__div__2,axiom,
% 0.35/0.60      ! [A: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.35/0.60       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.35/0.60          = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % even_succ_div_2
% 0.35/0.60  thf(fact_4117_even__succ__div__2,axiom,
% 0.35/0.60      ! [A: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.60       => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.60          = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % even_succ_div_2
% 0.35/0.60  thf(fact_4118_even__succ__div__2,axiom,
% 0.35/0.60      ! [A: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.60       => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.60          = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % even_succ_div_2
% 0.35/0.60  thf(fact_4119_even__succ__div__two,axiom,
% 0.35/0.60      ! [A: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.35/0.60       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.35/0.60          = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % even_succ_div_two
% 0.35/0.60  thf(fact_4120_even__succ__div__two,axiom,
% 0.35/0.60      ! [A: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.60       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.60          = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % even_succ_div_two
% 0.35/0.60  thf(fact_4121_even__succ__div__two,axiom,
% 0.35/0.60      ! [A: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.60       => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.60          = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % even_succ_div_two
% 0.35/0.60  thf(fact_4122_odd__succ__div__two,axiom,
% 0.35/0.60      ! [A: code_integer] :
% 0.35/0.60        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.35/0.60       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.35/0.60          = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % odd_succ_div_two
% 0.35/0.60  thf(fact_4123_odd__succ__div__two,axiom,
% 0.35/0.60      ! [A: nat] :
% 0.35/0.60        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.60       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.60          = ( plus_plus_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % odd_succ_div_two
% 0.35/0.60  thf(fact_4124_odd__succ__div__two,axiom,
% 0.35/0.60      ! [A: int] :
% 0.35/0.60        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.60       => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.60          = ( plus_plus_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % odd_succ_div_two
% 0.35/0.60  thf(fact_4125_even__power,axiom,
% 0.35/0.60      ! [A: code_integer,N: nat] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 0.35/0.60        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.35/0.60          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % even_power
% 0.35/0.60  thf(fact_4126_even__power,axiom,
% 0.35/0.60      ! [A: nat,N: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ A @ N ) )
% 0.35/0.60        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.60          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % even_power
% 0.35/0.60  thf(fact_4127_even__power,axiom,
% 0.35/0.60      ! [A: int,N: nat] :
% 0.35/0.60        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ A @ N ) )
% 0.35/0.60        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.60          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % even_power
% 0.35/0.60  thf(fact_4128_odd__two__times__div__two__nat,axiom,
% 0.35/0.60      ! [N: nat] :
% 0.35/0.60        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.60       => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.60          = ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % odd_two_times_div_two_nat
% 0.35/0.60  thf(fact_4129_divmod__algorithm__code_I5_J,axiom,
% 0.35/0.60      ! [M: num,N: num] :
% 0.35/0.60        ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.35/0.60        = ( produc2626176000494625587at_nat
% 0.35/0.60          @ ^ [Q4: nat,R5: nat] : ( product_Pair_nat_nat @ Q4 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) )
% 0.35/0.60          @ ( unique5055182867167087721od_nat @ M @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % divmod_algorithm_code(5)
% 0.35/0.60  thf(fact_4130_divmod__algorithm__code_I5_J,axiom,
% 0.35/0.60      ! [M: num,N: num] :
% 0.35/0.60        ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.35/0.60        = ( produc4245557441103728435nt_int
% 0.35/0.60          @ ^ [Q4: int,R5: int] : ( product_Pair_int_int @ Q4 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) )
% 0.35/0.60          @ ( unique5052692396658037445od_int @ M @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % divmod_algorithm_code(5)
% 0.35/0.60  thf(fact_4131_odd__two__times__div__two__succ,axiom,
% 0.35/0.60      ! [A: code_integer] :
% 0.35/0.60        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.35/0.60       => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ one_one_Code_integer )
% 0.35/0.60          = A ) ) ).
% 0.35/0.60  
% 0.35/0.60  % odd_two_times_div_two_succ
% 0.35/0.60  thf(fact_4132_odd__two__times__div__two__succ,axiom,
% 0.35/0.60      ! [A: nat] :
% 0.35/0.60        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.60       => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 0.35/0.60          = A ) ) ).
% 0.35/0.60  
% 0.35/0.60  % odd_two_times_div_two_succ
% 0.35/0.60  thf(fact_4133_odd__two__times__div__two__succ,axiom,
% 0.35/0.60      ! [A: int] :
% 0.35/0.60        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.60       => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 0.35/0.60          = A ) ) ).
% 0.35/0.60  
% 0.35/0.60  % odd_two_times_div_two_succ
% 0.35/0.60  thf(fact_4134_power__le__zero__eq__numeral,axiom,
% 0.35/0.60      ! [A: rat,W: num] :
% 0.35/0.60        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 0.35/0.60        = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 0.35/0.60          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.35/0.60              & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 0.35/0.60            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.35/0.60              & ( A = zero_zero_rat ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % power_le_zero_eq_numeral
% 0.35/0.60  thf(fact_4135_power__le__zero__eq__numeral,axiom,
% 0.35/0.60      ! [A: real,W: num] :
% 0.35/0.60        ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 0.35/0.60        = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 0.35/0.60          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.35/0.60              & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 0.35/0.60            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.35/0.60              & ( A = zero_zero_real ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % power_le_zero_eq_numeral
% 0.35/0.60  thf(fact_4136_power__le__zero__eq__numeral,axiom,
% 0.35/0.60      ! [A: int,W: num] :
% 0.35/0.60        ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 0.35/0.60        = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 0.35/0.60          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.35/0.60              & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 0.35/0.60            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.35/0.60              & ( A = zero_zero_int ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % power_le_zero_eq_numeral
% 0.35/0.60  thf(fact_4137_semiring__parity__class_Oeven__mask__iff,axiom,
% 0.35/0.60      ! [N: nat] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) )
% 0.35/0.60        = ( N = zero_zero_nat ) ) ).
% 0.35/0.60  
% 0.35/0.60  % semiring_parity_class.even_mask_iff
% 0.35/0.60  thf(fact_4138_semiring__parity__class_Oeven__mask__iff,axiom,
% 0.35/0.60      ! [N: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) )
% 0.35/0.60        = ( N = zero_zero_nat ) ) ).
% 0.35/0.60  
% 0.35/0.60  % semiring_parity_class.even_mask_iff
% 0.35/0.60  thf(fact_4139_semiring__parity__class_Oeven__mask__iff,axiom,
% 0.35/0.60      ! [N: nat] :
% 0.35/0.60        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 0.35/0.60        = ( N = zero_zero_nat ) ) ).
% 0.35/0.60  
% 0.35/0.60  % semiring_parity_class.even_mask_iff
% 0.35/0.60  thf(fact_4140_dvd__productE,axiom,
% 0.35/0.60      ! [P6: nat,A: nat,B: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ P6 @ ( times_times_nat @ A @ B ) )
% 0.35/0.60       => ~ ! [X3: nat,Y3: nat] :
% 0.35/0.60              ( ( P6
% 0.35/0.60                = ( times_times_nat @ X3 @ Y3 ) )
% 0.35/0.60             => ( ( dvd_dvd_nat @ X3 @ A )
% 0.35/0.60               => ~ ( dvd_dvd_nat @ Y3 @ B ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_productE
% 0.35/0.60  thf(fact_4141_dvd__productE,axiom,
% 0.35/0.60      ! [P6: int,A: int,B: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ P6 @ ( times_times_int @ A @ B ) )
% 0.35/0.60       => ~ ! [X3: int,Y3: int] :
% 0.35/0.60              ( ( P6
% 0.35/0.60                = ( times_times_int @ X3 @ Y3 ) )
% 0.35/0.60             => ( ( dvd_dvd_int @ X3 @ A )
% 0.35/0.60               => ~ ( dvd_dvd_int @ Y3 @ B ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_productE
% 0.35/0.60  thf(fact_4142_division__decomp,axiom,
% 0.35/0.60      ! [A: nat,B: nat,C: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.35/0.60       => ? [B7: nat,C5: nat] :
% 0.35/0.60            ( ( A
% 0.35/0.60              = ( times_times_nat @ B7 @ C5 ) )
% 0.35/0.60            & ( dvd_dvd_nat @ B7 @ B )
% 0.35/0.60            & ( dvd_dvd_nat @ C5 @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % division_decomp
% 0.35/0.60  thf(fact_4143_division__decomp,axiom,
% 0.35/0.60      ! [A: int,B: int,C: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 0.35/0.60       => ? [B7: int,C5: int] :
% 0.35/0.60            ( ( A
% 0.35/0.60              = ( times_times_int @ B7 @ C5 ) )
% 0.35/0.60            & ( dvd_dvd_int @ B7 @ B )
% 0.35/0.60            & ( dvd_dvd_int @ C5 @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % division_decomp
% 0.35/0.60  thf(fact_4144_dvdE,axiom,
% 0.35/0.60      ! [B: code_integer,A: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ B @ A )
% 0.35/0.60       => ~ ! [K2: code_integer] :
% 0.35/0.60              ( A
% 0.35/0.60             != ( times_3573771949741848930nteger @ B @ K2 ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvdE
% 0.35/0.60  thf(fact_4145_dvdE,axiom,
% 0.35/0.60      ! [B: complex,A: complex] :
% 0.35/0.60        ( ( dvd_dvd_complex @ B @ A )
% 0.35/0.60       => ~ ! [K2: complex] :
% 0.35/0.60              ( A
% 0.35/0.60             != ( times_times_complex @ B @ K2 ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvdE
% 0.35/0.60  thf(fact_4146_dvdE,axiom,
% 0.35/0.60      ! [B: real,A: real] :
% 0.35/0.60        ( ( dvd_dvd_real @ B @ A )
% 0.35/0.60       => ~ ! [K2: real] :
% 0.35/0.60              ( A
% 0.35/0.60             != ( times_times_real @ B @ K2 ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvdE
% 0.35/0.60  thf(fact_4147_dvdE,axiom,
% 0.35/0.60      ! [B: nat,A: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ B @ A )
% 0.35/0.60       => ~ ! [K2: nat] :
% 0.35/0.60              ( A
% 0.35/0.60             != ( times_times_nat @ B @ K2 ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvdE
% 0.35/0.60  thf(fact_4148_dvdE,axiom,
% 0.35/0.60      ! [B: int,A: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ B @ A )
% 0.35/0.60       => ~ ! [K2: int] :
% 0.35/0.60              ( A
% 0.35/0.60             != ( times_times_int @ B @ K2 ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvdE
% 0.35/0.60  thf(fact_4149_dvdI,axiom,
% 0.35/0.60      ! [A: code_integer,B: code_integer,K: code_integer] :
% 0.35/0.60        ( ( A
% 0.35/0.60          = ( times_3573771949741848930nteger @ B @ K ) )
% 0.35/0.60       => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvdI
% 0.35/0.60  thf(fact_4150_dvdI,axiom,
% 0.35/0.60      ! [A: complex,B: complex,K: complex] :
% 0.35/0.60        ( ( A
% 0.35/0.60          = ( times_times_complex @ B @ K ) )
% 0.35/0.60       => ( dvd_dvd_complex @ B @ A ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvdI
% 0.35/0.60  thf(fact_4151_dvdI,axiom,
% 0.35/0.60      ! [A: real,B: real,K: real] :
% 0.35/0.60        ( ( A
% 0.35/0.60          = ( times_times_real @ B @ K ) )
% 0.35/0.60       => ( dvd_dvd_real @ B @ A ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvdI
% 0.35/0.60  thf(fact_4152_dvdI,axiom,
% 0.35/0.60      ! [A: nat,B: nat,K: nat] :
% 0.35/0.60        ( ( A
% 0.35/0.60          = ( times_times_nat @ B @ K ) )
% 0.35/0.60       => ( dvd_dvd_nat @ B @ A ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvdI
% 0.35/0.60  thf(fact_4153_dvdI,axiom,
% 0.35/0.60      ! [A: int,B: int,K: int] :
% 0.35/0.60        ( ( A
% 0.35/0.60          = ( times_times_int @ B @ K ) )
% 0.35/0.60       => ( dvd_dvd_int @ B @ A ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvdI
% 0.35/0.60  thf(fact_4154_dvd__def,axiom,
% 0.35/0.60      ( dvd_dvd_Code_integer
% 0.35/0.60      = ( ^ [B4: code_integer,A3: code_integer] :
% 0.35/0.60          ? [K3: code_integer] :
% 0.35/0.60            ( A3
% 0.35/0.60            = ( times_3573771949741848930nteger @ B4 @ K3 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_def
% 0.35/0.60  thf(fact_4155_dvd__def,axiom,
% 0.35/0.60      ( dvd_dvd_complex
% 0.35/0.60      = ( ^ [B4: complex,A3: complex] :
% 0.35/0.60          ? [K3: complex] :
% 0.35/0.60            ( A3
% 0.35/0.60            = ( times_times_complex @ B4 @ K3 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_def
% 0.35/0.60  thf(fact_4156_dvd__def,axiom,
% 0.35/0.60      ( dvd_dvd_real
% 0.35/0.60      = ( ^ [B4: real,A3: real] :
% 0.35/0.60          ? [K3: real] :
% 0.35/0.60            ( A3
% 0.35/0.60            = ( times_times_real @ B4 @ K3 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_def
% 0.35/0.60  thf(fact_4157_dvd__def,axiom,
% 0.35/0.60      ( dvd_dvd_nat
% 0.35/0.60      = ( ^ [B4: nat,A3: nat] :
% 0.35/0.60          ? [K3: nat] :
% 0.35/0.60            ( A3
% 0.35/0.60            = ( times_times_nat @ B4 @ K3 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_def
% 0.35/0.60  thf(fact_4158_dvd__def,axiom,
% 0.35/0.60      ( dvd_dvd_int
% 0.35/0.60      = ( ^ [B4: int,A3: int] :
% 0.35/0.60          ? [K3: int] :
% 0.35/0.60            ( A3
% 0.35/0.60            = ( times_times_int @ B4 @ K3 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_def
% 0.35/0.60  thf(fact_4159_dvd__mult,axiom,
% 0.35/0.60      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ A @ C )
% 0.35/0.60       => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult
% 0.35/0.60  thf(fact_4160_dvd__mult,axiom,
% 0.35/0.60      ! [A: complex,C: complex,B: complex] :
% 0.35/0.60        ( ( dvd_dvd_complex @ A @ C )
% 0.35/0.60       => ( dvd_dvd_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult
% 0.35/0.60  thf(fact_4161_dvd__mult,axiom,
% 0.35/0.60      ! [A: real,C: real,B: real] :
% 0.35/0.60        ( ( dvd_dvd_real @ A @ C )
% 0.35/0.60       => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult
% 0.35/0.60  thf(fact_4162_dvd__mult,axiom,
% 0.35/0.60      ! [A: nat,C: nat,B: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ A @ C )
% 0.35/0.60       => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult
% 0.35/0.60  thf(fact_4163_dvd__mult,axiom,
% 0.35/0.60      ! [A: int,C: int,B: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ A @ C )
% 0.35/0.60       => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult
% 0.35/0.60  thf(fact_4164_dvd__mult2,axiom,
% 0.35/0.60      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ A @ B )
% 0.35/0.60       => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult2
% 0.35/0.60  thf(fact_4165_dvd__mult2,axiom,
% 0.35/0.60      ! [A: complex,B: complex,C: complex] :
% 0.35/0.60        ( ( dvd_dvd_complex @ A @ B )
% 0.35/0.60       => ( dvd_dvd_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult2
% 0.35/0.60  thf(fact_4166_dvd__mult2,axiom,
% 0.35/0.60      ! [A: real,B: real,C: real] :
% 0.35/0.60        ( ( dvd_dvd_real @ A @ B )
% 0.35/0.60       => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult2
% 0.35/0.60  thf(fact_4167_dvd__mult2,axiom,
% 0.35/0.60      ! [A: nat,B: nat,C: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ A @ B )
% 0.35/0.60       => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult2
% 0.35/0.60  thf(fact_4168_dvd__mult2,axiom,
% 0.35/0.60      ! [A: int,B: int,C: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ A @ B )
% 0.35/0.60       => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult2
% 0.35/0.60  thf(fact_4169_dvd__mult__left,axiom,
% 0.35/0.60      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 0.35/0.60       => ( dvd_dvd_Code_integer @ A @ C ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult_left
% 0.35/0.60  thf(fact_4170_dvd__mult__left,axiom,
% 0.35/0.60      ! [A: complex,B: complex,C: complex] :
% 0.35/0.60        ( ( dvd_dvd_complex @ ( times_times_complex @ A @ B ) @ C )
% 0.35/0.60       => ( dvd_dvd_complex @ A @ C ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult_left
% 0.35/0.60  thf(fact_4171_dvd__mult__left,axiom,
% 0.35/0.60      ! [A: real,B: real,C: real] :
% 0.35/0.60        ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 0.35/0.60       => ( dvd_dvd_real @ A @ C ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult_left
% 0.35/0.60  thf(fact_4172_dvd__mult__left,axiom,
% 0.35/0.60      ! [A: nat,B: nat,C: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.35/0.60       => ( dvd_dvd_nat @ A @ C ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult_left
% 0.35/0.60  thf(fact_4173_dvd__mult__left,axiom,
% 0.35/0.60      ! [A: int,B: int,C: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 0.35/0.60       => ( dvd_dvd_int @ A @ C ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult_left
% 0.35/0.60  thf(fact_4174_dvd__triv__left,axiom,
% 0.35/0.60      ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ A @ B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_triv_left
% 0.35/0.60  thf(fact_4175_dvd__triv__left,axiom,
% 0.35/0.60      ! [A: complex,B: complex] : ( dvd_dvd_complex @ A @ ( times_times_complex @ A @ B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_triv_left
% 0.35/0.60  thf(fact_4176_dvd__triv__left,axiom,
% 0.35/0.60      ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ A @ B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_triv_left
% 0.35/0.60  thf(fact_4177_dvd__triv__left,axiom,
% 0.35/0.60      ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_triv_left
% 0.35/0.60  thf(fact_4178_dvd__triv__left,axiom,
% 0.35/0.60      ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ A @ B ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_triv_left
% 0.35/0.60  thf(fact_4179_mult__dvd__mono,axiom,
% 0.35/0.60      ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ A @ B )
% 0.35/0.60       => ( ( dvd_dvd_Code_integer @ C @ D2 )
% 0.35/0.60         => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % mult_dvd_mono
% 0.35/0.60  thf(fact_4180_mult__dvd__mono,axiom,
% 0.35/0.60      ! [A: complex,B: complex,C: complex,D2: complex] :
% 0.35/0.60        ( ( dvd_dvd_complex @ A @ B )
% 0.35/0.60       => ( ( dvd_dvd_complex @ C @ D2 )
% 0.35/0.60         => ( dvd_dvd_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ D2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % mult_dvd_mono
% 0.35/0.60  thf(fact_4181_mult__dvd__mono,axiom,
% 0.35/0.60      ! [A: real,B: real,C: real,D2: real] :
% 0.35/0.60        ( ( dvd_dvd_real @ A @ B )
% 0.35/0.60       => ( ( dvd_dvd_real @ C @ D2 )
% 0.35/0.60         => ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % mult_dvd_mono
% 0.35/0.60  thf(fact_4182_mult__dvd__mono,axiom,
% 0.35/0.60      ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ A @ B )
% 0.35/0.60       => ( ( dvd_dvd_nat @ C @ D2 )
% 0.35/0.60         => ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % mult_dvd_mono
% 0.35/0.60  thf(fact_4183_mult__dvd__mono,axiom,
% 0.35/0.60      ! [A: int,B: int,C: int,D2: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ A @ B )
% 0.35/0.60       => ( ( dvd_dvd_int @ C @ D2 )
% 0.35/0.60         => ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % mult_dvd_mono
% 0.35/0.60  thf(fact_4184_dvd__mult__right,axiom,
% 0.35/0.60      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 0.35/0.60       => ( dvd_dvd_Code_integer @ B @ C ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult_right
% 0.35/0.60  thf(fact_4185_dvd__mult__right,axiom,
% 0.35/0.60      ! [A: complex,B: complex,C: complex] :
% 0.35/0.60        ( ( dvd_dvd_complex @ ( times_times_complex @ A @ B ) @ C )
% 0.35/0.60       => ( dvd_dvd_complex @ B @ C ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult_right
% 0.35/0.60  thf(fact_4186_dvd__mult__right,axiom,
% 0.35/0.60      ! [A: real,B: real,C: real] :
% 0.35/0.60        ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 0.35/0.60       => ( dvd_dvd_real @ B @ C ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult_right
% 0.35/0.60  thf(fact_4187_dvd__mult__right,axiom,
% 0.35/0.60      ! [A: nat,B: nat,C: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.35/0.60       => ( dvd_dvd_nat @ B @ C ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult_right
% 0.35/0.60  thf(fact_4188_dvd__mult__right,axiom,
% 0.35/0.60      ! [A: int,B: int,C: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 0.35/0.60       => ( dvd_dvd_int @ B @ C ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult_right
% 0.35/0.60  thf(fact_4189_dvd__triv__right,axiom,
% 0.35/0.60      ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ A ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_triv_right
% 0.35/0.60  thf(fact_4190_dvd__triv__right,axiom,
% 0.35/0.60      ! [A: complex,B: complex] : ( dvd_dvd_complex @ A @ ( times_times_complex @ B @ A ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_triv_right
% 0.35/0.60  thf(fact_4191_dvd__triv__right,axiom,
% 0.35/0.60      ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ B @ A ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_triv_right
% 0.35/0.60  thf(fact_4192_dvd__triv__right,axiom,
% 0.35/0.60      ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ A ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_triv_right
% 0.35/0.60  thf(fact_4193_dvd__triv__right,axiom,
% 0.35/0.60      ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ B @ A ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_triv_right
% 0.35/0.60  thf(fact_4194_dvd__unit__imp__unit,axiom,
% 0.35/0.60      ! [A: code_integer,B: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ A @ B )
% 0.35/0.60       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.35/0.60         => ( dvd_dvd_Code_integer @ A @ one_one_Code_integer ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_unit_imp_unit
% 0.35/0.60  thf(fact_4195_dvd__unit__imp__unit,axiom,
% 0.35/0.60      ! [A: nat,B: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ A @ B )
% 0.35/0.60       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.35/0.60         => ( dvd_dvd_nat @ A @ one_one_nat ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_unit_imp_unit
% 0.35/0.60  thf(fact_4196_dvd__unit__imp__unit,axiom,
% 0.35/0.60      ! [A: int,B: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ A @ B )
% 0.35/0.60       => ( ( dvd_dvd_int @ B @ one_one_int )
% 0.35/0.60         => ( dvd_dvd_int @ A @ one_one_int ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_unit_imp_unit
% 0.35/0.60  thf(fact_4197_unit__imp__dvd,axiom,
% 0.35/0.60      ! [B: code_integer,A: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.35/0.60       => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_imp_dvd
% 0.35/0.60  thf(fact_4198_unit__imp__dvd,axiom,
% 0.35/0.60      ! [B: nat,A: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.35/0.60       => ( dvd_dvd_nat @ B @ A ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_imp_dvd
% 0.35/0.60  thf(fact_4199_unit__imp__dvd,axiom,
% 0.35/0.60      ! [B: int,A: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.35/0.60       => ( dvd_dvd_int @ B @ A ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_imp_dvd
% 0.35/0.60  thf(fact_4200_one__dvd,axiom,
% 0.35/0.60      ! [A: code_integer] : ( dvd_dvd_Code_integer @ one_one_Code_integer @ A ) ).
% 0.35/0.60  
% 0.35/0.60  % one_dvd
% 0.35/0.60  thf(fact_4201_one__dvd,axiom,
% 0.35/0.60      ! [A: complex] : ( dvd_dvd_complex @ one_one_complex @ A ) ).
% 0.35/0.60  
% 0.35/0.60  % one_dvd
% 0.35/0.60  thf(fact_4202_one__dvd,axiom,
% 0.35/0.60      ! [A: real] : ( dvd_dvd_real @ one_one_real @ A ) ).
% 0.35/0.60  
% 0.35/0.60  % one_dvd
% 0.35/0.60  thf(fact_4203_one__dvd,axiom,
% 0.35/0.60      ! [A: rat] : ( dvd_dvd_rat @ one_one_rat @ A ) ).
% 0.35/0.60  
% 0.35/0.60  % one_dvd
% 0.35/0.60  thf(fact_4204_one__dvd,axiom,
% 0.35/0.60      ! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ) ).
% 0.35/0.60  
% 0.35/0.60  % one_dvd
% 0.35/0.60  thf(fact_4205_one__dvd,axiom,
% 0.35/0.60      ! [A: int] : ( dvd_dvd_int @ one_one_int @ A ) ).
% 0.35/0.60  
% 0.35/0.60  % one_dvd
% 0.35/0.60  thf(fact_4206_dvd__add__right__iff,axiom,
% 0.35/0.60      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ A @ B )
% 0.35/0.60       => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 0.35/0.60          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add_right_iff
% 0.35/0.60  thf(fact_4207_dvd__add__right__iff,axiom,
% 0.35/0.60      ! [A: real,B: real,C: real] :
% 0.35/0.60        ( ( dvd_dvd_real @ A @ B )
% 0.35/0.60       => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 0.35/0.60          = ( dvd_dvd_real @ A @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add_right_iff
% 0.35/0.60  thf(fact_4208_dvd__add__right__iff,axiom,
% 0.35/0.60      ! [A: rat,B: rat,C: rat] :
% 0.35/0.60        ( ( dvd_dvd_rat @ A @ B )
% 0.35/0.60       => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.35/0.60          = ( dvd_dvd_rat @ A @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add_right_iff
% 0.35/0.60  thf(fact_4209_dvd__add__right__iff,axiom,
% 0.35/0.60      ! [A: nat,B: nat,C: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ A @ B )
% 0.35/0.60       => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 0.35/0.60          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add_right_iff
% 0.35/0.60  thf(fact_4210_dvd__add__right__iff,axiom,
% 0.35/0.60      ! [A: int,B: int,C: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ A @ B )
% 0.35/0.60       => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.35/0.60          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add_right_iff
% 0.35/0.60  thf(fact_4211_dvd__add__right__iff,axiom,
% 0.35/0.60      ! [A: complex,B: complex,C: complex] :
% 0.35/0.60        ( ( dvd_dvd_complex @ A @ B )
% 0.35/0.60       => ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ B @ C ) )
% 0.35/0.60          = ( dvd_dvd_complex @ A @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add_right_iff
% 0.35/0.60  thf(fact_4212_dvd__add__left__iff,axiom,
% 0.35/0.60      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ A @ C )
% 0.35/0.60       => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 0.35/0.60          = ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add_left_iff
% 0.35/0.60  thf(fact_4213_dvd__add__left__iff,axiom,
% 0.35/0.60      ! [A: real,C: real,B: real] :
% 0.35/0.60        ( ( dvd_dvd_real @ A @ C )
% 0.35/0.60       => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 0.35/0.60          = ( dvd_dvd_real @ A @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add_left_iff
% 0.35/0.60  thf(fact_4214_dvd__add__left__iff,axiom,
% 0.35/0.60      ! [A: rat,C: rat,B: rat] :
% 0.35/0.60        ( ( dvd_dvd_rat @ A @ C )
% 0.35/0.60       => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.35/0.60          = ( dvd_dvd_rat @ A @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add_left_iff
% 0.35/0.60  thf(fact_4215_dvd__add__left__iff,axiom,
% 0.35/0.60      ! [A: nat,C: nat,B: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ A @ C )
% 0.35/0.60       => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 0.35/0.60          = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add_left_iff
% 0.35/0.60  thf(fact_4216_dvd__add__left__iff,axiom,
% 0.35/0.60      ! [A: int,C: int,B: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ A @ C )
% 0.35/0.60       => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.35/0.60          = ( dvd_dvd_int @ A @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add_left_iff
% 0.35/0.60  thf(fact_4217_dvd__add__left__iff,axiom,
% 0.35/0.60      ! [A: complex,C: complex,B: complex] :
% 0.35/0.60        ( ( dvd_dvd_complex @ A @ C )
% 0.35/0.60       => ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ B @ C ) )
% 0.35/0.60          = ( dvd_dvd_complex @ A @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add_left_iff
% 0.35/0.60  thf(fact_4218_dvd__add,axiom,
% 0.35/0.60      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ A @ B )
% 0.35/0.60       => ( ( dvd_dvd_Code_integer @ A @ C )
% 0.35/0.60         => ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add
% 0.35/0.60  thf(fact_4219_dvd__add,axiom,
% 0.35/0.60      ! [A: real,B: real,C: real] :
% 0.35/0.60        ( ( dvd_dvd_real @ A @ B )
% 0.35/0.60       => ( ( dvd_dvd_real @ A @ C )
% 0.35/0.60         => ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add
% 0.35/0.60  thf(fact_4220_dvd__add,axiom,
% 0.35/0.60      ! [A: rat,B: rat,C: rat] :
% 0.35/0.60        ( ( dvd_dvd_rat @ A @ B )
% 0.35/0.60       => ( ( dvd_dvd_rat @ A @ C )
% 0.35/0.60         => ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add
% 0.35/0.60  thf(fact_4221_dvd__add,axiom,
% 0.35/0.60      ! [A: nat,B: nat,C: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ A @ B )
% 0.35/0.60       => ( ( dvd_dvd_nat @ A @ C )
% 0.35/0.60         => ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add
% 0.35/0.60  thf(fact_4222_dvd__add,axiom,
% 0.35/0.60      ! [A: int,B: int,C: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ A @ B )
% 0.35/0.60       => ( ( dvd_dvd_int @ A @ C )
% 0.35/0.60         => ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add
% 0.35/0.60  thf(fact_4223_dvd__add,axiom,
% 0.35/0.60      ! [A: complex,B: complex,C: complex] :
% 0.35/0.60        ( ( dvd_dvd_complex @ A @ B )
% 0.35/0.60       => ( ( dvd_dvd_complex @ A @ C )
% 0.35/0.60         => ( dvd_dvd_complex @ A @ ( plus_plus_complex @ B @ C ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_add
% 0.35/0.60  thf(fact_4224_dvd__diff__commute,axiom,
% 0.35/0.60      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ C @ B ) )
% 0.35/0.60        = ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ B @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_diff_commute
% 0.35/0.60  thf(fact_4225_dvd__diff__commute,axiom,
% 0.35/0.60      ! [A: int,C: int,B: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ A @ ( minus_minus_int @ C @ B ) )
% 0.35/0.60        = ( dvd_dvd_int @ A @ ( minus_minus_int @ B @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_diff_commute
% 0.35/0.60  thf(fact_4226_dvd__diff,axiom,
% 0.35/0.60      ! [X: code_integer,Y2: code_integer,Z: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ X @ Y2 )
% 0.35/0.60       => ( ( dvd_dvd_Code_integer @ X @ Z )
% 0.35/0.60         => ( dvd_dvd_Code_integer @ X @ ( minus_8373710615458151222nteger @ Y2 @ Z ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_diff
% 0.35/0.60  thf(fact_4227_dvd__diff,axiom,
% 0.35/0.60      ! [X: rat,Y2: rat,Z: rat] :
% 0.35/0.60        ( ( dvd_dvd_rat @ X @ Y2 )
% 0.35/0.60       => ( ( dvd_dvd_rat @ X @ Z )
% 0.35/0.60         => ( dvd_dvd_rat @ X @ ( minus_minus_rat @ Y2 @ Z ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_diff
% 0.35/0.60  thf(fact_4228_dvd__diff,axiom,
% 0.35/0.60      ! [X: int,Y2: int,Z: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ X @ Y2 )
% 0.35/0.60       => ( ( dvd_dvd_int @ X @ Z )
% 0.35/0.60         => ( dvd_dvd_int @ X @ ( minus_minus_int @ Y2 @ Z ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_diff
% 0.35/0.60  thf(fact_4229_dvd__div__eq__iff,axiom,
% 0.35/0.60      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ C @ A )
% 0.35/0.60       => ( ( dvd_dvd_Code_integer @ C @ B )
% 0.35/0.60         => ( ( ( divide6298287555418463151nteger @ A @ C )
% 0.35/0.60              = ( divide6298287555418463151nteger @ B @ C ) )
% 0.35/0.60            = ( A = B ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_eq_iff
% 0.35/0.60  thf(fact_4230_dvd__div__eq__iff,axiom,
% 0.35/0.60      ! [C: complex,A: complex,B: complex] :
% 0.35/0.60        ( ( dvd_dvd_complex @ C @ A )
% 0.35/0.60       => ( ( dvd_dvd_complex @ C @ B )
% 0.35/0.60         => ( ( ( divide1717551699836669952omplex @ A @ C )
% 0.35/0.60              = ( divide1717551699836669952omplex @ B @ C ) )
% 0.35/0.60            = ( A = B ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_eq_iff
% 0.35/0.60  thf(fact_4231_dvd__div__eq__iff,axiom,
% 0.35/0.60      ! [C: real,A: real,B: real] :
% 0.35/0.60        ( ( dvd_dvd_real @ C @ A )
% 0.35/0.60       => ( ( dvd_dvd_real @ C @ B )
% 0.35/0.60         => ( ( ( divide_divide_real @ A @ C )
% 0.35/0.60              = ( divide_divide_real @ B @ C ) )
% 0.35/0.60            = ( A = B ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_eq_iff
% 0.35/0.60  thf(fact_4232_dvd__div__eq__iff,axiom,
% 0.35/0.60      ! [C: rat,A: rat,B: rat] :
% 0.35/0.60        ( ( dvd_dvd_rat @ C @ A )
% 0.35/0.60       => ( ( dvd_dvd_rat @ C @ B )
% 0.35/0.60         => ( ( ( divide_divide_rat @ A @ C )
% 0.35/0.60              = ( divide_divide_rat @ B @ C ) )
% 0.35/0.60            = ( A = B ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_eq_iff
% 0.35/0.60  thf(fact_4233_dvd__div__eq__iff,axiom,
% 0.35/0.60      ! [C: nat,A: nat,B: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ C @ A )
% 0.35/0.60       => ( ( dvd_dvd_nat @ C @ B )
% 0.35/0.60         => ( ( ( divide_divide_nat @ A @ C )
% 0.35/0.60              = ( divide_divide_nat @ B @ C ) )
% 0.35/0.60            = ( A = B ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_eq_iff
% 0.35/0.60  thf(fact_4234_dvd__div__eq__iff,axiom,
% 0.35/0.60      ! [C: int,A: int,B: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ C @ A )
% 0.35/0.60       => ( ( dvd_dvd_int @ C @ B )
% 0.35/0.60         => ( ( ( divide_divide_int @ A @ C )
% 0.35/0.60              = ( divide_divide_int @ B @ C ) )
% 0.35/0.60            = ( A = B ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_eq_iff
% 0.35/0.60  thf(fact_4235_dvd__div__eq__cancel,axiom,
% 0.35/0.60      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.35/0.60        ( ( ( divide6298287555418463151nteger @ A @ C )
% 0.35/0.60          = ( divide6298287555418463151nteger @ B @ C ) )
% 0.35/0.60       => ( ( dvd_dvd_Code_integer @ C @ A )
% 0.35/0.60         => ( ( dvd_dvd_Code_integer @ C @ B )
% 0.35/0.60           => ( A = B ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_eq_cancel
% 0.35/0.60  thf(fact_4236_dvd__div__eq__cancel,axiom,
% 0.35/0.60      ! [A: complex,C: complex,B: complex] :
% 0.35/0.60        ( ( ( divide1717551699836669952omplex @ A @ C )
% 0.35/0.60          = ( divide1717551699836669952omplex @ B @ C ) )
% 0.35/0.60       => ( ( dvd_dvd_complex @ C @ A )
% 0.35/0.60         => ( ( dvd_dvd_complex @ C @ B )
% 0.35/0.60           => ( A = B ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_eq_cancel
% 0.35/0.60  thf(fact_4237_dvd__div__eq__cancel,axiom,
% 0.35/0.60      ! [A: real,C: real,B: real] :
% 0.35/0.60        ( ( ( divide_divide_real @ A @ C )
% 0.35/0.60          = ( divide_divide_real @ B @ C ) )
% 0.35/0.60       => ( ( dvd_dvd_real @ C @ A )
% 0.35/0.60         => ( ( dvd_dvd_real @ C @ B )
% 0.35/0.60           => ( A = B ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_eq_cancel
% 0.35/0.60  thf(fact_4238_dvd__div__eq__cancel,axiom,
% 0.35/0.60      ! [A: rat,C: rat,B: rat] :
% 0.35/0.60        ( ( ( divide_divide_rat @ A @ C )
% 0.35/0.60          = ( divide_divide_rat @ B @ C ) )
% 0.35/0.60       => ( ( dvd_dvd_rat @ C @ A )
% 0.35/0.60         => ( ( dvd_dvd_rat @ C @ B )
% 0.35/0.60           => ( A = B ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_eq_cancel
% 0.35/0.60  thf(fact_4239_dvd__div__eq__cancel,axiom,
% 0.35/0.60      ! [A: nat,C: nat,B: nat] :
% 0.35/0.60        ( ( ( divide_divide_nat @ A @ C )
% 0.35/0.60          = ( divide_divide_nat @ B @ C ) )
% 0.35/0.60       => ( ( dvd_dvd_nat @ C @ A )
% 0.35/0.60         => ( ( dvd_dvd_nat @ C @ B )
% 0.35/0.60           => ( A = B ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_eq_cancel
% 0.35/0.60  thf(fact_4240_dvd__div__eq__cancel,axiom,
% 0.35/0.60      ! [A: int,C: int,B: int] :
% 0.35/0.60        ( ( ( divide_divide_int @ A @ C )
% 0.35/0.60          = ( divide_divide_int @ B @ C ) )
% 0.35/0.60       => ( ( dvd_dvd_int @ C @ A )
% 0.35/0.60         => ( ( dvd_dvd_int @ C @ B )
% 0.35/0.60           => ( A = B ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_eq_cancel
% 0.35/0.60  thf(fact_4241_div__div__div__same,axiom,
% 0.35/0.60      ! [D2: code_integer,B: code_integer,A: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ D2 @ B )
% 0.35/0.60       => ( ( dvd_dvd_Code_integer @ B @ A )
% 0.35/0.60         => ( ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ D2 ) @ ( divide6298287555418463151nteger @ B @ D2 ) )
% 0.35/0.60            = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_div_div_same
% 0.35/0.60  thf(fact_4242_div__div__div__same,axiom,
% 0.35/0.60      ! [D2: nat,B: nat,A: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ D2 @ B )
% 0.35/0.60       => ( ( dvd_dvd_nat @ B @ A )
% 0.35/0.60         => ( ( divide_divide_nat @ ( divide_divide_nat @ A @ D2 ) @ ( divide_divide_nat @ B @ D2 ) )
% 0.35/0.60            = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_div_div_same
% 0.35/0.60  thf(fact_4243_div__div__div__same,axiom,
% 0.35/0.60      ! [D2: int,B: int,A: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ D2 @ B )
% 0.35/0.60       => ( ( dvd_dvd_int @ B @ A )
% 0.35/0.60         => ( ( divide_divide_int @ ( divide_divide_int @ A @ D2 ) @ ( divide_divide_int @ B @ D2 ) )
% 0.35/0.60            = ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_div_div_same
% 0.35/0.60  thf(fact_4244_dvd__power__same,axiom,
% 0.35/0.60      ! [X: code_integer,Y2: code_integer,N: nat] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ X @ Y2 )
% 0.35/0.60       => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ N ) @ ( power_8256067586552552935nteger @ Y2 @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_power_same
% 0.35/0.60  thf(fact_4245_dvd__power__same,axiom,
% 0.35/0.60      ! [X: nat,Y2: nat,N: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ X @ Y2 )
% 0.35/0.60       => ( dvd_dvd_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y2 @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_power_same
% 0.35/0.60  thf(fact_4246_dvd__power__same,axiom,
% 0.35/0.60      ! [X: real,Y2: real,N: nat] :
% 0.35/0.60        ( ( dvd_dvd_real @ X @ Y2 )
% 0.35/0.60       => ( dvd_dvd_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y2 @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_power_same
% 0.35/0.60  thf(fact_4247_dvd__power__same,axiom,
% 0.35/0.60      ! [X: int,Y2: int,N: nat] :
% 0.35/0.60        ( ( dvd_dvd_int @ X @ Y2 )
% 0.35/0.60       => ( dvd_dvd_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y2 @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_power_same
% 0.35/0.60  thf(fact_4248_dvd__power__same,axiom,
% 0.35/0.60      ! [X: complex,Y2: complex,N: nat] :
% 0.35/0.60        ( ( dvd_dvd_complex @ X @ Y2 )
% 0.35/0.60       => ( dvd_dvd_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y2 @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_power_same
% 0.35/0.60  thf(fact_4249_old_Oprod_Ocase,axiom,
% 0.35/0.60      ! [F: nat > nat > nat,X1: nat,X23: nat] :
% 0.35/0.60        ( ( produc6842872674320459806at_nat @ F @ ( product_Pair_nat_nat @ X1 @ X23 ) )
% 0.35/0.60        = ( F @ X1 @ X23 ) ) ).
% 0.35/0.60  
% 0.35/0.60  % old.prod.case
% 0.35/0.60  thf(fact_4250_old_Oprod_Ocase,axiom,
% 0.35/0.60      ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X1: nat,X23: nat] :
% 0.35/0.60        ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ X1 @ X23 ) )
% 0.35/0.60        = ( F @ X1 @ X23 ) ) ).
% 0.35/0.60  
% 0.35/0.60  % old.prod.case
% 0.35/0.60  thf(fact_4251_old_Oprod_Ocase,axiom,
% 0.35/0.60      ! [F: nat > nat > product_prod_nat_nat > $o,X1: nat,X23: nat] :
% 0.35/0.60        ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ X1 @ X23 ) )
% 0.35/0.60        = ( F @ X1 @ X23 ) ) ).
% 0.35/0.60  
% 0.35/0.60  % old.prod.case
% 0.35/0.60  thf(fact_4252_old_Oprod_Ocase,axiom,
% 0.35/0.60      ! [F: int > int > product_prod_int_int,X1: int,X23: int] :
% 0.35/0.60        ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ X1 @ X23 ) )
% 0.35/0.60        = ( F @ X1 @ X23 ) ) ).
% 0.35/0.60  
% 0.35/0.60  % old.prod.case
% 0.35/0.60  thf(fact_4253_old_Oprod_Ocase,axiom,
% 0.35/0.60      ! [F: int > int > int,X1: int,X23: int] :
% 0.35/0.60        ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ X1 @ X23 ) )
% 0.35/0.60        = ( F @ X1 @ X23 ) ) ).
% 0.35/0.60  
% 0.35/0.60  % old.prod.case
% 0.35/0.60  thf(fact_4254_mod__mod__cancel,axiom,
% 0.35/0.60      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ C @ B )
% 0.35/0.60       => ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C )
% 0.35/0.60          = ( modulo364778990260209775nteger @ A @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % mod_mod_cancel
% 0.35/0.60  thf(fact_4255_mod__mod__cancel,axiom,
% 0.35/0.60      ! [C: nat,B: nat,A: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ C @ B )
% 0.35/0.60       => ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ C )
% 0.35/0.60          = ( modulo_modulo_nat @ A @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % mod_mod_cancel
% 0.35/0.60  thf(fact_4256_mod__mod__cancel,axiom,
% 0.35/0.60      ! [C: int,B: int,A: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ C @ B )
% 0.35/0.60       => ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ C )
% 0.35/0.60          = ( modulo_modulo_int @ A @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % mod_mod_cancel
% 0.35/0.60  thf(fact_4257_dvd__mod,axiom,
% 0.35/0.60      ! [K: code_integer,M: code_integer,N: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ K @ M )
% 0.35/0.60       => ( ( dvd_dvd_Code_integer @ K @ N )
% 0.35/0.60         => ( dvd_dvd_Code_integer @ K @ ( modulo364778990260209775nteger @ M @ N ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mod
% 0.35/0.60  thf(fact_4258_dvd__mod,axiom,
% 0.35/0.60      ! [K: nat,M: nat,N: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ K @ M )
% 0.35/0.60       => ( ( dvd_dvd_nat @ K @ N )
% 0.35/0.60         => ( dvd_dvd_nat @ K @ ( modulo_modulo_nat @ M @ N ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mod
% 0.35/0.60  thf(fact_4259_dvd__mod,axiom,
% 0.35/0.60      ! [K: int,M: int,N: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ K @ M )
% 0.35/0.60       => ( ( dvd_dvd_int @ K @ N )
% 0.35/0.60         => ( dvd_dvd_int @ K @ ( modulo_modulo_int @ M @ N ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mod
% 0.35/0.60  thf(fact_4260_dvd__diff__nat,axiom,
% 0.35/0.60      ! [K: nat,M: nat,N: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ K @ M )
% 0.35/0.60       => ( ( dvd_dvd_nat @ K @ N )
% 0.35/0.60         => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_diff_nat
% 0.35/0.60  thf(fact_4261_zdvd__zdiffD,axiom,
% 0.35/0.60      ! [K: int,M: int,N: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ K @ ( minus_minus_int @ M @ N ) )
% 0.35/0.60       => ( ( dvd_dvd_int @ K @ N )
% 0.35/0.60         => ( dvd_dvd_int @ K @ M ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % zdvd_zdiffD
% 0.35/0.60  thf(fact_4262_dvd__pos__nat,axiom,
% 0.35/0.60      ! [N: nat,M: nat] :
% 0.35/0.60        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.60       => ( ( dvd_dvd_nat @ M @ N )
% 0.35/0.60         => ( ord_less_nat @ zero_zero_nat @ M ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_pos_nat
% 0.35/0.60  thf(fact_4263_bezout__lemma__nat,axiom,
% 0.35/0.60      ! [D2: nat,A: nat,B: nat,X: nat,Y2: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ D2 @ A )
% 0.35/0.60       => ( ( dvd_dvd_nat @ D2 @ B )
% 0.35/0.60         => ( ( ( ( times_times_nat @ A @ X )
% 0.35/0.60                = ( plus_plus_nat @ ( times_times_nat @ B @ Y2 ) @ D2 ) )
% 0.35/0.60              | ( ( times_times_nat @ B @ X )
% 0.35/0.60                = ( plus_plus_nat @ ( times_times_nat @ A @ Y2 ) @ D2 ) ) )
% 0.35/0.60           => ? [X3: nat,Y3: nat] :
% 0.35/0.60                ( ( dvd_dvd_nat @ D2 @ A )
% 0.35/0.60                & ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ A @ B ) )
% 0.35/0.60                & ( ( ( times_times_nat @ A @ X3 )
% 0.35/0.60                    = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ Y3 ) @ D2 ) )
% 0.35/0.60                  | ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ X3 )
% 0.35/0.60                    = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D2 ) ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % bezout_lemma_nat
% 0.35/0.60  thf(fact_4264_bezout__add__nat,axiom,
% 0.35/0.60      ! [A: nat,B: nat] :
% 0.35/0.60      ? [D3: nat,X3: nat,Y3: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ D3 @ A )
% 0.35/0.60        & ( dvd_dvd_nat @ D3 @ B )
% 0.35/0.60        & ( ( ( times_times_nat @ A @ X3 )
% 0.35/0.60            = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D3 ) )
% 0.35/0.60          | ( ( times_times_nat @ B @ X3 )
% 0.35/0.60            = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D3 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % bezout_add_nat
% 0.35/0.60  thf(fact_4265_bezout1__nat,axiom,
% 0.35/0.60      ! [A: nat,B: nat] :
% 0.35/0.60      ? [D3: nat,X3: nat,Y3: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ D3 @ A )
% 0.35/0.60        & ( dvd_dvd_nat @ D3 @ B )
% 0.35/0.60        & ( ( ( minus_minus_nat @ ( times_times_nat @ A @ X3 ) @ ( times_times_nat @ B @ Y3 ) )
% 0.35/0.60            = D3 )
% 0.35/0.60          | ( ( minus_minus_nat @ ( times_times_nat @ B @ X3 ) @ ( times_times_nat @ A @ Y3 ) )
% 0.35/0.60            = D3 ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % bezout1_nat
% 0.35/0.60  thf(fact_4266_cond__case__prod__eta,axiom,
% 0.35/0.60      ! [F: nat > nat > nat,G: product_prod_nat_nat > nat] :
% 0.35/0.60        ( ! [X3: nat,Y3: nat] :
% 0.35/0.60            ( ( F @ X3 @ Y3 )
% 0.35/0.60            = ( G @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) )
% 0.35/0.60       => ( ( produc6842872674320459806at_nat @ F )
% 0.35/0.60          = G ) ) ).
% 0.35/0.60  
% 0.35/0.60  % cond_case_prod_eta
% 0.35/0.60  thf(fact_4267_cond__case__prod__eta,axiom,
% 0.35/0.60      ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,G: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 0.35/0.60        ( ! [X3: nat,Y3: nat] :
% 0.35/0.60            ( ( F @ X3 @ Y3 )
% 0.35/0.60            = ( G @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) )
% 0.35/0.60       => ( ( produc27273713700761075at_nat @ F )
% 0.35/0.60          = G ) ) ).
% 0.35/0.60  
% 0.35/0.60  % cond_case_prod_eta
% 0.35/0.60  thf(fact_4268_cond__case__prod__eta,axiom,
% 0.35/0.60      ! [F: nat > nat > product_prod_nat_nat > $o,G: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 0.35/0.60        ( ! [X3: nat,Y3: nat] :
% 0.35/0.60            ( ( F @ X3 @ Y3 )
% 0.35/0.60            = ( G @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) )
% 0.35/0.60       => ( ( produc8739625826339149834_nat_o @ F )
% 0.35/0.60          = G ) ) ).
% 0.35/0.60  
% 0.35/0.60  % cond_case_prod_eta
% 0.35/0.60  thf(fact_4269_cond__case__prod__eta,axiom,
% 0.35/0.60      ! [F: int > int > product_prod_int_int,G: product_prod_int_int > product_prod_int_int] :
% 0.35/0.60        ( ! [X3: int,Y3: int] :
% 0.35/0.60            ( ( F @ X3 @ Y3 )
% 0.35/0.60            = ( G @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 0.35/0.60       => ( ( produc4245557441103728435nt_int @ F )
% 0.35/0.60          = G ) ) ).
% 0.35/0.60  
% 0.35/0.60  % cond_case_prod_eta
% 0.35/0.60  thf(fact_4270_cond__case__prod__eta,axiom,
% 0.35/0.60      ! [F: int > int > int,G: product_prod_int_int > int] :
% 0.35/0.60        ( ! [X3: int,Y3: int] :
% 0.35/0.60            ( ( F @ X3 @ Y3 )
% 0.35/0.60            = ( G @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 0.35/0.60       => ( ( produc8211389475949308722nt_int @ F )
% 0.35/0.60          = G ) ) ).
% 0.35/0.60  
% 0.35/0.60  % cond_case_prod_eta
% 0.35/0.60  thf(fact_4271_case__prod__eta,axiom,
% 0.35/0.60      ! [F: product_prod_nat_nat > nat] :
% 0.35/0.60        ( ( produc6842872674320459806at_nat
% 0.35/0.60          @ ^ [X2: nat,Y: nat] : ( F @ ( product_Pair_nat_nat @ X2 @ Y ) ) )
% 0.35/0.60        = F ) ).
% 0.35/0.60  
% 0.35/0.60  % case_prod_eta
% 0.35/0.60  thf(fact_4272_case__prod__eta,axiom,
% 0.35/0.60      ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 0.35/0.60        ( ( produc27273713700761075at_nat
% 0.35/0.60          @ ^ [X2: nat,Y: nat] : ( F @ ( product_Pair_nat_nat @ X2 @ Y ) ) )
% 0.35/0.60        = F ) ).
% 0.35/0.60  
% 0.35/0.60  % case_prod_eta
% 0.35/0.60  thf(fact_4273_case__prod__eta,axiom,
% 0.35/0.60      ! [F: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 0.35/0.60        ( ( produc8739625826339149834_nat_o
% 0.35/0.60          @ ^ [X2: nat,Y: nat] : ( F @ ( product_Pair_nat_nat @ X2 @ Y ) ) )
% 0.35/0.60        = F ) ).
% 0.35/0.60  
% 0.35/0.60  % case_prod_eta
% 0.35/0.60  thf(fact_4274_case__prod__eta,axiom,
% 0.35/0.60      ! [F: product_prod_int_int > product_prod_int_int] :
% 0.35/0.60        ( ( produc4245557441103728435nt_int
% 0.35/0.60          @ ^ [X2: int,Y: int] : ( F @ ( product_Pair_int_int @ X2 @ Y ) ) )
% 0.35/0.60        = F ) ).
% 0.35/0.60  
% 0.35/0.60  % case_prod_eta
% 0.35/0.60  thf(fact_4275_case__prod__eta,axiom,
% 0.35/0.60      ! [F: product_prod_int_int > int] :
% 0.35/0.60        ( ( produc8211389475949308722nt_int
% 0.35/0.60          @ ^ [X2: int,Y: int] : ( F @ ( product_Pair_int_int @ X2 @ Y ) ) )
% 0.35/0.60        = F ) ).
% 0.35/0.60  
% 0.35/0.60  % case_prod_eta
% 0.35/0.60  thf(fact_4276_case__prodE2,axiom,
% 0.35/0.60      ! [Q: nat > $o,P: nat > nat > nat,Z: product_prod_nat_nat] :
% 0.35/0.60        ( ( Q @ ( produc6842872674320459806at_nat @ P @ Z ) )
% 0.35/0.60       => ~ ! [X3: nat,Y3: nat] :
% 0.35/0.60              ( ( Z
% 0.35/0.60                = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 0.35/0.60             => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % case_prodE2
% 0.35/0.60  thf(fact_4277_case__prodE2,axiom,
% 0.35/0.60      ! [Q: ( product_prod_nat_nat > product_prod_nat_nat ) > $o,P: nat > nat > product_prod_nat_nat > product_prod_nat_nat,Z: product_prod_nat_nat] :
% 0.35/0.60        ( ( Q @ ( produc27273713700761075at_nat @ P @ Z ) )
% 0.35/0.60       => ~ ! [X3: nat,Y3: nat] :
% 0.35/0.60              ( ( Z
% 0.35/0.60                = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 0.35/0.60             => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % case_prodE2
% 0.35/0.60  thf(fact_4278_case__prodE2,axiom,
% 0.35/0.60      ! [Q: ( product_prod_nat_nat > $o ) > $o,P: nat > nat > product_prod_nat_nat > $o,Z: product_prod_nat_nat] :
% 0.35/0.60        ( ( Q @ ( produc8739625826339149834_nat_o @ P @ Z ) )
% 0.35/0.60       => ~ ! [X3: nat,Y3: nat] :
% 0.35/0.60              ( ( Z
% 0.35/0.60                = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 0.35/0.60             => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % case_prodE2
% 0.35/0.60  thf(fact_4279_case__prodE2,axiom,
% 0.35/0.60      ! [Q: product_prod_int_int > $o,P: int > int > product_prod_int_int,Z: product_prod_int_int] :
% 0.35/0.60        ( ( Q @ ( produc4245557441103728435nt_int @ P @ Z ) )
% 0.35/0.60       => ~ ! [X3: int,Y3: int] :
% 0.35/0.60              ( ( Z
% 0.35/0.60                = ( product_Pair_int_int @ X3 @ Y3 ) )
% 0.35/0.60             => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % case_prodE2
% 0.35/0.60  thf(fact_4280_case__prodE2,axiom,
% 0.35/0.60      ! [Q: int > $o,P: int > int > int,Z: product_prod_int_int] :
% 0.35/0.60        ( ( Q @ ( produc8211389475949308722nt_int @ P @ Z ) )
% 0.35/0.60       => ~ ! [X3: int,Y3: int] :
% 0.35/0.60              ( ( Z
% 0.35/0.60                = ( product_Pair_int_int @ X3 @ Y3 ) )
% 0.35/0.60             => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % case_prodE2
% 0.35/0.60  thf(fact_4281_concat__bit__assoc,axiom,
% 0.35/0.60      ! [N: nat,K: int,M: nat,L2: int,R: int] :
% 0.35/0.60        ( ( bit_concat_bit @ N @ K @ ( bit_concat_bit @ M @ L2 @ R ) )
% 0.35/0.60        = ( bit_concat_bit @ ( plus_plus_nat @ M @ N ) @ ( bit_concat_bit @ N @ K @ L2 ) @ R ) ) ).
% 0.35/0.60  
% 0.35/0.60  % concat_bit_assoc
% 0.35/0.60  thf(fact_4282_not__is__unit__0,axiom,
% 0.35/0.60      ~ ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer ) ).
% 0.35/0.60  
% 0.35/0.60  % not_is_unit_0
% 0.35/0.60  thf(fact_4283_not__is__unit__0,axiom,
% 0.35/0.60      ~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ) ).
% 0.35/0.60  
% 0.35/0.60  % not_is_unit_0
% 0.35/0.60  thf(fact_4284_not__is__unit__0,axiom,
% 0.35/0.60      ~ ( dvd_dvd_int @ zero_zero_int @ one_one_int ) ).
% 0.35/0.60  
% 0.35/0.60  % not_is_unit_0
% 0.35/0.60  thf(fact_4285_pinf_I9_J,axiom,
% 0.35/0.60      ! [D2: code_integer,S3: code_integer] :
% 0.35/0.60      ? [Z3: code_integer] :
% 0.35/0.60      ! [X5: code_integer] :
% 0.35/0.60        ( ( ord_le6747313008572928689nteger @ Z3 @ X5 )
% 0.35/0.60       => ( ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X5 @ S3 ) )
% 0.35/0.60          = ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X5 @ S3 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % pinf(9)
% 0.35/0.60  thf(fact_4286_pinf_I9_J,axiom,
% 0.35/0.60      ! [D2: real,S3: real] :
% 0.35/0.60      ? [Z3: real] :
% 0.35/0.60      ! [X5: real] :
% 0.35/0.60        ( ( ord_less_real @ Z3 @ X5 )
% 0.35/0.60       => ( ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X5 @ S3 ) )
% 0.35/0.60          = ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X5 @ S3 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % pinf(9)
% 0.35/0.60  thf(fact_4287_pinf_I9_J,axiom,
% 0.35/0.60      ! [D2: rat,S3: rat] :
% 0.35/0.60      ? [Z3: rat] :
% 0.35/0.60      ! [X5: rat] :
% 0.35/0.60        ( ( ord_less_rat @ Z3 @ X5 )
% 0.35/0.60       => ( ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X5 @ S3 ) )
% 0.35/0.60          = ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X5 @ S3 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % pinf(9)
% 0.35/0.60  thf(fact_4288_pinf_I9_J,axiom,
% 0.35/0.60      ! [D2: nat,S3: nat] :
% 0.35/0.60      ? [Z3: nat] :
% 0.35/0.60      ! [X5: nat] :
% 0.35/0.60        ( ( ord_less_nat @ Z3 @ X5 )
% 0.35/0.60       => ( ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X5 @ S3 ) )
% 0.35/0.60          = ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X5 @ S3 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % pinf(9)
% 0.35/0.60  thf(fact_4289_pinf_I9_J,axiom,
% 0.35/0.60      ! [D2: int,S3: int] :
% 0.35/0.60      ? [Z3: int] :
% 0.35/0.60      ! [X5: int] :
% 0.35/0.60        ( ( ord_less_int @ Z3 @ X5 )
% 0.35/0.60       => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ S3 ) )
% 0.35/0.60          = ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ S3 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % pinf(9)
% 0.35/0.60  thf(fact_4290_pinf_I10_J,axiom,
% 0.35/0.60      ! [D2: code_integer,S3: code_integer] :
% 0.35/0.60      ? [Z3: code_integer] :
% 0.35/0.60      ! [X5: code_integer] :
% 0.35/0.60        ( ( ord_le6747313008572928689nteger @ Z3 @ X5 )
% 0.35/0.60       => ( ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X5 @ S3 ) ) )
% 0.35/0.60          = ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X5 @ S3 ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % pinf(10)
% 0.35/0.60  thf(fact_4291_pinf_I10_J,axiom,
% 0.35/0.60      ! [D2: real,S3: real] :
% 0.35/0.60      ? [Z3: real] :
% 0.35/0.60      ! [X5: real] :
% 0.35/0.60        ( ( ord_less_real @ Z3 @ X5 )
% 0.35/0.60       => ( ( ~ ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X5 @ S3 ) ) )
% 0.35/0.60          = ( ~ ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X5 @ S3 ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % pinf(10)
% 0.35/0.60  thf(fact_4292_pinf_I10_J,axiom,
% 0.35/0.60      ! [D2: rat,S3: rat] :
% 0.35/0.60      ? [Z3: rat] :
% 0.35/0.60      ! [X5: rat] :
% 0.35/0.60        ( ( ord_less_rat @ Z3 @ X5 )
% 0.35/0.60       => ( ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X5 @ S3 ) ) )
% 0.35/0.60          = ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X5 @ S3 ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % pinf(10)
% 0.35/0.60  thf(fact_4293_pinf_I10_J,axiom,
% 0.35/0.60      ! [D2: nat,S3: nat] :
% 0.35/0.60      ? [Z3: nat] :
% 0.35/0.60      ! [X5: nat] :
% 0.35/0.60        ( ( ord_less_nat @ Z3 @ X5 )
% 0.35/0.60       => ( ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X5 @ S3 ) ) )
% 0.35/0.60          = ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X5 @ S3 ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % pinf(10)
% 0.35/0.60  thf(fact_4294_pinf_I10_J,axiom,
% 0.35/0.60      ! [D2: int,S3: int] :
% 0.35/0.60      ? [Z3: int] :
% 0.35/0.60      ! [X5: int] :
% 0.35/0.60        ( ( ord_less_int @ Z3 @ X5 )
% 0.35/0.60       => ( ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ S3 ) ) )
% 0.35/0.60          = ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ S3 ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % pinf(10)
% 0.35/0.60  thf(fact_4295_minf_I9_J,axiom,
% 0.35/0.60      ! [D2: code_integer,S3: code_integer] :
% 0.35/0.60      ? [Z3: code_integer] :
% 0.35/0.60      ! [X5: code_integer] :
% 0.35/0.60        ( ( ord_le6747313008572928689nteger @ X5 @ Z3 )
% 0.35/0.60       => ( ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X5 @ S3 ) )
% 0.35/0.60          = ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X5 @ S3 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % minf(9)
% 0.35/0.60  thf(fact_4296_minf_I9_J,axiom,
% 0.35/0.60      ! [D2: real,S3: real] :
% 0.35/0.60      ? [Z3: real] :
% 0.35/0.60      ! [X5: real] :
% 0.35/0.60        ( ( ord_less_real @ X5 @ Z3 )
% 0.35/0.60       => ( ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X5 @ S3 ) )
% 0.35/0.60          = ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X5 @ S3 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % minf(9)
% 0.35/0.60  thf(fact_4297_minf_I9_J,axiom,
% 0.35/0.60      ! [D2: rat,S3: rat] :
% 0.35/0.60      ? [Z3: rat] :
% 0.35/0.60      ! [X5: rat] :
% 0.35/0.60        ( ( ord_less_rat @ X5 @ Z3 )
% 0.35/0.60       => ( ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X5 @ S3 ) )
% 0.35/0.60          = ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X5 @ S3 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % minf(9)
% 0.35/0.60  thf(fact_4298_minf_I9_J,axiom,
% 0.35/0.60      ! [D2: nat,S3: nat] :
% 0.35/0.60      ? [Z3: nat] :
% 0.35/0.60      ! [X5: nat] :
% 0.35/0.60        ( ( ord_less_nat @ X5 @ Z3 )
% 0.35/0.60       => ( ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X5 @ S3 ) )
% 0.35/0.60          = ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X5 @ S3 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % minf(9)
% 0.35/0.60  thf(fact_4299_minf_I9_J,axiom,
% 0.35/0.60      ! [D2: int,S3: int] :
% 0.35/0.60      ? [Z3: int] :
% 0.35/0.60      ! [X5: int] :
% 0.35/0.60        ( ( ord_less_int @ X5 @ Z3 )
% 0.35/0.60       => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ S3 ) )
% 0.35/0.60          = ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ S3 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % minf(9)
% 0.35/0.60  thf(fact_4300_minf_I10_J,axiom,
% 0.35/0.60      ! [D2: code_integer,S3: code_integer] :
% 0.35/0.60      ? [Z3: code_integer] :
% 0.35/0.60      ! [X5: code_integer] :
% 0.35/0.60        ( ( ord_le6747313008572928689nteger @ X5 @ Z3 )
% 0.35/0.60       => ( ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X5 @ S3 ) ) )
% 0.35/0.60          = ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X5 @ S3 ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % minf(10)
% 0.35/0.60  thf(fact_4301_minf_I10_J,axiom,
% 0.35/0.60      ! [D2: real,S3: real] :
% 0.35/0.60      ? [Z3: real] :
% 0.35/0.60      ! [X5: real] :
% 0.35/0.60        ( ( ord_less_real @ X5 @ Z3 )
% 0.35/0.60       => ( ( ~ ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X5 @ S3 ) ) )
% 0.35/0.60          = ( ~ ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X5 @ S3 ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % minf(10)
% 0.35/0.60  thf(fact_4302_minf_I10_J,axiom,
% 0.35/0.60      ! [D2: rat,S3: rat] :
% 0.35/0.60      ? [Z3: rat] :
% 0.35/0.60      ! [X5: rat] :
% 0.35/0.60        ( ( ord_less_rat @ X5 @ Z3 )
% 0.35/0.60       => ( ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X5 @ S3 ) ) )
% 0.35/0.60          = ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X5 @ S3 ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % minf(10)
% 0.35/0.60  thf(fact_4303_minf_I10_J,axiom,
% 0.35/0.60      ! [D2: nat,S3: nat] :
% 0.35/0.60      ? [Z3: nat] :
% 0.35/0.60      ! [X5: nat] :
% 0.35/0.60        ( ( ord_less_nat @ X5 @ Z3 )
% 0.35/0.60       => ( ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X5 @ S3 ) ) )
% 0.35/0.60          = ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X5 @ S3 ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % minf(10)
% 0.35/0.60  thf(fact_4304_minf_I10_J,axiom,
% 0.35/0.60      ! [D2: int,S3: int] :
% 0.35/0.60      ? [Z3: int] :
% 0.35/0.60      ! [X5: int] :
% 0.35/0.60        ( ( ord_less_int @ X5 @ Z3 )
% 0.35/0.60       => ( ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ S3 ) ) )
% 0.35/0.60          = ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ S3 ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % minf(10)
% 0.35/0.60  thf(fact_4305_dvd__div__eq__0__iff,axiom,
% 0.35/0.60      ! [B: code_integer,A: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ B @ A )
% 0.35/0.60       => ( ( ( divide6298287555418463151nteger @ A @ B )
% 0.35/0.60            = zero_z3403309356797280102nteger )
% 0.35/0.60          = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_eq_0_iff
% 0.35/0.60  thf(fact_4306_dvd__div__eq__0__iff,axiom,
% 0.35/0.60      ! [B: complex,A: complex] :
% 0.35/0.60        ( ( dvd_dvd_complex @ B @ A )
% 0.35/0.60       => ( ( ( divide1717551699836669952omplex @ A @ B )
% 0.35/0.60            = zero_zero_complex )
% 0.35/0.60          = ( A = zero_zero_complex ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_eq_0_iff
% 0.35/0.60  thf(fact_4307_dvd__div__eq__0__iff,axiom,
% 0.35/0.60      ! [B: real,A: real] :
% 0.35/0.60        ( ( dvd_dvd_real @ B @ A )
% 0.35/0.60       => ( ( ( divide_divide_real @ A @ B )
% 0.35/0.60            = zero_zero_real )
% 0.35/0.60          = ( A = zero_zero_real ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_eq_0_iff
% 0.35/0.60  thf(fact_4308_dvd__div__eq__0__iff,axiom,
% 0.35/0.60      ! [B: rat,A: rat] :
% 0.35/0.60        ( ( dvd_dvd_rat @ B @ A )
% 0.35/0.60       => ( ( ( divide_divide_rat @ A @ B )
% 0.35/0.60            = zero_zero_rat )
% 0.35/0.60          = ( A = zero_zero_rat ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_eq_0_iff
% 0.35/0.60  thf(fact_4309_dvd__div__eq__0__iff,axiom,
% 0.35/0.60      ! [B: nat,A: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ B @ A )
% 0.35/0.60       => ( ( ( divide_divide_nat @ A @ B )
% 0.35/0.60            = zero_zero_nat )
% 0.35/0.60          = ( A = zero_zero_nat ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_eq_0_iff
% 0.35/0.60  thf(fact_4310_dvd__div__eq__0__iff,axiom,
% 0.35/0.60      ! [B: int,A: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ B @ A )
% 0.35/0.60       => ( ( ( divide_divide_int @ A @ B )
% 0.35/0.60            = zero_zero_int )
% 0.35/0.60          = ( A = zero_zero_int ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_eq_0_iff
% 0.35/0.60  thf(fact_4311_unit__mult__right__cancel,axiom,
% 0.35/0.60      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.35/0.60       => ( ( ( times_3573771949741848930nteger @ B @ A )
% 0.35/0.60            = ( times_3573771949741848930nteger @ C @ A ) )
% 0.35/0.60          = ( B = C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_mult_right_cancel
% 0.35/0.60  thf(fact_4312_unit__mult__right__cancel,axiom,
% 0.35/0.60      ! [A: nat,B: nat,C: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.35/0.60       => ( ( ( times_times_nat @ B @ A )
% 0.35/0.60            = ( times_times_nat @ C @ A ) )
% 0.35/0.60          = ( B = C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_mult_right_cancel
% 0.35/0.60  thf(fact_4313_unit__mult__right__cancel,axiom,
% 0.35/0.60      ! [A: int,B: int,C: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.35/0.60       => ( ( ( times_times_int @ B @ A )
% 0.35/0.60            = ( times_times_int @ C @ A ) )
% 0.35/0.60          = ( B = C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_mult_right_cancel
% 0.35/0.60  thf(fact_4314_unit__mult__left__cancel,axiom,
% 0.35/0.60      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.35/0.60       => ( ( ( times_3573771949741848930nteger @ A @ B )
% 0.35/0.60            = ( times_3573771949741848930nteger @ A @ C ) )
% 0.35/0.60          = ( B = C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_mult_left_cancel
% 0.35/0.60  thf(fact_4315_unit__mult__left__cancel,axiom,
% 0.35/0.60      ! [A: nat,B: nat,C: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.35/0.60       => ( ( ( times_times_nat @ A @ B )
% 0.35/0.60            = ( times_times_nat @ A @ C ) )
% 0.35/0.60          = ( B = C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_mult_left_cancel
% 0.35/0.60  thf(fact_4316_unit__mult__left__cancel,axiom,
% 0.35/0.60      ! [A: int,B: int,C: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.35/0.60       => ( ( ( times_times_int @ A @ B )
% 0.35/0.60            = ( times_times_int @ A @ C ) )
% 0.35/0.60          = ( B = C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_mult_left_cancel
% 0.35/0.60  thf(fact_4317_mult__unit__dvd__iff_H,axiom,
% 0.35/0.60      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.35/0.60       => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 0.35/0.60          = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % mult_unit_dvd_iff'
% 0.35/0.60  thf(fact_4318_mult__unit__dvd__iff_H,axiom,
% 0.35/0.60      ! [A: nat,B: nat,C: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.35/0.60       => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.35/0.60          = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % mult_unit_dvd_iff'
% 0.35/0.60  thf(fact_4319_mult__unit__dvd__iff_H,axiom,
% 0.35/0.60      ! [A: int,B: int,C: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.35/0.60       => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 0.35/0.60          = ( dvd_dvd_int @ B @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % mult_unit_dvd_iff'
% 0.35/0.60  thf(fact_4320_dvd__mult__unit__iff_H,axiom,
% 0.35/0.60      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.35/0.60       => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.35/0.60          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult_unit_iff'
% 0.35/0.60  thf(fact_4321_dvd__mult__unit__iff_H,axiom,
% 0.35/0.60      ! [B: nat,A: nat,C: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.35/0.60       => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.35/0.60          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult_unit_iff'
% 0.35/0.60  thf(fact_4322_dvd__mult__unit__iff_H,axiom,
% 0.35/0.60      ! [B: int,A: int,C: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.35/0.60       => ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 0.35/0.60          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult_unit_iff'
% 0.35/0.60  thf(fact_4323_mult__unit__dvd__iff,axiom,
% 0.35/0.60      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.35/0.60       => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 0.35/0.60          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % mult_unit_dvd_iff
% 0.35/0.60  thf(fact_4324_mult__unit__dvd__iff,axiom,
% 0.35/0.60      ! [B: nat,A: nat,C: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.35/0.60       => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.35/0.60          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % mult_unit_dvd_iff
% 0.35/0.60  thf(fact_4325_mult__unit__dvd__iff,axiom,
% 0.35/0.60      ! [B: int,A: int,C: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.35/0.60       => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 0.35/0.60          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % mult_unit_dvd_iff
% 0.35/0.60  thf(fact_4326_dvd__mult__unit__iff,axiom,
% 0.35/0.60      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.35/0.60       => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.35/0.60          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult_unit_iff
% 0.35/0.60  thf(fact_4327_dvd__mult__unit__iff,axiom,
% 0.35/0.60      ! [B: nat,A: nat,C: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.35/0.60       => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) )
% 0.35/0.60          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult_unit_iff
% 0.35/0.60  thf(fact_4328_dvd__mult__unit__iff,axiom,
% 0.35/0.60      ! [B: int,A: int,C: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.35/0.60       => ( ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) )
% 0.35/0.60          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult_unit_iff
% 0.35/0.60  thf(fact_4329_is__unit__mult__iff,axiom,
% 0.35/0.60      ! [A: code_integer,B: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer )
% 0.35/0.60        = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.35/0.60          & ( dvd_dvd_Code_integer @ B @ one_one_Code_integer ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % is_unit_mult_iff
% 0.35/0.60  thf(fact_4330_is__unit__mult__iff,axiom,
% 0.35/0.60      ! [A: nat,B: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat )
% 0.35/0.60        = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.35/0.60          & ( dvd_dvd_nat @ B @ one_one_nat ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % is_unit_mult_iff
% 0.35/0.60  thf(fact_4331_is__unit__mult__iff,axiom,
% 0.35/0.60      ! [A: int,B: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int )
% 0.35/0.60        = ( ( dvd_dvd_int @ A @ one_one_int )
% 0.35/0.60          & ( dvd_dvd_int @ B @ one_one_int ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % is_unit_mult_iff
% 0.35/0.60  thf(fact_4332_dvd__div__mult,axiom,
% 0.35/0.60      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ C @ B )
% 0.35/0.60       => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ C ) @ A )
% 0.35/0.60          = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ B @ A ) @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_mult
% 0.35/0.60  thf(fact_4333_dvd__div__mult,axiom,
% 0.35/0.60      ! [C: nat,B: nat,A: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ C @ B )
% 0.35/0.60       => ( ( times_times_nat @ ( divide_divide_nat @ B @ C ) @ A )
% 0.35/0.60          = ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_mult
% 0.35/0.60  thf(fact_4334_dvd__div__mult,axiom,
% 0.35/0.60      ! [C: int,B: int,A: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ C @ B )
% 0.35/0.60       => ( ( times_times_int @ ( divide_divide_int @ B @ C ) @ A )
% 0.35/0.60          = ( divide_divide_int @ ( times_times_int @ B @ A ) @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_mult
% 0.35/0.60  thf(fact_4335_div__mult__swap,axiom,
% 0.35/0.60      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ C @ B )
% 0.35/0.60       => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 0.35/0.60          = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_mult_swap
% 0.35/0.60  thf(fact_4336_div__mult__swap,axiom,
% 0.35/0.60      ! [C: nat,B: nat,A: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ C @ B )
% 0.35/0.60       => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 0.35/0.60          = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_mult_swap
% 0.35/0.60  thf(fact_4337_div__mult__swap,axiom,
% 0.35/0.60      ! [C: int,B: int,A: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ C @ B )
% 0.35/0.60       => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 0.35/0.60          = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_mult_swap
% 0.35/0.60  thf(fact_4338_div__div__eq__right,axiom,
% 0.35/0.60      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ C @ B )
% 0.35/0.60       => ( ( dvd_dvd_Code_integer @ B @ A )
% 0.35/0.60         => ( ( divide6298287555418463151nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 0.35/0.60            = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_div_eq_right
% 0.35/0.60  thf(fact_4339_div__div__eq__right,axiom,
% 0.35/0.60      ! [C: nat,B: nat,A: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ C @ B )
% 0.35/0.60       => ( ( dvd_dvd_nat @ B @ A )
% 0.35/0.60         => ( ( divide_divide_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 0.35/0.60            = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_div_eq_right
% 0.35/0.60  thf(fact_4340_div__div__eq__right,axiom,
% 0.35/0.60      ! [C: int,B: int,A: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ C @ B )
% 0.35/0.60       => ( ( dvd_dvd_int @ B @ A )
% 0.35/0.60         => ( ( divide_divide_int @ A @ ( divide_divide_int @ B @ C ) )
% 0.35/0.60            = ( times_times_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_div_eq_right
% 0.35/0.60  thf(fact_4341_dvd__div__mult2__eq,axiom,
% 0.35/0.60      ! [B: code_integer,C: code_integer,A: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ C ) @ A )
% 0.35/0.60       => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.35/0.60          = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_mult2_eq
% 0.35/0.60  thf(fact_4342_dvd__div__mult2__eq,axiom,
% 0.35/0.60      ! [B: nat,C: nat,A: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ ( times_times_nat @ B @ C ) @ A )
% 0.35/0.60       => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.35/0.60          = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_mult2_eq
% 0.35/0.60  thf(fact_4343_dvd__div__mult2__eq,axiom,
% 0.35/0.60      ! [B: int,C: int,A: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ ( times_times_int @ B @ C ) @ A )
% 0.35/0.60       => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 0.35/0.60          = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_mult2_eq
% 0.35/0.60  thf(fact_4344_dvd__mult__imp__div,axiom,
% 0.35/0.60      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B )
% 0.35/0.60       => ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult_imp_div
% 0.35/0.60  thf(fact_4345_dvd__mult__imp__div,axiom,
% 0.35/0.60      ! [A: nat,C: nat,B: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B )
% 0.35/0.60       => ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult_imp_div
% 0.35/0.60  thf(fact_4346_dvd__mult__imp__div,axiom,
% 0.35/0.60      ! [A: int,C: int,B: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B )
% 0.35/0.60       => ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult_imp_div
% 0.35/0.60  thf(fact_4347_div__mult__div__if__dvd,axiom,
% 0.35/0.60      ! [B: code_integer,A: code_integer,D2: code_integer,C: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ B @ A )
% 0.35/0.60       => ( ( dvd_dvd_Code_integer @ D2 @ C )
% 0.35/0.60         => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ ( divide6298287555418463151nteger @ C @ D2 ) )
% 0.35/0.60            = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_mult_div_if_dvd
% 0.35/0.60  thf(fact_4348_div__mult__div__if__dvd,axiom,
% 0.35/0.60      ! [B: nat,A: nat,D2: nat,C: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ B @ A )
% 0.35/0.60       => ( ( dvd_dvd_nat @ D2 @ C )
% 0.35/0.60         => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ ( divide_divide_nat @ C @ D2 ) )
% 0.35/0.60            = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_mult_div_if_dvd
% 0.35/0.60  thf(fact_4349_div__mult__div__if__dvd,axiom,
% 0.35/0.60      ! [B: int,A: int,D2: int,C: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ B @ A )
% 0.35/0.60       => ( ( dvd_dvd_int @ D2 @ C )
% 0.35/0.60         => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ C @ D2 ) )
% 0.35/0.60            = ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_mult_div_if_dvd
% 0.35/0.60  thf(fact_4350_dvd__div__unit__iff,axiom,
% 0.35/0.60      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.35/0.60       => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ C @ B ) )
% 0.35/0.60          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_unit_iff
% 0.35/0.60  thf(fact_4351_dvd__div__unit__iff,axiom,
% 0.35/0.60      ! [B: nat,A: nat,C: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.35/0.60       => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ C @ B ) )
% 0.35/0.60          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_unit_iff
% 0.35/0.60  thf(fact_4352_dvd__div__unit__iff,axiom,
% 0.35/0.60      ! [B: int,A: int,C: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.35/0.60       => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ C @ B ) )
% 0.35/0.60          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_unit_iff
% 0.35/0.60  thf(fact_4353_div__unit__dvd__iff,axiom,
% 0.35/0.60      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.35/0.60       => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 0.35/0.60          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_unit_dvd_iff
% 0.35/0.60  thf(fact_4354_div__unit__dvd__iff,axiom,
% 0.35/0.60      ! [B: nat,A: nat,C: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.35/0.60       => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 0.35/0.60          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_unit_dvd_iff
% 0.35/0.60  thf(fact_4355_div__unit__dvd__iff,axiom,
% 0.35/0.60      ! [B: int,A: int,C: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.35/0.60       => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 0.35/0.60          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_unit_dvd_iff
% 0.35/0.60  thf(fact_4356_unit__div__cancel,axiom,
% 0.35/0.60      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.35/0.60       => ( ( ( divide6298287555418463151nteger @ B @ A )
% 0.35/0.60            = ( divide6298287555418463151nteger @ C @ A ) )
% 0.35/0.60          = ( B = C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_div_cancel
% 0.35/0.60  thf(fact_4357_unit__div__cancel,axiom,
% 0.35/0.60      ! [A: nat,B: nat,C: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.35/0.60       => ( ( ( divide_divide_nat @ B @ A )
% 0.35/0.60            = ( divide_divide_nat @ C @ A ) )
% 0.35/0.60          = ( B = C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_div_cancel
% 0.35/0.60  thf(fact_4358_unit__div__cancel,axiom,
% 0.35/0.60      ! [A: int,B: int,C: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.35/0.60       => ( ( ( divide_divide_int @ B @ A )
% 0.35/0.60            = ( divide_divide_int @ C @ A ) )
% 0.35/0.60          = ( B = C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_div_cancel
% 0.35/0.60  thf(fact_4359_div__plus__div__distrib__dvd__right,axiom,
% 0.35/0.60      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ C @ B )
% 0.35/0.60       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 0.35/0.60          = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_plus_div_distrib_dvd_right
% 0.35/0.60  thf(fact_4360_div__plus__div__distrib__dvd__right,axiom,
% 0.35/0.60      ! [C: nat,B: nat,A: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ C @ B )
% 0.35/0.60       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.35/0.60          = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_plus_div_distrib_dvd_right
% 0.35/0.60  thf(fact_4361_div__plus__div__distrib__dvd__right,axiom,
% 0.35/0.60      ! [C: int,B: int,A: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ C @ B )
% 0.35/0.60       => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.35/0.60          = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_plus_div_distrib_dvd_right
% 0.35/0.60  thf(fact_4362_div__plus__div__distrib__dvd__left,axiom,
% 0.35/0.60      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ C @ A )
% 0.35/0.60       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 0.35/0.60          = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_plus_div_distrib_dvd_left
% 0.35/0.60  thf(fact_4363_div__plus__div__distrib__dvd__left,axiom,
% 0.35/0.60      ! [C: nat,A: nat,B: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ C @ A )
% 0.35/0.60       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.35/0.60          = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_plus_div_distrib_dvd_left
% 0.35/0.60  thf(fact_4364_div__plus__div__distrib__dvd__left,axiom,
% 0.35/0.60      ! [C: int,A: int,B: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ C @ A )
% 0.35/0.60       => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.35/0.60          = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_plus_div_distrib_dvd_left
% 0.35/0.60  thf(fact_4365_div__power,axiom,
% 0.35/0.60      ! [B: code_integer,A: code_integer,N: nat] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ B @ A )
% 0.35/0.60       => ( ( power_8256067586552552935nteger @ ( divide6298287555418463151nteger @ A @ B ) @ N )
% 0.35/0.60          = ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_power
% 0.35/0.60  thf(fact_4366_div__power,axiom,
% 0.35/0.60      ! [B: nat,A: nat,N: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ B @ A )
% 0.35/0.60       => ( ( power_power_nat @ ( divide_divide_nat @ A @ B ) @ N )
% 0.35/0.60          = ( divide_divide_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_power
% 0.35/0.60  thf(fact_4367_div__power,axiom,
% 0.35/0.60      ! [B: int,A: int,N: nat] :
% 0.35/0.60        ( ( dvd_dvd_int @ B @ A )
% 0.35/0.60       => ( ( power_power_int @ ( divide_divide_int @ A @ B ) @ N )
% 0.35/0.60          = ( divide_divide_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_power
% 0.35/0.60  thf(fact_4368_dvd__power__le,axiom,
% 0.35/0.60      ! [X: code_integer,Y2: code_integer,N: nat,M: nat] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ X @ Y2 )
% 0.35/0.60       => ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.60         => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ N ) @ ( power_8256067586552552935nteger @ Y2 @ M ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_power_le
% 0.35/0.60  thf(fact_4369_dvd__power__le,axiom,
% 0.35/0.60      ! [X: nat,Y2: nat,N: nat,M: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ X @ Y2 )
% 0.35/0.60       => ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.60         => ( dvd_dvd_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y2 @ M ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_power_le
% 0.35/0.60  thf(fact_4370_dvd__power__le,axiom,
% 0.35/0.60      ! [X: real,Y2: real,N: nat,M: nat] :
% 0.35/0.60        ( ( dvd_dvd_real @ X @ Y2 )
% 0.35/0.60       => ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.60         => ( dvd_dvd_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y2 @ M ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_power_le
% 0.35/0.60  thf(fact_4371_dvd__power__le,axiom,
% 0.35/0.60      ! [X: int,Y2: int,N: nat,M: nat] :
% 0.35/0.60        ( ( dvd_dvd_int @ X @ Y2 )
% 0.35/0.60       => ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.60         => ( dvd_dvd_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y2 @ M ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_power_le
% 0.35/0.60  thf(fact_4372_dvd__power__le,axiom,
% 0.35/0.60      ! [X: complex,Y2: complex,N: nat,M: nat] :
% 0.35/0.60        ( ( dvd_dvd_complex @ X @ Y2 )
% 0.35/0.60       => ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.60         => ( dvd_dvd_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y2 @ M ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_power_le
% 0.35/0.60  thf(fact_4373_power__le__dvd,axiom,
% 0.35/0.60      ! [A: code_integer,N: nat,B: code_integer,M: nat] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ B )
% 0.35/0.60       => ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.60         => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % power_le_dvd
% 0.35/0.60  thf(fact_4374_power__le__dvd,axiom,
% 0.35/0.60      ! [A: nat,N: nat,B: nat,M: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ B )
% 0.35/0.60       => ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.60         => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % power_le_dvd
% 0.35/0.60  thf(fact_4375_power__le__dvd,axiom,
% 0.35/0.60      ! [A: real,N: nat,B: real,M: nat] :
% 0.35/0.60        ( ( dvd_dvd_real @ ( power_power_real @ A @ N ) @ B )
% 0.35/0.60       => ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.60         => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % power_le_dvd
% 0.35/0.60  thf(fact_4376_power__le__dvd,axiom,
% 0.35/0.60      ! [A: int,N: nat,B: int,M: nat] :
% 0.35/0.60        ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ B )
% 0.35/0.60       => ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.60         => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % power_le_dvd
% 0.35/0.60  thf(fact_4377_power__le__dvd,axiom,
% 0.35/0.60      ! [A: complex,N: nat,B: complex,M: nat] :
% 0.35/0.60        ( ( dvd_dvd_complex @ ( power_power_complex @ A @ N ) @ B )
% 0.35/0.60       => ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.60         => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % power_le_dvd
% 0.35/0.60  thf(fact_4378_le__imp__power__dvd,axiom,
% 0.35/0.60      ! [M: nat,N: nat,A: code_integer] :
% 0.35/0.60        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.60       => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % le_imp_power_dvd
% 0.35/0.60  thf(fact_4379_le__imp__power__dvd,axiom,
% 0.35/0.60      ! [M: nat,N: nat,A: nat] :
% 0.35/0.60        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.60       => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % le_imp_power_dvd
% 0.35/0.60  thf(fact_4380_le__imp__power__dvd,axiom,
% 0.35/0.60      ! [M: nat,N: nat,A: real] :
% 0.35/0.60        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.60       => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % le_imp_power_dvd
% 0.35/0.60  thf(fact_4381_le__imp__power__dvd,axiom,
% 0.35/0.60      ! [M: nat,N: nat,A: int] :
% 0.35/0.60        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.60       => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % le_imp_power_dvd
% 0.35/0.60  thf(fact_4382_le__imp__power__dvd,axiom,
% 0.35/0.60      ! [M: nat,N: nat,A: complex] :
% 0.35/0.60        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.60       => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % le_imp_power_dvd
% 0.35/0.60  thf(fact_4383_dvd__minus__mod,axiom,
% 0.35/0.60      ! [B: code_integer,A: code_integer] : ( dvd_dvd_Code_integer @ B @ ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_minus_mod
% 0.35/0.60  thf(fact_4384_dvd__minus__mod,axiom,
% 0.35/0.60      ! [B: nat,A: nat] : ( dvd_dvd_nat @ B @ ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_minus_mod
% 0.35/0.60  thf(fact_4385_dvd__minus__mod,axiom,
% 0.35/0.60      ! [B: int,A: int] : ( dvd_dvd_int @ B @ ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_minus_mod
% 0.35/0.60  thf(fact_4386_mod__eq__dvd__iff,axiom,
% 0.35/0.60      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.35/0.60        ( ( ( modulo364778990260209775nteger @ A @ C )
% 0.35/0.60          = ( modulo364778990260209775nteger @ B @ C ) )
% 0.35/0.60        = ( dvd_dvd_Code_integer @ C @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % mod_eq_dvd_iff
% 0.35/0.60  thf(fact_4387_mod__eq__dvd__iff,axiom,
% 0.35/0.60      ! [A: int,C: int,B: int] :
% 0.35/0.60        ( ( ( modulo_modulo_int @ A @ C )
% 0.35/0.60          = ( modulo_modulo_int @ B @ C ) )
% 0.35/0.60        = ( dvd_dvd_int @ C @ ( minus_minus_int @ A @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % mod_eq_dvd_iff
% 0.35/0.60  thf(fact_4388_bezout__add__strong__nat,axiom,
% 0.35/0.60      ! [A: nat,B: nat] :
% 0.35/0.60        ( ( A != zero_zero_nat )
% 0.35/0.60       => ? [D3: nat,X3: nat,Y3: nat] :
% 0.35/0.60            ( ( dvd_dvd_nat @ D3 @ A )
% 0.35/0.60            & ( dvd_dvd_nat @ D3 @ B )
% 0.35/0.60            & ( ( times_times_nat @ A @ X3 )
% 0.35/0.60              = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D3 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % bezout_add_strong_nat
% 0.35/0.60  thf(fact_4389_nat__dvd__not__less,axiom,
% 0.35/0.60      ! [M: nat,N: nat] :
% 0.35/0.60        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.35/0.60       => ( ( ord_less_nat @ M @ N )
% 0.35/0.60         => ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % nat_dvd_not_less
% 0.35/0.60  thf(fact_4390_dvd__minus__self,axiom,
% 0.35/0.60      ! [M: nat,N: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) )
% 0.35/0.60        = ( ( ord_less_nat @ N @ M )
% 0.35/0.60          | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_minus_self
% 0.35/0.60  thf(fact_4391_dvd__diffD,axiom,
% 0.35/0.60      ! [K: nat,M: nat,N: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 0.35/0.60       => ( ( dvd_dvd_nat @ K @ N )
% 0.35/0.60         => ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.60           => ( dvd_dvd_nat @ K @ M ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_diffD
% 0.35/0.60  thf(fact_4392_dvd__diffD1,axiom,
% 0.35/0.60      ! [K: nat,M: nat,N: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 0.35/0.60       => ( ( dvd_dvd_nat @ K @ M )
% 0.35/0.60         => ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.60           => ( dvd_dvd_nat @ K @ N ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_diffD1
% 0.35/0.60  thf(fact_4393_less__eq__dvd__minus,axiom,
% 0.35/0.60      ! [M: nat,N: nat] :
% 0.35/0.60        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.60       => ( ( dvd_dvd_nat @ M @ N )
% 0.35/0.60          = ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % less_eq_dvd_minus
% 0.35/0.60  thf(fact_4394_dbl__def,axiom,
% 0.35/0.60      ( neg_numeral_dbl_real
% 0.35/0.60      = ( ^ [X2: real] : ( plus_plus_real @ X2 @ X2 ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dbl_def
% 0.35/0.60  thf(fact_4395_dbl__def,axiom,
% 0.35/0.60      ( neg_numeral_dbl_rat
% 0.35/0.60      = ( ^ [X2: rat] : ( plus_plus_rat @ X2 @ X2 ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dbl_def
% 0.35/0.60  thf(fact_4396_dbl__def,axiom,
% 0.35/0.60      ( neg_numeral_dbl_int
% 0.35/0.60      = ( ^ [X2: int] : ( plus_plus_int @ X2 @ X2 ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dbl_def
% 0.35/0.60  thf(fact_4397_dbl__def,axiom,
% 0.35/0.60      ( neg_nu7009210354673126013omplex
% 0.35/0.60      = ( ^ [X2: complex] : ( plus_plus_complex @ X2 @ X2 ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dbl_def
% 0.35/0.60  thf(fact_4398_finite__divisors__nat,axiom,
% 0.35/0.60      ! [M: nat] :
% 0.35/0.60        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.35/0.60       => ( finite_finite_nat
% 0.35/0.60          @ ( collect_nat
% 0.35/0.60            @ ^ [D: nat] : ( dvd_dvd_nat @ D @ M ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % finite_divisors_nat
% 0.35/0.60  thf(fact_4399_div2__even__ext__nat,axiom,
% 0.35/0.60      ! [X: nat,Y2: nat] :
% 0.35/0.60        ( ( ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.60          = ( divide_divide_nat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.60       => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X )
% 0.35/0.60            = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y2 ) )
% 0.35/0.60         => ( X = Y2 ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div2_even_ext_nat
% 0.35/0.60  thf(fact_4400_unit__dvdE,axiom,
% 0.35/0.60      ! [A: code_integer,B: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.35/0.60       => ~ ( ( A != zero_z3403309356797280102nteger )
% 0.35/0.60           => ! [C2: code_integer] :
% 0.35/0.60                ( B
% 0.35/0.60               != ( times_3573771949741848930nteger @ A @ C2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_dvdE
% 0.35/0.60  thf(fact_4401_unit__dvdE,axiom,
% 0.35/0.60      ! [A: nat,B: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.35/0.60       => ~ ( ( A != zero_zero_nat )
% 0.35/0.60           => ! [C2: nat] :
% 0.35/0.60                ( B
% 0.35/0.60               != ( times_times_nat @ A @ C2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_dvdE
% 0.35/0.60  thf(fact_4402_unit__dvdE,axiom,
% 0.35/0.60      ! [A: int,B: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.35/0.60       => ~ ( ( A != zero_zero_int )
% 0.35/0.60           => ! [C2: int] :
% 0.35/0.60                ( B
% 0.35/0.60               != ( times_times_int @ A @ C2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_dvdE
% 0.35/0.60  thf(fact_4403_unity__coeff__ex,axiom,
% 0.35/0.60      ! [P: code_integer > $o,L2: code_integer] :
% 0.35/0.60        ( ( ? [X2: code_integer] : ( P @ ( times_3573771949741848930nteger @ L2 @ X2 ) ) )
% 0.35/0.60        = ( ? [X2: code_integer] :
% 0.35/0.60              ( ( dvd_dvd_Code_integer @ L2 @ ( plus_p5714425477246183910nteger @ X2 @ zero_z3403309356797280102nteger ) )
% 0.35/0.60              & ( P @ X2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unity_coeff_ex
% 0.35/0.60  thf(fact_4404_unity__coeff__ex,axiom,
% 0.35/0.60      ! [P: rat > $o,L2: rat] :
% 0.35/0.60        ( ( ? [X2: rat] : ( P @ ( times_times_rat @ L2 @ X2 ) ) )
% 0.35/0.60        = ( ? [X2: rat] :
% 0.35/0.60              ( ( dvd_dvd_rat @ L2 @ ( plus_plus_rat @ X2 @ zero_zero_rat ) )
% 0.35/0.60              & ( P @ X2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unity_coeff_ex
% 0.35/0.60  thf(fact_4405_unity__coeff__ex,axiom,
% 0.35/0.60      ! [P: complex > $o,L2: complex] :
% 0.35/0.60        ( ( ? [X2: complex] : ( P @ ( times_times_complex @ L2 @ X2 ) ) )
% 0.35/0.60        = ( ? [X2: complex] :
% 0.35/0.60              ( ( dvd_dvd_complex @ L2 @ ( plus_plus_complex @ X2 @ zero_zero_complex ) )
% 0.35/0.60              & ( P @ X2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unity_coeff_ex
% 0.35/0.60  thf(fact_4406_unity__coeff__ex,axiom,
% 0.35/0.60      ! [P: real > $o,L2: real] :
% 0.35/0.60        ( ( ? [X2: real] : ( P @ ( times_times_real @ L2 @ X2 ) ) )
% 0.35/0.60        = ( ? [X2: real] :
% 0.35/0.60              ( ( dvd_dvd_real @ L2 @ ( plus_plus_real @ X2 @ zero_zero_real ) )
% 0.35/0.60              & ( P @ X2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unity_coeff_ex
% 0.35/0.60  thf(fact_4407_unity__coeff__ex,axiom,
% 0.35/0.60      ! [P: nat > $o,L2: nat] :
% 0.35/0.60        ( ( ? [X2: nat] : ( P @ ( times_times_nat @ L2 @ X2 ) ) )
% 0.35/0.60        = ( ? [X2: nat] :
% 0.35/0.60              ( ( dvd_dvd_nat @ L2 @ ( plus_plus_nat @ X2 @ zero_zero_nat ) )
% 0.35/0.60              & ( P @ X2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unity_coeff_ex
% 0.35/0.60  thf(fact_4408_unity__coeff__ex,axiom,
% 0.35/0.60      ! [P: int > $o,L2: int] :
% 0.35/0.60        ( ( ? [X2: int] : ( P @ ( times_times_int @ L2 @ X2 ) ) )
% 0.35/0.60        = ( ? [X2: int] :
% 0.35/0.60              ( ( dvd_dvd_int @ L2 @ ( plus_plus_int @ X2 @ zero_zero_int ) )
% 0.35/0.60              & ( P @ X2 ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unity_coeff_ex
% 0.35/0.60  thf(fact_4409_even__numeral,axiom,
% 0.35/0.60      ! [N: num] : ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % even_numeral
% 0.35/0.60  thf(fact_4410_even__numeral,axiom,
% 0.35/0.60      ! [N: num] : ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % even_numeral
% 0.35/0.60  thf(fact_4411_even__numeral,axiom,
% 0.35/0.60      ! [N: num] : ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % even_numeral
% 0.35/0.60  thf(fact_4412_dvd__div__eq__mult,axiom,
% 0.35/0.60      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.35/0.60        ( ( A != zero_z3403309356797280102nteger )
% 0.35/0.60       => ( ( dvd_dvd_Code_integer @ A @ B )
% 0.35/0.60         => ( ( ( divide6298287555418463151nteger @ B @ A )
% 0.35/0.60              = C )
% 0.35/0.60            = ( B
% 0.35/0.60              = ( times_3573771949741848930nteger @ C @ A ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_eq_mult
% 0.35/0.60  thf(fact_4413_dvd__div__eq__mult,axiom,
% 0.35/0.60      ! [A: nat,B: nat,C: nat] :
% 0.35/0.60        ( ( A != zero_zero_nat )
% 0.35/0.60       => ( ( dvd_dvd_nat @ A @ B )
% 0.35/0.60         => ( ( ( divide_divide_nat @ B @ A )
% 0.35/0.60              = C )
% 0.35/0.60            = ( B
% 0.35/0.60              = ( times_times_nat @ C @ A ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_eq_mult
% 0.35/0.60  thf(fact_4414_dvd__div__eq__mult,axiom,
% 0.35/0.60      ! [A: int,B: int,C: int] :
% 0.35/0.60        ( ( A != zero_zero_int )
% 0.35/0.60       => ( ( dvd_dvd_int @ A @ B )
% 0.35/0.60         => ( ( ( divide_divide_int @ B @ A )
% 0.35/0.60              = C )
% 0.35/0.60            = ( B
% 0.35/0.60              = ( times_times_int @ C @ A ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_eq_mult
% 0.35/0.60  thf(fact_4415_div__dvd__iff__mult,axiom,
% 0.35/0.60      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.35/0.60        ( ( B != zero_z3403309356797280102nteger )
% 0.35/0.60       => ( ( dvd_dvd_Code_integer @ B @ A )
% 0.35/0.60         => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 0.35/0.60            = ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_dvd_iff_mult
% 0.35/0.60  thf(fact_4416_div__dvd__iff__mult,axiom,
% 0.35/0.60      ! [B: nat,A: nat,C: nat] :
% 0.35/0.60        ( ( B != zero_zero_nat )
% 0.35/0.60       => ( ( dvd_dvd_nat @ B @ A )
% 0.35/0.60         => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 0.35/0.60            = ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_dvd_iff_mult
% 0.35/0.60  thf(fact_4417_div__dvd__iff__mult,axiom,
% 0.35/0.60      ! [B: int,A: int,C: int] :
% 0.35/0.60        ( ( B != zero_zero_int )
% 0.35/0.60       => ( ( dvd_dvd_int @ B @ A )
% 0.35/0.60         => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 0.35/0.60            = ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_dvd_iff_mult
% 0.35/0.60  thf(fact_4418_dvd__div__iff__mult,axiom,
% 0.35/0.60      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.35/0.60        ( ( C != zero_z3403309356797280102nteger )
% 0.35/0.60       => ( ( dvd_dvd_Code_integer @ C @ B )
% 0.35/0.60         => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 0.35/0.60            = ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_iff_mult
% 0.35/0.60  thf(fact_4419_dvd__div__iff__mult,axiom,
% 0.35/0.60      ! [C: nat,B: nat,A: nat] :
% 0.35/0.60        ( ( C != zero_zero_nat )
% 0.35/0.60       => ( ( dvd_dvd_nat @ C @ B )
% 0.35/0.60         => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 0.35/0.60            = ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_iff_mult
% 0.35/0.60  thf(fact_4420_dvd__div__iff__mult,axiom,
% 0.35/0.60      ! [C: int,B: int,A: int] :
% 0.35/0.60        ( ( C != zero_zero_int )
% 0.35/0.60       => ( ( dvd_dvd_int @ C @ B )
% 0.35/0.60         => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) )
% 0.35/0.60            = ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_iff_mult
% 0.35/0.60  thf(fact_4421_dvd__div__div__eq__mult,axiom,
% 0.35/0.60      ! [A: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 0.35/0.60        ( ( A != zero_z3403309356797280102nteger )
% 0.35/0.60       => ( ( C != zero_z3403309356797280102nteger )
% 0.35/0.60         => ( ( dvd_dvd_Code_integer @ A @ B )
% 0.35/0.60           => ( ( dvd_dvd_Code_integer @ C @ D2 )
% 0.35/0.60             => ( ( ( divide6298287555418463151nteger @ B @ A )
% 0.35/0.60                  = ( divide6298287555418463151nteger @ D2 @ C ) )
% 0.35/0.60                = ( ( times_3573771949741848930nteger @ B @ C )
% 0.35/0.60                  = ( times_3573771949741848930nteger @ A @ D2 ) ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_div_eq_mult
% 0.35/0.60  thf(fact_4422_dvd__div__div__eq__mult,axiom,
% 0.35/0.60      ! [A: nat,C: nat,B: nat,D2: nat] :
% 0.35/0.60        ( ( A != zero_zero_nat )
% 0.35/0.60       => ( ( C != zero_zero_nat )
% 0.35/0.60         => ( ( dvd_dvd_nat @ A @ B )
% 0.35/0.60           => ( ( dvd_dvd_nat @ C @ D2 )
% 0.35/0.60             => ( ( ( divide_divide_nat @ B @ A )
% 0.35/0.60                  = ( divide_divide_nat @ D2 @ C ) )
% 0.35/0.60                = ( ( times_times_nat @ B @ C )
% 0.35/0.60                  = ( times_times_nat @ A @ D2 ) ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_div_eq_mult
% 0.35/0.60  thf(fact_4423_dvd__div__div__eq__mult,axiom,
% 0.35/0.60      ! [A: int,C: int,B: int,D2: int] :
% 0.35/0.60        ( ( A != zero_zero_int )
% 0.35/0.60       => ( ( C != zero_zero_int )
% 0.35/0.60         => ( ( dvd_dvd_int @ A @ B )
% 0.35/0.60           => ( ( dvd_dvd_int @ C @ D2 )
% 0.35/0.60             => ( ( ( divide_divide_int @ B @ A )
% 0.35/0.60                  = ( divide_divide_int @ D2 @ C ) )
% 0.35/0.60                = ( ( times_times_int @ B @ C )
% 0.35/0.60                  = ( times_times_int @ A @ D2 ) ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_div_div_eq_mult
% 0.35/0.60  thf(fact_4424_unit__div__eq__0__iff,axiom,
% 0.35/0.60      ! [B: code_integer,A: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.35/0.60       => ( ( ( divide6298287555418463151nteger @ A @ B )
% 0.35/0.60            = zero_z3403309356797280102nteger )
% 0.35/0.60          = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_div_eq_0_iff
% 0.35/0.60  thf(fact_4425_unit__div__eq__0__iff,axiom,
% 0.35/0.60      ! [B: nat,A: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.35/0.60       => ( ( ( divide_divide_nat @ A @ B )
% 0.35/0.60            = zero_zero_nat )
% 0.35/0.60          = ( A = zero_zero_nat ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_div_eq_0_iff
% 0.35/0.60  thf(fact_4426_unit__div__eq__0__iff,axiom,
% 0.35/0.60      ! [B: int,A: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.35/0.60       => ( ( ( divide_divide_int @ A @ B )
% 0.35/0.60            = zero_zero_int )
% 0.35/0.60          = ( A = zero_zero_int ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_div_eq_0_iff
% 0.35/0.60  thf(fact_4427_inf__period_I4_J,axiom,
% 0.35/0.60      ! [D2: code_integer,D4: code_integer,T: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ D2 @ D4 )
% 0.35/0.60       => ! [X5: code_integer,K4: code_integer] :
% 0.35/0.60            ( ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X5 @ T ) ) )
% 0.35/0.60            = ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X5 @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % inf_period(4)
% 0.35/0.60  thf(fact_4428_inf__period_I4_J,axiom,
% 0.35/0.60      ! [D2: rat,D4: rat,T: rat] :
% 0.35/0.60        ( ( dvd_dvd_rat @ D2 @ D4 )
% 0.35/0.60       => ! [X5: rat,K4: rat] :
% 0.35/0.60            ( ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X5 @ T ) ) )
% 0.35/0.60            = ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % inf_period(4)
% 0.35/0.60  thf(fact_4429_inf__period_I4_J,axiom,
% 0.35/0.60      ! [D2: complex,D4: complex,T: complex] :
% 0.35/0.60        ( ( dvd_dvd_complex @ D2 @ D4 )
% 0.35/0.60       => ! [X5: complex,K4: complex] :
% 0.35/0.60            ( ( ~ ( dvd_dvd_complex @ D2 @ ( plus_plus_complex @ X5 @ T ) ) )
% 0.35/0.60            = ( ~ ( dvd_dvd_complex @ D2 @ ( plus_plus_complex @ ( minus_minus_complex @ X5 @ ( times_times_complex @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % inf_period(4)
% 0.35/0.60  thf(fact_4430_inf__period_I4_J,axiom,
% 0.35/0.60      ! [D2: real,D4: real,T: real] :
% 0.35/0.60        ( ( dvd_dvd_real @ D2 @ D4 )
% 0.35/0.60       => ! [X5: real,K4: real] :
% 0.35/0.60            ( ( ~ ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X5 @ T ) ) )
% 0.35/0.60            = ( ~ ( dvd_dvd_real @ D2 @ ( plus_plus_real @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % inf_period(4)
% 0.35/0.60  thf(fact_4431_inf__period_I4_J,axiom,
% 0.35/0.60      ! [D2: int,D4: int,T: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ D2 @ D4 )
% 0.35/0.60       => ! [X5: int,K4: int] :
% 0.35/0.60            ( ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ T ) ) )
% 0.35/0.60            = ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % inf_period(4)
% 0.35/0.60  thf(fact_4432_inf__period_I3_J,axiom,
% 0.35/0.60      ! [D2: code_integer,D4: code_integer,T: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ D2 @ D4 )
% 0.35/0.60       => ! [X5: code_integer,K4: code_integer] :
% 0.35/0.60            ( ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X5 @ T ) )
% 0.35/0.60            = ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X5 @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % inf_period(3)
% 0.35/0.60  thf(fact_4433_inf__period_I3_J,axiom,
% 0.35/0.60      ! [D2: rat,D4: rat,T: rat] :
% 0.35/0.60        ( ( dvd_dvd_rat @ D2 @ D4 )
% 0.35/0.60       => ! [X5: rat,K4: rat] :
% 0.35/0.60            ( ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X5 @ T ) )
% 0.35/0.60            = ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % inf_period(3)
% 0.35/0.60  thf(fact_4434_inf__period_I3_J,axiom,
% 0.35/0.60      ! [D2: complex,D4: complex,T: complex] :
% 0.35/0.60        ( ( dvd_dvd_complex @ D2 @ D4 )
% 0.35/0.60       => ! [X5: complex,K4: complex] :
% 0.35/0.60            ( ( dvd_dvd_complex @ D2 @ ( plus_plus_complex @ X5 @ T ) )
% 0.35/0.60            = ( dvd_dvd_complex @ D2 @ ( plus_plus_complex @ ( minus_minus_complex @ X5 @ ( times_times_complex @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % inf_period(3)
% 0.35/0.60  thf(fact_4435_inf__period_I3_J,axiom,
% 0.35/0.60      ! [D2: real,D4: real,T: real] :
% 0.35/0.60        ( ( dvd_dvd_real @ D2 @ D4 )
% 0.35/0.60       => ! [X5: real,K4: real] :
% 0.35/0.60            ( ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X5 @ T ) )
% 0.35/0.60            = ( dvd_dvd_real @ D2 @ ( plus_plus_real @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % inf_period(3)
% 0.35/0.60  thf(fact_4436_inf__period_I3_J,axiom,
% 0.35/0.60      ! [D2: int,D4: int,T: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ D2 @ D4 )
% 0.35/0.60       => ! [X5: int,K4: int] :
% 0.35/0.60            ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ T ) )
% 0.35/0.60            = ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % inf_period(3)
% 0.35/0.60  thf(fact_4437_unit__eq__div1,axiom,
% 0.35/0.60      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.35/0.60       => ( ( ( divide6298287555418463151nteger @ A @ B )
% 0.35/0.60            = C )
% 0.35/0.60          = ( A
% 0.35/0.60            = ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_eq_div1
% 0.35/0.60  thf(fact_4438_unit__eq__div1,axiom,
% 0.35/0.60      ! [B: nat,A: nat,C: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.35/0.60       => ( ( ( divide_divide_nat @ A @ B )
% 0.35/0.60            = C )
% 0.35/0.60          = ( A
% 0.35/0.60            = ( times_times_nat @ C @ B ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_eq_div1
% 0.35/0.60  thf(fact_4439_unit__eq__div1,axiom,
% 0.35/0.60      ! [B: int,A: int,C: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.35/0.60       => ( ( ( divide_divide_int @ A @ B )
% 0.35/0.60            = C )
% 0.35/0.60          = ( A
% 0.35/0.60            = ( times_times_int @ C @ B ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_eq_div1
% 0.35/0.60  thf(fact_4440_unit__eq__div2,axiom,
% 0.35/0.60      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.35/0.60       => ( ( A
% 0.35/0.60            = ( divide6298287555418463151nteger @ C @ B ) )
% 0.35/0.60          = ( ( times_3573771949741848930nteger @ A @ B )
% 0.35/0.60            = C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_eq_div2
% 0.35/0.60  thf(fact_4441_unit__eq__div2,axiom,
% 0.35/0.60      ! [B: nat,A: nat,C: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.35/0.60       => ( ( A
% 0.35/0.60            = ( divide_divide_nat @ C @ B ) )
% 0.35/0.60          = ( ( times_times_nat @ A @ B )
% 0.35/0.60            = C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_eq_div2
% 0.35/0.60  thf(fact_4442_unit__eq__div2,axiom,
% 0.35/0.60      ! [B: int,A: int,C: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.35/0.60       => ( ( A
% 0.35/0.60            = ( divide_divide_int @ C @ B ) )
% 0.35/0.60          = ( ( times_times_int @ A @ B )
% 0.35/0.60            = C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_eq_div2
% 0.35/0.60  thf(fact_4443_div__mult__unit2,axiom,
% 0.35/0.60      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 0.35/0.60       => ( ( dvd_dvd_Code_integer @ B @ A )
% 0.35/0.60         => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.35/0.60            = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_mult_unit2
% 0.35/0.60  thf(fact_4444_div__mult__unit2,axiom,
% 0.35/0.60      ! [C: nat,B: nat,A: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ C @ one_one_nat )
% 0.35/0.60       => ( ( dvd_dvd_nat @ B @ A )
% 0.35/0.60         => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.35/0.60            = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_mult_unit2
% 0.35/0.60  thf(fact_4445_div__mult__unit2,axiom,
% 0.35/0.60      ! [C: int,B: int,A: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ C @ one_one_int )
% 0.35/0.60       => ( ( dvd_dvd_int @ B @ A )
% 0.35/0.60         => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 0.35/0.60            = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % div_mult_unit2
% 0.35/0.60  thf(fact_4446_unit__div__commute,axiom,
% 0.35/0.60      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.35/0.60       => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 0.35/0.60          = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_div_commute
% 0.35/0.60  thf(fact_4447_unit__div__commute,axiom,
% 0.35/0.60      ! [B: nat,A: nat,C: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.35/0.60       => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 0.35/0.60          = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_div_commute
% 0.35/0.60  thf(fact_4448_unit__div__commute,axiom,
% 0.35/0.60      ! [B: int,A: int,C: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.35/0.60       => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ C )
% 0.35/0.60          = ( divide_divide_int @ ( times_times_int @ A @ C ) @ B ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_div_commute
% 0.35/0.60  thf(fact_4449_unit__div__mult__swap,axiom,
% 0.35/0.60      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 0.35/0.60       => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 0.35/0.60          = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_div_mult_swap
% 0.35/0.60  thf(fact_4450_unit__div__mult__swap,axiom,
% 0.35/0.60      ! [C: nat,A: nat,B: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ C @ one_one_nat )
% 0.35/0.60       => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 0.35/0.60          = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_div_mult_swap
% 0.35/0.60  thf(fact_4451_unit__div__mult__swap,axiom,
% 0.35/0.60      ! [C: int,A: int,B: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ C @ one_one_int )
% 0.35/0.60       => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 0.35/0.60          = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_div_mult_swap
% 0.35/0.60  thf(fact_4452_is__unit__div__mult2__eq,axiom,
% 0.35/0.60      ! [B: code_integer,C: code_integer,A: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.35/0.60       => ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 0.35/0.60         => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.35/0.60            = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % is_unit_div_mult2_eq
% 0.35/0.60  thf(fact_4453_is__unit__div__mult2__eq,axiom,
% 0.35/0.60      ! [B: nat,C: nat,A: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.35/0.60       => ( ( dvd_dvd_nat @ C @ one_one_nat )
% 0.35/0.60         => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.35/0.60            = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % is_unit_div_mult2_eq
% 0.35/0.60  thf(fact_4454_is__unit__div__mult2__eq,axiom,
% 0.35/0.60      ! [B: int,C: int,A: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.35/0.60       => ( ( dvd_dvd_int @ C @ one_one_int )
% 0.35/0.60         => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 0.35/0.60            = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % is_unit_div_mult2_eq
% 0.35/0.60  thf(fact_4455_is__unit__power__iff,axiom,
% 0.35/0.60      ! [A: code_integer,N: nat] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ one_one_Code_integer )
% 0.35/0.60        = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.35/0.60          | ( N = zero_zero_nat ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % is_unit_power_iff
% 0.35/0.60  thf(fact_4456_is__unit__power__iff,axiom,
% 0.35/0.60      ! [A: nat,N: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ one_one_nat )
% 0.35/0.60        = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.35/0.60          | ( N = zero_zero_nat ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % is_unit_power_iff
% 0.35/0.60  thf(fact_4457_is__unit__power__iff,axiom,
% 0.35/0.60      ! [A: int,N: nat] :
% 0.35/0.60        ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ one_one_int )
% 0.35/0.60        = ( ( dvd_dvd_int @ A @ one_one_int )
% 0.35/0.60          | ( N = zero_zero_nat ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % is_unit_power_iff
% 0.35/0.60  thf(fact_4458_unit__imp__mod__eq__0,axiom,
% 0.35/0.60      ! [B: code_integer,A: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.35/0.60       => ( ( modulo364778990260209775nteger @ A @ B )
% 0.35/0.60          = zero_z3403309356797280102nteger ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_imp_mod_eq_0
% 0.35/0.60  thf(fact_4459_unit__imp__mod__eq__0,axiom,
% 0.35/0.60      ! [B: nat,A: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.35/0.60       => ( ( modulo_modulo_nat @ A @ B )
% 0.35/0.60          = zero_zero_nat ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_imp_mod_eq_0
% 0.35/0.60  thf(fact_4460_unit__imp__mod__eq__0,axiom,
% 0.35/0.60      ! [B: int,A: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.35/0.60       => ( ( modulo_modulo_int @ A @ B )
% 0.35/0.60          = zero_zero_int ) ) ).
% 0.35/0.60  
% 0.35/0.60  % unit_imp_mod_eq_0
% 0.35/0.60  thf(fact_4461_dvd__imp__le,axiom,
% 0.35/0.60      ! [K: nat,N: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ K @ N )
% 0.35/0.60       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.60         => ( ord_less_eq_nat @ K @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_imp_le
% 0.35/0.60  thf(fact_4462_dvd__mult__cancel,axiom,
% 0.35/0.60      ! [K: nat,M: nat,N: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.35/0.60       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.35/0.60         => ( dvd_dvd_nat @ M @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult_cancel
% 0.35/0.60  thf(fact_4463_nat__mult__dvd__cancel1,axiom,
% 0.35/0.60      ! [K: nat,M: nat,N: nat] :
% 0.35/0.60        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.35/0.60       => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.35/0.60          = ( dvd_dvd_nat @ M @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % nat_mult_dvd_cancel1
% 0.35/0.60  thf(fact_4464_mod__greater__zero__iff__not__dvd,axiom,
% 0.35/0.60      ! [M: nat,N: nat] :
% 0.35/0.60        ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ N ) )
% 0.35/0.60        = ( ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % mod_greater_zero_iff_not_dvd
% 0.35/0.60  thf(fact_4465_mod__eq__dvd__iff__nat,axiom,
% 0.35/0.60      ! [N: nat,M: nat,Q2: nat] :
% 0.35/0.60        ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.60       => ( ( ( modulo_modulo_nat @ M @ Q2 )
% 0.35/0.60            = ( modulo_modulo_nat @ N @ Q2 ) )
% 0.35/0.60          = ( dvd_dvd_nat @ Q2 @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % mod_eq_dvd_iff_nat
% 0.35/0.60  thf(fact_4466_prod__decode__aux_Ocases,axiom,
% 0.35/0.60      ! [X: product_prod_nat_nat] :
% 0.35/0.60        ~ ! [K2: nat,M4: nat] :
% 0.35/0.60            ( X
% 0.35/0.60           != ( product_Pair_nat_nat @ K2 @ M4 ) ) ).
% 0.35/0.60  
% 0.35/0.60  % prod_decode_aux.cases
% 0.35/0.60  thf(fact_4467_even__zero,axiom,
% 0.35/0.60      dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ zero_z3403309356797280102nteger ).
% 0.35/0.60  
% 0.35/0.60  % even_zero
% 0.35/0.60  thf(fact_4468_even__zero,axiom,
% 0.35/0.60      dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ zero_zero_nat ).
% 0.35/0.60  
% 0.35/0.60  % even_zero
% 0.35/0.60  thf(fact_4469_even__zero,axiom,
% 0.35/0.60      dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ zero_zero_int ).
% 0.35/0.60  
% 0.35/0.60  % even_zero
% 0.35/0.60  thf(fact_4470_evenE,axiom,
% 0.35/0.60      ! [A: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.35/0.60       => ~ ! [B3: code_integer] :
% 0.35/0.60              ( A
% 0.35/0.60             != ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B3 ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % evenE
% 0.35/0.60  thf(fact_4471_evenE,axiom,
% 0.35/0.60      ! [A: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.60       => ~ ! [B3: nat] :
% 0.35/0.60              ( A
% 0.35/0.60             != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % evenE
% 0.35/0.60  thf(fact_4472_evenE,axiom,
% 0.35/0.60      ! [A: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.60       => ~ ! [B3: int] :
% 0.35/0.60              ( A
% 0.35/0.60             != ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % evenE
% 0.35/0.60  thf(fact_4473_odd__one,axiom,
% 0.35/0.60      ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ one_one_Code_integer ) ).
% 0.35/0.60  
% 0.35/0.60  % odd_one
% 0.35/0.60  thf(fact_4474_odd__one,axiom,
% 0.35/0.60      ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ one_one_nat ) ).
% 0.35/0.60  
% 0.35/0.60  % odd_one
% 0.35/0.60  thf(fact_4475_odd__one,axiom,
% 0.35/0.60      ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ one_one_int ) ).
% 0.35/0.60  
% 0.35/0.60  % odd_one
% 0.35/0.60  thf(fact_4476_is__unitE,axiom,
% 0.35/0.60      ! [A: code_integer,C: code_integer] :
% 0.35/0.60        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.35/0.60       => ~ ( ( A != zero_z3403309356797280102nteger )
% 0.35/0.60           => ! [B3: code_integer] :
% 0.35/0.60                ( ( B3 != zero_z3403309356797280102nteger )
% 0.35/0.60               => ( ( dvd_dvd_Code_integer @ B3 @ one_one_Code_integer )
% 0.35/0.60                 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ A )
% 0.35/0.60                      = B3 )
% 0.35/0.60                   => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ B3 )
% 0.35/0.60                        = A )
% 0.35/0.60                     => ( ( ( times_3573771949741848930nteger @ A @ B3 )
% 0.35/0.60                          = one_one_Code_integer )
% 0.35/0.60                       => ( ( divide6298287555418463151nteger @ C @ A )
% 0.35/0.60                         != ( times_3573771949741848930nteger @ C @ B3 ) ) ) ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % is_unitE
% 0.35/0.60  thf(fact_4477_is__unitE,axiom,
% 0.35/0.60      ! [A: nat,C: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.35/0.60       => ~ ( ( A != zero_zero_nat )
% 0.35/0.60           => ! [B3: nat] :
% 0.35/0.60                ( ( B3 != zero_zero_nat )
% 0.35/0.60               => ( ( dvd_dvd_nat @ B3 @ one_one_nat )
% 0.35/0.60                 => ( ( ( divide_divide_nat @ one_one_nat @ A )
% 0.35/0.60                      = B3 )
% 0.35/0.60                   => ( ( ( divide_divide_nat @ one_one_nat @ B3 )
% 0.35/0.60                        = A )
% 0.35/0.60                     => ( ( ( times_times_nat @ A @ B3 )
% 0.35/0.60                          = one_one_nat )
% 0.35/0.60                       => ( ( divide_divide_nat @ C @ A )
% 0.35/0.60                         != ( times_times_nat @ C @ B3 ) ) ) ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % is_unitE
% 0.35/0.60  thf(fact_4478_is__unitE,axiom,
% 0.35/0.60      ! [A: int,C: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.35/0.60       => ~ ( ( A != zero_zero_int )
% 0.35/0.60           => ! [B3: int] :
% 0.35/0.60                ( ( B3 != zero_zero_int )
% 0.35/0.60               => ( ( dvd_dvd_int @ B3 @ one_one_int )
% 0.35/0.60                 => ( ( ( divide_divide_int @ one_one_int @ A )
% 0.35/0.60                      = B3 )
% 0.35/0.60                   => ( ( ( divide_divide_int @ one_one_int @ B3 )
% 0.35/0.60                        = A )
% 0.35/0.60                     => ( ( ( times_times_int @ A @ B3 )
% 0.35/0.60                          = one_one_int )
% 0.35/0.60                       => ( ( divide_divide_int @ C @ A )
% 0.35/0.60                         != ( times_times_int @ C @ B3 ) ) ) ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % is_unitE
% 0.35/0.60  thf(fact_4479_is__unit__div__mult__cancel__left,axiom,
% 0.35/0.60      ! [A: code_integer,B: code_integer] :
% 0.35/0.60        ( ( A != zero_z3403309356797280102nteger )
% 0.35/0.60       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.35/0.60         => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ A @ B ) )
% 0.35/0.60            = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % is_unit_div_mult_cancel_left
% 0.35/0.60  thf(fact_4480_is__unit__div__mult__cancel__left,axiom,
% 0.35/0.60      ! [A: nat,B: nat] :
% 0.35/0.60        ( ( A != zero_zero_nat )
% 0.35/0.60       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.35/0.60         => ( ( divide_divide_nat @ A @ ( times_times_nat @ A @ B ) )
% 0.35/0.60            = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % is_unit_div_mult_cancel_left
% 0.35/0.60  thf(fact_4481_is__unit__div__mult__cancel__left,axiom,
% 0.35/0.60      ! [A: int,B: int] :
% 0.35/0.60        ( ( A != zero_zero_int )
% 0.35/0.60       => ( ( dvd_dvd_int @ B @ one_one_int )
% 0.35/0.60         => ( ( divide_divide_int @ A @ ( times_times_int @ A @ B ) )
% 0.35/0.60            = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % is_unit_div_mult_cancel_left
% 0.35/0.60  thf(fact_4482_is__unit__div__mult__cancel__right,axiom,
% 0.35/0.60      ! [A: code_integer,B: code_integer] :
% 0.35/0.60        ( ( A != zero_z3403309356797280102nteger )
% 0.35/0.60       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.35/0.60         => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ A ) )
% 0.35/0.60            = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % is_unit_div_mult_cancel_right
% 0.35/0.60  thf(fact_4483_is__unit__div__mult__cancel__right,axiom,
% 0.35/0.60      ! [A: nat,B: nat] :
% 0.35/0.60        ( ( A != zero_zero_nat )
% 0.35/0.60       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.35/0.60         => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ A ) )
% 0.35/0.60            = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % is_unit_div_mult_cancel_right
% 0.35/0.60  thf(fact_4484_is__unit__div__mult__cancel__right,axiom,
% 0.35/0.60      ! [A: int,B: int] :
% 0.35/0.60        ( ( A != zero_zero_int )
% 0.35/0.60       => ( ( dvd_dvd_int @ B @ one_one_int )
% 0.35/0.60         => ( ( divide_divide_int @ A @ ( times_times_int @ B @ A ) )
% 0.35/0.60            = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % is_unit_div_mult_cancel_right
% 0.35/0.60  thf(fact_4485_odd__even__add,axiom,
% 0.35/0.60      ! [A: code_integer,B: code_integer] :
% 0.35/0.60        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.35/0.60       => ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B )
% 0.35/0.60         => ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % odd_even_add
% 0.35/0.60  thf(fact_4486_odd__even__add,axiom,
% 0.35/0.60      ! [A: nat,B: nat] :
% 0.35/0.60        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.60       => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.35/0.60         => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % odd_even_add
% 0.35/0.60  thf(fact_4487_odd__even__add,axiom,
% 0.35/0.60      ! [A: int,B: int] :
% 0.35/0.60        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.60       => ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B )
% 0.35/0.60         => ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % odd_even_add
% 0.35/0.60  thf(fact_4488_bit__eq__rec,axiom,
% 0.35/0.60      ( ( ^ [Y5: code_integer,Z5: code_integer] : ( Y5 = Z5 ) )
% 0.35/0.60      = ( ^ [A3: code_integer,B4: code_integer] :
% 0.35/0.60            ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 )
% 0.35/0.60              = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B4 ) )
% 0.35/0.60            & ( ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.35/0.60              = ( divide6298287555418463151nteger @ B4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % bit_eq_rec
% 0.35/0.60  thf(fact_4489_bit__eq__rec,axiom,
% 0.35/0.60      ( ( ^ [Y5: nat,Z5: nat] : ( Y5 = Z5 ) )
% 0.35/0.60      = ( ^ [A3: nat,B4: nat] :
% 0.35/0.60            ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 )
% 0.35/0.60              = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B4 ) )
% 0.35/0.60            & ( ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.60              = ( divide_divide_nat @ B4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % bit_eq_rec
% 0.35/0.60  thf(fact_4490_bit__eq__rec,axiom,
% 0.35/0.60      ( ( ^ [Y5: int,Z5: int] : ( Y5 = Z5 ) )
% 0.35/0.60      = ( ^ [A3: int,B4: int] :
% 0.35/0.60            ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 )
% 0.35/0.60              = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B4 ) )
% 0.35/0.60            & ( ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.60              = ( divide_divide_int @ B4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % bit_eq_rec
% 0.35/0.60  thf(fact_4491_odd__numeral,axiom,
% 0.35/0.60      ! [N: num] :
% 0.35/0.60        ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % odd_numeral
% 0.35/0.60  thf(fact_4492_odd__numeral,axiom,
% 0.35/0.60      ! [N: num] :
% 0.35/0.60        ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % odd_numeral
% 0.35/0.60  thf(fact_4493_odd__numeral,axiom,
% 0.35/0.60      ! [N: num] :
% 0.35/0.60        ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % odd_numeral
% 0.35/0.60  thf(fact_4494_dvd__power__iff,axiom,
% 0.35/0.60      ! [X: code_integer,M: nat,N: nat] :
% 0.35/0.60        ( ( X != zero_z3403309356797280102nteger )
% 0.35/0.60       => ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ M ) @ ( power_8256067586552552935nteger @ X @ N ) )
% 0.35/0.60          = ( ( dvd_dvd_Code_integer @ X @ one_one_Code_integer )
% 0.35/0.60            | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_power_iff
% 0.35/0.60  thf(fact_4495_dvd__power__iff,axiom,
% 0.35/0.60      ! [X: nat,M: nat,N: nat] :
% 0.35/0.60        ( ( X != zero_zero_nat )
% 0.35/0.60       => ( ( dvd_dvd_nat @ ( power_power_nat @ X @ M ) @ ( power_power_nat @ X @ N ) )
% 0.35/0.60          = ( ( dvd_dvd_nat @ X @ one_one_nat )
% 0.35/0.60            | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_power_iff
% 0.35/0.60  thf(fact_4496_dvd__power__iff,axiom,
% 0.35/0.60      ! [X: int,M: nat,N: nat] :
% 0.35/0.60        ( ( X != zero_zero_int )
% 0.35/0.60       => ( ( dvd_dvd_int @ ( power_power_int @ X @ M ) @ ( power_power_int @ X @ N ) )
% 0.35/0.60          = ( ( dvd_dvd_int @ X @ one_one_int )
% 0.35/0.60            | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_power_iff
% 0.35/0.60  thf(fact_4497_dvd__power,axiom,
% 0.35/0.60      ! [N: nat,X: code_integer] :
% 0.35/0.60        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.60          | ( X = one_one_Code_integer ) )
% 0.35/0.60       => ( dvd_dvd_Code_integer @ X @ ( power_8256067586552552935nteger @ X @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_power
% 0.35/0.60  thf(fact_4498_dvd__power,axiom,
% 0.35/0.60      ! [N: nat,X: rat] :
% 0.35/0.60        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.60          | ( X = one_one_rat ) )
% 0.35/0.60       => ( dvd_dvd_rat @ X @ ( power_power_rat @ X @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_power
% 0.35/0.60  thf(fact_4499_dvd__power,axiom,
% 0.35/0.60      ! [N: nat,X: nat] :
% 0.35/0.60        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.60          | ( X = one_one_nat ) )
% 0.35/0.60       => ( dvd_dvd_nat @ X @ ( power_power_nat @ X @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_power
% 0.35/0.60  thf(fact_4500_dvd__power,axiom,
% 0.35/0.60      ! [N: nat,X: real] :
% 0.35/0.60        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.60          | ( X = one_one_real ) )
% 0.35/0.60       => ( dvd_dvd_real @ X @ ( power_power_real @ X @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_power
% 0.35/0.60  thf(fact_4501_dvd__power,axiom,
% 0.35/0.60      ! [N: nat,X: int] :
% 0.35/0.60        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.60          | ( X = one_one_int ) )
% 0.35/0.60       => ( dvd_dvd_int @ X @ ( power_power_int @ X @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_power
% 0.35/0.60  thf(fact_4502_dvd__power,axiom,
% 0.35/0.60      ! [N: nat,X: complex] :
% 0.35/0.60        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.60          | ( X = one_one_complex ) )
% 0.35/0.60       => ( dvd_dvd_complex @ X @ ( power_power_complex @ X @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_power
% 0.35/0.60  thf(fact_4503_dvd__mult__cancel1,axiom,
% 0.35/0.60      ! [M: nat,N: nat] :
% 0.35/0.60        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.35/0.60       => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N ) @ M )
% 0.35/0.60          = ( N = one_one_nat ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult_cancel1
% 0.35/0.60  thf(fact_4504_dvd__mult__cancel2,axiom,
% 0.35/0.60      ! [M: nat,N: nat] :
% 0.35/0.60        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.35/0.60       => ( ( dvd_dvd_nat @ ( times_times_nat @ N @ M ) @ M )
% 0.35/0.60          = ( N = one_one_nat ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_mult_cancel2
% 0.35/0.60  thf(fact_4505_even__even__mod__4__iff,axiom,
% 0.35/0.60      ! [N: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.60        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % even_even_mod_4_iff
% 0.35/0.60  thf(fact_4506_odd__numeral__BitM,axiom,
% 0.35/0.60      ! [W: num] :
% 0.35/0.60        ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bitM @ W ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % odd_numeral_BitM
% 0.35/0.60  thf(fact_4507_odd__numeral__BitM,axiom,
% 0.35/0.60      ! [W: num] :
% 0.35/0.60        ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bitM @ W ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % odd_numeral_BitM
% 0.35/0.60  thf(fact_4508_odd__numeral__BitM,axiom,
% 0.35/0.60      ! [W: num] :
% 0.35/0.60        ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bitM @ W ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % odd_numeral_BitM
% 0.35/0.60  thf(fact_4509_power__dvd__imp__le,axiom,
% 0.35/0.60      ! [I2: nat,M: nat,N: nat] :
% 0.35/0.60        ( ( dvd_dvd_nat @ ( power_power_nat @ I2 @ M ) @ ( power_power_nat @ I2 @ N ) )
% 0.35/0.60       => ( ( ord_less_nat @ one_one_nat @ I2 )
% 0.35/0.60         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % power_dvd_imp_le
% 0.35/0.60  thf(fact_4510_dvd__minus__add,axiom,
% 0.35/0.60      ! [Q2: nat,N: nat,R: nat,M: nat] :
% 0.35/0.60        ( ( ord_less_eq_nat @ Q2 @ N )
% 0.35/0.60       => ( ( ord_less_eq_nat @ Q2 @ ( times_times_nat @ R @ M ) )
% 0.35/0.60         => ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ Q2 ) )
% 0.35/0.60            = ( dvd_dvd_nat @ M @ ( plus_plus_nat @ N @ ( minus_minus_nat @ ( times_times_nat @ R @ M ) @ Q2 ) ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % dvd_minus_add
% 0.35/0.60  thf(fact_4511_mod__nat__eqI,axiom,
% 0.35/0.60      ! [R: nat,N: nat,M: nat] :
% 0.35/0.60        ( ( ord_less_nat @ R @ N )
% 0.35/0.60       => ( ( ord_less_eq_nat @ R @ M )
% 0.35/0.60         => ( ( dvd_dvd_nat @ N @ ( minus_minus_nat @ M @ R ) )
% 0.35/0.60           => ( ( modulo_modulo_nat @ M @ N )
% 0.35/0.60              = R ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % mod_nat_eqI
% 0.35/0.60  thf(fact_4512_mod__int__pos__iff,axiom,
% 0.35/0.60      ! [K: int,L2: int] :
% 0.35/0.60        ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L2 ) )
% 0.35/0.60        = ( ( dvd_dvd_int @ L2 @ K )
% 0.35/0.60          | ( ( L2 = zero_zero_int )
% 0.35/0.60            & ( ord_less_eq_int @ zero_zero_int @ K ) )
% 0.35/0.60          | ( ord_less_int @ zero_zero_int @ L2 ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % mod_int_pos_iff
% 0.35/0.60  thf(fact_4513_aset_I10_J,axiom,
% 0.35/0.60      ! [D2: int,D4: int,A2: set_int,T: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ D2 @ D4 )
% 0.35/0.60       => ! [X5: int] :
% 0.35/0.60            ( ! [Xa3: int] :
% 0.35/0.60                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.35/0.60               => ! [Xb3: int] :
% 0.35/0.60                    ( ( member_int @ Xb3 @ A2 )
% 0.35/0.60                   => ( X5
% 0.35/0.60                     != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.35/0.60           => ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ T ) )
% 0.35/0.60             => ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( plus_plus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % aset(10)
% 0.35/0.60  thf(fact_4514_aset_I9_J,axiom,
% 0.35/0.60      ! [D2: int,D4: int,A2: set_int,T: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ D2 @ D4 )
% 0.35/0.60       => ! [X5: int] :
% 0.35/0.60            ( ! [Xa3: int] :
% 0.35/0.60                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.35/0.60               => ! [Xb3: int] :
% 0.35/0.60                    ( ( member_int @ Xb3 @ A2 )
% 0.35/0.60                   => ( X5
% 0.35/0.60                     != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.35/0.60           => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ T ) )
% 0.35/0.60             => ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( plus_plus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % aset(9)
% 0.35/0.60  thf(fact_4515_bset_I10_J,axiom,
% 0.35/0.60      ! [D2: int,D4: int,B2: set_int,T: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ D2 @ D4 )
% 0.35/0.60       => ! [X5: int] :
% 0.35/0.60            ( ! [Xa3: int] :
% 0.35/0.60                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.35/0.60               => ! [Xb3: int] :
% 0.35/0.60                    ( ( member_int @ Xb3 @ B2 )
% 0.35/0.60                   => ( X5
% 0.35/0.60                     != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.35/0.60           => ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ T ) )
% 0.35/0.60             => ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 0.35/0.60  
% 0.35/0.60  % bset(10)
% 0.35/0.60  thf(fact_4516_bset_I9_J,axiom,
% 0.35/0.60      ! [D2: int,D4: int,B2: set_int,T: int] :
% 0.35/0.60        ( ( dvd_dvd_int @ D2 @ D4 )
% 0.35/0.60       => ! [X5: int] :
% 0.35/0.60            ( ! [Xa3: int] :
% 0.35/0.60                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.35/0.60               => ! [Xb3: int] :
% 0.35/0.60                    ( ( member_int @ Xb3 @ B2 )
% 0.35/0.60                   => ( X5
% 0.35/0.60                     != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.35/0.61           => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ T ) )
% 0.35/0.61             => ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % bset(9)
% 0.35/0.61  thf(fact_4517_even__two__times__div__two,axiom,
% 0.35/0.61      ! [A: code_integer] :
% 0.35/0.61        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.35/0.61       => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 0.35/0.61          = A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % even_two_times_div_two
% 0.35/0.61  thf(fact_4518_even__two__times__div__two,axiom,
% 0.35/0.61      ! [A: nat] :
% 0.35/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.61       => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.61          = A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % even_two_times_div_two
% 0.35/0.61  thf(fact_4519_even__two__times__div__two,axiom,
% 0.35/0.61      ! [A: int] :
% 0.35/0.61        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.61       => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 0.35/0.61          = A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % even_two_times_div_two
% 0.35/0.61  thf(fact_4520_even__iff__mod__2__eq__zero,axiom,
% 0.35/0.61      ! [A: code_integer] :
% 0.35/0.61        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.35/0.61        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.35/0.61          = zero_z3403309356797280102nteger ) ) ).
% 0.35/0.61  
% 0.35/0.61  % even_iff_mod_2_eq_zero
% 0.35/0.61  thf(fact_4521_even__iff__mod__2__eq__zero,axiom,
% 0.35/0.61      ! [A: nat] :
% 0.35/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.61        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.61          = zero_zero_nat ) ) ).
% 0.35/0.61  
% 0.35/0.61  % even_iff_mod_2_eq_zero
% 0.35/0.61  thf(fact_4522_even__iff__mod__2__eq__zero,axiom,
% 0.35/0.61      ! [A: int] :
% 0.35/0.61        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.61        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.61          = zero_zero_int ) ) ).
% 0.35/0.61  
% 0.35/0.61  % even_iff_mod_2_eq_zero
% 0.35/0.61  thf(fact_4523_odd__iff__mod__2__eq__one,axiom,
% 0.35/0.61      ! [A: code_integer] :
% 0.35/0.61        ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 0.35/0.61        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.35/0.61          = one_one_Code_integer ) ) ).
% 0.35/0.61  
% 0.35/0.61  % odd_iff_mod_2_eq_one
% 0.35/0.61  thf(fact_4524_odd__iff__mod__2__eq__one,axiom,
% 0.35/0.61      ! [A: nat] :
% 0.35/0.61        ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 0.35/0.61        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.61          = one_one_nat ) ) ).
% 0.35/0.61  
% 0.35/0.61  % odd_iff_mod_2_eq_one
% 0.35/0.61  thf(fact_4525_odd__iff__mod__2__eq__one,axiom,
% 0.35/0.61      ! [A: int] :
% 0.35/0.61        ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 0.35/0.61        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.61          = one_one_int ) ) ).
% 0.35/0.61  
% 0.35/0.61  % odd_iff_mod_2_eq_one
% 0.35/0.61  thf(fact_4526_power__mono__odd,axiom,
% 0.35/0.61      ! [N: nat,A: real,B: real] :
% 0.35/0.61        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61       => ( ( ord_less_eq_real @ A @ B )
% 0.35/0.61         => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % power_mono_odd
% 0.35/0.61  thf(fact_4527_power__mono__odd,axiom,
% 0.35/0.61      ! [N: nat,A: int,B: int] :
% 0.35/0.61        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61       => ( ( ord_less_eq_int @ A @ B )
% 0.35/0.61         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % power_mono_odd
% 0.35/0.61  thf(fact_4528_odd__pos,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61       => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.35/0.61  
% 0.35/0.61  % odd_pos
% 0.35/0.61  thf(fact_4529_dvd__power__iff__le,axiom,
% 0.35/0.61      ! [K: nat,M: nat,N: nat] :
% 0.35/0.61        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 0.35/0.61       => ( ( dvd_dvd_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) )
% 0.35/0.61          = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % dvd_power_iff_le
% 0.35/0.61  thf(fact_4530_even__unset__bit__iff,axiom,
% 0.35/0.61      ! [M: nat,A: code_integer] :
% 0.35/0.61        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ M @ A ) )
% 0.35/0.61        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.35/0.61          | ( M = zero_zero_nat ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % even_unset_bit_iff
% 0.35/0.61  thf(fact_4531_even__unset__bit__iff,axiom,
% 0.35/0.61      ! [M: nat,A: int] :
% 0.35/0.61        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 0.35/0.61        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.61          | ( M = zero_zero_nat ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % even_unset_bit_iff
% 0.35/0.61  thf(fact_4532_even__unset__bit__iff,axiom,
% 0.35/0.61      ! [M: nat,A: nat] :
% 0.35/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 0.35/0.61        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.61          | ( M = zero_zero_nat ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % even_unset_bit_iff
% 0.35/0.61  thf(fact_4533_even__set__bit__iff,axiom,
% 0.35/0.61      ! [M: nat,A: code_integer] :
% 0.35/0.61        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ M @ A ) )
% 0.35/0.61        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.35/0.61          & ( M != zero_zero_nat ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % even_set_bit_iff
% 0.35/0.61  thf(fact_4534_even__set__bit__iff,axiom,
% 0.35/0.61      ! [M: nat,A: int] :
% 0.35/0.61        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 0.35/0.61        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.61          & ( M != zero_zero_nat ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % even_set_bit_iff
% 0.35/0.61  thf(fact_4535_even__set__bit__iff,axiom,
% 0.35/0.61      ! [M: nat,A: nat] :
% 0.35/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 0.35/0.61        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.61          & ( M != zero_zero_nat ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % even_set_bit_iff
% 0.35/0.61  thf(fact_4536_even__flip__bit__iff,axiom,
% 0.35/0.61      ! [M: nat,A: code_integer] :
% 0.35/0.61        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ M @ A ) )
% 0.35/0.61        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.35/0.61         != ( M = zero_zero_nat ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % even_flip_bit_iff
% 0.35/0.61  thf(fact_4537_even__flip__bit__iff,axiom,
% 0.35/0.61      ! [M: nat,A: int] :
% 0.35/0.61        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 0.35/0.61        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.61         != ( M = zero_zero_nat ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % even_flip_bit_iff
% 0.35/0.61  thf(fact_4538_even__flip__bit__iff,axiom,
% 0.35/0.61      ! [M: nat,A: nat] :
% 0.35/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 0.35/0.61        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.61         != ( M = zero_zero_nat ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % even_flip_bit_iff
% 0.35/0.61  thf(fact_4539_even__diff__iff,axiom,
% 0.35/0.61      ! [K: int,L2: int] :
% 0.35/0.61        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ K @ L2 ) )
% 0.35/0.61        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % even_diff_iff
% 0.35/0.61  thf(fact_4540_oddE,axiom,
% 0.35/0.61      ! [A: code_integer] :
% 0.35/0.61        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.35/0.61       => ~ ! [B3: code_integer] :
% 0.35/0.61              ( A
% 0.35/0.61             != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B3 ) @ one_one_Code_integer ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % oddE
% 0.35/0.61  thf(fact_4541_oddE,axiom,
% 0.35/0.61      ! [A: nat] :
% 0.35/0.61        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.61       => ~ ! [B3: nat] :
% 0.35/0.61              ( A
% 0.35/0.61             != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) @ one_one_nat ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % oddE
% 0.35/0.61  thf(fact_4542_oddE,axiom,
% 0.35/0.61      ! [A: int] :
% 0.35/0.61        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.61       => ~ ! [B3: int] :
% 0.35/0.61              ( A
% 0.35/0.61             != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) @ one_one_int ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % oddE
% 0.35/0.61  thf(fact_4543_parity__cases,axiom,
% 0.35/0.61      ! [A: code_integer] :
% 0.35/0.61        ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.35/0.61         => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.35/0.61           != zero_z3403309356797280102nteger ) )
% 0.35/0.61       => ~ ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.35/0.61           => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.35/0.61             != one_one_Code_integer ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % parity_cases
% 0.35/0.61  thf(fact_4544_parity__cases,axiom,
% 0.35/0.61      ! [A: nat] :
% 0.35/0.61        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.61         => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.61           != zero_zero_nat ) )
% 0.35/0.61       => ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.61           => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.61             != one_one_nat ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % parity_cases
% 0.35/0.61  thf(fact_4545_parity__cases,axiom,
% 0.35/0.61      ! [A: int] :
% 0.35/0.61        ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.61         => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.61           != zero_zero_int ) )
% 0.35/0.61       => ~ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.61           => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.61             != one_one_int ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % parity_cases
% 0.35/0.61  thf(fact_4546_mod2__eq__if,axiom,
% 0.35/0.61      ! [A: code_integer] :
% 0.35/0.61        ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.35/0.61         => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.35/0.61            = zero_z3403309356797280102nteger ) )
% 0.35/0.61        & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.35/0.61         => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.35/0.61            = one_one_Code_integer ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mod2_eq_if
% 0.35/0.61  thf(fact_4547_mod2__eq__if,axiom,
% 0.35/0.61      ! [A: nat] :
% 0.35/0.61        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.61         => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.61            = zero_zero_nat ) )
% 0.35/0.61        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.61         => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.61            = one_one_nat ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mod2_eq_if
% 0.35/0.61  thf(fact_4548_mod2__eq__if,axiom,
% 0.35/0.61      ! [A: int] :
% 0.35/0.61        ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.61         => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.61            = zero_zero_int ) )
% 0.35/0.61        & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.61         => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.61            = one_one_int ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mod2_eq_if
% 0.35/0.61  thf(fact_4549_zero__le__even__power,axiom,
% 0.35/0.61      ! [N: nat,A: rat] :
% 0.35/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61       => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % zero_le_even_power
% 0.35/0.61  thf(fact_4550_zero__le__even__power,axiom,
% 0.35/0.61      ! [N: nat,A: real] :
% 0.35/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61       => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % zero_le_even_power
% 0.35/0.61  thf(fact_4551_zero__le__even__power,axiom,
% 0.35/0.61      ! [N: nat,A: int] :
% 0.35/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61       => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % zero_le_even_power
% 0.35/0.61  thf(fact_4552_zero__le__odd__power,axiom,
% 0.35/0.61      ! [N: nat,A: rat] :
% 0.35/0.61        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61       => ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 0.35/0.61          = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % zero_le_odd_power
% 0.35/0.61  thf(fact_4553_zero__le__odd__power,axiom,
% 0.35/0.61      ! [N: nat,A: real] :
% 0.35/0.61        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61       => ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 0.35/0.61          = ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % zero_le_odd_power
% 0.35/0.61  thf(fact_4554_zero__le__odd__power,axiom,
% 0.35/0.61      ! [N: nat,A: int] :
% 0.35/0.61        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61       => ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 0.35/0.61          = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % zero_le_odd_power
% 0.35/0.61  thf(fact_4555_zero__le__power__eq,axiom,
% 0.35/0.61      ! [A: rat,N: nat] :
% 0.35/0.61        ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 0.35/0.61        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61            & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % zero_le_power_eq
% 0.35/0.61  thf(fact_4556_zero__le__power__eq,axiom,
% 0.35/0.61      ! [A: real,N: nat] :
% 0.35/0.61        ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 0.35/0.61        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61            & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % zero_le_power_eq
% 0.35/0.61  thf(fact_4557_zero__le__power__eq,axiom,
% 0.35/0.61      ! [A: int,N: nat] :
% 0.35/0.61        ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 0.35/0.61        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61            & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % zero_le_power_eq
% 0.35/0.61  thf(fact_4558_list__decode_Ocases,axiom,
% 0.35/0.61      ! [X: nat] :
% 0.35/0.61        ( ( X != zero_zero_nat )
% 0.35/0.61       => ~ ! [N3: nat] :
% 0.35/0.61              ( X
% 0.35/0.61             != ( suc @ N3 ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % list_decode.cases
% 0.35/0.61  thf(fact_4559_Euclid__induct,axiom,
% 0.35/0.61      ! [P: nat > nat > $o,A: nat,B: nat] :
% 0.35/0.61        ( ! [A4: nat,B3: nat] :
% 0.35/0.61            ( ( P @ A4 @ B3 )
% 0.35/0.61            = ( P @ B3 @ A4 ) )
% 0.35/0.61       => ( ! [A4: nat] : ( P @ A4 @ zero_zero_nat )
% 0.35/0.61         => ( ! [A4: nat,B3: nat] :
% 0.35/0.61                ( ( P @ A4 @ B3 )
% 0.35/0.61               => ( P @ A4 @ ( plus_plus_nat @ A4 @ B3 ) ) )
% 0.35/0.61           => ( P @ A @ B ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % Euclid_induct
% 0.35/0.61  thf(fact_4560_zero__less__power__eq,axiom,
% 0.35/0.61      ! [A: real,N: nat] :
% 0.35/0.61        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 0.35/0.61        = ( ( N = zero_zero_nat )
% 0.35/0.61          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61            & ( A != zero_zero_real ) )
% 0.35/0.61          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61            & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % zero_less_power_eq
% 0.35/0.61  thf(fact_4561_zero__less__power__eq,axiom,
% 0.35/0.61      ! [A: rat,N: nat] :
% 0.35/0.61        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 0.35/0.61        = ( ( N = zero_zero_nat )
% 0.35/0.61          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61            & ( A != zero_zero_rat ) )
% 0.35/0.61          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61            & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % zero_less_power_eq
% 0.35/0.61  thf(fact_4562_zero__less__power__eq,axiom,
% 0.35/0.61      ! [A: int,N: nat] :
% 0.35/0.61        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 0.35/0.61        = ( ( N = zero_zero_nat )
% 0.35/0.61          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61            & ( A != zero_zero_int ) )
% 0.35/0.61          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61            & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % zero_less_power_eq
% 0.35/0.61  thf(fact_4563_even__mask__div__iff_H,axiom,
% 0.35/0.61      ! [M: nat,N: nat] :
% 0.35/0.61        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.61        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.35/0.61  
% 0.35/0.61  % even_mask_div_iff'
% 0.35/0.61  thf(fact_4564_even__mask__div__iff_H,axiom,
% 0.35/0.61      ! [M: nat,N: nat] :
% 0.35/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.61        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.35/0.61  
% 0.35/0.61  % even_mask_div_iff'
% 0.35/0.61  thf(fact_4565_even__mask__div__iff_H,axiom,
% 0.35/0.61      ! [M: nat,N: nat] :
% 0.35/0.61        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.61        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.35/0.61  
% 0.35/0.61  % even_mask_div_iff'
% 0.35/0.61  thf(fact_4566_power__le__zero__eq,axiom,
% 0.35/0.61      ! [A: rat,N: nat] :
% 0.35/0.61        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 0.35/0.61        = ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.61          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61              & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 0.35/0.61            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61              & ( A = zero_zero_rat ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % power_le_zero_eq
% 0.35/0.61  thf(fact_4567_power__le__zero__eq,axiom,
% 0.35/0.61      ! [A: real,N: nat] :
% 0.35/0.61        ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 0.35/0.61        = ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.61          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61              & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 0.35/0.61            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61              & ( A = zero_zero_real ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % power_le_zero_eq
% 0.35/0.61  thf(fact_4568_power__le__zero__eq,axiom,
% 0.35/0.61      ! [A: int,N: nat] :
% 0.35/0.61        ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 0.35/0.61        = ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.61          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61              & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 0.35/0.61            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61              & ( A = zero_zero_int ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % power_le_zero_eq
% 0.35/0.61  thf(fact_4569_even__mod__4__div__2,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.35/0.61          = ( suc @ zero_zero_nat ) )
% 0.35/0.61       => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % even_mod_4_div_2
% 0.35/0.61  thf(fact_4570_divmod__step__nat__def,axiom,
% 0.35/0.61      ( unique5026877609467782581ep_nat
% 0.35/0.61      = ( ^ [L: num] :
% 0.35/0.61            ( produc2626176000494625587at_nat
% 0.35/0.61            @ ^ [Q4: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R5 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ one_one_nat ) @ ( minus_minus_nat @ R5 @ ( numeral_numeral_nat @ L ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % divmod_step_nat_def
% 0.35/0.61  thf(fact_4571_even__mask__div__iff,axiom,
% 0.35/0.61      ! [M: nat,N: nat] :
% 0.35/0.61        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.61        = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 0.35/0.61            = zero_z3403309356797280102nteger )
% 0.35/0.61          | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % even_mask_div_iff
% 0.35/0.61  thf(fact_4572_even__mask__div__iff,axiom,
% 0.35/0.61      ! [M: nat,N: nat] :
% 0.35/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.61        = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61            = zero_zero_nat )
% 0.35/0.61          | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % even_mask_div_iff
% 0.35/0.61  thf(fact_4573_even__mask__div__iff,axiom,
% 0.35/0.61      ! [M: nat,N: nat] :
% 0.35/0.61        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.61        = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 0.35/0.61            = zero_zero_int )
% 0.35/0.61          | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % even_mask_div_iff
% 0.35/0.61  thf(fact_4574_divmod__step__int__def,axiom,
% 0.35/0.61      ( unique5024387138958732305ep_int
% 0.35/0.61      = ( ^ [L: num] :
% 0.35/0.61            ( produc4245557441103728435nt_int
% 0.35/0.61            @ ^ [Q4: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R5 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ one_one_int ) @ ( minus_minus_int @ R5 @ ( numeral_numeral_int @ L ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % divmod_step_int_def
% 0.35/0.61  thf(fact_4575_odd__mod__4__div__2,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.35/0.61          = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.35/0.61       => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % odd_mod_4_div_2
% 0.35/0.61  thf(fact_4576_even__mult__exp__div__exp__iff,axiom,
% 0.35/0.61      ! [A: code_integer,M: nat,N: nat] :
% 0.35/0.61        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.61        = ( ( ord_less_nat @ N @ M )
% 0.35/0.61          | ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 0.35/0.61            = zero_z3403309356797280102nteger )
% 0.35/0.61          | ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.61            & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % even_mult_exp_div_exp_iff
% 0.35/0.61  thf(fact_4577_even__mult__exp__div__exp__iff,axiom,
% 0.35/0.61      ! [A: nat,M: nat,N: nat] :
% 0.35/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.61        = ( ( ord_less_nat @ N @ M )
% 0.35/0.61          | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61            = zero_zero_nat )
% 0.35/0.61          | ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.61            & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % even_mult_exp_div_exp_iff
% 0.35/0.61  thf(fact_4578_even__mult__exp__div__exp__iff,axiom,
% 0.35/0.61      ! [A: int,M: nat,N: nat] :
% 0.35/0.61        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.61        = ( ( ord_less_nat @ N @ M )
% 0.35/0.61          | ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 0.35/0.61            = zero_zero_int )
% 0.35/0.61          | ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.61            & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % even_mult_exp_div_exp_iff
% 0.35/0.61  thf(fact_4579_divmod__step__def,axiom,
% 0.35/0.61      ( unique5026877609467782581ep_nat
% 0.35/0.61      = ( ^ [L: num] :
% 0.35/0.61            ( produc2626176000494625587at_nat
% 0.35/0.61            @ ^ [Q4: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R5 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ one_one_nat ) @ ( minus_minus_nat @ R5 @ ( numeral_numeral_nat @ L ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % divmod_step_def
% 0.35/0.61  thf(fact_4580_divmod__step__def,axiom,
% 0.35/0.61      ( unique5024387138958732305ep_int
% 0.35/0.61      = ( ^ [L: num] :
% 0.35/0.61            ( produc4245557441103728435nt_int
% 0.35/0.61            @ ^ [Q4: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R5 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ one_one_int ) @ ( minus_minus_int @ R5 @ ( numeral_numeral_int @ L ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % divmod_step_def
% 0.35/0.61  thf(fact_4581_divmod__step__def,axiom,
% 0.35/0.61      ( unique4921790084139445826nteger
% 0.35/0.61      = ( ^ [L: num] :
% 0.35/0.61            ( produc6916734918728496179nteger
% 0.35/0.61            @ ^ [Q4: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % divmod_step_def
% 0.35/0.61  thf(fact_4582_set__encode__insert,axiom,
% 0.35/0.61      ! [A2: set_nat,N: nat] :
% 0.35/0.61        ( ( finite_finite_nat @ A2 )
% 0.35/0.61       => ( ~ ( member_nat @ N @ A2 )
% 0.35/0.61         => ( ( nat_set_encode @ ( insert_nat @ N @ A2 ) )
% 0.35/0.61            = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( nat_set_encode @ A2 ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % set_encode_insert
% 0.35/0.61  thf(fact_4583_triangle__def,axiom,
% 0.35/0.61      ( nat_triangle
% 0.35/0.61      = ( ^ [N2: nat] : ( divide_divide_nat @ ( times_times_nat @ N2 @ ( suc @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % triangle_def
% 0.35/0.61  thf(fact_4584_vebt__buildup_Oelims,axiom,
% 0.35/0.61      ! [X: nat,Y2: vEBT_VEBT] :
% 0.35/0.61        ( ( ( vEBT_vebt_buildup @ X )
% 0.35/0.61          = Y2 )
% 0.35/0.61       => ( ( ( X = zero_zero_nat )
% 0.35/0.61           => ( Y2
% 0.35/0.61             != ( vEBT_Leaf @ $false @ $false ) ) )
% 0.35/0.61         => ( ( ( X
% 0.35/0.61                = ( suc @ zero_zero_nat ) )
% 0.35/0.61             => ( Y2
% 0.35/0.61               != ( vEBT_Leaf @ $false @ $false ) ) )
% 0.35/0.61           => ~ ! [Va2: nat] :
% 0.35/0.61                  ( ( X
% 0.35/0.61                    = ( suc @ ( suc @ Va2 ) ) )
% 0.35/0.61                 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 0.35/0.61                       => ( Y2
% 0.35/0.61                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.35/0.61                      & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 0.35/0.61                       => ( Y2
% 0.35/0.61                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % vebt_buildup.elims
% 0.35/0.61  thf(fact_4585_divmod__nat__if,axiom,
% 0.35/0.61      ( divmod_nat
% 0.35/0.61      = ( ^ [M6: nat,N2: nat] :
% 0.35/0.61            ( if_Pro6206227464963214023at_nat
% 0.35/0.61            @ ( ( N2 = zero_zero_nat )
% 0.35/0.61              | ( ord_less_nat @ M6 @ N2 ) )
% 0.35/0.61            @ ( product_Pair_nat_nat @ zero_zero_nat @ M6 )
% 0.35/0.61            @ ( produc2626176000494625587at_nat
% 0.35/0.61              @ ^ [Q4: nat] : ( product_Pair_nat_nat @ ( suc @ Q4 ) )
% 0.35/0.61              @ ( divmod_nat @ ( minus_minus_nat @ M6 @ N2 ) @ N2 ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % divmod_nat_if
% 0.35/0.61  thf(fact_4586_flip__bit__0,axiom,
% 0.35/0.61      ! [A: code_integer] :
% 0.35/0.61        ( ( bit_se1345352211410354436nteger @ zero_zero_nat @ A )
% 0.35/0.61        = ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % flip_bit_0
% 0.35/0.61  thf(fact_4587_flip__bit__0,axiom,
% 0.35/0.61      ! [A: int] :
% 0.35/0.61        ( ( bit_se2159334234014336723it_int @ zero_zero_nat @ A )
% 0.35/0.61        = ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % flip_bit_0
% 0.35/0.61  thf(fact_4588_flip__bit__0,axiom,
% 0.35/0.61      ! [A: nat] :
% 0.35/0.61        ( ( bit_se2161824704523386999it_nat @ zero_zero_nat @ A )
% 0.35/0.61        = ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % flip_bit_0
% 0.35/0.61  thf(fact_4589_signed__take__bit__Suc,axiom,
% 0.35/0.61      ! [N: nat,A: int] :
% 0.35/0.61        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ A )
% 0.35/0.61        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % signed_take_bit_Suc
% 0.35/0.61  thf(fact_4590_option_Osize__gen_I2_J,axiom,
% 0.35/0.61      ! [X: product_prod_nat_nat > nat,X23: product_prod_nat_nat] :
% 0.35/0.61        ( ( size_o8335143837870341156at_nat @ X @ ( some_P7363390416028606310at_nat @ X23 ) )
% 0.35/0.61        = ( plus_plus_nat @ ( X @ X23 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % option.size_gen(2)
% 0.35/0.61  thf(fact_4591_option_Osize__gen_I2_J,axiom,
% 0.35/0.61      ! [X: nat > nat,X23: nat] :
% 0.35/0.61        ( ( size_option_nat @ X @ ( some_nat @ X23 ) )
% 0.35/0.61        = ( plus_plus_nat @ ( X @ X23 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % option.size_gen(2)
% 0.35/0.61  thf(fact_4592_option_Osize__gen_I2_J,axiom,
% 0.35/0.61      ! [X: num > nat,X23: num] :
% 0.35/0.61        ( ( size_option_num @ X @ ( some_num @ X23 ) )
% 0.35/0.61        = ( plus_plus_nat @ ( X @ X23 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % option.size_gen(2)
% 0.35/0.61  thf(fact_4593_intind,axiom,
% 0.35/0.61      ! [I2: nat,N: nat,P: nat > $o,X: nat] :
% 0.35/0.61        ( ( ord_less_nat @ I2 @ N )
% 0.35/0.61       => ( ( P @ X )
% 0.35/0.61         => ( P @ ( nth_nat @ ( replicate_nat @ N @ X ) @ I2 ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % intind
% 0.35/0.61  thf(fact_4594_intind,axiom,
% 0.35/0.61      ! [I2: nat,N: nat,P: vEBT_VEBT > $o,X: vEBT_VEBT] :
% 0.35/0.61        ( ( ord_less_nat @ I2 @ N )
% 0.35/0.61       => ( ( P @ X )
% 0.35/0.61         => ( P @ ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X ) @ I2 ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % intind
% 0.35/0.61  thf(fact_4595_case__prodI,axiom,
% 0.35/0.61      ! [F: product_prod_nat_nat > product_prod_nat_nat > $o,A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 0.35/0.61        ( ( F @ A @ B )
% 0.35/0.61       => ( produc6590410687421337004_nat_o @ F @ ( produc6161850002892822231at_nat @ A @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % case_prodI
% 0.35/0.61  thf(fact_4596_case__prodI,axiom,
% 0.35/0.61      ! [F: num > num > $o,A: num,B: num] :
% 0.35/0.61        ( ( F @ A @ B )
% 0.35/0.61       => ( produc5703948589228662326_num_o @ F @ ( product_Pair_num_num @ A @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % case_prodI
% 0.35/0.61  thf(fact_4597_case__prodI,axiom,
% 0.35/0.61      ! [F: nat > num > $o,A: nat,B: num] :
% 0.35/0.61        ( ( F @ A @ B )
% 0.35/0.61       => ( produc4927758841916487424_num_o @ F @ ( product_Pair_nat_num @ A @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % case_prodI
% 0.35/0.61  thf(fact_4598_case__prodI,axiom,
% 0.35/0.61      ! [F: nat > nat > $o,A: nat,B: nat] :
% 0.35/0.61        ( ( F @ A @ B )
% 0.35/0.61       => ( produc6081775807080527818_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % case_prodI
% 0.35/0.61  thf(fact_4599_case__prodI,axiom,
% 0.35/0.61      ! [F: int > int > $o,A: int,B: int] :
% 0.35/0.61        ( ( F @ A @ B )
% 0.35/0.61       => ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % case_prodI
% 0.35/0.61  thf(fact_4600_case__prodI2,axiom,
% 0.35/0.61      ! [P6: produc859450856879609959at_nat,C: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 0.35/0.61        ( ! [A4: product_prod_nat_nat,B3: product_prod_nat_nat] :
% 0.35/0.61            ( ( P6
% 0.35/0.61              = ( produc6161850002892822231at_nat @ A4 @ B3 ) )
% 0.35/0.61           => ( C @ A4 @ B3 ) )
% 0.35/0.61       => ( produc6590410687421337004_nat_o @ C @ P6 ) ) ).
% 0.35/0.61  
% 0.35/0.61  % case_prodI2
% 0.35/0.61  thf(fact_4601_case__prodI2,axiom,
% 0.35/0.61      ! [P6: product_prod_num_num,C: num > num > $o] :
% 0.35/0.61        ( ! [A4: num,B3: num] :
% 0.35/0.61            ( ( P6
% 0.35/0.61              = ( product_Pair_num_num @ A4 @ B3 ) )
% 0.35/0.61           => ( C @ A4 @ B3 ) )
% 0.35/0.61       => ( produc5703948589228662326_num_o @ C @ P6 ) ) ).
% 0.35/0.61  
% 0.35/0.61  % case_prodI2
% 0.35/0.61  thf(fact_4602_case__prodI2,axiom,
% 0.35/0.61      ! [P6: product_prod_nat_num,C: nat > num > $o] :
% 0.35/0.61        ( ! [A4: nat,B3: num] :
% 0.35/0.61            ( ( P6
% 0.35/0.61              = ( product_Pair_nat_num @ A4 @ B3 ) )
% 0.35/0.61           => ( C @ A4 @ B3 ) )
% 0.35/0.61       => ( produc4927758841916487424_num_o @ C @ P6 ) ) ).
% 0.35/0.61  
% 0.35/0.61  % case_prodI2
% 0.35/0.61  thf(fact_4603_case__prodI2,axiom,
% 0.35/0.61      ! [P6: product_prod_nat_nat,C: nat > nat > $o] :
% 0.35/0.61        ( ! [A4: nat,B3: nat] :
% 0.35/0.61            ( ( P6
% 0.35/0.61              = ( product_Pair_nat_nat @ A4 @ B3 ) )
% 0.35/0.61           => ( C @ A4 @ B3 ) )
% 0.35/0.61       => ( produc6081775807080527818_nat_o @ C @ P6 ) ) ).
% 0.35/0.61  
% 0.35/0.61  % case_prodI2
% 0.35/0.61  thf(fact_4604_case__prodI2,axiom,
% 0.35/0.61      ! [P6: product_prod_int_int,C: int > int > $o] :
% 0.35/0.61        ( ! [A4: int,B3: int] :
% 0.35/0.61            ( ( P6
% 0.35/0.61              = ( product_Pair_int_int @ A4 @ B3 ) )
% 0.35/0.61           => ( C @ A4 @ B3 ) )
% 0.35/0.61       => ( produc4947309494688390418_int_o @ C @ P6 ) ) ).
% 0.35/0.61  
% 0.35/0.61  % case_prodI2
% 0.35/0.61  thf(fact_4605_mem__case__prodI,axiom,
% 0.35/0.61      ! [Z: complex,C: num > num > set_complex,A: num,B: num] :
% 0.35/0.61        ( ( member_complex @ Z @ ( C @ A @ B ) )
% 0.35/0.61       => ( member_complex @ Z @ ( produc2866383454006189126omplex @ C @ ( product_Pair_num_num @ A @ B ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mem_case_prodI
% 0.35/0.61  thf(fact_4606_mem__case__prodI,axiom,
% 0.35/0.61      ! [Z: real,C: num > num > set_real,A: num,B: num] :
% 0.35/0.61        ( ( member_real @ Z @ ( C @ A @ B ) )
% 0.35/0.61       => ( member_real @ Z @ ( produc8296048397933160132t_real @ C @ ( product_Pair_num_num @ A @ B ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mem_case_prodI
% 0.35/0.61  thf(fact_4607_mem__case__prodI,axiom,
% 0.35/0.61      ! [Z: nat,C: num > num > set_nat,A: num,B: num] :
% 0.35/0.61        ( ( member_nat @ Z @ ( C @ A @ B ) )
% 0.35/0.61       => ( member_nat @ Z @ ( produc1361121860356118632et_nat @ C @ ( product_Pair_num_num @ A @ B ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mem_case_prodI
% 0.35/0.61  thf(fact_4608_mem__case__prodI,axiom,
% 0.35/0.61      ! [Z: int,C: num > num > set_int,A: num,B: num] :
% 0.35/0.61        ( ( member_int @ Z @ ( C @ A @ B ) )
% 0.35/0.61       => ( member_int @ Z @ ( produc6406642877701697732et_int @ C @ ( product_Pair_num_num @ A @ B ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mem_case_prodI
% 0.35/0.61  thf(fact_4609_mem__case__prodI,axiom,
% 0.35/0.61      ! [Z: complex,C: nat > num > set_complex,A: nat,B: num] :
% 0.35/0.61        ( ( member_complex @ Z @ ( C @ A @ B ) )
% 0.35/0.61       => ( member_complex @ Z @ ( produc6231982587499038204omplex @ C @ ( product_Pair_nat_num @ A @ B ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mem_case_prodI
% 0.35/0.61  thf(fact_4610_mem__case__prodI,axiom,
% 0.35/0.61      ! [Z: real,C: nat > num > set_real,A: nat,B: num] :
% 0.35/0.61        ( ( member_real @ Z @ ( C @ A @ B ) )
% 0.35/0.61       => ( member_real @ Z @ ( produc1435849484188172666t_real @ C @ ( product_Pair_nat_num @ A @ B ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mem_case_prodI
% 0.35/0.61  thf(fact_4611_mem__case__prodI,axiom,
% 0.35/0.61      ! [Z: nat,C: nat > num > set_nat,A: nat,B: num] :
% 0.35/0.61        ( ( member_nat @ Z @ ( C @ A @ B ) )
% 0.35/0.61       => ( member_nat @ Z @ ( produc4130284055270567454et_nat @ C @ ( product_Pair_nat_num @ A @ B ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mem_case_prodI
% 0.35/0.61  thf(fact_4612_mem__case__prodI,axiom,
% 0.35/0.61      ! [Z: int,C: nat > num > set_int,A: nat,B: num] :
% 0.35/0.61        ( ( member_int @ Z @ ( C @ A @ B ) )
% 0.35/0.61       => ( member_int @ Z @ ( produc9175805072616146554et_int @ C @ ( product_Pair_nat_num @ A @ B ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mem_case_prodI
% 0.35/0.61  thf(fact_4613_mem__case__prodI,axiom,
% 0.35/0.61      ! [Z: complex,C: nat > nat > set_complex,A: nat,B: nat] :
% 0.35/0.61        ( ( member_complex @ Z @ ( C @ A @ B ) )
% 0.35/0.61       => ( member_complex @ Z @ ( produc3453488052772718514omplex @ C @ ( product_Pair_nat_nat @ A @ B ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mem_case_prodI
% 0.35/0.61  thf(fact_4614_mem__case__prodI,axiom,
% 0.35/0.61      ! [Z: real,C: nat > nat > set_real,A: nat,B: nat] :
% 0.35/0.61        ( ( member_real @ Z @ ( C @ A @ B ) )
% 0.35/0.61       => ( member_real @ Z @ ( produc3668448655016342576t_real @ C @ ( product_Pair_nat_nat @ A @ B ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mem_case_prodI
% 0.35/0.61  thf(fact_4615_mem__case__prodI2,axiom,
% 0.35/0.61      ! [P6: product_prod_num_num,Z: complex,C: num > num > set_complex] :
% 0.35/0.61        ( ! [A4: num,B3: num] :
% 0.35/0.61            ( ( P6
% 0.35/0.61              = ( product_Pair_num_num @ A4 @ B3 ) )
% 0.35/0.61           => ( member_complex @ Z @ ( C @ A4 @ B3 ) ) )
% 0.35/0.61       => ( member_complex @ Z @ ( produc2866383454006189126omplex @ C @ P6 ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mem_case_prodI2
% 0.35/0.61  thf(fact_4616_mem__case__prodI2,axiom,
% 0.35/0.61      ! [P6: product_prod_num_num,Z: real,C: num > num > set_real] :
% 0.35/0.61        ( ! [A4: num,B3: num] :
% 0.35/0.61            ( ( P6
% 0.35/0.61              = ( product_Pair_num_num @ A4 @ B3 ) )
% 0.35/0.61           => ( member_real @ Z @ ( C @ A4 @ B3 ) ) )
% 0.35/0.61       => ( member_real @ Z @ ( produc8296048397933160132t_real @ C @ P6 ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mem_case_prodI2
% 0.35/0.61  thf(fact_4617_mem__case__prodI2,axiom,
% 0.35/0.61      ! [P6: product_prod_num_num,Z: nat,C: num > num > set_nat] :
% 0.35/0.61        ( ! [A4: num,B3: num] :
% 0.35/0.61            ( ( P6
% 0.35/0.61              = ( product_Pair_num_num @ A4 @ B3 ) )
% 0.35/0.61           => ( member_nat @ Z @ ( C @ A4 @ B3 ) ) )
% 0.35/0.61       => ( member_nat @ Z @ ( produc1361121860356118632et_nat @ C @ P6 ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mem_case_prodI2
% 0.35/0.61  thf(fact_4618_mem__case__prodI2,axiom,
% 0.35/0.61      ! [P6: product_prod_num_num,Z: int,C: num > num > set_int] :
% 0.35/0.61        ( ! [A4: num,B3: num] :
% 0.35/0.61            ( ( P6
% 0.35/0.61              = ( product_Pair_num_num @ A4 @ B3 ) )
% 0.35/0.61           => ( member_int @ Z @ ( C @ A4 @ B3 ) ) )
% 0.35/0.61       => ( member_int @ Z @ ( produc6406642877701697732et_int @ C @ P6 ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mem_case_prodI2
% 0.35/0.61  thf(fact_4619_mem__case__prodI2,axiom,
% 0.35/0.61      ! [P6: product_prod_nat_num,Z: complex,C: nat > num > set_complex] :
% 0.35/0.61        ( ! [A4: nat,B3: num] :
% 0.35/0.61            ( ( P6
% 0.35/0.61              = ( product_Pair_nat_num @ A4 @ B3 ) )
% 0.35/0.61           => ( member_complex @ Z @ ( C @ A4 @ B3 ) ) )
% 0.35/0.61       => ( member_complex @ Z @ ( produc6231982587499038204omplex @ C @ P6 ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mem_case_prodI2
% 0.35/0.61  thf(fact_4620_mem__case__prodI2,axiom,
% 0.35/0.61      ! [P6: product_prod_nat_num,Z: real,C: nat > num > set_real] :
% 0.35/0.61        ( ! [A4: nat,B3: num] :
% 0.35/0.61            ( ( P6
% 0.35/0.61              = ( product_Pair_nat_num @ A4 @ B3 ) )
% 0.35/0.61           => ( member_real @ Z @ ( C @ A4 @ B3 ) ) )
% 0.35/0.61       => ( member_real @ Z @ ( produc1435849484188172666t_real @ C @ P6 ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mem_case_prodI2
% 0.35/0.61  thf(fact_4621_mem__case__prodI2,axiom,
% 0.35/0.61      ! [P6: product_prod_nat_num,Z: nat,C: nat > num > set_nat] :
% 0.35/0.61        ( ! [A4: nat,B3: num] :
% 0.35/0.61            ( ( P6
% 0.35/0.61              = ( product_Pair_nat_num @ A4 @ B3 ) )
% 0.35/0.61           => ( member_nat @ Z @ ( C @ A4 @ B3 ) ) )
% 0.35/0.61       => ( member_nat @ Z @ ( produc4130284055270567454et_nat @ C @ P6 ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mem_case_prodI2
% 0.35/0.61  thf(fact_4622_mem__case__prodI2,axiom,
% 0.35/0.61      ! [P6: product_prod_nat_num,Z: int,C: nat > num > set_int] :
% 0.35/0.61        ( ! [A4: nat,B3: num] :
% 0.35/0.61            ( ( P6
% 0.35/0.61              = ( product_Pair_nat_num @ A4 @ B3 ) )
% 0.35/0.61           => ( member_int @ Z @ ( C @ A4 @ B3 ) ) )
% 0.35/0.61       => ( member_int @ Z @ ( produc9175805072616146554et_int @ C @ P6 ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mem_case_prodI2
% 0.35/0.61  thf(fact_4623_mem__case__prodI2,axiom,
% 0.35/0.61      ! [P6: product_prod_nat_nat,Z: complex,C: nat > nat > set_complex] :
% 0.35/0.61        ( ! [A4: nat,B3: nat] :
% 0.35/0.61            ( ( P6
% 0.35/0.61              = ( product_Pair_nat_nat @ A4 @ B3 ) )
% 0.35/0.61           => ( member_complex @ Z @ ( C @ A4 @ B3 ) ) )
% 0.35/0.61       => ( member_complex @ Z @ ( produc3453488052772718514omplex @ C @ P6 ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mem_case_prodI2
% 0.35/0.61  thf(fact_4624_mem__case__prodI2,axiom,
% 0.35/0.61      ! [P6: product_prod_nat_nat,Z: real,C: nat > nat > set_real] :
% 0.35/0.61        ( ! [A4: nat,B3: nat] :
% 0.35/0.61            ( ( P6
% 0.35/0.61              = ( product_Pair_nat_nat @ A4 @ B3 ) )
% 0.35/0.61           => ( member_real @ Z @ ( C @ A4 @ B3 ) ) )
% 0.35/0.61       => ( member_real @ Z @ ( produc3668448655016342576t_real @ C @ P6 ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mem_case_prodI2
% 0.35/0.61  thf(fact_4625_case__prodI2_H,axiom,
% 0.35/0.61      ! [P6: product_prod_nat_nat,C: nat > nat > product_prod_nat_nat > $o,X: product_prod_nat_nat] :
% 0.35/0.61        ( ! [A4: nat,B3: nat] :
% 0.35/0.61            ( ( ( product_Pair_nat_nat @ A4 @ B3 )
% 0.35/0.61              = P6 )
% 0.35/0.61           => ( C @ A4 @ B3 @ X ) )
% 0.35/0.61       => ( produc8739625826339149834_nat_o @ C @ P6 @ X ) ) ).
% 0.35/0.61  
% 0.35/0.61  % case_prodI2'
% 0.35/0.61  thf(fact_4626_of__bool__less__eq__iff,axiom,
% 0.35/0.61      ! [P: $o,Q: $o] :
% 0.35/0.61        ( ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 0.35/0.61        = ( P
% 0.35/0.61         => Q ) ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_less_eq_iff
% 0.35/0.61  thf(fact_4627_of__bool__less__eq__iff,axiom,
% 0.35/0.61      ! [P: $o,Q: $o] :
% 0.35/0.61        ( ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 0.35/0.61        = ( P
% 0.35/0.61         => Q ) ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_less_eq_iff
% 0.35/0.61  thf(fact_4628_of__bool__less__eq__iff,axiom,
% 0.35/0.61      ! [P: $o,Q: $o] :
% 0.35/0.61        ( ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 0.35/0.61        = ( P
% 0.35/0.61         => Q ) ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_less_eq_iff
% 0.35/0.61  thf(fact_4629_of__bool__less__iff,axiom,
% 0.35/0.61      ! [P: $o,Q: $o] :
% 0.35/0.61        ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) )
% 0.35/0.61        = ( ~ P
% 0.35/0.61          & Q ) ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_less_iff
% 0.35/0.61  thf(fact_4630_of__bool__less__iff,axiom,
% 0.35/0.61      ! [P: $o,Q: $o] :
% 0.35/0.61        ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 0.35/0.61        = ( ~ P
% 0.35/0.61          & Q ) ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_less_iff
% 0.35/0.61  thf(fact_4631_of__bool__less__iff,axiom,
% 0.35/0.61      ! [P: $o,Q: $o] :
% 0.35/0.61        ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 0.35/0.61        = ( ~ P
% 0.35/0.61          & Q ) ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_less_iff
% 0.35/0.61  thf(fact_4632_of__bool__less__iff,axiom,
% 0.35/0.61      ! [P: $o,Q: $o] :
% 0.35/0.61        ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 0.35/0.61        = ( ~ P
% 0.35/0.61          & Q ) ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_less_iff
% 0.35/0.61  thf(fact_4633_of__bool__less__iff,axiom,
% 0.35/0.61      ! [P: $o,Q: $o] :
% 0.35/0.61        ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 0.35/0.61        = ( ~ P
% 0.35/0.61          & Q ) ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_less_iff
% 0.35/0.61  thf(fact_4634_of__bool__eq_I2_J,axiom,
% 0.35/0.61      ( ( zero_n1201886186963655149omplex @ $true )
% 0.35/0.61      = one_one_complex ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_eq(2)
% 0.35/0.61  thf(fact_4635_of__bool__eq_I2_J,axiom,
% 0.35/0.61      ( ( zero_n3304061248610475627l_real @ $true )
% 0.35/0.61      = one_one_real ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_eq(2)
% 0.35/0.61  thf(fact_4636_of__bool__eq_I2_J,axiom,
% 0.35/0.61      ( ( zero_n2052037380579107095ol_rat @ $true )
% 0.35/0.61      = one_one_rat ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_eq(2)
% 0.35/0.61  thf(fact_4637_of__bool__eq_I2_J,axiom,
% 0.35/0.61      ( ( zero_n2687167440665602831ol_nat @ $true )
% 0.35/0.61      = one_one_nat ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_eq(2)
% 0.35/0.61  thf(fact_4638_of__bool__eq_I2_J,axiom,
% 0.35/0.61      ( ( zero_n2684676970156552555ol_int @ $true )
% 0.35/0.61      = one_one_int ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_eq(2)
% 0.35/0.61  thf(fact_4639_of__bool__eq_I2_J,axiom,
% 0.35/0.61      ( ( zero_n356916108424825756nteger @ $true )
% 0.35/0.61      = one_one_Code_integer ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_eq(2)
% 0.35/0.61  thf(fact_4640_of__bool__eq__1__iff,axiom,
% 0.35/0.61      ! [P: $o] :
% 0.35/0.61        ( ( ( zero_n1201886186963655149omplex @ P )
% 0.35/0.61          = one_one_complex )
% 0.35/0.61        = P ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_eq_1_iff
% 0.35/0.61  thf(fact_4641_of__bool__eq__1__iff,axiom,
% 0.35/0.61      ! [P: $o] :
% 0.35/0.61        ( ( ( zero_n3304061248610475627l_real @ P )
% 0.35/0.61          = one_one_real )
% 0.35/0.61        = P ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_eq_1_iff
% 0.35/0.61  thf(fact_4642_of__bool__eq__1__iff,axiom,
% 0.35/0.61      ! [P: $o] :
% 0.35/0.61        ( ( ( zero_n2052037380579107095ol_rat @ P )
% 0.35/0.61          = one_one_rat )
% 0.35/0.61        = P ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_eq_1_iff
% 0.35/0.61  thf(fact_4643_of__bool__eq__1__iff,axiom,
% 0.35/0.61      ! [P: $o] :
% 0.35/0.61        ( ( ( zero_n2687167440665602831ol_nat @ P )
% 0.35/0.61          = one_one_nat )
% 0.35/0.61        = P ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_eq_1_iff
% 0.35/0.61  thf(fact_4644_of__bool__eq__1__iff,axiom,
% 0.35/0.61      ! [P: $o] :
% 0.35/0.61        ( ( ( zero_n2684676970156552555ol_int @ P )
% 0.35/0.61          = one_one_int )
% 0.35/0.61        = P ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_eq_1_iff
% 0.35/0.61  thf(fact_4645_of__bool__eq__1__iff,axiom,
% 0.35/0.61      ! [P: $o] :
% 0.35/0.61        ( ( ( zero_n356916108424825756nteger @ P )
% 0.35/0.61          = one_one_Code_integer )
% 0.35/0.61        = P ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_eq_1_iff
% 0.35/0.61  thf(fact_4646_signed__take__bit__of__0,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ( bit_ri631733984087533419it_int @ N @ zero_zero_int )
% 0.35/0.61        = zero_zero_int ) ).
% 0.35/0.61  
% 0.35/0.61  % signed_take_bit_of_0
% 0.35/0.61  thf(fact_4647_length__replicate,axiom,
% 0.35/0.61      ! [N: nat,X: vEBT_VEBT] :
% 0.35/0.61        ( ( size_s6755466524823107622T_VEBT @ ( replicate_VEBT_VEBT @ N @ X ) )
% 0.35/0.61        = N ) ).
% 0.35/0.61  
% 0.35/0.61  % length_replicate
% 0.35/0.61  thf(fact_4648_length__replicate,axiom,
% 0.35/0.61      ! [N: nat,X: $o] :
% 0.35/0.61        ( ( size_size_list_o @ ( replicate_o @ N @ X ) )
% 0.35/0.61        = N ) ).
% 0.35/0.61  
% 0.35/0.61  % length_replicate
% 0.35/0.61  thf(fact_4649_length__replicate,axiom,
% 0.35/0.61      ! [N: nat,X: nat] :
% 0.35/0.61        ( ( size_size_list_nat @ ( replicate_nat @ N @ X ) )
% 0.35/0.61        = N ) ).
% 0.35/0.61  
% 0.35/0.61  % length_replicate
% 0.35/0.61  thf(fact_4650_length__replicate,axiom,
% 0.35/0.61      ! [N: nat,X: int] :
% 0.35/0.61        ( ( size_size_list_int @ ( replicate_int @ N @ X ) )
% 0.35/0.61        = N ) ).
% 0.35/0.61  
% 0.35/0.61  % length_replicate
% 0.35/0.61  thf(fact_4651_zero__less__of__bool__iff,axiom,
% 0.35/0.61      ! [P: $o] :
% 0.35/0.61        ( ( ord_less_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) )
% 0.35/0.61        = P ) ).
% 0.35/0.61  
% 0.35/0.61  % zero_less_of_bool_iff
% 0.35/0.61  thf(fact_4652_zero__less__of__bool__iff,axiom,
% 0.35/0.61      ! [P: $o] :
% 0.35/0.61        ( ( ord_less_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 0.35/0.61        = P ) ).
% 0.35/0.61  
% 0.35/0.61  % zero_less_of_bool_iff
% 0.35/0.61  thf(fact_4653_zero__less__of__bool__iff,axiom,
% 0.35/0.61      ! [P: $o] :
% 0.35/0.61        ( ( ord_less_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 0.35/0.61        = P ) ).
% 0.35/0.61  
% 0.35/0.61  % zero_less_of_bool_iff
% 0.35/0.61  thf(fact_4654_zero__less__of__bool__iff,axiom,
% 0.35/0.61      ! [P: $o] :
% 0.35/0.61        ( ( ord_less_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 0.35/0.61        = P ) ).
% 0.35/0.61  
% 0.35/0.61  % zero_less_of_bool_iff
% 0.35/0.61  thf(fact_4655_zero__less__of__bool__iff,axiom,
% 0.35/0.61      ! [P: $o] :
% 0.35/0.61        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) )
% 0.35/0.61        = P ) ).
% 0.35/0.61  
% 0.35/0.61  % zero_less_of_bool_iff
% 0.35/0.61  thf(fact_4656_of__bool__less__one__iff,axiom,
% 0.35/0.61      ! [P: $o] :
% 0.35/0.61        ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real )
% 0.35/0.61        = ( ~ P ) ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_less_one_iff
% 0.35/0.61  thf(fact_4657_of__bool__less__one__iff,axiom,
% 0.35/0.61      ! [P: $o] :
% 0.35/0.61        ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat )
% 0.35/0.61        = ( ~ P ) ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_less_one_iff
% 0.35/0.61  thf(fact_4658_of__bool__less__one__iff,axiom,
% 0.35/0.61      ! [P: $o] :
% 0.35/0.61        ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat )
% 0.35/0.61        = ( ~ P ) ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_less_one_iff
% 0.35/0.61  thf(fact_4659_of__bool__less__one__iff,axiom,
% 0.35/0.61      ! [P: $o] :
% 0.35/0.61        ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int )
% 0.35/0.61        = ( ~ P ) ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_less_one_iff
% 0.35/0.61  thf(fact_4660_of__bool__less__one__iff,axiom,
% 0.35/0.61      ! [P: $o] :
% 0.35/0.61        ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer )
% 0.35/0.61        = ( ~ P ) ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_less_one_iff
% 0.35/0.61  thf(fact_4661_of__bool__not__iff,axiom,
% 0.35/0.61      ! [P: $o] :
% 0.35/0.61        ( ( zero_n1201886186963655149omplex @ ~ P )
% 0.35/0.61        = ( minus_minus_complex @ one_one_complex @ ( zero_n1201886186963655149omplex @ P ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_not_iff
% 0.35/0.61  thf(fact_4662_of__bool__not__iff,axiom,
% 0.35/0.61      ! [P: $o] :
% 0.35/0.61        ( ( zero_n3304061248610475627l_real @ ~ P )
% 0.35/0.61        = ( minus_minus_real @ one_one_real @ ( zero_n3304061248610475627l_real @ P ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_not_iff
% 0.35/0.61  thf(fact_4663_of__bool__not__iff,axiom,
% 0.35/0.61      ! [P: $o] :
% 0.35/0.61        ( ( zero_n2052037380579107095ol_rat @ ~ P )
% 0.35/0.61        = ( minus_minus_rat @ one_one_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_not_iff
% 0.35/0.61  thf(fact_4664_of__bool__not__iff,axiom,
% 0.35/0.61      ! [P: $o] :
% 0.35/0.61        ( ( zero_n2684676970156552555ol_int @ ~ P )
% 0.35/0.61        = ( minus_minus_int @ one_one_int @ ( zero_n2684676970156552555ol_int @ P ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_not_iff
% 0.35/0.61  thf(fact_4665_of__bool__not__iff,axiom,
% 0.35/0.61      ! [P: $o] :
% 0.35/0.61        ( ( zero_n356916108424825756nteger @ ~ P )
% 0.35/0.61        = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( zero_n356916108424825756nteger @ P ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_not_iff
% 0.35/0.61  thf(fact_4666_Suc__0__mod__eq,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.35/0.61        = ( zero_n2687167440665602831ol_nat
% 0.35/0.61          @ ( N
% 0.35/0.61           != ( suc @ zero_zero_nat ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % Suc_0_mod_eq
% 0.35/0.61  thf(fact_4667_signed__take__bit__Suc__1,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ one_one_int )
% 0.35/0.61        = one_one_int ) ).
% 0.35/0.61  
% 0.35/0.61  % signed_take_bit_Suc_1
% 0.35/0.61  thf(fact_4668_signed__take__bit__numeral__of__1,axiom,
% 0.35/0.61      ! [K: num] :
% 0.35/0.61        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ K ) @ one_one_int )
% 0.35/0.61        = one_one_int ) ).
% 0.35/0.61  
% 0.35/0.61  % signed_take_bit_numeral_of_1
% 0.35/0.61  thf(fact_4669_Ball__set__replicate,axiom,
% 0.35/0.61      ! [N: nat,A: int,P: int > $o] :
% 0.35/0.61        ( ( ! [X2: int] :
% 0.35/0.61              ( ( member_int @ X2 @ ( set_int2 @ ( replicate_int @ N @ A ) ) )
% 0.35/0.61             => ( P @ X2 ) ) )
% 0.35/0.61        = ( ( P @ A )
% 0.35/0.61          | ( N = zero_zero_nat ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % Ball_set_replicate
% 0.35/0.61  thf(fact_4670_Ball__set__replicate,axiom,
% 0.35/0.61      ! [N: nat,A: nat,P: nat > $o] :
% 0.35/0.61        ( ( ! [X2: nat] :
% 0.35/0.61              ( ( member_nat @ X2 @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 0.35/0.61             => ( P @ X2 ) ) )
% 0.35/0.61        = ( ( P @ A )
% 0.35/0.61          | ( N = zero_zero_nat ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % Ball_set_replicate
% 0.35/0.61  thf(fact_4671_Ball__set__replicate,axiom,
% 0.35/0.61      ! [N: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 0.35/0.61        ( ( ! [X2: vEBT_VEBT] :
% 0.35/0.61              ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 0.35/0.61             => ( P @ X2 ) ) )
% 0.35/0.61        = ( ( P @ A )
% 0.35/0.61          | ( N = zero_zero_nat ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % Ball_set_replicate
% 0.35/0.61  thf(fact_4672_Bex__set__replicate,axiom,
% 0.35/0.61      ! [N: nat,A: int,P: int > $o] :
% 0.35/0.61        ( ( ? [X2: int] :
% 0.35/0.61              ( ( member_int @ X2 @ ( set_int2 @ ( replicate_int @ N @ A ) ) )
% 0.35/0.61              & ( P @ X2 ) ) )
% 0.35/0.61        = ( ( P @ A )
% 0.35/0.61          & ( N != zero_zero_nat ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % Bex_set_replicate
% 0.35/0.61  thf(fact_4673_Bex__set__replicate,axiom,
% 0.35/0.61      ! [N: nat,A: nat,P: nat > $o] :
% 0.35/0.61        ( ( ? [X2: nat] :
% 0.35/0.61              ( ( member_nat @ X2 @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 0.35/0.61              & ( P @ X2 ) ) )
% 0.35/0.61        = ( ( P @ A )
% 0.35/0.61          & ( N != zero_zero_nat ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % Bex_set_replicate
% 0.35/0.61  thf(fact_4674_Bex__set__replicate,axiom,
% 0.35/0.61      ! [N: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 0.35/0.61        ( ( ? [X2: vEBT_VEBT] :
% 0.35/0.61              ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 0.35/0.61              & ( P @ X2 ) ) )
% 0.35/0.61        = ( ( P @ A )
% 0.35/0.61          & ( N != zero_zero_nat ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % Bex_set_replicate
% 0.35/0.61  thf(fact_4675_in__set__replicate,axiom,
% 0.35/0.61      ! [X: product_prod_nat_nat,N: nat,Y2: product_prod_nat_nat] :
% 0.35/0.61        ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ ( replic4235873036481779905at_nat @ N @ Y2 ) ) )
% 0.35/0.61        = ( ( X = Y2 )
% 0.35/0.61          & ( N != zero_zero_nat ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % in_set_replicate
% 0.35/0.61  thf(fact_4676_in__set__replicate,axiom,
% 0.35/0.61      ! [X: complex,N: nat,Y2: complex] :
% 0.35/0.61        ( ( member_complex @ X @ ( set_complex2 @ ( replicate_complex @ N @ Y2 ) ) )
% 0.35/0.61        = ( ( X = Y2 )
% 0.35/0.61          & ( N != zero_zero_nat ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % in_set_replicate
% 0.35/0.61  thf(fact_4677_in__set__replicate,axiom,
% 0.35/0.61      ! [X: real,N: nat,Y2: real] :
% 0.35/0.61        ( ( member_real @ X @ ( set_real2 @ ( replicate_real @ N @ Y2 ) ) )
% 0.35/0.61        = ( ( X = Y2 )
% 0.35/0.61          & ( N != zero_zero_nat ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % in_set_replicate
% 0.35/0.61  thf(fact_4678_in__set__replicate,axiom,
% 0.35/0.61      ! [X: int,N: nat,Y2: int] :
% 0.35/0.61        ( ( member_int @ X @ ( set_int2 @ ( replicate_int @ N @ Y2 ) ) )
% 0.35/0.61        = ( ( X = Y2 )
% 0.35/0.61          & ( N != zero_zero_nat ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % in_set_replicate
% 0.35/0.61  thf(fact_4679_in__set__replicate,axiom,
% 0.35/0.61      ! [X: nat,N: nat,Y2: nat] :
% 0.35/0.61        ( ( member_nat @ X @ ( set_nat2 @ ( replicate_nat @ N @ Y2 ) ) )
% 0.35/0.61        = ( ( X = Y2 )
% 0.35/0.61          & ( N != zero_zero_nat ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % in_set_replicate
% 0.35/0.61  thf(fact_4680_in__set__replicate,axiom,
% 0.35/0.61      ! [X: vEBT_VEBT,N: nat,Y2: vEBT_VEBT] :
% 0.35/0.61        ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ Y2 ) ) )
% 0.35/0.61        = ( ( X = Y2 )
% 0.35/0.61          & ( N != zero_zero_nat ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % in_set_replicate
% 0.35/0.61  thf(fact_4681_nth__replicate,axiom,
% 0.35/0.61      ! [I2: nat,N: nat,X: nat] :
% 0.35/0.61        ( ( ord_less_nat @ I2 @ N )
% 0.35/0.61       => ( ( nth_nat @ ( replicate_nat @ N @ X ) @ I2 )
% 0.35/0.61          = X ) ) ).
% 0.35/0.61  
% 0.35/0.61  % nth_replicate
% 0.35/0.61  thf(fact_4682_nth__replicate,axiom,
% 0.35/0.61      ! [I2: nat,N: nat,X: vEBT_VEBT] :
% 0.35/0.61        ( ( ord_less_nat @ I2 @ N )
% 0.35/0.61       => ( ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X ) @ I2 )
% 0.35/0.61          = X ) ) ).
% 0.35/0.61  
% 0.35/0.61  % nth_replicate
% 0.35/0.61  thf(fact_4683_triangle__Suc,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ( nat_triangle @ ( suc @ N ) )
% 0.35/0.61        = ( plus_plus_nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % triangle_Suc
% 0.35/0.61  thf(fact_4684_signed__take__bit__Suc__bit0,axiom,
% 0.35/0.61      ! [N: nat,K: num] :
% 0.35/0.61        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 0.35/0.61        = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % signed_take_bit_Suc_bit0
% 0.35/0.61  thf(fact_4685_odd__of__bool__self,axiom,
% 0.35/0.61      ! [P6: $o] :
% 0.35/0.61        ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( zero_n2687167440665602831ol_nat @ P6 ) ) )
% 0.35/0.61        = P6 ) ).
% 0.35/0.61  
% 0.35/0.61  % odd_of_bool_self
% 0.35/0.61  thf(fact_4686_odd__of__bool__self,axiom,
% 0.35/0.61      ! [P6: $o] :
% 0.35/0.61        ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( zero_n2684676970156552555ol_int @ P6 ) ) )
% 0.35/0.61        = P6 ) ).
% 0.35/0.61  
% 0.35/0.61  % odd_of_bool_self
% 0.35/0.61  thf(fact_4687_odd__of__bool__self,axiom,
% 0.35/0.61      ! [P6: $o] :
% 0.35/0.61        ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( zero_n356916108424825756nteger @ P6 ) ) )
% 0.35/0.61        = P6 ) ).
% 0.35/0.61  
% 0.35/0.61  % odd_of_bool_self
% 0.35/0.61  thf(fact_4688_set__replicate,axiom,
% 0.35/0.61      ! [N: nat,X: vEBT_VEBT] :
% 0.35/0.61        ( ( N != zero_zero_nat )
% 0.35/0.61       => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X ) )
% 0.35/0.61          = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % set_replicate
% 0.35/0.61  thf(fact_4689_set__replicate,axiom,
% 0.35/0.61      ! [N: nat,X: nat] :
% 0.35/0.61        ( ( N != zero_zero_nat )
% 0.35/0.61       => ( ( set_nat2 @ ( replicate_nat @ N @ X ) )
% 0.35/0.61          = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % set_replicate
% 0.35/0.61  thf(fact_4690_set__replicate,axiom,
% 0.35/0.61      ! [N: nat,X: int] :
% 0.35/0.61        ( ( N != zero_zero_nat )
% 0.35/0.61       => ( ( set_int2 @ ( replicate_int @ N @ X ) )
% 0.35/0.61          = ( insert_int @ X @ bot_bot_set_int ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % set_replicate
% 0.35/0.61  thf(fact_4691_set__replicate,axiom,
% 0.35/0.61      ! [N: nat,X: real] :
% 0.35/0.61        ( ( N != zero_zero_nat )
% 0.35/0.61       => ( ( set_real2 @ ( replicate_real @ N @ X ) )
% 0.35/0.61          = ( insert_real @ X @ bot_bot_set_real ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % set_replicate
% 0.35/0.61  thf(fact_4692_of__bool__half__eq__0,axiom,
% 0.35/0.61      ! [B: $o] :
% 0.35/0.61        ( ( divide_divide_nat @ ( zero_n2687167440665602831ol_nat @ B ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.61        = zero_zero_nat ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_half_eq_0
% 0.35/0.61  thf(fact_4693_of__bool__half__eq__0,axiom,
% 0.35/0.61      ! [B: $o] :
% 0.35/0.61        ( ( divide_divide_int @ ( zero_n2684676970156552555ol_int @ B ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.61        = zero_zero_int ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_half_eq_0
% 0.35/0.61  thf(fact_4694_of__bool__half__eq__0,axiom,
% 0.35/0.61      ! [B: $o] :
% 0.35/0.61        ( ( divide6298287555418463151nteger @ ( zero_n356916108424825756nteger @ B ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.35/0.61        = zero_z3403309356797280102nteger ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_half_eq_0
% 0.35/0.61  thf(fact_4695_one__div__2__pow__eq,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61        = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % one_div_2_pow_eq
% 0.35/0.61  thf(fact_4696_one__div__2__pow__eq,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61        = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % one_div_2_pow_eq
% 0.35/0.61  thf(fact_4697_one__div__2__pow__eq,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61        = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % one_div_2_pow_eq
% 0.35/0.61  thf(fact_4698_bits__1__div__exp,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61        = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % bits_1_div_exp
% 0.35/0.61  thf(fact_4699_bits__1__div__exp,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61        = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % bits_1_div_exp
% 0.35/0.61  thf(fact_4700_bits__1__div__exp,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61        = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % bits_1_div_exp
% 0.35/0.61  thf(fact_4701_signed__take__bit__Suc__bit1,axiom,
% 0.35/0.61      ! [N: nat,K: num] :
% 0.35/0.61        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 0.35/0.61        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.35/0.61  
% 0.35/0.61  % signed_take_bit_Suc_bit1
% 0.35/0.61  thf(fact_4702_one__mod__2__pow__eq,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ( modulo_modulo_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61        = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % one_mod_2_pow_eq
% 0.35/0.61  thf(fact_4703_one__mod__2__pow__eq,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ( modulo_modulo_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61        = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % one_mod_2_pow_eq
% 0.35/0.61  thf(fact_4704_one__mod__2__pow__eq,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61        = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % one_mod_2_pow_eq
% 0.35/0.61  thf(fact_4705_dvd__antisym,axiom,
% 0.35/0.61      ! [M: nat,N: nat] :
% 0.35/0.61        ( ( dvd_dvd_nat @ M @ N )
% 0.35/0.61       => ( ( dvd_dvd_nat @ N @ M )
% 0.35/0.61         => ( M = N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % dvd_antisym
% 0.35/0.61  thf(fact_4706_of__bool__conj,axiom,
% 0.35/0.61      ! [P: $o,Q: $o] :
% 0.35/0.61        ( ( zero_n1201886186963655149omplex
% 0.35/0.61          @ ( P
% 0.35/0.61            & Q ) )
% 0.35/0.61        = ( times_times_complex @ ( zero_n1201886186963655149omplex @ P ) @ ( zero_n1201886186963655149omplex @ Q ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_conj
% 0.35/0.61  thf(fact_4707_of__bool__conj,axiom,
% 0.35/0.61      ! [P: $o,Q: $o] :
% 0.35/0.61        ( ( zero_n3304061248610475627l_real
% 0.35/0.61          @ ( P
% 0.35/0.61            & Q ) )
% 0.35/0.61        = ( times_times_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_conj
% 0.35/0.61  thf(fact_4708_of__bool__conj,axiom,
% 0.35/0.61      ! [P: $o,Q: $o] :
% 0.35/0.61        ( ( zero_n2687167440665602831ol_nat
% 0.35/0.61          @ ( P
% 0.35/0.61            & Q ) )
% 0.35/0.61        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_conj
% 0.35/0.61  thf(fact_4709_of__bool__conj,axiom,
% 0.35/0.61      ! [P: $o,Q: $o] :
% 0.35/0.61        ( ( zero_n2684676970156552555ol_int
% 0.35/0.61          @ ( P
% 0.35/0.61            & Q ) )
% 0.35/0.61        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_conj
% 0.35/0.61  thf(fact_4710_of__bool__conj,axiom,
% 0.35/0.61      ! [P: $o,Q: $o] :
% 0.35/0.61        ( ( zero_n356916108424825756nteger
% 0.35/0.61          @ ( P
% 0.35/0.61            & Q ) )
% 0.35/0.61        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_conj
% 0.35/0.61  thf(fact_4711_mem__case__prodE,axiom,
% 0.35/0.61      ! [Z: complex,C: num > num > set_complex,P6: product_prod_num_num] :
% 0.35/0.61        ( ( member_complex @ Z @ ( produc2866383454006189126omplex @ C @ P6 ) )
% 0.35/0.61       => ~ ! [X3: num,Y3: num] :
% 0.35/0.61              ( ( P6
% 0.35/0.61                = ( product_Pair_num_num @ X3 @ Y3 ) )
% 0.35/0.61             => ~ ( member_complex @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mem_case_prodE
% 0.35/0.61  thf(fact_4712_mem__case__prodE,axiom,
% 0.35/0.61      ! [Z: real,C: num > num > set_real,P6: product_prod_num_num] :
% 0.35/0.61        ( ( member_real @ Z @ ( produc8296048397933160132t_real @ C @ P6 ) )
% 0.35/0.61       => ~ ! [X3: num,Y3: num] :
% 0.35/0.61              ( ( P6
% 0.35/0.61                = ( product_Pair_num_num @ X3 @ Y3 ) )
% 0.35/0.61             => ~ ( member_real @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mem_case_prodE
% 0.35/0.61  thf(fact_4713_mem__case__prodE,axiom,
% 0.35/0.61      ! [Z: nat,C: num > num > set_nat,P6: product_prod_num_num] :
% 0.35/0.61        ( ( member_nat @ Z @ ( produc1361121860356118632et_nat @ C @ P6 ) )
% 0.35/0.61       => ~ ! [X3: num,Y3: num] :
% 0.35/0.61              ( ( P6
% 0.35/0.61                = ( product_Pair_num_num @ X3 @ Y3 ) )
% 0.35/0.61             => ~ ( member_nat @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mem_case_prodE
% 0.35/0.61  thf(fact_4714_mem__case__prodE,axiom,
% 0.35/0.61      ! [Z: int,C: num > num > set_int,P6: product_prod_num_num] :
% 0.35/0.61        ( ( member_int @ Z @ ( produc6406642877701697732et_int @ C @ P6 ) )
% 0.35/0.61       => ~ ! [X3: num,Y3: num] :
% 0.35/0.61              ( ( P6
% 0.35/0.61                = ( product_Pair_num_num @ X3 @ Y3 ) )
% 0.35/0.61             => ~ ( member_int @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mem_case_prodE
% 0.35/0.61  thf(fact_4715_mem__case__prodE,axiom,
% 0.35/0.61      ! [Z: complex,C: nat > num > set_complex,P6: product_prod_nat_num] :
% 0.35/0.61        ( ( member_complex @ Z @ ( produc6231982587499038204omplex @ C @ P6 ) )
% 0.35/0.61       => ~ ! [X3: nat,Y3: num] :
% 0.35/0.61              ( ( P6
% 0.35/0.61                = ( product_Pair_nat_num @ X3 @ Y3 ) )
% 0.35/0.61             => ~ ( member_complex @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mem_case_prodE
% 0.35/0.61  thf(fact_4716_mem__case__prodE,axiom,
% 0.35/0.61      ! [Z: real,C: nat > num > set_real,P6: product_prod_nat_num] :
% 0.35/0.61        ( ( member_real @ Z @ ( produc1435849484188172666t_real @ C @ P6 ) )
% 0.35/0.61       => ~ ! [X3: nat,Y3: num] :
% 0.35/0.61              ( ( P6
% 0.35/0.61                = ( product_Pair_nat_num @ X3 @ Y3 ) )
% 0.35/0.61             => ~ ( member_real @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mem_case_prodE
% 0.35/0.61  thf(fact_4717_mem__case__prodE,axiom,
% 0.35/0.61      ! [Z: nat,C: nat > num > set_nat,P6: product_prod_nat_num] :
% 0.35/0.61        ( ( member_nat @ Z @ ( produc4130284055270567454et_nat @ C @ P6 ) )
% 0.35/0.61       => ~ ! [X3: nat,Y3: num] :
% 0.35/0.61              ( ( P6
% 0.35/0.61                = ( product_Pair_nat_num @ X3 @ Y3 ) )
% 0.35/0.61             => ~ ( member_nat @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mem_case_prodE
% 0.35/0.61  thf(fact_4718_mem__case__prodE,axiom,
% 0.35/0.61      ! [Z: int,C: nat > num > set_int,P6: product_prod_nat_num] :
% 0.35/0.61        ( ( member_int @ Z @ ( produc9175805072616146554et_int @ C @ P6 ) )
% 0.35/0.61       => ~ ! [X3: nat,Y3: num] :
% 0.35/0.61              ( ( P6
% 0.35/0.61                = ( product_Pair_nat_num @ X3 @ Y3 ) )
% 0.35/0.61             => ~ ( member_int @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mem_case_prodE
% 0.35/0.61  thf(fact_4719_mem__case__prodE,axiom,
% 0.35/0.61      ! [Z: complex,C: nat > nat > set_complex,P6: product_prod_nat_nat] :
% 0.35/0.61        ( ( member_complex @ Z @ ( produc3453488052772718514omplex @ C @ P6 ) )
% 0.35/0.61       => ~ ! [X3: nat,Y3: nat] :
% 0.35/0.61              ( ( P6
% 0.35/0.61                = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 0.35/0.61             => ~ ( member_complex @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mem_case_prodE
% 0.35/0.61  thf(fact_4720_mem__case__prodE,axiom,
% 0.35/0.61      ! [Z: real,C: nat > nat > set_real,P6: product_prod_nat_nat] :
% 0.35/0.61        ( ( member_real @ Z @ ( produc3668448655016342576t_real @ C @ P6 ) )
% 0.35/0.61       => ~ ! [X3: nat,Y3: nat] :
% 0.35/0.61              ( ( P6
% 0.35/0.61                = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 0.35/0.61             => ~ ( member_real @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mem_case_prodE
% 0.35/0.61  thf(fact_4721_signed__take__bit__mult,axiom,
% 0.35/0.61      ! [N: nat,K: int,L2: int] :
% 0.35/0.61        ( ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L2 ) ) )
% 0.35/0.61        = ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ K @ L2 ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % signed_take_bit_mult
% 0.35/0.61  thf(fact_4722_signed__take__bit__add,axiom,
% 0.35/0.61      ! [N: nat,K: int,L2: int] :
% 0.35/0.61        ( ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L2 ) ) )
% 0.35/0.61        = ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % signed_take_bit_add
% 0.35/0.61  thf(fact_4723_signed__take__bit__diff,axiom,
% 0.35/0.61      ! [N: nat,K: int,L2: int] :
% 0.35/0.61        ( ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L2 ) ) )
% 0.35/0.61        = ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ K @ L2 ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % signed_take_bit_diff
% 0.35/0.61  thf(fact_4724_case__prodD,axiom,
% 0.35/0.61      ! [F: product_prod_nat_nat > product_prod_nat_nat > $o,A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 0.35/0.61        ( ( produc6590410687421337004_nat_o @ F @ ( produc6161850002892822231at_nat @ A @ B ) )
% 0.35/0.61       => ( F @ A @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % case_prodD
% 0.35/0.61  thf(fact_4725_case__prodD,axiom,
% 0.35/0.61      ! [F: num > num > $o,A: num,B: num] :
% 0.35/0.61        ( ( produc5703948589228662326_num_o @ F @ ( product_Pair_num_num @ A @ B ) )
% 0.35/0.61       => ( F @ A @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % case_prodD
% 0.35/0.61  thf(fact_4726_case__prodD,axiom,
% 0.35/0.61      ! [F: nat > num > $o,A: nat,B: num] :
% 0.35/0.61        ( ( produc4927758841916487424_num_o @ F @ ( product_Pair_nat_num @ A @ B ) )
% 0.35/0.61       => ( F @ A @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % case_prodD
% 0.35/0.61  thf(fact_4727_case__prodD,axiom,
% 0.35/0.61      ! [F: nat > nat > $o,A: nat,B: nat] :
% 0.35/0.61        ( ( produc6081775807080527818_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 0.35/0.61       => ( F @ A @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % case_prodD
% 0.35/0.61  thf(fact_4728_case__prodD,axiom,
% 0.35/0.61      ! [F: int > int > $o,A: int,B: int] :
% 0.35/0.61        ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) )
% 0.35/0.61       => ( F @ A @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % case_prodD
% 0.35/0.61  thf(fact_4729_case__prodE,axiom,
% 0.35/0.61      ! [C: product_prod_nat_nat > product_prod_nat_nat > $o,P6: produc859450856879609959at_nat] :
% 0.35/0.61        ( ( produc6590410687421337004_nat_o @ C @ P6 )
% 0.35/0.61       => ~ ! [X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 0.35/0.61              ( ( P6
% 0.35/0.61                = ( produc6161850002892822231at_nat @ X3 @ Y3 ) )
% 0.35/0.61             => ~ ( C @ X3 @ Y3 ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % case_prodE
% 0.35/0.61  thf(fact_4730_case__prodE,axiom,
% 0.35/0.61      ! [C: num > num > $o,P6: product_prod_num_num] :
% 0.35/0.61        ( ( produc5703948589228662326_num_o @ C @ P6 )
% 0.35/0.61       => ~ ! [X3: num,Y3: num] :
% 0.35/0.61              ( ( P6
% 0.35/0.61                = ( product_Pair_num_num @ X3 @ Y3 ) )
% 0.35/0.61             => ~ ( C @ X3 @ Y3 ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % case_prodE
% 0.35/0.61  thf(fact_4731_case__prodE,axiom,
% 0.35/0.61      ! [C: nat > num > $o,P6: product_prod_nat_num] :
% 0.35/0.61        ( ( produc4927758841916487424_num_o @ C @ P6 )
% 0.35/0.61       => ~ ! [X3: nat,Y3: num] :
% 0.35/0.61              ( ( P6
% 0.35/0.61                = ( product_Pair_nat_num @ X3 @ Y3 ) )
% 0.35/0.61             => ~ ( C @ X3 @ Y3 ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % case_prodE
% 0.35/0.61  thf(fact_4732_case__prodE,axiom,
% 0.35/0.61      ! [C: nat > nat > $o,P6: product_prod_nat_nat] :
% 0.35/0.61        ( ( produc6081775807080527818_nat_o @ C @ P6 )
% 0.35/0.61       => ~ ! [X3: nat,Y3: nat] :
% 0.35/0.61              ( ( P6
% 0.35/0.61                = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 0.35/0.61             => ~ ( C @ X3 @ Y3 ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % case_prodE
% 0.35/0.61  thf(fact_4733_case__prodE,axiom,
% 0.35/0.61      ! [C: int > int > $o,P6: product_prod_int_int] :
% 0.35/0.61        ( ( produc4947309494688390418_int_o @ C @ P6 )
% 0.35/0.61       => ~ ! [X3: int,Y3: int] :
% 0.35/0.61              ( ( P6
% 0.35/0.61                = ( product_Pair_int_int @ X3 @ Y3 ) )
% 0.35/0.61             => ~ ( C @ X3 @ Y3 ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % case_prodE
% 0.35/0.61  thf(fact_4734_case__prodD_H,axiom,
% 0.35/0.61      ! [R2: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat,C: product_prod_nat_nat] :
% 0.35/0.61        ( ( produc8739625826339149834_nat_o @ R2 @ ( product_Pair_nat_nat @ A @ B ) @ C )
% 0.35/0.61       => ( R2 @ A @ B @ C ) ) ).
% 0.35/0.61  
% 0.35/0.61  % case_prodD'
% 0.35/0.61  thf(fact_4735_case__prodE_H,axiom,
% 0.35/0.61      ! [C: nat > nat > product_prod_nat_nat > $o,P6: product_prod_nat_nat,Z: product_prod_nat_nat] :
% 0.35/0.61        ( ( produc8739625826339149834_nat_o @ C @ P6 @ Z )
% 0.35/0.61       => ~ ! [X3: nat,Y3: nat] :
% 0.35/0.61              ( ( P6
% 0.35/0.61                = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 0.35/0.61             => ~ ( C @ X3 @ Y3 @ Z ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % case_prodE'
% 0.35/0.61  thf(fact_4736_zero__less__eq__of__bool,axiom,
% 0.35/0.61      ! [P: $o] : ( ord_less_eq_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) ) ).
% 0.35/0.61  
% 0.35/0.61  % zero_less_eq_of_bool
% 0.35/0.61  thf(fact_4737_zero__less__eq__of__bool,axiom,
% 0.35/0.61      ! [P: $o] : ( ord_less_eq_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 0.35/0.61  
% 0.35/0.61  % zero_less_eq_of_bool
% 0.35/0.61  thf(fact_4738_zero__less__eq__of__bool,axiom,
% 0.35/0.61      ! [P: $o] : ( ord_less_eq_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 0.35/0.61  
% 0.35/0.61  % zero_less_eq_of_bool
% 0.35/0.61  thf(fact_4739_zero__less__eq__of__bool,axiom,
% 0.35/0.61      ! [P: $o] : ( ord_less_eq_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) ) ).
% 0.35/0.61  
% 0.35/0.61  % zero_less_eq_of_bool
% 0.35/0.61  thf(fact_4740_zero__less__eq__of__bool,axiom,
% 0.35/0.61      ! [P: $o] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) ) ).
% 0.35/0.61  
% 0.35/0.61  % zero_less_eq_of_bool
% 0.35/0.61  thf(fact_4741_of__bool__less__eq__one,axiom,
% 0.35/0.61      ! [P: $o] : ( ord_less_eq_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_less_eq_one
% 0.35/0.61  thf(fact_4742_of__bool__less__eq__one,axiom,
% 0.35/0.61      ! [P: $o] : ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_less_eq_one
% 0.35/0.61  thf(fact_4743_of__bool__less__eq__one,axiom,
% 0.35/0.61      ! [P: $o] : ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_less_eq_one
% 0.35/0.61  thf(fact_4744_of__bool__less__eq__one,axiom,
% 0.35/0.61      ! [P: $o] : ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_less_eq_one
% 0.35/0.61  thf(fact_4745_of__bool__less__eq__one,axiom,
% 0.35/0.61      ! [P: $o] : ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_less_eq_one
% 0.35/0.61  thf(fact_4746_of__bool__def,axiom,
% 0.35/0.61      ( zero_n1201886186963655149omplex
% 0.35/0.61      = ( ^ [P4: $o] : ( if_complex @ P4 @ one_one_complex @ zero_zero_complex ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_def
% 0.35/0.61  thf(fact_4747_of__bool__def,axiom,
% 0.35/0.61      ( zero_n3304061248610475627l_real
% 0.35/0.61      = ( ^ [P4: $o] : ( if_real @ P4 @ one_one_real @ zero_zero_real ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_def
% 0.35/0.61  thf(fact_4748_of__bool__def,axiom,
% 0.35/0.61      ( zero_n2052037380579107095ol_rat
% 0.35/0.61      = ( ^ [P4: $o] : ( if_rat @ P4 @ one_one_rat @ zero_zero_rat ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_def
% 0.35/0.61  thf(fact_4749_of__bool__def,axiom,
% 0.35/0.61      ( zero_n2687167440665602831ol_nat
% 0.35/0.61      = ( ^ [P4: $o] : ( if_nat @ P4 @ one_one_nat @ zero_zero_nat ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_def
% 0.35/0.61  thf(fact_4750_of__bool__def,axiom,
% 0.35/0.61      ( zero_n2684676970156552555ol_int
% 0.35/0.61      = ( ^ [P4: $o] : ( if_int @ P4 @ one_one_int @ zero_zero_int ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_def
% 0.35/0.61  thf(fact_4751_of__bool__def,axiom,
% 0.35/0.61      ( zero_n356916108424825756nteger
% 0.35/0.61      = ( ^ [P4: $o] : ( if_Code_integer @ P4 @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_def
% 0.35/0.61  thf(fact_4752_split__of__bool,axiom,
% 0.35/0.61      ! [P: complex > $o,P6: $o] :
% 0.35/0.61        ( ( P @ ( zero_n1201886186963655149omplex @ P6 ) )
% 0.35/0.61        = ( ( P6
% 0.35/0.61           => ( P @ one_one_complex ) )
% 0.35/0.61          & ( ~ P6
% 0.35/0.61           => ( P @ zero_zero_complex ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % split_of_bool
% 0.35/0.61  thf(fact_4753_split__of__bool,axiom,
% 0.35/0.61      ! [P: real > $o,P6: $o] :
% 0.35/0.61        ( ( P @ ( zero_n3304061248610475627l_real @ P6 ) )
% 0.35/0.61        = ( ( P6
% 0.35/0.61           => ( P @ one_one_real ) )
% 0.35/0.61          & ( ~ P6
% 0.35/0.61           => ( P @ zero_zero_real ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % split_of_bool
% 0.35/0.61  thf(fact_4754_split__of__bool,axiom,
% 0.35/0.61      ! [P: rat > $o,P6: $o] :
% 0.35/0.61        ( ( P @ ( zero_n2052037380579107095ol_rat @ P6 ) )
% 0.35/0.61        = ( ( P6
% 0.35/0.61           => ( P @ one_one_rat ) )
% 0.35/0.61          & ( ~ P6
% 0.35/0.61           => ( P @ zero_zero_rat ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % split_of_bool
% 0.35/0.61  thf(fact_4755_split__of__bool,axiom,
% 0.35/0.61      ! [P: nat > $o,P6: $o] :
% 0.35/0.61        ( ( P @ ( zero_n2687167440665602831ol_nat @ P6 ) )
% 0.35/0.61        = ( ( P6
% 0.35/0.61           => ( P @ one_one_nat ) )
% 0.35/0.61          & ( ~ P6
% 0.35/0.61           => ( P @ zero_zero_nat ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % split_of_bool
% 0.35/0.61  thf(fact_4756_split__of__bool,axiom,
% 0.35/0.61      ! [P: int > $o,P6: $o] :
% 0.35/0.61        ( ( P @ ( zero_n2684676970156552555ol_int @ P6 ) )
% 0.35/0.61        = ( ( P6
% 0.35/0.61           => ( P @ one_one_int ) )
% 0.35/0.61          & ( ~ P6
% 0.35/0.61           => ( P @ zero_zero_int ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % split_of_bool
% 0.35/0.61  thf(fact_4757_split__of__bool,axiom,
% 0.35/0.61      ! [P: code_integer > $o,P6: $o] :
% 0.35/0.61        ( ( P @ ( zero_n356916108424825756nteger @ P6 ) )
% 0.35/0.61        = ( ( P6
% 0.35/0.61           => ( P @ one_one_Code_integer ) )
% 0.35/0.61          & ( ~ P6
% 0.35/0.61           => ( P @ zero_z3403309356797280102nteger ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % split_of_bool
% 0.35/0.61  thf(fact_4758_split__of__bool__asm,axiom,
% 0.35/0.61      ! [P: complex > $o,P6: $o] :
% 0.35/0.61        ( ( P @ ( zero_n1201886186963655149omplex @ P6 ) )
% 0.35/0.61        = ( ~ ( ( P6
% 0.35/0.61                & ~ ( P @ one_one_complex ) )
% 0.35/0.61              | ( ~ P6
% 0.35/0.61                & ~ ( P @ zero_zero_complex ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % split_of_bool_asm
% 0.35/0.61  thf(fact_4759_split__of__bool__asm,axiom,
% 0.35/0.61      ! [P: real > $o,P6: $o] :
% 0.35/0.61        ( ( P @ ( zero_n3304061248610475627l_real @ P6 ) )
% 0.35/0.61        = ( ~ ( ( P6
% 0.35/0.61                & ~ ( P @ one_one_real ) )
% 0.35/0.61              | ( ~ P6
% 0.35/0.61                & ~ ( P @ zero_zero_real ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % split_of_bool_asm
% 0.35/0.61  thf(fact_4760_split__of__bool__asm,axiom,
% 0.35/0.61      ! [P: rat > $o,P6: $o] :
% 0.35/0.61        ( ( P @ ( zero_n2052037380579107095ol_rat @ P6 ) )
% 0.35/0.61        = ( ~ ( ( P6
% 0.35/0.61                & ~ ( P @ one_one_rat ) )
% 0.35/0.61              | ( ~ P6
% 0.35/0.61                & ~ ( P @ zero_zero_rat ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % split_of_bool_asm
% 0.35/0.61  thf(fact_4761_split__of__bool__asm,axiom,
% 0.35/0.61      ! [P: nat > $o,P6: $o] :
% 0.35/0.61        ( ( P @ ( zero_n2687167440665602831ol_nat @ P6 ) )
% 0.35/0.61        = ( ~ ( ( P6
% 0.35/0.61                & ~ ( P @ one_one_nat ) )
% 0.35/0.61              | ( ~ P6
% 0.35/0.61                & ~ ( P @ zero_zero_nat ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % split_of_bool_asm
% 0.35/0.61  thf(fact_4762_split__of__bool__asm,axiom,
% 0.35/0.61      ! [P: int > $o,P6: $o] :
% 0.35/0.61        ( ( P @ ( zero_n2684676970156552555ol_int @ P6 ) )
% 0.35/0.61        = ( ~ ( ( P6
% 0.35/0.61                & ~ ( P @ one_one_int ) )
% 0.35/0.61              | ( ~ P6
% 0.35/0.61                & ~ ( P @ zero_zero_int ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % split_of_bool_asm
% 0.35/0.61  thf(fact_4763_split__of__bool__asm,axiom,
% 0.35/0.61      ! [P: code_integer > $o,P6: $o] :
% 0.35/0.61        ( ( P @ ( zero_n356916108424825756nteger @ P6 ) )
% 0.35/0.61        = ( ~ ( ( P6
% 0.35/0.61                & ~ ( P @ one_one_Code_integer ) )
% 0.35/0.61              | ( ~ P6
% 0.35/0.61                & ~ ( P @ zero_z3403309356797280102nteger ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % split_of_bool_asm
% 0.35/0.61  thf(fact_4764_replicate__eqI,axiom,
% 0.35/0.61      ! [Xs2: list_P6011104703257516679at_nat,N: nat,X: product_prod_nat_nat] :
% 0.35/0.61        ( ( ( size_s5460976970255530739at_nat @ Xs2 )
% 0.35/0.61          = N )
% 0.35/0.61       => ( ! [Y3: product_prod_nat_nat] :
% 0.35/0.61              ( ( member8440522571783428010at_nat @ Y3 @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 0.35/0.61             => ( Y3 = X ) )
% 0.35/0.61         => ( Xs2
% 0.35/0.61            = ( replic4235873036481779905at_nat @ N @ X ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % replicate_eqI
% 0.35/0.61  thf(fact_4765_replicate__eqI,axiom,
% 0.35/0.61      ! [Xs2: list_complex,N: nat,X: complex] :
% 0.35/0.61        ( ( ( size_s3451745648224563538omplex @ Xs2 )
% 0.35/0.61          = N )
% 0.35/0.61       => ( ! [Y3: complex] :
% 0.35/0.61              ( ( member_complex @ Y3 @ ( set_complex2 @ Xs2 ) )
% 0.35/0.61             => ( Y3 = X ) )
% 0.35/0.61         => ( Xs2
% 0.35/0.61            = ( replicate_complex @ N @ X ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % replicate_eqI
% 0.35/0.61  thf(fact_4766_replicate__eqI,axiom,
% 0.35/0.61      ! [Xs2: list_real,N: nat,X: real] :
% 0.35/0.61        ( ( ( size_size_list_real @ Xs2 )
% 0.35/0.61          = N )
% 0.35/0.61       => ( ! [Y3: real] :
% 0.35/0.61              ( ( member_real @ Y3 @ ( set_real2 @ Xs2 ) )
% 0.35/0.61             => ( Y3 = X ) )
% 0.35/0.61         => ( Xs2
% 0.35/0.61            = ( replicate_real @ N @ X ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % replicate_eqI
% 0.35/0.61  thf(fact_4767_replicate__eqI,axiom,
% 0.35/0.61      ! [Xs2: list_VEBT_VEBT,N: nat,X: vEBT_VEBT] :
% 0.35/0.61        ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 0.35/0.61          = N )
% 0.35/0.61       => ( ! [Y3: vEBT_VEBT] :
% 0.35/0.61              ( ( member_VEBT_VEBT @ Y3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 0.35/0.61             => ( Y3 = X ) )
% 0.35/0.61         => ( Xs2
% 0.35/0.61            = ( replicate_VEBT_VEBT @ N @ X ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % replicate_eqI
% 0.35/0.61  thf(fact_4768_replicate__eqI,axiom,
% 0.35/0.61      ! [Xs2: list_o,N: nat,X: $o] :
% 0.35/0.61        ( ( ( size_size_list_o @ Xs2 )
% 0.35/0.61          = N )
% 0.35/0.61       => ( ! [Y3: $o] :
% 0.35/0.61              ( ( member_o @ Y3 @ ( set_o2 @ Xs2 ) )
% 0.35/0.61             => ( Y3 = X ) )
% 0.35/0.61         => ( Xs2
% 0.35/0.61            = ( replicate_o @ N @ X ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % replicate_eqI
% 0.35/0.61  thf(fact_4769_replicate__eqI,axiom,
% 0.35/0.61      ! [Xs2: list_nat,N: nat,X: nat] :
% 0.35/0.61        ( ( ( size_size_list_nat @ Xs2 )
% 0.35/0.61          = N )
% 0.35/0.61       => ( ! [Y3: nat] :
% 0.35/0.61              ( ( member_nat @ Y3 @ ( set_nat2 @ Xs2 ) )
% 0.35/0.61             => ( Y3 = X ) )
% 0.35/0.61         => ( Xs2
% 0.35/0.61            = ( replicate_nat @ N @ X ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % replicate_eqI
% 0.35/0.61  thf(fact_4770_replicate__eqI,axiom,
% 0.35/0.61      ! [Xs2: list_int,N: nat,X: int] :
% 0.35/0.61        ( ( ( size_size_list_int @ Xs2 )
% 0.35/0.61          = N )
% 0.35/0.61       => ( ! [Y3: int] :
% 0.35/0.61              ( ( member_int @ Y3 @ ( set_int2 @ Xs2 ) )
% 0.35/0.61             => ( Y3 = X ) )
% 0.35/0.61         => ( Xs2
% 0.35/0.61            = ( replicate_int @ N @ X ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % replicate_eqI
% 0.35/0.61  thf(fact_4771_replicate__length__same,axiom,
% 0.35/0.61      ! [Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 0.35/0.61        ( ! [X3: vEBT_VEBT] :
% 0.35/0.61            ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 0.35/0.61           => ( X3 = X ) )
% 0.35/0.61       => ( ( replicate_VEBT_VEBT @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ X )
% 0.35/0.61          = Xs2 ) ) ).
% 0.35/0.61  
% 0.35/0.61  % replicate_length_same
% 0.35/0.61  thf(fact_4772_replicate__length__same,axiom,
% 0.35/0.61      ! [Xs2: list_o,X: $o] :
% 0.35/0.61        ( ! [X3: $o] :
% 0.35/0.61            ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 0.35/0.61           => ( X3 = X ) )
% 0.35/0.61       => ( ( replicate_o @ ( size_size_list_o @ Xs2 ) @ X )
% 0.35/0.61          = Xs2 ) ) ).
% 0.35/0.61  
% 0.35/0.61  % replicate_length_same
% 0.35/0.61  thf(fact_4773_replicate__length__same,axiom,
% 0.35/0.61      ! [Xs2: list_nat,X: nat] :
% 0.35/0.61        ( ! [X3: nat] :
% 0.35/0.61            ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 0.35/0.61           => ( X3 = X ) )
% 0.35/0.61       => ( ( replicate_nat @ ( size_size_list_nat @ Xs2 ) @ X )
% 0.35/0.61          = Xs2 ) ) ).
% 0.35/0.61  
% 0.35/0.61  % replicate_length_same
% 0.35/0.61  thf(fact_4774_replicate__length__same,axiom,
% 0.35/0.61      ! [Xs2: list_int,X: int] :
% 0.35/0.61        ( ! [X3: int] :
% 0.35/0.61            ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 0.35/0.61           => ( X3 = X ) )
% 0.35/0.61       => ( ( replicate_int @ ( size_size_list_int @ Xs2 ) @ X )
% 0.35/0.61          = Xs2 ) ) ).
% 0.35/0.61  
% 0.35/0.61  % replicate_length_same
% 0.35/0.61  thf(fact_4775_set__replicate__Suc,axiom,
% 0.35/0.61      ! [N: nat,X: vEBT_VEBT] :
% 0.35/0.61        ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ ( suc @ N ) @ X ) )
% 0.35/0.61        = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ).
% 0.35/0.61  
% 0.35/0.61  % set_replicate_Suc
% 0.35/0.61  thf(fact_4776_set__replicate__Suc,axiom,
% 0.35/0.61      ! [N: nat,X: nat] :
% 0.35/0.61        ( ( set_nat2 @ ( replicate_nat @ ( suc @ N ) @ X ) )
% 0.35/0.61        = ( insert_nat @ X @ bot_bot_set_nat ) ) ).
% 0.35/0.61  
% 0.35/0.61  % set_replicate_Suc
% 0.35/0.61  thf(fact_4777_set__replicate__Suc,axiom,
% 0.35/0.61      ! [N: nat,X: int] :
% 0.35/0.61        ( ( set_int2 @ ( replicate_int @ ( suc @ N ) @ X ) )
% 0.35/0.61        = ( insert_int @ X @ bot_bot_set_int ) ) ).
% 0.35/0.61  
% 0.35/0.61  % set_replicate_Suc
% 0.35/0.61  thf(fact_4778_set__replicate__Suc,axiom,
% 0.35/0.61      ! [N: nat,X: real] :
% 0.35/0.61        ( ( set_real2 @ ( replicate_real @ ( suc @ N ) @ X ) )
% 0.35/0.61        = ( insert_real @ X @ bot_bot_set_real ) ) ).
% 0.35/0.61  
% 0.35/0.61  % set_replicate_Suc
% 0.35/0.61  thf(fact_4779_set__replicate__conv__if,axiom,
% 0.35/0.61      ! [N: nat,X: vEBT_VEBT] :
% 0.35/0.61        ( ( ( N = zero_zero_nat )
% 0.35/0.61         => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X ) )
% 0.35/0.61            = bot_bo8194388402131092736T_VEBT ) )
% 0.35/0.61        & ( ( N != zero_zero_nat )
% 0.35/0.61         => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X ) )
% 0.35/0.61            = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % set_replicate_conv_if
% 0.35/0.61  thf(fact_4780_set__replicate__conv__if,axiom,
% 0.35/0.61      ! [N: nat,X: nat] :
% 0.35/0.61        ( ( ( N = zero_zero_nat )
% 0.35/0.61         => ( ( set_nat2 @ ( replicate_nat @ N @ X ) )
% 0.35/0.61            = bot_bot_set_nat ) )
% 0.35/0.61        & ( ( N != zero_zero_nat )
% 0.35/0.61         => ( ( set_nat2 @ ( replicate_nat @ N @ X ) )
% 0.35/0.61            = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % set_replicate_conv_if
% 0.35/0.61  thf(fact_4781_set__replicate__conv__if,axiom,
% 0.35/0.61      ! [N: nat,X: int] :
% 0.35/0.61        ( ( ( N = zero_zero_nat )
% 0.35/0.61         => ( ( set_int2 @ ( replicate_int @ N @ X ) )
% 0.35/0.61            = bot_bot_set_int ) )
% 0.35/0.61        & ( ( N != zero_zero_nat )
% 0.35/0.61         => ( ( set_int2 @ ( replicate_int @ N @ X ) )
% 0.35/0.61            = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % set_replicate_conv_if
% 0.35/0.61  thf(fact_4782_set__replicate__conv__if,axiom,
% 0.35/0.61      ! [N: nat,X: real] :
% 0.35/0.61        ( ( ( N = zero_zero_nat )
% 0.35/0.61         => ( ( set_real2 @ ( replicate_real @ N @ X ) )
% 0.35/0.61            = bot_bot_set_real ) )
% 0.35/0.61        & ( ( N != zero_zero_nat )
% 0.35/0.61         => ( ( set_real2 @ ( replicate_real @ N @ X ) )
% 0.35/0.61            = ( insert_real @ X @ bot_bot_set_real ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % set_replicate_conv_if
% 0.35/0.61  thf(fact_4783_of__bool__odd__eq__mod__2,axiom,
% 0.35/0.61      ! [A: nat] :
% 0.35/0.61        ( ( zero_n2687167440665602831ol_nat
% 0.35/0.61          @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 0.35/0.61        = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_odd_eq_mod_2
% 0.35/0.61  thf(fact_4784_of__bool__odd__eq__mod__2,axiom,
% 0.35/0.61      ! [A: int] :
% 0.35/0.61        ( ( zero_n2684676970156552555ol_int
% 0.35/0.61          @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 0.35/0.61        = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_odd_eq_mod_2
% 0.35/0.61  thf(fact_4785_of__bool__odd__eq__mod__2,axiom,
% 0.35/0.61      ! [A: code_integer] :
% 0.35/0.61        ( ( zero_n356916108424825756nteger
% 0.35/0.61          @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 0.35/0.61        = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % of_bool_odd_eq_mod_2
% 0.35/0.61  thf(fact_4786_signed__take__bit__int__less__exp,axiom,
% 0.35/0.61      ! [N: nat,K: int] : ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 0.35/0.61  
% 0.35/0.61  % signed_take_bit_int_less_exp
% 0.35/0.61  thf(fact_4787_even__signed__take__bit__iff,axiom,
% 0.35/0.61      ! [M: nat,A: code_integer] :
% 0.35/0.61        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ M @ A ) )
% 0.35/0.61        = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % even_signed_take_bit_iff
% 0.35/0.61  thf(fact_4788_even__signed__take__bit__iff,axiom,
% 0.35/0.61      ! [M: nat,A: int] :
% 0.35/0.61        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ M @ A ) )
% 0.35/0.61        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % even_signed_take_bit_iff
% 0.35/0.61  thf(fact_4789_bits__induct,axiom,
% 0.35/0.61      ! [P: nat > $o,A: nat] :
% 0.35/0.61        ( ! [A4: nat] :
% 0.35/0.61            ( ( ( divide_divide_nat @ A4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.61              = A4 )
% 0.35/0.61           => ( P @ A4 ) )
% 0.35/0.61       => ( ! [A4: nat,B3: $o] :
% 0.35/0.61              ( ( P @ A4 )
% 0.35/0.61             => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B3 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.61                  = A4 )
% 0.35/0.61               => ( P @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B3 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A4 ) ) ) ) )
% 0.35/0.61         => ( P @ A ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % bits_induct
% 0.35/0.61  thf(fact_4790_bits__induct,axiom,
% 0.35/0.61      ! [P: int > $o,A: int] :
% 0.35/0.61        ( ! [A4: int] :
% 0.35/0.61            ( ( ( divide_divide_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.61              = A4 )
% 0.35/0.61           => ( P @ A4 ) )
% 0.35/0.61       => ( ! [A4: int,B3: $o] :
% 0.35/0.61              ( ( P @ A4 )
% 0.35/0.61             => ( ( ( divide_divide_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B3 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A4 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.61                  = A4 )
% 0.35/0.61               => ( P @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B3 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A4 ) ) ) ) )
% 0.35/0.61         => ( P @ A ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % bits_induct
% 0.35/0.61  thf(fact_4791_bits__induct,axiom,
% 0.35/0.61      ! [P: code_integer > $o,A: code_integer] :
% 0.35/0.61        ( ! [A4: code_integer] :
% 0.35/0.61            ( ( ( divide6298287555418463151nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.35/0.61              = A4 )
% 0.35/0.61           => ( P @ A4 ) )
% 0.35/0.61       => ( ! [A4: code_integer,B3: $o] :
% 0.35/0.61              ( ( P @ A4 )
% 0.35/0.61             => ( ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B3 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A4 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.35/0.61                  = A4 )
% 0.35/0.61               => ( P @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B3 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A4 ) ) ) ) )
% 0.35/0.61         => ( P @ A ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % bits_induct
% 0.35/0.61  thf(fact_4792_signed__take__bit__int__less__self__iff,axiom,
% 0.35/0.61      ! [N: nat,K: int] :
% 0.35/0.61        ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 0.35/0.61        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 0.35/0.61  
% 0.35/0.61  % signed_take_bit_int_less_self_iff
% 0.35/0.61  thf(fact_4793_signed__take__bit__int__greater__eq__self__iff,axiom,
% 0.35/0.61      ! [K: int,N: nat] :
% 0.35/0.61        ( ( ord_less_eq_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 0.35/0.61        = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % signed_take_bit_int_greater_eq_self_iff
% 0.35/0.61  thf(fact_4794_exp__mod__exp,axiom,
% 0.35/0.61      ! [M: nat,N: nat] :
% 0.35/0.61        ( ( modulo_modulo_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ M @ N ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % exp_mod_exp
% 0.35/0.61  thf(fact_4795_exp__mod__exp,axiom,
% 0.35/0.61      ! [M: nat,N: nat] :
% 0.35/0.61        ( ( modulo_modulo_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ M @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % exp_mod_exp
% 0.35/0.61  thf(fact_4796_exp__mod__exp,axiom,
% 0.35/0.61      ! [M: nat,N: nat] :
% 0.35/0.61        ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ M @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % exp_mod_exp
% 0.35/0.61  thf(fact_4797_divmod__nat__def,axiom,
% 0.35/0.61      ( divmod_nat
% 0.35/0.61      = ( ^ [M6: nat,N2: nat] : ( product_Pair_nat_nat @ ( divide_divide_nat @ M6 @ N2 ) @ ( modulo_modulo_nat @ M6 @ N2 ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % divmod_nat_def
% 0.35/0.61  thf(fact_4798_signed__take__bit__int__less__eq,axiom,
% 0.35/0.61      ! [N: nat,K: int] :
% 0.35/0.61        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 0.35/0.61       => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % signed_take_bit_int_less_eq
% 0.35/0.61  thf(fact_4799_option_Osize__gen_I1_J,axiom,
% 0.35/0.61      ! [X: product_prod_nat_nat > nat] :
% 0.35/0.61        ( ( size_o8335143837870341156at_nat @ X @ none_P5556105721700978146at_nat )
% 0.35/0.61        = ( suc @ zero_zero_nat ) ) ).
% 0.35/0.61  
% 0.35/0.61  % option.size_gen(1)
% 0.35/0.61  thf(fact_4800_option_Osize__gen_I1_J,axiom,
% 0.35/0.61      ! [X: nat > nat] :
% 0.35/0.61        ( ( size_option_nat @ X @ none_nat )
% 0.35/0.61        = ( suc @ zero_zero_nat ) ) ).
% 0.35/0.61  
% 0.35/0.61  % option.size_gen(1)
% 0.35/0.61  thf(fact_4801_option_Osize__gen_I1_J,axiom,
% 0.35/0.61      ! [X: num > nat] :
% 0.35/0.61        ( ( size_option_num @ X @ none_num )
% 0.35/0.61        = ( suc @ zero_zero_nat ) ) ).
% 0.35/0.61  
% 0.35/0.61  % option.size_gen(1)
% 0.35/0.61  thf(fact_4802_even__set__encode__iff,axiom,
% 0.35/0.61      ! [A2: set_nat] :
% 0.35/0.61        ( ( finite_finite_nat @ A2 )
% 0.35/0.61       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A2 ) )
% 0.35/0.61          = ( ~ ( member_nat @ zero_zero_nat @ A2 ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % even_set_encode_iff
% 0.35/0.61  thf(fact_4803_exp__div__exp__eq,axiom,
% 0.35/0.61      ! [M: nat,N: nat] :
% 0.35/0.61        ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61        = ( times_times_nat
% 0.35/0.61          @ ( zero_n2687167440665602831ol_nat
% 0.35/0.61            @ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 0.35/0.61               != zero_zero_nat )
% 0.35/0.61              & ( ord_less_eq_nat @ N @ M ) ) )
% 0.35/0.61          @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % exp_div_exp_eq
% 0.35/0.61  thf(fact_4804_exp__div__exp__eq,axiom,
% 0.35/0.61      ! [M: nat,N: nat] :
% 0.35/0.61        ( ( divide_divide_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61        = ( times_times_int
% 0.35/0.61          @ ( zero_n2684676970156552555ol_int
% 0.35/0.61            @ ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 0.35/0.61               != zero_zero_int )
% 0.35/0.61              & ( ord_less_eq_nat @ N @ M ) ) )
% 0.35/0.61          @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % exp_div_exp_eq
% 0.35/0.61  thf(fact_4805_exp__div__exp__eq,axiom,
% 0.35/0.61      ! [M: nat,N: nat] :
% 0.35/0.61        ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61        = ( times_3573771949741848930nteger
% 0.35/0.61          @ ( zero_n356916108424825756nteger
% 0.35/0.61            @ ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M )
% 0.35/0.61               != zero_z3403309356797280102nteger )
% 0.35/0.61              & ( ord_less_eq_nat @ N @ M ) ) )
% 0.35/0.61          @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % exp_div_exp_eq
% 0.35/0.61  thf(fact_4806_vebt__buildup_Osimps_I3_J,axiom,
% 0.35/0.61      ! [Va: nat] :
% 0.35/0.61        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 0.35/0.61         => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 0.35/0.61            = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.35/0.61        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 0.35/0.61         => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 0.35/0.61            = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % vebt_buildup.simps(3)
% 0.35/0.61  thf(fact_4807_Divides_Oadjust__div__eq,axiom,
% 0.35/0.61      ! [Q2: int,R: int] :
% 0.35/0.61        ( ( adjust_div @ ( product_Pair_int_int @ Q2 @ R ) )
% 0.35/0.61        = ( plus_plus_int @ Q2 @ ( zero_n2684676970156552555ol_int @ ( R != zero_zero_int ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % Divides.adjust_div_eq
% 0.35/0.61  thf(fact_4808_signed__take__bit__Suc__minus__bit1,axiom,
% 0.35/0.61      ! [N: nat,K: num] :
% 0.35/0.61        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.35/0.61        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.35/0.61  
% 0.35/0.61  % signed_take_bit_Suc_minus_bit1
% 0.35/0.61  thf(fact_4809_signed__take__bit__rec,axiom,
% 0.35/0.61      ( bit_ri6519982836138164636nteger
% 0.35/0.61      = ( ^ [N2: nat,A3: code_integer] : ( if_Code_integer @ ( N2 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % signed_take_bit_rec
% 0.35/0.61  thf(fact_4810_signed__take__bit__rec,axiom,
% 0.35/0.61      ( bit_ri631733984087533419it_int
% 0.35/0.61      = ( ^ [N2: nat,A3: int] : ( if_int @ ( N2 = zero_zero_nat ) @ ( uminus_uminus_int @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( plus_plus_int @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % signed_take_bit_rec
% 0.35/0.61  thf(fact_4811_signed__take__bit__numeral__bit1,axiom,
% 0.35/0.61      ! [L2: num,K: num] :
% 0.35/0.61        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 0.35/0.61        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.35/0.61  
% 0.35/0.61  % signed_take_bit_numeral_bit1
% 0.35/0.61  thf(fact_4812_vebt__buildup_Opelims,axiom,
% 0.35/0.61      ! [X: nat,Y2: vEBT_VEBT] :
% 0.35/0.61        ( ( ( vEBT_vebt_buildup @ X )
% 0.35/0.61          = Y2 )
% 0.35/0.61       => ( ( accp_nat @ vEBT_v4011308405150292612up_rel @ X )
% 0.35/0.61         => ( ( ( X = zero_zero_nat )
% 0.35/0.61             => ( ( Y2
% 0.35/0.61                  = ( vEBT_Leaf @ $false @ $false ) )
% 0.35/0.61               => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat ) ) )
% 0.35/0.61           => ( ( ( X
% 0.35/0.61                  = ( suc @ zero_zero_nat ) )
% 0.35/0.61               => ( ( Y2
% 0.35/0.61                    = ( vEBT_Leaf @ $false @ $false ) )
% 0.35/0.61                 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ zero_zero_nat ) ) ) )
% 0.35/0.61             => ~ ! [Va2: nat] :
% 0.35/0.61                    ( ( X
% 0.35/0.61                      = ( suc @ ( suc @ Va2 ) ) )
% 0.35/0.61                   => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 0.35/0.61                         => ( Y2
% 0.35/0.61                            = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.35/0.61                        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 0.35/0.61                         => ( Y2
% 0.35/0.61                            = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 0.35/0.61                     => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ ( suc @ Va2 ) ) ) ) ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % vebt_buildup.pelims
% 0.35/0.61  thf(fact_4813_set__decode__0,axiom,
% 0.35/0.61      ! [X: nat] :
% 0.35/0.61        ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X ) )
% 0.35/0.61        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % set_decode_0
% 0.35/0.61  thf(fact_4814_set__decode__Suc,axiom,
% 0.35/0.61      ! [N: nat,X: nat] :
% 0.35/0.61        ( ( member_nat @ ( suc @ N ) @ ( nat_set_decode @ X ) )
% 0.35/0.61        = ( member_nat @ N @ ( nat_set_decode @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % set_decode_Suc
% 0.35/0.61  thf(fact_4815_neg__le__iff__le,axiom,
% 0.35/0.61      ! [B: real,A: real] :
% 0.35/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 0.35/0.61        = ( ord_less_eq_real @ A @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_le_iff_le
% 0.35/0.61  thf(fact_4816_neg__le__iff__le,axiom,
% 0.35/0.61      ! [B: code_integer,A: code_integer] :
% 0.35/0.61        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 0.35/0.61        = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_le_iff_le
% 0.35/0.61  thf(fact_4817_neg__le__iff__le,axiom,
% 0.35/0.61      ! [B: rat,A: rat] :
% 0.35/0.61        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 0.35/0.61        = ( ord_less_eq_rat @ A @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_le_iff_le
% 0.35/0.61  thf(fact_4818_neg__le__iff__le,axiom,
% 0.35/0.61      ! [B: int,A: int] :
% 0.35/0.61        ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 0.35/0.61        = ( ord_less_eq_int @ A @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_le_iff_le
% 0.35/0.61  thf(fact_4819_neg__less__iff__less,axiom,
% 0.35/0.61      ! [B: int,A: int] :
% 0.35/0.61        ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 0.35/0.61        = ( ord_less_int @ A @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_less_iff_less
% 0.35/0.61  thf(fact_4820_neg__less__iff__less,axiom,
% 0.35/0.61      ! [B: real,A: real] :
% 0.35/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 0.35/0.61        = ( ord_less_real @ A @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_less_iff_less
% 0.35/0.61  thf(fact_4821_neg__less__iff__less,axiom,
% 0.35/0.61      ! [B: code_integer,A: code_integer] :
% 0.35/0.61        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 0.35/0.61        = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_less_iff_less
% 0.35/0.61  thf(fact_4822_neg__less__iff__less,axiom,
% 0.35/0.61      ! [B: rat,A: rat] :
% 0.35/0.61        ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 0.35/0.61        = ( ord_less_rat @ A @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_less_iff_less
% 0.35/0.61  thf(fact_4823_neg__numeral__eq__iff,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 0.35/0.61          = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.61        = ( M = N ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_numeral_eq_iff
% 0.35/0.61  thf(fact_4824_neg__numeral__eq__iff,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 0.35/0.61          = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.35/0.61        = ( M = N ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_numeral_eq_iff
% 0.35/0.61  thf(fact_4825_neg__numeral__eq__iff,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 0.35/0.61          = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 0.35/0.61        = ( M = N ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_numeral_eq_iff
% 0.35/0.61  thf(fact_4826_neg__numeral__eq__iff,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 0.35/0.61          = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.35/0.61        = ( M = N ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_numeral_eq_iff
% 0.35/0.61  thf(fact_4827_neg__numeral__eq__iff,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 0.35/0.61          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.35/0.61        = ( M = N ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_numeral_eq_iff
% 0.35/0.61  thf(fact_4828_mult__minus__left,axiom,
% 0.35/0.61      ! [A: int,B: int] :
% 0.35/0.61        ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 0.35/0.61        = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mult_minus_left
% 0.35/0.61  thf(fact_4829_mult__minus__left,axiom,
% 0.35/0.61      ! [A: real,B: real] :
% 0.35/0.61        ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 0.35/0.61        = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mult_minus_left
% 0.35/0.61  thf(fact_4830_mult__minus__left,axiom,
% 0.35/0.61      ! [A: complex,B: complex] :
% 0.35/0.61        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 0.35/0.61        = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mult_minus_left
% 0.35/0.61  thf(fact_4831_mult__minus__left,axiom,
% 0.35/0.61      ! [A: code_integer,B: code_integer] :
% 0.35/0.61        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.35/0.61        = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mult_minus_left
% 0.35/0.61  thf(fact_4832_mult__minus__left,axiom,
% 0.35/0.61      ! [A: rat,B: rat] :
% 0.35/0.61        ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.35/0.61        = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mult_minus_left
% 0.35/0.61  thf(fact_4833_minus__mult__minus,axiom,
% 0.35/0.61      ! [A: int,B: int] :
% 0.35/0.61        ( ( times_times_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 0.35/0.61        = ( times_times_int @ A @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_mult_minus
% 0.35/0.61  thf(fact_4834_minus__mult__minus,axiom,
% 0.35/0.61      ! [A: real,B: real] :
% 0.35/0.61        ( ( times_times_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 0.35/0.61        = ( times_times_real @ A @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_mult_minus
% 0.35/0.61  thf(fact_4835_minus__mult__minus,axiom,
% 0.35/0.61      ! [A: complex,B: complex] :
% 0.35/0.61        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 0.35/0.61        = ( times_times_complex @ A @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_mult_minus
% 0.35/0.61  thf(fact_4836_minus__mult__minus,axiom,
% 0.35/0.61      ! [A: code_integer,B: code_integer] :
% 0.35/0.61        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 0.35/0.61        = ( times_3573771949741848930nteger @ A @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_mult_minus
% 0.35/0.61  thf(fact_4837_minus__mult__minus,axiom,
% 0.35/0.61      ! [A: rat,B: rat] :
% 0.35/0.61        ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 0.35/0.61        = ( times_times_rat @ A @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_mult_minus
% 0.35/0.61  thf(fact_4838_mult__minus__right,axiom,
% 0.35/0.61      ! [A: int,B: int] :
% 0.35/0.61        ( ( times_times_int @ A @ ( uminus_uminus_int @ B ) )
% 0.35/0.61        = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mult_minus_right
% 0.35/0.61  thf(fact_4839_mult__minus__right,axiom,
% 0.35/0.61      ! [A: real,B: real] :
% 0.35/0.61        ( ( times_times_real @ A @ ( uminus_uminus_real @ B ) )
% 0.35/0.61        = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mult_minus_right
% 0.35/0.61  thf(fact_4840_mult__minus__right,axiom,
% 0.35/0.61      ! [A: complex,B: complex] :
% 0.35/0.61        ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 0.35/0.61        = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mult_minus_right
% 0.35/0.61  thf(fact_4841_mult__minus__right,axiom,
% 0.35/0.61      ! [A: code_integer,B: code_integer] :
% 0.35/0.61        ( ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.35/0.61        = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mult_minus_right
% 0.35/0.61  thf(fact_4842_mult__minus__right,axiom,
% 0.35/0.61      ! [A: rat,B: rat] :
% 0.35/0.61        ( ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.35/0.61        = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mult_minus_right
% 0.35/0.61  thf(fact_4843_minus__add__distrib,axiom,
% 0.35/0.61      ! [A: int,B: int] :
% 0.35/0.61        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 0.35/0.61        = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_add_distrib
% 0.35/0.61  thf(fact_4844_minus__add__distrib,axiom,
% 0.35/0.61      ! [A: real,B: real] :
% 0.35/0.61        ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 0.35/0.61        = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_add_distrib
% 0.35/0.61  thf(fact_4845_minus__add__distrib,axiom,
% 0.35/0.61      ! [A: complex,B: complex] :
% 0.35/0.61        ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 0.35/0.61        = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_add_distrib
% 0.35/0.61  thf(fact_4846_minus__add__distrib,axiom,
% 0.35/0.61      ! [A: code_integer,B: code_integer] :
% 0.35/0.61        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.35/0.61        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_add_distrib
% 0.35/0.61  thf(fact_4847_minus__add__distrib,axiom,
% 0.35/0.61      ! [A: rat,B: rat] :
% 0.35/0.61        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 0.35/0.61        = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_add_distrib
% 0.35/0.61  thf(fact_4848_minus__add__cancel,axiom,
% 0.35/0.61      ! [A: int,B: int] :
% 0.35/0.61        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 0.35/0.61        = B ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_add_cancel
% 0.35/0.61  thf(fact_4849_minus__add__cancel,axiom,
% 0.35/0.61      ! [A: real,B: real] :
% 0.35/0.61        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
% 0.35/0.61        = B ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_add_cancel
% 0.35/0.61  thf(fact_4850_minus__add__cancel,axiom,
% 0.35/0.61      ! [A: complex,B: complex] :
% 0.35/0.61        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( plus_plus_complex @ A @ B ) )
% 0.35/0.61        = B ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_add_cancel
% 0.35/0.61  thf(fact_4851_minus__add__cancel,axiom,
% 0.35/0.61      ! [A: code_integer,B: code_integer] :
% 0.35/0.61        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.35/0.61        = B ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_add_cancel
% 0.35/0.61  thf(fact_4852_minus__add__cancel,axiom,
% 0.35/0.61      ! [A: rat,B: rat] :
% 0.35/0.61        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 0.35/0.61        = B ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_add_cancel
% 0.35/0.61  thf(fact_4853_add__minus__cancel,axiom,
% 0.35/0.61      ! [A: int,B: int] :
% 0.35/0.61        ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 0.35/0.61        = B ) ).
% 0.35/0.61  
% 0.35/0.61  % add_minus_cancel
% 0.35/0.61  thf(fact_4854_add__minus__cancel,axiom,
% 0.35/0.61      ! [A: real,B: real] :
% 0.35/0.61        ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
% 0.35/0.61        = B ) ).
% 0.35/0.61  
% 0.35/0.61  % add_minus_cancel
% 0.35/0.61  thf(fact_4855_add__minus__cancel,axiom,
% 0.35/0.61      ! [A: complex,B: complex] :
% 0.35/0.61        ( ( plus_plus_complex @ A @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) )
% 0.35/0.61        = B ) ).
% 0.35/0.61  
% 0.35/0.61  % add_minus_cancel
% 0.35/0.61  thf(fact_4856_add__minus__cancel,axiom,
% 0.35/0.61      ! [A: code_integer,B: code_integer] :
% 0.35/0.61        ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) )
% 0.35/0.61        = B ) ).
% 0.35/0.61  
% 0.35/0.61  % add_minus_cancel
% 0.35/0.61  thf(fact_4857_add__minus__cancel,axiom,
% 0.35/0.61      ! [A: rat,B: rat] :
% 0.35/0.61        ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 0.35/0.61        = B ) ).
% 0.35/0.61  
% 0.35/0.61  % add_minus_cancel
% 0.35/0.61  thf(fact_4858_minus__diff__eq,axiom,
% 0.35/0.61      ! [A: int,B: int] :
% 0.35/0.61        ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
% 0.35/0.61        = ( minus_minus_int @ B @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_diff_eq
% 0.35/0.61  thf(fact_4859_minus__diff__eq,axiom,
% 0.35/0.61      ! [A: real,B: real] :
% 0.35/0.61        ( ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) )
% 0.35/0.61        = ( minus_minus_real @ B @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_diff_eq
% 0.35/0.61  thf(fact_4860_minus__diff__eq,axiom,
% 0.35/0.61      ! [A: complex,B: complex] :
% 0.35/0.61        ( ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) )
% 0.35/0.61        = ( minus_minus_complex @ B @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_diff_eq
% 0.35/0.61  thf(fact_4861_minus__diff__eq,axiom,
% 0.35/0.61      ! [A: code_integer,B: code_integer] :
% 0.35/0.61        ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.35/0.61        = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_diff_eq
% 0.35/0.61  thf(fact_4862_minus__diff__eq,axiom,
% 0.35/0.61      ! [A: rat,B: rat] :
% 0.35/0.61        ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) )
% 0.35/0.61        = ( minus_minus_rat @ B @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_diff_eq
% 0.35/0.61  thf(fact_4863_div__minus__minus,axiom,
% 0.35/0.61      ! [A: int,B: int] :
% 0.35/0.61        ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 0.35/0.61        = ( divide_divide_int @ A @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % div_minus_minus
% 0.35/0.61  thf(fact_4864_div__minus__minus,axiom,
% 0.35/0.61      ! [A: code_integer,B: code_integer] :
% 0.35/0.61        ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 0.35/0.61        = ( divide6298287555418463151nteger @ A @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % div_minus_minus
% 0.35/0.61  thf(fact_4865_mod__minus__minus,axiom,
% 0.35/0.61      ! [A: int,B: int] :
% 0.35/0.61        ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 0.35/0.61        = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mod_minus_minus
% 0.35/0.61  thf(fact_4866_mod__minus__minus,axiom,
% 0.35/0.61      ! [A: code_integer,B: code_integer] :
% 0.35/0.61        ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 0.35/0.61        = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mod_minus_minus
% 0.35/0.61  thf(fact_4867_real__add__minus__iff,axiom,
% 0.35/0.61      ! [X: real,A: real] :
% 0.35/0.61        ( ( ( plus_plus_real @ X @ ( uminus_uminus_real @ A ) )
% 0.35/0.61          = zero_zero_real )
% 0.35/0.61        = ( X = A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % real_add_minus_iff
% 0.35/0.61  thf(fact_4868_neg__less__eq__nonneg,axiom,
% 0.35/0.61      ! [A: real] :
% 0.35/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
% 0.35/0.61        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_less_eq_nonneg
% 0.35/0.61  thf(fact_4869_neg__less__eq__nonneg,axiom,
% 0.35/0.61      ! [A: code_integer] :
% 0.35/0.61        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 0.35/0.61        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_less_eq_nonneg
% 0.35/0.61  thf(fact_4870_neg__less__eq__nonneg,axiom,
% 0.35/0.61      ! [A: rat] :
% 0.35/0.61        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.35/0.61        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_less_eq_nonneg
% 0.35/0.61  thf(fact_4871_neg__less__eq__nonneg,axiom,
% 0.35/0.61      ! [A: int] :
% 0.35/0.61        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 0.35/0.61        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_less_eq_nonneg
% 0.35/0.61  thf(fact_4872_less__eq__neg__nonpos,axiom,
% 0.35/0.61      ! [A: real] :
% 0.35/0.61        ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
% 0.35/0.61        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.35/0.61  
% 0.35/0.61  % less_eq_neg_nonpos
% 0.35/0.61  thf(fact_4873_less__eq__neg__nonpos,axiom,
% 0.35/0.61      ! [A: code_integer] :
% 0.35/0.61        ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 0.35/0.61        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.35/0.61  
% 0.35/0.61  % less_eq_neg_nonpos
% 0.35/0.61  thf(fact_4874_less__eq__neg__nonpos,axiom,
% 0.35/0.61      ! [A: rat] :
% 0.35/0.61        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 0.35/0.61        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.35/0.61  
% 0.35/0.61  % less_eq_neg_nonpos
% 0.35/0.61  thf(fact_4875_less__eq__neg__nonpos,axiom,
% 0.35/0.61      ! [A: int] :
% 0.35/0.61        ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 0.35/0.61        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.35/0.61  
% 0.35/0.61  % less_eq_neg_nonpos
% 0.35/0.61  thf(fact_4876_neg__le__0__iff__le,axiom,
% 0.35/0.61      ! [A: real] :
% 0.35/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 0.35/0.61        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_le_0_iff_le
% 0.35/0.61  thf(fact_4877_neg__le__0__iff__le,axiom,
% 0.35/0.61      ! [A: code_integer] :
% 0.35/0.61        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 0.35/0.61        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_le_0_iff_le
% 0.35/0.61  thf(fact_4878_neg__le__0__iff__le,axiom,
% 0.35/0.61      ! [A: rat] :
% 0.35/0.61        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 0.35/0.61        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_le_0_iff_le
% 0.35/0.61  thf(fact_4879_neg__le__0__iff__le,axiom,
% 0.35/0.61      ! [A: int] :
% 0.35/0.61        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 0.35/0.61        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_le_0_iff_le
% 0.35/0.61  thf(fact_4880_neg__0__le__iff__le,axiom,
% 0.35/0.61      ! [A: real] :
% 0.35/0.61        ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 0.35/0.61        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_0_le_iff_le
% 0.35/0.61  thf(fact_4881_neg__0__le__iff__le,axiom,
% 0.35/0.61      ! [A: code_integer] :
% 0.35/0.61        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 0.35/0.61        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_0_le_iff_le
% 0.35/0.61  thf(fact_4882_neg__0__le__iff__le,axiom,
% 0.35/0.61      ! [A: rat] :
% 0.35/0.61        ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 0.35/0.61        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_0_le_iff_le
% 0.35/0.61  thf(fact_4883_neg__0__le__iff__le,axiom,
% 0.35/0.61      ! [A: int] :
% 0.35/0.61        ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 0.35/0.61        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_0_le_iff_le
% 0.35/0.61  thf(fact_4884_neg__less__0__iff__less,axiom,
% 0.35/0.61      ! [A: int] :
% 0.35/0.61        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 0.35/0.61        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_less_0_iff_less
% 0.35/0.61  thf(fact_4885_neg__less__0__iff__less,axiom,
% 0.35/0.61      ! [A: real] :
% 0.35/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 0.35/0.61        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_less_0_iff_less
% 0.35/0.61  thf(fact_4886_neg__less__0__iff__less,axiom,
% 0.35/0.61      ! [A: code_integer] :
% 0.35/0.61        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 0.35/0.61        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_less_0_iff_less
% 0.35/0.61  thf(fact_4887_neg__less__0__iff__less,axiom,
% 0.35/0.61      ! [A: rat] :
% 0.35/0.61        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 0.35/0.61        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_less_0_iff_less
% 0.35/0.61  thf(fact_4888_neg__0__less__iff__less,axiom,
% 0.35/0.61      ! [A: int] :
% 0.35/0.61        ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 0.35/0.61        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_0_less_iff_less
% 0.35/0.61  thf(fact_4889_neg__0__less__iff__less,axiom,
% 0.35/0.61      ! [A: real] :
% 0.35/0.61        ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 0.35/0.61        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_0_less_iff_less
% 0.35/0.61  thf(fact_4890_neg__0__less__iff__less,axiom,
% 0.35/0.61      ! [A: code_integer] :
% 0.35/0.61        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 0.35/0.61        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_0_less_iff_less
% 0.35/0.61  thf(fact_4891_neg__0__less__iff__less,axiom,
% 0.35/0.61      ! [A: rat] :
% 0.35/0.61        ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 0.35/0.61        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_0_less_iff_less
% 0.35/0.61  thf(fact_4892_neg__less__pos,axiom,
% 0.35/0.61      ! [A: int] :
% 0.35/0.61        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 0.35/0.61        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_less_pos
% 0.35/0.61  thf(fact_4893_neg__less__pos,axiom,
% 0.35/0.61      ! [A: real] :
% 0.35/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
% 0.35/0.61        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_less_pos
% 0.35/0.61  thf(fact_4894_neg__less__pos,axiom,
% 0.35/0.61      ! [A: code_integer] :
% 0.35/0.61        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 0.35/0.61        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_less_pos
% 0.35/0.61  thf(fact_4895_neg__less__pos,axiom,
% 0.35/0.61      ! [A: rat] :
% 0.35/0.61        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.35/0.61        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_less_pos
% 0.35/0.61  thf(fact_4896_less__neg__neg,axiom,
% 0.35/0.61      ! [A: int] :
% 0.35/0.61        ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 0.35/0.61        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.35/0.61  
% 0.35/0.61  % less_neg_neg
% 0.35/0.61  thf(fact_4897_less__neg__neg,axiom,
% 0.35/0.61      ! [A: real] :
% 0.35/0.61        ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
% 0.35/0.61        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.35/0.61  
% 0.35/0.61  % less_neg_neg
% 0.35/0.61  thf(fact_4898_less__neg__neg,axiom,
% 0.35/0.61      ! [A: code_integer] :
% 0.35/0.61        ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 0.35/0.61        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.35/0.61  
% 0.35/0.61  % less_neg_neg
% 0.35/0.61  thf(fact_4899_less__neg__neg,axiom,
% 0.35/0.61      ! [A: rat] :
% 0.35/0.61        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 0.35/0.61        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.35/0.61  
% 0.35/0.61  % less_neg_neg
% 0.35/0.61  thf(fact_4900_ab__left__minus,axiom,
% 0.35/0.61      ! [A: int] :
% 0.35/0.61        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 0.35/0.61        = zero_zero_int ) ).
% 0.35/0.61  
% 0.35/0.61  % ab_left_minus
% 0.35/0.61  thf(fact_4901_ab__left__minus,axiom,
% 0.35/0.61      ! [A: real] :
% 0.35/0.61        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 0.35/0.61        = zero_zero_real ) ).
% 0.35/0.61  
% 0.35/0.61  % ab_left_minus
% 0.35/0.61  thf(fact_4902_ab__left__minus,axiom,
% 0.35/0.61      ! [A: complex] :
% 0.35/0.61        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 0.35/0.61        = zero_zero_complex ) ).
% 0.35/0.61  
% 0.35/0.61  % ab_left_minus
% 0.35/0.61  thf(fact_4903_ab__left__minus,axiom,
% 0.35/0.61      ! [A: code_integer] :
% 0.35/0.61        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 0.35/0.61        = zero_z3403309356797280102nteger ) ).
% 0.35/0.61  
% 0.35/0.61  % ab_left_minus
% 0.35/0.61  thf(fact_4904_ab__left__minus,axiom,
% 0.35/0.61      ! [A: rat] :
% 0.35/0.61        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.35/0.61        = zero_zero_rat ) ).
% 0.35/0.61  
% 0.35/0.61  % ab_left_minus
% 0.35/0.61  thf(fact_4905_add_Oright__inverse,axiom,
% 0.35/0.61      ! [A: int] :
% 0.35/0.61        ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 0.35/0.61        = zero_zero_int ) ).
% 0.35/0.61  
% 0.35/0.61  % add.right_inverse
% 0.35/0.61  thf(fact_4906_add_Oright__inverse,axiom,
% 0.35/0.61      ! [A: real] :
% 0.35/0.61        ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
% 0.35/0.61        = zero_zero_real ) ).
% 0.35/0.61  
% 0.35/0.61  % add.right_inverse
% 0.35/0.61  thf(fact_4907_add_Oright__inverse,axiom,
% 0.35/0.61      ! [A: complex] :
% 0.35/0.61        ( ( plus_plus_complex @ A @ ( uminus1482373934393186551omplex @ A ) )
% 0.35/0.61        = zero_zero_complex ) ).
% 0.35/0.61  
% 0.35/0.61  % add.right_inverse
% 0.35/0.61  thf(fact_4908_add_Oright__inverse,axiom,
% 0.35/0.61      ! [A: code_integer] :
% 0.35/0.61        ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 0.35/0.61        = zero_z3403309356797280102nteger ) ).
% 0.35/0.61  
% 0.35/0.61  % add.right_inverse
% 0.35/0.61  thf(fact_4909_add_Oright__inverse,axiom,
% 0.35/0.61      ! [A: rat] :
% 0.35/0.61        ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 0.35/0.61        = zero_zero_rat ) ).
% 0.35/0.61  
% 0.35/0.61  % add.right_inverse
% 0.35/0.61  thf(fact_4910_diff__0,axiom,
% 0.35/0.61      ! [A: int] :
% 0.35/0.61        ( ( minus_minus_int @ zero_zero_int @ A )
% 0.35/0.61        = ( uminus_uminus_int @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_0
% 0.35/0.61  thf(fact_4911_diff__0,axiom,
% 0.35/0.61      ! [A: real] :
% 0.35/0.61        ( ( minus_minus_real @ zero_zero_real @ A )
% 0.35/0.61        = ( uminus_uminus_real @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_0
% 0.35/0.61  thf(fact_4912_diff__0,axiom,
% 0.35/0.61      ! [A: complex] :
% 0.35/0.61        ( ( minus_minus_complex @ zero_zero_complex @ A )
% 0.35/0.61        = ( uminus1482373934393186551omplex @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_0
% 0.35/0.61  thf(fact_4913_diff__0,axiom,
% 0.35/0.61      ! [A: code_integer] :
% 0.35/0.61        ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ A )
% 0.35/0.61        = ( uminus1351360451143612070nteger @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_0
% 0.35/0.61  thf(fact_4914_diff__0,axiom,
% 0.35/0.61      ! [A: rat] :
% 0.35/0.61        ( ( minus_minus_rat @ zero_zero_rat @ A )
% 0.35/0.61        = ( uminus_uminus_rat @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_0
% 0.35/0.61  thf(fact_4915_verit__minus__simplify_I3_J,axiom,
% 0.35/0.61      ! [B: int] :
% 0.35/0.61        ( ( minus_minus_int @ zero_zero_int @ B )
% 0.35/0.61        = ( uminus_uminus_int @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % verit_minus_simplify(3)
% 0.35/0.61  thf(fact_4916_verit__minus__simplify_I3_J,axiom,
% 0.35/0.61      ! [B: real] :
% 0.35/0.61        ( ( minus_minus_real @ zero_zero_real @ B )
% 0.35/0.61        = ( uminus_uminus_real @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % verit_minus_simplify(3)
% 0.35/0.61  thf(fact_4917_verit__minus__simplify_I3_J,axiom,
% 0.35/0.61      ! [B: complex] :
% 0.35/0.61        ( ( minus_minus_complex @ zero_zero_complex @ B )
% 0.35/0.61        = ( uminus1482373934393186551omplex @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % verit_minus_simplify(3)
% 0.35/0.61  thf(fact_4918_verit__minus__simplify_I3_J,axiom,
% 0.35/0.61      ! [B: code_integer] :
% 0.35/0.61        ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ B )
% 0.35/0.61        = ( uminus1351360451143612070nteger @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % verit_minus_simplify(3)
% 0.35/0.61  thf(fact_4919_verit__minus__simplify_I3_J,axiom,
% 0.35/0.61      ! [B: rat] :
% 0.35/0.61        ( ( minus_minus_rat @ zero_zero_rat @ B )
% 0.35/0.61        = ( uminus_uminus_rat @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % verit_minus_simplify(3)
% 0.35/0.61  thf(fact_4920_add__neg__numeral__simps_I3_J,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.61        = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % add_neg_numeral_simps(3)
% 0.35/0.61  thf(fact_4921_add__neg__numeral__simps_I3_J,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.35/0.61        = ( uminus_uminus_real @ ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % add_neg_numeral_simps(3)
% 0.35/0.61  thf(fact_4922_add__neg__numeral__simps_I3_J,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 0.35/0.61        = ( uminus1482373934393186551omplex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % add_neg_numeral_simps(3)
% 0.35/0.61  thf(fact_4923_add__neg__numeral__simps_I3_J,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.35/0.61        = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % add_neg_numeral_simps(3)
% 0.35/0.61  thf(fact_4924_add__neg__numeral__simps_I3_J,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.35/0.61        = ( uminus_uminus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % add_neg_numeral_simps(3)
% 0.35/0.61  thf(fact_4925_mult__minus1__right,axiom,
% 0.35/0.61      ! [Z: int] :
% 0.35/0.61        ( ( times_times_int @ Z @ ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.61        = ( uminus_uminus_int @ Z ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mult_minus1_right
% 0.35/0.61  thf(fact_4926_mult__minus1__right,axiom,
% 0.35/0.61      ! [Z: real] :
% 0.35/0.61        ( ( times_times_real @ Z @ ( uminus_uminus_real @ one_one_real ) )
% 0.35/0.61        = ( uminus_uminus_real @ Z ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mult_minus1_right
% 0.35/0.61  thf(fact_4927_mult__minus1__right,axiom,
% 0.35/0.61      ! [Z: complex] :
% 0.35/0.61        ( ( times_times_complex @ Z @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.35/0.61        = ( uminus1482373934393186551omplex @ Z ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mult_minus1_right
% 0.35/0.61  thf(fact_4928_mult__minus1__right,axiom,
% 0.35/0.61      ! [Z: code_integer] :
% 0.35/0.61        ( ( times_3573771949741848930nteger @ Z @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.61        = ( uminus1351360451143612070nteger @ Z ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mult_minus1_right
% 0.35/0.61  thf(fact_4929_mult__minus1__right,axiom,
% 0.35/0.61      ! [Z: rat] :
% 0.35/0.61        ( ( times_times_rat @ Z @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.35/0.61        = ( uminus_uminus_rat @ Z ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mult_minus1_right
% 0.35/0.61  thf(fact_4930_mult__minus1,axiom,
% 0.35/0.61      ! [Z: int] :
% 0.35/0.61        ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z )
% 0.35/0.61        = ( uminus_uminus_int @ Z ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mult_minus1
% 0.35/0.61  thf(fact_4931_mult__minus1,axiom,
% 0.35/0.61      ! [Z: real] :
% 0.35/0.61        ( ( times_times_real @ ( uminus_uminus_real @ one_one_real ) @ Z )
% 0.35/0.61        = ( uminus_uminus_real @ Z ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mult_minus1
% 0.35/0.61  thf(fact_4932_mult__minus1,axiom,
% 0.35/0.61      ! [Z: complex] :
% 0.35/0.61        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ Z )
% 0.35/0.61        = ( uminus1482373934393186551omplex @ Z ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mult_minus1
% 0.35/0.61  thf(fact_4933_mult__minus1,axiom,
% 0.35/0.61      ! [Z: code_integer] :
% 0.35/0.61        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z )
% 0.35/0.61        = ( uminus1351360451143612070nteger @ Z ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mult_minus1
% 0.35/0.61  thf(fact_4934_mult__minus1,axiom,
% 0.35/0.61      ! [Z: rat] :
% 0.35/0.61        ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z )
% 0.35/0.61        = ( uminus_uminus_rat @ Z ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mult_minus1
% 0.35/0.61  thf(fact_4935_diff__minus__eq__add,axiom,
% 0.35/0.61      ! [A: int,B: int] :
% 0.35/0.61        ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 0.35/0.61        = ( plus_plus_int @ A @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_minus_eq_add
% 0.35/0.61  thf(fact_4936_diff__minus__eq__add,axiom,
% 0.35/0.61      ! [A: real,B: real] :
% 0.35/0.61        ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
% 0.35/0.61        = ( plus_plus_real @ A @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_minus_eq_add
% 0.35/0.61  thf(fact_4937_diff__minus__eq__add,axiom,
% 0.35/0.61      ! [A: complex,B: complex] :
% 0.35/0.61        ( ( minus_minus_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 0.35/0.61        = ( plus_plus_complex @ A @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_minus_eq_add
% 0.35/0.61  thf(fact_4938_diff__minus__eq__add,axiom,
% 0.35/0.61      ! [A: code_integer,B: code_integer] :
% 0.35/0.61        ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.35/0.61        = ( plus_p5714425477246183910nteger @ A @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_minus_eq_add
% 0.35/0.61  thf(fact_4939_diff__minus__eq__add,axiom,
% 0.35/0.61      ! [A: rat,B: rat] :
% 0.35/0.61        ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.35/0.61        = ( plus_plus_rat @ A @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_minus_eq_add
% 0.35/0.61  thf(fact_4940_uminus__add__conv__diff,axiom,
% 0.35/0.61      ! [A: int,B: int] :
% 0.35/0.61        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 0.35/0.61        = ( minus_minus_int @ B @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % uminus_add_conv_diff
% 0.35/0.61  thf(fact_4941_uminus__add__conv__diff,axiom,
% 0.35/0.61      ! [A: real,B: real] :
% 0.35/0.61        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
% 0.35/0.61        = ( minus_minus_real @ B @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % uminus_add_conv_diff
% 0.35/0.61  thf(fact_4942_uminus__add__conv__diff,axiom,
% 0.35/0.61      ! [A: complex,B: complex] :
% 0.35/0.61        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 0.35/0.61        = ( minus_minus_complex @ B @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % uminus_add_conv_diff
% 0.35/0.61  thf(fact_4943_uminus__add__conv__diff,axiom,
% 0.35/0.61      ! [A: code_integer,B: code_integer] :
% 0.35/0.61        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.35/0.61        = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % uminus_add_conv_diff
% 0.35/0.61  thf(fact_4944_uminus__add__conv__diff,axiom,
% 0.35/0.61      ! [A: rat,B: rat] :
% 0.35/0.61        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.35/0.61        = ( minus_minus_rat @ B @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % uminus_add_conv_diff
% 0.35/0.61  thf(fact_4945_div__minus1__right,axiom,
% 0.35/0.61      ! [A: int] :
% 0.35/0.61        ( ( divide_divide_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.61        = ( uminus_uminus_int @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % div_minus1_right
% 0.35/0.61  thf(fact_4946_div__minus1__right,axiom,
% 0.35/0.61      ! [A: code_integer] :
% 0.35/0.61        ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.61        = ( uminus1351360451143612070nteger @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % div_minus1_right
% 0.35/0.61  thf(fact_4947_divide__minus1,axiom,
% 0.35/0.61      ! [X: real] :
% 0.35/0.61        ( ( divide_divide_real @ X @ ( uminus_uminus_real @ one_one_real ) )
% 0.35/0.61        = ( uminus_uminus_real @ X ) ) ).
% 0.35/0.61  
% 0.35/0.61  % divide_minus1
% 0.35/0.61  thf(fact_4948_divide__minus1,axiom,
% 0.35/0.61      ! [X: complex] :
% 0.35/0.61        ( ( divide1717551699836669952omplex @ X @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.35/0.61        = ( uminus1482373934393186551omplex @ X ) ) ).
% 0.35/0.61  
% 0.35/0.61  % divide_minus1
% 0.35/0.61  thf(fact_4949_divide__minus1,axiom,
% 0.35/0.61      ! [X: rat] :
% 0.35/0.61        ( ( divide_divide_rat @ X @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.35/0.61        = ( uminus_uminus_rat @ X ) ) ).
% 0.35/0.61  
% 0.35/0.61  % divide_minus1
% 0.35/0.61  thf(fact_4950_minus__mod__self1,axiom,
% 0.35/0.61      ! [B: int,A: int] :
% 0.35/0.61        ( ( modulo_modulo_int @ ( minus_minus_int @ B @ A ) @ B )
% 0.35/0.61        = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_mod_self1
% 0.35/0.61  thf(fact_4951_minus__mod__self1,axiom,
% 0.35/0.61      ! [B: code_integer,A: code_integer] :
% 0.35/0.61        ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ B )
% 0.35/0.61        = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_mod_self1
% 0.35/0.61  thf(fact_4952_signed__take__bit__of__minus__1,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ( bit_ri6519982836138164636nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.61        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.35/0.61  
% 0.35/0.61  % signed_take_bit_of_minus_1
% 0.35/0.61  thf(fact_4953_signed__take__bit__of__minus__1,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.61        = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.35/0.61  
% 0.35/0.61  % signed_take_bit_of_minus_1
% 0.35/0.61  thf(fact_4954_pred__numeral__simps_I1_J,axiom,
% 0.35/0.61      ( ( pred_numeral @ one )
% 0.35/0.61      = zero_zero_nat ) ).
% 0.35/0.61  
% 0.35/0.61  % pred_numeral_simps(1)
% 0.35/0.61  thf(fact_4955_Suc__eq__numeral,axiom,
% 0.35/0.61      ! [N: nat,K: num] :
% 0.35/0.61        ( ( ( suc @ N )
% 0.35/0.61          = ( numeral_numeral_nat @ K ) )
% 0.35/0.61        = ( N
% 0.35/0.61          = ( pred_numeral @ K ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % Suc_eq_numeral
% 0.35/0.61  thf(fact_4956_eq__numeral__Suc,axiom,
% 0.35/0.61      ! [K: num,N: nat] :
% 0.35/0.61        ( ( ( numeral_numeral_nat @ K )
% 0.35/0.61          = ( suc @ N ) )
% 0.35/0.61        = ( ( pred_numeral @ K )
% 0.35/0.61          = N ) ) ).
% 0.35/0.61  
% 0.35/0.61  % eq_numeral_Suc
% 0.35/0.61  thf(fact_4957_dbl__simps_I1_J,axiom,
% 0.35/0.61      ! [K: num] :
% 0.35/0.61        ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.35/0.61        = ( uminus_uminus_int @ ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % dbl_simps(1)
% 0.35/0.61  thf(fact_4958_dbl__simps_I1_J,axiom,
% 0.35/0.61      ! [K: num] :
% 0.35/0.61        ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 0.35/0.61        = ( uminus_uminus_real @ ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % dbl_simps(1)
% 0.35/0.61  thf(fact_4959_dbl__simps_I1_J,axiom,
% 0.35/0.61      ! [K: num] :
% 0.35/0.61        ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 0.35/0.61        = ( uminus1482373934393186551omplex @ ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % dbl_simps(1)
% 0.35/0.61  thf(fact_4960_dbl__simps_I1_J,axiom,
% 0.35/0.61      ! [K: num] :
% 0.35/0.61        ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 0.35/0.61        = ( uminus1351360451143612070nteger @ ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % dbl_simps(1)
% 0.35/0.61  thf(fact_4961_dbl__simps_I1_J,axiom,
% 0.35/0.61      ! [K: num] :
% 0.35/0.61        ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 0.35/0.61        = ( uminus_uminus_rat @ ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % dbl_simps(1)
% 0.35/0.61  thf(fact_4962_dbl__inc__simps_I4_J,axiom,
% 0.35/0.61      ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.61      = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.35/0.61  
% 0.35/0.61  % dbl_inc_simps(4)
% 0.35/0.61  thf(fact_4963_dbl__inc__simps_I4_J,axiom,
% 0.35/0.61      ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.35/0.61      = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.35/0.61  
% 0.35/0.61  % dbl_inc_simps(4)
% 0.35/0.61  thf(fact_4964_dbl__inc__simps_I4_J,axiom,
% 0.35/0.61      ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.35/0.61      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.35/0.61  
% 0.35/0.61  % dbl_inc_simps(4)
% 0.35/0.61  thf(fact_4965_dbl__inc__simps_I4_J,axiom,
% 0.35/0.61      ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.61      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.35/0.61  
% 0.35/0.61  % dbl_inc_simps(4)
% 0.35/0.61  thf(fact_4966_dbl__inc__simps_I4_J,axiom,
% 0.35/0.61      ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.35/0.61      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.35/0.61  
% 0.35/0.61  % dbl_inc_simps(4)
% 0.35/0.61  thf(fact_4967_add__neg__numeral__special_I7_J,axiom,
% 0.35/0.61      ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.61      = zero_zero_int ) ).
% 0.35/0.61  
% 0.35/0.61  % add_neg_numeral_special(7)
% 0.35/0.61  thf(fact_4968_add__neg__numeral__special_I7_J,axiom,
% 0.35/0.61      ( ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.35/0.61      = zero_zero_real ) ).
% 0.35/0.61  
% 0.35/0.61  % add_neg_numeral_special(7)
% 0.35/0.61  thf(fact_4969_add__neg__numeral__special_I7_J,axiom,
% 0.35/0.61      ( ( plus_plus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.35/0.61      = zero_zero_complex ) ).
% 0.35/0.61  
% 0.35/0.61  % add_neg_numeral_special(7)
% 0.35/0.61  thf(fact_4970_add__neg__numeral__special_I7_J,axiom,
% 0.35/0.61      ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.61      = zero_z3403309356797280102nteger ) ).
% 0.35/0.61  
% 0.35/0.61  % add_neg_numeral_special(7)
% 0.35/0.61  thf(fact_4971_add__neg__numeral__special_I7_J,axiom,
% 0.35/0.61      ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.35/0.61      = zero_zero_rat ) ).
% 0.35/0.61  
% 0.35/0.61  % add_neg_numeral_special(7)
% 0.35/0.61  thf(fact_4972_add__neg__numeral__special_I8_J,axiom,
% 0.35/0.61      ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 0.35/0.61      = zero_zero_int ) ).
% 0.35/0.61  
% 0.35/0.61  % add_neg_numeral_special(8)
% 0.35/0.61  thf(fact_4973_add__neg__numeral__special_I8_J,axiom,
% 0.35/0.61      ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 0.35/0.61      = zero_zero_real ) ).
% 0.35/0.61  
% 0.35/0.61  % add_neg_numeral_special(8)
% 0.35/0.61  thf(fact_4974_add__neg__numeral__special_I8_J,axiom,
% 0.35/0.61      ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 0.35/0.61      = zero_zero_complex ) ).
% 0.35/0.61  
% 0.35/0.61  % add_neg_numeral_special(8)
% 0.35/0.61  thf(fact_4975_add__neg__numeral__special_I8_J,axiom,
% 0.35/0.61      ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 0.35/0.61      = zero_z3403309356797280102nteger ) ).
% 0.35/0.61  
% 0.35/0.61  % add_neg_numeral_special(8)
% 0.35/0.61  thf(fact_4976_add__neg__numeral__special_I8_J,axiom,
% 0.35/0.61      ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 0.35/0.61      = zero_zero_rat ) ).
% 0.35/0.61  
% 0.35/0.61  % add_neg_numeral_special(8)
% 0.35/0.61  thf(fact_4977_diff__numeral__special_I12_J,axiom,
% 0.35/0.61      ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.61      = zero_zero_int ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_numeral_special(12)
% 0.35/0.61  thf(fact_4978_diff__numeral__special_I12_J,axiom,
% 0.35/0.61      ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 0.35/0.61      = zero_zero_real ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_numeral_special(12)
% 0.35/0.61  thf(fact_4979_diff__numeral__special_I12_J,axiom,
% 0.35/0.61      ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.35/0.61      = zero_zero_complex ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_numeral_special(12)
% 0.35/0.61  thf(fact_4980_diff__numeral__special_I12_J,axiom,
% 0.35/0.61      ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.61      = zero_z3403309356797280102nteger ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_numeral_special(12)
% 0.35/0.61  thf(fact_4981_diff__numeral__special_I12_J,axiom,
% 0.35/0.61      ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.35/0.61      = zero_zero_rat ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_numeral_special(12)
% 0.35/0.61  thf(fact_4982_numeral__eq__neg__one__iff,axiom,
% 0.35/0.61      ! [N: num] :
% 0.35/0.61        ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ N ) )
% 0.35/0.61          = ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.61        = ( N = one ) ) ).
% 0.35/0.61  
% 0.35/0.61  % numeral_eq_neg_one_iff
% 0.35/0.61  thf(fact_4983_numeral__eq__neg__one__iff,axiom,
% 0.35/0.61      ! [N: num] :
% 0.35/0.61        ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ N ) )
% 0.35/0.61          = ( uminus_uminus_real @ one_one_real ) )
% 0.35/0.61        = ( N = one ) ) ).
% 0.35/0.61  
% 0.35/0.61  % numeral_eq_neg_one_iff
% 0.35/0.61  thf(fact_4984_numeral__eq__neg__one__iff,axiom,
% 0.35/0.61      ! [N: num] :
% 0.35/0.61        ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) )
% 0.35/0.61          = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.35/0.61        = ( N = one ) ) ).
% 0.35/0.61  
% 0.35/0.61  % numeral_eq_neg_one_iff
% 0.35/0.61  thf(fact_4985_numeral__eq__neg__one__iff,axiom,
% 0.35/0.61      ! [N: num] :
% 0.35/0.61        ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) )
% 0.35/0.61          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.61        = ( N = one ) ) ).
% 0.35/0.61  
% 0.35/0.61  % numeral_eq_neg_one_iff
% 0.35/0.61  thf(fact_4986_numeral__eq__neg__one__iff,axiom,
% 0.35/0.61      ! [N: num] :
% 0.35/0.61        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) )
% 0.35/0.61          = ( uminus_uminus_rat @ one_one_rat ) )
% 0.35/0.61        = ( N = one ) ) ).
% 0.35/0.61  
% 0.35/0.61  % numeral_eq_neg_one_iff
% 0.35/0.61  thf(fact_4987_neg__one__eq__numeral__iff,axiom,
% 0.35/0.61      ! [N: num] :
% 0.35/0.61        ( ( ( uminus_uminus_int @ one_one_int )
% 0.35/0.61          = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.61        = ( N = one ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_one_eq_numeral_iff
% 0.35/0.61  thf(fact_4988_neg__one__eq__numeral__iff,axiom,
% 0.35/0.61      ! [N: num] :
% 0.35/0.61        ( ( ( uminus_uminus_real @ one_one_real )
% 0.35/0.61          = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.35/0.61        = ( N = one ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_one_eq_numeral_iff
% 0.35/0.61  thf(fact_4989_neg__one__eq__numeral__iff,axiom,
% 0.35/0.61      ! [N: num] :
% 0.35/0.61        ( ( ( uminus1482373934393186551omplex @ one_one_complex )
% 0.35/0.61          = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 0.35/0.61        = ( N = one ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_one_eq_numeral_iff
% 0.35/0.61  thf(fact_4990_neg__one__eq__numeral__iff,axiom,
% 0.35/0.61      ! [N: num] :
% 0.35/0.61        ( ( ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 0.35/0.61          = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.35/0.61        = ( N = one ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_one_eq_numeral_iff
% 0.35/0.61  thf(fact_4991_neg__one__eq__numeral__iff,axiom,
% 0.35/0.61      ! [N: num] :
% 0.35/0.61        ( ( ( uminus_uminus_rat @ one_one_rat )
% 0.35/0.61          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.35/0.61        = ( N = one ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_one_eq_numeral_iff
% 0.35/0.61  thf(fact_4992_left__minus__one__mult__self,axiom,
% 0.35/0.61      ! [N: nat,A: int] :
% 0.35/0.61        ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ A ) )
% 0.35/0.61        = A ) ).
% 0.35/0.61  
% 0.35/0.61  % left_minus_one_mult_self
% 0.35/0.61  thf(fact_4993_left__minus__one__mult__self,axiom,
% 0.35/0.61      ! [N: nat,A: real] :
% 0.35/0.61        ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ A ) )
% 0.35/0.61        = A ) ).
% 0.35/0.61  
% 0.35/0.61  % left_minus_one_mult_self
% 0.35/0.61  thf(fact_4994_left__minus__one__mult__self,axiom,
% 0.35/0.61      ! [N: nat,A: complex] :
% 0.35/0.61        ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ A ) )
% 0.35/0.61        = A ) ).
% 0.35/0.61  
% 0.35/0.61  % left_minus_one_mult_self
% 0.35/0.61  thf(fact_4995_left__minus__one__mult__self,axiom,
% 0.35/0.61      ! [N: nat,A: code_integer] :
% 0.35/0.61        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ A ) )
% 0.35/0.61        = A ) ).
% 0.35/0.61  
% 0.35/0.61  % left_minus_one_mult_self
% 0.35/0.61  thf(fact_4996_left__minus__one__mult__self,axiom,
% 0.35/0.61      ! [N: nat,A: rat] :
% 0.35/0.61        ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ A ) )
% 0.35/0.61        = A ) ).
% 0.35/0.61  
% 0.35/0.61  % left_minus_one_mult_self
% 0.35/0.61  thf(fact_4997_minus__one__mult__self,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) )
% 0.35/0.61        = one_one_int ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_one_mult_self
% 0.35/0.61  thf(fact_4998_minus__one__mult__self,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) )
% 0.35/0.61        = one_one_real ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_one_mult_self
% 0.35/0.61  thf(fact_4999_minus__one__mult__self,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) )
% 0.35/0.61        = one_one_complex ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_one_mult_self
% 0.35/0.61  thf(fact_5000_minus__one__mult__self,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) )
% 0.35/0.61        = one_one_Code_integer ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_one_mult_self
% 0.35/0.61  thf(fact_5001_minus__one__mult__self,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) )
% 0.35/0.61        = one_one_rat ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_one_mult_self
% 0.35/0.61  thf(fact_5002_mod__minus1__right,axiom,
% 0.35/0.61      ! [A: int] :
% 0.35/0.61        ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.61        = zero_zero_int ) ).
% 0.35/0.61  
% 0.35/0.61  % mod_minus1_right
% 0.35/0.61  thf(fact_5003_mod__minus1__right,axiom,
% 0.35/0.61      ! [A: code_integer] :
% 0.35/0.61        ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.61        = zero_z3403309356797280102nteger ) ).
% 0.35/0.61  
% 0.35/0.61  % mod_minus1_right
% 0.35/0.61  thf(fact_5004_max__number__of_I4_J,axiom,
% 0.35/0.61      ! [U: num,V: num] :
% 0.35/0.61        ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.35/0.61         => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.35/0.61            = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 0.35/0.61        & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.35/0.61         => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.35/0.61            = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % max_number_of(4)
% 0.35/0.61  thf(fact_5005_max__number__of_I4_J,axiom,
% 0.35/0.61      ! [U: num,V: num] :
% 0.35/0.61        ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 0.35/0.61         => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 0.35/0.61            = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 0.35/0.61        & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 0.35/0.61         => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 0.35/0.61            = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % max_number_of(4)
% 0.35/0.61  thf(fact_5006_max__number__of_I4_J,axiom,
% 0.35/0.61      ! [U: num,V: num] :
% 0.35/0.61        ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.35/0.61         => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.35/0.61            = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 0.35/0.61        & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.35/0.61         => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.35/0.61            = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % max_number_of(4)
% 0.35/0.61  thf(fact_5007_max__number__of_I4_J,axiom,
% 0.35/0.61      ! [U: num,V: num] :
% 0.35/0.61        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.35/0.61         => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.35/0.61            = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 0.35/0.61        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.35/0.61         => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.35/0.61            = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % max_number_of(4)
% 0.35/0.61  thf(fact_5008_max__number__of_I3_J,axiom,
% 0.35/0.61      ! [U: num,V: num] :
% 0.35/0.61        ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 0.35/0.61         => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 0.35/0.61            = ( numeral_numeral_real @ V ) ) )
% 0.35/0.61        & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 0.35/0.61         => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 0.35/0.61            = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % max_number_of(3)
% 0.35/0.61  thf(fact_5009_max__number__of_I3_J,axiom,
% 0.35/0.61      ! [U: num,V: num] :
% 0.35/0.61        ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 0.35/0.61         => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 0.35/0.61            = ( numera6620942414471956472nteger @ V ) ) )
% 0.35/0.61        & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 0.35/0.61         => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 0.35/0.61            = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % max_number_of(3)
% 0.35/0.61  thf(fact_5010_max__number__of_I3_J,axiom,
% 0.35/0.61      ! [U: num,V: num] :
% 0.35/0.61        ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 0.35/0.61         => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 0.35/0.61            = ( numeral_numeral_rat @ V ) ) )
% 0.35/0.61        & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 0.35/0.61         => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 0.35/0.61            = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % max_number_of(3)
% 0.35/0.61  thf(fact_5011_max__number__of_I3_J,axiom,
% 0.35/0.61      ! [U: num,V: num] :
% 0.35/0.61        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 0.35/0.61         => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 0.35/0.61            = ( numeral_numeral_int @ V ) ) )
% 0.35/0.61        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 0.35/0.61         => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 0.35/0.61            = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % max_number_of(3)
% 0.35/0.61  thf(fact_5012_max__number__of_I2_J,axiom,
% 0.35/0.61      ! [U: num,V: num] :
% 0.35/0.61        ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.35/0.61         => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.35/0.61            = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 0.35/0.61        & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.35/0.61         => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.35/0.61            = ( numeral_numeral_real @ U ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % max_number_of(2)
% 0.35/0.61  thf(fact_5013_max__number__of_I2_J,axiom,
% 0.35/0.61      ! [U: num,V: num] :
% 0.35/0.61        ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 0.35/0.61         => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 0.35/0.61            = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 0.35/0.61        & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 0.35/0.61         => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 0.35/0.61            = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % max_number_of(2)
% 0.35/0.61  thf(fact_5014_max__number__of_I2_J,axiom,
% 0.35/0.61      ! [U: num,V: num] :
% 0.35/0.61        ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.35/0.61         => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.35/0.61            = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 0.35/0.61        & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.35/0.61         => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.35/0.61            = ( numeral_numeral_rat @ U ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % max_number_of(2)
% 0.35/0.61  thf(fact_5015_max__number__of_I2_J,axiom,
% 0.35/0.61      ! [U: num,V: num] :
% 0.35/0.61        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.35/0.61         => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.35/0.61            = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 0.35/0.61        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.35/0.61         => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.35/0.61            = ( numeral_numeral_int @ U ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % max_number_of(2)
% 0.35/0.61  thf(fact_5016_semiring__norm_I168_J,axiom,
% 0.35/0.61      ! [V: num,W: num,Y2: int] :
% 0.35/0.61        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y2 ) )
% 0.35/0.61        = ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) ) @ Y2 ) ) ).
% 0.35/0.61  
% 0.35/0.61  % semiring_norm(168)
% 0.35/0.61  thf(fact_5017_semiring__norm_I168_J,axiom,
% 0.35/0.61      ! [V: num,W: num,Y2: real] :
% 0.35/0.61        ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y2 ) )
% 0.35/0.61        = ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) ) @ Y2 ) ) ).
% 0.35/0.61  
% 0.35/0.61  % semiring_norm(168)
% 0.35/0.61  thf(fact_5018_semiring__norm_I168_J,axiom,
% 0.35/0.61      ! [V: num,W: num,Y2: complex] :
% 0.35/0.61        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y2 ) )
% 0.35/0.61        = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) ) @ Y2 ) ) ).
% 0.35/0.61  
% 0.35/0.61  % semiring_norm(168)
% 0.35/0.61  thf(fact_5019_semiring__norm_I168_J,axiom,
% 0.35/0.61      ! [V: num,W: num,Y2: code_integer] :
% 0.35/0.61        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y2 ) )
% 0.35/0.61        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W ) ) ) @ Y2 ) ) ).
% 0.35/0.61  
% 0.35/0.61  % semiring_norm(168)
% 0.35/0.61  thf(fact_5020_semiring__norm_I168_J,axiom,
% 0.35/0.61      ! [V: num,W: num,Y2: rat] :
% 0.35/0.61        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y2 ) )
% 0.35/0.61        = ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) ) @ Y2 ) ) ).
% 0.35/0.61  
% 0.35/0.61  % semiring_norm(168)
% 0.35/0.61  thf(fact_5021_diff__numeral__simps_I3_J,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.35/0.61        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_numeral_simps(3)
% 0.35/0.61  thf(fact_5022_diff__numeral__simps_I3_J,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) )
% 0.35/0.61        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_numeral_simps(3)
% 0.35/0.61  thf(fact_5023_diff__numeral__simps_I3_J,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N ) )
% 0.35/0.61        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_numeral_simps(3)
% 0.35/0.61  thf(fact_5024_diff__numeral__simps_I3_J,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 0.35/0.61        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_numeral_simps(3)
% 0.35/0.61  thf(fact_5025_diff__numeral__simps_I3_J,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 0.35/0.61        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_numeral_simps(3)
% 0.35/0.61  thf(fact_5026_diff__numeral__simps_I2_J,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.61        = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_numeral_simps(2)
% 0.35/0.61  thf(fact_5027_diff__numeral__simps_I2_J,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.35/0.61        = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_numeral_simps(2)
% 0.35/0.61  thf(fact_5028_diff__numeral__simps_I2_J,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 0.35/0.61        = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_numeral_simps(2)
% 0.35/0.61  thf(fact_5029_diff__numeral__simps_I2_J,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.35/0.61        = ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_numeral_simps(2)
% 0.35/0.61  thf(fact_5030_diff__numeral__simps_I2_J,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.35/0.61        = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_numeral_simps(2)
% 0.35/0.61  thf(fact_5031_semiring__norm_I172_J,axiom,
% 0.35/0.61      ! [V: num,W: num,Y2: int] :
% 0.35/0.61        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y2 ) )
% 0.35/0.61        = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Y2 ) ) ).
% 0.35/0.61  
% 0.35/0.61  % semiring_norm(172)
% 0.35/0.61  thf(fact_5032_semiring__norm_I172_J,axiom,
% 0.35/0.61      ! [V: num,W: num,Y2: real] :
% 0.35/0.61        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y2 ) )
% 0.35/0.61        = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Y2 ) ) ).
% 0.35/0.61  
% 0.35/0.61  % semiring_norm(172)
% 0.35/0.61  thf(fact_5033_semiring__norm_I172_J,axiom,
% 0.35/0.61      ! [V: num,W: num,Y2: complex] :
% 0.35/0.61        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y2 ) )
% 0.35/0.61        = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Y2 ) ) ).
% 0.35/0.61  
% 0.35/0.61  % semiring_norm(172)
% 0.35/0.61  thf(fact_5034_semiring__norm_I172_J,axiom,
% 0.35/0.61      ! [V: num,W: num,Y2: code_integer] :
% 0.35/0.61        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y2 ) )
% 0.35/0.61        = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) @ Y2 ) ) ).
% 0.35/0.61  
% 0.35/0.61  % semiring_norm(172)
% 0.35/0.61  thf(fact_5035_semiring__norm_I172_J,axiom,
% 0.35/0.61      ! [V: num,W: num,Y2: rat] :
% 0.35/0.61        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y2 ) )
% 0.35/0.61        = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Y2 ) ) ).
% 0.35/0.61  
% 0.35/0.61  % semiring_norm(172)
% 0.35/0.61  thf(fact_5036_semiring__norm_I171_J,axiom,
% 0.35/0.61      ! [V: num,W: num,Y2: int] :
% 0.35/0.61        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y2 ) )
% 0.35/0.61        = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 0.35/0.61  
% 0.35/0.61  % semiring_norm(171)
% 0.35/0.61  thf(fact_5037_semiring__norm_I171_J,axiom,
% 0.35/0.61      ! [V: num,W: num,Y2: real] :
% 0.35/0.61        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y2 ) )
% 0.35/0.61        = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 0.35/0.61  
% 0.35/0.61  % semiring_norm(171)
% 0.35/0.61  thf(fact_5038_semiring__norm_I171_J,axiom,
% 0.35/0.61      ! [V: num,W: num,Y2: complex] :
% 0.35/0.61        ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y2 ) )
% 0.35/0.61        = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 0.35/0.61  
% 0.35/0.61  % semiring_norm(171)
% 0.35/0.61  thf(fact_5039_semiring__norm_I171_J,axiom,
% 0.35/0.61      ! [V: num,W: num,Y2: code_integer] :
% 0.35/0.61        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y2 ) )
% 0.35/0.61        = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 0.35/0.61  
% 0.35/0.61  % semiring_norm(171)
% 0.35/0.61  thf(fact_5040_semiring__norm_I171_J,axiom,
% 0.35/0.61      ! [V: num,W: num,Y2: rat] :
% 0.35/0.61        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y2 ) )
% 0.35/0.61        = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 0.35/0.61  
% 0.35/0.61  % semiring_norm(171)
% 0.35/0.61  thf(fact_5041_semiring__norm_I170_J,axiom,
% 0.35/0.61      ! [V: num,W: num,Y2: int] :
% 0.35/0.61        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Y2 ) )
% 0.35/0.61        = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 0.35/0.61  
% 0.35/0.61  % semiring_norm(170)
% 0.35/0.61  thf(fact_5042_semiring__norm_I170_J,axiom,
% 0.35/0.61      ! [V: num,W: num,Y2: real] :
% 0.35/0.61        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Y2 ) )
% 0.35/0.61        = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 0.35/0.61  
% 0.35/0.61  % semiring_norm(170)
% 0.35/0.61  thf(fact_5043_semiring__norm_I170_J,axiom,
% 0.35/0.61      ! [V: num,W: num,Y2: complex] :
% 0.35/0.61        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Y2 ) )
% 0.35/0.61        = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 0.35/0.61  
% 0.35/0.61  % semiring_norm(170)
% 0.35/0.61  thf(fact_5044_semiring__norm_I170_J,axiom,
% 0.35/0.61      ! [V: num,W: num,Y2: code_integer] :
% 0.35/0.61        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ Y2 ) )
% 0.35/0.61        = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 0.35/0.61  
% 0.35/0.61  % semiring_norm(170)
% 0.35/0.61  thf(fact_5045_semiring__norm_I170_J,axiom,
% 0.35/0.61      ! [V: num,W: num,Y2: rat] :
% 0.35/0.61        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Y2 ) )
% 0.35/0.61        = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 0.35/0.61  
% 0.35/0.61  % semiring_norm(170)
% 0.35/0.61  thf(fact_5046_mult__neg__numeral__simps_I3_J,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.61        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mult_neg_numeral_simps(3)
% 0.35/0.61  thf(fact_5047_mult__neg__numeral__simps_I3_J,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.35/0.61        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mult_neg_numeral_simps(3)
% 0.35/0.61  thf(fact_5048_mult__neg__numeral__simps_I3_J,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 0.35/0.61        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mult_neg_numeral_simps(3)
% 0.35/0.61  thf(fact_5049_mult__neg__numeral__simps_I3_J,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.35/0.61        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mult_neg_numeral_simps(3)
% 0.35/0.61  thf(fact_5050_mult__neg__numeral__simps_I3_J,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.35/0.61        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mult_neg_numeral_simps(3)
% 0.35/0.61  thf(fact_5051_mult__neg__numeral__simps_I2_J,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.35/0.61        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mult_neg_numeral_simps(2)
% 0.35/0.61  thf(fact_5052_mult__neg__numeral__simps_I2_J,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) )
% 0.35/0.61        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mult_neg_numeral_simps(2)
% 0.35/0.61  thf(fact_5053_mult__neg__numeral__simps_I2_J,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N ) )
% 0.35/0.61        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mult_neg_numeral_simps(2)
% 0.35/0.61  thf(fact_5054_mult__neg__numeral__simps_I2_J,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 0.35/0.61        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mult_neg_numeral_simps(2)
% 0.35/0.61  thf(fact_5055_mult__neg__numeral__simps_I2_J,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 0.35/0.61        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mult_neg_numeral_simps(2)
% 0.35/0.61  thf(fact_5056_mult__neg__numeral__simps_I1_J,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.61        = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mult_neg_numeral_simps(1)
% 0.35/0.61  thf(fact_5057_mult__neg__numeral__simps_I1_J,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.35/0.61        = ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mult_neg_numeral_simps(1)
% 0.35/0.61  thf(fact_5058_mult__neg__numeral__simps_I1_J,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 0.35/0.61        = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mult_neg_numeral_simps(1)
% 0.35/0.61  thf(fact_5059_mult__neg__numeral__simps_I1_J,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.35/0.61        = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mult_neg_numeral_simps(1)
% 0.35/0.61  thf(fact_5060_mult__neg__numeral__simps_I1_J,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.35/0.61        = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mult_neg_numeral_simps(1)
% 0.35/0.61  thf(fact_5061_less__Suc__numeral,axiom,
% 0.35/0.61      ! [N: nat,K: num] :
% 0.35/0.61        ( ( ord_less_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 0.35/0.61        = ( ord_less_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % less_Suc_numeral
% 0.35/0.61  thf(fact_5062_less__numeral__Suc,axiom,
% 0.35/0.61      ! [K: num,N: nat] :
% 0.35/0.61        ( ( ord_less_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 0.35/0.61        = ( ord_less_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 0.35/0.61  
% 0.35/0.61  % less_numeral_Suc
% 0.35/0.61  thf(fact_5063_pred__numeral__simps_I3_J,axiom,
% 0.35/0.61      ! [K: num] :
% 0.35/0.61        ( ( pred_numeral @ ( bit1 @ K ) )
% 0.35/0.61        = ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % pred_numeral_simps(3)
% 0.35/0.61  thf(fact_5064_le__Suc__numeral,axiom,
% 0.35/0.61      ! [N: nat,K: num] :
% 0.35/0.61        ( ( ord_less_eq_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 0.35/0.61        = ( ord_less_eq_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % le_Suc_numeral
% 0.35/0.61  thf(fact_5065_le__numeral__Suc,axiom,
% 0.35/0.61      ! [K: num,N: nat] :
% 0.35/0.61        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 0.35/0.61        = ( ord_less_eq_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 0.35/0.61  
% 0.35/0.61  % le_numeral_Suc
% 0.35/0.61  thf(fact_5066_diff__numeral__Suc,axiom,
% 0.35/0.61      ! [K: num,N: nat] :
% 0.35/0.61        ( ( minus_minus_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 0.35/0.61        = ( minus_minus_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_numeral_Suc
% 0.35/0.61  thf(fact_5067_diff__Suc__numeral,axiom,
% 0.35/0.61      ! [N: nat,K: num] :
% 0.35/0.61        ( ( minus_minus_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 0.35/0.61        = ( minus_minus_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_Suc_numeral
% 0.35/0.61  thf(fact_5068_neg__numeral__le__iff,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.35/0.61        = ( ord_less_eq_num @ N @ M ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_numeral_le_iff
% 0.35/0.61  thf(fact_5069_neg__numeral__le__iff,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.35/0.61        = ( ord_less_eq_num @ N @ M ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_numeral_le_iff
% 0.35/0.61  thf(fact_5070_neg__numeral__le__iff,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.35/0.61        = ( ord_less_eq_num @ N @ M ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_numeral_le_iff
% 0.35/0.61  thf(fact_5071_neg__numeral__le__iff,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.61        = ( ord_less_eq_num @ N @ M ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_numeral_le_iff
% 0.35/0.61  thf(fact_5072_neg__numeral__less__iff,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.61        = ( ord_less_num @ N @ M ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_numeral_less_iff
% 0.35/0.61  thf(fact_5073_neg__numeral__less__iff,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.35/0.61        = ( ord_less_num @ N @ M ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_numeral_less_iff
% 0.35/0.61  thf(fact_5074_neg__numeral__less__iff,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.35/0.61        = ( ord_less_num @ N @ M ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_numeral_less_iff
% 0.35/0.61  thf(fact_5075_neg__numeral__less__iff,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.35/0.61        = ( ord_less_num @ N @ M ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_numeral_less_iff
% 0.35/0.61  thf(fact_5076_max__numeral__Suc,axiom,
% 0.35/0.61      ! [K: num,N: nat] :
% 0.35/0.61        ( ( ord_max_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 0.35/0.61        = ( suc @ ( ord_max_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % max_numeral_Suc
% 0.35/0.61  thf(fact_5077_max__Suc__numeral,axiom,
% 0.35/0.61      ! [N: nat,K: num] :
% 0.35/0.61        ( ( ord_max_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 0.35/0.61        = ( suc @ ( ord_max_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % max_Suc_numeral
% 0.35/0.61  thf(fact_5078_pred__numeral__simps_I2_J,axiom,
% 0.35/0.61      ! [K: num] :
% 0.35/0.61        ( ( pred_numeral @ ( bit0 @ K ) )
% 0.35/0.61        = ( numeral_numeral_nat @ ( bitM @ K ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % pred_numeral_simps(2)
% 0.35/0.61  thf(fact_5079_not__neg__one__le__neg__numeral__iff,axiom,
% 0.35/0.61      ! [M: num] :
% 0.35/0.61        ( ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) )
% 0.35/0.61        = ( M != one ) ) ).
% 0.35/0.61  
% 0.35/0.61  % not_neg_one_le_neg_numeral_iff
% 0.35/0.61  thf(fact_5080_not__neg__one__le__neg__numeral__iff,axiom,
% 0.35/0.61      ! [M: num] :
% 0.35/0.61        ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) )
% 0.35/0.61        = ( M != one ) ) ).
% 0.35/0.61  
% 0.35/0.61  % not_neg_one_le_neg_numeral_iff
% 0.35/0.61  thf(fact_5081_not__neg__one__le__neg__numeral__iff,axiom,
% 0.35/0.61      ! [M: num] :
% 0.35/0.61        ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) )
% 0.35/0.61        = ( M != one ) ) ).
% 0.35/0.61  
% 0.35/0.61  % not_neg_one_le_neg_numeral_iff
% 0.35/0.61  thf(fact_5082_not__neg__one__le__neg__numeral__iff,axiom,
% 0.35/0.61      ! [M: num] :
% 0.35/0.61        ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) )
% 0.35/0.61        = ( M != one ) ) ).
% 0.35/0.61  
% 0.35/0.61  % not_neg_one_le_neg_numeral_iff
% 0.35/0.61  thf(fact_5083_neg__numeral__less__neg__one__iff,axiom,
% 0.35/0.61      ! [M: num] :
% 0.35/0.61        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.61        = ( M != one ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_numeral_less_neg_one_iff
% 0.35/0.61  thf(fact_5084_neg__numeral__less__neg__one__iff,axiom,
% 0.35/0.61      ! [M: num] :
% 0.35/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 0.35/0.61        = ( M != one ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_numeral_less_neg_one_iff
% 0.35/0.61  thf(fact_5085_neg__numeral__less__neg__one__iff,axiom,
% 0.35/0.61      ! [M: num] :
% 0.35/0.61        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.61        = ( M != one ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_numeral_less_neg_one_iff
% 0.35/0.61  thf(fact_5086_neg__numeral__less__neg__one__iff,axiom,
% 0.35/0.61      ! [M: num] :
% 0.35/0.61        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.35/0.61        = ( M != one ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_numeral_less_neg_one_iff
% 0.35/0.61  thf(fact_5087_divide__le__eq__numeral1_I2_J,axiom,
% 0.35/0.61      ! [B: real,W: num,A: real] :
% 0.35/0.61        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 0.35/0.61        = ( ord_less_eq_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % divide_le_eq_numeral1(2)
% 0.35/0.61  thf(fact_5088_divide__le__eq__numeral1_I2_J,axiom,
% 0.35/0.61      ! [B: rat,W: num,A: rat] :
% 0.35/0.61        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 0.35/0.61        = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % divide_le_eq_numeral1(2)
% 0.35/0.61  thf(fact_5089_le__divide__eq__numeral1_I2_J,axiom,
% 0.35/0.61      ! [A: real,B: real,W: num] :
% 0.35/0.61        ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 0.35/0.61        = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % le_divide_eq_numeral1(2)
% 0.35/0.61  thf(fact_5090_le__divide__eq__numeral1_I2_J,axiom,
% 0.35/0.61      ! [A: rat,B: rat,W: num] :
% 0.35/0.61        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 0.35/0.61        = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % le_divide_eq_numeral1(2)
% 0.35/0.61  thf(fact_5091_divide__eq__eq__numeral1_I2_J,axiom,
% 0.35/0.61      ! [B: real,W: num,A: real] :
% 0.35/0.61        ( ( ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 0.35/0.61          = A )
% 0.35/0.61        = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 0.35/0.61             != zero_zero_real )
% 0.35/0.61           => ( B
% 0.35/0.61              = ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) )
% 0.35/0.61          & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 0.35/0.61              = zero_zero_real )
% 0.35/0.61           => ( A = zero_zero_real ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % divide_eq_eq_numeral1(2)
% 0.35/0.61  thf(fact_5092_divide__eq__eq__numeral1_I2_J,axiom,
% 0.35/0.61      ! [B: complex,W: num,A: complex] :
% 0.35/0.61        ( ( ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 0.35/0.61          = A )
% 0.35/0.61        = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 0.35/0.61             != zero_zero_complex )
% 0.35/0.61           => ( B
% 0.35/0.61              = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) )
% 0.35/0.61          & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 0.35/0.61              = zero_zero_complex )
% 0.35/0.61           => ( A = zero_zero_complex ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % divide_eq_eq_numeral1(2)
% 0.35/0.61  thf(fact_5093_divide__eq__eq__numeral1_I2_J,axiom,
% 0.35/0.61      ! [B: rat,W: num,A: rat] :
% 0.35/0.61        ( ( ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 0.35/0.61          = A )
% 0.35/0.61        = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 0.35/0.61             != zero_zero_rat )
% 0.35/0.61           => ( B
% 0.35/0.61              = ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) )
% 0.35/0.61          & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 0.35/0.61              = zero_zero_rat )
% 0.35/0.61           => ( A = zero_zero_rat ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % divide_eq_eq_numeral1(2)
% 0.35/0.61  thf(fact_5094_eq__divide__eq__numeral1_I2_J,axiom,
% 0.35/0.61      ! [A: real,B: real,W: num] :
% 0.35/0.61        ( ( A
% 0.35/0.61          = ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 0.35/0.61        = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 0.35/0.61             != zero_zero_real )
% 0.35/0.61           => ( ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 0.35/0.61              = B ) )
% 0.35/0.61          & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 0.35/0.61              = zero_zero_real )
% 0.35/0.61           => ( A = zero_zero_real ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % eq_divide_eq_numeral1(2)
% 0.35/0.61  thf(fact_5095_eq__divide__eq__numeral1_I2_J,axiom,
% 0.35/0.61      ! [A: complex,B: complex,W: num] :
% 0.35/0.61        ( ( A
% 0.35/0.61          = ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) )
% 0.35/0.61        = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 0.35/0.61             != zero_zero_complex )
% 0.35/0.61           => ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 0.35/0.61              = B ) )
% 0.35/0.61          & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 0.35/0.61              = zero_zero_complex )
% 0.35/0.61           => ( A = zero_zero_complex ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % eq_divide_eq_numeral1(2)
% 0.35/0.61  thf(fact_5096_eq__divide__eq__numeral1_I2_J,axiom,
% 0.35/0.61      ! [A: rat,B: rat,W: num] :
% 0.35/0.61        ( ( A
% 0.35/0.61          = ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 0.35/0.61        = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 0.35/0.61             != zero_zero_rat )
% 0.35/0.61           => ( ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 0.35/0.61              = B ) )
% 0.35/0.61          & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 0.35/0.61              = zero_zero_rat )
% 0.35/0.61           => ( A = zero_zero_rat ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % eq_divide_eq_numeral1(2)
% 0.35/0.61  thf(fact_5097_divide__less__eq__numeral1_I2_J,axiom,
% 0.35/0.61      ! [B: real,W: num,A: real] :
% 0.35/0.61        ( ( ord_less_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 0.35/0.61        = ( ord_less_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % divide_less_eq_numeral1(2)
% 0.35/0.61  thf(fact_5098_divide__less__eq__numeral1_I2_J,axiom,
% 0.35/0.61      ! [B: rat,W: num,A: rat] :
% 0.35/0.61        ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 0.35/0.61        = ( ord_less_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % divide_less_eq_numeral1(2)
% 0.35/0.61  thf(fact_5099_less__divide__eq__numeral1_I2_J,axiom,
% 0.35/0.61      ! [A: real,B: real,W: num] :
% 0.35/0.61        ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 0.35/0.61        = ( ord_less_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % less_divide_eq_numeral1(2)
% 0.35/0.61  thf(fact_5100_less__divide__eq__numeral1_I2_J,axiom,
% 0.35/0.61      ! [A: rat,B: rat,W: num] :
% 0.35/0.61        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 0.35/0.61        = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % less_divide_eq_numeral1(2)
% 0.35/0.61  thf(fact_5101_power2__minus,axiom,
% 0.35/0.61      ! [A: int] :
% 0.35/0.61        ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.61        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % power2_minus
% 0.35/0.61  thf(fact_5102_power2__minus,axiom,
% 0.35/0.61      ! [A: real] :
% 0.35/0.61        ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.61        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % power2_minus
% 0.35/0.61  thf(fact_5103_power2__minus,axiom,
% 0.35/0.61      ! [A: complex] :
% 0.35/0.61        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.61        = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % power2_minus
% 0.35/0.61  thf(fact_5104_power2__minus,axiom,
% 0.35/0.61      ! [A: code_integer] :
% 0.35/0.61        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.61        = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % power2_minus
% 0.35/0.61  thf(fact_5105_power2__minus,axiom,
% 0.35/0.61      ! [A: rat] :
% 0.35/0.61        ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.61        = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % power2_minus
% 0.35/0.61  thf(fact_5106_add__neg__numeral__special_I9_J,axiom,
% 0.35/0.61      ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.61      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % add_neg_numeral_special(9)
% 0.35/0.61  thf(fact_5107_add__neg__numeral__special_I9_J,axiom,
% 0.35/0.61      ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 0.35/0.61      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % add_neg_numeral_special(9)
% 0.35/0.61  thf(fact_5108_add__neg__numeral__special_I9_J,axiom,
% 0.35/0.61      ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.35/0.61      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % add_neg_numeral_special(9)
% 0.35/0.61  thf(fact_5109_add__neg__numeral__special_I9_J,axiom,
% 0.35/0.61      ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.61      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % add_neg_numeral_special(9)
% 0.35/0.61  thf(fact_5110_add__neg__numeral__special_I9_J,axiom,
% 0.35/0.61      ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.35/0.61      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % add_neg_numeral_special(9)
% 0.35/0.61  thf(fact_5111_diff__numeral__special_I10_J,axiom,
% 0.35/0.61      ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 0.35/0.61      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_numeral_special(10)
% 0.35/0.61  thf(fact_5112_diff__numeral__special_I10_J,axiom,
% 0.35/0.61      ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 0.35/0.61      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_numeral_special(10)
% 0.35/0.61  thf(fact_5113_diff__numeral__special_I10_J,axiom,
% 0.35/0.61      ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 0.35/0.61      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_numeral_special(10)
% 0.35/0.61  thf(fact_5114_diff__numeral__special_I10_J,axiom,
% 0.35/0.61      ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 0.35/0.61      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_numeral_special(10)
% 0.35/0.61  thf(fact_5115_diff__numeral__special_I10_J,axiom,
% 0.35/0.61      ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 0.35/0.61      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_numeral_special(10)
% 0.35/0.61  thf(fact_5116_diff__numeral__special_I11_J,axiom,
% 0.35/0.61      ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.61      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_numeral_special(11)
% 0.35/0.61  thf(fact_5117_diff__numeral__special_I11_J,axiom,
% 0.35/0.61      ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.35/0.61      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_numeral_special(11)
% 0.35/0.61  thf(fact_5118_diff__numeral__special_I11_J,axiom,
% 0.35/0.61      ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.35/0.61      = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_numeral_special(11)
% 0.35/0.61  thf(fact_5119_diff__numeral__special_I11_J,axiom,
% 0.35/0.61      ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.61      = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_numeral_special(11)
% 0.35/0.61  thf(fact_5120_diff__numeral__special_I11_J,axiom,
% 0.35/0.61      ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.35/0.61      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_numeral_special(11)
% 0.35/0.61  thf(fact_5121_minus__1__div__2__eq,axiom,
% 0.35/0.61      ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.61      = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_1_div_2_eq
% 0.35/0.61  thf(fact_5122_minus__1__div__2__eq,axiom,
% 0.35/0.61      ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.35/0.61      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_1_div_2_eq
% 0.35/0.61  thf(fact_5123_bits__minus__1__mod__2__eq,axiom,
% 0.35/0.61      ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.61      = one_one_int ) ).
% 0.35/0.61  
% 0.35/0.61  % bits_minus_1_mod_2_eq
% 0.35/0.61  thf(fact_5124_bits__minus__1__mod__2__eq,axiom,
% 0.35/0.61      ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.35/0.61      = one_one_Code_integer ) ).
% 0.35/0.61  
% 0.35/0.61  % bits_minus_1_mod_2_eq
% 0.35/0.61  thf(fact_5125_minus__1__mod__2__eq,axiom,
% 0.35/0.61      ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.61      = one_one_int ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_1_mod_2_eq
% 0.35/0.61  thf(fact_5126_minus__1__mod__2__eq,axiom,
% 0.35/0.61      ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.35/0.61      = one_one_Code_integer ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_1_mod_2_eq
% 0.35/0.61  thf(fact_5127_Power_Oring__1__class_Opower__minus__even,axiom,
% 0.35/0.61      ! [A: int,N: nat] :
% 0.35/0.61        ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61        = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % Power.ring_1_class.power_minus_even
% 0.35/0.61  thf(fact_5128_Power_Oring__1__class_Opower__minus__even,axiom,
% 0.35/0.61      ! [A: real,N: nat] :
% 0.35/0.61        ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61        = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % Power.ring_1_class.power_minus_even
% 0.35/0.61  thf(fact_5129_Power_Oring__1__class_Opower__minus__even,axiom,
% 0.35/0.61      ! [A: complex,N: nat] :
% 0.35/0.61        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61        = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % Power.ring_1_class.power_minus_even
% 0.35/0.61  thf(fact_5130_Power_Oring__1__class_Opower__minus__even,axiom,
% 0.35/0.61      ! [A: code_integer,N: nat] :
% 0.35/0.61        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61        = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % Power.ring_1_class.power_minus_even
% 0.35/0.61  thf(fact_5131_Power_Oring__1__class_Opower__minus__even,axiom,
% 0.35/0.61      ! [A: rat,N: nat] :
% 0.35/0.61        ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61        = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % Power.ring_1_class.power_minus_even
% 0.35/0.61  thf(fact_5132_Parity_Oring__1__class_Opower__minus__even,axiom,
% 0.35/0.61      ! [N: nat,A: int] :
% 0.35/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61       => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 0.35/0.61          = ( power_power_int @ A @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % Parity.ring_1_class.power_minus_even
% 0.35/0.61  thf(fact_5133_Parity_Oring__1__class_Opower__minus__even,axiom,
% 0.35/0.61      ! [N: nat,A: real] :
% 0.35/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61       => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 0.35/0.61          = ( power_power_real @ A @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % Parity.ring_1_class.power_minus_even
% 0.35/0.61  thf(fact_5134_Parity_Oring__1__class_Opower__minus__even,axiom,
% 0.35/0.61      ! [N: nat,A: complex] :
% 0.35/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 0.35/0.61          = ( power_power_complex @ A @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % Parity.ring_1_class.power_minus_even
% 0.35/0.61  thf(fact_5135_Parity_Oring__1__class_Opower__minus__even,axiom,
% 0.35/0.61      ! [N: nat,A: code_integer] :
% 0.35/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 0.35/0.61          = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % Parity.ring_1_class.power_minus_even
% 0.35/0.61  thf(fact_5136_Parity_Oring__1__class_Opower__minus__even,axiom,
% 0.35/0.61      ! [N: nat,A: rat] :
% 0.35/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61       => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 0.35/0.61          = ( power_power_rat @ A @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % Parity.ring_1_class.power_minus_even
% 0.35/0.61  thf(fact_5137_power__minus__odd,axiom,
% 0.35/0.61      ! [N: nat,A: int] :
% 0.35/0.61        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61       => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 0.35/0.61          = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % power_minus_odd
% 0.35/0.61  thf(fact_5138_power__minus__odd,axiom,
% 0.35/0.61      ! [N: nat,A: real] :
% 0.35/0.61        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61       => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 0.35/0.61          = ( uminus_uminus_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % power_minus_odd
% 0.35/0.61  thf(fact_5139_power__minus__odd,axiom,
% 0.35/0.61      ! [N: nat,A: complex] :
% 0.35/0.61        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 0.35/0.61          = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % power_minus_odd
% 0.35/0.61  thf(fact_5140_power__minus__odd,axiom,
% 0.35/0.61      ! [N: nat,A: code_integer] :
% 0.35/0.61        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 0.35/0.61          = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % power_minus_odd
% 0.35/0.61  thf(fact_5141_power__minus__odd,axiom,
% 0.35/0.61      ! [N: nat,A: rat] :
% 0.35/0.61        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61       => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 0.35/0.61          = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % power_minus_odd
% 0.35/0.61  thf(fact_5142_diff__numeral__special_I3_J,axiom,
% 0.35/0.61      ! [N: num] :
% 0.35/0.61        ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.61        = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_numeral_special(3)
% 0.35/0.61  thf(fact_5143_diff__numeral__special_I3_J,axiom,
% 0.35/0.61      ! [N: num] :
% 0.35/0.61        ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.35/0.61        = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_numeral_special(3)
% 0.35/0.61  thf(fact_5144_diff__numeral__special_I3_J,axiom,
% 0.35/0.61      ! [N: num] :
% 0.35/0.61        ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 0.35/0.61        = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_numeral_special(3)
% 0.35/0.61  thf(fact_5145_diff__numeral__special_I3_J,axiom,
% 0.35/0.61      ! [N: num] :
% 0.35/0.61        ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.35/0.61        = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_numeral_special(3)
% 0.35/0.61  thf(fact_5146_diff__numeral__special_I3_J,axiom,
% 0.35/0.61      ! [N: num] :
% 0.35/0.61        ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.35/0.61        = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_numeral_special(3)
% 0.35/0.61  thf(fact_5147_diff__numeral__special_I4_J,axiom,
% 0.35/0.61      ! [M: num] :
% 0.35/0.61        ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int )
% 0.35/0.61        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_numeral_special(4)
% 0.35/0.61  thf(fact_5148_diff__numeral__special_I4_J,axiom,
% 0.35/0.61      ! [M: num] :
% 0.35/0.61        ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real )
% 0.35/0.61        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_numeral_special(4)
% 0.35/0.61  thf(fact_5149_diff__numeral__special_I4_J,axiom,
% 0.35/0.61      ! [M: num] :
% 0.35/0.61        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ one_one_complex )
% 0.35/0.61        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_numeral_special(4)
% 0.35/0.61  thf(fact_5150_diff__numeral__special_I4_J,axiom,
% 0.35/0.61      ! [M: num] :
% 0.35/0.61        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer )
% 0.35/0.61        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_numeral_special(4)
% 0.35/0.61  thf(fact_5151_diff__numeral__special_I4_J,axiom,
% 0.35/0.61      ! [M: num] :
% 0.35/0.61        ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat )
% 0.35/0.61        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % diff_numeral_special(4)
% 0.35/0.61  thf(fact_5152_numeral__div__minus__numeral,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( divide_divide_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.61        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % numeral_div_minus_numeral
% 0.35/0.61  thf(fact_5153_minus__numeral__div__numeral,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.35/0.61        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_numeral_div_numeral
% 0.35/0.61  thf(fact_5154_dbl__simps_I4_J,axiom,
% 0.35/0.61      ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.61      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % dbl_simps(4)
% 0.35/0.61  thf(fact_5155_dbl__simps_I4_J,axiom,
% 0.35/0.61      ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.35/0.61      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % dbl_simps(4)
% 0.35/0.61  thf(fact_5156_dbl__simps_I4_J,axiom,
% 0.35/0.61      ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.35/0.61      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % dbl_simps(4)
% 0.35/0.61  thf(fact_5157_dbl__simps_I4_J,axiom,
% 0.35/0.61      ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.61      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % dbl_simps(4)
% 0.35/0.61  thf(fact_5158_dbl__simps_I4_J,axiom,
% 0.35/0.61      ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.35/0.61      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % dbl_simps(4)
% 0.35/0.61  thf(fact_5159_power__minus1__even,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61        = one_one_int ) ).
% 0.35/0.61  
% 0.35/0.61  % power_minus1_even
% 0.35/0.61  thf(fact_5160_power__minus1__even,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61        = one_one_real ) ).
% 0.35/0.61  
% 0.35/0.61  % power_minus1_even
% 0.35/0.61  thf(fact_5161_power__minus1__even,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61        = one_one_complex ) ).
% 0.35/0.61  
% 0.35/0.61  % power_minus1_even
% 0.35/0.61  thf(fact_5162_power__minus1__even,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61        = one_one_Code_integer ) ).
% 0.35/0.61  
% 0.35/0.61  % power_minus1_even
% 0.35/0.61  thf(fact_5163_power__minus1__even,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61        = one_one_rat ) ).
% 0.35/0.61  
% 0.35/0.61  % power_minus1_even
% 0.35/0.61  thf(fact_5164_neg__one__even__power,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61       => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 0.35/0.61          = one_one_int ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_one_even_power
% 0.35/0.61  thf(fact_5165_neg__one__even__power,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61       => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 0.35/0.61          = one_one_real ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_one_even_power
% 0.35/0.61  thf(fact_5166_neg__one__even__power,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 0.35/0.61          = one_one_complex ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_one_even_power
% 0.35/0.61  thf(fact_5167_neg__one__even__power,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 0.35/0.61          = one_one_Code_integer ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_one_even_power
% 0.35/0.61  thf(fact_5168_neg__one__even__power,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61       => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 0.35/0.61          = one_one_rat ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_one_even_power
% 0.35/0.61  thf(fact_5169_neg__one__odd__power,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61       => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 0.35/0.61          = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_one_odd_power
% 0.35/0.61  thf(fact_5170_neg__one__odd__power,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61       => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 0.35/0.61          = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_one_odd_power
% 0.35/0.61  thf(fact_5171_neg__one__odd__power,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 0.35/0.61          = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_one_odd_power
% 0.35/0.61  thf(fact_5172_neg__one__odd__power,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 0.35/0.61          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_one_odd_power
% 0.35/0.61  thf(fact_5173_neg__one__odd__power,axiom,
% 0.35/0.61      ! [N: nat] :
% 0.35/0.61        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61       => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 0.35/0.61          = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_one_odd_power
% 0.35/0.61  thf(fact_5174_signed__take__bit__0,axiom,
% 0.35/0.61      ! [A: code_integer] :
% 0.35/0.61        ( ( bit_ri6519982836138164636nteger @ zero_zero_nat @ A )
% 0.35/0.61        = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % signed_take_bit_0
% 0.35/0.61  thf(fact_5175_signed__take__bit__0,axiom,
% 0.35/0.61      ! [A: int] :
% 0.35/0.61        ( ( bit_ri631733984087533419it_int @ zero_zero_nat @ A )
% 0.35/0.61        = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % signed_take_bit_0
% 0.35/0.61  thf(fact_5176_signed__take__bit__Suc__minus__bit0,axiom,
% 0.35/0.61      ! [N: nat,K: num] :
% 0.35/0.61        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 0.35/0.61        = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % signed_take_bit_Suc_minus_bit0
% 0.35/0.61  thf(fact_5177_signed__take__bit__numeral__bit0,axiom,
% 0.35/0.61      ! [L2: num,K: num] :
% 0.35/0.61        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 0.35/0.61        = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % signed_take_bit_numeral_bit0
% 0.35/0.61  thf(fact_5178_one__div__minus__numeral,axiom,
% 0.35/0.61      ! [N: num] :
% 0.35/0.61        ( ( divide_divide_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.61        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % one_div_minus_numeral
% 0.35/0.61  thf(fact_5179_minus__one__div__numeral,axiom,
% 0.35/0.61      ! [N: num] :
% 0.35/0.61        ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 0.35/0.61        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_one_div_numeral
% 0.35/0.61  thf(fact_5180_signed__take__bit__numeral__minus__bit0,axiom,
% 0.35/0.61      ! [L2: num,K: num] :
% 0.35/0.61        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 0.35/0.61        = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % signed_take_bit_numeral_minus_bit0
% 0.35/0.61  thf(fact_5181_signed__take__bit__numeral__minus__bit1,axiom,
% 0.35/0.61      ! [L2: num,K: num] :
% 0.35/0.61        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.35/0.61        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.35/0.61  
% 0.35/0.61  % signed_take_bit_numeral_minus_bit1
% 0.35/0.61  thf(fact_5182_signed__take__bit__minus,axiom,
% 0.35/0.61      ! [N: nat,K: int] :
% 0.35/0.61        ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( bit_ri631733984087533419it_int @ N @ K ) ) )
% 0.35/0.61        = ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % signed_take_bit_minus
% 0.35/0.61  thf(fact_5183_le__minus__iff,axiom,
% 0.35/0.61      ! [A: real,B: real] :
% 0.35/0.61        ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B ) )
% 0.35/0.61        = ( ord_less_eq_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % le_minus_iff
% 0.35/0.61  thf(fact_5184_le__minus__iff,axiom,
% 0.35/0.61      ! [A: code_integer,B: code_integer] :
% 0.35/0.61        ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.35/0.61        = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % le_minus_iff
% 0.35/0.61  thf(fact_5185_le__minus__iff,axiom,
% 0.35/0.61      ! [A: rat,B: rat] :
% 0.35/0.61        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.35/0.61        = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % le_minus_iff
% 0.35/0.61  thf(fact_5186_le__minus__iff,axiom,
% 0.35/0.61      ! [A: int,B: int] :
% 0.35/0.61        ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 0.35/0.61        = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % le_minus_iff
% 0.35/0.61  thf(fact_5187_minus__le__iff,axiom,
% 0.35/0.61      ! [A: real,B: real] :
% 0.35/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 0.35/0.61        = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_le_iff
% 0.35/0.61  thf(fact_5188_minus__le__iff,axiom,
% 0.35/0.61      ! [A: code_integer,B: code_integer] :
% 0.35/0.61        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.35/0.61        = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_le_iff
% 0.35/0.61  thf(fact_5189_minus__le__iff,axiom,
% 0.35/0.61      ! [A: rat,B: rat] :
% 0.35/0.61        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.35/0.61        = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_le_iff
% 0.35/0.61  thf(fact_5190_minus__le__iff,axiom,
% 0.35/0.61      ! [A: int,B: int] :
% 0.35/0.61        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 0.35/0.61        = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_le_iff
% 0.35/0.61  thf(fact_5191_le__imp__neg__le,axiom,
% 0.35/0.61      ! [A: real,B: real] :
% 0.35/0.61        ( ( ord_less_eq_real @ A @ B )
% 0.35/0.61       => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % le_imp_neg_le
% 0.35/0.61  thf(fact_5192_le__imp__neg__le,axiom,
% 0.35/0.61      ! [A: code_integer,B: code_integer] :
% 0.35/0.61        ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.35/0.61       => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % le_imp_neg_le
% 0.35/0.61  thf(fact_5193_le__imp__neg__le,axiom,
% 0.35/0.61      ! [A: rat,B: rat] :
% 0.35/0.61        ( ( ord_less_eq_rat @ A @ B )
% 0.35/0.61       => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % le_imp_neg_le
% 0.35/0.61  thf(fact_5194_le__imp__neg__le,axiom,
% 0.35/0.61      ! [A: int,B: int] :
% 0.35/0.61        ( ( ord_less_eq_int @ A @ B )
% 0.35/0.61       => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % le_imp_neg_le
% 0.35/0.61  thf(fact_5195_less__minus__iff,axiom,
% 0.35/0.61      ! [A: int,B: int] :
% 0.35/0.61        ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 0.35/0.61        = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % less_minus_iff
% 0.35/0.61  thf(fact_5196_less__minus__iff,axiom,
% 0.35/0.61      ! [A: real,B: real] :
% 0.35/0.61        ( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
% 0.35/0.61        = ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % less_minus_iff
% 0.35/0.61  thf(fact_5197_less__minus__iff,axiom,
% 0.35/0.61      ! [A: code_integer,B: code_integer] :
% 0.35/0.61        ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.35/0.61        = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % less_minus_iff
% 0.35/0.61  thf(fact_5198_less__minus__iff,axiom,
% 0.35/0.61      ! [A: rat,B: rat] :
% 0.35/0.61        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.35/0.61        = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % less_minus_iff
% 0.35/0.61  thf(fact_5199_minus__less__iff,axiom,
% 0.35/0.61      ! [A: int,B: int] :
% 0.35/0.61        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 0.35/0.61        = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_less_iff
% 0.35/0.61  thf(fact_5200_minus__less__iff,axiom,
% 0.35/0.61      ! [A: real,B: real] :
% 0.35/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
% 0.35/0.61        = ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_less_iff
% 0.35/0.61  thf(fact_5201_minus__less__iff,axiom,
% 0.35/0.61      ! [A: code_integer,B: code_integer] :
% 0.35/0.61        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.35/0.61        = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_less_iff
% 0.35/0.61  thf(fact_5202_minus__less__iff,axiom,
% 0.35/0.61      ! [A: rat,B: rat] :
% 0.35/0.61        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.35/0.61        = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_less_iff
% 0.35/0.61  thf(fact_5203_verit__negate__coefficient_I2_J,axiom,
% 0.35/0.61      ! [A: int,B: int] :
% 0.35/0.61        ( ( ord_less_int @ A @ B )
% 0.35/0.61       => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % verit_negate_coefficient(2)
% 0.35/0.61  thf(fact_5204_verit__negate__coefficient_I2_J,axiom,
% 0.35/0.61      ! [A: real,B: real] :
% 0.35/0.61        ( ( ord_less_real @ A @ B )
% 0.35/0.61       => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % verit_negate_coefficient(2)
% 0.35/0.61  thf(fact_5205_verit__negate__coefficient_I2_J,axiom,
% 0.35/0.61      ! [A: code_integer,B: code_integer] :
% 0.35/0.61        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.35/0.61       => ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % verit_negate_coefficient(2)
% 0.35/0.61  thf(fact_5206_verit__negate__coefficient_I2_J,axiom,
% 0.35/0.61      ! [A: rat,B: rat] :
% 0.35/0.61        ( ( ord_less_rat @ A @ B )
% 0.35/0.61       => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % verit_negate_coefficient(2)
% 0.35/0.61  thf(fact_5207_numeral__neq__neg__numeral,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( numeral_numeral_int @ M )
% 0.35/0.61       != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % numeral_neq_neg_numeral
% 0.35/0.61  thf(fact_5208_numeral__neq__neg__numeral,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( numeral_numeral_real @ M )
% 0.35/0.61       != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % numeral_neq_neg_numeral
% 0.35/0.61  thf(fact_5209_numeral__neq__neg__numeral,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( numera6690914467698888265omplex @ M )
% 0.35/0.61       != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % numeral_neq_neg_numeral
% 0.35/0.61  thf(fact_5210_numeral__neq__neg__numeral,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( numera6620942414471956472nteger @ M )
% 0.35/0.61       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % numeral_neq_neg_numeral
% 0.35/0.61  thf(fact_5211_numeral__neq__neg__numeral,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( numeral_numeral_rat @ M )
% 0.35/0.61       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % numeral_neq_neg_numeral
% 0.35/0.61  thf(fact_5212_neg__numeral__neq__numeral,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 0.35/0.61       != ( numeral_numeral_int @ N ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_numeral_neq_numeral
% 0.35/0.61  thf(fact_5213_neg__numeral__neq__numeral,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 0.35/0.61       != ( numeral_numeral_real @ N ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_numeral_neq_numeral
% 0.35/0.61  thf(fact_5214_neg__numeral__neq__numeral,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 0.35/0.61       != ( numera6690914467698888265omplex @ N ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_numeral_neq_numeral
% 0.35/0.61  thf(fact_5215_neg__numeral__neq__numeral,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 0.35/0.61       != ( numera6620942414471956472nteger @ N ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_numeral_neq_numeral
% 0.35/0.61  thf(fact_5216_neg__numeral__neq__numeral,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 0.35/0.61       != ( numeral_numeral_rat @ N ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_numeral_neq_numeral
% 0.35/0.61  thf(fact_5217_square__eq__iff,axiom,
% 0.35/0.61      ! [A: int,B: int] :
% 0.35/0.61        ( ( ( times_times_int @ A @ A )
% 0.35/0.61          = ( times_times_int @ B @ B ) )
% 0.35/0.61        = ( ( A = B )
% 0.35/0.61          | ( A
% 0.35/0.61            = ( uminus_uminus_int @ B ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % square_eq_iff
% 0.35/0.61  thf(fact_5218_square__eq__iff,axiom,
% 0.35/0.61      ! [A: real,B: real] :
% 0.35/0.61        ( ( ( times_times_real @ A @ A )
% 0.35/0.61          = ( times_times_real @ B @ B ) )
% 0.35/0.61        = ( ( A = B )
% 0.35/0.61          | ( A
% 0.35/0.61            = ( uminus_uminus_real @ B ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % square_eq_iff
% 0.35/0.61  thf(fact_5219_square__eq__iff,axiom,
% 0.35/0.61      ! [A: complex,B: complex] :
% 0.35/0.61        ( ( ( times_times_complex @ A @ A )
% 0.35/0.61          = ( times_times_complex @ B @ B ) )
% 0.35/0.61        = ( ( A = B )
% 0.35/0.61          | ( A
% 0.35/0.61            = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % square_eq_iff
% 0.35/0.61  thf(fact_5220_square__eq__iff,axiom,
% 0.35/0.61      ! [A: code_integer,B: code_integer] :
% 0.35/0.61        ( ( ( times_3573771949741848930nteger @ A @ A )
% 0.35/0.61          = ( times_3573771949741848930nteger @ B @ B ) )
% 0.35/0.61        = ( ( A = B )
% 0.35/0.61          | ( A
% 0.35/0.61            = ( uminus1351360451143612070nteger @ B ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % square_eq_iff
% 0.35/0.61  thf(fact_5221_square__eq__iff,axiom,
% 0.35/0.61      ! [A: rat,B: rat] :
% 0.35/0.61        ( ( ( times_times_rat @ A @ A )
% 0.35/0.61          = ( times_times_rat @ B @ B ) )
% 0.35/0.61        = ( ( A = B )
% 0.35/0.61          | ( A
% 0.35/0.61            = ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % square_eq_iff
% 0.35/0.61  thf(fact_5222_minus__mult__commute,axiom,
% 0.35/0.61      ! [A: int,B: int] :
% 0.35/0.61        ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 0.35/0.61        = ( times_times_int @ A @ ( uminus_uminus_int @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_mult_commute
% 0.35/0.61  thf(fact_5223_minus__mult__commute,axiom,
% 0.35/0.61      ! [A: real,B: real] :
% 0.35/0.61        ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 0.35/0.61        = ( times_times_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_mult_commute
% 0.35/0.61  thf(fact_5224_minus__mult__commute,axiom,
% 0.35/0.61      ! [A: complex,B: complex] :
% 0.35/0.61        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 0.35/0.61        = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_mult_commute
% 0.35/0.61  thf(fact_5225_minus__mult__commute,axiom,
% 0.35/0.61      ! [A: code_integer,B: code_integer] :
% 0.35/0.61        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.35/0.61        = ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_mult_commute
% 0.35/0.61  thf(fact_5226_minus__mult__commute,axiom,
% 0.35/0.61      ! [A: rat,B: rat] :
% 0.35/0.61        ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.35/0.61        = ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_mult_commute
% 0.35/0.61  thf(fact_5227_one__neq__neg__one,axiom,
% 0.35/0.61      ( one_one_int
% 0.35/0.61     != ( uminus_uminus_int @ one_one_int ) ) ).
% 0.35/0.61  
% 0.35/0.61  % one_neq_neg_one
% 0.35/0.61  thf(fact_5228_one__neq__neg__one,axiom,
% 0.35/0.61      ( one_one_real
% 0.35/0.61     != ( uminus_uminus_real @ one_one_real ) ) ).
% 0.35/0.61  
% 0.35/0.61  % one_neq_neg_one
% 0.35/0.61  thf(fact_5229_one__neq__neg__one,axiom,
% 0.35/0.61      ( one_one_complex
% 0.35/0.61     != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.35/0.61  
% 0.35/0.61  % one_neq_neg_one
% 0.35/0.61  thf(fact_5230_one__neq__neg__one,axiom,
% 0.35/0.61      ( one_one_Code_integer
% 0.35/0.61     != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.35/0.61  
% 0.35/0.61  % one_neq_neg_one
% 0.35/0.61  thf(fact_5231_one__neq__neg__one,axiom,
% 0.35/0.61      ( one_one_rat
% 0.35/0.61     != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.35/0.61  
% 0.35/0.61  % one_neq_neg_one
% 0.35/0.61  thf(fact_5232_is__num__normalize_I8_J,axiom,
% 0.35/0.61      ! [A: int,B: int] :
% 0.35/0.61        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 0.35/0.61        = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % is_num_normalize(8)
% 0.35/0.61  thf(fact_5233_is__num__normalize_I8_J,axiom,
% 0.35/0.61      ! [A: real,B: real] :
% 0.35/0.61        ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 0.35/0.61        = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % is_num_normalize(8)
% 0.35/0.61  thf(fact_5234_is__num__normalize_I8_J,axiom,
% 0.35/0.61      ! [A: complex,B: complex] :
% 0.35/0.61        ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 0.35/0.61        = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % is_num_normalize(8)
% 0.35/0.61  thf(fact_5235_is__num__normalize_I8_J,axiom,
% 0.35/0.61      ! [A: code_integer,B: code_integer] :
% 0.35/0.61        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.35/0.61        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % is_num_normalize(8)
% 0.35/0.61  thf(fact_5236_is__num__normalize_I8_J,axiom,
% 0.35/0.61      ! [A: rat,B: rat] :
% 0.35/0.61        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 0.35/0.61        = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % is_num_normalize(8)
% 0.35/0.61  thf(fact_5237_add_Oinverse__distrib__swap,axiom,
% 0.35/0.61      ! [A: int,B: int] :
% 0.35/0.61        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 0.35/0.61        = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % add.inverse_distrib_swap
% 0.35/0.61  thf(fact_5238_add_Oinverse__distrib__swap,axiom,
% 0.35/0.61      ! [A: real,B: real] :
% 0.35/0.61        ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 0.35/0.61        = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % add.inverse_distrib_swap
% 0.35/0.61  thf(fact_5239_add_Oinverse__distrib__swap,axiom,
% 0.35/0.61      ! [A: complex,B: complex] :
% 0.35/0.61        ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 0.35/0.61        = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % add.inverse_distrib_swap
% 0.35/0.61  thf(fact_5240_add_Oinverse__distrib__swap,axiom,
% 0.35/0.61      ! [A: code_integer,B: code_integer] :
% 0.35/0.61        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.35/0.61        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % add.inverse_distrib_swap
% 0.35/0.61  thf(fact_5241_add_Oinverse__distrib__swap,axiom,
% 0.35/0.61      ! [A: rat,B: rat] :
% 0.35/0.61        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 0.35/0.61        = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % add.inverse_distrib_swap
% 0.35/0.61  thf(fact_5242_group__cancel_Oneg1,axiom,
% 0.35/0.61      ! [A2: int,K: int,A: int] :
% 0.35/0.61        ( ( A2
% 0.35/0.61          = ( plus_plus_int @ K @ A ) )
% 0.35/0.61       => ( ( uminus_uminus_int @ A2 )
% 0.35/0.61          = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % group_cancel.neg1
% 0.35/0.61  thf(fact_5243_group__cancel_Oneg1,axiom,
% 0.35/0.61      ! [A2: real,K: real,A: real] :
% 0.35/0.61        ( ( A2
% 0.35/0.61          = ( plus_plus_real @ K @ A ) )
% 0.35/0.61       => ( ( uminus_uminus_real @ A2 )
% 0.35/0.61          = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( uminus_uminus_real @ A ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % group_cancel.neg1
% 0.35/0.61  thf(fact_5244_group__cancel_Oneg1,axiom,
% 0.35/0.61      ! [A2: complex,K: complex,A: complex] :
% 0.35/0.61        ( ( A2
% 0.35/0.61          = ( plus_plus_complex @ K @ A ) )
% 0.35/0.61       => ( ( uminus1482373934393186551omplex @ A2 )
% 0.35/0.61          = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % group_cancel.neg1
% 0.35/0.61  thf(fact_5245_group__cancel_Oneg1,axiom,
% 0.35/0.61      ! [A2: code_integer,K: code_integer,A: code_integer] :
% 0.35/0.61        ( ( A2
% 0.35/0.61          = ( plus_p5714425477246183910nteger @ K @ A ) )
% 0.35/0.61       => ( ( uminus1351360451143612070nteger @ A2 )
% 0.35/0.61          = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % group_cancel.neg1
% 0.35/0.61  thf(fact_5246_group__cancel_Oneg1,axiom,
% 0.35/0.61      ! [A2: rat,K: rat,A: rat] :
% 0.35/0.61        ( ( A2
% 0.35/0.61          = ( plus_plus_rat @ K @ A ) )
% 0.35/0.61       => ( ( uminus_uminus_rat @ A2 )
% 0.35/0.61          = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % group_cancel.neg1
% 0.35/0.61  thf(fact_5247_minus__diff__minus,axiom,
% 0.35/0.61      ! [A: int,B: int] :
% 0.35/0.61        ( ( minus_minus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 0.35/0.61        = ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_diff_minus
% 0.35/0.61  thf(fact_5248_minus__diff__minus,axiom,
% 0.35/0.61      ! [A: real,B: real] :
% 0.35/0.61        ( ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 0.35/0.61        = ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_diff_minus
% 0.35/0.61  thf(fact_5249_minus__diff__minus,axiom,
% 0.35/0.61      ! [A: complex,B: complex] :
% 0.35/0.61        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 0.35/0.61        = ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_diff_minus
% 0.35/0.61  thf(fact_5250_minus__diff__minus,axiom,
% 0.35/0.61      ! [A: code_integer,B: code_integer] :
% 0.35/0.61        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 0.35/0.61        = ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_diff_minus
% 0.35/0.61  thf(fact_5251_minus__diff__minus,axiom,
% 0.35/0.61      ! [A: rat,B: rat] :
% 0.35/0.61        ( ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 0.35/0.61        = ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_diff_minus
% 0.35/0.61  thf(fact_5252_minus__diff__commute,axiom,
% 0.35/0.61      ! [B: int,A: int] :
% 0.35/0.61        ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
% 0.35/0.61        = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_diff_commute
% 0.35/0.61  thf(fact_5253_minus__diff__commute,axiom,
% 0.35/0.61      ! [B: real,A: real] :
% 0.35/0.61        ( ( minus_minus_real @ ( uminus_uminus_real @ B ) @ A )
% 0.35/0.61        = ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_diff_commute
% 0.35/0.61  thf(fact_5254_minus__diff__commute,axiom,
% 0.35/0.61      ! [B: complex,A: complex] :
% 0.35/0.61        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ B ) @ A )
% 0.35/0.61        = ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_diff_commute
% 0.35/0.61  thf(fact_5255_minus__diff__commute,axiom,
% 0.35/0.61      ! [B: code_integer,A: code_integer] :
% 0.35/0.61        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ B ) @ A )
% 0.35/0.61        = ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_diff_commute
% 0.35/0.61  thf(fact_5256_minus__diff__commute,axiom,
% 0.35/0.61      ! [B: rat,A: rat] :
% 0.35/0.61        ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A )
% 0.35/0.61        = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_diff_commute
% 0.35/0.61  thf(fact_5257_div__minus__right,axiom,
% 0.35/0.61      ! [A: int,B: int] :
% 0.35/0.61        ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 0.35/0.61        = ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % div_minus_right
% 0.35/0.61  thf(fact_5258_div__minus__right,axiom,
% 0.35/0.61      ! [A: code_integer,B: code_integer] :
% 0.35/0.61        ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.35/0.61        = ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % div_minus_right
% 0.35/0.61  thf(fact_5259_minus__divide__right,axiom,
% 0.35/0.61      ! [A: real,B: real] :
% 0.35/0.61        ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 0.35/0.61        = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_divide_right
% 0.35/0.61  thf(fact_5260_minus__divide__right,axiom,
% 0.35/0.61      ! [A: complex,B: complex] :
% 0.35/0.61        ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.35/0.61        = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_divide_right
% 0.35/0.61  thf(fact_5261_minus__divide__right,axiom,
% 0.35/0.61      ! [A: rat,B: rat] :
% 0.35/0.61        ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 0.35/0.61        = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_divide_right
% 0.35/0.61  thf(fact_5262_minus__divide__divide,axiom,
% 0.35/0.61      ! [A: real,B: real] :
% 0.35/0.61        ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 0.35/0.61        = ( divide_divide_real @ A @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_divide_divide
% 0.35/0.61  thf(fact_5263_minus__divide__divide,axiom,
% 0.35/0.61      ! [A: complex,B: complex] :
% 0.35/0.61        ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 0.35/0.61        = ( divide1717551699836669952omplex @ A @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_divide_divide
% 0.35/0.61  thf(fact_5264_minus__divide__divide,axiom,
% 0.35/0.61      ! [A: rat,B: rat] :
% 0.35/0.61        ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 0.35/0.61        = ( divide_divide_rat @ A @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_divide_divide
% 0.35/0.61  thf(fact_5265_minus__divide__left,axiom,
% 0.35/0.61      ! [A: real,B: real] :
% 0.35/0.61        ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 0.35/0.61        = ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_divide_left
% 0.35/0.61  thf(fact_5266_minus__divide__left,axiom,
% 0.35/0.61      ! [A: complex,B: complex] :
% 0.35/0.61        ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.35/0.61        = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_divide_left
% 0.35/0.61  thf(fact_5267_minus__divide__left,axiom,
% 0.35/0.61      ! [A: rat,B: rat] :
% 0.35/0.61        ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 0.35/0.61        = ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % minus_divide_left
% 0.35/0.61  thf(fact_5268_mod__minus__right,axiom,
% 0.35/0.61      ! [A: int,B: int] :
% 0.35/0.61        ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 0.35/0.61        = ( uminus_uminus_int @ ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mod_minus_right
% 0.35/0.61  thf(fact_5269_mod__minus__right,axiom,
% 0.35/0.61      ! [A: code_integer,B: code_integer] :
% 0.35/0.61        ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.35/0.61        = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mod_minus_right
% 0.35/0.61  thf(fact_5270_mod__minus__cong,axiom,
% 0.35/0.61      ! [A: int,B: int,A5: int] :
% 0.35/0.61        ( ( ( modulo_modulo_int @ A @ B )
% 0.35/0.61          = ( modulo_modulo_int @ A5 @ B ) )
% 0.35/0.61       => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 0.35/0.61          = ( modulo_modulo_int @ ( uminus_uminus_int @ A5 ) @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mod_minus_cong
% 0.35/0.61  thf(fact_5271_mod__minus__cong,axiom,
% 0.35/0.61      ! [A: code_integer,B: code_integer,A5: code_integer] :
% 0.35/0.61        ( ( ( modulo364778990260209775nteger @ A @ B )
% 0.35/0.61          = ( modulo364778990260209775nteger @ A5 @ B ) )
% 0.35/0.61       => ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.35/0.61          = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A5 ) @ B ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mod_minus_cong
% 0.35/0.61  thf(fact_5272_mod__minus__eq,axiom,
% 0.35/0.61      ! [A: int,B: int] :
% 0.35/0.61        ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) @ B )
% 0.35/0.61        = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mod_minus_eq
% 0.35/0.61  thf(fact_5273_mod__minus__eq,axiom,
% 0.35/0.61      ! [A: code_integer,B: code_integer] :
% 0.35/0.61        ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) @ B )
% 0.35/0.61        = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 0.35/0.61  
% 0.35/0.61  % mod_minus_eq
% 0.35/0.61  thf(fact_5274_neg__numeral__le__numeral,axiom,
% 0.35/0.61      ! [M: num,N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_numeral_le_numeral
% 0.35/0.61  thf(fact_5275_neg__numeral__le__numeral,axiom,
% 0.35/0.61      ! [M: num,N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_numeral_le_numeral
% 0.35/0.61  thf(fact_5276_neg__numeral__le__numeral,axiom,
% 0.35/0.61      ! [M: num,N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_numeral_le_numeral
% 0.35/0.61  thf(fact_5277_neg__numeral__le__numeral,axiom,
% 0.35/0.61      ! [M: num,N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_numeral_le_numeral
% 0.35/0.61  thf(fact_5278_not__numeral__le__neg__numeral,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % not_numeral_le_neg_numeral
% 0.35/0.61  thf(fact_5279_not__numeral__le__neg__numeral,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % not_numeral_le_neg_numeral
% 0.35/0.61  thf(fact_5280_not__numeral__le__neg__numeral,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % not_numeral_le_neg_numeral
% 0.35/0.61  thf(fact_5281_not__numeral__le__neg__numeral,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % not_numeral_le_neg_numeral
% 0.35/0.61  thf(fact_5282_zero__neq__neg__numeral,axiom,
% 0.35/0.61      ! [N: num] :
% 0.35/0.61        ( zero_zero_int
% 0.35/0.61       != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % zero_neq_neg_numeral
% 0.35/0.61  thf(fact_5283_zero__neq__neg__numeral,axiom,
% 0.35/0.61      ! [N: num] :
% 0.35/0.61        ( zero_zero_real
% 0.35/0.61       != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % zero_neq_neg_numeral
% 0.35/0.61  thf(fact_5284_zero__neq__neg__numeral,axiom,
% 0.35/0.61      ! [N: num] :
% 0.35/0.61        ( zero_zero_complex
% 0.35/0.61       != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % zero_neq_neg_numeral
% 0.35/0.61  thf(fact_5285_zero__neq__neg__numeral,axiom,
% 0.35/0.61      ! [N: num] :
% 0.35/0.61        ( zero_z3403309356797280102nteger
% 0.35/0.61       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % zero_neq_neg_numeral
% 0.35/0.61  thf(fact_5286_zero__neq__neg__numeral,axiom,
% 0.35/0.61      ! [N: num] :
% 0.35/0.61        ( zero_zero_rat
% 0.35/0.61       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % zero_neq_neg_numeral
% 0.35/0.61  thf(fact_5287_not__numeral__less__neg__numeral,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % not_numeral_less_neg_numeral
% 0.35/0.61  thf(fact_5288_not__numeral__less__neg__numeral,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % not_numeral_less_neg_numeral
% 0.35/0.61  thf(fact_5289_not__numeral__less__neg__numeral,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % not_numeral_less_neg_numeral
% 0.35/0.61  thf(fact_5290_not__numeral__less__neg__numeral,axiom,
% 0.35/0.61      ! [M: num,N: num] :
% 0.35/0.61        ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % not_numeral_less_neg_numeral
% 0.35/0.61  thf(fact_5291_neg__numeral__less__numeral,axiom,
% 0.35/0.61      ! [M: num,N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_numeral_less_numeral
% 0.35/0.61  thf(fact_5292_neg__numeral__less__numeral,axiom,
% 0.35/0.61      ! [M: num,N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_numeral_less_numeral
% 0.35/0.61  thf(fact_5293_neg__numeral__less__numeral,axiom,
% 0.35/0.61      ! [M: num,N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_numeral_less_numeral
% 0.35/0.61  thf(fact_5294_neg__numeral__less__numeral,axiom,
% 0.35/0.61      ! [M: num,N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 0.35/0.61  
% 0.35/0.61  % neg_numeral_less_numeral
% 0.35/0.61  thf(fact_5295_le__minus__one__simps_I4_J,axiom,
% 0.35/0.61      ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.35/0.61  
% 0.35/0.61  % le_minus_one_simps(4)
% 0.35/0.61  thf(fact_5296_le__minus__one__simps_I4_J,axiom,
% 0.35/0.61      ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.35/0.61  
% 0.35/0.61  % le_minus_one_simps(4)
% 0.35/0.61  thf(fact_5297_le__minus__one__simps_I4_J,axiom,
% 0.35/0.61      ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.35/0.61  
% 0.35/0.61  % le_minus_one_simps(4)
% 0.35/0.61  thf(fact_5298_le__minus__one__simps_I4_J,axiom,
% 0.35/0.61      ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.35/0.61  
% 0.35/0.61  % le_minus_one_simps(4)
% 0.35/0.61  thf(fact_5299_le__minus__one__simps_I2_J,axiom,
% 0.35/0.61      ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 0.35/0.61  
% 0.35/0.61  % le_minus_one_simps(2)
% 0.35/0.61  thf(fact_5300_le__minus__one__simps_I2_J,axiom,
% 0.35/0.61      ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 0.35/0.61  
% 0.35/0.61  % le_minus_one_simps(2)
% 0.35/0.61  thf(fact_5301_le__minus__one__simps_I2_J,axiom,
% 0.35/0.61      ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 0.35/0.61  
% 0.35/0.61  % le_minus_one_simps(2)
% 0.35/0.61  thf(fact_5302_le__minus__one__simps_I2_J,axiom,
% 0.35/0.61      ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 0.35/0.61  
% 0.35/0.61  % le_minus_one_simps(2)
% 0.35/0.61  thf(fact_5303_zero__neq__neg__one,axiom,
% 0.35/0.61      ( zero_zero_int
% 0.35/0.61     != ( uminus_uminus_int @ one_one_int ) ) ).
% 0.35/0.61  
% 0.35/0.61  % zero_neq_neg_one
% 0.35/0.61  thf(fact_5304_zero__neq__neg__one,axiom,
% 0.35/0.61      ( zero_zero_real
% 0.35/0.61     != ( uminus_uminus_real @ one_one_real ) ) ).
% 0.35/0.61  
% 0.35/0.61  % zero_neq_neg_one
% 0.35/0.61  thf(fact_5305_zero__neq__neg__one,axiom,
% 0.35/0.61      ( zero_zero_complex
% 0.35/0.61     != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.35/0.61  
% 0.35/0.61  % zero_neq_neg_one
% 0.35/0.61  thf(fact_5306_zero__neq__neg__one,axiom,
% 0.35/0.61      ( zero_z3403309356797280102nteger
% 0.35/0.61     != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.35/0.61  
% 0.35/0.61  % zero_neq_neg_one
% 0.35/0.61  thf(fact_5307_zero__neq__neg__one,axiom,
% 0.35/0.61      ( zero_zero_rat
% 0.35/0.61     != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.35/0.61  
% 0.35/0.61  % zero_neq_neg_one
% 0.35/0.61  thf(fact_5308_add__eq__0__iff,axiom,
% 0.35/0.61      ! [A: int,B: int] :
% 0.35/0.61        ( ( ( plus_plus_int @ A @ B )
% 0.35/0.61          = zero_zero_int )
% 0.35/0.61        = ( B
% 0.35/0.61          = ( uminus_uminus_int @ A ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % add_eq_0_iff
% 0.35/0.61  thf(fact_5309_add__eq__0__iff,axiom,
% 0.35/0.61      ! [A: real,B: real] :
% 0.35/0.61        ( ( ( plus_plus_real @ A @ B )
% 0.35/0.61          = zero_zero_real )
% 0.35/0.61        = ( B
% 0.35/0.61          = ( uminus_uminus_real @ A ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % add_eq_0_iff
% 0.35/0.61  thf(fact_5310_add__eq__0__iff,axiom,
% 0.35/0.61      ! [A: complex,B: complex] :
% 0.35/0.61        ( ( ( plus_plus_complex @ A @ B )
% 0.35/0.61          = zero_zero_complex )
% 0.35/0.61        = ( B
% 0.35/0.61          = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % add_eq_0_iff
% 0.35/0.61  thf(fact_5311_add__eq__0__iff,axiom,
% 0.35/0.61      ! [A: code_integer,B: code_integer] :
% 0.35/0.61        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.35/0.61          = zero_z3403309356797280102nteger )
% 0.35/0.61        = ( B
% 0.35/0.61          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % add_eq_0_iff
% 0.35/0.61  thf(fact_5312_add__eq__0__iff,axiom,
% 0.35/0.61      ! [A: rat,B: rat] :
% 0.35/0.61        ( ( ( plus_plus_rat @ A @ B )
% 0.35/0.61          = zero_zero_rat )
% 0.35/0.61        = ( B
% 0.35/0.61          = ( uminus_uminus_rat @ A ) ) ) ).
% 0.35/0.61  
% 0.35/0.61  % add_eq_0_iff
% 0.35/0.61  thf(fact_5313_ab__group__add__class_Oab__left__minus,axiom,
% 0.35/0.61      ! [A: int] :
% 0.35/0.61        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 0.35/0.61        = zero_zero_int ) ).
% 0.35/0.61  
% 0.35/0.61  % ab_group_add_class.ab_left_minus
% 0.35/0.61  thf(fact_5314_ab__group__add__class_Oab__left__minus,axiom,
% 0.35/0.61      ! [A: real] :
% 0.35/0.61        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 0.35/0.61        = zero_zero_real ) ).
% 0.35/0.61  
% 0.35/0.61  % ab_group_add_class.ab_left_minus
% 0.35/0.61  thf(fact_5315_ab__group__add__class_Oab__left__minus,axiom,
% 0.35/0.61      ! [A: complex] :
% 0.35/0.61        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 0.35/0.61        = zero_zero_complex ) ).
% 0.35/0.61  
% 0.35/0.61  % ab_group_add_class.ab_left_minus
% 0.35/0.61  thf(fact_5316_ab__group__add__class_Oab__left__minus,axiom,
% 0.35/0.61      ! [A: code_integer] :
% 0.35/0.61        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 0.35/0.61        = zero_z3403309356797280102nteger ) ).
% 0.35/0.61  
% 0.35/0.61  % ab_group_add_class.ab_left_minus
% 0.35/0.61  thf(fact_5317_ab__group__add__class_Oab__left__minus,axiom,
% 0.35/0.61      ! [A: rat] :
% 0.35/0.61        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.35/0.61        = zero_zero_rat ) ).
% 0.35/0.61  
% 0.35/0.61  % ab_group_add_class.ab_left_minus
% 0.35/0.62  thf(fact_5318_add_Oinverse__unique,axiom,
% 0.35/0.62      ! [A: int,B: int] :
% 0.35/0.62        ( ( ( plus_plus_int @ A @ B )
% 0.35/0.62          = zero_zero_int )
% 0.35/0.62       => ( ( uminus_uminus_int @ A )
% 0.35/0.62          = B ) ) ).
% 0.35/0.62  
% 0.35/0.62  % add.inverse_unique
% 0.35/0.62  thf(fact_5319_add_Oinverse__unique,axiom,
% 0.35/0.62      ! [A: real,B: real] :
% 0.35/0.62        ( ( ( plus_plus_real @ A @ B )
% 0.35/0.62          = zero_zero_real )
% 0.35/0.62       => ( ( uminus_uminus_real @ A )
% 0.35/0.62          = B ) ) ).
% 0.35/0.62  
% 0.35/0.62  % add.inverse_unique
% 0.35/0.62  thf(fact_5320_add_Oinverse__unique,axiom,
% 0.35/0.62      ! [A: complex,B: complex] :
% 0.35/0.62        ( ( ( plus_plus_complex @ A @ B )
% 0.35/0.62          = zero_zero_complex )
% 0.35/0.62       => ( ( uminus1482373934393186551omplex @ A )
% 0.35/0.62          = B ) ) ).
% 0.35/0.62  
% 0.35/0.62  % add.inverse_unique
% 0.35/0.62  thf(fact_5321_add_Oinverse__unique,axiom,
% 0.35/0.62      ! [A: code_integer,B: code_integer] :
% 0.35/0.62        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.35/0.62          = zero_z3403309356797280102nteger )
% 0.35/0.62       => ( ( uminus1351360451143612070nteger @ A )
% 0.35/0.62          = B ) ) ).
% 0.35/0.62  
% 0.35/0.62  % add.inverse_unique
% 0.35/0.62  thf(fact_5322_add_Oinverse__unique,axiom,
% 0.35/0.62      ! [A: rat,B: rat] :
% 0.35/0.62        ( ( ( plus_plus_rat @ A @ B )
% 0.35/0.62          = zero_zero_rat )
% 0.35/0.62       => ( ( uminus_uminus_rat @ A )
% 0.35/0.62          = B ) ) ).
% 0.35/0.62  
% 0.35/0.62  % add.inverse_unique
% 0.35/0.62  thf(fact_5323_eq__neg__iff__add__eq__0,axiom,
% 0.35/0.62      ! [A: int,B: int] :
% 0.35/0.62        ( ( A
% 0.35/0.62          = ( uminus_uminus_int @ B ) )
% 0.35/0.62        = ( ( plus_plus_int @ A @ B )
% 0.35/0.62          = zero_zero_int ) ) ).
% 0.35/0.62  
% 0.35/0.62  % eq_neg_iff_add_eq_0
% 0.35/0.62  thf(fact_5324_eq__neg__iff__add__eq__0,axiom,
% 0.35/0.62      ! [A: real,B: real] :
% 0.35/0.62        ( ( A
% 0.35/0.62          = ( uminus_uminus_real @ B ) )
% 0.35/0.62        = ( ( plus_plus_real @ A @ B )
% 0.35/0.62          = zero_zero_real ) ) ).
% 0.35/0.62  
% 0.35/0.62  % eq_neg_iff_add_eq_0
% 0.35/0.62  thf(fact_5325_eq__neg__iff__add__eq__0,axiom,
% 0.35/0.62      ! [A: complex,B: complex] :
% 0.35/0.62        ( ( A
% 0.35/0.62          = ( uminus1482373934393186551omplex @ B ) )
% 0.35/0.62        = ( ( plus_plus_complex @ A @ B )
% 0.35/0.62          = zero_zero_complex ) ) ).
% 0.35/0.62  
% 0.35/0.62  % eq_neg_iff_add_eq_0
% 0.35/0.62  thf(fact_5326_eq__neg__iff__add__eq__0,axiom,
% 0.35/0.62      ! [A: code_integer,B: code_integer] :
% 0.35/0.62        ( ( A
% 0.35/0.62          = ( uminus1351360451143612070nteger @ B ) )
% 0.35/0.62        = ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.35/0.62          = zero_z3403309356797280102nteger ) ) ).
% 0.35/0.62  
% 0.35/0.62  % eq_neg_iff_add_eq_0
% 0.35/0.62  thf(fact_5327_eq__neg__iff__add__eq__0,axiom,
% 0.35/0.62      ! [A: rat,B: rat] :
% 0.35/0.62        ( ( A
% 0.35/0.62          = ( uminus_uminus_rat @ B ) )
% 0.35/0.62        = ( ( plus_plus_rat @ A @ B )
% 0.35/0.62          = zero_zero_rat ) ) ).
% 0.35/0.62  
% 0.35/0.62  % eq_neg_iff_add_eq_0
% 0.35/0.62  thf(fact_5328_neg__eq__iff__add__eq__0,axiom,
% 0.35/0.62      ! [A: int,B: int] :
% 0.35/0.62        ( ( ( uminus_uminus_int @ A )
% 0.35/0.62          = B )
% 0.35/0.62        = ( ( plus_plus_int @ A @ B )
% 0.35/0.62          = zero_zero_int ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_eq_iff_add_eq_0
% 0.35/0.62  thf(fact_5329_neg__eq__iff__add__eq__0,axiom,
% 0.35/0.62      ! [A: real,B: real] :
% 0.35/0.62        ( ( ( uminus_uminus_real @ A )
% 0.35/0.62          = B )
% 0.35/0.62        = ( ( plus_plus_real @ A @ B )
% 0.35/0.62          = zero_zero_real ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_eq_iff_add_eq_0
% 0.35/0.62  thf(fact_5330_neg__eq__iff__add__eq__0,axiom,
% 0.35/0.62      ! [A: complex,B: complex] :
% 0.35/0.62        ( ( ( uminus1482373934393186551omplex @ A )
% 0.35/0.62          = B )
% 0.35/0.62        = ( ( plus_plus_complex @ A @ B )
% 0.35/0.62          = zero_zero_complex ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_eq_iff_add_eq_0
% 0.35/0.62  thf(fact_5331_neg__eq__iff__add__eq__0,axiom,
% 0.35/0.62      ! [A: code_integer,B: code_integer] :
% 0.35/0.62        ( ( ( uminus1351360451143612070nteger @ A )
% 0.35/0.62          = B )
% 0.35/0.62        = ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.35/0.62          = zero_z3403309356797280102nteger ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_eq_iff_add_eq_0
% 0.35/0.62  thf(fact_5332_neg__eq__iff__add__eq__0,axiom,
% 0.35/0.62      ! [A: rat,B: rat] :
% 0.35/0.62        ( ( ( uminus_uminus_rat @ A )
% 0.35/0.62          = B )
% 0.35/0.62        = ( ( plus_plus_rat @ A @ B )
% 0.35/0.62          = zero_zero_rat ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_eq_iff_add_eq_0
% 0.35/0.62  thf(fact_5333_less__minus__one__simps_I2_J,axiom,
% 0.35/0.62      ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 0.35/0.62  
% 0.35/0.62  % less_minus_one_simps(2)
% 0.35/0.62  thf(fact_5334_less__minus__one__simps_I2_J,axiom,
% 0.35/0.62      ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 0.35/0.62  
% 0.35/0.62  % less_minus_one_simps(2)
% 0.35/0.62  thf(fact_5335_less__minus__one__simps_I2_J,axiom,
% 0.35/0.62      ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 0.35/0.62  
% 0.35/0.62  % less_minus_one_simps(2)
% 0.35/0.62  thf(fact_5336_less__minus__one__simps_I2_J,axiom,
% 0.35/0.62      ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 0.35/0.62  
% 0.35/0.62  % less_minus_one_simps(2)
% 0.35/0.62  thf(fact_5337_less__minus__one__simps_I4_J,axiom,
% 0.35/0.62      ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.35/0.62  
% 0.35/0.62  % less_minus_one_simps(4)
% 0.35/0.62  thf(fact_5338_less__minus__one__simps_I4_J,axiom,
% 0.35/0.62      ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.35/0.62  
% 0.35/0.62  % less_minus_one_simps(4)
% 0.35/0.62  thf(fact_5339_less__minus__one__simps_I4_J,axiom,
% 0.35/0.62      ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.35/0.62  
% 0.35/0.62  % less_minus_one_simps(4)
% 0.35/0.62  thf(fact_5340_less__minus__one__simps_I4_J,axiom,
% 0.35/0.62      ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.35/0.62  
% 0.35/0.62  % less_minus_one_simps(4)
% 0.35/0.62  thf(fact_5341_numeral__times__minus__swap,axiom,
% 0.35/0.62      ! [W: num,X: int] :
% 0.35/0.62        ( ( times_times_int @ ( numeral_numeral_int @ W ) @ ( uminus_uminus_int @ X ) )
% 0.35/0.62        = ( times_times_int @ X @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % numeral_times_minus_swap
% 0.35/0.62  thf(fact_5342_numeral__times__minus__swap,axiom,
% 0.35/0.62      ! [W: num,X: real] :
% 0.35/0.62        ( ( times_times_real @ ( numeral_numeral_real @ W ) @ ( uminus_uminus_real @ X ) )
% 0.35/0.62        = ( times_times_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % numeral_times_minus_swap
% 0.35/0.62  thf(fact_5343_numeral__times__minus__swap,axiom,
% 0.35/0.62      ! [W: num,X: complex] :
% 0.35/0.62        ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ ( uminus1482373934393186551omplex @ X ) )
% 0.35/0.62        = ( times_times_complex @ X @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % numeral_times_minus_swap
% 0.35/0.62  thf(fact_5344_numeral__times__minus__swap,axiom,
% 0.35/0.62      ! [W: num,X: code_integer] :
% 0.35/0.62        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ ( uminus1351360451143612070nteger @ X ) )
% 0.35/0.62        = ( times_3573771949741848930nteger @ X @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % numeral_times_minus_swap
% 0.35/0.62  thf(fact_5345_numeral__times__minus__swap,axiom,
% 0.35/0.62      ! [W: num,X: rat] :
% 0.35/0.62        ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ ( uminus_uminus_rat @ X ) )
% 0.35/0.62        = ( times_times_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % numeral_times_minus_swap
% 0.35/0.62  thf(fact_5346_one__neq__neg__numeral,axiom,
% 0.35/0.62      ! [N: num] :
% 0.35/0.62        ( one_one_int
% 0.35/0.62       != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % one_neq_neg_numeral
% 0.35/0.62  thf(fact_5347_one__neq__neg__numeral,axiom,
% 0.35/0.62      ! [N: num] :
% 0.35/0.62        ( one_one_real
% 0.35/0.62       != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % one_neq_neg_numeral
% 0.35/0.62  thf(fact_5348_one__neq__neg__numeral,axiom,
% 0.35/0.62      ! [N: num] :
% 0.35/0.62        ( one_one_complex
% 0.35/0.62       != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % one_neq_neg_numeral
% 0.35/0.62  thf(fact_5349_one__neq__neg__numeral,axiom,
% 0.35/0.62      ! [N: num] :
% 0.35/0.62        ( one_one_Code_integer
% 0.35/0.62       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % one_neq_neg_numeral
% 0.35/0.62  thf(fact_5350_one__neq__neg__numeral,axiom,
% 0.35/0.62      ! [N: num] :
% 0.35/0.62        ( one_one_rat
% 0.35/0.62       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % one_neq_neg_numeral
% 0.35/0.62  thf(fact_5351_numeral__neq__neg__one,axiom,
% 0.35/0.62      ! [N: num] :
% 0.35/0.62        ( ( numeral_numeral_int @ N )
% 0.35/0.62       != ( uminus_uminus_int @ one_one_int ) ) ).
% 0.35/0.62  
% 0.35/0.62  % numeral_neq_neg_one
% 0.35/0.62  thf(fact_5352_numeral__neq__neg__one,axiom,
% 0.35/0.62      ! [N: num] :
% 0.35/0.62        ( ( numeral_numeral_real @ N )
% 0.35/0.62       != ( uminus_uminus_real @ one_one_real ) ) ).
% 0.35/0.62  
% 0.35/0.62  % numeral_neq_neg_one
% 0.35/0.62  thf(fact_5353_numeral__neq__neg__one,axiom,
% 0.35/0.62      ! [N: num] :
% 0.35/0.62        ( ( numera6690914467698888265omplex @ N )
% 0.35/0.62       != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.35/0.62  
% 0.35/0.62  % numeral_neq_neg_one
% 0.35/0.62  thf(fact_5354_numeral__neq__neg__one,axiom,
% 0.35/0.62      ! [N: num] :
% 0.35/0.62        ( ( numera6620942414471956472nteger @ N )
% 0.35/0.62       != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.35/0.62  
% 0.35/0.62  % numeral_neq_neg_one
% 0.35/0.62  thf(fact_5355_numeral__neq__neg__one,axiom,
% 0.35/0.62      ! [N: num] :
% 0.35/0.62        ( ( numeral_numeral_rat @ N )
% 0.35/0.62       != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.35/0.62  
% 0.35/0.62  % numeral_neq_neg_one
% 0.35/0.62  thf(fact_5356_nonzero__minus__divide__right,axiom,
% 0.35/0.62      ! [B: real,A: real] :
% 0.35/0.62        ( ( B != zero_zero_real )
% 0.35/0.62       => ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 0.35/0.62          = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % nonzero_minus_divide_right
% 0.35/0.62  thf(fact_5357_nonzero__minus__divide__right,axiom,
% 0.35/0.62      ! [B: complex,A: complex] :
% 0.35/0.62        ( ( B != zero_zero_complex )
% 0.35/0.62       => ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.35/0.62          = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % nonzero_minus_divide_right
% 0.35/0.62  thf(fact_5358_nonzero__minus__divide__right,axiom,
% 0.35/0.62      ! [B: rat,A: rat] :
% 0.35/0.62        ( ( B != zero_zero_rat )
% 0.35/0.62       => ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 0.35/0.62          = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % nonzero_minus_divide_right
% 0.35/0.62  thf(fact_5359_nonzero__minus__divide__divide,axiom,
% 0.35/0.62      ! [B: real,A: real] :
% 0.35/0.62        ( ( B != zero_zero_real )
% 0.35/0.62       => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 0.35/0.62          = ( divide_divide_real @ A @ B ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % nonzero_minus_divide_divide
% 0.35/0.62  thf(fact_5360_nonzero__minus__divide__divide,axiom,
% 0.35/0.62      ! [B: complex,A: complex] :
% 0.35/0.62        ( ( B != zero_zero_complex )
% 0.35/0.62       => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 0.35/0.62          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % nonzero_minus_divide_divide
% 0.35/0.62  thf(fact_5361_nonzero__minus__divide__divide,axiom,
% 0.35/0.62      ! [B: rat,A: rat] :
% 0.35/0.62        ( ( B != zero_zero_rat )
% 0.35/0.62       => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 0.35/0.62          = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % nonzero_minus_divide_divide
% 0.35/0.62  thf(fact_5362_square__eq__1__iff,axiom,
% 0.35/0.62      ! [X: int] :
% 0.35/0.62        ( ( ( times_times_int @ X @ X )
% 0.35/0.62          = one_one_int )
% 0.35/0.62        = ( ( X = one_one_int )
% 0.35/0.62          | ( X
% 0.35/0.62            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % square_eq_1_iff
% 0.35/0.62  thf(fact_5363_square__eq__1__iff,axiom,
% 0.35/0.62      ! [X: real] :
% 0.35/0.62        ( ( ( times_times_real @ X @ X )
% 0.35/0.62          = one_one_real )
% 0.35/0.62        = ( ( X = one_one_real )
% 0.35/0.62          | ( X
% 0.35/0.62            = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % square_eq_1_iff
% 0.35/0.62  thf(fact_5364_square__eq__1__iff,axiom,
% 0.35/0.62      ! [X: complex] :
% 0.35/0.62        ( ( ( times_times_complex @ X @ X )
% 0.35/0.62          = one_one_complex )
% 0.35/0.62        = ( ( X = one_one_complex )
% 0.35/0.62          | ( X
% 0.35/0.62            = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % square_eq_1_iff
% 0.35/0.62  thf(fact_5365_square__eq__1__iff,axiom,
% 0.35/0.62      ! [X: code_integer] :
% 0.35/0.62        ( ( ( times_3573771949741848930nteger @ X @ X )
% 0.35/0.62          = one_one_Code_integer )
% 0.35/0.62        = ( ( X = one_one_Code_integer )
% 0.35/0.62          | ( X
% 0.35/0.62            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % square_eq_1_iff
% 0.35/0.62  thf(fact_5366_square__eq__1__iff,axiom,
% 0.35/0.62      ! [X: rat] :
% 0.35/0.62        ( ( ( times_times_rat @ X @ X )
% 0.35/0.62          = one_one_rat )
% 0.35/0.62        = ( ( X = one_one_rat )
% 0.35/0.62          | ( X
% 0.35/0.62            = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % square_eq_1_iff
% 0.35/0.62  thf(fact_5367_group__cancel_Osub2,axiom,
% 0.35/0.62      ! [B2: int,K: int,B: int,A: int] :
% 0.35/0.62        ( ( B2
% 0.35/0.62          = ( plus_plus_int @ K @ B ) )
% 0.35/0.62       => ( ( minus_minus_int @ A @ B2 )
% 0.35/0.62          = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % group_cancel.sub2
% 0.35/0.62  thf(fact_5368_group__cancel_Osub2,axiom,
% 0.35/0.62      ! [B2: real,K: real,B: real,A: real] :
% 0.35/0.62        ( ( B2
% 0.35/0.62          = ( plus_plus_real @ K @ B ) )
% 0.35/0.62       => ( ( minus_minus_real @ A @ B2 )
% 0.35/0.62          = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % group_cancel.sub2
% 0.35/0.62  thf(fact_5369_group__cancel_Osub2,axiom,
% 0.35/0.62      ! [B2: complex,K: complex,B: complex,A: complex] :
% 0.35/0.62        ( ( B2
% 0.35/0.62          = ( plus_plus_complex @ K @ B ) )
% 0.35/0.62       => ( ( minus_minus_complex @ A @ B2 )
% 0.35/0.62          = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( minus_minus_complex @ A @ B ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % group_cancel.sub2
% 0.35/0.62  thf(fact_5370_group__cancel_Osub2,axiom,
% 0.35/0.62      ! [B2: code_integer,K: code_integer,B: code_integer,A: code_integer] :
% 0.35/0.62        ( ( B2
% 0.35/0.62          = ( plus_p5714425477246183910nteger @ K @ B ) )
% 0.35/0.62       => ( ( minus_8373710615458151222nteger @ A @ B2 )
% 0.35/0.62          = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % group_cancel.sub2
% 0.35/0.62  thf(fact_5371_group__cancel_Osub2,axiom,
% 0.35/0.62      ! [B2: rat,K: rat,B: rat,A: rat] :
% 0.35/0.62        ( ( B2
% 0.35/0.62          = ( plus_plus_rat @ K @ B ) )
% 0.35/0.62       => ( ( minus_minus_rat @ A @ B2 )
% 0.35/0.62          = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % group_cancel.sub2
% 0.35/0.62  thf(fact_5372_diff__conv__add__uminus,axiom,
% 0.35/0.62      ( minus_minus_int
% 0.35/0.62      = ( ^ [A3: int,B4: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B4 ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % diff_conv_add_uminus
% 0.35/0.62  thf(fact_5373_diff__conv__add__uminus,axiom,
% 0.35/0.62      ( minus_minus_real
% 0.35/0.62      = ( ^ [A3: real,B4: real] : ( plus_plus_real @ A3 @ ( uminus_uminus_real @ B4 ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % diff_conv_add_uminus
% 0.35/0.62  thf(fact_5374_diff__conv__add__uminus,axiom,
% 0.35/0.62      ( minus_minus_complex
% 0.35/0.62      = ( ^ [A3: complex,B4: complex] : ( plus_plus_complex @ A3 @ ( uminus1482373934393186551omplex @ B4 ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % diff_conv_add_uminus
% 0.35/0.62  thf(fact_5375_diff__conv__add__uminus,axiom,
% 0.35/0.62      ( minus_8373710615458151222nteger
% 0.35/0.62      = ( ^ [A3: code_integer,B4: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B4 ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % diff_conv_add_uminus
% 0.35/0.62  thf(fact_5376_diff__conv__add__uminus,axiom,
% 0.35/0.62      ( minus_minus_rat
% 0.35/0.62      = ( ^ [A3: rat,B4: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B4 ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % diff_conv_add_uminus
% 0.35/0.62  thf(fact_5377_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.35/0.62      ( minus_minus_int
% 0.35/0.62      = ( ^ [A3: int,B4: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B4 ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % ab_group_add_class.ab_diff_conv_add_uminus
% 0.35/0.62  thf(fact_5378_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.35/0.62      ( minus_minus_real
% 0.35/0.62      = ( ^ [A3: real,B4: real] : ( plus_plus_real @ A3 @ ( uminus_uminus_real @ B4 ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % ab_group_add_class.ab_diff_conv_add_uminus
% 0.35/0.62  thf(fact_5379_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.35/0.62      ( minus_minus_complex
% 0.35/0.62      = ( ^ [A3: complex,B4: complex] : ( plus_plus_complex @ A3 @ ( uminus1482373934393186551omplex @ B4 ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % ab_group_add_class.ab_diff_conv_add_uminus
% 0.35/0.62  thf(fact_5380_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.35/0.62      ( minus_8373710615458151222nteger
% 0.35/0.62      = ( ^ [A3: code_integer,B4: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B4 ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % ab_group_add_class.ab_diff_conv_add_uminus
% 0.35/0.62  thf(fact_5381_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.35/0.62      ( minus_minus_rat
% 0.35/0.62      = ( ^ [A3: rat,B4: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B4 ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % ab_group_add_class.ab_diff_conv_add_uminus
% 0.35/0.62  thf(fact_5382_dvd__div__neg,axiom,
% 0.35/0.62      ! [B: int,A: int] :
% 0.35/0.62        ( ( dvd_dvd_int @ B @ A )
% 0.35/0.62       => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 0.35/0.62          = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dvd_div_neg
% 0.35/0.62  thf(fact_5383_dvd__div__neg,axiom,
% 0.35/0.62      ! [B: real,A: real] :
% 0.35/0.62        ( ( dvd_dvd_real @ B @ A )
% 0.35/0.62       => ( ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) )
% 0.35/0.62          = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dvd_div_neg
% 0.35/0.62  thf(fact_5384_dvd__div__neg,axiom,
% 0.35/0.62      ! [B: complex,A: complex] :
% 0.35/0.62        ( ( dvd_dvd_complex @ B @ A )
% 0.35/0.62       => ( ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 0.35/0.62          = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dvd_div_neg
% 0.35/0.62  thf(fact_5385_dvd__div__neg,axiom,
% 0.35/0.62      ! [B: code_integer,A: code_integer] :
% 0.35/0.62        ( ( dvd_dvd_Code_integer @ B @ A )
% 0.35/0.62       => ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.35/0.62          = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dvd_div_neg
% 0.35/0.62  thf(fact_5386_dvd__div__neg,axiom,
% 0.35/0.62      ! [B: rat,A: rat] :
% 0.35/0.62        ( ( dvd_dvd_rat @ B @ A )
% 0.35/0.62       => ( ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.35/0.62          = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dvd_div_neg
% 0.35/0.62  thf(fact_5387_dvd__neg__div,axiom,
% 0.35/0.62      ! [B: int,A: int] :
% 0.35/0.62        ( ( dvd_dvd_int @ B @ A )
% 0.35/0.62       => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 0.35/0.62          = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dvd_neg_div
% 0.35/0.62  thf(fact_5388_dvd__neg__div,axiom,
% 0.35/0.62      ! [B: real,A: real] :
% 0.35/0.62        ( ( dvd_dvd_real @ B @ A )
% 0.35/0.62       => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B )
% 0.35/0.62          = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dvd_neg_div
% 0.35/0.62  thf(fact_5389_dvd__neg__div,axiom,
% 0.35/0.62      ! [B: complex,A: complex] :
% 0.35/0.62        ( ( dvd_dvd_complex @ B @ A )
% 0.35/0.62       => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 0.35/0.62          = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dvd_neg_div
% 0.35/0.62  thf(fact_5390_dvd__neg__div,axiom,
% 0.35/0.62      ! [B: code_integer,A: code_integer] :
% 0.35/0.62        ( ( dvd_dvd_Code_integer @ B @ A )
% 0.35/0.62       => ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.35/0.62          = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dvd_neg_div
% 0.35/0.62  thf(fact_5391_dvd__neg__div,axiom,
% 0.35/0.62      ! [B: rat,A: rat] :
% 0.35/0.62        ( ( dvd_dvd_rat @ B @ A )
% 0.35/0.62       => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.35/0.62          = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dvd_neg_div
% 0.35/0.62  thf(fact_5392_real__minus__mult__self__le,axiom,
% 0.35/0.62      ! [U: real,X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( times_times_real @ U @ U ) ) @ ( times_times_real @ X @ X ) ) ).
% 0.35/0.62  
% 0.35/0.62  % real_minus_mult_self_le
% 0.35/0.62  thf(fact_5393_numeral__eq__Suc,axiom,
% 0.35/0.62      ( numeral_numeral_nat
% 0.35/0.62      = ( ^ [K3: num] : ( suc @ ( pred_numeral @ K3 ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % numeral_eq_Suc
% 0.35/0.62  thf(fact_5394_minus__int__code_I2_J,axiom,
% 0.35/0.62      ! [L2: int] :
% 0.35/0.62        ( ( minus_minus_int @ zero_zero_int @ L2 )
% 0.35/0.62        = ( uminus_uminus_int @ L2 ) ) ).
% 0.35/0.62  
% 0.35/0.62  % minus_int_code(2)
% 0.35/0.62  thf(fact_5395_zmod__zminus2__not__zero,axiom,
% 0.35/0.62      ! [K: int,L2: int] :
% 0.35/0.62        ( ( ( modulo_modulo_int @ K @ ( uminus_uminus_int @ L2 ) )
% 0.35/0.62         != zero_zero_int )
% 0.35/0.62       => ( ( modulo_modulo_int @ K @ L2 )
% 0.35/0.62         != zero_zero_int ) ) ).
% 0.35/0.62  
% 0.35/0.62  % zmod_zminus2_not_zero
% 0.35/0.62  thf(fact_5396_zmod__zminus1__not__zero,axiom,
% 0.35/0.62      ! [K: int,L2: int] :
% 0.35/0.62        ( ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L2 )
% 0.35/0.62         != zero_zero_int )
% 0.35/0.62       => ( ( modulo_modulo_int @ K @ L2 )
% 0.35/0.62         != zero_zero_int ) ) ).
% 0.35/0.62  
% 0.35/0.62  % zmod_zminus1_not_zero
% 0.35/0.62  thf(fact_5397_minus__real__def,axiom,
% 0.35/0.62      ( minus_minus_real
% 0.35/0.62      = ( ^ [X2: real,Y: real] : ( plus_plus_real @ X2 @ ( uminus_uminus_real @ Y ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % minus_real_def
% 0.35/0.62  thf(fact_5398_neg__numeral__le__zero,axiom,
% 0.35/0.62      ! [N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_numeral_le_zero
% 0.35/0.62  thf(fact_5399_neg__numeral__le__zero,axiom,
% 0.35/0.62      ! [N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_numeral_le_zero
% 0.35/0.62  thf(fact_5400_neg__numeral__le__zero,axiom,
% 0.35/0.62      ! [N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_numeral_le_zero
% 0.35/0.62  thf(fact_5401_neg__numeral__le__zero,axiom,
% 0.35/0.62      ! [N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_numeral_le_zero
% 0.35/0.62  thf(fact_5402_not__zero__le__neg__numeral,axiom,
% 0.35/0.62      ! [N: num] :
% 0.35/0.62        ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % not_zero_le_neg_numeral
% 0.35/0.62  thf(fact_5403_not__zero__le__neg__numeral,axiom,
% 0.35/0.62      ! [N: num] :
% 0.35/0.62        ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % not_zero_le_neg_numeral
% 0.35/0.62  thf(fact_5404_not__zero__le__neg__numeral,axiom,
% 0.35/0.62      ! [N: num] :
% 0.35/0.62        ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % not_zero_le_neg_numeral
% 0.35/0.62  thf(fact_5405_not__zero__le__neg__numeral,axiom,
% 0.35/0.62      ! [N: num] :
% 0.35/0.62        ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % not_zero_le_neg_numeral
% 0.35/0.62  thf(fact_5406_neg__numeral__less__zero,axiom,
% 0.35/0.62      ! [N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_numeral_less_zero
% 0.35/0.62  thf(fact_5407_neg__numeral__less__zero,axiom,
% 0.35/0.62      ! [N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_numeral_less_zero
% 0.35/0.62  thf(fact_5408_neg__numeral__less__zero,axiom,
% 0.35/0.62      ! [N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_numeral_less_zero
% 0.35/0.62  thf(fact_5409_neg__numeral__less__zero,axiom,
% 0.35/0.62      ! [N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_numeral_less_zero
% 0.35/0.62  thf(fact_5410_not__zero__less__neg__numeral,axiom,
% 0.35/0.62      ! [N: num] :
% 0.35/0.62        ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % not_zero_less_neg_numeral
% 0.35/0.62  thf(fact_5411_not__zero__less__neg__numeral,axiom,
% 0.35/0.62      ! [N: num] :
% 0.35/0.62        ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % not_zero_less_neg_numeral
% 0.35/0.62  thf(fact_5412_not__zero__less__neg__numeral,axiom,
% 0.35/0.62      ! [N: num] :
% 0.35/0.62        ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % not_zero_less_neg_numeral
% 0.35/0.62  thf(fact_5413_not__zero__less__neg__numeral,axiom,
% 0.35/0.62      ! [N: num] :
% 0.35/0.62        ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % not_zero_less_neg_numeral
% 0.35/0.62  thf(fact_5414_le__minus__one__simps_I3_J,axiom,
% 0.35/0.62      ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.35/0.62  
% 0.35/0.62  % le_minus_one_simps(3)
% 0.35/0.62  thf(fact_5415_le__minus__one__simps_I3_J,axiom,
% 0.35/0.62      ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.35/0.62  
% 0.35/0.62  % le_minus_one_simps(3)
% 0.35/0.62  thf(fact_5416_le__minus__one__simps_I3_J,axiom,
% 0.35/0.62      ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.35/0.62  
% 0.35/0.62  % le_minus_one_simps(3)
% 0.35/0.62  thf(fact_5417_le__minus__one__simps_I3_J,axiom,
% 0.35/0.62      ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.35/0.62  
% 0.35/0.62  % le_minus_one_simps(3)
% 0.35/0.62  thf(fact_5418_le__minus__one__simps_I1_J,axiom,
% 0.35/0.62      ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 0.35/0.62  
% 0.35/0.62  % le_minus_one_simps(1)
% 0.35/0.62  thf(fact_5419_le__minus__one__simps_I1_J,axiom,
% 0.35/0.62      ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 0.35/0.62  
% 0.35/0.62  % le_minus_one_simps(1)
% 0.35/0.62  thf(fact_5420_le__minus__one__simps_I1_J,axiom,
% 0.35/0.62      ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 0.35/0.62  
% 0.35/0.62  % le_minus_one_simps(1)
% 0.35/0.62  thf(fact_5421_le__minus__one__simps_I1_J,axiom,
% 0.35/0.62      ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 0.35/0.62  
% 0.35/0.62  % le_minus_one_simps(1)
% 0.35/0.62  thf(fact_5422_less__minus__one__simps_I3_J,axiom,
% 0.35/0.62      ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.35/0.62  
% 0.35/0.62  % less_minus_one_simps(3)
% 0.35/0.62  thf(fact_5423_less__minus__one__simps_I3_J,axiom,
% 0.35/0.62      ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.35/0.62  
% 0.35/0.62  % less_minus_one_simps(3)
% 0.35/0.62  thf(fact_5424_less__minus__one__simps_I3_J,axiom,
% 0.35/0.62      ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.35/0.62  
% 0.35/0.62  % less_minus_one_simps(3)
% 0.35/0.62  thf(fact_5425_less__minus__one__simps_I3_J,axiom,
% 0.35/0.62      ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.35/0.62  
% 0.35/0.62  % less_minus_one_simps(3)
% 0.35/0.62  thf(fact_5426_less__minus__one__simps_I1_J,axiom,
% 0.35/0.62      ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 0.35/0.62  
% 0.35/0.62  % less_minus_one_simps(1)
% 0.35/0.62  thf(fact_5427_less__minus__one__simps_I1_J,axiom,
% 0.35/0.62      ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 0.35/0.62  
% 0.35/0.62  % less_minus_one_simps(1)
% 0.35/0.62  thf(fact_5428_less__minus__one__simps_I1_J,axiom,
% 0.35/0.62      ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 0.35/0.62  
% 0.35/0.62  % less_minus_one_simps(1)
% 0.35/0.62  thf(fact_5429_less__minus__one__simps_I1_J,axiom,
% 0.35/0.62      ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 0.35/0.62  
% 0.35/0.62  % less_minus_one_simps(1)
% 0.35/0.62  thf(fact_5430_not__one__le__neg__numeral,axiom,
% 0.35/0.62      ! [M: num] :
% 0.35/0.62        ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % not_one_le_neg_numeral
% 0.35/0.62  thf(fact_5431_not__one__le__neg__numeral,axiom,
% 0.35/0.62      ! [M: num] :
% 0.35/0.62        ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % not_one_le_neg_numeral
% 0.35/0.62  thf(fact_5432_not__one__le__neg__numeral,axiom,
% 0.35/0.62      ! [M: num] :
% 0.35/0.62        ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % not_one_le_neg_numeral
% 0.35/0.62  thf(fact_5433_not__one__le__neg__numeral,axiom,
% 0.35/0.62      ! [M: num] :
% 0.35/0.62        ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % not_one_le_neg_numeral
% 0.35/0.62  thf(fact_5434_not__numeral__le__neg__one,axiom,
% 0.35/0.62      ! [M: num] :
% 0.35/0.62        ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.35/0.62  
% 0.35/0.62  % not_numeral_le_neg_one
% 0.35/0.62  thf(fact_5435_not__numeral__le__neg__one,axiom,
% 0.35/0.62      ! [M: num] :
% 0.35/0.62        ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.35/0.62  
% 0.35/0.62  % not_numeral_le_neg_one
% 0.35/0.62  thf(fact_5436_not__numeral__le__neg__one,axiom,
% 0.35/0.62      ! [M: num] :
% 0.35/0.62        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.35/0.62  
% 0.35/0.62  % not_numeral_le_neg_one
% 0.35/0.62  thf(fact_5437_not__numeral__le__neg__one,axiom,
% 0.35/0.62      ! [M: num] :
% 0.35/0.62        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.35/0.62  
% 0.35/0.62  % not_numeral_le_neg_one
% 0.35/0.62  thf(fact_5438_neg__numeral__le__neg__one,axiom,
% 0.35/0.62      ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_numeral_le_neg_one
% 0.35/0.62  thf(fact_5439_neg__numeral__le__neg__one,axiom,
% 0.35/0.62      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_numeral_le_neg_one
% 0.35/0.62  thf(fact_5440_neg__numeral__le__neg__one,axiom,
% 0.35/0.62      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_numeral_le_neg_one
% 0.35/0.62  thf(fact_5441_neg__numeral__le__neg__one,axiom,
% 0.35/0.62      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_numeral_le_neg_one
% 0.35/0.62  thf(fact_5442_neg__one__le__numeral,axiom,
% 0.35/0.62      ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_one_le_numeral
% 0.35/0.62  thf(fact_5443_neg__one__le__numeral,axiom,
% 0.35/0.62      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_one_le_numeral
% 0.35/0.62  thf(fact_5444_neg__one__le__numeral,axiom,
% 0.35/0.62      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_one_le_numeral
% 0.35/0.62  thf(fact_5445_neg__one__le__numeral,axiom,
% 0.35/0.62      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_one_le_numeral
% 0.35/0.62  thf(fact_5446_neg__numeral__le__one,axiom,
% 0.35/0.62      ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_numeral_le_one
% 0.35/0.62  thf(fact_5447_neg__numeral__le__one,axiom,
% 0.35/0.62      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_numeral_le_one
% 0.35/0.62  thf(fact_5448_neg__numeral__le__one,axiom,
% 0.35/0.62      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_numeral_le_one
% 0.35/0.62  thf(fact_5449_neg__numeral__le__one,axiom,
% 0.35/0.62      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_numeral_le_one
% 0.35/0.62  thf(fact_5450_not__neg__one__less__neg__numeral,axiom,
% 0.35/0.62      ! [M: num] :
% 0.35/0.62        ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % not_neg_one_less_neg_numeral
% 0.35/0.62  thf(fact_5451_not__neg__one__less__neg__numeral,axiom,
% 0.35/0.62      ! [M: num] :
% 0.35/0.62        ~ ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % not_neg_one_less_neg_numeral
% 0.35/0.62  thf(fact_5452_not__neg__one__less__neg__numeral,axiom,
% 0.35/0.62      ! [M: num] :
% 0.35/0.62        ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % not_neg_one_less_neg_numeral
% 0.35/0.62  thf(fact_5453_not__neg__one__less__neg__numeral,axiom,
% 0.35/0.62      ! [M: num] :
% 0.35/0.62        ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % not_neg_one_less_neg_numeral
% 0.35/0.62  thf(fact_5454_not__one__less__neg__numeral,axiom,
% 0.35/0.62      ! [M: num] :
% 0.35/0.62        ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % not_one_less_neg_numeral
% 0.35/0.62  thf(fact_5455_not__one__less__neg__numeral,axiom,
% 0.35/0.62      ! [M: num] :
% 0.35/0.62        ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % not_one_less_neg_numeral
% 0.35/0.62  thf(fact_5456_not__one__less__neg__numeral,axiom,
% 0.35/0.62      ! [M: num] :
% 0.35/0.62        ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % not_one_less_neg_numeral
% 0.35/0.62  thf(fact_5457_not__one__less__neg__numeral,axiom,
% 0.35/0.62      ! [M: num] :
% 0.35/0.62        ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % not_one_less_neg_numeral
% 0.35/0.62  thf(fact_5458_not__numeral__less__neg__one,axiom,
% 0.35/0.62      ! [M: num] :
% 0.35/0.62        ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.35/0.62  
% 0.35/0.62  % not_numeral_less_neg_one
% 0.35/0.62  thf(fact_5459_not__numeral__less__neg__one,axiom,
% 0.35/0.62      ! [M: num] :
% 0.35/0.62        ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.35/0.62  
% 0.35/0.62  % not_numeral_less_neg_one
% 0.35/0.62  thf(fact_5460_not__numeral__less__neg__one,axiom,
% 0.35/0.62      ! [M: num] :
% 0.35/0.62        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.35/0.62  
% 0.35/0.62  % not_numeral_less_neg_one
% 0.35/0.62  thf(fact_5461_not__numeral__less__neg__one,axiom,
% 0.35/0.62      ! [M: num] :
% 0.35/0.62        ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.35/0.62  
% 0.35/0.62  % not_numeral_less_neg_one
% 0.35/0.62  thf(fact_5462_neg__one__less__numeral,axiom,
% 0.35/0.62      ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_one_less_numeral
% 0.35/0.62  thf(fact_5463_neg__one__less__numeral,axiom,
% 0.35/0.62      ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_one_less_numeral
% 0.35/0.62  thf(fact_5464_neg__one__less__numeral,axiom,
% 0.35/0.62      ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_one_less_numeral
% 0.35/0.62  thf(fact_5465_neg__one__less__numeral,axiom,
% 0.35/0.62      ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_one_less_numeral
% 0.35/0.62  thf(fact_5466_neg__numeral__less__one,axiom,
% 0.35/0.62      ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_numeral_less_one
% 0.35/0.62  thf(fact_5467_neg__numeral__less__one,axiom,
% 0.35/0.62      ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_numeral_less_one
% 0.35/0.62  thf(fact_5468_neg__numeral__less__one,axiom,
% 0.35/0.62      ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_numeral_less_one
% 0.35/0.62  thf(fact_5469_neg__numeral__less__one,axiom,
% 0.35/0.62      ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_numeral_less_one
% 0.35/0.62  thf(fact_5470_mult__1s__ring__1_I1_J,axiom,
% 0.35/0.62      ! [B: int] :
% 0.35/0.62        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) @ B )
% 0.35/0.62        = ( uminus_uminus_int @ B ) ) ).
% 0.35/0.62  
% 0.35/0.62  % mult_1s_ring_1(1)
% 0.35/0.62  thf(fact_5471_mult__1s__ring__1_I1_J,axiom,
% 0.35/0.62      ! [B: real] :
% 0.35/0.62        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) @ B )
% 0.35/0.62        = ( uminus_uminus_real @ B ) ) ).
% 0.35/0.62  
% 0.35/0.62  % mult_1s_ring_1(1)
% 0.35/0.62  thf(fact_5472_mult__1s__ring__1_I1_J,axiom,
% 0.35/0.62      ! [B: complex] :
% 0.35/0.62        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) @ B )
% 0.35/0.62        = ( uminus1482373934393186551omplex @ B ) ) ).
% 0.35/0.62  
% 0.35/0.62  % mult_1s_ring_1(1)
% 0.35/0.62  thf(fact_5473_mult__1s__ring__1_I1_J,axiom,
% 0.35/0.62      ! [B: code_integer] :
% 0.35/0.62        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) @ B )
% 0.35/0.62        = ( uminus1351360451143612070nteger @ B ) ) ).
% 0.35/0.62  
% 0.35/0.62  % mult_1s_ring_1(1)
% 0.35/0.62  thf(fact_5474_mult__1s__ring__1_I1_J,axiom,
% 0.35/0.62      ! [B: rat] :
% 0.35/0.62        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) @ B )
% 0.35/0.62        = ( uminus_uminus_rat @ B ) ) ).
% 0.35/0.62  
% 0.35/0.62  % mult_1s_ring_1(1)
% 0.35/0.62  thf(fact_5475_mult__1s__ring__1_I2_J,axiom,
% 0.35/0.62      ! [B: int] :
% 0.35/0.62        ( ( times_times_int @ B @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) )
% 0.35/0.62        = ( uminus_uminus_int @ B ) ) ).
% 0.35/0.62  
% 0.35/0.62  % mult_1s_ring_1(2)
% 0.35/0.62  thf(fact_5476_mult__1s__ring__1_I2_J,axiom,
% 0.35/0.62      ! [B: real] :
% 0.35/0.62        ( ( times_times_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) )
% 0.35/0.62        = ( uminus_uminus_real @ B ) ) ).
% 0.35/0.62  
% 0.35/0.62  % mult_1s_ring_1(2)
% 0.35/0.62  thf(fact_5477_mult__1s__ring__1_I2_J,axiom,
% 0.35/0.62      ! [B: complex] :
% 0.35/0.62        ( ( times_times_complex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) )
% 0.35/0.62        = ( uminus1482373934393186551omplex @ B ) ) ).
% 0.35/0.62  
% 0.35/0.62  % mult_1s_ring_1(2)
% 0.35/0.62  thf(fact_5478_mult__1s__ring__1_I2_J,axiom,
% 0.35/0.62      ! [B: code_integer] :
% 0.35/0.62        ( ( times_3573771949741848930nteger @ B @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) )
% 0.35/0.62        = ( uminus1351360451143612070nteger @ B ) ) ).
% 0.35/0.62  
% 0.35/0.62  % mult_1s_ring_1(2)
% 0.35/0.62  thf(fact_5479_mult__1s__ring__1_I2_J,axiom,
% 0.35/0.62      ! [B: rat] :
% 0.35/0.62        ( ( times_times_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) )
% 0.35/0.62        = ( uminus_uminus_rat @ B ) ) ).
% 0.35/0.62  
% 0.35/0.62  % mult_1s_ring_1(2)
% 0.35/0.62  thf(fact_5480_uminus__numeral__One,axiom,
% 0.35/0.62      ( ( uminus_uminus_int @ ( numeral_numeral_int @ one ) )
% 0.35/0.62      = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.35/0.62  
% 0.35/0.62  % uminus_numeral_One
% 0.35/0.62  thf(fact_5481_uminus__numeral__One,axiom,
% 0.35/0.62      ( ( uminus_uminus_real @ ( numeral_numeral_real @ one ) )
% 0.35/0.62      = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.35/0.62  
% 0.35/0.62  % uminus_numeral_One
% 0.35/0.62  thf(fact_5482_uminus__numeral__One,axiom,
% 0.35/0.62      ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) )
% 0.35/0.62      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.35/0.62  
% 0.35/0.62  % uminus_numeral_One
% 0.35/0.62  thf(fact_5483_uminus__numeral__One,axiom,
% 0.35/0.62      ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) )
% 0.35/0.62      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.35/0.62  
% 0.35/0.62  % uminus_numeral_One
% 0.35/0.62  thf(fact_5484_uminus__numeral__One,axiom,
% 0.35/0.62      ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) )
% 0.35/0.62      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.35/0.62  
% 0.35/0.62  % uminus_numeral_One
% 0.35/0.62  thf(fact_5485_eq__minus__divide__eq,axiom,
% 0.35/0.62      ! [A: real,B: real,C: real] :
% 0.35/0.62        ( ( A
% 0.35/0.62          = ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 0.35/0.62        = ( ( ( C != zero_zero_real )
% 0.35/0.62           => ( ( times_times_real @ A @ C )
% 0.35/0.62              = ( uminus_uminus_real @ B ) ) )
% 0.35/0.62          & ( ( C = zero_zero_real )
% 0.35/0.62           => ( A = zero_zero_real ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % eq_minus_divide_eq
% 0.35/0.62  thf(fact_5486_eq__minus__divide__eq,axiom,
% 0.35/0.62      ! [A: complex,B: complex,C: complex] :
% 0.35/0.62        ( ( A
% 0.35/0.62          = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) ) )
% 0.35/0.62        = ( ( ( C != zero_zero_complex )
% 0.35/0.62           => ( ( times_times_complex @ A @ C )
% 0.35/0.62              = ( uminus1482373934393186551omplex @ B ) ) )
% 0.35/0.62          & ( ( C = zero_zero_complex )
% 0.35/0.62           => ( A = zero_zero_complex ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % eq_minus_divide_eq
% 0.35/0.62  thf(fact_5487_eq__minus__divide__eq,axiom,
% 0.35/0.62      ! [A: rat,B: rat,C: rat] :
% 0.35/0.62        ( ( A
% 0.35/0.62          = ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.35/0.62        = ( ( ( C != zero_zero_rat )
% 0.35/0.62           => ( ( times_times_rat @ A @ C )
% 0.35/0.62              = ( uminus_uminus_rat @ B ) ) )
% 0.35/0.62          & ( ( C = zero_zero_rat )
% 0.35/0.62           => ( A = zero_zero_rat ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % eq_minus_divide_eq
% 0.35/0.62  thf(fact_5488_minus__divide__eq__eq,axiom,
% 0.35/0.62      ! [B: real,C: real,A: real] :
% 0.35/0.62        ( ( ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) )
% 0.35/0.62          = A )
% 0.35/0.62        = ( ( ( C != zero_zero_real )
% 0.35/0.62           => ( ( uminus_uminus_real @ B )
% 0.35/0.62              = ( times_times_real @ A @ C ) ) )
% 0.35/0.62          & ( ( C = zero_zero_real )
% 0.35/0.62           => ( A = zero_zero_real ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % minus_divide_eq_eq
% 0.35/0.62  thf(fact_5489_minus__divide__eq__eq,axiom,
% 0.35/0.62      ! [B: complex,C: complex,A: complex] :
% 0.35/0.62        ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) )
% 0.35/0.62          = A )
% 0.35/0.62        = ( ( ( C != zero_zero_complex )
% 0.35/0.62           => ( ( uminus1482373934393186551omplex @ B )
% 0.35/0.62              = ( times_times_complex @ A @ C ) ) )
% 0.35/0.62          & ( ( C = zero_zero_complex )
% 0.35/0.62           => ( A = zero_zero_complex ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % minus_divide_eq_eq
% 0.35/0.62  thf(fact_5490_minus__divide__eq__eq,axiom,
% 0.35/0.62      ! [B: rat,C: rat,A: rat] :
% 0.35/0.62        ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) )
% 0.35/0.62          = A )
% 0.35/0.62        = ( ( ( C != zero_zero_rat )
% 0.35/0.62           => ( ( uminus_uminus_rat @ B )
% 0.35/0.62              = ( times_times_rat @ A @ C ) ) )
% 0.35/0.62          & ( ( C = zero_zero_rat )
% 0.35/0.62           => ( A = zero_zero_rat ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % minus_divide_eq_eq
% 0.35/0.62  thf(fact_5491_nonzero__neg__divide__eq__eq,axiom,
% 0.35/0.62      ! [B: real,A: real,C: real] :
% 0.35/0.62        ( ( B != zero_zero_real )
% 0.35/0.62       => ( ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 0.35/0.62            = C )
% 0.35/0.62          = ( ( uminus_uminus_real @ A )
% 0.35/0.62            = ( times_times_real @ C @ B ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % nonzero_neg_divide_eq_eq
% 0.35/0.62  thf(fact_5492_nonzero__neg__divide__eq__eq,axiom,
% 0.35/0.62      ! [B: complex,A: complex,C: complex] :
% 0.35/0.62        ( ( B != zero_zero_complex )
% 0.35/0.62       => ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.35/0.62            = C )
% 0.35/0.62          = ( ( uminus1482373934393186551omplex @ A )
% 0.35/0.62            = ( times_times_complex @ C @ B ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % nonzero_neg_divide_eq_eq
% 0.35/0.62  thf(fact_5493_nonzero__neg__divide__eq__eq,axiom,
% 0.35/0.62      ! [B: rat,A: rat,C: rat] :
% 0.35/0.62        ( ( B != zero_zero_rat )
% 0.35/0.62       => ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 0.35/0.62            = C )
% 0.35/0.62          = ( ( uminus_uminus_rat @ A )
% 0.35/0.62            = ( times_times_rat @ C @ B ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % nonzero_neg_divide_eq_eq
% 0.35/0.62  thf(fact_5494_nonzero__neg__divide__eq__eq2,axiom,
% 0.35/0.62      ! [B: real,C: real,A: real] :
% 0.35/0.62        ( ( B != zero_zero_real )
% 0.35/0.62       => ( ( C
% 0.35/0.62            = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) )
% 0.35/0.62          = ( ( times_times_real @ C @ B )
% 0.35/0.62            = ( uminus_uminus_real @ A ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % nonzero_neg_divide_eq_eq2
% 0.35/0.62  thf(fact_5495_nonzero__neg__divide__eq__eq2,axiom,
% 0.35/0.62      ! [B: complex,C: complex,A: complex] :
% 0.35/0.62        ( ( B != zero_zero_complex )
% 0.35/0.62       => ( ( C
% 0.35/0.62            = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 0.35/0.62          = ( ( times_times_complex @ C @ B )
% 0.35/0.62            = ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % nonzero_neg_divide_eq_eq2
% 0.35/0.62  thf(fact_5496_nonzero__neg__divide__eq__eq2,axiom,
% 0.35/0.62      ! [B: rat,C: rat,A: rat] :
% 0.35/0.62        ( ( B != zero_zero_rat )
% 0.35/0.62       => ( ( C
% 0.35/0.62            = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) )
% 0.35/0.62          = ( ( times_times_rat @ C @ B )
% 0.35/0.62            = ( uminus_uminus_rat @ A ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % nonzero_neg_divide_eq_eq2
% 0.35/0.62  thf(fact_5497_divide__eq__minus__1__iff,axiom,
% 0.35/0.62      ! [A: real,B: real] :
% 0.35/0.62        ( ( ( divide_divide_real @ A @ B )
% 0.35/0.62          = ( uminus_uminus_real @ one_one_real ) )
% 0.35/0.62        = ( ( B != zero_zero_real )
% 0.35/0.62          & ( A
% 0.35/0.62            = ( uminus_uminus_real @ B ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % divide_eq_minus_1_iff
% 0.35/0.62  thf(fact_5498_divide__eq__minus__1__iff,axiom,
% 0.35/0.62      ! [A: complex,B: complex] :
% 0.35/0.62        ( ( ( divide1717551699836669952omplex @ A @ B )
% 0.35/0.62          = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.35/0.62        = ( ( B != zero_zero_complex )
% 0.35/0.62          & ( A
% 0.35/0.62            = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % divide_eq_minus_1_iff
% 0.35/0.62  thf(fact_5499_divide__eq__minus__1__iff,axiom,
% 0.35/0.62      ! [A: rat,B: rat] :
% 0.35/0.62        ( ( ( divide_divide_rat @ A @ B )
% 0.35/0.62          = ( uminus_uminus_rat @ one_one_rat ) )
% 0.35/0.62        = ( ( B != zero_zero_rat )
% 0.35/0.62          & ( A
% 0.35/0.62            = ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % divide_eq_minus_1_iff
% 0.35/0.62  thf(fact_5500_power__minus,axiom,
% 0.35/0.62      ! [A: int,N: nat] :
% 0.35/0.62        ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 0.35/0.62        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ A @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power_minus
% 0.35/0.62  thf(fact_5501_power__minus,axiom,
% 0.35/0.62      ! [A: real,N: nat] :
% 0.35/0.62        ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 0.35/0.62        = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ A @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power_minus
% 0.35/0.62  thf(fact_5502_power__minus,axiom,
% 0.35/0.62      ! [A: complex,N: nat] :
% 0.35/0.62        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 0.35/0.62        = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ A @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power_minus
% 0.35/0.62  thf(fact_5503_power__minus,axiom,
% 0.35/0.62      ! [A: code_integer,N: nat] :
% 0.35/0.62        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 0.35/0.62        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power_minus
% 0.35/0.62  thf(fact_5504_power__minus,axiom,
% 0.35/0.62      ! [A: rat,N: nat] :
% 0.35/0.62        ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 0.35/0.62        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ A @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power_minus
% 0.35/0.62  thf(fact_5505_power__minus__Bit0,axiom,
% 0.35/0.62      ! [X: int,K: num] :
% 0.35/0.62        ( ( power_power_int @ ( uminus_uminus_int @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 0.35/0.62        = ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power_minus_Bit0
% 0.35/0.62  thf(fact_5506_power__minus__Bit0,axiom,
% 0.35/0.62      ! [X: real,K: num] :
% 0.35/0.62        ( ( power_power_real @ ( uminus_uminus_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 0.35/0.62        = ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power_minus_Bit0
% 0.35/0.62  thf(fact_5507_power__minus__Bit0,axiom,
% 0.35/0.62      ! [X: complex,K: num] :
% 0.35/0.62        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 0.35/0.62        = ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power_minus_Bit0
% 0.35/0.62  thf(fact_5508_power__minus__Bit0,axiom,
% 0.35/0.62      ! [X: code_integer,K: num] :
% 0.35/0.62        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 0.35/0.62        = ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power_minus_Bit0
% 0.35/0.62  thf(fact_5509_power__minus__Bit0,axiom,
% 0.35/0.62      ! [X: rat,K: num] :
% 0.35/0.62        ( ( power_power_rat @ ( uminus_uminus_rat @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 0.35/0.62        = ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power_minus_Bit0
% 0.35/0.62  thf(fact_5510_power__minus__Bit1,axiom,
% 0.35/0.62      ! [X: int,K: num] :
% 0.35/0.62        ( ( power_power_int @ ( uminus_uminus_int @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 0.35/0.62        = ( uminus_uminus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power_minus_Bit1
% 0.35/0.62  thf(fact_5511_power__minus__Bit1,axiom,
% 0.35/0.62      ! [X: real,K: num] :
% 0.35/0.62        ( ( power_power_real @ ( uminus_uminus_real @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 0.35/0.62        = ( uminus_uminus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power_minus_Bit1
% 0.35/0.62  thf(fact_5512_power__minus__Bit1,axiom,
% 0.35/0.62      ! [X: complex,K: num] :
% 0.35/0.62        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 0.35/0.62        = ( uminus1482373934393186551omplex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power_minus_Bit1
% 0.35/0.62  thf(fact_5513_power__minus__Bit1,axiom,
% 0.35/0.62      ! [X: code_integer,K: num] :
% 0.35/0.62        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 0.35/0.62        = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power_minus_Bit1
% 0.35/0.62  thf(fact_5514_power__minus__Bit1,axiom,
% 0.35/0.62      ! [X: rat,K: num] :
% 0.35/0.62        ( ( power_power_rat @ ( uminus_uminus_rat @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 0.35/0.62        = ( uminus_uminus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power_minus_Bit1
% 0.35/0.62  thf(fact_5515_Compl__insert,axiom,
% 0.35/0.62      ! [X: vEBT_VEBT,A2: set_VEBT_VEBT] :
% 0.35/0.62        ( ( uminus8041839845116263051T_VEBT @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 0.35/0.62        = ( minus_5127226145743854075T_VEBT @ ( uminus8041839845116263051T_VEBT @ A2 ) @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % Compl_insert
% 0.35/0.62  thf(fact_5516_Compl__insert,axiom,
% 0.35/0.62      ! [X: int,A2: set_int] :
% 0.35/0.62        ( ( uminus1532241313380277803et_int @ ( insert_int @ X @ A2 ) )
% 0.35/0.62        = ( minus_minus_set_int @ ( uminus1532241313380277803et_int @ A2 ) @ ( insert_int @ X @ bot_bot_set_int ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % Compl_insert
% 0.35/0.62  thf(fact_5517_Compl__insert,axiom,
% 0.35/0.62      ! [X: real,A2: set_real] :
% 0.35/0.62        ( ( uminus612125837232591019t_real @ ( insert_real @ X @ A2 ) )
% 0.35/0.62        = ( minus_minus_set_real @ ( uminus612125837232591019t_real @ A2 ) @ ( insert_real @ X @ bot_bot_set_real ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % Compl_insert
% 0.35/0.62  thf(fact_5518_Compl__insert,axiom,
% 0.35/0.62      ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 0.35/0.62        ( ( uminus6524753893492686040at_nat @ ( insert8211810215607154385at_nat @ X @ A2 ) )
% 0.35/0.62        = ( minus_1356011639430497352at_nat @ ( uminus6524753893492686040at_nat @ A2 ) @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % Compl_insert
% 0.35/0.62  thf(fact_5519_Compl__insert,axiom,
% 0.35/0.62      ! [X: nat,A2: set_nat] :
% 0.35/0.62        ( ( uminus5710092332889474511et_nat @ ( insert_nat @ X @ A2 ) )
% 0.35/0.62        = ( minus_minus_set_nat @ ( uminus5710092332889474511et_nat @ A2 ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % Compl_insert
% 0.35/0.62  thf(fact_5520_real__0__less__add__iff,axiom,
% 0.35/0.62      ! [X: real,Y2: real] :
% 0.35/0.62        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X @ Y2 ) )
% 0.35/0.62        = ( ord_less_real @ ( uminus_uminus_real @ X ) @ Y2 ) ) ).
% 0.35/0.62  
% 0.35/0.62  % real_0_less_add_iff
% 0.35/0.62  thf(fact_5521_real__add__less__0__iff,axiom,
% 0.35/0.62      ! [X: real,Y2: real] :
% 0.35/0.62        ( ( ord_less_real @ ( plus_plus_real @ X @ Y2 ) @ zero_zero_real )
% 0.35/0.62        = ( ord_less_real @ Y2 @ ( uminus_uminus_real @ X ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % real_add_less_0_iff
% 0.35/0.62  thf(fact_5522_real__0__le__add__iff,axiom,
% 0.35/0.62      ! [X: real,Y2: real] :
% 0.35/0.62        ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ X @ Y2 ) )
% 0.35/0.62        = ( ord_less_eq_real @ ( uminus_uminus_real @ X ) @ Y2 ) ) ).
% 0.35/0.62  
% 0.35/0.62  % real_0_le_add_iff
% 0.35/0.62  thf(fact_5523_real__add__le__0__iff,axiom,
% 0.35/0.62      ! [X: real,Y2: real] :
% 0.35/0.62        ( ( ord_less_eq_real @ ( plus_plus_real @ X @ Y2 ) @ zero_zero_real )
% 0.35/0.62        = ( ord_less_eq_real @ Y2 @ ( uminus_uminus_real @ X ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % real_add_le_0_iff
% 0.35/0.62  thf(fact_5524_pred__numeral__def,axiom,
% 0.35/0.62      ( pred_numeral
% 0.35/0.62      = ( ^ [K3: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K3 ) @ one_one_nat ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % pred_numeral_def
% 0.35/0.62  thf(fact_5525_zmod__zminus2__eq__if,axiom,
% 0.35/0.62      ! [A: int,B: int] :
% 0.35/0.62        ( ( ( ( modulo_modulo_int @ A @ B )
% 0.35/0.62            = zero_zero_int )
% 0.35/0.62         => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 0.35/0.62            = zero_zero_int ) )
% 0.35/0.62        & ( ( ( modulo_modulo_int @ A @ B )
% 0.35/0.62           != zero_zero_int )
% 0.35/0.62         => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 0.35/0.62            = ( minus_minus_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % zmod_zminus2_eq_if
% 0.35/0.62  thf(fact_5526_zmod__zminus1__eq__if,axiom,
% 0.35/0.62      ! [A: int,B: int] :
% 0.35/0.62        ( ( ( ( modulo_modulo_int @ A @ B )
% 0.35/0.62            = zero_zero_int )
% 0.35/0.62         => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 0.35/0.62            = zero_zero_int ) )
% 0.35/0.62        & ( ( ( modulo_modulo_int @ A @ B )
% 0.35/0.62           != zero_zero_int )
% 0.35/0.62         => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 0.35/0.62            = ( minus_minus_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % zmod_zminus1_eq_if
% 0.35/0.62  thf(fact_5527_less__minus__divide__eq,axiom,
% 0.35/0.62      ! [A: real,B: real,C: real] :
% 0.35/0.62        ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 0.35/0.62        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.62           => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 0.35/0.62          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.62           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.62               => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 0.35/0.62              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.62               => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % less_minus_divide_eq
% 0.35/0.62  thf(fact_5528_less__minus__divide__eq,axiom,
% 0.35/0.62      ! [A: rat,B: rat,C: rat] :
% 0.35/0.62        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.35/0.62        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.62           => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 0.35/0.62          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.62           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.62               => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 0.35/0.62              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.62               => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % less_minus_divide_eq
% 0.35/0.62  thf(fact_5529_minus__divide__less__eq,axiom,
% 0.35/0.62      ! [B: real,C: real,A: real] :
% 0.35/0.62        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 0.35/0.62        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.62           => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 0.35/0.62          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.62           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.62               => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 0.35/0.62              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.62               => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % minus_divide_less_eq
% 0.35/0.62  thf(fact_5530_minus__divide__less__eq,axiom,
% 0.35/0.62      ! [B: rat,C: rat,A: rat] :
% 0.35/0.62        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.35/0.62        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.62           => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 0.35/0.62          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.62           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.62               => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 0.35/0.62              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.62               => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % minus_divide_less_eq
% 0.35/0.62  thf(fact_5531_neg__less__minus__divide__eq,axiom,
% 0.35/0.62      ! [C: real,A: real,B: real] :
% 0.35/0.62        ( ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.62       => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 0.35/0.62          = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_less_minus_divide_eq
% 0.35/0.62  thf(fact_5532_neg__less__minus__divide__eq,axiom,
% 0.35/0.62      ! [C: rat,A: rat,B: rat] :
% 0.35/0.62        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.62       => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.35/0.62          = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_less_minus_divide_eq
% 0.35/0.62  thf(fact_5533_neg__minus__divide__less__eq,axiom,
% 0.35/0.62      ! [C: real,B: real,A: real] :
% 0.35/0.62        ( ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.62       => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 0.35/0.62          = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_minus_divide_less_eq
% 0.35/0.62  thf(fact_5534_neg__minus__divide__less__eq,axiom,
% 0.35/0.62      ! [C: rat,B: rat,A: rat] :
% 0.35/0.62        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.62       => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.35/0.62          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_minus_divide_less_eq
% 0.35/0.62  thf(fact_5535_pos__less__minus__divide__eq,axiom,
% 0.35/0.62      ! [C: real,A: real,B: real] :
% 0.35/0.62        ( ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.62       => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 0.35/0.62          = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % pos_less_minus_divide_eq
% 0.35/0.62  thf(fact_5536_pos__less__minus__divide__eq,axiom,
% 0.35/0.62      ! [C: rat,A: rat,B: rat] :
% 0.35/0.62        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.62       => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.35/0.62          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % pos_less_minus_divide_eq
% 0.35/0.62  thf(fact_5537_pos__minus__divide__less__eq,axiom,
% 0.35/0.62      ! [C: real,B: real,A: real] :
% 0.35/0.62        ( ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.62       => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 0.35/0.62          = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % pos_minus_divide_less_eq
% 0.35/0.62  thf(fact_5538_pos__minus__divide__less__eq,axiom,
% 0.35/0.62      ! [C: rat,B: rat,A: rat] :
% 0.35/0.62        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.62       => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.35/0.62          = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % pos_minus_divide_less_eq
% 0.35/0.62  thf(fact_5539_divide__eq__eq__numeral_I2_J,axiom,
% 0.35/0.62      ! [B: real,C: real,W: num] :
% 0.35/0.62        ( ( ( divide_divide_real @ B @ C )
% 0.35/0.62          = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 0.35/0.62        = ( ( ( C != zero_zero_real )
% 0.35/0.62           => ( B
% 0.35/0.62              = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 0.35/0.62          & ( ( C = zero_zero_real )
% 0.35/0.62           => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 0.35/0.62              = zero_zero_real ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % divide_eq_eq_numeral(2)
% 0.35/0.62  thf(fact_5540_divide__eq__eq__numeral_I2_J,axiom,
% 0.35/0.62      ! [B: complex,C: complex,W: num] :
% 0.35/0.62        ( ( ( divide1717551699836669952omplex @ B @ C )
% 0.35/0.62          = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 0.35/0.62        = ( ( ( C != zero_zero_complex )
% 0.35/0.62           => ( B
% 0.35/0.62              = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C ) ) )
% 0.35/0.62          & ( ( C = zero_zero_complex )
% 0.35/0.62           => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 0.35/0.62              = zero_zero_complex ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % divide_eq_eq_numeral(2)
% 0.35/0.62  thf(fact_5541_divide__eq__eq__numeral_I2_J,axiom,
% 0.35/0.62      ! [B: rat,C: rat,W: num] :
% 0.35/0.62        ( ( ( divide_divide_rat @ B @ C )
% 0.35/0.62          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 0.35/0.62        = ( ( ( C != zero_zero_rat )
% 0.35/0.62           => ( B
% 0.35/0.62              = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 0.35/0.62          & ( ( C = zero_zero_rat )
% 0.35/0.62           => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 0.35/0.62              = zero_zero_rat ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % divide_eq_eq_numeral(2)
% 0.35/0.62  thf(fact_5542_eq__divide__eq__numeral_I2_J,axiom,
% 0.35/0.62      ! [W: num,B: real,C: real] :
% 0.35/0.62        ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 0.35/0.62          = ( divide_divide_real @ B @ C ) )
% 0.35/0.62        = ( ( ( C != zero_zero_real )
% 0.35/0.62           => ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C )
% 0.35/0.62              = B ) )
% 0.35/0.62          & ( ( C = zero_zero_real )
% 0.35/0.62           => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 0.35/0.62              = zero_zero_real ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % eq_divide_eq_numeral(2)
% 0.35/0.62  thf(fact_5543_eq__divide__eq__numeral_I2_J,axiom,
% 0.35/0.62      ! [W: num,B: complex,C: complex] :
% 0.35/0.62        ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 0.35/0.62          = ( divide1717551699836669952omplex @ B @ C ) )
% 0.35/0.62        = ( ( ( C != zero_zero_complex )
% 0.35/0.62           => ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C )
% 0.35/0.62              = B ) )
% 0.35/0.62          & ( ( C = zero_zero_complex )
% 0.35/0.62           => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 0.35/0.62              = zero_zero_complex ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % eq_divide_eq_numeral(2)
% 0.35/0.62  thf(fact_5544_eq__divide__eq__numeral_I2_J,axiom,
% 0.35/0.62      ! [W: num,B: rat,C: rat] :
% 0.35/0.62        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 0.35/0.62          = ( divide_divide_rat @ B @ C ) )
% 0.35/0.62        = ( ( ( C != zero_zero_rat )
% 0.35/0.62           => ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C )
% 0.35/0.62              = B ) )
% 0.35/0.62          & ( ( C = zero_zero_rat )
% 0.35/0.62           => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 0.35/0.62              = zero_zero_rat ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % eq_divide_eq_numeral(2)
% 0.35/0.62  thf(fact_5545_add__divide__eq__if__simps_I3_J,axiom,
% 0.35/0.62      ! [Z: real,A: real,B: real] :
% 0.35/0.62        ( ( ( Z = zero_zero_real )
% 0.35/0.62         => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 0.35/0.62            = B ) )
% 0.35/0.62        & ( ( Z != zero_zero_real )
% 0.35/0.62         => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 0.35/0.62            = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % add_divide_eq_if_simps(3)
% 0.35/0.62  thf(fact_5546_add__divide__eq__if__simps_I3_J,axiom,
% 0.35/0.62      ! [Z: complex,A: complex,B: complex] :
% 0.35/0.62        ( ( ( Z = zero_zero_complex )
% 0.35/0.62         => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 0.35/0.62            = B ) )
% 0.35/0.62        & ( ( Z != zero_zero_complex )
% 0.35/0.62         => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 0.35/0.62            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % add_divide_eq_if_simps(3)
% 0.35/0.62  thf(fact_5547_add__divide__eq__if__simps_I3_J,axiom,
% 0.35/0.62      ! [Z: rat,A: rat,B: rat] :
% 0.35/0.62        ( ( ( Z = zero_zero_rat )
% 0.35/0.62         => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 0.35/0.62            = B ) )
% 0.35/0.62        & ( ( Z != zero_zero_rat )
% 0.35/0.62         => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 0.35/0.62            = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % add_divide_eq_if_simps(3)
% 0.35/0.62  thf(fact_5548_minus__divide__add__eq__iff,axiom,
% 0.35/0.62      ! [Z: real,X: real,Y2: real] :
% 0.35/0.62        ( ( Z != zero_zero_real )
% 0.35/0.62       => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X @ Z ) ) @ Y2 )
% 0.35/0.62          = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ Y2 @ Z ) ) @ Z ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % minus_divide_add_eq_iff
% 0.35/0.62  thf(fact_5549_minus__divide__add__eq__iff,axiom,
% 0.35/0.62      ! [Z: complex,X: complex,Y2: complex] :
% 0.35/0.62        ( ( Z != zero_zero_complex )
% 0.35/0.62       => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X @ Z ) ) @ Y2 )
% 0.35/0.62          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ X ) @ ( times_times_complex @ Y2 @ Z ) ) @ Z ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % minus_divide_add_eq_iff
% 0.35/0.62  thf(fact_5550_minus__divide__add__eq__iff,axiom,
% 0.35/0.62      ! [Z: rat,X: rat,Y2: rat] :
% 0.35/0.62        ( ( Z != zero_zero_rat )
% 0.35/0.62       => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z ) ) @ Y2 )
% 0.35/0.62          = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y2 @ Z ) ) @ Z ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % minus_divide_add_eq_iff
% 0.35/0.62  thf(fact_5551_subset__decode__imp__le,axiom,
% 0.35/0.62      ! [M: nat,N: nat] :
% 0.35/0.62        ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M ) @ ( nat_set_decode @ N ) )
% 0.35/0.62       => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.35/0.62  
% 0.35/0.62  % subset_decode_imp_le
% 0.35/0.62  thf(fact_5552_add__divide__eq__if__simps_I6_J,axiom,
% 0.35/0.62      ! [Z: real,A: real,B: real] :
% 0.35/0.62        ( ( ( Z = zero_zero_real )
% 0.35/0.62         => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 0.35/0.62            = ( uminus_uminus_real @ B ) ) )
% 0.35/0.62        & ( ( Z != zero_zero_real )
% 0.35/0.62         => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 0.35/0.62            = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % add_divide_eq_if_simps(6)
% 0.35/0.62  thf(fact_5553_add__divide__eq__if__simps_I6_J,axiom,
% 0.35/0.62      ! [Z: complex,A: complex,B: complex] :
% 0.35/0.62        ( ( ( Z = zero_zero_complex )
% 0.35/0.62         => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 0.35/0.62            = ( uminus1482373934393186551omplex @ B ) ) )
% 0.35/0.62        & ( ( Z != zero_zero_complex )
% 0.35/0.62         => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 0.35/0.62            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % add_divide_eq_if_simps(6)
% 0.35/0.62  thf(fact_5554_add__divide__eq__if__simps_I6_J,axiom,
% 0.35/0.62      ! [Z: rat,A: rat,B: rat] :
% 0.35/0.62        ( ( ( Z = zero_zero_rat )
% 0.35/0.62         => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 0.35/0.62            = ( uminus_uminus_rat @ B ) ) )
% 0.35/0.62        & ( ( Z != zero_zero_rat )
% 0.35/0.62         => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 0.35/0.62            = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % add_divide_eq_if_simps(6)
% 0.35/0.62  thf(fact_5555_add__divide__eq__if__simps_I5_J,axiom,
% 0.35/0.62      ! [Z: real,A: real,B: real] :
% 0.35/0.62        ( ( ( Z = zero_zero_real )
% 0.35/0.62         => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 0.35/0.62            = ( uminus_uminus_real @ B ) ) )
% 0.35/0.62        & ( ( Z != zero_zero_real )
% 0.35/0.62         => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 0.35/0.62            = ( divide_divide_real @ ( minus_minus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % add_divide_eq_if_simps(5)
% 0.35/0.62  thf(fact_5556_add__divide__eq__if__simps_I5_J,axiom,
% 0.35/0.62      ! [Z: complex,A: complex,B: complex] :
% 0.35/0.62        ( ( ( Z = zero_zero_complex )
% 0.35/0.62         => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 0.35/0.62            = ( uminus1482373934393186551omplex @ B ) ) )
% 0.35/0.62        & ( ( Z != zero_zero_complex )
% 0.35/0.62         => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 0.35/0.62            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % add_divide_eq_if_simps(5)
% 0.35/0.62  thf(fact_5557_add__divide__eq__if__simps_I5_J,axiom,
% 0.35/0.62      ! [Z: rat,A: rat,B: rat] :
% 0.35/0.62        ( ( ( Z = zero_zero_rat )
% 0.35/0.62         => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 0.35/0.62            = ( uminus_uminus_rat @ B ) ) )
% 0.35/0.62        & ( ( Z != zero_zero_rat )
% 0.35/0.62         => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 0.35/0.62            = ( divide_divide_rat @ ( minus_minus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % add_divide_eq_if_simps(5)
% 0.35/0.62  thf(fact_5558_minus__divide__diff__eq__iff,axiom,
% 0.35/0.62      ! [Z: real,X: real,Y2: real] :
% 0.35/0.62        ( ( Z != zero_zero_real )
% 0.35/0.62       => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X @ Z ) ) @ Y2 )
% 0.35/0.62          = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ Y2 @ Z ) ) @ Z ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % minus_divide_diff_eq_iff
% 0.35/0.62  thf(fact_5559_minus__divide__diff__eq__iff,axiom,
% 0.35/0.62      ! [Z: complex,X: complex,Y2: complex] :
% 0.35/0.62        ( ( Z != zero_zero_complex )
% 0.35/0.62       => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X @ Z ) ) @ Y2 )
% 0.35/0.62          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X ) @ ( times_times_complex @ Y2 @ Z ) ) @ Z ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % minus_divide_diff_eq_iff
% 0.35/0.62  thf(fact_5560_minus__divide__diff__eq__iff,axiom,
% 0.35/0.62      ! [Z: rat,X: rat,Y2: rat] :
% 0.35/0.62        ( ( Z != zero_zero_rat )
% 0.35/0.62       => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z ) ) @ Y2 )
% 0.35/0.62          = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y2 @ Z ) ) @ Z ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % minus_divide_diff_eq_iff
% 0.35/0.62  thf(fact_5561_even__minus,axiom,
% 0.35/0.62      ! [A: int] :
% 0.35/0.62        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( uminus_uminus_int @ A ) )
% 0.35/0.62        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % even_minus
% 0.35/0.62  thf(fact_5562_even__minus,axiom,
% 0.35/0.62      ! [A: code_integer] :
% 0.35/0.62        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( uminus1351360451143612070nteger @ A ) )
% 0.35/0.62        = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % even_minus
% 0.35/0.62  thf(fact_5563_power2__eq__iff,axiom,
% 0.35/0.62      ! [X: int,Y2: int] :
% 0.35/0.62        ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.62          = ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.62        = ( ( X = Y2 )
% 0.35/0.62          | ( X
% 0.35/0.62            = ( uminus_uminus_int @ Y2 ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power2_eq_iff
% 0.35/0.62  thf(fact_5564_power2__eq__iff,axiom,
% 0.35/0.62      ! [X: real,Y2: real] :
% 0.35/0.62        ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.62          = ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.62        = ( ( X = Y2 )
% 0.35/0.62          | ( X
% 0.35/0.62            = ( uminus_uminus_real @ Y2 ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power2_eq_iff
% 0.35/0.62  thf(fact_5565_power2__eq__iff,axiom,
% 0.35/0.62      ! [X: complex,Y2: complex] :
% 0.35/0.62        ( ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.62          = ( power_power_complex @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.62        = ( ( X = Y2 )
% 0.35/0.62          | ( X
% 0.35/0.62            = ( uminus1482373934393186551omplex @ Y2 ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power2_eq_iff
% 0.35/0.62  thf(fact_5566_power2__eq__iff,axiom,
% 0.35/0.62      ! [X: code_integer,Y2: code_integer] :
% 0.35/0.62        ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.62          = ( power_8256067586552552935nteger @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.62        = ( ( X = Y2 )
% 0.35/0.62          | ( X
% 0.35/0.62            = ( uminus1351360451143612070nteger @ Y2 ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power2_eq_iff
% 0.35/0.62  thf(fact_5567_power2__eq__iff,axiom,
% 0.35/0.62      ! [X: rat,Y2: rat] :
% 0.35/0.62        ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.62          = ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.62        = ( ( X = Y2 )
% 0.35/0.62          | ( X
% 0.35/0.62            = ( uminus_uminus_rat @ Y2 ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power2_eq_iff
% 0.35/0.62  thf(fact_5568_verit__less__mono__div__int2,axiom,
% 0.35/0.62      ! [A2: int,B2: int,N: int] :
% 0.35/0.62        ( ( ord_less_eq_int @ A2 @ B2 )
% 0.35/0.62       => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N ) )
% 0.35/0.62         => ( ord_less_eq_int @ ( divide_divide_int @ B2 @ N ) @ ( divide_divide_int @ A2 @ N ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % verit_less_mono_div_int2
% 0.35/0.62  thf(fact_5569_div__eq__minus1,axiom,
% 0.35/0.62      ! [B: int] :
% 0.35/0.62        ( ( ord_less_int @ zero_zero_int @ B )
% 0.35/0.62       => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 0.35/0.62          = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % div_eq_minus1
% 0.35/0.62  thf(fact_5570_le__minus__divide__eq,axiom,
% 0.35/0.62      ! [A: real,B: real,C: real] :
% 0.35/0.62        ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 0.35/0.62        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.62           => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 0.35/0.62          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.62           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.62               => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 0.35/0.62              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.62               => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % le_minus_divide_eq
% 0.35/0.62  thf(fact_5571_le__minus__divide__eq,axiom,
% 0.35/0.62      ! [A: rat,B: rat,C: rat] :
% 0.35/0.62        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.35/0.62        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.62           => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 0.35/0.62          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.62           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.62               => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 0.35/0.62              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.62               => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % le_minus_divide_eq
% 0.35/0.62  thf(fact_5572_minus__divide__le__eq,axiom,
% 0.35/0.62      ! [B: real,C: real,A: real] :
% 0.35/0.62        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 0.35/0.62        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.62           => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 0.35/0.62          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.62           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.62               => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 0.35/0.62              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.62               => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % minus_divide_le_eq
% 0.35/0.62  thf(fact_5573_minus__divide__le__eq,axiom,
% 0.35/0.62      ! [B: rat,C: rat,A: rat] :
% 0.35/0.62        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.35/0.62        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.62           => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 0.35/0.62          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.62           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.62               => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 0.35/0.62              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.62               => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % minus_divide_le_eq
% 0.35/0.62  thf(fact_5574_neg__le__minus__divide__eq,axiom,
% 0.35/0.62      ! [C: real,A: real,B: real] :
% 0.35/0.62        ( ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.62       => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 0.35/0.62          = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_le_minus_divide_eq
% 0.35/0.62  thf(fact_5575_neg__le__minus__divide__eq,axiom,
% 0.35/0.62      ! [C: rat,A: rat,B: rat] :
% 0.35/0.62        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.62       => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.35/0.62          = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_le_minus_divide_eq
% 0.35/0.62  thf(fact_5576_neg__minus__divide__le__eq,axiom,
% 0.35/0.62      ! [C: real,B: real,A: real] :
% 0.35/0.62        ( ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.62       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 0.35/0.62          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_minus_divide_le_eq
% 0.35/0.62  thf(fact_5577_neg__minus__divide__le__eq,axiom,
% 0.35/0.62      ! [C: rat,B: rat,A: rat] :
% 0.35/0.62        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.62       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.35/0.62          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_minus_divide_le_eq
% 0.35/0.62  thf(fact_5578_pos__le__minus__divide__eq,axiom,
% 0.35/0.62      ! [C: real,A: real,B: real] :
% 0.35/0.62        ( ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.62       => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 0.35/0.62          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % pos_le_minus_divide_eq
% 0.35/0.62  thf(fact_5579_pos__le__minus__divide__eq,axiom,
% 0.35/0.62      ! [C: rat,A: rat,B: rat] :
% 0.35/0.62        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.62       => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.35/0.62          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % pos_le_minus_divide_eq
% 0.35/0.62  thf(fact_5580_pos__minus__divide__le__eq,axiom,
% 0.35/0.62      ! [C: real,B: real,A: real] :
% 0.35/0.62        ( ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.62       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 0.35/0.62          = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % pos_minus_divide_le_eq
% 0.35/0.62  thf(fact_5581_pos__minus__divide__le__eq,axiom,
% 0.35/0.62      ! [C: rat,B: rat,A: rat] :
% 0.35/0.62        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.62       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.35/0.62          = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % pos_minus_divide_le_eq
% 0.35/0.62  thf(fact_5582_divide__less__eq__numeral_I2_J,axiom,
% 0.35/0.62      ! [B: real,C: real,W: num] :
% 0.35/0.62        ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 0.35/0.62        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.62           => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 0.35/0.62          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.62           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.62               => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 0.35/0.62              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.62               => ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % divide_less_eq_numeral(2)
% 0.35/0.62  thf(fact_5583_divide__less__eq__numeral_I2_J,axiom,
% 0.35/0.62      ! [B: rat,C: rat,W: num] :
% 0.35/0.62        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 0.35/0.62        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.62           => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 0.35/0.62          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.62           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.62               => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 0.35/0.62              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.62               => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % divide_less_eq_numeral(2)
% 0.35/0.62  thf(fact_5584_less__divide__eq__numeral_I2_J,axiom,
% 0.35/0.62      ! [W: num,B: real,C: real] :
% 0.35/0.62        ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 0.35/0.62        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.62           => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 0.35/0.62          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.62           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.62               => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 0.35/0.62              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.62               => ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % less_divide_eq_numeral(2)
% 0.35/0.62  thf(fact_5585_less__divide__eq__numeral_I2_J,axiom,
% 0.35/0.62      ! [W: num,B: rat,C: rat] :
% 0.35/0.62        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 0.35/0.62        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.62           => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 0.35/0.62          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.62           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.62               => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 0.35/0.62              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.62               => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % less_divide_eq_numeral(2)
% 0.35/0.62  thf(fact_5586_power2__eq__1__iff,axiom,
% 0.35/0.62      ! [A: int] :
% 0.35/0.62        ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.62          = one_one_int )
% 0.35/0.62        = ( ( A = one_one_int )
% 0.35/0.62          | ( A
% 0.35/0.62            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power2_eq_1_iff
% 0.35/0.62  thf(fact_5587_power2__eq__1__iff,axiom,
% 0.35/0.62      ! [A: real] :
% 0.35/0.62        ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.62          = one_one_real )
% 0.35/0.62        = ( ( A = one_one_real )
% 0.35/0.62          | ( A
% 0.35/0.62            = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power2_eq_1_iff
% 0.35/0.62  thf(fact_5588_power2__eq__1__iff,axiom,
% 0.35/0.62      ! [A: complex] :
% 0.35/0.62        ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.62          = one_one_complex )
% 0.35/0.62        = ( ( A = one_one_complex )
% 0.35/0.62          | ( A
% 0.35/0.62            = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power2_eq_1_iff
% 0.35/0.62  thf(fact_5589_power2__eq__1__iff,axiom,
% 0.35/0.62      ! [A: code_integer] :
% 0.35/0.62        ( ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.62          = one_one_Code_integer )
% 0.35/0.62        = ( ( A = one_one_Code_integer )
% 0.35/0.62          | ( A
% 0.35/0.62            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power2_eq_1_iff
% 0.35/0.62  thf(fact_5590_power2__eq__1__iff,axiom,
% 0.35/0.62      ! [A: rat] :
% 0.35/0.62        ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.62          = one_one_rat )
% 0.35/0.62        = ( ( A = one_one_rat )
% 0.35/0.62          | ( A
% 0.35/0.62            = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power2_eq_1_iff
% 0.35/0.62  thf(fact_5591_uminus__power__if,axiom,
% 0.35/0.62      ! [N: nat,A: int] :
% 0.35/0.62        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.62         => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 0.35/0.62            = ( power_power_int @ A @ N ) ) )
% 0.35/0.62        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.62         => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 0.35/0.62            = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % uminus_power_if
% 0.35/0.62  thf(fact_5592_uminus__power__if,axiom,
% 0.35/0.62      ! [N: nat,A: real] :
% 0.35/0.62        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.62         => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 0.35/0.62            = ( power_power_real @ A @ N ) ) )
% 0.35/0.62        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.62         => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 0.35/0.62            = ( uminus_uminus_real @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % uminus_power_if
% 0.35/0.62  thf(fact_5593_uminus__power__if,axiom,
% 0.35/0.62      ! [N: nat,A: complex] :
% 0.35/0.62        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.62         => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 0.35/0.62            = ( power_power_complex @ A @ N ) ) )
% 0.35/0.62        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.62         => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 0.35/0.62            = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % uminus_power_if
% 0.35/0.62  thf(fact_5594_uminus__power__if,axiom,
% 0.35/0.62      ! [N: nat,A: code_integer] :
% 0.35/0.62        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.62         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 0.35/0.62            = ( power_8256067586552552935nteger @ A @ N ) ) )
% 0.35/0.62        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.62         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 0.35/0.62            = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % uminus_power_if
% 0.35/0.62  thf(fact_5595_uminus__power__if,axiom,
% 0.35/0.62      ! [N: nat,A: rat] :
% 0.35/0.62        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.62         => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 0.35/0.62            = ( power_power_rat @ A @ N ) ) )
% 0.35/0.62        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.62         => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 0.35/0.62            = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % uminus_power_if
% 0.35/0.62  thf(fact_5596_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.35/0.62      ! [K: nat,N: nat] :
% 0.35/0.62        ( ( ord_less_eq_nat @ K @ N )
% 0.35/0.62       => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N @ K ) )
% 0.35/0.62          = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_one_power_add_eq_neg_one_power_diff
% 0.35/0.62  thf(fact_5597_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.35/0.62      ! [K: nat,N: nat] :
% 0.35/0.62        ( ( ord_less_eq_nat @ K @ N )
% 0.35/0.62       => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( plus_plus_nat @ N @ K ) )
% 0.35/0.62          = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_one_power_add_eq_neg_one_power_diff
% 0.35/0.62  thf(fact_5598_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.35/0.62      ! [K: nat,N: nat] :
% 0.35/0.62        ( ( ord_less_eq_nat @ K @ N )
% 0.35/0.62       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( plus_plus_nat @ N @ K ) )
% 0.35/0.62          = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_one_power_add_eq_neg_one_power_diff
% 0.35/0.62  thf(fact_5599_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.35/0.62      ! [K: nat,N: nat] :
% 0.35/0.62        ( ( ord_less_eq_nat @ K @ N )
% 0.35/0.62       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N @ K ) )
% 0.35/0.62          = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_one_power_add_eq_neg_one_power_diff
% 0.35/0.62  thf(fact_5600_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.35/0.62      ! [K: nat,N: nat] :
% 0.35/0.62        ( ( ord_less_eq_nat @ K @ N )
% 0.35/0.62       => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N @ K ) )
% 0.35/0.62          = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_one_power_add_eq_neg_one_power_diff
% 0.35/0.62  thf(fact_5601_realpow__square__minus__le,axiom,
% 0.35/0.62      ! [U: real,X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % realpow_square_minus_le
% 0.35/0.62  thf(fact_5602_signed__take__bit__int__greater__eq__minus__exp,axiom,
% 0.35/0.62      ! [N: nat,K: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ).
% 0.35/0.62  
% 0.35/0.62  % signed_take_bit_int_greater_eq_minus_exp
% 0.35/0.62  thf(fact_5603_signed__take__bit__int__less__eq__self__iff,axiom,
% 0.35/0.62      ! [N: nat,K: int] :
% 0.35/0.62        ( ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 0.35/0.62        = ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K ) ) ).
% 0.35/0.62  
% 0.35/0.62  % signed_take_bit_int_less_eq_self_iff
% 0.35/0.62  thf(fact_5604_signed__take__bit__int__greater__self__iff,axiom,
% 0.35/0.62      ! [K: int,N: nat] :
% 0.35/0.62        ( ( ord_less_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 0.35/0.62        = ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % signed_take_bit_int_greater_self_iff
% 0.35/0.62  thf(fact_5605_minus__mod__int__eq,axiom,
% 0.35/0.62      ! [L2: int,K: int] :
% 0.35/0.62        ( ( ord_less_eq_int @ zero_zero_int @ L2 )
% 0.35/0.62       => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L2 )
% 0.35/0.62          = ( minus_minus_int @ ( minus_minus_int @ L2 @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K @ one_one_int ) @ L2 ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % minus_mod_int_eq
% 0.35/0.62  thf(fact_5606_zmod__minus1,axiom,
% 0.35/0.62      ! [B: int] :
% 0.35/0.62        ( ( ord_less_int @ zero_zero_int @ B )
% 0.35/0.62       => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 0.35/0.62          = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % zmod_minus1
% 0.35/0.62  thf(fact_5607_zdiv__zminus2__eq__if,axiom,
% 0.35/0.62      ! [B: int,A: int] :
% 0.35/0.62        ( ( B != zero_zero_int )
% 0.35/0.62       => ( ( ( ( modulo_modulo_int @ A @ B )
% 0.35/0.62              = zero_zero_int )
% 0.35/0.62           => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 0.35/0.62              = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 0.35/0.62          & ( ( ( modulo_modulo_int @ A @ B )
% 0.35/0.62             != zero_zero_int )
% 0.35/0.62           => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 0.35/0.62              = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % zdiv_zminus2_eq_if
% 0.35/0.62  thf(fact_5608_zdiv__zminus1__eq__if,axiom,
% 0.35/0.62      ! [B: int,A: int] :
% 0.35/0.62        ( ( B != zero_zero_int )
% 0.35/0.62       => ( ( ( ( modulo_modulo_int @ A @ B )
% 0.35/0.62              = zero_zero_int )
% 0.35/0.62           => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 0.35/0.62              = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 0.35/0.62          & ( ( ( modulo_modulo_int @ A @ B )
% 0.35/0.62             != zero_zero_int )
% 0.35/0.62           => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 0.35/0.62              = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % zdiv_zminus1_eq_if
% 0.35/0.62  thf(fact_5609_zminus1__lemma,axiom,
% 0.35/0.62      ! [A: int,B: int,Q2: int,R: int] :
% 0.35/0.62        ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 0.35/0.62       => ( ( B != zero_zero_int )
% 0.35/0.62         => ( eucl_rel_int @ ( uminus_uminus_int @ A ) @ B @ ( product_Pair_int_int @ ( if_int @ ( R = zero_zero_int ) @ ( uminus_uminus_int @ Q2 ) @ ( minus_minus_int @ ( uminus_uminus_int @ Q2 ) @ one_one_int ) ) @ ( if_int @ ( R = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ B @ R ) ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % zminus1_lemma
% 0.35/0.62  thf(fact_5610_Divides_Oadjust__div__def,axiom,
% 0.35/0.62      ( adjust_div
% 0.35/0.62      = ( produc8211389475949308722nt_int
% 0.35/0.62        @ ^ [Q4: int,R5: int] : ( plus_plus_int @ Q4 @ ( zero_n2684676970156552555ol_int @ ( R5 != zero_zero_int ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % Divides.adjust_div_def
% 0.35/0.62  thf(fact_5611_divide__le__eq__numeral_I2_J,axiom,
% 0.35/0.62      ! [B: real,C: real,W: num] :
% 0.35/0.62        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 0.35/0.62        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.62           => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 0.35/0.62          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.62           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.62               => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 0.35/0.62              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.62               => ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % divide_le_eq_numeral(2)
% 0.35/0.62  thf(fact_5612_divide__le__eq__numeral_I2_J,axiom,
% 0.35/0.62      ! [B: rat,C: rat,W: num] :
% 0.35/0.62        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 0.35/0.62        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.62           => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 0.35/0.62          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.62           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.62               => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 0.35/0.62              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.62               => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % divide_le_eq_numeral(2)
% 0.35/0.62  thf(fact_5613_le__divide__eq__numeral_I2_J,axiom,
% 0.35/0.62      ! [W: num,B: real,C: real] :
% 0.35/0.62        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 0.35/0.62        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.62           => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 0.35/0.62          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.62           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.62               => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 0.35/0.62              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.35/0.62               => ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % le_divide_eq_numeral(2)
% 0.35/0.62  thf(fact_5614_le__divide__eq__numeral_I2_J,axiom,
% 0.35/0.62      ! [W: num,B: rat,C: rat] :
% 0.35/0.62        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 0.35/0.62        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.62           => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 0.35/0.62          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.35/0.62           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.62               => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 0.35/0.62              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.35/0.62               => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % le_divide_eq_numeral(2)
% 0.35/0.62  thf(fact_5615_square__le__1,axiom,
% 0.35/0.62      ! [X: real] :
% 0.35/0.62        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.35/0.62       => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.35/0.62         => ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % square_le_1
% 0.35/0.62  thf(fact_5616_square__le__1,axiom,
% 0.35/0.62      ! [X: code_integer] :
% 0.35/0.62        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 0.35/0.62       => ( ( ord_le3102999989581377725nteger @ X @ one_one_Code_integer )
% 0.35/0.62         => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % square_le_1
% 0.35/0.62  thf(fact_5617_square__le__1,axiom,
% 0.35/0.62      ! [X: rat] :
% 0.35/0.62        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X )
% 0.35/0.62       => ( ( ord_less_eq_rat @ X @ one_one_rat )
% 0.35/0.62         => ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % square_le_1
% 0.35/0.62  thf(fact_5618_square__le__1,axiom,
% 0.35/0.62      ! [X: int] :
% 0.35/0.62        ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 0.35/0.62       => ( ( ord_less_eq_int @ X @ one_one_int )
% 0.35/0.62         => ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % square_le_1
% 0.35/0.62  thf(fact_5619_minus__power__mult__self,axiom,
% 0.35/0.62      ! [A: int,N: nat] :
% 0.35/0.62        ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 0.35/0.62        = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % minus_power_mult_self
% 0.35/0.62  thf(fact_5620_minus__power__mult__self,axiom,
% 0.35/0.62      ! [A: real,N: nat] :
% 0.35/0.62        ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 0.35/0.62        = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % minus_power_mult_self
% 0.35/0.62  thf(fact_5621_minus__power__mult__self,axiom,
% 0.35/0.62      ! [A: complex,N: nat] :
% 0.35/0.62        ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) )
% 0.35/0.62        = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % minus_power_mult_self
% 0.35/0.62  thf(fact_5622_minus__power__mult__self,axiom,
% 0.35/0.62      ! [A: code_integer,N: nat] :
% 0.35/0.62        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 0.35/0.62        = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % minus_power_mult_self
% 0.35/0.62  thf(fact_5623_minus__power__mult__self,axiom,
% 0.35/0.62      ! [A: rat,N: nat] :
% 0.35/0.62        ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 0.35/0.62        = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % minus_power_mult_self
% 0.35/0.62  thf(fact_5624_minus__one__power__iff,axiom,
% 0.35/0.62      ! [N: nat] :
% 0.35/0.62        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.62         => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 0.35/0.62            = one_one_int ) )
% 0.35/0.62        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.62         => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 0.35/0.62            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % minus_one_power_iff
% 0.35/0.62  thf(fact_5625_minus__one__power__iff,axiom,
% 0.35/0.62      ! [N: nat] :
% 0.35/0.62        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.62         => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 0.35/0.62            = one_one_real ) )
% 0.35/0.62        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.62         => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 0.35/0.62            = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % minus_one_power_iff
% 0.35/0.62  thf(fact_5626_minus__one__power__iff,axiom,
% 0.35/0.62      ! [N: nat] :
% 0.35/0.62        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.62         => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 0.35/0.62            = one_one_complex ) )
% 0.35/0.62        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.62         => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 0.35/0.62            = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % minus_one_power_iff
% 0.35/0.62  thf(fact_5627_minus__one__power__iff,axiom,
% 0.35/0.62      ! [N: nat] :
% 0.35/0.62        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.62         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 0.35/0.62            = one_one_Code_integer ) )
% 0.35/0.62        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.62         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 0.35/0.62            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % minus_one_power_iff
% 0.35/0.62  thf(fact_5628_minus__one__power__iff,axiom,
% 0.35/0.62      ! [N: nat] :
% 0.35/0.62        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.62         => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 0.35/0.62            = one_one_rat ) )
% 0.35/0.62        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.62         => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 0.35/0.62            = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % minus_one_power_iff
% 0.35/0.62  thf(fact_5629_signed__take__bit__int__eq__self__iff,axiom,
% 0.35/0.62      ! [N: nat,K: int] :
% 0.35/0.62        ( ( ( bit_ri631733984087533419it_int @ N @ K )
% 0.35/0.62          = K )
% 0.35/0.62        = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 0.35/0.62          & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % signed_take_bit_int_eq_self_iff
% 0.35/0.62  thf(fact_5630_signed__take__bit__int__eq__self,axiom,
% 0.35/0.62      ! [N: nat,K: int] :
% 0.35/0.62        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 0.35/0.62       => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.62         => ( ( bit_ri631733984087533419it_int @ N @ K )
% 0.35/0.62            = K ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % signed_take_bit_int_eq_self
% 0.35/0.62  thf(fact_5631_minus__1__div__exp__eq__int,axiom,
% 0.35/0.62      ! [N: nat] :
% 0.35/0.62        ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.62        = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.35/0.62  
% 0.35/0.62  % minus_1_div_exp_eq_int
% 0.35/0.62  thf(fact_5632_div__pos__neg__trivial,axiom,
% 0.35/0.62      ! [K: int,L2: int] :
% 0.35/0.62        ( ( ord_less_int @ zero_zero_int @ K )
% 0.35/0.62       => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L2 ) @ zero_zero_int )
% 0.35/0.62         => ( ( divide_divide_int @ K @ L2 )
% 0.35/0.62            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % div_pos_neg_trivial
% 0.35/0.62  thf(fact_5633_power__minus1__odd,axiom,
% 0.35/0.62      ! [N: nat] :
% 0.35/0.62        ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.62        = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power_minus1_odd
% 0.35/0.62  thf(fact_5634_power__minus1__odd,axiom,
% 0.35/0.62      ! [N: nat] :
% 0.35/0.62        ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.62        = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power_minus1_odd
% 0.35/0.62  thf(fact_5635_power__minus1__odd,axiom,
% 0.35/0.62      ! [N: nat] :
% 0.35/0.62        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.62        = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power_minus1_odd
% 0.35/0.62  thf(fact_5636_power__minus1__odd,axiom,
% 0.35/0.62      ! [N: nat] :
% 0.35/0.62        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.62        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power_minus1_odd
% 0.35/0.62  thf(fact_5637_power__minus1__odd,axiom,
% 0.35/0.62      ! [N: nat] :
% 0.35/0.62        ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.62        = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power_minus1_odd
% 0.35/0.62  thf(fact_5638_int__bit__induct,axiom,
% 0.35/0.62      ! [P: int > $o,K: int] :
% 0.35/0.62        ( ( P @ zero_zero_int )
% 0.35/0.62       => ( ( P @ ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.62         => ( ! [K2: int] :
% 0.35/0.62                ( ( P @ K2 )
% 0.35/0.62               => ( ( K2 != zero_zero_int )
% 0.35/0.62                 => ( P @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.62           => ( ! [K2: int] :
% 0.35/0.62                  ( ( P @ K2 )
% 0.35/0.62                 => ( ( K2
% 0.35/0.62                     != ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.62                   => ( P @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 0.35/0.62             => ( P @ K ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % int_bit_induct
% 0.35/0.62  thf(fact_5639_signed__take__bit__int__greater__eq,axiom,
% 0.35/0.62      ! [K: int,N: nat] :
% 0.35/0.62        ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.62       => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % signed_take_bit_int_greater_eq
% 0.35/0.62  thf(fact_5640_set__decode__plus__power__2,axiom,
% 0.35/0.62      ! [N: nat,Z: nat] :
% 0.35/0.62        ( ~ ( member_nat @ N @ ( nat_set_decode @ Z ) )
% 0.35/0.62       => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ Z ) )
% 0.35/0.62          = ( insert_nat @ N @ ( nat_set_decode @ Z ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % set_decode_plus_power_2
% 0.35/0.62  thf(fact_5641_set__decode__def,axiom,
% 0.35/0.62      ( nat_set_decode
% 0.35/0.62      = ( ^ [X2: nat] :
% 0.35/0.62            ( collect_nat
% 0.35/0.62            @ ^ [N2: nat] :
% 0.35/0.62                ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % set_decode_def
% 0.35/0.62  thf(fact_5642_compl__le__compl__iff,axiom,
% 0.35/0.62      ! [X: set_real,Y2: set_real] :
% 0.35/0.62        ( ( ord_less_eq_set_real @ ( uminus612125837232591019t_real @ X ) @ ( uminus612125837232591019t_real @ Y2 ) )
% 0.35/0.62        = ( ord_less_eq_set_real @ Y2 @ X ) ) ).
% 0.35/0.62  
% 0.35/0.62  % compl_le_compl_iff
% 0.35/0.62  thf(fact_5643_compl__le__compl__iff,axiom,
% 0.35/0.62      ! [X: set_nat,Y2: set_nat] :
% 0.35/0.62        ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ ( uminus5710092332889474511et_nat @ Y2 ) )
% 0.35/0.62        = ( ord_less_eq_set_nat @ Y2 @ X ) ) ).
% 0.35/0.62  
% 0.35/0.62  % compl_le_compl_iff
% 0.35/0.62  thf(fact_5644_dbl__dec__simps_I4_J,axiom,
% 0.35/0.62      ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.62      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dbl_dec_simps(4)
% 0.35/0.62  thf(fact_5645_dbl__dec__simps_I4_J,axiom,
% 0.35/0.62      ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.35/0.62      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dbl_dec_simps(4)
% 0.35/0.62  thf(fact_5646_dbl__dec__simps_I4_J,axiom,
% 0.35/0.62      ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.35/0.62      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dbl_dec_simps(4)
% 0.35/0.62  thf(fact_5647_dbl__dec__simps_I4_J,axiom,
% 0.35/0.62      ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.62      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dbl_dec_simps(4)
% 0.35/0.62  thf(fact_5648_dbl__dec__simps_I4_J,axiom,
% 0.35/0.62      ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.35/0.62      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dbl_dec_simps(4)
% 0.35/0.62  thf(fact_5649_and__int_Osimps,axiom,
% 0.35/0.62      ( bit_se725231765392027082nd_int
% 0.35/0.62      = ( ^ [K3: int,L: int] :
% 0.35/0.62            ( if_int
% 0.35/0.62            @ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.35/0.62              & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.35/0.62            @ ( uminus_uminus_int
% 0.35/0.62              @ ( zero_n2684676970156552555ol_int
% 0.35/0.62                @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 0.35/0.62                  & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) )
% 0.35/0.62            @ ( plus_plus_int
% 0.35/0.62              @ ( zero_n2684676970156552555ol_int
% 0.35/0.62                @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 0.35/0.62                  & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 0.35/0.62              @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % and_int.simps
% 0.35/0.62  thf(fact_5650_and__int_Oelims,axiom,
% 0.35/0.62      ! [X: int,Xa2: int,Y2: int] :
% 0.35/0.62        ( ( ( bit_se725231765392027082nd_int @ X @ Xa2 )
% 0.35/0.62          = Y2 )
% 0.35/0.62       => ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.35/0.62              & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.35/0.62           => ( Y2
% 0.35/0.62              = ( uminus_uminus_int
% 0.35/0.62                @ ( zero_n2684676970156552555ol_int
% 0.35/0.62                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 0.35/0.62                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 0.35/0.62          & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.35/0.62                & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.35/0.62           => ( Y2
% 0.35/0.62              = ( plus_plus_int
% 0.35/0.62                @ ( zero_n2684676970156552555ol_int
% 0.35/0.62                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 0.35/0.62                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 0.35/0.62                @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % and_int.elims
% 0.35/0.62  thf(fact_5651_of__int__code__if,axiom,
% 0.35/0.62      ( ring_1_of_int_int
% 0.35/0.62      = ( ^ [K3: int] :
% 0.35/0.62            ( if_int @ ( K3 = zero_zero_int ) @ zero_zero_int
% 0.35/0.62            @ ( if_int @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_int @ ( ring_1_of_int_int @ ( uminus_uminus_int @ K3 ) ) )
% 0.35/0.62              @ ( if_int
% 0.35/0.62                @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.62                  = zero_zero_int )
% 0.35/0.62                @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.35/0.62                @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_int ) ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_code_if
% 0.35/0.62  thf(fact_5652_of__int__code__if,axiom,
% 0.35/0.62      ( ring_1_of_int_real
% 0.35/0.62      = ( ^ [K3: int] :
% 0.35/0.62            ( if_real @ ( K3 = zero_zero_int ) @ zero_zero_real
% 0.35/0.62            @ ( if_real @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_real @ ( ring_1_of_int_real @ ( uminus_uminus_int @ K3 ) ) )
% 0.35/0.62              @ ( if_real
% 0.35/0.62                @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.62                  = zero_zero_int )
% 0.35/0.62                @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.35/0.62                @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_code_if
% 0.35/0.62  thf(fact_5653_of__int__code__if,axiom,
% 0.35/0.62      ( ring_17405671764205052669omplex
% 0.35/0.62      = ( ^ [K3: int] :
% 0.35/0.62            ( if_complex @ ( K3 = zero_zero_int ) @ zero_zero_complex
% 0.35/0.62            @ ( if_complex @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ K3 ) ) )
% 0.35/0.62              @ ( if_complex
% 0.35/0.62                @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.62                  = zero_zero_int )
% 0.35/0.62                @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.35/0.62                @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_complex ) ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_code_if
% 0.35/0.62  thf(fact_5654_of__int__code__if,axiom,
% 0.35/0.62      ( ring_18347121197199848620nteger
% 0.35/0.62      = ( ^ [K3: int] :
% 0.35/0.62            ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 0.35/0.62            @ ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ K3 ) ) )
% 0.35/0.62              @ ( if_Code_integer
% 0.35/0.62                @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.62                  = zero_zero_int )
% 0.35/0.62                @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.35/0.62                @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_code_if
% 0.35/0.62  thf(fact_5655_of__int__code__if,axiom,
% 0.35/0.62      ( ring_1_of_int_rat
% 0.35/0.62      = ( ^ [K3: int] :
% 0.35/0.62            ( if_rat @ ( K3 = zero_zero_int ) @ zero_zero_rat
% 0.35/0.62            @ ( if_rat @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( ring_1_of_int_rat @ ( uminus_uminus_int @ K3 ) ) )
% 0.35/0.62              @ ( if_rat
% 0.35/0.62                @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.62                  = zero_zero_int )
% 0.35/0.62                @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.35/0.62                @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_rat ) ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_code_if
% 0.35/0.62  thf(fact_5656_diff__shunt__var,axiom,
% 0.35/0.62      ! [X: set_int,Y2: set_int] :
% 0.35/0.62        ( ( ( minus_minus_set_int @ X @ Y2 )
% 0.35/0.62          = bot_bot_set_int )
% 0.35/0.62        = ( ord_less_eq_set_int @ X @ Y2 ) ) ).
% 0.35/0.62  
% 0.35/0.62  % diff_shunt_var
% 0.35/0.62  thf(fact_5657_diff__shunt__var,axiom,
% 0.35/0.62      ! [X: set_Pr1261947904930325089at_nat,Y2: set_Pr1261947904930325089at_nat] :
% 0.35/0.62        ( ( ( minus_1356011639430497352at_nat @ X @ Y2 )
% 0.35/0.62          = bot_bo2099793752762293965at_nat )
% 0.35/0.62        = ( ord_le3146513528884898305at_nat @ X @ Y2 ) ) ).
% 0.35/0.62  
% 0.35/0.62  % diff_shunt_var
% 0.35/0.62  thf(fact_5658_diff__shunt__var,axiom,
% 0.35/0.62      ! [X: set_real,Y2: set_real] :
% 0.35/0.62        ( ( ( minus_minus_set_real @ X @ Y2 )
% 0.35/0.62          = bot_bot_set_real )
% 0.35/0.62        = ( ord_less_eq_set_real @ X @ Y2 ) ) ).
% 0.35/0.62  
% 0.35/0.62  % diff_shunt_var
% 0.35/0.62  thf(fact_5659_diff__shunt__var,axiom,
% 0.35/0.62      ! [X: set_nat,Y2: set_nat] :
% 0.35/0.62        ( ( ( minus_minus_set_nat @ X @ Y2 )
% 0.35/0.62          = bot_bot_set_nat )
% 0.35/0.62        = ( ord_less_eq_set_nat @ X @ Y2 ) ) ).
% 0.35/0.62  
% 0.35/0.62  % diff_shunt_var
% 0.35/0.62  thf(fact_5660_and_Oidem,axiom,
% 0.35/0.62      ! [A: int] :
% 0.35/0.62        ( ( bit_se725231765392027082nd_int @ A @ A )
% 0.35/0.62        = A ) ).
% 0.35/0.62  
% 0.35/0.62  % and.idem
% 0.35/0.62  thf(fact_5661_and_Oidem,axiom,
% 0.35/0.62      ! [A: nat] :
% 0.35/0.62        ( ( bit_se727722235901077358nd_nat @ A @ A )
% 0.35/0.62        = A ) ).
% 0.35/0.62  
% 0.35/0.62  % and.idem
% 0.35/0.62  thf(fact_5662_and_Oleft__idem,axiom,
% 0.35/0.62      ! [A: int,B: int] :
% 0.35/0.62        ( ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 0.35/0.62        = ( bit_se725231765392027082nd_int @ A @ B ) ) ).
% 0.35/0.62  
% 0.35/0.62  % and.left_idem
% 0.35/0.62  thf(fact_5663_and_Oleft__idem,axiom,
% 0.35/0.62      ! [A: nat,B: nat] :
% 0.35/0.62        ( ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 0.35/0.62        = ( bit_se727722235901077358nd_nat @ A @ B ) ) ).
% 0.35/0.62  
% 0.35/0.62  % and.left_idem
% 0.35/0.62  thf(fact_5664_and_Oright__idem,axiom,
% 0.35/0.62      ! [A: int,B: int] :
% 0.35/0.62        ( ( bit_se725231765392027082nd_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ B )
% 0.35/0.62        = ( bit_se725231765392027082nd_int @ A @ B ) ) ).
% 0.35/0.62  
% 0.35/0.62  % and.right_idem
% 0.35/0.62  thf(fact_5665_and_Oright__idem,axiom,
% 0.35/0.62      ! [A: nat,B: nat] :
% 0.35/0.62        ( ( bit_se727722235901077358nd_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ B )
% 0.35/0.62        = ( bit_se727722235901077358nd_nat @ A @ B ) ) ).
% 0.35/0.62  
% 0.35/0.62  % and.right_idem
% 0.35/0.62  thf(fact_5666_and__zero__eq,axiom,
% 0.35/0.62      ! [A: int] :
% 0.35/0.62        ( ( bit_se725231765392027082nd_int @ A @ zero_zero_int )
% 0.35/0.62        = zero_zero_int ) ).
% 0.35/0.62  
% 0.35/0.62  % and_zero_eq
% 0.35/0.62  thf(fact_5667_and__zero__eq,axiom,
% 0.35/0.62      ! [A: nat] :
% 0.35/0.62        ( ( bit_se727722235901077358nd_nat @ A @ zero_zero_nat )
% 0.35/0.62        = zero_zero_nat ) ).
% 0.35/0.62  
% 0.35/0.62  % and_zero_eq
% 0.35/0.62  thf(fact_5668_zero__and__eq,axiom,
% 0.35/0.62      ! [A: int] :
% 0.35/0.62        ( ( bit_se725231765392027082nd_int @ zero_zero_int @ A )
% 0.35/0.62        = zero_zero_int ) ).
% 0.35/0.62  
% 0.35/0.62  % zero_and_eq
% 0.35/0.62  thf(fact_5669_zero__and__eq,axiom,
% 0.35/0.62      ! [A: nat] :
% 0.35/0.62        ( ( bit_se727722235901077358nd_nat @ zero_zero_nat @ A )
% 0.35/0.62        = zero_zero_nat ) ).
% 0.35/0.62  
% 0.35/0.62  % zero_and_eq
% 0.35/0.62  thf(fact_5670_bit_Oconj__zero__left,axiom,
% 0.35/0.62      ! [X: int] :
% 0.35/0.62        ( ( bit_se725231765392027082nd_int @ zero_zero_int @ X )
% 0.35/0.62        = zero_zero_int ) ).
% 0.35/0.62  
% 0.35/0.62  % bit.conj_zero_left
% 0.35/0.62  thf(fact_5671_bit_Oconj__zero__right,axiom,
% 0.35/0.62      ! [X: int] :
% 0.35/0.62        ( ( bit_se725231765392027082nd_int @ X @ zero_zero_int )
% 0.35/0.62        = zero_zero_int ) ).
% 0.35/0.62  
% 0.35/0.62  % bit.conj_zero_right
% 0.35/0.62  thf(fact_5672_dbl__dec__simps_I3_J,axiom,
% 0.35/0.62      ( ( neg_nu6511756317524482435omplex @ one_one_complex )
% 0.35/0.62      = one_one_complex ) ).
% 0.35/0.62  
% 0.35/0.62  % dbl_dec_simps(3)
% 0.35/0.62  thf(fact_5673_dbl__dec__simps_I3_J,axiom,
% 0.35/0.62      ( ( neg_nu6075765906172075777c_real @ one_one_real )
% 0.35/0.62      = one_one_real ) ).
% 0.35/0.62  
% 0.35/0.62  % dbl_dec_simps(3)
% 0.35/0.62  thf(fact_5674_dbl__dec__simps_I3_J,axiom,
% 0.35/0.62      ( ( neg_nu3179335615603231917ec_rat @ one_one_rat )
% 0.35/0.62      = one_one_rat ) ).
% 0.35/0.62  
% 0.35/0.62  % dbl_dec_simps(3)
% 0.35/0.62  thf(fact_5675_dbl__dec__simps_I3_J,axiom,
% 0.35/0.62      ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 0.35/0.62      = one_one_int ) ).
% 0.35/0.62  
% 0.35/0.62  % dbl_dec_simps(3)
% 0.35/0.62  thf(fact_5676_bit_Oconj__one__right,axiom,
% 0.35/0.62      ! [X: code_integer] :
% 0.35/0.62        ( ( bit_se3949692690581998587nteger @ X @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.62        = X ) ).
% 0.35/0.62  
% 0.35/0.62  % bit.conj_one_right
% 0.35/0.62  thf(fact_5677_bit_Oconj__one__right,axiom,
% 0.35/0.62      ! [X: int] :
% 0.35/0.62        ( ( bit_se725231765392027082nd_int @ X @ ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.62        = X ) ).
% 0.35/0.62  
% 0.35/0.62  % bit.conj_one_right
% 0.35/0.62  thf(fact_5678_and_Oright__neutral,axiom,
% 0.35/0.62      ! [A: code_integer] :
% 0.35/0.62        ( ( bit_se3949692690581998587nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.62        = A ) ).
% 0.35/0.62  
% 0.35/0.62  % and.right_neutral
% 0.35/0.62  thf(fact_5679_and_Oright__neutral,axiom,
% 0.35/0.62      ! [A: int] :
% 0.35/0.62        ( ( bit_se725231765392027082nd_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.62        = A ) ).
% 0.35/0.62  
% 0.35/0.62  % and.right_neutral
% 0.35/0.62  thf(fact_5680_and_Oleft__neutral,axiom,
% 0.35/0.62      ! [A: code_integer] :
% 0.35/0.62        ( ( bit_se3949692690581998587nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ A )
% 0.35/0.62        = A ) ).
% 0.35/0.62  
% 0.35/0.62  % and.left_neutral
% 0.35/0.62  thf(fact_5681_and_Oleft__neutral,axiom,
% 0.35/0.62      ! [A: int] :
% 0.35/0.62        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ one_one_int ) @ A )
% 0.35/0.62        = A ) ).
% 0.35/0.62  
% 0.35/0.62  % and.left_neutral
% 0.35/0.62  thf(fact_5682_of__int__numeral,axiom,
% 0.35/0.62      ! [K: num] :
% 0.35/0.62        ( ( ring_17405671764205052669omplex @ ( numeral_numeral_int @ K ) )
% 0.35/0.62        = ( numera6690914467698888265omplex @ K ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_numeral
% 0.35/0.62  thf(fact_5683_of__int__numeral,axiom,
% 0.35/0.62      ! [K: num] :
% 0.35/0.62        ( ( ring_1_of_int_real @ ( numeral_numeral_int @ K ) )
% 0.35/0.62        = ( numeral_numeral_real @ K ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_numeral
% 0.35/0.62  thf(fact_5684_of__int__numeral,axiom,
% 0.35/0.62      ! [K: num] :
% 0.35/0.62        ( ( ring_1_of_int_rat @ ( numeral_numeral_int @ K ) )
% 0.35/0.62        = ( numeral_numeral_rat @ K ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_numeral
% 0.35/0.62  thf(fact_5685_of__int__numeral,axiom,
% 0.35/0.62      ! [K: num] :
% 0.35/0.62        ( ( ring_1_of_int_int @ ( numeral_numeral_int @ K ) )
% 0.35/0.62        = ( numeral_numeral_int @ K ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_numeral
% 0.35/0.62  thf(fact_5686_of__int__eq__numeral__iff,axiom,
% 0.35/0.62      ! [Z: int,N: num] :
% 0.35/0.62        ( ( ( ring_17405671764205052669omplex @ Z )
% 0.35/0.62          = ( numera6690914467698888265omplex @ N ) )
% 0.35/0.62        = ( Z
% 0.35/0.62          = ( numeral_numeral_int @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_eq_numeral_iff
% 0.35/0.62  thf(fact_5687_of__int__eq__numeral__iff,axiom,
% 0.35/0.62      ! [Z: int,N: num] :
% 0.35/0.62        ( ( ( ring_1_of_int_real @ Z )
% 0.35/0.62          = ( numeral_numeral_real @ N ) )
% 0.35/0.62        = ( Z
% 0.35/0.62          = ( numeral_numeral_int @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_eq_numeral_iff
% 0.35/0.62  thf(fact_5688_of__int__eq__numeral__iff,axiom,
% 0.35/0.62      ! [Z: int,N: num] :
% 0.35/0.62        ( ( ( ring_1_of_int_rat @ Z )
% 0.35/0.62          = ( numeral_numeral_rat @ N ) )
% 0.35/0.62        = ( Z
% 0.35/0.62          = ( numeral_numeral_int @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_eq_numeral_iff
% 0.35/0.62  thf(fact_5689_of__int__eq__numeral__iff,axiom,
% 0.35/0.62      ! [Z: int,N: num] :
% 0.35/0.62        ( ( ( ring_1_of_int_int @ Z )
% 0.35/0.62          = ( numeral_numeral_int @ N ) )
% 0.35/0.62        = ( Z
% 0.35/0.62          = ( numeral_numeral_int @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_eq_numeral_iff
% 0.35/0.62  thf(fact_5690_of__int__le__iff,axiom,
% 0.35/0.62      ! [W: int,Z: int] :
% 0.35/0.62        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 0.35/0.62        = ( ord_less_eq_int @ W @ Z ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_le_iff
% 0.35/0.62  thf(fact_5691_of__int__le__iff,axiom,
% 0.35/0.62      ! [W: int,Z: int] :
% 0.35/0.62        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 0.35/0.62        = ( ord_less_eq_int @ W @ Z ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_le_iff
% 0.35/0.62  thf(fact_5692_of__int__less__iff,axiom,
% 0.35/0.62      ! [W: int,Z: int] :
% 0.35/0.62        ( ( ord_less_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 0.35/0.62        = ( ord_less_int @ W @ Z ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_less_iff
% 0.35/0.62  thf(fact_5693_of__int__less__iff,axiom,
% 0.35/0.62      ! [W: int,Z: int] :
% 0.35/0.62        ( ( ord_less_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 0.35/0.62        = ( ord_less_int @ W @ Z ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_less_iff
% 0.35/0.62  thf(fact_5694_of__int__less__iff,axiom,
% 0.35/0.62      ! [W: int,Z: int] :
% 0.35/0.62        ( ( ord_less_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 0.35/0.62        = ( ord_less_int @ W @ Z ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_less_iff
% 0.35/0.62  thf(fact_5695_of__int__eq__1__iff,axiom,
% 0.35/0.62      ! [Z: int] :
% 0.35/0.62        ( ( ( ring_17405671764205052669omplex @ Z )
% 0.35/0.62          = one_one_complex )
% 0.35/0.62        = ( Z = one_one_int ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_eq_1_iff
% 0.35/0.62  thf(fact_5696_of__int__eq__1__iff,axiom,
% 0.35/0.62      ! [Z: int] :
% 0.35/0.62        ( ( ( ring_1_of_int_rat @ Z )
% 0.35/0.62          = one_one_rat )
% 0.35/0.62        = ( Z = one_one_int ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_eq_1_iff
% 0.35/0.62  thf(fact_5697_of__int__eq__1__iff,axiom,
% 0.35/0.62      ! [Z: int] :
% 0.35/0.62        ( ( ( ring_1_of_int_int @ Z )
% 0.35/0.62          = one_one_int )
% 0.35/0.62        = ( Z = one_one_int ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_eq_1_iff
% 0.35/0.62  thf(fact_5698_of__int__eq__1__iff,axiom,
% 0.35/0.62      ! [Z: int] :
% 0.35/0.62        ( ( ( ring_1_of_int_real @ Z )
% 0.35/0.62          = one_one_real )
% 0.35/0.62        = ( Z = one_one_int ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_eq_1_iff
% 0.35/0.62  thf(fact_5699_of__int__1,axiom,
% 0.35/0.62      ( ( ring_17405671764205052669omplex @ one_one_int )
% 0.35/0.62      = one_one_complex ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_1
% 0.35/0.62  thf(fact_5700_of__int__1,axiom,
% 0.35/0.62      ( ( ring_1_of_int_rat @ one_one_int )
% 0.35/0.62      = one_one_rat ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_1
% 0.35/0.62  thf(fact_5701_of__int__1,axiom,
% 0.35/0.62      ( ( ring_1_of_int_int @ one_one_int )
% 0.35/0.62      = one_one_int ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_1
% 0.35/0.62  thf(fact_5702_of__int__1,axiom,
% 0.35/0.62      ( ( ring_1_of_int_real @ one_one_int )
% 0.35/0.62      = one_one_real ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_1
% 0.35/0.62  thf(fact_5703_of__int__mult,axiom,
% 0.35/0.62      ! [W: int,Z: int] :
% 0.35/0.62        ( ( ring_17405671764205052669omplex @ ( times_times_int @ W @ Z ) )
% 0.35/0.62        = ( times_times_complex @ ( ring_17405671764205052669omplex @ W ) @ ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_mult
% 0.35/0.62  thf(fact_5704_of__int__mult,axiom,
% 0.35/0.62      ! [W: int,Z: int] :
% 0.35/0.62        ( ( ring_1_of_int_real @ ( times_times_int @ W @ Z ) )
% 0.35/0.62        = ( times_times_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_mult
% 0.35/0.62  thf(fact_5705_of__int__mult,axiom,
% 0.35/0.62      ! [W: int,Z: int] :
% 0.35/0.62        ( ( ring_1_of_int_int @ ( times_times_int @ W @ Z ) )
% 0.35/0.62        = ( times_times_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_mult
% 0.35/0.62  thf(fact_5706_of__int__add,axiom,
% 0.35/0.62      ! [W: int,Z: int] :
% 0.35/0.62        ( ( ring_1_of_int_rat @ ( plus_plus_int @ W @ Z ) )
% 0.35/0.62        = ( plus_plus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_add
% 0.35/0.62  thf(fact_5707_of__int__add,axiom,
% 0.35/0.62      ! [W: int,Z: int] :
% 0.35/0.62        ( ( ring_1_of_int_int @ ( plus_plus_int @ W @ Z ) )
% 0.35/0.62        = ( plus_plus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_add
% 0.35/0.62  thf(fact_5708_of__int__add,axiom,
% 0.35/0.62      ! [W: int,Z: int] :
% 0.35/0.62        ( ( ring_17405671764205052669omplex @ ( plus_plus_int @ W @ Z ) )
% 0.35/0.62        = ( plus_plus_complex @ ( ring_17405671764205052669omplex @ W ) @ ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_add
% 0.35/0.62  thf(fact_5709_of__int__add,axiom,
% 0.35/0.62      ! [W: int,Z: int] :
% 0.35/0.62        ( ( ring_1_of_int_real @ ( plus_plus_int @ W @ Z ) )
% 0.35/0.62        = ( plus_plus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_add
% 0.35/0.62  thf(fact_5710_of__int__diff,axiom,
% 0.35/0.62      ! [W: int,Z: int] :
% 0.35/0.62        ( ( ring_1_of_int_real @ ( minus_minus_int @ W @ Z ) )
% 0.35/0.62        = ( minus_minus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_diff
% 0.35/0.62  thf(fact_5711_of__int__diff,axiom,
% 0.35/0.62      ! [W: int,Z: int] :
% 0.35/0.62        ( ( ring_1_of_int_rat @ ( minus_minus_int @ W @ Z ) )
% 0.35/0.62        = ( minus_minus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_diff
% 0.35/0.62  thf(fact_5712_of__int__diff,axiom,
% 0.35/0.62      ! [W: int,Z: int] :
% 0.35/0.62        ( ( ring_1_of_int_int @ ( minus_minus_int @ W @ Z ) )
% 0.35/0.62        = ( minus_minus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_diff
% 0.35/0.62  thf(fact_5713_of__int__power,axiom,
% 0.35/0.62      ! [Z: int,N: nat] :
% 0.35/0.62        ( ( ring_1_of_int_real @ ( power_power_int @ Z @ N ) )
% 0.35/0.62        = ( power_power_real @ ( ring_1_of_int_real @ Z ) @ N ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_power
% 0.35/0.62  thf(fact_5714_of__int__power,axiom,
% 0.35/0.62      ! [Z: int,N: nat] :
% 0.35/0.62        ( ( ring_1_of_int_int @ ( power_power_int @ Z @ N ) )
% 0.35/0.62        = ( power_power_int @ ( ring_1_of_int_int @ Z ) @ N ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_power
% 0.35/0.62  thf(fact_5715_of__int__power,axiom,
% 0.35/0.62      ! [Z: int,N: nat] :
% 0.35/0.62        ( ( ring_17405671764205052669omplex @ ( power_power_int @ Z @ N ) )
% 0.35/0.62        = ( power_power_complex @ ( ring_17405671764205052669omplex @ Z ) @ N ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_power
% 0.35/0.62  thf(fact_5716_of__int__eq__of__int__power__cancel__iff,axiom,
% 0.35/0.62      ! [B: int,W: nat,X: int] :
% 0.35/0.62        ( ( ( power_power_real @ ( ring_1_of_int_real @ B ) @ W )
% 0.35/0.62          = ( ring_1_of_int_real @ X ) )
% 0.35/0.62        = ( ( power_power_int @ B @ W )
% 0.35/0.62          = X ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_eq_of_int_power_cancel_iff
% 0.35/0.62  thf(fact_5717_of__int__eq__of__int__power__cancel__iff,axiom,
% 0.35/0.62      ! [B: int,W: nat,X: int] :
% 0.35/0.62        ( ( ( power_power_int @ ( ring_1_of_int_int @ B ) @ W )
% 0.35/0.62          = ( ring_1_of_int_int @ X ) )
% 0.35/0.62        = ( ( power_power_int @ B @ W )
% 0.35/0.62          = X ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_eq_of_int_power_cancel_iff
% 0.35/0.62  thf(fact_5718_of__int__eq__of__int__power__cancel__iff,axiom,
% 0.35/0.62      ! [B: int,W: nat,X: int] :
% 0.35/0.62        ( ( ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W )
% 0.35/0.62          = ( ring_17405671764205052669omplex @ X ) )
% 0.35/0.62        = ( ( power_power_int @ B @ W )
% 0.35/0.62          = X ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_eq_of_int_power_cancel_iff
% 0.35/0.62  thf(fact_5719_of__int__power__eq__of__int__cancel__iff,axiom,
% 0.35/0.62      ! [X: int,B: int,W: nat] :
% 0.35/0.62        ( ( ( ring_1_of_int_real @ X )
% 0.35/0.62          = ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 0.35/0.62        = ( X
% 0.35/0.62          = ( power_power_int @ B @ W ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_power_eq_of_int_cancel_iff
% 0.35/0.62  thf(fact_5720_of__int__power__eq__of__int__cancel__iff,axiom,
% 0.35/0.62      ! [X: int,B: int,W: nat] :
% 0.35/0.62        ( ( ( ring_1_of_int_int @ X )
% 0.35/0.62          = ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 0.35/0.62        = ( X
% 0.35/0.62          = ( power_power_int @ B @ W ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_power_eq_of_int_cancel_iff
% 0.35/0.62  thf(fact_5721_of__int__power__eq__of__int__cancel__iff,axiom,
% 0.35/0.62      ! [X: int,B: int,W: nat] :
% 0.35/0.62        ( ( ( ring_17405671764205052669omplex @ X )
% 0.35/0.62          = ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W ) )
% 0.35/0.62        = ( X
% 0.35/0.62          = ( power_power_int @ B @ W ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_power_eq_of_int_cancel_iff
% 0.35/0.62  thf(fact_5722_and__nonnegative__int__iff,axiom,
% 0.35/0.62      ! [K: int,L2: int] :
% 0.35/0.62        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) )
% 0.35/0.62        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.35/0.62          | ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % and_nonnegative_int_iff
% 0.35/0.62  thf(fact_5723_and__negative__int__iff,axiom,
% 0.35/0.62      ! [K: int,L2: int] :
% 0.35/0.62        ( ( ord_less_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) @ zero_zero_int )
% 0.35/0.62        = ( ( ord_less_int @ K @ zero_zero_int )
% 0.35/0.62          & ( ord_less_int @ L2 @ zero_zero_int ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % and_negative_int_iff
% 0.35/0.62  thf(fact_5724_dbl__dec__simps_I5_J,axiom,
% 0.35/0.62      ! [K: num] :
% 0.35/0.62        ( ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) )
% 0.35/0.62        = ( numera6690914467698888265omplex @ ( bitM @ K ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dbl_dec_simps(5)
% 0.35/0.62  thf(fact_5725_dbl__dec__simps_I5_J,axiom,
% 0.35/0.62      ! [K: num] :
% 0.35/0.62        ( ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) )
% 0.35/0.62        = ( numeral_numeral_real @ ( bitM @ K ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dbl_dec_simps(5)
% 0.35/0.62  thf(fact_5726_dbl__dec__simps_I5_J,axiom,
% 0.35/0.62      ! [K: num] :
% 0.35/0.62        ( ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) )
% 0.35/0.62        = ( numeral_numeral_rat @ ( bitM @ K ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dbl_dec_simps(5)
% 0.35/0.62  thf(fact_5727_dbl__dec__simps_I5_J,axiom,
% 0.35/0.62      ! [K: num] :
% 0.35/0.62        ( ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) )
% 0.35/0.62        = ( numeral_numeral_int @ ( bitM @ K ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dbl_dec_simps(5)
% 0.35/0.62  thf(fact_5728_and__numerals_I8_J,axiom,
% 0.35/0.62      ! [X: num] :
% 0.35/0.62        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ one_one_int )
% 0.35/0.62        = one_one_int ) ).
% 0.35/0.62  
% 0.35/0.62  % and_numerals(8)
% 0.35/0.62  thf(fact_5729_and__numerals_I8_J,axiom,
% 0.35/0.62      ! [X: num] :
% 0.35/0.62        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ one_one_nat )
% 0.35/0.62        = one_one_nat ) ).
% 0.35/0.62  
% 0.35/0.62  % and_numerals(8)
% 0.35/0.62  thf(fact_5730_and__numerals_I2_J,axiom,
% 0.35/0.62      ! [Y2: num] :
% 0.35/0.62        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y2 ) ) )
% 0.35/0.62        = one_one_int ) ).
% 0.35/0.62  
% 0.35/0.62  % and_numerals(2)
% 0.35/0.62  thf(fact_5731_and__numerals_I2_J,axiom,
% 0.35/0.62      ! [Y2: num] :
% 0.35/0.62        ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) )
% 0.35/0.62        = one_one_nat ) ).
% 0.35/0.62  
% 0.35/0.62  % and_numerals(2)
% 0.35/0.62  thf(fact_5732_dbl__dec__simps_I2_J,axiom,
% 0.35/0.62      ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 0.35/0.62      = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dbl_dec_simps(2)
% 0.35/0.62  thf(fact_5733_dbl__dec__simps_I2_J,axiom,
% 0.35/0.62      ( ( neg_nu6075765906172075777c_real @ zero_zero_real )
% 0.35/0.62      = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dbl_dec_simps(2)
% 0.35/0.62  thf(fact_5734_dbl__dec__simps_I2_J,axiom,
% 0.35/0.62      ( ( neg_nu6511756317524482435omplex @ zero_zero_complex )
% 0.35/0.62      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dbl_dec_simps(2)
% 0.35/0.62  thf(fact_5735_dbl__dec__simps_I2_J,axiom,
% 0.35/0.62      ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 0.35/0.62      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dbl_dec_simps(2)
% 0.35/0.62  thf(fact_5736_dbl__dec__simps_I2_J,axiom,
% 0.35/0.62      ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 0.35/0.62      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dbl_dec_simps(2)
% 0.35/0.62  thf(fact_5737_dbl__dec__simps_I1_J,axiom,
% 0.35/0.62      ! [K: num] :
% 0.35/0.62        ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.35/0.62        = ( uminus_uminus_int @ ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dbl_dec_simps(1)
% 0.35/0.62  thf(fact_5738_dbl__dec__simps_I1_J,axiom,
% 0.35/0.62      ! [K: num] :
% 0.35/0.62        ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 0.35/0.62        = ( uminus_uminus_real @ ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dbl_dec_simps(1)
% 0.35/0.62  thf(fact_5739_dbl__dec__simps_I1_J,axiom,
% 0.35/0.62      ! [K: num] :
% 0.35/0.62        ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 0.35/0.62        = ( uminus1482373934393186551omplex @ ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dbl_dec_simps(1)
% 0.35/0.62  thf(fact_5740_dbl__dec__simps_I1_J,axiom,
% 0.35/0.62      ! [K: num] :
% 0.35/0.62        ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 0.35/0.62        = ( uminus1351360451143612070nteger @ ( neg_nu5831290666863070958nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dbl_dec_simps(1)
% 0.35/0.62  thf(fact_5741_dbl__dec__simps_I1_J,axiom,
% 0.35/0.62      ! [K: num] :
% 0.35/0.62        ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 0.35/0.62        = ( uminus_uminus_rat @ ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dbl_dec_simps(1)
% 0.35/0.62  thf(fact_5742_dbl__inc__simps_I1_J,axiom,
% 0.35/0.62      ! [K: num] :
% 0.35/0.62        ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.35/0.62        = ( uminus_uminus_int @ ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dbl_inc_simps(1)
% 0.35/0.62  thf(fact_5743_dbl__inc__simps_I1_J,axiom,
% 0.35/0.62      ! [K: num] :
% 0.35/0.62        ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 0.35/0.62        = ( uminus_uminus_real @ ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dbl_inc_simps(1)
% 0.35/0.62  thf(fact_5744_dbl__inc__simps_I1_J,axiom,
% 0.35/0.62      ! [K: num] :
% 0.35/0.62        ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 0.35/0.62        = ( uminus1482373934393186551omplex @ ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dbl_inc_simps(1)
% 0.35/0.62  thf(fact_5745_dbl__inc__simps_I1_J,axiom,
% 0.35/0.62      ! [K: num] :
% 0.35/0.62        ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 0.35/0.62        = ( uminus1351360451143612070nteger @ ( neg_nu7757733837767384882nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dbl_inc_simps(1)
% 0.35/0.62  thf(fact_5746_dbl__inc__simps_I1_J,axiom,
% 0.35/0.62      ! [K: num] :
% 0.35/0.62        ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 0.35/0.62        = ( uminus_uminus_rat @ ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dbl_inc_simps(1)
% 0.35/0.62  thf(fact_5747_and__numerals_I5_J,axiom,
% 0.35/0.62      ! [X: num] :
% 0.35/0.62        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ one_one_int )
% 0.35/0.62        = zero_zero_int ) ).
% 0.35/0.62  
% 0.35/0.62  % and_numerals(5)
% 0.35/0.62  thf(fact_5748_and__numerals_I5_J,axiom,
% 0.35/0.62      ! [X: num] :
% 0.35/0.62        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ one_one_nat )
% 0.35/0.62        = zero_zero_nat ) ).
% 0.35/0.62  
% 0.35/0.62  % and_numerals(5)
% 0.35/0.62  thf(fact_5749_and__numerals_I1_J,axiom,
% 0.35/0.62      ! [Y2: num] :
% 0.35/0.62        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y2 ) ) )
% 0.35/0.62        = zero_zero_int ) ).
% 0.35/0.62  
% 0.35/0.62  % and_numerals(1)
% 0.35/0.62  thf(fact_5750_and__numerals_I1_J,axiom,
% 0.35/0.62      ! [Y2: num] :
% 0.35/0.62        ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) )
% 0.35/0.62        = zero_zero_nat ) ).
% 0.35/0.62  
% 0.35/0.62  % and_numerals(1)
% 0.35/0.62  thf(fact_5751_and__numerals_I3_J,axiom,
% 0.35/0.62      ! [X: num,Y2: num] :
% 0.35/0.62        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y2 ) ) )
% 0.35/0.62        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y2 ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % and_numerals(3)
% 0.35/0.62  thf(fact_5752_and__numerals_I3_J,axiom,
% 0.35/0.62      ! [X: num,Y2: num] :
% 0.35/0.62        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) )
% 0.35/0.62        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y2 ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % and_numerals(3)
% 0.35/0.62  thf(fact_5753_of__int__0__le__iff,axiom,
% 0.35/0.62      ! [Z: int] :
% 0.35/0.62        ( ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 0.35/0.62        = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_0_le_iff
% 0.35/0.62  thf(fact_5754_of__int__0__le__iff,axiom,
% 0.35/0.62      ! [Z: int] :
% 0.35/0.62        ( ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 0.35/0.62        = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_0_le_iff
% 0.35/0.62  thf(fact_5755_of__int__0__le__iff,axiom,
% 0.35/0.62      ! [Z: int] :
% 0.35/0.62        ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 0.35/0.62        = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_0_le_iff
% 0.35/0.62  thf(fact_5756_of__int__le__0__iff,axiom,
% 0.35/0.62      ! [Z: int] :
% 0.35/0.62        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 0.35/0.62        = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_le_0_iff
% 0.35/0.62  thf(fact_5757_of__int__le__0__iff,axiom,
% 0.35/0.62      ! [Z: int] :
% 0.35/0.62        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 0.35/0.62        = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_le_0_iff
% 0.35/0.62  thf(fact_5758_of__int__le__0__iff,axiom,
% 0.35/0.62      ! [Z: int] :
% 0.35/0.62        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 0.35/0.62        = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_le_0_iff
% 0.35/0.62  thf(fact_5759_of__int__0__less__iff,axiom,
% 0.35/0.62      ! [Z: int] :
% 0.35/0.62        ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 0.35/0.62        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_0_less_iff
% 0.35/0.62  thf(fact_5760_of__int__0__less__iff,axiom,
% 0.35/0.62      ! [Z: int] :
% 0.35/0.62        ( ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 0.35/0.62        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_0_less_iff
% 0.35/0.62  thf(fact_5761_of__int__0__less__iff,axiom,
% 0.35/0.62      ! [Z: int] :
% 0.35/0.62        ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 0.35/0.62        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_0_less_iff
% 0.35/0.62  thf(fact_5762_of__int__less__0__iff,axiom,
% 0.35/0.62      ! [Z: int] :
% 0.35/0.62        ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 0.35/0.62        = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_less_0_iff
% 0.35/0.62  thf(fact_5763_of__int__less__0__iff,axiom,
% 0.35/0.62      ! [Z: int] :
% 0.35/0.62        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 0.35/0.62        = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_less_0_iff
% 0.35/0.62  thf(fact_5764_of__int__less__0__iff,axiom,
% 0.35/0.62      ! [Z: int] :
% 0.35/0.62        ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 0.35/0.62        = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_less_0_iff
% 0.35/0.62  thf(fact_5765_of__int__numeral__le__iff,axiom,
% 0.35/0.62      ! [N: num,Z: int] :
% 0.35/0.62        ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 0.35/0.62        = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_numeral_le_iff
% 0.35/0.62  thf(fact_5766_of__int__numeral__le__iff,axiom,
% 0.35/0.62      ! [N: num,Z: int] :
% 0.35/0.62        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 0.35/0.62        = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_numeral_le_iff
% 0.35/0.62  thf(fact_5767_of__int__numeral__le__iff,axiom,
% 0.35/0.62      ! [N: num,Z: int] :
% 0.35/0.62        ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 0.35/0.62        = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_numeral_le_iff
% 0.35/0.62  thf(fact_5768_of__int__le__numeral__iff,axiom,
% 0.35/0.62      ! [Z: int,N: num] :
% 0.35/0.62        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 0.35/0.62        = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_le_numeral_iff
% 0.35/0.62  thf(fact_5769_of__int__le__numeral__iff,axiom,
% 0.35/0.62      ! [Z: int,N: num] :
% 0.35/0.62        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 0.35/0.62        = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_le_numeral_iff
% 0.35/0.62  thf(fact_5770_of__int__le__numeral__iff,axiom,
% 0.35/0.62      ! [Z: int,N: num] :
% 0.35/0.62        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 0.35/0.62        = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_le_numeral_iff
% 0.35/0.62  thf(fact_5771_of__int__numeral__less__iff,axiom,
% 0.35/0.62      ! [N: num,Z: int] :
% 0.35/0.62        ( ( ord_less_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 0.35/0.62        = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_numeral_less_iff
% 0.35/0.62  thf(fact_5772_of__int__numeral__less__iff,axiom,
% 0.35/0.62      ! [N: num,Z: int] :
% 0.35/0.62        ( ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 0.35/0.62        = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_numeral_less_iff
% 0.35/0.62  thf(fact_5773_of__int__numeral__less__iff,axiom,
% 0.35/0.62      ! [N: num,Z: int] :
% 0.35/0.62        ( ( ord_less_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 0.35/0.62        = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_numeral_less_iff
% 0.35/0.62  thf(fact_5774_of__int__less__numeral__iff,axiom,
% 0.35/0.62      ! [Z: int,N: num] :
% 0.35/0.62        ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 0.35/0.62        = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_less_numeral_iff
% 0.35/0.62  thf(fact_5775_of__int__less__numeral__iff,axiom,
% 0.35/0.62      ! [Z: int,N: num] :
% 0.35/0.62        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 0.35/0.62        = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_less_numeral_iff
% 0.35/0.62  thf(fact_5776_of__int__less__numeral__iff,axiom,
% 0.35/0.62      ! [Z: int,N: num] :
% 0.35/0.62        ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 0.35/0.62        = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_less_numeral_iff
% 0.35/0.62  thf(fact_5777_of__int__le__1__iff,axiom,
% 0.35/0.62      ! [Z: int] :
% 0.35/0.62        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 0.35/0.62        = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_le_1_iff
% 0.35/0.62  thf(fact_5778_of__int__le__1__iff,axiom,
% 0.35/0.62      ! [Z: int] :
% 0.35/0.62        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 0.35/0.62        = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_le_1_iff
% 0.35/0.62  thf(fact_5779_of__int__le__1__iff,axiom,
% 0.35/0.62      ! [Z: int] :
% 0.35/0.62        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 0.35/0.62        = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_le_1_iff
% 0.35/0.62  thf(fact_5780_of__int__1__le__iff,axiom,
% 0.35/0.62      ! [Z: int] :
% 0.35/0.62        ( ( ord_less_eq_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 0.35/0.62        = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_1_le_iff
% 0.35/0.62  thf(fact_5781_of__int__1__le__iff,axiom,
% 0.35/0.62      ! [Z: int] :
% 0.35/0.62        ( ( ord_less_eq_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 0.35/0.62        = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_1_le_iff
% 0.35/0.62  thf(fact_5782_of__int__1__le__iff,axiom,
% 0.35/0.62      ! [Z: int] :
% 0.35/0.62        ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 0.35/0.62        = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_1_le_iff
% 0.35/0.62  thf(fact_5783_of__int__less__1__iff,axiom,
% 0.35/0.62      ! [Z: int] :
% 0.35/0.62        ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 0.35/0.62        = ( ord_less_int @ Z @ one_one_int ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_less_1_iff
% 0.35/0.62  thf(fact_5784_of__int__less__1__iff,axiom,
% 0.35/0.62      ! [Z: int] :
% 0.35/0.62        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 0.35/0.62        = ( ord_less_int @ Z @ one_one_int ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_less_1_iff
% 0.35/0.62  thf(fact_5785_of__int__less__1__iff,axiom,
% 0.35/0.62      ! [Z: int] :
% 0.35/0.62        ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 0.35/0.62        = ( ord_less_int @ Z @ one_one_int ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_less_1_iff
% 0.35/0.62  thf(fact_5786_of__int__1__less__iff,axiom,
% 0.35/0.62      ! [Z: int] :
% 0.35/0.62        ( ( ord_less_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 0.35/0.62        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_1_less_iff
% 0.35/0.62  thf(fact_5787_of__int__1__less__iff,axiom,
% 0.35/0.62      ! [Z: int] :
% 0.35/0.62        ( ( ord_less_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 0.35/0.62        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_1_less_iff
% 0.35/0.62  thf(fact_5788_of__int__1__less__iff,axiom,
% 0.35/0.62      ! [Z: int] :
% 0.35/0.62        ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 0.35/0.62        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_1_less_iff
% 0.35/0.62  thf(fact_5789_of__int__eq__numeral__power__cancel__iff,axiom,
% 0.35/0.62      ! [Y2: int,X: num,N: nat] :
% 0.35/0.62        ( ( ( ring_17405671764205052669omplex @ Y2 )
% 0.35/0.62          = ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N ) )
% 0.35/0.62        = ( Y2
% 0.35/0.62          = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_eq_numeral_power_cancel_iff
% 0.35/0.62  thf(fact_5790_of__int__eq__numeral__power__cancel__iff,axiom,
% 0.35/0.62      ! [Y2: int,X: num,N: nat] :
% 0.35/0.62        ( ( ( ring_1_of_int_real @ Y2 )
% 0.35/0.62          = ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 0.35/0.62        = ( Y2
% 0.35/0.62          = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_eq_numeral_power_cancel_iff
% 0.35/0.62  thf(fact_5791_of__int__eq__numeral__power__cancel__iff,axiom,
% 0.35/0.62      ! [Y2: int,X: num,N: nat] :
% 0.35/0.62        ( ( ( ring_1_of_int_rat @ Y2 )
% 0.35/0.62          = ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 0.35/0.62        = ( Y2
% 0.35/0.62          = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_eq_numeral_power_cancel_iff
% 0.35/0.62  thf(fact_5792_of__int__eq__numeral__power__cancel__iff,axiom,
% 0.35/0.62      ! [Y2: int,X: num,N: nat] :
% 0.35/0.62        ( ( ( ring_1_of_int_int @ Y2 )
% 0.35/0.62          = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 0.35/0.62        = ( Y2
% 0.35/0.62          = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_eq_numeral_power_cancel_iff
% 0.35/0.62  thf(fact_5793_numeral__power__eq__of__int__cancel__iff,axiom,
% 0.35/0.62      ! [X: num,N: nat,Y2: int] :
% 0.35/0.62        ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N )
% 0.35/0.62          = ( ring_17405671764205052669omplex @ Y2 ) )
% 0.35/0.62        = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 0.35/0.62          = Y2 ) ) ).
% 0.35/0.62  
% 0.35/0.62  % numeral_power_eq_of_int_cancel_iff
% 0.35/0.62  thf(fact_5794_numeral__power__eq__of__int__cancel__iff,axiom,
% 0.35/0.62      ! [X: num,N: nat,Y2: int] :
% 0.35/0.62        ( ( ( power_power_real @ ( numeral_numeral_real @ X ) @ N )
% 0.35/0.62          = ( ring_1_of_int_real @ Y2 ) )
% 0.35/0.62        = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 0.35/0.62          = Y2 ) ) ).
% 0.35/0.62  
% 0.35/0.62  % numeral_power_eq_of_int_cancel_iff
% 0.35/0.62  thf(fact_5795_numeral__power__eq__of__int__cancel__iff,axiom,
% 0.35/0.62      ! [X: num,N: nat,Y2: int] :
% 0.35/0.62        ( ( ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N )
% 0.35/0.62          = ( ring_1_of_int_rat @ Y2 ) )
% 0.35/0.62        = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 0.35/0.62          = Y2 ) ) ).
% 0.35/0.62  
% 0.35/0.62  % numeral_power_eq_of_int_cancel_iff
% 0.35/0.62  thf(fact_5796_numeral__power__eq__of__int__cancel__iff,axiom,
% 0.35/0.62      ! [X: num,N: nat,Y2: int] :
% 0.35/0.62        ( ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 0.35/0.62          = ( ring_1_of_int_int @ Y2 ) )
% 0.35/0.62        = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 0.35/0.62          = Y2 ) ) ).
% 0.35/0.62  
% 0.35/0.62  % numeral_power_eq_of_int_cancel_iff
% 0.35/0.62  thf(fact_5797_of__int__power__le__of__int__cancel__iff,axiom,
% 0.35/0.62      ! [X: int,B: int,W: nat] :
% 0.35/0.62        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 0.35/0.62        = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_power_le_of_int_cancel_iff
% 0.35/0.62  thf(fact_5798_of__int__power__le__of__int__cancel__iff,axiom,
% 0.35/0.62      ! [X: int,B: int,W: nat] :
% 0.35/0.62        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ X ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 0.35/0.62        = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_power_le_of_int_cancel_iff
% 0.35/0.62  thf(fact_5799_of__int__le__of__int__power__cancel__iff,axiom,
% 0.35/0.62      ! [B: int,W: nat,X: int] :
% 0.35/0.62        ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X ) )
% 0.35/0.62        = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_le_of_int_power_cancel_iff
% 0.35/0.62  thf(fact_5800_of__int__le__of__int__power__cancel__iff,axiom,
% 0.35/0.62      ! [B: int,W: nat,X: int] :
% 0.35/0.62        ( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X ) )
% 0.35/0.62        = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_le_of_int_power_cancel_iff
% 0.35/0.62  thf(fact_5801_of__int__power__less__of__int__cancel__iff,axiom,
% 0.35/0.62      ! [X: int,B: int,W: nat] :
% 0.35/0.62        ( ( ord_less_real @ ( ring_1_of_int_real @ X ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 0.35/0.62        = ( ord_less_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_power_less_of_int_cancel_iff
% 0.35/0.62  thf(fact_5802_of__int__power__less__of__int__cancel__iff,axiom,
% 0.35/0.62      ! [X: int,B: int,W: nat] :
% 0.35/0.62        ( ( ord_less_rat @ ( ring_1_of_int_rat @ X ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 0.35/0.62        = ( ord_less_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_power_less_of_int_cancel_iff
% 0.35/0.62  thf(fact_5803_of__int__power__less__of__int__cancel__iff,axiom,
% 0.35/0.62      ! [X: int,B: int,W: nat] :
% 0.35/0.62        ( ( ord_less_int @ ( ring_1_of_int_int @ X ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 0.35/0.62        = ( ord_less_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_power_less_of_int_cancel_iff
% 0.35/0.62  thf(fact_5804_of__int__less__of__int__power__cancel__iff,axiom,
% 0.35/0.62      ! [B: int,W: nat,X: int] :
% 0.35/0.62        ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X ) )
% 0.35/0.62        = ( ord_less_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_less_of_int_power_cancel_iff
% 0.35/0.62  thf(fact_5805_of__int__less__of__int__power__cancel__iff,axiom,
% 0.35/0.62      ! [B: int,W: nat,X: int] :
% 0.35/0.62        ( ( ord_less_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X ) )
% 0.35/0.62        = ( ord_less_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_less_of_int_power_cancel_iff
% 0.35/0.62  thf(fact_5806_of__int__less__of__int__power__cancel__iff,axiom,
% 0.35/0.62      ! [B: int,W: nat,X: int] :
% 0.35/0.62        ( ( ord_less_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X ) )
% 0.35/0.62        = ( ord_less_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_less_of_int_power_cancel_iff
% 0.35/0.62  thf(fact_5807_and__minus__numerals_I6_J,axiom,
% 0.35/0.62      ! [N: num] :
% 0.35/0.62        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 0.35/0.62        = one_one_int ) ).
% 0.35/0.62  
% 0.35/0.62  % and_minus_numerals(6)
% 0.35/0.62  thf(fact_5808_and__minus__numerals_I2_J,axiom,
% 0.35/0.62      ! [N: num] :
% 0.35/0.62        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.35/0.62        = one_one_int ) ).
% 0.35/0.62  
% 0.35/0.62  % and_minus_numerals(2)
% 0.35/0.62  thf(fact_5809_and__numerals_I6_J,axiom,
% 0.35/0.62      ! [X: num,Y2: num] :
% 0.35/0.62        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y2 ) ) )
% 0.35/0.62        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y2 ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % and_numerals(6)
% 0.35/0.62  thf(fact_5810_and__numerals_I6_J,axiom,
% 0.35/0.62      ! [X: num,Y2: num] :
% 0.35/0.62        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) )
% 0.35/0.62        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y2 ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % and_numerals(6)
% 0.35/0.62  thf(fact_5811_and__numerals_I4_J,axiom,
% 0.35/0.62      ! [X: num,Y2: num] :
% 0.35/0.62        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y2 ) ) )
% 0.35/0.62        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y2 ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % and_numerals(4)
% 0.35/0.62  thf(fact_5812_and__numerals_I4_J,axiom,
% 0.35/0.62      ! [X: num,Y2: num] :
% 0.35/0.62        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) )
% 0.35/0.62        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y2 ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % and_numerals(4)
% 0.35/0.62  thf(fact_5813_and__minus__numerals_I1_J,axiom,
% 0.35/0.62      ! [N: num] :
% 0.35/0.62        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.35/0.62        = zero_zero_int ) ).
% 0.35/0.62  
% 0.35/0.62  % and_minus_numerals(1)
% 0.35/0.62  thf(fact_5814_and__minus__numerals_I5_J,axiom,
% 0.35/0.62      ! [N: num] :
% 0.35/0.62        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 0.35/0.62        = zero_zero_int ) ).
% 0.35/0.62  
% 0.35/0.62  % and_minus_numerals(5)
% 0.35/0.62  thf(fact_5815_of__int__le__numeral__power__cancel__iff,axiom,
% 0.35/0.62      ! [A: int,X: num,N: nat] :
% 0.35/0.62        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 0.35/0.62        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_le_numeral_power_cancel_iff
% 0.35/0.62  thf(fact_5816_of__int__le__numeral__power__cancel__iff,axiom,
% 0.35/0.62      ! [A: int,X: num,N: nat] :
% 0.35/0.62        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 0.35/0.62        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_le_numeral_power_cancel_iff
% 0.35/0.62  thf(fact_5817_of__int__le__numeral__power__cancel__iff,axiom,
% 0.35/0.62      ! [A: int,X: num,N: nat] :
% 0.35/0.62        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 0.35/0.62        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_le_numeral_power_cancel_iff
% 0.35/0.62  thf(fact_5818_numeral__power__le__of__int__cancel__iff,axiom,
% 0.35/0.62      ! [X: num,N: nat,A: int] :
% 0.35/0.62        ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 0.35/0.62        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % numeral_power_le_of_int_cancel_iff
% 0.35/0.62  thf(fact_5819_numeral__power__le__of__int__cancel__iff,axiom,
% 0.35/0.62      ! [X: num,N: nat,A: int] :
% 0.35/0.62        ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 0.35/0.62        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % numeral_power_le_of_int_cancel_iff
% 0.35/0.62  thf(fact_5820_numeral__power__le__of__int__cancel__iff,axiom,
% 0.35/0.62      ! [X: num,N: nat,A: int] :
% 0.35/0.62        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 0.35/0.62        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % numeral_power_le_of_int_cancel_iff
% 0.35/0.62  thf(fact_5821_of__int__less__numeral__power__cancel__iff,axiom,
% 0.35/0.62      ! [A: int,X: num,N: nat] :
% 0.35/0.62        ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 0.35/0.62        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_less_numeral_power_cancel_iff
% 0.35/0.62  thf(fact_5822_of__int__less__numeral__power__cancel__iff,axiom,
% 0.35/0.62      ! [A: int,X: num,N: nat] :
% 0.35/0.62        ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 0.35/0.62        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_less_numeral_power_cancel_iff
% 0.35/0.62  thf(fact_5823_of__int__less__numeral__power__cancel__iff,axiom,
% 0.35/0.62      ! [A: int,X: num,N: nat] :
% 0.35/0.62        ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 0.35/0.62        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_less_numeral_power_cancel_iff
% 0.35/0.62  thf(fact_5824_numeral__power__less__of__int__cancel__iff,axiom,
% 0.35/0.62      ! [X: num,N: nat,A: int] :
% 0.35/0.62        ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 0.35/0.62        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % numeral_power_less_of_int_cancel_iff
% 0.35/0.62  thf(fact_5825_numeral__power__less__of__int__cancel__iff,axiom,
% 0.35/0.62      ! [X: num,N: nat,A: int] :
% 0.35/0.62        ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 0.35/0.62        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % numeral_power_less_of_int_cancel_iff
% 0.35/0.62  thf(fact_5826_numeral__power__less__of__int__cancel__iff,axiom,
% 0.35/0.62      ! [X: num,N: nat,A: int] :
% 0.35/0.62        ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 0.35/0.62        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % numeral_power_less_of_int_cancel_iff
% 0.35/0.62  thf(fact_5827_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 0.35/0.62      ! [Y2: int,X: num,N: nat] :
% 0.35/0.62        ( ( ( ring_1_of_int_int @ Y2 )
% 0.35/0.62          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 0.35/0.62        = ( Y2
% 0.35/0.62          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_eq_neg_numeral_power_cancel_iff
% 0.35/0.62  thf(fact_5828_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 0.35/0.62      ! [Y2: int,X: num,N: nat] :
% 0.35/0.62        ( ( ( ring_1_of_int_real @ Y2 )
% 0.35/0.62          = ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) )
% 0.35/0.62        = ( Y2
% 0.35/0.62          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_eq_neg_numeral_power_cancel_iff
% 0.35/0.62  thf(fact_5829_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 0.35/0.62      ! [Y2: int,X: num,N: nat] :
% 0.35/0.62        ( ( ( ring_17405671764205052669omplex @ Y2 )
% 0.35/0.62          = ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X ) ) @ N ) )
% 0.35/0.62        = ( Y2
% 0.35/0.62          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_eq_neg_numeral_power_cancel_iff
% 0.35/0.62  thf(fact_5830_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 0.35/0.62      ! [Y2: int,X: num,N: nat] :
% 0.35/0.62        ( ( ( ring_18347121197199848620nteger @ Y2 )
% 0.35/0.62          = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 0.35/0.62        = ( Y2
% 0.35/0.62          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_eq_neg_numeral_power_cancel_iff
% 0.35/0.62  thf(fact_5831_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 0.35/0.62      ! [Y2: int,X: num,N: nat] :
% 0.35/0.62        ( ( ( ring_1_of_int_rat @ Y2 )
% 0.35/0.62          = ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 0.35/0.62        = ( Y2
% 0.35/0.62          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_eq_neg_numeral_power_cancel_iff
% 0.35/0.62  thf(fact_5832_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 0.35/0.62      ! [X: num,N: nat,Y2: int] :
% 0.35/0.62        ( ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 0.35/0.62          = ( ring_1_of_int_int @ Y2 ) )
% 0.35/0.62        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 0.35/0.62          = Y2 ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_numeral_power_eq_of_int_cancel_iff
% 0.35/0.62  thf(fact_5833_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 0.35/0.62      ! [X: num,N: nat,Y2: int] :
% 0.35/0.62        ( ( ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N )
% 0.35/0.62          = ( ring_1_of_int_real @ Y2 ) )
% 0.35/0.62        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 0.35/0.62          = Y2 ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_numeral_power_eq_of_int_cancel_iff
% 0.35/0.62  thf(fact_5834_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 0.35/0.62      ! [X: num,N: nat,Y2: int] :
% 0.35/0.62        ( ( ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X ) ) @ N )
% 0.35/0.62          = ( ring_17405671764205052669omplex @ Y2 ) )
% 0.35/0.62        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 0.35/0.62          = Y2 ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_numeral_power_eq_of_int_cancel_iff
% 0.35/0.62  thf(fact_5835_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 0.35/0.62      ! [X: num,N: nat,Y2: int] :
% 0.35/0.62        ( ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N )
% 0.35/0.62          = ( ring_18347121197199848620nteger @ Y2 ) )
% 0.35/0.62        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 0.35/0.62          = Y2 ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_numeral_power_eq_of_int_cancel_iff
% 0.35/0.62  thf(fact_5836_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 0.35/0.62      ! [X: num,N: nat,Y2: int] :
% 0.35/0.62        ( ( ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N )
% 0.35/0.62          = ( ring_1_of_int_rat @ Y2 ) )
% 0.35/0.62        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 0.35/0.62          = Y2 ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_numeral_power_eq_of_int_cancel_iff
% 0.35/0.62  thf(fact_5837_and__numerals_I7_J,axiom,
% 0.35/0.62      ! [X: num,Y2: num] :
% 0.35/0.62        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y2 ) ) )
% 0.35/0.62        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y2 ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % and_numerals(7)
% 0.35/0.62  thf(fact_5838_and__numerals_I7_J,axiom,
% 0.35/0.62      ! [X: num,Y2: num] :
% 0.35/0.62        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) )
% 0.35/0.62        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y2 ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % and_numerals(7)
% 0.35/0.62  thf(fact_5839_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 0.35/0.62      ! [A: int,X: num,N: nat] :
% 0.35/0.62        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) )
% 0.35/0.62        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_le_neg_numeral_power_cancel_iff
% 0.35/0.62  thf(fact_5840_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 0.35/0.62      ! [A: int,X: num,N: nat] :
% 0.35/0.62        ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 0.35/0.62        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_le_neg_numeral_power_cancel_iff
% 0.35/0.62  thf(fact_5841_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 0.35/0.62      ! [A: int,X: num,N: nat] :
% 0.35/0.62        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 0.35/0.62        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_le_neg_numeral_power_cancel_iff
% 0.35/0.62  thf(fact_5842_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 0.35/0.62      ! [A: int,X: num,N: nat] :
% 0.35/0.62        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 0.35/0.62        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_le_neg_numeral_power_cancel_iff
% 0.35/0.62  thf(fact_5843_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 0.35/0.62      ! [X: num,N: nat,A: int] :
% 0.35/0.62        ( ( ord_less_eq_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 0.35/0.62        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_numeral_power_le_of_int_cancel_iff
% 0.35/0.62  thf(fact_5844_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 0.35/0.62      ! [X: num,N: nat,A: int] :
% 0.35/0.62        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 0.35/0.62        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_numeral_power_le_of_int_cancel_iff
% 0.35/0.62  thf(fact_5845_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 0.35/0.62      ! [X: num,N: nat,A: int] :
% 0.35/0.62        ( ( ord_less_eq_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 0.35/0.62        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_numeral_power_le_of_int_cancel_iff
% 0.35/0.62  thf(fact_5846_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 0.35/0.62      ! [X: num,N: nat,A: int] :
% 0.35/0.62        ( ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 0.35/0.62        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_numeral_power_le_of_int_cancel_iff
% 0.35/0.62  thf(fact_5847_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 0.35/0.62      ! [A: int,X: num,N: nat] :
% 0.35/0.62        ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 0.35/0.62        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_less_neg_numeral_power_cancel_iff
% 0.35/0.62  thf(fact_5848_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 0.35/0.62      ! [A: int,X: num,N: nat] :
% 0.35/0.62        ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) )
% 0.35/0.62        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_less_neg_numeral_power_cancel_iff
% 0.35/0.62  thf(fact_5849_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 0.35/0.62      ! [A: int,X: num,N: nat] :
% 0.35/0.62        ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 0.35/0.62        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_less_neg_numeral_power_cancel_iff
% 0.35/0.62  thf(fact_5850_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 0.35/0.62      ! [A: int,X: num,N: nat] :
% 0.35/0.62        ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 0.35/0.62        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_less_neg_numeral_power_cancel_iff
% 0.35/0.62  thf(fact_5851_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 0.35/0.62      ! [X: num,N: nat,A: int] :
% 0.35/0.62        ( ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 0.35/0.62        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_numeral_power_less_of_int_cancel_iff
% 0.35/0.62  thf(fact_5852_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 0.35/0.62      ! [X: num,N: nat,A: int] :
% 0.35/0.62        ( ( ord_less_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 0.35/0.62        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_numeral_power_less_of_int_cancel_iff
% 0.35/0.62  thf(fact_5853_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 0.35/0.62      ! [X: num,N: nat,A: int] :
% 0.35/0.62        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 0.35/0.62        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_numeral_power_less_of_int_cancel_iff
% 0.35/0.62  thf(fact_5854_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 0.35/0.62      ! [X: num,N: nat,A: int] :
% 0.35/0.62        ( ( ord_less_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 0.35/0.62        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % neg_numeral_power_less_of_int_cancel_iff
% 0.35/0.62  thf(fact_5855_of__int__and__eq,axiom,
% 0.35/0.62      ! [K: int,L2: int] :
% 0.35/0.62        ( ( ring_1_of_int_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) )
% 0.35/0.62        = ( bit_se725231765392027082nd_int @ ( ring_1_of_int_int @ K ) @ ( ring_1_of_int_int @ L2 ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_and_eq
% 0.35/0.62  thf(fact_5856_and_Oassoc,axiom,
% 0.35/0.62      ! [A: int,B: int,C: int] :
% 0.35/0.62        ( ( bit_se725231765392027082nd_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ C )
% 0.35/0.62        = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ B @ C ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % and.assoc
% 0.35/0.62  thf(fact_5857_and_Oassoc,axiom,
% 0.35/0.62      ! [A: nat,B: nat,C: nat] :
% 0.35/0.62        ( ( bit_se727722235901077358nd_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ C )
% 0.35/0.62        = ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ B @ C ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % and.assoc
% 0.35/0.62  thf(fact_5858_and_Ocommute,axiom,
% 0.35/0.62      ( bit_se725231765392027082nd_int
% 0.35/0.62      = ( ^ [A3: int,B4: int] : ( bit_se725231765392027082nd_int @ B4 @ A3 ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % and.commute
% 0.35/0.62  thf(fact_5859_and_Ocommute,axiom,
% 0.35/0.62      ( bit_se727722235901077358nd_nat
% 0.35/0.62      = ( ^ [A3: nat,B4: nat] : ( bit_se727722235901077358nd_nat @ B4 @ A3 ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % and.commute
% 0.35/0.62  thf(fact_5860_and_Oleft__commute,axiom,
% 0.35/0.62      ! [B: int,A: int,C: int] :
% 0.35/0.62        ( ( bit_se725231765392027082nd_int @ B @ ( bit_se725231765392027082nd_int @ A @ C ) )
% 0.35/0.62        = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ B @ C ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % and.left_commute
% 0.35/0.62  thf(fact_5861_and_Oleft__commute,axiom,
% 0.35/0.62      ! [B: nat,A: nat,C: nat] :
% 0.35/0.62        ( ( bit_se727722235901077358nd_nat @ B @ ( bit_se727722235901077358nd_nat @ A @ C ) )
% 0.35/0.62        = ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ B @ C ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % and.left_commute
% 0.35/0.62  thf(fact_5862_mult__of__int__commute,axiom,
% 0.35/0.62      ! [X: int,Y2: complex] :
% 0.35/0.62        ( ( times_times_complex @ ( ring_17405671764205052669omplex @ X ) @ Y2 )
% 0.35/0.62        = ( times_times_complex @ Y2 @ ( ring_17405671764205052669omplex @ X ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % mult_of_int_commute
% 0.35/0.62  thf(fact_5863_mult__of__int__commute,axiom,
% 0.35/0.62      ! [X: int,Y2: real] :
% 0.35/0.62        ( ( times_times_real @ ( ring_1_of_int_real @ X ) @ Y2 )
% 0.35/0.62        = ( times_times_real @ Y2 @ ( ring_1_of_int_real @ X ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % mult_of_int_commute
% 0.35/0.62  thf(fact_5864_mult__of__int__commute,axiom,
% 0.35/0.62      ! [X: int,Y2: int] :
% 0.35/0.62        ( ( times_times_int @ ( ring_1_of_int_int @ X ) @ Y2 )
% 0.35/0.62        = ( times_times_int @ Y2 @ ( ring_1_of_int_int @ X ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % mult_of_int_commute
% 0.35/0.62  thf(fact_5865_bot__nat__def,axiom,
% 0.35/0.62      bot_bot_nat = zero_zero_nat ).
% 0.35/0.62  
% 0.35/0.62  % bot_nat_def
% 0.35/0.62  thf(fact_5866_bot__enat__def,axiom,
% 0.35/0.62      bot_bo4199563552545308370d_enat = zero_z5237406670263579293d_enat ).
% 0.35/0.62  
% 0.35/0.62  % bot_enat_def
% 0.35/0.62  thf(fact_5867_and__eq__minus__1__iff,axiom,
% 0.35/0.62      ! [A: code_integer,B: code_integer] :
% 0.35/0.62        ( ( ( bit_se3949692690581998587nteger @ A @ B )
% 0.35/0.62          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.62        = ( ( A
% 0.35/0.62            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.62          & ( B
% 0.35/0.62            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % and_eq_minus_1_iff
% 0.35/0.62  thf(fact_5868_and__eq__minus__1__iff,axiom,
% 0.35/0.62      ! [A: int,B: int] :
% 0.35/0.62        ( ( ( bit_se725231765392027082nd_int @ A @ B )
% 0.35/0.62          = ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.62        = ( ( A
% 0.35/0.62            = ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.62          & ( B
% 0.35/0.62            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % and_eq_minus_1_iff
% 0.35/0.62  thf(fact_5869_AND__lower,axiom,
% 0.35/0.62      ! [X: int,Y2: int] :
% 0.35/0.62        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.35/0.62       => ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ X @ Y2 ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % AND_lower
% 0.35/0.62  thf(fact_5870_AND__upper1,axiom,
% 0.35/0.62      ! [X: int,Y2: int] :
% 0.35/0.62        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.35/0.62       => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y2 ) @ X ) ) ).
% 0.35/0.62  
% 0.35/0.62  % AND_upper1
% 0.35/0.62  thf(fact_5871_AND__upper2,axiom,
% 0.35/0.62      ! [Y2: int,X: int] :
% 0.35/0.62        ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 0.35/0.62       => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y2 ) @ Y2 ) ) ).
% 0.35/0.62  
% 0.35/0.62  % AND_upper2
% 0.35/0.62  thf(fact_5872_AND__upper1_H,axiom,
% 0.35/0.62      ! [Y2: int,Z: int,Ya: int] :
% 0.35/0.62        ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 0.35/0.62       => ( ( ord_less_eq_int @ Y2 @ Z )
% 0.35/0.62         => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ Y2 @ Ya ) @ Z ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % AND_upper1'
% 0.35/0.62  thf(fact_5873_AND__upper2_H,axiom,
% 0.35/0.62      ! [Y2: int,Z: int,X: int] :
% 0.35/0.62        ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 0.35/0.62       => ( ( ord_less_eq_int @ Y2 @ Z )
% 0.35/0.62         => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y2 ) @ Z ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % AND_upper2'
% 0.35/0.62  thf(fact_5874_and__less__eq,axiom,
% 0.35/0.62      ! [L2: int,K: int] :
% 0.35/0.62        ( ( ord_less_int @ L2 @ zero_zero_int )
% 0.35/0.62       => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) @ K ) ) ).
% 0.35/0.62  
% 0.35/0.62  % and_less_eq
% 0.35/0.62  thf(fact_5875_AND__upper1_H_H,axiom,
% 0.35/0.62      ! [Y2: int,Z: int,Ya: int] :
% 0.35/0.62        ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 0.35/0.62       => ( ( ord_less_int @ Y2 @ Z )
% 0.35/0.62         => ( ord_less_int @ ( bit_se725231765392027082nd_int @ Y2 @ Ya ) @ Z ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % AND_upper1''
% 0.35/0.62  thf(fact_5876_AND__upper2_H_H,axiom,
% 0.35/0.62      ! [Y2: int,Z: int,X: int] :
% 0.35/0.62        ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 0.35/0.62       => ( ( ord_less_int @ Y2 @ Z )
% 0.35/0.62         => ( ord_less_int @ ( bit_se725231765392027082nd_int @ X @ Y2 ) @ Z ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % AND_upper2''
% 0.35/0.62  thf(fact_5877_real__of__int__div4,axiom,
% 0.35/0.62      ! [N: int,X: int] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % real_of_int_div4
% 0.35/0.62  thf(fact_5878_real__of__int__div,axiom,
% 0.35/0.62      ! [D2: int,N: int] :
% 0.35/0.62        ( ( dvd_dvd_int @ D2 @ N )
% 0.35/0.62       => ( ( ring_1_of_int_real @ ( divide_divide_int @ N @ D2 ) )
% 0.35/0.62          = ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ D2 ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % real_of_int_div
% 0.35/0.62  thf(fact_5879_even__and__iff,axiom,
% 0.35/0.62      ! [A: code_integer,B: code_integer] :
% 0.35/0.62        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ A @ B ) )
% 0.35/0.62        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.35/0.62          | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % even_and_iff
% 0.35/0.62  thf(fact_5880_even__and__iff,axiom,
% 0.35/0.62      ! [A: int,B: int] :
% 0.35/0.62        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 0.35/0.62        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.62          | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % even_and_iff
% 0.35/0.62  thf(fact_5881_even__and__iff,axiom,
% 0.35/0.62      ! [A: nat,B: nat] :
% 0.35/0.62        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 0.35/0.62        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.62          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % even_and_iff
% 0.35/0.62  thf(fact_5882_of__int__nonneg,axiom,
% 0.35/0.62      ! [Z: int] :
% 0.35/0.62        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.35/0.62       => ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_nonneg
% 0.35/0.62  thf(fact_5883_of__int__nonneg,axiom,
% 0.35/0.62      ! [Z: int] :
% 0.35/0.62        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.35/0.62       => ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_nonneg
% 0.35/0.62  thf(fact_5884_of__int__nonneg,axiom,
% 0.35/0.62      ! [Z: int] :
% 0.35/0.62        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.35/0.62       => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_nonneg
% 0.35/0.62  thf(fact_5885_even__and__iff__int,axiom,
% 0.35/0.62      ! [K: int,L2: int] :
% 0.35/0.62        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ K @ L2 ) )
% 0.35/0.62        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 0.35/0.62          | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % even_and_iff_int
% 0.35/0.62  thf(fact_5886_of__int__pos,axiom,
% 0.35/0.62      ! [Z: int] :
% 0.35/0.62        ( ( ord_less_int @ zero_zero_int @ Z )
% 0.35/0.62       => ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_pos
% 0.35/0.62  thf(fact_5887_of__int__pos,axiom,
% 0.35/0.62      ! [Z: int] :
% 0.35/0.62        ( ( ord_less_int @ zero_zero_int @ Z )
% 0.35/0.62       => ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_pos
% 0.35/0.62  thf(fact_5888_of__int__pos,axiom,
% 0.35/0.62      ! [Z: int] :
% 0.35/0.62        ( ( ord_less_int @ zero_zero_int @ Z )
% 0.35/0.62       => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_pos
% 0.35/0.62  thf(fact_5889_of__int__neg__numeral,axiom,
% 0.35/0.62      ! [K: num] :
% 0.35/0.62        ( ( ring_1_of_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.35/0.62        = ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_neg_numeral
% 0.35/0.62  thf(fact_5890_of__int__neg__numeral,axiom,
% 0.35/0.62      ! [K: num] :
% 0.35/0.62        ( ( ring_1_of_int_real @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.35/0.62        = ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_neg_numeral
% 0.35/0.62  thf(fact_5891_of__int__neg__numeral,axiom,
% 0.35/0.62      ! [K: num] :
% 0.35/0.62        ( ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.35/0.62        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_neg_numeral
% 0.35/0.62  thf(fact_5892_of__int__neg__numeral,axiom,
% 0.35/0.62      ! [K: num] :
% 0.35/0.62        ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.35/0.62        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_neg_numeral
% 0.35/0.62  thf(fact_5893_of__int__neg__numeral,axiom,
% 0.35/0.62      ! [K: num] :
% 0.35/0.62        ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.35/0.62        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_neg_numeral
% 0.35/0.62  thf(fact_5894_int__le__real__less,axiom,
% 0.35/0.62      ( ord_less_eq_int
% 0.35/0.62      = ( ^ [N2: int,M6: int] : ( ord_less_real @ ( ring_1_of_int_real @ N2 ) @ ( plus_plus_real @ ( ring_1_of_int_real @ M6 ) @ one_one_real ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % int_le_real_less
% 0.35/0.62  thf(fact_5895_int__less__real__le,axiom,
% 0.35/0.62      ( ord_less_int
% 0.35/0.62      = ( ^ [N2: int,M6: int] : ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) @ ( ring_1_of_int_real @ M6 ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % int_less_real_le
% 0.35/0.62  thf(fact_5896_real__of__int__div__aux,axiom,
% 0.35/0.62      ! [X: int,D2: int] :
% 0.35/0.62        ( ( divide_divide_real @ ( ring_1_of_int_real @ X ) @ ( ring_1_of_int_real @ D2 ) )
% 0.35/0.62        = ( plus_plus_real @ ( ring_1_of_int_real @ ( divide_divide_int @ X @ D2 ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ ( modulo_modulo_int @ X @ D2 ) ) @ ( ring_1_of_int_real @ D2 ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % real_of_int_div_aux
% 0.35/0.62  thf(fact_5897_and__one__eq,axiom,
% 0.35/0.62      ! [A: int] :
% 0.35/0.62        ( ( bit_se725231765392027082nd_int @ A @ one_one_int )
% 0.35/0.62        = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % and_one_eq
% 0.35/0.62  thf(fact_5898_and__one__eq,axiom,
% 0.35/0.62      ! [A: nat] :
% 0.35/0.62        ( ( bit_se727722235901077358nd_nat @ A @ one_one_nat )
% 0.35/0.62        = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % and_one_eq
% 0.35/0.62  thf(fact_5899_one__and__eq,axiom,
% 0.35/0.62      ! [A: int] :
% 0.35/0.62        ( ( bit_se725231765392027082nd_int @ one_one_int @ A )
% 0.35/0.62        = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % one_and_eq
% 0.35/0.62  thf(fact_5900_one__and__eq,axiom,
% 0.35/0.62      ! [A: nat] :
% 0.35/0.62        ( ( bit_se727722235901077358nd_nat @ one_one_nat @ A )
% 0.35/0.62        = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % one_and_eq
% 0.35/0.62  thf(fact_5901_real__of__int__div2,axiom,
% 0.35/0.62      ! [N: int,X: int] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % real_of_int_div2
% 0.35/0.62  thf(fact_5902_real__of__int__div3,axiom,
% 0.35/0.62      ! [N: int,X: int] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X ) ) ) @ one_one_real ) ).
% 0.35/0.62  
% 0.35/0.62  % real_of_int_div3
% 0.35/0.62  thf(fact_5903_even__of__int__iff,axiom,
% 0.35/0.62      ! [K: int] :
% 0.35/0.62        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ K ) )
% 0.35/0.62        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 0.35/0.62  
% 0.35/0.62  % even_of_int_iff
% 0.35/0.62  thf(fact_5904_even__of__int__iff,axiom,
% 0.35/0.62      ! [K: int] :
% 0.35/0.62        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ K ) )
% 0.35/0.62        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 0.35/0.62  
% 0.35/0.62  % even_of_int_iff
% 0.35/0.62  thf(fact_5905_dbl__dec__def,axiom,
% 0.35/0.62      ( neg_nu6075765906172075777c_real
% 0.35/0.62      = ( ^ [X2: real] : ( minus_minus_real @ ( plus_plus_real @ X2 @ X2 ) @ one_one_real ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dbl_dec_def
% 0.35/0.62  thf(fact_5906_dbl__dec__def,axiom,
% 0.35/0.62      ( neg_nu6511756317524482435omplex
% 0.35/0.62      = ( ^ [X2: complex] : ( minus_minus_complex @ ( plus_plus_complex @ X2 @ X2 ) @ one_one_complex ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dbl_dec_def
% 0.35/0.62  thf(fact_5907_dbl__dec__def,axiom,
% 0.35/0.62      ( neg_nu3179335615603231917ec_rat
% 0.35/0.62      = ( ^ [X2: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X2 @ X2 ) @ one_one_rat ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dbl_dec_def
% 0.35/0.62  thf(fact_5908_dbl__dec__def,axiom,
% 0.35/0.62      ( neg_nu3811975205180677377ec_int
% 0.35/0.62      = ( ^ [X2: int] : ( minus_minus_int @ ( plus_plus_int @ X2 @ X2 ) @ one_one_int ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % dbl_dec_def
% 0.35/0.62  thf(fact_5909_compl__le__swap2,axiom,
% 0.35/0.62      ! [Y2: set_real,X: set_real] :
% 0.35/0.62        ( ( ord_less_eq_set_real @ ( uminus612125837232591019t_real @ Y2 ) @ X )
% 0.35/0.62       => ( ord_less_eq_set_real @ ( uminus612125837232591019t_real @ X ) @ Y2 ) ) ).
% 0.35/0.62  
% 0.35/0.62  % compl_le_swap2
% 0.35/0.62  thf(fact_5910_compl__le__swap2,axiom,
% 0.35/0.62      ! [Y2: set_nat,X: set_nat] :
% 0.35/0.62        ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y2 ) @ X )
% 0.35/0.62       => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ Y2 ) ) ).
% 0.35/0.62  
% 0.35/0.62  % compl_le_swap2
% 0.35/0.62  thf(fact_5911_compl__le__swap1,axiom,
% 0.35/0.62      ! [Y2: set_real,X: set_real] :
% 0.35/0.62        ( ( ord_less_eq_set_real @ Y2 @ ( uminus612125837232591019t_real @ X ) )
% 0.35/0.62       => ( ord_less_eq_set_real @ X @ ( uminus612125837232591019t_real @ Y2 ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % compl_le_swap1
% 0.35/0.62  thf(fact_5912_compl__le__swap1,axiom,
% 0.35/0.62      ! [Y2: set_nat,X: set_nat] :
% 0.35/0.62        ( ( ord_less_eq_set_nat @ Y2 @ ( uminus5710092332889474511et_nat @ X ) )
% 0.35/0.62       => ( ord_less_eq_set_nat @ X @ ( uminus5710092332889474511et_nat @ Y2 ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % compl_le_swap1
% 0.35/0.62  thf(fact_5913_compl__mono,axiom,
% 0.35/0.62      ! [X: set_real,Y2: set_real] :
% 0.35/0.62        ( ( ord_less_eq_set_real @ X @ Y2 )
% 0.35/0.62       => ( ord_less_eq_set_real @ ( uminus612125837232591019t_real @ Y2 ) @ ( uminus612125837232591019t_real @ X ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % compl_mono
% 0.35/0.62  thf(fact_5914_compl__mono,axiom,
% 0.35/0.62      ! [X: set_nat,Y2: set_nat] :
% 0.35/0.62        ( ( ord_less_eq_set_nat @ X @ Y2 )
% 0.35/0.62       => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y2 ) @ ( uminus5710092332889474511et_nat @ X ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % compl_mono
% 0.35/0.62  thf(fact_5915_and__int__rec,axiom,
% 0.35/0.62      ( bit_se725231765392027082nd_int
% 0.35/0.62      = ( ^ [K3: int,L: int] :
% 0.35/0.62            ( plus_plus_int
% 0.35/0.62            @ ( zero_n2684676970156552555ol_int
% 0.35/0.62              @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 0.35/0.62                & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 0.35/0.62            @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % and_int_rec
% 0.35/0.62  thf(fact_5916_and__int__unfold,axiom,
% 0.35/0.62      ( bit_se725231765392027082nd_int
% 0.35/0.62      = ( ^ [K3: int,L: int] :
% 0.35/0.62            ( if_int
% 0.35/0.62            @ ( ( K3 = zero_zero_int )
% 0.35/0.62              | ( L = zero_zero_int ) )
% 0.35/0.62            @ zero_zero_int
% 0.35/0.62            @ ( if_int
% 0.35/0.62              @ ( K3
% 0.35/0.62                = ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.62              @ L
% 0.35/0.62              @ ( if_int
% 0.35/0.62                @ ( L
% 0.35/0.62                  = ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.62                @ K3
% 0.35/0.62                @ ( plus_plus_int @ ( times_times_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % and_int_unfold
% 0.35/0.62  thf(fact_5917_floor__exists1,axiom,
% 0.35/0.62      ! [X: real] :
% 0.35/0.62      ? [X3: int] :
% 0.35/0.62        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X3 ) @ X )
% 0.35/0.62        & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ X3 @ one_one_int ) ) )
% 0.35/0.62        & ! [Y4: int] :
% 0.35/0.62            ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y4 ) @ X )
% 0.35/0.62              & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Y4 @ one_one_int ) ) ) )
% 0.35/0.62           => ( Y4 = X3 ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % floor_exists1
% 0.35/0.62  thf(fact_5918_floor__exists1,axiom,
% 0.35/0.62      ! [X: rat] :
% 0.35/0.62      ? [X3: int] :
% 0.35/0.62        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X3 ) @ X )
% 0.35/0.62        & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ X3 @ one_one_int ) ) )
% 0.35/0.62        & ! [Y4: int] :
% 0.35/0.62            ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y4 ) @ X )
% 0.35/0.62              & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Y4 @ one_one_int ) ) ) )
% 0.35/0.62           => ( Y4 = X3 ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % floor_exists1
% 0.35/0.62  thf(fact_5919_floor__exists,axiom,
% 0.35/0.62      ! [X: real] :
% 0.35/0.62      ? [Z3: int] :
% 0.35/0.62        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z3 ) @ X )
% 0.35/0.62        & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % floor_exists
% 0.35/0.62  thf(fact_5920_floor__exists,axiom,
% 0.35/0.62      ! [X: rat] :
% 0.35/0.62      ? [Z3: int] :
% 0.35/0.62        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z3 ) @ X )
% 0.35/0.62        & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % floor_exists
% 0.35/0.62  thf(fact_5921_and__int_Opelims,axiom,
% 0.35/0.62      ! [X: int,Xa2: int,Y2: int] :
% 0.35/0.62        ( ( ( bit_se725231765392027082nd_int @ X @ Xa2 )
% 0.35/0.62          = Y2 )
% 0.35/0.62       => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa2 ) )
% 0.35/0.62         => ~ ( ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.35/0.62                    & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.35/0.62                 => ( Y2
% 0.35/0.62                    = ( uminus_uminus_int
% 0.35/0.62                      @ ( zero_n2684676970156552555ol_int
% 0.35/0.62                        @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 0.35/0.62                          & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 0.35/0.62                & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.35/0.62                      & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.35/0.62                 => ( Y2
% 0.35/0.62                    = ( plus_plus_int
% 0.35/0.62                      @ ( zero_n2684676970156552555ol_int
% 0.35/0.62                        @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 0.35/0.62                          & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 0.35/0.62                      @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 0.35/0.62             => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa2 ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % and_int.pelims
% 0.35/0.62  thf(fact_5922_and__int_Opsimps,axiom,
% 0.35/0.62      ! [K: int,L2: int] :
% 0.35/0.62        ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L2 ) )
% 0.35/0.62       => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.35/0.62              & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.35/0.62           => ( ( bit_se725231765392027082nd_int @ K @ L2 )
% 0.35/0.62              = ( uminus_uminus_int
% 0.35/0.62                @ ( zero_n2684676970156552555ol_int
% 0.35/0.62                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 0.35/0.62                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) ) ) )
% 0.35/0.62          & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.35/0.62                & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.35/0.62           => ( ( bit_se725231765392027082nd_int @ K @ L2 )
% 0.35/0.62              = ( plus_plus_int
% 0.35/0.62                @ ( zero_n2684676970156552555ol_int
% 0.35/0.62                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 0.35/0.62                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 0.35/0.62                @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % and_int.psimps
% 0.35/0.62  thf(fact_5923_ln__one__minus__pos__lower__bound,axiom,
% 0.35/0.62      ! [X: real] :
% 0.35/0.62        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.62       => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.62         => ( ord_less_eq_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % ln_one_minus_pos_lower_bound
% 0.35/0.62  thf(fact_5924_add__scale__eq__noteq,axiom,
% 0.35/0.62      ! [R: rat,A: rat,B: rat,C: rat,D2: rat] :
% 0.35/0.62        ( ( R != zero_zero_rat )
% 0.35/0.62       => ( ( ( A = B )
% 0.35/0.62            & ( C != D2 ) )
% 0.35/0.62         => ( ( plus_plus_rat @ A @ ( times_times_rat @ R @ C ) )
% 0.35/0.62           != ( plus_plus_rat @ B @ ( times_times_rat @ R @ D2 ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % add_scale_eq_noteq
% 0.35/0.62  thf(fact_5925_add__scale__eq__noteq,axiom,
% 0.35/0.62      ! [R: complex,A: complex,B: complex,C: complex,D2: complex] :
% 0.35/0.62        ( ( R != zero_zero_complex )
% 0.35/0.62       => ( ( ( A = B )
% 0.35/0.62            & ( C != D2 ) )
% 0.35/0.62         => ( ( plus_plus_complex @ A @ ( times_times_complex @ R @ C ) )
% 0.35/0.62           != ( plus_plus_complex @ B @ ( times_times_complex @ R @ D2 ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % add_scale_eq_noteq
% 0.35/0.62  thf(fact_5926_add__scale__eq__noteq,axiom,
% 0.35/0.62      ! [R: real,A: real,B: real,C: real,D2: real] :
% 0.35/0.62        ( ( R != zero_zero_real )
% 0.35/0.62       => ( ( ( A = B )
% 0.35/0.62            & ( C != D2 ) )
% 0.35/0.62         => ( ( plus_plus_real @ A @ ( times_times_real @ R @ C ) )
% 0.35/0.62           != ( plus_plus_real @ B @ ( times_times_real @ R @ D2 ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % add_scale_eq_noteq
% 0.35/0.62  thf(fact_5927_add__scale__eq__noteq,axiom,
% 0.35/0.62      ! [R: nat,A: nat,B: nat,C: nat,D2: nat] :
% 0.35/0.62        ( ( R != zero_zero_nat )
% 0.35/0.62       => ( ( ( A = B )
% 0.35/0.62            & ( C != D2 ) )
% 0.35/0.62         => ( ( plus_plus_nat @ A @ ( times_times_nat @ R @ C ) )
% 0.35/0.62           != ( plus_plus_nat @ B @ ( times_times_nat @ R @ D2 ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % add_scale_eq_noteq
% 0.35/0.62  thf(fact_5928_add__scale__eq__noteq,axiom,
% 0.35/0.62      ! [R: int,A: int,B: int,C: int,D2: int] :
% 0.35/0.62        ( ( R != zero_zero_int )
% 0.35/0.62       => ( ( ( A = B )
% 0.35/0.62            & ( C != D2 ) )
% 0.35/0.62         => ( ( plus_plus_int @ A @ ( times_times_int @ R @ C ) )
% 0.35/0.62           != ( plus_plus_int @ B @ ( times_times_int @ R @ D2 ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % add_scale_eq_noteq
% 0.35/0.62  thf(fact_5929_ln__one,axiom,
% 0.35/0.62      ( ( ln_ln_real @ one_one_real )
% 0.35/0.62      = zero_zero_real ) ).
% 0.35/0.62  
% 0.35/0.62  % ln_one
% 0.35/0.62  thf(fact_5930_ln__less__cancel__iff,axiom,
% 0.35/0.62      ! [X: real,Y2: real] :
% 0.35/0.62        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.62       => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 0.35/0.62         => ( ( ord_less_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y2 ) )
% 0.35/0.62            = ( ord_less_real @ X @ Y2 ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % ln_less_cancel_iff
% 0.35/0.62  thf(fact_5931_ln__inj__iff,axiom,
% 0.35/0.62      ! [X: real,Y2: real] :
% 0.35/0.62        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.62       => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 0.35/0.62         => ( ( ( ln_ln_real @ X )
% 0.35/0.62              = ( ln_ln_real @ Y2 ) )
% 0.35/0.62            = ( X = Y2 ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % ln_inj_iff
% 0.35/0.62  thf(fact_5932_and__nat__numerals_I1_J,axiom,
% 0.35/0.62      ! [Y2: num] :
% 0.35/0.62        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) )
% 0.35/0.62        = zero_zero_nat ) ).
% 0.35/0.62  
% 0.35/0.62  % and_nat_numerals(1)
% 0.35/0.62  thf(fact_5933_and__nat__numerals_I3_J,axiom,
% 0.35/0.62      ! [X: num] :
% 0.35/0.62        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 0.35/0.62        = zero_zero_nat ) ).
% 0.35/0.62  
% 0.35/0.62  % and_nat_numerals(3)
% 0.35/0.62  thf(fact_5934_ln__le__cancel__iff,axiom,
% 0.35/0.62      ! [X: real,Y2: real] :
% 0.35/0.62        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.62       => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 0.35/0.62         => ( ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y2 ) )
% 0.35/0.62            = ( ord_less_eq_real @ X @ Y2 ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % ln_le_cancel_iff
% 0.35/0.62  thf(fact_5935_ln__eq__zero__iff,axiom,
% 0.35/0.62      ! [X: real] :
% 0.35/0.62        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.62       => ( ( ( ln_ln_real @ X )
% 0.35/0.62            = zero_zero_real )
% 0.35/0.62          = ( X = one_one_real ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % ln_eq_zero_iff
% 0.35/0.62  thf(fact_5936_ln__gt__zero__iff,axiom,
% 0.35/0.62      ! [X: real] :
% 0.35/0.62        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.62       => ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 0.35/0.62          = ( ord_less_real @ one_one_real @ X ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % ln_gt_zero_iff
% 0.35/0.62  thf(fact_5937_ln__less__zero__iff,axiom,
% 0.35/0.62      ! [X: real] :
% 0.35/0.62        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.62       => ( ( ord_less_real @ ( ln_ln_real @ X ) @ zero_zero_real )
% 0.35/0.62          = ( ord_less_real @ X @ one_one_real ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % ln_less_zero_iff
% 0.35/0.62  thf(fact_5938_and__nat__numerals_I2_J,axiom,
% 0.35/0.62      ! [Y2: num] :
% 0.35/0.62        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) )
% 0.35/0.62        = one_one_nat ) ).
% 0.35/0.62  
% 0.35/0.62  % and_nat_numerals(2)
% 0.35/0.62  thf(fact_5939_and__nat__numerals_I4_J,axiom,
% 0.35/0.62      ! [X: num] :
% 0.35/0.62        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 0.35/0.62        = one_one_nat ) ).
% 0.35/0.62  
% 0.35/0.62  % and_nat_numerals(4)
% 0.35/0.62  thf(fact_5940_ln__le__zero__iff,axiom,
% 0.35/0.62      ! [X: real] :
% 0.35/0.62        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.62       => ( ( ord_less_eq_real @ ( ln_ln_real @ X ) @ zero_zero_real )
% 0.35/0.62          = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % ln_le_zero_iff
% 0.35/0.62  thf(fact_5941_ln__ge__zero__iff,axiom,
% 0.35/0.62      ! [X: real] :
% 0.35/0.62        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.62       => ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 0.35/0.62          = ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % ln_ge_zero_iff
% 0.35/0.62  thf(fact_5942_and__Suc__0__eq,axiom,
% 0.35/0.62      ! [N: nat] :
% 0.35/0.62        ( ( bit_se727722235901077358nd_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.35/0.62        = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % and_Suc_0_eq
% 0.35/0.62  thf(fact_5943_Suc__0__and__eq,axiom,
% 0.35/0.62      ! [N: nat] :
% 0.35/0.62        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.35/0.62        = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % Suc_0_and_eq
% 0.35/0.62  thf(fact_5944_ln__less__self,axiom,
% 0.35/0.62      ! [X: real] :
% 0.35/0.62        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.62       => ( ord_less_real @ ( ln_ln_real @ X ) @ X ) ) ).
% 0.35/0.62  
% 0.35/0.62  % ln_less_self
% 0.35/0.62  thf(fact_5945_ln__bound,axiom,
% 0.35/0.62      ! [X: real] :
% 0.35/0.62        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.62       => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ X ) ) ).
% 0.35/0.62  
% 0.35/0.62  % ln_bound
% 0.35/0.62  thf(fact_5946_ln__gt__zero,axiom,
% 0.35/0.62      ! [X: real] :
% 0.35/0.62        ( ( ord_less_real @ one_one_real @ X )
% 0.35/0.62       => ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % ln_gt_zero
% 0.35/0.62  thf(fact_5947_ln__less__zero,axiom,
% 0.35/0.62      ! [X: real] :
% 0.35/0.62        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.62       => ( ( ord_less_real @ X @ one_one_real )
% 0.35/0.62         => ( ord_less_real @ ( ln_ln_real @ X ) @ zero_zero_real ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % ln_less_zero
% 0.35/0.62  thf(fact_5948_ln__gt__zero__imp__gt__one,axiom,
% 0.35/0.62      ! [X: real] :
% 0.35/0.62        ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 0.35/0.62       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.62         => ( ord_less_real @ one_one_real @ X ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % ln_gt_zero_imp_gt_one
% 0.35/0.62  thf(fact_5949_ln__ge__zero,axiom,
% 0.35/0.62      ! [X: real] :
% 0.35/0.62        ( ( ord_less_eq_real @ one_one_real @ X )
% 0.35/0.62       => ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % ln_ge_zero
% 0.35/0.62  thf(fact_5950_ln__ge__zero__imp__ge__one,axiom,
% 0.35/0.62      ! [X: real] :
% 0.35/0.62        ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 0.35/0.62       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.62         => ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % ln_ge_zero_imp_ge_one
% 0.35/0.62  thf(fact_5951_ln__add__one__self__le__self,axiom,
% 0.35/0.62      ! [X: real] :
% 0.35/0.62        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.62       => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) ).
% 0.35/0.62  
% 0.35/0.62  % ln_add_one_self_le_self
% 0.35/0.62  thf(fact_5952_ln__mult,axiom,
% 0.35/0.62      ! [X: real,Y2: real] :
% 0.35/0.62        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.62       => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 0.35/0.62         => ( ( ln_ln_real @ ( times_times_real @ X @ Y2 ) )
% 0.35/0.62            = ( plus_plus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y2 ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % ln_mult
% 0.35/0.62  thf(fact_5953_ln__eq__minus__one,axiom,
% 0.35/0.62      ! [X: real] :
% 0.35/0.62        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.62       => ( ( ( ln_ln_real @ X )
% 0.35/0.62            = ( minus_minus_real @ X @ one_one_real ) )
% 0.35/0.62         => ( X = one_one_real ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % ln_eq_minus_one
% 0.35/0.62  thf(fact_5954_ln__div,axiom,
% 0.35/0.62      ! [X: real,Y2: real] :
% 0.35/0.62        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.62       => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 0.35/0.62         => ( ( ln_ln_real @ ( divide_divide_real @ X @ Y2 ) )
% 0.35/0.62            = ( minus_minus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y2 ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % ln_div
% 0.35/0.62  thf(fact_5955_ln__2__less__1,axiom,
% 0.35/0.62      ord_less_real @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ one_one_real ).
% 0.35/0.62  
% 0.35/0.62  % ln_2_less_1
% 0.35/0.62  thf(fact_5956_ln__le__minus__one,axiom,
% 0.35/0.62      ! [X: real] :
% 0.35/0.62        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.62       => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % ln_le_minus_one
% 0.35/0.62  thf(fact_5957_ln__diff__le,axiom,
% 0.35/0.62      ! [X: real,Y2: real] :
% 0.35/0.62        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.62       => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 0.35/0.62         => ( ord_less_eq_real @ ( minus_minus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y2 ) ) @ ( divide_divide_real @ ( minus_minus_real @ X @ Y2 ) @ Y2 ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % ln_diff_le
% 0.35/0.62  thf(fact_5958_ln__add__one__self__le__self2,axiom,
% 0.35/0.62      ! [X: real] :
% 0.35/0.62        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.35/0.62       => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) ).
% 0.35/0.62  
% 0.35/0.62  % ln_add_one_self_le_self2
% 0.35/0.62  thf(fact_5959_ln__one__minus__pos__upper__bound,axiom,
% 0.35/0.62      ! [X: real] :
% 0.35/0.62        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.62       => ( ( ord_less_real @ X @ one_one_real )
% 0.35/0.62         => ( ord_less_eq_real @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X ) ) @ ( uminus_uminus_real @ X ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % ln_one_minus_pos_upper_bound
% 0.35/0.62  thf(fact_5960_add__0__iff,axiom,
% 0.35/0.62      ! [B: complex,A: complex] :
% 0.35/0.62        ( ( B
% 0.35/0.62          = ( plus_plus_complex @ B @ A ) )
% 0.35/0.62        = ( A = zero_zero_complex ) ) ).
% 0.35/0.62  
% 0.35/0.62  % add_0_iff
% 0.35/0.62  thf(fact_5961_add__0__iff,axiom,
% 0.35/0.62      ! [B: real,A: real] :
% 0.35/0.62        ( ( B
% 0.35/0.62          = ( plus_plus_real @ B @ A ) )
% 0.35/0.62        = ( A = zero_zero_real ) ) ).
% 0.35/0.62  
% 0.35/0.62  % add_0_iff
% 0.35/0.62  thf(fact_5962_add__0__iff,axiom,
% 0.35/0.62      ! [B: rat,A: rat] :
% 0.35/0.62        ( ( B
% 0.35/0.62          = ( plus_plus_rat @ B @ A ) )
% 0.35/0.62        = ( A = zero_zero_rat ) ) ).
% 0.35/0.62  
% 0.35/0.62  % add_0_iff
% 0.35/0.62  thf(fact_5963_add__0__iff,axiom,
% 0.35/0.62      ! [B: nat,A: nat] :
% 0.35/0.62        ( ( B
% 0.35/0.62          = ( plus_plus_nat @ B @ A ) )
% 0.35/0.62        = ( A = zero_zero_nat ) ) ).
% 0.35/0.62  
% 0.35/0.62  % add_0_iff
% 0.35/0.62  thf(fact_5964_add__0__iff,axiom,
% 0.35/0.62      ! [B: int,A: int] :
% 0.35/0.62        ( ( B
% 0.35/0.62          = ( plus_plus_int @ B @ A ) )
% 0.35/0.62        = ( A = zero_zero_int ) ) ).
% 0.35/0.62  
% 0.35/0.62  % add_0_iff
% 0.35/0.62  thf(fact_5965_crossproduct__noteq,axiom,
% 0.35/0.62      ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.35/0.62        ( ( ( A != B )
% 0.35/0.62          & ( C != D2 ) )
% 0.35/0.62        = ( ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) )
% 0.35/0.62         != ( plus_plus_rat @ ( times_times_rat @ A @ D2 ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % crossproduct_noteq
% 0.35/0.62  thf(fact_5966_crossproduct__noteq,axiom,
% 0.35/0.62      ! [A: complex,B: complex,C: complex,D2: complex] :
% 0.35/0.62        ( ( ( A != B )
% 0.35/0.62          & ( C != D2 ) )
% 0.35/0.62        = ( ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ D2 ) )
% 0.35/0.62         != ( plus_plus_complex @ ( times_times_complex @ A @ D2 ) @ ( times_times_complex @ B @ C ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % crossproduct_noteq
% 0.35/0.62  thf(fact_5967_crossproduct__noteq,axiom,
% 0.35/0.62      ! [A: real,B: real,C: real,D2: real] :
% 0.35/0.62        ( ( ( A != B )
% 0.35/0.62          & ( C != D2 ) )
% 0.35/0.62        = ( ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) )
% 0.35/0.62         != ( plus_plus_real @ ( times_times_real @ A @ D2 ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % crossproduct_noteq
% 0.35/0.62  thf(fact_5968_crossproduct__noteq,axiom,
% 0.35/0.62      ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.35/0.62        ( ( ( A != B )
% 0.35/0.62          & ( C != D2 ) )
% 0.35/0.62        = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) )
% 0.35/0.62         != ( plus_plus_nat @ ( times_times_nat @ A @ D2 ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % crossproduct_noteq
% 0.35/0.62  thf(fact_5969_crossproduct__noteq,axiom,
% 0.35/0.62      ! [A: int,B: int,C: int,D2: int] :
% 0.35/0.62        ( ( ( A != B )
% 0.35/0.62          & ( C != D2 ) )
% 0.35/0.62        = ( ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) )
% 0.35/0.62         != ( plus_plus_int @ ( times_times_int @ A @ D2 ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % crossproduct_noteq
% 0.35/0.62  thf(fact_5970_crossproduct__eq,axiom,
% 0.35/0.62      ! [W: rat,Y2: rat,X: rat,Z: rat] :
% 0.35/0.62        ( ( ( plus_plus_rat @ ( times_times_rat @ W @ Y2 ) @ ( times_times_rat @ X @ Z ) )
% 0.35/0.62          = ( plus_plus_rat @ ( times_times_rat @ W @ Z ) @ ( times_times_rat @ X @ Y2 ) ) )
% 0.35/0.62        = ( ( W = X )
% 0.35/0.62          | ( Y2 = Z ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % crossproduct_eq
% 0.35/0.62  thf(fact_5971_crossproduct__eq,axiom,
% 0.35/0.62      ! [W: complex,Y2: complex,X: complex,Z: complex] :
% 0.35/0.62        ( ( ( plus_plus_complex @ ( times_times_complex @ W @ Y2 ) @ ( times_times_complex @ X @ Z ) )
% 0.35/0.62          = ( plus_plus_complex @ ( times_times_complex @ W @ Z ) @ ( times_times_complex @ X @ Y2 ) ) )
% 0.35/0.62        = ( ( W = X )
% 0.35/0.62          | ( Y2 = Z ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % crossproduct_eq
% 0.35/0.62  thf(fact_5972_crossproduct__eq,axiom,
% 0.35/0.62      ! [W: real,Y2: real,X: real,Z: real] :
% 0.35/0.62        ( ( ( plus_plus_real @ ( times_times_real @ W @ Y2 ) @ ( times_times_real @ X @ Z ) )
% 0.35/0.62          = ( plus_plus_real @ ( times_times_real @ W @ Z ) @ ( times_times_real @ X @ Y2 ) ) )
% 0.35/0.62        = ( ( W = X )
% 0.35/0.62          | ( Y2 = Z ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % crossproduct_eq
% 0.35/0.62  thf(fact_5973_crossproduct__eq,axiom,
% 0.35/0.62      ! [W: nat,Y2: nat,X: nat,Z: nat] :
% 0.35/0.62        ( ( ( plus_plus_nat @ ( times_times_nat @ W @ Y2 ) @ ( times_times_nat @ X @ Z ) )
% 0.35/0.62          = ( plus_plus_nat @ ( times_times_nat @ W @ Z ) @ ( times_times_nat @ X @ Y2 ) ) )
% 0.35/0.62        = ( ( W = X )
% 0.35/0.62          | ( Y2 = Z ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % crossproduct_eq
% 0.35/0.62  thf(fact_5974_crossproduct__eq,axiom,
% 0.35/0.62      ! [W: int,Y2: int,X: int,Z: int] :
% 0.35/0.62        ( ( ( plus_plus_int @ ( times_times_int @ W @ Y2 ) @ ( times_times_int @ X @ Z ) )
% 0.35/0.62          = ( plus_plus_int @ ( times_times_int @ W @ Z ) @ ( times_times_int @ X @ Y2 ) ) )
% 0.35/0.62        = ( ( W = X )
% 0.35/0.62          | ( Y2 = Z ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % crossproduct_eq
% 0.35/0.62  thf(fact_5975_exists__least__lemma,axiom,
% 0.35/0.62      ! [P: nat > $o] :
% 0.35/0.62        ( ~ ( P @ zero_zero_nat )
% 0.35/0.62       => ( ? [X_1: nat] : ( P @ X_1 )
% 0.35/0.62         => ? [N3: nat] :
% 0.35/0.62              ( ~ ( P @ N3 )
% 0.35/0.62              & ( P @ ( suc @ N3 ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % exists_least_lemma
% 0.35/0.62  thf(fact_5976_ex__le__of__int,axiom,
% 0.35/0.62      ! [X: real] :
% 0.35/0.62      ? [Z3: int] : ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ Z3 ) ) ).
% 0.35/0.62  
% 0.35/0.62  % ex_le_of_int
% 0.35/0.62  thf(fact_5977_ex__of__int__less,axiom,
% 0.35/0.62      ! [X: real] :
% 0.35/0.62      ? [Z3: int] : ( ord_less_real @ ( ring_1_of_int_real @ Z3 ) @ X ) ).
% 0.35/0.62  
% 0.35/0.62  % ex_of_int_less
% 0.35/0.62  thf(fact_5978_ex__of__int__less,axiom,
% 0.35/0.62      ! [X: rat] :
% 0.35/0.62      ? [Z3: int] : ( ord_less_rat @ ( ring_1_of_int_rat @ Z3 ) @ X ) ).
% 0.35/0.62  
% 0.35/0.62  % ex_of_int_less
% 0.35/0.62  thf(fact_5979_ex__less__of__int,axiom,
% 0.35/0.62      ! [X: real] :
% 0.35/0.62      ? [Z3: int] : ( ord_less_real @ X @ ( ring_1_of_int_real @ Z3 ) ) ).
% 0.35/0.62  
% 0.35/0.62  % ex_less_of_int
% 0.35/0.62  thf(fact_5980_ex__less__of__int,axiom,
% 0.35/0.62      ! [X: rat] :
% 0.35/0.62      ? [Z3: int] : ( ord_less_rat @ X @ ( ring_1_of_int_rat @ Z3 ) ) ).
% 0.35/0.62  
% 0.35/0.62  % ex_less_of_int
% 0.35/0.62  thf(fact_5981_and__nat__unfold,axiom,
% 0.35/0.62      ( bit_se727722235901077358nd_nat
% 0.35/0.62      = ( ^ [M6: nat,N2: nat] :
% 0.35/0.62            ( if_nat
% 0.35/0.62            @ ( ( M6 = zero_zero_nat )
% 0.35/0.62              | ( N2 = zero_zero_nat ) )
% 0.35/0.62            @ zero_zero_nat
% 0.35/0.62            @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % and_nat_unfold
% 0.35/0.62  thf(fact_5982_and__nat__rec,axiom,
% 0.35/0.62      ( bit_se727722235901077358nd_nat
% 0.35/0.62      = ( ^ [M6: nat,N2: nat] :
% 0.35/0.62            ( plus_plus_nat
% 0.35/0.62            @ ( zero_n2687167440665602831ol_nat
% 0.35/0.62              @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 )
% 0.35/0.62                & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.35/0.62            @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % and_nat_rec
% 0.35/0.62  thf(fact_5983_and__int_Opinduct,axiom,
% 0.35/0.62      ! [A0: int,A12: int,P: int > int > $o] :
% 0.35/0.62        ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 0.35/0.62       => ( ! [K2: int,L4: int] :
% 0.35/0.62              ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K2 @ L4 ) )
% 0.35/0.62             => ( ( ~ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.35/0.62                      & ( member_int @ L4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.35/0.62                 => ( P @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.35/0.62               => ( P @ K2 @ L4 ) ) )
% 0.35/0.62         => ( P @ A0 @ A12 ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % and_int.pinduct
% 0.35/0.62  thf(fact_5984_ln__one__plus__pos__lower__bound,axiom,
% 0.35/0.62      ! [X: real] :
% 0.35/0.62        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.62       => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.35/0.62         => ( ord_less_eq_real @ ( minus_minus_real @ X @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % ln_one_plus_pos_lower_bound
% 0.35/0.62  thf(fact_5985_artanh__def,axiom,
% 0.35/0.62      ( artanh_real
% 0.35/0.62      = ( ^ [X2: real] : ( divide_divide_real @ ( ln_ln_real @ ( divide_divide_real @ ( plus_plus_real @ one_one_real @ X2 ) @ ( minus_minus_real @ one_one_real @ X2 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % artanh_def
% 0.35/0.62  thf(fact_5986_abs__ln__one__plus__x__minus__x__bound__nonpos,axiom,
% 0.35/0.62      ! [X: real] :
% 0.35/0.62        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.35/0.62       => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.35/0.62         => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_ln_one_plus_x_minus_x_bound_nonpos
% 0.35/0.62  thf(fact_5987_round__unique,axiom,
% 0.35/0.62      ! [X: real,Y2: int] :
% 0.35/0.62        ( ( ord_less_real @ ( minus_minus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ Y2 ) )
% 0.35/0.62       => ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y2 ) @ ( plus_plus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.35/0.62         => ( ( archim8280529875227126926d_real @ X )
% 0.35/0.62            = Y2 ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % round_unique
% 0.35/0.62  thf(fact_5988_round__unique,axiom,
% 0.35/0.62      ! [X: rat,Y2: int] :
% 0.35/0.62        ( ( ord_less_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ Y2 ) )
% 0.35/0.62       => ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y2 ) @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.62         => ( ( archim7778729529865785530nd_rat @ X )
% 0.35/0.62            = Y2 ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % round_unique
% 0.35/0.62  thf(fact_5989_tanh__ln__real,axiom,
% 0.35/0.62      ! [X: real] :
% 0.35/0.62        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.62       => ( ( tanh_real @ ( ln_ln_real @ X ) )
% 0.35/0.62          = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % tanh_ln_real
% 0.35/0.62  thf(fact_5990_abs__ln__one__plus__x__minus__x__bound,axiom,
% 0.35/0.62      ! [X: real] :
% 0.35/0.62        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.62       => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_ln_one_plus_x_minus_x_bound
% 0.35/0.62  thf(fact_5991_of__int__round__gt,axiom,
% 0.35/0.62      ! [X: real] : ( ord_less_real @ ( minus_minus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_round_gt
% 0.35/0.62  thf(fact_5992_of__int__round__gt,axiom,
% 0.35/0.62      ! [X: rat] : ( ord_less_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % of_int_round_gt
% 0.35/0.62  thf(fact_5993_abs__numeral,axiom,
% 0.35/0.62      ! [N: num] :
% 0.35/0.62        ( ( abs_abs_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 0.35/0.62        = ( numera6620942414471956472nteger @ N ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_numeral
% 0.35/0.62  thf(fact_5994_abs__numeral,axiom,
% 0.35/0.62      ! [N: num] :
% 0.35/0.62        ( ( abs_abs_real @ ( numeral_numeral_real @ N ) )
% 0.35/0.62        = ( numeral_numeral_real @ N ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_numeral
% 0.35/0.62  thf(fact_5995_abs__numeral,axiom,
% 0.35/0.62      ! [N: num] :
% 0.35/0.62        ( ( abs_abs_rat @ ( numeral_numeral_rat @ N ) )
% 0.35/0.62        = ( numeral_numeral_rat @ N ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_numeral
% 0.35/0.62  thf(fact_5996_abs__numeral,axiom,
% 0.35/0.62      ! [N: num] :
% 0.35/0.62        ( ( abs_abs_int @ ( numeral_numeral_int @ N ) )
% 0.35/0.62        = ( numeral_numeral_int @ N ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_numeral
% 0.35/0.62  thf(fact_5997_abs__mult__self__eq,axiom,
% 0.35/0.62      ! [A: code_integer] :
% 0.35/0.62        ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 0.35/0.62        = ( times_3573771949741848930nteger @ A @ A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_mult_self_eq
% 0.35/0.62  thf(fact_5998_abs__mult__self__eq,axiom,
% 0.35/0.62      ! [A: real] :
% 0.35/0.62        ( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
% 0.35/0.62        = ( times_times_real @ A @ A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_mult_self_eq
% 0.35/0.62  thf(fact_5999_abs__mult__self__eq,axiom,
% 0.35/0.62      ! [A: int] :
% 0.35/0.62        ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ A ) )
% 0.35/0.62        = ( times_times_int @ A @ A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_mult_self_eq
% 0.35/0.62  thf(fact_6000_abs__1,axiom,
% 0.35/0.62      ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 0.35/0.62      = one_one_Code_integer ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_1
% 0.35/0.62  thf(fact_6001_abs__1,axiom,
% 0.35/0.62      ( ( abs_abs_complex @ one_one_complex )
% 0.35/0.62      = one_one_complex ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_1
% 0.35/0.62  thf(fact_6002_abs__1,axiom,
% 0.35/0.62      ( ( abs_abs_real @ one_one_real )
% 0.35/0.62      = one_one_real ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_1
% 0.35/0.62  thf(fact_6003_abs__1,axiom,
% 0.35/0.62      ( ( abs_abs_rat @ one_one_rat )
% 0.35/0.62      = one_one_rat ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_1
% 0.35/0.62  thf(fact_6004_abs__1,axiom,
% 0.35/0.62      ( ( abs_abs_int @ one_one_int )
% 0.35/0.62      = one_one_int ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_1
% 0.35/0.62  thf(fact_6005_abs__add__abs,axiom,
% 0.35/0.62      ! [A: code_integer,B: code_integer] :
% 0.35/0.62        ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) )
% 0.35/0.62        = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_add_abs
% 0.35/0.62  thf(fact_6006_abs__add__abs,axiom,
% 0.35/0.62      ! [A: real,B: real] :
% 0.35/0.62        ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) )
% 0.35/0.62        = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_add_abs
% 0.35/0.62  thf(fact_6007_abs__add__abs,axiom,
% 0.35/0.62      ! [A: rat,B: rat] :
% 0.35/0.62        ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) )
% 0.35/0.62        = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_add_abs
% 0.35/0.62  thf(fact_6008_abs__add__abs,axiom,
% 0.35/0.62      ! [A: int,B: int] :
% 0.35/0.62        ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 0.35/0.62        = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_add_abs
% 0.35/0.62  thf(fact_6009_abs__divide,axiom,
% 0.35/0.62      ! [A: complex,B: complex] :
% 0.35/0.62        ( ( abs_abs_complex @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.35/0.62        = ( divide1717551699836669952omplex @ ( abs_abs_complex @ A ) @ ( abs_abs_complex @ B ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_divide
% 0.35/0.62  thf(fact_6010_abs__divide,axiom,
% 0.35/0.62      ! [A: real,B: real] :
% 0.35/0.62        ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 0.35/0.62        = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_divide
% 0.35/0.62  thf(fact_6011_abs__divide,axiom,
% 0.35/0.62      ! [A: rat,B: rat] :
% 0.35/0.62        ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 0.35/0.62        = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_divide
% 0.35/0.62  thf(fact_6012_tanh__real__less__iff,axiom,
% 0.35/0.62      ! [X: real,Y2: real] :
% 0.35/0.62        ( ( ord_less_real @ ( tanh_real @ X ) @ ( tanh_real @ Y2 ) )
% 0.35/0.62        = ( ord_less_real @ X @ Y2 ) ) ).
% 0.35/0.62  
% 0.35/0.62  % tanh_real_less_iff
% 0.35/0.62  thf(fact_6013_tanh__real__le__iff,axiom,
% 0.35/0.62      ! [X: real,Y2: real] :
% 0.35/0.62        ( ( ord_less_eq_real @ ( tanh_real @ X ) @ ( tanh_real @ Y2 ) )
% 0.35/0.62        = ( ord_less_eq_real @ X @ Y2 ) ) ).
% 0.35/0.62  
% 0.35/0.62  % tanh_real_le_iff
% 0.35/0.62  thf(fact_6014_abs__of__nonneg,axiom,
% 0.35/0.62      ! [A: code_integer] :
% 0.35/0.62        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.35/0.62       => ( ( abs_abs_Code_integer @ A )
% 0.35/0.62          = A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_of_nonneg
% 0.35/0.62  thf(fact_6015_abs__of__nonneg,axiom,
% 0.35/0.62      ! [A: real] :
% 0.35/0.62        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.35/0.62       => ( ( abs_abs_real @ A )
% 0.35/0.62          = A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_of_nonneg
% 0.35/0.62  thf(fact_6016_abs__of__nonneg,axiom,
% 0.35/0.62      ! [A: rat] :
% 0.35/0.62        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.35/0.62       => ( ( abs_abs_rat @ A )
% 0.35/0.62          = A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_of_nonneg
% 0.35/0.62  thf(fact_6017_abs__of__nonneg,axiom,
% 0.35/0.62      ! [A: int] :
% 0.35/0.62        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.35/0.62       => ( ( abs_abs_int @ A )
% 0.35/0.62          = A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_of_nonneg
% 0.35/0.62  thf(fact_6018_abs__le__self__iff,axiom,
% 0.35/0.62      ! [A: code_integer] :
% 0.35/0.62        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 0.35/0.62        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_le_self_iff
% 0.35/0.62  thf(fact_6019_abs__le__self__iff,axiom,
% 0.35/0.62      ! [A: real] :
% 0.35/0.62        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ A )
% 0.35/0.62        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_le_self_iff
% 0.35/0.62  thf(fact_6020_abs__le__self__iff,axiom,
% 0.35/0.62      ! [A: rat] :
% 0.35/0.62        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 0.35/0.62        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_le_self_iff
% 0.35/0.62  thf(fact_6021_abs__le__self__iff,axiom,
% 0.35/0.62      ! [A: int] :
% 0.35/0.62        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 0.35/0.62        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_le_self_iff
% 0.35/0.62  thf(fact_6022_abs__le__zero__iff,axiom,
% 0.35/0.62      ! [A: code_integer] :
% 0.35/0.62        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 0.35/0.62        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_le_zero_iff
% 0.35/0.62  thf(fact_6023_abs__le__zero__iff,axiom,
% 0.35/0.62      ! [A: real] :
% 0.35/0.62        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ zero_zero_real )
% 0.35/0.62        = ( A = zero_zero_real ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_le_zero_iff
% 0.35/0.62  thf(fact_6024_abs__le__zero__iff,axiom,
% 0.35/0.62      ! [A: rat] :
% 0.35/0.62        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 0.35/0.62        = ( A = zero_zero_rat ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_le_zero_iff
% 0.35/0.62  thf(fact_6025_abs__le__zero__iff,axiom,
% 0.35/0.62      ! [A: int] :
% 0.35/0.62        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 0.35/0.62        = ( A = zero_zero_int ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_le_zero_iff
% 0.35/0.62  thf(fact_6026_zero__less__abs__iff,axiom,
% 0.35/0.62      ! [A: code_integer] :
% 0.35/0.62        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 0.35/0.62        = ( A != zero_z3403309356797280102nteger ) ) ).
% 0.35/0.62  
% 0.35/0.62  % zero_less_abs_iff
% 0.35/0.62  thf(fact_6027_zero__less__abs__iff,axiom,
% 0.35/0.62      ! [A: real] :
% 0.35/0.62        ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ A ) )
% 0.35/0.62        = ( A != zero_zero_real ) ) ).
% 0.35/0.62  
% 0.35/0.62  % zero_less_abs_iff
% 0.35/0.62  thf(fact_6028_zero__less__abs__iff,axiom,
% 0.35/0.62      ! [A: rat] :
% 0.35/0.62        ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 0.35/0.62        = ( A != zero_zero_rat ) ) ).
% 0.35/0.62  
% 0.35/0.62  % zero_less_abs_iff
% 0.35/0.62  thf(fact_6029_zero__less__abs__iff,axiom,
% 0.35/0.62      ! [A: int] :
% 0.35/0.62        ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 0.35/0.62        = ( A != zero_zero_int ) ) ).
% 0.35/0.62  
% 0.35/0.62  % zero_less_abs_iff
% 0.35/0.62  thf(fact_6030_abs__neg__numeral,axiom,
% 0.35/0.62      ! [N: num] :
% 0.35/0.62        ( ( abs_abs_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.62        = ( numeral_numeral_int @ N ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_neg_numeral
% 0.35/0.62  thf(fact_6031_abs__neg__numeral,axiom,
% 0.35/0.62      ! [N: num] :
% 0.35/0.62        ( ( abs_abs_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.35/0.62        = ( numeral_numeral_real @ N ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_neg_numeral
% 0.35/0.62  thf(fact_6032_abs__neg__numeral,axiom,
% 0.35/0.62      ! [N: num] :
% 0.35/0.62        ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.35/0.62        = ( numera6620942414471956472nteger @ N ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_neg_numeral
% 0.35/0.62  thf(fact_6033_abs__neg__numeral,axiom,
% 0.35/0.62      ! [N: num] :
% 0.35/0.62        ( ( abs_abs_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.35/0.62        = ( numeral_numeral_rat @ N ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_neg_numeral
% 0.35/0.62  thf(fact_6034_abs__neg__one,axiom,
% 0.35/0.62      ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.62      = one_one_int ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_neg_one
% 0.35/0.62  thf(fact_6035_abs__neg__one,axiom,
% 0.35/0.62      ( ( abs_abs_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.35/0.62      = one_one_real ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_neg_one
% 0.35/0.62  thf(fact_6036_abs__neg__one,axiom,
% 0.35/0.62      ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.62      = one_one_Code_integer ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_neg_one
% 0.35/0.62  thf(fact_6037_abs__neg__one,axiom,
% 0.35/0.62      ( ( abs_abs_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.35/0.62      = one_one_rat ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_neg_one
% 0.35/0.62  thf(fact_6038_abs__power__minus,axiom,
% 0.35/0.62      ! [A: int,N: nat] :
% 0.35/0.62        ( ( abs_abs_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 0.35/0.62        = ( abs_abs_int @ ( power_power_int @ A @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_power_minus
% 0.35/0.62  thf(fact_6039_abs__power__minus,axiom,
% 0.35/0.62      ! [A: real,N: nat] :
% 0.35/0.62        ( ( abs_abs_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 0.35/0.62        = ( abs_abs_real @ ( power_power_real @ A @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_power_minus
% 0.35/0.62  thf(fact_6040_abs__power__minus,axiom,
% 0.35/0.62      ! [A: code_integer,N: nat] :
% 0.35/0.62        ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 0.35/0.62        = ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_power_minus
% 0.35/0.62  thf(fact_6041_abs__power__minus,axiom,
% 0.35/0.62      ! [A: rat,N: nat] :
% 0.35/0.62        ( ( abs_abs_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 0.35/0.62        = ( abs_abs_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_power_minus
% 0.35/0.62  thf(fact_6042_tanh__real__pos__iff,axiom,
% 0.35/0.62      ! [X: real] :
% 0.35/0.62        ( ( ord_less_real @ zero_zero_real @ ( tanh_real @ X ) )
% 0.35/0.62        = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 0.35/0.62  
% 0.35/0.62  % tanh_real_pos_iff
% 0.35/0.62  thf(fact_6043_tanh__real__neg__iff,axiom,
% 0.35/0.62      ! [X: real] :
% 0.35/0.62        ( ( ord_less_real @ ( tanh_real @ X ) @ zero_zero_real )
% 0.35/0.62        = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 0.35/0.62  
% 0.35/0.62  % tanh_real_neg_iff
% 0.35/0.62  thf(fact_6044_tanh__real__nonpos__iff,axiom,
% 0.35/0.62      ! [X: real] :
% 0.35/0.62        ( ( ord_less_eq_real @ ( tanh_real @ X ) @ zero_zero_real )
% 0.35/0.62        = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 0.35/0.62  
% 0.35/0.62  % tanh_real_nonpos_iff
% 0.35/0.62  thf(fact_6045_tanh__real__nonneg__iff,axiom,
% 0.35/0.62      ! [X: real] :
% 0.35/0.62        ( ( ord_less_eq_real @ zero_zero_real @ ( tanh_real @ X ) )
% 0.35/0.62        = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 0.35/0.62  
% 0.35/0.62  % tanh_real_nonneg_iff
% 0.35/0.62  thf(fact_6046_round__numeral,axiom,
% 0.35/0.62      ! [N: num] :
% 0.35/0.62        ( ( archim8280529875227126926d_real @ ( numeral_numeral_real @ N ) )
% 0.35/0.62        = ( numeral_numeral_int @ N ) ) ).
% 0.35/0.62  
% 0.35/0.62  % round_numeral
% 0.35/0.62  thf(fact_6047_round__numeral,axiom,
% 0.35/0.62      ! [N: num] :
% 0.35/0.62        ( ( archim7778729529865785530nd_rat @ ( numeral_numeral_rat @ N ) )
% 0.35/0.62        = ( numeral_numeral_int @ N ) ) ).
% 0.35/0.62  
% 0.35/0.62  % round_numeral
% 0.35/0.62  thf(fact_6048_round__1,axiom,
% 0.35/0.62      ( ( archim8280529875227126926d_real @ one_one_real )
% 0.35/0.62      = one_one_int ) ).
% 0.35/0.62  
% 0.35/0.62  % round_1
% 0.35/0.62  thf(fact_6049_round__1,axiom,
% 0.35/0.62      ( ( archim7778729529865785530nd_rat @ one_one_rat )
% 0.35/0.62      = one_one_int ) ).
% 0.35/0.62  
% 0.35/0.62  % round_1
% 0.35/0.62  thf(fact_6050_zero__le__divide__abs__iff,axiom,
% 0.35/0.62      ! [A: real,B: real] :
% 0.35/0.62        ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) )
% 0.35/0.62        = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.35/0.62          | ( B = zero_zero_real ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % zero_le_divide_abs_iff
% 0.35/0.62  thf(fact_6051_zero__le__divide__abs__iff,axiom,
% 0.35/0.62      ! [A: rat,B: rat] :
% 0.35/0.62        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) )
% 0.35/0.62        = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.35/0.62          | ( B = zero_zero_rat ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % zero_le_divide_abs_iff
% 0.35/0.62  thf(fact_6052_divide__le__0__abs__iff,axiom,
% 0.35/0.62      ! [A: real,B: real] :
% 0.35/0.62        ( ( ord_less_eq_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) @ zero_zero_real )
% 0.35/0.62        = ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.35/0.62          | ( B = zero_zero_real ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % divide_le_0_abs_iff
% 0.35/0.62  thf(fact_6053_divide__le__0__abs__iff,axiom,
% 0.35/0.62      ! [A: rat,B: rat] :
% 0.35/0.62        ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) @ zero_zero_rat )
% 0.35/0.62        = ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.35/0.62          | ( B = zero_zero_rat ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % divide_le_0_abs_iff
% 0.35/0.62  thf(fact_6054_abs__of__nonpos,axiom,
% 0.35/0.62      ! [A: real] :
% 0.35/0.62        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.35/0.62       => ( ( abs_abs_real @ A )
% 0.35/0.62          = ( uminus_uminus_real @ A ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_of_nonpos
% 0.35/0.62  thf(fact_6055_abs__of__nonpos,axiom,
% 0.35/0.62      ! [A: code_integer] :
% 0.35/0.62        ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 0.35/0.62       => ( ( abs_abs_Code_integer @ A )
% 0.35/0.62          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_of_nonpos
% 0.35/0.62  thf(fact_6056_abs__of__nonpos,axiom,
% 0.35/0.62      ! [A: rat] :
% 0.35/0.62        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.35/0.62       => ( ( abs_abs_rat @ A )
% 0.35/0.62          = ( uminus_uminus_rat @ A ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_of_nonpos
% 0.35/0.62  thf(fact_6057_abs__of__nonpos,axiom,
% 0.35/0.62      ! [A: int] :
% 0.35/0.62        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.35/0.62       => ( ( abs_abs_int @ A )
% 0.35/0.62          = ( uminus_uminus_int @ A ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_of_nonpos
% 0.35/0.62  thf(fact_6058_artanh__minus__real,axiom,
% 0.35/0.62      ! [X: real] :
% 0.35/0.62        ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.35/0.62       => ( ( artanh_real @ ( uminus_uminus_real @ X ) )
% 0.35/0.62          = ( uminus_uminus_real @ ( artanh_real @ X ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % artanh_minus_real
% 0.35/0.62  thf(fact_6059_zero__less__power__abs__iff,axiom,
% 0.35/0.62      ! [A: code_integer,N: nat] :
% 0.35/0.62        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) )
% 0.35/0.62        = ( ( A != zero_z3403309356797280102nteger )
% 0.35/0.62          | ( N = zero_zero_nat ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % zero_less_power_abs_iff
% 0.35/0.62  thf(fact_6060_zero__less__power__abs__iff,axiom,
% 0.35/0.62      ! [A: real,N: nat] :
% 0.35/0.62        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 0.35/0.62        = ( ( A != zero_zero_real )
% 0.35/0.62          | ( N = zero_zero_nat ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % zero_less_power_abs_iff
% 0.35/0.62  thf(fact_6061_zero__less__power__abs__iff,axiom,
% 0.35/0.62      ! [A: rat,N: nat] :
% 0.35/0.62        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) )
% 0.35/0.62        = ( ( A != zero_zero_rat )
% 0.35/0.62          | ( N = zero_zero_nat ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % zero_less_power_abs_iff
% 0.35/0.62  thf(fact_6062_zero__less__power__abs__iff,axiom,
% 0.35/0.62      ! [A: int,N: nat] :
% 0.35/0.62        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) )
% 0.35/0.62        = ( ( A != zero_zero_int )
% 0.35/0.62          | ( N = zero_zero_nat ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % zero_less_power_abs_iff
% 0.35/0.62  thf(fact_6063_abs__power2,axiom,
% 0.35/0.62      ! [A: code_integer] :
% 0.35/0.62        ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.62        = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_power2
% 0.35/0.62  thf(fact_6064_abs__power2,axiom,
% 0.35/0.62      ! [A: real] :
% 0.35/0.62        ( ( abs_abs_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.62        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_power2
% 0.35/0.62  thf(fact_6065_abs__power2,axiom,
% 0.35/0.62      ! [A: int] :
% 0.35/0.62        ( ( abs_abs_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.62        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_power2
% 0.35/0.62  thf(fact_6066_power2__abs,axiom,
% 0.35/0.62      ! [A: code_integer] :
% 0.35/0.62        ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.62        = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power2_abs
% 0.35/0.62  thf(fact_6067_power2__abs,axiom,
% 0.35/0.62      ! [A: real] :
% 0.35/0.62        ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.62        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power2_abs
% 0.35/0.62  thf(fact_6068_power2__abs,axiom,
% 0.35/0.62      ! [A: int] :
% 0.35/0.62        ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.62        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power2_abs
% 0.35/0.62  thf(fact_6069_round__neg__numeral,axiom,
% 0.35/0.62      ! [N: num] :
% 0.35/0.62        ( ( archim8280529875227126926d_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.35/0.62        = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % round_neg_numeral
% 0.35/0.62  thf(fact_6070_round__neg__numeral,axiom,
% 0.35/0.62      ! [N: num] :
% 0.35/0.62        ( ( archim7778729529865785530nd_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.35/0.62        = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % round_neg_numeral
% 0.35/0.62  thf(fact_6071_power__even__abs__numeral,axiom,
% 0.35/0.62      ! [W: num,A: code_integer] :
% 0.35/0.62        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.35/0.62       => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ W ) )
% 0.35/0.62          = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power_even_abs_numeral
% 0.35/0.62  thf(fact_6072_power__even__abs__numeral,axiom,
% 0.35/0.62      ! [W: num,A: real] :
% 0.35/0.62        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.35/0.62       => ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ W ) )
% 0.35/0.62          = ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power_even_abs_numeral
% 0.35/0.62  thf(fact_6073_power__even__abs__numeral,axiom,
% 0.35/0.62      ! [W: num,A: int] :
% 0.35/0.62        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.35/0.62       => ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ W ) )
% 0.35/0.62          = ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power_even_abs_numeral
% 0.35/0.62  thf(fact_6074_abs__ge__self,axiom,
% 0.35/0.62      ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_ge_self
% 0.35/0.62  thf(fact_6075_abs__ge__self,axiom,
% 0.35/0.62      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_ge_self
% 0.35/0.62  thf(fact_6076_abs__ge__self,axiom,
% 0.35/0.62      ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_ge_self
% 0.35/0.62  thf(fact_6077_abs__le__D1,axiom,
% 0.35/0.62      ! [A: real,B: real] :
% 0.35/0.62        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 0.35/0.62       => ( ord_less_eq_real @ A @ B ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_le_D1
% 0.35/0.62  thf(fact_6078_abs__le__D1,axiom,
% 0.35/0.62      ! [A: code_integer,B: code_integer] :
% 0.35/0.62        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 0.35/0.62       => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_le_D1
% 0.35/0.62  thf(fact_6079_abs__le__D1,axiom,
% 0.35/0.62      ! [A: int,B: int] :
% 0.35/0.62        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 0.35/0.62       => ( ord_less_eq_int @ A @ B ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_le_D1
% 0.35/0.62  thf(fact_6080_abs__mult,axiom,
% 0.35/0.62      ! [A: code_integer,B: code_integer] :
% 0.35/0.62        ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 0.35/0.62        = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_mult
% 0.35/0.62  thf(fact_6081_abs__mult,axiom,
% 0.35/0.62      ! [A: complex,B: complex] :
% 0.35/0.62        ( ( abs_abs_complex @ ( times_times_complex @ A @ B ) )
% 0.35/0.62        = ( times_times_complex @ ( abs_abs_complex @ A ) @ ( abs_abs_complex @ B ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_mult
% 0.35/0.62  thf(fact_6082_abs__mult,axiom,
% 0.35/0.62      ! [A: real,B: real] :
% 0.35/0.62        ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 0.35/0.62        = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_mult
% 0.35/0.62  thf(fact_6083_abs__mult,axiom,
% 0.35/0.62      ! [A: int,B: int] :
% 0.35/0.62        ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 0.35/0.62        = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_mult
% 0.35/0.62  thf(fact_6084_abs__one,axiom,
% 0.35/0.62      ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 0.35/0.62      = one_one_Code_integer ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_one
% 0.35/0.62  thf(fact_6085_abs__one,axiom,
% 0.35/0.62      ( ( abs_abs_real @ one_one_real )
% 0.35/0.62      = one_one_real ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_one
% 0.35/0.62  thf(fact_6086_abs__one,axiom,
% 0.35/0.62      ( ( abs_abs_rat @ one_one_rat )
% 0.35/0.62      = one_one_rat ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_one
% 0.35/0.62  thf(fact_6087_abs__one,axiom,
% 0.35/0.62      ( ( abs_abs_int @ one_one_int )
% 0.35/0.62      = one_one_int ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_one
% 0.35/0.62  thf(fact_6088_abs__minus__commute,axiom,
% 0.35/0.62      ! [A: real,B: real] :
% 0.35/0.62        ( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
% 0.35/0.62        = ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_minus_commute
% 0.35/0.62  thf(fact_6089_abs__minus__commute,axiom,
% 0.35/0.62      ! [A: code_integer,B: code_integer] :
% 0.35/0.62        ( ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.35/0.62        = ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_minus_commute
% 0.35/0.62  thf(fact_6090_abs__minus__commute,axiom,
% 0.35/0.62      ! [A: rat,B: rat] :
% 0.35/0.62        ( ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) )
% 0.35/0.62        = ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_minus_commute
% 0.35/0.62  thf(fact_6091_abs__minus__commute,axiom,
% 0.35/0.62      ! [A: int,B: int] :
% 0.35/0.62        ( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
% 0.35/0.62        = ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_minus_commute
% 0.35/0.62  thf(fact_6092_power__abs,axiom,
% 0.35/0.62      ! [A: code_integer,N: nat] :
% 0.35/0.62        ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) )
% 0.35/0.62        = ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power_abs
% 0.35/0.62  thf(fact_6093_power__abs,axiom,
% 0.35/0.62      ! [A: real,N: nat] :
% 0.35/0.62        ( ( abs_abs_real @ ( power_power_real @ A @ N ) )
% 0.35/0.62        = ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power_abs
% 0.35/0.62  thf(fact_6094_power__abs,axiom,
% 0.35/0.62      ! [A: int,N: nat] :
% 0.35/0.62        ( ( abs_abs_int @ ( power_power_int @ A @ N ) )
% 0.35/0.62        = ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 0.35/0.62  
% 0.35/0.62  % power_abs
% 0.35/0.62  thf(fact_6095_round__diff__minimal,axiom,
% 0.35/0.62      ! [Z: real,M: int] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ Z ) ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ Z @ ( ring_1_of_int_real @ M ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % round_diff_minimal
% 0.35/0.62  thf(fact_6096_round__diff__minimal,axiom,
% 0.35/0.62      ! [Z: rat,M: int] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ Z @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ Z ) ) ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ Z @ ( ring_1_of_int_rat @ M ) ) ) ) ).
% 0.35/0.62  
% 0.35/0.62  % round_diff_minimal
% 0.35/0.62  thf(fact_6097_abs__ge__zero,axiom,
% 0.35/0.62      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_ge_zero
% 0.35/0.62  thf(fact_6098_abs__ge__zero,axiom,
% 0.35/0.62      ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_ge_zero
% 0.35/0.62  thf(fact_6099_abs__ge__zero,axiom,
% 0.35/0.62      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_ge_zero
% 0.35/0.62  thf(fact_6100_abs__ge__zero,axiom,
% 0.35/0.62      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_ge_zero
% 0.35/0.62  thf(fact_6101_abs__not__less__zero,axiom,
% 0.35/0.62      ! [A: code_integer] :
% 0.35/0.62        ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_not_less_zero
% 0.35/0.62  thf(fact_6102_abs__not__less__zero,axiom,
% 0.35/0.62      ! [A: real] :
% 0.35/0.62        ~ ( ord_less_real @ ( abs_abs_real @ A ) @ zero_zero_real ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_not_less_zero
% 0.35/0.62  thf(fact_6103_abs__not__less__zero,axiom,
% 0.35/0.62      ! [A: rat] :
% 0.35/0.62        ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_not_less_zero
% 0.35/0.62  thf(fact_6104_abs__not__less__zero,axiom,
% 0.35/0.62      ! [A: int] :
% 0.35/0.62        ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_not_less_zero
% 0.35/0.62  thf(fact_6105_abs__of__pos,axiom,
% 0.35/0.62      ! [A: code_integer] :
% 0.35/0.62        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.35/0.62       => ( ( abs_abs_Code_integer @ A )
% 0.35/0.62          = A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_of_pos
% 0.35/0.62  thf(fact_6106_abs__of__pos,axiom,
% 0.35/0.62      ! [A: real] :
% 0.35/0.62        ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.62       => ( ( abs_abs_real @ A )
% 0.35/0.62          = A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_of_pos
% 0.35/0.62  thf(fact_6107_abs__of__pos,axiom,
% 0.35/0.62      ! [A: rat] :
% 0.35/0.62        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.35/0.62       => ( ( abs_abs_rat @ A )
% 0.35/0.62          = A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_of_pos
% 0.35/0.62  thf(fact_6108_abs__of__pos,axiom,
% 0.35/0.62      ! [A: int] :
% 0.35/0.62        ( ( ord_less_int @ zero_zero_int @ A )
% 0.35/0.62       => ( ( abs_abs_int @ A )
% 0.35/0.62          = A ) ) ).
% 0.35/0.62  
% 0.35/0.62  % abs_of_pos
% 0.35/0.62  thf(fact_6109_abs__triangle__ineq,axiom,
% 0.35/0.62      ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_triangle_ineq
% 0.35/0.63  thf(fact_6110_abs__triangle__ineq,axiom,
% 0.35/0.63      ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_triangle_ineq
% 0.35/0.63  thf(fact_6111_abs__triangle__ineq,axiom,
% 0.35/0.63      ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( plus_plus_rat @ A @ B ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_triangle_ineq
% 0.35/0.63  thf(fact_6112_abs__triangle__ineq,axiom,
% 0.35/0.63      ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_triangle_ineq
% 0.35/0.63  thf(fact_6113_abs__mult__less,axiom,
% 0.35/0.63      ! [A: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 0.35/0.63        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ C )
% 0.35/0.63       => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ B ) @ D2 )
% 0.35/0.63         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( times_3573771949741848930nteger @ C @ D2 ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_mult_less
% 0.35/0.63  thf(fact_6114_abs__mult__less,axiom,
% 0.35/0.63      ! [A: real,C: real,B: real,D2: real] :
% 0.35/0.63        ( ( ord_less_real @ ( abs_abs_real @ A ) @ C )
% 0.35/0.63       => ( ( ord_less_real @ ( abs_abs_real @ B ) @ D2 )
% 0.35/0.63         => ( ord_less_real @ ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( times_times_real @ C @ D2 ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_mult_less
% 0.35/0.63  thf(fact_6115_abs__mult__less,axiom,
% 0.35/0.63      ! [A: rat,C: rat,B: rat,D2: rat] :
% 0.35/0.63        ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ C )
% 0.35/0.63       => ( ( ord_less_rat @ ( abs_abs_rat @ B ) @ D2 )
% 0.35/0.63         => ( ord_less_rat @ ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( times_times_rat @ C @ D2 ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_mult_less
% 0.35/0.63  thf(fact_6116_abs__mult__less,axiom,
% 0.35/0.63      ! [A: int,C: int,B: int,D2: int] :
% 0.35/0.63        ( ( ord_less_int @ ( abs_abs_int @ A ) @ C )
% 0.35/0.63       => ( ( ord_less_int @ ( abs_abs_int @ B ) @ D2 )
% 0.35/0.63         => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( times_times_int @ C @ D2 ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_mult_less
% 0.35/0.63  thf(fact_6117_abs__triangle__ineq2__sym,axiom,
% 0.35/0.63      ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_triangle_ineq2_sym
% 0.35/0.63  thf(fact_6118_abs__triangle__ineq2__sym,axiom,
% 0.35/0.63      ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_triangle_ineq2_sym
% 0.35/0.63  thf(fact_6119_abs__triangle__ineq2__sym,axiom,
% 0.35/0.63      ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_triangle_ineq2_sym
% 0.35/0.63  thf(fact_6120_abs__triangle__ineq2__sym,axiom,
% 0.35/0.63      ! [A: int,B: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_triangle_ineq2_sym
% 0.35/0.63  thf(fact_6121_abs__triangle__ineq3,axiom,
% 0.35/0.63      ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_triangle_ineq3
% 0.35/0.63  thf(fact_6122_abs__triangle__ineq3,axiom,
% 0.35/0.63      ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_triangle_ineq3
% 0.35/0.63  thf(fact_6123_abs__triangle__ineq3,axiom,
% 0.35/0.63      ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_triangle_ineq3
% 0.35/0.63  thf(fact_6124_abs__triangle__ineq3,axiom,
% 0.35/0.63      ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_triangle_ineq3
% 0.35/0.63  thf(fact_6125_abs__triangle__ineq2,axiom,
% 0.35/0.63      ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_triangle_ineq2
% 0.35/0.63  thf(fact_6126_abs__triangle__ineq2,axiom,
% 0.35/0.63      ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_triangle_ineq2
% 0.35/0.63  thf(fact_6127_abs__triangle__ineq2,axiom,
% 0.35/0.63      ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_triangle_ineq2
% 0.35/0.63  thf(fact_6128_abs__triangle__ineq2,axiom,
% 0.35/0.63      ! [A: int,B: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_triangle_ineq2
% 0.35/0.63  thf(fact_6129_nonzero__abs__divide,axiom,
% 0.35/0.63      ! [B: real,A: real] :
% 0.35/0.63        ( ( B != zero_zero_real )
% 0.35/0.63       => ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 0.35/0.63          = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % nonzero_abs_divide
% 0.35/0.63  thf(fact_6130_nonzero__abs__divide,axiom,
% 0.35/0.63      ! [B: rat,A: rat] :
% 0.35/0.63        ( ( B != zero_zero_rat )
% 0.35/0.63       => ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 0.35/0.63          = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % nonzero_abs_divide
% 0.35/0.63  thf(fact_6131_abs__ge__minus__self,axiom,
% 0.35/0.63      ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ ( abs_abs_real @ A ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_ge_minus_self
% 0.35/0.63  thf(fact_6132_abs__ge__minus__self,axiom,
% 0.35/0.63      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_ge_minus_self
% 0.35/0.63  thf(fact_6133_abs__ge__minus__self,axiom,
% 0.35/0.63      ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_ge_minus_self
% 0.35/0.63  thf(fact_6134_abs__ge__minus__self,axiom,
% 0.35/0.63      ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_ge_minus_self
% 0.35/0.63  thf(fact_6135_abs__le__iff,axiom,
% 0.35/0.63      ! [A: real,B: real] :
% 0.35/0.63        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 0.35/0.63        = ( ( ord_less_eq_real @ A @ B )
% 0.35/0.63          & ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_le_iff
% 0.35/0.63  thf(fact_6136_abs__le__iff,axiom,
% 0.35/0.63      ! [A: code_integer,B: code_integer] :
% 0.35/0.63        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 0.35/0.63        = ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.35/0.63          & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_le_iff
% 0.35/0.63  thf(fact_6137_abs__le__iff,axiom,
% 0.35/0.63      ! [A: rat,B: rat] :
% 0.35/0.63        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 0.35/0.63        = ( ( ord_less_eq_rat @ A @ B )
% 0.35/0.63          & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_le_iff
% 0.35/0.63  thf(fact_6138_abs__le__iff,axiom,
% 0.35/0.63      ! [A: int,B: int] :
% 0.35/0.63        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 0.35/0.63        = ( ( ord_less_eq_int @ A @ B )
% 0.35/0.63          & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_le_iff
% 0.35/0.63  thf(fact_6139_abs__le__D2,axiom,
% 0.35/0.63      ! [A: real,B: real] :
% 0.35/0.63        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 0.35/0.63       => ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_le_D2
% 0.35/0.63  thf(fact_6140_abs__le__D2,axiom,
% 0.35/0.63      ! [A: code_integer,B: code_integer] :
% 0.35/0.63        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 0.35/0.63       => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_le_D2
% 0.35/0.63  thf(fact_6141_abs__le__D2,axiom,
% 0.35/0.63      ! [A: rat,B: rat] :
% 0.35/0.63        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 0.35/0.63       => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_le_D2
% 0.35/0.63  thf(fact_6142_abs__le__D2,axiom,
% 0.35/0.63      ! [A: int,B: int] :
% 0.35/0.63        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 0.35/0.63       => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_le_D2
% 0.35/0.63  thf(fact_6143_abs__leI,axiom,
% 0.35/0.63      ! [A: real,B: real] :
% 0.35/0.63        ( ( ord_less_eq_real @ A @ B )
% 0.35/0.63       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 0.35/0.63         => ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_leI
% 0.35/0.63  thf(fact_6144_abs__leI,axiom,
% 0.35/0.63      ! [A: code_integer,B: code_integer] :
% 0.35/0.63        ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.35/0.63       => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.35/0.63         => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_leI
% 0.35/0.63  thf(fact_6145_abs__leI,axiom,
% 0.35/0.63      ! [A: rat,B: rat] :
% 0.35/0.63        ( ( ord_less_eq_rat @ A @ B )
% 0.35/0.63       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.35/0.63         => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_leI
% 0.35/0.63  thf(fact_6146_abs__leI,axiom,
% 0.35/0.63      ! [A: int,B: int] :
% 0.35/0.63        ( ( ord_less_eq_int @ A @ B )
% 0.35/0.63       => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 0.35/0.63         => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_leI
% 0.35/0.63  thf(fact_6147_abs__less__iff,axiom,
% 0.35/0.63      ! [A: int,B: int] :
% 0.35/0.63        ( ( ord_less_int @ ( abs_abs_int @ A ) @ B )
% 0.35/0.63        = ( ( ord_less_int @ A @ B )
% 0.35/0.63          & ( ord_less_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_less_iff
% 0.35/0.63  thf(fact_6148_abs__less__iff,axiom,
% 0.35/0.63      ! [A: real,B: real] :
% 0.35/0.63        ( ( ord_less_real @ ( abs_abs_real @ A ) @ B )
% 0.35/0.63        = ( ( ord_less_real @ A @ B )
% 0.35/0.63          & ( ord_less_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_less_iff
% 0.35/0.63  thf(fact_6149_abs__less__iff,axiom,
% 0.35/0.63      ! [A: code_integer,B: code_integer] :
% 0.35/0.63        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 0.35/0.63        = ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.35/0.63          & ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_less_iff
% 0.35/0.63  thf(fact_6150_abs__less__iff,axiom,
% 0.35/0.63      ! [A: rat,B: rat] :
% 0.35/0.63        ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ B )
% 0.35/0.63        = ( ( ord_less_rat @ A @ B )
% 0.35/0.63          & ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_less_iff
% 0.35/0.63  thf(fact_6151_tanh__real__lt__1,axiom,
% 0.35/0.63      ! [X: real] : ( ord_less_real @ ( tanh_real @ X ) @ one_one_real ) ).
% 0.35/0.63  
% 0.35/0.63  % tanh_real_lt_1
% 0.35/0.63  thf(fact_6152_dense__eq0__I,axiom,
% 0.35/0.63      ! [X: real] :
% 0.35/0.63        ( ! [E2: real] :
% 0.35/0.63            ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.35/0.63           => ( ord_less_eq_real @ ( abs_abs_real @ X ) @ E2 ) )
% 0.35/0.63       => ( X = zero_zero_real ) ) ).
% 0.35/0.63  
% 0.35/0.63  % dense_eq0_I
% 0.35/0.63  thf(fact_6153_dense__eq0__I,axiom,
% 0.35/0.63      ! [X: rat] :
% 0.35/0.63        ( ! [E2: rat] :
% 0.35/0.63            ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 0.35/0.63           => ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ E2 ) )
% 0.35/0.63       => ( X = zero_zero_rat ) ) ).
% 0.35/0.63  
% 0.35/0.63  % dense_eq0_I
% 0.35/0.63  thf(fact_6154_abs__eq__mult,axiom,
% 0.35/0.63      ! [A: code_integer,B: code_integer] :
% 0.35/0.63        ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.35/0.63            | ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 0.35/0.63          & ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.35/0.63            | ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 0.35/0.63       => ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 0.35/0.63          = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_eq_mult
% 0.35/0.63  thf(fact_6155_abs__eq__mult,axiom,
% 0.35/0.63      ! [A: rat,B: rat] :
% 0.35/0.63        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.35/0.63            | ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 0.35/0.63          & ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.35/0.63            | ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 0.35/0.63       => ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 0.35/0.63          = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_eq_mult
% 0.35/0.63  thf(fact_6156_abs__eq__mult,axiom,
% 0.35/0.63      ! [A: real,B: real] :
% 0.35/0.63        ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.35/0.63            | ( ord_less_eq_real @ A @ zero_zero_real ) )
% 0.35/0.63          & ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.35/0.63            | ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 0.35/0.63       => ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 0.35/0.63          = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_eq_mult
% 0.35/0.63  thf(fact_6157_abs__eq__mult,axiom,
% 0.35/0.63      ! [A: int,B: int] :
% 0.35/0.63        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.35/0.63            | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 0.35/0.63          & ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.35/0.63            | ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 0.35/0.63       => ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 0.35/0.63          = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_eq_mult
% 0.35/0.63  thf(fact_6158_abs__mult__pos,axiom,
% 0.35/0.63      ! [X: code_integer,Y2: code_integer] :
% 0.35/0.63        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 0.35/0.63       => ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ Y2 ) @ X )
% 0.35/0.63          = ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ Y2 @ X ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_mult_pos
% 0.35/0.63  thf(fact_6159_abs__mult__pos,axiom,
% 0.35/0.63      ! [X: rat,Y2: rat] :
% 0.35/0.63        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.35/0.63       => ( ( times_times_rat @ ( abs_abs_rat @ Y2 ) @ X )
% 0.35/0.63          = ( abs_abs_rat @ ( times_times_rat @ Y2 @ X ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_mult_pos
% 0.35/0.63  thf(fact_6160_abs__mult__pos,axiom,
% 0.35/0.63      ! [X: real,Y2: real] :
% 0.35/0.63        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.63       => ( ( times_times_real @ ( abs_abs_real @ Y2 ) @ X )
% 0.35/0.63          = ( abs_abs_real @ ( times_times_real @ Y2 @ X ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_mult_pos
% 0.35/0.63  thf(fact_6161_abs__mult__pos,axiom,
% 0.35/0.63      ! [X: int,Y2: int] :
% 0.35/0.63        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.35/0.63       => ( ( times_times_int @ ( abs_abs_int @ Y2 ) @ X )
% 0.35/0.63          = ( abs_abs_int @ ( times_times_int @ Y2 @ X ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_mult_pos
% 0.35/0.63  thf(fact_6162_eq__abs__iff_H,axiom,
% 0.35/0.63      ! [A: real,B: real] :
% 0.35/0.63        ( ( A
% 0.35/0.63          = ( abs_abs_real @ B ) )
% 0.35/0.63        = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.35/0.63          & ( ( B = A )
% 0.35/0.63            | ( B
% 0.35/0.63              = ( uminus_uminus_real @ A ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % eq_abs_iff'
% 0.35/0.63  thf(fact_6163_eq__abs__iff_H,axiom,
% 0.35/0.63      ! [A: code_integer,B: code_integer] :
% 0.35/0.63        ( ( A
% 0.35/0.63          = ( abs_abs_Code_integer @ B ) )
% 0.35/0.63        = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.35/0.63          & ( ( B = A )
% 0.35/0.63            | ( B
% 0.35/0.63              = ( uminus1351360451143612070nteger @ A ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % eq_abs_iff'
% 0.35/0.63  thf(fact_6164_eq__abs__iff_H,axiom,
% 0.35/0.63      ! [A: rat,B: rat] :
% 0.35/0.63        ( ( A
% 0.35/0.63          = ( abs_abs_rat @ B ) )
% 0.35/0.63        = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.35/0.63          & ( ( B = A )
% 0.35/0.63            | ( B
% 0.35/0.63              = ( uminus_uminus_rat @ A ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % eq_abs_iff'
% 0.35/0.63  thf(fact_6165_eq__abs__iff_H,axiom,
% 0.35/0.63      ! [A: int,B: int] :
% 0.35/0.63        ( ( A
% 0.35/0.63          = ( abs_abs_int @ B ) )
% 0.35/0.63        = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.35/0.63          & ( ( B = A )
% 0.35/0.63            | ( B
% 0.35/0.63              = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % eq_abs_iff'
% 0.35/0.63  thf(fact_6166_abs__eq__iff_H,axiom,
% 0.35/0.63      ! [A: real,B: real] :
% 0.35/0.63        ( ( ( abs_abs_real @ A )
% 0.35/0.63          = B )
% 0.35/0.63        = ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.35/0.63          & ( ( A = B )
% 0.35/0.63            | ( A
% 0.35/0.63              = ( uminus_uminus_real @ B ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_eq_iff'
% 0.35/0.63  thf(fact_6167_abs__eq__iff_H,axiom,
% 0.35/0.63      ! [A: code_integer,B: code_integer] :
% 0.35/0.63        ( ( ( abs_abs_Code_integer @ A )
% 0.35/0.63          = B )
% 0.35/0.63        = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.35/0.63          & ( ( A = B )
% 0.35/0.63            | ( A
% 0.35/0.63              = ( uminus1351360451143612070nteger @ B ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_eq_iff'
% 0.35/0.63  thf(fact_6168_abs__eq__iff_H,axiom,
% 0.35/0.63      ! [A: rat,B: rat] :
% 0.35/0.63        ( ( ( abs_abs_rat @ A )
% 0.35/0.63          = B )
% 0.35/0.63        = ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.35/0.63          & ( ( A = B )
% 0.35/0.63            | ( A
% 0.35/0.63              = ( uminus_uminus_rat @ B ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_eq_iff'
% 0.35/0.63  thf(fact_6169_abs__eq__iff_H,axiom,
% 0.35/0.63      ! [A: int,B: int] :
% 0.35/0.63        ( ( ( abs_abs_int @ A )
% 0.35/0.63          = B )
% 0.35/0.63        = ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.35/0.63          & ( ( A = B )
% 0.35/0.63            | ( A
% 0.35/0.63              = ( uminus_uminus_int @ B ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_eq_iff'
% 0.35/0.63  thf(fact_6170_abs__minus__le__zero,axiom,
% 0.35/0.63      ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( abs_abs_real @ A ) ) @ zero_zero_real ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_minus_le_zero
% 0.35/0.63  thf(fact_6171_abs__minus__le__zero,axiom,
% 0.35/0.63      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_minus_le_zero
% 0.35/0.63  thf(fact_6172_abs__minus__le__zero,axiom,
% 0.35/0.63      ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_minus_le_zero
% 0.35/0.63  thf(fact_6173_abs__minus__le__zero,axiom,
% 0.35/0.63      ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_minus_le_zero
% 0.35/0.63  thf(fact_6174_abs__div__pos,axiom,
% 0.35/0.63      ! [Y2: real,X: real] :
% 0.35/0.63        ( ( ord_less_real @ zero_zero_real @ Y2 )
% 0.35/0.63       => ( ( divide_divide_real @ ( abs_abs_real @ X ) @ Y2 )
% 0.35/0.63          = ( abs_abs_real @ ( divide_divide_real @ X @ Y2 ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_div_pos
% 0.35/0.63  thf(fact_6175_abs__div__pos,axiom,
% 0.35/0.63      ! [Y2: rat,X: rat] :
% 0.35/0.63        ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 0.35/0.63       => ( ( divide_divide_rat @ ( abs_abs_rat @ X ) @ Y2 )
% 0.35/0.63          = ( abs_abs_rat @ ( divide_divide_rat @ X @ Y2 ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_div_pos
% 0.35/0.63  thf(fact_6176_zero__le__power__abs,axiom,
% 0.35/0.63      ! [A: code_integer,N: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 0.35/0.63  
% 0.35/0.63  % zero_le_power_abs
% 0.35/0.63  thf(fact_6177_zero__le__power__abs,axiom,
% 0.35/0.63      ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 0.35/0.63  
% 0.35/0.63  % zero_le_power_abs
% 0.35/0.63  thf(fact_6178_zero__le__power__abs,axiom,
% 0.35/0.63      ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 0.35/0.63  
% 0.35/0.63  % zero_le_power_abs
% 0.35/0.63  thf(fact_6179_zero__le__power__abs,axiom,
% 0.35/0.63      ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 0.35/0.63  
% 0.35/0.63  % zero_le_power_abs
% 0.35/0.63  thf(fact_6180_abs__if__raw,axiom,
% 0.35/0.63      ( abs_abs_int
% 0.35/0.63      = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_if_raw
% 0.35/0.63  thf(fact_6181_abs__if__raw,axiom,
% 0.35/0.63      ( abs_abs_real
% 0.35/0.63      = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_if_raw
% 0.35/0.63  thf(fact_6182_abs__if__raw,axiom,
% 0.35/0.63      ( abs_abs_Code_integer
% 0.35/0.63      = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_if_raw
% 0.35/0.63  thf(fact_6183_abs__if__raw,axiom,
% 0.35/0.63      ( abs_abs_rat
% 0.35/0.63      = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_if_raw
% 0.35/0.63  thf(fact_6184_abs__if,axiom,
% 0.35/0.63      ( abs_abs_int
% 0.35/0.63      = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_if
% 0.35/0.63  thf(fact_6185_abs__if,axiom,
% 0.35/0.63      ( abs_abs_real
% 0.35/0.63      = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_if
% 0.35/0.63  thf(fact_6186_abs__if,axiom,
% 0.35/0.63      ( abs_abs_Code_integer
% 0.35/0.63      = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_if
% 0.35/0.63  thf(fact_6187_abs__if,axiom,
% 0.35/0.63      ( abs_abs_rat
% 0.35/0.63      = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_if
% 0.35/0.63  thf(fact_6188_abs__of__neg,axiom,
% 0.35/0.63      ! [A: int] :
% 0.35/0.63        ( ( ord_less_int @ A @ zero_zero_int )
% 0.35/0.63       => ( ( abs_abs_int @ A )
% 0.35/0.63          = ( uminus_uminus_int @ A ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_of_neg
% 0.35/0.63  thf(fact_6189_abs__of__neg,axiom,
% 0.35/0.63      ! [A: real] :
% 0.35/0.63        ( ( ord_less_real @ A @ zero_zero_real )
% 0.35/0.63       => ( ( abs_abs_real @ A )
% 0.35/0.63          = ( uminus_uminus_real @ A ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_of_neg
% 0.35/0.63  thf(fact_6190_abs__of__neg,axiom,
% 0.35/0.63      ! [A: code_integer] :
% 0.35/0.63        ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 0.35/0.63       => ( ( abs_abs_Code_integer @ A )
% 0.35/0.63          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_of_neg
% 0.35/0.63  thf(fact_6191_abs__of__neg,axiom,
% 0.35/0.63      ! [A: rat] :
% 0.35/0.63        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.35/0.63       => ( ( abs_abs_rat @ A )
% 0.35/0.63          = ( uminus_uminus_rat @ A ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_of_neg
% 0.35/0.63  thf(fact_6192_abs__diff__triangle__ineq,axiom,
% 0.35/0.63      ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( plus_p5714425477246183910nteger @ C @ D2 ) ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ C ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ D2 ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_diff_triangle_ineq
% 0.35/0.63  thf(fact_6193_abs__diff__triangle__ineq,axiom,
% 0.35/0.63      ! [A: real,B: real,C: real,D2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D2 ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ ( minus_minus_real @ A @ C ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ D2 ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_diff_triangle_ineq
% 0.35/0.63  thf(fact_6194_abs__diff__triangle__ineq,axiom,
% 0.35/0.63      ! [A: rat,B: rat,C: rat,D2: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ C @ D2 ) ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ C ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ D2 ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_diff_triangle_ineq
% 0.35/0.63  thf(fact_6195_abs__diff__triangle__ineq,axiom,
% 0.35/0.63      ! [A: int,B: int,C: int,D2: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D2 ) ) ) @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ A @ C ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ D2 ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_diff_triangle_ineq
% 0.35/0.63  thf(fact_6196_abs__triangle__ineq4,axiom,
% 0.35/0.63      ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_triangle_ineq4
% 0.35/0.63  thf(fact_6197_abs__triangle__ineq4,axiom,
% 0.35/0.63      ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_triangle_ineq4
% 0.35/0.63  thf(fact_6198_abs__triangle__ineq4,axiom,
% 0.35/0.63      ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_triangle_ineq4
% 0.35/0.63  thf(fact_6199_abs__triangle__ineq4,axiom,
% 0.35/0.63      ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_triangle_ineq4
% 0.35/0.63  thf(fact_6200_abs__diff__le__iff,axiom,
% 0.35/0.63      ! [X: code_integer,A: code_integer,R: code_integer] :
% 0.35/0.63        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R )
% 0.35/0.63        = ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ R ) @ X )
% 0.35/0.63          & ( ord_le3102999989581377725nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_diff_le_iff
% 0.35/0.63  thf(fact_6201_abs__diff__le__iff,axiom,
% 0.35/0.63      ! [X: real,A: real,R: real] :
% 0.35/0.63        ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ X @ A ) ) @ R )
% 0.35/0.63        = ( ( ord_less_eq_real @ ( minus_minus_real @ A @ R ) @ X )
% 0.35/0.63          & ( ord_less_eq_real @ X @ ( plus_plus_real @ A @ R ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_diff_le_iff
% 0.35/0.63  thf(fact_6202_abs__diff__le__iff,axiom,
% 0.35/0.63      ! [X: rat,A: rat,R: rat] :
% 0.35/0.63        ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R )
% 0.35/0.63        = ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ R ) @ X )
% 0.35/0.63          & ( ord_less_eq_rat @ X @ ( plus_plus_rat @ A @ R ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_diff_le_iff
% 0.35/0.63  thf(fact_6203_abs__diff__le__iff,axiom,
% 0.35/0.63      ! [X: int,A: int,R: int] :
% 0.35/0.63        ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R )
% 0.35/0.63        = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R ) @ X )
% 0.35/0.63          & ( ord_less_eq_int @ X @ ( plus_plus_int @ A @ R ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_diff_le_iff
% 0.35/0.63  thf(fact_6204_abs__diff__less__iff,axiom,
% 0.35/0.63      ! [X: code_integer,A: code_integer,R: code_integer] :
% 0.35/0.63        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R )
% 0.35/0.63        = ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ R ) @ X )
% 0.35/0.63          & ( ord_le6747313008572928689nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_diff_less_iff
% 0.35/0.63  thf(fact_6205_abs__diff__less__iff,axiom,
% 0.35/0.63      ! [X: real,A: real,R: real] :
% 0.35/0.63        ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ A ) ) @ R )
% 0.35/0.63        = ( ( ord_less_real @ ( minus_minus_real @ A @ R ) @ X )
% 0.35/0.63          & ( ord_less_real @ X @ ( plus_plus_real @ A @ R ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_diff_less_iff
% 0.35/0.63  thf(fact_6206_abs__diff__less__iff,axiom,
% 0.35/0.63      ! [X: rat,A: rat,R: rat] :
% 0.35/0.63        ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R )
% 0.35/0.63        = ( ( ord_less_rat @ ( minus_minus_rat @ A @ R ) @ X )
% 0.35/0.63          & ( ord_less_rat @ X @ ( plus_plus_rat @ A @ R ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_diff_less_iff
% 0.35/0.63  thf(fact_6207_abs__diff__less__iff,axiom,
% 0.35/0.63      ! [X: int,A: int,R: int] :
% 0.35/0.63        ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R )
% 0.35/0.63        = ( ( ord_less_int @ ( minus_minus_int @ A @ R ) @ X )
% 0.35/0.63          & ( ord_less_int @ X @ ( plus_plus_int @ A @ R ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_diff_less_iff
% 0.35/0.63  thf(fact_6208_abs__real__def,axiom,
% 0.35/0.63      ( abs_abs_real
% 0.35/0.63      = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_real_def
% 0.35/0.63  thf(fact_6209_lemma__interval__lt,axiom,
% 0.35/0.63      ! [A: real,X: real,B: real] :
% 0.35/0.63        ( ( ord_less_real @ A @ X )
% 0.35/0.63       => ( ( ord_less_real @ X @ B )
% 0.35/0.63         => ? [D3: real] :
% 0.35/0.63              ( ( ord_less_real @ zero_zero_real @ D3 )
% 0.35/0.63              & ! [Y4: real] :
% 0.35/0.63                  ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y4 ) ) @ D3 )
% 0.35/0.63                 => ( ( ord_less_real @ A @ Y4 )
% 0.35/0.63                    & ( ord_less_real @ Y4 @ B ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % lemma_interval_lt
% 0.35/0.63  thf(fact_6210_sin__bound__lemma,axiom,
% 0.35/0.63      ! [X: real,Y2: real,U: real,V: real] :
% 0.35/0.63        ( ( X = Y2 )
% 0.35/0.63       => ( ( ord_less_eq_real @ ( abs_abs_real @ U ) @ V )
% 0.35/0.63         => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ X @ U ) @ Y2 ) ) @ V ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sin_bound_lemma
% 0.35/0.63  thf(fact_6211_tanh__real__gt__neg1,axiom,
% 0.35/0.63      ! [X: real] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( tanh_real @ X ) ) ).
% 0.35/0.63  
% 0.35/0.63  % tanh_real_gt_neg1
% 0.35/0.63  thf(fact_6212_abs__add__one__gt__zero,axiom,
% 0.35/0.63      ! [X: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_add_one_gt_zero
% 0.35/0.63  thf(fact_6213_abs__add__one__gt__zero,axiom,
% 0.35/0.63      ! [X: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ ( abs_abs_real @ X ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_add_one_gt_zero
% 0.35/0.63  thf(fact_6214_abs__add__one__gt__zero,axiom,
% 0.35/0.63      ! [X: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_add_one_gt_zero
% 0.35/0.63  thf(fact_6215_abs__add__one__gt__zero,axiom,
% 0.35/0.63      ! [X: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_add_one_gt_zero
% 0.35/0.63  thf(fact_6216_of__int__leD,axiom,
% 0.35/0.63      ! [N: int,X: code_integer] :
% 0.35/0.63        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X )
% 0.35/0.63       => ( ( N = zero_zero_int )
% 0.35/0.63          | ( ord_le3102999989581377725nteger @ one_one_Code_integer @ X ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % of_int_leD
% 0.35/0.63  thf(fact_6217_of__int__leD,axiom,
% 0.35/0.63      ! [N: int,X: rat] :
% 0.35/0.63        ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X )
% 0.35/0.63       => ( ( N = zero_zero_int )
% 0.35/0.63          | ( ord_less_eq_rat @ one_one_rat @ X ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % of_int_leD
% 0.35/0.63  thf(fact_6218_of__int__leD,axiom,
% 0.35/0.63      ! [N: int,X: real] :
% 0.35/0.63        ( ( ord_less_eq_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X )
% 0.35/0.63       => ( ( N = zero_zero_int )
% 0.35/0.63          | ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % of_int_leD
% 0.35/0.63  thf(fact_6219_of__int__leD,axiom,
% 0.35/0.63      ! [N: int,X: int] :
% 0.35/0.63        ( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X )
% 0.35/0.63       => ( ( N = zero_zero_int )
% 0.35/0.63          | ( ord_less_eq_int @ one_one_int @ X ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % of_int_leD
% 0.35/0.63  thf(fact_6220_of__int__lessD,axiom,
% 0.35/0.63      ! [N: int,X: code_integer] :
% 0.35/0.63        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X )
% 0.35/0.63       => ( ( N = zero_zero_int )
% 0.35/0.63          | ( ord_le6747313008572928689nteger @ one_one_Code_integer @ X ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % of_int_lessD
% 0.35/0.63  thf(fact_6221_of__int__lessD,axiom,
% 0.35/0.63      ! [N: int,X: real] :
% 0.35/0.63        ( ( ord_less_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X )
% 0.35/0.63       => ( ( N = zero_zero_int )
% 0.35/0.63          | ( ord_less_real @ one_one_real @ X ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % of_int_lessD
% 0.35/0.63  thf(fact_6222_of__int__lessD,axiom,
% 0.35/0.63      ! [N: int,X: rat] :
% 0.35/0.63        ( ( ord_less_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X )
% 0.35/0.63       => ( ( N = zero_zero_int )
% 0.35/0.63          | ( ord_less_rat @ one_one_rat @ X ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % of_int_lessD
% 0.35/0.63  thf(fact_6223_of__int__lessD,axiom,
% 0.35/0.63      ! [N: int,X: int] :
% 0.35/0.63        ( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X )
% 0.35/0.63       => ( ( N = zero_zero_int )
% 0.35/0.63          | ( ord_less_int @ one_one_int @ X ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % of_int_lessD
% 0.35/0.63  thf(fact_6224_lemma__interval,axiom,
% 0.35/0.63      ! [A: real,X: real,B: real] :
% 0.35/0.63        ( ( ord_less_real @ A @ X )
% 0.35/0.63       => ( ( ord_less_real @ X @ B )
% 0.35/0.63         => ? [D3: real] :
% 0.35/0.63              ( ( ord_less_real @ zero_zero_real @ D3 )
% 0.35/0.63              & ! [Y4: real] :
% 0.35/0.63                  ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y4 ) ) @ D3 )
% 0.35/0.63                 => ( ( ord_less_eq_real @ A @ Y4 )
% 0.35/0.63                    & ( ord_less_eq_real @ Y4 @ B ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % lemma_interval
% 0.35/0.63  thf(fact_6225_of__int__round__abs__le,axiom,
% 0.35/0.63      ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) @ X ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % of_int_round_abs_le
% 0.35/0.63  thf(fact_6226_of__int__round__abs__le,axiom,
% 0.35/0.63      ! [X: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) @ X ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % of_int_round_abs_le
% 0.35/0.63  thf(fact_6227_round__unique_H,axiom,
% 0.35/0.63      ! [X: real,N: int] :
% 0.35/0.63        ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ ( ring_1_of_int_real @ N ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.63       => ( ( archim8280529875227126926d_real @ X )
% 0.35/0.63          = N ) ) ).
% 0.35/0.63  
% 0.35/0.63  % round_unique'
% 0.35/0.63  thf(fact_6228_round__unique_H,axiom,
% 0.35/0.63      ! [X: rat,N: int] :
% 0.35/0.63        ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ ( ring_1_of_int_rat @ N ) ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 0.35/0.63       => ( ( archim7778729529865785530nd_rat @ X )
% 0.35/0.63          = N ) ) ).
% 0.35/0.63  
% 0.35/0.63  % round_unique'
% 0.35/0.63  thf(fact_6229_abs__le__square__iff,axiom,
% 0.35/0.63      ! [X: code_integer,Y2: code_integer] :
% 0.35/0.63        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ ( abs_abs_Code_integer @ Y2 ) )
% 0.35/0.63        = ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_le_square_iff
% 0.35/0.63  thf(fact_6230_abs__le__square__iff,axiom,
% 0.35/0.63      ! [X: real,Y2: real] :
% 0.35/0.63        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ Y2 ) )
% 0.35/0.63        = ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_le_square_iff
% 0.35/0.63  thf(fact_6231_abs__le__square__iff,axiom,
% 0.35/0.63      ! [X: int,Y2: int] :
% 0.35/0.63        ( ( ord_less_eq_int @ ( abs_abs_int @ X ) @ ( abs_abs_int @ Y2 ) )
% 0.35/0.63        = ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_le_square_iff
% 0.35/0.63  thf(fact_6232_abs__square__eq__1,axiom,
% 0.35/0.63      ! [X: code_integer] :
% 0.35/0.63        ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.63          = one_one_Code_integer )
% 0.35/0.63        = ( ( abs_abs_Code_integer @ X )
% 0.35/0.63          = one_one_Code_integer ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_square_eq_1
% 0.35/0.63  thf(fact_6233_abs__square__eq__1,axiom,
% 0.35/0.63      ! [X: rat] :
% 0.35/0.63        ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.63          = one_one_rat )
% 0.35/0.63        = ( ( abs_abs_rat @ X )
% 0.35/0.63          = one_one_rat ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_square_eq_1
% 0.35/0.63  thf(fact_6234_abs__square__eq__1,axiom,
% 0.35/0.63      ! [X: real] :
% 0.35/0.63        ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.63          = one_one_real )
% 0.35/0.63        = ( ( abs_abs_real @ X )
% 0.35/0.63          = one_one_real ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_square_eq_1
% 0.35/0.63  thf(fact_6235_abs__square__eq__1,axiom,
% 0.35/0.63      ! [X: int] :
% 0.35/0.63        ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.63          = one_one_int )
% 0.35/0.63        = ( ( abs_abs_int @ X )
% 0.35/0.63          = one_one_int ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_square_eq_1
% 0.35/0.63  thf(fact_6236_power__even__abs,axiom,
% 0.35/0.63      ! [N: nat,A: code_integer] :
% 0.35/0.63        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.63       => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N )
% 0.35/0.63          = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % power_even_abs
% 0.35/0.63  thf(fact_6237_power__even__abs,axiom,
% 0.35/0.63      ! [N: nat,A: real] :
% 0.35/0.63        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.63       => ( ( power_power_real @ ( abs_abs_real @ A ) @ N )
% 0.35/0.63          = ( power_power_real @ A @ N ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % power_even_abs
% 0.35/0.63  thf(fact_6238_power__even__abs,axiom,
% 0.35/0.63      ! [N: nat,A: int] :
% 0.35/0.63        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.63       => ( ( power_power_int @ ( abs_abs_int @ A ) @ N )
% 0.35/0.63          = ( power_power_int @ A @ N ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % power_even_abs
% 0.35/0.63  thf(fact_6239_power2__le__iff__abs__le,axiom,
% 0.35/0.63      ! [Y2: code_integer,X: code_integer] :
% 0.35/0.63        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y2 )
% 0.35/0.63       => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.63          = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ Y2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % power2_le_iff_abs_le
% 0.35/0.63  thf(fact_6240_power2__le__iff__abs__le,axiom,
% 0.35/0.63      ! [Y2: rat,X: rat] :
% 0.35/0.63        ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 0.35/0.63       => ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.63          = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ Y2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % power2_le_iff_abs_le
% 0.35/0.63  thf(fact_6241_power2__le__iff__abs__le,axiom,
% 0.35/0.63      ! [Y2: real,X: real] :
% 0.35/0.63        ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 0.35/0.63       => ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.63          = ( ord_less_eq_real @ ( abs_abs_real @ X ) @ Y2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % power2_le_iff_abs_le
% 0.35/0.63  thf(fact_6242_power2__le__iff__abs__le,axiom,
% 0.35/0.63      ! [Y2: int,X: int] :
% 0.35/0.63        ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 0.35/0.63       => ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.63          = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ Y2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % power2_le_iff_abs_le
% 0.35/0.63  thf(fact_6243_abs__sqrt__wlog,axiom,
% 0.35/0.63      ! [P: code_integer > code_integer > $o,X: code_integer] :
% 0.35/0.63        ( ! [X3: code_integer] :
% 0.35/0.63            ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X3 )
% 0.35/0.63           => ( P @ X3 @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.63       => ( P @ ( abs_abs_Code_integer @ X ) @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_sqrt_wlog
% 0.35/0.63  thf(fact_6244_abs__sqrt__wlog,axiom,
% 0.35/0.63      ! [P: rat > rat > $o,X: rat] :
% 0.35/0.63        ( ! [X3: rat] :
% 0.35/0.63            ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 0.35/0.63           => ( P @ X3 @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.63       => ( P @ ( abs_abs_rat @ X ) @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_sqrt_wlog
% 0.35/0.63  thf(fact_6245_abs__sqrt__wlog,axiom,
% 0.35/0.63      ! [P: real > real > $o,X: real] :
% 0.35/0.63        ( ! [X3: real] :
% 0.35/0.63            ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.35/0.63           => ( P @ X3 @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.63       => ( P @ ( abs_abs_real @ X ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_sqrt_wlog
% 0.35/0.63  thf(fact_6246_abs__sqrt__wlog,axiom,
% 0.35/0.63      ! [P: int > int > $o,X: int] :
% 0.35/0.63        ( ! [X3: int] :
% 0.35/0.63            ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 0.35/0.63           => ( P @ X3 @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.63       => ( P @ ( abs_abs_int @ X ) @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_sqrt_wlog
% 0.35/0.63  thf(fact_6247_abs__square__le__1,axiom,
% 0.35/0.63      ! [X: code_integer] :
% 0.35/0.63        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 0.35/0.63        = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_square_le_1
% 0.35/0.63  thf(fact_6248_abs__square__le__1,axiom,
% 0.35/0.63      ! [X: rat] :
% 0.35/0.63        ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 0.35/0.63        = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_square_le_1
% 0.35/0.63  thf(fact_6249_abs__square__le__1,axiom,
% 0.35/0.63      ! [X: real] :
% 0.35/0.63        ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 0.35/0.63        = ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_square_le_1
% 0.35/0.63  thf(fact_6250_abs__square__le__1,axiom,
% 0.35/0.63      ! [X: int] :
% 0.35/0.63        ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 0.35/0.63        = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_square_le_1
% 0.35/0.63  thf(fact_6251_abs__square__less__1,axiom,
% 0.35/0.63      ! [X: code_integer] :
% 0.35/0.63        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 0.35/0.63        = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_square_less_1
% 0.35/0.63  thf(fact_6252_abs__square__less__1,axiom,
% 0.35/0.63      ! [X: real] :
% 0.35/0.63        ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 0.35/0.63        = ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_square_less_1
% 0.35/0.63  thf(fact_6253_abs__square__less__1,axiom,
% 0.35/0.63      ! [X: rat] :
% 0.35/0.63        ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 0.35/0.63        = ( ord_less_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_square_less_1
% 0.35/0.63  thf(fact_6254_abs__square__less__1,axiom,
% 0.35/0.63      ! [X: int] :
% 0.35/0.63        ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 0.35/0.63        = ( ord_less_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_square_less_1
% 0.35/0.63  thf(fact_6255_power__mono__even,axiom,
% 0.35/0.63      ! [N: nat,A: code_integer,B: code_integer] :
% 0.35/0.63        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.63       => ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) )
% 0.35/0.63         => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % power_mono_even
% 0.35/0.63  thf(fact_6256_power__mono__even,axiom,
% 0.35/0.63      ! [N: nat,A: real,B: real] :
% 0.35/0.63        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.63       => ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) )
% 0.35/0.63         => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % power_mono_even
% 0.35/0.63  thf(fact_6257_power__mono__even,axiom,
% 0.35/0.63      ! [N: nat,A: int,B: int] :
% 0.35/0.63        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.63       => ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) )
% 0.35/0.63         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % power_mono_even
% 0.35/0.63  thf(fact_6258_abs__ln__one__plus__x__minus__x__bound__nonneg,axiom,
% 0.35/0.63      ! [X: real] :
% 0.35/0.63        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.63       => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.35/0.63         => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_ln_one_plus_x_minus_x_bound_nonneg
% 0.35/0.63  thf(fact_6259_of__int__round__le,axiom,
% 0.35/0.63      ! [X: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) @ ( plus_plus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % of_int_round_le
% 0.35/0.63  thf(fact_6260_of__int__round__le,axiom,
% 0.35/0.63      ! [X: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % of_int_round_le
% 0.35/0.63  thf(fact_6261_of__int__round__ge,axiom,
% 0.35/0.63      ! [X: real] : ( ord_less_eq_real @ ( minus_minus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % of_int_round_ge
% 0.35/0.63  thf(fact_6262_of__int__round__ge,axiom,
% 0.35/0.63      ! [X: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % of_int_round_ge
% 0.35/0.63  thf(fact_6263_arctan__double,axiom,
% 0.35/0.63      ! [X: real] :
% 0.35/0.63        ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.35/0.63       => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ X ) )
% 0.35/0.63          = ( arctan @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % arctan_double
% 0.35/0.63  thf(fact_6264_Sum__Icc__int,axiom,
% 0.35/0.63      ! [M: int,N: int] :
% 0.35/0.63        ( ( ord_less_eq_int @ M @ N )
% 0.35/0.63       => ( ( groups4538972089207619220nt_int
% 0.35/0.63            @ ^ [X2: int] : X2
% 0.35/0.63            @ ( set_or1266510415728281911st_int @ M @ N ) )
% 0.35/0.63          = ( divide_divide_int @ ( minus_minus_int @ ( times_times_int @ N @ ( plus_plus_int @ N @ one_one_int ) ) @ ( times_times_int @ M @ ( minus_minus_int @ M @ one_one_int ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % Sum_Icc_int
% 0.35/0.63  thf(fact_6265_mask__numeral,axiom,
% 0.35/0.63      ! [N: num] :
% 0.35/0.63        ( ( bit_se2002935070580805687sk_nat @ ( numeral_numeral_nat @ N ) )
% 0.35/0.63        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ ( pred_numeral @ N ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % mask_numeral
% 0.35/0.63  thf(fact_6266_mask__numeral,axiom,
% 0.35/0.63      ! [N: num] :
% 0.35/0.63        ( ( bit_se2000444600071755411sk_int @ ( numeral_numeral_nat @ N ) )
% 0.35/0.63        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ ( pred_numeral @ N ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % mask_numeral
% 0.35/0.63  thf(fact_6267_take__bit__rec,axiom,
% 0.35/0.63      ( bit_se2923211474154528505it_int
% 0.35/0.63      = ( ^ [N2: nat,A3: int] : ( if_int @ ( N2 = zero_zero_nat ) @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_rec
% 0.35/0.63  thf(fact_6268_take__bit__rec,axiom,
% 0.35/0.63      ( bit_se2925701944663578781it_nat
% 0.35/0.63      = ( ^ [N2: nat,A3: nat] : ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_rec
% 0.35/0.63  thf(fact_6269_num_Osize__gen_I3_J,axiom,
% 0.35/0.63      ! [X33: num] :
% 0.35/0.63        ( ( size_num @ ( bit1 @ X33 ) )
% 0.35/0.63        = ( plus_plus_nat @ ( size_num @ X33 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % num.size_gen(3)
% 0.35/0.63  thf(fact_6270_tanh__real__altdef,axiom,
% 0.35/0.63      ( tanh_real
% 0.35/0.63      = ( ^ [X2: real] : ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 ) ) ) @ ( plus_plus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % tanh_real_altdef
% 0.35/0.63  thf(fact_6271_mask__nat__positive__iff,axiom,
% 0.35/0.63      ! [N: nat] :
% 0.35/0.63        ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 0.35/0.63        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.35/0.63  
% 0.35/0.63  % mask_nat_positive_iff
% 0.35/0.63  thf(fact_6272_take__bit__of__0,axiom,
% 0.35/0.63      ! [N: nat] :
% 0.35/0.63        ( ( bit_se2923211474154528505it_int @ N @ zero_zero_int )
% 0.35/0.63        = zero_zero_int ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_of_0
% 0.35/0.63  thf(fact_6273_take__bit__of__0,axiom,
% 0.35/0.63      ! [N: nat] :
% 0.35/0.63        ( ( bit_se2925701944663578781it_nat @ N @ zero_zero_nat )
% 0.35/0.63        = zero_zero_nat ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_of_0
% 0.35/0.63  thf(fact_6274_exp__less__cancel__iff,axiom,
% 0.35/0.63      ! [X: real,Y2: real] :
% 0.35/0.63        ( ( ord_less_real @ ( exp_real @ X ) @ ( exp_real @ Y2 ) )
% 0.35/0.63        = ( ord_less_real @ X @ Y2 ) ) ).
% 0.35/0.63  
% 0.35/0.63  % exp_less_cancel_iff
% 0.35/0.63  thf(fact_6275_exp__less__mono,axiom,
% 0.35/0.63      ! [X: real,Y2: real] :
% 0.35/0.63        ( ( ord_less_real @ X @ Y2 )
% 0.35/0.63       => ( ord_less_real @ ( exp_real @ X ) @ ( exp_real @ Y2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % exp_less_mono
% 0.35/0.63  thf(fact_6276_take__bit__and,axiom,
% 0.35/0.63      ! [N: nat,A: int,B: int] :
% 0.35/0.63        ( ( bit_se2923211474154528505it_int @ N @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 0.35/0.63        = ( bit_se725231765392027082nd_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_se2923211474154528505it_int @ N @ B ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_and
% 0.35/0.63  thf(fact_6277_take__bit__and,axiom,
% 0.35/0.63      ! [N: nat,A: nat,B: nat] :
% 0.35/0.63        ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 0.35/0.63        = ( bit_se727722235901077358nd_nat @ ( bit_se2925701944663578781it_nat @ N @ A ) @ ( bit_se2925701944663578781it_nat @ N @ B ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_and
% 0.35/0.63  thf(fact_6278_exp__le__cancel__iff,axiom,
% 0.35/0.63      ! [X: real,Y2: real] :
% 0.35/0.63        ( ( ord_less_eq_real @ ( exp_real @ X ) @ ( exp_real @ Y2 ) )
% 0.35/0.63        = ( ord_less_eq_real @ X @ Y2 ) ) ).
% 0.35/0.63  
% 0.35/0.63  % exp_le_cancel_iff
% 0.35/0.63  thf(fact_6279_concat__bit__of__zero__2,axiom,
% 0.35/0.63      ! [N: nat,K: int] :
% 0.35/0.63        ( ( bit_concat_bit @ N @ K @ zero_zero_int )
% 0.35/0.63        = ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 0.35/0.63  
% 0.35/0.63  % concat_bit_of_zero_2
% 0.35/0.63  thf(fact_6280_exp__zero,axiom,
% 0.35/0.63      ( ( exp_complex @ zero_zero_complex )
% 0.35/0.63      = one_one_complex ) ).
% 0.35/0.63  
% 0.35/0.63  % exp_zero
% 0.35/0.63  thf(fact_6281_exp__zero,axiom,
% 0.35/0.63      ( ( exp_real @ zero_zero_real )
% 0.35/0.63      = one_one_real ) ).
% 0.35/0.63  
% 0.35/0.63  % exp_zero
% 0.35/0.63  thf(fact_6282_take__bit__0,axiom,
% 0.35/0.63      ! [A: int] :
% 0.35/0.63        ( ( bit_se2923211474154528505it_int @ zero_zero_nat @ A )
% 0.35/0.63        = zero_zero_int ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_0
% 0.35/0.63  thf(fact_6283_take__bit__0,axiom,
% 0.35/0.63      ! [A: nat] :
% 0.35/0.63        ( ( bit_se2925701944663578781it_nat @ zero_zero_nat @ A )
% 0.35/0.63        = zero_zero_nat ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_0
% 0.35/0.63  thf(fact_6284_take__bit__Suc__1,axiom,
% 0.35/0.63      ! [N: nat] :
% 0.35/0.63        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ one_one_int )
% 0.35/0.63        = one_one_int ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_Suc_1
% 0.35/0.63  thf(fact_6285_take__bit__Suc__1,axiom,
% 0.35/0.63      ! [N: nat] :
% 0.35/0.63        ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ one_one_nat )
% 0.35/0.63        = one_one_nat ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_Suc_1
% 0.35/0.63  thf(fact_6286_take__bit__numeral__1,axiom,
% 0.35/0.63      ! [L2: num] :
% 0.35/0.63        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ one_one_int )
% 0.35/0.63        = one_one_int ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_numeral_1
% 0.35/0.63  thf(fact_6287_take__bit__numeral__1,axiom,
% 0.35/0.63      ! [L2: num] :
% 0.35/0.63        ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L2 ) @ one_one_nat )
% 0.35/0.63        = one_one_nat ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_numeral_1
% 0.35/0.63  thf(fact_6288_mask__eq__0__iff,axiom,
% 0.35/0.63      ! [N: nat] :
% 0.35/0.63        ( ( ( bit_se2002935070580805687sk_nat @ N )
% 0.35/0.63          = zero_zero_nat )
% 0.35/0.63        = ( N = zero_zero_nat ) ) ).
% 0.35/0.63  
% 0.35/0.63  % mask_eq_0_iff
% 0.35/0.63  thf(fact_6289_mask__eq__0__iff,axiom,
% 0.35/0.63      ! [N: nat] :
% 0.35/0.63        ( ( ( bit_se2000444600071755411sk_int @ N )
% 0.35/0.63          = zero_zero_int )
% 0.35/0.63        = ( N = zero_zero_nat ) ) ).
% 0.35/0.63  
% 0.35/0.63  % mask_eq_0_iff
% 0.35/0.63  thf(fact_6290_mask__0,axiom,
% 0.35/0.63      ( ( bit_se2002935070580805687sk_nat @ zero_zero_nat )
% 0.35/0.63      = zero_zero_nat ) ).
% 0.35/0.63  
% 0.35/0.63  % mask_0
% 0.35/0.63  thf(fact_6291_mask__0,axiom,
% 0.35/0.63      ( ( bit_se2000444600071755411sk_int @ zero_zero_nat )
% 0.35/0.63      = zero_zero_int ) ).
% 0.35/0.63  
% 0.35/0.63  % mask_0
% 0.35/0.63  thf(fact_6292_arctan__less__zero__iff,axiom,
% 0.35/0.63      ! [X: real] :
% 0.35/0.63        ( ( ord_less_real @ ( arctan @ X ) @ zero_zero_real )
% 0.35/0.63        = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 0.35/0.63  
% 0.35/0.63  % arctan_less_zero_iff
% 0.35/0.63  thf(fact_6293_zero__less__arctan__iff,axiom,
% 0.35/0.63      ! [X: real] :
% 0.35/0.63        ( ( ord_less_real @ zero_zero_real @ ( arctan @ X ) )
% 0.35/0.63        = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 0.35/0.63  
% 0.35/0.63  % zero_less_arctan_iff
% 0.35/0.63  thf(fact_6294_exp__eq__one__iff,axiom,
% 0.35/0.63      ! [X: real] :
% 0.35/0.63        ( ( ( exp_real @ X )
% 0.35/0.63          = one_one_real )
% 0.35/0.63        = ( X = zero_zero_real ) ) ).
% 0.35/0.63  
% 0.35/0.63  % exp_eq_one_iff
% 0.35/0.63  thf(fact_6295_arctan__le__zero__iff,axiom,
% 0.35/0.63      ! [X: real] :
% 0.35/0.63        ( ( ord_less_eq_real @ ( arctan @ X ) @ zero_zero_real )
% 0.35/0.63        = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 0.35/0.63  
% 0.35/0.63  % arctan_le_zero_iff
% 0.35/0.63  thf(fact_6296_zero__le__arctan__iff,axiom,
% 0.35/0.63      ! [X: real] :
% 0.35/0.63        ( ( ord_less_eq_real @ zero_zero_real @ ( arctan @ X ) )
% 0.35/0.63        = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 0.35/0.63  
% 0.35/0.63  % zero_le_arctan_iff
% 0.35/0.63  thf(fact_6297_sum__abs,axiom,
% 0.35/0.63      ! [F: int > int,A2: set_int] :
% 0.35/0.63        ( ord_less_eq_int @ ( abs_abs_int @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 0.35/0.63        @ ( groups4538972089207619220nt_int
% 0.35/0.63          @ ^ [I3: int] : ( abs_abs_int @ ( F @ I3 ) )
% 0.35/0.63          @ A2 ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_abs
% 0.35/0.63  thf(fact_6298_sum__abs,axiom,
% 0.35/0.63      ! [F: nat > real,A2: set_nat] :
% 0.35/0.63        ( ord_less_eq_real @ ( abs_abs_real @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 0.35/0.63        @ ( groups6591440286371151544t_real
% 0.35/0.63          @ ^ [I3: nat] : ( abs_abs_real @ ( F @ I3 ) )
% 0.35/0.63          @ A2 ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_abs
% 0.35/0.63  thf(fact_6299_sum_Oinsert,axiom,
% 0.35/0.63      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > real] :
% 0.35/0.63        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.35/0.63       => ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 0.35/0.63         => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 0.35/0.63            = ( plus_plus_real @ ( G @ X ) @ ( groups2240296850493347238T_real @ G @ A2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.insert
% 0.35/0.63  thf(fact_6300_sum_Oinsert,axiom,
% 0.35/0.63      ! [A2: set_real,X: real,G: real > real] :
% 0.35/0.63        ( ( finite_finite_real @ A2 )
% 0.35/0.63       => ( ~ ( member_real @ X @ A2 )
% 0.35/0.63         => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X @ A2 ) )
% 0.35/0.63            = ( plus_plus_real @ ( G @ X ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.insert
% 0.35/0.63  thf(fact_6301_sum_Oinsert,axiom,
% 0.35/0.63      ! [A2: set_int,X: int,G: int > real] :
% 0.35/0.63        ( ( finite_finite_int @ A2 )
% 0.35/0.63       => ( ~ ( member_int @ X @ A2 )
% 0.35/0.63         => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X @ A2 ) )
% 0.35/0.63            = ( plus_plus_real @ ( G @ X ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.insert
% 0.35/0.63  thf(fact_6302_sum_Oinsert,axiom,
% 0.35/0.63      ! [A2: set_complex,X: complex,G: complex > real] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.63       => ( ~ ( member_complex @ X @ A2 )
% 0.35/0.63         => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A2 ) )
% 0.35/0.63            = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.insert
% 0.35/0.63  thf(fact_6303_sum_Oinsert,axiom,
% 0.35/0.63      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 0.35/0.63        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.35/0.63       => ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 0.35/0.63         => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 0.35/0.63            = ( plus_plus_rat @ ( G @ X ) @ ( groups136491112297645522BT_rat @ G @ A2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.insert
% 0.35/0.63  thf(fact_6304_sum_Oinsert,axiom,
% 0.35/0.63      ! [A2: set_real,X: real,G: real > rat] :
% 0.35/0.63        ( ( finite_finite_real @ A2 )
% 0.35/0.63       => ( ~ ( member_real @ X @ A2 )
% 0.35/0.63         => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X @ A2 ) )
% 0.35/0.63            = ( plus_plus_rat @ ( G @ X ) @ ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.insert
% 0.35/0.63  thf(fact_6305_sum_Oinsert,axiom,
% 0.35/0.63      ! [A2: set_int,X: int,G: int > rat] :
% 0.35/0.63        ( ( finite_finite_int @ A2 )
% 0.35/0.63       => ( ~ ( member_int @ X @ A2 )
% 0.35/0.63         => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X @ A2 ) )
% 0.35/0.63            = ( plus_plus_rat @ ( G @ X ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.insert
% 0.35/0.63  thf(fact_6306_sum_Oinsert,axiom,
% 0.35/0.63      ! [A2: set_nat,X: nat,G: nat > rat] :
% 0.35/0.63        ( ( finite_finite_nat @ A2 )
% 0.35/0.63       => ( ~ ( member_nat @ X @ A2 )
% 0.35/0.63         => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A2 ) )
% 0.35/0.63            = ( plus_plus_rat @ ( G @ X ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.insert
% 0.35/0.63  thf(fact_6307_sum_Oinsert,axiom,
% 0.35/0.63      ! [A2: set_complex,X: complex,G: complex > rat] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.63       => ( ~ ( member_complex @ X @ A2 )
% 0.35/0.63         => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X @ A2 ) )
% 0.35/0.63            = ( plus_plus_rat @ ( G @ X ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.insert
% 0.35/0.63  thf(fact_6308_sum_Oinsert,axiom,
% 0.35/0.63      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > nat] :
% 0.35/0.63        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.35/0.63       => ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 0.35/0.63         => ( ( groups771621172384141258BT_nat @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 0.35/0.63            = ( plus_plus_nat @ ( G @ X ) @ ( groups771621172384141258BT_nat @ G @ A2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.insert
% 0.35/0.63  thf(fact_6309_take__bit__of__1__eq__0__iff,axiom,
% 0.35/0.63      ! [N: nat] :
% 0.35/0.63        ( ( ( bit_se2923211474154528505it_int @ N @ one_one_int )
% 0.35/0.63          = zero_zero_int )
% 0.35/0.63        = ( N = zero_zero_nat ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_of_1_eq_0_iff
% 0.35/0.63  thf(fact_6310_take__bit__of__1__eq__0__iff,axiom,
% 0.35/0.63      ! [N: nat] :
% 0.35/0.63        ( ( ( bit_se2925701944663578781it_nat @ N @ one_one_nat )
% 0.35/0.63          = zero_zero_nat )
% 0.35/0.63        = ( N = zero_zero_nat ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_of_1_eq_0_iff
% 0.35/0.63  thf(fact_6311_mask__Suc__0,axiom,
% 0.35/0.63      ( ( bit_se2002935070580805687sk_nat @ ( suc @ zero_zero_nat ) )
% 0.35/0.63      = one_one_nat ) ).
% 0.35/0.63  
% 0.35/0.63  % mask_Suc_0
% 0.35/0.63  thf(fact_6312_mask__Suc__0,axiom,
% 0.35/0.63      ( ( bit_se2000444600071755411sk_int @ ( suc @ zero_zero_nat ) )
% 0.35/0.63      = one_one_int ) ).
% 0.35/0.63  
% 0.35/0.63  % mask_Suc_0
% 0.35/0.63  thf(fact_6313_exp__less__one__iff,axiom,
% 0.35/0.63      ! [X: real] :
% 0.35/0.63        ( ( ord_less_real @ ( exp_real @ X ) @ one_one_real )
% 0.35/0.63        = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 0.35/0.63  
% 0.35/0.63  % exp_less_one_iff
% 0.35/0.63  thf(fact_6314_one__less__exp__iff,axiom,
% 0.35/0.63      ! [X: real] :
% 0.35/0.63        ( ( ord_less_real @ one_one_real @ ( exp_real @ X ) )
% 0.35/0.63        = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 0.35/0.63  
% 0.35/0.63  % one_less_exp_iff
% 0.35/0.63  thf(fact_6315_one__le__exp__iff,axiom,
% 0.35/0.63      ! [X: real] :
% 0.35/0.63        ( ( ord_less_eq_real @ one_one_real @ ( exp_real @ X ) )
% 0.35/0.63        = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 0.35/0.63  
% 0.35/0.63  % one_le_exp_iff
% 0.35/0.63  thf(fact_6316_exp__le__one__iff,axiom,
% 0.35/0.63      ! [X: real] :
% 0.35/0.63        ( ( ord_less_eq_real @ ( exp_real @ X ) @ one_one_real )
% 0.35/0.63        = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 0.35/0.63  
% 0.35/0.63  % exp_le_one_iff
% 0.35/0.63  thf(fact_6317_take__bit__minus__one__eq__mask,axiom,
% 0.35/0.63      ! [N: nat] :
% 0.35/0.63        ( ( bit_se1745604003318907178nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.63        = ( bit_se2119862282449309892nteger @ N ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_minus_one_eq_mask
% 0.35/0.63  thf(fact_6318_take__bit__minus__one__eq__mask,axiom,
% 0.35/0.63      ! [N: nat] :
% 0.35/0.63        ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.63        = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_minus_one_eq_mask
% 0.35/0.63  thf(fact_6319_exp__ln__iff,axiom,
% 0.35/0.63      ! [X: real] :
% 0.35/0.63        ( ( ( exp_real @ ( ln_ln_real @ X ) )
% 0.35/0.63          = X )
% 0.35/0.63        = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 0.35/0.63  
% 0.35/0.63  % exp_ln_iff
% 0.35/0.63  thf(fact_6320_exp__ln,axiom,
% 0.35/0.63      ! [X: real] :
% 0.35/0.63        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.63       => ( ( exp_real @ ( ln_ln_real @ X ) )
% 0.35/0.63          = X ) ) ).
% 0.35/0.63  
% 0.35/0.63  % exp_ln
% 0.35/0.63  thf(fact_6321_take__bit__of__Suc__0,axiom,
% 0.35/0.63      ! [N: nat] :
% 0.35/0.63        ( ( bit_se2925701944663578781it_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.35/0.63        = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_of_Suc_0
% 0.35/0.63  thf(fact_6322_sum__abs__ge__zero,axiom,
% 0.35/0.63      ! [F: int > int,A2: set_int] :
% 0.35/0.63        ( ord_less_eq_int @ zero_zero_int
% 0.35/0.63        @ ( groups4538972089207619220nt_int
% 0.35/0.63          @ ^ [I3: int] : ( abs_abs_int @ ( F @ I3 ) )
% 0.35/0.63          @ A2 ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_abs_ge_zero
% 0.35/0.63  thf(fact_6323_sum__abs__ge__zero,axiom,
% 0.35/0.63      ! [F: nat > real,A2: set_nat] :
% 0.35/0.63        ( ord_less_eq_real @ zero_zero_real
% 0.35/0.63        @ ( groups6591440286371151544t_real
% 0.35/0.63          @ ^ [I3: nat] : ( abs_abs_real @ ( F @ I3 ) )
% 0.35/0.63          @ A2 ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_abs_ge_zero
% 0.35/0.63  thf(fact_6324_take__bit__of__1,axiom,
% 0.35/0.63      ! [N: nat] :
% 0.35/0.63        ( ( bit_se1745604003318907178nteger @ N @ one_one_Code_integer )
% 0.35/0.63        = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_of_1
% 0.35/0.63  thf(fact_6325_take__bit__of__1,axiom,
% 0.35/0.63      ! [N: nat] :
% 0.35/0.63        ( ( bit_se2923211474154528505it_int @ N @ one_one_int )
% 0.35/0.63        = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_of_1
% 0.35/0.63  thf(fact_6326_take__bit__of__1,axiom,
% 0.35/0.63      ! [N: nat] :
% 0.35/0.63        ( ( bit_se2925701944663578781it_nat @ N @ one_one_nat )
% 0.35/0.63        = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_of_1
% 0.35/0.63  thf(fact_6327_even__take__bit__eq,axiom,
% 0.35/0.63      ! [N: nat,A: code_integer] :
% 0.35/0.63        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1745604003318907178nteger @ N @ A ) )
% 0.35/0.63        = ( ( N = zero_zero_nat )
% 0.35/0.63          | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % even_take_bit_eq
% 0.35/0.63  thf(fact_6328_even__take__bit__eq,axiom,
% 0.35/0.63      ! [N: nat,A: int] :
% 0.35/0.63        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2923211474154528505it_int @ N @ A ) )
% 0.35/0.63        = ( ( N = zero_zero_nat )
% 0.35/0.63          | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % even_take_bit_eq
% 0.35/0.63  thf(fact_6329_even__take__bit__eq,axiom,
% 0.35/0.63      ! [N: nat,A: nat] :
% 0.35/0.63        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2925701944663578781it_nat @ N @ A ) )
% 0.35/0.63        = ( ( N = zero_zero_nat )
% 0.35/0.63          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % even_take_bit_eq
% 0.35/0.63  thf(fact_6330_take__bit__Suc__0,axiom,
% 0.35/0.63      ! [A: int] :
% 0.35/0.63        ( ( bit_se2923211474154528505it_int @ ( suc @ zero_zero_nat ) @ A )
% 0.35/0.63        = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_Suc_0
% 0.35/0.63  thf(fact_6331_take__bit__Suc__0,axiom,
% 0.35/0.63      ! [A: nat] :
% 0.35/0.63        ( ( bit_se2925701944663578781it_nat @ ( suc @ zero_zero_nat ) @ A )
% 0.35/0.63        = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_Suc_0
% 0.35/0.63  thf(fact_6332_take__bit__of__exp,axiom,
% 0.35/0.63      ! [M: nat,N: nat] :
% 0.35/0.63        ( ( bit_se1745604003318907178nteger @ M @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.63        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ N @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_of_exp
% 0.35/0.63  thf(fact_6333_take__bit__of__exp,axiom,
% 0.35/0.63      ! [M: nat,N: nat] :
% 0.35/0.63        ( ( bit_se2923211474154528505it_int @ M @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.63        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ N @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_of_exp
% 0.35/0.63  thf(fact_6334_take__bit__of__exp,axiom,
% 0.35/0.63      ! [M: nat,N: nat] :
% 0.35/0.63        ( ( bit_se2925701944663578781it_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.63        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ N @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_of_exp
% 0.35/0.63  thf(fact_6335_take__bit__of__2,axiom,
% 0.35/0.63      ! [N: nat] :
% 0.35/0.63        ( ( bit_se1745604003318907178nteger @ N @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.35/0.63        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_of_2
% 0.35/0.63  thf(fact_6336_take__bit__of__2,axiom,
% 0.35/0.63      ! [N: nat] :
% 0.35/0.63        ( ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.63        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_of_2
% 0.35/0.63  thf(fact_6337_take__bit__of__2,axiom,
% 0.35/0.63      ! [N: nat] :
% 0.35/0.63        ( ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.63        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_of_2
% 0.35/0.63  thf(fact_6338_take__bit__eq__mask,axiom,
% 0.35/0.63      ( bit_se2923211474154528505it_int
% 0.35/0.63      = ( ^ [N2: nat,A3: int] : ( bit_se725231765392027082nd_int @ A3 @ ( bit_se2000444600071755411sk_int @ N2 ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_eq_mask
% 0.35/0.63  thf(fact_6339_take__bit__eq__mask,axiom,
% 0.35/0.63      ( bit_se2925701944663578781it_nat
% 0.35/0.63      = ( ^ [N2: nat,A3: nat] : ( bit_se727722235901077358nd_nat @ A3 @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_eq_mask
% 0.35/0.63  thf(fact_6340_take__bit__of__int,axiom,
% 0.35/0.63      ! [N: nat,K: int] :
% 0.35/0.63        ( ( bit_se2923211474154528505it_int @ N @ ( ring_1_of_int_int @ K ) )
% 0.35/0.63        = ( ring_1_of_int_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_of_int
% 0.35/0.63  thf(fact_6341_of__int__mask__eq,axiom,
% 0.35/0.63      ! [N: nat] :
% 0.35/0.63        ( ( ring_1_of_int_int @ ( bit_se2000444600071755411sk_int @ N ) )
% 0.35/0.63        = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 0.35/0.63  
% 0.35/0.63  % of_int_mask_eq
% 0.35/0.63  thf(fact_6342_take__bit__add,axiom,
% 0.35/0.63      ! [N: nat,A: int,B: int] :
% 0.35/0.63        ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_se2923211474154528505it_int @ N @ B ) ) )
% 0.35/0.63        = ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ A @ B ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_add
% 0.35/0.63  thf(fact_6343_take__bit__add,axiom,
% 0.35/0.63      ! [N: nat,A: nat,B: nat] :
% 0.35/0.63        ( ( bit_se2925701944663578781it_nat @ N @ ( plus_plus_nat @ ( bit_se2925701944663578781it_nat @ N @ A ) @ ( bit_se2925701944663578781it_nat @ N @ B ) ) )
% 0.35/0.63        = ( bit_se2925701944663578781it_nat @ N @ ( plus_plus_nat @ A @ B ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_add
% 0.35/0.63  thf(fact_6344_take__bit__tightened,axiom,
% 0.35/0.63      ! [N: nat,A: int,B: int,M: nat] :
% 0.35/0.63        ( ( ( bit_se2923211474154528505it_int @ N @ A )
% 0.35/0.63          = ( bit_se2923211474154528505it_int @ N @ B ) )
% 0.35/0.63       => ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.63         => ( ( bit_se2923211474154528505it_int @ M @ A )
% 0.35/0.63            = ( bit_se2923211474154528505it_int @ M @ B ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_tightened
% 0.35/0.63  thf(fact_6345_take__bit__tightened,axiom,
% 0.35/0.63      ! [N: nat,A: nat,B: nat,M: nat] :
% 0.35/0.63        ( ( ( bit_se2925701944663578781it_nat @ N @ A )
% 0.35/0.63          = ( bit_se2925701944663578781it_nat @ N @ B ) )
% 0.35/0.63       => ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.63         => ( ( bit_se2925701944663578781it_nat @ M @ A )
% 0.35/0.63            = ( bit_se2925701944663578781it_nat @ M @ B ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_tightened
% 0.35/0.63  thf(fact_6346_take__bit__nat__less__eq__self,axiom,
% 0.35/0.63      ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_nat_less_eq_self
% 0.35/0.63  thf(fact_6347_take__bit__tightened__less__eq__nat,axiom,
% 0.35/0.63      ! [M: nat,N: nat,Q2: nat] :
% 0.35/0.63        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.63       => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M @ Q2 ) @ ( bit_se2925701944663578781it_nat @ N @ Q2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_tightened_less_eq_nat
% 0.35/0.63  thf(fact_6348_exp__less__cancel,axiom,
% 0.35/0.63      ! [X: real,Y2: real] :
% 0.35/0.63        ( ( ord_less_real @ ( exp_real @ X ) @ ( exp_real @ Y2 ) )
% 0.35/0.63       => ( ord_less_real @ X @ Y2 ) ) ).
% 0.35/0.63  
% 0.35/0.63  % exp_less_cancel
% 0.35/0.63  thf(fact_6349_exp__times__arg__commute,axiom,
% 0.35/0.63      ! [A2: complex] :
% 0.35/0.63        ( ( times_times_complex @ ( exp_complex @ A2 ) @ A2 )
% 0.35/0.63        = ( times_times_complex @ A2 @ ( exp_complex @ A2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % exp_times_arg_commute
% 0.35/0.63  thf(fact_6350_exp__times__arg__commute,axiom,
% 0.35/0.63      ! [A2: real] :
% 0.35/0.63        ( ( times_times_real @ ( exp_real @ A2 ) @ A2 )
% 0.35/0.63        = ( times_times_real @ A2 @ ( exp_real @ A2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % exp_times_arg_commute
% 0.35/0.63  thf(fact_6351_take__bit__minus,axiom,
% 0.35/0.63      ! [N: nat,K: int] :
% 0.35/0.63        ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 0.35/0.63        = ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_minus
% 0.35/0.63  thf(fact_6352_take__bit__mult,axiom,
% 0.35/0.63      ! [N: nat,K: int,L2: int] :
% 0.35/0.63        ( ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( bit_se2923211474154528505it_int @ N @ L2 ) ) )
% 0.35/0.63        = ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ K @ L2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_mult
% 0.35/0.63  thf(fact_6353_take__bit__diff,axiom,
% 0.35/0.63      ! [N: nat,K: int,L2: int] :
% 0.35/0.63        ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( bit_se2923211474154528505it_int @ N @ L2 ) ) )
% 0.35/0.63        = ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ L2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_diff
% 0.35/0.63  thf(fact_6354_arctan__monotone,axiom,
% 0.35/0.63      ! [X: real,Y2: real] :
% 0.35/0.63        ( ( ord_less_real @ X @ Y2 )
% 0.35/0.63       => ( ord_less_real @ ( arctan @ X ) @ ( arctan @ Y2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % arctan_monotone
% 0.35/0.63  thf(fact_6355_arctan__less__iff,axiom,
% 0.35/0.63      ! [X: real,Y2: real] :
% 0.35/0.63        ( ( ord_less_real @ ( arctan @ X ) @ ( arctan @ Y2 ) )
% 0.35/0.63        = ( ord_less_real @ X @ Y2 ) ) ).
% 0.35/0.63  
% 0.35/0.63  % arctan_less_iff
% 0.35/0.63  thf(fact_6356_arctan__le__iff,axiom,
% 0.35/0.63      ! [X: real,Y2: real] :
% 0.35/0.63        ( ( ord_less_eq_real @ ( arctan @ X ) @ ( arctan @ Y2 ) )
% 0.35/0.63        = ( ord_less_eq_real @ X @ Y2 ) ) ).
% 0.35/0.63  
% 0.35/0.63  % arctan_le_iff
% 0.35/0.63  thf(fact_6357_arctan__monotone_H,axiom,
% 0.35/0.63      ! [X: real,Y2: real] :
% 0.35/0.63        ( ( ord_less_eq_real @ X @ Y2 )
% 0.35/0.63       => ( ord_less_eq_real @ ( arctan @ X ) @ ( arctan @ Y2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % arctan_monotone'
% 0.35/0.63  thf(fact_6358_concat__bit__take__bit__eq,axiom,
% 0.35/0.63      ! [N: nat,B: int] :
% 0.35/0.63        ( ( bit_concat_bit @ N @ ( bit_se2923211474154528505it_int @ N @ B ) )
% 0.35/0.63        = ( bit_concat_bit @ N @ B ) ) ).
% 0.35/0.63  
% 0.35/0.63  % concat_bit_take_bit_eq
% 0.35/0.63  thf(fact_6359_concat__bit__eq__iff,axiom,
% 0.35/0.63      ! [N: nat,K: int,L2: int,R: int,S3: int] :
% 0.35/0.63        ( ( ( bit_concat_bit @ N @ K @ L2 )
% 0.35/0.63          = ( bit_concat_bit @ N @ R @ S3 ) )
% 0.35/0.63        = ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 0.35/0.63            = ( bit_se2923211474154528505it_int @ N @ R ) )
% 0.35/0.63          & ( L2 = S3 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % concat_bit_eq_iff
% 0.35/0.63  thf(fact_6360_less__eq__mask,axiom,
% 0.35/0.63      ! [N: nat] : ( ord_less_eq_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 0.35/0.63  
% 0.35/0.63  % less_eq_mask
% 0.35/0.63  thf(fact_6361_sum__mono,axiom,
% 0.35/0.63      ! [K5: set_complex,F: complex > nat,G: complex > nat] :
% 0.35/0.63        ( ! [I4: complex] :
% 0.35/0.63            ( ( member_complex @ I4 @ K5 )
% 0.35/0.63           => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.35/0.63       => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ K5 ) @ ( groups5693394587270226106ex_nat @ G @ K5 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_mono
% 0.35/0.63  thf(fact_6362_sum__mono,axiom,
% 0.35/0.63      ! [K5: set_real,F: real > nat,G: real > nat] :
% 0.35/0.63        ( ! [I4: real] :
% 0.35/0.63            ( ( member_real @ I4 @ K5 )
% 0.35/0.63           => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.35/0.63       => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ K5 ) @ ( groups1935376822645274424al_nat @ G @ K5 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_mono
% 0.35/0.63  thf(fact_6363_sum__mono,axiom,
% 0.35/0.63      ! [K5: set_int,F: int > nat,G: int > nat] :
% 0.35/0.63        ( ! [I4: int] :
% 0.35/0.63            ( ( member_int @ I4 @ K5 )
% 0.35/0.63           => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.35/0.63       => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ K5 ) @ ( groups4541462559716669496nt_nat @ G @ K5 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_mono
% 0.35/0.63  thf(fact_6364_sum__mono,axiom,
% 0.35/0.63      ! [K5: set_complex,F: complex > int,G: complex > int] :
% 0.35/0.63        ( ! [I4: complex] :
% 0.35/0.63            ( ( member_complex @ I4 @ K5 )
% 0.35/0.63           => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.35/0.63       => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F @ K5 ) @ ( groups5690904116761175830ex_int @ G @ K5 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_mono
% 0.35/0.63  thf(fact_6365_sum__mono,axiom,
% 0.35/0.63      ! [K5: set_real,F: real > int,G: real > int] :
% 0.35/0.63        ( ! [I4: real] :
% 0.35/0.63            ( ( member_real @ I4 @ K5 )
% 0.35/0.63           => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.35/0.63       => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ K5 ) @ ( groups1932886352136224148al_int @ G @ K5 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_mono
% 0.35/0.63  thf(fact_6366_sum__mono,axiom,
% 0.35/0.63      ! [K5: set_nat,F: nat > int,G: nat > int] :
% 0.35/0.63        ( ! [I4: nat] :
% 0.35/0.63            ( ( member_nat @ I4 @ K5 )
% 0.35/0.63           => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.35/0.63       => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ K5 ) @ ( groups3539618377306564664at_int @ G @ K5 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_mono
% 0.35/0.63  thf(fact_6367_sum__mono,axiom,
% 0.35/0.63      ! [K5: set_int,F: int > int,G: int > int] :
% 0.35/0.63        ( ! [I4: int] :
% 0.35/0.63            ( ( member_int @ I4 @ K5 )
% 0.35/0.63           => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.35/0.63       => ( ord_less_eq_int @ ( groups4538972089207619220nt_int @ F @ K5 ) @ ( groups4538972089207619220nt_int @ G @ K5 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_mono
% 0.35/0.63  thf(fact_6368_sum__mono,axiom,
% 0.35/0.63      ! [K5: set_nat,F: nat > nat,G: nat > nat] :
% 0.35/0.63        ( ! [I4: nat] :
% 0.35/0.63            ( ( member_nat @ I4 @ K5 )
% 0.35/0.63           => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.35/0.63       => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ K5 ) @ ( groups3542108847815614940at_nat @ G @ K5 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_mono
% 0.35/0.63  thf(fact_6369_sum__mono,axiom,
% 0.35/0.63      ! [K5: set_nat,F: nat > real,G: nat > real] :
% 0.35/0.63        ( ! [I4: nat] :
% 0.35/0.63            ( ( member_nat @ I4 @ K5 )
% 0.35/0.63           => ( ord_less_eq_real @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.35/0.63       => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ K5 ) @ ( groups6591440286371151544t_real @ G @ K5 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_mono
% 0.35/0.63  thf(fact_6370_sum__mono,axiom,
% 0.35/0.63      ! [K5: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat,G: product_prod_nat_nat > nat] :
% 0.35/0.63        ( ! [I4: product_prod_nat_nat] :
% 0.35/0.63            ( ( member8440522571783428010at_nat @ I4 @ K5 )
% 0.35/0.63           => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.35/0.63       => ( ord_less_eq_nat @ ( groups977919841031483927at_nat @ F @ K5 ) @ ( groups977919841031483927at_nat @ G @ K5 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_mono
% 0.35/0.63  thf(fact_6371_sum__product,axiom,
% 0.35/0.63      ! [F: int > int,A2: set_int,G: int > int,B2: set_int] :
% 0.35/0.63        ( ( times_times_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ G @ B2 ) )
% 0.35/0.63        = ( groups4538972089207619220nt_int
% 0.35/0.63          @ ^ [I3: int] :
% 0.35/0.63              ( groups4538972089207619220nt_int
% 0.35/0.63              @ ^ [J3: int] : ( times_times_int @ ( F @ I3 ) @ ( G @ J3 ) )
% 0.35/0.63              @ B2 )
% 0.35/0.63          @ A2 ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_product
% 0.35/0.63  thf(fact_6372_sum__product,axiom,
% 0.35/0.63      ! [F: complex > complex,A2: set_complex,G: complex > complex,B2: set_complex] :
% 0.35/0.63        ( ( times_times_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ ( groups7754918857620584856omplex @ G @ B2 ) )
% 0.35/0.63        = ( groups7754918857620584856omplex
% 0.35/0.63          @ ^ [I3: complex] :
% 0.35/0.63              ( groups7754918857620584856omplex
% 0.35/0.63              @ ^ [J3: complex] : ( times_times_complex @ ( F @ I3 ) @ ( G @ J3 ) )
% 0.35/0.63              @ B2 )
% 0.35/0.63          @ A2 ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_product
% 0.35/0.63  thf(fact_6373_sum__product,axiom,
% 0.35/0.63      ! [F: nat > nat,A2: set_nat,G: nat > nat,B2: set_nat] :
% 0.35/0.63        ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ B2 ) )
% 0.35/0.63        = ( groups3542108847815614940at_nat
% 0.35/0.63          @ ^ [I3: nat] :
% 0.35/0.63              ( groups3542108847815614940at_nat
% 0.35/0.63              @ ^ [J3: nat] : ( times_times_nat @ ( F @ I3 ) @ ( G @ J3 ) )
% 0.35/0.63              @ B2 )
% 0.35/0.63          @ A2 ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_product
% 0.35/0.63  thf(fact_6374_sum__product,axiom,
% 0.35/0.63      ! [F: nat > real,A2: set_nat,G: nat > real,B2: set_nat] :
% 0.35/0.63        ( ( times_times_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ G @ B2 ) )
% 0.35/0.63        = ( groups6591440286371151544t_real
% 0.35/0.63          @ ^ [I3: nat] :
% 0.35/0.63              ( groups6591440286371151544t_real
% 0.35/0.63              @ ^ [J3: nat] : ( times_times_real @ ( F @ I3 ) @ ( G @ J3 ) )
% 0.35/0.63              @ B2 )
% 0.35/0.63          @ A2 ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_product
% 0.35/0.63  thf(fact_6375_sum__distrib__right,axiom,
% 0.35/0.63      ! [F: int > int,A2: set_int,R: int] :
% 0.35/0.63        ( ( times_times_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ R )
% 0.35/0.63        = ( groups4538972089207619220nt_int
% 0.35/0.63          @ ^ [N2: int] : ( times_times_int @ ( F @ N2 ) @ R )
% 0.35/0.63          @ A2 ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_distrib_right
% 0.35/0.63  thf(fact_6376_sum__distrib__right,axiom,
% 0.35/0.63      ! [F: complex > complex,A2: set_complex,R: complex] :
% 0.35/0.63        ( ( times_times_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ R )
% 0.35/0.63        = ( groups7754918857620584856omplex
% 0.35/0.63          @ ^ [N2: complex] : ( times_times_complex @ ( F @ N2 ) @ R )
% 0.35/0.63          @ A2 ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_distrib_right
% 0.35/0.63  thf(fact_6377_sum__distrib__right,axiom,
% 0.35/0.63      ! [F: nat > nat,A2: set_nat,R: nat] :
% 0.35/0.63        ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ R )
% 0.35/0.63        = ( groups3542108847815614940at_nat
% 0.35/0.63          @ ^ [N2: nat] : ( times_times_nat @ ( F @ N2 ) @ R )
% 0.35/0.63          @ A2 ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_distrib_right
% 0.35/0.63  thf(fact_6378_sum__distrib__right,axiom,
% 0.35/0.63      ! [F: nat > real,A2: set_nat,R: real] :
% 0.35/0.63        ( ( times_times_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ R )
% 0.35/0.63        = ( groups6591440286371151544t_real
% 0.35/0.63          @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ R )
% 0.35/0.63          @ A2 ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_distrib_right
% 0.35/0.63  thf(fact_6379_sum__distrib__left,axiom,
% 0.35/0.63      ! [R: int,F: int > int,A2: set_int] :
% 0.35/0.63        ( ( times_times_int @ R @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 0.35/0.63        = ( groups4538972089207619220nt_int
% 0.35/0.63          @ ^ [N2: int] : ( times_times_int @ R @ ( F @ N2 ) )
% 0.35/0.63          @ A2 ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_distrib_left
% 0.35/0.63  thf(fact_6380_sum__distrib__left,axiom,
% 0.35/0.63      ! [R: complex,F: complex > complex,A2: set_complex] :
% 0.35/0.63        ( ( times_times_complex @ R @ ( groups7754918857620584856omplex @ F @ A2 ) )
% 0.35/0.63        = ( groups7754918857620584856omplex
% 0.35/0.63          @ ^ [N2: complex] : ( times_times_complex @ R @ ( F @ N2 ) )
% 0.35/0.63          @ A2 ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_distrib_left
% 0.35/0.63  thf(fact_6381_sum__distrib__left,axiom,
% 0.35/0.63      ! [R: nat,F: nat > nat,A2: set_nat] :
% 0.35/0.63        ( ( times_times_nat @ R @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 0.35/0.63        = ( groups3542108847815614940at_nat
% 0.35/0.63          @ ^ [N2: nat] : ( times_times_nat @ R @ ( F @ N2 ) )
% 0.35/0.63          @ A2 ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_distrib_left
% 0.35/0.63  thf(fact_6382_sum__distrib__left,axiom,
% 0.35/0.63      ! [R: real,F: nat > real,A2: set_nat] :
% 0.35/0.63        ( ( times_times_real @ R @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 0.35/0.63        = ( groups6591440286371151544t_real
% 0.35/0.63          @ ^ [N2: nat] : ( times_times_real @ R @ ( F @ N2 ) )
% 0.35/0.63          @ A2 ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_distrib_left
% 0.35/0.63  thf(fact_6383_sum_Odistrib,axiom,
% 0.35/0.63      ! [G: int > int,H2: int > int,A2: set_int] :
% 0.35/0.63        ( ( groups4538972089207619220nt_int
% 0.35/0.63          @ ^ [X2: int] : ( plus_plus_int @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 0.35/0.63          @ A2 )
% 0.35/0.63        = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ A2 ) @ ( groups4538972089207619220nt_int @ H2 @ A2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.distrib
% 0.35/0.63  thf(fact_6384_sum_Odistrib,axiom,
% 0.35/0.63      ! [G: complex > complex,H2: complex > complex,A2: set_complex] :
% 0.35/0.63        ( ( groups7754918857620584856omplex
% 0.35/0.63          @ ^ [X2: complex] : ( plus_plus_complex @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 0.35/0.63          @ A2 )
% 0.35/0.63        = ( plus_plus_complex @ ( groups7754918857620584856omplex @ G @ A2 ) @ ( groups7754918857620584856omplex @ H2 @ A2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.distrib
% 0.35/0.63  thf(fact_6385_sum_Odistrib,axiom,
% 0.35/0.63      ! [G: nat > nat,H2: nat > nat,A2: set_nat] :
% 0.35/0.63        ( ( groups3542108847815614940at_nat
% 0.35/0.63          @ ^ [X2: nat] : ( plus_plus_nat @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 0.35/0.63          @ A2 )
% 0.35/0.63        = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ A2 ) @ ( groups3542108847815614940at_nat @ H2 @ A2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.distrib
% 0.35/0.63  thf(fact_6386_sum_Odistrib,axiom,
% 0.35/0.63      ! [G: nat > real,H2: nat > real,A2: set_nat] :
% 0.35/0.63        ( ( groups6591440286371151544t_real
% 0.35/0.63          @ ^ [X2: nat] : ( plus_plus_real @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 0.35/0.63          @ A2 )
% 0.35/0.63        = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ A2 ) @ ( groups6591440286371151544t_real @ H2 @ A2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.distrib
% 0.35/0.63  thf(fact_6387_sum__subtractf,axiom,
% 0.35/0.63      ! [F: int > int,G: int > int,A2: set_int] :
% 0.35/0.63        ( ( groups4538972089207619220nt_int
% 0.35/0.63          @ ^ [X2: int] : ( minus_minus_int @ ( F @ X2 ) @ ( G @ X2 ) )
% 0.35/0.63          @ A2 )
% 0.35/0.63        = ( minus_minus_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ G @ A2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_subtractf
% 0.35/0.63  thf(fact_6388_sum__subtractf,axiom,
% 0.35/0.63      ! [F: complex > complex,G: complex > complex,A2: set_complex] :
% 0.35/0.63        ( ( groups7754918857620584856omplex
% 0.35/0.63          @ ^ [X2: complex] : ( minus_minus_complex @ ( F @ X2 ) @ ( G @ X2 ) )
% 0.35/0.63          @ A2 )
% 0.35/0.63        = ( minus_minus_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ ( groups7754918857620584856omplex @ G @ A2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_subtractf
% 0.35/0.63  thf(fact_6389_sum__subtractf,axiom,
% 0.35/0.63      ! [F: nat > real,G: nat > real,A2: set_nat] :
% 0.35/0.63        ( ( groups6591440286371151544t_real
% 0.35/0.63          @ ^ [X2: nat] : ( minus_minus_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 0.35/0.63          @ A2 )
% 0.35/0.63        = ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ G @ A2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_subtractf
% 0.35/0.63  thf(fact_6390_sum__divide__distrib,axiom,
% 0.35/0.63      ! [F: complex > complex,A2: set_complex,R: complex] :
% 0.35/0.63        ( ( divide1717551699836669952omplex @ ( groups7754918857620584856omplex @ F @ A2 ) @ R )
% 0.35/0.63        = ( groups7754918857620584856omplex
% 0.35/0.63          @ ^ [N2: complex] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ R )
% 0.35/0.63          @ A2 ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_divide_distrib
% 0.35/0.63  thf(fact_6391_sum__divide__distrib,axiom,
% 0.35/0.63      ! [F: nat > real,A2: set_nat,R: real] :
% 0.35/0.63        ( ( divide_divide_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ R )
% 0.35/0.63        = ( groups6591440286371151544t_real
% 0.35/0.63          @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ R )
% 0.35/0.63          @ A2 ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_divide_distrib
% 0.35/0.63  thf(fact_6392_mod__sum__eq,axiom,
% 0.35/0.63      ! [F: int > int,A: int,A2: set_int] :
% 0.35/0.63        ( ( modulo_modulo_int
% 0.35/0.63          @ ( groups4538972089207619220nt_int
% 0.35/0.63            @ ^ [I3: int] : ( modulo_modulo_int @ ( F @ I3 ) @ A )
% 0.35/0.63            @ A2 )
% 0.35/0.63          @ A )
% 0.35/0.63        = ( modulo_modulo_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ A ) ) ).
% 0.35/0.63  
% 0.35/0.63  % mod_sum_eq
% 0.35/0.63  thf(fact_6393_mod__sum__eq,axiom,
% 0.35/0.63      ! [F: nat > nat,A: nat,A2: set_nat] :
% 0.35/0.63        ( ( modulo_modulo_nat
% 0.35/0.63          @ ( groups3542108847815614940at_nat
% 0.35/0.63            @ ^ [I3: nat] : ( modulo_modulo_nat @ ( F @ I3 ) @ A )
% 0.35/0.63            @ A2 )
% 0.35/0.63          @ A )
% 0.35/0.63        = ( modulo_modulo_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ A ) ) ).
% 0.35/0.63  
% 0.35/0.63  % mod_sum_eq
% 0.35/0.63  thf(fact_6394_take__bit__eq__mask__iff,axiom,
% 0.35/0.63      ! [N: nat,K: int] :
% 0.35/0.63        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 0.35/0.63          = ( bit_se2000444600071755411sk_int @ N ) )
% 0.35/0.63        = ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 0.35/0.63          = zero_zero_int ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_eq_mask_iff
% 0.35/0.63  thf(fact_6395_sum__nonpos,axiom,
% 0.35/0.63      ! [A2: set_complex,F: complex > real] :
% 0.35/0.63        ( ! [X3: complex] :
% 0.35/0.63            ( ( member_complex @ X3 @ A2 )
% 0.35/0.63           => ( ord_less_eq_real @ ( F @ X3 ) @ zero_zero_real ) )
% 0.35/0.63       => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonpos
% 0.35/0.63  thf(fact_6396_sum__nonpos,axiom,
% 0.35/0.63      ! [A2: set_real,F: real > real] :
% 0.35/0.63        ( ! [X3: real] :
% 0.35/0.63            ( ( member_real @ X3 @ A2 )
% 0.35/0.63           => ( ord_less_eq_real @ ( F @ X3 ) @ zero_zero_real ) )
% 0.35/0.63       => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonpos
% 0.35/0.63  thf(fact_6397_sum__nonpos,axiom,
% 0.35/0.63      ! [A2: set_int,F: int > real] :
% 0.35/0.63        ( ! [X3: int] :
% 0.35/0.63            ( ( member_int @ X3 @ A2 )
% 0.35/0.63           => ( ord_less_eq_real @ ( F @ X3 ) @ zero_zero_real ) )
% 0.35/0.63       => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonpos
% 0.35/0.63  thf(fact_6398_sum__nonpos,axiom,
% 0.35/0.63      ! [A2: set_complex,F: complex > rat] :
% 0.35/0.63        ( ! [X3: complex] :
% 0.35/0.63            ( ( member_complex @ X3 @ A2 )
% 0.35/0.63           => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 0.35/0.63       => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonpos
% 0.35/0.63  thf(fact_6399_sum__nonpos,axiom,
% 0.35/0.63      ! [A2: set_real,F: real > rat] :
% 0.35/0.63        ( ! [X3: real] :
% 0.35/0.63            ( ( member_real @ X3 @ A2 )
% 0.35/0.63           => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 0.35/0.63       => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonpos
% 0.35/0.63  thf(fact_6400_sum__nonpos,axiom,
% 0.35/0.63      ! [A2: set_nat,F: nat > rat] :
% 0.35/0.63        ( ! [X3: nat] :
% 0.35/0.63            ( ( member_nat @ X3 @ A2 )
% 0.35/0.63           => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 0.35/0.63       => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonpos
% 0.35/0.63  thf(fact_6401_sum__nonpos,axiom,
% 0.35/0.63      ! [A2: set_int,F: int > rat] :
% 0.35/0.63        ( ! [X3: int] :
% 0.35/0.63            ( ( member_int @ X3 @ A2 )
% 0.35/0.63           => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 0.35/0.63       => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonpos
% 0.35/0.63  thf(fact_6402_sum__nonpos,axiom,
% 0.35/0.63      ! [A2: set_complex,F: complex > nat] :
% 0.35/0.63        ( ! [X3: complex] :
% 0.35/0.63            ( ( member_complex @ X3 @ A2 )
% 0.35/0.63           => ( ord_less_eq_nat @ ( F @ X3 ) @ zero_zero_nat ) )
% 0.35/0.63       => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonpos
% 0.35/0.63  thf(fact_6403_sum__nonpos,axiom,
% 0.35/0.63      ! [A2: set_real,F: real > nat] :
% 0.35/0.63        ( ! [X3: real] :
% 0.35/0.63            ( ( member_real @ X3 @ A2 )
% 0.35/0.63           => ( ord_less_eq_nat @ ( F @ X3 ) @ zero_zero_nat ) )
% 0.35/0.63       => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonpos
% 0.35/0.63  thf(fact_6404_sum__nonpos,axiom,
% 0.35/0.63      ! [A2: set_int,F: int > nat] :
% 0.35/0.63        ( ! [X3: int] :
% 0.35/0.63            ( ( member_int @ X3 @ A2 )
% 0.35/0.63           => ( ord_less_eq_nat @ ( F @ X3 ) @ zero_zero_nat ) )
% 0.35/0.63       => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonpos
% 0.35/0.63  thf(fact_6405_sum__nonneg,axiom,
% 0.35/0.63      ! [A2: set_complex,F: complex > real] :
% 0.35/0.63        ( ! [X3: complex] :
% 0.35/0.63            ( ( member_complex @ X3 @ A2 )
% 0.35/0.63           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 0.35/0.63       => ( ord_less_eq_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ A2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg
% 0.35/0.63  thf(fact_6406_sum__nonneg,axiom,
% 0.35/0.63      ! [A2: set_real,F: real > real] :
% 0.35/0.63        ( ! [X3: real] :
% 0.35/0.63            ( ( member_real @ X3 @ A2 )
% 0.35/0.63           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 0.35/0.63       => ( ord_less_eq_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ A2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg
% 0.35/0.63  thf(fact_6407_sum__nonneg,axiom,
% 0.35/0.63      ! [A2: set_int,F: int > real] :
% 0.35/0.63        ( ! [X3: int] :
% 0.35/0.63            ( ( member_int @ X3 @ A2 )
% 0.35/0.63           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 0.35/0.63       => ( ord_less_eq_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ A2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg
% 0.35/0.63  thf(fact_6408_sum__nonneg,axiom,
% 0.35/0.63      ! [A2: set_complex,F: complex > rat] :
% 0.35/0.63        ( ! [X3: complex] :
% 0.35/0.63            ( ( member_complex @ X3 @ A2 )
% 0.35/0.63           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 0.35/0.63       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg
% 0.35/0.63  thf(fact_6409_sum__nonneg,axiom,
% 0.35/0.63      ! [A2: set_real,F: real > rat] :
% 0.35/0.63        ( ! [X3: real] :
% 0.35/0.63            ( ( member_real @ X3 @ A2 )
% 0.35/0.63           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 0.35/0.63       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg
% 0.35/0.63  thf(fact_6410_sum__nonneg,axiom,
% 0.35/0.63      ! [A2: set_nat,F: nat > rat] :
% 0.35/0.63        ( ! [X3: nat] :
% 0.35/0.63            ( ( member_nat @ X3 @ A2 )
% 0.35/0.63           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 0.35/0.63       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg
% 0.35/0.63  thf(fact_6411_sum__nonneg,axiom,
% 0.35/0.63      ! [A2: set_int,F: int > rat] :
% 0.35/0.63        ( ! [X3: int] :
% 0.35/0.63            ( ( member_int @ X3 @ A2 )
% 0.35/0.63           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 0.35/0.63       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg
% 0.35/0.63  thf(fact_6412_sum__nonneg,axiom,
% 0.35/0.63      ! [A2: set_complex,F: complex > nat] :
% 0.35/0.63        ( ! [X3: complex] :
% 0.35/0.63            ( ( member_complex @ X3 @ A2 )
% 0.35/0.63           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 0.35/0.63       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg
% 0.35/0.63  thf(fact_6413_sum__nonneg,axiom,
% 0.35/0.63      ! [A2: set_real,F: real > nat] :
% 0.35/0.63        ( ! [X3: real] :
% 0.35/0.63            ( ( member_real @ X3 @ A2 )
% 0.35/0.63           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 0.35/0.63       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg
% 0.35/0.63  thf(fact_6414_sum__nonneg,axiom,
% 0.35/0.63      ! [A2: set_int,F: int > nat] :
% 0.35/0.63        ( ! [X3: int] :
% 0.35/0.63            ( ( member_int @ X3 @ A2 )
% 0.35/0.63           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 0.35/0.63       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg
% 0.35/0.63  thf(fact_6415_sum__mono__inv,axiom,
% 0.35/0.63      ! [F: real > nat,I6: set_real,G: real > nat,I2: real] :
% 0.35/0.63        ( ( ( groups1935376822645274424al_nat @ F @ I6 )
% 0.35/0.63          = ( groups1935376822645274424al_nat @ G @ I6 ) )
% 0.35/0.63       => ( ! [I4: real] :
% 0.35/0.63              ( ( member_real @ I4 @ I6 )
% 0.35/0.63             => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.35/0.63         => ( ( member_real @ I2 @ I6 )
% 0.35/0.63           => ( ( finite_finite_real @ I6 )
% 0.35/0.63             => ( ( F @ I2 )
% 0.35/0.63                = ( G @ I2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_mono_inv
% 0.35/0.63  thf(fact_6416_sum__mono__inv,axiom,
% 0.35/0.63      ! [F: int > nat,I6: set_int,G: int > nat,I2: int] :
% 0.35/0.63        ( ( ( groups4541462559716669496nt_nat @ F @ I6 )
% 0.35/0.63          = ( groups4541462559716669496nt_nat @ G @ I6 ) )
% 0.35/0.63       => ( ! [I4: int] :
% 0.35/0.63              ( ( member_int @ I4 @ I6 )
% 0.35/0.63             => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.35/0.63         => ( ( member_int @ I2 @ I6 )
% 0.35/0.63           => ( ( finite_finite_int @ I6 )
% 0.35/0.63             => ( ( F @ I2 )
% 0.35/0.63                = ( G @ I2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_mono_inv
% 0.35/0.63  thf(fact_6417_sum__mono__inv,axiom,
% 0.35/0.63      ! [F: complex > nat,I6: set_complex,G: complex > nat,I2: complex] :
% 0.35/0.63        ( ( ( groups5693394587270226106ex_nat @ F @ I6 )
% 0.35/0.63          = ( groups5693394587270226106ex_nat @ G @ I6 ) )
% 0.35/0.63       => ( ! [I4: complex] :
% 0.35/0.63              ( ( member_complex @ I4 @ I6 )
% 0.35/0.63             => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.35/0.63         => ( ( member_complex @ I2 @ I6 )
% 0.35/0.63           => ( ( finite3207457112153483333omplex @ I6 )
% 0.35/0.63             => ( ( F @ I2 )
% 0.35/0.63                = ( G @ I2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_mono_inv
% 0.35/0.63  thf(fact_6418_sum__mono__inv,axiom,
% 0.35/0.63      ! [F: real > int,I6: set_real,G: real > int,I2: real] :
% 0.35/0.63        ( ( ( groups1932886352136224148al_int @ F @ I6 )
% 0.35/0.63          = ( groups1932886352136224148al_int @ G @ I6 ) )
% 0.35/0.63       => ( ! [I4: real] :
% 0.35/0.63              ( ( member_real @ I4 @ I6 )
% 0.35/0.63             => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.35/0.63         => ( ( member_real @ I2 @ I6 )
% 0.35/0.63           => ( ( finite_finite_real @ I6 )
% 0.35/0.63             => ( ( F @ I2 )
% 0.35/0.63                = ( G @ I2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_mono_inv
% 0.35/0.63  thf(fact_6419_sum__mono__inv,axiom,
% 0.35/0.63      ! [F: nat > int,I6: set_nat,G: nat > int,I2: nat] :
% 0.35/0.63        ( ( ( groups3539618377306564664at_int @ F @ I6 )
% 0.35/0.63          = ( groups3539618377306564664at_int @ G @ I6 ) )
% 0.35/0.63       => ( ! [I4: nat] :
% 0.35/0.63              ( ( member_nat @ I4 @ I6 )
% 0.35/0.63             => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.35/0.63         => ( ( member_nat @ I2 @ I6 )
% 0.35/0.63           => ( ( finite_finite_nat @ I6 )
% 0.35/0.63             => ( ( F @ I2 )
% 0.35/0.63                = ( G @ I2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_mono_inv
% 0.35/0.63  thf(fact_6420_sum__mono__inv,axiom,
% 0.35/0.63      ! [F: complex > int,I6: set_complex,G: complex > int,I2: complex] :
% 0.35/0.63        ( ( ( groups5690904116761175830ex_int @ F @ I6 )
% 0.35/0.63          = ( groups5690904116761175830ex_int @ G @ I6 ) )
% 0.35/0.63       => ( ! [I4: complex] :
% 0.35/0.63              ( ( member_complex @ I4 @ I6 )
% 0.35/0.63             => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.35/0.63         => ( ( member_complex @ I2 @ I6 )
% 0.35/0.63           => ( ( finite3207457112153483333omplex @ I6 )
% 0.35/0.63             => ( ( F @ I2 )
% 0.35/0.63                = ( G @ I2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_mono_inv
% 0.35/0.63  thf(fact_6421_sum__mono__inv,axiom,
% 0.35/0.63      ! [F: int > int,I6: set_int,G: int > int,I2: int] :
% 0.35/0.63        ( ( ( groups4538972089207619220nt_int @ F @ I6 )
% 0.35/0.63          = ( groups4538972089207619220nt_int @ G @ I6 ) )
% 0.35/0.63       => ( ! [I4: int] :
% 0.35/0.63              ( ( member_int @ I4 @ I6 )
% 0.35/0.63             => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.35/0.63         => ( ( member_int @ I2 @ I6 )
% 0.35/0.63           => ( ( finite_finite_int @ I6 )
% 0.35/0.63             => ( ( F @ I2 )
% 0.35/0.63                = ( G @ I2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_mono_inv
% 0.35/0.63  thf(fact_6422_sum__mono__inv,axiom,
% 0.35/0.63      ! [F: nat > nat,I6: set_nat,G: nat > nat,I2: nat] :
% 0.35/0.63        ( ( ( groups3542108847815614940at_nat @ F @ I6 )
% 0.35/0.63          = ( groups3542108847815614940at_nat @ G @ I6 ) )
% 0.35/0.63       => ( ! [I4: nat] :
% 0.35/0.63              ( ( member_nat @ I4 @ I6 )
% 0.35/0.63             => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.35/0.63         => ( ( member_nat @ I2 @ I6 )
% 0.35/0.63           => ( ( finite_finite_nat @ I6 )
% 0.35/0.63             => ( ( F @ I2 )
% 0.35/0.63                = ( G @ I2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_mono_inv
% 0.35/0.63  thf(fact_6423_sum__mono__inv,axiom,
% 0.35/0.63      ! [F: nat > real,I6: set_nat,G: nat > real,I2: nat] :
% 0.35/0.63        ( ( ( groups6591440286371151544t_real @ F @ I6 )
% 0.35/0.63          = ( groups6591440286371151544t_real @ G @ I6 ) )
% 0.35/0.63       => ( ! [I4: nat] :
% 0.35/0.63              ( ( member_nat @ I4 @ I6 )
% 0.35/0.63             => ( ord_less_eq_real @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.35/0.63         => ( ( member_nat @ I2 @ I6 )
% 0.35/0.63           => ( ( finite_finite_nat @ I6 )
% 0.35/0.63             => ( ( F @ I2 )
% 0.35/0.63                = ( G @ I2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_mono_inv
% 0.35/0.63  thf(fact_6424_sum__mono__inv,axiom,
% 0.35/0.63      ! [F: product_prod_nat_nat > nat,I6: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > nat,I2: product_prod_nat_nat] :
% 0.35/0.63        ( ( ( groups977919841031483927at_nat @ F @ I6 )
% 0.35/0.63          = ( groups977919841031483927at_nat @ G @ I6 ) )
% 0.35/0.63       => ( ! [I4: product_prod_nat_nat] :
% 0.35/0.63              ( ( member8440522571783428010at_nat @ I4 @ I6 )
% 0.35/0.63             => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.35/0.63         => ( ( member8440522571783428010at_nat @ I2 @ I6 )
% 0.35/0.63           => ( ( finite6177210948735845034at_nat @ I6 )
% 0.35/0.63             => ( ( F @ I2 )
% 0.35/0.63                = ( G @ I2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_mono_inv
% 0.35/0.63  thf(fact_6425_not__exp__less__zero,axiom,
% 0.35/0.63      ! [X: real] :
% 0.35/0.63        ~ ( ord_less_real @ ( exp_real @ X ) @ zero_zero_real ) ).
% 0.35/0.63  
% 0.35/0.63  % not_exp_less_zero
% 0.35/0.63  thf(fact_6426_exp__gt__zero,axiom,
% 0.35/0.63      ! [X: real] : ( ord_less_real @ zero_zero_real @ ( exp_real @ X ) ) ).
% 0.35/0.63  
% 0.35/0.63  % exp_gt_zero
% 0.35/0.63  thf(fact_6427_exp__total,axiom,
% 0.35/0.63      ! [Y2: real] :
% 0.35/0.63        ( ( ord_less_real @ zero_zero_real @ Y2 )
% 0.35/0.63       => ? [X3: real] :
% 0.35/0.63            ( ( exp_real @ X3 )
% 0.35/0.63            = Y2 ) ) ).
% 0.35/0.63  
% 0.35/0.63  % exp_total
% 0.35/0.63  thf(fact_6428_not__exp__le__zero,axiom,
% 0.35/0.63      ! [X: real] :
% 0.35/0.63        ~ ( ord_less_eq_real @ ( exp_real @ X ) @ zero_zero_real ) ).
% 0.35/0.63  
% 0.35/0.63  % not_exp_le_zero
% 0.35/0.63  thf(fact_6429_exp__ge__zero,axiom,
% 0.35/0.63      ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( exp_real @ X ) ) ).
% 0.35/0.63  
% 0.35/0.63  % exp_ge_zero
% 0.35/0.63  thf(fact_6430_take__bit__tightened__less__eq__int,axiom,
% 0.35/0.63      ! [M: nat,N: nat,K: int] :
% 0.35/0.63        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.63       => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M @ K ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_tightened_less_eq_int
% 0.35/0.63  thf(fact_6431_signed__take__bit__eq__iff__take__bit__eq,axiom,
% 0.35/0.63      ! [N: nat,A: int,B: int] :
% 0.35/0.63        ( ( ( bit_ri631733984087533419it_int @ N @ A )
% 0.35/0.63          = ( bit_ri631733984087533419it_int @ N @ B ) )
% 0.35/0.63        = ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A )
% 0.35/0.63          = ( bit_se2923211474154528505it_int @ ( suc @ N ) @ B ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % signed_take_bit_eq_iff_take_bit_eq
% 0.35/0.63  thf(fact_6432_take__bit__int__less__eq__self__iff,axiom,
% 0.35/0.63      ! [N: nat,K: int] :
% 0.35/0.63        ( ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 0.35/0.63        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_int_less_eq_self_iff
% 0.35/0.63  thf(fact_6433_take__bit__nonnegative,axiom,
% 0.35/0.63      ! [N: nat,K: int] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_nonnegative
% 0.35/0.63  thf(fact_6434_not__take__bit__negative,axiom,
% 0.35/0.63      ! [N: nat,K: int] :
% 0.35/0.63        ~ ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ zero_zero_int ) ).
% 0.35/0.63  
% 0.35/0.63  % not_take_bit_negative
% 0.35/0.63  thf(fact_6435_take__bit__int__greater__self__iff,axiom,
% 0.35/0.63      ! [K: int,N: nat] :
% 0.35/0.63        ( ( ord_less_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 0.35/0.63        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_int_greater_self_iff
% 0.35/0.63  thf(fact_6436_signed__take__bit__take__bit,axiom,
% 0.35/0.63      ! [M: nat,N: nat,A: int] :
% 0.35/0.63        ( ( bit_ri631733984087533419it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) )
% 0.35/0.63        = ( if_int_int @ ( ord_less_eq_nat @ N @ M ) @ ( bit_se2923211474154528505it_int @ N ) @ ( bit_ri631733984087533419it_int @ M ) @ A ) ) ).
% 0.35/0.63  
% 0.35/0.63  % signed_take_bit_take_bit
% 0.35/0.63  thf(fact_6437_exp__add__commuting,axiom,
% 0.35/0.63      ! [X: complex,Y2: complex] :
% 0.35/0.63        ( ( ( times_times_complex @ X @ Y2 )
% 0.35/0.63          = ( times_times_complex @ Y2 @ X ) )
% 0.35/0.63       => ( ( exp_complex @ ( plus_plus_complex @ X @ Y2 ) )
% 0.35/0.63          = ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ Y2 ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % exp_add_commuting
% 0.35/0.63  thf(fact_6438_exp__add__commuting,axiom,
% 0.35/0.63      ! [X: real,Y2: real] :
% 0.35/0.63        ( ( ( times_times_real @ X @ Y2 )
% 0.35/0.63          = ( times_times_real @ Y2 @ X ) )
% 0.35/0.63       => ( ( exp_real @ ( plus_plus_real @ X @ Y2 ) )
% 0.35/0.63          = ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ Y2 ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % exp_add_commuting
% 0.35/0.63  thf(fact_6439_mult__exp__exp,axiom,
% 0.35/0.63      ! [X: complex,Y2: complex] :
% 0.35/0.63        ( ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ Y2 ) )
% 0.35/0.63        = ( exp_complex @ ( plus_plus_complex @ X @ Y2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % mult_exp_exp
% 0.35/0.63  thf(fact_6440_mult__exp__exp,axiom,
% 0.35/0.63      ! [X: real,Y2: real] :
% 0.35/0.63        ( ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ Y2 ) )
% 0.35/0.63        = ( exp_real @ ( plus_plus_real @ X @ Y2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % mult_exp_exp
% 0.35/0.63  thf(fact_6441_exp__diff,axiom,
% 0.35/0.63      ! [X: complex,Y2: complex] :
% 0.35/0.63        ( ( exp_complex @ ( minus_minus_complex @ X @ Y2 ) )
% 0.35/0.63        = ( divide1717551699836669952omplex @ ( exp_complex @ X ) @ ( exp_complex @ Y2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % exp_diff
% 0.35/0.63  thf(fact_6442_exp__diff,axiom,
% 0.35/0.63      ! [X: real,Y2: real] :
% 0.35/0.63        ( ( exp_real @ ( minus_minus_real @ X @ Y2 ) )
% 0.35/0.63        = ( divide_divide_real @ ( exp_real @ X ) @ ( exp_real @ Y2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % exp_diff
% 0.35/0.63  thf(fact_6443_take__bit__unset__bit__eq,axiom,
% 0.35/0.63      ! [N: nat,M: nat,A: int] :
% 0.35/0.63        ( ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.63         => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 0.35/0.63            = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 0.35/0.63        & ( ~ ( ord_less_eq_nat @ N @ M )
% 0.35/0.63         => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 0.35/0.63            = ( bit_se4203085406695923979it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_unset_bit_eq
% 0.35/0.63  thf(fact_6444_take__bit__unset__bit__eq,axiom,
% 0.35/0.63      ! [N: nat,M: nat,A: nat] :
% 0.35/0.63        ( ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.63         => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 0.35/0.63            = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 0.35/0.63        & ( ~ ( ord_less_eq_nat @ N @ M )
% 0.35/0.63         => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 0.35/0.63            = ( bit_se4205575877204974255it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_unset_bit_eq
% 0.35/0.63  thf(fact_6445_take__bit__set__bit__eq,axiom,
% 0.35/0.63      ! [N: nat,M: nat,A: int] :
% 0.35/0.63        ( ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.63         => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 0.35/0.63            = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 0.35/0.63        & ( ~ ( ord_less_eq_nat @ N @ M )
% 0.35/0.63         => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 0.35/0.63            = ( bit_se7879613467334960850it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_set_bit_eq
% 0.35/0.63  thf(fact_6446_take__bit__set__bit__eq,axiom,
% 0.35/0.63      ! [N: nat,M: nat,A: nat] :
% 0.35/0.63        ( ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.63         => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 0.35/0.63            = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 0.35/0.63        & ( ~ ( ord_less_eq_nat @ N @ M )
% 0.35/0.63         => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 0.35/0.63            = ( bit_se7882103937844011126it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_set_bit_eq
% 0.35/0.63  thf(fact_6447_take__bit__flip__bit__eq,axiom,
% 0.35/0.63      ! [N: nat,M: nat,A: int] :
% 0.35/0.63        ( ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.63         => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 0.35/0.63            = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 0.35/0.63        & ( ~ ( ord_less_eq_nat @ N @ M )
% 0.35/0.63         => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 0.35/0.63            = ( bit_se2159334234014336723it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_flip_bit_eq
% 0.35/0.63  thf(fact_6448_take__bit__flip__bit__eq,axiom,
% 0.35/0.63      ! [N: nat,M: nat,A: nat] :
% 0.35/0.63        ( ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.63         => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 0.35/0.63            = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 0.35/0.63        & ( ~ ( ord_less_eq_nat @ N @ M )
% 0.35/0.63         => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 0.35/0.63            = ( bit_se2161824704523386999it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_flip_bit_eq
% 0.35/0.63  thf(fact_6449_abs__div,axiom,
% 0.35/0.63      ! [Y2: int,X: int] :
% 0.35/0.63        ( ( dvd_dvd_int @ Y2 @ X )
% 0.35/0.63       => ( ( abs_abs_int @ ( divide_divide_int @ X @ Y2 ) )
% 0.35/0.63          = ( divide_divide_int @ ( abs_abs_int @ X ) @ ( abs_abs_int @ Y2 ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_div
% 0.35/0.63  thf(fact_6450_mask__nonnegative__int,axiom,
% 0.35/0.63      ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2000444600071755411sk_int @ N ) ) ).
% 0.35/0.63  
% 0.35/0.63  % mask_nonnegative_int
% 0.35/0.63  thf(fact_6451_not__mask__negative__int,axiom,
% 0.35/0.63      ! [N: nat] :
% 0.35/0.63        ~ ( ord_less_int @ ( bit_se2000444600071755411sk_int @ N ) @ zero_zero_int ) ).
% 0.35/0.63  
% 0.35/0.63  % not_mask_negative_int
% 0.35/0.63  thf(fact_6452_sum__nonneg__eq__0__iff,axiom,
% 0.35/0.63      ! [A2: set_real,F: real > real] :
% 0.35/0.63        ( ( finite_finite_real @ A2 )
% 0.35/0.63       => ( ! [X3: real] :
% 0.35/0.63              ( ( member_real @ X3 @ A2 )
% 0.35/0.63             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 0.35/0.63         => ( ( ( groups8097168146408367636l_real @ F @ A2 )
% 0.35/0.63              = zero_zero_real )
% 0.35/0.63            = ( ! [X2: real] :
% 0.35/0.63                  ( ( member_real @ X2 @ A2 )
% 0.35/0.63                 => ( ( F @ X2 )
% 0.35/0.63                    = zero_zero_real ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg_eq_0_iff
% 0.35/0.63  thf(fact_6453_sum__nonneg__eq__0__iff,axiom,
% 0.35/0.63      ! [A2: set_int,F: int > real] :
% 0.35/0.63        ( ( finite_finite_int @ A2 )
% 0.35/0.63       => ( ! [X3: int] :
% 0.35/0.63              ( ( member_int @ X3 @ A2 )
% 0.35/0.63             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 0.35/0.63         => ( ( ( groups8778361861064173332t_real @ F @ A2 )
% 0.35/0.63              = zero_zero_real )
% 0.35/0.63            = ( ! [X2: int] :
% 0.35/0.63                  ( ( member_int @ X2 @ A2 )
% 0.35/0.63                 => ( ( F @ X2 )
% 0.35/0.63                    = zero_zero_real ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg_eq_0_iff
% 0.35/0.63  thf(fact_6454_sum__nonneg__eq__0__iff,axiom,
% 0.35/0.63      ! [A2: set_complex,F: complex > real] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.63       => ( ! [X3: complex] :
% 0.35/0.63              ( ( member_complex @ X3 @ A2 )
% 0.35/0.63             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 0.35/0.63         => ( ( ( groups5808333547571424918x_real @ F @ A2 )
% 0.35/0.63              = zero_zero_real )
% 0.35/0.63            = ( ! [X2: complex] :
% 0.35/0.63                  ( ( member_complex @ X2 @ A2 )
% 0.35/0.63                 => ( ( F @ X2 )
% 0.35/0.63                    = zero_zero_real ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg_eq_0_iff
% 0.35/0.63  thf(fact_6455_sum__nonneg__eq__0__iff,axiom,
% 0.35/0.63      ! [A2: set_real,F: real > rat] :
% 0.35/0.63        ( ( finite_finite_real @ A2 )
% 0.35/0.63       => ( ! [X3: real] :
% 0.35/0.63              ( ( member_real @ X3 @ A2 )
% 0.35/0.63             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 0.35/0.63         => ( ( ( groups1300246762558778688al_rat @ F @ A2 )
% 0.35/0.63              = zero_zero_rat )
% 0.35/0.63            = ( ! [X2: real] :
% 0.35/0.63                  ( ( member_real @ X2 @ A2 )
% 0.35/0.63                 => ( ( F @ X2 )
% 0.35/0.63                    = zero_zero_rat ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg_eq_0_iff
% 0.35/0.63  thf(fact_6456_sum__nonneg__eq__0__iff,axiom,
% 0.35/0.63      ! [A2: set_int,F: int > rat] :
% 0.35/0.63        ( ( finite_finite_int @ A2 )
% 0.35/0.63       => ( ! [X3: int] :
% 0.35/0.63              ( ( member_int @ X3 @ A2 )
% 0.35/0.63             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 0.35/0.63         => ( ( ( groups3906332499630173760nt_rat @ F @ A2 )
% 0.35/0.63              = zero_zero_rat )
% 0.35/0.63            = ( ! [X2: int] :
% 0.35/0.63                  ( ( member_int @ X2 @ A2 )
% 0.35/0.63                 => ( ( F @ X2 )
% 0.35/0.63                    = zero_zero_rat ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg_eq_0_iff
% 0.35/0.63  thf(fact_6457_sum__nonneg__eq__0__iff,axiom,
% 0.35/0.63      ! [A2: set_nat,F: nat > rat] :
% 0.35/0.63        ( ( finite_finite_nat @ A2 )
% 0.35/0.63       => ( ! [X3: nat] :
% 0.35/0.63              ( ( member_nat @ X3 @ A2 )
% 0.35/0.63             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 0.35/0.63         => ( ( ( groups2906978787729119204at_rat @ F @ A2 )
% 0.35/0.63              = zero_zero_rat )
% 0.35/0.63            = ( ! [X2: nat] :
% 0.35/0.63                  ( ( member_nat @ X2 @ A2 )
% 0.35/0.63                 => ( ( F @ X2 )
% 0.35/0.63                    = zero_zero_rat ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg_eq_0_iff
% 0.35/0.63  thf(fact_6458_sum__nonneg__eq__0__iff,axiom,
% 0.35/0.63      ! [A2: set_complex,F: complex > rat] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.63       => ( ! [X3: complex] :
% 0.35/0.63              ( ( member_complex @ X3 @ A2 )
% 0.35/0.63             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 0.35/0.63         => ( ( ( groups5058264527183730370ex_rat @ F @ A2 )
% 0.35/0.63              = zero_zero_rat )
% 0.35/0.63            = ( ! [X2: complex] :
% 0.35/0.63                  ( ( member_complex @ X2 @ A2 )
% 0.35/0.63                 => ( ( F @ X2 )
% 0.35/0.63                    = zero_zero_rat ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg_eq_0_iff
% 0.35/0.63  thf(fact_6459_sum__nonneg__eq__0__iff,axiom,
% 0.35/0.63      ! [A2: set_real,F: real > nat] :
% 0.35/0.63        ( ( finite_finite_real @ A2 )
% 0.35/0.63       => ( ! [X3: real] :
% 0.35/0.63              ( ( member_real @ X3 @ A2 )
% 0.35/0.63             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 0.35/0.63         => ( ( ( groups1935376822645274424al_nat @ F @ A2 )
% 0.35/0.63              = zero_zero_nat )
% 0.35/0.63            = ( ! [X2: real] :
% 0.35/0.63                  ( ( member_real @ X2 @ A2 )
% 0.35/0.63                 => ( ( F @ X2 )
% 0.35/0.63                    = zero_zero_nat ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg_eq_0_iff
% 0.35/0.63  thf(fact_6460_sum__nonneg__eq__0__iff,axiom,
% 0.35/0.63      ! [A2: set_int,F: int > nat] :
% 0.35/0.63        ( ( finite_finite_int @ A2 )
% 0.35/0.63       => ( ! [X3: int] :
% 0.35/0.63              ( ( member_int @ X3 @ A2 )
% 0.35/0.63             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 0.35/0.63         => ( ( ( groups4541462559716669496nt_nat @ F @ A2 )
% 0.35/0.63              = zero_zero_nat )
% 0.35/0.63            = ( ! [X2: int] :
% 0.35/0.63                  ( ( member_int @ X2 @ A2 )
% 0.35/0.63                 => ( ( F @ X2 )
% 0.35/0.63                    = zero_zero_nat ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg_eq_0_iff
% 0.35/0.63  thf(fact_6461_sum__nonneg__eq__0__iff,axiom,
% 0.35/0.63      ! [A2: set_complex,F: complex > nat] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.63       => ( ! [X3: complex] :
% 0.35/0.63              ( ( member_complex @ X3 @ A2 )
% 0.35/0.63             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 0.35/0.63         => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 0.35/0.63              = zero_zero_nat )
% 0.35/0.63            = ( ! [X2: complex] :
% 0.35/0.63                  ( ( member_complex @ X2 @ A2 )
% 0.35/0.63                 => ( ( F @ X2 )
% 0.35/0.63                    = zero_zero_nat ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg_eq_0_iff
% 0.35/0.63  thf(fact_6462_sum__le__included,axiom,
% 0.35/0.63      ! [S3: set_complex,T: set_complex,G: complex > real,I2: complex > complex,F: complex > real] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ S3 )
% 0.35/0.63       => ( ( finite3207457112153483333omplex @ T )
% 0.35/0.63         => ( ! [X3: complex] :
% 0.35/0.63                ( ( member_complex @ X3 @ T )
% 0.35/0.63               => ( ord_less_eq_real @ zero_zero_real @ ( G @ X3 ) ) )
% 0.35/0.63           => ( ! [X3: complex] :
% 0.35/0.63                  ( ( member_complex @ X3 @ S3 )
% 0.35/0.63                 => ? [Xa: complex] :
% 0.35/0.63                      ( ( member_complex @ Xa @ T )
% 0.35/0.63                      & ( ( I2 @ Xa )
% 0.35/0.63                        = X3 )
% 0.35/0.63                      & ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 0.35/0.63             => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S3 ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_le_included
% 0.35/0.63  thf(fact_6463_sum__le__included,axiom,
% 0.35/0.63      ! [S3: set_nat,T: set_nat,G: nat > rat,I2: nat > nat,F: nat > rat] :
% 0.35/0.63        ( ( finite_finite_nat @ S3 )
% 0.35/0.63       => ( ( finite_finite_nat @ T )
% 0.35/0.63         => ( ! [X3: nat] :
% 0.35/0.63                ( ( member_nat @ X3 @ T )
% 0.35/0.63               => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 0.35/0.63           => ( ! [X3: nat] :
% 0.35/0.63                  ( ( member_nat @ X3 @ S3 )
% 0.35/0.63                 => ? [Xa: nat] :
% 0.35/0.63                      ( ( member_nat @ Xa @ T )
% 0.35/0.63                      & ( ( I2 @ Xa )
% 0.35/0.63                        = X3 )
% 0.35/0.63                      & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 0.35/0.63             => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S3 ) @ ( groups2906978787729119204at_rat @ G @ T ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_le_included
% 0.35/0.63  thf(fact_6464_sum__le__included,axiom,
% 0.35/0.63      ! [S3: set_nat,T: set_complex,G: complex > rat,I2: complex > nat,F: nat > rat] :
% 0.35/0.63        ( ( finite_finite_nat @ S3 )
% 0.35/0.63       => ( ( finite3207457112153483333omplex @ T )
% 0.35/0.63         => ( ! [X3: complex] :
% 0.35/0.63                ( ( member_complex @ X3 @ T )
% 0.35/0.63               => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 0.35/0.63           => ( ! [X3: nat] :
% 0.35/0.63                  ( ( member_nat @ X3 @ S3 )
% 0.35/0.63                 => ? [Xa: complex] :
% 0.35/0.63                      ( ( member_complex @ Xa @ T )
% 0.35/0.63                      & ( ( I2 @ Xa )
% 0.35/0.63                        = X3 )
% 0.35/0.63                      & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 0.35/0.63             => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S3 ) @ ( groups5058264527183730370ex_rat @ G @ T ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_le_included
% 0.35/0.63  thf(fact_6465_sum__le__included,axiom,
% 0.35/0.63      ! [S3: set_complex,T: set_nat,G: nat > rat,I2: nat > complex,F: complex > rat] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ S3 )
% 0.35/0.63       => ( ( finite_finite_nat @ T )
% 0.35/0.63         => ( ! [X3: nat] :
% 0.35/0.63                ( ( member_nat @ X3 @ T )
% 0.35/0.63               => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 0.35/0.63           => ( ! [X3: complex] :
% 0.35/0.63                  ( ( member_complex @ X3 @ S3 )
% 0.35/0.63                 => ? [Xa: nat] :
% 0.35/0.63                      ( ( member_nat @ Xa @ T )
% 0.35/0.63                      & ( ( I2 @ Xa )
% 0.35/0.63                        = X3 )
% 0.35/0.63                      & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 0.35/0.63             => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ S3 ) @ ( groups2906978787729119204at_rat @ G @ T ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_le_included
% 0.35/0.63  thf(fact_6466_sum__le__included,axiom,
% 0.35/0.63      ! [S3: set_complex,T: set_complex,G: complex > rat,I2: complex > complex,F: complex > rat] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ S3 )
% 0.35/0.63       => ( ( finite3207457112153483333omplex @ T )
% 0.35/0.63         => ( ! [X3: complex] :
% 0.35/0.63                ( ( member_complex @ X3 @ T )
% 0.35/0.63               => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 0.35/0.63           => ( ! [X3: complex] :
% 0.35/0.63                  ( ( member_complex @ X3 @ S3 )
% 0.35/0.63                 => ? [Xa: complex] :
% 0.35/0.63                      ( ( member_complex @ Xa @ T )
% 0.35/0.63                      & ( ( I2 @ Xa )
% 0.35/0.63                        = X3 )
% 0.35/0.63                      & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 0.35/0.63             => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ S3 ) @ ( groups5058264527183730370ex_rat @ G @ T ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_le_included
% 0.35/0.63  thf(fact_6467_sum__le__included,axiom,
% 0.35/0.63      ! [S3: set_complex,T: set_complex,G: complex > nat,I2: complex > complex,F: complex > nat] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ S3 )
% 0.35/0.63       => ( ( finite3207457112153483333omplex @ T )
% 0.35/0.63         => ( ! [X3: complex] :
% 0.35/0.63                ( ( member_complex @ X3 @ T )
% 0.35/0.63               => ( ord_less_eq_nat @ zero_zero_nat @ ( G @ X3 ) ) )
% 0.35/0.63           => ( ! [X3: complex] :
% 0.35/0.63                  ( ( member_complex @ X3 @ S3 )
% 0.35/0.63                 => ? [Xa: complex] :
% 0.35/0.63                      ( ( member_complex @ Xa @ T )
% 0.35/0.63                      & ( ( I2 @ Xa )
% 0.35/0.63                        = X3 )
% 0.35/0.63                      & ( ord_less_eq_nat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 0.35/0.63             => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ S3 ) @ ( groups5693394587270226106ex_nat @ G @ T ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_le_included
% 0.35/0.63  thf(fact_6468_sum__le__included,axiom,
% 0.35/0.63      ! [S3: set_nat,T: set_nat,G: nat > int,I2: nat > nat,F: nat > int] :
% 0.35/0.63        ( ( finite_finite_nat @ S3 )
% 0.35/0.63       => ( ( finite_finite_nat @ T )
% 0.35/0.63         => ( ! [X3: nat] :
% 0.35/0.63                ( ( member_nat @ X3 @ T )
% 0.35/0.63               => ( ord_less_eq_int @ zero_zero_int @ ( G @ X3 ) ) )
% 0.35/0.63           => ( ! [X3: nat] :
% 0.35/0.63                  ( ( member_nat @ X3 @ S3 )
% 0.35/0.63                 => ? [Xa: nat] :
% 0.35/0.63                      ( ( member_nat @ Xa @ T )
% 0.35/0.63                      & ( ( I2 @ Xa )
% 0.35/0.63                        = X3 )
% 0.35/0.63                      & ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 0.35/0.63             => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ S3 ) @ ( groups3539618377306564664at_int @ G @ T ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_le_included
% 0.35/0.63  thf(fact_6469_sum__le__included,axiom,
% 0.35/0.63      ! [S3: set_nat,T: set_complex,G: complex > int,I2: complex > nat,F: nat > int] :
% 0.35/0.63        ( ( finite_finite_nat @ S3 )
% 0.35/0.63       => ( ( finite3207457112153483333omplex @ T )
% 0.35/0.63         => ( ! [X3: complex] :
% 0.35/0.63                ( ( member_complex @ X3 @ T )
% 0.35/0.63               => ( ord_less_eq_int @ zero_zero_int @ ( G @ X3 ) ) )
% 0.35/0.63           => ( ! [X3: nat] :
% 0.35/0.63                  ( ( member_nat @ X3 @ S3 )
% 0.35/0.63                 => ? [Xa: complex] :
% 0.35/0.63                      ( ( member_complex @ Xa @ T )
% 0.35/0.63                      & ( ( I2 @ Xa )
% 0.35/0.63                        = X3 )
% 0.35/0.63                      & ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 0.35/0.63             => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ S3 ) @ ( groups5690904116761175830ex_int @ G @ T ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_le_included
% 0.35/0.63  thf(fact_6470_sum__le__included,axiom,
% 0.35/0.63      ! [S3: set_complex,T: set_nat,G: nat > int,I2: nat > complex,F: complex > int] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ S3 )
% 0.35/0.63       => ( ( finite_finite_nat @ T )
% 0.35/0.63         => ( ! [X3: nat] :
% 0.35/0.63                ( ( member_nat @ X3 @ T )
% 0.35/0.63               => ( ord_less_eq_int @ zero_zero_int @ ( G @ X3 ) ) )
% 0.35/0.63           => ( ! [X3: complex] :
% 0.35/0.63                  ( ( member_complex @ X3 @ S3 )
% 0.35/0.63                 => ? [Xa: nat] :
% 0.35/0.63                      ( ( member_nat @ Xa @ T )
% 0.35/0.63                      & ( ( I2 @ Xa )
% 0.35/0.63                        = X3 )
% 0.35/0.63                      & ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 0.35/0.63             => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F @ S3 ) @ ( groups3539618377306564664at_int @ G @ T ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_le_included
% 0.35/0.63  thf(fact_6471_sum__le__included,axiom,
% 0.35/0.63      ! [S3: set_complex,T: set_complex,G: complex > int,I2: complex > complex,F: complex > int] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ S3 )
% 0.35/0.63       => ( ( finite3207457112153483333omplex @ T )
% 0.35/0.63         => ( ! [X3: complex] :
% 0.35/0.63                ( ( member_complex @ X3 @ T )
% 0.35/0.63               => ( ord_less_eq_int @ zero_zero_int @ ( G @ X3 ) ) )
% 0.35/0.63           => ( ! [X3: complex] :
% 0.35/0.63                  ( ( member_complex @ X3 @ S3 )
% 0.35/0.63                 => ? [Xa: complex] :
% 0.35/0.63                      ( ( member_complex @ Xa @ T )
% 0.35/0.63                      & ( ( I2 @ Xa )
% 0.35/0.63                        = X3 )
% 0.35/0.63                      & ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 0.35/0.63             => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F @ S3 ) @ ( groups5690904116761175830ex_int @ G @ T ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_le_included
% 0.35/0.63  thf(fact_6472_sum__strict__mono__ex1,axiom,
% 0.35/0.63      ! [A2: set_complex,F: complex > real,G: complex > real] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.63       => ( ! [X3: complex] :
% 0.35/0.63              ( ( member_complex @ X3 @ A2 )
% 0.35/0.63             => ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.63         => ( ? [X5: complex] :
% 0.35/0.63                ( ( member_complex @ X5 @ A2 )
% 0.35/0.63                & ( ord_less_real @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 0.35/0.63           => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_strict_mono_ex1
% 0.35/0.63  thf(fact_6473_sum__strict__mono__ex1,axiom,
% 0.35/0.63      ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 0.35/0.63        ( ( finite_finite_nat @ A2 )
% 0.35/0.63       => ( ! [X3: nat] :
% 0.35/0.63              ( ( member_nat @ X3 @ A2 )
% 0.35/0.63             => ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.63         => ( ? [X5: nat] :
% 0.35/0.63                ( ( member_nat @ X5 @ A2 )
% 0.35/0.63                & ( ord_less_rat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 0.35/0.63           => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_strict_mono_ex1
% 0.35/0.63  thf(fact_6474_sum__strict__mono__ex1,axiom,
% 0.35/0.63      ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.63       => ( ! [X3: complex] :
% 0.35/0.63              ( ( member_complex @ X3 @ A2 )
% 0.35/0.63             => ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.63         => ( ? [X5: complex] :
% 0.35/0.63                ( ( member_complex @ X5 @ A2 )
% 0.35/0.63                & ( ord_less_rat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 0.35/0.63           => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_strict_mono_ex1
% 0.35/0.63  thf(fact_6475_sum__strict__mono__ex1,axiom,
% 0.35/0.63      ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.63       => ( ! [X3: complex] :
% 0.35/0.63              ( ( member_complex @ X3 @ A2 )
% 0.35/0.63             => ( ord_less_eq_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.63         => ( ? [X5: complex] :
% 0.35/0.63                ( ( member_complex @ X5 @ A2 )
% 0.35/0.63                & ( ord_less_nat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 0.35/0.63           => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_strict_mono_ex1
% 0.35/0.63  thf(fact_6476_sum__strict__mono__ex1,axiom,
% 0.35/0.63      ! [A2: set_nat,F: nat > int,G: nat > int] :
% 0.35/0.63        ( ( finite_finite_nat @ A2 )
% 0.35/0.63       => ( ! [X3: nat] :
% 0.35/0.63              ( ( member_nat @ X3 @ A2 )
% 0.35/0.63             => ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.63         => ( ? [X5: nat] :
% 0.35/0.63                ( ( member_nat @ X5 @ A2 )
% 0.35/0.63                & ( ord_less_int @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 0.35/0.63           => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ G @ A2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_strict_mono_ex1
% 0.35/0.63  thf(fact_6477_sum__strict__mono__ex1,axiom,
% 0.35/0.63      ! [A2: set_complex,F: complex > int,G: complex > int] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.63       => ( ! [X3: complex] :
% 0.35/0.63              ( ( member_complex @ X3 @ A2 )
% 0.35/0.63             => ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.63         => ( ? [X5: complex] :
% 0.35/0.63                ( ( member_complex @ X5 @ A2 )
% 0.35/0.63                & ( ord_less_int @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 0.35/0.63           => ( ord_less_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ G @ A2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_strict_mono_ex1
% 0.35/0.63  thf(fact_6478_sum__strict__mono__ex1,axiom,
% 0.35/0.63      ! [A2: set_int,F: int > int,G: int > int] :
% 0.35/0.63        ( ( finite_finite_int @ A2 )
% 0.35/0.63       => ( ! [X3: int] :
% 0.35/0.63              ( ( member_int @ X3 @ A2 )
% 0.35/0.63             => ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.63         => ( ? [X5: int] :
% 0.35/0.63                ( ( member_int @ X5 @ A2 )
% 0.35/0.63                & ( ord_less_int @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 0.35/0.63           => ( ord_less_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ G @ A2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_strict_mono_ex1
% 0.35/0.63  thf(fact_6479_sum__strict__mono__ex1,axiom,
% 0.35/0.63      ! [A2: set_nat,F: nat > nat,G: nat > nat] :
% 0.35/0.63        ( ( finite_finite_nat @ A2 )
% 0.35/0.63       => ( ! [X3: nat] :
% 0.35/0.63              ( ( member_nat @ X3 @ A2 )
% 0.35/0.63             => ( ord_less_eq_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.63         => ( ? [X5: nat] :
% 0.35/0.63                ( ( member_nat @ X5 @ A2 )
% 0.35/0.63                & ( ord_less_nat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 0.35/0.63           => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_strict_mono_ex1
% 0.35/0.63  thf(fact_6480_sum__strict__mono__ex1,axiom,
% 0.35/0.63      ! [A2: set_nat,F: nat > real,G: nat > real] :
% 0.35/0.63        ( ( finite_finite_nat @ A2 )
% 0.35/0.63       => ( ! [X3: nat] :
% 0.35/0.63              ( ( member_nat @ X3 @ A2 )
% 0.35/0.63             => ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.63         => ( ? [X5: nat] :
% 0.35/0.63                ( ( member_nat @ X5 @ A2 )
% 0.35/0.63                & ( ord_less_real @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 0.35/0.63           => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ G @ A2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_strict_mono_ex1
% 0.35/0.63  thf(fact_6481_sum_Orelated,axiom,
% 0.35/0.63      ! [R2: complex > complex > $o,S2: set_nat,H2: nat > complex,G: nat > complex] :
% 0.35/0.63        ( ( R2 @ zero_zero_complex @ zero_zero_complex )
% 0.35/0.63       => ( ! [X15: complex,Y15: complex,X22: complex,Y23: complex] :
% 0.35/0.63              ( ( ( R2 @ X15 @ X22 )
% 0.35/0.63                & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.63             => ( R2 @ ( plus_plus_complex @ X15 @ Y15 ) @ ( plus_plus_complex @ X22 @ Y23 ) ) )
% 0.35/0.63         => ( ( finite_finite_nat @ S2 )
% 0.35/0.63           => ( ! [X3: nat] :
% 0.35/0.63                  ( ( member_nat @ X3 @ S2 )
% 0.35/0.63                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.63             => ( R2 @ ( groups2073611262835488442omplex @ H2 @ S2 ) @ ( groups2073611262835488442omplex @ G @ S2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.related
% 0.35/0.63  thf(fact_6482_sum_Orelated,axiom,
% 0.35/0.63      ! [R2: real > real > $o,S2: set_complex,H2: complex > real,G: complex > real] :
% 0.35/0.63        ( ( R2 @ zero_zero_real @ zero_zero_real )
% 0.35/0.63       => ( ! [X15: real,Y15: real,X22: real,Y23: real] :
% 0.35/0.63              ( ( ( R2 @ X15 @ X22 )
% 0.35/0.63                & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.63             => ( R2 @ ( plus_plus_real @ X15 @ Y15 ) @ ( plus_plus_real @ X22 @ Y23 ) ) )
% 0.35/0.63         => ( ( finite3207457112153483333omplex @ S2 )
% 0.35/0.63           => ( ! [X3: complex] :
% 0.35/0.63                  ( ( member_complex @ X3 @ S2 )
% 0.35/0.63                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.63             => ( R2 @ ( groups5808333547571424918x_real @ H2 @ S2 ) @ ( groups5808333547571424918x_real @ G @ S2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.related
% 0.35/0.63  thf(fact_6483_sum_Orelated,axiom,
% 0.35/0.63      ! [R2: rat > rat > $o,S2: set_nat,H2: nat > rat,G: nat > rat] :
% 0.35/0.63        ( ( R2 @ zero_zero_rat @ zero_zero_rat )
% 0.35/0.63       => ( ! [X15: rat,Y15: rat,X22: rat,Y23: rat] :
% 0.35/0.63              ( ( ( R2 @ X15 @ X22 )
% 0.35/0.63                & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.63             => ( R2 @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X22 @ Y23 ) ) )
% 0.35/0.63         => ( ( finite_finite_nat @ S2 )
% 0.35/0.63           => ( ! [X3: nat] :
% 0.35/0.63                  ( ( member_nat @ X3 @ S2 )
% 0.35/0.63                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.63             => ( R2 @ ( groups2906978787729119204at_rat @ H2 @ S2 ) @ ( groups2906978787729119204at_rat @ G @ S2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.related
% 0.35/0.63  thf(fact_6484_sum_Orelated,axiom,
% 0.35/0.63      ! [R2: rat > rat > $o,S2: set_complex,H2: complex > rat,G: complex > rat] :
% 0.35/0.63        ( ( R2 @ zero_zero_rat @ zero_zero_rat )
% 0.35/0.63       => ( ! [X15: rat,Y15: rat,X22: rat,Y23: rat] :
% 0.35/0.63              ( ( ( R2 @ X15 @ X22 )
% 0.35/0.63                & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.63             => ( R2 @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X22 @ Y23 ) ) )
% 0.35/0.63         => ( ( finite3207457112153483333omplex @ S2 )
% 0.35/0.63           => ( ! [X3: complex] :
% 0.35/0.63                  ( ( member_complex @ X3 @ S2 )
% 0.35/0.63                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.63             => ( R2 @ ( groups5058264527183730370ex_rat @ H2 @ S2 ) @ ( groups5058264527183730370ex_rat @ G @ S2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.related
% 0.35/0.63  thf(fact_6485_sum_Orelated,axiom,
% 0.35/0.63      ! [R2: nat > nat > $o,S2: set_complex,H2: complex > nat,G: complex > nat] :
% 0.35/0.63        ( ( R2 @ zero_zero_nat @ zero_zero_nat )
% 0.35/0.63       => ( ! [X15: nat,Y15: nat,X22: nat,Y23: nat] :
% 0.35/0.63              ( ( ( R2 @ X15 @ X22 )
% 0.35/0.63                & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.63             => ( R2 @ ( plus_plus_nat @ X15 @ Y15 ) @ ( plus_plus_nat @ X22 @ Y23 ) ) )
% 0.35/0.63         => ( ( finite3207457112153483333omplex @ S2 )
% 0.35/0.63           => ( ! [X3: complex] :
% 0.35/0.63                  ( ( member_complex @ X3 @ S2 )
% 0.35/0.63                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.63             => ( R2 @ ( groups5693394587270226106ex_nat @ H2 @ S2 ) @ ( groups5693394587270226106ex_nat @ G @ S2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.related
% 0.35/0.63  thf(fact_6486_sum_Orelated,axiom,
% 0.35/0.63      ! [R2: int > int > $o,S2: set_nat,H2: nat > int,G: nat > int] :
% 0.35/0.63        ( ( R2 @ zero_zero_int @ zero_zero_int )
% 0.35/0.63       => ( ! [X15: int,Y15: int,X22: int,Y23: int] :
% 0.35/0.63              ( ( ( R2 @ X15 @ X22 )
% 0.35/0.63                & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.63             => ( R2 @ ( plus_plus_int @ X15 @ Y15 ) @ ( plus_plus_int @ X22 @ Y23 ) ) )
% 0.35/0.63         => ( ( finite_finite_nat @ S2 )
% 0.35/0.63           => ( ! [X3: nat] :
% 0.35/0.63                  ( ( member_nat @ X3 @ S2 )
% 0.35/0.63                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.63             => ( R2 @ ( groups3539618377306564664at_int @ H2 @ S2 ) @ ( groups3539618377306564664at_int @ G @ S2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.related
% 0.35/0.63  thf(fact_6487_sum_Orelated,axiom,
% 0.35/0.63      ! [R2: int > int > $o,S2: set_complex,H2: complex > int,G: complex > int] :
% 0.35/0.63        ( ( R2 @ zero_zero_int @ zero_zero_int )
% 0.35/0.63       => ( ! [X15: int,Y15: int,X22: int,Y23: int] :
% 0.35/0.63              ( ( ( R2 @ X15 @ X22 )
% 0.35/0.63                & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.63             => ( R2 @ ( plus_plus_int @ X15 @ Y15 ) @ ( plus_plus_int @ X22 @ Y23 ) ) )
% 0.35/0.63         => ( ( finite3207457112153483333omplex @ S2 )
% 0.35/0.63           => ( ! [X3: complex] :
% 0.35/0.63                  ( ( member_complex @ X3 @ S2 )
% 0.35/0.63                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.63             => ( R2 @ ( groups5690904116761175830ex_int @ H2 @ S2 ) @ ( groups5690904116761175830ex_int @ G @ S2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.related
% 0.35/0.63  thf(fact_6488_sum_Orelated,axiom,
% 0.35/0.63      ! [R2: int > int > $o,S2: set_int,H2: int > int,G: int > int] :
% 0.35/0.63        ( ( R2 @ zero_zero_int @ zero_zero_int )
% 0.35/0.63       => ( ! [X15: int,Y15: int,X22: int,Y23: int] :
% 0.35/0.63              ( ( ( R2 @ X15 @ X22 )
% 0.35/0.63                & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.63             => ( R2 @ ( plus_plus_int @ X15 @ Y15 ) @ ( plus_plus_int @ X22 @ Y23 ) ) )
% 0.35/0.63         => ( ( finite_finite_int @ S2 )
% 0.35/0.63           => ( ! [X3: int] :
% 0.35/0.63                  ( ( member_int @ X3 @ S2 )
% 0.35/0.63                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.63             => ( R2 @ ( groups4538972089207619220nt_int @ H2 @ S2 ) @ ( groups4538972089207619220nt_int @ G @ S2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.related
% 0.35/0.63  thf(fact_6489_sum_Orelated,axiom,
% 0.35/0.63      ! [R2: complex > complex > $o,S2: set_complex,H2: complex > complex,G: complex > complex] :
% 0.35/0.63        ( ( R2 @ zero_zero_complex @ zero_zero_complex )
% 0.35/0.63       => ( ! [X15: complex,Y15: complex,X22: complex,Y23: complex] :
% 0.35/0.63              ( ( ( R2 @ X15 @ X22 )
% 0.35/0.63                & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.63             => ( R2 @ ( plus_plus_complex @ X15 @ Y15 ) @ ( plus_plus_complex @ X22 @ Y23 ) ) )
% 0.35/0.63         => ( ( finite3207457112153483333omplex @ S2 )
% 0.35/0.63           => ( ! [X3: complex] :
% 0.35/0.63                  ( ( member_complex @ X3 @ S2 )
% 0.35/0.63                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.63             => ( R2 @ ( groups7754918857620584856omplex @ H2 @ S2 ) @ ( groups7754918857620584856omplex @ G @ S2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.related
% 0.35/0.63  thf(fact_6490_sum_Orelated,axiom,
% 0.35/0.63      ! [R2: nat > nat > $o,S2: set_nat,H2: nat > nat,G: nat > nat] :
% 0.35/0.63        ( ( R2 @ zero_zero_nat @ zero_zero_nat )
% 0.35/0.63       => ( ! [X15: nat,Y15: nat,X22: nat,Y23: nat] :
% 0.35/0.63              ( ( ( R2 @ X15 @ X22 )
% 0.35/0.63                & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.63             => ( R2 @ ( plus_plus_nat @ X15 @ Y15 ) @ ( plus_plus_nat @ X22 @ Y23 ) ) )
% 0.35/0.63         => ( ( finite_finite_nat @ S2 )
% 0.35/0.63           => ( ! [X3: nat] :
% 0.35/0.63                  ( ( member_nat @ X3 @ S2 )
% 0.35/0.63                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.63             => ( R2 @ ( groups3542108847815614940at_nat @ H2 @ S2 ) @ ( groups3542108847815614940at_nat @ G @ S2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.related
% 0.35/0.63  thf(fact_6491_sum__strict__mono,axiom,
% 0.35/0.63      ! [A2: set_complex,F: complex > real,G: complex > real] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.63       => ( ( A2 != bot_bot_set_complex )
% 0.35/0.63         => ( ! [X3: complex] :
% 0.35/0.63                ( ( member_complex @ X3 @ A2 )
% 0.35/0.63               => ( ord_less_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.63           => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_strict_mono
% 0.35/0.63  thf(fact_6492_sum__strict__mono,axiom,
% 0.35/0.63      ! [A2: set_int,F: int > real,G: int > real] :
% 0.35/0.63        ( ( finite_finite_int @ A2 )
% 0.35/0.63       => ( ( A2 != bot_bot_set_int )
% 0.35/0.63         => ( ! [X3: int] :
% 0.35/0.63                ( ( member_int @ X3 @ A2 )
% 0.35/0.63               => ( ord_less_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.63           => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_strict_mono
% 0.35/0.63  thf(fact_6493_sum__strict__mono,axiom,
% 0.35/0.63      ! [A2: set_real,F: real > real,G: real > real] :
% 0.35/0.63        ( ( finite_finite_real @ A2 )
% 0.35/0.63       => ( ( A2 != bot_bot_set_real )
% 0.35/0.63         => ( ! [X3: real] :
% 0.35/0.63                ( ( member_real @ X3 @ A2 )
% 0.35/0.63               => ( ord_less_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.63           => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_strict_mono
% 0.35/0.63  thf(fact_6494_sum__strict__mono,axiom,
% 0.35/0.63      ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.63       => ( ( A2 != bot_bot_set_complex )
% 0.35/0.63         => ( ! [X3: complex] :
% 0.35/0.63                ( ( member_complex @ X3 @ A2 )
% 0.35/0.63               => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.63           => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_strict_mono
% 0.35/0.63  thf(fact_6495_sum__strict__mono,axiom,
% 0.35/0.63      ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 0.35/0.63        ( ( finite_finite_nat @ A2 )
% 0.35/0.63       => ( ( A2 != bot_bot_set_nat )
% 0.35/0.63         => ( ! [X3: nat] :
% 0.35/0.63                ( ( member_nat @ X3 @ A2 )
% 0.35/0.63               => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.63           => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_strict_mono
% 0.35/0.63  thf(fact_6496_sum__strict__mono,axiom,
% 0.35/0.63      ! [A2: set_int,F: int > rat,G: int > rat] :
% 0.35/0.63        ( ( finite_finite_int @ A2 )
% 0.35/0.63       => ( ( A2 != bot_bot_set_int )
% 0.35/0.63         => ( ! [X3: int] :
% 0.35/0.63                ( ( member_int @ X3 @ A2 )
% 0.35/0.63               => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.63           => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_strict_mono
% 0.35/0.63  thf(fact_6497_sum__strict__mono,axiom,
% 0.35/0.63      ! [A2: set_real,F: real > rat,G: real > rat] :
% 0.35/0.63        ( ( finite_finite_real @ A2 )
% 0.35/0.63       => ( ( A2 != bot_bot_set_real )
% 0.35/0.63         => ( ! [X3: real] :
% 0.35/0.63                ( ( member_real @ X3 @ A2 )
% 0.35/0.63               => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.63           => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_strict_mono
% 0.35/0.63  thf(fact_6498_sum__strict__mono,axiom,
% 0.35/0.63      ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.63       => ( ( A2 != bot_bot_set_complex )
% 0.35/0.63         => ( ! [X3: complex] :
% 0.35/0.63                ( ( member_complex @ X3 @ A2 )
% 0.35/0.63               => ( ord_less_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.63           => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_strict_mono
% 0.35/0.63  thf(fact_6499_sum__strict__mono,axiom,
% 0.35/0.63      ! [A2: set_int,F: int > nat,G: int > nat] :
% 0.35/0.63        ( ( finite_finite_int @ A2 )
% 0.35/0.63       => ( ( A2 != bot_bot_set_int )
% 0.35/0.63         => ( ! [X3: int] :
% 0.35/0.63                ( ( member_int @ X3 @ A2 )
% 0.35/0.63               => ( ord_less_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.63           => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_strict_mono
% 0.35/0.63  thf(fact_6500_sum__strict__mono,axiom,
% 0.35/0.63      ! [A2: set_real,F: real > nat,G: real > nat] :
% 0.35/0.63        ( ( finite_finite_real @ A2 )
% 0.35/0.63       => ( ( A2 != bot_bot_set_real )
% 0.35/0.63         => ( ! [X3: real] :
% 0.35/0.63                ( ( member_real @ X3 @ A2 )
% 0.35/0.63               => ( ord_less_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.63           => ( ord_less_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_strict_mono
% 0.35/0.63  thf(fact_6501_sum_Oinsert__if,axiom,
% 0.35/0.63      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > real] :
% 0.35/0.63        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.35/0.63       => ( ( ( member_VEBT_VEBT @ X @ A2 )
% 0.35/0.63           => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 0.35/0.63              = ( groups2240296850493347238T_real @ G @ A2 ) ) )
% 0.35/0.63          & ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 0.35/0.63           => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 0.35/0.63              = ( plus_plus_real @ ( G @ X ) @ ( groups2240296850493347238T_real @ G @ A2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.insert_if
% 0.35/0.63  thf(fact_6502_sum_Oinsert__if,axiom,
% 0.35/0.63      ! [A2: set_real,X: real,G: real > real] :
% 0.35/0.63        ( ( finite_finite_real @ A2 )
% 0.35/0.63       => ( ( ( member_real @ X @ A2 )
% 0.35/0.63           => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X @ A2 ) )
% 0.35/0.63              = ( groups8097168146408367636l_real @ G @ A2 ) ) )
% 0.35/0.63          & ( ~ ( member_real @ X @ A2 )
% 0.35/0.63           => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X @ A2 ) )
% 0.35/0.63              = ( plus_plus_real @ ( G @ X ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.insert_if
% 0.35/0.63  thf(fact_6503_sum_Oinsert__if,axiom,
% 0.35/0.63      ! [A2: set_int,X: int,G: int > real] :
% 0.35/0.63        ( ( finite_finite_int @ A2 )
% 0.35/0.63       => ( ( ( member_int @ X @ A2 )
% 0.35/0.63           => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X @ A2 ) )
% 0.35/0.63              = ( groups8778361861064173332t_real @ G @ A2 ) ) )
% 0.35/0.63          & ( ~ ( member_int @ X @ A2 )
% 0.35/0.63           => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X @ A2 ) )
% 0.35/0.63              = ( plus_plus_real @ ( G @ X ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.insert_if
% 0.35/0.63  thf(fact_6504_sum_Oinsert__if,axiom,
% 0.35/0.63      ! [A2: set_complex,X: complex,G: complex > real] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.63       => ( ( ( member_complex @ X @ A2 )
% 0.35/0.63           => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A2 ) )
% 0.35/0.63              = ( groups5808333547571424918x_real @ G @ A2 ) ) )
% 0.35/0.63          & ( ~ ( member_complex @ X @ A2 )
% 0.35/0.63           => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A2 ) )
% 0.35/0.63              = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.insert_if
% 0.35/0.63  thf(fact_6505_sum_Oinsert__if,axiom,
% 0.35/0.63      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 0.35/0.63        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.35/0.63       => ( ( ( member_VEBT_VEBT @ X @ A2 )
% 0.35/0.63           => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 0.35/0.63              = ( groups136491112297645522BT_rat @ G @ A2 ) ) )
% 0.35/0.63          & ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 0.35/0.63           => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 0.35/0.63              = ( plus_plus_rat @ ( G @ X ) @ ( groups136491112297645522BT_rat @ G @ A2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.insert_if
% 0.35/0.63  thf(fact_6506_sum_Oinsert__if,axiom,
% 0.35/0.63      ! [A2: set_real,X: real,G: real > rat] :
% 0.35/0.63        ( ( finite_finite_real @ A2 )
% 0.35/0.63       => ( ( ( member_real @ X @ A2 )
% 0.35/0.63           => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X @ A2 ) )
% 0.35/0.63              = ( groups1300246762558778688al_rat @ G @ A2 ) ) )
% 0.35/0.63          & ( ~ ( member_real @ X @ A2 )
% 0.35/0.63           => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X @ A2 ) )
% 0.35/0.63              = ( plus_plus_rat @ ( G @ X ) @ ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.insert_if
% 0.35/0.63  thf(fact_6507_sum_Oinsert__if,axiom,
% 0.35/0.63      ! [A2: set_int,X: int,G: int > rat] :
% 0.35/0.63        ( ( finite_finite_int @ A2 )
% 0.35/0.63       => ( ( ( member_int @ X @ A2 )
% 0.35/0.63           => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X @ A2 ) )
% 0.35/0.63              = ( groups3906332499630173760nt_rat @ G @ A2 ) ) )
% 0.35/0.63          & ( ~ ( member_int @ X @ A2 )
% 0.35/0.63           => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X @ A2 ) )
% 0.35/0.63              = ( plus_plus_rat @ ( G @ X ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.insert_if
% 0.35/0.63  thf(fact_6508_sum_Oinsert__if,axiom,
% 0.35/0.63      ! [A2: set_nat,X: nat,G: nat > rat] :
% 0.35/0.63        ( ( finite_finite_nat @ A2 )
% 0.35/0.63       => ( ( ( member_nat @ X @ A2 )
% 0.35/0.63           => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A2 ) )
% 0.35/0.63              = ( groups2906978787729119204at_rat @ G @ A2 ) ) )
% 0.35/0.63          & ( ~ ( member_nat @ X @ A2 )
% 0.35/0.63           => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A2 ) )
% 0.35/0.63              = ( plus_plus_rat @ ( G @ X ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.insert_if
% 0.35/0.63  thf(fact_6509_sum_Oinsert__if,axiom,
% 0.35/0.63      ! [A2: set_complex,X: complex,G: complex > rat] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.63       => ( ( ( member_complex @ X @ A2 )
% 0.35/0.63           => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X @ A2 ) )
% 0.35/0.63              = ( groups5058264527183730370ex_rat @ G @ A2 ) ) )
% 0.35/0.63          & ( ~ ( member_complex @ X @ A2 )
% 0.35/0.63           => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X @ A2 ) )
% 0.35/0.63              = ( plus_plus_rat @ ( G @ X ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.insert_if
% 0.35/0.63  thf(fact_6510_sum_Oinsert__if,axiom,
% 0.35/0.63      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > nat] :
% 0.35/0.63        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.35/0.63       => ( ( ( member_VEBT_VEBT @ X @ A2 )
% 0.35/0.63           => ( ( groups771621172384141258BT_nat @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 0.35/0.63              = ( groups771621172384141258BT_nat @ G @ A2 ) ) )
% 0.35/0.63          & ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 0.35/0.63           => ( ( groups771621172384141258BT_nat @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 0.35/0.63              = ( plus_plus_nat @ ( G @ X ) @ ( groups771621172384141258BT_nat @ G @ A2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.insert_if
% 0.35/0.63  thf(fact_6511_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.35/0.63      ! [S5: set_real,T5: set_real,S2: set_real,I2: real > real,J: real > real,T4: set_real,G: real > complex,H2: real > complex] :
% 0.35/0.63        ( ( finite_finite_real @ S5 )
% 0.35/0.63       => ( ( finite_finite_real @ T5 )
% 0.35/0.63         => ( ! [A4: real] :
% 0.35/0.63                ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 0.35/0.63               => ( ( I2 @ ( J @ A4 ) )
% 0.35/0.63                  = A4 ) )
% 0.35/0.63           => ( ! [A4: real] :
% 0.35/0.63                  ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 0.35/0.63                 => ( member_real @ ( J @ A4 ) @ ( minus_minus_set_real @ T4 @ T5 ) ) )
% 0.35/0.63             => ( ! [B3: real] :
% 0.35/0.63                    ( ( member_real @ B3 @ ( minus_minus_set_real @ T4 @ T5 ) )
% 0.35/0.63                   => ( ( J @ ( I2 @ B3 ) )
% 0.35/0.63                      = B3 ) )
% 0.35/0.63               => ( ! [B3: real] :
% 0.35/0.63                      ( ( member_real @ B3 @ ( minus_minus_set_real @ T4 @ T5 ) )
% 0.35/0.63                     => ( member_real @ ( I2 @ B3 ) @ ( minus_minus_set_real @ S2 @ S5 ) ) )
% 0.35/0.63                 => ( ! [A4: real] :
% 0.35/0.63                        ( ( member_real @ A4 @ S5 )
% 0.35/0.63                       => ( ( G @ A4 )
% 0.35/0.63                          = zero_zero_complex ) )
% 0.35/0.63                   => ( ! [B3: real] :
% 0.35/0.63                          ( ( member_real @ B3 @ T5 )
% 0.35/0.63                         => ( ( H2 @ B3 )
% 0.35/0.63                            = zero_zero_complex ) )
% 0.35/0.63                     => ( ! [A4: real] :
% 0.35/0.63                            ( ( member_real @ A4 @ S2 )
% 0.35/0.63                           => ( ( H2 @ ( J @ A4 ) )
% 0.35/0.63                              = ( G @ A4 ) ) )
% 0.35/0.63                       => ( ( groups5754745047067104278omplex @ G @ S2 )
% 0.35/0.63                          = ( groups5754745047067104278omplex @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.reindex_bij_witness_not_neutral
% 0.35/0.63  thf(fact_6512_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.35/0.63      ! [S5: set_real,T5: set_int,S2: set_real,I2: int > real,J: real > int,T4: set_int,G: real > complex,H2: int > complex] :
% 0.35/0.63        ( ( finite_finite_real @ S5 )
% 0.35/0.63       => ( ( finite_finite_int @ T5 )
% 0.35/0.63         => ( ! [A4: real] :
% 0.35/0.63                ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 0.35/0.63               => ( ( I2 @ ( J @ A4 ) )
% 0.35/0.63                  = A4 ) )
% 0.35/0.63           => ( ! [A4: real] :
% 0.35/0.63                  ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 0.35/0.63                 => ( member_int @ ( J @ A4 ) @ ( minus_minus_set_int @ T4 @ T5 ) ) )
% 0.35/0.63             => ( ! [B3: int] :
% 0.35/0.63                    ( ( member_int @ B3 @ ( minus_minus_set_int @ T4 @ T5 ) )
% 0.35/0.63                   => ( ( J @ ( I2 @ B3 ) )
% 0.35/0.63                      = B3 ) )
% 0.35/0.63               => ( ! [B3: int] :
% 0.35/0.63                      ( ( member_int @ B3 @ ( minus_minus_set_int @ T4 @ T5 ) )
% 0.35/0.63                     => ( member_real @ ( I2 @ B3 ) @ ( minus_minus_set_real @ S2 @ S5 ) ) )
% 0.35/0.63                 => ( ! [A4: real] :
% 0.35/0.63                        ( ( member_real @ A4 @ S5 )
% 0.35/0.63                       => ( ( G @ A4 )
% 0.35/0.63                          = zero_zero_complex ) )
% 0.35/0.63                   => ( ! [B3: int] :
% 0.35/0.63                          ( ( member_int @ B3 @ T5 )
% 0.35/0.63                         => ( ( H2 @ B3 )
% 0.35/0.63                            = zero_zero_complex ) )
% 0.35/0.63                     => ( ! [A4: real] :
% 0.35/0.63                            ( ( member_real @ A4 @ S2 )
% 0.35/0.63                           => ( ( H2 @ ( J @ A4 ) )
% 0.35/0.63                              = ( G @ A4 ) ) )
% 0.35/0.63                       => ( ( groups5754745047067104278omplex @ G @ S2 )
% 0.35/0.63                          = ( groups3049146728041665814omplex @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.reindex_bij_witness_not_neutral
% 0.35/0.63  thf(fact_6513_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.35/0.63      ! [S5: set_int,T5: set_real,S2: set_int,I2: real > int,J: int > real,T4: set_real,G: int > complex,H2: real > complex] :
% 0.35/0.63        ( ( finite_finite_int @ S5 )
% 0.35/0.63       => ( ( finite_finite_real @ T5 )
% 0.35/0.63         => ( ! [A4: int] :
% 0.35/0.63                ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 0.35/0.63               => ( ( I2 @ ( J @ A4 ) )
% 0.35/0.63                  = A4 ) )
% 0.35/0.63           => ( ! [A4: int] :
% 0.35/0.63                  ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 0.35/0.63                 => ( member_real @ ( J @ A4 ) @ ( minus_minus_set_real @ T4 @ T5 ) ) )
% 0.35/0.63             => ( ! [B3: real] :
% 0.35/0.63                    ( ( member_real @ B3 @ ( minus_minus_set_real @ T4 @ T5 ) )
% 0.35/0.63                   => ( ( J @ ( I2 @ B3 ) )
% 0.35/0.63                      = B3 ) )
% 0.35/0.63               => ( ! [B3: real] :
% 0.35/0.63                      ( ( member_real @ B3 @ ( minus_minus_set_real @ T4 @ T5 ) )
% 0.35/0.63                     => ( member_int @ ( I2 @ B3 ) @ ( minus_minus_set_int @ S2 @ S5 ) ) )
% 0.35/0.63                 => ( ! [A4: int] :
% 0.35/0.63                        ( ( member_int @ A4 @ S5 )
% 0.35/0.63                       => ( ( G @ A4 )
% 0.35/0.63                          = zero_zero_complex ) )
% 0.35/0.63                   => ( ! [B3: real] :
% 0.35/0.63                          ( ( member_real @ B3 @ T5 )
% 0.35/0.63                         => ( ( H2 @ B3 )
% 0.35/0.63                            = zero_zero_complex ) )
% 0.35/0.63                     => ( ! [A4: int] :
% 0.35/0.63                            ( ( member_int @ A4 @ S2 )
% 0.35/0.63                           => ( ( H2 @ ( J @ A4 ) )
% 0.35/0.63                              = ( G @ A4 ) ) )
% 0.35/0.63                       => ( ( groups3049146728041665814omplex @ G @ S2 )
% 0.35/0.63                          = ( groups5754745047067104278omplex @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.reindex_bij_witness_not_neutral
% 0.35/0.63  thf(fact_6514_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.35/0.63      ! [S5: set_int,T5: set_int,S2: set_int,I2: int > int,J: int > int,T4: set_int,G: int > complex,H2: int > complex] :
% 0.35/0.63        ( ( finite_finite_int @ S5 )
% 0.35/0.63       => ( ( finite_finite_int @ T5 )
% 0.35/0.63         => ( ! [A4: int] :
% 0.35/0.63                ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 0.35/0.63               => ( ( I2 @ ( J @ A4 ) )
% 0.35/0.63                  = A4 ) )
% 0.35/0.63           => ( ! [A4: int] :
% 0.35/0.63                  ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 0.35/0.63                 => ( member_int @ ( J @ A4 ) @ ( minus_minus_set_int @ T4 @ T5 ) ) )
% 0.35/0.63             => ( ! [B3: int] :
% 0.35/0.63                    ( ( member_int @ B3 @ ( minus_minus_set_int @ T4 @ T5 ) )
% 0.35/0.63                   => ( ( J @ ( I2 @ B3 ) )
% 0.35/0.63                      = B3 ) )
% 0.35/0.63               => ( ! [B3: int] :
% 0.35/0.63                      ( ( member_int @ B3 @ ( minus_minus_set_int @ T4 @ T5 ) )
% 0.35/0.63                     => ( member_int @ ( I2 @ B3 ) @ ( minus_minus_set_int @ S2 @ S5 ) ) )
% 0.35/0.63                 => ( ! [A4: int] :
% 0.35/0.63                        ( ( member_int @ A4 @ S5 )
% 0.35/0.63                       => ( ( G @ A4 )
% 0.35/0.63                          = zero_zero_complex ) )
% 0.35/0.63                   => ( ! [B3: int] :
% 0.35/0.63                          ( ( member_int @ B3 @ T5 )
% 0.35/0.63                         => ( ( H2 @ B3 )
% 0.35/0.63                            = zero_zero_complex ) )
% 0.35/0.63                     => ( ! [A4: int] :
% 0.35/0.63                            ( ( member_int @ A4 @ S2 )
% 0.35/0.63                           => ( ( H2 @ ( J @ A4 ) )
% 0.35/0.63                              = ( G @ A4 ) ) )
% 0.35/0.63                       => ( ( groups3049146728041665814omplex @ G @ S2 )
% 0.35/0.63                          = ( groups3049146728041665814omplex @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.reindex_bij_witness_not_neutral
% 0.35/0.63  thf(fact_6515_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.35/0.63      ! [S5: set_real,T5: set_real,S2: set_real,I2: real > real,J: real > real,T4: set_real,G: real > real,H2: real > real] :
% 0.35/0.63        ( ( finite_finite_real @ S5 )
% 0.35/0.63       => ( ( finite_finite_real @ T5 )
% 0.35/0.63         => ( ! [A4: real] :
% 0.35/0.63                ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 0.35/0.63               => ( ( I2 @ ( J @ A4 ) )
% 0.35/0.63                  = A4 ) )
% 0.35/0.63           => ( ! [A4: real] :
% 0.35/0.63                  ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 0.35/0.63                 => ( member_real @ ( J @ A4 ) @ ( minus_minus_set_real @ T4 @ T5 ) ) )
% 0.35/0.63             => ( ! [B3: real] :
% 0.35/0.63                    ( ( member_real @ B3 @ ( minus_minus_set_real @ T4 @ T5 ) )
% 0.35/0.63                   => ( ( J @ ( I2 @ B3 ) )
% 0.35/0.63                      = B3 ) )
% 0.35/0.63               => ( ! [B3: real] :
% 0.35/0.63                      ( ( member_real @ B3 @ ( minus_minus_set_real @ T4 @ T5 ) )
% 0.35/0.63                     => ( member_real @ ( I2 @ B3 ) @ ( minus_minus_set_real @ S2 @ S5 ) ) )
% 0.35/0.63                 => ( ! [A4: real] :
% 0.35/0.63                        ( ( member_real @ A4 @ S5 )
% 0.35/0.63                       => ( ( G @ A4 )
% 0.35/0.63                          = zero_zero_real ) )
% 0.35/0.63                   => ( ! [B3: real] :
% 0.35/0.63                          ( ( member_real @ B3 @ T5 )
% 0.35/0.63                         => ( ( H2 @ B3 )
% 0.35/0.63                            = zero_zero_real ) )
% 0.35/0.63                     => ( ! [A4: real] :
% 0.35/0.63                            ( ( member_real @ A4 @ S2 )
% 0.35/0.63                           => ( ( H2 @ ( J @ A4 ) )
% 0.35/0.63                              = ( G @ A4 ) ) )
% 0.35/0.63                       => ( ( groups8097168146408367636l_real @ G @ S2 )
% 0.35/0.63                          = ( groups8097168146408367636l_real @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.reindex_bij_witness_not_neutral
% 0.35/0.63  thf(fact_6516_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.35/0.63      ! [S5: set_real,T5: set_int,S2: set_real,I2: int > real,J: real > int,T4: set_int,G: real > real,H2: int > real] :
% 0.35/0.63        ( ( finite_finite_real @ S5 )
% 0.35/0.63       => ( ( finite_finite_int @ T5 )
% 0.35/0.63         => ( ! [A4: real] :
% 0.35/0.63                ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 0.35/0.63               => ( ( I2 @ ( J @ A4 ) )
% 0.35/0.63                  = A4 ) )
% 0.35/0.63           => ( ! [A4: real] :
% 0.35/0.63                  ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 0.35/0.63                 => ( member_int @ ( J @ A4 ) @ ( minus_minus_set_int @ T4 @ T5 ) ) )
% 0.35/0.63             => ( ! [B3: int] :
% 0.35/0.63                    ( ( member_int @ B3 @ ( minus_minus_set_int @ T4 @ T5 ) )
% 0.35/0.63                   => ( ( J @ ( I2 @ B3 ) )
% 0.35/0.63                      = B3 ) )
% 0.35/0.63               => ( ! [B3: int] :
% 0.35/0.63                      ( ( member_int @ B3 @ ( minus_minus_set_int @ T4 @ T5 ) )
% 0.35/0.63                     => ( member_real @ ( I2 @ B3 ) @ ( minus_minus_set_real @ S2 @ S5 ) ) )
% 0.35/0.63                 => ( ! [A4: real] :
% 0.35/0.63                        ( ( member_real @ A4 @ S5 )
% 0.35/0.63                       => ( ( G @ A4 )
% 0.35/0.63                          = zero_zero_real ) )
% 0.35/0.63                   => ( ! [B3: int] :
% 0.35/0.63                          ( ( member_int @ B3 @ T5 )
% 0.35/0.63                         => ( ( H2 @ B3 )
% 0.35/0.63                            = zero_zero_real ) )
% 0.35/0.63                     => ( ! [A4: real] :
% 0.35/0.63                            ( ( member_real @ A4 @ S2 )
% 0.35/0.63                           => ( ( H2 @ ( J @ A4 ) )
% 0.35/0.63                              = ( G @ A4 ) ) )
% 0.35/0.63                       => ( ( groups8097168146408367636l_real @ G @ S2 )
% 0.35/0.63                          = ( groups8778361861064173332t_real @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.reindex_bij_witness_not_neutral
% 0.35/0.63  thf(fact_6517_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.35/0.63      ! [S5: set_int,T5: set_real,S2: set_int,I2: real > int,J: int > real,T4: set_real,G: int > real,H2: real > real] :
% 0.35/0.63        ( ( finite_finite_int @ S5 )
% 0.35/0.63       => ( ( finite_finite_real @ T5 )
% 0.35/0.63         => ( ! [A4: int] :
% 0.35/0.63                ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 0.35/0.63               => ( ( I2 @ ( J @ A4 ) )
% 0.35/0.63                  = A4 ) )
% 0.35/0.63           => ( ! [A4: int] :
% 0.35/0.63                  ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 0.35/0.63                 => ( member_real @ ( J @ A4 ) @ ( minus_minus_set_real @ T4 @ T5 ) ) )
% 0.35/0.63             => ( ! [B3: real] :
% 0.35/0.63                    ( ( member_real @ B3 @ ( minus_minus_set_real @ T4 @ T5 ) )
% 0.35/0.63                   => ( ( J @ ( I2 @ B3 ) )
% 0.35/0.63                      = B3 ) )
% 0.35/0.63               => ( ! [B3: real] :
% 0.35/0.63                      ( ( member_real @ B3 @ ( minus_minus_set_real @ T4 @ T5 ) )
% 0.35/0.63                     => ( member_int @ ( I2 @ B3 ) @ ( minus_minus_set_int @ S2 @ S5 ) ) )
% 0.35/0.63                 => ( ! [A4: int] :
% 0.35/0.63                        ( ( member_int @ A4 @ S5 )
% 0.35/0.63                       => ( ( G @ A4 )
% 0.35/0.63                          = zero_zero_real ) )
% 0.35/0.63                   => ( ! [B3: real] :
% 0.35/0.63                          ( ( member_real @ B3 @ T5 )
% 0.35/0.63                         => ( ( H2 @ B3 )
% 0.35/0.63                            = zero_zero_real ) )
% 0.35/0.63                     => ( ! [A4: int] :
% 0.35/0.63                            ( ( member_int @ A4 @ S2 )
% 0.35/0.63                           => ( ( H2 @ ( J @ A4 ) )
% 0.35/0.63                              = ( G @ A4 ) ) )
% 0.35/0.63                       => ( ( groups8778361861064173332t_real @ G @ S2 )
% 0.35/0.63                          = ( groups8097168146408367636l_real @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.reindex_bij_witness_not_neutral
% 0.35/0.63  thf(fact_6518_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.35/0.63      ! [S5: set_int,T5: set_int,S2: set_int,I2: int > int,J: int > int,T4: set_int,G: int > real,H2: int > real] :
% 0.35/0.63        ( ( finite_finite_int @ S5 )
% 0.35/0.63       => ( ( finite_finite_int @ T5 )
% 0.35/0.63         => ( ! [A4: int] :
% 0.35/0.63                ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 0.35/0.63               => ( ( I2 @ ( J @ A4 ) )
% 0.35/0.63                  = A4 ) )
% 0.35/0.63           => ( ! [A4: int] :
% 0.35/0.63                  ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 0.35/0.63                 => ( member_int @ ( J @ A4 ) @ ( minus_minus_set_int @ T4 @ T5 ) ) )
% 0.35/0.63             => ( ! [B3: int] :
% 0.35/0.63                    ( ( member_int @ B3 @ ( minus_minus_set_int @ T4 @ T5 ) )
% 0.35/0.63                   => ( ( J @ ( I2 @ B3 ) )
% 0.35/0.63                      = B3 ) )
% 0.35/0.63               => ( ! [B3: int] :
% 0.35/0.63                      ( ( member_int @ B3 @ ( minus_minus_set_int @ T4 @ T5 ) )
% 0.35/0.63                     => ( member_int @ ( I2 @ B3 ) @ ( minus_minus_set_int @ S2 @ S5 ) ) )
% 0.35/0.63                 => ( ! [A4: int] :
% 0.35/0.63                        ( ( member_int @ A4 @ S5 )
% 0.35/0.63                       => ( ( G @ A4 )
% 0.35/0.63                          = zero_zero_real ) )
% 0.35/0.63                   => ( ! [B3: int] :
% 0.35/0.63                          ( ( member_int @ B3 @ T5 )
% 0.35/0.63                         => ( ( H2 @ B3 )
% 0.35/0.63                            = zero_zero_real ) )
% 0.35/0.63                     => ( ! [A4: int] :
% 0.35/0.63                            ( ( member_int @ A4 @ S2 )
% 0.35/0.63                           => ( ( H2 @ ( J @ A4 ) )
% 0.35/0.63                              = ( G @ A4 ) ) )
% 0.35/0.63                       => ( ( groups8778361861064173332t_real @ G @ S2 )
% 0.35/0.63                          = ( groups8778361861064173332t_real @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.reindex_bij_witness_not_neutral
% 0.35/0.63  thf(fact_6519_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.35/0.63      ! [S5: set_real,T5: set_complex,S2: set_real,I2: complex > real,J: real > complex,T4: set_complex,G: real > real,H2: complex > real] :
% 0.35/0.63        ( ( finite_finite_real @ S5 )
% 0.35/0.63       => ( ( finite3207457112153483333omplex @ T5 )
% 0.35/0.63         => ( ! [A4: real] :
% 0.35/0.63                ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 0.35/0.63               => ( ( I2 @ ( J @ A4 ) )
% 0.35/0.63                  = A4 ) )
% 0.35/0.63           => ( ! [A4: real] :
% 0.35/0.63                  ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 0.35/0.63                 => ( member_complex @ ( J @ A4 ) @ ( minus_811609699411566653omplex @ T4 @ T5 ) ) )
% 0.35/0.63             => ( ! [B3: complex] :
% 0.35/0.63                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T4 @ T5 ) )
% 0.35/0.63                   => ( ( J @ ( I2 @ B3 ) )
% 0.35/0.63                      = B3 ) )
% 0.35/0.63               => ( ! [B3: complex] :
% 0.35/0.63                      ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T4 @ T5 ) )
% 0.35/0.63                     => ( member_real @ ( I2 @ B3 ) @ ( minus_minus_set_real @ S2 @ S5 ) ) )
% 0.35/0.63                 => ( ! [A4: real] :
% 0.35/0.63                        ( ( member_real @ A4 @ S5 )
% 0.35/0.63                       => ( ( G @ A4 )
% 0.35/0.63                          = zero_zero_real ) )
% 0.35/0.63                   => ( ! [B3: complex] :
% 0.35/0.63                          ( ( member_complex @ B3 @ T5 )
% 0.35/0.63                         => ( ( H2 @ B3 )
% 0.35/0.63                            = zero_zero_real ) )
% 0.35/0.63                     => ( ! [A4: real] :
% 0.35/0.63                            ( ( member_real @ A4 @ S2 )
% 0.35/0.63                           => ( ( H2 @ ( J @ A4 ) )
% 0.35/0.63                              = ( G @ A4 ) ) )
% 0.35/0.63                       => ( ( groups8097168146408367636l_real @ G @ S2 )
% 0.35/0.63                          = ( groups5808333547571424918x_real @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.reindex_bij_witness_not_neutral
% 0.35/0.63  thf(fact_6520_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.35/0.63      ! [S5: set_int,T5: set_complex,S2: set_int,I2: complex > int,J: int > complex,T4: set_complex,G: int > real,H2: complex > real] :
% 0.35/0.63        ( ( finite_finite_int @ S5 )
% 0.35/0.63       => ( ( finite3207457112153483333omplex @ T5 )
% 0.35/0.63         => ( ! [A4: int] :
% 0.35/0.63                ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 0.35/0.63               => ( ( I2 @ ( J @ A4 ) )
% 0.35/0.63                  = A4 ) )
% 0.35/0.63           => ( ! [A4: int] :
% 0.35/0.63                  ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 0.35/0.63                 => ( member_complex @ ( J @ A4 ) @ ( minus_811609699411566653omplex @ T4 @ T5 ) ) )
% 0.35/0.63             => ( ! [B3: complex] :
% 0.35/0.63                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T4 @ T5 ) )
% 0.35/0.63                   => ( ( J @ ( I2 @ B3 ) )
% 0.35/0.63                      = B3 ) )
% 0.35/0.63               => ( ! [B3: complex] :
% 0.35/0.63                      ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T4 @ T5 ) )
% 0.35/0.63                     => ( member_int @ ( I2 @ B3 ) @ ( minus_minus_set_int @ S2 @ S5 ) ) )
% 0.35/0.63                 => ( ! [A4: int] :
% 0.35/0.63                        ( ( member_int @ A4 @ S5 )
% 0.35/0.63                       => ( ( G @ A4 )
% 0.35/0.63                          = zero_zero_real ) )
% 0.35/0.63                   => ( ! [B3: complex] :
% 0.35/0.63                          ( ( member_complex @ B3 @ T5 )
% 0.35/0.63                         => ( ( H2 @ B3 )
% 0.35/0.63                            = zero_zero_real ) )
% 0.35/0.63                     => ( ! [A4: int] :
% 0.35/0.63                            ( ( member_int @ A4 @ S2 )
% 0.35/0.63                           => ( ( H2 @ ( J @ A4 ) )
% 0.35/0.63                              = ( G @ A4 ) ) )
% 0.35/0.63                       => ( ( groups8778361861064173332t_real @ G @ S2 )
% 0.35/0.63                          = ( groups5808333547571424918x_real @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.reindex_bij_witness_not_neutral
% 0.35/0.63  thf(fact_6521_exp__gt__one,axiom,
% 0.35/0.63      ! [X: real] :
% 0.35/0.63        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.63       => ( ord_less_real @ one_one_real @ ( exp_real @ X ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % exp_gt_one
% 0.35/0.63  thf(fact_6522_take__bit__signed__take__bit,axiom,
% 0.35/0.63      ! [M: nat,N: nat,A: int] :
% 0.35/0.63        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.35/0.63       => ( ( bit_se2923211474154528505it_int @ M @ ( bit_ri631733984087533419it_int @ N @ A ) )
% 0.35/0.63          = ( bit_se2923211474154528505it_int @ M @ A ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_signed_take_bit
% 0.35/0.63  thf(fact_6523_exp__ge__add__one__self,axiom,
% 0.35/0.63      ! [X: real] : ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X ) @ ( exp_real @ X ) ) ).
% 0.35/0.63  
% 0.35/0.63  % exp_ge_add_one_self
% 0.35/0.63  thf(fact_6524_exp__minus__inverse,axiom,
% 0.35/0.63      ! [X: real] :
% 0.35/0.63        ( ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) )
% 0.35/0.63        = one_one_real ) ).
% 0.35/0.63  
% 0.35/0.63  % exp_minus_inverse
% 0.35/0.63  thf(fact_6525_exp__minus__inverse,axiom,
% 0.35/0.63      ! [X: complex] :
% 0.35/0.63        ( ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) )
% 0.35/0.63        = one_one_complex ) ).
% 0.35/0.63  
% 0.35/0.63  % exp_minus_inverse
% 0.35/0.63  thf(fact_6526_take__bit__decr__eq,axiom,
% 0.35/0.63      ! [N: nat,K: int] :
% 0.35/0.63        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 0.35/0.63         != zero_zero_int )
% 0.35/0.63       => ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ one_one_int ) )
% 0.35/0.63          = ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ one_one_int ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_decr_eq
% 0.35/0.63  thf(fact_6527_sum__nonneg__0,axiom,
% 0.35/0.63      ! [S3: set_real,F: real > real,I2: real] :
% 0.35/0.63        ( ( finite_finite_real @ S3 )
% 0.35/0.63       => ( ! [I4: real] :
% 0.35/0.63              ( ( member_real @ I4 @ S3 )
% 0.35/0.63             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 0.35/0.63         => ( ( ( groups8097168146408367636l_real @ F @ S3 )
% 0.35/0.63              = zero_zero_real )
% 0.35/0.63           => ( ( member_real @ I2 @ S3 )
% 0.35/0.63             => ( ( F @ I2 )
% 0.35/0.63                = zero_zero_real ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg_0
% 0.35/0.63  thf(fact_6528_sum__nonneg__0,axiom,
% 0.35/0.63      ! [S3: set_int,F: int > real,I2: int] :
% 0.35/0.63        ( ( finite_finite_int @ S3 )
% 0.35/0.63       => ( ! [I4: int] :
% 0.35/0.63              ( ( member_int @ I4 @ S3 )
% 0.35/0.63             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 0.35/0.63         => ( ( ( groups8778361861064173332t_real @ F @ S3 )
% 0.35/0.63              = zero_zero_real )
% 0.35/0.63           => ( ( member_int @ I2 @ S3 )
% 0.35/0.63             => ( ( F @ I2 )
% 0.35/0.63                = zero_zero_real ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg_0
% 0.35/0.63  thf(fact_6529_sum__nonneg__0,axiom,
% 0.35/0.63      ! [S3: set_complex,F: complex > real,I2: complex] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ S3 )
% 0.35/0.63       => ( ! [I4: complex] :
% 0.35/0.63              ( ( member_complex @ I4 @ S3 )
% 0.35/0.63             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 0.35/0.63         => ( ( ( groups5808333547571424918x_real @ F @ S3 )
% 0.35/0.63              = zero_zero_real )
% 0.35/0.63           => ( ( member_complex @ I2 @ S3 )
% 0.35/0.63             => ( ( F @ I2 )
% 0.35/0.63                = zero_zero_real ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg_0
% 0.35/0.63  thf(fact_6530_sum__nonneg__0,axiom,
% 0.35/0.63      ! [S3: set_real,F: real > rat,I2: real] :
% 0.35/0.63        ( ( finite_finite_real @ S3 )
% 0.35/0.63       => ( ! [I4: real] :
% 0.35/0.63              ( ( member_real @ I4 @ S3 )
% 0.35/0.63             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 0.35/0.63         => ( ( ( groups1300246762558778688al_rat @ F @ S3 )
% 0.35/0.63              = zero_zero_rat )
% 0.35/0.63           => ( ( member_real @ I2 @ S3 )
% 0.35/0.63             => ( ( F @ I2 )
% 0.35/0.63                = zero_zero_rat ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg_0
% 0.35/0.63  thf(fact_6531_sum__nonneg__0,axiom,
% 0.35/0.63      ! [S3: set_int,F: int > rat,I2: int] :
% 0.35/0.63        ( ( finite_finite_int @ S3 )
% 0.35/0.63       => ( ! [I4: int] :
% 0.35/0.63              ( ( member_int @ I4 @ S3 )
% 0.35/0.63             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 0.35/0.63         => ( ( ( groups3906332499630173760nt_rat @ F @ S3 )
% 0.35/0.63              = zero_zero_rat )
% 0.35/0.63           => ( ( member_int @ I2 @ S3 )
% 0.35/0.63             => ( ( F @ I2 )
% 0.35/0.63                = zero_zero_rat ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg_0
% 0.35/0.63  thf(fact_6532_sum__nonneg__0,axiom,
% 0.35/0.63      ! [S3: set_nat,F: nat > rat,I2: nat] :
% 0.35/0.63        ( ( finite_finite_nat @ S3 )
% 0.35/0.63       => ( ! [I4: nat] :
% 0.35/0.63              ( ( member_nat @ I4 @ S3 )
% 0.35/0.63             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 0.35/0.63         => ( ( ( groups2906978787729119204at_rat @ F @ S3 )
% 0.35/0.63              = zero_zero_rat )
% 0.35/0.63           => ( ( member_nat @ I2 @ S3 )
% 0.35/0.63             => ( ( F @ I2 )
% 0.35/0.63                = zero_zero_rat ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg_0
% 0.35/0.63  thf(fact_6533_sum__nonneg__0,axiom,
% 0.35/0.63      ! [S3: set_complex,F: complex > rat,I2: complex] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ S3 )
% 0.35/0.63       => ( ! [I4: complex] :
% 0.35/0.63              ( ( member_complex @ I4 @ S3 )
% 0.35/0.63             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 0.35/0.63         => ( ( ( groups5058264527183730370ex_rat @ F @ S3 )
% 0.35/0.63              = zero_zero_rat )
% 0.35/0.63           => ( ( member_complex @ I2 @ S3 )
% 0.35/0.63             => ( ( F @ I2 )
% 0.35/0.63                = zero_zero_rat ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg_0
% 0.35/0.63  thf(fact_6534_sum__nonneg__0,axiom,
% 0.35/0.63      ! [S3: set_real,F: real > nat,I2: real] :
% 0.35/0.63        ( ( finite_finite_real @ S3 )
% 0.35/0.63       => ( ! [I4: real] :
% 0.35/0.63              ( ( member_real @ I4 @ S3 )
% 0.35/0.63             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 0.35/0.63         => ( ( ( groups1935376822645274424al_nat @ F @ S3 )
% 0.35/0.63              = zero_zero_nat )
% 0.35/0.63           => ( ( member_real @ I2 @ S3 )
% 0.35/0.63             => ( ( F @ I2 )
% 0.35/0.63                = zero_zero_nat ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg_0
% 0.35/0.63  thf(fact_6535_sum__nonneg__0,axiom,
% 0.35/0.63      ! [S3: set_int,F: int > nat,I2: int] :
% 0.35/0.63        ( ( finite_finite_int @ S3 )
% 0.35/0.63       => ( ! [I4: int] :
% 0.35/0.63              ( ( member_int @ I4 @ S3 )
% 0.35/0.63             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 0.35/0.63         => ( ( ( groups4541462559716669496nt_nat @ F @ S3 )
% 0.35/0.63              = zero_zero_nat )
% 0.35/0.63           => ( ( member_int @ I2 @ S3 )
% 0.35/0.63             => ( ( F @ I2 )
% 0.35/0.63                = zero_zero_nat ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg_0
% 0.35/0.63  thf(fact_6536_sum__nonneg__0,axiom,
% 0.35/0.63      ! [S3: set_complex,F: complex > nat,I2: complex] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ S3 )
% 0.35/0.63       => ( ! [I4: complex] :
% 0.35/0.63              ( ( member_complex @ I4 @ S3 )
% 0.35/0.63             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 0.35/0.63         => ( ( ( groups5693394587270226106ex_nat @ F @ S3 )
% 0.35/0.63              = zero_zero_nat )
% 0.35/0.63           => ( ( member_complex @ I2 @ S3 )
% 0.35/0.63             => ( ( F @ I2 )
% 0.35/0.63                = zero_zero_nat ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg_0
% 0.35/0.63  thf(fact_6537_sum__nonneg__leq__bound,axiom,
% 0.35/0.63      ! [S3: set_real,F: real > real,B2: real,I2: real] :
% 0.35/0.63        ( ( finite_finite_real @ S3 )
% 0.35/0.63       => ( ! [I4: real] :
% 0.35/0.63              ( ( member_real @ I4 @ S3 )
% 0.35/0.63             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 0.35/0.63         => ( ( ( groups8097168146408367636l_real @ F @ S3 )
% 0.35/0.63              = B2 )
% 0.35/0.63           => ( ( member_real @ I2 @ S3 )
% 0.35/0.63             => ( ord_less_eq_real @ ( F @ I2 ) @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg_leq_bound
% 0.35/0.63  thf(fact_6538_sum__nonneg__leq__bound,axiom,
% 0.35/0.63      ! [S3: set_int,F: int > real,B2: real,I2: int] :
% 0.35/0.63        ( ( finite_finite_int @ S3 )
% 0.35/0.63       => ( ! [I4: int] :
% 0.35/0.63              ( ( member_int @ I4 @ S3 )
% 0.35/0.63             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 0.35/0.63         => ( ( ( groups8778361861064173332t_real @ F @ S3 )
% 0.35/0.63              = B2 )
% 0.35/0.63           => ( ( member_int @ I2 @ S3 )
% 0.35/0.63             => ( ord_less_eq_real @ ( F @ I2 ) @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg_leq_bound
% 0.35/0.63  thf(fact_6539_sum__nonneg__leq__bound,axiom,
% 0.35/0.63      ! [S3: set_complex,F: complex > real,B2: real,I2: complex] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ S3 )
% 0.35/0.63       => ( ! [I4: complex] :
% 0.35/0.63              ( ( member_complex @ I4 @ S3 )
% 0.35/0.63             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 0.35/0.63         => ( ( ( groups5808333547571424918x_real @ F @ S3 )
% 0.35/0.63              = B2 )
% 0.35/0.63           => ( ( member_complex @ I2 @ S3 )
% 0.35/0.63             => ( ord_less_eq_real @ ( F @ I2 ) @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg_leq_bound
% 0.35/0.63  thf(fact_6540_sum__nonneg__leq__bound,axiom,
% 0.35/0.63      ! [S3: set_real,F: real > rat,B2: rat,I2: real] :
% 0.35/0.63        ( ( finite_finite_real @ S3 )
% 0.35/0.63       => ( ! [I4: real] :
% 0.35/0.63              ( ( member_real @ I4 @ S3 )
% 0.35/0.63             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 0.35/0.63         => ( ( ( groups1300246762558778688al_rat @ F @ S3 )
% 0.35/0.63              = B2 )
% 0.35/0.63           => ( ( member_real @ I2 @ S3 )
% 0.35/0.63             => ( ord_less_eq_rat @ ( F @ I2 ) @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg_leq_bound
% 0.35/0.63  thf(fact_6541_sum__nonneg__leq__bound,axiom,
% 0.35/0.63      ! [S3: set_int,F: int > rat,B2: rat,I2: int] :
% 0.35/0.63        ( ( finite_finite_int @ S3 )
% 0.35/0.63       => ( ! [I4: int] :
% 0.35/0.63              ( ( member_int @ I4 @ S3 )
% 0.35/0.63             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 0.35/0.63         => ( ( ( groups3906332499630173760nt_rat @ F @ S3 )
% 0.35/0.63              = B2 )
% 0.35/0.63           => ( ( member_int @ I2 @ S3 )
% 0.35/0.63             => ( ord_less_eq_rat @ ( F @ I2 ) @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg_leq_bound
% 0.35/0.63  thf(fact_6542_sum__nonneg__leq__bound,axiom,
% 0.35/0.63      ! [S3: set_nat,F: nat > rat,B2: rat,I2: nat] :
% 0.35/0.63        ( ( finite_finite_nat @ S3 )
% 0.35/0.63       => ( ! [I4: nat] :
% 0.35/0.63              ( ( member_nat @ I4 @ S3 )
% 0.35/0.63             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 0.35/0.63         => ( ( ( groups2906978787729119204at_rat @ F @ S3 )
% 0.35/0.63              = B2 )
% 0.35/0.63           => ( ( member_nat @ I2 @ S3 )
% 0.35/0.63             => ( ord_less_eq_rat @ ( F @ I2 ) @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg_leq_bound
% 0.35/0.63  thf(fact_6543_sum__nonneg__leq__bound,axiom,
% 0.35/0.63      ! [S3: set_complex,F: complex > rat,B2: rat,I2: complex] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ S3 )
% 0.35/0.63       => ( ! [I4: complex] :
% 0.35/0.63              ( ( member_complex @ I4 @ S3 )
% 0.35/0.63             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 0.35/0.63         => ( ( ( groups5058264527183730370ex_rat @ F @ S3 )
% 0.35/0.63              = B2 )
% 0.35/0.63           => ( ( member_complex @ I2 @ S3 )
% 0.35/0.63             => ( ord_less_eq_rat @ ( F @ I2 ) @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg_leq_bound
% 0.35/0.63  thf(fact_6544_sum__nonneg__leq__bound,axiom,
% 0.35/0.63      ! [S3: set_real,F: real > nat,B2: nat,I2: real] :
% 0.35/0.63        ( ( finite_finite_real @ S3 )
% 0.35/0.63       => ( ! [I4: real] :
% 0.35/0.63              ( ( member_real @ I4 @ S3 )
% 0.35/0.63             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 0.35/0.63         => ( ( ( groups1935376822645274424al_nat @ F @ S3 )
% 0.35/0.63              = B2 )
% 0.35/0.63           => ( ( member_real @ I2 @ S3 )
% 0.35/0.63             => ( ord_less_eq_nat @ ( F @ I2 ) @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg_leq_bound
% 0.35/0.63  thf(fact_6545_sum__nonneg__leq__bound,axiom,
% 0.35/0.63      ! [S3: set_int,F: int > nat,B2: nat,I2: int] :
% 0.35/0.63        ( ( finite_finite_int @ S3 )
% 0.35/0.63       => ( ! [I4: int] :
% 0.35/0.63              ( ( member_int @ I4 @ S3 )
% 0.35/0.63             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 0.35/0.63         => ( ( ( groups4541462559716669496nt_nat @ F @ S3 )
% 0.35/0.63              = B2 )
% 0.35/0.63           => ( ( member_int @ I2 @ S3 )
% 0.35/0.63             => ( ord_less_eq_nat @ ( F @ I2 ) @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg_leq_bound
% 0.35/0.63  thf(fact_6546_sum__nonneg__leq__bound,axiom,
% 0.35/0.63      ! [S3: set_complex,F: complex > nat,B2: nat,I2: complex] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ S3 )
% 0.35/0.63       => ( ! [I4: complex] :
% 0.35/0.63              ( ( member_complex @ I4 @ S3 )
% 0.35/0.63             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 0.35/0.63         => ( ( ( groups5693394587270226106ex_nat @ F @ S3 )
% 0.35/0.63              = B2 )
% 0.35/0.63           => ( ( member_complex @ I2 @ S3 )
% 0.35/0.63             => ( ord_less_eq_nat @ ( F @ I2 ) @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_nonneg_leq_bound
% 0.35/0.63  thf(fact_6547_abs__mod__less,axiom,
% 0.35/0.63      ! [L2: int,K: int] :
% 0.35/0.63        ( ( L2 != zero_zero_int )
% 0.35/0.63       => ( ord_less_int @ ( abs_abs_int @ ( modulo_modulo_int @ K @ L2 ) ) @ ( abs_abs_int @ L2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % abs_mod_less
% 0.35/0.63  thf(fact_6548_sum_Osetdiff__irrelevant,axiom,
% 0.35/0.63      ! [A2: set_real,G: real > complex] :
% 0.35/0.63        ( ( finite_finite_real @ A2 )
% 0.35/0.63       => ( ( groups5754745047067104278omplex @ G
% 0.35/0.63            @ ( minus_minus_set_real @ A2
% 0.35/0.63              @ ( collect_real
% 0.35/0.63                @ ^ [X2: real] :
% 0.35/0.63                    ( ( G @ X2 )
% 0.35/0.63                    = zero_zero_complex ) ) ) )
% 0.35/0.63          = ( groups5754745047067104278omplex @ G @ A2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.setdiff_irrelevant
% 0.35/0.63  thf(fact_6549_sum_Osetdiff__irrelevant,axiom,
% 0.35/0.63      ! [A2: set_real,G: real > real] :
% 0.35/0.63        ( ( finite_finite_real @ A2 )
% 0.35/0.63       => ( ( groups8097168146408367636l_real @ G
% 0.35/0.63            @ ( minus_minus_set_real @ A2
% 0.35/0.63              @ ( collect_real
% 0.35/0.63                @ ^ [X2: real] :
% 0.35/0.63                    ( ( G @ X2 )
% 0.35/0.63                    = zero_zero_real ) ) ) )
% 0.35/0.63          = ( groups8097168146408367636l_real @ G @ A2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.setdiff_irrelevant
% 0.35/0.63  thf(fact_6550_sum_Osetdiff__irrelevant,axiom,
% 0.35/0.63      ! [A2: set_complex,G: complex > real] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.63       => ( ( groups5808333547571424918x_real @ G
% 0.35/0.63            @ ( minus_811609699411566653omplex @ A2
% 0.35/0.63              @ ( collect_complex
% 0.35/0.63                @ ^ [X2: complex] :
% 0.35/0.63                    ( ( G @ X2 )
% 0.35/0.63                    = zero_zero_real ) ) ) )
% 0.35/0.63          = ( groups5808333547571424918x_real @ G @ A2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.setdiff_irrelevant
% 0.35/0.63  thf(fact_6551_sum_Osetdiff__irrelevant,axiom,
% 0.35/0.63      ! [A2: set_real,G: real > rat] :
% 0.35/0.63        ( ( finite_finite_real @ A2 )
% 0.35/0.63       => ( ( groups1300246762558778688al_rat @ G
% 0.35/0.63            @ ( minus_minus_set_real @ A2
% 0.35/0.63              @ ( collect_real
% 0.35/0.63                @ ^ [X2: real] :
% 0.35/0.63                    ( ( G @ X2 )
% 0.35/0.63                    = zero_zero_rat ) ) ) )
% 0.35/0.63          = ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.setdiff_irrelevant
% 0.35/0.63  thf(fact_6552_sum_Osetdiff__irrelevant,axiom,
% 0.35/0.63      ! [A2: set_complex,G: complex > rat] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.63       => ( ( groups5058264527183730370ex_rat @ G
% 0.35/0.63            @ ( minus_811609699411566653omplex @ A2
% 0.35/0.63              @ ( collect_complex
% 0.35/0.63                @ ^ [X2: complex] :
% 0.35/0.63                    ( ( G @ X2 )
% 0.35/0.63                    = zero_zero_rat ) ) ) )
% 0.35/0.63          = ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.setdiff_irrelevant
% 0.35/0.63  thf(fact_6553_sum_Osetdiff__irrelevant,axiom,
% 0.35/0.63      ! [A2: set_real,G: real > nat] :
% 0.35/0.63        ( ( finite_finite_real @ A2 )
% 0.35/0.63       => ( ( groups1935376822645274424al_nat @ G
% 0.35/0.63            @ ( minus_minus_set_real @ A2
% 0.35/0.63              @ ( collect_real
% 0.35/0.63                @ ^ [X2: real] :
% 0.35/0.63                    ( ( G @ X2 )
% 0.35/0.63                    = zero_zero_nat ) ) ) )
% 0.35/0.63          = ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.setdiff_irrelevant
% 0.35/0.63  thf(fact_6554_sum_Osetdiff__irrelevant,axiom,
% 0.35/0.63      ! [A2: set_complex,G: complex > nat] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.63       => ( ( groups5693394587270226106ex_nat @ G
% 0.35/0.63            @ ( minus_811609699411566653omplex @ A2
% 0.35/0.63              @ ( collect_complex
% 0.35/0.63                @ ^ [X2: complex] :
% 0.35/0.63                    ( ( G @ X2 )
% 0.35/0.63                    = zero_zero_nat ) ) ) )
% 0.35/0.63          = ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.setdiff_irrelevant
% 0.35/0.63  thf(fact_6555_sum_Osetdiff__irrelevant,axiom,
% 0.35/0.63      ! [A2: set_real,G: real > int] :
% 0.35/0.63        ( ( finite_finite_real @ A2 )
% 0.35/0.63       => ( ( groups1932886352136224148al_int @ G
% 0.35/0.63            @ ( minus_minus_set_real @ A2
% 0.35/0.63              @ ( collect_real
% 0.35/0.63                @ ^ [X2: real] :
% 0.35/0.63                    ( ( G @ X2 )
% 0.35/0.63                    = zero_zero_int ) ) ) )
% 0.35/0.63          = ( groups1932886352136224148al_int @ G @ A2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.setdiff_irrelevant
% 0.35/0.63  thf(fact_6556_sum_Osetdiff__irrelevant,axiom,
% 0.35/0.63      ! [A2: set_complex,G: complex > int] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.63       => ( ( groups5690904116761175830ex_int @ G
% 0.35/0.63            @ ( minus_811609699411566653omplex @ A2
% 0.35/0.63              @ ( collect_complex
% 0.35/0.63                @ ^ [X2: complex] :
% 0.35/0.63                    ( ( G @ X2 )
% 0.35/0.63                    = zero_zero_int ) ) ) )
% 0.35/0.63          = ( groups5690904116761175830ex_int @ G @ A2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.setdiff_irrelevant
% 0.35/0.63  thf(fact_6557_sum_Osetdiff__irrelevant,axiom,
% 0.35/0.63      ! [A2: set_nat,G: nat > complex] :
% 0.35/0.63        ( ( finite_finite_nat @ A2 )
% 0.35/0.63       => ( ( groups2073611262835488442omplex @ G
% 0.35/0.63            @ ( minus_minus_set_nat @ A2
% 0.35/0.63              @ ( collect_nat
% 0.35/0.63                @ ^ [X2: nat] :
% 0.35/0.63                    ( ( G @ X2 )
% 0.35/0.63                    = zero_zero_complex ) ) ) )
% 0.35/0.63          = ( groups2073611262835488442omplex @ G @ A2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.setdiff_irrelevant
% 0.35/0.63  thf(fact_6558_less__mask,axiom,
% 0.35/0.63      ! [N: nat] :
% 0.35/0.63        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.35/0.63       => ( ord_less_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % less_mask
% 0.35/0.63  thf(fact_6559_take__bit__eq__mask__iff__exp__dvd,axiom,
% 0.35/0.63      ! [N: nat,K: int] :
% 0.35/0.63        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 0.35/0.63          = ( bit_se2000444600071755411sk_int @ N ) )
% 0.35/0.63        = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( plus_plus_int @ K @ one_one_int ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_eq_mask_iff_exp_dvd
% 0.35/0.63  thf(fact_6560_sum__pos2,axiom,
% 0.35/0.63      ! [I6: set_real,I2: real,F: real > real] :
% 0.35/0.63        ( ( finite_finite_real @ I6 )
% 0.35/0.63       => ( ( member_real @ I2 @ I6 )
% 0.35/0.63         => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 0.35/0.63           => ( ! [I4: real] :
% 0.35/0.63                  ( ( member_real @ I4 @ I6 )
% 0.35/0.63                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 0.35/0.63             => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I6 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_pos2
% 0.35/0.63  thf(fact_6561_sum__pos2,axiom,
% 0.35/0.63      ! [I6: set_int,I2: int,F: int > real] :
% 0.35/0.63        ( ( finite_finite_int @ I6 )
% 0.35/0.63       => ( ( member_int @ I2 @ I6 )
% 0.35/0.63         => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 0.35/0.63           => ( ! [I4: int] :
% 0.35/0.63                  ( ( member_int @ I4 @ I6 )
% 0.35/0.63                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 0.35/0.63             => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I6 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_pos2
% 0.35/0.63  thf(fact_6562_sum__pos2,axiom,
% 0.35/0.63      ! [I6: set_complex,I2: complex,F: complex > real] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ I6 )
% 0.35/0.63       => ( ( member_complex @ I2 @ I6 )
% 0.35/0.63         => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 0.35/0.63           => ( ! [I4: complex] :
% 0.35/0.63                  ( ( member_complex @ I4 @ I6 )
% 0.35/0.63                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 0.35/0.63             => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I6 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_pos2
% 0.35/0.63  thf(fact_6563_sum__pos2,axiom,
% 0.35/0.63      ! [I6: set_real,I2: real,F: real > rat] :
% 0.35/0.63        ( ( finite_finite_real @ I6 )
% 0.35/0.63       => ( ( member_real @ I2 @ I6 )
% 0.35/0.63         => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) )
% 0.35/0.63           => ( ! [I4: real] :
% 0.35/0.63                  ( ( member_real @ I4 @ I6 )
% 0.35/0.63                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 0.35/0.63             => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I6 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_pos2
% 0.35/0.63  thf(fact_6564_sum__pos2,axiom,
% 0.35/0.63      ! [I6: set_int,I2: int,F: int > rat] :
% 0.35/0.63        ( ( finite_finite_int @ I6 )
% 0.35/0.63       => ( ( member_int @ I2 @ I6 )
% 0.35/0.63         => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) )
% 0.35/0.63           => ( ! [I4: int] :
% 0.35/0.63                  ( ( member_int @ I4 @ I6 )
% 0.35/0.63                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 0.35/0.63             => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I6 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_pos2
% 0.35/0.63  thf(fact_6565_sum__pos2,axiom,
% 0.35/0.63      ! [I6: set_nat,I2: nat,F: nat > rat] :
% 0.35/0.63        ( ( finite_finite_nat @ I6 )
% 0.35/0.63       => ( ( member_nat @ I2 @ I6 )
% 0.35/0.63         => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) )
% 0.35/0.63           => ( ! [I4: nat] :
% 0.35/0.63                  ( ( member_nat @ I4 @ I6 )
% 0.35/0.63                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 0.35/0.63             => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I6 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_pos2
% 0.35/0.63  thf(fact_6566_sum__pos2,axiom,
% 0.35/0.63      ! [I6: set_complex,I2: complex,F: complex > rat] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ I6 )
% 0.35/0.63       => ( ( member_complex @ I2 @ I6 )
% 0.35/0.63         => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) )
% 0.35/0.63           => ( ! [I4: complex] :
% 0.35/0.63                  ( ( member_complex @ I4 @ I6 )
% 0.35/0.63                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 0.35/0.63             => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I6 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_pos2
% 0.35/0.63  thf(fact_6567_sum__pos2,axiom,
% 0.35/0.63      ! [I6: set_real,I2: real,F: real > nat] :
% 0.35/0.63        ( ( finite_finite_real @ I6 )
% 0.35/0.63       => ( ( member_real @ I2 @ I6 )
% 0.35/0.63         => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 0.35/0.63           => ( ! [I4: real] :
% 0.35/0.63                  ( ( member_real @ I4 @ I6 )
% 0.35/0.63                 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 0.35/0.63             => ( ord_less_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ I6 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_pos2
% 0.35/0.63  thf(fact_6568_sum__pos2,axiom,
% 0.35/0.63      ! [I6: set_int,I2: int,F: int > nat] :
% 0.35/0.63        ( ( finite_finite_int @ I6 )
% 0.35/0.63       => ( ( member_int @ I2 @ I6 )
% 0.35/0.63         => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 0.35/0.63           => ( ! [I4: int] :
% 0.35/0.63                  ( ( member_int @ I4 @ I6 )
% 0.35/0.63                 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 0.35/0.63             => ( ord_less_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ I6 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_pos2
% 0.35/0.63  thf(fact_6569_sum__pos2,axiom,
% 0.35/0.63      ! [I6: set_complex,I2: complex,F: complex > nat] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ I6 )
% 0.35/0.63       => ( ( member_complex @ I2 @ I6 )
% 0.35/0.63         => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 0.35/0.63           => ( ! [I4: complex] :
% 0.35/0.63                  ( ( member_complex @ I4 @ I6 )
% 0.35/0.63                 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 0.35/0.63             => ( ord_less_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ I6 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_pos2
% 0.35/0.63  thf(fact_6570_sum__pos,axiom,
% 0.35/0.63      ! [I6: set_complex,F: complex > real] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ I6 )
% 0.35/0.63       => ( ( I6 != bot_bot_set_complex )
% 0.35/0.63         => ( ! [I4: complex] :
% 0.35/0.63                ( ( member_complex @ I4 @ I6 )
% 0.35/0.63               => ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) )
% 0.35/0.63           => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I6 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_pos
% 0.35/0.63  thf(fact_6571_sum__pos,axiom,
% 0.35/0.63      ! [I6: set_int,F: int > real] :
% 0.35/0.63        ( ( finite_finite_int @ I6 )
% 0.35/0.63       => ( ( I6 != bot_bot_set_int )
% 0.35/0.63         => ( ! [I4: int] :
% 0.35/0.63                ( ( member_int @ I4 @ I6 )
% 0.35/0.63               => ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) )
% 0.35/0.63           => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I6 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_pos
% 0.35/0.63  thf(fact_6572_sum__pos,axiom,
% 0.35/0.63      ! [I6: set_real,F: real > real] :
% 0.35/0.63        ( ( finite_finite_real @ I6 )
% 0.35/0.63       => ( ( I6 != bot_bot_set_real )
% 0.35/0.63         => ( ! [I4: real] :
% 0.35/0.63                ( ( member_real @ I4 @ I6 )
% 0.35/0.63               => ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) )
% 0.35/0.63           => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I6 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_pos
% 0.35/0.63  thf(fact_6573_sum__pos,axiom,
% 0.35/0.63      ! [I6: set_complex,F: complex > rat] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ I6 )
% 0.35/0.63       => ( ( I6 != bot_bot_set_complex )
% 0.35/0.63         => ( ! [I4: complex] :
% 0.35/0.63                ( ( member_complex @ I4 @ I6 )
% 0.35/0.63               => ( ord_less_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 0.35/0.63           => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I6 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_pos
% 0.35/0.63  thf(fact_6574_sum__pos,axiom,
% 0.35/0.63      ! [I6: set_nat,F: nat > rat] :
% 0.35/0.63        ( ( finite_finite_nat @ I6 )
% 0.35/0.63       => ( ( I6 != bot_bot_set_nat )
% 0.35/0.63         => ( ! [I4: nat] :
% 0.35/0.63                ( ( member_nat @ I4 @ I6 )
% 0.35/0.63               => ( ord_less_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 0.35/0.63           => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I6 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_pos
% 0.35/0.63  thf(fact_6575_sum__pos,axiom,
% 0.35/0.63      ! [I6: set_int,F: int > rat] :
% 0.35/0.63        ( ( finite_finite_int @ I6 )
% 0.35/0.63       => ( ( I6 != bot_bot_set_int )
% 0.35/0.63         => ( ! [I4: int] :
% 0.35/0.63                ( ( member_int @ I4 @ I6 )
% 0.35/0.63               => ( ord_less_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 0.35/0.63           => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I6 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_pos
% 0.35/0.63  thf(fact_6576_sum__pos,axiom,
% 0.35/0.63      ! [I6: set_real,F: real > rat] :
% 0.35/0.63        ( ( finite_finite_real @ I6 )
% 0.35/0.63       => ( ( I6 != bot_bot_set_real )
% 0.35/0.63         => ( ! [I4: real] :
% 0.35/0.63                ( ( member_real @ I4 @ I6 )
% 0.35/0.63               => ( ord_less_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 0.35/0.63           => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I6 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_pos
% 0.35/0.63  thf(fact_6577_sum__pos,axiom,
% 0.35/0.63      ! [I6: set_complex,F: complex > nat] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ I6 )
% 0.35/0.63       => ( ( I6 != bot_bot_set_complex )
% 0.35/0.63         => ( ! [I4: complex] :
% 0.35/0.63                ( ( member_complex @ I4 @ I6 )
% 0.35/0.63               => ( ord_less_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 0.35/0.63           => ( ord_less_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ I6 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_pos
% 0.35/0.63  thf(fact_6578_sum__pos,axiom,
% 0.35/0.63      ! [I6: set_int,F: int > nat] :
% 0.35/0.63        ( ( finite_finite_int @ I6 )
% 0.35/0.63       => ( ( I6 != bot_bot_set_int )
% 0.35/0.63         => ( ! [I4: int] :
% 0.35/0.63                ( ( member_int @ I4 @ I6 )
% 0.35/0.63               => ( ord_less_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 0.35/0.63           => ( ord_less_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ I6 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_pos
% 0.35/0.63  thf(fact_6579_sum__pos,axiom,
% 0.35/0.63      ! [I6: set_real,F: real > nat] :
% 0.35/0.63        ( ( finite_finite_real @ I6 )
% 0.35/0.63       => ( ( I6 != bot_bot_set_real )
% 0.35/0.63         => ( ! [I4: real] :
% 0.35/0.63                ( ( member_real @ I4 @ I6 )
% 0.35/0.63               => ( ord_less_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 0.35/0.63           => ( ord_less_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ I6 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_pos
% 0.35/0.63  thf(fact_6580_sum_Osame__carrier,axiom,
% 0.35/0.63      ! [C4: set_int,A2: set_int,B2: set_int,G: int > complex,H2: int > complex] :
% 0.35/0.63        ( ( finite_finite_int @ C4 )
% 0.35/0.63       => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 0.35/0.63         => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 0.35/0.63           => ( ! [A4: int] :
% 0.35/0.63                  ( ( member_int @ A4 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 0.35/0.63                 => ( ( G @ A4 )
% 0.35/0.63                    = zero_zero_complex ) )
% 0.35/0.63             => ( ! [B3: int] :
% 0.35/0.63                    ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 0.35/0.63                   => ( ( H2 @ B3 )
% 0.35/0.63                      = zero_zero_complex ) )
% 0.35/0.63               => ( ( ( groups3049146728041665814omplex @ G @ A2 )
% 0.35/0.63                    = ( groups3049146728041665814omplex @ H2 @ B2 ) )
% 0.35/0.63                  = ( ( groups3049146728041665814omplex @ G @ C4 )
% 0.35/0.63                    = ( groups3049146728041665814omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.same_carrier
% 0.35/0.63  thf(fact_6581_sum_Osame__carrier,axiom,
% 0.35/0.63      ! [C4: set_int,A2: set_int,B2: set_int,G: int > real,H2: int > real] :
% 0.35/0.63        ( ( finite_finite_int @ C4 )
% 0.35/0.63       => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 0.35/0.63         => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 0.35/0.63           => ( ! [A4: int] :
% 0.35/0.63                  ( ( member_int @ A4 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 0.35/0.63                 => ( ( G @ A4 )
% 0.35/0.63                    = zero_zero_real ) )
% 0.35/0.63             => ( ! [B3: int] :
% 0.35/0.63                    ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 0.35/0.63                   => ( ( H2 @ B3 )
% 0.35/0.63                      = zero_zero_real ) )
% 0.35/0.63               => ( ( ( groups8778361861064173332t_real @ G @ A2 )
% 0.35/0.63                    = ( groups8778361861064173332t_real @ H2 @ B2 ) )
% 0.35/0.63                  = ( ( groups8778361861064173332t_real @ G @ C4 )
% 0.35/0.63                    = ( groups8778361861064173332t_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.same_carrier
% 0.35/0.63  thf(fact_6582_sum_Osame__carrier,axiom,
% 0.35/0.63      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > real,H2: complex > real] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ C4 )
% 0.35/0.63       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 0.35/0.63         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 0.35/0.63           => ( ! [A4: complex] :
% 0.35/0.63                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 0.35/0.63                 => ( ( G @ A4 )
% 0.35/0.63                    = zero_zero_real ) )
% 0.35/0.63             => ( ! [B3: complex] :
% 0.35/0.63                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 0.35/0.63                   => ( ( H2 @ B3 )
% 0.35/0.63                      = zero_zero_real ) )
% 0.35/0.63               => ( ( ( groups5808333547571424918x_real @ G @ A2 )
% 0.35/0.63                    = ( groups5808333547571424918x_real @ H2 @ B2 ) )
% 0.35/0.63                  = ( ( groups5808333547571424918x_real @ G @ C4 )
% 0.35/0.63                    = ( groups5808333547571424918x_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.same_carrier
% 0.35/0.63  thf(fact_6583_sum_Osame__carrier,axiom,
% 0.35/0.63      ! [C4: set_int,A2: set_int,B2: set_int,G: int > rat,H2: int > rat] :
% 0.35/0.63        ( ( finite_finite_int @ C4 )
% 0.35/0.63       => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 0.35/0.63         => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 0.35/0.63           => ( ! [A4: int] :
% 0.35/0.63                  ( ( member_int @ A4 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 0.35/0.63                 => ( ( G @ A4 )
% 0.35/0.63                    = zero_zero_rat ) )
% 0.35/0.63             => ( ! [B3: int] :
% 0.35/0.63                    ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 0.35/0.63                   => ( ( H2 @ B3 )
% 0.35/0.63                      = zero_zero_rat ) )
% 0.35/0.63               => ( ( ( groups3906332499630173760nt_rat @ G @ A2 )
% 0.35/0.63                    = ( groups3906332499630173760nt_rat @ H2 @ B2 ) )
% 0.35/0.63                  = ( ( groups3906332499630173760nt_rat @ G @ C4 )
% 0.35/0.63                    = ( groups3906332499630173760nt_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.same_carrier
% 0.35/0.63  thf(fact_6584_sum_Osame__carrier,axiom,
% 0.35/0.63      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > rat,H2: complex > rat] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ C4 )
% 0.35/0.63       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 0.35/0.63         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 0.35/0.63           => ( ! [A4: complex] :
% 0.35/0.63                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 0.35/0.63                 => ( ( G @ A4 )
% 0.35/0.63                    = zero_zero_rat ) )
% 0.35/0.63             => ( ! [B3: complex] :
% 0.35/0.63                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 0.35/0.63                   => ( ( H2 @ B3 )
% 0.35/0.63                      = zero_zero_rat ) )
% 0.35/0.63               => ( ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 0.35/0.63                    = ( groups5058264527183730370ex_rat @ H2 @ B2 ) )
% 0.35/0.63                  = ( ( groups5058264527183730370ex_rat @ G @ C4 )
% 0.35/0.63                    = ( groups5058264527183730370ex_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.same_carrier
% 0.35/0.63  thf(fact_6585_sum_Osame__carrier,axiom,
% 0.35/0.63      ! [C4: set_int,A2: set_int,B2: set_int,G: int > nat,H2: int > nat] :
% 0.35/0.63        ( ( finite_finite_int @ C4 )
% 0.35/0.63       => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 0.35/0.63         => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 0.35/0.63           => ( ! [A4: int] :
% 0.35/0.63                  ( ( member_int @ A4 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 0.35/0.63                 => ( ( G @ A4 )
% 0.35/0.63                    = zero_zero_nat ) )
% 0.35/0.63             => ( ! [B3: int] :
% 0.35/0.63                    ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 0.35/0.63                   => ( ( H2 @ B3 )
% 0.35/0.63                      = zero_zero_nat ) )
% 0.35/0.63               => ( ( ( groups4541462559716669496nt_nat @ G @ A2 )
% 0.35/0.63                    = ( groups4541462559716669496nt_nat @ H2 @ B2 ) )
% 0.35/0.63                  = ( ( groups4541462559716669496nt_nat @ G @ C4 )
% 0.35/0.63                    = ( groups4541462559716669496nt_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.same_carrier
% 0.35/0.63  thf(fact_6586_sum_Osame__carrier,axiom,
% 0.35/0.63      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > nat,H2: complex > nat] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ C4 )
% 0.35/0.63       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 0.35/0.63         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 0.35/0.63           => ( ! [A4: complex] :
% 0.35/0.63                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 0.35/0.63                 => ( ( G @ A4 )
% 0.35/0.63                    = zero_zero_nat ) )
% 0.35/0.63             => ( ! [B3: complex] :
% 0.35/0.63                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 0.35/0.63                   => ( ( H2 @ B3 )
% 0.35/0.63                      = zero_zero_nat ) )
% 0.35/0.63               => ( ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 0.35/0.63                    = ( groups5693394587270226106ex_nat @ H2 @ B2 ) )
% 0.35/0.63                  = ( ( groups5693394587270226106ex_nat @ G @ C4 )
% 0.35/0.63                    = ( groups5693394587270226106ex_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.same_carrier
% 0.35/0.63  thf(fact_6587_sum_Osame__carrier,axiom,
% 0.35/0.63      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > int,H2: complex > int] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ C4 )
% 0.35/0.63       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 0.35/0.63         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 0.35/0.63           => ( ! [A4: complex] :
% 0.35/0.63                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 0.35/0.63                 => ( ( G @ A4 )
% 0.35/0.63                    = zero_zero_int ) )
% 0.35/0.63             => ( ! [B3: complex] :
% 0.35/0.63                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 0.35/0.63                   => ( ( H2 @ B3 )
% 0.35/0.63                      = zero_zero_int ) )
% 0.35/0.63               => ( ( ( groups5690904116761175830ex_int @ G @ A2 )
% 0.35/0.63                    = ( groups5690904116761175830ex_int @ H2 @ B2 ) )
% 0.35/0.63                  = ( ( groups5690904116761175830ex_int @ G @ C4 )
% 0.35/0.63                    = ( groups5690904116761175830ex_int @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.same_carrier
% 0.35/0.63  thf(fact_6588_sum_Osame__carrier,axiom,
% 0.35/0.63      ! [C4: set_real,A2: set_real,B2: set_real,G: real > complex,H2: real > complex] :
% 0.35/0.63        ( ( finite_finite_real @ C4 )
% 0.35/0.63       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 0.35/0.63         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 0.35/0.63           => ( ! [A4: real] :
% 0.35/0.63                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 0.35/0.63                 => ( ( G @ A4 )
% 0.35/0.63                    = zero_zero_complex ) )
% 0.35/0.63             => ( ! [B3: real] :
% 0.35/0.63                    ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 0.35/0.63                   => ( ( H2 @ B3 )
% 0.35/0.63                      = zero_zero_complex ) )
% 0.35/0.63               => ( ( ( groups5754745047067104278omplex @ G @ A2 )
% 0.35/0.63                    = ( groups5754745047067104278omplex @ H2 @ B2 ) )
% 0.35/0.63                  = ( ( groups5754745047067104278omplex @ G @ C4 )
% 0.35/0.63                    = ( groups5754745047067104278omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.same_carrier
% 0.35/0.63  thf(fact_6589_sum_Osame__carrier,axiom,
% 0.35/0.63      ! [C4: set_real,A2: set_real,B2: set_real,G: real > real,H2: real > real] :
% 0.35/0.63        ( ( finite_finite_real @ C4 )
% 0.35/0.63       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 0.35/0.63         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 0.35/0.63           => ( ! [A4: real] :
% 0.35/0.63                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 0.35/0.63                 => ( ( G @ A4 )
% 0.35/0.63                    = zero_zero_real ) )
% 0.35/0.63             => ( ! [B3: real] :
% 0.35/0.63                    ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 0.35/0.63                   => ( ( H2 @ B3 )
% 0.35/0.63                      = zero_zero_real ) )
% 0.35/0.63               => ( ( ( groups8097168146408367636l_real @ G @ A2 )
% 0.35/0.63                    = ( groups8097168146408367636l_real @ H2 @ B2 ) )
% 0.35/0.63                  = ( ( groups8097168146408367636l_real @ G @ C4 )
% 0.35/0.63                    = ( groups8097168146408367636l_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.same_carrier
% 0.35/0.63  thf(fact_6590_sum_Osame__carrierI,axiom,
% 0.35/0.63      ! [C4: set_int,A2: set_int,B2: set_int,G: int > complex,H2: int > complex] :
% 0.35/0.63        ( ( finite_finite_int @ C4 )
% 0.35/0.63       => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 0.35/0.63         => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 0.35/0.63           => ( ! [A4: int] :
% 0.35/0.63                  ( ( member_int @ A4 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 0.35/0.63                 => ( ( G @ A4 )
% 0.35/0.63                    = zero_zero_complex ) )
% 0.35/0.63             => ( ! [B3: int] :
% 0.35/0.63                    ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 0.35/0.63                   => ( ( H2 @ B3 )
% 0.35/0.63                      = zero_zero_complex ) )
% 0.35/0.63               => ( ( ( groups3049146728041665814omplex @ G @ C4 )
% 0.35/0.63                    = ( groups3049146728041665814omplex @ H2 @ C4 ) )
% 0.35/0.63                 => ( ( groups3049146728041665814omplex @ G @ A2 )
% 0.35/0.63                    = ( groups3049146728041665814omplex @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.same_carrierI
% 0.35/0.63  thf(fact_6591_sum_Osame__carrierI,axiom,
% 0.35/0.63      ! [C4: set_int,A2: set_int,B2: set_int,G: int > real,H2: int > real] :
% 0.35/0.63        ( ( finite_finite_int @ C4 )
% 0.35/0.63       => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 0.35/0.63         => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 0.35/0.63           => ( ! [A4: int] :
% 0.35/0.63                  ( ( member_int @ A4 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 0.35/0.63                 => ( ( G @ A4 )
% 0.35/0.63                    = zero_zero_real ) )
% 0.35/0.63             => ( ! [B3: int] :
% 0.35/0.63                    ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 0.35/0.63                   => ( ( H2 @ B3 )
% 0.35/0.63                      = zero_zero_real ) )
% 0.35/0.63               => ( ( ( groups8778361861064173332t_real @ G @ C4 )
% 0.35/0.63                    = ( groups8778361861064173332t_real @ H2 @ C4 ) )
% 0.35/0.63                 => ( ( groups8778361861064173332t_real @ G @ A2 )
% 0.35/0.63                    = ( groups8778361861064173332t_real @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.same_carrierI
% 0.35/0.63  thf(fact_6592_sum_Osame__carrierI,axiom,
% 0.35/0.63      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > real,H2: complex > real] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ C4 )
% 0.35/0.63       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 0.35/0.63         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 0.35/0.63           => ( ! [A4: complex] :
% 0.35/0.63                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 0.35/0.63                 => ( ( G @ A4 )
% 0.35/0.63                    = zero_zero_real ) )
% 0.35/0.63             => ( ! [B3: complex] :
% 0.35/0.63                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 0.35/0.63                   => ( ( H2 @ B3 )
% 0.35/0.63                      = zero_zero_real ) )
% 0.35/0.63               => ( ( ( groups5808333547571424918x_real @ G @ C4 )
% 0.35/0.63                    = ( groups5808333547571424918x_real @ H2 @ C4 ) )
% 0.35/0.63                 => ( ( groups5808333547571424918x_real @ G @ A2 )
% 0.35/0.63                    = ( groups5808333547571424918x_real @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.same_carrierI
% 0.35/0.63  thf(fact_6593_sum_Osame__carrierI,axiom,
% 0.35/0.63      ! [C4: set_int,A2: set_int,B2: set_int,G: int > rat,H2: int > rat] :
% 0.35/0.63        ( ( finite_finite_int @ C4 )
% 0.35/0.63       => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 0.35/0.63         => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 0.35/0.63           => ( ! [A4: int] :
% 0.35/0.63                  ( ( member_int @ A4 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 0.35/0.63                 => ( ( G @ A4 )
% 0.35/0.63                    = zero_zero_rat ) )
% 0.35/0.63             => ( ! [B3: int] :
% 0.35/0.63                    ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 0.35/0.63                   => ( ( H2 @ B3 )
% 0.35/0.63                      = zero_zero_rat ) )
% 0.35/0.63               => ( ( ( groups3906332499630173760nt_rat @ G @ C4 )
% 0.35/0.63                    = ( groups3906332499630173760nt_rat @ H2 @ C4 ) )
% 0.35/0.63                 => ( ( groups3906332499630173760nt_rat @ G @ A2 )
% 0.35/0.63                    = ( groups3906332499630173760nt_rat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.same_carrierI
% 0.35/0.63  thf(fact_6594_sum_Osame__carrierI,axiom,
% 0.35/0.63      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > rat,H2: complex > rat] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ C4 )
% 0.35/0.63       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 0.35/0.63         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 0.35/0.63           => ( ! [A4: complex] :
% 0.35/0.63                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 0.35/0.63                 => ( ( G @ A4 )
% 0.35/0.63                    = zero_zero_rat ) )
% 0.35/0.63             => ( ! [B3: complex] :
% 0.35/0.63                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 0.35/0.63                   => ( ( H2 @ B3 )
% 0.35/0.63                      = zero_zero_rat ) )
% 0.35/0.63               => ( ( ( groups5058264527183730370ex_rat @ G @ C4 )
% 0.35/0.63                    = ( groups5058264527183730370ex_rat @ H2 @ C4 ) )
% 0.35/0.63                 => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 0.35/0.63                    = ( groups5058264527183730370ex_rat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.same_carrierI
% 0.35/0.63  thf(fact_6595_sum_Osame__carrierI,axiom,
% 0.35/0.63      ! [C4: set_int,A2: set_int,B2: set_int,G: int > nat,H2: int > nat] :
% 0.35/0.63        ( ( finite_finite_int @ C4 )
% 0.35/0.63       => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 0.35/0.63         => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 0.35/0.63           => ( ! [A4: int] :
% 0.35/0.63                  ( ( member_int @ A4 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 0.35/0.63                 => ( ( G @ A4 )
% 0.35/0.63                    = zero_zero_nat ) )
% 0.35/0.63             => ( ! [B3: int] :
% 0.35/0.63                    ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 0.35/0.63                   => ( ( H2 @ B3 )
% 0.35/0.63                      = zero_zero_nat ) )
% 0.35/0.63               => ( ( ( groups4541462559716669496nt_nat @ G @ C4 )
% 0.35/0.63                    = ( groups4541462559716669496nt_nat @ H2 @ C4 ) )
% 0.35/0.63                 => ( ( groups4541462559716669496nt_nat @ G @ A2 )
% 0.35/0.63                    = ( groups4541462559716669496nt_nat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.same_carrierI
% 0.35/0.63  thf(fact_6596_sum_Osame__carrierI,axiom,
% 0.35/0.63      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > nat,H2: complex > nat] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ C4 )
% 0.35/0.63       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 0.35/0.63         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 0.35/0.63           => ( ! [A4: complex] :
% 0.35/0.63                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 0.35/0.63                 => ( ( G @ A4 )
% 0.35/0.63                    = zero_zero_nat ) )
% 0.35/0.63             => ( ! [B3: complex] :
% 0.35/0.63                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 0.35/0.63                   => ( ( H2 @ B3 )
% 0.35/0.63                      = zero_zero_nat ) )
% 0.35/0.63               => ( ( ( groups5693394587270226106ex_nat @ G @ C4 )
% 0.35/0.63                    = ( groups5693394587270226106ex_nat @ H2 @ C4 ) )
% 0.35/0.63                 => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 0.35/0.63                    = ( groups5693394587270226106ex_nat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.same_carrierI
% 0.35/0.63  thf(fact_6597_sum_Osame__carrierI,axiom,
% 0.35/0.63      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > int,H2: complex > int] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ C4 )
% 0.35/0.63       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 0.35/0.63         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 0.35/0.63           => ( ! [A4: complex] :
% 0.35/0.63                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 0.35/0.63                 => ( ( G @ A4 )
% 0.35/0.63                    = zero_zero_int ) )
% 0.35/0.63             => ( ! [B3: complex] :
% 0.35/0.63                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 0.35/0.63                   => ( ( H2 @ B3 )
% 0.35/0.63                      = zero_zero_int ) )
% 0.35/0.63               => ( ( ( groups5690904116761175830ex_int @ G @ C4 )
% 0.35/0.63                    = ( groups5690904116761175830ex_int @ H2 @ C4 ) )
% 0.35/0.63                 => ( ( groups5690904116761175830ex_int @ G @ A2 )
% 0.35/0.63                    = ( groups5690904116761175830ex_int @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.same_carrierI
% 0.35/0.63  thf(fact_6598_sum_Osame__carrierI,axiom,
% 0.35/0.63      ! [C4: set_real,A2: set_real,B2: set_real,G: real > complex,H2: real > complex] :
% 0.35/0.63        ( ( finite_finite_real @ C4 )
% 0.35/0.63       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 0.35/0.63         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 0.35/0.63           => ( ! [A4: real] :
% 0.35/0.63                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 0.35/0.63                 => ( ( G @ A4 )
% 0.35/0.63                    = zero_zero_complex ) )
% 0.35/0.63             => ( ! [B3: real] :
% 0.35/0.63                    ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 0.35/0.63                   => ( ( H2 @ B3 )
% 0.35/0.63                      = zero_zero_complex ) )
% 0.35/0.63               => ( ( ( groups5754745047067104278omplex @ G @ C4 )
% 0.35/0.63                    = ( groups5754745047067104278omplex @ H2 @ C4 ) )
% 0.35/0.63                 => ( ( groups5754745047067104278omplex @ G @ A2 )
% 0.35/0.63                    = ( groups5754745047067104278omplex @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.same_carrierI
% 0.35/0.63  thf(fact_6599_sum_Osame__carrierI,axiom,
% 0.35/0.63      ! [C4: set_real,A2: set_real,B2: set_real,G: real > real,H2: real > real] :
% 0.35/0.63        ( ( finite_finite_real @ C4 )
% 0.35/0.63       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 0.35/0.63         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 0.35/0.63           => ( ! [A4: real] :
% 0.35/0.63                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 0.35/0.63                 => ( ( G @ A4 )
% 0.35/0.63                    = zero_zero_real ) )
% 0.35/0.63             => ( ! [B3: real] :
% 0.35/0.63                    ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 0.35/0.63                   => ( ( H2 @ B3 )
% 0.35/0.63                      = zero_zero_real ) )
% 0.35/0.63               => ( ( ( groups8097168146408367636l_real @ G @ C4 )
% 0.35/0.63                    = ( groups8097168146408367636l_real @ H2 @ C4 ) )
% 0.35/0.63                 => ( ( groups8097168146408367636l_real @ G @ A2 )
% 0.35/0.63                    = ( groups8097168146408367636l_real @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.same_carrierI
% 0.35/0.63  thf(fact_6600_sum_Omono__neutral__left,axiom,
% 0.35/0.63      ! [T4: set_complex,S2: set_complex,G: complex > real] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.63       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: complex] :
% 0.35/0.63                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 0.35/0.63               => ( ( G @ X3 )
% 0.35/0.63                  = zero_zero_real ) )
% 0.35/0.63           => ( ( groups5808333547571424918x_real @ G @ S2 )
% 0.35/0.63              = ( groups5808333547571424918x_real @ G @ T4 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_left
% 0.35/0.63  thf(fact_6601_sum_Omono__neutral__left,axiom,
% 0.35/0.63      ! [T4: set_complex,S2: set_complex,G: complex > rat] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.63       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: complex] :
% 0.35/0.63                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 0.35/0.63               => ( ( G @ X3 )
% 0.35/0.63                  = zero_zero_rat ) )
% 0.35/0.63           => ( ( groups5058264527183730370ex_rat @ G @ S2 )
% 0.35/0.63              = ( groups5058264527183730370ex_rat @ G @ T4 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_left
% 0.35/0.63  thf(fact_6602_sum_Omono__neutral__left,axiom,
% 0.35/0.63      ! [T4: set_complex,S2: set_complex,G: complex > nat] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.63       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: complex] :
% 0.35/0.63                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 0.35/0.63               => ( ( G @ X3 )
% 0.35/0.63                  = zero_zero_nat ) )
% 0.35/0.63           => ( ( groups5693394587270226106ex_nat @ G @ S2 )
% 0.35/0.63              = ( groups5693394587270226106ex_nat @ G @ T4 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_left
% 0.35/0.63  thf(fact_6603_sum_Omono__neutral__left,axiom,
% 0.35/0.63      ! [T4: set_complex,S2: set_complex,G: complex > int] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.63       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: complex] :
% 0.35/0.63                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 0.35/0.63               => ( ( G @ X3 )
% 0.35/0.63                  = zero_zero_int ) )
% 0.35/0.63           => ( ( groups5690904116761175830ex_int @ G @ S2 )
% 0.35/0.63              = ( groups5690904116761175830ex_int @ G @ T4 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_left
% 0.35/0.63  thf(fact_6604_sum_Omono__neutral__left,axiom,
% 0.35/0.63      ! [T4: set_real,S2: set_real,G: real > complex] :
% 0.35/0.63        ( ( finite_finite_real @ T4 )
% 0.35/0.63       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: real] :
% 0.35/0.63                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 0.35/0.63               => ( ( G @ X3 )
% 0.35/0.63                  = zero_zero_complex ) )
% 0.35/0.63           => ( ( groups5754745047067104278omplex @ G @ S2 )
% 0.35/0.63              = ( groups5754745047067104278omplex @ G @ T4 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_left
% 0.35/0.63  thf(fact_6605_sum_Omono__neutral__left,axiom,
% 0.35/0.63      ! [T4: set_real,S2: set_real,G: real > real] :
% 0.35/0.63        ( ( finite_finite_real @ T4 )
% 0.35/0.63       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: real] :
% 0.35/0.63                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 0.35/0.63               => ( ( G @ X3 )
% 0.35/0.63                  = zero_zero_real ) )
% 0.35/0.63           => ( ( groups8097168146408367636l_real @ G @ S2 )
% 0.35/0.63              = ( groups8097168146408367636l_real @ G @ T4 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_left
% 0.35/0.63  thf(fact_6606_sum_Omono__neutral__left,axiom,
% 0.35/0.63      ! [T4: set_real,S2: set_real,G: real > rat] :
% 0.35/0.63        ( ( finite_finite_real @ T4 )
% 0.35/0.63       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: real] :
% 0.35/0.63                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 0.35/0.63               => ( ( G @ X3 )
% 0.35/0.63                  = zero_zero_rat ) )
% 0.35/0.63           => ( ( groups1300246762558778688al_rat @ G @ S2 )
% 0.35/0.63              = ( groups1300246762558778688al_rat @ G @ T4 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_left
% 0.35/0.63  thf(fact_6607_sum_Omono__neutral__left,axiom,
% 0.35/0.63      ! [T4: set_real,S2: set_real,G: real > nat] :
% 0.35/0.63        ( ( finite_finite_real @ T4 )
% 0.35/0.63       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: real] :
% 0.35/0.63                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 0.35/0.63               => ( ( G @ X3 )
% 0.35/0.63                  = zero_zero_nat ) )
% 0.35/0.63           => ( ( groups1935376822645274424al_nat @ G @ S2 )
% 0.35/0.63              = ( groups1935376822645274424al_nat @ G @ T4 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_left
% 0.35/0.63  thf(fact_6608_sum_Omono__neutral__left,axiom,
% 0.35/0.63      ! [T4: set_real,S2: set_real,G: real > int] :
% 0.35/0.63        ( ( finite_finite_real @ T4 )
% 0.35/0.63       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: real] :
% 0.35/0.63                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 0.35/0.63               => ( ( G @ X3 )
% 0.35/0.63                  = zero_zero_int ) )
% 0.35/0.63           => ( ( groups1932886352136224148al_int @ G @ S2 )
% 0.35/0.63              = ( groups1932886352136224148al_int @ G @ T4 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_left
% 0.35/0.63  thf(fact_6609_sum_Omono__neutral__left,axiom,
% 0.35/0.63      ! [T4: set_nat,S2: set_nat,G: nat > complex] :
% 0.35/0.63        ( ( finite_finite_nat @ T4 )
% 0.35/0.63       => ( ( ord_less_eq_set_nat @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: nat] :
% 0.35/0.63                ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T4 @ S2 ) )
% 0.35/0.63               => ( ( G @ X3 )
% 0.35/0.63                  = zero_zero_complex ) )
% 0.35/0.63           => ( ( groups2073611262835488442omplex @ G @ S2 )
% 0.35/0.63              = ( groups2073611262835488442omplex @ G @ T4 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_left
% 0.35/0.63  thf(fact_6610_sum_Omono__neutral__right,axiom,
% 0.35/0.63      ! [T4: set_complex,S2: set_complex,G: complex > real] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.63       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: complex] :
% 0.35/0.63                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 0.35/0.63               => ( ( G @ X3 )
% 0.35/0.63                  = zero_zero_real ) )
% 0.35/0.63           => ( ( groups5808333547571424918x_real @ G @ T4 )
% 0.35/0.63              = ( groups5808333547571424918x_real @ G @ S2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_right
% 0.35/0.63  thf(fact_6611_sum_Omono__neutral__right,axiom,
% 0.35/0.63      ! [T4: set_complex,S2: set_complex,G: complex > rat] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.63       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: complex] :
% 0.35/0.63                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 0.35/0.63               => ( ( G @ X3 )
% 0.35/0.63                  = zero_zero_rat ) )
% 0.35/0.63           => ( ( groups5058264527183730370ex_rat @ G @ T4 )
% 0.35/0.63              = ( groups5058264527183730370ex_rat @ G @ S2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_right
% 0.35/0.63  thf(fact_6612_sum_Omono__neutral__right,axiom,
% 0.35/0.63      ! [T4: set_complex,S2: set_complex,G: complex > nat] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.63       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: complex] :
% 0.35/0.63                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 0.35/0.63               => ( ( G @ X3 )
% 0.35/0.63                  = zero_zero_nat ) )
% 0.35/0.63           => ( ( groups5693394587270226106ex_nat @ G @ T4 )
% 0.35/0.63              = ( groups5693394587270226106ex_nat @ G @ S2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_right
% 0.35/0.63  thf(fact_6613_sum_Omono__neutral__right,axiom,
% 0.35/0.63      ! [T4: set_complex,S2: set_complex,G: complex > int] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.63       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: complex] :
% 0.35/0.63                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 0.35/0.63               => ( ( G @ X3 )
% 0.35/0.63                  = zero_zero_int ) )
% 0.35/0.63           => ( ( groups5690904116761175830ex_int @ G @ T4 )
% 0.35/0.63              = ( groups5690904116761175830ex_int @ G @ S2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_right
% 0.35/0.63  thf(fact_6614_sum_Omono__neutral__right,axiom,
% 0.35/0.63      ! [T4: set_real,S2: set_real,G: real > complex] :
% 0.35/0.63        ( ( finite_finite_real @ T4 )
% 0.35/0.63       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: real] :
% 0.35/0.63                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 0.35/0.63               => ( ( G @ X3 )
% 0.35/0.63                  = zero_zero_complex ) )
% 0.35/0.63           => ( ( groups5754745047067104278omplex @ G @ T4 )
% 0.35/0.63              = ( groups5754745047067104278omplex @ G @ S2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_right
% 0.35/0.63  thf(fact_6615_sum_Omono__neutral__right,axiom,
% 0.35/0.63      ! [T4: set_real,S2: set_real,G: real > real] :
% 0.35/0.63        ( ( finite_finite_real @ T4 )
% 0.35/0.63       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: real] :
% 0.35/0.63                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 0.35/0.63               => ( ( G @ X3 )
% 0.35/0.63                  = zero_zero_real ) )
% 0.35/0.63           => ( ( groups8097168146408367636l_real @ G @ T4 )
% 0.35/0.63              = ( groups8097168146408367636l_real @ G @ S2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_right
% 0.35/0.63  thf(fact_6616_sum_Omono__neutral__right,axiom,
% 0.35/0.63      ! [T4: set_real,S2: set_real,G: real > rat] :
% 0.35/0.63        ( ( finite_finite_real @ T4 )
% 0.35/0.63       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: real] :
% 0.35/0.63                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 0.35/0.63               => ( ( G @ X3 )
% 0.35/0.63                  = zero_zero_rat ) )
% 0.35/0.63           => ( ( groups1300246762558778688al_rat @ G @ T4 )
% 0.35/0.63              = ( groups1300246762558778688al_rat @ G @ S2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_right
% 0.35/0.63  thf(fact_6617_sum_Omono__neutral__right,axiom,
% 0.35/0.63      ! [T4: set_real,S2: set_real,G: real > nat] :
% 0.35/0.63        ( ( finite_finite_real @ T4 )
% 0.35/0.63       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: real] :
% 0.35/0.63                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 0.35/0.63               => ( ( G @ X3 )
% 0.35/0.63                  = zero_zero_nat ) )
% 0.35/0.63           => ( ( groups1935376822645274424al_nat @ G @ T4 )
% 0.35/0.63              = ( groups1935376822645274424al_nat @ G @ S2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_right
% 0.35/0.63  thf(fact_6618_sum_Omono__neutral__right,axiom,
% 0.35/0.63      ! [T4: set_real,S2: set_real,G: real > int] :
% 0.35/0.63        ( ( finite_finite_real @ T4 )
% 0.35/0.63       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: real] :
% 0.35/0.63                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 0.35/0.63               => ( ( G @ X3 )
% 0.35/0.63                  = zero_zero_int ) )
% 0.35/0.63           => ( ( groups1932886352136224148al_int @ G @ T4 )
% 0.35/0.63              = ( groups1932886352136224148al_int @ G @ S2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_right
% 0.35/0.63  thf(fact_6619_sum_Omono__neutral__right,axiom,
% 0.35/0.63      ! [T4: set_nat,S2: set_nat,G: nat > complex] :
% 0.35/0.63        ( ( finite_finite_nat @ T4 )
% 0.35/0.63       => ( ( ord_less_eq_set_nat @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: nat] :
% 0.35/0.63                ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T4 @ S2 ) )
% 0.35/0.63               => ( ( G @ X3 )
% 0.35/0.63                  = zero_zero_complex ) )
% 0.35/0.63           => ( ( groups2073611262835488442omplex @ G @ T4 )
% 0.35/0.63              = ( groups2073611262835488442omplex @ G @ S2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_right
% 0.35/0.63  thf(fact_6620_sum_Omono__neutral__cong__left,axiom,
% 0.35/0.63      ! [T4: set_int,S2: set_int,H2: int > complex,G: int > complex] :
% 0.35/0.63        ( ( finite_finite_int @ T4 )
% 0.35/0.63       => ( ( ord_less_eq_set_int @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: int] :
% 0.35/0.63                ( ( member_int @ X3 @ ( minus_minus_set_int @ T4 @ S2 ) )
% 0.35/0.63               => ( ( H2 @ X3 )
% 0.35/0.63                  = zero_zero_complex ) )
% 0.35/0.63           => ( ! [X3: int] :
% 0.35/0.63                  ( ( member_int @ X3 @ S2 )
% 0.35/0.63                 => ( ( G @ X3 )
% 0.35/0.63                    = ( H2 @ X3 ) ) )
% 0.35/0.63             => ( ( groups3049146728041665814omplex @ G @ S2 )
% 0.35/0.63                = ( groups3049146728041665814omplex @ H2 @ T4 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_cong_left
% 0.35/0.63  thf(fact_6621_sum_Omono__neutral__cong__left,axiom,
% 0.35/0.63      ! [T4: set_int,S2: set_int,H2: int > real,G: int > real] :
% 0.35/0.63        ( ( finite_finite_int @ T4 )
% 0.35/0.63       => ( ( ord_less_eq_set_int @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: int] :
% 0.35/0.63                ( ( member_int @ X3 @ ( minus_minus_set_int @ T4 @ S2 ) )
% 0.35/0.63               => ( ( H2 @ X3 )
% 0.35/0.63                  = zero_zero_real ) )
% 0.35/0.63           => ( ! [X3: int] :
% 0.35/0.63                  ( ( member_int @ X3 @ S2 )
% 0.35/0.63                 => ( ( G @ X3 )
% 0.35/0.63                    = ( H2 @ X3 ) ) )
% 0.35/0.63             => ( ( groups8778361861064173332t_real @ G @ S2 )
% 0.35/0.63                = ( groups8778361861064173332t_real @ H2 @ T4 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_cong_left
% 0.35/0.63  thf(fact_6622_sum_Omono__neutral__cong__left,axiom,
% 0.35/0.63      ! [T4: set_complex,S2: set_complex,H2: complex > real,G: complex > real] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.63       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: complex] :
% 0.35/0.63                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 0.35/0.63               => ( ( H2 @ X3 )
% 0.35/0.63                  = zero_zero_real ) )
% 0.35/0.63           => ( ! [X3: complex] :
% 0.35/0.63                  ( ( member_complex @ X3 @ S2 )
% 0.35/0.63                 => ( ( G @ X3 )
% 0.35/0.63                    = ( H2 @ X3 ) ) )
% 0.35/0.63             => ( ( groups5808333547571424918x_real @ G @ S2 )
% 0.35/0.63                = ( groups5808333547571424918x_real @ H2 @ T4 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_cong_left
% 0.35/0.63  thf(fact_6623_sum_Omono__neutral__cong__left,axiom,
% 0.35/0.63      ! [T4: set_int,S2: set_int,H2: int > rat,G: int > rat] :
% 0.35/0.63        ( ( finite_finite_int @ T4 )
% 0.35/0.63       => ( ( ord_less_eq_set_int @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: int] :
% 0.35/0.63                ( ( member_int @ X3 @ ( minus_minus_set_int @ T4 @ S2 ) )
% 0.35/0.63               => ( ( H2 @ X3 )
% 0.35/0.63                  = zero_zero_rat ) )
% 0.35/0.63           => ( ! [X3: int] :
% 0.35/0.63                  ( ( member_int @ X3 @ S2 )
% 0.35/0.63                 => ( ( G @ X3 )
% 0.35/0.63                    = ( H2 @ X3 ) ) )
% 0.35/0.63             => ( ( groups3906332499630173760nt_rat @ G @ S2 )
% 0.35/0.63                = ( groups3906332499630173760nt_rat @ H2 @ T4 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_cong_left
% 0.35/0.63  thf(fact_6624_sum_Omono__neutral__cong__left,axiom,
% 0.35/0.63      ! [T4: set_complex,S2: set_complex,H2: complex > rat,G: complex > rat] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.63       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: complex] :
% 0.35/0.63                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 0.35/0.63               => ( ( H2 @ X3 )
% 0.35/0.63                  = zero_zero_rat ) )
% 0.35/0.63           => ( ! [X3: complex] :
% 0.35/0.63                  ( ( member_complex @ X3 @ S2 )
% 0.35/0.63                 => ( ( G @ X3 )
% 0.35/0.63                    = ( H2 @ X3 ) ) )
% 0.35/0.63             => ( ( groups5058264527183730370ex_rat @ G @ S2 )
% 0.35/0.63                = ( groups5058264527183730370ex_rat @ H2 @ T4 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_cong_left
% 0.35/0.63  thf(fact_6625_sum_Omono__neutral__cong__left,axiom,
% 0.35/0.63      ! [T4: set_int,S2: set_int,H2: int > nat,G: int > nat] :
% 0.35/0.63        ( ( finite_finite_int @ T4 )
% 0.35/0.63       => ( ( ord_less_eq_set_int @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: int] :
% 0.35/0.63                ( ( member_int @ X3 @ ( minus_minus_set_int @ T4 @ S2 ) )
% 0.35/0.63               => ( ( H2 @ X3 )
% 0.35/0.63                  = zero_zero_nat ) )
% 0.35/0.63           => ( ! [X3: int] :
% 0.35/0.63                  ( ( member_int @ X3 @ S2 )
% 0.35/0.63                 => ( ( G @ X3 )
% 0.35/0.63                    = ( H2 @ X3 ) ) )
% 0.35/0.63             => ( ( groups4541462559716669496nt_nat @ G @ S2 )
% 0.35/0.63                = ( groups4541462559716669496nt_nat @ H2 @ T4 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_cong_left
% 0.35/0.63  thf(fact_6626_sum_Omono__neutral__cong__left,axiom,
% 0.35/0.63      ! [T4: set_complex,S2: set_complex,H2: complex > nat,G: complex > nat] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.63       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: complex] :
% 0.35/0.63                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 0.35/0.63               => ( ( H2 @ X3 )
% 0.35/0.63                  = zero_zero_nat ) )
% 0.35/0.63           => ( ! [X3: complex] :
% 0.35/0.63                  ( ( member_complex @ X3 @ S2 )
% 0.35/0.63                 => ( ( G @ X3 )
% 0.35/0.63                    = ( H2 @ X3 ) ) )
% 0.35/0.63             => ( ( groups5693394587270226106ex_nat @ G @ S2 )
% 0.35/0.63                = ( groups5693394587270226106ex_nat @ H2 @ T4 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_cong_left
% 0.35/0.63  thf(fact_6627_sum_Omono__neutral__cong__left,axiom,
% 0.35/0.63      ! [T4: set_complex,S2: set_complex,H2: complex > int,G: complex > int] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.63       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: complex] :
% 0.35/0.63                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 0.35/0.63               => ( ( H2 @ X3 )
% 0.35/0.63                  = zero_zero_int ) )
% 0.35/0.63           => ( ! [X3: complex] :
% 0.35/0.63                  ( ( member_complex @ X3 @ S2 )
% 0.35/0.63                 => ( ( G @ X3 )
% 0.35/0.63                    = ( H2 @ X3 ) ) )
% 0.35/0.63             => ( ( groups5690904116761175830ex_int @ G @ S2 )
% 0.35/0.63                = ( groups5690904116761175830ex_int @ H2 @ T4 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_cong_left
% 0.35/0.63  thf(fact_6628_sum_Omono__neutral__cong__left,axiom,
% 0.35/0.63      ! [T4: set_real,S2: set_real,H2: real > complex,G: real > complex] :
% 0.35/0.63        ( ( finite_finite_real @ T4 )
% 0.35/0.63       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: real] :
% 0.35/0.63                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 0.35/0.63               => ( ( H2 @ X3 )
% 0.35/0.63                  = zero_zero_complex ) )
% 0.35/0.63           => ( ! [X3: real] :
% 0.35/0.63                  ( ( member_real @ X3 @ S2 )
% 0.35/0.63                 => ( ( G @ X3 )
% 0.35/0.63                    = ( H2 @ X3 ) ) )
% 0.35/0.63             => ( ( groups5754745047067104278omplex @ G @ S2 )
% 0.35/0.63                = ( groups5754745047067104278omplex @ H2 @ T4 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_cong_left
% 0.35/0.63  thf(fact_6629_sum_Omono__neutral__cong__left,axiom,
% 0.35/0.63      ! [T4: set_real,S2: set_real,H2: real > real,G: real > real] :
% 0.35/0.63        ( ( finite_finite_real @ T4 )
% 0.35/0.63       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: real] :
% 0.35/0.63                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 0.35/0.63               => ( ( H2 @ X3 )
% 0.35/0.63                  = zero_zero_real ) )
% 0.35/0.63           => ( ! [X3: real] :
% 0.35/0.63                  ( ( member_real @ X3 @ S2 )
% 0.35/0.63                 => ( ( G @ X3 )
% 0.35/0.63                    = ( H2 @ X3 ) ) )
% 0.35/0.63             => ( ( groups8097168146408367636l_real @ G @ S2 )
% 0.35/0.63                = ( groups8097168146408367636l_real @ H2 @ T4 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_cong_left
% 0.35/0.63  thf(fact_6630_sum_Omono__neutral__cong__right,axiom,
% 0.35/0.63      ! [T4: set_int,S2: set_int,G: int > complex,H2: int > complex] :
% 0.35/0.63        ( ( finite_finite_int @ T4 )
% 0.35/0.63       => ( ( ord_less_eq_set_int @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: int] :
% 0.35/0.63                ( ( member_int @ X3 @ ( minus_minus_set_int @ T4 @ S2 ) )
% 0.35/0.63               => ( ( G @ X3 )
% 0.35/0.63                  = zero_zero_complex ) )
% 0.35/0.63           => ( ! [X3: int] :
% 0.35/0.63                  ( ( member_int @ X3 @ S2 )
% 0.35/0.63                 => ( ( G @ X3 )
% 0.35/0.63                    = ( H2 @ X3 ) ) )
% 0.35/0.63             => ( ( groups3049146728041665814omplex @ G @ T4 )
% 0.35/0.63                = ( groups3049146728041665814omplex @ H2 @ S2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_cong_right
% 0.35/0.63  thf(fact_6631_sum_Omono__neutral__cong__right,axiom,
% 0.35/0.63      ! [T4: set_int,S2: set_int,G: int > real,H2: int > real] :
% 0.35/0.63        ( ( finite_finite_int @ T4 )
% 0.35/0.63       => ( ( ord_less_eq_set_int @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: int] :
% 0.35/0.63                ( ( member_int @ X3 @ ( minus_minus_set_int @ T4 @ S2 ) )
% 0.35/0.63               => ( ( G @ X3 )
% 0.35/0.63                  = zero_zero_real ) )
% 0.35/0.63           => ( ! [X3: int] :
% 0.35/0.63                  ( ( member_int @ X3 @ S2 )
% 0.35/0.63                 => ( ( G @ X3 )
% 0.35/0.63                    = ( H2 @ X3 ) ) )
% 0.35/0.63             => ( ( groups8778361861064173332t_real @ G @ T4 )
% 0.35/0.63                = ( groups8778361861064173332t_real @ H2 @ S2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_cong_right
% 0.35/0.63  thf(fact_6632_sum_Omono__neutral__cong__right,axiom,
% 0.35/0.63      ! [T4: set_complex,S2: set_complex,G: complex > real,H2: complex > real] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.63       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: complex] :
% 0.35/0.63                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 0.35/0.63               => ( ( G @ X3 )
% 0.35/0.63                  = zero_zero_real ) )
% 0.35/0.63           => ( ! [X3: complex] :
% 0.35/0.63                  ( ( member_complex @ X3 @ S2 )
% 0.35/0.63                 => ( ( G @ X3 )
% 0.35/0.63                    = ( H2 @ X3 ) ) )
% 0.35/0.63             => ( ( groups5808333547571424918x_real @ G @ T4 )
% 0.35/0.63                = ( groups5808333547571424918x_real @ H2 @ S2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_cong_right
% 0.35/0.63  thf(fact_6633_sum_Omono__neutral__cong__right,axiom,
% 0.35/0.63      ! [T4: set_int,S2: set_int,G: int > rat,H2: int > rat] :
% 0.35/0.63        ( ( finite_finite_int @ T4 )
% 0.35/0.63       => ( ( ord_less_eq_set_int @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: int] :
% 0.35/0.63                ( ( member_int @ X3 @ ( minus_minus_set_int @ T4 @ S2 ) )
% 0.35/0.63               => ( ( G @ X3 )
% 0.35/0.63                  = zero_zero_rat ) )
% 0.35/0.63           => ( ! [X3: int] :
% 0.35/0.63                  ( ( member_int @ X3 @ S2 )
% 0.35/0.63                 => ( ( G @ X3 )
% 0.35/0.63                    = ( H2 @ X3 ) ) )
% 0.35/0.63             => ( ( groups3906332499630173760nt_rat @ G @ T4 )
% 0.35/0.63                = ( groups3906332499630173760nt_rat @ H2 @ S2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_cong_right
% 0.35/0.63  thf(fact_6634_sum_Omono__neutral__cong__right,axiom,
% 0.35/0.63      ! [T4: set_complex,S2: set_complex,G: complex > rat,H2: complex > rat] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.63       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: complex] :
% 0.35/0.63                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 0.35/0.63               => ( ( G @ X3 )
% 0.35/0.63                  = zero_zero_rat ) )
% 0.35/0.63           => ( ! [X3: complex] :
% 0.35/0.63                  ( ( member_complex @ X3 @ S2 )
% 0.35/0.63                 => ( ( G @ X3 )
% 0.35/0.63                    = ( H2 @ X3 ) ) )
% 0.35/0.63             => ( ( groups5058264527183730370ex_rat @ G @ T4 )
% 0.35/0.63                = ( groups5058264527183730370ex_rat @ H2 @ S2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_cong_right
% 0.35/0.63  thf(fact_6635_sum_Omono__neutral__cong__right,axiom,
% 0.35/0.63      ! [T4: set_int,S2: set_int,G: int > nat,H2: int > nat] :
% 0.35/0.63        ( ( finite_finite_int @ T4 )
% 0.35/0.63       => ( ( ord_less_eq_set_int @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: int] :
% 0.35/0.63                ( ( member_int @ X3 @ ( minus_minus_set_int @ T4 @ S2 ) )
% 0.35/0.63               => ( ( G @ X3 )
% 0.35/0.63                  = zero_zero_nat ) )
% 0.35/0.63           => ( ! [X3: int] :
% 0.35/0.63                  ( ( member_int @ X3 @ S2 )
% 0.35/0.63                 => ( ( G @ X3 )
% 0.35/0.63                    = ( H2 @ X3 ) ) )
% 0.35/0.63             => ( ( groups4541462559716669496nt_nat @ G @ T4 )
% 0.35/0.63                = ( groups4541462559716669496nt_nat @ H2 @ S2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_cong_right
% 0.35/0.63  thf(fact_6636_sum_Omono__neutral__cong__right,axiom,
% 0.35/0.63      ! [T4: set_complex,S2: set_complex,G: complex > nat,H2: complex > nat] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.63       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: complex] :
% 0.35/0.63                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 0.35/0.63               => ( ( G @ X3 )
% 0.35/0.63                  = zero_zero_nat ) )
% 0.35/0.63           => ( ! [X3: complex] :
% 0.35/0.63                  ( ( member_complex @ X3 @ S2 )
% 0.35/0.63                 => ( ( G @ X3 )
% 0.35/0.63                    = ( H2 @ X3 ) ) )
% 0.35/0.63             => ( ( groups5693394587270226106ex_nat @ G @ T4 )
% 0.35/0.63                = ( groups5693394587270226106ex_nat @ H2 @ S2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_cong_right
% 0.35/0.63  thf(fact_6637_sum_Omono__neutral__cong__right,axiom,
% 0.35/0.63      ! [T4: set_complex,S2: set_complex,G: complex > int,H2: complex > int] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.63       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: complex] :
% 0.35/0.63                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 0.35/0.63               => ( ( G @ X3 )
% 0.35/0.63                  = zero_zero_int ) )
% 0.35/0.63           => ( ! [X3: complex] :
% 0.35/0.63                  ( ( member_complex @ X3 @ S2 )
% 0.35/0.63                 => ( ( G @ X3 )
% 0.35/0.63                    = ( H2 @ X3 ) ) )
% 0.35/0.63             => ( ( groups5690904116761175830ex_int @ G @ T4 )
% 0.35/0.63                = ( groups5690904116761175830ex_int @ H2 @ S2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_cong_right
% 0.35/0.63  thf(fact_6638_sum_Omono__neutral__cong__right,axiom,
% 0.35/0.63      ! [T4: set_real,S2: set_real,G: real > complex,H2: real > complex] :
% 0.35/0.63        ( ( finite_finite_real @ T4 )
% 0.35/0.63       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: real] :
% 0.35/0.63                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 0.35/0.63               => ( ( G @ X3 )
% 0.35/0.63                  = zero_zero_complex ) )
% 0.35/0.63           => ( ! [X3: real] :
% 0.35/0.63                  ( ( member_real @ X3 @ S2 )
% 0.35/0.63                 => ( ( G @ X3 )
% 0.35/0.63                    = ( H2 @ X3 ) ) )
% 0.35/0.63             => ( ( groups5754745047067104278omplex @ G @ T4 )
% 0.35/0.63                = ( groups5754745047067104278omplex @ H2 @ S2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_cong_right
% 0.35/0.63  thf(fact_6639_sum_Omono__neutral__cong__right,axiom,
% 0.35/0.63      ! [T4: set_real,S2: set_real,G: real > real,H2: real > real] :
% 0.35/0.63        ( ( finite_finite_real @ T4 )
% 0.35/0.63       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 0.35/0.63         => ( ! [X3: real] :
% 0.35/0.63                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 0.35/0.63               => ( ( G @ X3 )
% 0.35/0.63                  = zero_zero_real ) )
% 0.35/0.63           => ( ! [X3: real] :
% 0.35/0.63                  ( ( member_real @ X3 @ S2 )
% 0.35/0.63                 => ( ( G @ X3 )
% 0.35/0.63                    = ( H2 @ X3 ) ) )
% 0.35/0.63             => ( ( groups8097168146408367636l_real @ G @ T4 )
% 0.35/0.63                = ( groups8097168146408367636l_real @ H2 @ S2 ) ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.mono_neutral_cong_right
% 0.35/0.63  thf(fact_6640_sum_Osubset__diff,axiom,
% 0.35/0.63      ! [B2: set_complex,A2: set_complex,G: complex > real] :
% 0.35/0.63        ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 0.35/0.63       => ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.63         => ( ( groups5808333547571424918x_real @ G @ A2 )
% 0.35/0.63            = ( plus_plus_real @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups5808333547571424918x_real @ G @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.subset_diff
% 0.35/0.63  thf(fact_6641_sum_Osubset__diff,axiom,
% 0.35/0.63      ! [B2: set_complex,A2: set_complex,G: complex > rat] :
% 0.35/0.63        ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 0.35/0.63       => ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.63         => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 0.35/0.63            = ( plus_plus_rat @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups5058264527183730370ex_rat @ G @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.subset_diff
% 0.35/0.63  thf(fact_6642_sum_Osubset__diff,axiom,
% 0.35/0.63      ! [B2: set_complex,A2: set_complex,G: complex > nat] :
% 0.35/0.63        ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 0.35/0.63       => ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.63         => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 0.35/0.63            = ( plus_plus_nat @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups5693394587270226106ex_nat @ G @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.subset_diff
% 0.35/0.63  thf(fact_6643_sum_Osubset__diff,axiom,
% 0.35/0.63      ! [B2: set_complex,A2: set_complex,G: complex > int] :
% 0.35/0.63        ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 0.35/0.63       => ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.63         => ( ( groups5690904116761175830ex_int @ G @ A2 )
% 0.35/0.63            = ( plus_plus_int @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups5690904116761175830ex_int @ G @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.subset_diff
% 0.35/0.63  thf(fact_6644_sum_Osubset__diff,axiom,
% 0.35/0.63      ! [B2: set_real,A2: set_real,G: real > real] :
% 0.35/0.63        ( ( ord_less_eq_set_real @ B2 @ A2 )
% 0.35/0.63       => ( ( finite_finite_real @ A2 )
% 0.35/0.63         => ( ( groups8097168146408367636l_real @ G @ A2 )
% 0.35/0.63            = ( plus_plus_real @ ( groups8097168146408367636l_real @ G @ ( minus_minus_set_real @ A2 @ B2 ) ) @ ( groups8097168146408367636l_real @ G @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.subset_diff
% 0.35/0.63  thf(fact_6645_sum_Osubset__diff,axiom,
% 0.35/0.63      ! [B2: set_real,A2: set_real,G: real > rat] :
% 0.35/0.63        ( ( ord_less_eq_set_real @ B2 @ A2 )
% 0.35/0.63       => ( ( finite_finite_real @ A2 )
% 0.35/0.63         => ( ( groups1300246762558778688al_rat @ G @ A2 )
% 0.35/0.63            = ( plus_plus_rat @ ( groups1300246762558778688al_rat @ G @ ( minus_minus_set_real @ A2 @ B2 ) ) @ ( groups1300246762558778688al_rat @ G @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.subset_diff
% 0.35/0.63  thf(fact_6646_sum_Osubset__diff,axiom,
% 0.35/0.63      ! [B2: set_real,A2: set_real,G: real > nat] :
% 0.35/0.63        ( ( ord_less_eq_set_real @ B2 @ A2 )
% 0.35/0.63       => ( ( finite_finite_real @ A2 )
% 0.35/0.63         => ( ( groups1935376822645274424al_nat @ G @ A2 )
% 0.35/0.63            = ( plus_plus_nat @ ( groups1935376822645274424al_nat @ G @ ( minus_minus_set_real @ A2 @ B2 ) ) @ ( groups1935376822645274424al_nat @ G @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.subset_diff
% 0.35/0.63  thf(fact_6647_sum_Osubset__diff,axiom,
% 0.35/0.63      ! [B2: set_real,A2: set_real,G: real > int] :
% 0.35/0.63        ( ( ord_less_eq_set_real @ B2 @ A2 )
% 0.35/0.63       => ( ( finite_finite_real @ A2 )
% 0.35/0.63         => ( ( groups1932886352136224148al_int @ G @ A2 )
% 0.35/0.63            = ( plus_plus_int @ ( groups1932886352136224148al_int @ G @ ( minus_minus_set_real @ A2 @ B2 ) ) @ ( groups1932886352136224148al_int @ G @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.subset_diff
% 0.35/0.63  thf(fact_6648_sum_Osubset__diff,axiom,
% 0.35/0.63      ! [B2: set_real,A2: set_real,G: real > complex] :
% 0.35/0.63        ( ( ord_less_eq_set_real @ B2 @ A2 )
% 0.35/0.63       => ( ( finite_finite_real @ A2 )
% 0.35/0.63         => ( ( groups5754745047067104278omplex @ G @ A2 )
% 0.35/0.63            = ( plus_plus_complex @ ( groups5754745047067104278omplex @ G @ ( minus_minus_set_real @ A2 @ B2 ) ) @ ( groups5754745047067104278omplex @ G @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.subset_diff
% 0.35/0.63  thf(fact_6649_sum_Osubset__diff,axiom,
% 0.35/0.63      ! [B2: set_nat,A2: set_nat,G: nat > rat] :
% 0.35/0.63        ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 0.35/0.63       => ( ( finite_finite_nat @ A2 )
% 0.35/0.63         => ( ( groups2906978787729119204at_rat @ G @ A2 )
% 0.35/0.63            = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups2906978787729119204at_rat @ G @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum.subset_diff
% 0.35/0.63  thf(fact_6650_sum__diff,axiom,
% 0.35/0.63      ! [A2: set_complex,B2: set_complex,F: complex > rat] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.63       => ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 0.35/0.63         => ( ( groups5058264527183730370ex_rat @ F @ ( minus_811609699411566653omplex @ A2 @ B2 ) )
% 0.35/0.63            = ( minus_minus_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ F @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_diff
% 0.35/0.63  thf(fact_6651_sum__diff,axiom,
% 0.35/0.63      ! [A2: set_complex,B2: set_complex,F: complex > int] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.63       => ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 0.35/0.63         => ( ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ B2 ) )
% 0.35/0.63            = ( minus_minus_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ F @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_diff
% 0.35/0.63  thf(fact_6652_sum__diff,axiom,
% 0.35/0.63      ! [A2: set_real,B2: set_real,F: real > rat] :
% 0.35/0.63        ( ( finite_finite_real @ A2 )
% 0.35/0.63       => ( ( ord_less_eq_set_real @ B2 @ A2 )
% 0.35/0.63         => ( ( groups1300246762558778688al_rat @ F @ ( minus_minus_set_real @ A2 @ B2 ) )
% 0.35/0.63            = ( minus_minus_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ F @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_diff
% 0.35/0.63  thf(fact_6653_sum__diff,axiom,
% 0.35/0.63      ! [A2: set_real,B2: set_real,F: real > int] :
% 0.35/0.63        ( ( finite_finite_real @ A2 )
% 0.35/0.63       => ( ( ord_less_eq_set_real @ B2 @ A2 )
% 0.35/0.63         => ( ( groups1932886352136224148al_int @ F @ ( minus_minus_set_real @ A2 @ B2 ) )
% 0.35/0.63            = ( minus_minus_int @ ( groups1932886352136224148al_int @ F @ A2 ) @ ( groups1932886352136224148al_int @ F @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_diff
% 0.35/0.63  thf(fact_6654_sum__diff,axiom,
% 0.35/0.63      ! [A2: set_nat,B2: set_nat,F: nat > rat] :
% 0.35/0.63        ( ( finite_finite_nat @ A2 )
% 0.35/0.63       => ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 0.35/0.63         => ( ( groups2906978787729119204at_rat @ F @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 0.35/0.63            = ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ F @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_diff
% 0.35/0.63  thf(fact_6655_sum__diff,axiom,
% 0.35/0.63      ! [A2: set_nat,B2: set_nat,F: nat > int] :
% 0.35/0.63        ( ( finite_finite_nat @ A2 )
% 0.35/0.63       => ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 0.35/0.63         => ( ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 0.35/0.63            = ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ F @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_diff
% 0.35/0.63  thf(fact_6656_sum__diff,axiom,
% 0.35/0.63      ! [A2: set_int,B2: set_int,F: int > int] :
% 0.35/0.63        ( ( finite_finite_int @ A2 )
% 0.35/0.63       => ( ( ord_less_eq_set_int @ B2 @ A2 )
% 0.35/0.63         => ( ( groups4538972089207619220nt_int @ F @ ( minus_minus_set_int @ A2 @ B2 ) )
% 0.35/0.63            = ( minus_minus_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ F @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_diff
% 0.35/0.63  thf(fact_6657_sum__diff,axiom,
% 0.35/0.63      ! [A2: set_complex,B2: set_complex,F: complex > complex] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.63       => ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 0.35/0.63         => ( ( groups7754918857620584856omplex @ F @ ( minus_811609699411566653omplex @ A2 @ B2 ) )
% 0.35/0.63            = ( minus_minus_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ ( groups7754918857620584856omplex @ F @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_diff
% 0.35/0.63  thf(fact_6658_sum__diff,axiom,
% 0.35/0.63      ! [A2: set_nat,B2: set_nat,F: nat > real] :
% 0.35/0.63        ( ( finite_finite_nat @ A2 )
% 0.35/0.63       => ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 0.35/0.63         => ( ( groups6591440286371151544t_real @ F @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 0.35/0.63            = ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ F @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_diff
% 0.35/0.63  thf(fact_6659_sum__diff,axiom,
% 0.35/0.63      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > rat] :
% 0.35/0.63        ( ( finite6177210948735845034at_nat @ A2 )
% 0.35/0.63       => ( ( ord_le3146513528884898305at_nat @ B2 @ A2 )
% 0.35/0.63         => ( ( groups342789780944988191at_rat @ F @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) )
% 0.35/0.63            = ( minus_minus_rat @ ( groups342789780944988191at_rat @ F @ A2 ) @ ( groups342789780944988191at_rat @ F @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_diff
% 0.35/0.63  thf(fact_6660_exp__ge__add__one__self__aux,axiom,
% 0.35/0.63      ! [X: real] :
% 0.35/0.63        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.63       => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X ) @ ( exp_real @ X ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % exp_ge_add_one_self_aux
% 0.35/0.63  thf(fact_6661_lemma__exp__total,axiom,
% 0.35/0.63      ! [Y2: real] :
% 0.35/0.63        ( ( ord_less_eq_real @ one_one_real @ Y2 )
% 0.35/0.63       => ? [X3: real] :
% 0.35/0.63            ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.35/0.63            & ( ord_less_eq_real @ X3 @ ( minus_minus_real @ Y2 @ one_one_real ) )
% 0.35/0.63            & ( ( exp_real @ X3 )
% 0.35/0.63              = Y2 ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % lemma_exp_total
% 0.35/0.63  thf(fact_6662_ln__ge__iff,axiom,
% 0.35/0.63      ! [X: real,Y2: real] :
% 0.35/0.63        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.63       => ( ( ord_less_eq_real @ Y2 @ ( ln_ln_real @ X ) )
% 0.35/0.63          = ( ord_less_eq_real @ ( exp_real @ Y2 ) @ X ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % ln_ge_iff
% 0.35/0.63  thf(fact_6663_ln__x__over__x__mono,axiom,
% 0.35/0.63      ! [X: real,Y2: real] :
% 0.35/0.63        ( ( ord_less_eq_real @ ( exp_real @ one_one_real ) @ X )
% 0.35/0.63       => ( ( ord_less_eq_real @ X @ Y2 )
% 0.35/0.63         => ( ord_less_eq_real @ ( divide_divide_real @ ( ln_ln_real @ Y2 ) @ Y2 ) @ ( divide_divide_real @ ( ln_ln_real @ X ) @ X ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % ln_x_over_x_mono
% 0.35/0.63  thf(fact_6664_take__bit__Suc__bit0,axiom,
% 0.35/0.63      ! [N: nat,K: num] :
% 0.35/0.63        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 0.35/0.63        = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_Suc_bit0
% 0.35/0.63  thf(fact_6665_take__bit__Suc__bit0,axiom,
% 0.35/0.63      ! [N: nat,K: num] :
% 0.35/0.63        ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 0.35/0.63        = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_Suc_bit0
% 0.35/0.63  thf(fact_6666_take__bit__eq__mod,axiom,
% 0.35/0.63      ( bit_se2923211474154528505it_int
% 0.35/0.63      = ( ^ [N2: nat,A3: int] : ( modulo_modulo_int @ A3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_eq_mod
% 0.35/0.63  thf(fact_6667_take__bit__eq__mod,axiom,
% 0.35/0.63      ( bit_se2925701944663578781it_nat
% 0.35/0.63      = ( ^ [N2: nat,A3: nat] : ( modulo_modulo_nat @ A3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % take_bit_eq_mod
% 0.35/0.63  thf(fact_6668_sum__mono2,axiom,
% 0.35/0.63      ! [B2: set_int,A2: set_int,F: int > real] :
% 0.35/0.63        ( ( finite_finite_int @ B2 )
% 0.35/0.63       => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 0.35/0.63         => ( ! [B3: int] :
% 0.35/0.63                ( ( member_int @ B3 @ ( minus_minus_set_int @ B2 @ A2 ) )
% 0.35/0.63               => ( ord_less_eq_real @ zero_zero_real @ ( F @ B3 ) ) )
% 0.35/0.63           => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ F @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_mono2
% 0.35/0.63  thf(fact_6669_sum__mono2,axiom,
% 0.35/0.63      ! [B2: set_complex,A2: set_complex,F: complex > real] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ B2 )
% 0.35/0.63       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 0.35/0.63         => ( ! [B3: complex] :
% 0.35/0.63                ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 0.35/0.63               => ( ord_less_eq_real @ zero_zero_real @ ( F @ B3 ) ) )
% 0.35/0.63           => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_mono2
% 0.35/0.63  thf(fact_6670_sum__mono2,axiom,
% 0.35/0.63      ! [B2: set_int,A2: set_int,F: int > rat] :
% 0.35/0.63        ( ( finite_finite_int @ B2 )
% 0.35/0.63       => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 0.35/0.63         => ( ! [B3: int] :
% 0.35/0.63                ( ( member_int @ B3 @ ( minus_minus_set_int @ B2 @ A2 ) )
% 0.35/0.63               => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B3 ) ) )
% 0.35/0.63           => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ F @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_mono2
% 0.35/0.63  thf(fact_6671_sum__mono2,axiom,
% 0.35/0.63      ! [B2: set_complex,A2: set_complex,F: complex > rat] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ B2 )
% 0.35/0.63       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 0.35/0.63         => ( ! [B3: complex] :
% 0.35/0.63                ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 0.35/0.63               => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B3 ) ) )
% 0.35/0.63           => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ F @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_mono2
% 0.35/0.63  thf(fact_6672_sum__mono2,axiom,
% 0.35/0.63      ! [B2: set_int,A2: set_int,F: int > nat] :
% 0.35/0.63        ( ( finite_finite_int @ B2 )
% 0.35/0.63       => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 0.35/0.63         => ( ! [B3: int] :
% 0.35/0.63                ( ( member_int @ B3 @ ( minus_minus_set_int @ B2 @ A2 ) )
% 0.35/0.63               => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B3 ) ) )
% 0.35/0.63           => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ F @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_mono2
% 0.35/0.63  thf(fact_6673_sum__mono2,axiom,
% 0.35/0.63      ! [B2: set_complex,A2: set_complex,F: complex > nat] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ B2 )
% 0.35/0.63       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 0.35/0.63         => ( ! [B3: complex] :
% 0.35/0.63                ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 0.35/0.63               => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B3 ) ) )
% 0.35/0.63           => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_mono2
% 0.35/0.63  thf(fact_6674_sum__mono2,axiom,
% 0.35/0.63      ! [B2: set_complex,A2: set_complex,F: complex > int] :
% 0.35/0.63        ( ( finite3207457112153483333omplex @ B2 )
% 0.35/0.63       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 0.35/0.63         => ( ! [B3: complex] :
% 0.35/0.63                ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 0.35/0.63               => ( ord_less_eq_int @ zero_zero_int @ ( F @ B3 ) ) )
% 0.35/0.63           => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ F @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_mono2
% 0.35/0.63  thf(fact_6675_sum__mono2,axiom,
% 0.35/0.63      ! [B2: set_real,A2: set_real,F: real > real] :
% 0.35/0.63        ( ( finite_finite_real @ B2 )
% 0.35/0.63       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 0.35/0.63         => ( ! [B3: real] :
% 0.35/0.63                ( ( member_real @ B3 @ ( minus_minus_set_real @ B2 @ A2 ) )
% 0.35/0.63               => ( ord_less_eq_real @ zero_zero_real @ ( F @ B3 ) ) )
% 0.35/0.63           => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ F @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_mono2
% 0.35/0.63  thf(fact_6676_sum__mono2,axiom,
% 0.35/0.63      ! [B2: set_real,A2: set_real,F: real > rat] :
% 0.35/0.63        ( ( finite_finite_real @ B2 )
% 0.35/0.63       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 0.35/0.63         => ( ! [B3: real] :
% 0.35/0.63                ( ( member_real @ B3 @ ( minus_minus_set_real @ B2 @ A2 ) )
% 0.35/0.63               => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B3 ) ) )
% 0.35/0.63           => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ F @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_mono2
% 0.35/0.63  thf(fact_6677_sum__mono2,axiom,
% 0.35/0.63      ! [B2: set_real,A2: set_real,F: real > nat] :
% 0.35/0.63        ( ( finite_finite_real @ B2 )
% 0.35/0.63       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 0.35/0.63         => ( ! [B3: real] :
% 0.35/0.63                ( ( member_real @ B3 @ ( minus_minus_set_real @ B2 @ A2 ) )
% 0.35/0.63               => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B3 ) ) )
% 0.35/0.63           => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ F @ B2 ) ) ) ) ) ).
% 0.35/0.63  
% 0.35/0.63  % sum_mono2
% 0.35/0.63  thf(fact_6678_take__bit__nat__eq__self__iff,axiom,
% 0.35/0.63      ! [N: nat,M: nat] :
% 0.35/0.64        ( ( ( bit_se2925701944663578781it_nat @ N @ M )
% 0.35/0.64          = M )
% 0.35/0.64        = ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_nat_eq_self_iff
% 0.35/0.64  thf(fact_6679_take__bit__nat__less__exp,axiom,
% 0.35/0.64      ! [N: nat,M: nat] : ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_nat_less_exp
% 0.35/0.64  thf(fact_6680_take__bit__nat__eq__self,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.64       => ( ( bit_se2925701944663578781it_nat @ N @ M )
% 0.35/0.64          = M ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_nat_eq_self
% 0.35/0.64  thf(fact_6681_sum_Oinsert__remove,axiom,
% 0.35/0.64      ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > real,X: vEBT_VEBT] :
% 0.35/0.64        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.35/0.64       => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 0.35/0.64          = ( plus_plus_real @ ( G @ X ) @ ( groups2240296850493347238T_real @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.insert_remove
% 0.35/0.64  thf(fact_6682_sum_Oinsert__remove,axiom,
% 0.35/0.64      ! [A2: set_complex,G: complex > real,X: complex] :
% 0.35/0.64        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.64       => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A2 ) )
% 0.35/0.64          = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.insert_remove
% 0.35/0.64  thf(fact_6683_sum_Oinsert__remove,axiom,
% 0.35/0.64      ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > rat,X: vEBT_VEBT] :
% 0.35/0.64        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.35/0.64       => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 0.35/0.64          = ( plus_plus_rat @ ( G @ X ) @ ( groups136491112297645522BT_rat @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.insert_remove
% 0.35/0.64  thf(fact_6684_sum_Oinsert__remove,axiom,
% 0.35/0.64      ! [A2: set_complex,G: complex > rat,X: complex] :
% 0.35/0.64        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.64       => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X @ A2 ) )
% 0.35/0.64          = ( plus_plus_rat @ ( G @ X ) @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.insert_remove
% 0.35/0.64  thf(fact_6685_sum_Oinsert__remove,axiom,
% 0.35/0.64      ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > nat,X: vEBT_VEBT] :
% 0.35/0.64        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.35/0.64       => ( ( groups771621172384141258BT_nat @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 0.35/0.64          = ( plus_plus_nat @ ( G @ X ) @ ( groups771621172384141258BT_nat @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.insert_remove
% 0.35/0.64  thf(fact_6686_sum_Oinsert__remove,axiom,
% 0.35/0.64      ! [A2: set_complex,G: complex > nat,X: complex] :
% 0.35/0.64        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.64       => ( ( groups5693394587270226106ex_nat @ G @ ( insert_complex @ X @ A2 ) )
% 0.35/0.64          = ( plus_plus_nat @ ( G @ X ) @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.insert_remove
% 0.35/0.64  thf(fact_6687_sum_Oinsert__remove,axiom,
% 0.35/0.64      ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > int,X: vEBT_VEBT] :
% 0.35/0.64        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.35/0.64       => ( ( groups769130701875090982BT_int @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 0.35/0.64          = ( plus_plus_int @ ( G @ X ) @ ( groups769130701875090982BT_int @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.insert_remove
% 0.35/0.64  thf(fact_6688_sum_Oinsert__remove,axiom,
% 0.35/0.64      ! [A2: set_complex,G: complex > int,X: complex] :
% 0.35/0.64        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.64       => ( ( groups5690904116761175830ex_int @ G @ ( insert_complex @ X @ A2 ) )
% 0.35/0.64          = ( plus_plus_int @ ( G @ X ) @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.insert_remove
% 0.35/0.64  thf(fact_6689_sum_Oinsert__remove,axiom,
% 0.35/0.64      ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > complex,X: vEBT_VEBT] :
% 0.35/0.64        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.35/0.64       => ( ( groups1794756597179926696omplex @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 0.35/0.64          = ( plus_plus_complex @ ( G @ X ) @ ( groups1794756597179926696omplex @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.insert_remove
% 0.35/0.64  thf(fact_6690_sum_Oinsert__remove,axiom,
% 0.35/0.64      ! [A2: set_int,G: int > real,X: int] :
% 0.35/0.64        ( ( finite_finite_int @ A2 )
% 0.35/0.64       => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X @ A2 ) )
% 0.35/0.64          = ( plus_plus_real @ ( G @ X ) @ ( groups8778361861064173332t_real @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.insert_remove
% 0.35/0.64  thf(fact_6691_sum_Oremove,axiom,
% 0.35/0.64      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > real] :
% 0.35/0.64        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.35/0.64       => ( ( member_VEBT_VEBT @ X @ A2 )
% 0.35/0.64         => ( ( groups2240296850493347238T_real @ G @ A2 )
% 0.35/0.64            = ( plus_plus_real @ ( G @ X ) @ ( groups2240296850493347238T_real @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.remove
% 0.35/0.64  thf(fact_6692_sum_Oremove,axiom,
% 0.35/0.64      ! [A2: set_complex,X: complex,G: complex > real] :
% 0.35/0.64        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.64       => ( ( member_complex @ X @ A2 )
% 0.35/0.64         => ( ( groups5808333547571424918x_real @ G @ A2 )
% 0.35/0.64            = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.remove
% 0.35/0.64  thf(fact_6693_sum_Oremove,axiom,
% 0.35/0.64      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 0.35/0.64        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.35/0.64       => ( ( member_VEBT_VEBT @ X @ A2 )
% 0.35/0.64         => ( ( groups136491112297645522BT_rat @ G @ A2 )
% 0.35/0.64            = ( plus_plus_rat @ ( G @ X ) @ ( groups136491112297645522BT_rat @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.remove
% 0.35/0.64  thf(fact_6694_sum_Oremove,axiom,
% 0.35/0.64      ! [A2: set_complex,X: complex,G: complex > rat] :
% 0.35/0.64        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.64       => ( ( member_complex @ X @ A2 )
% 0.35/0.64         => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 0.35/0.64            = ( plus_plus_rat @ ( G @ X ) @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.remove
% 0.35/0.64  thf(fact_6695_sum_Oremove,axiom,
% 0.35/0.64      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > nat] :
% 0.35/0.64        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.35/0.64       => ( ( member_VEBT_VEBT @ X @ A2 )
% 0.35/0.64         => ( ( groups771621172384141258BT_nat @ G @ A2 )
% 0.35/0.64            = ( plus_plus_nat @ ( G @ X ) @ ( groups771621172384141258BT_nat @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.remove
% 0.35/0.64  thf(fact_6696_sum_Oremove,axiom,
% 0.35/0.64      ! [A2: set_complex,X: complex,G: complex > nat] :
% 0.35/0.64        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.64       => ( ( member_complex @ X @ A2 )
% 0.35/0.64         => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 0.35/0.64            = ( plus_plus_nat @ ( G @ X ) @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.remove
% 0.35/0.64  thf(fact_6697_sum_Oremove,axiom,
% 0.35/0.64      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > int] :
% 0.35/0.64        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.35/0.64       => ( ( member_VEBT_VEBT @ X @ A2 )
% 0.35/0.64         => ( ( groups769130701875090982BT_int @ G @ A2 )
% 0.35/0.64            = ( plus_plus_int @ ( G @ X ) @ ( groups769130701875090982BT_int @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.remove
% 0.35/0.64  thf(fact_6698_sum_Oremove,axiom,
% 0.35/0.64      ! [A2: set_complex,X: complex,G: complex > int] :
% 0.35/0.64        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.64       => ( ( member_complex @ X @ A2 )
% 0.35/0.64         => ( ( groups5690904116761175830ex_int @ G @ A2 )
% 0.35/0.64            = ( plus_plus_int @ ( G @ X ) @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.remove
% 0.35/0.64  thf(fact_6699_sum_Oremove,axiom,
% 0.35/0.64      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > complex] :
% 0.35/0.64        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.35/0.64       => ( ( member_VEBT_VEBT @ X @ A2 )
% 0.35/0.64         => ( ( groups1794756597179926696omplex @ G @ A2 )
% 0.35/0.64            = ( plus_plus_complex @ ( G @ X ) @ ( groups1794756597179926696omplex @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.remove
% 0.35/0.64  thf(fact_6700_sum_Oremove,axiom,
% 0.35/0.64      ! [A2: set_int,X: int,G: int > real] :
% 0.35/0.64        ( ( finite_finite_int @ A2 )
% 0.35/0.64       => ( ( member_int @ X @ A2 )
% 0.35/0.64         => ( ( groups8778361861064173332t_real @ G @ A2 )
% 0.35/0.64            = ( plus_plus_real @ ( G @ X ) @ ( groups8778361861064173332t_real @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.remove
% 0.35/0.64  thf(fact_6701_sum__diff1,axiom,
% 0.35/0.64      ! [A2: set_VEBT_VEBT,A: vEBT_VEBT,F: vEBT_VEBT > rat] :
% 0.35/0.64        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.35/0.64       => ( ( ( member_VEBT_VEBT @ A @ A2 )
% 0.35/0.64           => ( ( groups136491112297645522BT_rat @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.35/0.64              = ( minus_minus_rat @ ( groups136491112297645522BT_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.35/0.64          & ( ~ ( member_VEBT_VEBT @ A @ A2 )
% 0.35/0.64           => ( ( groups136491112297645522BT_rat @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.35/0.64              = ( groups136491112297645522BT_rat @ F @ A2 ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_diff1
% 0.35/0.64  thf(fact_6702_sum__diff1,axiom,
% 0.35/0.64      ! [A2: set_complex,A: complex,F: complex > rat] :
% 0.35/0.64        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.64       => ( ( ( member_complex @ A @ A2 )
% 0.35/0.64           => ( ( groups5058264527183730370ex_rat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.35/0.64              = ( minus_minus_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.35/0.64          & ( ~ ( member_complex @ A @ A2 )
% 0.35/0.64           => ( ( groups5058264527183730370ex_rat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.35/0.64              = ( groups5058264527183730370ex_rat @ F @ A2 ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_diff1
% 0.35/0.64  thf(fact_6703_sum__diff1,axiom,
% 0.35/0.64      ! [A2: set_int,A: int,F: int > rat] :
% 0.35/0.64        ( ( finite_finite_int @ A2 )
% 0.35/0.64       => ( ( ( member_int @ A @ A2 )
% 0.35/0.64           => ( ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.35/0.64              = ( minus_minus_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.35/0.64          & ( ~ ( member_int @ A @ A2 )
% 0.35/0.64           => ( ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.35/0.64              = ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_diff1
% 0.35/0.64  thf(fact_6704_sum__diff1,axiom,
% 0.35/0.64      ! [A2: set_real,A: real,F: real > rat] :
% 0.35/0.64        ( ( finite_finite_real @ A2 )
% 0.35/0.64       => ( ( ( member_real @ A @ A2 )
% 0.35/0.64           => ( ( groups1300246762558778688al_rat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.35/0.64              = ( minus_minus_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.35/0.64          & ( ~ ( member_real @ A @ A2 )
% 0.35/0.64           => ( ( groups1300246762558778688al_rat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.35/0.64              = ( groups1300246762558778688al_rat @ F @ A2 ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_diff1
% 0.35/0.64  thf(fact_6705_sum__diff1,axiom,
% 0.35/0.64      ! [A2: set_VEBT_VEBT,A: vEBT_VEBT,F: vEBT_VEBT > int] :
% 0.35/0.64        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.35/0.64       => ( ( ( member_VEBT_VEBT @ A @ A2 )
% 0.35/0.64           => ( ( groups769130701875090982BT_int @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.35/0.64              = ( minus_minus_int @ ( groups769130701875090982BT_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.35/0.64          & ( ~ ( member_VEBT_VEBT @ A @ A2 )
% 0.35/0.64           => ( ( groups769130701875090982BT_int @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.35/0.64              = ( groups769130701875090982BT_int @ F @ A2 ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_diff1
% 0.35/0.64  thf(fact_6706_sum__diff1,axiom,
% 0.35/0.64      ! [A2: set_complex,A: complex,F: complex > int] :
% 0.35/0.64        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.64       => ( ( ( member_complex @ A @ A2 )
% 0.35/0.64           => ( ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.35/0.64              = ( minus_minus_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.35/0.64          & ( ~ ( member_complex @ A @ A2 )
% 0.35/0.64           => ( ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.35/0.64              = ( groups5690904116761175830ex_int @ F @ A2 ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_diff1
% 0.35/0.64  thf(fact_6707_sum__diff1,axiom,
% 0.35/0.64      ! [A2: set_real,A: real,F: real > int] :
% 0.35/0.64        ( ( finite_finite_real @ A2 )
% 0.35/0.64       => ( ( ( member_real @ A @ A2 )
% 0.35/0.64           => ( ( groups1932886352136224148al_int @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.35/0.64              = ( minus_minus_int @ ( groups1932886352136224148al_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.35/0.64          & ( ~ ( member_real @ A @ A2 )
% 0.35/0.64           => ( ( groups1932886352136224148al_int @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.35/0.64              = ( groups1932886352136224148al_int @ F @ A2 ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_diff1
% 0.35/0.64  thf(fact_6708_sum__diff1,axiom,
% 0.35/0.64      ! [A2: set_nat,A: nat,F: nat > rat] :
% 0.35/0.64        ( ( finite_finite_nat @ A2 )
% 0.35/0.64       => ( ( ( member_nat @ A @ A2 )
% 0.35/0.64           => ( ( groups2906978787729119204at_rat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.35/0.64              = ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.35/0.64          & ( ~ ( member_nat @ A @ A2 )
% 0.35/0.64           => ( ( groups2906978787729119204at_rat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.35/0.64              = ( groups2906978787729119204at_rat @ F @ A2 ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_diff1
% 0.35/0.64  thf(fact_6709_sum__diff1,axiom,
% 0.35/0.64      ! [A2: set_nat,A: nat,F: nat > int] :
% 0.35/0.64        ( ( finite_finite_nat @ A2 )
% 0.35/0.64       => ( ( ( member_nat @ A @ A2 )
% 0.35/0.64           => ( ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.35/0.64              = ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.35/0.64          & ( ~ ( member_nat @ A @ A2 )
% 0.35/0.64           => ( ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.35/0.64              = ( groups3539618377306564664at_int @ F @ A2 ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_diff1
% 0.35/0.64  thf(fact_6710_sum__diff1,axiom,
% 0.35/0.64      ! [A2: set_int,A: int,F: int > int] :
% 0.35/0.64        ( ( finite_finite_int @ A2 )
% 0.35/0.64       => ( ( ( member_int @ A @ A2 )
% 0.35/0.64           => ( ( groups4538972089207619220nt_int @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.35/0.64              = ( minus_minus_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.35/0.64          & ( ~ ( member_int @ A @ A2 )
% 0.35/0.64           => ( ( groups4538972089207619220nt_int @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.35/0.64              = ( groups4538972089207619220nt_int @ F @ A2 ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_diff1
% 0.35/0.64  thf(fact_6711_take__bit__nat__def,axiom,
% 0.35/0.64      ( bit_se2925701944663578781it_nat
% 0.35/0.64      = ( ^ [N2: nat,M6: nat] : ( modulo_modulo_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_nat_def
% 0.35/0.64  thf(fact_6712_exp__le,axiom,
% 0.35/0.64      ord_less_eq_real @ ( exp_real @ one_one_real ) @ ( numeral_numeral_real @ ( bit1 @ one ) ) ).
% 0.35/0.64  
% 0.35/0.64  % exp_le
% 0.35/0.64  thf(fact_6713_take__bit__int__less__exp,axiom,
% 0.35/0.64      ! [N: nat,K: int] : ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_int_less_exp
% 0.35/0.64  thf(fact_6714_take__bit__int__def,axiom,
% 0.35/0.64      ( bit_se2923211474154528505it_int
% 0.35/0.64      = ( ^ [N2: nat,K3: int] : ( modulo_modulo_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_int_def
% 0.35/0.64  thf(fact_6715_even__abs__add__iff,axiom,
% 0.35/0.64      ! [K: int,L2: int] :
% 0.35/0.64        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ ( abs_abs_int @ K ) @ L2 ) )
% 0.35/0.64        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % even_abs_add_iff
% 0.35/0.64  thf(fact_6716_even__add__abs__iff,axiom,
% 0.35/0.64      ! [K: int,L2: int] :
% 0.35/0.64        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ ( abs_abs_int @ L2 ) ) )
% 0.35/0.64        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % even_add_abs_iff
% 0.35/0.64  thf(fact_6717_sum_Odelta__remove,axiom,
% 0.35/0.64      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > real,C: vEBT_VEBT > real] :
% 0.35/0.64        ( ( finite5795047828879050333T_VEBT @ S2 )
% 0.35/0.64       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 0.35/0.64           => ( ( groups2240296850493347238T_real
% 0.35/0.64                @ ^ [K3: vEBT_VEBT] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.64                @ S2 )
% 0.35/0.64              = ( plus_plus_real @ ( B @ A ) @ ( groups2240296850493347238T_real @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 0.35/0.64          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 0.35/0.64           => ( ( groups2240296850493347238T_real
% 0.35/0.64                @ ^ [K3: vEBT_VEBT] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.64                @ S2 )
% 0.35/0.64              = ( groups2240296850493347238T_real @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.delta_remove
% 0.35/0.64  thf(fact_6718_sum_Odelta__remove,axiom,
% 0.35/0.64      ! [S2: set_complex,A: complex,B: complex > real,C: complex > real] :
% 0.35/0.64        ( ( finite3207457112153483333omplex @ S2 )
% 0.35/0.64       => ( ( ( member_complex @ A @ S2 )
% 0.35/0.64           => ( ( groups5808333547571424918x_real
% 0.35/0.64                @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.64                @ S2 )
% 0.35/0.64              = ( plus_plus_real @ ( B @ A ) @ ( groups5808333547571424918x_real @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 0.35/0.64          & ( ~ ( member_complex @ A @ S2 )
% 0.35/0.64           => ( ( groups5808333547571424918x_real
% 0.35/0.64                @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.64                @ S2 )
% 0.35/0.64              = ( groups5808333547571424918x_real @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.delta_remove
% 0.35/0.64  thf(fact_6719_sum_Odelta__remove,axiom,
% 0.35/0.64      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > rat,C: vEBT_VEBT > rat] :
% 0.35/0.64        ( ( finite5795047828879050333T_VEBT @ S2 )
% 0.35/0.64       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 0.35/0.64           => ( ( groups136491112297645522BT_rat
% 0.35/0.64                @ ^ [K3: vEBT_VEBT] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.64                @ S2 )
% 0.35/0.64              = ( plus_plus_rat @ ( B @ A ) @ ( groups136491112297645522BT_rat @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 0.35/0.64          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 0.35/0.64           => ( ( groups136491112297645522BT_rat
% 0.35/0.64                @ ^ [K3: vEBT_VEBT] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.64                @ S2 )
% 0.35/0.64              = ( groups136491112297645522BT_rat @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.delta_remove
% 0.35/0.64  thf(fact_6720_sum_Odelta__remove,axiom,
% 0.35/0.64      ! [S2: set_complex,A: complex,B: complex > rat,C: complex > rat] :
% 0.35/0.64        ( ( finite3207457112153483333omplex @ S2 )
% 0.35/0.64       => ( ( ( member_complex @ A @ S2 )
% 0.35/0.64           => ( ( groups5058264527183730370ex_rat
% 0.35/0.64                @ ^ [K3: complex] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.64                @ S2 )
% 0.35/0.64              = ( plus_plus_rat @ ( B @ A ) @ ( groups5058264527183730370ex_rat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 0.35/0.64          & ( ~ ( member_complex @ A @ S2 )
% 0.35/0.64           => ( ( groups5058264527183730370ex_rat
% 0.35/0.64                @ ^ [K3: complex] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.64                @ S2 )
% 0.35/0.64              = ( groups5058264527183730370ex_rat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.delta_remove
% 0.35/0.64  thf(fact_6721_sum_Odelta__remove,axiom,
% 0.35/0.64      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > nat,C: vEBT_VEBT > nat] :
% 0.35/0.64        ( ( finite5795047828879050333T_VEBT @ S2 )
% 0.35/0.64       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 0.35/0.64           => ( ( groups771621172384141258BT_nat
% 0.35/0.64                @ ^ [K3: vEBT_VEBT] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.64                @ S2 )
% 0.35/0.64              = ( plus_plus_nat @ ( B @ A ) @ ( groups771621172384141258BT_nat @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 0.35/0.64          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 0.35/0.64           => ( ( groups771621172384141258BT_nat
% 0.35/0.64                @ ^ [K3: vEBT_VEBT] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.64                @ S2 )
% 0.35/0.64              = ( groups771621172384141258BT_nat @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.delta_remove
% 0.35/0.64  thf(fact_6722_sum_Odelta__remove,axiom,
% 0.35/0.64      ! [S2: set_complex,A: complex,B: complex > nat,C: complex > nat] :
% 0.35/0.64        ( ( finite3207457112153483333omplex @ S2 )
% 0.35/0.64       => ( ( ( member_complex @ A @ S2 )
% 0.35/0.64           => ( ( groups5693394587270226106ex_nat
% 0.35/0.64                @ ^ [K3: complex] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.64                @ S2 )
% 0.35/0.64              = ( plus_plus_nat @ ( B @ A ) @ ( groups5693394587270226106ex_nat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 0.35/0.64          & ( ~ ( member_complex @ A @ S2 )
% 0.35/0.64           => ( ( groups5693394587270226106ex_nat
% 0.35/0.64                @ ^ [K3: complex] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.64                @ S2 )
% 0.35/0.64              = ( groups5693394587270226106ex_nat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.delta_remove
% 0.35/0.64  thf(fact_6723_sum_Odelta__remove,axiom,
% 0.35/0.64      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > int,C: vEBT_VEBT > int] :
% 0.35/0.64        ( ( finite5795047828879050333T_VEBT @ S2 )
% 0.35/0.64       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 0.35/0.64           => ( ( groups769130701875090982BT_int
% 0.35/0.64                @ ^ [K3: vEBT_VEBT] : ( if_int @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.64                @ S2 )
% 0.35/0.64              = ( plus_plus_int @ ( B @ A ) @ ( groups769130701875090982BT_int @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 0.35/0.64          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 0.35/0.64           => ( ( groups769130701875090982BT_int
% 0.35/0.64                @ ^ [K3: vEBT_VEBT] : ( if_int @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.64                @ S2 )
% 0.35/0.64              = ( groups769130701875090982BT_int @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.delta_remove
% 0.35/0.64  thf(fact_6724_sum_Odelta__remove,axiom,
% 0.35/0.64      ! [S2: set_complex,A: complex,B: complex > int,C: complex > int] :
% 0.35/0.64        ( ( finite3207457112153483333omplex @ S2 )
% 0.35/0.64       => ( ( ( member_complex @ A @ S2 )
% 0.35/0.64           => ( ( groups5690904116761175830ex_int
% 0.35/0.64                @ ^ [K3: complex] : ( if_int @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.64                @ S2 )
% 0.35/0.64              = ( plus_plus_int @ ( B @ A ) @ ( groups5690904116761175830ex_int @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 0.35/0.64          & ( ~ ( member_complex @ A @ S2 )
% 0.35/0.64           => ( ( groups5690904116761175830ex_int
% 0.35/0.64                @ ^ [K3: complex] : ( if_int @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.64                @ S2 )
% 0.35/0.64              = ( groups5690904116761175830ex_int @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.delta_remove
% 0.35/0.64  thf(fact_6725_sum_Odelta__remove,axiom,
% 0.35/0.64      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > complex,C: vEBT_VEBT > complex] :
% 0.35/0.64        ( ( finite5795047828879050333T_VEBT @ S2 )
% 0.35/0.64       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 0.35/0.64           => ( ( groups1794756597179926696omplex
% 0.35/0.64                @ ^ [K3: vEBT_VEBT] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.64                @ S2 )
% 0.35/0.64              = ( plus_plus_complex @ ( B @ A ) @ ( groups1794756597179926696omplex @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 0.35/0.64          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 0.35/0.64           => ( ( groups1794756597179926696omplex
% 0.35/0.64                @ ^ [K3: vEBT_VEBT] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.64                @ S2 )
% 0.35/0.64              = ( groups1794756597179926696omplex @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.delta_remove
% 0.35/0.64  thf(fact_6726_sum_Odelta__remove,axiom,
% 0.35/0.64      ! [S2: set_int,A: int,B: int > real,C: int > real] :
% 0.35/0.64        ( ( finite_finite_int @ S2 )
% 0.35/0.64       => ( ( ( member_int @ A @ S2 )
% 0.35/0.64           => ( ( groups8778361861064173332t_real
% 0.35/0.64                @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.64                @ S2 )
% 0.35/0.64              = ( plus_plus_real @ ( B @ A ) @ ( groups8778361861064173332t_real @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 0.35/0.64          & ( ~ ( member_int @ A @ S2 )
% 0.35/0.64           => ( ( groups8778361861064173332t_real
% 0.35/0.64                @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.64                @ S2 )
% 0.35/0.64              = ( groups8778361861064173332t_real @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.delta_remove
% 0.35/0.64  thf(fact_6727_tanh__altdef,axiom,
% 0.35/0.64      ( tanh_real
% 0.35/0.64      = ( ^ [X2: real] : ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X2 ) @ ( exp_real @ ( uminus_uminus_real @ X2 ) ) ) @ ( plus_plus_real @ ( exp_real @ X2 ) @ ( exp_real @ ( uminus_uminus_real @ X2 ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % tanh_altdef
% 0.35/0.64  thf(fact_6728_tanh__altdef,axiom,
% 0.35/0.64      ( tanh_complex
% 0.35/0.64      = ( ^ [X2: complex] : ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( exp_complex @ X2 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X2 ) ) ) @ ( plus_plus_complex @ ( exp_complex @ X2 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X2 ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % tanh_altdef
% 0.35/0.64  thf(fact_6729_num_Osize__gen_I1_J,axiom,
% 0.35/0.64      ( ( size_num @ one )
% 0.35/0.64      = zero_zero_nat ) ).
% 0.35/0.64  
% 0.35/0.64  % num.size_gen(1)
% 0.35/0.64  thf(fact_6730_take__bit__eq__0__iff,axiom,
% 0.35/0.64      ! [N: nat,A: code_integer] :
% 0.35/0.64        ( ( ( bit_se1745604003318907178nteger @ N @ A )
% 0.35/0.64          = zero_z3403309356797280102nteger )
% 0.35/0.64        = ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_eq_0_iff
% 0.35/0.64  thf(fact_6731_take__bit__eq__0__iff,axiom,
% 0.35/0.64      ! [N: nat,A: int] :
% 0.35/0.64        ( ( ( bit_se2923211474154528505it_int @ N @ A )
% 0.35/0.64          = zero_zero_int )
% 0.35/0.64        = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_eq_0_iff
% 0.35/0.64  thf(fact_6732_take__bit__eq__0__iff,axiom,
% 0.35/0.64      ! [N: nat,A: nat] :
% 0.35/0.64        ( ( ( bit_se2925701944663578781it_nat @ N @ A )
% 0.35/0.64          = zero_zero_nat )
% 0.35/0.64        = ( dvd_dvd_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_eq_0_iff
% 0.35/0.64  thf(fact_6733_sum__strict__mono2,axiom,
% 0.35/0.64      ! [B2: set_int,A2: set_int,B: int,F: int > real] :
% 0.35/0.64        ( ( finite_finite_int @ B2 )
% 0.35/0.64       => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 0.35/0.64         => ( ( member_int @ B @ ( minus_minus_set_int @ B2 @ A2 ) )
% 0.35/0.64           => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 0.35/0.64             => ( ! [X3: int] :
% 0.35/0.64                    ( ( member_int @ X3 @ B2 )
% 0.35/0.64                   => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 0.35/0.64               => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ F @ B2 ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_strict_mono2
% 0.35/0.64  thf(fact_6734_sum__strict__mono2,axiom,
% 0.35/0.64      ! [B2: set_complex,A2: set_complex,B: complex,F: complex > real] :
% 0.35/0.64        ( ( finite3207457112153483333omplex @ B2 )
% 0.35/0.64       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 0.35/0.64         => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 0.35/0.64           => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 0.35/0.64             => ( ! [X3: complex] :
% 0.35/0.64                    ( ( member_complex @ X3 @ B2 )
% 0.35/0.64                   => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 0.35/0.64               => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B2 ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_strict_mono2
% 0.35/0.64  thf(fact_6735_sum__strict__mono2,axiom,
% 0.35/0.64      ! [B2: set_int,A2: set_int,B: int,F: int > rat] :
% 0.35/0.64        ( ( finite_finite_int @ B2 )
% 0.35/0.64       => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 0.35/0.64         => ( ( member_int @ B @ ( minus_minus_set_int @ B2 @ A2 ) )
% 0.35/0.64           => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 0.35/0.64             => ( ! [X3: int] :
% 0.35/0.64                    ( ( member_int @ X3 @ B2 )
% 0.35/0.64                   => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 0.35/0.64               => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ F @ B2 ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_strict_mono2
% 0.35/0.64  thf(fact_6736_sum__strict__mono2,axiom,
% 0.35/0.64      ! [B2: set_complex,A2: set_complex,B: complex,F: complex > rat] :
% 0.35/0.64        ( ( finite3207457112153483333omplex @ B2 )
% 0.35/0.64       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 0.35/0.64         => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 0.35/0.64           => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 0.35/0.64             => ( ! [X3: complex] :
% 0.35/0.64                    ( ( member_complex @ X3 @ B2 )
% 0.35/0.64                   => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 0.35/0.64               => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ F @ B2 ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_strict_mono2
% 0.35/0.64  thf(fact_6737_sum__strict__mono2,axiom,
% 0.35/0.64      ! [B2: set_int,A2: set_int,B: int,F: int > nat] :
% 0.35/0.64        ( ( finite_finite_int @ B2 )
% 0.35/0.64       => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 0.35/0.64         => ( ( member_int @ B @ ( minus_minus_set_int @ B2 @ A2 ) )
% 0.35/0.64           => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 0.35/0.64             => ( ! [X3: int] :
% 0.35/0.64                    ( ( member_int @ X3 @ B2 )
% 0.35/0.64                   => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 0.35/0.64               => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ F @ B2 ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_strict_mono2
% 0.35/0.64  thf(fact_6738_sum__strict__mono2,axiom,
% 0.35/0.64      ! [B2: set_complex,A2: set_complex,B: complex,F: complex > nat] :
% 0.35/0.64        ( ( finite3207457112153483333omplex @ B2 )
% 0.35/0.64       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 0.35/0.64         => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 0.35/0.64           => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 0.35/0.64             => ( ! [X3: complex] :
% 0.35/0.64                    ( ( member_complex @ X3 @ B2 )
% 0.35/0.64                   => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 0.35/0.64               => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B2 ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_strict_mono2
% 0.35/0.64  thf(fact_6739_sum__strict__mono2,axiom,
% 0.35/0.64      ! [B2: set_complex,A2: set_complex,B: complex,F: complex > int] :
% 0.35/0.64        ( ( finite3207457112153483333omplex @ B2 )
% 0.35/0.64       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 0.35/0.64         => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 0.35/0.64           => ( ( ord_less_int @ zero_zero_int @ ( F @ B ) )
% 0.35/0.64             => ( ! [X3: complex] :
% 0.35/0.64                    ( ( member_complex @ X3 @ B2 )
% 0.35/0.64                   => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 0.35/0.64               => ( ord_less_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ F @ B2 ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_strict_mono2
% 0.35/0.64  thf(fact_6740_sum__strict__mono2,axiom,
% 0.35/0.64      ! [B2: set_real,A2: set_real,B: real,F: real > real] :
% 0.35/0.64        ( ( finite_finite_real @ B2 )
% 0.35/0.64       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 0.35/0.64         => ( ( member_real @ B @ ( minus_minus_set_real @ B2 @ A2 ) )
% 0.35/0.64           => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 0.35/0.64             => ( ! [X3: real] :
% 0.35/0.64                    ( ( member_real @ X3 @ B2 )
% 0.35/0.64                   => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 0.35/0.64               => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ F @ B2 ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_strict_mono2
% 0.35/0.64  thf(fact_6741_sum__strict__mono2,axiom,
% 0.35/0.64      ! [B2: set_real,A2: set_real,B: real,F: real > rat] :
% 0.35/0.64        ( ( finite_finite_real @ B2 )
% 0.35/0.64       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 0.35/0.64         => ( ( member_real @ B @ ( minus_minus_set_real @ B2 @ A2 ) )
% 0.35/0.64           => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 0.35/0.64             => ( ! [X3: real] :
% 0.35/0.64                    ( ( member_real @ X3 @ B2 )
% 0.35/0.64                   => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 0.35/0.64               => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ F @ B2 ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_strict_mono2
% 0.35/0.64  thf(fact_6742_sum__strict__mono2,axiom,
% 0.35/0.64      ! [B2: set_real,A2: set_real,B: real,F: real > nat] :
% 0.35/0.64        ( ( finite_finite_real @ B2 )
% 0.35/0.64       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 0.35/0.64         => ( ( member_real @ B @ ( minus_minus_set_real @ B2 @ A2 ) )
% 0.35/0.64           => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 0.35/0.64             => ( ! [X3: real] :
% 0.35/0.64                    ( ( member_real @ X3 @ B2 )
% 0.35/0.64                   => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 0.35/0.64               => ( ord_less_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ F @ B2 ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_strict_mono2
% 0.35/0.64  thf(fact_6743_member__le__sum,axiom,
% 0.35/0.64      ! [I2: vEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 0.35/0.64        ( ( member_VEBT_VEBT @ I2 @ A2 )
% 0.35/0.64       => ( ! [X3: vEBT_VEBT] :
% 0.35/0.64              ( ( member_VEBT_VEBT @ X3 @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ I2 @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.35/0.64             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 0.35/0.64         => ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.35/0.64           => ( ord_less_eq_real @ ( F @ I2 ) @ ( groups2240296850493347238T_real @ F @ A2 ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % member_le_sum
% 0.35/0.64  thf(fact_6744_member__le__sum,axiom,
% 0.35/0.64      ! [I2: complex,A2: set_complex,F: complex > real] :
% 0.35/0.64        ( ( member_complex @ I2 @ A2 )
% 0.35/0.64       => ( ! [X3: complex] :
% 0.35/0.64              ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ I2 @ bot_bot_set_complex ) ) )
% 0.35/0.64             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 0.35/0.64         => ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.64           => ( ord_less_eq_real @ ( F @ I2 ) @ ( groups5808333547571424918x_real @ F @ A2 ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % member_le_sum
% 0.35/0.64  thf(fact_6745_member__le__sum,axiom,
% 0.35/0.64      ! [I2: vEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 0.35/0.64        ( ( member_VEBT_VEBT @ I2 @ A2 )
% 0.35/0.64       => ( ! [X3: vEBT_VEBT] :
% 0.35/0.64              ( ( member_VEBT_VEBT @ X3 @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ I2 @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.35/0.64             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 0.35/0.64         => ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.35/0.64           => ( ord_less_eq_rat @ ( F @ I2 ) @ ( groups136491112297645522BT_rat @ F @ A2 ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % member_le_sum
% 0.35/0.64  thf(fact_6746_member__le__sum,axiom,
% 0.35/0.64      ! [I2: complex,A2: set_complex,F: complex > rat] :
% 0.35/0.64        ( ( member_complex @ I2 @ A2 )
% 0.35/0.64       => ( ! [X3: complex] :
% 0.35/0.64              ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ I2 @ bot_bot_set_complex ) ) )
% 0.35/0.64             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 0.35/0.64         => ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.64           => ( ord_less_eq_rat @ ( F @ I2 ) @ ( groups5058264527183730370ex_rat @ F @ A2 ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % member_le_sum
% 0.35/0.64  thf(fact_6747_member__le__sum,axiom,
% 0.35/0.64      ! [I2: int,A2: set_int,F: int > real] :
% 0.35/0.64        ( ( member_int @ I2 @ A2 )
% 0.35/0.64       => ( ! [X3: int] :
% 0.35/0.64              ( ( member_int @ X3 @ ( minus_minus_set_int @ A2 @ ( insert_int @ I2 @ bot_bot_set_int ) ) )
% 0.35/0.64             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 0.35/0.64         => ( ( finite_finite_int @ A2 )
% 0.35/0.64           => ( ord_less_eq_real @ ( F @ I2 ) @ ( groups8778361861064173332t_real @ F @ A2 ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % member_le_sum
% 0.35/0.64  thf(fact_6748_member__le__sum,axiom,
% 0.35/0.64      ! [I2: int,A2: set_int,F: int > rat] :
% 0.35/0.64        ( ( member_int @ I2 @ A2 )
% 0.35/0.64       => ( ! [X3: int] :
% 0.35/0.64              ( ( member_int @ X3 @ ( minus_minus_set_int @ A2 @ ( insert_int @ I2 @ bot_bot_set_int ) ) )
% 0.35/0.64             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 0.35/0.64         => ( ( finite_finite_int @ A2 )
% 0.35/0.64           => ( ord_less_eq_rat @ ( F @ I2 ) @ ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % member_le_sum
% 0.35/0.64  thf(fact_6749_member__le__sum,axiom,
% 0.35/0.64      ! [I2: real,A2: set_real,F: real > real] :
% 0.35/0.64        ( ( member_real @ I2 @ A2 )
% 0.35/0.64       => ( ! [X3: real] :
% 0.35/0.64              ( ( member_real @ X3 @ ( minus_minus_set_real @ A2 @ ( insert_real @ I2 @ bot_bot_set_real ) ) )
% 0.35/0.64             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 0.35/0.64         => ( ( finite_finite_real @ A2 )
% 0.35/0.64           => ( ord_less_eq_real @ ( F @ I2 ) @ ( groups8097168146408367636l_real @ F @ A2 ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % member_le_sum
% 0.35/0.64  thf(fact_6750_member__le__sum,axiom,
% 0.35/0.64      ! [I2: real,A2: set_real,F: real > rat] :
% 0.35/0.64        ( ( member_real @ I2 @ A2 )
% 0.35/0.64       => ( ! [X3: real] :
% 0.35/0.64              ( ( member_real @ X3 @ ( minus_minus_set_real @ A2 @ ( insert_real @ I2 @ bot_bot_set_real ) ) )
% 0.35/0.64             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 0.35/0.64         => ( ( finite_finite_real @ A2 )
% 0.35/0.64           => ( ord_less_eq_rat @ ( F @ I2 ) @ ( groups1300246762558778688al_rat @ F @ A2 ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % member_le_sum
% 0.35/0.64  thf(fact_6751_member__le__sum,axiom,
% 0.35/0.64      ! [I2: nat,A2: set_nat,F: nat > rat] :
% 0.35/0.64        ( ( member_nat @ I2 @ A2 )
% 0.35/0.64       => ( ! [X3: nat] :
% 0.35/0.64              ( ( member_nat @ X3 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ I2 @ bot_bot_set_nat ) ) )
% 0.35/0.64             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 0.35/0.64         => ( ( finite_finite_nat @ A2 )
% 0.35/0.64           => ( ord_less_eq_rat @ ( F @ I2 ) @ ( groups2906978787729119204at_rat @ F @ A2 ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % member_le_sum
% 0.35/0.64  thf(fact_6752_member__le__sum,axiom,
% 0.35/0.64      ! [I2: vEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 0.35/0.64        ( ( member_VEBT_VEBT @ I2 @ A2 )
% 0.35/0.64       => ( ! [X3: vEBT_VEBT] :
% 0.35/0.64              ( ( member_VEBT_VEBT @ X3 @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ I2 @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.35/0.64             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 0.35/0.64         => ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.35/0.64           => ( ord_less_eq_nat @ ( F @ I2 ) @ ( groups771621172384141258BT_nat @ F @ A2 ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % member_le_sum
% 0.35/0.64  thf(fact_6753_take__bit__numeral__bit0,axiom,
% 0.35/0.64      ! [L2: num,K: num] :
% 0.35/0.64        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 0.35/0.64        = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_numeral_bit0
% 0.35/0.64  thf(fact_6754_take__bit__numeral__bit0,axiom,
% 0.35/0.64      ! [L2: num,K: num] :
% 0.35/0.64        ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 0.35/0.64        = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L2 ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_numeral_bit0
% 0.35/0.64  thf(fact_6755_take__bit__nat__less__self__iff,axiom,
% 0.35/0.64      ! [N: nat,M: nat] :
% 0.35/0.64        ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M )
% 0.35/0.64        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_nat_less_self_iff
% 0.35/0.64  thf(fact_6756_Suc__mask__eq__exp,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( suc @ ( bit_se2002935070580805687sk_nat @ N ) )
% 0.35/0.64        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % Suc_mask_eq_exp
% 0.35/0.64  thf(fact_6757_mask__nat__less__exp,axiom,
% 0.35/0.64      ! [N: nat] : ( ord_less_nat @ ( bit_se2002935070580805687sk_nat @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % mask_nat_less_exp
% 0.35/0.64  thf(fact_6758_exp__half__le2,axiom,
% 0.35/0.64      ord_less_eq_real @ ( exp_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 0.35/0.64  
% 0.35/0.64  % exp_half_le2
% 0.35/0.64  thf(fact_6759_take__bit__Suc__minus__bit0,axiom,
% 0.35/0.64      ! [N: nat,K: num] :
% 0.35/0.64        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 0.35/0.64        = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_Suc_minus_bit0
% 0.35/0.64  thf(fact_6760_convex__sum__bound__le,axiom,
% 0.35/0.64      ! [I6: set_complex,X: complex > code_integer,A: complex > code_integer,B: code_integer,Delta: code_integer] :
% 0.35/0.64        ( ! [I4: complex] :
% 0.35/0.64            ( ( member_complex @ I4 @ I6 )
% 0.35/0.64           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I4 ) ) )
% 0.35/0.64       => ( ( ( groups6621422865394947399nteger @ X @ I6 )
% 0.35/0.64            = one_one_Code_integer )
% 0.35/0.64         => ( ! [I4: complex] :
% 0.35/0.64                ( ( member_complex @ I4 @ I6 )
% 0.35/0.64               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 0.35/0.64           => ( ord_le3102999989581377725nteger
% 0.35/0.64              @ ( abs_abs_Code_integer
% 0.35/0.64                @ ( minus_8373710615458151222nteger
% 0.35/0.64                  @ ( groups6621422865394947399nteger
% 0.35/0.64                    @ ^ [I3: complex] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X @ I3 ) )
% 0.35/0.64                    @ I6 )
% 0.35/0.64                  @ B ) )
% 0.35/0.64              @ Delta ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % convex_sum_bound_le
% 0.35/0.64  thf(fact_6761_convex__sum__bound__le,axiom,
% 0.35/0.64      ! [I6: set_real,X: real > code_integer,A: real > code_integer,B: code_integer,Delta: code_integer] :
% 0.35/0.64        ( ! [I4: real] :
% 0.35/0.64            ( ( member_real @ I4 @ I6 )
% 0.35/0.64           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I4 ) ) )
% 0.35/0.64       => ( ( ( groups7713935264441627589nteger @ X @ I6 )
% 0.35/0.64            = one_one_Code_integer )
% 0.35/0.64         => ( ! [I4: real] :
% 0.35/0.64                ( ( member_real @ I4 @ I6 )
% 0.35/0.64               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 0.35/0.64           => ( ord_le3102999989581377725nteger
% 0.35/0.64              @ ( abs_abs_Code_integer
% 0.35/0.64                @ ( minus_8373710615458151222nteger
% 0.35/0.64                  @ ( groups7713935264441627589nteger
% 0.35/0.64                    @ ^ [I3: real] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X @ I3 ) )
% 0.35/0.64                    @ I6 )
% 0.35/0.64                  @ B ) )
% 0.35/0.64              @ Delta ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % convex_sum_bound_le
% 0.35/0.64  thf(fact_6762_convex__sum__bound__le,axiom,
% 0.35/0.64      ! [I6: set_nat,X: nat > code_integer,A: nat > code_integer,B: code_integer,Delta: code_integer] :
% 0.35/0.64        ( ! [I4: nat] :
% 0.35/0.64            ( ( member_nat @ I4 @ I6 )
% 0.35/0.64           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I4 ) ) )
% 0.35/0.64       => ( ( ( groups7501900531339628137nteger @ X @ I6 )
% 0.35/0.64            = one_one_Code_integer )
% 0.35/0.64         => ( ! [I4: nat] :
% 0.35/0.64                ( ( member_nat @ I4 @ I6 )
% 0.35/0.64               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 0.35/0.64           => ( ord_le3102999989581377725nteger
% 0.35/0.64              @ ( abs_abs_Code_integer
% 0.35/0.64                @ ( minus_8373710615458151222nteger
% 0.35/0.64                  @ ( groups7501900531339628137nteger
% 0.35/0.64                    @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X @ I3 ) )
% 0.35/0.64                    @ I6 )
% 0.35/0.64                  @ B ) )
% 0.35/0.64              @ Delta ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % convex_sum_bound_le
% 0.35/0.64  thf(fact_6763_convex__sum__bound__le,axiom,
% 0.35/0.64      ! [I6: set_int,X: int > code_integer,A: int > code_integer,B: code_integer,Delta: code_integer] :
% 0.35/0.64        ( ! [I4: int] :
% 0.35/0.64            ( ( member_int @ I4 @ I6 )
% 0.35/0.64           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I4 ) ) )
% 0.35/0.64       => ( ( ( groups7873554091576472773nteger @ X @ I6 )
% 0.35/0.64            = one_one_Code_integer )
% 0.35/0.64         => ( ! [I4: int] :
% 0.35/0.64                ( ( member_int @ I4 @ I6 )
% 0.35/0.64               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 0.35/0.64           => ( ord_le3102999989581377725nteger
% 0.35/0.64              @ ( abs_abs_Code_integer
% 0.35/0.64                @ ( minus_8373710615458151222nteger
% 0.35/0.64                  @ ( groups7873554091576472773nteger
% 0.35/0.64                    @ ^ [I3: int] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X @ I3 ) )
% 0.35/0.64                    @ I6 )
% 0.35/0.64                  @ B ) )
% 0.35/0.64              @ Delta ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % convex_sum_bound_le
% 0.35/0.64  thf(fact_6764_convex__sum__bound__le,axiom,
% 0.35/0.64      ! [I6: set_complex,X: complex > rat,A: complex > rat,B: rat,Delta: rat] :
% 0.35/0.64        ( ! [I4: complex] :
% 0.35/0.64            ( ( member_complex @ I4 @ I6 )
% 0.35/0.64           => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I4 ) ) )
% 0.35/0.64       => ( ( ( groups5058264527183730370ex_rat @ X @ I6 )
% 0.35/0.64            = one_one_rat )
% 0.35/0.64         => ( ! [I4: complex] :
% 0.35/0.64                ( ( member_complex @ I4 @ I6 )
% 0.35/0.64               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 0.35/0.64           => ( ord_less_eq_rat
% 0.35/0.64              @ ( abs_abs_rat
% 0.35/0.64                @ ( minus_minus_rat
% 0.35/0.64                  @ ( groups5058264527183730370ex_rat
% 0.35/0.64                    @ ^ [I3: complex] : ( times_times_rat @ ( A @ I3 ) @ ( X @ I3 ) )
% 0.35/0.64                    @ I6 )
% 0.35/0.64                  @ B ) )
% 0.35/0.64              @ Delta ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % convex_sum_bound_le
% 0.35/0.64  thf(fact_6765_convex__sum__bound__le,axiom,
% 0.35/0.64      ! [I6: set_real,X: real > rat,A: real > rat,B: rat,Delta: rat] :
% 0.35/0.64        ( ! [I4: real] :
% 0.35/0.64            ( ( member_real @ I4 @ I6 )
% 0.35/0.64           => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I4 ) ) )
% 0.35/0.64       => ( ( ( groups1300246762558778688al_rat @ X @ I6 )
% 0.35/0.64            = one_one_rat )
% 0.35/0.64         => ( ! [I4: real] :
% 0.35/0.64                ( ( member_real @ I4 @ I6 )
% 0.35/0.64               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 0.35/0.64           => ( ord_less_eq_rat
% 0.35/0.64              @ ( abs_abs_rat
% 0.35/0.64                @ ( minus_minus_rat
% 0.35/0.64                  @ ( groups1300246762558778688al_rat
% 0.35/0.64                    @ ^ [I3: real] : ( times_times_rat @ ( A @ I3 ) @ ( X @ I3 ) )
% 0.35/0.64                    @ I6 )
% 0.35/0.64                  @ B ) )
% 0.35/0.64              @ Delta ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % convex_sum_bound_le
% 0.35/0.64  thf(fact_6766_convex__sum__bound__le,axiom,
% 0.35/0.64      ! [I6: set_nat,X: nat > rat,A: nat > rat,B: rat,Delta: rat] :
% 0.35/0.64        ( ! [I4: nat] :
% 0.35/0.64            ( ( member_nat @ I4 @ I6 )
% 0.35/0.64           => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I4 ) ) )
% 0.35/0.64       => ( ( ( groups2906978787729119204at_rat @ X @ I6 )
% 0.35/0.64            = one_one_rat )
% 0.35/0.64         => ( ! [I4: nat] :
% 0.35/0.64                ( ( member_nat @ I4 @ I6 )
% 0.35/0.64               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 0.35/0.64           => ( ord_less_eq_rat
% 0.35/0.64              @ ( abs_abs_rat
% 0.35/0.64                @ ( minus_minus_rat
% 0.35/0.64                  @ ( groups2906978787729119204at_rat
% 0.35/0.64                    @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( X @ I3 ) )
% 0.35/0.64                    @ I6 )
% 0.35/0.64                  @ B ) )
% 0.35/0.64              @ Delta ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % convex_sum_bound_le
% 0.35/0.64  thf(fact_6767_convex__sum__bound__le,axiom,
% 0.35/0.64      ! [I6: set_int,X: int > rat,A: int > rat,B: rat,Delta: rat] :
% 0.35/0.64        ( ! [I4: int] :
% 0.35/0.64            ( ( member_int @ I4 @ I6 )
% 0.35/0.64           => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I4 ) ) )
% 0.35/0.64       => ( ( ( groups3906332499630173760nt_rat @ X @ I6 )
% 0.35/0.64            = one_one_rat )
% 0.35/0.64         => ( ! [I4: int] :
% 0.35/0.64                ( ( member_int @ I4 @ I6 )
% 0.35/0.64               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 0.35/0.64           => ( ord_less_eq_rat
% 0.35/0.64              @ ( abs_abs_rat
% 0.35/0.64                @ ( minus_minus_rat
% 0.35/0.64                  @ ( groups3906332499630173760nt_rat
% 0.35/0.64                    @ ^ [I3: int] : ( times_times_rat @ ( A @ I3 ) @ ( X @ I3 ) )
% 0.35/0.64                    @ I6 )
% 0.35/0.64                  @ B ) )
% 0.35/0.64              @ Delta ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % convex_sum_bound_le
% 0.35/0.64  thf(fact_6768_convex__sum__bound__le,axiom,
% 0.35/0.64      ! [I6: set_complex,X: complex > real,A: complex > real,B: real,Delta: real] :
% 0.35/0.64        ( ! [I4: complex] :
% 0.35/0.64            ( ( member_complex @ I4 @ I6 )
% 0.35/0.64           => ( ord_less_eq_real @ zero_zero_real @ ( X @ I4 ) ) )
% 0.35/0.64       => ( ( ( groups5808333547571424918x_real @ X @ I6 )
% 0.35/0.64            = one_one_real )
% 0.35/0.64         => ( ! [I4: complex] :
% 0.35/0.64                ( ( member_complex @ I4 @ I6 )
% 0.35/0.64               => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 0.35/0.64           => ( ord_less_eq_real
% 0.35/0.64              @ ( abs_abs_real
% 0.35/0.64                @ ( minus_minus_real
% 0.35/0.64                  @ ( groups5808333547571424918x_real
% 0.35/0.64                    @ ^ [I3: complex] : ( times_times_real @ ( A @ I3 ) @ ( X @ I3 ) )
% 0.35/0.64                    @ I6 )
% 0.35/0.64                  @ B ) )
% 0.35/0.64              @ Delta ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % convex_sum_bound_le
% 0.35/0.64  thf(fact_6769_convex__sum__bound__le,axiom,
% 0.35/0.64      ! [I6: set_real,X: real > real,A: real > real,B: real,Delta: real] :
% 0.35/0.64        ( ! [I4: real] :
% 0.35/0.64            ( ( member_real @ I4 @ I6 )
% 0.35/0.64           => ( ord_less_eq_real @ zero_zero_real @ ( X @ I4 ) ) )
% 0.35/0.64       => ( ( ( groups8097168146408367636l_real @ X @ I6 )
% 0.35/0.64            = one_one_real )
% 0.35/0.64         => ( ! [I4: real] :
% 0.35/0.64                ( ( member_real @ I4 @ I6 )
% 0.35/0.64               => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 0.35/0.64           => ( ord_less_eq_real
% 0.35/0.64              @ ( abs_abs_real
% 0.35/0.64                @ ( minus_minus_real
% 0.35/0.64                  @ ( groups8097168146408367636l_real
% 0.35/0.64                    @ ^ [I3: real] : ( times_times_real @ ( A @ I3 ) @ ( X @ I3 ) )
% 0.35/0.64                    @ I6 )
% 0.35/0.64                  @ B ) )
% 0.35/0.64              @ Delta ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % convex_sum_bound_le
% 0.35/0.64  thf(fact_6770_take__bit__int__greater__eq__self__iff,axiom,
% 0.35/0.64      ! [K: int,N: nat] :
% 0.35/0.64        ( ( ord_less_eq_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 0.35/0.64        = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_int_greater_eq_self_iff
% 0.35/0.64  thf(fact_6771_take__bit__int__less__self__iff,axiom,
% 0.35/0.64      ! [N: nat,K: int] :
% 0.35/0.64        ( ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 0.35/0.64        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_int_less_self_iff
% 0.35/0.64  thf(fact_6772_exp__double,axiom,
% 0.35/0.64      ! [Z: complex] :
% 0.35/0.64        ( ( exp_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) )
% 0.35/0.64        = ( power_power_complex @ ( exp_complex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % exp_double
% 0.35/0.64  thf(fact_6773_exp__double,axiom,
% 0.35/0.64      ! [Z: real] :
% 0.35/0.64        ( ( exp_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) )
% 0.35/0.64        = ( power_power_real @ ( exp_real @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % exp_double
% 0.35/0.64  thf(fact_6774_nat__intermed__int__val,axiom,
% 0.35/0.64      ! [M: nat,N: nat,F: nat > int,K: int] :
% 0.35/0.64        ( ! [I4: nat] :
% 0.35/0.64            ( ( ( ord_less_eq_nat @ M @ I4 )
% 0.35/0.64              & ( ord_less_nat @ I4 @ N ) )
% 0.35/0.64           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
% 0.35/0.64       => ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.64         => ( ( ord_less_eq_int @ ( F @ M ) @ K )
% 0.35/0.64           => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 0.35/0.64             => ? [I4: nat] :
% 0.35/0.64                  ( ( ord_less_eq_nat @ M @ I4 )
% 0.35/0.64                  & ( ord_less_eq_nat @ I4 @ N )
% 0.35/0.64                  & ( ( F @ I4 )
% 0.35/0.64                    = K ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % nat_intermed_int_val
% 0.35/0.64  thf(fact_6775_decr__lemma,axiom,
% 0.35/0.64      ! [D2: int,X: int,Z: int] :
% 0.35/0.64        ( ( ord_less_int @ zero_zero_int @ D2 )
% 0.35/0.64       => ( ord_less_int @ ( minus_minus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D2 ) ) @ Z ) ) ).
% 0.35/0.64  
% 0.35/0.64  % decr_lemma
% 0.35/0.64  thf(fact_6776_incr__lemma,axiom,
% 0.35/0.64      ! [D2: int,Z: int,X: int] :
% 0.35/0.64        ( ( ord_less_int @ zero_zero_int @ D2 )
% 0.35/0.64       => ( ord_less_int @ Z @ ( plus_plus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D2 ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % incr_lemma
% 0.35/0.64  thf(fact_6777_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2119862282449309892nteger @ N ) )
% 0.35/0.64        = ( N = zero_zero_nat ) ) ).
% 0.35/0.64  
% 0.35/0.64  % semiring_bit_operations_class.even_mask_iff
% 0.35/0.64  thf(fact_6778_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ N ) )
% 0.35/0.64        = ( N = zero_zero_nat ) ) ).
% 0.35/0.64  
% 0.35/0.64  % semiring_bit_operations_class.even_mask_iff
% 0.35/0.64  thf(fact_6779_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ N ) )
% 0.35/0.64        = ( N = zero_zero_nat ) ) ).
% 0.35/0.64  
% 0.35/0.64  % semiring_bit_operations_class.even_mask_iff
% 0.35/0.64  thf(fact_6780_mask__nat__def,axiom,
% 0.35/0.64      ( bit_se2002935070580805687sk_nat
% 0.35/0.64      = ( ^ [N2: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % mask_nat_def
% 0.35/0.64  thf(fact_6781_take__bit__int__eq__self__iff,axiom,
% 0.35/0.64      ! [N: nat,K: int] :
% 0.35/0.64        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 0.35/0.64          = K )
% 0.35/0.64        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.35/0.64          & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_int_eq_self_iff
% 0.35/0.64  thf(fact_6782_take__bit__int__eq__self,axiom,
% 0.35/0.64      ! [K: int,N: nat] :
% 0.35/0.64        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.35/0.64       => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.64         => ( ( bit_se2923211474154528505it_int @ N @ K )
% 0.35/0.64            = K ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_int_eq_self
% 0.35/0.64  thf(fact_6783_mask__half__int,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( divide_divide_int @ ( bit_se2000444600071755411sk_int @ N ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.64        = ( bit_se2000444600071755411sk_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % mask_half_int
% 0.35/0.64  thf(fact_6784_take__bit__numeral__minus__bit0,axiom,
% 0.35/0.64      ! [L2: num,K: num] :
% 0.35/0.64        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 0.35/0.64        = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_numeral_minus_bit0
% 0.35/0.64  thf(fact_6785_take__bit__incr__eq,axiom,
% 0.35/0.64      ! [N: nat,K: int] :
% 0.35/0.64        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 0.35/0.64         != ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 0.35/0.64       => ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 0.35/0.64          = ( plus_plus_int @ one_one_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_incr_eq
% 0.35/0.64  thf(fact_6786_mask__int__def,axiom,
% 0.35/0.64      ( bit_se2000444600071755411sk_int
% 0.35/0.64      = ( ^ [N2: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % mask_int_def
% 0.35/0.64  thf(fact_6787_nat__ivt__aux,axiom,
% 0.35/0.64      ! [N: nat,F: nat > int,K: int] :
% 0.35/0.64        ( ! [I4: nat] :
% 0.35/0.64            ( ( ord_less_nat @ I4 @ N )
% 0.35/0.64           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
% 0.35/0.64       => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 0.35/0.64         => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 0.35/0.64           => ? [I4: nat] :
% 0.35/0.64                ( ( ord_less_eq_nat @ I4 @ N )
% 0.35/0.64                & ( ( F @ I4 )
% 0.35/0.64                  = K ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % nat_ivt_aux
% 0.35/0.64  thf(fact_6788_take__bit__Suc__bit1,axiom,
% 0.35/0.64      ! [N: nat,K: num] :
% 0.35/0.64        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 0.35/0.64        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_Suc_bit1
% 0.35/0.64  thf(fact_6789_take__bit__Suc__bit1,axiom,
% 0.35/0.64      ! [N: nat,K: num] :
% 0.35/0.64        ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 0.35/0.64        = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_Suc_bit1
% 0.35/0.64  thf(fact_6790_take__bit__Suc__minus__1__eq,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.64        = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_Code_integer ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_Suc_minus_1_eq
% 0.35/0.64  thf(fact_6791_take__bit__Suc__minus__1__eq,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.64        = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_int ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_Suc_minus_1_eq
% 0.35/0.64  thf(fact_6792_take__bit__numeral__minus__1__eq,axiom,
% 0.35/0.64      ! [K: num] :
% 0.35/0.64        ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ K ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.64        = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_Code_integer ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_numeral_minus_1_eq
% 0.35/0.64  thf(fact_6793_take__bit__numeral__minus__1__eq,axiom,
% 0.35/0.64      ! [K: num] :
% 0.35/0.64        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ K ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.64        = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_int ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_numeral_minus_1_eq
% 0.35/0.64  thf(fact_6794_take__bit__Suc,axiom,
% 0.35/0.64      ! [N: nat,A: int] :
% 0.35/0.64        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A )
% 0.35/0.64        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_Suc
% 0.35/0.64  thf(fact_6795_take__bit__Suc,axiom,
% 0.35/0.64      ! [N: nat,A: nat] :
% 0.35/0.64        ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ A )
% 0.35/0.64        = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_Suc
% 0.35/0.64  thf(fact_6796_mask__eq__exp__minus__1,axiom,
% 0.35/0.64      ( bit_se2002935070580805687sk_nat
% 0.35/0.64      = ( ^ [N2: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % mask_eq_exp_minus_1
% 0.35/0.64  thf(fact_6797_mask__eq__exp__minus__1,axiom,
% 0.35/0.64      ( bit_se2000444600071755411sk_int
% 0.35/0.64      = ( ^ [N2: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % mask_eq_exp_minus_1
% 0.35/0.64  thf(fact_6798_exp__bound,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.64       => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.35/0.64         => ( ord_less_eq_real @ ( exp_real @ X ) @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % exp_bound
% 0.35/0.64  thf(fact_6799_take__bit__int__less__eq,axiom,
% 0.35/0.64      ! [N: nat,K: int] :
% 0.35/0.64        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 0.35/0.64       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.64         => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_int_less_eq
% 0.35/0.64  thf(fact_6800_take__bit__int__greater__eq,axiom,
% 0.35/0.64      ! [K: int,N: nat] :
% 0.35/0.64        ( ( ord_less_int @ K @ zero_zero_int )
% 0.35/0.64       => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_int_greater_eq
% 0.35/0.64  thf(fact_6801_signed__take__bit__eq__take__bit__shift,axiom,
% 0.35/0.64      ( bit_ri631733984087533419it_int
% 0.35/0.64      = ( ^ [N2: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( plus_plus_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % signed_take_bit_eq_take_bit_shift
% 0.35/0.64  thf(fact_6802_nat0__intermed__int__val,axiom,
% 0.35/0.64      ! [N: nat,F: nat > int,K: int] :
% 0.35/0.64        ( ! [I4: nat] :
% 0.35/0.64            ( ( ord_less_nat @ I4 @ N )
% 0.35/0.64           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I4 @ one_one_nat ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
% 0.35/0.64       => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 0.35/0.64         => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 0.35/0.64           => ? [I4: nat] :
% 0.35/0.64                ( ( ord_less_eq_nat @ I4 @ N )
% 0.35/0.64                & ( ( F @ I4 )
% 0.35/0.64                  = K ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % nat0_intermed_int_val
% 0.35/0.64  thf(fact_6803_stable__imp__take__bit__eq,axiom,
% 0.35/0.64      ! [A: code_integer,N: nat] :
% 0.35/0.64        ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.35/0.64          = A )
% 0.35/0.64       => ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.35/0.64           => ( ( bit_se1745604003318907178nteger @ N @ A )
% 0.35/0.64              = zero_z3403309356797280102nteger ) )
% 0.35/0.64          & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.35/0.64           => ( ( bit_se1745604003318907178nteger @ N @ A )
% 0.35/0.64              = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % stable_imp_take_bit_eq
% 0.35/0.64  thf(fact_6804_stable__imp__take__bit__eq,axiom,
% 0.35/0.64      ! [A: int,N: nat] :
% 0.35/0.64        ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.64          = A )
% 0.35/0.64       => ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.64           => ( ( bit_se2923211474154528505it_int @ N @ A )
% 0.35/0.64              = zero_zero_int ) )
% 0.35/0.64          & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.64           => ( ( bit_se2923211474154528505it_int @ N @ A )
% 0.35/0.64              = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % stable_imp_take_bit_eq
% 0.35/0.64  thf(fact_6805_stable__imp__take__bit__eq,axiom,
% 0.35/0.64      ! [A: nat,N: nat] :
% 0.35/0.64        ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.64          = A )
% 0.35/0.64       => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.64           => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 0.35/0.64              = zero_zero_nat ) )
% 0.35/0.64          & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.64           => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 0.35/0.64              = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % stable_imp_take_bit_eq
% 0.35/0.64  thf(fact_6806_take__bit__numeral__bit1,axiom,
% 0.35/0.64      ! [L2: num,K: num] :
% 0.35/0.64        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 0.35/0.64        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_numeral_bit1
% 0.35/0.64  thf(fact_6807_take__bit__numeral__bit1,axiom,
% 0.35/0.64      ! [L2: num,K: num] :
% 0.35/0.64        ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 0.35/0.64        = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L2 ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_numeral_bit1
% 0.35/0.64  thf(fact_6808_real__exp__bound__lemma,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.64       => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.64         => ( ord_less_eq_real @ ( exp_real @ X ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_exp_bound_lemma
% 0.35/0.64  thf(fact_6809_arctan__add,axiom,
% 0.35/0.64      ! [X: real,Y2: real] :
% 0.35/0.64        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.35/0.64       => ( ( ord_less_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 0.35/0.64         => ( ( plus_plus_real @ ( arctan @ X ) @ ( arctan @ Y2 ) )
% 0.35/0.64            = ( arctan @ ( divide_divide_real @ ( plus_plus_real @ X @ Y2 ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ X @ Y2 ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % arctan_add
% 0.35/0.64  thf(fact_6810_take__bit__minus__small__eq,axiom,
% 0.35/0.64      ! [K: int,N: nat] :
% 0.35/0.64        ( ( ord_less_int @ zero_zero_int @ K )
% 0.35/0.64       => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.64         => ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) )
% 0.35/0.64            = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_minus_small_eq
% 0.35/0.64  thf(fact_6811_exp__lower__Taylor__quadratic,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.64       => ( ord_less_eq_real @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X ) @ ( divide_divide_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( exp_real @ X ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % exp_lower_Taylor_quadratic
% 0.35/0.64  thf(fact_6812_num_Osize__gen_I2_J,axiom,
% 0.35/0.64      ! [X23: num] :
% 0.35/0.64        ( ( size_num @ ( bit0 @ X23 ) )
% 0.35/0.64        = ( plus_plus_nat @ ( size_num @ X23 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % num.size_gen(2)
% 0.35/0.64  thf(fact_6813_take__bit__numeral__minus__bit1,axiom,
% 0.35/0.64      ! [L2: num,K: num] :
% 0.35/0.64        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.35/0.64        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_numeral_minus_bit1
% 0.35/0.64  thf(fact_6814_take__bit__Suc__minus__bit1,axiom,
% 0.35/0.64      ! [N: nat,K: num] :
% 0.35/0.64        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.35/0.64        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_Suc_minus_bit1
% 0.35/0.64  thf(fact_6815_log__base__10__eq1,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.64       => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 0.35/0.64          = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( ln_ln_real @ X ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % log_base_10_eq1
% 0.35/0.64  thf(fact_6816_power__numeral,axiom,
% 0.35/0.64      ! [K: num,L2: num] :
% 0.35/0.64        ( ( power_power_complex @ ( numera6690914467698888265omplex @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 0.35/0.64        = ( numera6690914467698888265omplex @ ( pow @ K @ L2 ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % power_numeral
% 0.35/0.64  thf(fact_6817_power__numeral,axiom,
% 0.35/0.64      ! [K: num,L2: num] :
% 0.35/0.64        ( ( power_power_real @ ( numeral_numeral_real @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 0.35/0.64        = ( numeral_numeral_real @ ( pow @ K @ L2 ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % power_numeral
% 0.35/0.64  thf(fact_6818_power__numeral,axiom,
% 0.35/0.64      ! [K: num,L2: num] :
% 0.35/0.64        ( ( power_power_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 0.35/0.64        = ( numeral_numeral_rat @ ( pow @ K @ L2 ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % power_numeral
% 0.35/0.64  thf(fact_6819_power__numeral,axiom,
% 0.35/0.64      ! [K: num,L2: num] :
% 0.35/0.64        ( ( power_power_nat @ ( numeral_numeral_nat @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 0.35/0.64        = ( numeral_numeral_nat @ ( pow @ K @ L2 ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % power_numeral
% 0.35/0.64  thf(fact_6820_power__numeral,axiom,
% 0.35/0.64      ! [K: num,L2: num] :
% 0.35/0.64        ( ( power_power_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 0.35/0.64        = ( numeral_numeral_int @ ( pow @ K @ L2 ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % power_numeral
% 0.35/0.64  thf(fact_6821_or__int__unfold,axiom,
% 0.35/0.64      ( bit_se1409905431419307370or_int
% 0.35/0.64      = ( ^ [K3: int,L: int] :
% 0.35/0.64            ( if_int
% 0.35/0.64            @ ( ( K3
% 0.35/0.64                = ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.64              | ( L
% 0.35/0.64                = ( uminus_uminus_int @ one_one_int ) ) )
% 0.35/0.64            @ ( uminus_uminus_int @ one_one_int )
% 0.35/0.64            @ ( if_int @ ( K3 = zero_zero_int ) @ L @ ( if_int @ ( L = zero_zero_int ) @ K3 @ ( plus_plus_int @ ( ord_max_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or_int_unfold
% 0.35/0.64  thf(fact_6822_arctan__half,axiom,
% 0.35/0.64      ( arctan
% 0.35/0.64      = ( ^ [X2: real] : ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ ( divide_divide_real @ X2 @ ( plus_plus_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % arctan_half
% 0.35/0.64  thf(fact_6823_or_Oidem,axiom,
% 0.35/0.64      ! [A: int] :
% 0.35/0.64        ( ( bit_se1409905431419307370or_int @ A @ A )
% 0.35/0.64        = A ) ).
% 0.35/0.64  
% 0.35/0.64  % or.idem
% 0.35/0.64  thf(fact_6824_or_Oidem,axiom,
% 0.35/0.64      ! [A: nat] :
% 0.35/0.64        ( ( bit_se1412395901928357646or_nat @ A @ A )
% 0.35/0.64        = A ) ).
% 0.35/0.64  
% 0.35/0.64  % or.idem
% 0.35/0.64  thf(fact_6825_or_Oleft__idem,axiom,
% 0.35/0.64      ! [A: int,B: int] :
% 0.35/0.64        ( ( bit_se1409905431419307370or_int @ A @ ( bit_se1409905431419307370or_int @ A @ B ) )
% 0.35/0.64        = ( bit_se1409905431419307370or_int @ A @ B ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or.left_idem
% 0.35/0.64  thf(fact_6826_or_Oleft__idem,axiom,
% 0.35/0.64      ! [A: nat,B: nat] :
% 0.35/0.64        ( ( bit_se1412395901928357646or_nat @ A @ ( bit_se1412395901928357646or_nat @ A @ B ) )
% 0.35/0.64        = ( bit_se1412395901928357646or_nat @ A @ B ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or.left_idem
% 0.35/0.64  thf(fact_6827_or_Oright__idem,axiom,
% 0.35/0.64      ! [A: int,B: int] :
% 0.35/0.64        ( ( bit_se1409905431419307370or_int @ ( bit_se1409905431419307370or_int @ A @ B ) @ B )
% 0.35/0.64        = ( bit_se1409905431419307370or_int @ A @ B ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or.right_idem
% 0.35/0.64  thf(fact_6828_or_Oright__idem,axiom,
% 0.35/0.64      ! [A: nat,B: nat] :
% 0.35/0.64        ( ( bit_se1412395901928357646or_nat @ ( bit_se1412395901928357646or_nat @ A @ B ) @ B )
% 0.35/0.64        = ( bit_se1412395901928357646or_nat @ A @ B ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or.right_idem
% 0.35/0.64  thf(fact_6829_real__sqrt__eq__iff,axiom,
% 0.35/0.64      ! [X: real,Y2: real] :
% 0.35/0.64        ( ( ( sqrt @ X )
% 0.35/0.64          = ( sqrt @ Y2 ) )
% 0.35/0.64        = ( X = Y2 ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_eq_iff
% 0.35/0.64  thf(fact_6830_or_Oleft__neutral,axiom,
% 0.35/0.64      ! [A: int] :
% 0.35/0.64        ( ( bit_se1409905431419307370or_int @ zero_zero_int @ A )
% 0.35/0.64        = A ) ).
% 0.35/0.64  
% 0.35/0.64  % or.left_neutral
% 0.35/0.64  thf(fact_6831_or_Oleft__neutral,axiom,
% 0.35/0.64      ! [A: nat] :
% 0.35/0.64        ( ( bit_se1412395901928357646or_nat @ zero_zero_nat @ A )
% 0.35/0.64        = A ) ).
% 0.35/0.64  
% 0.35/0.64  % or.left_neutral
% 0.35/0.64  thf(fact_6832_or_Oright__neutral,axiom,
% 0.35/0.64      ! [A: int] :
% 0.35/0.64        ( ( bit_se1409905431419307370or_int @ A @ zero_zero_int )
% 0.35/0.64        = A ) ).
% 0.35/0.64  
% 0.35/0.64  % or.right_neutral
% 0.35/0.64  thf(fact_6833_or_Oright__neutral,axiom,
% 0.35/0.64      ! [A: nat] :
% 0.35/0.64        ( ( bit_se1412395901928357646or_nat @ A @ zero_zero_nat )
% 0.35/0.64        = A ) ).
% 0.35/0.64  
% 0.35/0.64  % or.right_neutral
% 0.35/0.64  thf(fact_6834_real__sqrt__zero,axiom,
% 0.35/0.64      ( ( sqrt @ zero_zero_real )
% 0.35/0.64      = zero_zero_real ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_zero
% 0.35/0.64  thf(fact_6835_real__sqrt__eq__zero__cancel__iff,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64        ( ( ( sqrt @ X )
% 0.35/0.64          = zero_zero_real )
% 0.35/0.64        = ( X = zero_zero_real ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_eq_zero_cancel_iff
% 0.35/0.64  thf(fact_6836_real__sqrt__less__iff,axiom,
% 0.35/0.64      ! [X: real,Y2: real] :
% 0.35/0.64        ( ( ord_less_real @ ( sqrt @ X ) @ ( sqrt @ Y2 ) )
% 0.35/0.64        = ( ord_less_real @ X @ Y2 ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_less_iff
% 0.35/0.64  thf(fact_6837_real__sqrt__le__iff,axiom,
% 0.35/0.64      ! [X: real,Y2: real] :
% 0.35/0.64        ( ( ord_less_eq_real @ ( sqrt @ X ) @ ( sqrt @ Y2 ) )
% 0.35/0.64        = ( ord_less_eq_real @ X @ Y2 ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_le_iff
% 0.35/0.64  thf(fact_6838_real__sqrt__eq__1__iff,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64        ( ( ( sqrt @ X )
% 0.35/0.64          = one_one_real )
% 0.35/0.64        = ( X = one_one_real ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_eq_1_iff
% 0.35/0.64  thf(fact_6839_real__sqrt__one,axiom,
% 0.35/0.64      ( ( sqrt @ one_one_real )
% 0.35/0.64      = one_one_real ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_one
% 0.35/0.64  thf(fact_6840_take__bit__or,axiom,
% 0.35/0.64      ! [N: nat,A: int,B: int] :
% 0.35/0.64        ( ( bit_se2923211474154528505it_int @ N @ ( bit_se1409905431419307370or_int @ A @ B ) )
% 0.35/0.64        = ( bit_se1409905431419307370or_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_se2923211474154528505it_int @ N @ B ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_or
% 0.35/0.64  thf(fact_6841_take__bit__or,axiom,
% 0.35/0.64      ! [N: nat,A: nat,B: nat] :
% 0.35/0.64        ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se1412395901928357646or_nat @ A @ B ) )
% 0.35/0.64        = ( bit_se1412395901928357646or_nat @ ( bit_se2925701944663578781it_nat @ N @ A ) @ ( bit_se2925701944663578781it_nat @ N @ B ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_or
% 0.35/0.64  thf(fact_6842_bit_Odisj__one__right,axiom,
% 0.35/0.64      ! [X: code_integer] :
% 0.35/0.64        ( ( bit_se1080825931792720795nteger @ X @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.64        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.35/0.64  
% 0.35/0.64  % bit.disj_one_right
% 0.35/0.64  thf(fact_6843_bit_Odisj__one__right,axiom,
% 0.35/0.64      ! [X: int] :
% 0.35/0.64        ( ( bit_se1409905431419307370or_int @ X @ ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.64        = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.35/0.64  
% 0.35/0.64  % bit.disj_one_right
% 0.35/0.64  thf(fact_6844_bit_Odisj__one__left,axiom,
% 0.35/0.64      ! [X: code_integer] :
% 0.35/0.64        ( ( bit_se1080825931792720795nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 0.35/0.64        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.35/0.64  
% 0.35/0.64  % bit.disj_one_left
% 0.35/0.64  thf(fact_6845_bit_Odisj__one__left,axiom,
% 0.35/0.64      ! [X: int] :
% 0.35/0.64        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 0.35/0.64        = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.35/0.64  
% 0.35/0.64  % bit.disj_one_left
% 0.35/0.64  thf(fact_6846_real__sqrt__lt__0__iff,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64        ( ( ord_less_real @ ( sqrt @ X ) @ zero_zero_real )
% 0.35/0.64        = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_lt_0_iff
% 0.35/0.64  thf(fact_6847_real__sqrt__gt__0__iff,axiom,
% 0.35/0.64      ! [Y2: real] :
% 0.35/0.64        ( ( ord_less_real @ zero_zero_real @ ( sqrt @ Y2 ) )
% 0.35/0.64        = ( ord_less_real @ zero_zero_real @ Y2 ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_gt_0_iff
% 0.35/0.64  thf(fact_6848_real__sqrt__le__0__iff,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64        ( ( ord_less_eq_real @ ( sqrt @ X ) @ zero_zero_real )
% 0.35/0.64        = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_le_0_iff
% 0.35/0.64  thf(fact_6849_real__sqrt__ge__0__iff,axiom,
% 0.35/0.64      ! [Y2: real] :
% 0.35/0.64        ( ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ Y2 ) )
% 0.35/0.64        = ( ord_less_eq_real @ zero_zero_real @ Y2 ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_ge_0_iff
% 0.35/0.64  thf(fact_6850_real__sqrt__lt__1__iff,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64        ( ( ord_less_real @ ( sqrt @ X ) @ one_one_real )
% 0.35/0.64        = ( ord_less_real @ X @ one_one_real ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_lt_1_iff
% 0.35/0.64  thf(fact_6851_real__sqrt__gt__1__iff,axiom,
% 0.35/0.64      ! [Y2: real] :
% 0.35/0.64        ( ( ord_less_real @ one_one_real @ ( sqrt @ Y2 ) )
% 0.35/0.64        = ( ord_less_real @ one_one_real @ Y2 ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_gt_1_iff
% 0.35/0.64  thf(fact_6852_real__sqrt__le__1__iff,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64        ( ( ord_less_eq_real @ ( sqrt @ X ) @ one_one_real )
% 0.35/0.64        = ( ord_less_eq_real @ X @ one_one_real ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_le_1_iff
% 0.35/0.64  thf(fact_6853_real__sqrt__ge__1__iff,axiom,
% 0.35/0.64      ! [Y2: real] :
% 0.35/0.64        ( ( ord_less_eq_real @ one_one_real @ ( sqrt @ Y2 ) )
% 0.35/0.64        = ( ord_less_eq_real @ one_one_real @ Y2 ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_ge_1_iff
% 0.35/0.64  thf(fact_6854_log__one,axiom,
% 0.35/0.64      ! [A: real] :
% 0.35/0.64        ( ( log @ A @ one_one_real )
% 0.35/0.64        = zero_zero_real ) ).
% 0.35/0.64  
% 0.35/0.64  % log_one
% 0.35/0.64  thf(fact_6855_real__sqrt__mult__self,axiom,
% 0.35/0.64      ! [A: real] :
% 0.35/0.64        ( ( times_times_real @ ( sqrt @ A ) @ ( sqrt @ A ) )
% 0.35/0.64        = ( abs_abs_real @ A ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_mult_self
% 0.35/0.64  thf(fact_6856_real__sqrt__abs2,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64        ( ( sqrt @ ( times_times_real @ X @ X ) )
% 0.35/0.64        = ( abs_abs_real @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_abs2
% 0.35/0.64  thf(fact_6857_or__nonnegative__int__iff,axiom,
% 0.35/0.64      ! [K: int,L2: int] :
% 0.35/0.64        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) )
% 0.35/0.64        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.35/0.64          & ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or_nonnegative_int_iff
% 0.35/0.64  thf(fact_6858_or__negative__int__iff,axiom,
% 0.35/0.64      ! [K: int,L2: int] :
% 0.35/0.64        ( ( ord_less_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) @ zero_zero_int )
% 0.35/0.64        = ( ( ord_less_int @ K @ zero_zero_int )
% 0.35/0.64          | ( ord_less_int @ L2 @ zero_zero_int ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or_negative_int_iff
% 0.35/0.64  thf(fact_6859_pred__numeral__inc,axiom,
% 0.35/0.64      ! [K: num] :
% 0.35/0.64        ( ( pred_numeral @ ( inc @ K ) )
% 0.35/0.64        = ( numeral_numeral_nat @ K ) ) ).
% 0.35/0.64  
% 0.35/0.64  % pred_numeral_inc
% 0.35/0.64  thf(fact_6860_or__numerals_I8_J,axiom,
% 0.35/0.64      ! [X: num] :
% 0.35/0.64        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ one_one_int )
% 0.35/0.64        = ( numeral_numeral_int @ ( bit1 @ X ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or_numerals(8)
% 0.35/0.64  thf(fact_6861_or__numerals_I8_J,axiom,
% 0.35/0.64      ! [X: num] :
% 0.35/0.64        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ one_one_nat )
% 0.35/0.64        = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or_numerals(8)
% 0.35/0.64  thf(fact_6862_or__numerals_I2_J,axiom,
% 0.35/0.64      ! [Y2: num] :
% 0.35/0.64        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y2 ) ) )
% 0.35/0.64        = ( numeral_numeral_int @ ( bit1 @ Y2 ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or_numerals(2)
% 0.35/0.64  thf(fact_6863_or__numerals_I2_J,axiom,
% 0.35/0.64      ! [Y2: num] :
% 0.35/0.64        ( ( bit_se1412395901928357646or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) )
% 0.35/0.64        = ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or_numerals(2)
% 0.35/0.64  thf(fact_6864_real__sqrt__four,axiom,
% 0.35/0.64      ( ( sqrt @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.35/0.64      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_four
% 0.35/0.64  thf(fact_6865_zero__less__log__cancel__iff,axiom,
% 0.35/0.64      ! [A: real,X: real] :
% 0.35/0.64        ( ( ord_less_real @ one_one_real @ A )
% 0.35/0.64       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.64         => ( ( ord_less_real @ zero_zero_real @ ( log @ A @ X ) )
% 0.35/0.64            = ( ord_less_real @ one_one_real @ X ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % zero_less_log_cancel_iff
% 0.35/0.64  thf(fact_6866_log__less__zero__cancel__iff,axiom,
% 0.35/0.64      ! [A: real,X: real] :
% 0.35/0.64        ( ( ord_less_real @ one_one_real @ A )
% 0.35/0.64       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.64         => ( ( ord_less_real @ ( log @ A @ X ) @ zero_zero_real )
% 0.35/0.64            = ( ord_less_real @ X @ one_one_real ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % log_less_zero_cancel_iff
% 0.35/0.64  thf(fact_6867_one__less__log__cancel__iff,axiom,
% 0.35/0.64      ! [A: real,X: real] :
% 0.35/0.64        ( ( ord_less_real @ one_one_real @ A )
% 0.35/0.64       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.64         => ( ( ord_less_real @ one_one_real @ ( log @ A @ X ) )
% 0.35/0.64            = ( ord_less_real @ A @ X ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % one_less_log_cancel_iff
% 0.35/0.64  thf(fact_6868_log__less__one__cancel__iff,axiom,
% 0.35/0.64      ! [A: real,X: real] :
% 0.35/0.64        ( ( ord_less_real @ one_one_real @ A )
% 0.35/0.64       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.64         => ( ( ord_less_real @ ( log @ A @ X ) @ one_one_real )
% 0.35/0.64            = ( ord_less_real @ X @ A ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % log_less_one_cancel_iff
% 0.35/0.64  thf(fact_6869_log__less__cancel__iff,axiom,
% 0.35/0.64      ! [A: real,X: real,Y2: real] :
% 0.35/0.64        ( ( ord_less_real @ one_one_real @ A )
% 0.35/0.64       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.64         => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 0.35/0.64           => ( ( ord_less_real @ ( log @ A @ X ) @ ( log @ A @ Y2 ) )
% 0.35/0.64              = ( ord_less_real @ X @ Y2 ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % log_less_cancel_iff
% 0.35/0.64  thf(fact_6870_log__eq__one,axiom,
% 0.35/0.64      ! [A: real] :
% 0.35/0.64        ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.64       => ( ( A != one_one_real )
% 0.35/0.64         => ( ( log @ A @ A )
% 0.35/0.64            = one_one_real ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % log_eq_one
% 0.35/0.64  thf(fact_6871_or__numerals_I3_J,axiom,
% 0.35/0.64      ! [X: num,Y2: num] :
% 0.35/0.64        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y2 ) ) )
% 0.35/0.64        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y2 ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or_numerals(3)
% 0.35/0.64  thf(fact_6872_or__numerals_I3_J,axiom,
% 0.35/0.64      ! [X: num,Y2: num] :
% 0.35/0.64        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) )
% 0.35/0.64        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y2 ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or_numerals(3)
% 0.35/0.64  thf(fact_6873_sum_Ocl__ivl__Suc,axiom,
% 0.35/0.64      ! [N: nat,M: nat,G: nat > complex] :
% 0.35/0.64        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.35/0.64         => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.35/0.64            = zero_zero_complex ) )
% 0.35/0.64        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 0.35/0.64         => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.35/0.64            = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.cl_ivl_Suc
% 0.35/0.64  thf(fact_6874_sum_Ocl__ivl__Suc,axiom,
% 0.35/0.64      ! [N: nat,M: nat,G: nat > rat] :
% 0.35/0.64        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.35/0.64         => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.35/0.64            = zero_zero_rat ) )
% 0.35/0.64        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 0.35/0.64         => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.35/0.64            = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.cl_ivl_Suc
% 0.35/0.64  thf(fact_6875_sum_Ocl__ivl__Suc,axiom,
% 0.35/0.64      ! [N: nat,M: nat,G: nat > int] :
% 0.35/0.64        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.35/0.64         => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.35/0.64            = zero_zero_int ) )
% 0.35/0.64        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 0.35/0.64         => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.35/0.64            = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.cl_ivl_Suc
% 0.35/0.64  thf(fact_6876_sum_Ocl__ivl__Suc,axiom,
% 0.35/0.64      ! [N: nat,M: nat,G: nat > nat] :
% 0.35/0.64        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.35/0.64         => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.35/0.64            = zero_zero_nat ) )
% 0.35/0.64        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 0.35/0.64         => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.35/0.64            = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.cl_ivl_Suc
% 0.35/0.64  thf(fact_6877_sum_Ocl__ivl__Suc,axiom,
% 0.35/0.64      ! [N: nat,M: nat,G: nat > real] :
% 0.35/0.64        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.35/0.64         => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.35/0.64            = zero_zero_real ) )
% 0.35/0.64        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 0.35/0.64         => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.35/0.64            = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.cl_ivl_Suc
% 0.35/0.64  thf(fact_6878_or__numerals_I5_J,axiom,
% 0.35/0.64      ! [X: num] :
% 0.35/0.64        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ one_one_int )
% 0.35/0.64        = ( numeral_numeral_int @ ( bit1 @ X ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or_numerals(5)
% 0.35/0.64  thf(fact_6879_or__numerals_I5_J,axiom,
% 0.35/0.64      ! [X: num] :
% 0.35/0.64        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ one_one_nat )
% 0.35/0.64        = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or_numerals(5)
% 0.35/0.64  thf(fact_6880_or__numerals_I1_J,axiom,
% 0.35/0.64      ! [Y2: num] :
% 0.35/0.64        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y2 ) ) )
% 0.35/0.64        = ( numeral_numeral_int @ ( bit1 @ Y2 ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or_numerals(1)
% 0.35/0.64  thf(fact_6881_or__numerals_I1_J,axiom,
% 0.35/0.64      ! [Y2: num] :
% 0.35/0.64        ( ( bit_se1412395901928357646or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) )
% 0.35/0.64        = ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or_numerals(1)
% 0.35/0.64  thf(fact_6882_log__le__cancel__iff,axiom,
% 0.35/0.64      ! [A: real,X: real,Y2: real] :
% 0.35/0.64        ( ( ord_less_real @ one_one_real @ A )
% 0.35/0.64       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.64         => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 0.35/0.64           => ( ( ord_less_eq_real @ ( log @ A @ X ) @ ( log @ A @ Y2 ) )
% 0.35/0.64              = ( ord_less_eq_real @ X @ Y2 ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % log_le_cancel_iff
% 0.35/0.64  thf(fact_6883_log__le__one__cancel__iff,axiom,
% 0.35/0.64      ! [A: real,X: real] :
% 0.35/0.64        ( ( ord_less_real @ one_one_real @ A )
% 0.35/0.64       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.64         => ( ( ord_less_eq_real @ ( log @ A @ X ) @ one_one_real )
% 0.35/0.64            = ( ord_less_eq_real @ X @ A ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % log_le_one_cancel_iff
% 0.35/0.64  thf(fact_6884_one__le__log__cancel__iff,axiom,
% 0.35/0.64      ! [A: real,X: real] :
% 0.35/0.64        ( ( ord_less_real @ one_one_real @ A )
% 0.35/0.64       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.64         => ( ( ord_less_eq_real @ one_one_real @ ( log @ A @ X ) )
% 0.35/0.64            = ( ord_less_eq_real @ A @ X ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % one_le_log_cancel_iff
% 0.35/0.64  thf(fact_6885_log__le__zero__cancel__iff,axiom,
% 0.35/0.64      ! [A: real,X: real] :
% 0.35/0.64        ( ( ord_less_real @ one_one_real @ A )
% 0.35/0.64       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.64         => ( ( ord_less_eq_real @ ( log @ A @ X ) @ zero_zero_real )
% 0.35/0.64            = ( ord_less_eq_real @ X @ one_one_real ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % log_le_zero_cancel_iff
% 0.35/0.64  thf(fact_6886_zero__le__log__cancel__iff,axiom,
% 0.35/0.64      ! [A: real,X: real] :
% 0.35/0.64        ( ( ord_less_real @ one_one_real @ A )
% 0.35/0.64       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.64         => ( ( ord_less_eq_real @ zero_zero_real @ ( log @ A @ X ) )
% 0.35/0.64            = ( ord_less_eq_real @ one_one_real @ X ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % zero_le_log_cancel_iff
% 0.35/0.64  thf(fact_6887_add__neg__numeral__special_I6_J,axiom,
% 0.35/0.64      ! [M: num] :
% 0.35/0.64        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ M ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % add_neg_numeral_special(6)
% 0.35/0.64  thf(fact_6888_add__neg__numeral__special_I6_J,axiom,
% 0.35/0.64      ! [M: num] :
% 0.35/0.64        ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 0.35/0.64        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ M ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % add_neg_numeral_special(6)
% 0.35/0.64  thf(fact_6889_add__neg__numeral__special_I6_J,axiom,
% 0.35/0.64      ! [M: num] :
% 0.35/0.64        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.35/0.64        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % add_neg_numeral_special(6)
% 0.35/0.64  thf(fact_6890_add__neg__numeral__special_I6_J,axiom,
% 0.35/0.64      ! [M: num] :
% 0.35/0.64        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.64        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % add_neg_numeral_special(6)
% 0.35/0.64  thf(fact_6891_add__neg__numeral__special_I6_J,axiom,
% 0.35/0.64      ! [M: num] :
% 0.35/0.64        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.35/0.64        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ M ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % add_neg_numeral_special(6)
% 0.35/0.64  thf(fact_6892_add__neg__numeral__special_I5_J,axiom,
% 0.35/0.64      ! [N: num] :
% 0.35/0.64        ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % add_neg_numeral_special(5)
% 0.35/0.64  thf(fact_6893_add__neg__numeral__special_I5_J,axiom,
% 0.35/0.64      ! [N: num] :
% 0.35/0.64        ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.35/0.64        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % add_neg_numeral_special(5)
% 0.35/0.64  thf(fact_6894_add__neg__numeral__special_I5_J,axiom,
% 0.35/0.64      ! [N: num] :
% 0.35/0.64        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 0.35/0.64        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % add_neg_numeral_special(5)
% 0.35/0.64  thf(fact_6895_add__neg__numeral__special_I5_J,axiom,
% 0.35/0.64      ! [N: num] :
% 0.35/0.64        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.35/0.64        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % add_neg_numeral_special(5)
% 0.35/0.64  thf(fact_6896_add__neg__numeral__special_I5_J,axiom,
% 0.35/0.64      ! [N: num] :
% 0.35/0.64        ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.35/0.64        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % add_neg_numeral_special(5)
% 0.35/0.64  thf(fact_6897_diff__numeral__special_I6_J,axiom,
% 0.35/0.64      ! [M: num] :
% 0.35/0.64        ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.64        = ( numeral_numeral_int @ ( inc @ M ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % diff_numeral_special(6)
% 0.35/0.64  thf(fact_6898_diff__numeral__special_I6_J,axiom,
% 0.35/0.64      ! [M: num] :
% 0.35/0.64        ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) )
% 0.35/0.64        = ( numeral_numeral_real @ ( inc @ M ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % diff_numeral_special(6)
% 0.35/0.64  thf(fact_6899_diff__numeral__special_I6_J,axiom,
% 0.35/0.64      ! [M: num] :
% 0.35/0.64        ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.35/0.64        = ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % diff_numeral_special(6)
% 0.35/0.64  thf(fact_6900_diff__numeral__special_I6_J,axiom,
% 0.35/0.64      ! [M: num] :
% 0.35/0.64        ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.64        = ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % diff_numeral_special(6)
% 0.35/0.64  thf(fact_6901_diff__numeral__special_I6_J,axiom,
% 0.35/0.64      ! [M: num] :
% 0.35/0.64        ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.35/0.64        = ( numeral_numeral_rat @ ( inc @ M ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % diff_numeral_special(6)
% 0.35/0.64  thf(fact_6902_diff__numeral__special_I5_J,axiom,
% 0.35/0.64      ! [N: num] :
% 0.35/0.64        ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 0.35/0.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % diff_numeral_special(5)
% 0.35/0.64  thf(fact_6903_diff__numeral__special_I5_J,axiom,
% 0.35/0.64      ! [N: num] :
% 0.35/0.64        ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ N ) )
% 0.35/0.64        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % diff_numeral_special(5)
% 0.35/0.64  thf(fact_6904_diff__numeral__special_I5_J,axiom,
% 0.35/0.64      ! [N: num] :
% 0.35/0.64        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( numera6690914467698888265omplex @ N ) )
% 0.35/0.64        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % diff_numeral_special(5)
% 0.35/0.64  thf(fact_6905_diff__numeral__special_I5_J,axiom,
% 0.35/0.64      ! [N: num] :
% 0.35/0.64        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ N ) )
% 0.35/0.64        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % diff_numeral_special(5)
% 0.35/0.64  thf(fact_6906_diff__numeral__special_I5_J,axiom,
% 0.35/0.64      ! [N: num] :
% 0.35/0.64        ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ N ) )
% 0.35/0.64        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % diff_numeral_special(5)
% 0.35/0.64  thf(fact_6907_or__minus__numerals_I6_J,axiom,
% 0.35/0.64      ! [N: num] :
% 0.35/0.64        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 0.35/0.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or_minus_numerals(6)
% 0.35/0.64  thf(fact_6908_or__minus__numerals_I2_J,axiom,
% 0.35/0.64      ! [N: num] :
% 0.35/0.64        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.35/0.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or_minus_numerals(2)
% 0.35/0.64  thf(fact_6909_sum__zero__power,axiom,
% 0.35/0.64      ! [A2: set_nat,C: nat > rat] :
% 0.35/0.64        ( ( ( ( finite_finite_nat @ A2 )
% 0.35/0.64            & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.35/0.64         => ( ( groups2906978787729119204at_rat
% 0.35/0.64              @ ^ [I3: nat] : ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ zero_zero_rat @ I3 ) )
% 0.35/0.64              @ A2 )
% 0.35/0.64            = ( C @ zero_zero_nat ) ) )
% 0.35/0.64        & ( ~ ( ( finite_finite_nat @ A2 )
% 0.35/0.64              & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.35/0.64         => ( ( groups2906978787729119204at_rat
% 0.35/0.64              @ ^ [I3: nat] : ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ zero_zero_rat @ I3 ) )
% 0.35/0.64              @ A2 )
% 0.35/0.64            = zero_zero_rat ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_zero_power
% 0.35/0.64  thf(fact_6910_sum__zero__power,axiom,
% 0.35/0.64      ! [A2: set_nat,C: nat > complex] :
% 0.35/0.64        ( ( ( ( finite_finite_nat @ A2 )
% 0.35/0.64            & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.35/0.64         => ( ( groups2073611262835488442omplex
% 0.35/0.64              @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ zero_zero_complex @ I3 ) )
% 0.35/0.64              @ A2 )
% 0.35/0.64            = ( C @ zero_zero_nat ) ) )
% 0.35/0.64        & ( ~ ( ( finite_finite_nat @ A2 )
% 0.35/0.64              & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.35/0.64         => ( ( groups2073611262835488442omplex
% 0.35/0.64              @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ zero_zero_complex @ I3 ) )
% 0.35/0.64              @ A2 )
% 0.35/0.64            = zero_zero_complex ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_zero_power
% 0.35/0.64  thf(fact_6911_sum__zero__power,axiom,
% 0.35/0.64      ! [A2: set_nat,C: nat > real] :
% 0.35/0.64        ( ( ( ( finite_finite_nat @ A2 )
% 0.35/0.64            & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.35/0.64         => ( ( groups6591440286371151544t_real
% 0.35/0.64              @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ zero_zero_real @ I3 ) )
% 0.35/0.64              @ A2 )
% 0.35/0.64            = ( C @ zero_zero_nat ) ) )
% 0.35/0.64        & ( ~ ( ( finite_finite_nat @ A2 )
% 0.35/0.64              & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.35/0.64         => ( ( groups6591440286371151544t_real
% 0.35/0.64              @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ zero_zero_real @ I3 ) )
% 0.35/0.64              @ A2 )
% 0.35/0.64            = zero_zero_real ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_zero_power
% 0.35/0.64  thf(fact_6912_real__sqrt__abs,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64        ( ( sqrt @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.64        = ( abs_abs_real @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_abs
% 0.35/0.64  thf(fact_6913_sum__zero__power_H,axiom,
% 0.35/0.64      ! [A2: set_nat,C: nat > complex,D2: nat > complex] :
% 0.35/0.64        ( ( ( ( finite_finite_nat @ A2 )
% 0.35/0.64            & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.35/0.64         => ( ( groups2073611262835488442omplex
% 0.35/0.64              @ ^ [I3: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ zero_zero_complex @ I3 ) ) @ ( D2 @ I3 ) )
% 0.35/0.64              @ A2 )
% 0.35/0.64            = ( divide1717551699836669952omplex @ ( C @ zero_zero_nat ) @ ( D2 @ zero_zero_nat ) ) ) )
% 0.35/0.64        & ( ~ ( ( finite_finite_nat @ A2 )
% 0.35/0.64              & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.35/0.64         => ( ( groups2073611262835488442omplex
% 0.35/0.64              @ ^ [I3: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ zero_zero_complex @ I3 ) ) @ ( D2 @ I3 ) )
% 0.35/0.64              @ A2 )
% 0.35/0.64            = zero_zero_complex ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_zero_power'
% 0.35/0.64  thf(fact_6914_sum__zero__power_H,axiom,
% 0.35/0.64      ! [A2: set_nat,C: nat > rat,D2: nat > rat] :
% 0.35/0.64        ( ( ( ( finite_finite_nat @ A2 )
% 0.35/0.64            & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.35/0.64         => ( ( groups2906978787729119204at_rat
% 0.35/0.64              @ ^ [I3: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ zero_zero_rat @ I3 ) ) @ ( D2 @ I3 ) )
% 0.35/0.64              @ A2 )
% 0.35/0.64            = ( divide_divide_rat @ ( C @ zero_zero_nat ) @ ( D2 @ zero_zero_nat ) ) ) )
% 0.35/0.64        & ( ~ ( ( finite_finite_nat @ A2 )
% 0.35/0.64              & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.35/0.64         => ( ( groups2906978787729119204at_rat
% 0.35/0.64              @ ^ [I3: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ zero_zero_rat @ I3 ) ) @ ( D2 @ I3 ) )
% 0.35/0.64              @ A2 )
% 0.35/0.64            = zero_zero_rat ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_zero_power'
% 0.35/0.64  thf(fact_6915_sum__zero__power_H,axiom,
% 0.35/0.64      ! [A2: set_nat,C: nat > real,D2: nat > real] :
% 0.35/0.64        ( ( ( ( finite_finite_nat @ A2 )
% 0.35/0.64            & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.35/0.64         => ( ( groups6591440286371151544t_real
% 0.35/0.64              @ ^ [I3: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ zero_zero_real @ I3 ) ) @ ( D2 @ I3 ) )
% 0.35/0.64              @ A2 )
% 0.35/0.64            = ( divide_divide_real @ ( C @ zero_zero_nat ) @ ( D2 @ zero_zero_nat ) ) ) )
% 0.35/0.64        & ( ~ ( ( finite_finite_nat @ A2 )
% 0.35/0.64              & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.35/0.64         => ( ( groups6591440286371151544t_real
% 0.35/0.64              @ ^ [I3: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ zero_zero_real @ I3 ) ) @ ( D2 @ I3 ) )
% 0.35/0.64              @ A2 )
% 0.35/0.64            = zero_zero_real ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_zero_power'
% 0.35/0.64  thf(fact_6916_real__sqrt__pow2,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.64       => ( ( power_power_real @ ( sqrt @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.64          = X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_pow2
% 0.35/0.64  thf(fact_6917_real__sqrt__pow2__iff,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64        ( ( ( power_power_real @ ( sqrt @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.64          = X )
% 0.35/0.64        = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_pow2_iff
% 0.35/0.64  thf(fact_6918_real__sqrt__sum__squares__mult__squared__eq,axiom,
% 0.35/0.64      ! [X: real,Y2: real,Xa2: real,Ya: real] :
% 0.35/0.64        ( ( power_power_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.64        = ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_sum_squares_mult_squared_eq
% 0.35/0.64  thf(fact_6919_or__numerals_I7_J,axiom,
% 0.35/0.64      ! [X: num,Y2: num] :
% 0.35/0.64        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y2 ) ) )
% 0.35/0.64        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y2 ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or_numerals(7)
% 0.35/0.64  thf(fact_6920_or__numerals_I7_J,axiom,
% 0.35/0.64      ! [X: num,Y2: num] :
% 0.35/0.64        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) )
% 0.35/0.64        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y2 ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or_numerals(7)
% 0.35/0.64  thf(fact_6921_or__numerals_I6_J,axiom,
% 0.35/0.64      ! [X: num,Y2: num] :
% 0.35/0.64        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y2 ) ) )
% 0.35/0.64        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y2 ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or_numerals(6)
% 0.35/0.64  thf(fact_6922_or__numerals_I6_J,axiom,
% 0.35/0.64      ! [X: num,Y2: num] :
% 0.35/0.64        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) )
% 0.35/0.64        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y2 ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or_numerals(6)
% 0.35/0.64  thf(fact_6923_or__numerals_I4_J,axiom,
% 0.35/0.64      ! [X: num,Y2: num] :
% 0.35/0.64        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y2 ) ) )
% 0.35/0.64        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y2 ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or_numerals(4)
% 0.35/0.64  thf(fact_6924_or__numerals_I4_J,axiom,
% 0.35/0.64      ! [X: num,Y2: num] :
% 0.35/0.64        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) )
% 0.35/0.64        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y2 ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or_numerals(4)
% 0.35/0.64  thf(fact_6925_of__int__or__eq,axiom,
% 0.35/0.64      ! [K: int,L2: int] :
% 0.35/0.64        ( ( ring_1_of_int_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) )
% 0.35/0.64        = ( bit_se1409905431419307370or_int @ ( ring_1_of_int_int @ K ) @ ( ring_1_of_int_int @ L2 ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_int_or_eq
% 0.35/0.64  thf(fact_6926_or_Oassoc,axiom,
% 0.35/0.64      ! [A: int,B: int,C: int] :
% 0.35/0.64        ( ( bit_se1409905431419307370or_int @ ( bit_se1409905431419307370or_int @ A @ B ) @ C )
% 0.35/0.64        = ( bit_se1409905431419307370or_int @ A @ ( bit_se1409905431419307370or_int @ B @ C ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or.assoc
% 0.35/0.64  thf(fact_6927_or_Oassoc,axiom,
% 0.35/0.64      ! [A: nat,B: nat,C: nat] :
% 0.35/0.64        ( ( bit_se1412395901928357646or_nat @ ( bit_se1412395901928357646or_nat @ A @ B ) @ C )
% 0.35/0.64        = ( bit_se1412395901928357646or_nat @ A @ ( bit_se1412395901928357646or_nat @ B @ C ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or.assoc
% 0.35/0.64  thf(fact_6928_or_Ocommute,axiom,
% 0.35/0.64      ( bit_se1409905431419307370or_int
% 0.35/0.64      = ( ^ [A3: int,B4: int] : ( bit_se1409905431419307370or_int @ B4 @ A3 ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or.commute
% 0.35/0.64  thf(fact_6929_or_Ocommute,axiom,
% 0.35/0.64      ( bit_se1412395901928357646or_nat
% 0.35/0.64      = ( ^ [A3: nat,B4: nat] : ( bit_se1412395901928357646or_nat @ B4 @ A3 ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or.commute
% 0.35/0.64  thf(fact_6930_or_Oleft__commute,axiom,
% 0.35/0.64      ! [B: int,A: int,C: int] :
% 0.35/0.64        ( ( bit_se1409905431419307370or_int @ B @ ( bit_se1409905431419307370or_int @ A @ C ) )
% 0.35/0.64        = ( bit_se1409905431419307370or_int @ A @ ( bit_se1409905431419307370or_int @ B @ C ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or.left_commute
% 0.35/0.64  thf(fact_6931_or_Oleft__commute,axiom,
% 0.35/0.64      ! [B: nat,A: nat,C: nat] :
% 0.35/0.64        ( ( bit_se1412395901928357646or_nat @ B @ ( bit_se1412395901928357646or_nat @ A @ C ) )
% 0.35/0.64        = ( bit_se1412395901928357646or_nat @ A @ ( bit_se1412395901928357646or_nat @ B @ C ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or.left_commute
% 0.35/0.64  thf(fact_6932_or__eq__0__iff,axiom,
% 0.35/0.64      ! [A: int,B: int] :
% 0.35/0.64        ( ( ( bit_se1409905431419307370or_int @ A @ B )
% 0.35/0.64          = zero_zero_int )
% 0.35/0.64        = ( ( A = zero_zero_int )
% 0.35/0.64          & ( B = zero_zero_int ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or_eq_0_iff
% 0.35/0.64  thf(fact_6933_or__eq__0__iff,axiom,
% 0.35/0.64      ! [A: nat,B: nat] :
% 0.35/0.64        ( ( ( bit_se1412395901928357646or_nat @ A @ B )
% 0.35/0.64          = zero_zero_nat )
% 0.35/0.64        = ( ( A = zero_zero_nat )
% 0.35/0.64          & ( B = zero_zero_nat ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or_eq_0_iff
% 0.35/0.64  thf(fact_6934_bit_Odisj__zero__right,axiom,
% 0.35/0.64      ! [X: int] :
% 0.35/0.64        ( ( bit_se1409905431419307370or_int @ X @ zero_zero_int )
% 0.35/0.64        = X ) ).
% 0.35/0.64  
% 0.35/0.64  % bit.disj_zero_right
% 0.35/0.64  thf(fact_6935_real__sqrt__less__mono,axiom,
% 0.35/0.64      ! [X: real,Y2: real] :
% 0.35/0.64        ( ( ord_less_real @ X @ Y2 )
% 0.35/0.64       => ( ord_less_real @ ( sqrt @ X ) @ ( sqrt @ Y2 ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_less_mono
% 0.35/0.64  thf(fact_6936_real__sqrt__le__mono,axiom,
% 0.35/0.64      ! [X: real,Y2: real] :
% 0.35/0.64        ( ( ord_less_eq_real @ X @ Y2 )
% 0.35/0.64       => ( ord_less_eq_real @ ( sqrt @ X ) @ ( sqrt @ Y2 ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_le_mono
% 0.35/0.64  thf(fact_6937_real__sqrt__divide,axiom,
% 0.35/0.64      ! [X: real,Y2: real] :
% 0.35/0.64        ( ( sqrt @ ( divide_divide_real @ X @ Y2 ) )
% 0.35/0.64        = ( divide_divide_real @ ( sqrt @ X ) @ ( sqrt @ Y2 ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_divide
% 0.35/0.64  thf(fact_6938_real__sqrt__mult,axiom,
% 0.35/0.64      ! [X: real,Y2: real] :
% 0.35/0.64        ( ( sqrt @ ( times_times_real @ X @ Y2 ) )
% 0.35/0.64        = ( times_times_real @ ( sqrt @ X ) @ ( sqrt @ Y2 ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_mult
% 0.35/0.64  thf(fact_6939_real__sqrt__power,axiom,
% 0.35/0.64      ! [X: real,K: nat] :
% 0.35/0.64        ( ( sqrt @ ( power_power_real @ X @ K ) )
% 0.35/0.64        = ( power_power_real @ ( sqrt @ X ) @ K ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_power
% 0.35/0.64  thf(fact_6940_real__sqrt__minus,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64        ( ( sqrt @ ( uminus_uminus_real @ X ) )
% 0.35/0.64        = ( uminus_uminus_real @ ( sqrt @ X ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_minus
% 0.35/0.64  thf(fact_6941_bit_Oconj__disj__distrib,axiom,
% 0.35/0.64      ! [X: int,Y2: int,Z: int] :
% 0.35/0.64        ( ( bit_se725231765392027082nd_int @ X @ ( bit_se1409905431419307370or_int @ Y2 @ Z ) )
% 0.35/0.64        = ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ X @ Y2 ) @ ( bit_se725231765392027082nd_int @ X @ Z ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % bit.conj_disj_distrib
% 0.35/0.64  thf(fact_6942_bit_Odisj__conj__distrib,axiom,
% 0.35/0.64      ! [X: int,Y2: int,Z: int] :
% 0.35/0.64        ( ( bit_se1409905431419307370or_int @ X @ ( bit_se725231765392027082nd_int @ Y2 @ Z ) )
% 0.35/0.64        = ( bit_se725231765392027082nd_int @ ( bit_se1409905431419307370or_int @ X @ Y2 ) @ ( bit_se1409905431419307370or_int @ X @ Z ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % bit.disj_conj_distrib
% 0.35/0.64  thf(fact_6943_bit_Oconj__disj__distrib2,axiom,
% 0.35/0.64      ! [Y2: int,Z: int,X: int] :
% 0.35/0.64        ( ( bit_se725231765392027082nd_int @ ( bit_se1409905431419307370or_int @ Y2 @ Z ) @ X )
% 0.35/0.64        = ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ Y2 @ X ) @ ( bit_se725231765392027082nd_int @ Z @ X ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % bit.conj_disj_distrib2
% 0.35/0.64  thf(fact_6944_bit_Odisj__conj__distrib2,axiom,
% 0.35/0.64      ! [Y2: int,Z: int,X: int] :
% 0.35/0.64        ( ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ Y2 @ Z ) @ X )
% 0.35/0.64        = ( bit_se725231765392027082nd_int @ ( bit_se1409905431419307370or_int @ Y2 @ X ) @ ( bit_se1409905431419307370or_int @ Z @ X ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % bit.disj_conj_distrib2
% 0.35/0.64  thf(fact_6945_num__induct,axiom,
% 0.35/0.64      ! [P: num > $o,X: num] :
% 0.35/0.64        ( ( P @ one )
% 0.35/0.64       => ( ! [X3: num] :
% 0.35/0.64              ( ( P @ X3 )
% 0.35/0.64             => ( P @ ( inc @ X3 ) ) )
% 0.35/0.64         => ( P @ X ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % num_induct
% 0.35/0.64  thf(fact_6946_add__inc,axiom,
% 0.35/0.64      ! [X: num,Y2: num] :
% 0.35/0.64        ( ( plus_plus_num @ X @ ( inc @ Y2 ) )
% 0.35/0.64        = ( inc @ ( plus_plus_num @ X @ Y2 ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % add_inc
% 0.35/0.64  thf(fact_6947_real__sqrt__gt__zero,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.64       => ( ord_less_real @ zero_zero_real @ ( sqrt @ X ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_gt_zero
% 0.35/0.64  thf(fact_6948_real__sqrt__eq__zero__cancel,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.64       => ( ( ( sqrt @ X )
% 0.35/0.64            = zero_zero_real )
% 0.35/0.64         => ( X = zero_zero_real ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_eq_zero_cancel
% 0.35/0.64  thf(fact_6949_real__sqrt__ge__zero,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.64       => ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ X ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_ge_zero
% 0.35/0.64  thf(fact_6950_sum__cong__Suc,axiom,
% 0.35/0.64      ! [A2: set_nat,F: nat > nat,G: nat > nat] :
% 0.35/0.64        ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 0.35/0.64       => ( ! [X3: nat] :
% 0.35/0.64              ( ( member_nat @ ( suc @ X3 ) @ A2 )
% 0.35/0.64             => ( ( F @ ( suc @ X3 ) )
% 0.35/0.64                = ( G @ ( suc @ X3 ) ) ) )
% 0.35/0.64         => ( ( groups3542108847815614940at_nat @ F @ A2 )
% 0.35/0.64            = ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_cong_Suc
% 0.35/0.64  thf(fact_6951_sum__cong__Suc,axiom,
% 0.35/0.64      ! [A2: set_nat,F: nat > real,G: nat > real] :
% 0.35/0.64        ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 0.35/0.64       => ( ! [X3: nat] :
% 0.35/0.64              ( ( member_nat @ ( suc @ X3 ) @ A2 )
% 0.35/0.64             => ( ( F @ ( suc @ X3 ) )
% 0.35/0.64                = ( G @ ( suc @ X3 ) ) ) )
% 0.35/0.64         => ( ( groups6591440286371151544t_real @ F @ A2 )
% 0.35/0.64            = ( groups6591440286371151544t_real @ G @ A2 ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_cong_Suc
% 0.35/0.64  thf(fact_6952_real__sqrt__ge__one,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64        ( ( ord_less_eq_real @ one_one_real @ X )
% 0.35/0.64       => ( ord_less_eq_real @ one_one_real @ ( sqrt @ X ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_ge_one
% 0.35/0.64  thf(fact_6953_OR__lower,axiom,
% 0.35/0.64      ! [X: int,Y2: int] :
% 0.35/0.64        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.35/0.64       => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 0.35/0.64         => ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ X @ Y2 ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % OR_lower
% 0.35/0.64  thf(fact_6954_or__greater__eq,axiom,
% 0.35/0.64      ! [L2: int,K: int] :
% 0.35/0.64        ( ( ord_less_eq_int @ zero_zero_int @ L2 )
% 0.35/0.64       => ( ord_less_eq_int @ K @ ( bit_se1409905431419307370or_int @ K @ L2 ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or_greater_eq
% 0.35/0.64  thf(fact_6955_log__def,axiom,
% 0.35/0.64      ( log
% 0.35/0.64      = ( ^ [A3: real,X2: real] : ( divide_divide_real @ ( ln_ln_real @ X2 ) @ ( ln_ln_real @ A3 ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % log_def
% 0.35/0.64  thf(fact_6956_plus__and__or,axiom,
% 0.35/0.64      ! [X: int,Y2: int] :
% 0.35/0.64        ( ( plus_plus_int @ ( bit_se725231765392027082nd_int @ X @ Y2 ) @ ( bit_se1409905431419307370or_int @ X @ Y2 ) )
% 0.35/0.64        = ( plus_plus_int @ X @ Y2 ) ) ).
% 0.35/0.64  
% 0.35/0.64  % plus_and_or
% 0.35/0.64  thf(fact_6957_sum__subtractf__nat,axiom,
% 0.35/0.64      ! [A2: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > nat,F: product_prod_nat_nat > nat] :
% 0.35/0.64        ( ! [X3: product_prod_nat_nat] :
% 0.35/0.64            ( ( member8440522571783428010at_nat @ X3 @ A2 )
% 0.35/0.64           => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 0.35/0.64       => ( ( groups977919841031483927at_nat
% 0.35/0.64            @ ^ [X2: product_prod_nat_nat] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 0.35/0.64            @ A2 )
% 0.35/0.64          = ( minus_minus_nat @ ( groups977919841031483927at_nat @ F @ A2 ) @ ( groups977919841031483927at_nat @ G @ A2 ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_subtractf_nat
% 0.35/0.64  thf(fact_6958_sum__subtractf__nat,axiom,
% 0.35/0.64      ! [A2: set_complex,G: complex > nat,F: complex > nat] :
% 0.35/0.64        ( ! [X3: complex] :
% 0.35/0.64            ( ( member_complex @ X3 @ A2 )
% 0.35/0.64           => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 0.35/0.64       => ( ( groups5693394587270226106ex_nat
% 0.35/0.64            @ ^ [X2: complex] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 0.35/0.64            @ A2 )
% 0.35/0.64          = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_subtractf_nat
% 0.35/0.64  thf(fact_6959_sum__subtractf__nat,axiom,
% 0.35/0.64      ! [A2: set_real,G: real > nat,F: real > nat] :
% 0.35/0.64        ( ! [X3: real] :
% 0.35/0.64            ( ( member_real @ X3 @ A2 )
% 0.35/0.64           => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 0.35/0.64       => ( ( groups1935376822645274424al_nat
% 0.35/0.64            @ ^ [X2: real] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 0.35/0.64            @ A2 )
% 0.35/0.64          = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_subtractf_nat
% 0.35/0.64  thf(fact_6960_sum__subtractf__nat,axiom,
% 0.35/0.64      ! [A2: set_int,G: int > nat,F: int > nat] :
% 0.35/0.64        ( ! [X3: int] :
% 0.35/0.64            ( ( member_int @ X3 @ A2 )
% 0.35/0.64           => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 0.35/0.64       => ( ( groups4541462559716669496nt_nat
% 0.35/0.64            @ ^ [X2: int] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 0.35/0.64            @ A2 )
% 0.35/0.64          = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_subtractf_nat
% 0.35/0.64  thf(fact_6961_sum__subtractf__nat,axiom,
% 0.35/0.64      ! [A2: set_nat,G: nat > nat,F: nat > nat] :
% 0.35/0.64        ( ! [X3: nat] :
% 0.35/0.64            ( ( member_nat @ X3 @ A2 )
% 0.35/0.64           => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 0.35/0.64       => ( ( groups3542108847815614940at_nat
% 0.35/0.64            @ ^ [X2: nat] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 0.35/0.64            @ A2 )
% 0.35/0.64          = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_subtractf_nat
% 0.35/0.64  thf(fact_6962_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 0.35/0.64      ! [G: nat > nat,M: nat,N: nat] :
% 0.35/0.64        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 0.35/0.64        = ( groups3542108847815614940at_nat
% 0.35/0.64          @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.35/0.64          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.shift_bounds_cl_Suc_ivl
% 0.35/0.64  thf(fact_6963_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 0.35/0.64      ! [G: nat > real,M: nat,N: nat] :
% 0.35/0.64        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 0.35/0.64        = ( groups6591440286371151544t_real
% 0.35/0.64          @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.35/0.64          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.shift_bounds_cl_Suc_ivl
% 0.35/0.64  thf(fact_6964_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 0.35/0.64      ! [G: nat > nat,M: nat,K: nat,N: nat] :
% 0.35/0.64        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 0.35/0.64        = ( groups3542108847815614940at_nat
% 0.35/0.64          @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 0.35/0.64          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.shift_bounds_cl_nat_ivl
% 0.35/0.64  thf(fact_6965_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 0.35/0.64      ! [G: nat > real,M: nat,K: nat,N: nat] :
% 0.35/0.64        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 0.35/0.64        = ( groups6591440286371151544t_real
% 0.35/0.64          @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 0.35/0.64          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.shift_bounds_cl_nat_ivl
% 0.35/0.64  thf(fact_6966_pow_Osimps_I1_J,axiom,
% 0.35/0.64      ! [X: num] :
% 0.35/0.64        ( ( pow @ X @ one )
% 0.35/0.64        = X ) ).
% 0.35/0.64  
% 0.35/0.64  % pow.simps(1)
% 0.35/0.64  thf(fact_6967_inc_Osimps_I1_J,axiom,
% 0.35/0.64      ( ( inc @ one )
% 0.35/0.64      = ( bit0 @ one ) ) ).
% 0.35/0.64  
% 0.35/0.64  % inc.simps(1)
% 0.35/0.64  thf(fact_6968_inc_Osimps_I3_J,axiom,
% 0.35/0.64      ! [X: num] :
% 0.35/0.64        ( ( inc @ ( bit1 @ X ) )
% 0.35/0.64        = ( bit0 @ ( inc @ X ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % inc.simps(3)
% 0.35/0.64  thf(fact_6969_inc_Osimps_I2_J,axiom,
% 0.35/0.64      ! [X: num] :
% 0.35/0.64        ( ( inc @ ( bit0 @ X ) )
% 0.35/0.64        = ( bit1 @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % inc.simps(2)
% 0.35/0.64  thf(fact_6970_sum__eq__Suc0__iff,axiom,
% 0.35/0.64      ! [A2: set_complex,F: complex > nat] :
% 0.35/0.64        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.64       => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 0.35/0.64            = ( suc @ zero_zero_nat ) )
% 0.35/0.64          = ( ? [X2: complex] :
% 0.35/0.64                ( ( member_complex @ X2 @ A2 )
% 0.35/0.64                & ( ( F @ X2 )
% 0.35/0.64                  = ( suc @ zero_zero_nat ) )
% 0.35/0.64                & ! [Y: complex] :
% 0.35/0.64                    ( ( member_complex @ Y @ A2 )
% 0.35/0.64                   => ( ( X2 != Y )
% 0.35/0.64                     => ( ( F @ Y )
% 0.35/0.64                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_eq_Suc0_iff
% 0.35/0.64  thf(fact_6971_sum__eq__Suc0__iff,axiom,
% 0.35/0.64      ! [A2: set_nat,F: nat > nat] :
% 0.35/0.64        ( ( finite_finite_nat @ A2 )
% 0.35/0.64       => ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 0.35/0.64            = ( suc @ zero_zero_nat ) )
% 0.35/0.64          = ( ? [X2: nat] :
% 0.35/0.64                ( ( member_nat @ X2 @ A2 )
% 0.35/0.64                & ( ( F @ X2 )
% 0.35/0.64                  = ( suc @ zero_zero_nat ) )
% 0.35/0.64                & ! [Y: nat] :
% 0.35/0.64                    ( ( member_nat @ Y @ A2 )
% 0.35/0.64                   => ( ( X2 != Y )
% 0.35/0.64                     => ( ( F @ Y )
% 0.35/0.64                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_eq_Suc0_iff
% 0.35/0.64  thf(fact_6972_sum__SucD,axiom,
% 0.35/0.64      ! [F: nat > nat,A2: set_nat,N: nat] :
% 0.35/0.64        ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 0.35/0.64          = ( suc @ N ) )
% 0.35/0.64       => ? [X3: nat] :
% 0.35/0.64            ( ( member_nat @ X3 @ A2 )
% 0.35/0.64            & ( ord_less_nat @ zero_zero_nat @ ( F @ X3 ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_SucD
% 0.35/0.64  thf(fact_6973_sum__eq__1__iff,axiom,
% 0.35/0.64      ! [A2: set_complex,F: complex > nat] :
% 0.35/0.64        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.64       => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 0.35/0.64            = one_one_nat )
% 0.35/0.64          = ( ? [X2: complex] :
% 0.35/0.64                ( ( member_complex @ X2 @ A2 )
% 0.35/0.64                & ( ( F @ X2 )
% 0.35/0.64                  = one_one_nat )
% 0.35/0.64                & ! [Y: complex] :
% 0.35/0.64                    ( ( member_complex @ Y @ A2 )
% 0.35/0.64                   => ( ( X2 != Y )
% 0.35/0.64                     => ( ( F @ Y )
% 0.35/0.64                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_eq_1_iff
% 0.35/0.64  thf(fact_6974_sum__eq__1__iff,axiom,
% 0.35/0.64      ! [A2: set_nat,F: nat > nat] :
% 0.35/0.64        ( ( finite_finite_nat @ A2 )
% 0.35/0.64       => ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 0.35/0.64            = one_one_nat )
% 0.35/0.64          = ( ? [X2: nat] :
% 0.35/0.64                ( ( member_nat @ X2 @ A2 )
% 0.35/0.64                & ( ( F @ X2 )
% 0.35/0.64                  = one_one_nat )
% 0.35/0.64                & ! [Y: nat] :
% 0.35/0.64                    ( ( member_nat @ Y @ A2 )
% 0.35/0.64                   => ( ( X2 != Y )
% 0.35/0.64                     => ( ( F @ Y )
% 0.35/0.64                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_eq_1_iff
% 0.35/0.64  thf(fact_6975_real__div__sqrt,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.64       => ( ( divide_divide_real @ X @ ( sqrt @ X ) )
% 0.35/0.64          = ( sqrt @ X ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_div_sqrt
% 0.35/0.64  thf(fact_6976_add__One,axiom,
% 0.35/0.64      ! [X: num] :
% 0.35/0.64        ( ( plus_plus_num @ X @ one )
% 0.35/0.64        = ( inc @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % add_One
% 0.35/0.64  thf(fact_6977_sqrt__add__le__add__sqrt,axiom,
% 0.35/0.64      ! [X: real,Y2: real] :
% 0.35/0.64        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.64       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 0.35/0.64         => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ X @ Y2 ) ) @ ( plus_plus_real @ ( sqrt @ X ) @ ( sqrt @ Y2 ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sqrt_add_le_add_sqrt
% 0.35/0.64  thf(fact_6978_le__real__sqrt__sumsq,axiom,
% 0.35/0.64      ! [X: real,Y2: real] : ( ord_less_eq_real @ X @ ( sqrt @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y2 @ Y2 ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % le_real_sqrt_sumsq
% 0.35/0.64  thf(fact_6979_inc__BitM__eq,axiom,
% 0.35/0.64      ! [N: num] :
% 0.35/0.64        ( ( inc @ ( bitM @ N ) )
% 0.35/0.64        = ( bit0 @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % inc_BitM_eq
% 0.35/0.64  thf(fact_6980_BitM__inc__eq,axiom,
% 0.35/0.64      ! [N: num] :
% 0.35/0.64        ( ( bitM @ ( inc @ N ) )
% 0.35/0.64        = ( bit1 @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % BitM_inc_eq
% 0.35/0.64  thf(fact_6981_log__ln,axiom,
% 0.35/0.64      ( ln_ln_real
% 0.35/0.64      = ( log @ ( exp_real @ one_one_real ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % log_ln
% 0.35/0.64  thf(fact_6982_mult__inc,axiom,
% 0.35/0.64      ! [X: num,Y2: num] :
% 0.35/0.64        ( ( times_times_num @ X @ ( inc @ Y2 ) )
% 0.35/0.64        = ( plus_plus_num @ ( times_times_num @ X @ Y2 ) @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % mult_inc
% 0.35/0.64  thf(fact_6983_sum__power__add,axiom,
% 0.35/0.64      ! [X: complex,M: nat,I6: set_nat] :
% 0.35/0.64        ( ( groups2073611262835488442omplex
% 0.35/0.64          @ ^ [I3: nat] : ( power_power_complex @ X @ ( plus_plus_nat @ M @ I3 ) )
% 0.35/0.64          @ I6 )
% 0.35/0.64        = ( times_times_complex @ ( power_power_complex @ X @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ I6 ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_power_add
% 0.35/0.64  thf(fact_6984_sum__power__add,axiom,
% 0.35/0.64      ! [X: int,M: nat,I6: set_nat] :
% 0.35/0.64        ( ( groups3539618377306564664at_int
% 0.35/0.64          @ ^ [I3: nat] : ( power_power_int @ X @ ( plus_plus_nat @ M @ I3 ) )
% 0.35/0.64          @ I6 )
% 0.35/0.64        = ( times_times_int @ ( power_power_int @ X @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ I6 ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_power_add
% 0.35/0.64  thf(fact_6985_sum__power__add,axiom,
% 0.35/0.64      ! [X: real,M: nat,I6: set_nat] :
% 0.35/0.64        ( ( groups6591440286371151544t_real
% 0.35/0.64          @ ^ [I3: nat] : ( power_power_real @ X @ ( plus_plus_nat @ M @ I3 ) )
% 0.35/0.64          @ I6 )
% 0.35/0.64        = ( times_times_real @ ( power_power_real @ X @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ I6 ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_power_add
% 0.35/0.64  thf(fact_6986_sum_OatLeastAtMost__rev,axiom,
% 0.35/0.64      ! [G: nat > nat,N: nat,M: nat] :
% 0.35/0.64        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 0.35/0.64        = ( groups3542108847815614940at_nat
% 0.35/0.64          @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I3 ) )
% 0.35/0.64          @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.atLeastAtMost_rev
% 0.35/0.64  thf(fact_6987_sum_OatLeastAtMost__rev,axiom,
% 0.35/0.64      ! [G: nat > real,N: nat,M: nat] :
% 0.35/0.64        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 0.35/0.64        = ( groups6591440286371151544t_real
% 0.35/0.64          @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I3 ) )
% 0.35/0.64          @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.atLeastAtMost_rev
% 0.35/0.64  thf(fact_6988_sum__roots__unity,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( ord_less_nat @ one_one_nat @ N )
% 0.35/0.64       => ( ( groups7754918857620584856omplex
% 0.35/0.64            @ ^ [X2: complex] : X2
% 0.35/0.64            @ ( collect_complex
% 0.35/0.64              @ ^ [Z4: complex] :
% 0.35/0.64                  ( ( power_power_complex @ Z4 @ N )
% 0.35/0.64                  = one_one_complex ) ) )
% 0.35/0.64          = zero_zero_complex ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_roots_unity
% 0.35/0.64  thf(fact_6989_sum__nth__roots,axiom,
% 0.35/0.64      ! [N: nat,C: complex] :
% 0.35/0.64        ( ( ord_less_nat @ one_one_nat @ N )
% 0.35/0.64       => ( ( groups7754918857620584856omplex
% 0.35/0.64            @ ^ [X2: complex] : X2
% 0.35/0.64            @ ( collect_complex
% 0.35/0.64              @ ^ [Z4: complex] :
% 0.35/0.64                  ( ( power_power_complex @ Z4 @ N )
% 0.35/0.64                  = C ) ) )
% 0.35/0.64          = zero_zero_complex ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_nth_roots
% 0.35/0.64  thf(fact_6990_sqrt2__less__2,axiom,
% 0.35/0.64      ord_less_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sqrt2_less_2
% 0.35/0.64  thf(fact_6991_even__or__iff,axiom,
% 0.35/0.64      ! [A: code_integer,B: code_integer] :
% 0.35/0.64        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1080825931792720795nteger @ A @ B ) )
% 0.35/0.64        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.35/0.64          & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % even_or_iff
% 0.35/0.64  thf(fact_6992_even__or__iff,axiom,
% 0.35/0.64      ! [A: int,B: int] :
% 0.35/0.64        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ A @ B ) )
% 0.35/0.64        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.64          & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % even_or_iff
% 0.35/0.64  thf(fact_6993_even__or__iff,axiom,
% 0.35/0.64      ! [A: nat,B: nat] :
% 0.35/0.64        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ A @ B ) )
% 0.35/0.64        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.64          & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % even_or_iff
% 0.35/0.64  thf(fact_6994_log__base__change,axiom,
% 0.35/0.64      ! [A: real,B: real,X: real] :
% 0.35/0.64        ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.64       => ( ( A != one_one_real )
% 0.35/0.64         => ( ( log @ B @ X )
% 0.35/0.64            = ( divide_divide_real @ ( log @ A @ X ) @ ( log @ A @ B ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % log_base_change
% 0.35/0.64  thf(fact_6995_sum__diff__nat,axiom,
% 0.35/0.64      ! [B2: set_complex,A2: set_complex,F: complex > nat] :
% 0.35/0.64        ( ( finite3207457112153483333omplex @ B2 )
% 0.35/0.64       => ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 0.35/0.64         => ( ( groups5693394587270226106ex_nat @ F @ ( minus_811609699411566653omplex @ A2 @ B2 ) )
% 0.35/0.64            = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B2 ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_diff_nat
% 0.35/0.64  thf(fact_6996_sum__diff__nat,axiom,
% 0.35/0.64      ! [B2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 0.35/0.64        ( ( finite6177210948735845034at_nat @ B2 )
% 0.35/0.64       => ( ( ord_le3146513528884898305at_nat @ B2 @ A2 )
% 0.35/0.64         => ( ( groups977919841031483927at_nat @ F @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) )
% 0.35/0.64            = ( minus_minus_nat @ ( groups977919841031483927at_nat @ F @ A2 ) @ ( groups977919841031483927at_nat @ F @ B2 ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_diff_nat
% 0.35/0.64  thf(fact_6997_sum__diff__nat,axiom,
% 0.35/0.64      ! [B2: set_real,A2: set_real,F: real > nat] :
% 0.35/0.64        ( ( finite_finite_real @ B2 )
% 0.35/0.64       => ( ( ord_less_eq_set_real @ B2 @ A2 )
% 0.35/0.64         => ( ( groups1935376822645274424al_nat @ F @ ( minus_minus_set_real @ A2 @ B2 ) )
% 0.35/0.64            = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ F @ B2 ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_diff_nat
% 0.35/0.64  thf(fact_6998_sum__diff__nat,axiom,
% 0.35/0.64      ! [B2: set_nat,A2: set_nat,F: nat > nat] :
% 0.35/0.64        ( ( finite_finite_nat @ B2 )
% 0.35/0.64       => ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 0.35/0.64         => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 0.35/0.64            = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ F @ B2 ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_diff_nat
% 0.35/0.64  thf(fact_6999_bit_Ocomplement__unique,axiom,
% 0.35/0.64      ! [A: code_integer,X: code_integer,Y2: code_integer] :
% 0.35/0.64        ( ( ( bit_se3949692690581998587nteger @ A @ X )
% 0.35/0.64          = zero_z3403309356797280102nteger )
% 0.35/0.64       => ( ( ( bit_se1080825931792720795nteger @ A @ X )
% 0.35/0.64            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.64         => ( ( ( bit_se3949692690581998587nteger @ A @ Y2 )
% 0.35/0.64              = zero_z3403309356797280102nteger )
% 0.35/0.64           => ( ( ( bit_se1080825931792720795nteger @ A @ Y2 )
% 0.35/0.64                = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.64             => ( X = Y2 ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % bit.complement_unique
% 0.35/0.64  thf(fact_7000_bit_Ocomplement__unique,axiom,
% 0.35/0.64      ! [A: int,X: int,Y2: int] :
% 0.35/0.64        ( ( ( bit_se725231765392027082nd_int @ A @ X )
% 0.35/0.64          = zero_zero_int )
% 0.35/0.64       => ( ( ( bit_se1409905431419307370or_int @ A @ X )
% 0.35/0.64            = ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.64         => ( ( ( bit_se725231765392027082nd_int @ A @ Y2 )
% 0.35/0.64              = zero_zero_int )
% 0.35/0.64           => ( ( ( bit_se1409905431419307370or_int @ A @ Y2 )
% 0.35/0.64                = ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.64             => ( X = Y2 ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % bit.complement_unique
% 0.35/0.64  thf(fact_7001_sum__diff1__nat,axiom,
% 0.35/0.64      ! [A: vEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 0.35/0.64        ( ( ( member_VEBT_VEBT @ A @ A2 )
% 0.35/0.64         => ( ( groups771621172384141258BT_nat @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.35/0.64            = ( minus_minus_nat @ ( groups771621172384141258BT_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.35/0.64        & ( ~ ( member_VEBT_VEBT @ A @ A2 )
% 0.35/0.64         => ( ( groups771621172384141258BT_nat @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.35/0.64            = ( groups771621172384141258BT_nat @ F @ A2 ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_diff1_nat
% 0.35/0.64  thf(fact_7002_sum__diff1__nat,axiom,
% 0.35/0.64      ! [A: complex,A2: set_complex,F: complex > nat] :
% 0.35/0.64        ( ( ( member_complex @ A @ A2 )
% 0.35/0.64         => ( ( groups5693394587270226106ex_nat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.35/0.64            = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.35/0.64        & ( ~ ( member_complex @ A @ A2 )
% 0.35/0.64         => ( ( groups5693394587270226106ex_nat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.35/0.64            = ( groups5693394587270226106ex_nat @ F @ A2 ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_diff1_nat
% 0.35/0.64  thf(fact_7003_sum__diff1__nat,axiom,
% 0.35/0.64      ! [A: int,A2: set_int,F: int > nat] :
% 0.35/0.64        ( ( ( member_int @ A @ A2 )
% 0.35/0.64         => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.35/0.64            = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.35/0.64        & ( ~ ( member_int @ A @ A2 )
% 0.35/0.64         => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.35/0.64            = ( groups4541462559716669496nt_nat @ F @ A2 ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_diff1_nat
% 0.35/0.64  thf(fact_7004_sum__diff1__nat,axiom,
% 0.35/0.64      ! [A: real,A2: set_real,F: real > nat] :
% 0.35/0.64        ( ( ( member_real @ A @ A2 )
% 0.35/0.64         => ( ( groups1935376822645274424al_nat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.35/0.64            = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.35/0.64        & ( ~ ( member_real @ A @ A2 )
% 0.35/0.64         => ( ( groups1935376822645274424al_nat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.35/0.64            = ( groups1935376822645274424al_nat @ F @ A2 ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_diff1_nat
% 0.35/0.64  thf(fact_7005_sum__diff1__nat,axiom,
% 0.35/0.64      ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 0.35/0.64        ( ( ( member8440522571783428010at_nat @ A @ A2 )
% 0.35/0.64         => ( ( groups977919841031483927at_nat @ F @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 0.35/0.64            = ( minus_minus_nat @ ( groups977919841031483927at_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.35/0.64        & ( ~ ( member8440522571783428010at_nat @ A @ A2 )
% 0.35/0.64         => ( ( groups977919841031483927at_nat @ F @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 0.35/0.64            = ( groups977919841031483927at_nat @ F @ A2 ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_diff1_nat
% 0.35/0.64  thf(fact_7006_sum__diff1__nat,axiom,
% 0.35/0.64      ! [A: nat,A2: set_nat,F: nat > nat] :
% 0.35/0.64        ( ( ( member_nat @ A @ A2 )
% 0.35/0.64         => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.35/0.64            = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.35/0.64        & ( ~ ( member_nat @ A @ A2 )
% 0.35/0.64         => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.35/0.64            = ( groups3542108847815614940at_nat @ F @ A2 ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_diff1_nat
% 0.35/0.64  thf(fact_7007_sum__shift__lb__Suc0__0,axiom,
% 0.35/0.64      ! [F: nat > complex,K: nat] :
% 0.35/0.64        ( ( ( F @ zero_zero_nat )
% 0.35/0.64          = zero_zero_complex )
% 0.35/0.64       => ( ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.35/0.64          = ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_shift_lb_Suc0_0
% 0.35/0.64  thf(fact_7008_sum__shift__lb__Suc0__0,axiom,
% 0.35/0.64      ! [F: nat > rat,K: nat] :
% 0.35/0.64        ( ( ( F @ zero_zero_nat )
% 0.35/0.64          = zero_zero_rat )
% 0.35/0.64       => ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.35/0.64          = ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_shift_lb_Suc0_0
% 0.35/0.64  thf(fact_7009_sum__shift__lb__Suc0__0,axiom,
% 0.35/0.64      ! [F: nat > int,K: nat] :
% 0.35/0.64        ( ( ( F @ zero_zero_nat )
% 0.35/0.64          = zero_zero_int )
% 0.35/0.64       => ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.35/0.64          = ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_shift_lb_Suc0_0
% 0.35/0.64  thf(fact_7010_sum__shift__lb__Suc0__0,axiom,
% 0.35/0.64      ! [F: nat > nat,K: nat] :
% 0.35/0.64        ( ( ( F @ zero_zero_nat )
% 0.35/0.64          = zero_zero_nat )
% 0.35/0.64       => ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.35/0.64          = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_shift_lb_Suc0_0
% 0.35/0.64  thf(fact_7011_sum__shift__lb__Suc0__0,axiom,
% 0.35/0.64      ! [F: nat > real,K: nat] :
% 0.35/0.64        ( ( ( F @ zero_zero_nat )
% 0.35/0.64          = zero_zero_real )
% 0.35/0.64       => ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.35/0.64          = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_shift_lb_Suc0_0
% 0.35/0.64  thf(fact_7012_sum_OatLeast0__atMost__Suc,axiom,
% 0.35/0.64      ! [G: nat > rat,N: nat] :
% 0.35/0.64        ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.35/0.64        = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.atLeast0_atMost_Suc
% 0.35/0.64  thf(fact_7013_sum_OatLeast0__atMost__Suc,axiom,
% 0.35/0.64      ! [G: nat > int,N: nat] :
% 0.35/0.64        ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.35/0.64        = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.atLeast0_atMost_Suc
% 0.35/0.64  thf(fact_7014_sum_OatLeast0__atMost__Suc,axiom,
% 0.35/0.64      ! [G: nat > complex,N: nat] :
% 0.35/0.64        ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.35/0.64        = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.atLeast0_atMost_Suc
% 0.35/0.64  thf(fact_7015_sum_OatLeast0__atMost__Suc,axiom,
% 0.35/0.64      ! [G: nat > nat,N: nat] :
% 0.35/0.64        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.35/0.64        = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.atLeast0_atMost_Suc
% 0.35/0.64  thf(fact_7016_sum_OatLeast0__atMost__Suc,axiom,
% 0.35/0.64      ! [G: nat > real,N: nat] :
% 0.35/0.64        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.35/0.64        = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.atLeast0_atMost_Suc
% 0.35/0.64  thf(fact_7017_sum_Onat__ivl__Suc_H,axiom,
% 0.35/0.64      ! [M: nat,N: nat,G: nat > rat] :
% 0.35/0.64        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.35/0.64       => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.35/0.64          = ( plus_plus_rat @ ( G @ ( suc @ N ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.nat_ivl_Suc'
% 0.35/0.64  thf(fact_7018_sum_Onat__ivl__Suc_H,axiom,
% 0.35/0.64      ! [M: nat,N: nat,G: nat > int] :
% 0.35/0.64        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.35/0.64       => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.35/0.64          = ( plus_plus_int @ ( G @ ( suc @ N ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.nat_ivl_Suc'
% 0.35/0.64  thf(fact_7019_sum_Onat__ivl__Suc_H,axiom,
% 0.35/0.64      ! [M: nat,N: nat,G: nat > complex] :
% 0.35/0.64        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.35/0.64       => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.35/0.64          = ( plus_plus_complex @ ( G @ ( suc @ N ) ) @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.nat_ivl_Suc'
% 0.35/0.64  thf(fact_7020_sum_Onat__ivl__Suc_H,axiom,
% 0.35/0.64      ! [M: nat,N: nat,G: nat > nat] :
% 0.35/0.64        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.35/0.64       => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.35/0.64          = ( plus_plus_nat @ ( G @ ( suc @ N ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.nat_ivl_Suc'
% 0.35/0.64  thf(fact_7021_sum_Onat__ivl__Suc_H,axiom,
% 0.35/0.64      ! [M: nat,N: nat,G: nat > real] :
% 0.35/0.64        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.35/0.64       => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.35/0.64          = ( plus_plus_real @ ( G @ ( suc @ N ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.nat_ivl_Suc'
% 0.35/0.64  thf(fact_7022_sum_OatLeast__Suc__atMost,axiom,
% 0.35/0.64      ! [M: nat,N: nat,G: nat > rat] :
% 0.35/0.64        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.64       => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.35/0.64          = ( plus_plus_rat @ ( G @ M ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.atLeast_Suc_atMost
% 0.35/0.64  thf(fact_7023_sum_OatLeast__Suc__atMost,axiom,
% 0.35/0.64      ! [M: nat,N: nat,G: nat > int] :
% 0.35/0.64        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.64       => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.35/0.64          = ( plus_plus_int @ ( G @ M ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.atLeast_Suc_atMost
% 0.35/0.64  thf(fact_7024_sum_OatLeast__Suc__atMost,axiom,
% 0.35/0.64      ! [M: nat,N: nat,G: nat > complex] :
% 0.35/0.64        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.64       => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.35/0.64          = ( plus_plus_complex @ ( G @ M ) @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.atLeast_Suc_atMost
% 0.35/0.64  thf(fact_7025_sum_OatLeast__Suc__atMost,axiom,
% 0.35/0.64      ! [M: nat,N: nat,G: nat > nat] :
% 0.35/0.64        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.64       => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.35/0.64          = ( plus_plus_nat @ ( G @ M ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.atLeast_Suc_atMost
% 0.35/0.64  thf(fact_7026_sum_OatLeast__Suc__atMost,axiom,
% 0.35/0.64      ! [M: nat,N: nat,G: nat > real] :
% 0.35/0.64        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.64       => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.35/0.64          = ( plus_plus_real @ ( G @ M ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.atLeast_Suc_atMost
% 0.35/0.64  thf(fact_7027_numeral__inc,axiom,
% 0.35/0.64      ! [X: num] :
% 0.35/0.64        ( ( numera6690914467698888265omplex @ ( inc @ X ) )
% 0.35/0.64        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X ) @ one_one_complex ) ) ).
% 0.35/0.64  
% 0.35/0.64  % numeral_inc
% 0.35/0.64  thf(fact_7028_numeral__inc,axiom,
% 0.35/0.64      ! [X: num] :
% 0.35/0.64        ( ( numeral_numeral_real @ ( inc @ X ) )
% 0.35/0.64        = ( plus_plus_real @ ( numeral_numeral_real @ X ) @ one_one_real ) ) ).
% 0.35/0.64  
% 0.35/0.64  % numeral_inc
% 0.35/0.64  thf(fact_7029_numeral__inc,axiom,
% 0.35/0.64      ! [X: num] :
% 0.35/0.64        ( ( numeral_numeral_rat @ ( inc @ X ) )
% 0.35/0.64        = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 0.35/0.64  
% 0.35/0.64  % numeral_inc
% 0.35/0.64  thf(fact_7030_numeral__inc,axiom,
% 0.35/0.64      ! [X: num] :
% 0.35/0.64        ( ( numeral_numeral_nat @ ( inc @ X ) )
% 0.35/0.64        = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 0.35/0.64  
% 0.35/0.64  % numeral_inc
% 0.35/0.64  thf(fact_7031_numeral__inc,axiom,
% 0.35/0.64      ! [X: num] :
% 0.35/0.64        ( ( numeral_numeral_int @ ( inc @ X ) )
% 0.35/0.64        = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 0.35/0.64  
% 0.35/0.64  % numeral_inc
% 0.35/0.64  thf(fact_7032_sum_OSuc__reindex__ivl,axiom,
% 0.35/0.64      ! [M: nat,N: nat,G: nat > rat] :
% 0.35/0.64        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.64       => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 0.35/0.64          = ( plus_plus_rat @ ( G @ M )
% 0.35/0.64            @ ( groups2906978787729119204at_rat
% 0.35/0.64              @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.35/0.64              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.Suc_reindex_ivl
% 0.35/0.64  thf(fact_7033_sum_OSuc__reindex__ivl,axiom,
% 0.35/0.64      ! [M: nat,N: nat,G: nat > int] :
% 0.35/0.64        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.64       => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 0.35/0.64          = ( plus_plus_int @ ( G @ M )
% 0.35/0.64            @ ( groups3539618377306564664at_int
% 0.35/0.64              @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.35/0.64              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.Suc_reindex_ivl
% 0.35/0.64  thf(fact_7034_sum_OSuc__reindex__ivl,axiom,
% 0.35/0.64      ! [M: nat,N: nat,G: nat > complex] :
% 0.35/0.64        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.64       => ( ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 0.35/0.64          = ( plus_plus_complex @ ( G @ M )
% 0.35/0.64            @ ( groups2073611262835488442omplex
% 0.35/0.64              @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.35/0.64              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.Suc_reindex_ivl
% 0.35/0.64  thf(fact_7035_sum_OSuc__reindex__ivl,axiom,
% 0.35/0.64      ! [M: nat,N: nat,G: nat > nat] :
% 0.35/0.64        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.64       => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 0.35/0.64          = ( plus_plus_nat @ ( G @ M )
% 0.35/0.64            @ ( groups3542108847815614940at_nat
% 0.35/0.64              @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.35/0.64              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.Suc_reindex_ivl
% 0.35/0.64  thf(fact_7036_sum_OSuc__reindex__ivl,axiom,
% 0.35/0.64      ! [M: nat,N: nat,G: nat > real] :
% 0.35/0.64        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.64       => ( ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 0.35/0.64          = ( plus_plus_real @ ( G @ M )
% 0.35/0.64            @ ( groups6591440286371151544t_real
% 0.35/0.64              @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.35/0.64              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.Suc_reindex_ivl
% 0.35/0.64  thf(fact_7037_sum__Suc__diff,axiom,
% 0.35/0.64      ! [M: nat,N: nat,F: nat > rat] :
% 0.35/0.64        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.35/0.64       => ( ( groups2906978787729119204at_rat
% 0.35/0.64            @ ^ [I3: nat] : ( minus_minus_rat @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 0.35/0.64            @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.35/0.64          = ( minus_minus_rat @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_Suc_diff
% 0.35/0.64  thf(fact_7038_sum__Suc__diff,axiom,
% 0.35/0.64      ! [M: nat,N: nat,F: nat > int] :
% 0.35/0.64        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.35/0.64       => ( ( groups3539618377306564664at_int
% 0.35/0.64            @ ^ [I3: nat] : ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 0.35/0.64            @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.35/0.64          = ( minus_minus_int @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_Suc_diff
% 0.35/0.64  thf(fact_7039_sum__Suc__diff,axiom,
% 0.35/0.64      ! [M: nat,N: nat,F: nat > real] :
% 0.35/0.64        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.35/0.64       => ( ( groups6591440286371151544t_real
% 0.35/0.64            @ ^ [I3: nat] : ( minus_minus_real @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 0.35/0.64            @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.35/0.64          = ( minus_minus_real @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_Suc_diff
% 0.35/0.64  thf(fact_7040_real__less__rsqrt,axiom,
% 0.35/0.64      ! [X: real,Y2: real] :
% 0.35/0.64        ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y2 )
% 0.35/0.64       => ( ord_less_real @ X @ ( sqrt @ Y2 ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_less_rsqrt
% 0.35/0.64  thf(fact_7041_sqrt__le__D,axiom,
% 0.35/0.64      ! [X: real,Y2: real] :
% 0.35/0.64        ( ( ord_less_eq_real @ ( sqrt @ X ) @ Y2 )
% 0.35/0.64       => ( ord_less_eq_real @ X @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sqrt_le_D
% 0.35/0.64  thf(fact_7042_real__le__rsqrt,axiom,
% 0.35/0.64      ! [X: real,Y2: real] :
% 0.35/0.64        ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y2 )
% 0.35/0.64       => ( ord_less_eq_real @ X @ ( sqrt @ Y2 ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_le_rsqrt
% 0.35/0.64  thf(fact_7043_log__mult,axiom,
% 0.35/0.64      ! [A: real,X: real,Y2: real] :
% 0.35/0.64        ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.64       => ( ( A != one_one_real )
% 0.35/0.64         => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.64           => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 0.35/0.64             => ( ( log @ A @ ( times_times_real @ X @ Y2 ) )
% 0.35/0.64                = ( plus_plus_real @ ( log @ A @ X ) @ ( log @ A @ Y2 ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % log_mult
% 0.35/0.64  thf(fact_7044_log__divide,axiom,
% 0.35/0.64      ! [A: real,X: real,Y2: real] :
% 0.35/0.64        ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.64       => ( ( A != one_one_real )
% 0.35/0.64         => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.64           => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 0.35/0.64             => ( ( log @ A @ ( divide_divide_real @ X @ Y2 ) )
% 0.35/0.64                = ( minus_minus_real @ ( log @ A @ X ) @ ( log @ A @ Y2 ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % log_divide
% 0.35/0.64  thf(fact_7045_sum_Oub__add__nat,axiom,
% 0.35/0.64      ! [M: nat,N: nat,G: nat > rat,P6: nat] :
% 0.35/0.64        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 0.35/0.64       => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 0.35/0.64          = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.ub_add_nat
% 0.35/0.64  thf(fact_7046_sum_Oub__add__nat,axiom,
% 0.35/0.64      ! [M: nat,N: nat,G: nat > int,P6: nat] :
% 0.35/0.64        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 0.35/0.64       => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 0.35/0.64          = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.ub_add_nat
% 0.35/0.64  thf(fact_7047_sum_Oub__add__nat,axiom,
% 0.35/0.64      ! [M: nat,N: nat,G: nat > complex,P6: nat] :
% 0.35/0.64        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 0.35/0.64       => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 0.35/0.64          = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.ub_add_nat
% 0.35/0.64  thf(fact_7048_sum_Oub__add__nat,axiom,
% 0.35/0.64      ! [M: nat,N: nat,G: nat > nat,P6: nat] :
% 0.35/0.64        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 0.35/0.64       => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 0.35/0.64          = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.ub_add_nat
% 0.35/0.64  thf(fact_7049_sum_Oub__add__nat,axiom,
% 0.35/0.64      ! [M: nat,N: nat,G: nat > real,P6: nat] :
% 0.35/0.64        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 0.35/0.64       => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 0.35/0.64          = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.ub_add_nat
% 0.35/0.64  thf(fact_7050_set__encode__def,axiom,
% 0.35/0.64      ( nat_set_encode
% 0.35/0.64      = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % set_encode_def
% 0.35/0.64  thf(fact_7051_real__le__lsqrt,axiom,
% 0.35/0.64      ! [X: real,Y2: real] :
% 0.35/0.64        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.64       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 0.35/0.64         => ( ( ord_less_eq_real @ X @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.64           => ( ord_less_eq_real @ ( sqrt @ X ) @ Y2 ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_le_lsqrt
% 0.35/0.64  thf(fact_7052_real__sqrt__unique,axiom,
% 0.35/0.64      ! [Y2: real,X: real] :
% 0.35/0.64        ( ( ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.64          = X )
% 0.35/0.64       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 0.35/0.64         => ( ( sqrt @ X )
% 0.35/0.64            = Y2 ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_unique
% 0.35/0.64  thf(fact_7053_lemma__real__divide__sqrt__less,axiom,
% 0.35/0.64      ! [U: real] :
% 0.35/0.64        ( ( ord_less_real @ zero_zero_real @ U )
% 0.35/0.64       => ( ord_less_real @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ U ) ) ).
% 0.35/0.64  
% 0.35/0.64  % lemma_real_divide_sqrt_less
% 0.35/0.64  thf(fact_7054_real__sqrt__sum__squares__eq__cancel,axiom,
% 0.35/0.64      ! [X: real,Y2: real] :
% 0.35/0.64        ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.64          = X )
% 0.35/0.64       => ( Y2 = zero_zero_real ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_sum_squares_eq_cancel
% 0.35/0.64  thf(fact_7055_real__sqrt__sum__squares__eq__cancel2,axiom,
% 0.35/0.64      ! [X: real,Y2: real] :
% 0.35/0.64        ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.64          = Y2 )
% 0.35/0.64       => ( X = zero_zero_real ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_sum_squares_eq_cancel2
% 0.35/0.64  thf(fact_7056_real__sqrt__sum__squares__ge1,axiom,
% 0.35/0.64      ! [X: real,Y2: real] : ( ord_less_eq_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_sum_squares_ge1
% 0.35/0.64  thf(fact_7057_real__sqrt__sum__squares__ge2,axiom,
% 0.35/0.64      ! [Y2: real,X: real] : ( ord_less_eq_real @ Y2 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_sum_squares_ge2
% 0.35/0.64  thf(fact_7058_real__sqrt__sum__squares__triangle__ineq,axiom,
% 0.35/0.64      ! [A: real,C: real,B: real,D2: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ ( plus_plus_real @ A @ C ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( plus_plus_real @ B @ D2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ C @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ D2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_sum_squares_triangle_ineq
% 0.35/0.64  thf(fact_7059_sqrt__ge__absD,axiom,
% 0.35/0.64      ! [X: real,Y2: real] :
% 0.35/0.64        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( sqrt @ Y2 ) )
% 0.35/0.64       => ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y2 ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sqrt_ge_absD
% 0.35/0.64  thf(fact_7060_log__eq__div__ln__mult__log,axiom,
% 0.35/0.64      ! [A: real,B: real,X: real] :
% 0.35/0.64        ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.64       => ( ( A != one_one_real )
% 0.35/0.64         => ( ( ord_less_real @ zero_zero_real @ B )
% 0.35/0.64           => ( ( B != one_one_real )
% 0.35/0.64             => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.64               => ( ( log @ A @ X )
% 0.35/0.64                  = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ B ) @ ( ln_ln_real @ A ) ) @ ( log @ B @ X ) ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % log_eq_div_ln_mult_log
% 0.35/0.64  thf(fact_7061_mask__Suc__exp,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( bit_se2002935070580805687sk_nat @ ( suc @ N ) )
% 0.35/0.64        = ( bit_se1412395901928357646or_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % mask_Suc_exp
% 0.35/0.64  thf(fact_7062_mask__Suc__exp,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( bit_se2000444600071755411sk_int @ ( suc @ N ) )
% 0.35/0.64        = ( bit_se1409905431419307370or_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( bit_se2000444600071755411sk_int @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % mask_Suc_exp
% 0.35/0.64  thf(fact_7063_sum__natinterval__diff,axiom,
% 0.35/0.64      ! [M: nat,N: nat,F: nat > complex] :
% 0.35/0.64        ( ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.64         => ( ( groups2073611262835488442omplex
% 0.35/0.64              @ ^ [K3: nat] : ( minus_minus_complex @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 0.35/0.64              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.35/0.64            = ( minus_minus_complex @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 0.35/0.64        & ( ~ ( ord_less_eq_nat @ M @ N )
% 0.35/0.64         => ( ( groups2073611262835488442omplex
% 0.35/0.64              @ ^ [K3: nat] : ( minus_minus_complex @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 0.35/0.64              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.35/0.64            = zero_zero_complex ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_natinterval_diff
% 0.35/0.64  thf(fact_7064_sum__natinterval__diff,axiom,
% 0.35/0.64      ! [M: nat,N: nat,F: nat > rat] :
% 0.35/0.64        ( ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.64         => ( ( groups2906978787729119204at_rat
% 0.35/0.64              @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 0.35/0.64              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.35/0.64            = ( minus_minus_rat @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 0.35/0.64        & ( ~ ( ord_less_eq_nat @ M @ N )
% 0.35/0.64         => ( ( groups2906978787729119204at_rat
% 0.35/0.64              @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 0.35/0.64              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.35/0.64            = zero_zero_rat ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_natinterval_diff
% 0.35/0.64  thf(fact_7065_sum__natinterval__diff,axiom,
% 0.35/0.64      ! [M: nat,N: nat,F: nat > int] :
% 0.35/0.64        ( ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.64         => ( ( groups3539618377306564664at_int
% 0.35/0.64              @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 0.35/0.64              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.35/0.64            = ( minus_minus_int @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 0.35/0.64        & ( ~ ( ord_less_eq_nat @ M @ N )
% 0.35/0.64         => ( ( groups3539618377306564664at_int
% 0.35/0.64              @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 0.35/0.64              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.35/0.64            = zero_zero_int ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_natinterval_diff
% 0.35/0.64  thf(fact_7066_sum__natinterval__diff,axiom,
% 0.35/0.64      ! [M: nat,N: nat,F: nat > real] :
% 0.35/0.64        ( ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.64         => ( ( groups6591440286371151544t_real
% 0.35/0.64              @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 0.35/0.64              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.35/0.64            = ( minus_minus_real @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 0.35/0.64        & ( ~ ( ord_less_eq_nat @ M @ N )
% 0.35/0.64         => ( ( groups6591440286371151544t_real
% 0.35/0.64              @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 0.35/0.64              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.35/0.64            = zero_zero_real ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_natinterval_diff
% 0.35/0.64  thf(fact_7067_sum__telescope_H_H,axiom,
% 0.35/0.64      ! [M: nat,N: nat,F: nat > rat] :
% 0.35/0.64        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.64       => ( ( groups2906978787729119204at_rat
% 0.35/0.64            @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 0.35/0.64            @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 0.35/0.64          = ( minus_minus_rat @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_telescope''
% 0.35/0.64  thf(fact_7068_sum__telescope_H_H,axiom,
% 0.35/0.64      ! [M: nat,N: nat,F: nat > int] :
% 0.35/0.64        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.64       => ( ( groups3539618377306564664at_int
% 0.35/0.64            @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 0.35/0.64            @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 0.35/0.64          = ( minus_minus_int @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_telescope''
% 0.35/0.64  thf(fact_7069_sum__telescope_H_H,axiom,
% 0.35/0.64      ! [M: nat,N: nat,F: nat > real] :
% 0.35/0.64        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.64       => ( ( groups6591440286371151544t_real
% 0.35/0.64            @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 0.35/0.64            @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 0.35/0.64          = ( minus_minus_real @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_telescope''
% 0.35/0.64  thf(fact_7070_real__less__lsqrt,axiom,
% 0.35/0.64      ! [X: real,Y2: real] :
% 0.35/0.64        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.64       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 0.35/0.64         => ( ( ord_less_real @ X @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.64           => ( ord_less_real @ ( sqrt @ X ) @ Y2 ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_less_lsqrt
% 0.35/0.64  thf(fact_7071_sqrt__sum__squares__le__sum,axiom,
% 0.35/0.64      ! [X: real,Y2: real] :
% 0.35/0.64        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.64       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 0.35/0.64         => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ X @ Y2 ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sqrt_sum_squares_le_sum
% 0.35/0.64  thf(fact_7072_one__or__eq,axiom,
% 0.35/0.64      ! [A: code_integer] :
% 0.35/0.64        ( ( bit_se1080825931792720795nteger @ one_one_Code_integer @ A )
% 0.35/0.64        = ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % one_or_eq
% 0.35/0.64  thf(fact_7073_one__or__eq,axiom,
% 0.35/0.64      ! [A: int] :
% 0.35/0.64        ( ( bit_se1409905431419307370or_int @ one_one_int @ A )
% 0.35/0.64        = ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % one_or_eq
% 0.35/0.64  thf(fact_7074_one__or__eq,axiom,
% 0.35/0.64      ! [A: nat] :
% 0.35/0.64        ( ( bit_se1412395901928357646or_nat @ one_one_nat @ A )
% 0.35/0.64        = ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % one_or_eq
% 0.35/0.64  thf(fact_7075_or__one__eq,axiom,
% 0.35/0.64      ! [A: code_integer] :
% 0.35/0.64        ( ( bit_se1080825931792720795nteger @ A @ one_one_Code_integer )
% 0.35/0.64        = ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or_one_eq
% 0.35/0.64  thf(fact_7076_or__one__eq,axiom,
% 0.35/0.64      ! [A: int] :
% 0.35/0.64        ( ( bit_se1409905431419307370or_int @ A @ one_one_int )
% 0.35/0.64        = ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or_one_eq
% 0.35/0.64  thf(fact_7077_or__one__eq,axiom,
% 0.35/0.64      ! [A: nat] :
% 0.35/0.64        ( ( bit_se1412395901928357646or_nat @ A @ one_one_nat )
% 0.35/0.64        = ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or_one_eq
% 0.35/0.64  thf(fact_7078_sqrt__even__pow2,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.64       => ( ( sqrt @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.64          = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sqrt_even_pow2
% 0.35/0.64  thf(fact_7079_mask__Suc__double,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( bit_se2002935070580805687sk_nat @ ( suc @ N ) )
% 0.35/0.64        = ( bit_se1412395901928357646or_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % mask_Suc_double
% 0.35/0.64  thf(fact_7080_mask__Suc__double,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( bit_se2000444600071755411sk_int @ ( suc @ N ) )
% 0.35/0.64        = ( bit_se1409905431419307370or_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ N ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % mask_Suc_double
% 0.35/0.64  thf(fact_7081_sqrt__sum__squares__le__sum__abs,axiom,
% 0.35/0.64      ! [X: real,Y2: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ Y2 ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sqrt_sum_squares_le_sum_abs
% 0.35/0.64  thf(fact_7082_real__sqrt__ge__abs2,axiom,
% 0.35/0.64      ! [Y2: real,X: real] : ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_ge_abs2
% 0.35/0.64  thf(fact_7083_real__sqrt__ge__abs1,axiom,
% 0.35/0.64      ! [X: real,Y2: real] : ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_ge_abs1
% 0.35/0.64  thf(fact_7084_ln__sqrt,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.64       => ( ( ln_ln_real @ ( sqrt @ X ) )
% 0.35/0.64          = ( divide_divide_real @ ( ln_ln_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ln_sqrt
% 0.35/0.64  thf(fact_7085_OR__upper,axiom,
% 0.35/0.64      ! [X: int,N: nat,Y2: int] :
% 0.35/0.64        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.35/0.64       => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.64         => ( ( ord_less_int @ Y2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.64           => ( ord_less_int @ ( bit_se1409905431419307370or_int @ X @ Y2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % OR_upper
% 0.35/0.64  thf(fact_7086_mask__eq__sum__exp,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int )
% 0.35/0.64        = ( groups3539618377306564664at_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.64          @ ( collect_nat
% 0.35/0.64            @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % mask_eq_sum_exp
% 0.35/0.64  thf(fact_7087_mask__eq__sum__exp,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat )
% 0.35/0.64        = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.64          @ ( collect_nat
% 0.35/0.64            @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % mask_eq_sum_exp
% 0.35/0.64  thf(fact_7088_sum__gp__multiplied,axiom,
% 0.35/0.64      ! [M: nat,N: nat,X: rat] :
% 0.35/0.64        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.64       => ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 0.35/0.64          = ( minus_minus_rat @ ( power_power_rat @ X @ M ) @ ( power_power_rat @ X @ ( suc @ N ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_gp_multiplied
% 0.35/0.64  thf(fact_7089_sum__gp__multiplied,axiom,
% 0.35/0.64      ! [M: nat,N: nat,X: complex] :
% 0.35/0.64        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.64       => ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 0.35/0.64          = ( minus_minus_complex @ ( power_power_complex @ X @ M ) @ ( power_power_complex @ X @ ( suc @ N ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_gp_multiplied
% 0.35/0.64  thf(fact_7090_sum__gp__multiplied,axiom,
% 0.35/0.64      ! [M: nat,N: nat,X: int] :
% 0.35/0.64        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.64       => ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 0.35/0.64          = ( minus_minus_int @ ( power_power_int @ X @ M ) @ ( power_power_int @ X @ ( suc @ N ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_gp_multiplied
% 0.35/0.64  thf(fact_7091_sum__gp__multiplied,axiom,
% 0.35/0.64      ! [M: nat,N: nat,X: real] :
% 0.35/0.64        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.64       => ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 0.35/0.64          = ( minus_minus_real @ ( power_power_real @ X @ M ) @ ( power_power_real @ X @ ( suc @ N ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum_gp_multiplied
% 0.35/0.64  thf(fact_7092_sum_Oin__pairs,axiom,
% 0.35/0.64      ! [G: nat > rat,M: nat,N: nat] :
% 0.35/0.64        ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.35/0.64        = ( groups2906978787729119204at_rat
% 0.35/0.64          @ ^ [I3: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.35/0.64          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.in_pairs
% 0.35/0.64  thf(fact_7093_sum_Oin__pairs,axiom,
% 0.35/0.64      ! [G: nat > int,M: nat,N: nat] :
% 0.35/0.64        ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.35/0.64        = ( groups3539618377306564664at_int
% 0.35/0.64          @ ^ [I3: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.35/0.64          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.in_pairs
% 0.35/0.64  thf(fact_7094_sum_Oin__pairs,axiom,
% 0.35/0.64      ! [G: nat > complex,M: nat,N: nat] :
% 0.35/0.64        ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.35/0.64        = ( groups2073611262835488442omplex
% 0.35/0.64          @ ^ [I3: nat] : ( plus_plus_complex @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.35/0.64          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.in_pairs
% 0.35/0.64  thf(fact_7095_sum_Oin__pairs,axiom,
% 0.35/0.64      ! [G: nat > nat,M: nat,N: nat] :
% 0.35/0.64        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.35/0.64        = ( groups3542108847815614940at_nat
% 0.35/0.64          @ ^ [I3: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.35/0.64          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.in_pairs
% 0.35/0.64  thf(fact_7096_sum_Oin__pairs,axiom,
% 0.35/0.64      ! [G: nat > real,M: nat,N: nat] :
% 0.35/0.64        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.35/0.64        = ( groups6591440286371151544t_real
% 0.35/0.64          @ ^ [I3: nat] : ( plus_plus_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.35/0.64          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sum.in_pairs
% 0.35/0.64  thf(fact_7097_real__sqrt__power__even,axiom,
% 0.35/0.64      ! [N: nat,X: real] :
% 0.35/0.64        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.64       => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.64         => ( ( power_power_real @ ( sqrt @ X ) @ N )
% 0.35/0.64            = ( power_power_real @ X @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_power_even
% 0.35/0.64  thf(fact_7098_arsinh__real__aux,axiom,
% 0.35/0.64      ! [X: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % arsinh_real_aux
% 0.35/0.64  thf(fact_7099_real__sqrt__sum__squares__mult__ge__zero,axiom,
% 0.35/0.64      ! [X: real,Y2: real,Xa2: real,Ya: real] : ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_sum_squares_mult_ge_zero
% 0.35/0.64  thf(fact_7100_arith__geo__mean__sqrt,axiom,
% 0.35/0.64      ! [X: real,Y2: real] :
% 0.35/0.64        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.64       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 0.35/0.64         => ( ord_less_eq_real @ ( sqrt @ ( times_times_real @ X @ Y2 ) ) @ ( divide_divide_real @ ( plus_plus_real @ X @ Y2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % arith_geo_mean_sqrt
% 0.35/0.64  thf(fact_7101_or__int__rec,axiom,
% 0.35/0.64      ( bit_se1409905431419307370or_int
% 0.35/0.64      = ( ^ [K3: int,L: int] :
% 0.35/0.64            ( plus_plus_int
% 0.35/0.64            @ ( zero_n2684676970156552555ol_int
% 0.35/0.64              @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 0.35/0.64                | ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 0.35/0.64            @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or_int_rec
% 0.35/0.64  thf(fact_7102_mask__eq__sum__exp__nat,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( suc @ zero_zero_nat ) )
% 0.35/0.64        = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.64          @ ( collect_nat
% 0.35/0.64            @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % mask_eq_sum_exp_nat
% 0.35/0.64  thf(fact_7103_gauss__sum__nat,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( groups3542108847815614940at_nat
% 0.35/0.64          @ ^ [X2: nat] : X2
% 0.35/0.64          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.35/0.64        = ( divide_divide_nat @ ( times_times_nat @ N @ ( suc @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % gauss_sum_nat
% 0.35/0.64  thf(fact_7104_cos__x__y__le__one,axiom,
% 0.35/0.64      ! [X: real,Y2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( divide_divide_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ one_one_real ) ).
% 0.35/0.64  
% 0.35/0.64  % cos_x_y_le_one
% 0.35/0.64  thf(fact_7105_real__sqrt__sum__squares__less,axiom,
% 0.35/0.64      ! [X: real,U: real,Y2: real] :
% 0.35/0.64        ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.35/0.64       => ( ( ord_less_real @ ( abs_abs_real @ Y2 ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.35/0.64         => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_sqrt_sum_squares_less
% 0.35/0.64  thf(fact_7106_arcosh__real__def,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64        ( ( ord_less_eq_real @ one_one_real @ X )
% 0.35/0.64       => ( ( arcosh_real @ X )
% 0.35/0.64          = ( ln_ln_real @ ( plus_plus_real @ X @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % arcosh_real_def
% 0.35/0.64  thf(fact_7107_arith__series__nat,axiom,
% 0.35/0.64      ! [A: nat,D2: nat,N: nat] :
% 0.35/0.64        ( ( groups3542108847815614940at_nat
% 0.35/0.64          @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I3 @ D2 ) )
% 0.35/0.64          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.35/0.64        = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ N @ D2 ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % arith_series_nat
% 0.35/0.64  thf(fact_7108_Sum__Icc__nat,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( groups3542108847815614940at_nat
% 0.35/0.64          @ ^ [X2: nat] : X2
% 0.35/0.64          @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.35/0.64        = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( plus_plus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % Sum_Icc_nat
% 0.35/0.64  thf(fact_7109_sqrt__sum__squares__half__less,axiom,
% 0.35/0.64      ! [X: real,U: real,Y2: real] :
% 0.35/0.64        ( ( ord_less_real @ X @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.64       => ( ( ord_less_real @ Y2 @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.64         => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.64           => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 0.35/0.64             => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % sqrt_sum_squares_half_less
% 0.35/0.64  thf(fact_7110_log__base__10__eq2,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.64       => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 0.35/0.64          = ( times_times_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ X ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % log_base_10_eq2
% 0.35/0.64  thf(fact_7111_height__double__log__univ__size,axiom,
% 0.35/0.64      ! [U: real,Deg: nat,T: vEBT_VEBT] :
% 0.35/0.64        ( ( U
% 0.35/0.64          = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Deg ) )
% 0.35/0.64       => ( ( vEBT_invar_vebt @ T @ Deg )
% 0.35/0.64         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_VEBT_height @ T ) ) @ ( plus_plus_real @ one_one_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % height_double_log_univ_size
% 0.35/0.64  thf(fact_7112_log__ceil__idem,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64        ( ( ord_less_eq_real @ one_one_real @ X )
% 0.35/0.64       => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 0.35/0.64          = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % log_ceil_idem
% 0.35/0.64  thf(fact_7113_arsinh__real__def,axiom,
% 0.35/0.64      ( arsinh_real
% 0.35/0.64      = ( ^ [X2: real] : ( ln_ln_real @ ( plus_plus_real @ X2 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % arsinh_real_def
% 0.35/0.64  thf(fact_7114_member__bound__size__univ,axiom,
% 0.35/0.64      ! [T: vEBT_VEBT,N: nat,U: real,X: nat] :
% 0.35/0.64        ( ( vEBT_invar_vebt @ T @ N )
% 0.35/0.64       => ( ( U
% 0.35/0.64            = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.64         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_m_e_m_b_e_r @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % member_bound_size_univ
% 0.35/0.64  thf(fact_7115_succ__bound__size__univ,axiom,
% 0.35/0.64      ! [T: vEBT_VEBT,N: nat,U: real,X: nat] :
% 0.35/0.64        ( ( vEBT_invar_vebt @ T @ N )
% 0.35/0.64       => ( ( U
% 0.35/0.64            = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.64         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_s_u_c_c @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % succ_bound_size_univ
% 0.35/0.64  thf(fact_7116_pred__bound__size__univ,axiom,
% 0.35/0.64      ! [T: vEBT_VEBT,N: nat,U: real,X: nat] :
% 0.35/0.64        ( ( vEBT_invar_vebt @ T @ N )
% 0.35/0.64       => ( ( U
% 0.35/0.64            = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.64         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_p_r_e_d @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % pred_bound_size_univ
% 0.35/0.64  thf(fact_7117_of__nat__eq__iff,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( ( semiri5074537144036343181t_real @ M )
% 0.35/0.64          = ( semiri5074537144036343181t_real @ N ) )
% 0.35/0.64        = ( M = N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_eq_iff
% 0.35/0.64  thf(fact_7118_of__nat__eq__iff,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( ( semiri1314217659103216013at_int @ M )
% 0.35/0.64          = ( semiri1314217659103216013at_int @ N ) )
% 0.35/0.64        = ( M = N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_eq_iff
% 0.35/0.64  thf(fact_7119_of__nat__eq__iff,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( ( semiri1316708129612266289at_nat @ M )
% 0.35/0.64          = ( semiri1316708129612266289at_nat @ N ) )
% 0.35/0.64        = ( M = N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_eq_iff
% 0.35/0.64  thf(fact_7120_of__nat__eq__iff,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( ( semiri8010041392384452111omplex @ M )
% 0.35/0.64          = ( semiri8010041392384452111omplex @ N ) )
% 0.35/0.64        = ( M = N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_eq_iff
% 0.35/0.64  thf(fact_7121_abs__of__nat,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( abs_abs_Code_integer @ ( semiri4939895301339042750nteger @ N ) )
% 0.35/0.64        = ( semiri4939895301339042750nteger @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % abs_of_nat
% 0.35/0.64  thf(fact_7122_abs__of__nat,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( abs_abs_real @ ( semiri5074537144036343181t_real @ N ) )
% 0.35/0.64        = ( semiri5074537144036343181t_real @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % abs_of_nat
% 0.35/0.64  thf(fact_7123_abs__of__nat,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( abs_abs_int @ ( semiri1314217659103216013at_int @ N ) )
% 0.35/0.64        = ( semiri1314217659103216013at_int @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % abs_of_nat
% 0.35/0.64  thf(fact_7124_of__int__ceiling__cancel,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64        ( ( ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) )
% 0.35/0.64          = X )
% 0.35/0.64        = ( ? [N2: int] :
% 0.35/0.64              ( X
% 0.35/0.64              = ( ring_1_of_int_real @ N2 ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_int_ceiling_cancel
% 0.35/0.64  thf(fact_7125_of__nat__eq__0__iff,axiom,
% 0.35/0.64      ! [M: nat] :
% 0.35/0.64        ( ( ( semiri681578069525770553at_rat @ M )
% 0.35/0.64          = zero_zero_rat )
% 0.35/0.64        = ( M = zero_zero_nat ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_eq_0_iff
% 0.35/0.64  thf(fact_7126_of__nat__eq__0__iff,axiom,
% 0.35/0.64      ! [M: nat] :
% 0.35/0.64        ( ( ( semiri5074537144036343181t_real @ M )
% 0.35/0.64          = zero_zero_real )
% 0.35/0.64        = ( M = zero_zero_nat ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_eq_0_iff
% 0.35/0.64  thf(fact_7127_of__nat__eq__0__iff,axiom,
% 0.35/0.64      ! [M: nat] :
% 0.35/0.64        ( ( ( semiri1314217659103216013at_int @ M )
% 0.35/0.64          = zero_zero_int )
% 0.35/0.64        = ( M = zero_zero_nat ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_eq_0_iff
% 0.35/0.64  thf(fact_7128_of__nat__eq__0__iff,axiom,
% 0.35/0.64      ! [M: nat] :
% 0.35/0.64        ( ( ( semiri1316708129612266289at_nat @ M )
% 0.35/0.64          = zero_zero_nat )
% 0.35/0.64        = ( M = zero_zero_nat ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_eq_0_iff
% 0.35/0.64  thf(fact_7129_of__nat__eq__0__iff,axiom,
% 0.35/0.64      ! [M: nat] :
% 0.35/0.64        ( ( ( semiri8010041392384452111omplex @ M )
% 0.35/0.64          = zero_zero_complex )
% 0.35/0.64        = ( M = zero_zero_nat ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_eq_0_iff
% 0.35/0.64  thf(fact_7130_of__nat__0__eq__iff,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( zero_zero_rat
% 0.35/0.64          = ( semiri681578069525770553at_rat @ N ) )
% 0.35/0.64        = ( zero_zero_nat = N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_0_eq_iff
% 0.35/0.64  thf(fact_7131_of__nat__0__eq__iff,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( zero_zero_real
% 0.35/0.64          = ( semiri5074537144036343181t_real @ N ) )
% 0.35/0.64        = ( zero_zero_nat = N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_0_eq_iff
% 0.35/0.64  thf(fact_7132_of__nat__0__eq__iff,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( zero_zero_int
% 0.35/0.64          = ( semiri1314217659103216013at_int @ N ) )
% 0.35/0.64        = ( zero_zero_nat = N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_0_eq_iff
% 0.35/0.64  thf(fact_7133_of__nat__0__eq__iff,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( zero_zero_nat
% 0.35/0.64          = ( semiri1316708129612266289at_nat @ N ) )
% 0.35/0.64        = ( zero_zero_nat = N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_0_eq_iff
% 0.35/0.64  thf(fact_7134_of__nat__0__eq__iff,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( zero_zero_complex
% 0.35/0.64          = ( semiri8010041392384452111omplex @ N ) )
% 0.35/0.64        = ( zero_zero_nat = N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_0_eq_iff
% 0.35/0.64  thf(fact_7135_of__nat__0,axiom,
% 0.35/0.64      ( ( semiri681578069525770553at_rat @ zero_zero_nat )
% 0.35/0.64      = zero_zero_rat ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_0
% 0.35/0.64  thf(fact_7136_of__nat__0,axiom,
% 0.35/0.64      ( ( semiri5074537144036343181t_real @ zero_zero_nat )
% 0.35/0.64      = zero_zero_real ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_0
% 0.35/0.64  thf(fact_7137_of__nat__0,axiom,
% 0.35/0.64      ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 0.35/0.64      = zero_zero_int ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_0
% 0.35/0.64  thf(fact_7138_of__nat__0,axiom,
% 0.35/0.64      ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 0.35/0.64      = zero_zero_nat ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_0
% 0.35/0.64  thf(fact_7139_of__nat__0,axiom,
% 0.35/0.64      ( ( semiri8010041392384452111omplex @ zero_zero_nat )
% 0.35/0.64      = zero_zero_complex ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_0
% 0.35/0.64  thf(fact_7140_of__nat__numeral,axiom,
% 0.35/0.64      ! [N: num] :
% 0.35/0.64        ( ( semiri681578069525770553at_rat @ ( numeral_numeral_nat @ N ) )
% 0.35/0.64        = ( numeral_numeral_rat @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_numeral
% 0.35/0.64  thf(fact_7141_of__nat__numeral,axiom,
% 0.35/0.64      ! [N: num] :
% 0.35/0.64        ( ( semiri5074537144036343181t_real @ ( numeral_numeral_nat @ N ) )
% 0.35/0.64        = ( numeral_numeral_real @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_numeral
% 0.35/0.64  thf(fact_7142_of__nat__numeral,axiom,
% 0.35/0.64      ! [N: num] :
% 0.35/0.64        ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 0.35/0.64        = ( numeral_numeral_int @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_numeral
% 0.35/0.64  thf(fact_7143_of__nat__numeral,axiom,
% 0.35/0.64      ! [N: num] :
% 0.35/0.64        ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N ) )
% 0.35/0.64        = ( numeral_numeral_nat @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_numeral
% 0.35/0.64  thf(fact_7144_of__nat__numeral,axiom,
% 0.35/0.64      ! [N: num] :
% 0.35/0.64        ( ( semiri8010041392384452111omplex @ ( numeral_numeral_nat @ N ) )
% 0.35/0.64        = ( numera6690914467698888265omplex @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_numeral
% 0.35/0.64  thf(fact_7145_of__nat__less__iff,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 0.35/0.64        = ( ord_less_nat @ M @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_less_iff
% 0.35/0.64  thf(fact_7146_of__nat__less__iff,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 0.35/0.64        = ( ord_less_nat @ M @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_less_iff
% 0.35/0.64  thf(fact_7147_of__nat__less__iff,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.35/0.64        = ( ord_less_nat @ M @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_less_iff
% 0.35/0.64  thf(fact_7148_of__nat__less__iff,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 0.35/0.64        = ( ord_less_nat @ M @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_less_iff
% 0.35/0.64  thf(fact_7149_of__nat__le__iff,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 0.35/0.64        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_le_iff
% 0.35/0.64  thf(fact_7150_of__nat__le__iff,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 0.35/0.64        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_le_iff
% 0.35/0.64  thf(fact_7151_of__nat__le__iff,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.35/0.64        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_le_iff
% 0.35/0.64  thf(fact_7152_of__nat__add,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ N ) )
% 0.35/0.64        = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_add
% 0.35/0.64  thf(fact_7153_of__nat__add,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ N ) )
% 0.35/0.64        = ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_add
% 0.35/0.64  thf(fact_7154_of__nat__add,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) )
% 0.35/0.64        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_add
% 0.35/0.64  thf(fact_7155_of__nat__add,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N ) )
% 0.35/0.64        = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_add
% 0.35/0.64  thf(fact_7156_of__nat__add,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( semiri8010041392384452111omplex @ ( plus_plus_nat @ M @ N ) )
% 0.35/0.64        = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_add
% 0.35/0.64  thf(fact_7157_of__nat__eq__1__iff,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( ( semiri681578069525770553at_rat @ N )
% 0.35/0.64          = one_one_rat )
% 0.35/0.64        = ( N = one_one_nat ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_eq_1_iff
% 0.35/0.64  thf(fact_7158_of__nat__eq__1__iff,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( ( semiri5074537144036343181t_real @ N )
% 0.35/0.64          = one_one_real )
% 0.35/0.64        = ( N = one_one_nat ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_eq_1_iff
% 0.35/0.64  thf(fact_7159_of__nat__eq__1__iff,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( ( semiri1314217659103216013at_int @ N )
% 0.35/0.64          = one_one_int )
% 0.35/0.64        = ( N = one_one_nat ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_eq_1_iff
% 0.35/0.64  thf(fact_7160_of__nat__eq__1__iff,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( ( semiri1316708129612266289at_nat @ N )
% 0.35/0.64          = one_one_nat )
% 0.35/0.64        = ( N = one_one_nat ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_eq_1_iff
% 0.35/0.64  thf(fact_7161_of__nat__eq__1__iff,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( ( semiri8010041392384452111omplex @ N )
% 0.35/0.64          = one_one_complex )
% 0.35/0.64        = ( N = one_one_nat ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_eq_1_iff
% 0.35/0.64  thf(fact_7162_of__nat__1__eq__iff,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( one_one_rat
% 0.35/0.64          = ( semiri681578069525770553at_rat @ N ) )
% 0.35/0.64        = ( N = one_one_nat ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_1_eq_iff
% 0.35/0.64  thf(fact_7163_of__nat__1__eq__iff,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( one_one_real
% 0.35/0.64          = ( semiri5074537144036343181t_real @ N ) )
% 0.35/0.64        = ( N = one_one_nat ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_1_eq_iff
% 0.35/0.64  thf(fact_7164_of__nat__1__eq__iff,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( one_one_int
% 0.35/0.64          = ( semiri1314217659103216013at_int @ N ) )
% 0.35/0.64        = ( N = one_one_nat ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_1_eq_iff
% 0.35/0.64  thf(fact_7165_of__nat__1__eq__iff,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( one_one_nat
% 0.35/0.64          = ( semiri1316708129612266289at_nat @ N ) )
% 0.35/0.64        = ( N = one_one_nat ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_1_eq_iff
% 0.35/0.64  thf(fact_7166_of__nat__1__eq__iff,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( one_one_complex
% 0.35/0.64          = ( semiri8010041392384452111omplex @ N ) )
% 0.35/0.64        = ( N = one_one_nat ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_1_eq_iff
% 0.35/0.64  thf(fact_7167_of__nat__1,axiom,
% 0.35/0.64      ( ( semiri681578069525770553at_rat @ one_one_nat )
% 0.35/0.64      = one_one_rat ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_1
% 0.35/0.64  thf(fact_7168_of__nat__1,axiom,
% 0.35/0.64      ( ( semiri5074537144036343181t_real @ one_one_nat )
% 0.35/0.64      = one_one_real ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_1
% 0.35/0.64  thf(fact_7169_of__nat__1,axiom,
% 0.35/0.64      ( ( semiri1314217659103216013at_int @ one_one_nat )
% 0.35/0.64      = one_one_int ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_1
% 0.35/0.64  thf(fact_7170_of__nat__1,axiom,
% 0.35/0.64      ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 0.35/0.64      = one_one_nat ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_1
% 0.35/0.64  thf(fact_7171_of__nat__1,axiom,
% 0.35/0.64      ( ( semiri8010041392384452111omplex @ one_one_nat )
% 0.35/0.64      = one_one_complex ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_1
% 0.35/0.64  thf(fact_7172_of__nat__mult,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( semiri5074537144036343181t_real @ ( times_times_nat @ M @ N ) )
% 0.35/0.64        = ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_mult
% 0.35/0.64  thf(fact_7173_of__nat__mult,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M @ N ) )
% 0.35/0.64        = ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_mult
% 0.35/0.64  thf(fact_7174_of__nat__mult,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N ) )
% 0.35/0.64        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_mult
% 0.35/0.64  thf(fact_7175_of__nat__mult,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( semiri8010041392384452111omplex @ ( times_times_nat @ M @ N ) )
% 0.35/0.64        = ( times_times_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_mult
% 0.35/0.64  thf(fact_7176_of__nat__power,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( semiri5074537144036343181t_real @ ( power_power_nat @ M @ N ) )
% 0.35/0.64        = ( power_power_real @ ( semiri5074537144036343181t_real @ M ) @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_power
% 0.35/0.64  thf(fact_7177_of__nat__power,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( semiri1314217659103216013at_int @ ( power_power_nat @ M @ N ) )
% 0.35/0.64        = ( power_power_int @ ( semiri1314217659103216013at_int @ M ) @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_power
% 0.35/0.64  thf(fact_7178_of__nat__power,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( semiri1316708129612266289at_nat @ ( power_power_nat @ M @ N ) )
% 0.35/0.64        = ( power_power_nat @ ( semiri1316708129612266289at_nat @ M ) @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_power
% 0.35/0.64  thf(fact_7179_of__nat__power,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( semiri8010041392384452111omplex @ ( power_power_nat @ M @ N ) )
% 0.35/0.64        = ( power_power_complex @ ( semiri8010041392384452111omplex @ M ) @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_power
% 0.35/0.64  thf(fact_7180_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 0.35/0.64      ! [B: nat,W: nat,X: nat] :
% 0.35/0.64        ( ( ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W )
% 0.35/0.64          = ( semiri5074537144036343181t_real @ X ) )
% 0.35/0.64        = ( ( power_power_nat @ B @ W )
% 0.35/0.64          = X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_eq_of_nat_power_cancel_iff
% 0.35/0.64  thf(fact_7181_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 0.35/0.64      ! [B: nat,W: nat,X: nat] :
% 0.35/0.64        ( ( ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W )
% 0.35/0.64          = ( semiri1314217659103216013at_int @ X ) )
% 0.35/0.64        = ( ( power_power_nat @ B @ W )
% 0.35/0.64          = X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_eq_of_nat_power_cancel_iff
% 0.35/0.64  thf(fact_7182_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 0.35/0.64      ! [B: nat,W: nat,X: nat] :
% 0.35/0.64        ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W )
% 0.35/0.64          = ( semiri1316708129612266289at_nat @ X ) )
% 0.35/0.64        = ( ( power_power_nat @ B @ W )
% 0.35/0.64          = X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_eq_of_nat_power_cancel_iff
% 0.35/0.64  thf(fact_7183_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 0.35/0.64      ! [B: nat,W: nat,X: nat] :
% 0.35/0.64        ( ( ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W )
% 0.35/0.64          = ( semiri8010041392384452111omplex @ X ) )
% 0.35/0.64        = ( ( power_power_nat @ B @ W )
% 0.35/0.64          = X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_eq_of_nat_power_cancel_iff
% 0.35/0.64  thf(fact_7184_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 0.35/0.64      ! [X: nat,B: nat,W: nat] :
% 0.35/0.64        ( ( ( semiri5074537144036343181t_real @ X )
% 0.35/0.64          = ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 0.35/0.64        = ( X
% 0.35/0.64          = ( power_power_nat @ B @ W ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_power_eq_of_nat_cancel_iff
% 0.35/0.64  thf(fact_7185_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 0.35/0.64      ! [X: nat,B: nat,W: nat] :
% 0.35/0.64        ( ( ( semiri1314217659103216013at_int @ X )
% 0.35/0.64          = ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 0.35/0.64        = ( X
% 0.35/0.64          = ( power_power_nat @ B @ W ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_power_eq_of_nat_cancel_iff
% 0.35/0.64  thf(fact_7186_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 0.35/0.64      ! [X: nat,B: nat,W: nat] :
% 0.35/0.64        ( ( ( semiri1316708129612266289at_nat @ X )
% 0.35/0.64          = ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 0.35/0.64        = ( X
% 0.35/0.64          = ( power_power_nat @ B @ W ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_power_eq_of_nat_cancel_iff
% 0.35/0.64  thf(fact_7187_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 0.35/0.64      ! [X: nat,B: nat,W: nat] :
% 0.35/0.64        ( ( ( semiri8010041392384452111omplex @ X )
% 0.35/0.64          = ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W ) )
% 0.35/0.64        = ( X
% 0.35/0.64          = ( power_power_nat @ B @ W ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_power_eq_of_nat_cancel_iff
% 0.35/0.64  thf(fact_7188_ceiling__numeral,axiom,
% 0.35/0.64      ! [V: num] :
% 0.35/0.64        ( ( archim7802044766580827645g_real @ ( numeral_numeral_real @ V ) )
% 0.35/0.64        = ( numeral_numeral_int @ V ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_numeral
% 0.35/0.64  thf(fact_7189_ceiling__numeral,axiom,
% 0.35/0.64      ! [V: num] :
% 0.35/0.64        ( ( archim2889992004027027881ng_rat @ ( numeral_numeral_rat @ V ) )
% 0.35/0.64        = ( numeral_numeral_int @ V ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_numeral
% 0.35/0.64  thf(fact_7190_ceiling__one,axiom,
% 0.35/0.64      ( ( archim2889992004027027881ng_rat @ one_one_rat )
% 0.35/0.64      = one_one_int ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_one
% 0.35/0.64  thf(fact_7191_ceiling__one,axiom,
% 0.35/0.64      ( ( archim7802044766580827645g_real @ one_one_real )
% 0.35/0.64      = one_one_int ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_one
% 0.35/0.64  thf(fact_7192_of__nat__of__bool,axiom,
% 0.35/0.64      ! [P: $o] :
% 0.35/0.64        ( ( semiri5074537144036343181t_real @ ( zero_n2687167440665602831ol_nat @ P ) )
% 0.35/0.64        = ( zero_n3304061248610475627l_real @ P ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_of_bool
% 0.35/0.64  thf(fact_7193_of__nat__of__bool,axiom,
% 0.35/0.64      ! [P: $o] :
% 0.35/0.64        ( ( semiri8010041392384452111omplex @ ( zero_n2687167440665602831ol_nat @ P ) )
% 0.35/0.64        = ( zero_n1201886186963655149omplex @ P ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_of_bool
% 0.35/0.64  thf(fact_7194_of__nat__of__bool,axiom,
% 0.35/0.64      ! [P: $o] :
% 0.35/0.64        ( ( semiri1316708129612266289at_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 0.35/0.64        = ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_of_bool
% 0.35/0.64  thf(fact_7195_of__nat__of__bool,axiom,
% 0.35/0.64      ! [P: $o] :
% 0.35/0.64        ( ( semiri1314217659103216013at_int @ ( zero_n2687167440665602831ol_nat @ P ) )
% 0.35/0.64        = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_of_bool
% 0.35/0.64  thf(fact_7196_of__nat__of__bool,axiom,
% 0.35/0.64      ! [P: $o] :
% 0.35/0.64        ( ( semiri4939895301339042750nteger @ ( zero_n2687167440665602831ol_nat @ P ) )
% 0.35/0.64        = ( zero_n356916108424825756nteger @ P ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_of_bool
% 0.35/0.64  thf(fact_7197_of__nat__le__0__iff,axiom,
% 0.35/0.64      ! [M: nat] :
% 0.35/0.64        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat )
% 0.35/0.64        = ( M = zero_zero_nat ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_le_0_iff
% 0.35/0.64  thf(fact_7198_of__nat__le__0__iff,axiom,
% 0.35/0.64      ! [M: nat] :
% 0.35/0.64        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real )
% 0.35/0.64        = ( M = zero_zero_nat ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_le_0_iff
% 0.35/0.64  thf(fact_7199_of__nat__le__0__iff,axiom,
% 0.35/0.64      ! [M: nat] :
% 0.35/0.64        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat )
% 0.35/0.64        = ( M = zero_zero_nat ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_le_0_iff
% 0.35/0.64  thf(fact_7200_of__nat__le__0__iff,axiom,
% 0.35/0.64      ! [M: nat] :
% 0.35/0.64        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int )
% 0.35/0.64        = ( M = zero_zero_nat ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_le_0_iff
% 0.35/0.64  thf(fact_7201_of__nat__Suc,axiom,
% 0.35/0.64      ! [M: nat] :
% 0.35/0.64        ( ( semiri681578069525770553at_rat @ ( suc @ M ) )
% 0.35/0.64        = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_Suc
% 0.35/0.64  thf(fact_7202_of__nat__Suc,axiom,
% 0.35/0.64      ! [M: nat] :
% 0.35/0.64        ( ( semiri5074537144036343181t_real @ ( suc @ M ) )
% 0.35/0.64        = ( plus_plus_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_Suc
% 0.35/0.64  thf(fact_7203_of__nat__Suc,axiom,
% 0.35/0.64      ! [M: nat] :
% 0.35/0.64        ( ( semiri1314217659103216013at_int @ ( suc @ M ) )
% 0.35/0.64        = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_Suc
% 0.35/0.64  thf(fact_7204_of__nat__Suc,axiom,
% 0.35/0.64      ! [M: nat] :
% 0.35/0.64        ( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
% 0.35/0.64        = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_Suc
% 0.35/0.64  thf(fact_7205_of__nat__Suc,axiom,
% 0.35/0.64      ! [M: nat] :
% 0.35/0.64        ( ( semiri8010041392384452111omplex @ ( suc @ M ) )
% 0.35/0.64        = ( plus_plus_complex @ one_one_complex @ ( semiri8010041392384452111omplex @ M ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_Suc
% 0.35/0.64  thf(fact_7206_or__nat__numerals_I2_J,axiom,
% 0.35/0.64      ! [Y2: num] :
% 0.35/0.64        ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) )
% 0.35/0.64        = ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or_nat_numerals(2)
% 0.35/0.64  thf(fact_7207_or__nat__numerals_I4_J,axiom,
% 0.35/0.64      ! [X: num] :
% 0.35/0.64        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 0.35/0.64        = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or_nat_numerals(4)
% 0.35/0.64  thf(fact_7208_ceiling__add__of__int,axiom,
% 0.35/0.64      ! [X: rat,Z: int] :
% 0.35/0.64        ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ ( ring_1_of_int_rat @ Z ) ) )
% 0.35/0.64        = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ Z ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_add_of_int
% 0.35/0.64  thf(fact_7209_ceiling__add__of__int,axiom,
% 0.35/0.64      ! [X: real,Z: int] :
% 0.35/0.64        ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X @ ( ring_1_of_int_real @ Z ) ) )
% 0.35/0.64        = ( plus_plus_int @ ( archim7802044766580827645g_real @ X ) @ Z ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_add_of_int
% 0.35/0.64  thf(fact_7210_ceiling__diff__of__int,axiom,
% 0.35/0.64      ! [X: rat,Z: int] :
% 0.35/0.64        ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X @ ( ring_1_of_int_rat @ Z ) ) )
% 0.35/0.64        = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X ) @ Z ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_diff_of_int
% 0.35/0.64  thf(fact_7211_ceiling__diff__of__int,axiom,
% 0.35/0.64      ! [X: real,Z: int] :
% 0.35/0.64        ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X @ ( ring_1_of_int_real @ Z ) ) )
% 0.35/0.64        = ( minus_minus_int @ ( archim7802044766580827645g_real @ X ) @ Z ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_diff_of_int
% 0.35/0.64  thf(fact_7212_of__nat__0__less__iff,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) )
% 0.35/0.64        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_0_less_iff
% 0.35/0.64  thf(fact_7213_of__nat__0__less__iff,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( ord_less_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) )
% 0.35/0.64        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_0_less_iff
% 0.35/0.64  thf(fact_7214_of__nat__0__less__iff,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) )
% 0.35/0.64        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_0_less_iff
% 0.35/0.64  thf(fact_7215_of__nat__0__less__iff,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) )
% 0.35/0.64        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_0_less_iff
% 0.35/0.64  thf(fact_7216_or__nat__numerals_I1_J,axiom,
% 0.35/0.64      ! [Y2: num] :
% 0.35/0.64        ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) )
% 0.35/0.64        = ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or_nat_numerals(1)
% 0.35/0.64  thf(fact_7217_or__nat__numerals_I3_J,axiom,
% 0.35/0.64      ! [X: num] :
% 0.35/0.64        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 0.35/0.64        = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % or_nat_numerals(3)
% 0.35/0.64  thf(fact_7218_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 0.35/0.64      ! [Y2: nat,X: num,N: nat] :
% 0.35/0.64        ( ( ( semiri681578069525770553at_rat @ Y2 )
% 0.35/0.64          = ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 0.35/0.64        = ( Y2
% 0.35/0.64          = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_of_nat_eq_numeral_power_cancel_iff
% 0.35/0.64  thf(fact_7219_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 0.35/0.64      ! [Y2: nat,X: num,N: nat] :
% 0.35/0.64        ( ( ( semiri5074537144036343181t_real @ Y2 )
% 0.35/0.64          = ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 0.35/0.64        = ( Y2
% 0.35/0.64          = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_of_nat_eq_numeral_power_cancel_iff
% 0.35/0.64  thf(fact_7220_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 0.35/0.64      ! [Y2: nat,X: num,N: nat] :
% 0.35/0.64        ( ( ( semiri1314217659103216013at_int @ Y2 )
% 0.35/0.64          = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 0.35/0.64        = ( Y2
% 0.35/0.64          = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_of_nat_eq_numeral_power_cancel_iff
% 0.35/0.64  thf(fact_7221_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 0.35/0.64      ! [Y2: nat,X: num,N: nat] :
% 0.35/0.64        ( ( ( semiri1316708129612266289at_nat @ Y2 )
% 0.35/0.64          = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 0.35/0.64        = ( Y2
% 0.35/0.64          = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_of_nat_eq_numeral_power_cancel_iff
% 0.35/0.64  thf(fact_7222_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 0.35/0.64      ! [Y2: nat,X: num,N: nat] :
% 0.35/0.64        ( ( ( semiri8010041392384452111omplex @ Y2 )
% 0.35/0.64          = ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N ) )
% 0.35/0.64        = ( Y2
% 0.35/0.64          = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_of_nat_eq_numeral_power_cancel_iff
% 0.35/0.64  thf(fact_7223_numeral__power__eq__of__nat__cancel__iff,axiom,
% 0.35/0.64      ! [X: num,N: nat,Y2: nat] :
% 0.35/0.64        ( ( ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N )
% 0.35/0.64          = ( semiri681578069525770553at_rat @ Y2 ) )
% 0.35/0.64        = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 0.35/0.64          = Y2 ) ) ).
% 0.35/0.64  
% 0.35/0.64  % numeral_power_eq_of_nat_cancel_iff
% 0.35/0.64  thf(fact_7224_numeral__power__eq__of__nat__cancel__iff,axiom,
% 0.35/0.64      ! [X: num,N: nat,Y2: nat] :
% 0.35/0.64        ( ( ( power_power_real @ ( numeral_numeral_real @ X ) @ N )
% 0.35/0.64          = ( semiri5074537144036343181t_real @ Y2 ) )
% 0.35/0.64        = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 0.35/0.64          = Y2 ) ) ).
% 0.35/0.64  
% 0.35/0.64  % numeral_power_eq_of_nat_cancel_iff
% 0.35/0.64  thf(fact_7225_numeral__power__eq__of__nat__cancel__iff,axiom,
% 0.35/0.64      ! [X: num,N: nat,Y2: nat] :
% 0.35/0.64        ( ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 0.35/0.64          = ( semiri1314217659103216013at_int @ Y2 ) )
% 0.35/0.64        = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 0.35/0.64          = Y2 ) ) ).
% 0.35/0.64  
% 0.35/0.64  % numeral_power_eq_of_nat_cancel_iff
% 0.35/0.64  thf(fact_7226_numeral__power__eq__of__nat__cancel__iff,axiom,
% 0.35/0.64      ! [X: num,N: nat,Y2: nat] :
% 0.35/0.64        ( ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 0.35/0.64          = ( semiri1316708129612266289at_nat @ Y2 ) )
% 0.35/0.64        = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 0.35/0.64          = Y2 ) ) ).
% 0.35/0.64  
% 0.35/0.64  % numeral_power_eq_of_nat_cancel_iff
% 0.35/0.64  thf(fact_7227_numeral__power__eq__of__nat__cancel__iff,axiom,
% 0.35/0.64      ! [X: num,N: nat,Y2: nat] :
% 0.35/0.64        ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N )
% 0.35/0.64          = ( semiri8010041392384452111omplex @ Y2 ) )
% 0.35/0.64        = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 0.35/0.64          = Y2 ) ) ).
% 0.35/0.64  
% 0.35/0.64  % numeral_power_eq_of_nat_cancel_iff
% 0.35/0.64  thf(fact_7228_of__nat__less__of__nat__power__cancel__iff,axiom,
% 0.35/0.64      ! [B: nat,W: nat,X: nat] :
% 0.35/0.64        ( ( ord_less_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X ) )
% 0.35/0.64        = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_less_of_nat_power_cancel_iff
% 0.35/0.64  thf(fact_7229_of__nat__less__of__nat__power__cancel__iff,axiom,
% 0.35/0.64      ! [B: nat,W: nat,X: nat] :
% 0.35/0.64        ( ( ord_less_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X ) )
% 0.35/0.64        = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_less_of_nat_power_cancel_iff
% 0.35/0.64  thf(fact_7230_of__nat__less__of__nat__power__cancel__iff,axiom,
% 0.35/0.64      ! [B: nat,W: nat,X: nat] :
% 0.35/0.64        ( ( ord_less_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X ) )
% 0.35/0.64        = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_less_of_nat_power_cancel_iff
% 0.35/0.64  thf(fact_7231_of__nat__less__of__nat__power__cancel__iff,axiom,
% 0.35/0.64      ! [B: nat,W: nat,X: nat] :
% 0.35/0.64        ( ( ord_less_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X ) )
% 0.35/0.64        = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_less_of_nat_power_cancel_iff
% 0.35/0.64  thf(fact_7232_of__nat__power__less__of__nat__cancel__iff,axiom,
% 0.35/0.64      ! [X: nat,B: nat,W: nat] :
% 0.35/0.64        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 0.35/0.64        = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_power_less_of_nat_cancel_iff
% 0.35/0.64  thf(fact_7233_of__nat__power__less__of__nat__cancel__iff,axiom,
% 0.35/0.64      ! [X: nat,B: nat,W: nat] :
% 0.35/0.64        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 0.35/0.64        = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_power_less_of_nat_cancel_iff
% 0.35/0.64  thf(fact_7234_of__nat__power__less__of__nat__cancel__iff,axiom,
% 0.35/0.64      ! [X: nat,B: nat,W: nat] :
% 0.35/0.64        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 0.35/0.64        = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_power_less_of_nat_cancel_iff
% 0.35/0.64  thf(fact_7235_of__nat__power__less__of__nat__cancel__iff,axiom,
% 0.35/0.64      ! [X: nat,B: nat,W: nat] :
% 0.35/0.64        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 0.35/0.64        = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_power_less_of_nat_cancel_iff
% 0.35/0.64  thf(fact_7236_of__nat__le__of__nat__power__cancel__iff,axiom,
% 0.35/0.64      ! [B: nat,W: nat,X: nat] :
% 0.35/0.64        ( ( ord_less_eq_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X ) )
% 0.35/0.64        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_le_of_nat_power_cancel_iff
% 0.35/0.64  thf(fact_7237_of__nat__le__of__nat__power__cancel__iff,axiom,
% 0.35/0.64      ! [B: nat,W: nat,X: nat] :
% 0.35/0.64        ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X ) )
% 0.35/0.64        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_le_of_nat_power_cancel_iff
% 0.35/0.64  thf(fact_7238_of__nat__le__of__nat__power__cancel__iff,axiom,
% 0.35/0.64      ! [B: nat,W: nat,X: nat] :
% 0.35/0.64        ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X ) )
% 0.35/0.64        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_le_of_nat_power_cancel_iff
% 0.35/0.64  thf(fact_7239_of__nat__power__le__of__nat__cancel__iff,axiom,
% 0.35/0.64      ! [X: nat,B: nat,W: nat] :
% 0.35/0.64        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 0.35/0.64        = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_power_le_of_nat_cancel_iff
% 0.35/0.64  thf(fact_7240_of__nat__power__le__of__nat__cancel__iff,axiom,
% 0.35/0.64      ! [X: nat,B: nat,W: nat] :
% 0.35/0.64        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 0.35/0.64        = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_power_le_of_nat_cancel_iff
% 0.35/0.64  thf(fact_7241_of__nat__power__le__of__nat__cancel__iff,axiom,
% 0.35/0.64      ! [X: nat,B: nat,W: nat] :
% 0.35/0.64        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 0.35/0.64        = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_power_le_of_nat_cancel_iff
% 0.35/0.64  thf(fact_7242_ceiling__le__zero,axiom,
% 0.35/0.64      ! [X: rat] :
% 0.35/0.64        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ zero_zero_int )
% 0.35/0.64        = ( ord_less_eq_rat @ X @ zero_zero_rat ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_le_zero
% 0.35/0.64  thf(fact_7243_ceiling__le__zero,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64        ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ zero_zero_int )
% 0.35/0.64        = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_le_zero
% 0.35/0.64  thf(fact_7244_zero__less__ceiling,axiom,
% 0.35/0.64      ! [X: rat] :
% 0.35/0.64        ( ( ord_less_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X ) )
% 0.35/0.64        = ( ord_less_rat @ zero_zero_rat @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % zero_less_ceiling
% 0.35/0.64  thf(fact_7245_zero__less__ceiling,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64        ( ( ord_less_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X ) )
% 0.35/0.64        = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % zero_less_ceiling
% 0.35/0.64  thf(fact_7246_numeral__less__real__of__nat__iff,axiom,
% 0.35/0.64      ! [W: num,N: nat] :
% 0.35/0.64        ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( semiri5074537144036343181t_real @ N ) )
% 0.35/0.64        = ( ord_less_nat @ ( numeral_numeral_nat @ W ) @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % numeral_less_real_of_nat_iff
% 0.35/0.64  thf(fact_7247_real__of__nat__less__numeral__iff,axiom,
% 0.35/0.64      ! [N: nat,W: num] :
% 0.35/0.64        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( numeral_numeral_real @ W ) )
% 0.35/0.64        = ( ord_less_nat @ N @ ( numeral_numeral_nat @ W ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_of_nat_less_numeral_iff
% 0.35/0.64  thf(fact_7248_ceiling__le__numeral,axiom,
% 0.35/0.64      ! [X: real,V: num] :
% 0.35/0.64        ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ ( numeral_numeral_int @ V ) )
% 0.35/0.64        = ( ord_less_eq_real @ X @ ( numeral_numeral_real @ V ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_le_numeral
% 0.35/0.64  thf(fact_7249_ceiling__le__numeral,axiom,
% 0.35/0.64      ! [X: rat,V: num] :
% 0.35/0.64        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 0.35/0.64        = ( ord_less_eq_rat @ X @ ( numeral_numeral_rat @ V ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_le_numeral
% 0.35/0.64  thf(fact_7250_numeral__less__ceiling,axiom,
% 0.35/0.64      ! [V: num,X: real] :
% 0.35/0.64        ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X ) )
% 0.35/0.64        = ( ord_less_real @ ( numeral_numeral_real @ V ) @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % numeral_less_ceiling
% 0.35/0.64  thf(fact_7251_numeral__less__ceiling,axiom,
% 0.35/0.64      ! [V: num,X: rat] :
% 0.35/0.64        ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X ) )
% 0.35/0.64        = ( ord_less_rat @ ( numeral_numeral_rat @ V ) @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % numeral_less_ceiling
% 0.35/0.64  thf(fact_7252_ceiling__less__one,axiom,
% 0.35/0.64      ! [X: rat] :
% 0.35/0.64        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int )
% 0.35/0.64        = ( ord_less_eq_rat @ X @ zero_zero_rat ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_less_one
% 0.35/0.64  thf(fact_7253_ceiling__less__one,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64        ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int )
% 0.35/0.64        = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_less_one
% 0.35/0.64  thf(fact_7254_numeral__le__real__of__nat__iff,axiom,
% 0.35/0.64      ! [N: num,M: nat] :
% 0.35/0.64        ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( semiri5074537144036343181t_real @ M ) )
% 0.35/0.64        = ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ M ) ) ).
% 0.35/0.64  
% 0.35/0.64  % numeral_le_real_of_nat_iff
% 0.35/0.64  thf(fact_7255_one__le__ceiling,axiom,
% 0.35/0.64      ! [X: rat] :
% 0.35/0.64        ( ( ord_less_eq_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X ) )
% 0.35/0.64        = ( ord_less_rat @ zero_zero_rat @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % one_le_ceiling
% 0.35/0.64  thf(fact_7256_one__le__ceiling,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64        ( ( ord_less_eq_int @ one_one_int @ ( archim7802044766580827645g_real @ X ) )
% 0.35/0.64        = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % one_le_ceiling
% 0.35/0.64  thf(fact_7257_ceiling__le__one,axiom,
% 0.35/0.64      ! [X: rat] :
% 0.35/0.64        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int )
% 0.35/0.64        = ( ord_less_eq_rat @ X @ one_one_rat ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_le_one
% 0.35/0.64  thf(fact_7258_ceiling__le__one,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64        ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int )
% 0.35/0.64        = ( ord_less_eq_real @ X @ one_one_real ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_le_one
% 0.35/0.64  thf(fact_7259_one__less__ceiling,axiom,
% 0.35/0.64      ! [X: rat] :
% 0.35/0.64        ( ( ord_less_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X ) )
% 0.35/0.64        = ( ord_less_rat @ one_one_rat @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % one_less_ceiling
% 0.35/0.64  thf(fact_7260_one__less__ceiling,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64        ( ( ord_less_int @ one_one_int @ ( archim7802044766580827645g_real @ X ) )
% 0.35/0.64        = ( ord_less_real @ one_one_real @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % one_less_ceiling
% 0.35/0.64  thf(fact_7261_ceiling__add__numeral,axiom,
% 0.35/0.64      ! [X: real,V: num] :
% 0.35/0.64        ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X @ ( numeral_numeral_real @ V ) ) )
% 0.35/0.64        = ( plus_plus_int @ ( archim7802044766580827645g_real @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_add_numeral
% 0.35/0.64  thf(fact_7262_ceiling__add__numeral,axiom,
% 0.35/0.64      ! [X: rat,V: num] :
% 0.35/0.64        ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ ( numeral_numeral_rat @ V ) ) )
% 0.35/0.64        = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_add_numeral
% 0.35/0.64  thf(fact_7263_ceiling__neg__numeral,axiom,
% 0.35/0.64      ! [V: num] :
% 0.35/0.64        ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.35/0.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_neg_numeral
% 0.35/0.64  thf(fact_7264_ceiling__neg__numeral,axiom,
% 0.35/0.64      ! [V: num] :
% 0.35/0.64        ( ( archim2889992004027027881ng_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.35/0.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_neg_numeral
% 0.35/0.64  thf(fact_7265_ceiling__add__one,axiom,
% 0.35/0.64      ! [X: rat] :
% 0.35/0.64        ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ one_one_rat ) )
% 0.35/0.64        = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_add_one
% 0.35/0.64  thf(fact_7266_ceiling__add__one,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64        ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X @ one_one_real ) )
% 0.35/0.64        = ( plus_plus_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_add_one
% 0.35/0.64  thf(fact_7267_ceiling__diff__numeral,axiom,
% 0.35/0.64      ! [X: real,V: num] :
% 0.35/0.64        ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X @ ( numeral_numeral_real @ V ) ) )
% 0.35/0.64        = ( minus_minus_int @ ( archim7802044766580827645g_real @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_diff_numeral
% 0.35/0.64  thf(fact_7268_ceiling__diff__numeral,axiom,
% 0.35/0.64      ! [X: rat,V: num] :
% 0.35/0.64        ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X @ ( numeral_numeral_rat @ V ) ) )
% 0.35/0.64        = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_diff_numeral
% 0.35/0.64  thf(fact_7269_ceiling__diff__one,axiom,
% 0.35/0.64      ! [X: rat] :
% 0.35/0.64        ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X @ one_one_rat ) )
% 0.35/0.64        = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_diff_one
% 0.35/0.64  thf(fact_7270_ceiling__diff__one,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64        ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X @ one_one_real ) )
% 0.35/0.64        = ( minus_minus_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_diff_one
% 0.35/0.64  thf(fact_7271_ceiling__numeral__power,axiom,
% 0.35/0.64      ! [X: num,N: nat] :
% 0.35/0.64        ( ( archim7802044766580827645g_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 0.35/0.64        = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_numeral_power
% 0.35/0.64  thf(fact_7272_ceiling__numeral__power,axiom,
% 0.35/0.64      ! [X: num,N: nat] :
% 0.35/0.64        ( ( archim2889992004027027881ng_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 0.35/0.64        = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_numeral_power
% 0.35/0.64  thf(fact_7273_of__nat__zero__less__power__iff,axiom,
% 0.35/0.64      ! [X: nat,N: nat] :
% 0.35/0.64        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X ) @ N ) )
% 0.35/0.64        = ( ( ord_less_nat @ zero_zero_nat @ X )
% 0.35/0.64          | ( N = zero_zero_nat ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_zero_less_power_iff
% 0.35/0.64  thf(fact_7274_of__nat__zero__less__power__iff,axiom,
% 0.35/0.64      ! [X: nat,N: nat] :
% 0.35/0.64        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ X ) @ N ) )
% 0.35/0.64        = ( ( ord_less_nat @ zero_zero_nat @ X )
% 0.35/0.64          | ( N = zero_zero_nat ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_zero_less_power_iff
% 0.35/0.64  thf(fact_7275_of__nat__zero__less__power__iff,axiom,
% 0.35/0.64      ! [X: nat,N: nat] :
% 0.35/0.64        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X ) @ N ) )
% 0.35/0.64        = ( ( ord_less_nat @ zero_zero_nat @ X )
% 0.35/0.64          | ( N = zero_zero_nat ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_zero_less_power_iff
% 0.35/0.64  thf(fact_7276_of__nat__zero__less__power__iff,axiom,
% 0.35/0.64      ! [X: nat,N: nat] :
% 0.35/0.64        ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X ) @ N ) )
% 0.35/0.64        = ( ( ord_less_nat @ zero_zero_nat @ X )
% 0.35/0.64          | ( N = zero_zero_nat ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_zero_less_power_iff
% 0.35/0.64  thf(fact_7277_ceiling__less__zero,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64        ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ zero_zero_int )
% 0.35/0.64        = ( ord_less_eq_real @ X @ ( uminus_uminus_real @ one_one_real ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_less_zero
% 0.35/0.64  thf(fact_7278_ceiling__less__zero,axiom,
% 0.35/0.64      ! [X: rat] :
% 0.35/0.64        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ zero_zero_int )
% 0.35/0.64        = ( ord_less_eq_rat @ X @ ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_less_zero
% 0.35/0.64  thf(fact_7279_zero__le__ceiling,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64        ( ( ord_less_eq_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X ) )
% 0.35/0.64        = ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % zero_le_ceiling
% 0.35/0.64  thf(fact_7280_zero__le__ceiling,axiom,
% 0.35/0.64      ! [X: rat] :
% 0.35/0.64        ( ( ord_less_eq_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X ) )
% 0.35/0.64        = ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % zero_le_ceiling
% 0.35/0.64  thf(fact_7281_log__pow__cancel,axiom,
% 0.35/0.64      ! [A: real,B: nat] :
% 0.35/0.64        ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.64       => ( ( A != one_one_real )
% 0.35/0.64         => ( ( log @ A @ ( power_power_real @ A @ B ) )
% 0.35/0.64            = ( semiri5074537144036343181t_real @ B ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % log_pow_cancel
% 0.35/0.64  thf(fact_7282_ceiling__divide__eq__div__numeral,axiom,
% 0.35/0.64      ! [A: num,B: num] :
% 0.35/0.64        ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 0.35/0.64        = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_divide_eq_div_numeral
% 0.35/0.64  thf(fact_7283_of__nat__less__numeral__power__cancel__iff,axiom,
% 0.35/0.64      ! [X: nat,I2: num,N: nat] :
% 0.35/0.64        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N ) )
% 0.35/0.64        = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_less_numeral_power_cancel_iff
% 0.35/0.64  thf(fact_7284_of__nat__less__numeral__power__cancel__iff,axiom,
% 0.35/0.64      ! [X: nat,I2: num,N: nat] :
% 0.35/0.64        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N ) )
% 0.35/0.64        = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_less_numeral_power_cancel_iff
% 0.35/0.64  thf(fact_7285_of__nat__less__numeral__power__cancel__iff,axiom,
% 0.35/0.64      ! [X: nat,I2: num,N: nat] :
% 0.35/0.64        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N ) )
% 0.35/0.64        = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_less_numeral_power_cancel_iff
% 0.35/0.64  thf(fact_7286_of__nat__less__numeral__power__cancel__iff,axiom,
% 0.35/0.64      ! [X: nat,I2: num,N: nat] :
% 0.35/0.64        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) )
% 0.35/0.64        = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_less_numeral_power_cancel_iff
% 0.35/0.64  thf(fact_7287_numeral__power__less__of__nat__cancel__iff,axiom,
% 0.35/0.64      ! [I2: num,N: nat,X: nat] :
% 0.35/0.64        ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N ) @ ( semiri681578069525770553at_rat @ X ) )
% 0.35/0.64        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % numeral_power_less_of_nat_cancel_iff
% 0.35/0.64  thf(fact_7288_numeral__power__less__of__nat__cancel__iff,axiom,
% 0.35/0.64      ! [I2: num,N: nat,X: nat] :
% 0.35/0.64        ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N ) @ ( semiri5074537144036343181t_real @ X ) )
% 0.35/0.64        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % numeral_power_less_of_nat_cancel_iff
% 0.35/0.64  thf(fact_7289_numeral__power__less__of__nat__cancel__iff,axiom,
% 0.35/0.64      ! [I2: num,N: nat,X: nat] :
% 0.35/0.64        ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N ) @ ( semiri1314217659103216013at_int @ X ) )
% 0.35/0.64        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % numeral_power_less_of_nat_cancel_iff
% 0.35/0.64  thf(fact_7290_numeral__power__less__of__nat__cancel__iff,axiom,
% 0.35/0.64      ! [I2: num,N: nat,X: nat] :
% 0.35/0.64        ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ ( semiri1316708129612266289at_nat @ X ) )
% 0.35/0.64        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % numeral_power_less_of_nat_cancel_iff
% 0.35/0.64  thf(fact_7291_even__of__nat,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( semiri4939895301339042750nteger @ N ) )
% 0.35/0.64        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % even_of_nat
% 0.35/0.64  thf(fact_7292_even__of__nat,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.35/0.64        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % even_of_nat
% 0.35/0.64  thf(fact_7293_even__of__nat,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ N ) )
% 0.35/0.64        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % even_of_nat
% 0.35/0.64  thf(fact_7294_numeral__power__le__of__nat__cancel__iff,axiom,
% 0.35/0.64      ! [I2: num,N: nat,X: nat] :
% 0.35/0.64        ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N ) @ ( semiri681578069525770553at_rat @ X ) )
% 0.35/0.64        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % numeral_power_le_of_nat_cancel_iff
% 0.35/0.64  thf(fact_7295_numeral__power__le__of__nat__cancel__iff,axiom,
% 0.35/0.64      ! [I2: num,N: nat,X: nat] :
% 0.35/0.64        ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N ) @ ( semiri5074537144036343181t_real @ X ) )
% 0.35/0.64        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % numeral_power_le_of_nat_cancel_iff
% 0.35/0.64  thf(fact_7296_numeral__power__le__of__nat__cancel__iff,axiom,
% 0.35/0.64      ! [I2: num,N: nat,X: nat] :
% 0.35/0.64        ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ ( semiri1316708129612266289at_nat @ X ) )
% 0.35/0.64        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % numeral_power_le_of_nat_cancel_iff
% 0.35/0.64  thf(fact_7297_numeral__power__le__of__nat__cancel__iff,axiom,
% 0.35/0.64      ! [I2: num,N: nat,X: nat] :
% 0.35/0.64        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N ) @ ( semiri1314217659103216013at_int @ X ) )
% 0.35/0.64        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % numeral_power_le_of_nat_cancel_iff
% 0.35/0.64  thf(fact_7298_of__nat__le__numeral__power__cancel__iff,axiom,
% 0.35/0.64      ! [X: nat,I2: num,N: nat] :
% 0.35/0.64        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N ) )
% 0.35/0.64        = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_le_numeral_power_cancel_iff
% 0.35/0.64  thf(fact_7299_of__nat__le__numeral__power__cancel__iff,axiom,
% 0.35/0.64      ! [X: nat,I2: num,N: nat] :
% 0.35/0.64        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N ) )
% 0.35/0.64        = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_le_numeral_power_cancel_iff
% 0.35/0.64  thf(fact_7300_of__nat__le__numeral__power__cancel__iff,axiom,
% 0.35/0.64      ! [X: nat,I2: num,N: nat] :
% 0.35/0.64        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) )
% 0.35/0.64        = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_le_numeral_power_cancel_iff
% 0.35/0.64  thf(fact_7301_of__nat__le__numeral__power__cancel__iff,axiom,
% 0.35/0.64      ! [X: nat,I2: num,N: nat] :
% 0.35/0.64        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N ) )
% 0.35/0.64        = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_le_numeral_power_cancel_iff
% 0.35/0.64  thf(fact_7302_ceiling__less__numeral,axiom,
% 0.35/0.64      ! [X: real,V: num] :
% 0.35/0.64        ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ ( numeral_numeral_int @ V ) )
% 0.35/0.64        = ( ord_less_eq_real @ X @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_less_numeral
% 0.35/0.64  thf(fact_7303_ceiling__less__numeral,axiom,
% 0.35/0.64      ! [X: rat,V: num] :
% 0.35/0.64        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 0.35/0.64        = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_less_numeral
% 0.35/0.64  thf(fact_7304_numeral__le__ceiling,axiom,
% 0.35/0.64      ! [V: num,X: real] :
% 0.35/0.64        ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X ) )
% 0.35/0.64        = ( ord_less_real @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % numeral_le_ceiling
% 0.35/0.64  thf(fact_7305_numeral__le__ceiling,axiom,
% 0.35/0.64      ! [V: num,X: rat] :
% 0.35/0.64        ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X ) )
% 0.35/0.64        = ( ord_less_rat @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % numeral_le_ceiling
% 0.35/0.64  thf(fact_7306_ceiling__le__neg__numeral,axiom,
% 0.35/0.64      ! [X: real,V: num] :
% 0.35/0.64        ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.35/0.64        = ( ord_less_eq_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_le_neg_numeral
% 0.35/0.64  thf(fact_7307_ceiling__le__neg__numeral,axiom,
% 0.35/0.64      ! [X: rat,V: num] :
% 0.35/0.64        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.35/0.64        = ( ord_less_eq_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_le_neg_numeral
% 0.35/0.64  thf(fact_7308_neg__numeral__less__ceiling,axiom,
% 0.35/0.64      ! [V: num,X: real] :
% 0.35/0.64        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X ) )
% 0.35/0.64        = ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % neg_numeral_less_ceiling
% 0.35/0.64  thf(fact_7309_neg__numeral__less__ceiling,axiom,
% 0.35/0.64      ! [V: num,X: rat] :
% 0.35/0.64        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X ) )
% 0.35/0.64        = ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % neg_numeral_less_ceiling
% 0.35/0.64  thf(fact_7310_ceiling__minus__divide__eq__div__numeral,axiom,
% 0.35/0.64      ! [A: num,B: num] :
% 0.35/0.64        ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 0.35/0.64        = ( uminus_uminus_int @ ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_minus_divide_eq_div_numeral
% 0.35/0.64  thf(fact_7311_ceiling__less__neg__numeral,axiom,
% 0.35/0.64      ! [X: real,V: num] :
% 0.35/0.64        ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.35/0.64        = ( ord_less_eq_real @ X @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_less_neg_numeral
% 0.35/0.64  thf(fact_7312_ceiling__less__neg__numeral,axiom,
% 0.35/0.64      ! [X: rat,V: num] :
% 0.35/0.64        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.35/0.64        = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_less_neg_numeral
% 0.35/0.64  thf(fact_7313_neg__numeral__le__ceiling,axiom,
% 0.35/0.64      ! [V: num,X: real] :
% 0.35/0.64        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X ) )
% 0.35/0.64        = ( ord_less_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % neg_numeral_le_ceiling
% 0.35/0.64  thf(fact_7314_neg__numeral__le__ceiling,axiom,
% 0.35/0.64      ! [V: num,X: rat] :
% 0.35/0.64        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X ) )
% 0.35/0.64        = ( ord_less_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % neg_numeral_le_ceiling
% 0.35/0.64  thf(fact_7315_real__arch__simple,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64      ? [N3: nat] : ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_arch_simple
% 0.35/0.64  thf(fact_7316_reals__Archimedean2,axiom,
% 0.35/0.64      ! [X: rat] :
% 0.35/0.64      ? [N3: nat] : ( ord_less_rat @ X @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 0.35/0.64  
% 0.35/0.64  % reals_Archimedean2
% 0.35/0.64  thf(fact_7317_reals__Archimedean2,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64      ? [N3: nat] : ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 0.35/0.64  
% 0.35/0.64  % reals_Archimedean2
% 0.35/0.64  thf(fact_7318_mult__of__nat__commute,axiom,
% 0.35/0.64      ! [X: nat,Y2: real] :
% 0.35/0.64        ( ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ Y2 )
% 0.35/0.64        = ( times_times_real @ Y2 @ ( semiri5074537144036343181t_real @ X ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % mult_of_nat_commute
% 0.35/0.64  thf(fact_7319_mult__of__nat__commute,axiom,
% 0.35/0.64      ! [X: nat,Y2: int] :
% 0.35/0.64        ( ( times_times_int @ ( semiri1314217659103216013at_int @ X ) @ Y2 )
% 0.35/0.64        = ( times_times_int @ Y2 @ ( semiri1314217659103216013at_int @ X ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % mult_of_nat_commute
% 0.35/0.64  thf(fact_7320_mult__of__nat__commute,axiom,
% 0.35/0.64      ! [X: nat,Y2: nat] :
% 0.35/0.64        ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X ) @ Y2 )
% 0.35/0.64        = ( times_times_nat @ Y2 @ ( semiri1316708129612266289at_nat @ X ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % mult_of_nat_commute
% 0.35/0.64  thf(fact_7321_mult__of__nat__commute,axiom,
% 0.35/0.64      ! [X: nat,Y2: complex] :
% 0.35/0.64        ( ( times_times_complex @ ( semiri8010041392384452111omplex @ X ) @ Y2 )
% 0.35/0.64        = ( times_times_complex @ Y2 @ ( semiri8010041392384452111omplex @ X ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % mult_of_nat_commute
% 0.35/0.64  thf(fact_7322_of__nat__or__eq,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( semiri1314217659103216013at_int @ ( bit_se1412395901928357646or_nat @ M @ N ) )
% 0.35/0.64        = ( bit_se1409905431419307370or_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_or_eq
% 0.35/0.64  thf(fact_7323_of__nat__or__eq,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( semiri1316708129612266289at_nat @ ( bit_se1412395901928357646or_nat @ M @ N ) )
% 0.35/0.64        = ( bit_se1412395901928357646or_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_or_eq
% 0.35/0.64  thf(fact_7324_of__nat__less__of__int__iff,axiom,
% 0.35/0.64      ! [N: nat,X: int] :
% 0.35/0.64        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( ring_1_of_int_rat @ X ) )
% 0.35/0.64        = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_less_of_int_iff
% 0.35/0.64  thf(fact_7325_of__nat__less__of__int__iff,axiom,
% 0.35/0.64      ! [N: nat,X: int] :
% 0.35/0.64        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( ring_1_of_int_real @ X ) )
% 0.35/0.64        = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_less_of_int_iff
% 0.35/0.64  thf(fact_7326_of__nat__less__of__int__iff,axiom,
% 0.35/0.64      ! [N: nat,X: int] :
% 0.35/0.64        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( ring_1_of_int_int @ X ) )
% 0.35/0.64        = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_less_of_int_iff
% 0.35/0.64  thf(fact_7327_of__nat__0__le__iff,axiom,
% 0.35/0.64      ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_0_le_iff
% 0.35/0.64  thf(fact_7328_of__nat__0__le__iff,axiom,
% 0.35/0.64      ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_0_le_iff
% 0.35/0.64  thf(fact_7329_of__nat__0__le__iff,axiom,
% 0.35/0.64      ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_0_le_iff
% 0.35/0.64  thf(fact_7330_of__nat__0__le__iff,axiom,
% 0.35/0.64      ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_0_le_iff
% 0.35/0.64  thf(fact_7331_of__nat__less__0__iff,axiom,
% 0.35/0.64      ! [M: nat] :
% 0.35/0.64        ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_less_0_iff
% 0.35/0.64  thf(fact_7332_of__nat__less__0__iff,axiom,
% 0.35/0.64      ! [M: nat] :
% 0.35/0.64        ~ ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_less_0_iff
% 0.35/0.64  thf(fact_7333_of__nat__less__0__iff,axiom,
% 0.35/0.64      ! [M: nat] :
% 0.35/0.64        ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_less_0_iff
% 0.35/0.64  thf(fact_7334_of__nat__less__0__iff,axiom,
% 0.35/0.64      ! [M: nat] :
% 0.35/0.64        ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_less_0_iff
% 0.35/0.64  thf(fact_7335_ceiling__mono,axiom,
% 0.35/0.64      ! [Y2: real,X: real] :
% 0.35/0.64        ( ( ord_less_eq_real @ Y2 @ X )
% 0.35/0.64       => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ Y2 ) @ ( archim7802044766580827645g_real @ X ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_mono
% 0.35/0.64  thf(fact_7336_of__nat__neq__0,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( semiri681578069525770553at_rat @ ( suc @ N ) )
% 0.35/0.64       != zero_zero_rat ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_neq_0
% 0.35/0.64  thf(fact_7337_of__nat__neq__0,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( semiri5074537144036343181t_real @ ( suc @ N ) )
% 0.35/0.64       != zero_zero_real ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_neq_0
% 0.35/0.64  thf(fact_7338_of__nat__neq__0,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 0.35/0.64       != zero_zero_int ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_neq_0
% 0.35/0.64  thf(fact_7339_of__nat__neq__0,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( semiri1316708129612266289at_nat @ ( suc @ N ) )
% 0.35/0.64       != zero_zero_nat ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_neq_0
% 0.35/0.64  thf(fact_7340_of__nat__neq__0,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( semiri8010041392384452111omplex @ ( suc @ N ) )
% 0.35/0.64       != zero_zero_complex ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_neq_0
% 0.35/0.64  thf(fact_7341_le__of__int__ceiling,axiom,
% 0.35/0.64      ! [X: real] : ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % le_of_int_ceiling
% 0.35/0.64  thf(fact_7342_ceiling__less__cancel,axiom,
% 0.35/0.64      ! [X: rat,Y2: rat] :
% 0.35/0.64        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ ( archim2889992004027027881ng_rat @ Y2 ) )
% 0.35/0.64       => ( ord_less_rat @ X @ Y2 ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_less_cancel
% 0.35/0.64  thf(fact_7343_ceiling__less__cancel,axiom,
% 0.35/0.64      ! [X: real,Y2: real] :
% 0.35/0.64        ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ ( archim7802044766580827645g_real @ Y2 ) )
% 0.35/0.64       => ( ord_less_real @ X @ Y2 ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_less_cancel
% 0.35/0.64  thf(fact_7344_div__mult2__eq_H,axiom,
% 0.35/0.64      ! [A: int,M: nat,N: nat] :
% 0.35/0.64        ( ( divide_divide_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.35/0.64        = ( divide_divide_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % div_mult2_eq'
% 0.35/0.64  thf(fact_7345_div__mult2__eq_H,axiom,
% 0.35/0.64      ! [A: nat,M: nat,N: nat] :
% 0.35/0.64        ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 0.35/0.64        = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % div_mult2_eq'
% 0.35/0.64  thf(fact_7346_less__imp__of__nat__less,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( ord_less_nat @ M @ N )
% 0.35/0.64       => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % less_imp_of_nat_less
% 0.35/0.64  thf(fact_7347_less__imp__of__nat__less,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( ord_less_nat @ M @ N )
% 0.35/0.64       => ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % less_imp_of_nat_less
% 0.35/0.64  thf(fact_7348_less__imp__of__nat__less,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( ord_less_nat @ M @ N )
% 0.35/0.64       => ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % less_imp_of_nat_less
% 0.35/0.64  thf(fact_7349_less__imp__of__nat__less,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( ord_less_nat @ M @ N )
% 0.35/0.64       => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % less_imp_of_nat_less
% 0.35/0.64  thf(fact_7350_of__nat__less__imp__less,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 0.35/0.64       => ( ord_less_nat @ M @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_less_imp_less
% 0.35/0.64  thf(fact_7351_of__nat__less__imp__less,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 0.35/0.64       => ( ord_less_nat @ M @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_less_imp_less
% 0.35/0.64  thf(fact_7352_of__nat__less__imp__less,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.35/0.64       => ( ord_less_nat @ M @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_less_imp_less
% 0.35/0.64  thf(fact_7353_of__nat__less__imp__less,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 0.35/0.64       => ( ord_less_nat @ M @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_less_imp_less
% 0.35/0.64  thf(fact_7354_of__nat__mono,axiom,
% 0.35/0.64      ! [I2: nat,J: nat] :
% 0.35/0.64        ( ( ord_less_eq_nat @ I2 @ J )
% 0.35/0.64       => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ I2 ) @ ( semiri5074537144036343181t_real @ J ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_mono
% 0.35/0.64  thf(fact_7355_of__nat__mono,axiom,
% 0.35/0.64      ! [I2: nat,J: nat] :
% 0.35/0.64        ( ( ord_less_eq_nat @ I2 @ J )
% 0.35/0.64       => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I2 ) @ ( semiri1316708129612266289at_nat @ J ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_mono
% 0.35/0.64  thf(fact_7356_of__nat__mono,axiom,
% 0.35/0.64      ! [I2: nat,J: nat] :
% 0.35/0.64        ( ( ord_less_eq_nat @ I2 @ J )
% 0.35/0.64       => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ J ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_mono
% 0.35/0.64  thf(fact_7357_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) )
% 0.35/0.64        = ( divide_divide_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % unique_euclidean_semiring_with_nat_class.of_nat_div
% 0.35/0.64  thf(fact_7358_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( semiri1316708129612266289at_nat @ ( divide_divide_nat @ M @ N ) )
% 0.35/0.64        = ( divide_divide_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % unique_euclidean_semiring_with_nat_class.of_nat_div
% 0.35/0.64  thf(fact_7359_of__nat__dvd__iff,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( dvd_dvd_Code_integer @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) )
% 0.35/0.64        = ( dvd_dvd_nat @ M @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_dvd_iff
% 0.35/0.64  thf(fact_7360_of__nat__dvd__iff,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.35/0.64        = ( dvd_dvd_nat @ M @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_dvd_iff
% 0.35/0.64  thf(fact_7361_of__nat__dvd__iff,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( dvd_dvd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 0.35/0.64        = ( dvd_dvd_nat @ M @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_dvd_iff
% 0.35/0.64  thf(fact_7362_of__nat__mod,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) )
% 0.35/0.64        = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_mod
% 0.35/0.64  thf(fact_7363_of__nat__mod,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( semiri1316708129612266289at_nat @ ( modulo_modulo_nat @ M @ N ) )
% 0.35/0.64        = ( modulo_modulo_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_mod
% 0.35/0.64  thf(fact_7364_of__nat__max,axiom,
% 0.35/0.64      ! [X: nat,Y2: nat] :
% 0.35/0.64        ( ( semiri4216267220026989637d_enat @ ( ord_max_nat @ X @ Y2 ) )
% 0.35/0.64        = ( ord_ma741700101516333627d_enat @ ( semiri4216267220026989637d_enat @ X ) @ ( semiri4216267220026989637d_enat @ Y2 ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_max
% 0.35/0.64  thf(fact_7365_of__nat__max,axiom,
% 0.35/0.64      ! [X: nat,Y2: nat] :
% 0.35/0.64        ( ( semiri5074537144036343181t_real @ ( ord_max_nat @ X @ Y2 ) )
% 0.35/0.64        = ( ord_max_real @ ( semiri5074537144036343181t_real @ X ) @ ( semiri5074537144036343181t_real @ Y2 ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_max
% 0.35/0.64  thf(fact_7366_of__nat__max,axiom,
% 0.35/0.64      ! [X: nat,Y2: nat] :
% 0.35/0.64        ( ( semiri1314217659103216013at_int @ ( ord_max_nat @ X @ Y2 ) )
% 0.35/0.64        = ( ord_max_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y2 ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_max
% 0.35/0.64  thf(fact_7367_of__nat__max,axiom,
% 0.35/0.64      ! [X: nat,Y2: nat] :
% 0.35/0.64        ( ( semiri1316708129612266289at_nat @ ( ord_max_nat @ X @ Y2 ) )
% 0.35/0.64        = ( ord_max_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( semiri1316708129612266289at_nat @ Y2 ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_max
% 0.35/0.64  thf(fact_7368_take__bit__of__nat,axiom,
% 0.35/0.64      ! [N: nat,M: nat] :
% 0.35/0.64        ( ( bit_se2923211474154528505it_int @ N @ ( semiri1314217659103216013at_int @ M ) )
% 0.35/0.64        = ( semiri1314217659103216013at_int @ ( bit_se2925701944663578781it_nat @ N @ M ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_of_nat
% 0.35/0.64  thf(fact_7369_take__bit__of__nat,axiom,
% 0.35/0.64      ! [N: nat,M: nat] :
% 0.35/0.64        ( ( bit_se2925701944663578781it_nat @ N @ ( semiri1316708129612266289at_nat @ M ) )
% 0.35/0.64        = ( semiri1316708129612266289at_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % take_bit_of_nat
% 0.35/0.64  thf(fact_7370_of__nat__and__eq,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( semiri1314217659103216013at_int @ ( bit_se727722235901077358nd_nat @ M @ N ) )
% 0.35/0.64        = ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_and_eq
% 0.35/0.64  thf(fact_7371_of__nat__and__eq,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( semiri1316708129612266289at_nat @ ( bit_se727722235901077358nd_nat @ M @ N ) )
% 0.35/0.64        = ( bit_se727722235901077358nd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_and_eq
% 0.35/0.64  thf(fact_7372_of__nat__mask__eq,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( semiri1316708129612266289at_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 0.35/0.64        = ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_mask_eq
% 0.35/0.64  thf(fact_7373_of__nat__mask__eq,axiom,
% 0.35/0.64      ! [N: nat] :
% 0.35/0.64        ( ( semiri1314217659103216013at_int @ ( bit_se2002935070580805687sk_nat @ N ) )
% 0.35/0.64        = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_mask_eq
% 0.35/0.64  thf(fact_7374_ex__less__of__nat__mult,axiom,
% 0.35/0.64      ! [X: rat,Y2: rat] :
% 0.35/0.64        ( ( ord_less_rat @ zero_zero_rat @ X )
% 0.35/0.64       => ? [N3: nat] : ( ord_less_rat @ Y2 @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N3 ) @ X ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ex_less_of_nat_mult
% 0.35/0.64  thf(fact_7375_ex__less__of__nat__mult,axiom,
% 0.35/0.64      ! [X: real,Y2: real] :
% 0.35/0.64        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.64       => ? [N3: nat] : ( ord_less_real @ Y2 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ex_less_of_nat_mult
% 0.35/0.64  thf(fact_7376_ceiling__le__iff,axiom,
% 0.35/0.64      ! [X: real,Z: int] :
% 0.35/0.64        ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ Z )
% 0.35/0.64        = ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ Z ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_le_iff
% 0.35/0.64  thf(fact_7377_ceiling__le,axiom,
% 0.35/0.64      ! [X: real,A: int] :
% 0.35/0.64        ( ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ A ) )
% 0.35/0.64       => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ A ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_le
% 0.35/0.64  thf(fact_7378_less__ceiling__iff,axiom,
% 0.35/0.64      ! [Z: int,X: rat] :
% 0.35/0.64        ( ( ord_less_int @ Z @ ( archim2889992004027027881ng_rat @ X ) )
% 0.35/0.64        = ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % less_ceiling_iff
% 0.35/0.64  thf(fact_7379_less__ceiling__iff,axiom,
% 0.35/0.64      ! [Z: int,X: real] :
% 0.35/0.64        ( ( ord_less_int @ Z @ ( archim7802044766580827645g_real @ X ) )
% 0.35/0.64        = ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ X ) ) ).
% 0.35/0.64  
% 0.35/0.64  % less_ceiling_iff
% 0.35/0.64  thf(fact_7380_ceiling__add__le,axiom,
% 0.35/0.64      ! [X: rat,Y2: rat] : ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ Y2 ) ) @ ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ ( archim2889992004027027881ng_rat @ Y2 ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_add_le
% 0.35/0.64  thf(fact_7381_ceiling__add__le,axiom,
% 0.35/0.64      ! [X: real,Y2: real] : ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( plus_plus_real @ X @ Y2 ) ) @ ( plus_plus_int @ ( archim7802044766580827645g_real @ X ) @ ( archim7802044766580827645g_real @ Y2 ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_add_le
% 0.35/0.64  thf(fact_7382_of__nat__diff,axiom,
% 0.35/0.64      ! [N: nat,M: nat] :
% 0.35/0.64        ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.64       => ( ( semiri681578069525770553at_rat @ ( minus_minus_nat @ M @ N ) )
% 0.35/0.64          = ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_diff
% 0.35/0.64  thf(fact_7383_of__nat__diff,axiom,
% 0.35/0.64      ! [N: nat,M: nat] :
% 0.35/0.64        ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.64       => ( ( semiri5074537144036343181t_real @ ( minus_minus_nat @ M @ N ) )
% 0.35/0.64          = ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_diff
% 0.35/0.64  thf(fact_7384_of__nat__diff,axiom,
% 0.35/0.64      ! [N: nat,M: nat] :
% 0.35/0.64        ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.64       => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M @ N ) )
% 0.35/0.64          = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_diff
% 0.35/0.64  thf(fact_7385_of__nat__diff,axiom,
% 0.35/0.64      ! [N: nat,M: nat] :
% 0.35/0.64        ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.64       => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M @ N ) )
% 0.35/0.64          = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_diff
% 0.35/0.64  thf(fact_7386_of__nat__diff,axiom,
% 0.35/0.64      ! [N: nat,M: nat] :
% 0.35/0.64        ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.64       => ( ( semiri8010041392384452111omplex @ ( minus_minus_nat @ M @ N ) )
% 0.35/0.64          = ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_nat_diff
% 0.35/0.64  thf(fact_7387_exp__of__nat2__mult,axiom,
% 0.35/0.64      ! [X: real,N: nat] :
% 0.35/0.64        ( ( exp_real @ ( times_times_real @ X @ ( semiri5074537144036343181t_real @ N ) ) )
% 0.35/0.64        = ( power_power_real @ ( exp_real @ X ) @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % exp_of_nat2_mult
% 0.35/0.64  thf(fact_7388_exp__of__nat2__mult,axiom,
% 0.35/0.64      ! [X: complex,N: nat] :
% 0.35/0.64        ( ( exp_complex @ ( times_times_complex @ X @ ( semiri8010041392384452111omplex @ N ) ) )
% 0.35/0.64        = ( power_power_complex @ ( exp_complex @ X ) @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % exp_of_nat2_mult
% 0.35/0.64  thf(fact_7389_exp__of__nat__mult,axiom,
% 0.35/0.64      ! [N: nat,X: real] :
% 0.35/0.64        ( ( exp_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) )
% 0.35/0.64        = ( power_power_real @ ( exp_real @ X ) @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % exp_of_nat_mult
% 0.35/0.64  thf(fact_7390_exp__of__nat__mult,axiom,
% 0.35/0.64      ! [N: nat,X: complex] :
% 0.35/0.64        ( ( exp_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ X ) )
% 0.35/0.64        = ( power_power_complex @ ( exp_complex @ X ) @ N ) ) ).
% 0.35/0.64  
% 0.35/0.64  % exp_of_nat_mult
% 0.35/0.64  thf(fact_7391_reals__Archimedean3,axiom,
% 0.35/0.64      ! [X: real] :
% 0.35/0.64        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.64       => ! [Y4: real] :
% 0.35/0.64          ? [N3: nat] : ( ord_less_real @ Y4 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % reals_Archimedean3
% 0.35/0.64  thf(fact_7392_real__of__nat__div4,axiom,
% 0.35/0.64      ! [N: nat,X: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_of_nat_div4
% 0.35/0.64  thf(fact_7393_real__of__nat__div,axiom,
% 0.35/0.64      ! [D2: nat,N: nat] :
% 0.35/0.64        ( ( dvd_dvd_nat @ D2 @ N )
% 0.35/0.64       => ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ D2 ) )
% 0.35/0.64          = ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ D2 ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % real_of_nat_div
% 0.35/0.64  thf(fact_7394_of__int__ceiling__le__add__one,axiom,
% 0.35/0.64      ! [R: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R ) ) @ ( plus_plus_rat @ R @ one_one_rat ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_int_ceiling_le_add_one
% 0.35/0.64  thf(fact_7395_of__int__ceiling__le__add__one,axiom,
% 0.35/0.64      ! [R: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R ) ) @ ( plus_plus_real @ R @ one_one_real ) ) ).
% 0.35/0.64  
% 0.35/0.64  % of_int_ceiling_le_add_one
% 0.35/0.64  thf(fact_7396_of__int__ceiling__diff__one__le,axiom,
% 0.35/0.64      ! [R: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R ) ) @ one_one_rat ) @ R ) ).
% 0.35/0.64  
% 0.35/0.64  % of_int_ceiling_diff_one_le
% 0.35/0.64  thf(fact_7397_of__int__ceiling__diff__one__le,axiom,
% 0.35/0.64      ! [R: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R ) ) @ one_one_real ) @ R ) ).
% 0.35/0.64  
% 0.35/0.64  % of_int_ceiling_diff_one_le
% 0.35/0.64  thf(fact_7398_mod__mult2__eq_H,axiom,
% 0.35/0.64      ! [A: int,M: nat,N: nat] :
% 0.35/0.64        ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.35/0.64        = ( plus_plus_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( modulo_modulo_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) @ ( modulo_modulo_int @ A @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % mod_mult2_eq'
% 0.35/0.64  thf(fact_7399_mod__mult2__eq_H,axiom,
% 0.35/0.64      ! [A: nat,M: nat,N: nat] :
% 0.35/0.64        ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 0.35/0.64        = ( plus_plus_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) @ ( modulo_modulo_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % mod_mult2_eq'
% 0.35/0.64  thf(fact_7400_ceiling__divide__eq__div,axiom,
% 0.35/0.64      ! [A: int,B: int] :
% 0.35/0.64        ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B ) ) )
% 0.35/0.64        = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_divide_eq_div
% 0.35/0.64  thf(fact_7401_ceiling__divide__eq__div,axiom,
% 0.35/0.64      ! [A: int,B: int] :
% 0.35/0.64        ( ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ A ) @ ( ring_1_of_int_rat @ B ) ) )
% 0.35/0.64        = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 0.35/0.64  
% 0.35/0.64  % ceiling_divide_eq_div
% 0.35/0.64  thf(fact_7402_field__char__0__class_Oof__nat__div,axiom,
% 0.35/0.64      ! [M: nat,N: nat] :
% 0.35/0.64        ( ( semiri681578069525770553at_rat @ ( divide_divide_nat @ M @ N ) )
% 0.35/0.64        = ( divide_divide_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % field_char_0_class.of_nat_div
% 0.35/0.65  thf(fact_7403_field__char__0__class_Oof__nat__div,axiom,
% 0.35/0.65      ! [M: nat,N: nat] :
% 0.35/0.65        ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ M @ N ) )
% 0.35/0.65        = ( divide_divide_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % field_char_0_class.of_nat_div
% 0.35/0.65  thf(fact_7404_field__char__0__class_Oof__nat__div,axiom,
% 0.35/0.65      ! [M: nat,N: nat] :
% 0.35/0.65        ( ( semiri8010041392384452111omplex @ ( divide_divide_nat @ M @ N ) )
% 0.35/0.65        = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % field_char_0_class.of_nat_div
% 0.35/0.65  thf(fact_7405_nat__less__real__le,axiom,
% 0.35/0.65      ( ord_less_nat
% 0.35/0.65      = ( ^ [N2: nat,M6: nat] : ( ord_less_eq_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ M6 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % nat_less_real_le
% 0.35/0.65  thf(fact_7406_nat__le__real__less,axiom,
% 0.35/0.65      ( ord_less_eq_nat
% 0.35/0.65      = ( ^ [N2: nat,M6: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M6 ) @ one_one_real ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % nat_le_real_less
% 0.35/0.65  thf(fact_7407_less__log__of__power,axiom,
% 0.35/0.65      ! [B: real,N: nat,M: real] :
% 0.35/0.65        ( ( ord_less_real @ ( power_power_real @ B @ N ) @ M )
% 0.35/0.65       => ( ( ord_less_real @ one_one_real @ B )
% 0.35/0.65         => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % less_log_of_power
% 0.35/0.65  thf(fact_7408_log__of__power__eq,axiom,
% 0.35/0.65      ! [M: nat,B: real,N: nat] :
% 0.35/0.65        ( ( ( semiri5074537144036343181t_real @ M )
% 0.35/0.65          = ( power_power_real @ B @ N ) )
% 0.35/0.65       => ( ( ord_less_real @ one_one_real @ B )
% 0.35/0.65         => ( ( semiri5074537144036343181t_real @ N )
% 0.35/0.65            = ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % log_of_power_eq
% 0.35/0.65  thf(fact_7409_real__of__nat__div__aux,axiom,
% 0.35/0.65      ! [X: nat,D2: nat] :
% 0.35/0.65        ( ( divide_divide_real @ ( semiri5074537144036343181t_real @ X ) @ ( semiri5074537144036343181t_real @ D2 ) )
% 0.35/0.65        = ( plus_plus_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ X @ D2 ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ X @ D2 ) ) @ ( semiri5074537144036343181t_real @ D2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % real_of_nat_div_aux
% 0.35/0.65  thf(fact_7410_ceiling__split,axiom,
% 0.35/0.65      ! [P: int > $o,T: rat] :
% 0.35/0.65        ( ( P @ ( archim2889992004027027881ng_rat @ T ) )
% 0.35/0.65        = ( ! [I3: int] :
% 0.35/0.65              ( ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ I3 ) @ one_one_rat ) @ T )
% 0.35/0.65                & ( ord_less_eq_rat @ T @ ( ring_1_of_int_rat @ I3 ) ) )
% 0.35/0.65             => ( P @ I3 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % ceiling_split
% 0.35/0.65  thf(fact_7411_ceiling__split,axiom,
% 0.35/0.65      ! [P: int > $o,T: real] :
% 0.35/0.65        ( ( P @ ( archim7802044766580827645g_real @ T ) )
% 0.35/0.65        = ( ! [I3: int] :
% 0.35/0.65              ( ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ I3 ) @ one_one_real ) @ T )
% 0.35/0.65                & ( ord_less_eq_real @ T @ ( ring_1_of_int_real @ I3 ) ) )
% 0.35/0.65             => ( P @ I3 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % ceiling_split
% 0.35/0.65  thf(fact_7412_ceiling__eq__iff,axiom,
% 0.35/0.65      ! [X: rat,A: int] :
% 0.35/0.65        ( ( ( archim2889992004027027881ng_rat @ X )
% 0.35/0.65          = A )
% 0.35/0.65        = ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) @ X )
% 0.35/0.65          & ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ A ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % ceiling_eq_iff
% 0.35/0.65  thf(fact_7413_ceiling__eq__iff,axiom,
% 0.35/0.65      ! [X: real,A: int] :
% 0.35/0.65        ( ( ( archim7802044766580827645g_real @ X )
% 0.35/0.65          = A )
% 0.35/0.65        = ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) @ X )
% 0.35/0.65          & ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ A ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % ceiling_eq_iff
% 0.35/0.65  thf(fact_7414_ceiling__unique,axiom,
% 0.35/0.65      ! [Z: int,X: rat] :
% 0.35/0.65        ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X )
% 0.35/0.65       => ( ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ Z ) )
% 0.35/0.65         => ( ( archim2889992004027027881ng_rat @ X )
% 0.35/0.65            = Z ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % ceiling_unique
% 0.35/0.65  thf(fact_7415_ceiling__unique,axiom,
% 0.35/0.65      ! [Z: int,X: real] :
% 0.35/0.65        ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X )
% 0.35/0.65       => ( ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ Z ) )
% 0.35/0.65         => ( ( archim7802044766580827645g_real @ X )
% 0.35/0.65            = Z ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % ceiling_unique
% 0.35/0.65  thf(fact_7416_ceiling__correct,axiom,
% 0.35/0.65      ! [X: rat] :
% 0.35/0.65        ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X ) ) @ one_one_rat ) @ X )
% 0.35/0.65        & ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % ceiling_correct
% 0.35/0.65  thf(fact_7417_ceiling__correct,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) ) @ one_one_real ) @ X )
% 0.35/0.65        & ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % ceiling_correct
% 0.35/0.65  thf(fact_7418_mult__ceiling__le,axiom,
% 0.35/0.65      ! [A: rat,B: rat] :
% 0.35/0.65        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.35/0.65       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.35/0.65         => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % mult_ceiling_le
% 0.35/0.65  thf(fact_7419_mult__ceiling__le,axiom,
% 0.35/0.65      ! [A: real,B: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.35/0.65       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.35/0.65         => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B ) ) @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % mult_ceiling_le
% 0.35/0.65  thf(fact_7420_nat__approx__posE,axiom,
% 0.35/0.65      ! [E: rat] :
% 0.35/0.65        ( ( ord_less_rat @ zero_zero_rat @ E )
% 0.35/0.65       => ~ ! [N3: nat] :
% 0.35/0.65              ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N3 ) ) ) @ E ) ) ).
% 0.35/0.65  
% 0.35/0.65  % nat_approx_posE
% 0.35/0.65  thf(fact_7421_nat__approx__posE,axiom,
% 0.35/0.65      ! [E: real] :
% 0.35/0.65        ( ( ord_less_real @ zero_zero_real @ E )
% 0.35/0.65       => ~ ! [N3: nat] :
% 0.35/0.65              ~ ( ord_less_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ E ) ) ).
% 0.35/0.65  
% 0.35/0.65  % nat_approx_posE
% 0.35/0.65  thf(fact_7422_of__nat__less__two__power,axiom,
% 0.35/0.65      ! [N: nat] : ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.35/0.65  
% 0.35/0.65  % of_nat_less_two_power
% 0.35/0.65  thf(fact_7423_of__nat__less__two__power,axiom,
% 0.35/0.65      ! [N: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 0.35/0.65  
% 0.35/0.65  % of_nat_less_two_power
% 0.35/0.65  thf(fact_7424_of__nat__less__two__power,axiom,
% 0.35/0.65      ! [N: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 0.35/0.65  
% 0.35/0.65  % of_nat_less_two_power
% 0.35/0.65  thf(fact_7425_ceiling__less__iff,axiom,
% 0.35/0.65      ! [X: rat,Z: int] :
% 0.35/0.65        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ Z )
% 0.35/0.65        = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % ceiling_less_iff
% 0.35/0.65  thf(fact_7426_ceiling__less__iff,axiom,
% 0.35/0.65      ! [X: real,Z: int] :
% 0.35/0.65        ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ Z )
% 0.35/0.65        = ( ord_less_eq_real @ X @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % ceiling_less_iff
% 0.35/0.65  thf(fact_7427_le__ceiling__iff,axiom,
% 0.35/0.65      ! [Z: int,X: rat] :
% 0.35/0.65        ( ( ord_less_eq_int @ Z @ ( archim2889992004027027881ng_rat @ X ) )
% 0.35/0.65        = ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X ) ) ).
% 0.35/0.65  
% 0.35/0.65  % le_ceiling_iff
% 0.35/0.65  thf(fact_7428_le__ceiling__iff,axiom,
% 0.35/0.65      ! [Z: int,X: real] :
% 0.35/0.65        ( ( ord_less_eq_int @ Z @ ( archim7802044766580827645g_real @ X ) )
% 0.35/0.65        = ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X ) ) ).
% 0.35/0.65  
% 0.35/0.65  % le_ceiling_iff
% 0.35/0.65  thf(fact_7429_inverse__of__nat__le,axiom,
% 0.35/0.65      ! [N: nat,M: nat] :
% 0.35/0.65        ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.65       => ( ( N != zero_zero_nat )
% 0.35/0.65         => ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ N ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % inverse_of_nat_le
% 0.35/0.65  thf(fact_7430_inverse__of__nat__le,axiom,
% 0.35/0.65      ! [N: nat,M: nat] :
% 0.35/0.65        ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.65       => ( ( N != zero_zero_nat )
% 0.35/0.65         => ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % inverse_of_nat_le
% 0.35/0.65  thf(fact_7431_exp__divide__power__eq,axiom,
% 0.35/0.65      ! [N: nat,X: real] :
% 0.35/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.65       => ( ( power_power_real @ ( exp_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N )
% 0.35/0.65          = ( exp_real @ X ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % exp_divide_power_eq
% 0.35/0.65  thf(fact_7432_exp__divide__power__eq,axiom,
% 0.35/0.65      ! [N: nat,X: complex] :
% 0.35/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.65       => ( ( power_power_complex @ ( exp_complex @ ( divide1717551699836669952omplex @ X @ ( semiri8010041392384452111omplex @ N ) ) ) @ N )
% 0.35/0.65          = ( exp_complex @ X ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % exp_divide_power_eq
% 0.35/0.65  thf(fact_7433_real__archimedian__rdiv__eq__0,axiom,
% 0.35/0.65      ! [X: real,C: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.65       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.35/0.65         => ( ! [M4: nat] :
% 0.35/0.65                ( ( ord_less_nat @ zero_zero_nat @ M4 )
% 0.35/0.65               => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M4 ) @ X ) @ C ) )
% 0.35/0.65           => ( X = zero_zero_real ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % real_archimedian_rdiv_eq_0
% 0.35/0.65  thf(fact_7434_real__of__nat__div2,axiom,
% 0.35/0.65      ! [N: nat,X: nat] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % real_of_nat_div2
% 0.35/0.65  thf(fact_7435_real__of__nat__div3,axiom,
% 0.35/0.65      ! [N: nat,X: nat] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) ) @ one_one_real ) ).
% 0.35/0.65  
% 0.35/0.65  % real_of_nat_div3
% 0.35/0.65  thf(fact_7436_le__log__of__power,axiom,
% 0.35/0.65      ! [B: real,N: nat,M: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ ( power_power_real @ B @ N ) @ M )
% 0.35/0.65       => ( ( ord_less_real @ one_one_real @ B )
% 0.35/0.65         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % le_log_of_power
% 0.35/0.65  thf(fact_7437_log__base__pow,axiom,
% 0.35/0.65      ! [A: real,N: nat,X: real] :
% 0.35/0.65        ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.65       => ( ( log @ ( power_power_real @ A @ N ) @ X )
% 0.35/0.65          = ( divide_divide_real @ ( log @ A @ X ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % log_base_pow
% 0.35/0.65  thf(fact_7438_log__nat__power,axiom,
% 0.35/0.65      ! [X: real,B: real,N: nat] :
% 0.35/0.65        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.65       => ( ( log @ B @ ( power_power_real @ X @ N ) )
% 0.35/0.65          = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % log_nat_power
% 0.35/0.65  thf(fact_7439_ln__realpow,axiom,
% 0.35/0.65      ! [X: real,N: nat] :
% 0.35/0.65        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.65       => ( ( ln_ln_real @ ( power_power_real @ X @ N ) )
% 0.35/0.65          = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( ln_ln_real @ X ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % ln_realpow
% 0.35/0.65  thf(fact_7440_ceiling__divide__upper,axiom,
% 0.35/0.65      ! [Q2: real,P6: real] :
% 0.35/0.65        ( ( ord_less_real @ zero_zero_real @ Q2 )
% 0.35/0.65       => ( ord_less_eq_real @ P6 @ ( times_times_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P6 @ Q2 ) ) ) @ Q2 ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % ceiling_divide_upper
% 0.35/0.65  thf(fact_7441_ceiling__divide__upper,axiom,
% 0.35/0.65      ! [Q2: rat,P6: rat] :
% 0.35/0.65        ( ( ord_less_rat @ zero_zero_rat @ Q2 )
% 0.35/0.65       => ( ord_less_eq_rat @ P6 @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P6 @ Q2 ) ) ) @ Q2 ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % ceiling_divide_upper
% 0.35/0.65  thf(fact_7442_ceiling__log2__div2,axiom,
% 0.35/0.65      ! [N: nat] :
% 0.35/0.65        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.65       => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 0.35/0.65          = ( plus_plus_int @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( divide_divide_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) @ one_one_int ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % ceiling_log2_div2
% 0.35/0.65  thf(fact_7443_log2__of__power__eq,axiom,
% 0.35/0.65      ! [M: nat,N: nat] :
% 0.35/0.65        ( ( M
% 0.35/0.65          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.65       => ( ( semiri5074537144036343181t_real @ N )
% 0.35/0.65          = ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % log2_of_power_eq
% 0.35/0.65  thf(fact_7444_log__of__power__less,axiom,
% 0.35/0.65      ! [M: nat,B: real,N: nat] :
% 0.35/0.65        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 0.35/0.65       => ( ( ord_less_real @ one_one_real @ B )
% 0.35/0.65         => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.35/0.65           => ( ord_less_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % log_of_power_less
% 0.35/0.65  thf(fact_7445_linear__plus__1__le__power,axiom,
% 0.35/0.65      ! [X: real,N: nat] :
% 0.35/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.65       => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) @ one_one_real ) @ ( power_power_real @ ( plus_plus_real @ X @ one_one_real ) @ N ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % linear_plus_1_le_power
% 0.35/0.65  thf(fact_7446_Bernoulli__inequality,axiom,
% 0.35/0.65      ! [X: real,N: nat] :
% 0.35/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.35/0.65       => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X ) @ N ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % Bernoulli_inequality
% 0.35/0.65  thf(fact_7447_ceiling__divide__lower,axiom,
% 0.35/0.65      ! [Q2: real,P6: real] :
% 0.35/0.65        ( ( ord_less_real @ zero_zero_real @ Q2 )
% 0.35/0.65       => ( ord_less_real @ ( times_times_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P6 @ Q2 ) ) ) @ one_one_real ) @ Q2 ) @ P6 ) ) ).
% 0.35/0.65  
% 0.35/0.65  % ceiling_divide_lower
% 0.35/0.65  thf(fact_7448_ceiling__divide__lower,axiom,
% 0.35/0.65      ! [Q2: rat,P6: rat] :
% 0.35/0.65        ( ( ord_less_rat @ zero_zero_rat @ Q2 )
% 0.35/0.65       => ( ord_less_rat @ ( times_times_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P6 @ Q2 ) ) ) @ one_one_rat ) @ Q2 ) @ P6 ) ) ).
% 0.35/0.65  
% 0.35/0.65  % ceiling_divide_lower
% 0.35/0.65  thf(fact_7449_ceiling__eq,axiom,
% 0.35/0.65      ! [N: int,X: rat] :
% 0.35/0.65        ( ( ord_less_rat @ ( ring_1_of_int_rat @ N ) @ X )
% 0.35/0.65       => ( ( ord_less_eq_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ N ) @ one_one_rat ) )
% 0.35/0.65         => ( ( archim2889992004027027881ng_rat @ X )
% 0.35/0.65            = ( plus_plus_int @ N @ one_one_int ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % ceiling_eq
% 0.35/0.65  thf(fact_7450_ceiling__eq,axiom,
% 0.35/0.65      ! [N: int,X: real] :
% 0.35/0.65        ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X )
% 0.35/0.65       => ( ( ord_less_eq_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 0.35/0.65         => ( ( archim7802044766580827645g_real @ X )
% 0.35/0.65            = ( plus_plus_int @ N @ one_one_int ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % ceiling_eq
% 0.35/0.65  thf(fact_7451_log__of__power__le,axiom,
% 0.35/0.65      ! [M: nat,B: real,N: nat] :
% 0.35/0.65        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 0.35/0.65       => ( ( ord_less_real @ one_one_real @ B )
% 0.35/0.65         => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.35/0.65           => ( ord_less_eq_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % log_of_power_le
% 0.35/0.65  thf(fact_7452_or__Suc__0__eq,axiom,
% 0.35/0.65      ! [N: nat] :
% 0.35/0.65        ( ( bit_se1412395901928357646or_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.35/0.65        = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % or_Suc_0_eq
% 0.35/0.65  thf(fact_7453_Suc__0__or__eq,axiom,
% 0.35/0.65      ! [N: nat] :
% 0.35/0.65        ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.35/0.65        = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % Suc_0_or_eq
% 0.35/0.65  thf(fact_7454_or__nat__rec,axiom,
% 0.35/0.65      ( bit_se1412395901928357646or_nat
% 0.35/0.65      = ( ^ [M6: nat,N2: nat] :
% 0.35/0.65            ( plus_plus_nat
% 0.35/0.65            @ ( zero_n2687167440665602831ol_nat
% 0.35/0.65              @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 )
% 0.35/0.65                | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.35/0.65            @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % or_nat_rec
% 0.35/0.65  thf(fact_7455_double__arith__series,axiom,
% 0.35/0.65      ! [A: rat,D2: rat,N: nat] :
% 0.35/0.65        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 0.35/0.65          @ ( groups2906978787729119204at_rat
% 0.35/0.65            @ ^ [I3: nat] : ( plus_plus_rat @ A @ ( times_times_rat @ ( semiri681578069525770553at_rat @ I3 ) @ D2 ) )
% 0.35/0.65            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.35/0.65        = ( times_times_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ D2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % double_arith_series
% 0.35/0.65  thf(fact_7456_double__arith__series,axiom,
% 0.35/0.65      ! [A: int,D2: int,N: nat] :
% 0.35/0.65        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 0.35/0.65          @ ( groups3539618377306564664at_int
% 0.35/0.65            @ ^ [I3: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I3 ) @ D2 ) )
% 0.35/0.65            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.35/0.65        = ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ D2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % double_arith_series
% 0.35/0.65  thf(fact_7457_double__arith__series,axiom,
% 0.35/0.65      ! [A: complex,D2: complex,N: nat] :
% 0.35/0.65        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 0.35/0.65          @ ( groups2073611262835488442omplex
% 0.35/0.65            @ ^ [I3: nat] : ( plus_plus_complex @ A @ ( times_times_complex @ ( semiri8010041392384452111omplex @ I3 ) @ D2 ) )
% 0.35/0.65            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.35/0.65        = ( times_times_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ D2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % double_arith_series
% 0.35/0.65  thf(fact_7458_double__arith__series,axiom,
% 0.35/0.65      ! [A: nat,D2: nat,N: nat] :
% 0.35/0.65        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.35/0.65          @ ( groups3542108847815614940at_nat
% 0.35/0.65            @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I3 ) @ D2 ) )
% 0.35/0.65            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.35/0.65        = ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ D2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % double_arith_series
% 0.35/0.65  thf(fact_7459_double__arith__series,axiom,
% 0.35/0.65      ! [A: real,D2: real,N: nat] :
% 0.35/0.65        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 0.35/0.65          @ ( groups6591440286371151544t_real
% 0.35/0.65            @ ^ [I3: nat] : ( plus_plus_real @ A @ ( times_times_real @ ( semiri5074537144036343181t_real @ I3 ) @ D2 ) )
% 0.35/0.65            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.35/0.65        = ( times_times_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ D2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % double_arith_series
% 0.35/0.65  thf(fact_7460_double__gauss__sum,axiom,
% 0.35/0.65      ! [N: nat] :
% 0.35/0.65        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.35/0.65        = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % double_gauss_sum
% 0.35/0.65  thf(fact_7461_double__gauss__sum,axiom,
% 0.35/0.65      ! [N: nat] :
% 0.35/0.65        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.35/0.65        = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % double_gauss_sum
% 0.35/0.65  thf(fact_7462_double__gauss__sum,axiom,
% 0.35/0.65      ! [N: nat] :
% 0.35/0.65        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.35/0.65        = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % double_gauss_sum
% 0.35/0.65  thf(fact_7463_double__gauss__sum,axiom,
% 0.35/0.65      ! [N: nat] :
% 0.35/0.65        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.35/0.65        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % double_gauss_sum
% 0.35/0.65  thf(fact_7464_double__gauss__sum,axiom,
% 0.35/0.65      ! [N: nat] :
% 0.35/0.65        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.35/0.65        = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % double_gauss_sum
% 0.35/0.65  thf(fact_7465_less__log2__of__power,axiom,
% 0.35/0.65      ! [N: nat,M: nat] :
% 0.35/0.65        ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 0.35/0.65       => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % less_log2_of_power
% 0.35/0.65  thf(fact_7466_le__log2__of__power,axiom,
% 0.35/0.65      ! [N: nat,M: nat] :
% 0.35/0.65        ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 0.35/0.65       => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % le_log2_of_power
% 0.35/0.65  thf(fact_7467_or__nat__unfold,axiom,
% 0.35/0.65      ( bit_se1412395901928357646or_nat
% 0.35/0.65      = ( ^ [M6: nat,N2: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N2 @ ( if_nat @ ( N2 = zero_zero_nat ) @ M6 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % or_nat_unfold
% 0.35/0.65  thf(fact_7468_double__gauss__sum__from__Suc__0,axiom,
% 0.35/0.65      ! [N: nat] :
% 0.35/0.65        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 0.35/0.65        = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % double_gauss_sum_from_Suc_0
% 0.35/0.65  thf(fact_7469_double__gauss__sum__from__Suc__0,axiom,
% 0.35/0.65      ! [N: nat] :
% 0.35/0.65        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 0.35/0.65        = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % double_gauss_sum_from_Suc_0
% 0.35/0.65  thf(fact_7470_double__gauss__sum__from__Suc__0,axiom,
% 0.35/0.65      ! [N: nat] :
% 0.35/0.65        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 0.35/0.65        = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % double_gauss_sum_from_Suc_0
% 0.35/0.65  thf(fact_7471_double__gauss__sum__from__Suc__0,axiom,
% 0.35/0.65      ! [N: nat] :
% 0.35/0.65        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 0.35/0.65        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % double_gauss_sum_from_Suc_0
% 0.35/0.65  thf(fact_7472_double__gauss__sum__from__Suc__0,axiom,
% 0.35/0.65      ! [N: nat] :
% 0.35/0.65        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 0.35/0.65        = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % double_gauss_sum_from_Suc_0
% 0.35/0.65  thf(fact_7473_arith__series,axiom,
% 0.35/0.65      ! [A: int,D2: int,N: nat] :
% 0.35/0.65        ( ( groups3539618377306564664at_int
% 0.35/0.65          @ ^ [I3: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I3 ) @ D2 ) )
% 0.35/0.65          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.35/0.65        = ( divide_divide_int @ ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ D2 ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % arith_series
% 0.35/0.65  thf(fact_7474_arith__series,axiom,
% 0.35/0.65      ! [A: nat,D2: nat,N: nat] :
% 0.35/0.65        ( ( groups3542108847815614940at_nat
% 0.35/0.65          @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I3 ) @ D2 ) )
% 0.35/0.65          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.35/0.65        = ( divide_divide_nat @ ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ D2 ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % arith_series
% 0.35/0.65  thf(fact_7475_gauss__sum,axiom,
% 0.35/0.65      ! [N: nat] :
% 0.35/0.65        ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.35/0.65        = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % gauss_sum
% 0.35/0.65  thf(fact_7476_gauss__sum,axiom,
% 0.35/0.65      ! [N: nat] :
% 0.35/0.65        ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.35/0.65        = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % gauss_sum
% 0.35/0.65  thf(fact_7477_log2__of__power__less,axiom,
% 0.35/0.65      ! [M: nat,N: nat] :
% 0.35/0.65        ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.65       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.35/0.65         => ( ord_less_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % log2_of_power_less
% 0.35/0.65  thf(fact_7478_sum__gp__offset,axiom,
% 0.35/0.65      ! [X: rat,M: nat,N: nat] :
% 0.35/0.65        ( ( ( X = one_one_rat )
% 0.35/0.65         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 0.35/0.65            = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) )
% 0.35/0.65        & ( ( X != one_one_rat )
% 0.35/0.65         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 0.35/0.65            = ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ X @ M ) @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N ) ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum_gp_offset
% 0.35/0.65  thf(fact_7479_sum__gp__offset,axiom,
% 0.35/0.65      ! [X: complex,M: nat,N: nat] :
% 0.35/0.65        ( ( ( X = one_one_complex )
% 0.35/0.65         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 0.35/0.65            = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) )
% 0.35/0.65        & ( ( X != one_one_complex )
% 0.35/0.65         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 0.35/0.65            = ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ X @ M ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ ( suc @ N ) ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum_gp_offset
% 0.35/0.65  thf(fact_7480_sum__gp__offset,axiom,
% 0.35/0.65      ! [X: real,M: nat,N: nat] :
% 0.35/0.65        ( ( ( X = one_one_real )
% 0.35/0.65         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 0.35/0.65            = ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) )
% 0.35/0.65        & ( ( X != one_one_real )
% 0.35/0.65         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 0.35/0.65            = ( divide_divide_real @ ( times_times_real @ ( power_power_real @ X @ M ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( suc @ N ) ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum_gp_offset
% 0.35/0.65  thf(fact_7481_Bernoulli__inequality__even,axiom,
% 0.35/0.65      ! [N: nat,X: real] :
% 0.35/0.65        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.65       => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X ) @ N ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % Bernoulli_inequality_even
% 0.35/0.65  thf(fact_7482_exp__ge__one__plus__x__over__n__power__n,axiom,
% 0.35/0.65      ! [N: nat,X: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ X )
% 0.35/0.65       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.65         => ( ord_less_eq_real @ ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ X ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % exp_ge_one_plus_x_over_n_power_n
% 0.35/0.65  thf(fact_7483_exp__ge__one__minus__x__over__n__power__n,axiom,
% 0.35/0.65      ! [X: real,N: nat] :
% 0.35/0.65        ( ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N ) )
% 0.35/0.65       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.65         => ( ord_less_eq_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % exp_ge_one_minus_x_over_n_power_n
% 0.35/0.65  thf(fact_7484_pred__bound__size__univ_H,axiom,
% 0.35/0.65      ! [T: vEBT_VEBT,N: nat,U: real,X: nat] :
% 0.35/0.65        ( ( vEBT_invar_vebt @ T @ N )
% 0.35/0.65       => ( ( U
% 0.35/0.65            = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.65         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_p_r_e_d2 @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % pred_bound_size_univ'
% 0.35/0.65  thf(fact_7485_succ__bound__size__univ_H,axiom,
% 0.35/0.65      ! [T: vEBT_VEBT,N: nat,U: real,X: nat] :
% 0.35/0.65        ( ( vEBT_invar_vebt @ T @ N )
% 0.35/0.65       => ( ( U
% 0.35/0.65            = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.65         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_s_u_c_c2 @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % succ_bound_size_univ'
% 0.35/0.65  thf(fact_7486_gauss__sum__from__Suc__0,axiom,
% 0.35/0.65      ! [N: nat] :
% 0.35/0.65        ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 0.35/0.65        = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % gauss_sum_from_Suc_0
% 0.35/0.65  thf(fact_7487_gauss__sum__from__Suc__0,axiom,
% 0.35/0.65      ! [N: nat] :
% 0.35/0.65        ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 0.35/0.65        = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % gauss_sum_from_Suc_0
% 0.35/0.65  thf(fact_7488_log2__of__power__le,axiom,
% 0.35/0.65      ! [M: nat,N: nat] :
% 0.35/0.65        ( ( ord_less_eq_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.65       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.35/0.65         => ( ord_less_eq_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % log2_of_power_le
% 0.35/0.65  thf(fact_7489_sum__gp,axiom,
% 0.35/0.65      ! [N: nat,M: nat,X: rat] :
% 0.35/0.65        ( ( ( ord_less_nat @ N @ M )
% 0.35/0.65         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.35/0.65            = zero_zero_rat ) )
% 0.35/0.65        & ( ~ ( ord_less_nat @ N @ M )
% 0.35/0.65         => ( ( ( X = one_one_rat )
% 0.35/0.65             => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.35/0.65                = ( semiri681578069525770553at_rat @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 0.35/0.65            & ( ( X != one_one_rat )
% 0.35/0.65             => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.35/0.65                = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ M ) @ ( power_power_rat @ X @ ( suc @ N ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum_gp
% 0.35/0.65  thf(fact_7490_sum__gp,axiom,
% 0.35/0.65      ! [N: nat,M: nat,X: complex] :
% 0.35/0.65        ( ( ( ord_less_nat @ N @ M )
% 0.35/0.65         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.35/0.65            = zero_zero_complex ) )
% 0.35/0.65        & ( ~ ( ord_less_nat @ N @ M )
% 0.35/0.65         => ( ( ( X = one_one_complex )
% 0.35/0.65             => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.35/0.65                = ( semiri8010041392384452111omplex @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 0.35/0.65            & ( ( X != one_one_complex )
% 0.35/0.65             => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.35/0.65                = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X @ M ) @ ( power_power_complex @ X @ ( suc @ N ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum_gp
% 0.35/0.65  thf(fact_7491_sum__gp,axiom,
% 0.35/0.65      ! [N: nat,M: nat,X: real] :
% 0.35/0.65        ( ( ( ord_less_nat @ N @ M )
% 0.35/0.65         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.35/0.65            = zero_zero_real ) )
% 0.35/0.65        & ( ~ ( ord_less_nat @ N @ M )
% 0.35/0.65         => ( ( ( X = one_one_real )
% 0.35/0.65             => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.35/0.65                = ( semiri5074537144036343181t_real @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 0.35/0.65            & ( ( X != one_one_real )
% 0.35/0.65             => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.35/0.65                = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ M ) @ ( power_power_real @ X @ ( suc @ N ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum_gp
% 0.35/0.65  thf(fact_7492_insert__bound__size__univ,axiom,
% 0.35/0.65      ! [T: vEBT_VEBT,N: nat,U: real,X: nat] :
% 0.35/0.65        ( ( vEBT_invar_vebt @ T @ N )
% 0.35/0.65       => ( ( U
% 0.35/0.65            = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.65         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_i_n_s_e_r_t @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % insert_bound_size_univ
% 0.35/0.65  thf(fact_7493_of__nat__code__if,axiom,
% 0.35/0.65      ( semiri681578069525770553at_rat
% 0.35/0.65      = ( ^ [N2: nat] :
% 0.35/0.65            ( if_rat @ ( N2 = zero_zero_nat ) @ zero_zero_rat
% 0.35/0.65            @ ( produc6207742614233964070at_rat
% 0.35/0.65              @ ^ [M6: nat,Q4: nat] : ( if_rat @ ( Q4 = zero_zero_nat ) @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M6 ) ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M6 ) ) @ one_one_rat ) )
% 0.35/0.65              @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % of_nat_code_if
% 0.35/0.65  thf(fact_7494_of__nat__code__if,axiom,
% 0.35/0.65      ( semiri5074537144036343181t_real
% 0.35/0.65      = ( ^ [N2: nat] :
% 0.35/0.65            ( if_real @ ( N2 = zero_zero_nat ) @ zero_zero_real
% 0.35/0.65            @ ( produc1703576794950452218t_real
% 0.35/0.65              @ ^ [M6: nat,Q4: nat] : ( if_real @ ( Q4 = zero_zero_nat ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M6 ) ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M6 ) ) @ one_one_real ) )
% 0.35/0.65              @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % of_nat_code_if
% 0.35/0.65  thf(fact_7495_of__nat__code__if,axiom,
% 0.35/0.65      ( semiri1314217659103216013at_int
% 0.35/0.65      = ( ^ [N2: nat] :
% 0.35/0.65            ( if_int @ ( N2 = zero_zero_nat ) @ zero_zero_int
% 0.35/0.65            @ ( produc6840382203811409530at_int
% 0.35/0.65              @ ^ [M6: nat,Q4: nat] : ( if_int @ ( Q4 = zero_zero_nat ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ M6 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ M6 ) ) @ one_one_int ) )
% 0.35/0.65              @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % of_nat_code_if
% 0.35/0.65  thf(fact_7496_of__nat__code__if,axiom,
% 0.35/0.65      ( semiri8010041392384452111omplex
% 0.35/0.65      = ( ^ [N2: nat] :
% 0.35/0.65            ( if_complex @ ( N2 = zero_zero_nat ) @ zero_zero_complex
% 0.35/0.65            @ ( produc1917071388513777916omplex
% 0.35/0.65              @ ^ [M6: nat,Q4: nat] : ( if_complex @ ( Q4 = zero_zero_nat ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M6 ) ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M6 ) ) @ one_one_complex ) )
% 0.35/0.65              @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % of_nat_code_if
% 0.35/0.65  thf(fact_7497_of__nat__code__if,axiom,
% 0.35/0.65      ( semiri1316708129612266289at_nat
% 0.35/0.65      = ( ^ [N2: nat] :
% 0.35/0.65            ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat
% 0.35/0.65            @ ( produc6842872674320459806at_nat
% 0.35/0.65              @ ^ [M6: nat,Q4: nat] : ( if_nat @ ( Q4 = zero_zero_nat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ M6 ) ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ M6 ) ) @ one_one_nat ) )
% 0.35/0.65              @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % of_nat_code_if
% 0.35/0.65  thf(fact_7498_heigt__uplog__rel,axiom,
% 0.35/0.65      ! [T: vEBT_VEBT,N: nat] :
% 0.35/0.65        ( ( vEBT_invar_vebt @ T @ N )
% 0.35/0.65       => ( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ T ) )
% 0.35/0.65          = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % heigt_uplog_rel
% 0.35/0.65  thf(fact_7499_monoseq__arctan__series,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.35/0.65       => ( topolo6980174941875973593q_real
% 0.35/0.65          @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % monoseq_arctan_series
% 0.35/0.65  thf(fact_7500_lemma__termdiff3,axiom,
% 0.35/0.65      ! [H2: real,Z: real,K5: real,N: nat] :
% 0.35/0.65        ( ( H2 != zero_zero_real )
% 0.35/0.65       => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ K5 )
% 0.35/0.65         => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ Z @ H2 ) ) @ K5 )
% 0.35/0.65           => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ N ) @ ( power_power_real @ Z @ N ) ) @ H2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V7735802525324610683m_real @ H2 ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % lemma_termdiff3
% 0.35/0.65  thf(fact_7501_lemma__termdiff3,axiom,
% 0.35/0.65      ! [H2: complex,Z: complex,K5: real,N: nat] :
% 0.35/0.65        ( ( H2 != zero_zero_complex )
% 0.35/0.65       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ K5 )
% 0.35/0.65         => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ Z @ H2 ) ) @ K5 )
% 0.35/0.65           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ N ) @ ( power_power_complex @ Z @ N ) ) @ H2 ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V1022390504157884413omplex @ H2 ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % lemma_termdiff3
% 0.35/0.65  thf(fact_7502_ln__series,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.65       => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.35/0.65         => ( ( ln_ln_real @ X )
% 0.35/0.65            = ( suminf_real
% 0.35/0.65              @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) @ ( power_power_real @ ( minus_minus_real @ X @ one_one_real ) @ ( suc @ N2 ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % ln_series
% 0.35/0.65  thf(fact_7503_int__eq__iff__numeral,axiom,
% 0.35/0.65      ! [M: nat,V: num] :
% 0.35/0.65        ( ( ( semiri1314217659103216013at_int @ M )
% 0.35/0.65          = ( numeral_numeral_int @ V ) )
% 0.35/0.65        = ( M
% 0.35/0.65          = ( numeral_numeral_nat @ V ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % int_eq_iff_numeral
% 0.35/0.65  thf(fact_7504_negative__zless,axiom,
% 0.35/0.65      ! [N: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 0.35/0.65  
% 0.35/0.65  % negative_zless
% 0.35/0.65  thf(fact_7505_powser__zero,axiom,
% 0.35/0.65      ! [F: nat > complex] :
% 0.35/0.65        ( ( suminf_complex
% 0.35/0.65          @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) ) )
% 0.35/0.65        = ( F @ zero_zero_nat ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powser_zero
% 0.35/0.65  thf(fact_7506_powser__zero,axiom,
% 0.35/0.65      ! [F: nat > real] :
% 0.35/0.65        ( ( suminf_real
% 0.35/0.65          @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) ) )
% 0.35/0.65        = ( F @ zero_zero_nat ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powser_zero
% 0.35/0.65  thf(fact_7507_int__diff__cases,axiom,
% 0.35/0.65      ! [Z: int] :
% 0.35/0.65        ~ ! [M4: nat,N3: nat] :
% 0.35/0.65            ( Z
% 0.35/0.65           != ( minus_minus_int @ ( semiri1314217659103216013at_int @ M4 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % int_diff_cases
% 0.35/0.65  thf(fact_7508_int__ops_I3_J,axiom,
% 0.35/0.65      ! [N: num] :
% 0.35/0.65        ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 0.35/0.65        = ( numeral_numeral_int @ N ) ) ).
% 0.35/0.65  
% 0.35/0.65  % int_ops(3)
% 0.35/0.65  thf(fact_7509_complex__mod__minus__le__complex__mod,axiom,
% 0.35/0.65      ! [X: complex] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 0.35/0.65  
% 0.35/0.65  % complex_mod_minus_le_complex_mod
% 0.35/0.65  thf(fact_7510_int__of__nat__induct,axiom,
% 0.35/0.65      ! [P: int > $o,Z: int] :
% 0.35/0.65        ( ! [N3: nat] : ( P @ ( semiri1314217659103216013at_int @ N3 ) )
% 0.35/0.65       => ( ! [N3: nat] : ( P @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) )
% 0.35/0.65         => ( P @ Z ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % int_of_nat_induct
% 0.35/0.65  thf(fact_7511_int__cases,axiom,
% 0.35/0.65      ! [Z: int] :
% 0.35/0.65        ( ! [N3: nat] :
% 0.35/0.65            ( Z
% 0.35/0.65           != ( semiri1314217659103216013at_int @ N3 ) )
% 0.35/0.65       => ~ ! [N3: nat] :
% 0.35/0.65              ( Z
% 0.35/0.65             != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % int_cases
% 0.35/0.65  thf(fact_7512_nat__int__comparison_I2_J,axiom,
% 0.35/0.65      ( ord_less_nat
% 0.35/0.65      = ( ^ [A3: nat,B4: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % nat_int_comparison(2)
% 0.35/0.65  thf(fact_7513_nat__int__comparison_I3_J,axiom,
% 0.35/0.65      ( ord_less_eq_nat
% 0.35/0.65      = ( ^ [A3: nat,B4: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % nat_int_comparison(3)
% 0.35/0.65  thf(fact_7514_zle__int,axiom,
% 0.35/0.65      ! [M: nat,N: nat] :
% 0.35/0.65        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.35/0.65        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.35/0.65  
% 0.35/0.65  % zle_int
% 0.35/0.65  thf(fact_7515_int__ops_I2_J,axiom,
% 0.35/0.65      ( ( semiri1314217659103216013at_int @ one_one_nat )
% 0.35/0.65      = one_one_int ) ).
% 0.35/0.65  
% 0.35/0.65  % int_ops(2)
% 0.35/0.65  thf(fact_7516_complex__mod__triangle__ineq2,axiom,
% 0.35/0.65      ! [B: complex,A: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ B @ A ) ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ A ) ) ).
% 0.35/0.65  
% 0.35/0.65  % complex_mod_triangle_ineq2
% 0.35/0.65  thf(fact_7517_int__ops_I5_J,axiom,
% 0.35/0.65      ! [A: nat,B: nat] :
% 0.35/0.65        ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B ) )
% 0.35/0.65        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % int_ops(5)
% 0.35/0.65  thf(fact_7518_int__plus,axiom,
% 0.35/0.65      ! [N: nat,M: nat] :
% 0.35/0.65        ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N @ M ) )
% 0.35/0.65        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % int_plus
% 0.35/0.65  thf(fact_7519_zadd__int__left,axiom,
% 0.35/0.65      ! [M: nat,N: nat,Z: int] :
% 0.35/0.65        ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ Z ) )
% 0.35/0.65        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) ) @ Z ) ) ).
% 0.35/0.65  
% 0.35/0.65  % zadd_int_left
% 0.35/0.65  thf(fact_7520_int__ops_I7_J,axiom,
% 0.35/0.65      ! [A: nat,B: nat] :
% 0.35/0.65        ( ( semiri1314217659103216013at_int @ ( times_times_nat @ A @ B ) )
% 0.35/0.65        = ( times_times_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % int_ops(7)
% 0.35/0.65  thf(fact_7521_zdiv__int,axiom,
% 0.35/0.65      ! [A: nat,B: nat] :
% 0.35/0.65        ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ A @ B ) )
% 0.35/0.65        = ( divide_divide_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % zdiv_int
% 0.35/0.65  thf(fact_7522_zmod__int,axiom,
% 0.35/0.65      ! [A: nat,B: nat] :
% 0.35/0.65        ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ A @ B ) )
% 0.35/0.65        = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % zmod_int
% 0.35/0.65  thf(fact_7523_nat__less__as__int,axiom,
% 0.35/0.65      ( ord_less_nat
% 0.35/0.65      = ( ^ [A3: nat,B4: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % nat_less_as_int
% 0.35/0.65  thf(fact_7524_nat__leq__as__int,axiom,
% 0.35/0.65      ( ord_less_eq_nat
% 0.35/0.65      = ( ^ [A3: nat,B4: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % nat_leq_as_int
% 0.35/0.65  thf(fact_7525_int__cases4,axiom,
% 0.35/0.65      ! [M: int] :
% 0.35/0.65        ( ! [N3: nat] :
% 0.35/0.65            ( M
% 0.35/0.65           != ( semiri1314217659103216013at_int @ N3 ) )
% 0.35/0.65       => ~ ! [N3: nat] :
% 0.35/0.65              ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.35/0.65             => ( M
% 0.35/0.65               != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % int_cases4
% 0.35/0.65  thf(fact_7526_int__Suc,axiom,
% 0.35/0.65      ! [N: nat] :
% 0.35/0.65        ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 0.35/0.65        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ).
% 0.35/0.65  
% 0.35/0.65  % int_Suc
% 0.35/0.65  thf(fact_7527_int__ops_I4_J,axiom,
% 0.35/0.65      ! [A: nat] :
% 0.35/0.65        ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 0.35/0.65        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 0.35/0.65  
% 0.35/0.65  % int_ops(4)
% 0.35/0.65  thf(fact_7528_zless__iff__Suc__zadd,axiom,
% 0.35/0.65      ( ord_less_int
% 0.35/0.65      = ( ^ [W2: int,Z4: int] :
% 0.35/0.65          ? [N2: nat] :
% 0.35/0.65            ( Z4
% 0.35/0.65            = ( plus_plus_int @ W2 @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % zless_iff_Suc_zadd
% 0.35/0.65  thf(fact_7529_norm__exp,axiom,
% 0.35/0.65      ! [X: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ X ) ) @ ( exp_real @ ( real_V7735802525324610683m_real @ X ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_exp
% 0.35/0.65  thf(fact_7530_norm__exp,axiom,
% 0.35/0.65      ! [X: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ X ) ) @ ( exp_real @ ( real_V1022390504157884413omplex @ X ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_exp
% 0.35/0.65  thf(fact_7531_pos__int__cases,axiom,
% 0.35/0.65      ! [K: int] :
% 0.35/0.65        ( ( ord_less_int @ zero_zero_int @ K )
% 0.35/0.65       => ~ ! [N3: nat] :
% 0.35/0.65              ( ( K
% 0.35/0.65                = ( semiri1314217659103216013at_int @ N3 ) )
% 0.35/0.65             => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % pos_int_cases
% 0.35/0.65  thf(fact_7532_zero__less__imp__eq__int,axiom,
% 0.35/0.65      ! [K: int] :
% 0.35/0.65        ( ( ord_less_int @ zero_zero_int @ K )
% 0.35/0.65       => ? [N3: nat] :
% 0.35/0.65            ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.35/0.65            & ( K
% 0.35/0.65              = ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % zero_less_imp_eq_int
% 0.35/0.65  thf(fact_7533_int__cases3,axiom,
% 0.35/0.65      ! [K: int] :
% 0.35/0.65        ( ( K != zero_zero_int )
% 0.35/0.65       => ( ! [N3: nat] :
% 0.35/0.65              ( ( K
% 0.35/0.65                = ( semiri1314217659103216013at_int @ N3 ) )
% 0.35/0.65             => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) )
% 0.35/0.65         => ~ ! [N3: nat] :
% 0.35/0.65                ( ( K
% 0.35/0.65                  = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 0.35/0.65               => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % int_cases3
% 0.35/0.65  thf(fact_7534_zmult__zless__mono2__lemma,axiom,
% 0.35/0.65      ! [I2: int,J: int,K: nat] :
% 0.35/0.65        ( ( ord_less_int @ I2 @ J )
% 0.35/0.65       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.35/0.65         => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I2 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % zmult_zless_mono2_lemma
% 0.35/0.65  thf(fact_7535_not__zle__0__negative,axiom,
% 0.35/0.65      ! [N: nat] :
% 0.35/0.65        ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % not_zle_0_negative
% 0.35/0.65  thf(fact_7536_negative__zless__0,axiom,
% 0.35/0.65      ! [N: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ zero_zero_int ) ).
% 0.35/0.65  
% 0.35/0.65  % negative_zless_0
% 0.35/0.65  thf(fact_7537_negD,axiom,
% 0.35/0.65      ! [X: int] :
% 0.35/0.65        ( ( ord_less_int @ X @ zero_zero_int )
% 0.35/0.65       => ? [N3: nat] :
% 0.35/0.65            ( X
% 0.35/0.65            = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % negD
% 0.35/0.65  thf(fact_7538_int__ops_I6_J,axiom,
% 0.35/0.65      ! [A: nat,B: nat] :
% 0.35/0.65        ( ( ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 0.35/0.65         => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 0.35/0.65            = zero_zero_int ) )
% 0.35/0.65        & ( ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 0.35/0.65         => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 0.35/0.65            = ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % int_ops(6)
% 0.35/0.65  thf(fact_7539_neg__int__cases,axiom,
% 0.35/0.65      ! [K: int] :
% 0.35/0.65        ( ( ord_less_int @ K @ zero_zero_int )
% 0.35/0.65       => ~ ! [N3: nat] :
% 0.35/0.65              ( ( K
% 0.35/0.65                = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 0.35/0.65             => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % neg_int_cases
% 0.35/0.65  thf(fact_7540_zdiff__int__split,axiom,
% 0.35/0.65      ! [P: int > $o,X: nat,Y2: nat] :
% 0.35/0.65        ( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X @ Y2 ) ) )
% 0.35/0.65        = ( ( ( ord_less_eq_nat @ Y2 @ X )
% 0.35/0.65           => ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y2 ) ) ) )
% 0.35/0.65          & ( ( ord_less_nat @ X @ Y2 )
% 0.35/0.65           => ( P @ zero_zero_int ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % zdiff_int_split
% 0.35/0.65  thf(fact_7541_monoseq__realpow,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.65       => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.35/0.65         => ( topolo6980174941875973593q_real @ ( power_power_real @ X ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % monoseq_realpow
% 0.35/0.65  thf(fact_7542_exp__bound__half,axiom,
% 0.35/0.65      ! [Z: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.65       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % exp_bound_half
% 0.35/0.65  thf(fact_7543_exp__bound__half,axiom,
% 0.35/0.65      ! [Z: complex] :
% 0.35/0.65        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.65       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % exp_bound_half
% 0.35/0.65  thf(fact_7544_exp__bound__lemma,axiom,
% 0.35/0.65      ! [Z: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.65       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ Z ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( real_V7735802525324610683m_real @ Z ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % exp_bound_lemma
% 0.35/0.65  thf(fact_7545_exp__bound__lemma,axiom,
% 0.35/0.65      ! [Z: complex] :
% 0.35/0.65        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.65       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ Z ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % exp_bound_lemma
% 0.35/0.65  thf(fact_7546_ceiling__log__nat__eq__if,axiom,
% 0.35/0.65      ! [B: nat,N: nat,K: nat] :
% 0.35/0.65        ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 0.35/0.65       => ( ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 0.35/0.65         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.35/0.65           => ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 0.35/0.65              = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % ceiling_log_nat_eq_if
% 0.35/0.65  thf(fact_7547_arctan__series,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.35/0.65       => ( ( arctan @ X )
% 0.35/0.65          = ( suminf_real
% 0.35/0.65            @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % arctan_series
% 0.35/0.65  thf(fact_7548_ceiling__log__nat__eq__powr__iff,axiom,
% 0.35/0.65      ! [B: nat,K: nat,N: nat] :
% 0.35/0.65        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.35/0.65       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.35/0.65         => ( ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 0.35/0.65              = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) )
% 0.35/0.65            = ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 0.35/0.65              & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % ceiling_log_nat_eq_powr_iff
% 0.35/0.65  thf(fact_7549_norm__divide__numeral,axiom,
% 0.35/0.65      ! [A: real,W: num] :
% 0.35/0.65        ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ W ) ) )
% 0.35/0.65        = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_divide_numeral
% 0.35/0.65  thf(fact_7550_norm__divide__numeral,axiom,
% 0.35/0.65      ! [A: complex,W: num] :
% 0.35/0.65        ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 0.35/0.65        = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_divide_numeral
% 0.35/0.65  thf(fact_7551_norm__mult__numeral2,axiom,
% 0.35/0.65      ! [A: real,W: num] :
% 0.35/0.65        ( ( real_V7735802525324610683m_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) )
% 0.35/0.65        = ( times_times_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_mult_numeral2
% 0.35/0.65  thf(fact_7552_norm__mult__numeral2,axiom,
% 0.35/0.65      ! [A: complex,W: num] :
% 0.35/0.65        ( ( real_V1022390504157884413omplex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 0.35/0.65        = ( times_times_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_mult_numeral2
% 0.35/0.65  thf(fact_7553_norm__mult__numeral1,axiom,
% 0.35/0.65      ! [W: num,A: real] :
% 0.35/0.65        ( ( real_V7735802525324610683m_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 0.35/0.65        = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V7735802525324610683m_real @ A ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_mult_numeral1
% 0.35/0.65  thf(fact_7554_norm__mult__numeral1,axiom,
% 0.35/0.65      ! [W: num,A: complex] :
% 0.35/0.65        ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 0.35/0.65        = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V1022390504157884413omplex @ A ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_mult_numeral1
% 0.35/0.65  thf(fact_7555_norm__neg__numeral,axiom,
% 0.35/0.65      ! [W: num] :
% 0.35/0.65        ( ( real_V7735802525324610683m_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 0.35/0.65        = ( numeral_numeral_real @ W ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_neg_numeral
% 0.35/0.65  thf(fact_7556_norm__neg__numeral,axiom,
% 0.35/0.65      ! [W: num] :
% 0.35/0.65        ( ( real_V1022390504157884413omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 0.35/0.65        = ( numeral_numeral_real @ W ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_neg_numeral
% 0.35/0.65  thf(fact_7557_norm__le__zero__iff,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X ) @ zero_zero_real )
% 0.35/0.65        = ( X = zero_zero_real ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_le_zero_iff
% 0.35/0.65  thf(fact_7558_norm__le__zero__iff,axiom,
% 0.35/0.65      ! [X: complex] :
% 0.35/0.65        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ zero_zero_real )
% 0.35/0.65        = ( X = zero_zero_complex ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_le_zero_iff
% 0.35/0.65  thf(fact_7559_norm__one,axiom,
% 0.35/0.65      ( ( real_V7735802525324610683m_real @ one_one_real )
% 0.35/0.65      = one_one_real ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_one
% 0.35/0.65  thf(fact_7560_norm__one,axiom,
% 0.35/0.65      ( ( real_V1022390504157884413omplex @ one_one_complex )
% 0.35/0.65      = one_one_real ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_one
% 0.35/0.65  thf(fact_7561_norm__numeral,axiom,
% 0.35/0.65      ! [W: num] :
% 0.35/0.65        ( ( real_V7735802525324610683m_real @ ( numeral_numeral_real @ W ) )
% 0.35/0.65        = ( numeral_numeral_real @ W ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_numeral
% 0.35/0.65  thf(fact_7562_norm__numeral,axiom,
% 0.35/0.65      ! [W: num] :
% 0.35/0.65        ( ( real_V1022390504157884413omplex @ ( numera6690914467698888265omplex @ W ) )
% 0.35/0.65        = ( numeral_numeral_real @ W ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_numeral
% 0.35/0.65  thf(fact_7563_zero__less__norm__iff,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ord_less_real @ zero_zero_real @ ( real_V7735802525324610683m_real @ X ) )
% 0.35/0.65        = ( X != zero_zero_real ) ) ).
% 0.35/0.65  
% 0.35/0.65  % zero_less_norm_iff
% 0.35/0.65  thf(fact_7564_zero__less__norm__iff,axiom,
% 0.35/0.65      ! [X: complex] :
% 0.35/0.65        ( ( ord_less_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X ) )
% 0.35/0.65        = ( X != zero_zero_complex ) ) ).
% 0.35/0.65  
% 0.35/0.65  % zero_less_norm_iff
% 0.35/0.65  thf(fact_7565_norm__minus__commute,axiom,
% 0.35/0.65      ! [A: complex,B: complex] :
% 0.35/0.65        ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) )
% 0.35/0.65        = ( real_V1022390504157884413omplex @ ( minus_minus_complex @ B @ A ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_minus_commute
% 0.35/0.65  thf(fact_7566_norm__not__less__zero,axiom,
% 0.35/0.65      ! [X: complex] :
% 0.35/0.65        ~ ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ zero_zero_real ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_not_less_zero
% 0.35/0.65  thf(fact_7567_norm__ge__zero,axiom,
% 0.35/0.65      ! [X: complex] : ( ord_less_eq_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_ge_zero
% 0.35/0.65  thf(fact_7568_norm__mult,axiom,
% 0.35/0.65      ! [X: real,Y2: real] :
% 0.35/0.65        ( ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y2 ) )
% 0.35/0.65        = ( times_times_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y2 ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_mult
% 0.35/0.65  thf(fact_7569_norm__mult,axiom,
% 0.35/0.65      ! [X: complex,Y2: complex] :
% 0.35/0.65        ( ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y2 ) )
% 0.35/0.65        = ( times_times_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y2 ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_mult
% 0.35/0.65  thf(fact_7570_norm__divide,axiom,
% 0.35/0.65      ! [A: real,B: real] :
% 0.35/0.65        ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 0.35/0.65        = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_divide
% 0.35/0.65  thf(fact_7571_norm__divide,axiom,
% 0.35/0.65      ! [A: complex,B: complex] :
% 0.35/0.65        ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.35/0.65        = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_divide
% 0.35/0.65  thf(fact_7572_sum__norm__le,axiom,
% 0.35/0.65      ! [S2: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > complex,G: product_prod_nat_nat > real] :
% 0.35/0.65        ( ! [X3: product_prod_nat_nat] :
% 0.35/0.65            ( ( member8440522571783428010at_nat @ X3 @ S2 )
% 0.35/0.65           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X3 ) ) @ ( G @ X3 ) ) )
% 0.35/0.65       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups6381953495645901045omplex @ F @ S2 ) ) @ ( groups4567486121110086003t_real @ G @ S2 ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum_norm_le
% 0.35/0.65  thf(fact_7573_sum__norm__le,axiom,
% 0.35/0.65      ! [S2: set_real,F: real > complex,G: real > real] :
% 0.35/0.65        ( ! [X3: real] :
% 0.35/0.65            ( ( member_real @ X3 @ S2 )
% 0.35/0.65           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X3 ) ) @ ( G @ X3 ) ) )
% 0.35/0.65       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups5754745047067104278omplex @ F @ S2 ) ) @ ( groups8097168146408367636l_real @ G @ S2 ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum_norm_le
% 0.35/0.65  thf(fact_7574_sum__norm__le,axiom,
% 0.35/0.65      ! [S2: set_int,F: int > complex,G: int > real] :
% 0.35/0.65        ( ! [X3: int] :
% 0.35/0.65            ( ( member_int @ X3 @ S2 )
% 0.35/0.65           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X3 ) ) @ ( G @ X3 ) ) )
% 0.35/0.65       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups3049146728041665814omplex @ F @ S2 ) ) @ ( groups8778361861064173332t_real @ G @ S2 ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum_norm_le
% 0.35/0.65  thf(fact_7575_sum__norm__le,axiom,
% 0.35/0.65      ! [S2: set_nat,F: nat > complex,G: nat > real] :
% 0.35/0.65        ( ! [X3: nat] :
% 0.35/0.65            ( ( member_nat @ X3 @ S2 )
% 0.35/0.65           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X3 ) ) @ ( G @ X3 ) ) )
% 0.35/0.65       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ S2 ) ) @ ( groups6591440286371151544t_real @ G @ S2 ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum_norm_le
% 0.35/0.65  thf(fact_7576_sum__norm__le,axiom,
% 0.35/0.65      ! [S2: set_complex,F: complex > complex,G: complex > real] :
% 0.35/0.65        ( ! [X3: complex] :
% 0.35/0.65            ( ( member_complex @ X3 @ S2 )
% 0.35/0.65           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X3 ) ) @ ( G @ X3 ) ) )
% 0.35/0.65       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ S2 ) ) @ ( groups5808333547571424918x_real @ G @ S2 ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum_norm_le
% 0.35/0.65  thf(fact_7577_sum__norm__le,axiom,
% 0.35/0.65      ! [S2: set_nat,F: nat > real,G: nat > real] :
% 0.35/0.65        ( ! [X3: nat] :
% 0.35/0.65            ( ( member_nat @ X3 @ S2 )
% 0.35/0.65           => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ X3 ) ) @ ( G @ X3 ) ) )
% 0.35/0.65       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ S2 ) ) @ ( groups6591440286371151544t_real @ G @ S2 ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum_norm_le
% 0.35/0.65  thf(fact_7578_norm__power,axiom,
% 0.35/0.65      ! [X: real,N: nat] :
% 0.35/0.65        ( ( real_V7735802525324610683m_real @ ( power_power_real @ X @ N ) )
% 0.35/0.65        = ( power_power_real @ ( real_V7735802525324610683m_real @ X ) @ N ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_power
% 0.35/0.65  thf(fact_7579_norm__power,axiom,
% 0.35/0.65      ! [X: complex,N: nat] :
% 0.35/0.65        ( ( real_V1022390504157884413omplex @ ( power_power_complex @ X @ N ) )
% 0.35/0.65        = ( power_power_real @ ( real_V1022390504157884413omplex @ X ) @ N ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_power
% 0.35/0.65  thf(fact_7580_norm__sum,axiom,
% 0.35/0.65      ! [F: nat > complex,A2: set_nat] :
% 0.35/0.65        ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ A2 ) )
% 0.35/0.65        @ ( groups6591440286371151544t_real
% 0.35/0.65          @ ^ [I3: nat] : ( real_V1022390504157884413omplex @ ( F @ I3 ) )
% 0.35/0.65          @ A2 ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_sum
% 0.35/0.65  thf(fact_7581_norm__sum,axiom,
% 0.35/0.65      ! [F: complex > complex,A2: set_complex] :
% 0.35/0.65        ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ A2 ) )
% 0.35/0.65        @ ( groups5808333547571424918x_real
% 0.35/0.65          @ ^ [I3: complex] : ( real_V1022390504157884413omplex @ ( F @ I3 ) )
% 0.35/0.65          @ A2 ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_sum
% 0.35/0.65  thf(fact_7582_norm__sum,axiom,
% 0.35/0.65      ! [F: nat > real,A2: set_nat] :
% 0.35/0.65        ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 0.35/0.65        @ ( groups6591440286371151544t_real
% 0.35/0.65          @ ^ [I3: nat] : ( real_V7735802525324610683m_real @ ( F @ I3 ) )
% 0.35/0.65          @ A2 ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_sum
% 0.35/0.65  thf(fact_7583_norm__uminus__minus,axiom,
% 0.35/0.65      ! [X: real,Y2: real] :
% 0.35/0.65        ( ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ Y2 ) )
% 0.35/0.65        = ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y2 ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_uminus_minus
% 0.35/0.65  thf(fact_7584_norm__uminus__minus,axiom,
% 0.35/0.65      ! [X: complex,Y2: complex] :
% 0.35/0.65        ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X ) @ Y2 ) )
% 0.35/0.65        = ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y2 ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_uminus_minus
% 0.35/0.65  thf(fact_7585_nonzero__norm__divide,axiom,
% 0.35/0.65      ! [B: real,A: real] :
% 0.35/0.65        ( ( B != zero_zero_real )
% 0.35/0.65       => ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 0.35/0.65          = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % nonzero_norm_divide
% 0.35/0.65  thf(fact_7586_nonzero__norm__divide,axiom,
% 0.35/0.65      ! [B: complex,A: complex] :
% 0.35/0.65        ( ( B != zero_zero_complex )
% 0.35/0.65       => ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.35/0.65          = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % nonzero_norm_divide
% 0.35/0.65  thf(fact_7587_power__eq__imp__eq__norm,axiom,
% 0.35/0.65      ! [W: real,N: nat,Z: real] :
% 0.35/0.65        ( ( ( power_power_real @ W @ N )
% 0.35/0.65          = ( power_power_real @ Z @ N ) )
% 0.35/0.65       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.65         => ( ( real_V7735802525324610683m_real @ W )
% 0.35/0.65            = ( real_V7735802525324610683m_real @ Z ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % power_eq_imp_eq_norm
% 0.35/0.65  thf(fact_7588_power__eq__imp__eq__norm,axiom,
% 0.35/0.65      ! [W: complex,N: nat,Z: complex] :
% 0.35/0.65        ( ( ( power_power_complex @ W @ N )
% 0.35/0.65          = ( power_power_complex @ Z @ N ) )
% 0.35/0.65       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.65         => ( ( real_V1022390504157884413omplex @ W )
% 0.35/0.65            = ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % power_eq_imp_eq_norm
% 0.35/0.65  thf(fact_7589_norm__mult__less,axiom,
% 0.35/0.65      ! [X: real,R: real,Y2: real,S3: real] :
% 0.35/0.65        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ R )
% 0.35/0.65       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y2 ) @ S3 )
% 0.35/0.65         => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y2 ) ) @ ( times_times_real @ R @ S3 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_mult_less
% 0.35/0.65  thf(fact_7590_norm__mult__less,axiom,
% 0.35/0.65      ! [X: complex,R: real,Y2: complex,S3: real] :
% 0.35/0.65        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ R )
% 0.35/0.65       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y2 ) @ S3 )
% 0.35/0.65         => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y2 ) ) @ ( times_times_real @ R @ S3 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_mult_less
% 0.35/0.65  thf(fact_7591_norm__mult__ineq,axiom,
% 0.35/0.65      ! [X: real,Y2: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y2 ) ) @ ( times_times_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y2 ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_mult_ineq
% 0.35/0.65  thf(fact_7592_norm__mult__ineq,axiom,
% 0.35/0.65      ! [X: complex,Y2: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y2 ) ) @ ( times_times_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y2 ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_mult_ineq
% 0.35/0.65  thf(fact_7593_norm__triangle__lt,axiom,
% 0.35/0.65      ! [X: real,Y2: real,E: real] :
% 0.35/0.65        ( ( ord_less_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y2 ) ) @ E )
% 0.35/0.65       => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y2 ) ) @ E ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_triangle_lt
% 0.35/0.65  thf(fact_7594_norm__triangle__lt,axiom,
% 0.35/0.65      ! [X: complex,Y2: complex,E: real] :
% 0.35/0.65        ( ( ord_less_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y2 ) ) @ E )
% 0.35/0.65       => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y2 ) ) @ E ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_triangle_lt
% 0.35/0.65  thf(fact_7595_norm__add__less,axiom,
% 0.35/0.65      ! [X: real,R: real,Y2: real,S3: real] :
% 0.35/0.65        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ R )
% 0.35/0.65       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y2 ) @ S3 )
% 0.35/0.65         => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y2 ) ) @ ( plus_plus_real @ R @ S3 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_add_less
% 0.35/0.65  thf(fact_7596_norm__add__less,axiom,
% 0.35/0.65      ! [X: complex,R: real,Y2: complex,S3: real] :
% 0.35/0.65        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ R )
% 0.35/0.65       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y2 ) @ S3 )
% 0.35/0.65         => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y2 ) ) @ ( plus_plus_real @ R @ S3 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_add_less
% 0.35/0.65  thf(fact_7597_norm__triangle__mono,axiom,
% 0.35/0.65      ! [A: real,R: real,B: real,S3: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ A ) @ R )
% 0.35/0.65       => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ S3 )
% 0.35/0.65         => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ R @ S3 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_triangle_mono
% 0.35/0.65  thf(fact_7598_norm__triangle__mono,axiom,
% 0.35/0.65      ! [A: complex,R: real,B: complex,S3: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ A ) @ R )
% 0.35/0.65       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ S3 )
% 0.35/0.65         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ ( plus_plus_real @ R @ S3 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_triangle_mono
% 0.35/0.65  thf(fact_7599_norm__triangle__ineq,axiom,
% 0.35/0.65      ! [X: real,Y2: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y2 ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y2 ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_triangle_ineq
% 0.35/0.65  thf(fact_7600_norm__triangle__ineq,axiom,
% 0.35/0.65      ! [X: complex,Y2: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y2 ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y2 ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_triangle_ineq
% 0.35/0.65  thf(fact_7601_norm__triangle__le,axiom,
% 0.35/0.65      ! [X: real,Y2: real,E: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y2 ) ) @ E )
% 0.35/0.65       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y2 ) ) @ E ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_triangle_le
% 0.35/0.65  thf(fact_7602_norm__triangle__le,axiom,
% 0.35/0.65      ! [X: complex,Y2: complex,E: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y2 ) ) @ E )
% 0.35/0.65       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y2 ) ) @ E ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_triangle_le
% 0.35/0.65  thf(fact_7603_norm__add__leD,axiom,
% 0.35/0.65      ! [A: real,B: real,C: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ C )
% 0.35/0.65       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ C ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_add_leD
% 0.35/0.65  thf(fact_7604_norm__add__leD,axiom,
% 0.35/0.65      ! [A: complex,B: complex,C: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ C )
% 0.35/0.65       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ C ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_add_leD
% 0.35/0.65  thf(fact_7605_norm__power__ineq,axiom,
% 0.35/0.65      ! [X: real,N: nat] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( power_power_real @ X @ N ) ) @ ( power_power_real @ ( real_V7735802525324610683m_real @ X ) @ N ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_power_ineq
% 0.35/0.65  thf(fact_7606_norm__power__ineq,axiom,
% 0.35/0.65      ! [X: complex,N: nat] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( power_power_complex @ X @ N ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ X ) @ N ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_power_ineq
% 0.35/0.65  thf(fact_7607_norm__diff__triangle__less,axiom,
% 0.35/0.65      ! [X: complex,Y2: complex,E1: real,Z: complex,E22: real] :
% 0.35/0.65        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y2 ) ) @ E1 )
% 0.35/0.65       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y2 @ Z ) ) @ E22 )
% 0.35/0.65         => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_diff_triangle_less
% 0.35/0.65  thf(fact_7608_norm__triangle__sub,axiom,
% 0.35/0.65      ! [X: complex,Y2: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Y2 ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_triangle_sub
% 0.35/0.65  thf(fact_7609_norm__triangle__ineq4,axiom,
% 0.35/0.65      ! [A: complex,B: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_triangle_ineq4
% 0.35/0.65  thf(fact_7610_norm__diff__triangle__le,axiom,
% 0.35/0.65      ! [X: complex,Y2: complex,E1: real,Z: complex,E22: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y2 ) ) @ E1 )
% 0.35/0.65       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y2 @ Z ) ) @ E22 )
% 0.35/0.65         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_diff_triangle_le
% 0.35/0.65  thf(fact_7611_norm__triangle__le__diff,axiom,
% 0.35/0.65      ! [X: complex,Y2: complex,E: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y2 ) ) @ E )
% 0.35/0.65       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y2 ) ) @ E ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_triangle_le_diff
% 0.35/0.65  thf(fact_7612_norm__diff__ineq,axiom,
% 0.35/0.65      ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_diff_ineq
% 0.35/0.65  thf(fact_7613_norm__diff__ineq,axiom,
% 0.35/0.65      ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_diff_ineq
% 0.35/0.65  thf(fact_7614_norm__triangle__ineq2,axiom,
% 0.35/0.65      ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_triangle_ineq2
% 0.35/0.65  thf(fact_7615_power__eq__1__iff,axiom,
% 0.35/0.65      ! [W: real,N: nat] :
% 0.35/0.65        ( ( ( power_power_real @ W @ N )
% 0.35/0.65          = one_one_real )
% 0.35/0.65       => ( ( ( real_V7735802525324610683m_real @ W )
% 0.35/0.65            = one_one_real )
% 0.35/0.65          | ( N = zero_zero_nat ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % power_eq_1_iff
% 0.35/0.65  thf(fact_7616_power__eq__1__iff,axiom,
% 0.35/0.65      ! [W: complex,N: nat] :
% 0.35/0.65        ( ( ( power_power_complex @ W @ N )
% 0.35/0.65          = one_one_complex )
% 0.35/0.65       => ( ( ( real_V1022390504157884413omplex @ W )
% 0.35/0.65            = one_one_real )
% 0.35/0.65          | ( N = zero_zero_nat ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % power_eq_1_iff
% 0.35/0.65  thf(fact_7617_norm__diff__triangle__ineq,axiom,
% 0.35/0.65      ! [A: real,B: real,C: real,D2: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D2 ) ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ C ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ B @ D2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_diff_triangle_ineq
% 0.35/0.65  thf(fact_7618_norm__diff__triangle__ineq,axiom,
% 0.35/0.65      ! [A: complex,B: complex,C: complex,D2: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ ( plus_plus_complex @ C @ D2 ) ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ C ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ B @ D2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_diff_triangle_ineq
% 0.35/0.65  thf(fact_7619_norm__triangle__ineq3,axiom,
% 0.35/0.65      ! [A: complex,B: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_triangle_ineq3
% 0.35/0.65  thf(fact_7620_square__norm__one,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.65          = one_one_real )
% 0.35/0.65       => ( ( real_V7735802525324610683m_real @ X )
% 0.35/0.65          = one_one_real ) ) ).
% 0.35/0.65  
% 0.35/0.65  % square_norm_one
% 0.35/0.65  thf(fact_7621_square__norm__one,axiom,
% 0.35/0.65      ! [X: complex] :
% 0.35/0.65        ( ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.65          = one_one_complex )
% 0.35/0.65       => ( ( real_V1022390504157884413omplex @ X )
% 0.35/0.65          = one_one_real ) ) ).
% 0.35/0.65  
% 0.35/0.65  % square_norm_one
% 0.35/0.65  thf(fact_7622_norm__power__diff,axiom,
% 0.35/0.65      ! [Z: real,W: real,M: nat] :
% 0.35/0.65        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 0.35/0.65       => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ W ) @ one_one_real )
% 0.35/0.65         => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( power_power_real @ Z @ M ) @ ( power_power_real @ W @ M ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Z @ W ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_power_diff
% 0.35/0.65  thf(fact_7623_norm__power__diff,axiom,
% 0.35/0.65      ! [Z: complex,W: complex,M: nat] :
% 0.35/0.65        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 0.35/0.65       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ W ) @ one_one_real )
% 0.35/0.65         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( power_power_complex @ Z @ M ) @ ( power_power_complex @ W @ M ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Z @ W ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_power_diff
% 0.35/0.65  thf(fact_7624_suminf__geometric,axiom,
% 0.35/0.65      ! [C: real] :
% 0.35/0.65        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 0.35/0.65       => ( ( suminf_real @ ( power_power_real @ C ) )
% 0.35/0.65          = ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_geometric
% 0.35/0.65  thf(fact_7625_suminf__geometric,axiom,
% 0.35/0.65      ! [C: complex] :
% 0.35/0.65        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 0.35/0.65       => ( ( suminf_complex @ ( power_power_complex @ C ) )
% 0.35/0.65          = ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_geometric
% 0.35/0.65  thf(fact_7626_pi__series,axiom,
% 0.35/0.65      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.35/0.65      = ( suminf_real
% 0.35/0.65        @ ^ [K3: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % pi_series
% 0.35/0.65  thf(fact_7627_lemma__termdiff2,axiom,
% 0.35/0.65      ! [H2: rat,Z: rat,N: nat] :
% 0.35/0.65        ( ( H2 != zero_zero_rat )
% 0.35/0.65       => ( ( minus_minus_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ N ) @ ( power_power_rat @ Z @ N ) ) @ H2 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.35/0.65          = ( times_times_rat @ H2
% 0.35/0.65            @ ( groups2906978787729119204at_rat
% 0.35/0.65              @ ^ [P4: nat] :
% 0.35/0.65                  ( groups2906978787729119204at_rat
% 0.35/0.65                  @ ^ [Q4: nat] : ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ Q4 ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q4 ) ) )
% 0.35/0.65                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P4 ) ) )
% 0.35/0.65              @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % lemma_termdiff2
% 0.35/0.65  thf(fact_7628_lemma__termdiff2,axiom,
% 0.35/0.65      ! [H2: complex,Z: complex,N: nat] :
% 0.35/0.65        ( ( H2 != zero_zero_complex )
% 0.35/0.65       => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ N ) @ ( power_power_complex @ Z @ N ) ) @ H2 ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.35/0.65          = ( times_times_complex @ H2
% 0.35/0.65            @ ( groups2073611262835488442omplex
% 0.35/0.65              @ ^ [P4: nat] :
% 0.35/0.65                  ( groups2073611262835488442omplex
% 0.35/0.65                  @ ^ [Q4: nat] : ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ Q4 ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q4 ) ) )
% 0.35/0.65                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P4 ) ) )
% 0.35/0.65              @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % lemma_termdiff2
% 0.35/0.65  thf(fact_7629_lemma__termdiff2,axiom,
% 0.35/0.65      ! [H2: real,Z: real,N: nat] :
% 0.35/0.65        ( ( H2 != zero_zero_real )
% 0.35/0.65       => ( ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ N ) @ ( power_power_real @ Z @ N ) ) @ H2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.35/0.65          = ( times_times_real @ H2
% 0.35/0.65            @ ( groups6591440286371151544t_real
% 0.35/0.65              @ ^ [P4: nat] :
% 0.35/0.65                  ( groups6591440286371151544t_real
% 0.35/0.65                  @ ^ [Q4: nat] : ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ Q4 ) @ ( power_power_real @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q4 ) ) )
% 0.35/0.65                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P4 ) ) )
% 0.35/0.65              @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % lemma_termdiff2
% 0.35/0.65  thf(fact_7630_summable__arctan__series,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.35/0.65       => ( summable_real
% 0.35/0.65          @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_arctan_series
% 0.35/0.65  thf(fact_7631_ceiling__log__eq__powr__iff,axiom,
% 0.35/0.65      ! [X: real,B: real,K: nat] :
% 0.35/0.65        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.65       => ( ( ord_less_real @ one_one_real @ B )
% 0.35/0.65         => ( ( ( archim7802044766580827645g_real @ ( log @ B @ X ) )
% 0.35/0.65              = ( plus_plus_int @ ( semiri1314217659103216013at_int @ K ) @ one_one_int ) )
% 0.35/0.65            = ( ( ord_less_real @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ X )
% 0.35/0.65              & ( ord_less_eq_real @ X @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % ceiling_log_eq_powr_iff
% 0.35/0.65  thf(fact_7632_lessThan__iff,axiom,
% 0.35/0.65      ! [I2: rat,K: rat] :
% 0.35/0.65        ( ( member_rat @ I2 @ ( set_ord_lessThan_rat @ K ) )
% 0.35/0.65        = ( ord_less_rat @ I2 @ K ) ) ).
% 0.35/0.65  
% 0.35/0.65  % lessThan_iff
% 0.35/0.65  thf(fact_7633_lessThan__iff,axiom,
% 0.35/0.65      ! [I2: num,K: num] :
% 0.35/0.65        ( ( member_num @ I2 @ ( set_ord_lessThan_num @ K ) )
% 0.35/0.65        = ( ord_less_num @ I2 @ K ) ) ).
% 0.35/0.65  
% 0.35/0.65  % lessThan_iff
% 0.35/0.65  thf(fact_7634_lessThan__iff,axiom,
% 0.35/0.65      ! [I2: int,K: int] :
% 0.35/0.65        ( ( member_int @ I2 @ ( set_ord_lessThan_int @ K ) )
% 0.35/0.65        = ( ord_less_int @ I2 @ K ) ) ).
% 0.35/0.65  
% 0.35/0.65  % lessThan_iff
% 0.35/0.65  thf(fact_7635_lessThan__iff,axiom,
% 0.35/0.65      ! [I2: nat,K: nat] :
% 0.35/0.65        ( ( member_nat @ I2 @ ( set_ord_lessThan_nat @ K ) )
% 0.35/0.65        = ( ord_less_nat @ I2 @ K ) ) ).
% 0.35/0.65  
% 0.35/0.65  % lessThan_iff
% 0.35/0.65  thf(fact_7636_lessThan__iff,axiom,
% 0.35/0.65      ! [I2: real,K: real] :
% 0.35/0.65        ( ( member_real @ I2 @ ( set_or5984915006950818249n_real @ K ) )
% 0.35/0.65        = ( ord_less_real @ I2 @ K ) ) ).
% 0.35/0.65  
% 0.35/0.65  % lessThan_iff
% 0.35/0.65  thf(fact_7637_powr__one__eq__one,axiom,
% 0.35/0.65      ! [A: real] :
% 0.35/0.65        ( ( powr_real @ one_one_real @ A )
% 0.35/0.65        = one_one_real ) ).
% 0.35/0.65  
% 0.35/0.65  % powr_one_eq_one
% 0.35/0.65  thf(fact_7638_summable__iff__shift,axiom,
% 0.35/0.65      ! [F: nat > real,K: nat] :
% 0.35/0.65        ( ( summable_real
% 0.35/0.65          @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ K ) ) )
% 0.35/0.65        = ( summable_real @ F ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_iff_shift
% 0.35/0.65  thf(fact_7639_lessThan__subset__iff,axiom,
% 0.35/0.65      ! [X: num,Y2: num] :
% 0.35/0.65        ( ( ord_less_eq_set_num @ ( set_ord_lessThan_num @ X ) @ ( set_ord_lessThan_num @ Y2 ) )
% 0.35/0.65        = ( ord_less_eq_num @ X @ Y2 ) ) ).
% 0.35/0.65  
% 0.35/0.65  % lessThan_subset_iff
% 0.35/0.65  thf(fact_7640_lessThan__subset__iff,axiom,
% 0.35/0.65      ! [X: int,Y2: int] :
% 0.35/0.65        ( ( ord_less_eq_set_int @ ( set_ord_lessThan_int @ X ) @ ( set_ord_lessThan_int @ Y2 ) )
% 0.35/0.65        = ( ord_less_eq_int @ X @ Y2 ) ) ).
% 0.35/0.65  
% 0.35/0.65  % lessThan_subset_iff
% 0.35/0.65  thf(fact_7641_lessThan__subset__iff,axiom,
% 0.35/0.65      ! [X: nat,Y2: nat] :
% 0.35/0.65        ( ( ord_less_eq_set_nat @ ( set_ord_lessThan_nat @ X ) @ ( set_ord_lessThan_nat @ Y2 ) )
% 0.35/0.65        = ( ord_less_eq_nat @ X @ Y2 ) ) ).
% 0.35/0.65  
% 0.35/0.65  % lessThan_subset_iff
% 0.35/0.65  thf(fact_7642_lessThan__subset__iff,axiom,
% 0.35/0.65      ! [X: real,Y2: real] :
% 0.35/0.65        ( ( ord_less_eq_set_real @ ( set_or5984915006950818249n_real @ X ) @ ( set_or5984915006950818249n_real @ Y2 ) )
% 0.35/0.65        = ( ord_less_eq_real @ X @ Y2 ) ) ).
% 0.35/0.65  
% 0.35/0.65  % lessThan_subset_iff
% 0.35/0.65  thf(fact_7643_powr__zero__eq__one,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ( X = zero_zero_real )
% 0.35/0.65         => ( ( powr_real @ X @ zero_zero_real )
% 0.35/0.65            = zero_zero_real ) )
% 0.35/0.65        & ( ( X != zero_zero_real )
% 0.35/0.65         => ( ( powr_real @ X @ zero_zero_real )
% 0.35/0.65            = one_one_real ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powr_zero_eq_one
% 0.35/0.65  thf(fact_7644_powr__gt__zero,axiom,
% 0.35/0.65      ! [X: real,A: real] :
% 0.35/0.65        ( ( ord_less_real @ zero_zero_real @ ( powr_real @ X @ A ) )
% 0.35/0.65        = ( X != zero_zero_real ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powr_gt_zero
% 0.35/0.65  thf(fact_7645_powr__nonneg__iff,axiom,
% 0.35/0.65      ! [A: real,X: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ ( powr_real @ A @ X ) @ zero_zero_real )
% 0.35/0.65        = ( A = zero_zero_real ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powr_nonneg_iff
% 0.35/0.65  thf(fact_7646_powr__less__cancel__iff,axiom,
% 0.35/0.65      ! [X: real,A: real,B: real] :
% 0.35/0.65        ( ( ord_less_real @ one_one_real @ X )
% 0.35/0.65       => ( ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 0.35/0.65          = ( ord_less_real @ A @ B ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powr_less_cancel_iff
% 0.35/0.65  thf(fact_7647_summable__cmult__iff,axiom,
% 0.35/0.65      ! [C: complex,F: nat > complex] :
% 0.35/0.65        ( ( summable_complex
% 0.35/0.65          @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) ) )
% 0.35/0.65        = ( ( C = zero_zero_complex )
% 0.35/0.65          | ( summable_complex @ F ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_cmult_iff
% 0.35/0.65  thf(fact_7648_summable__cmult__iff,axiom,
% 0.35/0.65      ! [C: real,F: nat > real] :
% 0.35/0.65        ( ( summable_real
% 0.35/0.65          @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) ) )
% 0.35/0.65        = ( ( C = zero_zero_real )
% 0.35/0.65          | ( summable_real @ F ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_cmult_iff
% 0.35/0.65  thf(fact_7649_summable__divide__iff,axiom,
% 0.35/0.65      ! [F: nat > complex,C: complex] :
% 0.35/0.65        ( ( summable_complex
% 0.35/0.65          @ ^ [N2: nat] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ C ) )
% 0.35/0.65        = ( ( C = zero_zero_complex )
% 0.35/0.65          | ( summable_complex @ F ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_divide_iff
% 0.35/0.65  thf(fact_7650_summable__divide__iff,axiom,
% 0.35/0.65      ! [F: nat > real,C: real] :
% 0.35/0.65        ( ( summable_real
% 0.35/0.65          @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ C ) )
% 0.35/0.65        = ( ( C = zero_zero_real )
% 0.35/0.65          | ( summable_real @ F ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_divide_iff
% 0.35/0.65  thf(fact_7651_sum_OlessThan__Suc,axiom,
% 0.35/0.65      ! [G: nat > rat,N: nat] :
% 0.35/0.65        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.35/0.65        = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum.lessThan_Suc
% 0.35/0.65  thf(fact_7652_sum_OlessThan__Suc,axiom,
% 0.35/0.65      ! [G: nat > int,N: nat] :
% 0.35/0.65        ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.35/0.65        = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum.lessThan_Suc
% 0.35/0.65  thf(fact_7653_sum_OlessThan__Suc,axiom,
% 0.35/0.65      ! [G: nat > complex,N: nat] :
% 0.35/0.65        ( ( groups2073611262835488442omplex @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.35/0.65        = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum.lessThan_Suc
% 0.35/0.65  thf(fact_7654_sum_OlessThan__Suc,axiom,
% 0.35/0.65      ! [G: nat > nat,N: nat] :
% 0.35/0.65        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.35/0.65        = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum.lessThan_Suc
% 0.35/0.65  thf(fact_7655_sum_OlessThan__Suc,axiom,
% 0.35/0.65      ! [G: nat > real,N: nat] :
% 0.35/0.65        ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.35/0.65        = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum.lessThan_Suc
% 0.35/0.65  thf(fact_7656_single__Diff__lessThan,axiom,
% 0.35/0.65      ! [K: int] :
% 0.35/0.65        ( ( minus_minus_set_int @ ( insert_int @ K @ bot_bot_set_int ) @ ( set_ord_lessThan_int @ K ) )
% 0.35/0.65        = ( insert_int @ K @ bot_bot_set_int ) ) ).
% 0.35/0.65  
% 0.35/0.65  % single_Diff_lessThan
% 0.35/0.65  thf(fact_7657_single__Diff__lessThan,axiom,
% 0.35/0.65      ! [K: nat] :
% 0.35/0.65        ( ( minus_minus_set_nat @ ( insert_nat @ K @ bot_bot_set_nat ) @ ( set_ord_lessThan_nat @ K ) )
% 0.35/0.65        = ( insert_nat @ K @ bot_bot_set_nat ) ) ).
% 0.35/0.65  
% 0.35/0.65  % single_Diff_lessThan
% 0.35/0.65  thf(fact_7658_single__Diff__lessThan,axiom,
% 0.35/0.65      ! [K: real] :
% 0.35/0.65        ( ( minus_minus_set_real @ ( insert_real @ K @ bot_bot_set_real ) @ ( set_or5984915006950818249n_real @ K ) )
% 0.35/0.65        = ( insert_real @ K @ bot_bot_set_real ) ) ).
% 0.35/0.65  
% 0.35/0.65  % single_Diff_lessThan
% 0.35/0.65  thf(fact_7659_powr__eq__one__iff,axiom,
% 0.35/0.65      ! [A: real,X: real] :
% 0.35/0.65        ( ( ord_less_real @ one_one_real @ A )
% 0.35/0.65       => ( ( ( powr_real @ A @ X )
% 0.35/0.65            = one_one_real )
% 0.35/0.65          = ( X = zero_zero_real ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powr_eq_one_iff
% 0.35/0.65  thf(fact_7660_powr__one,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.65       => ( ( powr_real @ X @ one_one_real )
% 0.35/0.65          = X ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powr_one
% 0.35/0.65  thf(fact_7661_powr__one__gt__zero__iff,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ( powr_real @ X @ one_one_real )
% 0.35/0.65          = X )
% 0.35/0.65        = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powr_one_gt_zero_iff
% 0.35/0.65  thf(fact_7662_powr__le__cancel__iff,axiom,
% 0.35/0.65      ! [X: real,A: real,B: real] :
% 0.35/0.65        ( ( ord_less_real @ one_one_real @ X )
% 0.35/0.65       => ( ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 0.35/0.65          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powr_le_cancel_iff
% 0.35/0.65  thf(fact_7663_numeral__powr__numeral__real,axiom,
% 0.35/0.65      ! [M: num,N: num] :
% 0.35/0.65        ( ( powr_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 0.35/0.65        = ( power_power_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % numeral_powr_numeral_real
% 0.35/0.65  thf(fact_7664_log__powr__cancel,axiom,
% 0.35/0.65      ! [A: real,Y2: real] :
% 0.35/0.65        ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.65       => ( ( A != one_one_real )
% 0.35/0.65         => ( ( log @ A @ ( powr_real @ A @ Y2 ) )
% 0.35/0.65            = Y2 ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % log_powr_cancel
% 0.35/0.65  thf(fact_7665_powr__log__cancel,axiom,
% 0.35/0.65      ! [A: real,X: real] :
% 0.35/0.65        ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.65       => ( ( A != one_one_real )
% 0.35/0.65         => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.65           => ( ( powr_real @ A @ ( log @ A @ X ) )
% 0.35/0.65              = X ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powr_log_cancel
% 0.35/0.65  thf(fact_7666_summable__geometric__iff,axiom,
% 0.35/0.65      ! [C: real] :
% 0.35/0.65        ( ( summable_real @ ( power_power_real @ C ) )
% 0.35/0.65        = ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_geometric_iff
% 0.35/0.65  thf(fact_7667_summable__geometric__iff,axiom,
% 0.35/0.65      ! [C: complex] :
% 0.35/0.65        ( ( summable_complex @ ( power_power_complex @ C ) )
% 0.35/0.65        = ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_geometric_iff
% 0.35/0.65  thf(fact_7668_powr__numeral,axiom,
% 0.35/0.65      ! [X: real,N: num] :
% 0.35/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.65       => ( ( powr_real @ X @ ( numeral_numeral_real @ N ) )
% 0.35/0.65          = ( power_power_real @ X @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powr_numeral
% 0.35/0.65  thf(fact_7669_square__powr__half,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( powr_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.65        = ( abs_abs_real @ X ) ) ).
% 0.35/0.65  
% 0.35/0.65  % square_powr_half
% 0.35/0.65  thf(fact_7670_suminf__le__const,axiom,
% 0.35/0.65      ! [F: nat > int,X: int] :
% 0.35/0.65        ( ( summable_int @ F )
% 0.35/0.65       => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X )
% 0.35/0.65         => ( ord_less_eq_int @ ( suminf_int @ F ) @ X ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_le_const
% 0.35/0.65  thf(fact_7671_suminf__le__const,axiom,
% 0.35/0.65      ! [F: nat > nat,X: nat] :
% 0.35/0.65        ( ( summable_nat @ F )
% 0.35/0.65       => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X )
% 0.35/0.65         => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ X ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_le_const
% 0.35/0.65  thf(fact_7672_suminf__le__const,axiom,
% 0.35/0.65      ! [F: nat > real,X: real] :
% 0.35/0.65        ( ( summable_real @ F )
% 0.35/0.65       => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X )
% 0.35/0.65         => ( ord_less_eq_real @ ( suminf_real @ F ) @ X ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_le_const
% 0.35/0.65  thf(fact_7673_summable__comparison__test,axiom,
% 0.35/0.65      ! [F: nat > real,G: nat > real] :
% 0.35/0.65        ( ? [N7: nat] :
% 0.35/0.65          ! [N3: nat] :
% 0.35/0.65            ( ( ord_less_eq_nat @ N7 @ N3 )
% 0.35/0.65           => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 0.35/0.65       => ( ( summable_real @ G )
% 0.35/0.65         => ( summable_real @ F ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_comparison_test
% 0.35/0.65  thf(fact_7674_summable__comparison__test,axiom,
% 0.35/0.65      ! [F: nat > complex,G: nat > real] :
% 0.35/0.65        ( ? [N7: nat] :
% 0.35/0.65          ! [N3: nat] :
% 0.35/0.65            ( ( ord_less_eq_nat @ N7 @ N3 )
% 0.35/0.65           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 0.35/0.65       => ( ( summable_real @ G )
% 0.35/0.65         => ( summable_complex @ F ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_comparison_test
% 0.35/0.65  thf(fact_7675_summable__comparison__test_H,axiom,
% 0.35/0.65      ! [G: nat > real,N4: nat,F: nat > real] :
% 0.35/0.65        ( ( summable_real @ G )
% 0.35/0.65       => ( ! [N3: nat] :
% 0.35/0.65              ( ( ord_less_eq_nat @ N4 @ N3 )
% 0.35/0.65             => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 0.35/0.65         => ( summable_real @ F ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_comparison_test'
% 0.35/0.65  thf(fact_7676_summable__comparison__test_H,axiom,
% 0.35/0.65      ! [G: nat > real,N4: nat,F: nat > complex] :
% 0.35/0.65        ( ( summable_real @ G )
% 0.35/0.65       => ( ! [N3: nat] :
% 0.35/0.65              ( ( ord_less_eq_nat @ N4 @ N3 )
% 0.35/0.65             => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 0.35/0.65         => ( summable_complex @ F ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_comparison_test'
% 0.35/0.65  thf(fact_7677_summable__add,axiom,
% 0.35/0.65      ! [F: nat > real,G: nat > real] :
% 0.35/0.65        ( ( summable_real @ F )
% 0.35/0.65       => ( ( summable_real @ G )
% 0.35/0.65         => ( summable_real
% 0.35/0.65            @ ^ [N2: nat] : ( plus_plus_real @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_add
% 0.35/0.65  thf(fact_7678_summable__add,axiom,
% 0.35/0.65      ! [F: nat > nat,G: nat > nat] :
% 0.35/0.65        ( ( summable_nat @ F )
% 0.35/0.65       => ( ( summable_nat @ G )
% 0.35/0.65         => ( summable_nat
% 0.35/0.65            @ ^ [N2: nat] : ( plus_plus_nat @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_add
% 0.35/0.65  thf(fact_7679_summable__add,axiom,
% 0.35/0.65      ! [F: nat > int,G: nat > int] :
% 0.35/0.65        ( ( summable_int @ F )
% 0.35/0.65       => ( ( summable_int @ G )
% 0.35/0.65         => ( summable_int
% 0.35/0.65            @ ^ [N2: nat] : ( plus_plus_int @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_add
% 0.35/0.65  thf(fact_7680_summable__add,axiom,
% 0.35/0.65      ! [F: nat > complex,G: nat > complex] :
% 0.35/0.65        ( ( summable_complex @ F )
% 0.35/0.65       => ( ( summable_complex @ G )
% 0.35/0.65         => ( summable_complex
% 0.35/0.65            @ ^ [N2: nat] : ( plus_plus_complex @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_add
% 0.35/0.65  thf(fact_7681_summable__ignore__initial__segment,axiom,
% 0.35/0.65      ! [F: nat > real,K: nat] :
% 0.35/0.65        ( ( summable_real @ F )
% 0.35/0.65       => ( summable_real
% 0.35/0.65          @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ K ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_ignore_initial_segment
% 0.35/0.65  thf(fact_7682_powr__powr,axiom,
% 0.35/0.65      ! [X: real,A: real,B: real] :
% 0.35/0.65        ( ( powr_real @ ( powr_real @ X @ A ) @ B )
% 0.35/0.65        = ( powr_real @ X @ ( times_times_real @ A @ B ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powr_powr
% 0.35/0.65  thf(fact_7683_summable__divide,axiom,
% 0.35/0.65      ! [F: nat > complex,C: complex] :
% 0.35/0.65        ( ( summable_complex @ F )
% 0.35/0.65       => ( summable_complex
% 0.35/0.65          @ ^ [N2: nat] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ C ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_divide
% 0.35/0.65  thf(fact_7684_summable__divide,axiom,
% 0.35/0.65      ! [F: nat > real,C: real] :
% 0.35/0.65        ( ( summable_real @ F )
% 0.35/0.65       => ( summable_real
% 0.35/0.65          @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ C ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_divide
% 0.35/0.65  thf(fact_7685_summable__diff,axiom,
% 0.35/0.65      ! [F: nat > real,G: nat > real] :
% 0.35/0.65        ( ( summable_real @ F )
% 0.35/0.65       => ( ( summable_real @ G )
% 0.35/0.65         => ( summable_real
% 0.35/0.65            @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_diff
% 0.35/0.65  thf(fact_7686_summable__Suc__iff,axiom,
% 0.35/0.65      ! [F: nat > real] :
% 0.35/0.65        ( ( summable_real
% 0.35/0.65          @ ^ [N2: nat] : ( F @ ( suc @ N2 ) ) )
% 0.35/0.65        = ( summable_real @ F ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_Suc_iff
% 0.35/0.65  thf(fact_7687_summable__mult2,axiom,
% 0.35/0.65      ! [F: nat > complex,C: complex] :
% 0.35/0.65        ( ( summable_complex @ F )
% 0.35/0.65       => ( summable_complex
% 0.35/0.65          @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ C ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_mult2
% 0.35/0.65  thf(fact_7688_summable__mult2,axiom,
% 0.35/0.65      ! [F: nat > real,C: real] :
% 0.35/0.65        ( ( summable_real @ F )
% 0.35/0.65       => ( summable_real
% 0.35/0.65          @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ C ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_mult2
% 0.35/0.65  thf(fact_7689_summable__mult,axiom,
% 0.35/0.65      ! [F: nat > complex,C: complex] :
% 0.35/0.65        ( ( summable_complex @ F )
% 0.35/0.65       => ( summable_complex
% 0.35/0.65          @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_mult
% 0.35/0.65  thf(fact_7690_summable__mult,axiom,
% 0.35/0.65      ! [F: nat > real,C: real] :
% 0.35/0.65        ( ( summable_real @ F )
% 0.35/0.65       => ( summable_real
% 0.35/0.65          @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_mult
% 0.35/0.65  thf(fact_7691_summableI__nonneg__bounded,axiom,
% 0.35/0.65      ! [F: nat > int,X: int] :
% 0.35/0.65        ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 0.35/0.65       => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X )
% 0.35/0.65         => ( summable_int @ F ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summableI_nonneg_bounded
% 0.35/0.65  thf(fact_7692_summableI__nonneg__bounded,axiom,
% 0.35/0.65      ! [F: nat > nat,X: nat] :
% 0.35/0.65        ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 0.35/0.65       => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X )
% 0.35/0.65         => ( summable_nat @ F ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summableI_nonneg_bounded
% 0.35/0.65  thf(fact_7693_summableI__nonneg__bounded,axiom,
% 0.35/0.65      ! [F: nat > real,X: real] :
% 0.35/0.65        ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 0.35/0.65       => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X )
% 0.35/0.65         => ( summable_real @ F ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summableI_nonneg_bounded
% 0.35/0.65  thf(fact_7694_suminf__le,axiom,
% 0.35/0.65      ! [F: nat > real,G: nat > real] :
% 0.35/0.65        ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 0.35/0.65       => ( ( summable_real @ F )
% 0.35/0.65         => ( ( summable_real @ G )
% 0.35/0.65           => ( ord_less_eq_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_le
% 0.35/0.65  thf(fact_7695_suminf__le,axiom,
% 0.35/0.65      ! [F: nat > nat,G: nat > nat] :
% 0.35/0.65        ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( G @ N3 ) )
% 0.35/0.65       => ( ( summable_nat @ F )
% 0.35/0.65         => ( ( summable_nat @ G )
% 0.35/0.65           => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_le
% 0.35/0.65  thf(fact_7696_suminf__le,axiom,
% 0.35/0.65      ! [F: nat > int,G: nat > int] :
% 0.35/0.65        ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( G @ N3 ) )
% 0.35/0.65       => ( ( summable_int @ F )
% 0.35/0.65         => ( ( summable_int @ G )
% 0.35/0.65           => ( ord_less_eq_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_le
% 0.35/0.65  thf(fact_7697_summable__mult__D,axiom,
% 0.35/0.65      ! [C: complex,F: nat > complex] :
% 0.35/0.65        ( ( summable_complex
% 0.35/0.65          @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) ) )
% 0.35/0.65       => ( ( C != zero_zero_complex )
% 0.35/0.65         => ( summable_complex @ F ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_mult_D
% 0.35/0.65  thf(fact_7698_summable__mult__D,axiom,
% 0.35/0.65      ! [C: real,F: nat > real] :
% 0.35/0.65        ( ( summable_real
% 0.35/0.65          @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) ) )
% 0.35/0.65       => ( ( C != zero_zero_real )
% 0.35/0.65         => ( summable_real @ F ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_mult_D
% 0.35/0.65  thf(fact_7699_summable__zero__power,axiom,
% 0.35/0.65      summable_real @ ( power_power_real @ zero_zero_real ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_zero_power
% 0.35/0.65  thf(fact_7700_summable__zero__power,axiom,
% 0.35/0.65      summable_int @ ( power_power_int @ zero_zero_int ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_zero_power
% 0.35/0.65  thf(fact_7701_summable__zero__power,axiom,
% 0.35/0.65      summable_complex @ ( power_power_complex @ zero_zero_complex ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_zero_power
% 0.35/0.65  thf(fact_7702_lessThan__def,axiom,
% 0.35/0.65      ( set_ord_lessThan_rat
% 0.35/0.65      = ( ^ [U2: rat] :
% 0.35/0.65            ( collect_rat
% 0.35/0.65            @ ^ [X2: rat] : ( ord_less_rat @ X2 @ U2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % lessThan_def
% 0.35/0.65  thf(fact_7703_lessThan__def,axiom,
% 0.35/0.65      ( set_ord_lessThan_num
% 0.35/0.65      = ( ^ [U2: num] :
% 0.35/0.65            ( collect_num
% 0.35/0.65            @ ^ [X2: num] : ( ord_less_num @ X2 @ U2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % lessThan_def
% 0.35/0.65  thf(fact_7704_lessThan__def,axiom,
% 0.35/0.65      ( set_ord_lessThan_int
% 0.35/0.65      = ( ^ [U2: int] :
% 0.35/0.65            ( collect_int
% 0.35/0.65            @ ^ [X2: int] : ( ord_less_int @ X2 @ U2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % lessThan_def
% 0.35/0.65  thf(fact_7705_lessThan__def,axiom,
% 0.35/0.65      ( set_ord_lessThan_nat
% 0.35/0.65      = ( ^ [U2: nat] :
% 0.35/0.65            ( collect_nat
% 0.35/0.65            @ ^ [X2: nat] : ( ord_less_nat @ X2 @ U2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % lessThan_def
% 0.35/0.65  thf(fact_7706_lessThan__def,axiom,
% 0.35/0.65      ( set_or5984915006950818249n_real
% 0.35/0.65      = ( ^ [U2: real] :
% 0.35/0.65            ( collect_real
% 0.35/0.65            @ ^ [X2: real] : ( ord_less_real @ X2 @ U2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % lessThan_def
% 0.35/0.65  thf(fact_7707_suminf__mult,axiom,
% 0.35/0.65      ! [F: nat > complex,C: complex] :
% 0.35/0.65        ( ( summable_complex @ F )
% 0.35/0.65       => ( ( suminf_complex
% 0.35/0.65            @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) ) )
% 0.35/0.65          = ( times_times_complex @ C @ ( suminf_complex @ F ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_mult
% 0.35/0.65  thf(fact_7708_suminf__mult,axiom,
% 0.35/0.65      ! [F: nat > real,C: real] :
% 0.35/0.65        ( ( summable_real @ F )
% 0.35/0.65       => ( ( suminf_real
% 0.35/0.65            @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) ) )
% 0.35/0.65          = ( times_times_real @ C @ ( suminf_real @ F ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_mult
% 0.35/0.65  thf(fact_7709_suminf__mult2,axiom,
% 0.35/0.65      ! [F: nat > complex,C: complex] :
% 0.35/0.65        ( ( summable_complex @ F )
% 0.35/0.65       => ( ( times_times_complex @ ( suminf_complex @ F ) @ C )
% 0.35/0.65          = ( suminf_complex
% 0.35/0.65            @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ C ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_mult2
% 0.35/0.65  thf(fact_7710_suminf__mult2,axiom,
% 0.35/0.65      ! [F: nat > real,C: real] :
% 0.35/0.65        ( ( summable_real @ F )
% 0.35/0.65       => ( ( times_times_real @ ( suminf_real @ F ) @ C )
% 0.35/0.65          = ( suminf_real
% 0.35/0.65            @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ C ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_mult2
% 0.35/0.65  thf(fact_7711_suminf__add,axiom,
% 0.35/0.65      ! [F: nat > real,G: nat > real] :
% 0.35/0.65        ( ( summable_real @ F )
% 0.35/0.65       => ( ( summable_real @ G )
% 0.35/0.65         => ( ( plus_plus_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) )
% 0.35/0.65            = ( suminf_real
% 0.35/0.65              @ ^ [N2: nat] : ( plus_plus_real @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_add
% 0.35/0.65  thf(fact_7712_suminf__add,axiom,
% 0.35/0.65      ! [F: nat > nat,G: nat > nat] :
% 0.35/0.65        ( ( summable_nat @ F )
% 0.35/0.65       => ( ( summable_nat @ G )
% 0.35/0.65         => ( ( plus_plus_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) )
% 0.35/0.65            = ( suminf_nat
% 0.35/0.65              @ ^ [N2: nat] : ( plus_plus_nat @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_add
% 0.35/0.65  thf(fact_7713_suminf__add,axiom,
% 0.35/0.65      ! [F: nat > int,G: nat > int] :
% 0.35/0.65        ( ( summable_int @ F )
% 0.35/0.65       => ( ( summable_int @ G )
% 0.35/0.65         => ( ( plus_plus_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) )
% 0.35/0.65            = ( suminf_int
% 0.35/0.65              @ ^ [N2: nat] : ( plus_plus_int @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_add
% 0.35/0.65  thf(fact_7714_suminf__add,axiom,
% 0.35/0.65      ! [F: nat > complex,G: nat > complex] :
% 0.35/0.65        ( ( summable_complex @ F )
% 0.35/0.65       => ( ( summable_complex @ G )
% 0.35/0.65         => ( ( plus_plus_complex @ ( suminf_complex @ F ) @ ( suminf_complex @ G ) )
% 0.35/0.65            = ( suminf_complex
% 0.35/0.65              @ ^ [N2: nat] : ( plus_plus_complex @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_add
% 0.35/0.65  thf(fact_7715_suminf__diff,axiom,
% 0.35/0.65      ! [F: nat > real,G: nat > real] :
% 0.35/0.65        ( ( summable_real @ F )
% 0.35/0.65       => ( ( summable_real @ G )
% 0.35/0.65         => ( ( minus_minus_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) )
% 0.35/0.65            = ( suminf_real
% 0.35/0.65              @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_diff
% 0.35/0.65  thf(fact_7716_suminf__divide,axiom,
% 0.35/0.65      ! [F: nat > complex,C: complex] :
% 0.35/0.65        ( ( summable_complex @ F )
% 0.35/0.65       => ( ( suminf_complex
% 0.35/0.65            @ ^ [N2: nat] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ C ) )
% 0.35/0.65          = ( divide1717551699836669952omplex @ ( suminf_complex @ F ) @ C ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_divide
% 0.35/0.65  thf(fact_7717_suminf__divide,axiom,
% 0.35/0.65      ! [F: nat > real,C: real] :
% 0.35/0.65        ( ( summable_real @ F )
% 0.35/0.65       => ( ( suminf_real
% 0.35/0.65            @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ C ) )
% 0.35/0.65          = ( divide_divide_real @ ( suminf_real @ F ) @ C ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_divide
% 0.35/0.65  thf(fact_7718_suminf__split__initial__segment,axiom,
% 0.35/0.65      ! [F: nat > complex,K: nat] :
% 0.35/0.65        ( ( summable_complex @ F )
% 0.35/0.65       => ( ( suminf_complex @ F )
% 0.35/0.65          = ( plus_plus_complex
% 0.35/0.65            @ ( suminf_complex
% 0.35/0.65              @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ K ) ) )
% 0.35/0.65            @ ( groups2073611262835488442omplex @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_split_initial_segment
% 0.35/0.65  thf(fact_7719_suminf__split__initial__segment,axiom,
% 0.35/0.65      ! [F: nat > real,K: nat] :
% 0.35/0.65        ( ( summable_real @ F )
% 0.35/0.65       => ( ( suminf_real @ F )
% 0.35/0.65          = ( plus_plus_real
% 0.35/0.65            @ ( suminf_real
% 0.35/0.65              @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ K ) ) )
% 0.35/0.65            @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_split_initial_segment
% 0.35/0.65  thf(fact_7720_suminf__minus__initial__segment,axiom,
% 0.35/0.65      ! [F: nat > real,K: nat] :
% 0.35/0.65        ( ( summable_real @ F )
% 0.35/0.65       => ( ( suminf_real
% 0.35/0.65            @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ K ) ) )
% 0.35/0.65          = ( minus_minus_real @ ( suminf_real @ F ) @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_minus_initial_segment
% 0.35/0.65  thf(fact_7721_sum__less__suminf,axiom,
% 0.35/0.65      ! [F: nat > int,N: nat] :
% 0.35/0.65        ( ( summable_int @ F )
% 0.35/0.65       => ( ! [M4: nat] :
% 0.35/0.65              ( ( ord_less_eq_nat @ N @ M4 )
% 0.35/0.65             => ( ord_less_int @ zero_zero_int @ ( F @ M4 ) ) )
% 0.35/0.65         => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_int @ F ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum_less_suminf
% 0.35/0.65  thf(fact_7722_sum__less__suminf,axiom,
% 0.35/0.65      ! [F: nat > nat,N: nat] :
% 0.35/0.65        ( ( summable_nat @ F )
% 0.35/0.65       => ( ! [M4: nat] :
% 0.35/0.65              ( ( ord_less_eq_nat @ N @ M4 )
% 0.35/0.65             => ( ord_less_nat @ zero_zero_nat @ ( F @ M4 ) ) )
% 0.35/0.65         => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_nat @ F ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum_less_suminf
% 0.35/0.65  thf(fact_7723_sum__less__suminf,axiom,
% 0.35/0.65      ! [F: nat > real,N: nat] :
% 0.35/0.65        ( ( summable_real @ F )
% 0.35/0.65       => ( ! [M4: nat] :
% 0.35/0.65              ( ( ord_less_eq_nat @ N @ M4 )
% 0.35/0.65             => ( ord_less_real @ zero_zero_real @ ( F @ M4 ) ) )
% 0.35/0.65         => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_real @ F ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum_less_suminf
% 0.35/0.65  thf(fact_7724_powser__insidea,axiom,
% 0.35/0.65      ! [F: nat > real,X: real,Z: real] :
% 0.35/0.65        ( ( summable_real
% 0.35/0.65          @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ X @ N2 ) ) )
% 0.35/0.65       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ ( real_V7735802525324610683m_real @ X ) )
% 0.35/0.65         => ( summable_real
% 0.35/0.65            @ ^ [N2: nat] : ( real_V7735802525324610683m_real @ ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powser_insidea
% 0.35/0.65  thf(fact_7725_powser__insidea,axiom,
% 0.35/0.65      ! [F: nat > complex,X: complex,Z: complex] :
% 0.35/0.65        ( ( summable_complex
% 0.35/0.65          @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ X @ N2 ) ) )
% 0.35/0.65       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ ( real_V1022390504157884413omplex @ X ) )
% 0.35/0.65         => ( summable_real
% 0.35/0.65            @ ^ [N2: nat] : ( real_V1022390504157884413omplex @ ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powser_insidea
% 0.35/0.65  thf(fact_7726_suminf__eq__zero__iff,axiom,
% 0.35/0.65      ! [F: nat > real] :
% 0.35/0.65        ( ( summable_real @ F )
% 0.35/0.65       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 0.35/0.65         => ( ( ( suminf_real @ F )
% 0.35/0.65              = zero_zero_real )
% 0.35/0.65            = ( ! [N2: nat] :
% 0.35/0.65                  ( ( F @ N2 )
% 0.35/0.65                  = zero_zero_real ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_eq_zero_iff
% 0.35/0.65  thf(fact_7727_suminf__eq__zero__iff,axiom,
% 0.35/0.65      ! [F: nat > nat] :
% 0.35/0.65        ( ( summable_nat @ F )
% 0.35/0.65       => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 0.35/0.65         => ( ( ( suminf_nat @ F )
% 0.35/0.65              = zero_zero_nat )
% 0.35/0.65            = ( ! [N2: nat] :
% 0.35/0.65                  ( ( F @ N2 )
% 0.35/0.65                  = zero_zero_nat ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_eq_zero_iff
% 0.35/0.65  thf(fact_7728_suminf__eq__zero__iff,axiom,
% 0.35/0.65      ! [F: nat > int] :
% 0.35/0.65        ( ( summable_int @ F )
% 0.35/0.65       => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 0.35/0.65         => ( ( ( suminf_int @ F )
% 0.35/0.65              = zero_zero_int )
% 0.35/0.65            = ( ! [N2: nat] :
% 0.35/0.65                  ( ( F @ N2 )
% 0.35/0.65                  = zero_zero_int ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_eq_zero_iff
% 0.35/0.65  thf(fact_7729_suminf__nonneg,axiom,
% 0.35/0.65      ! [F: nat > real] :
% 0.35/0.65        ( ( summable_real @ F )
% 0.35/0.65       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 0.35/0.65         => ( ord_less_eq_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_nonneg
% 0.35/0.65  thf(fact_7730_suminf__nonneg,axiom,
% 0.35/0.65      ! [F: nat > nat] :
% 0.35/0.65        ( ( summable_nat @ F )
% 0.35/0.65       => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 0.35/0.65         => ( ord_less_eq_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_nonneg
% 0.35/0.65  thf(fact_7731_suminf__nonneg,axiom,
% 0.35/0.65      ! [F: nat > int] :
% 0.35/0.65        ( ( summable_int @ F )
% 0.35/0.65       => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 0.35/0.65         => ( ord_less_eq_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_nonneg
% 0.35/0.65  thf(fact_7732_suminf__pos,axiom,
% 0.35/0.65      ! [F: nat > real] :
% 0.35/0.65        ( ( summable_real @ F )
% 0.35/0.65       => ( ! [N3: nat] : ( ord_less_real @ zero_zero_real @ ( F @ N3 ) )
% 0.35/0.65         => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_pos
% 0.35/0.65  thf(fact_7733_suminf__pos,axiom,
% 0.35/0.65      ! [F: nat > nat] :
% 0.35/0.65        ( ( summable_nat @ F )
% 0.35/0.65       => ( ! [N3: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ N3 ) )
% 0.35/0.65         => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_pos
% 0.35/0.65  thf(fact_7734_suminf__pos,axiom,
% 0.35/0.65      ! [F: nat > int] :
% 0.35/0.65        ( ( summable_int @ F )
% 0.35/0.65       => ( ! [N3: nat] : ( ord_less_int @ zero_zero_int @ ( F @ N3 ) )
% 0.35/0.65         => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_pos
% 0.35/0.65  thf(fact_7735_powr__non__neg,axiom,
% 0.35/0.65      ! [A: real,X: real] :
% 0.35/0.65        ~ ( ord_less_real @ ( powr_real @ A @ X ) @ zero_zero_real ) ).
% 0.35/0.65  
% 0.35/0.65  % powr_non_neg
% 0.35/0.65  thf(fact_7736_powr__less__mono2__neg,axiom,
% 0.35/0.65      ! [A: real,X: real,Y2: real] :
% 0.35/0.65        ( ( ord_less_real @ A @ zero_zero_real )
% 0.35/0.65       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.65         => ( ( ord_less_real @ X @ Y2 )
% 0.35/0.65           => ( ord_less_real @ ( powr_real @ Y2 @ A ) @ ( powr_real @ X @ A ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powr_less_mono2_neg
% 0.35/0.65  thf(fact_7737_powr__mono2,axiom,
% 0.35/0.65      ! [A: real,X: real,Y2: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.35/0.65       => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.65         => ( ( ord_less_eq_real @ X @ Y2 )
% 0.35/0.65           => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y2 @ A ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powr_mono2
% 0.35/0.65  thf(fact_7738_powr__ge__pzero,axiom,
% 0.35/0.65      ! [X: real,Y2: real] : ( ord_less_eq_real @ zero_zero_real @ ( powr_real @ X @ Y2 ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powr_ge_pzero
% 0.35/0.65  thf(fact_7739_powr__less__cancel,axiom,
% 0.35/0.65      ! [X: real,A: real,B: real] :
% 0.35/0.65        ( ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 0.35/0.65       => ( ( ord_less_real @ one_one_real @ X )
% 0.35/0.65         => ( ord_less_real @ A @ B ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powr_less_cancel
% 0.35/0.65  thf(fact_7740_powr__less__mono,axiom,
% 0.35/0.65      ! [A: real,B: real,X: real] :
% 0.35/0.65        ( ( ord_less_real @ A @ B )
% 0.35/0.65       => ( ( ord_less_real @ one_one_real @ X )
% 0.35/0.65         => ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powr_less_mono
% 0.35/0.65  thf(fact_7741_powr__mono,axiom,
% 0.35/0.65      ! [A: real,B: real,X: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ A @ B )
% 0.35/0.65       => ( ( ord_less_eq_real @ one_one_real @ X )
% 0.35/0.65         => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powr_mono
% 0.35/0.65  thf(fact_7742_lessThan__strict__subset__iff,axiom,
% 0.35/0.65      ! [M: rat,N: rat] :
% 0.35/0.65        ( ( ord_less_set_rat @ ( set_ord_lessThan_rat @ M ) @ ( set_ord_lessThan_rat @ N ) )
% 0.35/0.65        = ( ord_less_rat @ M @ N ) ) ).
% 0.35/0.65  
% 0.35/0.65  % lessThan_strict_subset_iff
% 0.35/0.65  thf(fact_7743_lessThan__strict__subset__iff,axiom,
% 0.35/0.65      ! [M: num,N: num] :
% 0.35/0.65        ( ( ord_less_set_num @ ( set_ord_lessThan_num @ M ) @ ( set_ord_lessThan_num @ N ) )
% 0.35/0.65        = ( ord_less_num @ M @ N ) ) ).
% 0.35/0.65  
% 0.35/0.65  % lessThan_strict_subset_iff
% 0.35/0.65  thf(fact_7744_lessThan__strict__subset__iff,axiom,
% 0.35/0.65      ! [M: int,N: int] :
% 0.35/0.65        ( ( ord_less_set_int @ ( set_ord_lessThan_int @ M ) @ ( set_ord_lessThan_int @ N ) )
% 0.35/0.65        = ( ord_less_int @ M @ N ) ) ).
% 0.35/0.65  
% 0.35/0.65  % lessThan_strict_subset_iff
% 0.35/0.65  thf(fact_7745_lessThan__strict__subset__iff,axiom,
% 0.35/0.65      ! [M: nat,N: nat] :
% 0.35/0.65        ( ( ord_less_set_nat @ ( set_ord_lessThan_nat @ M ) @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.65        = ( ord_less_nat @ M @ N ) ) ).
% 0.35/0.65  
% 0.35/0.65  % lessThan_strict_subset_iff
% 0.35/0.65  thf(fact_7746_lessThan__strict__subset__iff,axiom,
% 0.35/0.65      ! [M: real,N: real] :
% 0.35/0.65        ( ( ord_less_set_real @ ( set_or5984915006950818249n_real @ M ) @ ( set_or5984915006950818249n_real @ N ) )
% 0.35/0.65        = ( ord_less_real @ M @ N ) ) ).
% 0.35/0.65  
% 0.35/0.65  % lessThan_strict_subset_iff
% 0.35/0.65  thf(fact_7747_summable__0__powser,axiom,
% 0.35/0.65      ! [F: nat > complex] :
% 0.35/0.65        ( summable_complex
% 0.35/0.65        @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_0_powser
% 0.35/0.65  thf(fact_7748_summable__0__powser,axiom,
% 0.35/0.65      ! [F: nat > real] :
% 0.35/0.65        ( summable_real
% 0.35/0.65        @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_0_powser
% 0.35/0.65  thf(fact_7749_summable__zero__power_H,axiom,
% 0.35/0.65      ! [F: nat > complex] :
% 0.35/0.65        ( summable_complex
% 0.35/0.65        @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_zero_power'
% 0.35/0.65  thf(fact_7750_summable__zero__power_H,axiom,
% 0.35/0.65      ! [F: nat > real] :
% 0.35/0.65        ( summable_real
% 0.35/0.65        @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_zero_power'
% 0.35/0.65  thf(fact_7751_summable__zero__power_H,axiom,
% 0.35/0.65      ! [F: nat > int] :
% 0.35/0.65        ( summable_int
% 0.35/0.65        @ ^ [N2: nat] : ( times_times_int @ ( F @ N2 ) @ ( power_power_int @ zero_zero_int @ N2 ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_zero_power'
% 0.35/0.65  thf(fact_7752_summable__powser__split__head,axiom,
% 0.35/0.65      ! [F: nat > complex,Z: complex] :
% 0.35/0.65        ( ( summable_complex
% 0.35/0.65          @ ^ [N2: nat] : ( times_times_complex @ ( F @ ( suc @ N2 ) ) @ ( power_power_complex @ Z @ N2 ) ) )
% 0.35/0.65        = ( summable_complex
% 0.35/0.65          @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_powser_split_head
% 0.35/0.65  thf(fact_7753_summable__powser__split__head,axiom,
% 0.35/0.65      ! [F: nat > real,Z: real] :
% 0.35/0.65        ( ( summable_real
% 0.35/0.65          @ ^ [N2: nat] : ( times_times_real @ ( F @ ( suc @ N2 ) ) @ ( power_power_real @ Z @ N2 ) ) )
% 0.35/0.65        = ( summable_real
% 0.35/0.65          @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_powser_split_head
% 0.35/0.65  thf(fact_7754_powser__split__head_I3_J,axiom,
% 0.35/0.65      ! [F: nat > complex,Z: complex] :
% 0.35/0.65        ( ( summable_complex
% 0.35/0.65          @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) )
% 0.35/0.65       => ( summable_complex
% 0.35/0.65          @ ^ [N2: nat] : ( times_times_complex @ ( F @ ( suc @ N2 ) ) @ ( power_power_complex @ Z @ N2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powser_split_head(3)
% 0.35/0.65  thf(fact_7755_powser__split__head_I3_J,axiom,
% 0.35/0.65      ! [F: nat > real,Z: real] :
% 0.35/0.65        ( ( summable_real
% 0.35/0.65          @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) )
% 0.35/0.65       => ( summable_real
% 0.35/0.65          @ ^ [N2: nat] : ( times_times_real @ ( F @ ( suc @ N2 ) ) @ ( power_power_real @ Z @ N2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powser_split_head(3)
% 0.35/0.65  thf(fact_7756_summable__powser__ignore__initial__segment,axiom,
% 0.35/0.65      ! [F: nat > complex,M: nat,Z: complex] :
% 0.35/0.65        ( ( summable_complex
% 0.35/0.65          @ ^ [N2: nat] : ( times_times_complex @ ( F @ ( plus_plus_nat @ N2 @ M ) ) @ ( power_power_complex @ Z @ N2 ) ) )
% 0.35/0.65        = ( summable_complex
% 0.35/0.65          @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_powser_ignore_initial_segment
% 0.35/0.65  thf(fact_7757_summable__powser__ignore__initial__segment,axiom,
% 0.35/0.65      ! [F: nat > real,M: nat,Z: real] :
% 0.35/0.65        ( ( summable_real
% 0.35/0.65          @ ^ [N2: nat] : ( times_times_real @ ( F @ ( plus_plus_nat @ N2 @ M ) ) @ ( power_power_real @ Z @ N2 ) ) )
% 0.35/0.65        = ( summable_real
% 0.35/0.65          @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_powser_ignore_initial_segment
% 0.35/0.65  thf(fact_7758_pi__gt__zero,axiom,
% 0.35/0.65      ord_less_real @ zero_zero_real @ pi ).
% 0.35/0.65  
% 0.35/0.65  % pi_gt_zero
% 0.35/0.65  thf(fact_7759_pi__not__less__zero,axiom,
% 0.35/0.65      ~ ( ord_less_real @ pi @ zero_zero_real ) ).
% 0.35/0.65  
% 0.35/0.65  % pi_not_less_zero
% 0.35/0.65  thf(fact_7760_pi__ge__zero,axiom,
% 0.35/0.65      ord_less_eq_real @ zero_zero_real @ pi ).
% 0.35/0.65  
% 0.35/0.65  % pi_ge_zero
% 0.35/0.65  thf(fact_7761_sum__less__suminf2,axiom,
% 0.35/0.65      ! [F: nat > int,N: nat,I2: nat] :
% 0.35/0.65        ( ( summable_int @ F )
% 0.35/0.65       => ( ! [M4: nat] :
% 0.35/0.65              ( ( ord_less_eq_nat @ N @ M4 )
% 0.35/0.65             => ( ord_less_eq_int @ zero_zero_int @ ( F @ M4 ) ) )
% 0.35/0.65         => ( ( ord_less_eq_nat @ N @ I2 )
% 0.35/0.65           => ( ( ord_less_int @ zero_zero_int @ ( F @ I2 ) )
% 0.35/0.65             => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_int @ F ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum_less_suminf2
% 0.35/0.65  thf(fact_7762_sum__less__suminf2,axiom,
% 0.35/0.65      ! [F: nat > nat,N: nat,I2: nat] :
% 0.35/0.65        ( ( summable_nat @ F )
% 0.35/0.65       => ( ! [M4: nat] :
% 0.35/0.65              ( ( ord_less_eq_nat @ N @ M4 )
% 0.35/0.65             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ M4 ) ) )
% 0.35/0.65         => ( ( ord_less_eq_nat @ N @ I2 )
% 0.35/0.65           => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 0.35/0.65             => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_nat @ F ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum_less_suminf2
% 0.35/0.65  thf(fact_7763_sum__less__suminf2,axiom,
% 0.35/0.65      ! [F: nat > real,N: nat,I2: nat] :
% 0.35/0.65        ( ( summable_real @ F )
% 0.35/0.65       => ( ! [M4: nat] :
% 0.35/0.65              ( ( ord_less_eq_nat @ N @ M4 )
% 0.35/0.65             => ( ord_less_eq_real @ zero_zero_real @ ( F @ M4 ) ) )
% 0.35/0.65         => ( ( ord_less_eq_nat @ N @ I2 )
% 0.35/0.65           => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 0.35/0.65             => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_real @ F ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum_less_suminf2
% 0.35/0.65  thf(fact_7764_lessThan__Suc,axiom,
% 0.35/0.65      ! [K: nat] :
% 0.35/0.65        ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 0.35/0.65        = ( insert_nat @ K @ ( set_ord_lessThan_nat @ K ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % lessThan_Suc
% 0.35/0.65  thf(fact_7765_summable__norm__comparison__test,axiom,
% 0.35/0.65      ! [F: nat > complex,G: nat > real] :
% 0.35/0.65        ( ? [N7: nat] :
% 0.35/0.65          ! [N3: nat] :
% 0.35/0.65            ( ( ord_less_eq_nat @ N7 @ N3 )
% 0.35/0.65           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 0.35/0.65       => ( ( summable_real @ G )
% 0.35/0.65         => ( summable_real
% 0.35/0.65            @ ^ [N2: nat] : ( real_V1022390504157884413omplex @ ( F @ N2 ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_norm_comparison_test
% 0.35/0.65  thf(fact_7766_summable__rabs__comparison__test,axiom,
% 0.35/0.65      ! [F: nat > real,G: nat > real] :
% 0.35/0.65        ( ? [N7: nat] :
% 0.35/0.65          ! [N3: nat] :
% 0.35/0.65            ( ( ord_less_eq_nat @ N7 @ N3 )
% 0.35/0.65           => ( ord_less_eq_real @ ( abs_abs_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 0.35/0.65       => ( ( summable_real @ G )
% 0.35/0.65         => ( summable_real
% 0.35/0.65            @ ^ [N2: nat] : ( abs_abs_real @ ( F @ N2 ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_rabs_comparison_test
% 0.35/0.65  thf(fact_7767_summable__rabs,axiom,
% 0.35/0.65      ! [F: nat > real] :
% 0.35/0.65        ( ( summable_real
% 0.35/0.65          @ ^ [N2: nat] : ( abs_abs_real @ ( F @ N2 ) ) )
% 0.35/0.65       => ( ord_less_eq_real @ ( abs_abs_real @ ( suminf_real @ F ) )
% 0.35/0.65          @ ( suminf_real
% 0.35/0.65            @ ^ [N2: nat] : ( abs_abs_real @ ( F @ N2 ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_rabs
% 0.35/0.65  thf(fact_7768_suminf__pos2,axiom,
% 0.35/0.65      ! [F: nat > real,I2: nat] :
% 0.35/0.65        ( ( summable_real @ F )
% 0.35/0.65       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 0.35/0.65         => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 0.35/0.65           => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_pos2
% 0.35/0.65  thf(fact_7769_suminf__pos2,axiom,
% 0.35/0.65      ! [F: nat > nat,I2: nat] :
% 0.35/0.65        ( ( summable_nat @ F )
% 0.35/0.65       => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 0.35/0.65         => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 0.35/0.65           => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_pos2
% 0.35/0.65  thf(fact_7770_suminf__pos2,axiom,
% 0.35/0.65      ! [F: nat > int,I2: nat] :
% 0.35/0.65        ( ( summable_int @ F )
% 0.35/0.65       => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 0.35/0.65         => ( ( ord_less_int @ zero_zero_int @ ( F @ I2 ) )
% 0.35/0.65           => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_pos2
% 0.35/0.65  thf(fact_7771_suminf__pos__iff,axiom,
% 0.35/0.65      ! [F: nat > real] :
% 0.35/0.65        ( ( summable_real @ F )
% 0.35/0.65       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 0.35/0.65         => ( ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) )
% 0.35/0.65            = ( ? [I3: nat] : ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_pos_iff
% 0.35/0.65  thf(fact_7772_suminf__pos__iff,axiom,
% 0.35/0.65      ! [F: nat > nat] :
% 0.35/0.65        ( ( summable_nat @ F )
% 0.35/0.65       => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 0.35/0.65         => ( ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) )
% 0.35/0.65            = ( ? [I3: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ I3 ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_pos_iff
% 0.35/0.65  thf(fact_7773_suminf__pos__iff,axiom,
% 0.35/0.65      ! [F: nat > int] :
% 0.35/0.65        ( ( summable_int @ F )
% 0.35/0.65       => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 0.35/0.65         => ( ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) )
% 0.35/0.65            = ( ? [I3: nat] : ( ord_less_int @ zero_zero_int @ ( F @ I3 ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_pos_iff
% 0.35/0.65  thf(fact_7774_powr__mono2_H,axiom,
% 0.35/0.65      ! [A: real,X: real,Y2: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.35/0.65       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.65         => ( ( ord_less_eq_real @ X @ Y2 )
% 0.35/0.65           => ( ord_less_eq_real @ ( powr_real @ Y2 @ A ) @ ( powr_real @ X @ A ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powr_mono2'
% 0.35/0.65  thf(fact_7775_powr__less__mono2,axiom,
% 0.35/0.65      ! [A: real,X: real,Y2: real] :
% 0.35/0.65        ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.65       => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.65         => ( ( ord_less_real @ X @ Y2 )
% 0.35/0.65           => ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y2 @ A ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powr_less_mono2
% 0.35/0.65  thf(fact_7776_gr__one__powr,axiom,
% 0.35/0.65      ! [X: real,Y2: real] :
% 0.35/0.65        ( ( ord_less_real @ one_one_real @ X )
% 0.35/0.65       => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 0.35/0.65         => ( ord_less_real @ one_one_real @ ( powr_real @ X @ Y2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % gr_one_powr
% 0.35/0.65  thf(fact_7777_powr__inj,axiom,
% 0.35/0.65      ! [A: real,X: real,Y2: real] :
% 0.35/0.65        ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.65       => ( ( A != one_one_real )
% 0.35/0.65         => ( ( ( powr_real @ A @ X )
% 0.35/0.65              = ( powr_real @ A @ Y2 ) )
% 0.35/0.65            = ( X = Y2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powr_inj
% 0.35/0.65  thf(fact_7778_powr__le1,axiom,
% 0.35/0.65      ! [A: real,X: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.35/0.65       => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.65         => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.35/0.65           => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ one_one_real ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powr_le1
% 0.35/0.65  thf(fact_7779_powr__mono__both,axiom,
% 0.35/0.65      ! [A: real,B: real,X: real,Y2: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.35/0.65       => ( ( ord_less_eq_real @ A @ B )
% 0.35/0.65         => ( ( ord_less_eq_real @ one_one_real @ X )
% 0.35/0.65           => ( ( ord_less_eq_real @ X @ Y2 )
% 0.35/0.65             => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y2 @ B ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powr_mono_both
% 0.35/0.65  thf(fact_7780_ge__one__powr__ge__zero,axiom,
% 0.35/0.65      ! [X: real,A: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ one_one_real @ X )
% 0.35/0.65       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.35/0.65         => ( ord_less_eq_real @ one_one_real @ ( powr_real @ X @ A ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % ge_one_powr_ge_zero
% 0.35/0.65  thf(fact_7781_complete__algebra__summable__geometric,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ one_one_real )
% 0.35/0.65       => ( summable_real @ ( power_power_real @ X ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % complete_algebra_summable_geometric
% 0.35/0.65  thf(fact_7782_complete__algebra__summable__geometric,axiom,
% 0.35/0.65      ! [X: complex] :
% 0.35/0.65        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ one_one_real )
% 0.35/0.65       => ( summable_complex @ ( power_power_complex @ X ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % complete_algebra_summable_geometric
% 0.35/0.65  thf(fact_7783_summable__geometric,axiom,
% 0.35/0.65      ! [C: real] :
% 0.35/0.65        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 0.35/0.65       => ( summable_real @ ( power_power_real @ C ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_geometric
% 0.35/0.65  thf(fact_7784_summable__geometric,axiom,
% 0.35/0.65      ! [C: complex] :
% 0.35/0.65        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 0.35/0.65       => ( summable_complex @ ( power_power_complex @ C ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_geometric
% 0.35/0.65  thf(fact_7785_suminf__split__head,axiom,
% 0.35/0.65      ! [F: nat > real] :
% 0.35/0.65        ( ( summable_real @ F )
% 0.35/0.65       => ( ( suminf_real
% 0.35/0.65            @ ^ [N2: nat] : ( F @ ( suc @ N2 ) ) )
% 0.35/0.65          = ( minus_minus_real @ ( suminf_real @ F ) @ ( F @ zero_zero_nat ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_split_head
% 0.35/0.65  thf(fact_7786_powr__divide,axiom,
% 0.35/0.65      ! [X: real,Y2: real,A: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.65       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 0.35/0.65         => ( ( powr_real @ ( divide_divide_real @ X @ Y2 ) @ A )
% 0.35/0.65            = ( divide_divide_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y2 @ A ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powr_divide
% 0.35/0.65  thf(fact_7787_powr__mult,axiom,
% 0.35/0.65      ! [X: real,Y2: real,A: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.65       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 0.35/0.65         => ( ( powr_real @ ( times_times_real @ X @ Y2 ) @ A )
% 0.35/0.65            = ( times_times_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y2 @ A ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powr_mult
% 0.35/0.65  thf(fact_7788_divide__powr__uminus,axiom,
% 0.35/0.65      ! [A: real,B: real,C: real] :
% 0.35/0.65        ( ( divide_divide_real @ A @ ( powr_real @ B @ C ) )
% 0.35/0.65        = ( times_times_real @ A @ ( powr_real @ B @ ( uminus_uminus_real @ C ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % divide_powr_uminus
% 0.35/0.65  thf(fact_7789_log__base__powr,axiom,
% 0.35/0.65      ! [A: real,B: real,X: real] :
% 0.35/0.65        ( ( A != zero_zero_real )
% 0.35/0.65       => ( ( log @ ( powr_real @ A @ B ) @ X )
% 0.35/0.65          = ( divide_divide_real @ ( log @ A @ X ) @ B ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % log_base_powr
% 0.35/0.65  thf(fact_7790_log__powr,axiom,
% 0.35/0.65      ! [X: real,B: real,Y2: real] :
% 0.35/0.65        ( ( X != zero_zero_real )
% 0.35/0.65       => ( ( log @ B @ ( powr_real @ X @ Y2 ) )
% 0.35/0.65          = ( times_times_real @ Y2 @ ( log @ B @ X ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % log_powr
% 0.35/0.65  thf(fact_7791_ln__powr,axiom,
% 0.35/0.65      ! [X: real,Y2: real] :
% 0.35/0.65        ( ( X != zero_zero_real )
% 0.35/0.65       => ( ( ln_ln_real @ ( powr_real @ X @ Y2 ) )
% 0.35/0.65          = ( times_times_real @ Y2 @ ( ln_ln_real @ X ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % ln_powr
% 0.35/0.65  thf(fact_7792_powr__add,axiom,
% 0.35/0.65      ! [X: real,A: real,B: real] :
% 0.35/0.65        ( ( powr_real @ X @ ( plus_plus_real @ A @ B ) )
% 0.35/0.65        = ( times_times_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powr_add
% 0.35/0.65  thf(fact_7793_powr__diff,axiom,
% 0.35/0.65      ! [W: real,Z1: real,Z22: real] :
% 0.35/0.65        ( ( powr_real @ W @ ( minus_minus_real @ Z1 @ Z22 ) )
% 0.35/0.65        = ( divide_divide_real @ ( powr_real @ W @ Z1 ) @ ( powr_real @ W @ Z22 ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powr_diff
% 0.35/0.65  thf(fact_7794_summable__norm,axiom,
% 0.35/0.65      ! [F: nat > real] :
% 0.35/0.65        ( ( summable_real
% 0.35/0.65          @ ^ [N2: nat] : ( real_V7735802525324610683m_real @ ( F @ N2 ) ) )
% 0.35/0.65       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( suminf_real @ F ) )
% 0.35/0.65          @ ( suminf_real
% 0.35/0.65            @ ^ [N2: nat] : ( real_V7735802525324610683m_real @ ( F @ N2 ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_norm
% 0.35/0.65  thf(fact_7795_summable__norm,axiom,
% 0.35/0.65      ! [F: nat > complex] :
% 0.35/0.65        ( ( summable_real
% 0.35/0.65          @ ^ [N2: nat] : ( real_V1022390504157884413omplex @ ( F @ N2 ) ) )
% 0.35/0.65       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( suminf_complex @ F ) )
% 0.35/0.65          @ ( suminf_real
% 0.35/0.65            @ ^ [N2: nat] : ( real_V1022390504157884413omplex @ ( F @ N2 ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_norm
% 0.35/0.65  thf(fact_7796_lessThan__nat__numeral,axiom,
% 0.35/0.65      ! [K: num] :
% 0.35/0.65        ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K ) )
% 0.35/0.65        = ( insert_nat @ ( pred_numeral @ K ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % lessThan_nat_numeral
% 0.35/0.65  thf(fact_7797_sum_Onat__diff__reindex,axiom,
% 0.35/0.65      ! [G: nat > nat,N: nat] :
% 0.35/0.65        ( ( groups3542108847815614940at_nat
% 0.35/0.65          @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 0.35/0.65          @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.65        = ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum.nat_diff_reindex
% 0.35/0.65  thf(fact_7798_sum_Onat__diff__reindex,axiom,
% 0.35/0.65      ! [G: nat > real,N: nat] :
% 0.35/0.65        ( ( groups6591440286371151544t_real
% 0.35/0.65          @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 0.35/0.65          @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.65        = ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum.nat_diff_reindex
% 0.35/0.65  thf(fact_7799_sum__le__suminf,axiom,
% 0.35/0.65      ! [F: nat > int,I6: set_nat] :
% 0.35/0.65        ( ( summable_int @ F )
% 0.35/0.65       => ( ( finite_finite_nat @ I6 )
% 0.35/0.65         => ( ! [N3: nat] :
% 0.35/0.65                ( ( member_nat @ N3 @ ( uminus5710092332889474511et_nat @ I6 ) )
% 0.35/0.65               => ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) ) )
% 0.35/0.65           => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ I6 ) @ ( suminf_int @ F ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum_le_suminf
% 0.35/0.65  thf(fact_7800_sum__le__suminf,axiom,
% 0.35/0.65      ! [F: nat > nat,I6: set_nat] :
% 0.35/0.65        ( ( summable_nat @ F )
% 0.35/0.65       => ( ( finite_finite_nat @ I6 )
% 0.35/0.65         => ( ! [N3: nat] :
% 0.35/0.65                ( ( member_nat @ N3 @ ( uminus5710092332889474511et_nat @ I6 ) )
% 0.35/0.65               => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) ) )
% 0.35/0.65           => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ I6 ) @ ( suminf_nat @ F ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum_le_suminf
% 0.35/0.65  thf(fact_7801_sum__le__suminf,axiom,
% 0.35/0.65      ! [F: nat > real,I6: set_nat] :
% 0.35/0.65        ( ( summable_real @ F )
% 0.35/0.65       => ( ( finite_finite_nat @ I6 )
% 0.35/0.65         => ( ! [N3: nat] :
% 0.35/0.65                ( ( member_nat @ N3 @ ( uminus5710092332889474511et_nat @ I6 ) )
% 0.35/0.65               => ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) ) )
% 0.35/0.65           => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ I6 ) @ ( suminf_real @ F ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum_le_suminf
% 0.35/0.65  thf(fact_7802_sum__diff__distrib,axiom,
% 0.35/0.65      ! [Q: real > nat,P: real > nat,N: real] :
% 0.35/0.65        ( ! [X3: real] : ( ord_less_eq_nat @ ( Q @ X3 ) @ ( P @ X3 ) )
% 0.35/0.65       => ( ( minus_minus_nat @ ( groups1935376822645274424al_nat @ P @ ( set_or5984915006950818249n_real @ N ) ) @ ( groups1935376822645274424al_nat @ Q @ ( set_or5984915006950818249n_real @ N ) ) )
% 0.35/0.65          = ( groups1935376822645274424al_nat
% 0.35/0.65            @ ^ [X2: real] : ( minus_minus_nat @ ( P @ X2 ) @ ( Q @ X2 ) )
% 0.35/0.65            @ ( set_or5984915006950818249n_real @ N ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum_diff_distrib
% 0.35/0.65  thf(fact_7803_sum__diff__distrib,axiom,
% 0.35/0.65      ! [Q: nat > nat,P: nat > nat,N: nat] :
% 0.35/0.65        ( ! [X3: nat] : ( ord_less_eq_nat @ ( Q @ X3 ) @ ( P @ X3 ) )
% 0.35/0.65       => ( ( minus_minus_nat @ ( groups3542108847815614940at_nat @ P @ ( set_ord_lessThan_nat @ N ) ) @ ( groups3542108847815614940at_nat @ Q @ ( set_ord_lessThan_nat @ N ) ) )
% 0.35/0.65          = ( groups3542108847815614940at_nat
% 0.35/0.65            @ ^ [X2: nat] : ( minus_minus_nat @ ( P @ X2 ) @ ( Q @ X2 ) )
% 0.35/0.65            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum_diff_distrib
% 0.35/0.65  thf(fact_7804_powr__realpow,axiom,
% 0.35/0.65      ! [X: real,N: nat] :
% 0.35/0.65        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.65       => ( ( powr_real @ X @ ( semiri5074537144036343181t_real @ N ) )
% 0.35/0.65          = ( power_power_real @ X @ N ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powr_realpow
% 0.35/0.65  thf(fact_7805_less__log__iff,axiom,
% 0.35/0.65      ! [B: real,X: real,Y2: real] :
% 0.35/0.65        ( ( ord_less_real @ one_one_real @ B )
% 0.35/0.65       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.65         => ( ( ord_less_real @ Y2 @ ( log @ B @ X ) )
% 0.35/0.65            = ( ord_less_real @ ( powr_real @ B @ Y2 ) @ X ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % less_log_iff
% 0.35/0.65  thf(fact_7806_log__less__iff,axiom,
% 0.35/0.65      ! [B: real,X: real,Y2: real] :
% 0.35/0.65        ( ( ord_less_real @ one_one_real @ B )
% 0.35/0.65       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.65         => ( ( ord_less_real @ ( log @ B @ X ) @ Y2 )
% 0.35/0.65            = ( ord_less_real @ X @ ( powr_real @ B @ Y2 ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % log_less_iff
% 0.35/0.65  thf(fact_7807_less__powr__iff,axiom,
% 0.35/0.65      ! [B: real,X: real,Y2: real] :
% 0.35/0.65        ( ( ord_less_real @ one_one_real @ B )
% 0.35/0.65       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.65         => ( ( ord_less_real @ X @ ( powr_real @ B @ Y2 ) )
% 0.35/0.65            = ( ord_less_real @ ( log @ B @ X ) @ Y2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % less_powr_iff
% 0.35/0.65  thf(fact_7808_powr__less__iff,axiom,
% 0.35/0.65      ! [B: real,X: real,Y2: real] :
% 0.35/0.65        ( ( ord_less_real @ one_one_real @ B )
% 0.35/0.65       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.65         => ( ( ord_less_real @ ( powr_real @ B @ Y2 ) @ X )
% 0.35/0.65            = ( ord_less_real @ Y2 @ ( log @ B @ X ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powr_less_iff
% 0.35/0.65  thf(fact_7809_powser__inside,axiom,
% 0.35/0.65      ! [F: nat > real,X: real,Z: real] :
% 0.35/0.65        ( ( summable_real
% 0.35/0.65          @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ X @ N2 ) ) )
% 0.35/0.65       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ ( real_V7735802525324610683m_real @ X ) )
% 0.35/0.65         => ( summable_real
% 0.35/0.65            @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powser_inside
% 0.35/0.65  thf(fact_7810_powser__inside,axiom,
% 0.35/0.65      ! [F: nat > complex,X: complex,Z: complex] :
% 0.35/0.65        ( ( summable_complex
% 0.35/0.65          @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ X @ N2 ) ) )
% 0.35/0.65       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ ( real_V1022390504157884413omplex @ X ) )
% 0.35/0.65         => ( summable_complex
% 0.35/0.65            @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powser_inside
% 0.35/0.65  thf(fact_7811_pi__less__4,axiom,
% 0.35/0.65      ord_less_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % pi_less_4
% 0.35/0.65  thf(fact_7812_pi__ge__two,axiom,
% 0.35/0.65      ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ).
% 0.35/0.65  
% 0.35/0.65  % pi_ge_two
% 0.35/0.65  thf(fact_7813_pi__half__neq__two,axiom,
% 0.35/0.65      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.35/0.65     != ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % pi_half_neq_two
% 0.35/0.65  thf(fact_7814_sum__pos__lt__pair,axiom,
% 0.35/0.65      ! [F: nat > real,K: nat] :
% 0.35/0.65        ( ( summable_real @ F )
% 0.35/0.65       => ( ! [D3: nat] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( F @ ( plus_plus_nat @ K @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D3 ) ) ) @ ( F @ ( plus_plus_nat @ K @ ( plus_plus_nat @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D3 ) @ one_one_nat ) ) ) ) )
% 0.35/0.65         => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) @ ( suminf_real @ F ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum_pos_lt_pair
% 0.35/0.65  thf(fact_7815_powser__split__head_I1_J,axiom,
% 0.35/0.65      ! [F: nat > complex,Z: complex] :
% 0.35/0.65        ( ( summable_complex
% 0.35/0.65          @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) )
% 0.35/0.65       => ( ( suminf_complex
% 0.35/0.65            @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) )
% 0.35/0.65          = ( plus_plus_complex @ ( F @ zero_zero_nat )
% 0.35/0.65            @ ( times_times_complex
% 0.35/0.65              @ ( suminf_complex
% 0.35/0.65                @ ^ [N2: nat] : ( times_times_complex @ ( F @ ( suc @ N2 ) ) @ ( power_power_complex @ Z @ N2 ) ) )
% 0.35/0.65              @ Z ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powser_split_head(1)
% 0.35/0.65  thf(fact_7816_powser__split__head_I1_J,axiom,
% 0.35/0.65      ! [F: nat > real,Z: real] :
% 0.35/0.65        ( ( summable_real
% 0.35/0.65          @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) )
% 0.35/0.65       => ( ( suminf_real
% 0.35/0.65            @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) )
% 0.35/0.65          = ( plus_plus_real @ ( F @ zero_zero_nat )
% 0.35/0.65            @ ( times_times_real
% 0.35/0.65              @ ( suminf_real
% 0.35/0.65                @ ^ [N2: nat] : ( times_times_real @ ( F @ ( suc @ N2 ) ) @ ( power_power_real @ Z @ N2 ) ) )
% 0.35/0.65              @ Z ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powser_split_head(1)
% 0.35/0.65  thf(fact_7817_sum_OlessThan__Suc__shift,axiom,
% 0.35/0.65      ! [G: nat > rat,N: nat] :
% 0.35/0.65        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.35/0.65        = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 0.35/0.65          @ ( groups2906978787729119204at_rat
% 0.35/0.65            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.35/0.65            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum.lessThan_Suc_shift
% 0.35/0.65  thf(fact_7818_sum_OlessThan__Suc__shift,axiom,
% 0.35/0.65      ! [G: nat > int,N: nat] :
% 0.35/0.65        ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.35/0.65        = ( plus_plus_int @ ( G @ zero_zero_nat )
% 0.35/0.65          @ ( groups3539618377306564664at_int
% 0.35/0.65            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.35/0.65            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum.lessThan_Suc_shift
% 0.35/0.65  thf(fact_7819_sum_OlessThan__Suc__shift,axiom,
% 0.35/0.65      ! [G: nat > complex,N: nat] :
% 0.35/0.65        ( ( groups2073611262835488442omplex @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.35/0.65        = ( plus_plus_complex @ ( G @ zero_zero_nat )
% 0.35/0.65          @ ( groups2073611262835488442omplex
% 0.35/0.65            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.35/0.65            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum.lessThan_Suc_shift
% 0.35/0.65  thf(fact_7820_sum_OlessThan__Suc__shift,axiom,
% 0.35/0.65      ! [G: nat > nat,N: nat] :
% 0.35/0.65        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.35/0.65        = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 0.35/0.65          @ ( groups3542108847815614940at_nat
% 0.35/0.65            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.35/0.65            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum.lessThan_Suc_shift
% 0.35/0.65  thf(fact_7821_sum_OlessThan__Suc__shift,axiom,
% 0.35/0.65      ! [G: nat > real,N: nat] :
% 0.35/0.65        ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.35/0.65        = ( plus_plus_real @ ( G @ zero_zero_nat )
% 0.35/0.65          @ ( groups6591440286371151544t_real
% 0.35/0.65            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.35/0.65            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum.lessThan_Suc_shift
% 0.35/0.65  thf(fact_7822_powser__split__head_I2_J,axiom,
% 0.35/0.65      ! [F: nat > complex,Z: complex] :
% 0.35/0.65        ( ( summable_complex
% 0.35/0.65          @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) )
% 0.35/0.65       => ( ( times_times_complex
% 0.35/0.65            @ ( suminf_complex
% 0.35/0.65              @ ^ [N2: nat] : ( times_times_complex @ ( F @ ( suc @ N2 ) ) @ ( power_power_complex @ Z @ N2 ) ) )
% 0.35/0.65            @ Z )
% 0.35/0.65          = ( minus_minus_complex
% 0.35/0.65            @ ( suminf_complex
% 0.35/0.65              @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) )
% 0.35/0.65            @ ( F @ zero_zero_nat ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powser_split_head(2)
% 0.35/0.65  thf(fact_7823_powser__split__head_I2_J,axiom,
% 0.35/0.65      ! [F: nat > real,Z: real] :
% 0.35/0.65        ( ( summable_real
% 0.35/0.65          @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) )
% 0.35/0.65       => ( ( times_times_real
% 0.35/0.65            @ ( suminf_real
% 0.35/0.65              @ ^ [N2: nat] : ( times_times_real @ ( F @ ( suc @ N2 ) ) @ ( power_power_real @ Z @ N2 ) ) )
% 0.35/0.65            @ Z )
% 0.35/0.65          = ( minus_minus_real
% 0.35/0.65            @ ( suminf_real
% 0.35/0.65              @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) )
% 0.35/0.65            @ ( F @ zero_zero_nat ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powser_split_head(2)
% 0.35/0.65  thf(fact_7824_sum__lessThan__telescope_H,axiom,
% 0.35/0.65      ! [F: nat > rat,M: nat] :
% 0.35/0.65        ( ( groups2906978787729119204at_rat
% 0.35/0.65          @ ^ [N2: nat] : ( minus_minus_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.35/0.65          @ ( set_ord_lessThan_nat @ M ) )
% 0.35/0.65        = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum_lessThan_telescope'
% 0.35/0.65  thf(fact_7825_sum__lessThan__telescope_H,axiom,
% 0.35/0.65      ! [F: nat > int,M: nat] :
% 0.35/0.65        ( ( groups3539618377306564664at_int
% 0.35/0.65          @ ^ [N2: nat] : ( minus_minus_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.35/0.65          @ ( set_ord_lessThan_nat @ M ) )
% 0.35/0.65        = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum_lessThan_telescope'
% 0.35/0.65  thf(fact_7826_sum__lessThan__telescope_H,axiom,
% 0.35/0.65      ! [F: nat > real,M: nat] :
% 0.35/0.65        ( ( groups6591440286371151544t_real
% 0.35/0.65          @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.35/0.65          @ ( set_ord_lessThan_nat @ M ) )
% 0.35/0.65        = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum_lessThan_telescope'
% 0.35/0.65  thf(fact_7827_sum__lessThan__telescope,axiom,
% 0.35/0.65      ! [F: nat > rat,M: nat] :
% 0.35/0.65        ( ( groups2906978787729119204at_rat
% 0.35/0.65          @ ^ [N2: nat] : ( minus_minus_rat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 0.35/0.65          @ ( set_ord_lessThan_nat @ M ) )
% 0.35/0.65        = ( minus_minus_rat @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum_lessThan_telescope
% 0.35/0.65  thf(fact_7828_sum__lessThan__telescope,axiom,
% 0.35/0.65      ! [F: nat > int,M: nat] :
% 0.35/0.65        ( ( groups3539618377306564664at_int
% 0.35/0.65          @ ^ [N2: nat] : ( minus_minus_int @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 0.35/0.65          @ ( set_ord_lessThan_nat @ M ) )
% 0.35/0.65        = ( minus_minus_int @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum_lessThan_telescope
% 0.35/0.65  thf(fact_7829_sum__lessThan__telescope,axiom,
% 0.35/0.65      ! [F: nat > real,M: nat] :
% 0.35/0.65        ( ( groups6591440286371151544t_real
% 0.35/0.65          @ ^ [N2: nat] : ( minus_minus_real @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 0.35/0.65          @ ( set_ord_lessThan_nat @ M ) )
% 0.35/0.65        = ( minus_minus_real @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum_lessThan_telescope
% 0.35/0.65  thf(fact_7830_sumr__diff__mult__const2,axiom,
% 0.35/0.65      ! [F: nat > rat,N: nat,R: rat] :
% 0.35/0.65        ( ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ R ) )
% 0.35/0.65        = ( groups2906978787729119204at_rat
% 0.35/0.65          @ ^ [I3: nat] : ( minus_minus_rat @ ( F @ I3 ) @ R )
% 0.35/0.65          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sumr_diff_mult_const2
% 0.35/0.65  thf(fact_7831_sumr__diff__mult__const2,axiom,
% 0.35/0.65      ! [F: nat > int,N: nat,R: int] :
% 0.35/0.65        ( ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ R ) )
% 0.35/0.65        = ( groups3539618377306564664at_int
% 0.35/0.65          @ ^ [I3: nat] : ( minus_minus_int @ ( F @ I3 ) @ R )
% 0.35/0.65          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sumr_diff_mult_const2
% 0.35/0.65  thf(fact_7832_sumr__diff__mult__const2,axiom,
% 0.35/0.65      ! [F: nat > complex,N: nat,R: complex] :
% 0.35/0.65        ( ( minus_minus_complex @ ( groups2073611262835488442omplex @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ R ) )
% 0.35/0.65        = ( groups2073611262835488442omplex
% 0.35/0.65          @ ^ [I3: nat] : ( minus_minus_complex @ ( F @ I3 ) @ R )
% 0.35/0.65          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sumr_diff_mult_const2
% 0.35/0.65  thf(fact_7833_sumr__diff__mult__const2,axiom,
% 0.35/0.65      ! [F: nat > real,N: nat,R: real] :
% 0.35/0.65        ( ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ R ) )
% 0.35/0.65        = ( groups6591440286371151544t_real
% 0.35/0.65          @ ^ [I3: nat] : ( minus_minus_real @ ( F @ I3 ) @ R )
% 0.35/0.65          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sumr_diff_mult_const2
% 0.35/0.65  thf(fact_7834_sum_OatLeast1__atMost__eq,axiom,
% 0.35/0.65      ! [G: nat > nat,N: nat] :
% 0.35/0.65        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 0.35/0.65        = ( groups3542108847815614940at_nat
% 0.35/0.65          @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 0.35/0.65          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum.atLeast1_atMost_eq
% 0.35/0.65  thf(fact_7835_sum_OatLeast1__atMost__eq,axiom,
% 0.35/0.65      ! [G: nat > real,N: nat] :
% 0.35/0.65        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 0.35/0.65        = ( groups6591440286371151544t_real
% 0.35/0.65          @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 0.35/0.65          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum.atLeast1_atMost_eq
% 0.35/0.65  thf(fact_7836_suminf__exist__split,axiom,
% 0.35/0.65      ! [R: real,F: nat > real] :
% 0.35/0.65        ( ( ord_less_real @ zero_zero_real @ R )
% 0.35/0.65       => ( ( summable_real @ F )
% 0.35/0.65         => ? [N8: nat] :
% 0.35/0.65            ! [N9: nat] :
% 0.35/0.65              ( ( ord_less_eq_nat @ N8 @ N9 )
% 0.35/0.65             => ( ord_less_real
% 0.35/0.65                @ ( real_V7735802525324610683m_real
% 0.35/0.65                  @ ( suminf_real
% 0.35/0.65                    @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N9 ) ) ) )
% 0.35/0.65                @ R ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_exist_split
% 0.35/0.65  thf(fact_7837_suminf__exist__split,axiom,
% 0.35/0.65      ! [R: real,F: nat > complex] :
% 0.35/0.65        ( ( ord_less_real @ zero_zero_real @ R )
% 0.35/0.65       => ( ( summable_complex @ F )
% 0.35/0.65         => ? [N8: nat] :
% 0.35/0.65            ! [N9: nat] :
% 0.35/0.65              ( ( ord_less_eq_nat @ N8 @ N9 )
% 0.35/0.65             => ( ord_less_real
% 0.35/0.65                @ ( real_V1022390504157884413omplex
% 0.35/0.65                  @ ( suminf_complex
% 0.35/0.65                    @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N9 ) ) ) )
% 0.35/0.65                @ R ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % suminf_exist_split
% 0.35/0.65  thf(fact_7838_summable__partial__sum__bound,axiom,
% 0.35/0.65      ! [F: nat > complex,E: real] :
% 0.35/0.65        ( ( summable_complex @ F )
% 0.35/0.65       => ( ( ord_less_real @ zero_zero_real @ E )
% 0.35/0.65         => ~ ! [N8: nat] :
% 0.35/0.65                ~ ! [M5: nat] :
% 0.35/0.65                    ( ( ord_less_eq_nat @ N8 @ M5 )
% 0.35/0.65                   => ! [N9: nat] : ( ord_less_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ M5 @ N9 ) ) ) @ E ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_partial_sum_bound
% 0.35/0.65  thf(fact_7839_summable__partial__sum__bound,axiom,
% 0.35/0.65      ! [F: nat > real,E: real] :
% 0.35/0.65        ( ( summable_real @ F )
% 0.35/0.65       => ( ( ord_less_real @ zero_zero_real @ E )
% 0.35/0.65         => ~ ! [N8: nat] :
% 0.35/0.65                ~ ! [M5: nat] :
% 0.35/0.65                    ( ( ord_less_eq_nat @ N8 @ M5 )
% 0.35/0.65                   => ! [N9: nat] : ( ord_less_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ M5 @ N9 ) ) ) @ E ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_partial_sum_bound
% 0.35/0.65  thf(fact_7840_summable__power__series,axiom,
% 0.35/0.65      ! [F: nat > real,Z: real] :
% 0.35/0.65        ( ! [I4: nat] : ( ord_less_eq_real @ ( F @ I4 ) @ one_one_real )
% 0.35/0.65       => ( ! [I4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 0.35/0.65         => ( ( ord_less_eq_real @ zero_zero_real @ Z )
% 0.35/0.65           => ( ( ord_less_real @ Z @ one_one_real )
% 0.35/0.65             => ( summable_real
% 0.35/0.65                @ ^ [I3: nat] : ( times_times_real @ ( F @ I3 ) @ ( power_power_real @ Z @ I3 ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_power_series
% 0.35/0.65  thf(fact_7841_Abel__lemma,axiom,
% 0.35/0.65      ! [R: real,R0: real,A: nat > complex,M7: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ zero_zero_real @ R )
% 0.35/0.65       => ( ( ord_less_real @ R @ R0 )
% 0.35/0.65         => ( ! [N3: nat] : ( ord_less_eq_real @ ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N3 ) ) @ ( power_power_real @ R0 @ N3 ) ) @ M7 )
% 0.35/0.65           => ( summable_real
% 0.35/0.65              @ ^ [N2: nat] : ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N2 ) ) @ ( power_power_real @ R @ N2 ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % Abel_lemma
% 0.35/0.65  thf(fact_7842_powr__minus__divide,axiom,
% 0.35/0.65      ! [X: real,A: real] :
% 0.35/0.65        ( ( powr_real @ X @ ( uminus_uminus_real @ A ) )
% 0.35/0.65        = ( divide_divide_real @ one_one_real @ ( powr_real @ X @ A ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powr_minus_divide
% 0.35/0.65  thf(fact_7843_summable__ratio__test,axiom,
% 0.35/0.65      ! [C: real,N4: nat,F: nat > real] :
% 0.35/0.65        ( ( ord_less_real @ C @ one_one_real )
% 0.35/0.65       => ( ! [N3: nat] :
% 0.35/0.65              ( ( ord_less_eq_nat @ N4 @ N3 )
% 0.35/0.65             => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ ( suc @ N3 ) ) ) @ ( times_times_real @ C @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) ) ) )
% 0.35/0.65         => ( summable_real @ F ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_ratio_test
% 0.35/0.65  thf(fact_7844_summable__ratio__test,axiom,
% 0.35/0.65      ! [C: real,N4: nat,F: nat > complex] :
% 0.35/0.65        ( ( ord_less_real @ C @ one_one_real )
% 0.35/0.65       => ( ! [N3: nat] :
% 0.35/0.65              ( ( ord_less_eq_nat @ N4 @ N3 )
% 0.35/0.65             => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ ( suc @ N3 ) ) ) @ ( times_times_real @ C @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) ) ) )
% 0.35/0.65         => ( summable_complex @ F ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % summable_ratio_test
% 0.35/0.65  thf(fact_7845_powr__neg__one,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.65       => ( ( powr_real @ X @ ( uminus_uminus_real @ one_one_real ) )
% 0.35/0.65          = ( divide_divide_real @ one_one_real @ X ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powr_neg_one
% 0.35/0.65  thf(fact_7846_powr__mult__base,axiom,
% 0.35/0.65      ! [X: real,Y2: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.65       => ( ( times_times_real @ X @ ( powr_real @ X @ Y2 ) )
% 0.35/0.65          = ( powr_real @ X @ ( plus_plus_real @ one_one_real @ Y2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powr_mult_base
% 0.35/0.65  thf(fact_7847_le__log__iff,axiom,
% 0.35/0.65      ! [B: real,X: real,Y2: real] :
% 0.35/0.65        ( ( ord_less_real @ one_one_real @ B )
% 0.35/0.65       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.65         => ( ( ord_less_eq_real @ Y2 @ ( log @ B @ X ) )
% 0.35/0.65            = ( ord_less_eq_real @ ( powr_real @ B @ Y2 ) @ X ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % le_log_iff
% 0.35/0.65  thf(fact_7848_log__le__iff,axiom,
% 0.35/0.65      ! [B: real,X: real,Y2: real] :
% 0.35/0.65        ( ( ord_less_real @ one_one_real @ B )
% 0.35/0.65       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.65         => ( ( ord_less_eq_real @ ( log @ B @ X ) @ Y2 )
% 0.35/0.65            = ( ord_less_eq_real @ X @ ( powr_real @ B @ Y2 ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % log_le_iff
% 0.35/0.65  thf(fact_7849_le__powr__iff,axiom,
% 0.35/0.65      ! [B: real,X: real,Y2: real] :
% 0.35/0.65        ( ( ord_less_real @ one_one_real @ B )
% 0.35/0.65       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.65         => ( ( ord_less_eq_real @ X @ ( powr_real @ B @ Y2 ) )
% 0.35/0.65            = ( ord_less_eq_real @ ( log @ B @ X ) @ Y2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % le_powr_iff
% 0.35/0.65  thf(fact_7850_powr__le__iff,axiom,
% 0.35/0.65      ! [B: real,X: real,Y2: real] :
% 0.35/0.65        ( ( ord_less_real @ one_one_real @ B )
% 0.35/0.65       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.65         => ( ( ord_less_eq_real @ ( powr_real @ B @ Y2 ) @ X )
% 0.35/0.65            = ( ord_less_eq_real @ Y2 @ ( log @ B @ X ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powr_le_iff
% 0.35/0.65  thf(fact_7851_pi__half__neq__zero,axiom,
% 0.35/0.65      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.35/0.65     != zero_zero_real ) ).
% 0.35/0.65  
% 0.35/0.65  % pi_half_neq_zero
% 0.35/0.65  thf(fact_7852_pi__half__less__two,axiom,
% 0.35/0.65      ord_less_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 0.35/0.65  
% 0.35/0.65  % pi_half_less_two
% 0.35/0.65  thf(fact_7853_pi__half__le__two,axiom,
% 0.35/0.65      ord_less_eq_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 0.35/0.65  
% 0.35/0.65  % pi_half_le_two
% 0.35/0.65  thf(fact_7854_one__diff__power__eq,axiom,
% 0.35/0.65      ! [X: rat,N: nat] :
% 0.35/0.65        ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) )
% 0.35/0.65        = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % one_diff_power_eq
% 0.35/0.65  thf(fact_7855_one__diff__power__eq,axiom,
% 0.35/0.65      ! [X: complex,N: nat] :
% 0.35/0.65        ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N ) )
% 0.35/0.65        = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % one_diff_power_eq
% 0.35/0.65  thf(fact_7856_one__diff__power__eq,axiom,
% 0.35/0.65      ! [X: int,N: nat] :
% 0.35/0.65        ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N ) )
% 0.35/0.65        = ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % one_diff_power_eq
% 0.35/0.65  thf(fact_7857_one__diff__power__eq,axiom,
% 0.35/0.65      ! [X: real,N: nat] :
% 0.35/0.65        ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N ) )
% 0.35/0.65        = ( times_times_real @ ( minus_minus_real @ one_one_real @ X ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % one_diff_power_eq
% 0.35/0.65  thf(fact_7858_power__diff__1__eq,axiom,
% 0.35/0.65      ! [X: rat,N: nat] :
% 0.35/0.65        ( ( minus_minus_rat @ ( power_power_rat @ X @ N ) @ one_one_rat )
% 0.35/0.65        = ( times_times_rat @ ( minus_minus_rat @ X @ one_one_rat ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % power_diff_1_eq
% 0.35/0.65  thf(fact_7859_power__diff__1__eq,axiom,
% 0.35/0.65      ! [X: complex,N: nat] :
% 0.35/0.65        ( ( minus_minus_complex @ ( power_power_complex @ X @ N ) @ one_one_complex )
% 0.35/0.65        = ( times_times_complex @ ( minus_minus_complex @ X @ one_one_complex ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % power_diff_1_eq
% 0.35/0.65  thf(fact_7860_power__diff__1__eq,axiom,
% 0.35/0.65      ! [X: int,N: nat] :
% 0.35/0.65        ( ( minus_minus_int @ ( power_power_int @ X @ N ) @ one_one_int )
% 0.35/0.65        = ( times_times_int @ ( minus_minus_int @ X @ one_one_int ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % power_diff_1_eq
% 0.35/0.65  thf(fact_7861_power__diff__1__eq,axiom,
% 0.35/0.65      ! [X: real,N: nat] :
% 0.35/0.65        ( ( minus_minus_real @ ( power_power_real @ X @ N ) @ one_one_real )
% 0.35/0.65        = ( times_times_real @ ( minus_minus_real @ X @ one_one_real ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % power_diff_1_eq
% 0.35/0.65  thf(fact_7862_geometric__sum,axiom,
% 0.35/0.65      ! [X: complex,N: nat] :
% 0.35/0.65        ( ( X != one_one_complex )
% 0.35/0.65       => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.65          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X @ N ) @ one_one_complex ) @ ( minus_minus_complex @ X @ one_one_complex ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % geometric_sum
% 0.35/0.65  thf(fact_7863_geometric__sum,axiom,
% 0.35/0.65      ! [X: rat,N: nat] :
% 0.35/0.65        ( ( X != one_one_rat )
% 0.35/0.65       => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.65          = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ N ) @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % geometric_sum
% 0.35/0.65  thf(fact_7864_geometric__sum,axiom,
% 0.35/0.65      ! [X: real,N: nat] :
% 0.35/0.65        ( ( X != one_one_real )
% 0.35/0.65       => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.65          = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ N ) @ one_one_real ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % geometric_sum
% 0.35/0.65  thf(fact_7865_ln__powr__bound,axiom,
% 0.35/0.65      ! [X: real,A: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ one_one_real @ X )
% 0.35/0.65       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.65         => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( divide_divide_real @ ( powr_real @ X @ A ) @ A ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % ln_powr_bound
% 0.35/0.65  thf(fact_7866_ln__powr__bound2,axiom,
% 0.35/0.65      ! [X: real,A: real] :
% 0.35/0.65        ( ( ord_less_real @ one_one_real @ X )
% 0.35/0.65       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.65         => ( ord_less_eq_real @ ( powr_real @ ( ln_ln_real @ X ) @ A ) @ ( times_times_real @ ( powr_real @ A @ A ) @ X ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % ln_powr_bound2
% 0.35/0.65  thf(fact_7867_log__add__eq__powr,axiom,
% 0.35/0.65      ! [B: real,X: real,Y2: real] :
% 0.35/0.65        ( ( ord_less_real @ zero_zero_real @ B )
% 0.35/0.65       => ( ( B != one_one_real )
% 0.35/0.65         => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.65           => ( ( plus_plus_real @ ( log @ B @ X ) @ Y2 )
% 0.35/0.65              = ( log @ B @ ( times_times_real @ X @ ( powr_real @ B @ Y2 ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % log_add_eq_powr
% 0.35/0.65  thf(fact_7868_add__log__eq__powr,axiom,
% 0.35/0.65      ! [B: real,X: real,Y2: real] :
% 0.35/0.65        ( ( ord_less_real @ zero_zero_real @ B )
% 0.35/0.65       => ( ( B != one_one_real )
% 0.35/0.65         => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.65           => ( ( plus_plus_real @ Y2 @ ( log @ B @ X ) )
% 0.35/0.65              = ( log @ B @ ( times_times_real @ ( powr_real @ B @ Y2 ) @ X ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % add_log_eq_powr
% 0.35/0.65  thf(fact_7869_minus__log__eq__powr,axiom,
% 0.35/0.65      ! [B: real,X: real,Y2: real] :
% 0.35/0.65        ( ( ord_less_real @ zero_zero_real @ B )
% 0.35/0.65       => ( ( B != one_one_real )
% 0.35/0.65         => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.65           => ( ( minus_minus_real @ Y2 @ ( log @ B @ X ) )
% 0.35/0.65              = ( log @ B @ ( divide_divide_real @ ( powr_real @ B @ Y2 ) @ X ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % minus_log_eq_powr
% 0.35/0.65  thf(fact_7870_sum__gp__strict,axiom,
% 0.35/0.65      ! [X: rat,N: nat] :
% 0.35/0.65        ( ( ( X = one_one_rat )
% 0.35/0.65         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.65            = ( semiri681578069525770553at_rat @ N ) ) )
% 0.35/0.65        & ( ( X != one_one_rat )
% 0.35/0.65         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.65            = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum_gp_strict
% 0.35/0.65  thf(fact_7871_sum__gp__strict,axiom,
% 0.35/0.65      ! [X: complex,N: nat] :
% 0.35/0.65        ( ( ( X = one_one_complex )
% 0.35/0.65         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.65            = ( semiri8010041392384452111omplex @ N ) ) )
% 0.35/0.65        & ( ( X != one_one_complex )
% 0.35/0.65         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.65            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum_gp_strict
% 0.35/0.65  thf(fact_7872_sum__gp__strict,axiom,
% 0.35/0.65      ! [X: real,N: nat] :
% 0.35/0.65        ( ( ( X = one_one_real )
% 0.35/0.65         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.65            = ( semiri5074537144036343181t_real @ N ) ) )
% 0.35/0.65        & ( ( X != one_one_real )
% 0.35/0.65         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.65            = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum_gp_strict
% 0.35/0.65  thf(fact_7873_lemma__termdiff1,axiom,
% 0.35/0.65      ! [Z: rat,H2: rat,M: nat] :
% 0.35/0.65        ( ( groups2906978787729119204at_rat
% 0.35/0.65          @ ^ [P4: nat] : ( minus_minus_rat @ ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_rat @ Z @ P4 ) ) @ ( power_power_rat @ Z @ M ) )
% 0.35/0.65          @ ( set_ord_lessThan_nat @ M ) )
% 0.35/0.65        = ( groups2906978787729119204at_rat
% 0.35/0.65          @ ^ [P4: nat] : ( times_times_rat @ ( power_power_rat @ Z @ P4 ) @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ M @ P4 ) ) ) )
% 0.35/0.65          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % lemma_termdiff1
% 0.35/0.65  thf(fact_7874_lemma__termdiff1,axiom,
% 0.35/0.65      ! [Z: complex,H2: complex,M: nat] :
% 0.35/0.65        ( ( groups2073611262835488442omplex
% 0.35/0.65          @ ^ [P4: nat] : ( minus_minus_complex @ ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_complex @ Z @ P4 ) ) @ ( power_power_complex @ Z @ M ) )
% 0.35/0.65          @ ( set_ord_lessThan_nat @ M ) )
% 0.35/0.65        = ( groups2073611262835488442omplex
% 0.35/0.65          @ ^ [P4: nat] : ( times_times_complex @ ( power_power_complex @ Z @ P4 ) @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ M @ P4 ) ) ) )
% 0.35/0.65          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % lemma_termdiff1
% 0.35/0.65  thf(fact_7875_lemma__termdiff1,axiom,
% 0.35/0.65      ! [Z: int,H2: int,M: nat] :
% 0.35/0.65        ( ( groups3539618377306564664at_int
% 0.35/0.65          @ ^ [P4: nat] : ( minus_minus_int @ ( times_times_int @ ( power_power_int @ ( plus_plus_int @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_int @ Z @ P4 ) ) @ ( power_power_int @ Z @ M ) )
% 0.35/0.65          @ ( set_ord_lessThan_nat @ M ) )
% 0.35/0.65        = ( groups3539618377306564664at_int
% 0.35/0.65          @ ^ [P4: nat] : ( times_times_int @ ( power_power_int @ Z @ P4 ) @ ( minus_minus_int @ ( power_power_int @ ( plus_plus_int @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_int @ Z @ ( minus_minus_nat @ M @ P4 ) ) ) )
% 0.35/0.65          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % lemma_termdiff1
% 0.35/0.65  thf(fact_7876_lemma__termdiff1,axiom,
% 0.35/0.65      ! [Z: real,H2: real,M: nat] :
% 0.35/0.65        ( ( groups6591440286371151544t_real
% 0.35/0.65          @ ^ [P4: nat] : ( minus_minus_real @ ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_real @ Z @ P4 ) ) @ ( power_power_real @ Z @ M ) )
% 0.35/0.65          @ ( set_ord_lessThan_nat @ M ) )
% 0.35/0.65        = ( groups6591440286371151544t_real
% 0.35/0.65          @ ^ [P4: nat] : ( times_times_real @ ( power_power_real @ Z @ P4 ) @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_real @ Z @ ( minus_minus_nat @ M @ P4 ) ) ) )
% 0.35/0.65          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % lemma_termdiff1
% 0.35/0.65  thf(fact_7877_pi__half__gt__zero,axiom,
% 0.35/0.65      ord_less_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % pi_half_gt_zero
% 0.35/0.65  thf(fact_7878_pi__half__ge__zero,axiom,
% 0.35/0.65      ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % pi_half_ge_zero
% 0.35/0.65  thf(fact_7879_power__diff__sumr2,axiom,
% 0.35/0.65      ! [X: rat,N: nat,Y2: rat] :
% 0.35/0.65        ( ( minus_minus_rat @ ( power_power_rat @ X @ N ) @ ( power_power_rat @ Y2 @ N ) )
% 0.35/0.65        = ( times_times_rat @ ( minus_minus_rat @ X @ Y2 )
% 0.35/0.65          @ ( groups2906978787729119204at_rat
% 0.35/0.65            @ ^ [I3: nat] : ( times_times_rat @ ( power_power_rat @ Y2 @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) ) @ ( power_power_rat @ X @ I3 ) )
% 0.35/0.65            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % power_diff_sumr2
% 0.35/0.65  thf(fact_7880_power__diff__sumr2,axiom,
% 0.35/0.65      ! [X: complex,N: nat,Y2: complex] :
% 0.35/0.65        ( ( minus_minus_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y2 @ N ) )
% 0.35/0.65        = ( times_times_complex @ ( minus_minus_complex @ X @ Y2 )
% 0.35/0.65          @ ( groups2073611262835488442omplex
% 0.35/0.65            @ ^ [I3: nat] : ( times_times_complex @ ( power_power_complex @ Y2 @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) ) @ ( power_power_complex @ X @ I3 ) )
% 0.35/0.65            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % power_diff_sumr2
% 0.35/0.65  thf(fact_7881_power__diff__sumr2,axiom,
% 0.35/0.65      ! [X: int,N: nat,Y2: int] :
% 0.35/0.65        ( ( minus_minus_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y2 @ N ) )
% 0.35/0.65        = ( times_times_int @ ( minus_minus_int @ X @ Y2 )
% 0.35/0.65          @ ( groups3539618377306564664at_int
% 0.35/0.65            @ ^ [I3: nat] : ( times_times_int @ ( power_power_int @ Y2 @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) ) @ ( power_power_int @ X @ I3 ) )
% 0.35/0.65            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % power_diff_sumr2
% 0.35/0.65  thf(fact_7882_power__diff__sumr2,axiom,
% 0.35/0.65      ! [X: real,N: nat,Y2: real] :
% 0.35/0.65        ( ( minus_minus_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y2 @ N ) )
% 0.35/0.65        = ( times_times_real @ ( minus_minus_real @ X @ Y2 )
% 0.35/0.65          @ ( groups6591440286371151544t_real
% 0.35/0.65            @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ Y2 @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) ) @ ( power_power_real @ X @ I3 ) )
% 0.35/0.65            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % power_diff_sumr2
% 0.35/0.65  thf(fact_7883_diff__power__eq__sum,axiom,
% 0.35/0.65      ! [X: rat,N: nat,Y2: rat] :
% 0.35/0.65        ( ( minus_minus_rat @ ( power_power_rat @ X @ ( suc @ N ) ) @ ( power_power_rat @ Y2 @ ( suc @ N ) ) )
% 0.35/0.65        = ( times_times_rat @ ( minus_minus_rat @ X @ Y2 )
% 0.35/0.65          @ ( groups2906978787729119204at_rat
% 0.35/0.65            @ ^ [P4: nat] : ( times_times_rat @ ( power_power_rat @ X @ P4 ) @ ( power_power_rat @ Y2 @ ( minus_minus_nat @ N @ P4 ) ) )
% 0.35/0.65            @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % diff_power_eq_sum
% 0.35/0.65  thf(fact_7884_diff__power__eq__sum,axiom,
% 0.35/0.65      ! [X: complex,N: nat,Y2: complex] :
% 0.35/0.65        ( ( minus_minus_complex @ ( power_power_complex @ X @ ( suc @ N ) ) @ ( power_power_complex @ Y2 @ ( suc @ N ) ) )
% 0.35/0.65        = ( times_times_complex @ ( minus_minus_complex @ X @ Y2 )
% 0.35/0.65          @ ( groups2073611262835488442omplex
% 0.35/0.65            @ ^ [P4: nat] : ( times_times_complex @ ( power_power_complex @ X @ P4 ) @ ( power_power_complex @ Y2 @ ( minus_minus_nat @ N @ P4 ) ) )
% 0.35/0.65            @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % diff_power_eq_sum
% 0.35/0.65  thf(fact_7885_diff__power__eq__sum,axiom,
% 0.35/0.65      ! [X: int,N: nat,Y2: int] :
% 0.35/0.65        ( ( minus_minus_int @ ( power_power_int @ X @ ( suc @ N ) ) @ ( power_power_int @ Y2 @ ( suc @ N ) ) )
% 0.35/0.65        = ( times_times_int @ ( minus_minus_int @ X @ Y2 )
% 0.35/0.65          @ ( groups3539618377306564664at_int
% 0.35/0.65            @ ^ [P4: nat] : ( times_times_int @ ( power_power_int @ X @ P4 ) @ ( power_power_int @ Y2 @ ( minus_minus_nat @ N @ P4 ) ) )
% 0.35/0.65            @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % diff_power_eq_sum
% 0.35/0.65  thf(fact_7886_diff__power__eq__sum,axiom,
% 0.35/0.65      ! [X: real,N: nat,Y2: real] :
% 0.35/0.65        ( ( minus_minus_real @ ( power_power_real @ X @ ( suc @ N ) ) @ ( power_power_real @ Y2 @ ( suc @ N ) ) )
% 0.35/0.65        = ( times_times_real @ ( minus_minus_real @ X @ Y2 )
% 0.35/0.65          @ ( groups6591440286371151544t_real
% 0.35/0.65            @ ^ [P4: nat] : ( times_times_real @ ( power_power_real @ X @ P4 ) @ ( power_power_real @ Y2 @ ( minus_minus_nat @ N @ P4 ) ) )
% 0.35/0.65            @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % diff_power_eq_sum
% 0.35/0.65  thf(fact_7887_m2pi__less__pi,axiom,
% 0.35/0.65      ord_less_real @ ( uminus_uminus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) @ pi ).
% 0.35/0.65  
% 0.35/0.65  % m2pi_less_pi
% 0.35/0.65  thf(fact_7888_powr__def,axiom,
% 0.35/0.65      ( powr_real
% 0.35/0.65      = ( ^ [X2: real,A3: real] : ( if_real @ ( X2 = zero_zero_real ) @ zero_zero_real @ ( exp_real @ ( times_times_real @ A3 @ ( ln_ln_real @ X2 ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powr_def
% 0.35/0.65  thf(fact_7889_arctan__ubound,axiom,
% 0.35/0.65      ! [Y2: real] : ( ord_less_real @ ( arctan @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % arctan_ubound
% 0.35/0.65  thf(fact_7890_arctan__one,axiom,
% 0.35/0.65      ( ( arctan @ one_one_real )
% 0.35/0.65      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % arctan_one
% 0.35/0.65  thf(fact_7891_real__sum__nat__ivl__bounded2,axiom,
% 0.35/0.65      ! [N: nat,F: nat > rat,K5: rat,K: nat] :
% 0.35/0.65        ( ! [P7: nat] :
% 0.35/0.65            ( ( ord_less_nat @ P7 @ N )
% 0.35/0.65           => ( ord_less_eq_rat @ ( F @ P7 ) @ K5 ) )
% 0.35/0.65       => ( ( ord_less_eq_rat @ zero_zero_rat @ K5 )
% 0.35/0.65         => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ K5 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % real_sum_nat_ivl_bounded2
% 0.35/0.65  thf(fact_7892_real__sum__nat__ivl__bounded2,axiom,
% 0.35/0.65      ! [N: nat,F: nat > int,K5: int,K: nat] :
% 0.35/0.65        ( ! [P7: nat] :
% 0.35/0.65            ( ( ord_less_nat @ P7 @ N )
% 0.35/0.65           => ( ord_less_eq_int @ ( F @ P7 ) @ K5 ) )
% 0.35/0.65       => ( ( ord_less_eq_int @ zero_zero_int @ K5 )
% 0.35/0.65         => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ K5 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % real_sum_nat_ivl_bounded2
% 0.35/0.65  thf(fact_7893_real__sum__nat__ivl__bounded2,axiom,
% 0.35/0.65      ! [N: nat,F: nat > nat,K5: nat,K: nat] :
% 0.35/0.65        ( ! [P7: nat] :
% 0.35/0.65            ( ( ord_less_nat @ P7 @ N )
% 0.35/0.65           => ( ord_less_eq_nat @ ( F @ P7 ) @ K5 ) )
% 0.35/0.65       => ( ( ord_less_eq_nat @ zero_zero_nat @ K5 )
% 0.35/0.65         => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ K5 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % real_sum_nat_ivl_bounded2
% 0.35/0.65  thf(fact_7894_real__sum__nat__ivl__bounded2,axiom,
% 0.35/0.65      ! [N: nat,F: nat > real,K5: real,K: nat] :
% 0.35/0.65        ( ! [P7: nat] :
% 0.35/0.65            ( ( ord_less_nat @ P7 @ N )
% 0.35/0.65           => ( ord_less_eq_real @ ( F @ P7 ) @ K5 ) )
% 0.35/0.65       => ( ( ord_less_eq_real @ zero_zero_real @ K5 )
% 0.35/0.65         => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ K5 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % real_sum_nat_ivl_bounded2
% 0.35/0.65  thf(fact_7895_log__minus__eq__powr,axiom,
% 0.35/0.65      ! [B: real,X: real,Y2: real] :
% 0.35/0.65        ( ( ord_less_real @ zero_zero_real @ B )
% 0.35/0.65       => ( ( B != one_one_real )
% 0.35/0.65         => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.65           => ( ( minus_minus_real @ ( log @ B @ X ) @ Y2 )
% 0.35/0.65              = ( log @ B @ ( times_times_real @ X @ ( powr_real @ B @ ( uminus_uminus_real @ Y2 ) ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % log_minus_eq_powr
% 0.35/0.65  thf(fact_7896_one__diff__power__eq_H,axiom,
% 0.35/0.65      ! [X: rat,N: nat] :
% 0.35/0.65        ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) )
% 0.35/0.65        = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X )
% 0.35/0.65          @ ( groups2906978787729119204at_rat
% 0.35/0.65            @ ^ [I3: nat] : ( power_power_rat @ X @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 0.35/0.65            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % one_diff_power_eq'
% 0.35/0.65  thf(fact_7897_one__diff__power__eq_H,axiom,
% 0.35/0.65      ! [X: complex,N: nat] :
% 0.35/0.65        ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N ) )
% 0.35/0.65        = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X )
% 0.35/0.65          @ ( groups2073611262835488442omplex
% 0.35/0.65            @ ^ [I3: nat] : ( power_power_complex @ X @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 0.35/0.65            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % one_diff_power_eq'
% 0.35/0.65  thf(fact_7898_one__diff__power__eq_H,axiom,
% 0.35/0.65      ! [X: int,N: nat] :
% 0.35/0.65        ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N ) )
% 0.35/0.65        = ( times_times_int @ ( minus_minus_int @ one_one_int @ X )
% 0.35/0.65          @ ( groups3539618377306564664at_int
% 0.35/0.65            @ ^ [I3: nat] : ( power_power_int @ X @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 0.35/0.65            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % one_diff_power_eq'
% 0.35/0.65  thf(fact_7899_one__diff__power__eq_H,axiom,
% 0.35/0.65      ! [X: real,N: nat] :
% 0.35/0.65        ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N ) )
% 0.35/0.65        = ( times_times_real @ ( minus_minus_real @ one_one_real @ X )
% 0.35/0.65          @ ( groups6591440286371151544t_real
% 0.35/0.65            @ ^ [I3: nat] : ( power_power_real @ X @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 0.35/0.65            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % one_diff_power_eq'
% 0.35/0.65  thf(fact_7900_minus__pi__half__less__zero,axiom,
% 0.35/0.65      ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ zero_zero_real ).
% 0.35/0.65  
% 0.35/0.65  % minus_pi_half_less_zero
% 0.35/0.65  thf(fact_7901_arctan__lbound,axiom,
% 0.35/0.65      ! [Y2: real] : ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y2 ) ) ).
% 0.35/0.65  
% 0.35/0.65  % arctan_lbound
% 0.35/0.65  thf(fact_7902_arctan__bounded,axiom,
% 0.35/0.65      ! [Y2: real] :
% 0.35/0.65        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y2 ) )
% 0.35/0.65        & ( ord_less_real @ ( arctan @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % arctan_bounded
% 0.35/0.65  thf(fact_7903_powr__half__sqrt,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.65       => ( ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.65          = ( sqrt @ X ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powr_half_sqrt
% 0.35/0.65  thf(fact_7904_powr__neg__numeral,axiom,
% 0.35/0.65      ! [X: real,N: num] :
% 0.35/0.65        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.65       => ( ( powr_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.35/0.65          = ( divide_divide_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ N ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % powr_neg_numeral
% 0.35/0.65  thf(fact_7905_sum__split__even__odd,axiom,
% 0.35/0.65      ! [F: nat > real,G: nat > real,N: nat] :
% 0.35/0.65        ( ( groups6591440286371151544t_real
% 0.35/0.65          @ ^ [I3: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( F @ I3 ) @ ( G @ I3 ) )
% 0.35/0.65          @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.65        = ( plus_plus_real
% 0.35/0.65          @ ( groups6591440286371151544t_real
% 0.35/0.65            @ ^ [I3: nat] : ( F @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) )
% 0.35/0.65            @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.65          @ ( groups6591440286371151544t_real
% 0.35/0.65            @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ one_one_nat ) )
% 0.35/0.65            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum_split_even_odd
% 0.35/0.65  thf(fact_7906_machin__Euler,axiom,
% 0.35/0.65      ( ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ one ) ) ) @ ( arctan @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.35/0.65      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % machin_Euler
% 0.35/0.65  thf(fact_7907_machin,axiom,
% 0.35/0.65      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.35/0.65      = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( arctan @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( arctan @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % machin
% 0.35/0.65  thf(fact_7908_sum__bounds__lt__plus1,axiom,
% 0.35/0.65      ! [F: nat > nat,Mm: nat] :
% 0.35/0.65        ( ( groups3542108847815614940at_nat
% 0.35/0.65          @ ^ [K3: nat] : ( F @ ( suc @ K3 ) )
% 0.35/0.65          @ ( set_ord_lessThan_nat @ Mm ) )
% 0.35/0.65        = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum_bounds_lt_plus1
% 0.35/0.65  thf(fact_7909_sum__bounds__lt__plus1,axiom,
% 0.35/0.65      ! [F: nat > real,Mm: nat] :
% 0.35/0.65        ( ( groups6591440286371151544t_real
% 0.35/0.65          @ ^ [K3: nat] : ( F @ ( suc @ K3 ) )
% 0.35/0.65          @ ( set_ord_lessThan_nat @ Mm ) )
% 0.35/0.65        = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sum_bounds_lt_plus1
% 0.35/0.65  thf(fact_7910_sin__cos__npi,axiom,
% 0.35/0.65      ! [N: nat] :
% 0.35/0.65        ( ( sin_real @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.65        = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_cos_npi
% 0.35/0.65  thf(fact_7911_sumr__cos__zero__one,axiom,
% 0.35/0.65      ! [N: nat] :
% 0.35/0.65        ( ( groups6591440286371151544t_real
% 0.35/0.65          @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ zero_zero_real @ M6 ) )
% 0.35/0.65          @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.35/0.65        = one_one_real ) ).
% 0.35/0.65  
% 0.35/0.65  % sumr_cos_zero_one
% 0.35/0.65  thf(fact_7912_cos__pi__eq__zero,axiom,
% 0.35/0.65      ! [M: nat] :
% 0.35/0.65        ( ( cos_real @ ( divide_divide_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.65        = zero_zero_real ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_pi_eq_zero
% 0.35/0.65  thf(fact_7913_arcosh__def,axiom,
% 0.35/0.65      ( arcosh_real
% 0.35/0.65      = ( ^ [X2: real] : ( ln_ln_real @ ( plus_plus_real @ X2 @ ( powr_real @ ( minus_minus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( real_V1803761363581548252l_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % arcosh_def
% 0.35/0.65  thf(fact_7914_cos__zero,axiom,
% 0.35/0.65      ( ( cos_complex @ zero_zero_complex )
% 0.35/0.65      = one_one_complex ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_zero
% 0.35/0.65  thf(fact_7915_cos__zero,axiom,
% 0.35/0.65      ( ( cos_real @ zero_zero_real )
% 0.35/0.65      = one_one_real ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_zero
% 0.35/0.65  thf(fact_7916_of__real__eq__1__iff,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ( real_V1803761363581548252l_real @ X )
% 0.35/0.65          = one_one_real )
% 0.35/0.65        = ( X = one_one_real ) ) ).
% 0.35/0.65  
% 0.35/0.65  % of_real_eq_1_iff
% 0.35/0.65  thf(fact_7917_of__real__eq__1__iff,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ( real_V4546457046886955230omplex @ X )
% 0.35/0.65          = one_one_complex )
% 0.35/0.65        = ( X = one_one_real ) ) ).
% 0.35/0.65  
% 0.35/0.65  % of_real_eq_1_iff
% 0.35/0.65  thf(fact_7918_of__real__1,axiom,
% 0.35/0.65      ( ( real_V1803761363581548252l_real @ one_one_real )
% 0.35/0.65      = one_one_real ) ).
% 0.35/0.65  
% 0.35/0.65  % of_real_1
% 0.35/0.65  thf(fact_7919_of__real__1,axiom,
% 0.35/0.65      ( ( real_V4546457046886955230omplex @ one_one_real )
% 0.35/0.65      = one_one_complex ) ).
% 0.35/0.65  
% 0.35/0.65  % of_real_1
% 0.35/0.65  thf(fact_7920_of__real__numeral,axiom,
% 0.35/0.65      ! [W: num] :
% 0.35/0.65        ( ( real_V1803761363581548252l_real @ ( numeral_numeral_real @ W ) )
% 0.35/0.65        = ( numeral_numeral_real @ W ) ) ).
% 0.35/0.65  
% 0.35/0.65  % of_real_numeral
% 0.35/0.65  thf(fact_7921_of__real__numeral,axiom,
% 0.35/0.65      ! [W: num] :
% 0.35/0.65        ( ( real_V4546457046886955230omplex @ ( numeral_numeral_real @ W ) )
% 0.35/0.65        = ( numera6690914467698888265omplex @ W ) ) ).
% 0.35/0.65  
% 0.35/0.65  % of_real_numeral
% 0.35/0.65  thf(fact_7922_of__real__mult,axiom,
% 0.35/0.65      ! [X: real,Y2: real] :
% 0.35/0.65        ( ( real_V1803761363581548252l_real @ ( times_times_real @ X @ Y2 ) )
% 0.35/0.65        = ( times_times_real @ ( real_V1803761363581548252l_real @ X ) @ ( real_V1803761363581548252l_real @ Y2 ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % of_real_mult
% 0.35/0.65  thf(fact_7923_of__real__mult,axiom,
% 0.35/0.65      ! [X: real,Y2: real] :
% 0.35/0.65        ( ( real_V4546457046886955230omplex @ ( times_times_real @ X @ Y2 ) )
% 0.35/0.65        = ( times_times_complex @ ( real_V4546457046886955230omplex @ X ) @ ( real_V4546457046886955230omplex @ Y2 ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % of_real_mult
% 0.35/0.65  thf(fact_7924_of__real__divide,axiom,
% 0.35/0.65      ! [X: real,Y2: real] :
% 0.35/0.65        ( ( real_V1803761363581548252l_real @ ( divide_divide_real @ X @ Y2 ) )
% 0.35/0.65        = ( divide_divide_real @ ( real_V1803761363581548252l_real @ X ) @ ( real_V1803761363581548252l_real @ Y2 ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % of_real_divide
% 0.35/0.65  thf(fact_7925_of__real__divide,axiom,
% 0.35/0.65      ! [X: real,Y2: real] :
% 0.35/0.65        ( ( real_V4546457046886955230omplex @ ( divide_divide_real @ X @ Y2 ) )
% 0.35/0.65        = ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ X ) @ ( real_V4546457046886955230omplex @ Y2 ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % of_real_divide
% 0.35/0.65  thf(fact_7926_of__real__add,axiom,
% 0.35/0.65      ! [X: real,Y2: real] :
% 0.35/0.65        ( ( real_V1803761363581548252l_real @ ( plus_plus_real @ X @ Y2 ) )
% 0.35/0.65        = ( plus_plus_real @ ( real_V1803761363581548252l_real @ X ) @ ( real_V1803761363581548252l_real @ Y2 ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % of_real_add
% 0.35/0.65  thf(fact_7927_of__real__add,axiom,
% 0.35/0.65      ! [X: real,Y2: real] :
% 0.35/0.65        ( ( real_V4546457046886955230omplex @ ( plus_plus_real @ X @ Y2 ) )
% 0.35/0.65        = ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X ) @ ( real_V4546457046886955230omplex @ Y2 ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % of_real_add
% 0.35/0.65  thf(fact_7928_of__real__power,axiom,
% 0.35/0.65      ! [X: real,N: nat] :
% 0.35/0.65        ( ( real_V1803761363581548252l_real @ ( power_power_real @ X @ N ) )
% 0.35/0.65        = ( power_power_real @ ( real_V1803761363581548252l_real @ X ) @ N ) ) ).
% 0.35/0.65  
% 0.35/0.65  % of_real_power
% 0.35/0.65  thf(fact_7929_of__real__power,axiom,
% 0.35/0.65      ! [X: real,N: nat] :
% 0.35/0.65        ( ( real_V4546457046886955230omplex @ ( power_power_real @ X @ N ) )
% 0.35/0.65        = ( power_power_complex @ ( real_V4546457046886955230omplex @ X ) @ N ) ) ).
% 0.35/0.65  
% 0.35/0.65  % of_real_power
% 0.35/0.65  thf(fact_7930_of__real__diff,axiom,
% 0.35/0.65      ! [X: real,Y2: real] :
% 0.35/0.65        ( ( real_V4546457046886955230omplex @ ( minus_minus_real @ X @ Y2 ) )
% 0.35/0.65        = ( minus_minus_complex @ ( real_V4546457046886955230omplex @ X ) @ ( real_V4546457046886955230omplex @ Y2 ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % of_real_diff
% 0.35/0.65  thf(fact_7931_sin__pi__minus,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( sin_real @ ( minus_minus_real @ pi @ X ) )
% 0.35/0.65        = ( sin_real @ X ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_pi_minus
% 0.35/0.65  thf(fact_7932_cos__coeff__0,axiom,
% 0.35/0.65      ( ( cos_coeff @ zero_zero_nat )
% 0.35/0.65      = one_one_real ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_coeff_0
% 0.35/0.65  thf(fact_7933_cos__pi,axiom,
% 0.35/0.65      ( ( cos_real @ pi )
% 0.35/0.65      = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_pi
% 0.35/0.65  thf(fact_7934_cos__periodic__pi,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( cos_real @ ( plus_plus_real @ X @ pi ) )
% 0.35/0.65        = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_periodic_pi
% 0.35/0.65  thf(fact_7935_cos__periodic__pi2,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( cos_real @ ( plus_plus_real @ pi @ X ) )
% 0.35/0.65        = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_periodic_pi2
% 0.35/0.65  thf(fact_7936_sin__periodic__pi,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( sin_real @ ( plus_plus_real @ X @ pi ) )
% 0.35/0.65        = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_periodic_pi
% 0.35/0.65  thf(fact_7937_sin__periodic__pi2,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( sin_real @ ( plus_plus_real @ pi @ X ) )
% 0.35/0.65        = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_periodic_pi2
% 0.35/0.65  thf(fact_7938_cos__minus__pi,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( cos_real @ ( minus_minus_real @ X @ pi ) )
% 0.35/0.65        = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_minus_pi
% 0.35/0.65  thf(fact_7939_cos__pi__minus,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( cos_real @ ( minus_minus_real @ pi @ X ) )
% 0.35/0.65        = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_pi_minus
% 0.35/0.65  thf(fact_7940_sin__minus__pi,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( sin_real @ ( minus_minus_real @ X @ pi ) )
% 0.35/0.65        = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_minus_pi
% 0.35/0.65  thf(fact_7941_sin__cos__squared__add3,axiom,
% 0.35/0.65      ! [X: complex] :
% 0.35/0.65        ( ( plus_plus_complex @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ X ) ) @ ( times_times_complex @ ( sin_complex @ X ) @ ( sin_complex @ X ) ) )
% 0.35/0.65        = one_one_complex ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_cos_squared_add3
% 0.35/0.65  thf(fact_7942_sin__cos__squared__add3,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( plus_plus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ X ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ X ) ) )
% 0.35/0.65        = one_one_real ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_cos_squared_add3
% 0.35/0.65  thf(fact_7943_of__real__neg__numeral,axiom,
% 0.35/0.65      ! [W: num] :
% 0.35/0.65        ( ( real_V1803761363581548252l_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 0.35/0.65        = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % of_real_neg_numeral
% 0.35/0.65  thf(fact_7944_of__real__neg__numeral,axiom,
% 0.35/0.65      ! [W: num] :
% 0.35/0.65        ( ( real_V4546457046886955230omplex @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 0.35/0.65        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % of_real_neg_numeral
% 0.35/0.65  thf(fact_7945_cos__of__real__pi,axiom,
% 0.35/0.65      ( ( cos_real @ ( real_V1803761363581548252l_real @ pi ) )
% 0.35/0.65      = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_of_real_pi
% 0.35/0.65  thf(fact_7946_cos__of__real__pi,axiom,
% 0.35/0.65      ( ( cos_complex @ ( real_V4546457046886955230omplex @ pi ) )
% 0.35/0.65      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_of_real_pi
% 0.35/0.65  thf(fact_7947_sin__npi2,axiom,
% 0.35/0.65      ! [N: nat] :
% 0.35/0.65        ( ( sin_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 0.35/0.65        = zero_zero_real ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_npi2
% 0.35/0.65  thf(fact_7948_sin__npi,axiom,
% 0.35/0.65      ! [N: nat] :
% 0.35/0.65        ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 0.35/0.65        = zero_zero_real ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_npi
% 0.35/0.65  thf(fact_7949_sin__npi__int,axiom,
% 0.35/0.65      ! [N: int] :
% 0.35/0.65        ( ( sin_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 0.35/0.65        = zero_zero_real ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_npi_int
% 0.35/0.65  thf(fact_7950_cos__pi__half,axiom,
% 0.35/0.65      ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.65      = zero_zero_real ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_pi_half
% 0.35/0.65  thf(fact_7951_sin__two__pi,axiom,
% 0.35/0.65      ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.35/0.65      = zero_zero_real ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_two_pi
% 0.35/0.65  thf(fact_7952_sin__pi__half,axiom,
% 0.35/0.65      ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.65      = one_one_real ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_pi_half
% 0.35/0.65  thf(fact_7953_cos__two__pi,axiom,
% 0.35/0.65      ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.35/0.65      = one_one_real ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_two_pi
% 0.35/0.65  thf(fact_7954_norm__of__real__add1,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ X ) @ one_one_real ) )
% 0.35/0.65        = ( abs_abs_real @ ( plus_plus_real @ X @ one_one_real ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_of_real_add1
% 0.35/0.65  thf(fact_7955_norm__of__real__add1,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X ) @ one_one_complex ) )
% 0.35/0.65        = ( abs_abs_real @ ( plus_plus_real @ X @ one_one_real ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_of_real_add1
% 0.35/0.65  thf(fact_7956_norm__of__real__addn,axiom,
% 0.35/0.65      ! [X: real,B: num] :
% 0.35/0.65        ( ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ X ) @ ( numeral_numeral_real @ B ) ) )
% 0.35/0.65        = ( abs_abs_real @ ( plus_plus_real @ X @ ( numeral_numeral_real @ B ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_of_real_addn
% 0.35/0.65  thf(fact_7957_norm__of__real__addn,axiom,
% 0.35/0.65      ! [X: real,B: num] :
% 0.35/0.65        ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X ) @ ( numera6690914467698888265omplex @ B ) ) )
% 0.35/0.65        = ( abs_abs_real @ ( plus_plus_real @ X @ ( numeral_numeral_real @ B ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_of_real_addn
% 0.35/0.65  thf(fact_7958_cos__periodic,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( cos_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 0.35/0.65        = ( cos_real @ X ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_periodic
% 0.35/0.65  thf(fact_7959_sin__periodic,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( sin_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 0.35/0.65        = ( sin_real @ X ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_periodic
% 0.35/0.65  thf(fact_7960_cos__2pi__minus,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( cos_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X ) )
% 0.35/0.65        = ( cos_real @ X ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_2pi_minus
% 0.35/0.65  thf(fact_7961_cos__npi,axiom,
% 0.35/0.65      ! [N: nat] :
% 0.35/0.65        ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 0.35/0.65        = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_npi
% 0.35/0.65  thf(fact_7962_cos__npi2,axiom,
% 0.35/0.65      ! [N: nat] :
% 0.35/0.65        ( ( cos_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 0.35/0.65        = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_npi2
% 0.35/0.65  thf(fact_7963_sin__cos__squared__add2,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( plus_plus_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.65        = one_one_real ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_cos_squared_add2
% 0.35/0.65  thf(fact_7964_sin__cos__squared__add2,axiom,
% 0.35/0.65      ! [X: complex] :
% 0.35/0.65        ( ( plus_plus_complex @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.65        = one_one_complex ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_cos_squared_add2
% 0.35/0.65  thf(fact_7965_sin__cos__squared__add,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( plus_plus_real @ ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.65        = one_one_real ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_cos_squared_add
% 0.35/0.65  thf(fact_7966_sin__cos__squared__add,axiom,
% 0.35/0.65      ! [X: complex] :
% 0.35/0.65        ( ( plus_plus_complex @ ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.65        = one_one_complex ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_cos_squared_add
% 0.35/0.65  thf(fact_7967_cos__of__real__pi__half,axiom,
% 0.35/0.65      ( ( cos_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.65      = zero_zero_real ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_of_real_pi_half
% 0.35/0.65  thf(fact_7968_cos__of__real__pi__half,axiom,
% 0.35/0.65      ( ( cos_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 0.35/0.65      = zero_zero_complex ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_of_real_pi_half
% 0.35/0.65  thf(fact_7969_sin__of__real__pi__half,axiom,
% 0.35/0.65      ( ( sin_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.65      = one_one_real ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_of_real_pi_half
% 0.35/0.65  thf(fact_7970_sin__of__real__pi__half,axiom,
% 0.35/0.65      ( ( sin_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 0.35/0.65      = one_one_complex ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_of_real_pi_half
% 0.35/0.65  thf(fact_7971_sin__2npi,axiom,
% 0.35/0.65      ! [N: nat] :
% 0.35/0.65        ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 0.35/0.65        = zero_zero_real ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_2npi
% 0.35/0.65  thf(fact_7972_cos__2npi,axiom,
% 0.35/0.65      ! [N: nat] :
% 0.35/0.65        ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 0.35/0.65        = one_one_real ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_2npi
% 0.35/0.65  thf(fact_7973_sin__2pi__minus,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( sin_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X ) )
% 0.35/0.65        = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_2pi_minus
% 0.35/0.65  thf(fact_7974_sin__int__2pin,axiom,
% 0.35/0.65      ! [N: int] :
% 0.35/0.65        ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 0.35/0.65        = zero_zero_real ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_int_2pin
% 0.35/0.65  thf(fact_7975_cos__int__2pin,axiom,
% 0.35/0.65      ! [N: int] :
% 0.35/0.65        ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 0.35/0.65        = one_one_real ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_int_2pin
% 0.35/0.65  thf(fact_7976_cos__3over2__pi,axiom,
% 0.35/0.65      ( ( cos_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 0.35/0.65      = zero_zero_real ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_3over2_pi
% 0.35/0.65  thf(fact_7977_sin__3over2__pi,axiom,
% 0.35/0.65      ( ( sin_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 0.35/0.65      = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_3over2_pi
% 0.35/0.65  thf(fact_7978_cos__npi__int,axiom,
% 0.35/0.65      ! [N: int] :
% 0.35/0.65        ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 0.35/0.65         => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 0.35/0.65            = one_one_real ) )
% 0.35/0.65        & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 0.35/0.65         => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 0.35/0.65            = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_npi_int
% 0.35/0.65  thf(fact_7979_sin__diff,axiom,
% 0.35/0.65      ! [X: complex,Y2: complex] :
% 0.35/0.65        ( ( sin_complex @ ( minus_minus_complex @ X @ Y2 ) )
% 0.35/0.65        = ( minus_minus_complex @ ( times_times_complex @ ( sin_complex @ X ) @ ( cos_complex @ Y2 ) ) @ ( times_times_complex @ ( cos_complex @ X ) @ ( sin_complex @ Y2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_diff
% 0.35/0.65  thf(fact_7980_sin__diff,axiom,
% 0.35/0.65      ! [X: real,Y2: real] :
% 0.35/0.65        ( ( sin_real @ ( minus_minus_real @ X @ Y2 ) )
% 0.35/0.65        = ( minus_minus_real @ ( times_times_real @ ( sin_real @ X ) @ ( cos_real @ Y2 ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( sin_real @ Y2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_diff
% 0.35/0.65  thf(fact_7981_polar__Ex,axiom,
% 0.35/0.65      ! [X: real,Y2: real] :
% 0.35/0.65      ? [R3: real,A4: real] :
% 0.35/0.65        ( ( X
% 0.35/0.65          = ( times_times_real @ R3 @ ( cos_real @ A4 ) ) )
% 0.35/0.65        & ( Y2
% 0.35/0.65          = ( times_times_real @ R3 @ ( sin_real @ A4 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % polar_Ex
% 0.35/0.65  thf(fact_7982_cos__one__sin__zero,axiom,
% 0.35/0.65      ! [X: complex] :
% 0.35/0.65        ( ( ( cos_complex @ X )
% 0.35/0.65          = one_one_complex )
% 0.35/0.65       => ( ( sin_complex @ X )
% 0.35/0.65          = zero_zero_complex ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_one_sin_zero
% 0.35/0.65  thf(fact_7983_cos__one__sin__zero,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ( cos_real @ X )
% 0.35/0.65          = one_one_real )
% 0.35/0.65       => ( ( sin_real @ X )
% 0.35/0.65          = zero_zero_real ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_one_sin_zero
% 0.35/0.65  thf(fact_7984_cos__int__times__real,axiom,
% 0.35/0.65      ! [M: int,X: real] :
% 0.35/0.65        ( ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ ( real_V1803761363581548252l_real @ X ) ) )
% 0.35/0.65        = ( real_V1803761363581548252l_real @ ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_int_times_real
% 0.35/0.65  thf(fact_7985_cos__int__times__real,axiom,
% 0.35/0.65      ! [M: int,X: real] :
% 0.35/0.65        ( ( cos_complex @ ( times_times_complex @ ( ring_17405671764205052669omplex @ M ) @ ( real_V4546457046886955230omplex @ X ) ) )
% 0.35/0.65        = ( real_V4546457046886955230omplex @ ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_int_times_real
% 0.35/0.65  thf(fact_7986_sin__add,axiom,
% 0.35/0.65      ! [X: complex,Y2: complex] :
% 0.35/0.65        ( ( sin_complex @ ( plus_plus_complex @ X @ Y2 ) )
% 0.35/0.65        = ( plus_plus_complex @ ( times_times_complex @ ( sin_complex @ X ) @ ( cos_complex @ Y2 ) ) @ ( times_times_complex @ ( cos_complex @ X ) @ ( sin_complex @ Y2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_add
% 0.35/0.65  thf(fact_7987_sin__add,axiom,
% 0.35/0.65      ! [X: real,Y2: real] :
% 0.35/0.65        ( ( sin_real @ ( plus_plus_real @ X @ Y2 ) )
% 0.35/0.65        = ( plus_plus_real @ ( times_times_real @ ( sin_real @ X ) @ ( cos_real @ Y2 ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( sin_real @ Y2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_add
% 0.35/0.65  thf(fact_7988_sin__int__times__real,axiom,
% 0.35/0.65      ! [M: int,X: real] :
% 0.35/0.65        ( ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ ( real_V1803761363581548252l_real @ X ) ) )
% 0.35/0.65        = ( real_V1803761363581548252l_real @ ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_int_times_real
% 0.35/0.65  thf(fact_7989_sin__int__times__real,axiom,
% 0.35/0.65      ! [M: int,X: real] :
% 0.35/0.65        ( ( sin_complex @ ( times_times_complex @ ( ring_17405671764205052669omplex @ M ) @ ( real_V4546457046886955230omplex @ X ) ) )
% 0.35/0.65        = ( real_V4546457046886955230omplex @ ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_int_times_real
% 0.35/0.65  thf(fact_7990_cos__diff,axiom,
% 0.35/0.65      ! [X: complex,Y2: complex] :
% 0.35/0.65        ( ( cos_complex @ ( minus_minus_complex @ X @ Y2 ) )
% 0.35/0.65        = ( plus_plus_complex @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ Y2 ) ) @ ( times_times_complex @ ( sin_complex @ X ) @ ( sin_complex @ Y2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_diff
% 0.35/0.65  thf(fact_7991_cos__diff,axiom,
% 0.35/0.65      ! [X: real,Y2: real] :
% 0.35/0.65        ( ( cos_real @ ( minus_minus_real @ X @ Y2 ) )
% 0.35/0.65        = ( plus_plus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y2 ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_diff
% 0.35/0.65  thf(fact_7992_cos__add,axiom,
% 0.35/0.65      ! [X: complex,Y2: complex] :
% 0.35/0.65        ( ( cos_complex @ ( plus_plus_complex @ X @ Y2 ) )
% 0.35/0.65        = ( minus_minus_complex @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ Y2 ) ) @ ( times_times_complex @ ( sin_complex @ X ) @ ( sin_complex @ Y2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_add
% 0.35/0.65  thf(fact_7993_cos__add,axiom,
% 0.35/0.65      ! [X: real,Y2: real] :
% 0.35/0.65        ( ( cos_real @ ( plus_plus_real @ X @ Y2 ) )
% 0.35/0.65        = ( minus_minus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y2 ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_add
% 0.35/0.65  thf(fact_7994_sin__zero__norm__cos__one,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ( sin_real @ X )
% 0.35/0.65          = zero_zero_real )
% 0.35/0.65       => ( ( real_V7735802525324610683m_real @ ( cos_real @ X ) )
% 0.35/0.65          = one_one_real ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_zero_norm_cos_one
% 0.35/0.65  thf(fact_7995_sin__zero__norm__cos__one,axiom,
% 0.35/0.65      ! [X: complex] :
% 0.35/0.65        ( ( ( sin_complex @ X )
% 0.35/0.65          = zero_zero_complex )
% 0.35/0.65       => ( ( real_V1022390504157884413omplex @ ( cos_complex @ X ) )
% 0.35/0.65          = one_one_real ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_zero_norm_cos_one
% 0.35/0.65  thf(fact_7996_sin__zero__abs__cos__one,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ( sin_real @ X )
% 0.35/0.65          = zero_zero_real )
% 0.35/0.65       => ( ( abs_abs_real @ ( cos_real @ X ) )
% 0.35/0.65          = one_one_real ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_zero_abs_cos_one
% 0.35/0.65  thf(fact_7997_sin__cos__eq,axiom,
% 0.35/0.65      ( sin_real
% 0.35/0.65      = ( ^ [X2: real] : ( cos_real @ ( minus_minus_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_cos_eq
% 0.35/0.65  thf(fact_7998_sin__cos__eq,axiom,
% 0.35/0.65      ( sin_complex
% 0.35/0.65      = ( ^ [X2: complex] : ( cos_complex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ X2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_cos_eq
% 0.35/0.65  thf(fact_7999_cos__sin__eq,axiom,
% 0.35/0.65      ( cos_real
% 0.35/0.65      = ( ^ [X2: real] : ( sin_real @ ( minus_minus_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_sin_eq
% 0.35/0.65  thf(fact_8000_cos__sin__eq,axiom,
% 0.35/0.65      ( cos_complex
% 0.35/0.65      = ( ^ [X2: complex] : ( sin_complex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ X2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_sin_eq
% 0.35/0.65  thf(fact_8001_sin__double,axiom,
% 0.35/0.65      ! [X: complex] :
% 0.35/0.65        ( ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 0.35/0.65        = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ X ) ) @ ( cos_complex @ X ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_double
% 0.35/0.65  thf(fact_8002_sin__double,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 0.35/0.65        = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ X ) ) @ ( cos_real @ X ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_double
% 0.35/0.65  thf(fact_8003_sincos__principal__value,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65      ? [Y3: real] :
% 0.35/0.65        ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ Y3 )
% 0.35/0.65        & ( ord_less_eq_real @ Y3 @ pi )
% 0.35/0.65        & ( ( sin_real @ Y3 )
% 0.35/0.65          = ( sin_real @ X ) )
% 0.35/0.65        & ( ( cos_real @ Y3 )
% 0.35/0.65          = ( cos_real @ X ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sincos_principal_value
% 0.35/0.65  thf(fact_8004_sin__x__le__x,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.65       => ( ord_less_eq_real @ ( sin_real @ X ) @ X ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_x_le_x
% 0.35/0.65  thf(fact_8005_minus__sin__cos__eq,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( uminus_uminus_real @ ( sin_real @ X ) )
% 0.35/0.65        = ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % minus_sin_cos_eq
% 0.35/0.65  thf(fact_8006_minus__sin__cos__eq,axiom,
% 0.35/0.65      ! [X: complex] :
% 0.35/0.65        ( ( uminus1482373934393186551omplex @ ( sin_complex @ X ) )
% 0.35/0.65        = ( cos_complex @ ( plus_plus_complex @ X @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % minus_sin_cos_eq
% 0.35/0.65  thf(fact_8007_sin__le__one,axiom,
% 0.35/0.65      ! [X: real] : ( ord_less_eq_real @ ( sin_real @ X ) @ one_one_real ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_le_one
% 0.35/0.65  thf(fact_8008_cos__le__one,axiom,
% 0.35/0.65      ! [X: real] : ( ord_less_eq_real @ ( cos_real @ X ) @ one_one_real ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_le_one
% 0.35/0.65  thf(fact_8009_abs__sin__x__le__abs__x,axiom,
% 0.35/0.65      ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X ) ) @ ( abs_abs_real @ X ) ) ).
% 0.35/0.65  
% 0.35/0.65  % abs_sin_x_le_abs_x
% 0.35/0.65  thf(fact_8010_sin__cos__le1,axiom,
% 0.35/0.65      ! [X: real,Y2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y2 ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y2 ) ) ) ) @ one_one_real ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_cos_le1
% 0.35/0.65  thf(fact_8011_sin__squared__eq,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.65        = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_squared_eq
% 0.35/0.65  thf(fact_8012_sin__squared__eq,axiom,
% 0.35/0.65      ! [X: complex] :
% 0.35/0.65        ( ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.65        = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_squared_eq
% 0.35/0.65  thf(fact_8013_cos__squared__eq,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.65        = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_squared_eq
% 0.35/0.65  thf(fact_8014_cos__squared__eq,axiom,
% 0.35/0.65      ! [X: complex] :
% 0.35/0.65        ( ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.65        = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_squared_eq
% 0.35/0.65  thf(fact_8015_nonzero__of__real__divide,axiom,
% 0.35/0.65      ! [Y2: real,X: real] :
% 0.35/0.65        ( ( Y2 != zero_zero_real )
% 0.35/0.65       => ( ( real_V1803761363581548252l_real @ ( divide_divide_real @ X @ Y2 ) )
% 0.35/0.65          = ( divide_divide_real @ ( real_V1803761363581548252l_real @ X ) @ ( real_V1803761363581548252l_real @ Y2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % nonzero_of_real_divide
% 0.35/0.65  thf(fact_8016_nonzero__of__real__divide,axiom,
% 0.35/0.65      ! [Y2: real,X: real] :
% 0.35/0.65        ( ( Y2 != zero_zero_real )
% 0.35/0.65       => ( ( real_V4546457046886955230omplex @ ( divide_divide_real @ X @ Y2 ) )
% 0.35/0.65          = ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ X ) @ ( real_V4546457046886955230omplex @ Y2 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % nonzero_of_real_divide
% 0.35/0.65  thf(fact_8017_sin__gt__zero,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.65       => ( ( ord_less_real @ X @ pi )
% 0.35/0.65         => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_gt_zero
% 0.35/0.65  thf(fact_8018_sin__x__ge__neg__x,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.65       => ( ord_less_eq_real @ ( uminus_uminus_real @ X ) @ ( sin_real @ X ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_x_ge_neg_x
% 0.35/0.65  thf(fact_8019_sin__ge__zero,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.65       => ( ( ord_less_eq_real @ X @ pi )
% 0.35/0.65         => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_ge_zero
% 0.35/0.65  thf(fact_8020_sin__ge__minus__one,axiom,
% 0.35/0.65      ! [X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( sin_real @ X ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_ge_minus_one
% 0.35/0.65  thf(fact_8021_cos__inj__pi,axiom,
% 0.35/0.65      ! [X: real,Y2: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.65       => ( ( ord_less_eq_real @ X @ pi )
% 0.35/0.65         => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 0.35/0.65           => ( ( ord_less_eq_real @ Y2 @ pi )
% 0.35/0.65             => ( ( ( cos_real @ X )
% 0.35/0.65                  = ( cos_real @ Y2 ) )
% 0.35/0.65               => ( X = Y2 ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_inj_pi
% 0.35/0.65  thf(fact_8022_cos__mono__le__eq,axiom,
% 0.35/0.65      ! [X: real,Y2: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.65       => ( ( ord_less_eq_real @ X @ pi )
% 0.35/0.65         => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 0.35/0.65           => ( ( ord_less_eq_real @ Y2 @ pi )
% 0.35/0.65             => ( ( ord_less_eq_real @ ( cos_real @ X ) @ ( cos_real @ Y2 ) )
% 0.35/0.65                = ( ord_less_eq_real @ Y2 @ X ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_mono_le_eq
% 0.35/0.65  thf(fact_8023_cos__monotone__0__pi__le,axiom,
% 0.35/0.65      ! [Y2: real,X: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 0.35/0.65       => ( ( ord_less_eq_real @ Y2 @ X )
% 0.35/0.65         => ( ( ord_less_eq_real @ X @ pi )
% 0.35/0.65           => ( ord_less_eq_real @ ( cos_real @ X ) @ ( cos_real @ Y2 ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_monotone_0_pi_le
% 0.35/0.65  thf(fact_8024_cos__ge__minus__one,axiom,
% 0.35/0.65      ! [X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( cos_real @ X ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_ge_minus_one
% 0.35/0.65  thf(fact_8025_abs__sin__le__one,axiom,
% 0.35/0.65      ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X ) ) @ one_one_real ) ).
% 0.35/0.65  
% 0.35/0.65  % abs_sin_le_one
% 0.35/0.65  thf(fact_8026_abs__cos__le__one,axiom,
% 0.35/0.65      ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( cos_real @ X ) ) @ one_one_real ) ).
% 0.35/0.65  
% 0.35/0.65  % abs_cos_le_one
% 0.35/0.65  thf(fact_8027_sin__times__sin,axiom,
% 0.35/0.65      ! [W: complex,Z: complex] :
% 0.35/0.65        ( ( times_times_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 0.35/0.65        = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_times_sin
% 0.35/0.65  thf(fact_8028_sin__times__sin,axiom,
% 0.35/0.65      ! [W: real,Z: real] :
% 0.35/0.65        ( ( times_times_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 0.35/0.65        = ( divide_divide_real @ ( minus_minus_real @ ( cos_real @ ( minus_minus_real @ W @ Z ) ) @ ( cos_real @ ( plus_plus_real @ W @ Z ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_times_sin
% 0.35/0.65  thf(fact_8029_sin__times__cos,axiom,
% 0.35/0.65      ! [W: complex,Z: complex] :
% 0.35/0.65        ( ( times_times_complex @ ( sin_complex @ W ) @ ( cos_complex @ Z ) )
% 0.35/0.65        = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_times_cos
% 0.35/0.65  thf(fact_8030_sin__times__cos,axiom,
% 0.35/0.65      ! [W: real,Z: real] :
% 0.35/0.65        ( ( times_times_real @ ( sin_real @ W ) @ ( cos_real @ Z ) )
% 0.35/0.65        = ( divide_divide_real @ ( plus_plus_real @ ( sin_real @ ( plus_plus_real @ W @ Z ) ) @ ( sin_real @ ( minus_minus_real @ W @ Z ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_times_cos
% 0.35/0.65  thf(fact_8031_cos__times__sin,axiom,
% 0.35/0.65      ! [W: complex,Z: complex] :
% 0.35/0.65        ( ( times_times_complex @ ( cos_complex @ W ) @ ( sin_complex @ Z ) )
% 0.35/0.65        = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_times_sin
% 0.35/0.65  thf(fact_8032_cos__times__sin,axiom,
% 0.35/0.65      ! [W: real,Z: real] :
% 0.35/0.65        ( ( times_times_real @ ( cos_real @ W ) @ ( sin_real @ Z ) )
% 0.35/0.65        = ( divide_divide_real @ ( minus_minus_real @ ( sin_real @ ( plus_plus_real @ W @ Z ) ) @ ( sin_real @ ( minus_minus_real @ W @ Z ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_times_sin
% 0.35/0.65  thf(fact_8033_sin__plus__sin,axiom,
% 0.35/0.65      ! [W: complex,Z: complex] :
% 0.35/0.65        ( ( plus_plus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 0.35/0.65        = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_plus_sin
% 0.35/0.65  thf(fact_8034_sin__plus__sin,axiom,
% 0.35/0.65      ! [W: real,Z: real] :
% 0.35/0.65        ( ( plus_plus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 0.35/0.65        = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( minus_minus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_plus_sin
% 0.35/0.65  thf(fact_8035_sin__diff__sin,axiom,
% 0.35/0.65      ! [W: complex,Z: complex] :
% 0.35/0.65        ( ( minus_minus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 0.35/0.65        = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_diff_sin
% 0.35/0.65  thf(fact_8036_sin__diff__sin,axiom,
% 0.35/0.65      ! [W: real,Z: real] :
% 0.35/0.65        ( ( minus_minus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 0.35/0.65        = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( minus_minus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_diff_sin
% 0.35/0.65  thf(fact_8037_cos__diff__cos,axiom,
% 0.35/0.65      ! [W: complex,Z: complex] :
% 0.35/0.65        ( ( minus_minus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 0.35/0.65        = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ Z @ W ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_diff_cos
% 0.35/0.65  thf(fact_8038_cos__diff__cos,axiom,
% 0.35/0.65      ! [W: real,Z: real] :
% 0.35/0.65        ( ( minus_minus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 0.35/0.65        = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( sin_real @ ( divide_divide_real @ ( minus_minus_real @ Z @ W ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_diff_cos
% 0.35/0.65  thf(fact_8039_cos__double,axiom,
% 0.35/0.65      ! [X: complex] :
% 0.35/0.65        ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 0.35/0.65        = ( minus_minus_complex @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_double
% 0.35/0.65  thf(fact_8040_cos__double,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 0.35/0.65        = ( minus_minus_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_double
% 0.35/0.65  thf(fact_8041_cos__double__sin,axiom,
% 0.35/0.65      ! [W: complex] :
% 0.35/0.65        ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 0.35/0.65        = ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( sin_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_double_sin
% 0.35/0.65  thf(fact_8042_cos__double__sin,axiom,
% 0.35/0.65      ! [W: real] :
% 0.35/0.65        ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 0.35/0.65        = ( minus_minus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( sin_real @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_double_sin
% 0.35/0.65  thf(fact_8043_norm__less__p1,axiom,
% 0.35/0.65      ! [X: real] : ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ ( real_V7735802525324610683m_real @ X ) ) @ one_one_real ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_less_p1
% 0.35/0.65  thf(fact_8044_norm__less__p1,axiom,
% 0.35/0.65      ! [X: complex] : ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( real_V1022390504157884413omplex @ X ) ) @ one_one_complex ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_less_p1
% 0.35/0.65  thf(fact_8045_cos__two__neq__zero,axiom,
% 0.35/0.65      ( ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.35/0.65     != zero_zero_real ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_two_neq_zero
% 0.35/0.65  thf(fact_8046_cos__monotone__0__pi,axiom,
% 0.35/0.65      ! [Y2: real,X: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 0.35/0.65       => ( ( ord_less_real @ Y2 @ X )
% 0.35/0.65         => ( ( ord_less_eq_real @ X @ pi )
% 0.35/0.65           => ( ord_less_real @ ( cos_real @ X ) @ ( cos_real @ Y2 ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_monotone_0_pi
% 0.35/0.65  thf(fact_8047_cos__mono__less__eq,axiom,
% 0.35/0.65      ! [X: real,Y2: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.65       => ( ( ord_less_eq_real @ X @ pi )
% 0.35/0.65         => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 0.35/0.65           => ( ( ord_less_eq_real @ Y2 @ pi )
% 0.35/0.65             => ( ( ord_less_real @ ( cos_real @ X ) @ ( cos_real @ Y2 ) )
% 0.35/0.65                = ( ord_less_real @ Y2 @ X ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_mono_less_eq
% 0.35/0.65  thf(fact_8048_sin__eq__0__pi,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X )
% 0.35/0.65       => ( ( ord_less_real @ X @ pi )
% 0.35/0.65         => ( ( ( sin_real @ X )
% 0.35/0.65              = zero_zero_real )
% 0.35/0.65           => ( X = zero_zero_real ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_eq_0_pi
% 0.35/0.65  thf(fact_8049_sin__zero__pi__iff,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ord_less_real @ ( abs_abs_real @ X ) @ pi )
% 0.35/0.65       => ( ( ( sin_real @ X )
% 0.35/0.65            = zero_zero_real )
% 0.35/0.65          = ( X = zero_zero_real ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_zero_pi_iff
% 0.35/0.65  thf(fact_8050_cos__monotone__minus__pi__0_H,axiom,
% 0.35/0.65      ! [Y2: real,X: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y2 )
% 0.35/0.65       => ( ( ord_less_eq_real @ Y2 @ X )
% 0.35/0.65         => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.35/0.65           => ( ord_less_eq_real @ ( cos_real @ Y2 ) @ ( cos_real @ X ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_monotone_minus_pi_0'
% 0.35/0.65  thf(fact_8051_sin__zero__iff__int2,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ( sin_real @ X )
% 0.35/0.65          = zero_zero_real )
% 0.35/0.65        = ( ? [I3: int] :
% 0.35/0.65              ( X
% 0.35/0.65              = ( times_times_real @ ( ring_1_of_int_real @ I3 ) @ pi ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_zero_iff_int2
% 0.35/0.65  thf(fact_8052_sincos__total__pi,axiom,
% 0.35/0.65      ! [Y2: real,X: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 0.35/0.65       => ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.65            = one_one_real )
% 0.35/0.65         => ? [T6: real] :
% 0.35/0.65              ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 0.35/0.65              & ( ord_less_eq_real @ T6 @ pi )
% 0.35/0.65              & ( X
% 0.35/0.65                = ( cos_real @ T6 ) )
% 0.35/0.65              & ( Y2
% 0.35/0.65                = ( sin_real @ T6 ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sincos_total_pi
% 0.35/0.65  thf(fact_8053_sin__cos__sqrt,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X ) )
% 0.35/0.65       => ( ( sin_real @ X )
% 0.35/0.65          = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_cos_sqrt
% 0.35/0.65  thf(fact_8054_sin__expansion__lemma,axiom,
% 0.35/0.65      ! [X: real,M: nat] :
% 0.35/0.65        ( ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.35/0.65        = ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_expansion_lemma
% 0.35/0.65  thf(fact_8055_cos__expansion__lemma,axiom,
% 0.35/0.65      ! [X: real,M: nat] :
% 0.35/0.65        ( ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.35/0.65        = ( uminus_uminus_real @ ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_expansion_lemma
% 0.35/0.65  thf(fact_8056_sin__gt__zero__02,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.65       => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.35/0.65         => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_gt_zero_02
% 0.35/0.65  thf(fact_8057_cos__two__less__zero,axiom,
% 0.35/0.65      ord_less_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 0.35/0.65  
% 0.35/0.65  % cos_two_less_zero
% 0.35/0.65  thf(fact_8058_cos__is__zero,axiom,
% 0.35/0.65      ? [X3: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.35/0.65        & ( ord_less_eq_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.35/0.65        & ( ( cos_real @ X3 )
% 0.35/0.65          = zero_zero_real )
% 0.35/0.65        & ! [Y4: real] :
% 0.35/0.65            ( ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 0.35/0.65              & ( ord_less_eq_real @ Y4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.35/0.65              & ( ( cos_real @ Y4 )
% 0.35/0.65                = zero_zero_real ) )
% 0.35/0.65           => ( Y4 = X3 ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_is_zero
% 0.35/0.65  thf(fact_8059_cos__two__le__zero,axiom,
% 0.35/0.65      ord_less_eq_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 0.35/0.65  
% 0.35/0.65  % cos_two_le_zero
% 0.35/0.65  thf(fact_8060_norm__of__real__diff,axiom,
% 0.35/0.65      ! [B: real,A: real] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( real_V4546457046886955230omplex @ B ) @ ( real_V4546457046886955230omplex @ A ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % norm_of_real_diff
% 0.35/0.65  thf(fact_8061_cos__monotone__minus__pi__0,axiom,
% 0.35/0.65      ! [Y2: real,X: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y2 )
% 0.35/0.65       => ( ( ord_less_real @ Y2 @ X )
% 0.35/0.65         => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.35/0.65           => ( ord_less_real @ ( cos_real @ Y2 ) @ ( cos_real @ X ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_monotone_minus_pi_0
% 0.35/0.65  thf(fact_8062_cos__total,axiom,
% 0.35/0.65      ! [Y2: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 0.35/0.65       => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 0.35/0.65         => ? [X3: real] :
% 0.35/0.65              ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.35/0.65              & ( ord_less_eq_real @ X3 @ pi )
% 0.35/0.65              & ( ( cos_real @ X3 )
% 0.35/0.65                = Y2 )
% 0.35/0.65              & ! [Y4: real] :
% 0.35/0.65                  ( ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 0.35/0.65                    & ( ord_less_eq_real @ Y4 @ pi )
% 0.35/0.65                    & ( ( cos_real @ Y4 )
% 0.35/0.65                      = Y2 ) )
% 0.35/0.65                 => ( Y4 = X3 ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_total
% 0.35/0.65  thf(fact_8063_sincos__total__pi__half,axiom,
% 0.35/0.65      ! [X: real,Y2: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.65       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 0.35/0.65         => ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.65              = one_one_real )
% 0.35/0.65           => ? [T6: real] :
% 0.35/0.65                ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 0.35/0.65                & ( ord_less_eq_real @ T6 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.65                & ( X
% 0.35/0.65                  = ( cos_real @ T6 ) )
% 0.35/0.65                & ( Y2
% 0.35/0.65                  = ( sin_real @ T6 ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sincos_total_pi_half
% 0.35/0.65  thf(fact_8064_sincos__total__2pi__le,axiom,
% 0.35/0.65      ! [X: real,Y2: real] :
% 0.35/0.65        ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.65          = one_one_real )
% 0.35/0.65       => ? [T6: real] :
% 0.35/0.65            ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 0.35/0.65            & ( ord_less_eq_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.35/0.65            & ( X
% 0.35/0.65              = ( cos_real @ T6 ) )
% 0.35/0.65            & ( Y2
% 0.35/0.65              = ( sin_real @ T6 ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sincos_total_2pi_le
% 0.35/0.65  thf(fact_8065_sincos__total__2pi,axiom,
% 0.35/0.65      ! [X: real,Y2: real] :
% 0.35/0.65        ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.65          = one_one_real )
% 0.35/0.65       => ~ ! [T6: real] :
% 0.35/0.65              ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 0.35/0.65             => ( ( ord_less_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.35/0.65               => ( ( X
% 0.35/0.65                    = ( cos_real @ T6 ) )
% 0.35/0.65                 => ( Y2
% 0.35/0.65                   != ( sin_real @ T6 ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sincos_total_2pi
% 0.35/0.65  thf(fact_8066_sin__pi__divide__n__ge__0,axiom,
% 0.35/0.65      ! [N: nat] :
% 0.35/0.65        ( ( N != zero_zero_nat )
% 0.35/0.65       => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_pi_divide_n_ge_0
% 0.35/0.65  thf(fact_8067_sin__45,axiom,
% 0.35/0.65      ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 0.35/0.65      = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_45
% 0.35/0.65  thf(fact_8068_cos__45,axiom,
% 0.35/0.65      ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 0.35/0.65      = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_45
% 0.35/0.65  thf(fact_8069_cos__times__cos,axiom,
% 0.35/0.65      ! [W: complex,Z: complex] :
% 0.35/0.65        ( ( times_times_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 0.35/0.65        = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_times_cos
% 0.35/0.65  thf(fact_8070_cos__times__cos,axiom,
% 0.35/0.65      ! [W: real,Z: real] :
% 0.35/0.65        ( ( times_times_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 0.35/0.65        = ( divide_divide_real @ ( plus_plus_real @ ( cos_real @ ( minus_minus_real @ W @ Z ) ) @ ( cos_real @ ( plus_plus_real @ W @ Z ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_times_cos
% 0.35/0.65  thf(fact_8071_cos__plus__cos,axiom,
% 0.35/0.65      ! [W: complex,Z: complex] :
% 0.35/0.65        ( ( plus_plus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 0.35/0.65        = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_plus_cos
% 0.35/0.65  thf(fact_8072_cos__plus__cos,axiom,
% 0.35/0.65      ! [W: real,Z: real] :
% 0.35/0.65        ( ( plus_plus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 0.35/0.65        = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( cos_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( minus_minus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_plus_cos
% 0.35/0.65  thf(fact_8073_sin__gt__zero2,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.65       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.65         => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_gt_zero2
% 0.35/0.65  thf(fact_8074_sin__lt__zero,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ord_less_real @ pi @ X )
% 0.35/0.65       => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.35/0.65         => ( ord_less_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_lt_zero
% 0.35/0.65  thf(fact_8075_cos__double__less__one,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.65       => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.35/0.65         => ( ord_less_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) @ one_one_real ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_double_less_one
% 0.35/0.65  thf(fact_8076_sin__30,axiom,
% 0.35/0.65      ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 0.35/0.65      = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_30
% 0.35/0.65  thf(fact_8077_cos__gt__zero,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.65       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.65         => ( ord_less_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_gt_zero
% 0.35/0.65  thf(fact_8078_sin__inj__pi,axiom,
% 0.35/0.65      ! [X: real,Y2: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.35/0.65       => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.65         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 0.35/0.65           => ( ( ord_less_eq_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.65             => ( ( ( sin_real @ X )
% 0.35/0.65                  = ( sin_real @ Y2 ) )
% 0.35/0.65               => ( X = Y2 ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_inj_pi
% 0.35/0.65  thf(fact_8079_sin__mono__le__eq,axiom,
% 0.35/0.65      ! [X: real,Y2: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.35/0.65       => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.65         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 0.35/0.65           => ( ( ord_less_eq_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.65             => ( ( ord_less_eq_real @ ( sin_real @ X ) @ ( sin_real @ Y2 ) )
% 0.35/0.65                = ( ord_less_eq_real @ X @ Y2 ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_mono_le_eq
% 0.35/0.65  thf(fact_8080_sin__monotone__2pi__le,axiom,
% 0.35/0.65      ! [Y2: real,X: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 0.35/0.65       => ( ( ord_less_eq_real @ Y2 @ X )
% 0.35/0.65         => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.65           => ( ord_less_eq_real @ ( sin_real @ Y2 ) @ ( sin_real @ X ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_monotone_2pi_le
% 0.35/0.65  thf(fact_8081_cos__60,axiom,
% 0.35/0.65      ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 0.35/0.65      = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_60
% 0.35/0.65  thf(fact_8082_sin__60,axiom,
% 0.35/0.65      ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 0.35/0.65      = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_60
% 0.35/0.65  thf(fact_8083_cos__30,axiom,
% 0.35/0.65      ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 0.35/0.65      = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_30
% 0.35/0.65  thf(fact_8084_cos__one__2pi__int,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ( cos_real @ X )
% 0.35/0.65          = one_one_real )
% 0.35/0.65        = ( ? [X2: int] :
% 0.35/0.65              ( X
% 0.35/0.65              = ( times_times_real @ ( times_times_real @ ( ring_1_of_int_real @ X2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_one_2pi_int
% 0.35/0.65  thf(fact_8085_cos__double__cos,axiom,
% 0.35/0.65      ! [W: complex] :
% 0.35/0.65        ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 0.35/0.65        = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( cos_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_complex ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_double_cos
% 0.35/0.65  thf(fact_8086_cos__double__cos,axiom,
% 0.35/0.65      ! [W: real] :
% 0.35/0.65        ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 0.35/0.65        = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( cos_real @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_real ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_double_cos
% 0.35/0.65  thf(fact_8087_cos__treble__cos,axiom,
% 0.35/0.65      ! [X: complex] :
% 0.35/0.65        ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ X ) )
% 0.35/0.65        = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ ( cos_complex @ X ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_treble_cos
% 0.35/0.65  thf(fact_8088_cos__treble__cos,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ X ) )
% 0.35/0.65        = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( cos_real @ X ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_treble_cos
% 0.35/0.65  thf(fact_8089_sin__le__zero,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ pi @ X )
% 0.35/0.65       => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.35/0.65         => ( ord_less_eq_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_le_zero
% 0.35/0.65  thf(fact_8090_sin__less__zero,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 0.35/0.65       => ( ( ord_less_real @ X @ zero_zero_real )
% 0.35/0.65         => ( ord_less_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_less_zero
% 0.35/0.65  thf(fact_8091_sin__mono__less__eq,axiom,
% 0.35/0.65      ! [X: real,Y2: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.35/0.65       => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.65         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 0.35/0.65           => ( ( ord_less_eq_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.65             => ( ( ord_less_real @ ( sin_real @ X ) @ ( sin_real @ Y2 ) )
% 0.35/0.65                = ( ord_less_real @ X @ Y2 ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_mono_less_eq
% 0.35/0.65  thf(fact_8092_sin__monotone__2pi,axiom,
% 0.35/0.65      ! [Y2: real,X: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 0.35/0.65       => ( ( ord_less_real @ Y2 @ X )
% 0.35/0.65         => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.65           => ( ord_less_real @ ( sin_real @ Y2 ) @ ( sin_real @ X ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_monotone_2pi
% 0.35/0.65  thf(fact_8093_sin__total,axiom,
% 0.35/0.65      ! [Y2: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 0.35/0.65       => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 0.35/0.65         => ? [X3: real] :
% 0.35/0.65              ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 0.35/0.65              & ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.65              & ( ( sin_real @ X3 )
% 0.35/0.65                = Y2 )
% 0.35/0.65              & ! [Y4: real] :
% 0.35/0.65                  ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 0.35/0.65                    & ( ord_less_eq_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.65                    & ( ( sin_real @ Y4 )
% 0.35/0.65                      = Y2 ) )
% 0.35/0.65                 => ( Y4 = X3 ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_total
% 0.35/0.65  thf(fact_8094_cos__gt__zero__pi,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.35/0.65       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.65         => ( ord_less_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_gt_zero_pi
% 0.35/0.65  thf(fact_8095_cos__ge__zero,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.35/0.65       => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.65         => ( ord_less_eq_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_ge_zero
% 0.35/0.65  thf(fact_8096_cos__one__2pi,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ( cos_real @ X )
% 0.35/0.65          = one_one_real )
% 0.35/0.65        = ( ? [X2: nat] :
% 0.35/0.65              ( X
% 0.35/0.65              = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 0.35/0.65          | ? [X2: nat] :
% 0.35/0.65              ( X
% 0.35/0.65              = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_one_2pi
% 0.35/0.65  thf(fact_8097_sin__pi__divide__n__gt__0,axiom,
% 0.35/0.65      ! [N: nat] :
% 0.35/0.65        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.65       => ( ord_less_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_pi_divide_n_gt_0
% 0.35/0.65  thf(fact_8098_sin__arctan,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( sin_real @ ( arctan @ X ) )
% 0.35/0.65        = ( divide_divide_real @ X @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_arctan
% 0.35/0.65  thf(fact_8099_cos__arctan,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( cos_real @ ( arctan @ X ) )
% 0.35/0.65        = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_arctan
% 0.35/0.65  thf(fact_8100_sin__zero__iff__int,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ( sin_real @ X )
% 0.35/0.65          = zero_zero_real )
% 0.35/0.65        = ( ? [I3: int] :
% 0.35/0.65              ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I3 )
% 0.35/0.65              & ( X
% 0.35/0.65                = ( times_times_real @ ( ring_1_of_int_real @ I3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_zero_iff_int
% 0.35/0.65  thf(fact_8101_cos__zero__iff__int,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ( cos_real @ X )
% 0.35/0.65          = zero_zero_real )
% 0.35/0.65        = ( ? [I3: int] :
% 0.35/0.65              ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I3 )
% 0.35/0.65              & ( X
% 0.35/0.65                = ( times_times_real @ ( ring_1_of_int_real @ I3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_zero_iff_int
% 0.35/0.65  thf(fact_8102_sin__zero__lemma,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.65       => ( ( ( sin_real @ X )
% 0.35/0.65            = zero_zero_real )
% 0.35/0.65         => ? [N3: nat] :
% 0.35/0.65              ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 0.35/0.65              & ( X
% 0.35/0.65                = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_zero_lemma
% 0.35/0.65  thf(fact_8103_sin__zero__iff,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ( sin_real @ X )
% 0.35/0.65          = zero_zero_real )
% 0.35/0.65        = ( ? [N2: nat] :
% 0.35/0.65              ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.35/0.65              & ( X
% 0.35/0.65                = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.65          | ? [N2: nat] :
% 0.35/0.65              ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.35/0.65              & ( X
% 0.35/0.65                = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_zero_iff
% 0.35/0.65  thf(fact_8104_cos__zero__lemma,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.65       => ( ( ( cos_real @ X )
% 0.35/0.65            = zero_zero_real )
% 0.35/0.65         => ? [N3: nat] :
% 0.35/0.65              ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 0.35/0.65              & ( X
% 0.35/0.65                = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_zero_lemma
% 0.35/0.65  thf(fact_8105_cos__zero__iff,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ( cos_real @ X )
% 0.35/0.65          = zero_zero_real )
% 0.35/0.65        = ( ? [N2: nat] :
% 0.35/0.65              ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.35/0.65              & ( X
% 0.35/0.65                = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.65          | ? [N2: nat] :
% 0.35/0.65              ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.35/0.65              & ( X
% 0.35/0.65                = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % cos_zero_iff
% 0.35/0.65  thf(fact_8106_arsinh__def,axiom,
% 0.35/0.65      ( arsinh_real
% 0.35/0.65      = ( ^ [X2: real] : ( ln_ln_real @ ( plus_plus_real @ X2 @ ( powr_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( real_V1803761363581548252l_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % arsinh_def
% 0.35/0.65  thf(fact_8107_Maclaurin__cos__expansion2,axiom,
% 0.35/0.65      ! [X: real,N: nat] :
% 0.35/0.65        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.65       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.65         => ? [T6: real] :
% 0.35/0.65              ( ( ord_less_real @ zero_zero_real @ T6 )
% 0.35/0.65              & ( ord_less_real @ T6 @ X )
% 0.35/0.65              & ( ( cos_real @ X )
% 0.35/0.65                = ( plus_plus_real
% 0.35/0.65                  @ ( groups6591440286371151544t_real
% 0.35/0.65                    @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 0.35/0.65                    @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.65                  @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % Maclaurin_cos_expansion2
% 0.35/0.65  thf(fact_8108_Maclaurin__minus__cos__expansion,axiom,
% 0.35/0.65      ! [N: nat,X: real] :
% 0.35/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.65       => ( ( ord_less_real @ X @ zero_zero_real )
% 0.35/0.65         => ? [T6: real] :
% 0.35/0.65              ( ( ord_less_real @ X @ T6 )
% 0.35/0.65              & ( ord_less_real @ T6 @ zero_zero_real )
% 0.35/0.65              & ( ( cos_real @ X )
% 0.35/0.65                = ( plus_plus_real
% 0.35/0.65                  @ ( groups6591440286371151544t_real
% 0.35/0.65                    @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 0.35/0.65                    @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.65                  @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % Maclaurin_minus_cos_expansion
% 0.35/0.65  thf(fact_8109_Maclaurin__cos__expansion,axiom,
% 0.35/0.65      ! [X: real,N: nat] :
% 0.35/0.65      ? [T6: real] :
% 0.35/0.65        ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 0.35/0.65        & ( ( cos_real @ X )
% 0.35/0.65          = ( plus_plus_real
% 0.35/0.65            @ ( groups6591440286371151544t_real
% 0.35/0.65              @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 0.35/0.65              @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.65            @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % Maclaurin_cos_expansion
% 0.35/0.65  thf(fact_8110_tan__double,axiom,
% 0.35/0.65      ! [X: complex] :
% 0.35/0.65        ( ( ( cos_complex @ X )
% 0.35/0.65         != zero_zero_complex )
% 0.35/0.65       => ( ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 0.35/0.65           != zero_zero_complex )
% 0.35/0.65         => ( ( tan_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 0.35/0.65            = ( divide1717551699836669952omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( tan_complex @ X ) ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( tan_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % tan_double
% 0.35/0.65  thf(fact_8111_tan__double,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ( cos_real @ X )
% 0.35/0.65         != zero_zero_real )
% 0.35/0.65       => ( ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 0.35/0.65           != zero_zero_real )
% 0.35/0.65         => ( ( tan_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 0.35/0.65            = ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( tan_real @ X ) ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % tan_double
% 0.35/0.65  thf(fact_8112_sin__tan,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.65       => ( ( sin_real @ X )
% 0.35/0.65          = ( divide_divide_real @ ( tan_real @ X ) @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % sin_tan
% 0.35/0.65  thf(fact_8113_fact__0,axiom,
% 0.35/0.65      ( ( semiri5044797733671781792omplex @ zero_zero_nat )
% 0.35/0.65      = one_one_complex ) ).
% 0.35/0.65  
% 0.35/0.65  % fact_0
% 0.35/0.65  thf(fact_8114_fact__0,axiom,
% 0.35/0.65      ( ( semiri773545260158071498ct_rat @ zero_zero_nat )
% 0.35/0.65      = one_one_rat ) ).
% 0.35/0.65  
% 0.35/0.65  % fact_0
% 0.35/0.65  thf(fact_8115_fact__0,axiom,
% 0.35/0.65      ( ( semiri1406184849735516958ct_int @ zero_zero_nat )
% 0.35/0.65      = one_one_int ) ).
% 0.35/0.65  
% 0.35/0.65  % fact_0
% 0.35/0.65  thf(fact_8116_fact__0,axiom,
% 0.35/0.65      ( ( semiri2265585572941072030t_real @ zero_zero_nat )
% 0.35/0.65      = one_one_real ) ).
% 0.35/0.65  
% 0.35/0.65  % fact_0
% 0.35/0.65  thf(fact_8117_fact__0,axiom,
% 0.35/0.65      ( ( semiri1408675320244567234ct_nat @ zero_zero_nat )
% 0.35/0.65      = one_one_nat ) ).
% 0.35/0.65  
% 0.35/0.65  % fact_0
% 0.35/0.65  thf(fact_8118_fact__1,axiom,
% 0.35/0.65      ( ( semiri5044797733671781792omplex @ one_one_nat )
% 0.35/0.65      = one_one_complex ) ).
% 0.35/0.65  
% 0.35/0.65  % fact_1
% 0.35/0.65  thf(fact_8119_fact__1,axiom,
% 0.35/0.65      ( ( semiri773545260158071498ct_rat @ one_one_nat )
% 0.35/0.65      = one_one_rat ) ).
% 0.35/0.65  
% 0.35/0.65  % fact_1
% 0.35/0.65  thf(fact_8120_fact__1,axiom,
% 0.35/0.65      ( ( semiri1406184849735516958ct_int @ one_one_nat )
% 0.35/0.65      = one_one_int ) ).
% 0.35/0.65  
% 0.35/0.65  % fact_1
% 0.35/0.65  thf(fact_8121_fact__1,axiom,
% 0.35/0.65      ( ( semiri2265585572941072030t_real @ one_one_nat )
% 0.35/0.65      = one_one_real ) ).
% 0.35/0.65  
% 0.35/0.65  % fact_1
% 0.35/0.65  thf(fact_8122_fact__1,axiom,
% 0.35/0.65      ( ( semiri1408675320244567234ct_nat @ one_one_nat )
% 0.35/0.65      = one_one_nat ) ).
% 0.35/0.65  
% 0.35/0.65  % fact_1
% 0.35/0.65  thf(fact_8123_tan__periodic__pi,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( tan_real @ ( plus_plus_real @ X @ pi ) )
% 0.35/0.65        = ( tan_real @ X ) ) ).
% 0.35/0.65  
% 0.35/0.65  % tan_periodic_pi
% 0.35/0.65  thf(fact_8124_fact__Suc__0,axiom,
% 0.35/0.65      ( ( semiri5044797733671781792omplex @ ( suc @ zero_zero_nat ) )
% 0.35/0.65      = one_one_complex ) ).
% 0.35/0.65  
% 0.35/0.65  % fact_Suc_0
% 0.35/0.65  thf(fact_8125_fact__Suc__0,axiom,
% 0.35/0.65      ( ( semiri773545260158071498ct_rat @ ( suc @ zero_zero_nat ) )
% 0.35/0.65      = one_one_rat ) ).
% 0.35/0.65  
% 0.35/0.65  % fact_Suc_0
% 0.35/0.65  thf(fact_8126_fact__Suc__0,axiom,
% 0.35/0.65      ( ( semiri1406184849735516958ct_int @ ( suc @ zero_zero_nat ) )
% 0.35/0.65      = one_one_int ) ).
% 0.35/0.65  
% 0.35/0.65  % fact_Suc_0
% 0.35/0.65  thf(fact_8127_fact__Suc__0,axiom,
% 0.35/0.65      ( ( semiri2265585572941072030t_real @ ( suc @ zero_zero_nat ) )
% 0.35/0.65      = one_one_real ) ).
% 0.35/0.65  
% 0.35/0.65  % fact_Suc_0
% 0.35/0.65  thf(fact_8128_fact__Suc__0,axiom,
% 0.35/0.65      ( ( semiri1408675320244567234ct_nat @ ( suc @ zero_zero_nat ) )
% 0.35/0.65      = one_one_nat ) ).
% 0.35/0.65  
% 0.35/0.65  % fact_Suc_0
% 0.35/0.65  thf(fact_8129_fact__Suc,axiom,
% 0.35/0.65      ! [N: nat] :
% 0.35/0.65        ( ( semiri1406184849735516958ct_int @ ( suc @ N ) )
% 0.35/0.65        = ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % fact_Suc
% 0.35/0.65  thf(fact_8130_fact__Suc,axiom,
% 0.35/0.65      ! [N: nat] :
% 0.35/0.65        ( ( semiri5044797733671781792omplex @ ( suc @ N ) )
% 0.35/0.65        = ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N ) ) @ ( semiri5044797733671781792omplex @ N ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % fact_Suc
% 0.35/0.65  thf(fact_8131_fact__Suc,axiom,
% 0.35/0.65      ! [N: nat] :
% 0.35/0.65        ( ( semiri2265585572941072030t_real @ ( suc @ N ) )
% 0.35/0.65        = ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % fact_Suc
% 0.35/0.65  thf(fact_8132_fact__Suc,axiom,
% 0.35/0.65      ! [N: nat] :
% 0.35/0.65        ( ( semiri1408675320244567234ct_nat @ ( suc @ N ) )
% 0.35/0.65        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( suc @ N ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % fact_Suc
% 0.35/0.65  thf(fact_8133_fact__2,axiom,
% 0.35/0.65      ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.65      = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % fact_2
% 0.35/0.65  thf(fact_8134_fact__2,axiom,
% 0.35/0.65      ( ( semiri773545260158071498ct_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.65      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % fact_2
% 0.35/0.65  thf(fact_8135_fact__2,axiom,
% 0.35/0.65      ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.65      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % fact_2
% 0.35/0.65  thf(fact_8136_fact__2,axiom,
% 0.35/0.65      ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.65      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % fact_2
% 0.35/0.65  thf(fact_8137_fact__2,axiom,
% 0.35/0.65      ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.65      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.35/0.65  
% 0.35/0.65  % fact_2
% 0.35/0.65  thf(fact_8138_tan__npi,axiom,
% 0.35/0.65      ! [N: nat] :
% 0.35/0.65        ( ( tan_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 0.35/0.65        = zero_zero_real ) ).
% 0.35/0.65  
% 0.35/0.65  % tan_npi
% 0.35/0.65  thf(fact_8139_tan__periodic__n,axiom,
% 0.35/0.65      ! [X: real,N: num] :
% 0.35/0.65        ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ N ) @ pi ) ) )
% 0.35/0.65        = ( tan_real @ X ) ) ).
% 0.35/0.65  
% 0.35/0.65  % tan_periodic_n
% 0.35/0.65  thf(fact_8140_tan__periodic__nat,axiom,
% 0.35/0.65      ! [X: real,N: nat] :
% 0.35/0.65        ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) ) )
% 0.35/0.65        = ( tan_real @ X ) ) ).
% 0.35/0.65  
% 0.35/0.65  % tan_periodic_nat
% 0.35/0.65  thf(fact_8141_tan__periodic__int,axiom,
% 0.35/0.65      ! [X: real,I2: int] :
% 0.35/0.65        ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( ring_1_of_int_real @ I2 ) @ pi ) ) )
% 0.35/0.65        = ( tan_real @ X ) ) ).
% 0.35/0.65  
% 0.35/0.65  % tan_periodic_int
% 0.35/0.65  thf(fact_8142_tan__periodic,axiom,
% 0.35/0.65      ! [X: real] :
% 0.35/0.65        ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 0.35/0.65        = ( tan_real @ X ) ) ).
% 0.35/0.65  
% 0.35/0.65  % tan_periodic
% 0.35/0.65  thf(fact_8143_fact__ge__zero,axiom,
% 0.35/0.65      ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 0.35/0.65  
% 0.35/0.65  % fact_ge_zero
% 0.35/0.65  thf(fact_8144_fact__ge__zero,axiom,
% 0.35/0.65      ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 0.35/0.65  
% 0.35/0.65  % fact_ge_zero
% 0.35/0.65  thf(fact_8145_fact__ge__zero,axiom,
% 0.35/0.65      ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 0.35/0.65  
% 0.35/0.65  % fact_ge_zero
% 0.35/0.65  thf(fact_8146_fact__ge__zero,axiom,
% 0.35/0.65      ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 0.35/0.65  
% 0.35/0.65  % fact_ge_zero
% 0.35/0.65  thf(fact_8147_fact__gt__zero,axiom,
% 0.35/0.66      ! [N: nat] : ( ord_less_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_gt_zero
% 0.35/0.66  thf(fact_8148_fact__gt__zero,axiom,
% 0.35/0.66      ! [N: nat] : ( ord_less_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_gt_zero
% 0.35/0.66  thf(fact_8149_fact__gt__zero,axiom,
% 0.35/0.66      ! [N: nat] : ( ord_less_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_gt_zero
% 0.35/0.66  thf(fact_8150_fact__gt__zero,axiom,
% 0.35/0.66      ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_gt_zero
% 0.35/0.66  thf(fact_8151_fact__not__neg,axiom,
% 0.35/0.66      ! [N: nat] :
% 0.35/0.66        ~ ( ord_less_rat @ ( semiri773545260158071498ct_rat @ N ) @ zero_zero_rat ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_not_neg
% 0.35/0.66  thf(fact_8152_fact__not__neg,axiom,
% 0.35/0.66      ! [N: nat] :
% 0.35/0.66        ~ ( ord_less_int @ ( semiri1406184849735516958ct_int @ N ) @ zero_zero_int ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_not_neg
% 0.35/0.66  thf(fact_8153_fact__not__neg,axiom,
% 0.35/0.66      ! [N: nat] :
% 0.35/0.66        ~ ( ord_less_real @ ( semiri2265585572941072030t_real @ N ) @ zero_zero_real ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_not_neg
% 0.35/0.66  thf(fact_8154_fact__not__neg,axiom,
% 0.35/0.66      ! [N: nat] :
% 0.35/0.66        ~ ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ N ) @ zero_zero_nat ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_not_neg
% 0.35/0.66  thf(fact_8155_fact__ge__1,axiom,
% 0.35/0.66      ! [N: nat] : ( ord_less_eq_rat @ one_one_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_ge_1
% 0.35/0.66  thf(fact_8156_fact__ge__1,axiom,
% 0.35/0.66      ! [N: nat] : ( ord_less_eq_int @ one_one_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_ge_1
% 0.35/0.66  thf(fact_8157_fact__ge__1,axiom,
% 0.35/0.66      ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_ge_1
% 0.35/0.66  thf(fact_8158_fact__ge__1,axiom,
% 0.35/0.66      ! [N: nat] : ( ord_less_eq_nat @ one_one_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_ge_1
% 0.35/0.66  thf(fact_8159_fact__mono,axiom,
% 0.35/0.66      ! [M: nat,N: nat] :
% 0.35/0.66        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.66       => ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_mono
% 0.35/0.66  thf(fact_8160_fact__mono,axiom,
% 0.35/0.66      ! [M: nat,N: nat] :
% 0.35/0.66        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.66       => ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ M ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_mono
% 0.35/0.66  thf(fact_8161_fact__mono,axiom,
% 0.35/0.66      ! [M: nat,N: nat] :
% 0.35/0.66        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.66       => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_mono
% 0.35/0.66  thf(fact_8162_fact__dvd,axiom,
% 0.35/0.66      ! [N: nat,M: nat] :
% 0.35/0.66        ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.66       => ( dvd_dvd_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1406184849735516958ct_int @ M ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_dvd
% 0.35/0.66  thf(fact_8163_fact__dvd,axiom,
% 0.35/0.66      ! [N: nat,M: nat] :
% 0.35/0.66        ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.66       => ( dvd_dvd_Code_integer @ ( semiri3624122377584611663nteger @ N ) @ ( semiri3624122377584611663nteger @ M ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_dvd
% 0.35/0.66  thf(fact_8164_fact__dvd,axiom,
% 0.35/0.66      ! [N: nat,M: nat] :
% 0.35/0.66        ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.66       => ( dvd_dvd_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ M ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_dvd
% 0.35/0.66  thf(fact_8165_fact__dvd,axiom,
% 0.35/0.66      ! [N: nat,M: nat] :
% 0.35/0.66        ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.66       => ( dvd_dvd_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ M ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_dvd
% 0.35/0.66  thf(fact_8166_fact__less__mono,axiom,
% 0.35/0.66      ! [M: nat,N: nat] :
% 0.35/0.66        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.35/0.66       => ( ( ord_less_nat @ M @ N )
% 0.35/0.66         => ( ord_less_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_less_mono
% 0.35/0.66  thf(fact_8167_fact__less__mono,axiom,
% 0.35/0.66      ! [M: nat,N: nat] :
% 0.35/0.66        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.35/0.66       => ( ( ord_less_nat @ M @ N )
% 0.35/0.66         => ( ord_less_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_less_mono
% 0.35/0.66  thf(fact_8168_fact__less__mono,axiom,
% 0.35/0.66      ! [M: nat,N: nat] :
% 0.35/0.66        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.35/0.66       => ( ( ord_less_nat @ M @ N )
% 0.35/0.66         => ( ord_less_real @ ( semiri2265585572941072030t_real @ M ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_less_mono
% 0.35/0.66  thf(fact_8169_fact__less__mono,axiom,
% 0.35/0.66      ! [M: nat,N: nat] :
% 0.35/0.66        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.35/0.66       => ( ( ord_less_nat @ M @ N )
% 0.35/0.66         => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_less_mono
% 0.35/0.66  thf(fact_8170_fact__fact__dvd__fact,axiom,
% 0.35/0.66      ! [K: nat,N: nat] : ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ N ) ) @ ( semiri3624122377584611663nteger @ ( plus_plus_nat @ K @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_fact_dvd_fact
% 0.35/0.66  thf(fact_8171_fact__fact__dvd__fact,axiom,
% 0.35/0.66      ! [K: nat,N: nat] : ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ N ) ) @ ( semiri1406184849735516958ct_int @ ( plus_plus_nat @ K @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_fact_dvd_fact
% 0.35/0.66  thf(fact_8172_fact__fact__dvd__fact,axiom,
% 0.35/0.66      ! [K: nat,N: nat] : ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ K @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_fact_dvd_fact
% 0.35/0.66  thf(fact_8173_fact__fact__dvd__fact,axiom,
% 0.35/0.66      ! [K: nat,N: nat] : ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ N ) ) @ ( semiri1408675320244567234ct_nat @ ( plus_plus_nat @ K @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_fact_dvd_fact
% 0.35/0.66  thf(fact_8174_fact__mod,axiom,
% 0.35/0.66      ! [M: nat,N: nat] :
% 0.35/0.66        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.66       => ( ( modulo_modulo_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1406184849735516958ct_int @ M ) )
% 0.35/0.66          = zero_zero_int ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_mod
% 0.35/0.66  thf(fact_8175_fact__mod,axiom,
% 0.35/0.66      ! [M: nat,N: nat] :
% 0.35/0.66        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.66       => ( ( modulo_modulo_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ M ) )
% 0.35/0.66          = zero_zero_nat ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_mod
% 0.35/0.66  thf(fact_8176_fact__le__power,axiom,
% 0.35/0.66      ! [N: nat] : ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1314217659103216013at_int @ ( power_power_nat @ N @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_le_power
% 0.35/0.66  thf(fact_8177_fact__le__power,axiom,
% 0.35/0.66      ! [N: nat] : ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri5074537144036343181t_real @ ( power_power_nat @ N @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_le_power
% 0.35/0.66  thf(fact_8178_fact__le__power,axiom,
% 0.35/0.66      ! [N: nat] : ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1316708129612266289at_nat @ ( power_power_nat @ N @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_le_power
% 0.35/0.66  thf(fact_8179_tan__def,axiom,
% 0.35/0.66      ( tan_complex
% 0.35/0.66      = ( ^ [X2: complex] : ( divide1717551699836669952omplex @ ( sin_complex @ X2 ) @ ( cos_complex @ X2 ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % tan_def
% 0.35/0.66  thf(fact_8180_tan__def,axiom,
% 0.35/0.66      ( tan_real
% 0.35/0.66      = ( ^ [X2: real] : ( divide_divide_real @ ( sin_real @ X2 ) @ ( cos_real @ X2 ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % tan_def
% 0.35/0.66  thf(fact_8181_choose__dvd,axiom,
% 0.35/0.66      ! [K: nat,N: nat] :
% 0.35/0.66        ( ( ord_less_eq_nat @ K @ N )
% 0.35/0.66       => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % choose_dvd
% 0.35/0.66  thf(fact_8182_choose__dvd,axiom,
% 0.35/0.66      ! [K: nat,N: nat] :
% 0.35/0.66        ( ( ord_less_eq_nat @ K @ N )
% 0.35/0.66       => ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % choose_dvd
% 0.35/0.66  thf(fact_8183_choose__dvd,axiom,
% 0.35/0.66      ! [K: nat,N: nat] :
% 0.35/0.66        ( ( ord_less_eq_nat @ K @ N )
% 0.35/0.66       => ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % choose_dvd
% 0.35/0.66  thf(fact_8184_choose__dvd,axiom,
% 0.35/0.66      ! [K: nat,N: nat] :
% 0.35/0.66        ( ( ord_less_eq_nat @ K @ N )
% 0.35/0.66       => ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % choose_dvd
% 0.35/0.66  thf(fact_8185_fact__numeral,axiom,
% 0.35/0.66      ! [K: num] :
% 0.35/0.66        ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ K ) )
% 0.35/0.66        = ( times_times_complex @ ( numera6690914467698888265omplex @ K ) @ ( semiri5044797733671781792omplex @ ( pred_numeral @ K ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_numeral
% 0.35/0.66  thf(fact_8186_fact__numeral,axiom,
% 0.35/0.66      ! [K: num] :
% 0.35/0.66        ( ( semiri773545260158071498ct_rat @ ( numeral_numeral_nat @ K ) )
% 0.35/0.66        = ( times_times_rat @ ( numeral_numeral_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( pred_numeral @ K ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_numeral
% 0.35/0.66  thf(fact_8187_fact__numeral,axiom,
% 0.35/0.66      ! [K: num] :
% 0.35/0.66        ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ K ) )
% 0.35/0.66        = ( times_times_int @ ( numeral_numeral_int @ K ) @ ( semiri1406184849735516958ct_int @ ( pred_numeral @ K ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_numeral
% 0.35/0.66  thf(fact_8188_fact__numeral,axiom,
% 0.35/0.66      ! [K: num] :
% 0.35/0.66        ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ K ) )
% 0.35/0.66        = ( times_times_real @ ( numeral_numeral_real @ K ) @ ( semiri2265585572941072030t_real @ ( pred_numeral @ K ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_numeral
% 0.35/0.66  thf(fact_8189_fact__numeral,axiom,
% 0.35/0.66      ! [K: num] :
% 0.35/0.66        ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ K ) )
% 0.35/0.66        = ( times_times_nat @ ( numeral_numeral_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( pred_numeral @ K ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_numeral
% 0.35/0.66  thf(fact_8190_square__fact__le__2__fact,axiom,
% 0.35/0.66      ! [N: nat] : ( ord_less_eq_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % square_fact_le_2_fact
% 0.35/0.66  thf(fact_8191_tan__45,axiom,
% 0.35/0.66      ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 0.35/0.66      = one_one_real ) ).
% 0.35/0.66  
% 0.35/0.66  % tan_45
% 0.35/0.66  thf(fact_8192_tan__60,axiom,
% 0.35/0.66      ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 0.35/0.66      = ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % tan_60
% 0.35/0.66  thf(fact_8193_fact__num__eq__if,axiom,
% 0.35/0.66      ( semiri773545260158071498ct_rat
% 0.35/0.66      = ( ^ [M6: nat] : ( if_rat @ ( M6 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ M6 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_num_eq_if
% 0.35/0.66  thf(fact_8194_fact__num__eq__if,axiom,
% 0.35/0.66      ( semiri1406184849735516958ct_int
% 0.35/0.66      = ( ^ [M6: nat] : ( if_int @ ( M6 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_num_eq_if
% 0.35/0.66  thf(fact_8195_fact__num__eq__if,axiom,
% 0.35/0.66      ( semiri5044797733671781792omplex
% 0.35/0.66      = ( ^ [M6: nat] : ( if_complex @ ( M6 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ M6 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_num_eq_if
% 0.35/0.66  thf(fact_8196_fact__num__eq__if,axiom,
% 0.35/0.66      ( semiri2265585572941072030t_real
% 0.35/0.66      = ( ^ [M6: nat] : ( if_real @ ( M6 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M6 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_num_eq_if
% 0.35/0.66  thf(fact_8197_fact__num__eq__if,axiom,
% 0.35/0.66      ( semiri1408675320244567234ct_nat
% 0.35/0.66      = ( ^ [M6: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M6 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_num_eq_if
% 0.35/0.66  thf(fact_8198_fact__reduce,axiom,
% 0.35/0.66      ! [N: nat] :
% 0.35/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.66       => ( ( semiri1406184849735516958ct_int @ N )
% 0.35/0.66          = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_reduce
% 0.35/0.66  thf(fact_8199_fact__reduce,axiom,
% 0.35/0.66      ! [N: nat] :
% 0.35/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.66       => ( ( semiri5044797733671781792omplex @ N )
% 0.35/0.66          = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_reduce
% 0.35/0.66  thf(fact_8200_fact__reduce,axiom,
% 0.35/0.66      ! [N: nat] :
% 0.35/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.66       => ( ( semiri2265585572941072030t_real @ N )
% 0.35/0.66          = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_reduce
% 0.35/0.66  thf(fact_8201_fact__reduce,axiom,
% 0.35/0.66      ! [N: nat] :
% 0.35/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.66       => ( ( semiri1408675320244567234ct_nat @ N )
% 0.35/0.66          = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_reduce
% 0.35/0.66  thf(fact_8202_tan__gt__zero,axiom,
% 0.35/0.66      ! [X: real] :
% 0.35/0.66        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.66       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.66         => ( ord_less_real @ zero_zero_real @ ( tan_real @ X ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % tan_gt_zero
% 0.35/0.66  thf(fact_8203_lemma__tan__total,axiom,
% 0.35/0.66      ! [Y2: real] :
% 0.35/0.66        ( ( ord_less_real @ zero_zero_real @ Y2 )
% 0.35/0.66       => ? [X3: real] :
% 0.35/0.66            ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.35/0.66            & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.66            & ( ord_less_real @ Y2 @ ( tan_real @ X3 ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % lemma_tan_total
% 0.35/0.66  thf(fact_8204_lemma__tan__total1,axiom,
% 0.35/0.66      ! [Y2: real] :
% 0.35/0.66      ? [X3: real] :
% 0.35/0.66        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 0.35/0.66        & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.66        & ( ( tan_real @ X3 )
% 0.35/0.66          = Y2 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % lemma_tan_total1
% 0.35/0.66  thf(fact_8205_tan__mono__lt__eq,axiom,
% 0.35/0.66      ! [X: real,Y2: real] :
% 0.35/0.66        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.35/0.66       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.66         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 0.35/0.66           => ( ( ord_less_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.66             => ( ( ord_less_real @ ( tan_real @ X ) @ ( tan_real @ Y2 ) )
% 0.35/0.66                = ( ord_less_real @ X @ Y2 ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % tan_mono_lt_eq
% 0.35/0.66  thf(fact_8206_tan__monotone_H,axiom,
% 0.35/0.66      ! [Y2: real,X: real] :
% 0.35/0.66        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 0.35/0.66       => ( ( ord_less_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.66         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.35/0.66           => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.66             => ( ( ord_less_real @ Y2 @ X )
% 0.35/0.66                = ( ord_less_real @ ( tan_real @ Y2 ) @ ( tan_real @ X ) ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % tan_monotone'
% 0.35/0.66  thf(fact_8207_tan__monotone,axiom,
% 0.35/0.66      ! [Y2: real,X: real] :
% 0.35/0.66        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 0.35/0.66       => ( ( ord_less_real @ Y2 @ X )
% 0.35/0.66         => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.66           => ( ord_less_real @ ( tan_real @ Y2 ) @ ( tan_real @ X ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % tan_monotone
% 0.35/0.66  thf(fact_8208_tan__total,axiom,
% 0.35/0.66      ! [Y2: real] :
% 0.35/0.66      ? [X3: real] :
% 0.35/0.66        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 0.35/0.66        & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.66        & ( ( tan_real @ X3 )
% 0.35/0.66          = Y2 )
% 0.35/0.66        & ! [Y4: real] :
% 0.35/0.66            ( ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 0.35/0.66              & ( ord_less_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.66              & ( ( tan_real @ Y4 )
% 0.35/0.66                = Y2 ) )
% 0.35/0.66           => ( Y4 = X3 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % tan_total
% 0.35/0.66  thf(fact_8209_tan__minus__45,axiom,
% 0.35/0.66      ( ( tan_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.66      = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.35/0.66  
% 0.35/0.66  % tan_minus_45
% 0.35/0.66  thf(fact_8210_tan__inverse,axiom,
% 0.35/0.66      ! [Y2: real] :
% 0.35/0.66        ( ( divide_divide_real @ one_one_real @ ( tan_real @ Y2 ) )
% 0.35/0.66        = ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % tan_inverse
% 0.35/0.66  thf(fact_8211_add__tan__eq,axiom,
% 0.35/0.66      ! [X: complex,Y2: complex] :
% 0.35/0.66        ( ( ( cos_complex @ X )
% 0.35/0.66         != zero_zero_complex )
% 0.35/0.66       => ( ( ( cos_complex @ Y2 )
% 0.35/0.66           != zero_zero_complex )
% 0.35/0.66         => ( ( plus_plus_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y2 ) )
% 0.35/0.66            = ( divide1717551699836669952omplex @ ( sin_complex @ ( plus_plus_complex @ X @ Y2 ) ) @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ Y2 ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % add_tan_eq
% 0.35/0.66  thf(fact_8212_add__tan__eq,axiom,
% 0.35/0.66      ! [X: real,Y2: real] :
% 0.35/0.66        ( ( ( cos_real @ X )
% 0.35/0.66         != zero_zero_real )
% 0.35/0.66       => ( ( ( cos_real @ Y2 )
% 0.35/0.66           != zero_zero_real )
% 0.35/0.66         => ( ( plus_plus_real @ ( tan_real @ X ) @ ( tan_real @ Y2 ) )
% 0.35/0.66            = ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ X @ Y2 ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y2 ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % add_tan_eq
% 0.35/0.66  thf(fact_8213_tan__total__pos,axiom,
% 0.35/0.66      ! [Y2: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 0.35/0.66       => ? [X3: real] :
% 0.35/0.66            ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.35/0.66            & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.66            & ( ( tan_real @ X3 )
% 0.35/0.66              = Y2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % tan_total_pos
% 0.35/0.66  thf(fact_8214_tan__pos__pi2__le,axiom,
% 0.35/0.66      ! [X: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.66       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.66         => ( ord_less_eq_real @ zero_zero_real @ ( tan_real @ X ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % tan_pos_pi2_le
% 0.35/0.66  thf(fact_8215_tan__less__zero,axiom,
% 0.35/0.66      ! [X: real] :
% 0.35/0.66        ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 0.35/0.66       => ( ( ord_less_real @ X @ zero_zero_real )
% 0.35/0.66         => ( ord_less_real @ ( tan_real @ X ) @ zero_zero_real ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % tan_less_zero
% 0.35/0.66  thf(fact_8216_tan__mono__le__eq,axiom,
% 0.35/0.66      ! [X: real,Y2: real] :
% 0.35/0.66        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.35/0.66       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.66         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 0.35/0.66           => ( ( ord_less_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.66             => ( ( ord_less_eq_real @ ( tan_real @ X ) @ ( tan_real @ Y2 ) )
% 0.35/0.66                = ( ord_less_eq_real @ X @ Y2 ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % tan_mono_le_eq
% 0.35/0.66  thf(fact_8217_tan__mono__le,axiom,
% 0.35/0.66      ! [X: real,Y2: real] :
% 0.35/0.66        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.35/0.66       => ( ( ord_less_eq_real @ X @ Y2 )
% 0.35/0.66         => ( ( ord_less_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.66           => ( ord_less_eq_real @ ( tan_real @ X ) @ ( tan_real @ Y2 ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % tan_mono_le
% 0.35/0.66  thf(fact_8218_tan__bound__pi2,axiom,
% 0.35/0.66      ! [X: real] :
% 0.35/0.66        ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 0.35/0.66       => ( ord_less_real @ ( abs_abs_real @ ( tan_real @ X ) ) @ one_one_real ) ) ).
% 0.35/0.66  
% 0.35/0.66  % tan_bound_pi2
% 0.35/0.66  thf(fact_8219_tan__30,axiom,
% 0.35/0.66      ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 0.35/0.66      = ( divide_divide_real @ one_one_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % tan_30
% 0.35/0.66  thf(fact_8220_arctan__unique,axiom,
% 0.35/0.66      ! [X: real,Y2: real] :
% 0.35/0.66        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.35/0.66       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.66         => ( ( ( tan_real @ X )
% 0.35/0.66              = Y2 )
% 0.35/0.66           => ( ( arctan @ Y2 )
% 0.35/0.66              = X ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % arctan_unique
% 0.35/0.66  thf(fact_8221_arctan__tan,axiom,
% 0.35/0.66      ! [X: real] :
% 0.35/0.66        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.35/0.66       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.66         => ( ( arctan @ ( tan_real @ X ) )
% 0.35/0.66            = X ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % arctan_tan
% 0.35/0.66  thf(fact_8222_arctan,axiom,
% 0.35/0.66      ! [Y2: real] :
% 0.35/0.66        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y2 ) )
% 0.35/0.66        & ( ord_less_real @ ( arctan @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.66        & ( ( tan_real @ ( arctan @ Y2 ) )
% 0.35/0.66          = Y2 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % arctan
% 0.35/0.66  thf(fact_8223_Maclaurin__zero,axiom,
% 0.35/0.66      ! [X: real,N: nat,Diff: nat > complex > real] :
% 0.35/0.66        ( ( X = zero_zero_real )
% 0.35/0.66       => ( ( N != zero_zero_nat )
% 0.35/0.66         => ( ( groups6591440286371151544t_real
% 0.35/0.66              @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_complex ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 0.35/0.66              @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.66            = ( Diff @ zero_zero_nat @ zero_zero_complex ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % Maclaurin_zero
% 0.35/0.66  thf(fact_8224_Maclaurin__zero,axiom,
% 0.35/0.66      ! [X: real,N: nat,Diff: nat > real > real] :
% 0.35/0.66        ( ( X = zero_zero_real )
% 0.35/0.66       => ( ( N != zero_zero_nat )
% 0.35/0.66         => ( ( groups6591440286371151544t_real
% 0.35/0.66              @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 0.35/0.66              @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.66            = ( Diff @ zero_zero_nat @ zero_zero_real ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % Maclaurin_zero
% 0.35/0.66  thf(fact_8225_Maclaurin__zero,axiom,
% 0.35/0.66      ! [X: real,N: nat,Diff: nat > rat > real] :
% 0.35/0.66        ( ( X = zero_zero_real )
% 0.35/0.66       => ( ( N != zero_zero_nat )
% 0.35/0.66         => ( ( groups6591440286371151544t_real
% 0.35/0.66              @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_rat ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 0.35/0.66              @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.66            = ( Diff @ zero_zero_nat @ zero_zero_rat ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % Maclaurin_zero
% 0.35/0.66  thf(fact_8226_Maclaurin__zero,axiom,
% 0.35/0.66      ! [X: real,N: nat,Diff: nat > nat > real] :
% 0.35/0.66        ( ( X = zero_zero_real )
% 0.35/0.66       => ( ( N != zero_zero_nat )
% 0.35/0.66         => ( ( groups6591440286371151544t_real
% 0.35/0.66              @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_nat ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 0.35/0.66              @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.66            = ( Diff @ zero_zero_nat @ zero_zero_nat ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % Maclaurin_zero
% 0.35/0.66  thf(fact_8227_Maclaurin__zero,axiom,
% 0.35/0.66      ! [X: real,N: nat,Diff: nat > int > real] :
% 0.35/0.66        ( ( X = zero_zero_real )
% 0.35/0.66       => ( ( N != zero_zero_nat )
% 0.35/0.66         => ( ( groups6591440286371151544t_real
% 0.35/0.66              @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_int ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 0.35/0.66              @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.66            = ( Diff @ zero_zero_nat @ zero_zero_int ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % Maclaurin_zero
% 0.35/0.66  thf(fact_8228_Maclaurin__lemma,axiom,
% 0.35/0.66      ! [H2: real,F: real > real,J: nat > real,N: nat] :
% 0.35/0.66        ( ( ord_less_real @ zero_zero_real @ H2 )
% 0.35/0.66       => ? [B8: real] :
% 0.35/0.66            ( ( F @ H2 )
% 0.35/0.66            = ( plus_plus_real
% 0.35/0.66              @ ( groups6591440286371151544t_real
% 0.35/0.66                @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( J @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 0.35/0.66                @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.66              @ ( times_times_real @ B8 @ ( divide_divide_real @ ( power_power_real @ H2 @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % Maclaurin_lemma
% 0.35/0.66  thf(fact_8229_lemma__tan__add1,axiom,
% 0.35/0.66      ! [X: complex,Y2: complex] :
% 0.35/0.66        ( ( ( cos_complex @ X )
% 0.35/0.66         != zero_zero_complex )
% 0.35/0.66       => ( ( ( cos_complex @ Y2 )
% 0.35/0.66           != zero_zero_complex )
% 0.35/0.66         => ( ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y2 ) ) )
% 0.35/0.66            = ( divide1717551699836669952omplex @ ( cos_complex @ ( plus_plus_complex @ X @ Y2 ) ) @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ Y2 ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % lemma_tan_add1
% 0.35/0.66  thf(fact_8230_lemma__tan__add1,axiom,
% 0.35/0.66      ! [X: real,Y2: real] :
% 0.35/0.66        ( ( ( cos_real @ X )
% 0.35/0.66         != zero_zero_real )
% 0.35/0.66       => ( ( ( cos_real @ Y2 )
% 0.35/0.66           != zero_zero_real )
% 0.35/0.66         => ( ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X ) @ ( tan_real @ Y2 ) ) )
% 0.35/0.66            = ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ X @ Y2 ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y2 ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % lemma_tan_add1
% 0.35/0.66  thf(fact_8231_tan__diff,axiom,
% 0.35/0.66      ! [X: complex,Y2: complex] :
% 0.35/0.66        ( ( ( cos_complex @ X )
% 0.35/0.66         != zero_zero_complex )
% 0.35/0.66       => ( ( ( cos_complex @ Y2 )
% 0.35/0.66           != zero_zero_complex )
% 0.35/0.66         => ( ( ( cos_complex @ ( minus_minus_complex @ X @ Y2 ) )
% 0.35/0.66             != zero_zero_complex )
% 0.35/0.66           => ( ( tan_complex @ ( minus_minus_complex @ X @ Y2 ) )
% 0.35/0.66              = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y2 ) ) @ ( plus_plus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y2 ) ) ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % tan_diff
% 0.35/0.66  thf(fact_8232_tan__diff,axiom,
% 0.35/0.66      ! [X: real,Y2: real] :
% 0.35/0.66        ( ( ( cos_real @ X )
% 0.35/0.66         != zero_zero_real )
% 0.35/0.66       => ( ( ( cos_real @ Y2 )
% 0.35/0.66           != zero_zero_real )
% 0.35/0.66         => ( ( ( cos_real @ ( minus_minus_real @ X @ Y2 ) )
% 0.35/0.66             != zero_zero_real )
% 0.35/0.66           => ( ( tan_real @ ( minus_minus_real @ X @ Y2 ) )
% 0.35/0.66              = ( divide_divide_real @ ( minus_minus_real @ ( tan_real @ X ) @ ( tan_real @ Y2 ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X ) @ ( tan_real @ Y2 ) ) ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % tan_diff
% 0.35/0.66  thf(fact_8233_tan__add,axiom,
% 0.35/0.66      ! [X: complex,Y2: complex] :
% 0.35/0.66        ( ( ( cos_complex @ X )
% 0.35/0.66         != zero_zero_complex )
% 0.35/0.66       => ( ( ( cos_complex @ Y2 )
% 0.35/0.66           != zero_zero_complex )
% 0.35/0.66         => ( ( ( cos_complex @ ( plus_plus_complex @ X @ Y2 ) )
% 0.35/0.66             != zero_zero_complex )
% 0.35/0.66           => ( ( tan_complex @ ( plus_plus_complex @ X @ Y2 ) )
% 0.35/0.66              = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y2 ) ) @ ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y2 ) ) ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % tan_add
% 0.35/0.66  thf(fact_8234_tan__add,axiom,
% 0.35/0.66      ! [X: real,Y2: real] :
% 0.35/0.66        ( ( ( cos_real @ X )
% 0.35/0.66         != zero_zero_real )
% 0.35/0.66       => ( ( ( cos_real @ Y2 )
% 0.35/0.66           != zero_zero_real )
% 0.35/0.66         => ( ( ( cos_real @ ( plus_plus_real @ X @ Y2 ) )
% 0.35/0.66             != zero_zero_real )
% 0.35/0.66           => ( ( tan_real @ ( plus_plus_real @ X @ Y2 ) )
% 0.35/0.66              = ( divide_divide_real @ ( plus_plus_real @ ( tan_real @ X ) @ ( tan_real @ Y2 ) ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X ) @ ( tan_real @ Y2 ) ) ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % tan_add
% 0.35/0.66  thf(fact_8235_tan__total__pi4,axiom,
% 0.35/0.66      ! [X: real] :
% 0.35/0.66        ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.35/0.66       => ? [Z3: real] :
% 0.35/0.66            ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) @ Z3 )
% 0.35/0.66            & ( ord_less_real @ Z3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 0.35/0.66            & ( ( tan_real @ Z3 )
% 0.35/0.66              = X ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % tan_total_pi4
% 0.35/0.66  thf(fact_8236_Maclaurin__exp__le,axiom,
% 0.35/0.66      ! [X: real,N: nat] :
% 0.35/0.66      ? [T6: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 0.35/0.66        & ( ( exp_real @ X )
% 0.35/0.66          = ( plus_plus_real
% 0.35/0.66            @ ( groups6591440286371151544t_real
% 0.35/0.66              @ ^ [M6: nat] : ( divide_divide_real @ ( power_power_real @ X @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) )
% 0.35/0.66              @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.66            @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % Maclaurin_exp_le
% 0.35/0.66  thf(fact_8237_tan__half,axiom,
% 0.35/0.66      ( tan_complex
% 0.35/0.66      = ( ^ [X2: complex] : ( divide1717551699836669952omplex @ ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) ) @ ( plus_plus_complex @ ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) ) @ one_one_complex ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % tan_half
% 0.35/0.66  thf(fact_8238_tan__half,axiom,
% 0.35/0.66      ( tan_real
% 0.35/0.66      = ( ^ [X2: real] : ( divide_divide_real @ ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) ) @ ( plus_plus_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) ) @ one_one_real ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % tan_half
% 0.35/0.66  thf(fact_8239_cos__coeff__def,axiom,
% 0.35/0.66      ( cos_coeff
% 0.35/0.66      = ( ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ zero_zero_real ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % cos_coeff_def
% 0.35/0.66  thf(fact_8240_Maclaurin__exp__lt,axiom,
% 0.35/0.66      ! [X: real,N: nat] :
% 0.35/0.66        ( ( X != zero_zero_real )
% 0.35/0.66       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.66         => ? [T6: real] :
% 0.35/0.66              ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T6 ) )
% 0.35/0.66              & ( ord_less_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 0.35/0.66              & ( ( exp_real @ X )
% 0.35/0.66                = ( plus_plus_real
% 0.35/0.66                  @ ( groups6591440286371151544t_real
% 0.35/0.66                    @ ^ [M6: nat] : ( divide_divide_real @ ( power_power_real @ X @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) )
% 0.35/0.66                    @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.66                  @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % Maclaurin_exp_lt
% 0.35/0.66  thf(fact_8241_cos__tan,axiom,
% 0.35/0.66      ! [X: real] :
% 0.35/0.66        ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.66       => ( ( cos_real @ X )
% 0.35/0.66          = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % cos_tan
% 0.35/0.66  thf(fact_8242_Maclaurin__sin__expansion3,axiom,
% 0.35/0.66      ! [N: nat,X: real] :
% 0.35/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.66       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.66         => ? [T6: real] :
% 0.35/0.66              ( ( ord_less_real @ zero_zero_real @ T6 )
% 0.35/0.66              & ( ord_less_real @ T6 @ X )
% 0.35/0.66              & ( ( sin_real @ X )
% 0.35/0.66                = ( plus_plus_real
% 0.35/0.66                  @ ( groups6591440286371151544t_real
% 0.35/0.66                    @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 0.35/0.66                    @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.66                  @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % Maclaurin_sin_expansion3
% 0.35/0.66  thf(fact_8243_Maclaurin__sin__expansion4,axiom,
% 0.35/0.66      ! [X: real,N: nat] :
% 0.35/0.66        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.66       => ? [T6: real] :
% 0.35/0.66            ( ( ord_less_real @ zero_zero_real @ T6 )
% 0.35/0.66            & ( ord_less_eq_real @ T6 @ X )
% 0.35/0.66            & ( ( sin_real @ X )
% 0.35/0.66              = ( plus_plus_real
% 0.35/0.66                @ ( groups6591440286371151544t_real
% 0.35/0.66                  @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 0.35/0.66                  @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.66                @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % Maclaurin_sin_expansion4
% 0.35/0.66  thf(fact_8244_Maclaurin__sin__expansion2,axiom,
% 0.35/0.66      ! [X: real,N: nat] :
% 0.35/0.66      ? [T6: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 0.35/0.66        & ( ( sin_real @ X )
% 0.35/0.66          = ( plus_plus_real
% 0.35/0.66            @ ( groups6591440286371151544t_real
% 0.35/0.66              @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 0.35/0.66              @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.66            @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % Maclaurin_sin_expansion2
% 0.35/0.66  thf(fact_8245_Maclaurin__sin__expansion,axiom,
% 0.35/0.66      ! [X: real,N: nat] :
% 0.35/0.66      ? [T6: real] :
% 0.35/0.66        ( ( sin_real @ X )
% 0.35/0.66        = ( plus_plus_real
% 0.35/0.66          @ ( groups6591440286371151544t_real
% 0.35/0.66            @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 0.35/0.66            @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.66          @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % Maclaurin_sin_expansion
% 0.35/0.66  thf(fact_8246_sin__coeff__def,axiom,
% 0.35/0.66      ( sin_coeff
% 0.35/0.66      = ( ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ zero_zero_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sin_coeff_def
% 0.35/0.66  thf(fact_8247_fact__ge__self,axiom,
% 0.35/0.66      ! [N: nat] : ( ord_less_eq_nat @ N @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_ge_self
% 0.35/0.66  thf(fact_8248_fact__mono__nat,axiom,
% 0.35/0.66      ! [M: nat,N: nat] :
% 0.35/0.66        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.66       => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_mono_nat
% 0.35/0.66  thf(fact_8249_fact__less__mono__nat,axiom,
% 0.35/0.66      ! [M: nat,N: nat] :
% 0.35/0.66        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.35/0.66       => ( ( ord_less_nat @ M @ N )
% 0.35/0.66         => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_less_mono_nat
% 0.35/0.66  thf(fact_8250_fact__ge__Suc__0__nat,axiom,
% 0.35/0.66      ! [N: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_ge_Suc_0_nat
% 0.35/0.66  thf(fact_8251_dvd__fact,axiom,
% 0.35/0.66      ! [M: nat,N: nat] :
% 0.35/0.66        ( ( ord_less_eq_nat @ one_one_nat @ M )
% 0.35/0.66       => ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.66         => ( dvd_dvd_nat @ M @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % dvd_fact
% 0.35/0.66  thf(fact_8252_fact__diff__Suc,axiom,
% 0.35/0.66      ! [N: nat,M: nat] :
% 0.35/0.66        ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.35/0.66       => ( ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) )
% 0.35/0.66          = ( times_times_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M @ N ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_diff_Suc
% 0.35/0.66  thf(fact_8253_fact__div__fact__le__pow,axiom,
% 0.35/0.66      ! [R: nat,N: nat] :
% 0.35/0.66        ( ( ord_less_eq_nat @ R @ N )
% 0.35/0.66       => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ R ) ) ) @ ( power_power_nat @ N @ R ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_div_fact_le_pow
% 0.35/0.66  thf(fact_8254_sin__coeff__Suc,axiom,
% 0.35/0.66      ! [N: nat] :
% 0.35/0.66        ( ( sin_coeff @ ( suc @ N ) )
% 0.35/0.66        = ( divide_divide_real @ ( cos_coeff @ N ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sin_coeff_Suc
% 0.35/0.66  thf(fact_8255_cos__coeff__Suc,axiom,
% 0.35/0.66      ! [N: nat] :
% 0.35/0.66        ( ( cos_coeff @ ( suc @ N ) )
% 0.35/0.66        = ( divide_divide_real @ ( uminus_uminus_real @ ( sin_coeff @ N ) ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % cos_coeff_Suc
% 0.35/0.66  thf(fact_8256_complex__unimodular__polar,axiom,
% 0.35/0.66      ! [Z: complex] :
% 0.35/0.66        ( ( ( real_V1022390504157884413omplex @ Z )
% 0.35/0.66          = one_one_real )
% 0.35/0.66       => ~ ! [T6: real] :
% 0.35/0.66              ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 0.35/0.66             => ( ( ord_less_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.35/0.66               => ( Z
% 0.35/0.66                 != ( complex2 @ ( cos_real @ T6 ) @ ( sin_real @ T6 ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % complex_unimodular_polar
% 0.35/0.66  thf(fact_8257_sin__paired,axiom,
% 0.35/0.66      ! [X: real] :
% 0.35/0.66        ( sums_real
% 0.35/0.66        @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 0.35/0.66        @ ( sin_real @ X ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sin_paired
% 0.35/0.66  thf(fact_8258_cos__arcsin,axiom,
% 0.35/0.66      ! [X: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.35/0.66       => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.35/0.66         => ( ( cos_real @ ( arcsin @ X ) )
% 0.35/0.66            = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % cos_arcsin
% 0.35/0.66  thf(fact_8259_sin__arccos__abs,axiom,
% 0.35/0.66      ! [Y2: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 0.35/0.66       => ( ( sin_real @ ( arccos @ Y2 ) )
% 0.35/0.66          = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sin_arccos_abs
% 0.35/0.66  thf(fact_8260_arccos__1,axiom,
% 0.35/0.66      ( ( arccos @ one_one_real )
% 0.35/0.66      = zero_zero_real ) ).
% 0.35/0.66  
% 0.35/0.66  % arccos_1
% 0.35/0.66  thf(fact_8261_arccos__minus__1,axiom,
% 0.35/0.66      ( ( arccos @ ( uminus_uminus_real @ one_one_real ) )
% 0.35/0.66      = pi ) ).
% 0.35/0.66  
% 0.35/0.66  % arccos_minus_1
% 0.35/0.66  thf(fact_8262_cos__arccos,axiom,
% 0.35/0.66      ! [Y2: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 0.35/0.66       => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 0.35/0.66         => ( ( cos_real @ ( arccos @ Y2 ) )
% 0.35/0.66            = Y2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % cos_arccos
% 0.35/0.66  thf(fact_8263_sin__arcsin,axiom,
% 0.35/0.66      ! [Y2: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 0.35/0.66       => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 0.35/0.66         => ( ( sin_real @ ( arcsin @ Y2 ) )
% 0.35/0.66            = Y2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sin_arcsin
% 0.35/0.66  thf(fact_8264_powser__sums__zero__iff,axiom,
% 0.35/0.66      ! [A: nat > complex,X: complex] :
% 0.35/0.66        ( ( sums_complex
% 0.35/0.66          @ ^ [N2: nat] : ( times_times_complex @ ( A @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) )
% 0.35/0.66          @ X )
% 0.35/0.66        = ( ( A @ zero_zero_nat )
% 0.35/0.66          = X ) ) ).
% 0.35/0.66  
% 0.35/0.66  % powser_sums_zero_iff
% 0.35/0.66  thf(fact_8265_powser__sums__zero__iff,axiom,
% 0.35/0.66      ! [A: nat > real,X: real] :
% 0.35/0.66        ( ( sums_real
% 0.35/0.66          @ ^ [N2: nat] : ( times_times_real @ ( A @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) )
% 0.35/0.66          @ X )
% 0.35/0.66        = ( ( A @ zero_zero_nat )
% 0.35/0.66          = X ) ) ).
% 0.35/0.66  
% 0.35/0.66  % powser_sums_zero_iff
% 0.35/0.66  thf(fact_8266_norm__cos__sin,axiom,
% 0.35/0.66      ! [T: real] :
% 0.35/0.66        ( ( real_V1022390504157884413omplex @ ( complex2 @ ( cos_real @ T ) @ ( sin_real @ T ) ) )
% 0.35/0.66        = one_one_real ) ).
% 0.35/0.66  
% 0.35/0.66  % norm_cos_sin
% 0.35/0.66  thf(fact_8267_arccos__0,axiom,
% 0.35/0.66      ( ( arccos @ zero_zero_real )
% 0.35/0.66      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % arccos_0
% 0.35/0.66  thf(fact_8268_arcsin__1,axiom,
% 0.35/0.66      ( ( arcsin @ one_one_real )
% 0.35/0.66      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % arcsin_1
% 0.35/0.66  thf(fact_8269_arcsin__minus__1,axiom,
% 0.35/0.66      ( ( arcsin @ ( uminus_uminus_real @ one_one_real ) )
% 0.35/0.66      = ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % arcsin_minus_1
% 0.35/0.66  thf(fact_8270_complex__of__real__mult__Complex,axiom,
% 0.35/0.66      ! [R: real,X: real,Y2: real] :
% 0.35/0.66        ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R ) @ ( complex2 @ X @ Y2 ) )
% 0.35/0.66        = ( complex2 @ ( times_times_real @ R @ X ) @ ( times_times_real @ R @ Y2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % complex_of_real_mult_Complex
% 0.35/0.66  thf(fact_8271_Complex__mult__complex__of__real,axiom,
% 0.35/0.66      ! [X: real,Y2: real,R: real] :
% 0.35/0.66        ( ( times_times_complex @ ( complex2 @ X @ Y2 ) @ ( real_V4546457046886955230omplex @ R ) )
% 0.35/0.66        = ( complex2 @ ( times_times_real @ X @ R ) @ ( times_times_real @ Y2 @ R ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % Complex_mult_complex_of_real
% 0.35/0.66  thf(fact_8272_complex__diff,axiom,
% 0.35/0.66      ! [A: real,B: real,C: real,D2: real] :
% 0.35/0.66        ( ( minus_minus_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D2 ) )
% 0.35/0.66        = ( complex2 @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % complex_diff
% 0.35/0.66  thf(fact_8273_sums__le,axiom,
% 0.35/0.66      ! [F: nat > real,G: nat > real,S3: real,T: real] :
% 0.35/0.66        ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 0.35/0.66       => ( ( sums_real @ F @ S3 )
% 0.35/0.66         => ( ( sums_real @ G @ T )
% 0.35/0.66           => ( ord_less_eq_real @ S3 @ T ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_le
% 0.35/0.66  thf(fact_8274_sums__le,axiom,
% 0.35/0.66      ! [F: nat > nat,G: nat > nat,S3: nat,T: nat] :
% 0.35/0.66        ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( G @ N3 ) )
% 0.35/0.66       => ( ( sums_nat @ F @ S3 )
% 0.35/0.66         => ( ( sums_nat @ G @ T )
% 0.35/0.66           => ( ord_less_eq_nat @ S3 @ T ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_le
% 0.35/0.66  thf(fact_8275_sums__le,axiom,
% 0.35/0.66      ! [F: nat > int,G: nat > int,S3: int,T: int] :
% 0.35/0.66        ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( G @ N3 ) )
% 0.35/0.66       => ( ( sums_int @ F @ S3 )
% 0.35/0.66         => ( ( sums_int @ G @ T )
% 0.35/0.66           => ( ord_less_eq_int @ S3 @ T ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_le
% 0.35/0.66  thf(fact_8276_sums__divide,axiom,
% 0.35/0.66      ! [F: nat > complex,A: complex,C: complex] :
% 0.35/0.66        ( ( sums_complex @ F @ A )
% 0.35/0.66       => ( sums_complex
% 0.35/0.66          @ ^ [N2: nat] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ C )
% 0.35/0.66          @ ( divide1717551699836669952omplex @ A @ C ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_divide
% 0.35/0.66  thf(fact_8277_sums__divide,axiom,
% 0.35/0.66      ! [F: nat > real,A: real,C: real] :
% 0.35/0.66        ( ( sums_real @ F @ A )
% 0.35/0.66       => ( sums_real
% 0.35/0.66          @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ C )
% 0.35/0.66          @ ( divide_divide_real @ A @ C ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_divide
% 0.35/0.66  thf(fact_8278_sums__diff,axiom,
% 0.35/0.66      ! [F: nat > real,A: real,G: nat > real,B: real] :
% 0.35/0.66        ( ( sums_real @ F @ A )
% 0.35/0.66       => ( ( sums_real @ G @ B )
% 0.35/0.66         => ( sums_real
% 0.35/0.66            @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 0.35/0.66            @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_diff
% 0.35/0.66  thf(fact_8279_sums__add,axiom,
% 0.35/0.66      ! [F: nat > real,A: real,G: nat > real,B: real] :
% 0.35/0.66        ( ( sums_real @ F @ A )
% 0.35/0.66       => ( ( sums_real @ G @ B )
% 0.35/0.66         => ( sums_real
% 0.35/0.66            @ ^ [N2: nat] : ( plus_plus_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 0.35/0.66            @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_add
% 0.35/0.66  thf(fact_8280_sums__add,axiom,
% 0.35/0.66      ! [F: nat > nat,A: nat,G: nat > nat,B: nat] :
% 0.35/0.66        ( ( sums_nat @ F @ A )
% 0.35/0.66       => ( ( sums_nat @ G @ B )
% 0.35/0.66         => ( sums_nat
% 0.35/0.66            @ ^ [N2: nat] : ( plus_plus_nat @ ( F @ N2 ) @ ( G @ N2 ) )
% 0.35/0.66            @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_add
% 0.35/0.66  thf(fact_8281_sums__add,axiom,
% 0.35/0.66      ! [F: nat > int,A: int,G: nat > int,B: int] :
% 0.35/0.66        ( ( sums_int @ F @ A )
% 0.35/0.66       => ( ( sums_int @ G @ B )
% 0.35/0.66         => ( sums_int
% 0.35/0.66            @ ^ [N2: nat] : ( plus_plus_int @ ( F @ N2 ) @ ( G @ N2 ) )
% 0.35/0.66            @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_add
% 0.35/0.66  thf(fact_8282_sums__add,axiom,
% 0.35/0.66      ! [F: nat > complex,A: complex,G: nat > complex,B: complex] :
% 0.35/0.66        ( ( sums_complex @ F @ A )
% 0.35/0.66       => ( ( sums_complex @ G @ B )
% 0.35/0.66         => ( sums_complex
% 0.35/0.66            @ ^ [N2: nat] : ( plus_plus_complex @ ( F @ N2 ) @ ( G @ N2 ) )
% 0.35/0.66            @ ( plus_plus_complex @ A @ B ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_add
% 0.35/0.66  thf(fact_8283_sums__mult,axiom,
% 0.35/0.66      ! [F: nat > complex,A: complex,C: complex] :
% 0.35/0.66        ( ( sums_complex @ F @ A )
% 0.35/0.66       => ( sums_complex
% 0.35/0.66          @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) )
% 0.35/0.66          @ ( times_times_complex @ C @ A ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_mult
% 0.35/0.66  thf(fact_8284_sums__mult,axiom,
% 0.35/0.66      ! [F: nat > real,A: real,C: real] :
% 0.35/0.66        ( ( sums_real @ F @ A )
% 0.35/0.66       => ( sums_real
% 0.35/0.66          @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) )
% 0.35/0.66          @ ( times_times_real @ C @ A ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_mult
% 0.35/0.66  thf(fact_8285_sums__mult2,axiom,
% 0.35/0.66      ! [F: nat > complex,A: complex,C: complex] :
% 0.35/0.66        ( ( sums_complex @ F @ A )
% 0.35/0.66       => ( sums_complex
% 0.35/0.66          @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ C )
% 0.35/0.66          @ ( times_times_complex @ A @ C ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_mult2
% 0.35/0.66  thf(fact_8286_sums__mult2,axiom,
% 0.35/0.66      ! [F: nat > real,A: real,C: real] :
% 0.35/0.66        ( ( sums_real @ F @ A )
% 0.35/0.66       => ( sums_real
% 0.35/0.66          @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ C )
% 0.35/0.66          @ ( times_times_real @ A @ C ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_mult2
% 0.35/0.66  thf(fact_8287_sums__mult2__iff,axiom,
% 0.35/0.66      ! [C: complex,F: nat > complex,D2: complex] :
% 0.35/0.66        ( ( C != zero_zero_complex )
% 0.35/0.66       => ( ( sums_complex
% 0.35/0.66            @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ C )
% 0.35/0.66            @ ( times_times_complex @ D2 @ C ) )
% 0.35/0.66          = ( sums_complex @ F @ D2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_mult2_iff
% 0.35/0.66  thf(fact_8288_sums__mult2__iff,axiom,
% 0.35/0.66      ! [C: real,F: nat > real,D2: real] :
% 0.35/0.66        ( ( C != zero_zero_real )
% 0.35/0.66       => ( ( sums_real
% 0.35/0.66            @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ C )
% 0.35/0.66            @ ( times_times_real @ D2 @ C ) )
% 0.35/0.66          = ( sums_real @ F @ D2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_mult2_iff
% 0.35/0.66  thf(fact_8289_sums__mult__iff,axiom,
% 0.35/0.66      ! [C: complex,F: nat > complex,D2: complex] :
% 0.35/0.66        ( ( C != zero_zero_complex )
% 0.35/0.66       => ( ( sums_complex
% 0.35/0.66            @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) )
% 0.35/0.66            @ ( times_times_complex @ C @ D2 ) )
% 0.35/0.66          = ( sums_complex @ F @ D2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_mult_iff
% 0.35/0.66  thf(fact_8290_sums__mult__iff,axiom,
% 0.35/0.66      ! [C: real,F: nat > real,D2: real] :
% 0.35/0.66        ( ( C != zero_zero_real )
% 0.35/0.66       => ( ( sums_real
% 0.35/0.66            @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) )
% 0.35/0.66            @ ( times_times_real @ C @ D2 ) )
% 0.35/0.66          = ( sums_real @ F @ D2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_mult_iff
% 0.35/0.66  thf(fact_8291_Complex__eq__numeral,axiom,
% 0.35/0.66      ! [A: real,B: real,W: num] :
% 0.35/0.66        ( ( ( complex2 @ A @ B )
% 0.35/0.66          = ( numera6690914467698888265omplex @ W ) )
% 0.35/0.66        = ( ( A
% 0.35/0.66            = ( numeral_numeral_real @ W ) )
% 0.35/0.66          & ( B = zero_zero_real ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % Complex_eq_numeral
% 0.35/0.66  thf(fact_8292_complex__add,axiom,
% 0.35/0.66      ! [A: real,B: real,C: real,D2: real] :
% 0.35/0.66        ( ( plus_plus_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D2 ) )
% 0.35/0.66        = ( complex2 @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % complex_add
% 0.35/0.66  thf(fact_8293_complex__of__real__add__Complex,axiom,
% 0.35/0.66      ! [R: real,X: real,Y2: real] :
% 0.35/0.66        ( ( plus_plus_complex @ ( real_V4546457046886955230omplex @ R ) @ ( complex2 @ X @ Y2 ) )
% 0.35/0.66        = ( complex2 @ ( plus_plus_real @ R @ X ) @ Y2 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % complex_of_real_add_Complex
% 0.35/0.66  thf(fact_8294_Complex__add__complex__of__real,axiom,
% 0.35/0.66      ! [X: real,Y2: real,R: real] :
% 0.35/0.66        ( ( plus_plus_complex @ ( complex2 @ X @ Y2 ) @ ( real_V4546457046886955230omplex @ R ) )
% 0.35/0.66        = ( complex2 @ ( plus_plus_real @ X @ R ) @ Y2 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % Complex_add_complex_of_real
% 0.35/0.66  thf(fact_8295_sums__mult__D,axiom,
% 0.35/0.66      ! [C: complex,F: nat > complex,A: complex] :
% 0.35/0.66        ( ( sums_complex
% 0.35/0.66          @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) )
% 0.35/0.66          @ A )
% 0.35/0.66       => ( ( C != zero_zero_complex )
% 0.35/0.66         => ( sums_complex @ F @ ( divide1717551699836669952omplex @ A @ C ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_mult_D
% 0.35/0.66  thf(fact_8296_sums__mult__D,axiom,
% 0.35/0.66      ! [C: real,F: nat > real,A: real] :
% 0.35/0.66        ( ( sums_real
% 0.35/0.66          @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) )
% 0.35/0.66          @ A )
% 0.35/0.66       => ( ( C != zero_zero_real )
% 0.35/0.66         => ( sums_real @ F @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_mult_D
% 0.35/0.66  thf(fact_8297_sums__Suc__imp,axiom,
% 0.35/0.66      ! [F: nat > complex,S3: complex] :
% 0.35/0.66        ( ( ( F @ zero_zero_nat )
% 0.35/0.66          = zero_zero_complex )
% 0.35/0.66       => ( ( sums_complex
% 0.35/0.66            @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 0.35/0.66            @ S3 )
% 0.35/0.66         => ( sums_complex @ F @ S3 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_Suc_imp
% 0.35/0.66  thf(fact_8298_sums__Suc__imp,axiom,
% 0.35/0.66      ! [F: nat > real,S3: real] :
% 0.35/0.66        ( ( ( F @ zero_zero_nat )
% 0.35/0.66          = zero_zero_real )
% 0.35/0.66       => ( ( sums_real
% 0.35/0.66            @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 0.35/0.66            @ S3 )
% 0.35/0.66         => ( sums_real @ F @ S3 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_Suc_imp
% 0.35/0.66  thf(fact_8299_sums__Suc,axiom,
% 0.35/0.66      ! [F: nat > real,L2: real] :
% 0.35/0.66        ( ( sums_real
% 0.35/0.66          @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 0.35/0.66          @ L2 )
% 0.35/0.66       => ( sums_real @ F @ ( plus_plus_real @ L2 @ ( F @ zero_zero_nat ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_Suc
% 0.35/0.66  thf(fact_8300_sums__Suc,axiom,
% 0.35/0.66      ! [F: nat > nat,L2: nat] :
% 0.35/0.66        ( ( sums_nat
% 0.35/0.66          @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 0.35/0.66          @ L2 )
% 0.35/0.66       => ( sums_nat @ F @ ( plus_plus_nat @ L2 @ ( F @ zero_zero_nat ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_Suc
% 0.35/0.66  thf(fact_8301_sums__Suc,axiom,
% 0.35/0.66      ! [F: nat > int,L2: int] :
% 0.35/0.66        ( ( sums_int
% 0.35/0.66          @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 0.35/0.66          @ L2 )
% 0.35/0.66       => ( sums_int @ F @ ( plus_plus_int @ L2 @ ( F @ zero_zero_nat ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_Suc
% 0.35/0.66  thf(fact_8302_sums__Suc,axiom,
% 0.35/0.66      ! [F: nat > complex,L2: complex] :
% 0.35/0.66        ( ( sums_complex
% 0.35/0.66          @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 0.35/0.66          @ L2 )
% 0.35/0.66       => ( sums_complex @ F @ ( plus_plus_complex @ L2 @ ( F @ zero_zero_nat ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_Suc
% 0.35/0.66  thf(fact_8303_sums__Suc__iff,axiom,
% 0.35/0.66      ! [F: nat > real,S3: real] :
% 0.35/0.66        ( ( sums_real
% 0.35/0.66          @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 0.35/0.66          @ S3 )
% 0.35/0.66        = ( sums_real @ F @ ( plus_plus_real @ S3 @ ( F @ zero_zero_nat ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_Suc_iff
% 0.35/0.66  thf(fact_8304_sums__Suc__iff,axiom,
% 0.35/0.66      ! [F: nat > complex,S3: complex] :
% 0.35/0.66        ( ( sums_complex
% 0.35/0.66          @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 0.35/0.66          @ S3 )
% 0.35/0.66        = ( sums_complex @ F @ ( plus_plus_complex @ S3 @ ( F @ zero_zero_nat ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_Suc_iff
% 0.35/0.66  thf(fact_8305_sums__zero__iff__shift,axiom,
% 0.35/0.66      ! [N: nat,F: nat > complex,S3: complex] :
% 0.35/0.66        ( ! [I4: nat] :
% 0.35/0.66            ( ( ord_less_nat @ I4 @ N )
% 0.35/0.66           => ( ( F @ I4 )
% 0.35/0.66              = zero_zero_complex ) )
% 0.35/0.66       => ( ( sums_complex
% 0.35/0.66            @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N ) )
% 0.35/0.66            @ S3 )
% 0.35/0.66          = ( sums_complex @ F @ S3 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_zero_iff_shift
% 0.35/0.66  thf(fact_8306_sums__zero__iff__shift,axiom,
% 0.35/0.66      ! [N: nat,F: nat > real,S3: real] :
% 0.35/0.66        ( ! [I4: nat] :
% 0.35/0.66            ( ( ord_less_nat @ I4 @ N )
% 0.35/0.66           => ( ( F @ I4 )
% 0.35/0.66              = zero_zero_real ) )
% 0.35/0.66       => ( ( sums_real
% 0.35/0.66            @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N ) )
% 0.35/0.66            @ S3 )
% 0.35/0.66          = ( sums_real @ F @ S3 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_zero_iff_shift
% 0.35/0.66  thf(fact_8307_Complex__eq__neg__numeral,axiom,
% 0.35/0.66      ! [A: real,B: real,W: num] :
% 0.35/0.66        ( ( ( complex2 @ A @ B )
% 0.35/0.66          = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 0.35/0.66        = ( ( A
% 0.35/0.66            = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 0.35/0.66          & ( B = zero_zero_real ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % Complex_eq_neg_numeral
% 0.35/0.66  thf(fact_8308_complex__mult,axiom,
% 0.35/0.66      ! [A: real,B: real,C: real,D2: real] :
% 0.35/0.66        ( ( times_times_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D2 ) )
% 0.35/0.66        = ( complex2 @ ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) @ ( plus_plus_real @ ( times_times_real @ A @ D2 ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % complex_mult
% 0.35/0.66  thf(fact_8309_Complex__eq__1,axiom,
% 0.35/0.66      ! [A: real,B: real] :
% 0.35/0.66        ( ( ( complex2 @ A @ B )
% 0.35/0.66          = one_one_complex )
% 0.35/0.66        = ( ( A = one_one_real )
% 0.35/0.66          & ( B = zero_zero_real ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % Complex_eq_1
% 0.35/0.66  thf(fact_8310_one__complex_Ocode,axiom,
% 0.35/0.66      ( one_one_complex
% 0.35/0.66      = ( complex2 @ one_one_real @ zero_zero_real ) ) ).
% 0.35/0.66  
% 0.35/0.66  % one_complex.code
% 0.35/0.66  thf(fact_8311_arccos__le__arccos,axiom,
% 0.35/0.66      ! [X: real,Y2: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.35/0.66       => ( ( ord_less_eq_real @ X @ Y2 )
% 0.35/0.66         => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 0.35/0.66           => ( ord_less_eq_real @ ( arccos @ Y2 ) @ ( arccos @ X ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % arccos_le_arccos
% 0.35/0.66  thf(fact_8312_arccos__le__mono,axiom,
% 0.35/0.66      ! [X: real,Y2: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.35/0.66       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 0.35/0.66         => ( ( ord_less_eq_real @ ( arccos @ X ) @ ( arccos @ Y2 ) )
% 0.35/0.66            = ( ord_less_eq_real @ Y2 @ X ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % arccos_le_mono
% 0.35/0.66  thf(fact_8313_arccos__eq__iff,axiom,
% 0.35/0.66      ! [X: real,Y2: real] :
% 0.35/0.66        ( ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.35/0.66          & ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real ) )
% 0.35/0.66       => ( ( ( arccos @ X )
% 0.35/0.66            = ( arccos @ Y2 ) )
% 0.35/0.66          = ( X = Y2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % arccos_eq_iff
% 0.35/0.66  thf(fact_8314_arcsin__minus,axiom,
% 0.35/0.66      ! [X: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.35/0.66       => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.35/0.66         => ( ( arcsin @ ( uminus_uminus_real @ X ) )
% 0.35/0.66            = ( uminus_uminus_real @ ( arcsin @ X ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % arcsin_minus
% 0.35/0.66  thf(fact_8315_arcsin__le__arcsin,axiom,
% 0.35/0.66      ! [X: real,Y2: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.35/0.66       => ( ( ord_less_eq_real @ X @ Y2 )
% 0.35/0.66         => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 0.35/0.66           => ( ord_less_eq_real @ ( arcsin @ X ) @ ( arcsin @ Y2 ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % arcsin_le_arcsin
% 0.35/0.66  thf(fact_8316_arcsin__le__mono,axiom,
% 0.35/0.66      ! [X: real,Y2: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.35/0.66       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 0.35/0.66         => ( ( ord_less_eq_real @ ( arcsin @ X ) @ ( arcsin @ Y2 ) )
% 0.35/0.66            = ( ord_less_eq_real @ X @ Y2 ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % arcsin_le_mono
% 0.35/0.66  thf(fact_8317_arcsin__eq__iff,axiom,
% 0.35/0.66      ! [X: real,Y2: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.35/0.66       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 0.35/0.66         => ( ( ( arcsin @ X )
% 0.35/0.66              = ( arcsin @ Y2 ) )
% 0.35/0.66            = ( X = Y2 ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % arcsin_eq_iff
% 0.35/0.66  thf(fact_8318_powser__sums__if,axiom,
% 0.35/0.66      ! [M: nat,Z: complex] :
% 0.35/0.66        ( sums_complex
% 0.35/0.66        @ ^ [N2: nat] : ( times_times_complex @ ( if_complex @ ( N2 = M ) @ one_one_complex @ zero_zero_complex ) @ ( power_power_complex @ Z @ N2 ) )
% 0.35/0.66        @ ( power_power_complex @ Z @ M ) ) ).
% 0.35/0.66  
% 0.35/0.66  % powser_sums_if
% 0.35/0.66  thf(fact_8319_powser__sums__if,axiom,
% 0.35/0.66      ! [M: nat,Z: real] :
% 0.35/0.66        ( sums_real
% 0.35/0.66        @ ^ [N2: nat] : ( times_times_real @ ( if_real @ ( N2 = M ) @ one_one_real @ zero_zero_real ) @ ( power_power_real @ Z @ N2 ) )
% 0.35/0.66        @ ( power_power_real @ Z @ M ) ) ).
% 0.35/0.66  
% 0.35/0.66  % powser_sums_if
% 0.35/0.66  thf(fact_8320_powser__sums__if,axiom,
% 0.35/0.66      ! [M: nat,Z: int] :
% 0.35/0.66        ( sums_int
% 0.35/0.66        @ ^ [N2: nat] : ( times_times_int @ ( if_int @ ( N2 = M ) @ one_one_int @ zero_zero_int ) @ ( power_power_int @ Z @ N2 ) )
% 0.35/0.66        @ ( power_power_int @ Z @ M ) ) ).
% 0.35/0.66  
% 0.35/0.66  % powser_sums_if
% 0.35/0.66  thf(fact_8321_powser__sums__zero,axiom,
% 0.35/0.66      ! [A: nat > complex] :
% 0.35/0.66        ( sums_complex
% 0.35/0.66        @ ^ [N2: nat] : ( times_times_complex @ ( A @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) )
% 0.35/0.66        @ ( A @ zero_zero_nat ) ) ).
% 0.35/0.66  
% 0.35/0.66  % powser_sums_zero
% 0.35/0.66  thf(fact_8322_powser__sums__zero,axiom,
% 0.35/0.66      ! [A: nat > real] :
% 0.35/0.66        ( sums_real
% 0.35/0.66        @ ^ [N2: nat] : ( times_times_real @ ( A @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) )
% 0.35/0.66        @ ( A @ zero_zero_nat ) ) ).
% 0.35/0.66  
% 0.35/0.66  % powser_sums_zero
% 0.35/0.66  thf(fact_8323_sums__iff__shift,axiom,
% 0.35/0.66      ! [F: nat > complex,N: nat,S3: complex] :
% 0.35/0.66        ( ( sums_complex
% 0.35/0.66          @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N ) )
% 0.35/0.66          @ S3 )
% 0.35/0.66        = ( sums_complex @ F @ ( plus_plus_complex @ S3 @ ( groups2073611262835488442omplex @ F @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_iff_shift
% 0.35/0.66  thf(fact_8324_sums__iff__shift,axiom,
% 0.35/0.66      ! [F: nat > real,N: nat,S3: real] :
% 0.35/0.66        ( ( sums_real
% 0.35/0.66          @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N ) )
% 0.35/0.66          @ S3 )
% 0.35/0.66        = ( sums_real @ F @ ( plus_plus_real @ S3 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_iff_shift
% 0.35/0.66  thf(fact_8325_sums__split__initial__segment,axiom,
% 0.35/0.66      ! [F: nat > real,S3: real,N: nat] :
% 0.35/0.66        ( ( sums_real @ F @ S3 )
% 0.35/0.66       => ( sums_real
% 0.35/0.66          @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N ) )
% 0.35/0.66          @ ( minus_minus_real @ S3 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_split_initial_segment
% 0.35/0.66  thf(fact_8326_sums__iff__shift_H,axiom,
% 0.35/0.66      ! [F: nat > real,N: nat,S3: real] :
% 0.35/0.66        ( ( sums_real
% 0.35/0.66          @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N ) )
% 0.35/0.66          @ ( minus_minus_real @ S3 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) ) )
% 0.35/0.66        = ( sums_real @ F @ S3 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_iff_shift'
% 0.35/0.66  thf(fact_8327_sums__If__finite__set_H,axiom,
% 0.35/0.66      ! [G: nat > complex,S2: complex,A2: set_nat,S5: complex,F: nat > complex] :
% 0.35/0.66        ( ( sums_complex @ G @ S2 )
% 0.35/0.66       => ( ( finite_finite_nat @ A2 )
% 0.35/0.66         => ( ( S5
% 0.35/0.66              = ( plus_plus_complex @ S2
% 0.35/0.66                @ ( groups2073611262835488442omplex
% 0.35/0.66                  @ ^ [N2: nat] : ( minus_minus_complex @ ( F @ N2 ) @ ( G @ N2 ) )
% 0.35/0.66                  @ A2 ) ) )
% 0.35/0.66           => ( sums_complex
% 0.35/0.66              @ ^ [N2: nat] : ( if_complex @ ( member_nat @ N2 @ A2 ) @ ( F @ N2 ) @ ( G @ N2 ) )
% 0.35/0.66              @ S5 ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_If_finite_set'
% 0.35/0.66  thf(fact_8328_sums__If__finite__set_H,axiom,
% 0.35/0.66      ! [G: nat > real,S2: real,A2: set_nat,S5: real,F: nat > real] :
% 0.35/0.66        ( ( sums_real @ G @ S2 )
% 0.35/0.66       => ( ( finite_finite_nat @ A2 )
% 0.35/0.66         => ( ( S5
% 0.35/0.66              = ( plus_plus_real @ S2
% 0.35/0.66                @ ( groups6591440286371151544t_real
% 0.35/0.66                  @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 0.35/0.66                  @ A2 ) ) )
% 0.35/0.66           => ( sums_real
% 0.35/0.66              @ ^ [N2: nat] : ( if_real @ ( member_nat @ N2 @ A2 ) @ ( F @ N2 ) @ ( G @ N2 ) )
% 0.35/0.66              @ S5 ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_If_finite_set'
% 0.35/0.66  thf(fact_8329_Complex__eq__neg__1,axiom,
% 0.35/0.66      ! [A: real,B: real] :
% 0.35/0.66        ( ( ( complex2 @ A @ B )
% 0.35/0.66          = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.35/0.66        = ( ( A
% 0.35/0.66            = ( uminus_uminus_real @ one_one_real ) )
% 0.35/0.66          & ( B = zero_zero_real ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % Complex_eq_neg_1
% 0.35/0.66  thf(fact_8330_arccos__lbound,axiom,
% 0.35/0.66      ! [Y2: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 0.35/0.66       => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 0.35/0.66         => ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y2 ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % arccos_lbound
% 0.35/0.66  thf(fact_8331_arccos__less__arccos,axiom,
% 0.35/0.66      ! [X: real,Y2: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.35/0.66       => ( ( ord_less_real @ X @ Y2 )
% 0.35/0.66         => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 0.35/0.66           => ( ord_less_real @ ( arccos @ Y2 ) @ ( arccos @ X ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % arccos_less_arccos
% 0.35/0.66  thf(fact_8332_arccos__less__mono,axiom,
% 0.35/0.66      ! [X: real,Y2: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.35/0.66       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 0.35/0.66         => ( ( ord_less_real @ ( arccos @ X ) @ ( arccos @ Y2 ) )
% 0.35/0.66            = ( ord_less_real @ Y2 @ X ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % arccos_less_mono
% 0.35/0.66  thf(fact_8333_arccos__ubound,axiom,
% 0.35/0.66      ! [Y2: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 0.35/0.66       => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 0.35/0.66         => ( ord_less_eq_real @ ( arccos @ Y2 ) @ pi ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % arccos_ubound
% 0.35/0.66  thf(fact_8334_arccos__cos,axiom,
% 0.35/0.66      ! [X: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.66       => ( ( ord_less_eq_real @ X @ pi )
% 0.35/0.66         => ( ( arccos @ ( cos_real @ X ) )
% 0.35/0.66            = X ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % arccos_cos
% 0.35/0.66  thf(fact_8335_arcsin__less__arcsin,axiom,
% 0.35/0.66      ! [X: real,Y2: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.35/0.66       => ( ( ord_less_real @ X @ Y2 )
% 0.35/0.66         => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 0.35/0.66           => ( ord_less_real @ ( arcsin @ X ) @ ( arcsin @ Y2 ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % arcsin_less_arcsin
% 0.35/0.66  thf(fact_8336_arcsin__less__mono,axiom,
% 0.35/0.66      ! [X: real,Y2: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.35/0.66       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 0.35/0.66         => ( ( ord_less_real @ ( arcsin @ X ) @ ( arcsin @ Y2 ) )
% 0.35/0.66            = ( ord_less_real @ X @ Y2 ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % arcsin_less_mono
% 0.35/0.66  thf(fact_8337_cos__arccos__abs,axiom,
% 0.35/0.66      ! [Y2: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 0.35/0.66       => ( ( cos_real @ ( arccos @ Y2 ) )
% 0.35/0.66          = Y2 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % cos_arccos_abs
% 0.35/0.66  thf(fact_8338_arccos__cos__eq__abs,axiom,
% 0.35/0.66      ! [Theta: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ ( abs_abs_real @ Theta ) @ pi )
% 0.35/0.66       => ( ( arccos @ ( cos_real @ Theta ) )
% 0.35/0.66          = ( abs_abs_real @ Theta ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % arccos_cos_eq_abs
% 0.35/0.66  thf(fact_8339_arccos__lt__bounded,axiom,
% 0.35/0.66      ! [Y2: real] :
% 0.35/0.66        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 0.35/0.66       => ( ( ord_less_real @ Y2 @ one_one_real )
% 0.35/0.66         => ( ( ord_less_real @ zero_zero_real @ ( arccos @ Y2 ) )
% 0.35/0.66            & ( ord_less_real @ ( arccos @ Y2 ) @ pi ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % arccos_lt_bounded
% 0.35/0.66  thf(fact_8340_arccos__bounded,axiom,
% 0.35/0.66      ! [Y2: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 0.35/0.66       => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 0.35/0.66         => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y2 ) )
% 0.35/0.66            & ( ord_less_eq_real @ ( arccos @ Y2 ) @ pi ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % arccos_bounded
% 0.35/0.66  thf(fact_8341_sin__arccos__nonzero,axiom,
% 0.35/0.66      ! [X: real] :
% 0.35/0.66        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.35/0.66       => ( ( ord_less_real @ X @ one_one_real )
% 0.35/0.66         => ( ( sin_real @ ( arccos @ X ) )
% 0.35/0.66           != zero_zero_real ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sin_arccos_nonzero
% 0.35/0.66  thf(fact_8342_arccos__cos2,axiom,
% 0.35/0.66      ! [X: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.35/0.66       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ X )
% 0.35/0.66         => ( ( arccos @ ( cos_real @ X ) )
% 0.35/0.66            = ( uminus_uminus_real @ X ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % arccos_cos2
% 0.35/0.66  thf(fact_8343_arccos__minus,axiom,
% 0.35/0.66      ! [X: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.35/0.66       => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.35/0.66         => ( ( arccos @ ( uminus_uminus_real @ X ) )
% 0.35/0.66            = ( minus_minus_real @ pi @ ( arccos @ X ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % arccos_minus
% 0.35/0.66  thf(fact_8344_cos__arcsin__nonzero,axiom,
% 0.35/0.66      ! [X: real] :
% 0.35/0.66        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.35/0.66       => ( ( ord_less_real @ X @ one_one_real )
% 0.35/0.66         => ( ( cos_real @ ( arcsin @ X ) )
% 0.35/0.66           != zero_zero_real ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % cos_arcsin_nonzero
% 0.35/0.66  thf(fact_8345_geometric__sums,axiom,
% 0.35/0.66      ! [C: real] :
% 0.35/0.66        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 0.35/0.66       => ( sums_real @ ( power_power_real @ C ) @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % geometric_sums
% 0.35/0.66  thf(fact_8346_geometric__sums,axiom,
% 0.35/0.66      ! [C: complex] :
% 0.35/0.66        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 0.35/0.66       => ( sums_complex @ ( power_power_complex @ C ) @ ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % geometric_sums
% 0.35/0.66  thf(fact_8347_power__half__series,axiom,
% 0.35/0.66      ( sums_real
% 0.35/0.66      @ ^ [N2: nat] : ( power_power_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( suc @ N2 ) )
% 0.35/0.66      @ one_one_real ) ).
% 0.35/0.66  
% 0.35/0.66  % power_half_series
% 0.35/0.66  thf(fact_8348_arccos,axiom,
% 0.35/0.66      ! [Y2: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 0.35/0.66       => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 0.35/0.66         => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y2 ) )
% 0.35/0.66            & ( ord_less_eq_real @ ( arccos @ Y2 ) @ pi )
% 0.35/0.66            & ( ( cos_real @ ( arccos @ Y2 ) )
% 0.35/0.66              = Y2 ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % arccos
% 0.35/0.66  thf(fact_8349_complex__norm,axiom,
% 0.35/0.66      ! [X: real,Y2: real] :
% 0.35/0.66        ( ( real_V1022390504157884413omplex @ ( complex2 @ X @ Y2 ) )
% 0.35/0.66        = ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % complex_norm
% 0.35/0.66  thf(fact_8350_arccos__minus__abs,axiom,
% 0.35/0.66      ! [X: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.35/0.66       => ( ( arccos @ ( uminus_uminus_real @ X ) )
% 0.35/0.66          = ( minus_minus_real @ pi @ ( arccos @ X ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % arccos_minus_abs
% 0.35/0.66  thf(fact_8351_sums__if_H,axiom,
% 0.35/0.66      ! [G: nat > real,X: real] :
% 0.35/0.66        ( ( sums_real @ G @ X )
% 0.35/0.66       => ( sums_real
% 0.35/0.66          @ ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ zero_zero_real @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.66          @ X ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_if'
% 0.35/0.66  thf(fact_8352_sums__if,axiom,
% 0.35/0.66      ! [G: nat > real,X: real,F: nat > real,Y2: real] :
% 0.35/0.66        ( ( sums_real @ G @ X )
% 0.35/0.66       => ( ( sums_real @ F @ Y2 )
% 0.35/0.66         => ( sums_real
% 0.35/0.66            @ ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( F @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.66            @ ( plus_plus_real @ X @ Y2 ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sums_if
% 0.35/0.66  thf(fact_8353_arccos__le__pi2,axiom,
% 0.35/0.66      ! [Y2: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 0.35/0.66       => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 0.35/0.66         => ( ord_less_eq_real @ ( arccos @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % arccos_le_pi2
% 0.35/0.66  thf(fact_8354_arcsin__lt__bounded,axiom,
% 0.35/0.66      ! [Y2: real] :
% 0.35/0.66        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 0.35/0.66       => ( ( ord_less_real @ Y2 @ one_one_real )
% 0.35/0.66         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y2 ) )
% 0.35/0.66            & ( ord_less_real @ ( arcsin @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % arcsin_lt_bounded
% 0.35/0.66  thf(fact_8355_arcsin__lbound,axiom,
% 0.35/0.66      ! [Y2: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 0.35/0.66       => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 0.35/0.66         => ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y2 ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % arcsin_lbound
% 0.35/0.66  thf(fact_8356_arcsin__ubound,axiom,
% 0.35/0.66      ! [Y2: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 0.35/0.66       => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 0.35/0.66         => ( ord_less_eq_real @ ( arcsin @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % arcsin_ubound
% 0.35/0.66  thf(fact_8357_arcsin__bounded,axiom,
% 0.35/0.66      ! [Y2: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 0.35/0.66       => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 0.35/0.66         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y2 ) )
% 0.35/0.66            & ( ord_less_eq_real @ ( arcsin @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % arcsin_bounded
% 0.35/0.66  thf(fact_8358_arcsin__sin,axiom,
% 0.35/0.66      ! [X: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.35/0.66       => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.66         => ( ( arcsin @ ( sin_real @ X ) )
% 0.35/0.66            = X ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % arcsin_sin
% 0.35/0.66  thf(fact_8359_cos__paired,axiom,
% 0.35/0.66      ! [X: real] :
% 0.35/0.66        ( sums_real
% 0.35/0.66        @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( power_power_real @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.35/0.66        @ ( cos_real @ X ) ) ).
% 0.35/0.66  
% 0.35/0.66  % cos_paired
% 0.35/0.66  thf(fact_8360_le__arcsin__iff,axiom,
% 0.35/0.66      ! [X: real,Y2: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.35/0.66       => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.35/0.66         => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y2 )
% 0.35/0.66           => ( ( ord_less_eq_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.66             => ( ( ord_less_eq_real @ Y2 @ ( arcsin @ X ) )
% 0.35/0.66                = ( ord_less_eq_real @ ( sin_real @ Y2 ) @ X ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % le_arcsin_iff
% 0.35/0.66  thf(fact_8361_arcsin__le__iff,axiom,
% 0.35/0.66      ! [X: real,Y2: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.35/0.66       => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.35/0.66         => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y2 )
% 0.35/0.66           => ( ( ord_less_eq_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.66             => ( ( ord_less_eq_real @ ( arcsin @ X ) @ Y2 )
% 0.35/0.66                = ( ord_less_eq_real @ X @ ( sin_real @ Y2 ) ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % arcsin_le_iff
% 0.35/0.66  thf(fact_8362_arcsin__pi,axiom,
% 0.35/0.66      ! [Y2: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 0.35/0.66       => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 0.35/0.66         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y2 ) )
% 0.35/0.66            & ( ord_less_eq_real @ ( arcsin @ Y2 ) @ pi )
% 0.35/0.66            & ( ( sin_real @ ( arcsin @ Y2 ) )
% 0.35/0.66              = Y2 ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % arcsin_pi
% 0.35/0.66  thf(fact_8363_arcsin,axiom,
% 0.35/0.66      ! [Y2: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 0.35/0.66       => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 0.35/0.66         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y2 ) )
% 0.35/0.66            & ( ord_less_eq_real @ ( arcsin @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.66            & ( ( sin_real @ ( arcsin @ Y2 ) )
% 0.35/0.66              = Y2 ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % arcsin
% 0.35/0.66  thf(fact_8364_arccos__cos__eq__abs__2pi,axiom,
% 0.35/0.66      ! [Theta: real] :
% 0.35/0.66        ~ ! [K2: int] :
% 0.35/0.66            ( ( arccos @ ( cos_real @ Theta ) )
% 0.35/0.66           != ( abs_abs_real @ ( minus_minus_real @ Theta @ ( times_times_real @ ( ring_1_of_int_real @ K2 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % arccos_cos_eq_abs_2pi
% 0.35/0.66  thf(fact_8365_geometric__deriv__sums,axiom,
% 0.35/0.66      ! [Z: real] :
% 0.35/0.66        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 0.35/0.66       => ( sums_real
% 0.35/0.66          @ ^ [N2: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) @ ( power_power_real @ Z @ N2 ) )
% 0.35/0.66          @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % geometric_deriv_sums
% 0.35/0.66  thf(fact_8366_geometric__deriv__sums,axiom,
% 0.35/0.66      ! [Z: complex] :
% 0.35/0.66        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 0.35/0.66       => ( sums_complex
% 0.35/0.66          @ ^ [N2: nat] : ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N2 ) ) @ ( power_power_complex @ Z @ N2 ) )
% 0.35/0.66          @ ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ ( minus_minus_complex @ one_one_complex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % geometric_deriv_sums
% 0.35/0.66  thf(fact_8367_sin__arccos,axiom,
% 0.35/0.66      ! [X: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.35/0.66       => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.35/0.66         => ( ( sin_real @ ( arccos @ X ) )
% 0.35/0.66            = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % sin_arccos
% 0.35/0.66  thf(fact_8368_diffs__equiv,axiom,
% 0.35/0.66      ! [C: nat > real,X: real] :
% 0.35/0.66        ( ( summable_real
% 0.35/0.66          @ ^ [N2: nat] : ( times_times_real @ ( diffs_real @ C @ N2 ) @ ( power_power_real @ X @ N2 ) ) )
% 0.35/0.66       => ( sums_real
% 0.35/0.66          @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( C @ N2 ) ) @ ( power_power_real @ X @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) )
% 0.35/0.66          @ ( suminf_real
% 0.35/0.66            @ ^ [N2: nat] : ( times_times_real @ ( diffs_real @ C @ N2 ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % diffs_equiv
% 0.35/0.66  thf(fact_8369_diffs__equiv,axiom,
% 0.35/0.66      ! [C: nat > complex,X: complex] :
% 0.35/0.66        ( ( summable_complex
% 0.35/0.66          @ ^ [N2: nat] : ( times_times_complex @ ( diffs_complex @ C @ N2 ) @ ( power_power_complex @ X @ N2 ) ) )
% 0.35/0.66       => ( sums_complex
% 0.35/0.66          @ ^ [N2: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( C @ N2 ) ) @ ( power_power_complex @ X @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) )
% 0.35/0.66          @ ( suminf_complex
% 0.35/0.66            @ ^ [N2: nat] : ( times_times_complex @ ( diffs_complex @ C @ N2 ) @ ( power_power_complex @ X @ N2 ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % diffs_equiv
% 0.35/0.66  thf(fact_8370_monoseq__def,axiom,
% 0.35/0.66      ( topolo6980174941875973593q_real
% 0.35/0.66      = ( ^ [X4: nat > real] :
% 0.35/0.66            ( ! [M6: nat,N2: nat] :
% 0.35/0.66                ( ( ord_less_eq_nat @ M6 @ N2 )
% 0.35/0.66               => ( ord_less_eq_real @ ( X4 @ M6 ) @ ( X4 @ N2 ) ) )
% 0.35/0.66            | ! [M6: nat,N2: nat] :
% 0.35/0.66                ( ( ord_less_eq_nat @ M6 @ N2 )
% 0.35/0.66               => ( ord_less_eq_real @ ( X4 @ N2 ) @ ( X4 @ M6 ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % monoseq_def
% 0.35/0.66  thf(fact_8371_monoseq__def,axiom,
% 0.35/0.66      ( topolo2489691266198938127t_real
% 0.35/0.66      = ( ^ [X4: nat > set_real] :
% 0.35/0.66            ( ! [M6: nat,N2: nat] :
% 0.35/0.66                ( ( ord_less_eq_nat @ M6 @ N2 )
% 0.35/0.66               => ( ord_less_eq_set_real @ ( X4 @ M6 ) @ ( X4 @ N2 ) ) )
% 0.35/0.66            | ! [M6: nat,N2: nat] :
% 0.35/0.66                ( ( ord_less_eq_nat @ M6 @ N2 )
% 0.35/0.66               => ( ord_less_eq_set_real @ ( X4 @ N2 ) @ ( X4 @ M6 ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % monoseq_def
% 0.35/0.66  thf(fact_8372_monoseq__def,axiom,
% 0.35/0.66      ( topolo7278393974255667507et_nat
% 0.35/0.66      = ( ^ [X4: nat > set_nat] :
% 0.35/0.66            ( ! [M6: nat,N2: nat] :
% 0.35/0.66                ( ( ord_less_eq_nat @ M6 @ N2 )
% 0.35/0.66               => ( ord_less_eq_set_nat @ ( X4 @ M6 ) @ ( X4 @ N2 ) ) )
% 0.35/0.66            | ! [M6: nat,N2: nat] :
% 0.35/0.66                ( ( ord_less_eq_nat @ M6 @ N2 )
% 0.35/0.66               => ( ord_less_eq_set_nat @ ( X4 @ N2 ) @ ( X4 @ M6 ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % monoseq_def
% 0.35/0.66  thf(fact_8373_monoseq__def,axiom,
% 0.35/0.66      ( topolo1459490580787246023eq_num
% 0.35/0.66      = ( ^ [X4: nat > num] :
% 0.35/0.66            ( ! [M6: nat,N2: nat] :
% 0.35/0.66                ( ( ord_less_eq_nat @ M6 @ N2 )
% 0.35/0.66               => ( ord_less_eq_num @ ( X4 @ M6 ) @ ( X4 @ N2 ) ) )
% 0.35/0.66            | ! [M6: nat,N2: nat] :
% 0.35/0.66                ( ( ord_less_eq_nat @ M6 @ N2 )
% 0.35/0.66               => ( ord_less_eq_num @ ( X4 @ N2 ) @ ( X4 @ M6 ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % monoseq_def
% 0.35/0.66  thf(fact_8374_monoseq__def,axiom,
% 0.35/0.66      ( topolo4902158794631467389eq_nat
% 0.35/0.66      = ( ^ [X4: nat > nat] :
% 0.35/0.66            ( ! [M6: nat,N2: nat] :
% 0.35/0.66                ( ( ord_less_eq_nat @ M6 @ N2 )
% 0.35/0.66               => ( ord_less_eq_nat @ ( X4 @ M6 ) @ ( X4 @ N2 ) ) )
% 0.35/0.66            | ! [M6: nat,N2: nat] :
% 0.35/0.66                ( ( ord_less_eq_nat @ M6 @ N2 )
% 0.35/0.66               => ( ord_less_eq_nat @ ( X4 @ N2 ) @ ( X4 @ M6 ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % monoseq_def
% 0.35/0.66  thf(fact_8375_monoseq__def,axiom,
% 0.35/0.66      ( topolo4899668324122417113eq_int
% 0.35/0.66      = ( ^ [X4: nat > int] :
% 0.35/0.66            ( ! [M6: nat,N2: nat] :
% 0.35/0.66                ( ( ord_less_eq_nat @ M6 @ N2 )
% 0.35/0.66               => ( ord_less_eq_int @ ( X4 @ M6 ) @ ( X4 @ N2 ) ) )
% 0.35/0.66            | ! [M6: nat,N2: nat] :
% 0.35/0.66                ( ( ord_less_eq_nat @ M6 @ N2 )
% 0.35/0.66               => ( ord_less_eq_int @ ( X4 @ N2 ) @ ( X4 @ M6 ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % monoseq_def
% 0.35/0.66  thf(fact_8376_monoI2,axiom,
% 0.35/0.66      ! [X8: nat > real] :
% 0.35/0.66        ( ! [M4: nat,N3: nat] :
% 0.35/0.66            ( ( ord_less_eq_nat @ M4 @ N3 )
% 0.35/0.66           => ( ord_less_eq_real @ ( X8 @ N3 ) @ ( X8 @ M4 ) ) )
% 0.35/0.66       => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % monoI2
% 0.35/0.66  thf(fact_8377_monoI2,axiom,
% 0.35/0.66      ! [X8: nat > set_real] :
% 0.35/0.66        ( ! [M4: nat,N3: nat] :
% 0.35/0.66            ( ( ord_less_eq_nat @ M4 @ N3 )
% 0.35/0.66           => ( ord_less_eq_set_real @ ( X8 @ N3 ) @ ( X8 @ M4 ) ) )
% 0.35/0.66       => ( topolo2489691266198938127t_real @ X8 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % monoI2
% 0.35/0.66  thf(fact_8378_monoI2,axiom,
% 0.35/0.66      ! [X8: nat > set_nat] :
% 0.35/0.66        ( ! [M4: nat,N3: nat] :
% 0.35/0.66            ( ( ord_less_eq_nat @ M4 @ N3 )
% 0.35/0.66           => ( ord_less_eq_set_nat @ ( X8 @ N3 ) @ ( X8 @ M4 ) ) )
% 0.35/0.66       => ( topolo7278393974255667507et_nat @ X8 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % monoI2
% 0.35/0.66  thf(fact_8379_monoI2,axiom,
% 0.35/0.66      ! [X8: nat > num] :
% 0.35/0.66        ( ! [M4: nat,N3: nat] :
% 0.35/0.66            ( ( ord_less_eq_nat @ M4 @ N3 )
% 0.35/0.66           => ( ord_less_eq_num @ ( X8 @ N3 ) @ ( X8 @ M4 ) ) )
% 0.35/0.66       => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % monoI2
% 0.35/0.66  thf(fact_8380_monoI2,axiom,
% 0.35/0.66      ! [X8: nat > nat] :
% 0.35/0.66        ( ! [M4: nat,N3: nat] :
% 0.35/0.66            ( ( ord_less_eq_nat @ M4 @ N3 )
% 0.35/0.66           => ( ord_less_eq_nat @ ( X8 @ N3 ) @ ( X8 @ M4 ) ) )
% 0.35/0.66       => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % monoI2
% 0.35/0.66  thf(fact_8381_monoI2,axiom,
% 0.35/0.66      ! [X8: nat > int] :
% 0.35/0.66        ( ! [M4: nat,N3: nat] :
% 0.35/0.66            ( ( ord_less_eq_nat @ M4 @ N3 )
% 0.35/0.66           => ( ord_less_eq_int @ ( X8 @ N3 ) @ ( X8 @ M4 ) ) )
% 0.35/0.66       => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % monoI2
% 0.35/0.66  thf(fact_8382_monoI1,axiom,
% 0.35/0.66      ! [X8: nat > real] :
% 0.35/0.66        ( ! [M4: nat,N3: nat] :
% 0.35/0.66            ( ( ord_less_eq_nat @ M4 @ N3 )
% 0.35/0.66           => ( ord_less_eq_real @ ( X8 @ M4 ) @ ( X8 @ N3 ) ) )
% 0.35/0.66       => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % monoI1
% 0.35/0.66  thf(fact_8383_monoI1,axiom,
% 0.35/0.66      ! [X8: nat > set_real] :
% 0.35/0.66        ( ! [M4: nat,N3: nat] :
% 0.35/0.66            ( ( ord_less_eq_nat @ M4 @ N3 )
% 0.35/0.66           => ( ord_less_eq_set_real @ ( X8 @ M4 ) @ ( X8 @ N3 ) ) )
% 0.35/0.66       => ( topolo2489691266198938127t_real @ X8 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % monoI1
% 0.35/0.66  thf(fact_8384_monoI1,axiom,
% 0.35/0.66      ! [X8: nat > set_nat] :
% 0.35/0.66        ( ! [M4: nat,N3: nat] :
% 0.35/0.66            ( ( ord_less_eq_nat @ M4 @ N3 )
% 0.35/0.66           => ( ord_less_eq_set_nat @ ( X8 @ M4 ) @ ( X8 @ N3 ) ) )
% 0.35/0.66       => ( topolo7278393974255667507et_nat @ X8 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % monoI1
% 0.35/0.66  thf(fact_8385_monoI1,axiom,
% 0.35/0.66      ! [X8: nat > num] :
% 0.35/0.66        ( ! [M4: nat,N3: nat] :
% 0.35/0.66            ( ( ord_less_eq_nat @ M4 @ N3 )
% 0.35/0.66           => ( ord_less_eq_num @ ( X8 @ M4 ) @ ( X8 @ N3 ) ) )
% 0.35/0.66       => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % monoI1
% 0.35/0.66  thf(fact_8386_monoI1,axiom,
% 0.35/0.66      ! [X8: nat > nat] :
% 0.35/0.66        ( ! [M4: nat,N3: nat] :
% 0.35/0.66            ( ( ord_less_eq_nat @ M4 @ N3 )
% 0.35/0.66           => ( ord_less_eq_nat @ ( X8 @ M4 ) @ ( X8 @ N3 ) ) )
% 0.35/0.66       => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % monoI1
% 0.35/0.66  thf(fact_8387_monoI1,axiom,
% 0.35/0.66      ! [X8: nat > int] :
% 0.35/0.66        ( ! [M4: nat,N3: nat] :
% 0.35/0.66            ( ( ord_less_eq_nat @ M4 @ N3 )
% 0.35/0.66           => ( ord_less_eq_int @ ( X8 @ M4 ) @ ( X8 @ N3 ) ) )
% 0.35/0.66       => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % monoI1
% 0.35/0.66  thf(fact_8388_diffs__def,axiom,
% 0.35/0.66      ( diffs_real
% 0.35/0.66      = ( ^ [C3: nat > real,N2: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) @ ( C3 @ ( suc @ N2 ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % diffs_def
% 0.35/0.66  thf(fact_8389_diffs__def,axiom,
% 0.35/0.66      ( diffs_int
% 0.35/0.66      = ( ^ [C3: nat > int,N2: nat] : ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) @ ( C3 @ ( suc @ N2 ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % diffs_def
% 0.35/0.66  thf(fact_8390_diffs__def,axiom,
% 0.35/0.66      ( diffs_complex
% 0.35/0.66      = ( ^ [C3: nat > complex,N2: nat] : ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N2 ) ) @ ( C3 @ ( suc @ N2 ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % diffs_def
% 0.35/0.66  thf(fact_8391_termdiff__converges__all,axiom,
% 0.35/0.66      ! [C: nat > complex,X: complex] :
% 0.35/0.66        ( ! [X3: complex] :
% 0.35/0.66            ( summable_complex
% 0.35/0.66            @ ^ [N2: nat] : ( times_times_complex @ ( C @ N2 ) @ ( power_power_complex @ X3 @ N2 ) ) )
% 0.35/0.66       => ( summable_complex
% 0.35/0.66          @ ^ [N2: nat] : ( times_times_complex @ ( diffs_complex @ C @ N2 ) @ ( power_power_complex @ X @ N2 ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % termdiff_converges_all
% 0.35/0.66  thf(fact_8392_termdiff__converges__all,axiom,
% 0.35/0.66      ! [C: nat > real,X: real] :
% 0.35/0.66        ( ! [X3: real] :
% 0.35/0.66            ( summable_real
% 0.35/0.66            @ ^ [N2: nat] : ( times_times_real @ ( C @ N2 ) @ ( power_power_real @ X3 @ N2 ) ) )
% 0.35/0.66       => ( summable_real
% 0.35/0.66          @ ^ [N2: nat] : ( times_times_real @ ( diffs_real @ C @ N2 ) @ ( power_power_real @ X @ N2 ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % termdiff_converges_all
% 0.35/0.66  thf(fact_8393_termdiff__converges,axiom,
% 0.35/0.66      ! [X: real,K5: real,C: nat > real] :
% 0.35/0.66        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ K5 )
% 0.35/0.66       => ( ! [X3: real] :
% 0.35/0.66              ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X3 ) @ K5 )
% 0.35/0.66             => ( summable_real
% 0.35/0.66                @ ^ [N2: nat] : ( times_times_real @ ( C @ N2 ) @ ( power_power_real @ X3 @ N2 ) ) ) )
% 0.35/0.66         => ( summable_real
% 0.35/0.66            @ ^ [N2: nat] : ( times_times_real @ ( diffs_real @ C @ N2 ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % termdiff_converges
% 0.35/0.66  thf(fact_8394_termdiff__converges,axiom,
% 0.35/0.66      ! [X: complex,K5: real,C: nat > complex] :
% 0.35/0.66        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ K5 )
% 0.35/0.66       => ( ! [X3: complex] :
% 0.35/0.66              ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X3 ) @ K5 )
% 0.35/0.66             => ( summable_complex
% 0.35/0.66                @ ^ [N2: nat] : ( times_times_complex @ ( C @ N2 ) @ ( power_power_complex @ X3 @ N2 ) ) ) )
% 0.35/0.66         => ( summable_complex
% 0.35/0.66            @ ^ [N2: nat] : ( times_times_complex @ ( diffs_complex @ C @ N2 ) @ ( power_power_complex @ X @ N2 ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % termdiff_converges
% 0.35/0.66  thf(fact_8395_mono__SucI1,axiom,
% 0.35/0.66      ! [X8: nat > real] :
% 0.35/0.66        ( ! [N3: nat] : ( ord_less_eq_real @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 0.35/0.66       => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % mono_SucI1
% 0.35/0.66  thf(fact_8396_mono__SucI1,axiom,
% 0.35/0.66      ! [X8: nat > set_real] :
% 0.35/0.66        ( ! [N3: nat] : ( ord_less_eq_set_real @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 0.35/0.66       => ( topolo2489691266198938127t_real @ X8 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % mono_SucI1
% 0.35/0.66  thf(fact_8397_mono__SucI1,axiom,
% 0.35/0.66      ! [X8: nat > set_nat] :
% 0.35/0.66        ( ! [N3: nat] : ( ord_less_eq_set_nat @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 0.35/0.66       => ( topolo7278393974255667507et_nat @ X8 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % mono_SucI1
% 0.35/0.66  thf(fact_8398_mono__SucI1,axiom,
% 0.35/0.66      ! [X8: nat > num] :
% 0.35/0.66        ( ! [N3: nat] : ( ord_less_eq_num @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 0.35/0.66       => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % mono_SucI1
% 0.35/0.66  thf(fact_8399_mono__SucI1,axiom,
% 0.35/0.66      ! [X8: nat > nat] :
% 0.35/0.66        ( ! [N3: nat] : ( ord_less_eq_nat @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 0.35/0.66       => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % mono_SucI1
% 0.35/0.66  thf(fact_8400_mono__SucI1,axiom,
% 0.35/0.66      ! [X8: nat > int] :
% 0.35/0.66        ( ! [N3: nat] : ( ord_less_eq_int @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 0.35/0.66       => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % mono_SucI1
% 0.35/0.66  thf(fact_8401_mono__SucI2,axiom,
% 0.35/0.66      ! [X8: nat > real] :
% 0.35/0.66        ( ! [N3: nat] : ( ord_less_eq_real @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 0.35/0.66       => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % mono_SucI2
% 0.35/0.66  thf(fact_8402_mono__SucI2,axiom,
% 0.35/0.66      ! [X8: nat > set_real] :
% 0.35/0.66        ( ! [N3: nat] : ( ord_less_eq_set_real @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 0.35/0.66       => ( topolo2489691266198938127t_real @ X8 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % mono_SucI2
% 0.35/0.66  thf(fact_8403_mono__SucI2,axiom,
% 0.35/0.66      ! [X8: nat > set_nat] :
% 0.35/0.66        ( ! [N3: nat] : ( ord_less_eq_set_nat @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 0.35/0.66       => ( topolo7278393974255667507et_nat @ X8 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % mono_SucI2
% 0.35/0.66  thf(fact_8404_mono__SucI2,axiom,
% 0.35/0.66      ! [X8: nat > num] :
% 0.35/0.66        ( ! [N3: nat] : ( ord_less_eq_num @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 0.35/0.66       => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % mono_SucI2
% 0.35/0.66  thf(fact_8405_mono__SucI2,axiom,
% 0.35/0.66      ! [X8: nat > nat] :
% 0.35/0.66        ( ! [N3: nat] : ( ord_less_eq_nat @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 0.35/0.66       => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % mono_SucI2
% 0.35/0.66  thf(fact_8406_mono__SucI2,axiom,
% 0.35/0.66      ! [X8: nat > int] :
% 0.35/0.66        ( ! [N3: nat] : ( ord_less_eq_int @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 0.35/0.66       => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % mono_SucI2
% 0.35/0.66  thf(fact_8407_monoseq__Suc,axiom,
% 0.35/0.66      ( topolo6980174941875973593q_real
% 0.35/0.66      = ( ^ [X4: nat > real] :
% 0.35/0.66            ( ! [N2: nat] : ( ord_less_eq_real @ ( X4 @ N2 ) @ ( X4 @ ( suc @ N2 ) ) )
% 0.35/0.66            | ! [N2: nat] : ( ord_less_eq_real @ ( X4 @ ( suc @ N2 ) ) @ ( X4 @ N2 ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % monoseq_Suc
% 0.35/0.66  thf(fact_8408_monoseq__Suc,axiom,
% 0.35/0.66      ( topolo2489691266198938127t_real
% 0.35/0.66      = ( ^ [X4: nat > set_real] :
% 0.35/0.66            ( ! [N2: nat] : ( ord_less_eq_set_real @ ( X4 @ N2 ) @ ( X4 @ ( suc @ N2 ) ) )
% 0.35/0.66            | ! [N2: nat] : ( ord_less_eq_set_real @ ( X4 @ ( suc @ N2 ) ) @ ( X4 @ N2 ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % monoseq_Suc
% 0.35/0.66  thf(fact_8409_monoseq__Suc,axiom,
% 0.35/0.66      ( topolo7278393974255667507et_nat
% 0.35/0.66      = ( ^ [X4: nat > set_nat] :
% 0.35/0.66            ( ! [N2: nat] : ( ord_less_eq_set_nat @ ( X4 @ N2 ) @ ( X4 @ ( suc @ N2 ) ) )
% 0.35/0.66            | ! [N2: nat] : ( ord_less_eq_set_nat @ ( X4 @ ( suc @ N2 ) ) @ ( X4 @ N2 ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % monoseq_Suc
% 0.35/0.66  thf(fact_8410_monoseq__Suc,axiom,
% 0.35/0.66      ( topolo1459490580787246023eq_num
% 0.35/0.66      = ( ^ [X4: nat > num] :
% 0.35/0.66            ( ! [N2: nat] : ( ord_less_eq_num @ ( X4 @ N2 ) @ ( X4 @ ( suc @ N2 ) ) )
% 0.35/0.66            | ! [N2: nat] : ( ord_less_eq_num @ ( X4 @ ( suc @ N2 ) ) @ ( X4 @ N2 ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % monoseq_Suc
% 0.35/0.66  thf(fact_8411_monoseq__Suc,axiom,
% 0.35/0.66      ( topolo4902158794631467389eq_nat
% 0.35/0.66      = ( ^ [X4: nat > nat] :
% 0.35/0.66            ( ! [N2: nat] : ( ord_less_eq_nat @ ( X4 @ N2 ) @ ( X4 @ ( suc @ N2 ) ) )
% 0.35/0.66            | ! [N2: nat] : ( ord_less_eq_nat @ ( X4 @ ( suc @ N2 ) ) @ ( X4 @ N2 ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % monoseq_Suc
% 0.35/0.66  thf(fact_8412_monoseq__Suc,axiom,
% 0.35/0.66      ( topolo4899668324122417113eq_int
% 0.35/0.66      = ( ^ [X4: nat > int] :
% 0.35/0.66            ( ! [N2: nat] : ( ord_less_eq_int @ ( X4 @ N2 ) @ ( X4 @ ( suc @ N2 ) ) )
% 0.35/0.66            | ! [N2: nat] : ( ord_less_eq_int @ ( X4 @ ( suc @ N2 ) ) @ ( X4 @ N2 ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % monoseq_Suc
% 0.35/0.66  thf(fact_8413_or__minus__numerals_I1_J,axiom,
% 0.35/0.66      ! [N: num] :
% 0.35/0.66        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.35/0.66        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % or_minus_numerals(1)
% 0.35/0.66  thf(fact_8414_or__minus__numerals_I5_J,axiom,
% 0.35/0.66      ! [N: num] :
% 0.35/0.66        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 0.35/0.66        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % or_minus_numerals(5)
% 0.35/0.66  thf(fact_8415_pochhammer__double,axiom,
% 0.35/0.66      ! [Z: rat,N: nat] :
% 0.35/0.66        ( ( comm_s4028243227959126397er_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.66        = ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_double
% 0.35/0.66  thf(fact_8416_pochhammer__double,axiom,
% 0.35/0.66      ! [Z: real,N: nat] :
% 0.35/0.66        ( ( comm_s7457072308508201937r_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.66        = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s7457072308508201937r_real @ Z @ N ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_double
% 0.35/0.66  thf(fact_8417_pochhammer__double,axiom,
% 0.35/0.66      ! [Z: complex,N: nat] :
% 0.35/0.66        ( ( comm_s2602460028002588243omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.66        = ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s2602460028002588243omplex @ Z @ N ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_double
% 0.35/0.66  thf(fact_8418_floor__log__nat__eq__powr__iff,axiom,
% 0.35/0.66      ! [B: nat,K: nat,N: nat] :
% 0.35/0.66        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.35/0.66       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.35/0.66         => ( ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 0.35/0.66              = ( semiri1314217659103216013at_int @ N ) )
% 0.35/0.66            = ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 0.35/0.66              & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_log_nat_eq_powr_iff
% 0.35/0.66  thf(fact_8419_of__int__floor__cancel,axiom,
% 0.35/0.66      ! [X: real] :
% 0.35/0.66        ( ( ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) )
% 0.35/0.66          = X )
% 0.35/0.66        = ( ? [N2: int] :
% 0.35/0.66              ( X
% 0.35/0.66              = ( ring_1_of_int_real @ N2 ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % of_int_floor_cancel
% 0.35/0.66  thf(fact_8420_of__int__floor__cancel,axiom,
% 0.35/0.66      ! [X: rat] :
% 0.35/0.66        ( ( ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) )
% 0.35/0.66          = X )
% 0.35/0.66        = ( ? [N2: int] :
% 0.35/0.66              ( X
% 0.35/0.66              = ( ring_1_of_int_rat @ N2 ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % of_int_floor_cancel
% 0.35/0.66  thf(fact_8421_floor__numeral,axiom,
% 0.35/0.66      ! [V: num] :
% 0.35/0.66        ( ( archim6058952711729229775r_real @ ( numeral_numeral_real @ V ) )
% 0.35/0.66        = ( numeral_numeral_int @ V ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_numeral
% 0.35/0.66  thf(fact_8422_floor__numeral,axiom,
% 0.35/0.66      ! [V: num] :
% 0.35/0.66        ( ( archim3151403230148437115or_rat @ ( numeral_numeral_rat @ V ) )
% 0.35/0.66        = ( numeral_numeral_int @ V ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_numeral
% 0.35/0.66  thf(fact_8423_floor__one,axiom,
% 0.35/0.66      ( ( archim6058952711729229775r_real @ one_one_real )
% 0.35/0.66      = one_one_int ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_one
% 0.35/0.66  thf(fact_8424_floor__one,axiom,
% 0.35/0.66      ( ( archim3151403230148437115or_rat @ one_one_rat )
% 0.35/0.66      = one_one_int ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_one
% 0.35/0.66  thf(fact_8425_pochhammer__0,axiom,
% 0.35/0.66      ! [A: complex] :
% 0.35/0.66        ( ( comm_s2602460028002588243omplex @ A @ zero_zero_nat )
% 0.35/0.66        = one_one_complex ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_0
% 0.35/0.66  thf(fact_8426_pochhammer__0,axiom,
% 0.35/0.66      ! [A: real] :
% 0.35/0.66        ( ( comm_s7457072308508201937r_real @ A @ zero_zero_nat )
% 0.35/0.66        = one_one_real ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_0
% 0.35/0.66  thf(fact_8427_pochhammer__0,axiom,
% 0.35/0.66      ! [A: rat] :
% 0.35/0.66        ( ( comm_s4028243227959126397er_rat @ A @ zero_zero_nat )
% 0.35/0.66        = one_one_rat ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_0
% 0.35/0.66  thf(fact_8428_pochhammer__0,axiom,
% 0.35/0.66      ! [A: nat] :
% 0.35/0.66        ( ( comm_s4663373288045622133er_nat @ A @ zero_zero_nat )
% 0.35/0.66        = one_one_nat ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_0
% 0.35/0.66  thf(fact_8429_pochhammer__0,axiom,
% 0.35/0.66      ! [A: int] :
% 0.35/0.66        ( ( comm_s4660882817536571857er_int @ A @ zero_zero_nat )
% 0.35/0.66        = one_one_int ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_0
% 0.35/0.66  thf(fact_8430_floor__diff__of__int,axiom,
% 0.35/0.66      ! [X: real,Z: int] :
% 0.35/0.66        ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X @ ( ring_1_of_int_real @ Z ) ) )
% 0.35/0.66        = ( minus_minus_int @ ( archim6058952711729229775r_real @ X ) @ Z ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_diff_of_int
% 0.35/0.66  thf(fact_8431_floor__diff__of__int,axiom,
% 0.35/0.66      ! [X: rat,Z: int] :
% 0.35/0.66        ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X @ ( ring_1_of_int_rat @ Z ) ) )
% 0.35/0.66        = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X ) @ Z ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_diff_of_int
% 0.35/0.66  thf(fact_8432_zero__le__floor,axiom,
% 0.35/0.66      ! [X: real] :
% 0.35/0.66        ( ( ord_less_eq_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X ) )
% 0.35/0.66        = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 0.35/0.66  
% 0.35/0.66  % zero_le_floor
% 0.35/0.66  thf(fact_8433_zero__le__floor,axiom,
% 0.35/0.66      ! [X: rat] :
% 0.35/0.66        ( ( ord_less_eq_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X ) )
% 0.35/0.66        = ( ord_less_eq_rat @ zero_zero_rat @ X ) ) ).
% 0.35/0.66  
% 0.35/0.66  % zero_le_floor
% 0.35/0.66  thf(fact_8434_floor__less__zero,axiom,
% 0.35/0.66      ! [X: real] :
% 0.35/0.66        ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ zero_zero_int )
% 0.35/0.66        = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_less_zero
% 0.35/0.66  thf(fact_8435_floor__less__zero,axiom,
% 0.35/0.66      ! [X: rat] :
% 0.35/0.66        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ zero_zero_int )
% 0.35/0.66        = ( ord_less_rat @ X @ zero_zero_rat ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_less_zero
% 0.35/0.66  thf(fact_8436_numeral__le__floor,axiom,
% 0.35/0.66      ! [V: num,X: real] :
% 0.35/0.66        ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X ) )
% 0.35/0.66        = ( ord_less_eq_real @ ( numeral_numeral_real @ V ) @ X ) ) ).
% 0.35/0.66  
% 0.35/0.66  % numeral_le_floor
% 0.35/0.66  thf(fact_8437_numeral__le__floor,axiom,
% 0.35/0.66      ! [V: num,X: rat] :
% 0.35/0.66        ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X ) )
% 0.35/0.66        = ( ord_less_eq_rat @ ( numeral_numeral_rat @ V ) @ X ) ) ).
% 0.35/0.66  
% 0.35/0.66  % numeral_le_floor
% 0.35/0.66  thf(fact_8438_zero__less__floor,axiom,
% 0.35/0.66      ! [X: real] :
% 0.35/0.66        ( ( ord_less_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X ) )
% 0.35/0.66        = ( ord_less_eq_real @ one_one_real @ X ) ) ).
% 0.35/0.66  
% 0.35/0.66  % zero_less_floor
% 0.35/0.66  thf(fact_8439_zero__less__floor,axiom,
% 0.35/0.66      ! [X: rat] :
% 0.35/0.66        ( ( ord_less_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X ) )
% 0.35/0.66        = ( ord_less_eq_rat @ one_one_rat @ X ) ) ).
% 0.35/0.66  
% 0.35/0.66  % zero_less_floor
% 0.35/0.66  thf(fact_8440_floor__le__zero,axiom,
% 0.35/0.66      ! [X: real] :
% 0.35/0.66        ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ zero_zero_int )
% 0.35/0.66        = ( ord_less_real @ X @ one_one_real ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_le_zero
% 0.35/0.66  thf(fact_8441_floor__le__zero,axiom,
% 0.35/0.66      ! [X: rat] :
% 0.35/0.66        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ zero_zero_int )
% 0.35/0.66        = ( ord_less_rat @ X @ one_one_rat ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_le_zero
% 0.35/0.66  thf(fact_8442_floor__less__numeral,axiom,
% 0.35/0.66      ! [X: real,V: num] :
% 0.35/0.66        ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ ( numeral_numeral_int @ V ) )
% 0.35/0.66        = ( ord_less_real @ X @ ( numeral_numeral_real @ V ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_less_numeral
% 0.35/0.66  thf(fact_8443_floor__less__numeral,axiom,
% 0.35/0.66      ! [X: rat,V: num] :
% 0.35/0.66        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 0.35/0.66        = ( ord_less_rat @ X @ ( numeral_numeral_rat @ V ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_less_numeral
% 0.35/0.66  thf(fact_8444_one__le__floor,axiom,
% 0.35/0.66      ! [X: real] :
% 0.35/0.66        ( ( ord_less_eq_int @ one_one_int @ ( archim6058952711729229775r_real @ X ) )
% 0.35/0.66        = ( ord_less_eq_real @ one_one_real @ X ) ) ).
% 0.35/0.66  
% 0.35/0.66  % one_le_floor
% 0.35/0.66  thf(fact_8445_one__le__floor,axiom,
% 0.35/0.66      ! [X: rat] :
% 0.35/0.66        ( ( ord_less_eq_int @ one_one_int @ ( archim3151403230148437115or_rat @ X ) )
% 0.35/0.66        = ( ord_less_eq_rat @ one_one_rat @ X ) ) ).
% 0.35/0.66  
% 0.35/0.66  % one_le_floor
% 0.35/0.66  thf(fact_8446_floor__less__one,axiom,
% 0.35/0.66      ! [X: real] :
% 0.35/0.66        ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int )
% 0.35/0.66        = ( ord_less_real @ X @ one_one_real ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_less_one
% 0.35/0.66  thf(fact_8447_floor__less__one,axiom,
% 0.35/0.66      ! [X: rat] :
% 0.35/0.66        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int )
% 0.35/0.66        = ( ord_less_rat @ X @ one_one_rat ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_less_one
% 0.35/0.66  thf(fact_8448_floor__neg__numeral,axiom,
% 0.35/0.66      ! [V: num] :
% 0.35/0.66        ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.35/0.66        = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_neg_numeral
% 0.35/0.66  thf(fact_8449_floor__neg__numeral,axiom,
% 0.35/0.66      ! [V: num] :
% 0.35/0.66        ( ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.35/0.66        = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_neg_numeral
% 0.35/0.66  thf(fact_8450_floor__diff__numeral,axiom,
% 0.35/0.66      ! [X: real,V: num] :
% 0.35/0.66        ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X @ ( numeral_numeral_real @ V ) ) )
% 0.35/0.66        = ( minus_minus_int @ ( archim6058952711729229775r_real @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_diff_numeral
% 0.35/0.66  thf(fact_8451_floor__diff__numeral,axiom,
% 0.35/0.66      ! [X: rat,V: num] :
% 0.35/0.66        ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X @ ( numeral_numeral_rat @ V ) ) )
% 0.35/0.66        = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_diff_numeral
% 0.35/0.66  thf(fact_8452_floor__diff__one,axiom,
% 0.35/0.66      ! [X: real] :
% 0.35/0.66        ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X @ one_one_real ) )
% 0.35/0.66        = ( minus_minus_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_diff_one
% 0.35/0.66  thf(fact_8453_floor__diff__one,axiom,
% 0.35/0.66      ! [X: rat] :
% 0.35/0.66        ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X @ one_one_rat ) )
% 0.35/0.66        = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_diff_one
% 0.35/0.66  thf(fact_8454_floor__numeral__power,axiom,
% 0.35/0.66      ! [X: num,N: nat] :
% 0.35/0.66        ( ( archim6058952711729229775r_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 0.35/0.66        = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_numeral_power
% 0.35/0.66  thf(fact_8455_floor__numeral__power,axiom,
% 0.35/0.66      ! [X: num,N: nat] :
% 0.35/0.66        ( ( archim3151403230148437115or_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 0.35/0.66        = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_numeral_power
% 0.35/0.66  thf(fact_8456_floor__divide__eq__div__numeral,axiom,
% 0.35/0.66      ! [A: num,B: num] :
% 0.35/0.66        ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 0.35/0.66        = ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_divide_eq_div_numeral
% 0.35/0.66  thf(fact_8457_or__minus__numerals_I4_J,axiom,
% 0.35/0.66      ! [M: num,N: num] :
% 0.35/0.66        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.35/0.66        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % or_minus_numerals(4)
% 0.35/0.66  thf(fact_8458_or__minus__numerals_I8_J,axiom,
% 0.35/0.66      ! [N: num,M: num] :
% 0.35/0.66        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 0.35/0.66        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % or_minus_numerals(8)
% 0.35/0.66  thf(fact_8459_or__minus__numerals_I7_J,axiom,
% 0.35/0.66      ! [N: num,M: num] :
% 0.35/0.66        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 0.35/0.66        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % or_minus_numerals(7)
% 0.35/0.66  thf(fact_8460_or__minus__numerals_I3_J,axiom,
% 0.35/0.66      ! [M: num,N: num] :
% 0.35/0.66        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.35/0.66        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % or_minus_numerals(3)
% 0.35/0.66  thf(fact_8461_numeral__less__floor,axiom,
% 0.35/0.66      ! [V: num,X: real] :
% 0.35/0.66        ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X ) )
% 0.35/0.66        = ( ord_less_eq_real @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X ) ) ).
% 0.35/0.66  
% 0.35/0.66  % numeral_less_floor
% 0.35/0.66  thf(fact_8462_numeral__less__floor,axiom,
% 0.35/0.66      ! [V: num,X: rat] :
% 0.35/0.66        ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X ) )
% 0.35/0.66        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X ) ) ).
% 0.35/0.66  
% 0.35/0.66  % numeral_less_floor
% 0.35/0.66  thf(fact_8463_floor__le__numeral,axiom,
% 0.35/0.66      ! [X: real,V: num] :
% 0.35/0.66        ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ ( numeral_numeral_int @ V ) )
% 0.35/0.66        = ( ord_less_real @ X @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_le_numeral
% 0.35/0.66  thf(fact_8464_floor__le__numeral,axiom,
% 0.35/0.66      ! [X: rat,V: num] :
% 0.35/0.66        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 0.35/0.66        = ( ord_less_rat @ X @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_le_numeral
% 0.35/0.66  thf(fact_8465_one__less__floor,axiom,
% 0.35/0.66      ! [X: real] :
% 0.35/0.66        ( ( ord_less_int @ one_one_int @ ( archim6058952711729229775r_real @ X ) )
% 0.35/0.66        = ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) ).
% 0.35/0.66  
% 0.35/0.66  % one_less_floor
% 0.35/0.66  thf(fact_8466_one__less__floor,axiom,
% 0.35/0.66      ! [X: rat] :
% 0.35/0.66        ( ( ord_less_int @ one_one_int @ ( archim3151403230148437115or_rat @ X ) )
% 0.35/0.66        = ( ord_less_eq_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) ) ).
% 0.35/0.66  
% 0.35/0.66  % one_less_floor
% 0.35/0.66  thf(fact_8467_floor__le__one,axiom,
% 0.35/0.66      ! [X: real] :
% 0.35/0.66        ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int )
% 0.35/0.66        = ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_le_one
% 0.35/0.66  thf(fact_8468_floor__le__one,axiom,
% 0.35/0.66      ! [X: rat] :
% 0.35/0.66        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int )
% 0.35/0.66        = ( ord_less_rat @ X @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_le_one
% 0.35/0.66  thf(fact_8469_neg__numeral__le__floor,axiom,
% 0.35/0.66      ! [V: num,X: real] :
% 0.35/0.66        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X ) )
% 0.35/0.66        = ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X ) ) ).
% 0.35/0.66  
% 0.35/0.66  % neg_numeral_le_floor
% 0.35/0.66  thf(fact_8470_neg__numeral__le__floor,axiom,
% 0.35/0.66      ! [V: num,X: rat] :
% 0.35/0.66        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X ) )
% 0.35/0.66        = ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X ) ) ).
% 0.35/0.66  
% 0.35/0.66  % neg_numeral_le_floor
% 0.35/0.66  thf(fact_8471_floor__less__neg__numeral,axiom,
% 0.35/0.66      ! [X: real,V: num] :
% 0.35/0.66        ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.35/0.66        = ( ord_less_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_less_neg_numeral
% 0.35/0.66  thf(fact_8472_floor__less__neg__numeral,axiom,
% 0.35/0.66      ! [X: rat,V: num] :
% 0.35/0.66        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.35/0.66        = ( ord_less_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_less_neg_numeral
% 0.35/0.66  thf(fact_8473_floor__one__divide__eq__div__numeral,axiom,
% 0.35/0.66      ! [B: num] :
% 0.35/0.66        ( ( archim6058952711729229775r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) )
% 0.35/0.66        = ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ B ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_one_divide_eq_div_numeral
% 0.35/0.66  thf(fact_8474_floor__minus__divide__eq__div__numeral,axiom,
% 0.35/0.66      ! [A: num,B: num] :
% 0.35/0.66        ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 0.35/0.66        = ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_minus_divide_eq_div_numeral
% 0.35/0.66  thf(fact_8475_neg__numeral__less__floor,axiom,
% 0.35/0.66      ! [V: num,X: real] :
% 0.35/0.66        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X ) )
% 0.35/0.66        = ( ord_less_eq_real @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X ) ) ).
% 0.35/0.66  
% 0.35/0.66  % neg_numeral_less_floor
% 0.35/0.66  thf(fact_8476_neg__numeral__less__floor,axiom,
% 0.35/0.66      ! [V: num,X: rat] :
% 0.35/0.66        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X ) )
% 0.35/0.66        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X ) ) ).
% 0.35/0.66  
% 0.35/0.66  % neg_numeral_less_floor
% 0.35/0.66  thf(fact_8477_floor__le__neg__numeral,axiom,
% 0.35/0.66      ! [X: real,V: num] :
% 0.35/0.66        ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.35/0.66        = ( ord_less_real @ X @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_le_neg_numeral
% 0.35/0.66  thf(fact_8478_floor__le__neg__numeral,axiom,
% 0.35/0.66      ! [X: rat,V: num] :
% 0.35/0.66        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.35/0.66        = ( ord_less_rat @ X @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_le_neg_numeral
% 0.35/0.66  thf(fact_8479_floor__minus__one__divide__eq__div__numeral,axiom,
% 0.35/0.66      ! [B: num] :
% 0.35/0.66        ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) ) )
% 0.35/0.66        = ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ B ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_minus_one_divide_eq_div_numeral
% 0.35/0.66  thf(fact_8480_or__not__num__neg_Osimps_I1_J,axiom,
% 0.35/0.66      ( ( bit_or_not_num_neg @ one @ one )
% 0.35/0.66      = one ) ).
% 0.35/0.66  
% 0.35/0.66  % or_not_num_neg.simps(1)
% 0.35/0.66  thf(fact_8481_floor__mono,axiom,
% 0.35/0.66      ! [X: real,Y2: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ X @ Y2 )
% 0.35/0.66       => ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_mono
% 0.35/0.66  thf(fact_8482_floor__mono,axiom,
% 0.35/0.66      ! [X: rat,Y2: rat] :
% 0.35/0.66        ( ( ord_less_eq_rat @ X @ Y2 )
% 0.35/0.66       => ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_mono
% 0.35/0.66  thf(fact_8483_of__int__floor__le,axiom,
% 0.35/0.66      ! [X: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) ) @ X ) ).
% 0.35/0.66  
% 0.35/0.66  % of_int_floor_le
% 0.35/0.66  thf(fact_8484_of__int__floor__le,axiom,
% 0.35/0.66      ! [X: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) ) @ X ) ).
% 0.35/0.66  
% 0.35/0.66  % of_int_floor_le
% 0.35/0.66  thf(fact_8485_floor__less__cancel,axiom,
% 0.35/0.66      ! [X: real,Y2: real] :
% 0.35/0.66        ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y2 ) )
% 0.35/0.66       => ( ord_less_real @ X @ Y2 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_less_cancel
% 0.35/0.66  thf(fact_8486_floor__less__cancel,axiom,
% 0.35/0.66      ! [X: rat,Y2: rat] :
% 0.35/0.66        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y2 ) )
% 0.35/0.66       => ( ord_less_rat @ X @ Y2 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_less_cancel
% 0.35/0.66  thf(fact_8487_pochhammer__pos,axiom,
% 0.35/0.66      ! [X: real,N: nat] :
% 0.35/0.66        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.66       => ( ord_less_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_pos
% 0.35/0.66  thf(fact_8488_pochhammer__pos,axiom,
% 0.35/0.66      ! [X: rat,N: nat] :
% 0.35/0.66        ( ( ord_less_rat @ zero_zero_rat @ X )
% 0.35/0.66       => ( ord_less_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_pos
% 0.35/0.66  thf(fact_8489_pochhammer__pos,axiom,
% 0.35/0.66      ! [X: nat,N: nat] :
% 0.35/0.66        ( ( ord_less_nat @ zero_zero_nat @ X )
% 0.35/0.66       => ( ord_less_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_pos
% 0.35/0.66  thf(fact_8490_pochhammer__pos,axiom,
% 0.35/0.66      ! [X: int,N: nat] :
% 0.35/0.66        ( ( ord_less_int @ zero_zero_int @ X )
% 0.35/0.66       => ( ord_less_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_pos
% 0.35/0.66  thf(fact_8491_pochhammer__eq__0__mono,axiom,
% 0.35/0.66      ! [A: complex,N: nat,M: nat] :
% 0.35/0.66        ( ( ( comm_s2602460028002588243omplex @ A @ N )
% 0.35/0.66          = zero_zero_complex )
% 0.35/0.66       => ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.66         => ( ( comm_s2602460028002588243omplex @ A @ M )
% 0.35/0.66            = zero_zero_complex ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_eq_0_mono
% 0.35/0.66  thf(fact_8492_pochhammer__eq__0__mono,axiom,
% 0.35/0.66      ! [A: real,N: nat,M: nat] :
% 0.35/0.66        ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 0.35/0.66          = zero_zero_real )
% 0.35/0.66       => ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.66         => ( ( comm_s7457072308508201937r_real @ A @ M )
% 0.35/0.66            = zero_zero_real ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_eq_0_mono
% 0.35/0.66  thf(fact_8493_pochhammer__eq__0__mono,axiom,
% 0.35/0.66      ! [A: rat,N: nat,M: nat] :
% 0.35/0.66        ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 0.35/0.66          = zero_zero_rat )
% 0.35/0.66       => ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.66         => ( ( comm_s4028243227959126397er_rat @ A @ M )
% 0.35/0.66            = zero_zero_rat ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_eq_0_mono
% 0.35/0.66  thf(fact_8494_pochhammer__neq__0__mono,axiom,
% 0.35/0.66      ! [A: complex,M: nat,N: nat] :
% 0.35/0.66        ( ( ( comm_s2602460028002588243omplex @ A @ M )
% 0.35/0.66         != zero_zero_complex )
% 0.35/0.66       => ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.66         => ( ( comm_s2602460028002588243omplex @ A @ N )
% 0.35/0.66           != zero_zero_complex ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_neq_0_mono
% 0.35/0.66  thf(fact_8495_pochhammer__neq__0__mono,axiom,
% 0.35/0.66      ! [A: real,M: nat,N: nat] :
% 0.35/0.66        ( ( ( comm_s7457072308508201937r_real @ A @ M )
% 0.35/0.66         != zero_zero_real )
% 0.35/0.66       => ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.66         => ( ( comm_s7457072308508201937r_real @ A @ N )
% 0.35/0.66           != zero_zero_real ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_neq_0_mono
% 0.35/0.66  thf(fact_8496_pochhammer__neq__0__mono,axiom,
% 0.35/0.66      ! [A: rat,M: nat,N: nat] :
% 0.35/0.66        ( ( ( comm_s4028243227959126397er_rat @ A @ M )
% 0.35/0.66         != zero_zero_rat )
% 0.35/0.66       => ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.66         => ( ( comm_s4028243227959126397er_rat @ A @ N )
% 0.35/0.66           != zero_zero_rat ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_neq_0_mono
% 0.35/0.66  thf(fact_8497_pochhammer__fact,axiom,
% 0.35/0.66      ( semiri5044797733671781792omplex
% 0.35/0.66      = ( comm_s2602460028002588243omplex @ one_one_complex ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_fact
% 0.35/0.66  thf(fact_8498_pochhammer__fact,axiom,
% 0.35/0.66      ( semiri773545260158071498ct_rat
% 0.35/0.66      = ( comm_s4028243227959126397er_rat @ one_one_rat ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_fact
% 0.35/0.66  thf(fact_8499_pochhammer__fact,axiom,
% 0.35/0.66      ( semiri1406184849735516958ct_int
% 0.35/0.66      = ( comm_s4660882817536571857er_int @ one_one_int ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_fact
% 0.35/0.66  thf(fact_8500_pochhammer__fact,axiom,
% 0.35/0.66      ( semiri2265585572941072030t_real
% 0.35/0.66      = ( comm_s7457072308508201937r_real @ one_one_real ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_fact
% 0.35/0.66  thf(fact_8501_pochhammer__fact,axiom,
% 0.35/0.66      ( semiri1408675320244567234ct_nat
% 0.35/0.66      = ( comm_s4663373288045622133er_nat @ one_one_nat ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_fact
% 0.35/0.66  thf(fact_8502_or__not__num__neg_Osimps_I4_J,axiom,
% 0.35/0.66      ! [N: num] :
% 0.35/0.66        ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ one )
% 0.35/0.66        = ( bit0 @ one ) ) ).
% 0.35/0.66  
% 0.35/0.66  % or_not_num_neg.simps(4)
% 0.35/0.66  thf(fact_8503_or__not__num__neg_Osimps_I6_J,axiom,
% 0.35/0.66      ! [N: num,M: num] :
% 0.35/0.66        ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit1 @ M ) )
% 0.35/0.66        = ( bit0 @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % or_not_num_neg.simps(6)
% 0.35/0.66  thf(fact_8504_or__not__num__neg_Osimps_I7_J,axiom,
% 0.35/0.66      ! [N: num] :
% 0.35/0.66        ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ one )
% 0.35/0.66        = one ) ).
% 0.35/0.66  
% 0.35/0.66  % or_not_num_neg.simps(7)
% 0.35/0.66  thf(fact_8505_or__not__num__neg_Osimps_I3_J,axiom,
% 0.35/0.66      ! [M: num] :
% 0.35/0.66        ( ( bit_or_not_num_neg @ one @ ( bit1 @ M ) )
% 0.35/0.66        = ( bit1 @ M ) ) ).
% 0.35/0.66  
% 0.35/0.66  % or_not_num_neg.simps(3)
% 0.35/0.66  thf(fact_8506_or__not__num__neg_Osimps_I5_J,axiom,
% 0.35/0.66      ! [N: num,M: num] :
% 0.35/0.66        ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit0 @ M ) )
% 0.35/0.66        = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % or_not_num_neg.simps(5)
% 0.35/0.66  thf(fact_8507_or__not__num__neg_Osimps_I9_J,axiom,
% 0.35/0.66      ! [N: num,M: num] :
% 0.35/0.66        ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ ( bit1 @ M ) )
% 0.35/0.66        = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % or_not_num_neg.simps(9)
% 0.35/0.66  thf(fact_8508_le__floor__iff,axiom,
% 0.35/0.66      ! [Z: int,X: real] :
% 0.35/0.66        ( ( ord_less_eq_int @ Z @ ( archim6058952711729229775r_real @ X ) )
% 0.35/0.66        = ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ X ) ) ).
% 0.35/0.66  
% 0.35/0.66  % le_floor_iff
% 0.35/0.66  thf(fact_8509_le__floor__iff,axiom,
% 0.35/0.66      ! [Z: int,X: rat] :
% 0.35/0.66        ( ( ord_less_eq_int @ Z @ ( archim3151403230148437115or_rat @ X ) )
% 0.35/0.66        = ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X ) ) ).
% 0.35/0.66  
% 0.35/0.66  % le_floor_iff
% 0.35/0.66  thf(fact_8510_floor__less__iff,axiom,
% 0.35/0.66      ! [X: real,Z: int] :
% 0.35/0.66        ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ Z )
% 0.35/0.66        = ( ord_less_real @ X @ ( ring_1_of_int_real @ Z ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_less_iff
% 0.35/0.66  thf(fact_8511_floor__less__iff,axiom,
% 0.35/0.66      ! [X: rat,Z: int] :
% 0.35/0.66        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ Z )
% 0.35/0.66        = ( ord_less_rat @ X @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_less_iff
% 0.35/0.66  thf(fact_8512_le__floor__add,axiom,
% 0.35/0.66      ! [X: real,Y2: real] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y2 ) ) @ ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ Y2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % le_floor_add
% 0.35/0.66  thf(fact_8513_le__floor__add,axiom,
% 0.35/0.66      ! [X: rat,Y2: rat] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y2 ) ) @ ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ Y2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % le_floor_add
% 0.35/0.66  thf(fact_8514_int__add__floor,axiom,
% 0.35/0.66      ! [Z: int,X: real] :
% 0.35/0.66        ( ( plus_plus_int @ Z @ ( archim6058952711729229775r_real @ X ) )
% 0.35/0.66        = ( archim6058952711729229775r_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ X ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % int_add_floor
% 0.35/0.66  thf(fact_8515_int__add__floor,axiom,
% 0.35/0.66      ! [Z: int,X: rat] :
% 0.35/0.66        ( ( plus_plus_int @ Z @ ( archim3151403230148437115or_rat @ X ) )
% 0.35/0.66        = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ X ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % int_add_floor
% 0.35/0.66  thf(fact_8516_floor__add__int,axiom,
% 0.35/0.66      ! [X: real,Z: int] :
% 0.35/0.66        ( ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ Z )
% 0.35/0.66        = ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ ( ring_1_of_int_real @ Z ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_add_int
% 0.35/0.66  thf(fact_8517_floor__add__int,axiom,
% 0.35/0.66      ! [X: rat,Z: int] :
% 0.35/0.66        ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ Z )
% 0.35/0.66        = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ ( ring_1_of_int_rat @ Z ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_add_int
% 0.35/0.66  thf(fact_8518_floor__divide__of__int__eq,axiom,
% 0.35/0.66      ! [K: int,L2: int] :
% 0.35/0.66        ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( ring_1_of_int_real @ K ) @ ( ring_1_of_int_real @ L2 ) ) )
% 0.35/0.66        = ( divide_divide_int @ K @ L2 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_divide_of_int_eq
% 0.35/0.66  thf(fact_8519_floor__divide__of__int__eq,axiom,
% 0.35/0.66      ! [K: int,L2: int] :
% 0.35/0.66        ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ K ) @ ( ring_1_of_int_rat @ L2 ) ) )
% 0.35/0.66        = ( divide_divide_int @ K @ L2 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_divide_of_int_eq
% 0.35/0.66  thf(fact_8520_floor__power,axiom,
% 0.35/0.66      ! [X: real,N: nat] :
% 0.35/0.66        ( ( X
% 0.35/0.66          = ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) ) )
% 0.35/0.66       => ( ( archim6058952711729229775r_real @ ( power_power_real @ X @ N ) )
% 0.35/0.66          = ( power_power_int @ ( archim6058952711729229775r_real @ X ) @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_power
% 0.35/0.66  thf(fact_8521_floor__power,axiom,
% 0.35/0.66      ! [X: rat,N: nat] :
% 0.35/0.66        ( ( X
% 0.35/0.66          = ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) ) )
% 0.35/0.66       => ( ( archim3151403230148437115or_rat @ ( power_power_rat @ X @ N ) )
% 0.35/0.66          = ( power_power_int @ ( archim3151403230148437115or_rat @ X ) @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_power
% 0.35/0.66  thf(fact_8522_pochhammer__nonneg,axiom,
% 0.35/0.66      ! [X: real,N: nat] :
% 0.35/0.66        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.66       => ( ord_less_eq_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_nonneg
% 0.35/0.66  thf(fact_8523_pochhammer__nonneg,axiom,
% 0.35/0.66      ! [X: rat,N: nat] :
% 0.35/0.66        ( ( ord_less_rat @ zero_zero_rat @ X )
% 0.35/0.66       => ( ord_less_eq_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_nonneg
% 0.35/0.66  thf(fact_8524_pochhammer__nonneg,axiom,
% 0.35/0.66      ! [X: nat,N: nat] :
% 0.35/0.66        ( ( ord_less_nat @ zero_zero_nat @ X )
% 0.35/0.66       => ( ord_less_eq_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_nonneg
% 0.35/0.66  thf(fact_8525_pochhammer__nonneg,axiom,
% 0.35/0.66      ! [X: int,N: nat] :
% 0.35/0.66        ( ( ord_less_int @ zero_zero_int @ X )
% 0.35/0.66       => ( ord_less_eq_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_nonneg
% 0.35/0.66  thf(fact_8526_pochhammer__0__left,axiom,
% 0.35/0.66      ! [N: nat] :
% 0.35/0.66        ( ( ( N = zero_zero_nat )
% 0.35/0.66         => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 0.35/0.66            = one_one_complex ) )
% 0.35/0.66        & ( ( N != zero_zero_nat )
% 0.35/0.66         => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 0.35/0.66            = zero_zero_complex ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_0_left
% 0.35/0.66  thf(fact_8527_pochhammer__0__left,axiom,
% 0.35/0.66      ! [N: nat] :
% 0.35/0.66        ( ( ( N = zero_zero_nat )
% 0.35/0.66         => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 0.35/0.66            = one_one_real ) )
% 0.35/0.66        & ( ( N != zero_zero_nat )
% 0.35/0.66         => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 0.35/0.66            = zero_zero_real ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_0_left
% 0.35/0.66  thf(fact_8528_pochhammer__0__left,axiom,
% 0.35/0.66      ! [N: nat] :
% 0.35/0.66        ( ( ( N = zero_zero_nat )
% 0.35/0.66         => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 0.35/0.66            = one_one_rat ) )
% 0.35/0.66        & ( ( N != zero_zero_nat )
% 0.35/0.66         => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 0.35/0.66            = zero_zero_rat ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_0_left
% 0.35/0.66  thf(fact_8529_pochhammer__0__left,axiom,
% 0.35/0.66      ! [N: nat] :
% 0.35/0.66        ( ( ( N = zero_zero_nat )
% 0.35/0.66         => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 0.35/0.66            = one_one_nat ) )
% 0.35/0.66        & ( ( N != zero_zero_nat )
% 0.35/0.66         => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 0.35/0.66            = zero_zero_nat ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_0_left
% 0.35/0.66  thf(fact_8530_pochhammer__0__left,axiom,
% 0.35/0.66      ! [N: nat] :
% 0.35/0.66        ( ( ( N = zero_zero_nat )
% 0.35/0.66         => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 0.35/0.66            = one_one_int ) )
% 0.35/0.66        & ( ( N != zero_zero_nat )
% 0.35/0.66         => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 0.35/0.66            = zero_zero_int ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_0_left
% 0.35/0.66  thf(fact_8531_or__not__num__neg_Osimps_I2_J,axiom,
% 0.35/0.66      ! [M: num] :
% 0.35/0.66        ( ( bit_or_not_num_neg @ one @ ( bit0 @ M ) )
% 0.35/0.66        = ( bit1 @ M ) ) ).
% 0.35/0.66  
% 0.35/0.66  % or_not_num_neg.simps(2)
% 0.35/0.66  thf(fact_8532_one__add__floor,axiom,
% 0.35/0.66      ! [X: real] :
% 0.35/0.66        ( ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int )
% 0.35/0.66        = ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ one_one_real ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % one_add_floor
% 0.35/0.66  thf(fact_8533_one__add__floor,axiom,
% 0.35/0.66      ! [X: rat] :
% 0.35/0.66        ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int )
% 0.35/0.66        = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ one_one_rat ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % one_add_floor
% 0.35/0.66  thf(fact_8534_floor__divide__of__nat__eq,axiom,
% 0.35/0.66      ! [M: nat,N: nat] :
% 0.35/0.66        ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 0.35/0.66        = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_divide_of_nat_eq
% 0.35/0.66  thf(fact_8535_floor__divide__of__nat__eq,axiom,
% 0.35/0.66      ! [M: nat,N: nat] :
% 0.35/0.66        ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) )
% 0.35/0.66        = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_divide_of_nat_eq
% 0.35/0.66  thf(fact_8536_ceiling__diff__floor__le__1,axiom,
% 0.35/0.66      ! [X: real] : ( ord_less_eq_int @ ( minus_minus_int @ ( archim7802044766580827645g_real @ X ) @ ( archim6058952711729229775r_real @ X ) ) @ one_one_int ) ).
% 0.35/0.66  
% 0.35/0.66  % ceiling_diff_floor_le_1
% 0.35/0.66  thf(fact_8537_ceiling__diff__floor__le__1,axiom,
% 0.35/0.66      ! [X: rat] : ( ord_less_eq_int @ ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X ) @ ( archim3151403230148437115or_rat @ X ) ) @ one_one_int ) ).
% 0.35/0.66  
% 0.35/0.66  % ceiling_diff_floor_le_1
% 0.35/0.66  thf(fact_8538_real__of__int__floor__add__one__gt,axiom,
% 0.35/0.66      ! [R: real] : ( ord_less_real @ R @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) @ one_one_real ) ) ).
% 0.35/0.66  
% 0.35/0.66  % real_of_int_floor_add_one_gt
% 0.35/0.66  thf(fact_8539_floor__eq,axiom,
% 0.35/0.66      ! [N: int,X: real] :
% 0.35/0.66        ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X )
% 0.35/0.66       => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 0.35/0.66         => ( ( archim6058952711729229775r_real @ X )
% 0.35/0.66            = N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_eq
% 0.35/0.66  thf(fact_8540_real__of__int__floor__add__one__ge,axiom,
% 0.35/0.66      ! [R: real] : ( ord_less_eq_real @ R @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) @ one_one_real ) ) ).
% 0.35/0.66  
% 0.35/0.66  % real_of_int_floor_add_one_ge
% 0.35/0.66  thf(fact_8541_or__not__num__neg_Osimps_I8_J,axiom,
% 0.35/0.66      ! [N: num,M: num] :
% 0.35/0.66        ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ ( bit0 @ M ) )
% 0.35/0.66        = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % or_not_num_neg.simps(8)
% 0.35/0.66  thf(fact_8542_real__of__int__floor__gt__diff__one,axiom,
% 0.35/0.66      ! [R: real] : ( ord_less_real @ ( minus_minus_real @ R @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % real_of_int_floor_gt_diff_one
% 0.35/0.66  thf(fact_8543_real__of__int__floor__ge__diff__one,axiom,
% 0.35/0.66      ! [R: real] : ( ord_less_eq_real @ ( minus_minus_real @ R @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % real_of_int_floor_ge_diff_one
% 0.35/0.66  thf(fact_8544_pochhammer__rec,axiom,
% 0.35/0.66      ! [A: rat,N: nat] :
% 0.35/0.66        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 0.35/0.66        = ( times_times_rat @ A @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_rec
% 0.35/0.66  thf(fact_8545_pochhammer__rec,axiom,
% 0.35/0.66      ! [A: complex,N: nat] :
% 0.35/0.66        ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 0.35/0.66        = ( times_times_complex @ A @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_rec
% 0.35/0.66  thf(fact_8546_pochhammer__rec,axiom,
% 0.35/0.66      ! [A: real,N: nat] :
% 0.35/0.66        ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 0.35/0.66        = ( times_times_real @ A @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ one_one_real ) @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_rec
% 0.35/0.66  thf(fact_8547_pochhammer__rec,axiom,
% 0.35/0.66      ! [A: nat,N: nat] :
% 0.35/0.66        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 0.35/0.66        = ( times_times_nat @ A @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_rec
% 0.35/0.66  thf(fact_8548_pochhammer__rec,axiom,
% 0.35/0.66      ! [A: int,N: nat] :
% 0.35/0.66        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 0.35/0.66        = ( times_times_int @ A @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ one_one_int ) @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_rec
% 0.35/0.66  thf(fact_8549_pochhammer__rec_H,axiom,
% 0.35/0.66      ! [Z: rat,N: nat] :
% 0.35/0.66        ( ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N ) )
% 0.35/0.66        = ( times_times_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_rec'
% 0.35/0.66  thf(fact_8550_pochhammer__rec_H,axiom,
% 0.35/0.66      ! [Z: real,N: nat] :
% 0.35/0.66        ( ( comm_s7457072308508201937r_real @ Z @ ( suc @ N ) )
% 0.35/0.66        = ( times_times_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N ) ) @ ( comm_s7457072308508201937r_real @ Z @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_rec'
% 0.35/0.66  thf(fact_8551_pochhammer__rec_H,axiom,
% 0.35/0.66      ! [Z: int,N: nat] :
% 0.35/0.66        ( ( comm_s4660882817536571857er_int @ Z @ ( suc @ N ) )
% 0.35/0.66        = ( times_times_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N ) ) @ ( comm_s4660882817536571857er_int @ Z @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_rec'
% 0.35/0.66  thf(fact_8552_pochhammer__rec_H,axiom,
% 0.35/0.66      ! [Z: nat,N: nat] :
% 0.35/0.66        ( ( comm_s4663373288045622133er_nat @ Z @ ( suc @ N ) )
% 0.35/0.66        = ( times_times_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N ) ) @ ( comm_s4663373288045622133er_nat @ Z @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_rec'
% 0.35/0.66  thf(fact_8553_pochhammer__rec_H,axiom,
% 0.35/0.66      ! [Z: complex,N: nat] :
% 0.35/0.66        ( ( comm_s2602460028002588243omplex @ Z @ ( suc @ N ) )
% 0.35/0.66        = ( times_times_complex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ N ) ) @ ( comm_s2602460028002588243omplex @ Z @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_rec'
% 0.35/0.66  thf(fact_8554_pochhammer__Suc,axiom,
% 0.35/0.66      ! [A: rat,N: nat] :
% 0.35/0.66        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 0.35/0.66        = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ A @ N ) @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_Suc
% 0.35/0.66  thf(fact_8555_pochhammer__Suc,axiom,
% 0.35/0.66      ! [A: real,N: nat] :
% 0.35/0.66        ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 0.35/0.66        = ( times_times_real @ ( comm_s7457072308508201937r_real @ A @ N ) @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_Suc
% 0.35/0.66  thf(fact_8556_pochhammer__Suc,axiom,
% 0.35/0.66      ! [A: int,N: nat] :
% 0.35/0.66        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 0.35/0.66        = ( times_times_int @ ( comm_s4660882817536571857er_int @ A @ N ) @ ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_Suc
% 0.35/0.66  thf(fact_8557_pochhammer__Suc,axiom,
% 0.35/0.66      ! [A: nat,N: nat] :
% 0.35/0.66        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 0.35/0.66        = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ A @ N ) @ ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_Suc
% 0.35/0.66  thf(fact_8558_pochhammer__Suc,axiom,
% 0.35/0.66      ! [A: complex,N: nat] :
% 0.35/0.66        ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 0.35/0.66        = ( times_times_complex @ ( comm_s2602460028002588243omplex @ A @ N ) @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ N ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_Suc
% 0.35/0.66  thf(fact_8559_pochhammer__eq__0__iff,axiom,
% 0.35/0.66      ! [A: rat,N: nat] :
% 0.35/0.66        ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 0.35/0.66          = zero_zero_rat )
% 0.35/0.66        = ( ? [K3: nat] :
% 0.35/0.66              ( ( ord_less_nat @ K3 @ N )
% 0.35/0.66              & ( A
% 0.35/0.66                = ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K3 ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_eq_0_iff
% 0.35/0.66  thf(fact_8560_pochhammer__eq__0__iff,axiom,
% 0.35/0.66      ! [A: real,N: nat] :
% 0.35/0.66        ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 0.35/0.66          = zero_zero_real )
% 0.35/0.66        = ( ? [K3: nat] :
% 0.35/0.66              ( ( ord_less_nat @ K3 @ N )
% 0.35/0.66              & ( A
% 0.35/0.66                = ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K3 ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_eq_0_iff
% 0.35/0.66  thf(fact_8561_pochhammer__eq__0__iff,axiom,
% 0.35/0.66      ! [A: complex,N: nat] :
% 0.35/0.66        ( ( ( comm_s2602460028002588243omplex @ A @ N )
% 0.35/0.66          = zero_zero_complex )
% 0.35/0.66        = ( ? [K3: nat] :
% 0.35/0.66              ( ( ord_less_nat @ K3 @ N )
% 0.35/0.66              & ( A
% 0.35/0.66                = ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K3 ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_eq_0_iff
% 0.35/0.66  thf(fact_8562_pochhammer__of__nat__eq__0__iff,axiom,
% 0.35/0.66      ! [N: nat,K: nat] :
% 0.35/0.66        ( ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 0.35/0.66          = zero_z3403309356797280102nteger )
% 0.35/0.66        = ( ord_less_nat @ N @ K ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_of_nat_eq_0_iff
% 0.35/0.66  thf(fact_8563_pochhammer__of__nat__eq__0__iff,axiom,
% 0.35/0.66      ! [N: nat,K: nat] :
% 0.35/0.66        ( ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 0.35/0.66          = zero_zero_rat )
% 0.35/0.66        = ( ord_less_nat @ N @ K ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_of_nat_eq_0_iff
% 0.35/0.66  thf(fact_8564_pochhammer__of__nat__eq__0__iff,axiom,
% 0.35/0.66      ! [N: nat,K: nat] :
% 0.35/0.66        ( ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 0.35/0.66          = zero_zero_real )
% 0.35/0.66        = ( ord_less_nat @ N @ K ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_of_nat_eq_0_iff
% 0.35/0.66  thf(fact_8565_pochhammer__of__nat__eq__0__iff,axiom,
% 0.35/0.66      ! [N: nat,K: nat] :
% 0.35/0.66        ( ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 0.35/0.66          = zero_zero_int )
% 0.35/0.66        = ( ord_less_nat @ N @ K ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_of_nat_eq_0_iff
% 0.35/0.66  thf(fact_8566_pochhammer__of__nat__eq__0__iff,axiom,
% 0.35/0.66      ! [N: nat,K: nat] :
% 0.35/0.66        ( ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 0.35/0.66          = zero_zero_complex )
% 0.35/0.66        = ( ord_less_nat @ N @ K ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_of_nat_eq_0_iff
% 0.35/0.66  thf(fact_8567_pochhammer__of__nat__eq__0__lemma,axiom,
% 0.35/0.66      ! [N: nat,K: nat] :
% 0.35/0.66        ( ( ord_less_nat @ N @ K )
% 0.35/0.66       => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 0.35/0.66          = zero_z3403309356797280102nteger ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_of_nat_eq_0_lemma
% 0.35/0.66  thf(fact_8568_pochhammer__of__nat__eq__0__lemma,axiom,
% 0.35/0.66      ! [N: nat,K: nat] :
% 0.35/0.66        ( ( ord_less_nat @ N @ K )
% 0.35/0.66       => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 0.35/0.66          = zero_zero_rat ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_of_nat_eq_0_lemma
% 0.35/0.66  thf(fact_8569_pochhammer__of__nat__eq__0__lemma,axiom,
% 0.35/0.66      ! [N: nat,K: nat] :
% 0.35/0.66        ( ( ord_less_nat @ N @ K )
% 0.35/0.66       => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 0.35/0.66          = zero_zero_real ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_of_nat_eq_0_lemma
% 0.35/0.66  thf(fact_8570_pochhammer__of__nat__eq__0__lemma,axiom,
% 0.35/0.66      ! [N: nat,K: nat] :
% 0.35/0.66        ( ( ord_less_nat @ N @ K )
% 0.35/0.66       => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 0.35/0.66          = zero_zero_int ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_of_nat_eq_0_lemma
% 0.35/0.66  thf(fact_8571_pochhammer__of__nat__eq__0__lemma,axiom,
% 0.35/0.66      ! [N: nat,K: nat] :
% 0.35/0.66        ( ( ord_less_nat @ N @ K )
% 0.35/0.66       => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 0.35/0.66          = zero_zero_complex ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_of_nat_eq_0_lemma
% 0.35/0.66  thf(fact_8572_pochhammer__product_H,axiom,
% 0.35/0.66      ! [Z: rat,N: nat,M: nat] :
% 0.35/0.66        ( ( comm_s4028243227959126397er_rat @ Z @ ( plus_plus_nat @ N @ M ) )
% 0.35/0.66        = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ N ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N ) ) @ M ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_product'
% 0.35/0.66  thf(fact_8573_pochhammer__product_H,axiom,
% 0.35/0.66      ! [Z: real,N: nat,M: nat] :
% 0.35/0.66        ( ( comm_s7457072308508201937r_real @ Z @ ( plus_plus_nat @ N @ M ) )
% 0.35/0.66        = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ N ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N ) ) @ M ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_product'
% 0.35/0.66  thf(fact_8574_pochhammer__product_H,axiom,
% 0.35/0.66      ! [Z: int,N: nat,M: nat] :
% 0.35/0.66        ( ( comm_s4660882817536571857er_int @ Z @ ( plus_plus_nat @ N @ M ) )
% 0.35/0.66        = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ N ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N ) ) @ M ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_product'
% 0.35/0.66  thf(fact_8575_pochhammer__product_H,axiom,
% 0.35/0.66      ! [Z: nat,N: nat,M: nat] :
% 0.35/0.66        ( ( comm_s4663373288045622133er_nat @ Z @ ( plus_plus_nat @ N @ M ) )
% 0.35/0.66        = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ N ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N ) ) @ M ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_product'
% 0.35/0.66  thf(fact_8576_pochhammer__product_H,axiom,
% 0.35/0.66      ! [Z: complex,N: nat,M: nat] :
% 0.35/0.66        ( ( comm_s2602460028002588243omplex @ Z @ ( plus_plus_nat @ N @ M ) )
% 0.35/0.66        = ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ N ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ N ) ) @ M ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_product'
% 0.35/0.66  thf(fact_8577_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 0.35/0.66      ! [K: nat,N: nat] :
% 0.35/0.66        ( ( ord_less_eq_nat @ K @ N )
% 0.35/0.66       => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 0.35/0.66         != zero_z3403309356797280102nteger ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_of_nat_eq_0_lemma'
% 0.35/0.66  thf(fact_8578_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 0.35/0.66      ! [K: nat,N: nat] :
% 0.35/0.66        ( ( ord_less_eq_nat @ K @ N )
% 0.35/0.66       => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 0.35/0.66         != zero_zero_rat ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_of_nat_eq_0_lemma'
% 0.35/0.66  thf(fact_8579_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 0.35/0.66      ! [K: nat,N: nat] :
% 0.35/0.66        ( ( ord_less_eq_nat @ K @ N )
% 0.35/0.66       => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 0.35/0.66         != zero_zero_real ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_of_nat_eq_0_lemma'
% 0.35/0.66  thf(fact_8580_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 0.35/0.66      ! [K: nat,N: nat] :
% 0.35/0.66        ( ( ord_less_eq_nat @ K @ N )
% 0.35/0.66       => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 0.35/0.66         != zero_zero_int ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_of_nat_eq_0_lemma'
% 0.35/0.66  thf(fact_8581_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 0.35/0.66      ! [K: nat,N: nat] :
% 0.35/0.66        ( ( ord_less_eq_nat @ K @ N )
% 0.35/0.66       => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 0.35/0.66         != zero_zero_complex ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_of_nat_eq_0_lemma'
% 0.35/0.66  thf(fact_8582_floor__unique,axiom,
% 0.35/0.66      ! [Z: int,X: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ X )
% 0.35/0.66       => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) )
% 0.35/0.66         => ( ( archim6058952711729229775r_real @ X )
% 0.35/0.66            = Z ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_unique
% 0.35/0.66  thf(fact_8583_floor__unique,axiom,
% 0.35/0.66      ! [Z: int,X: rat] :
% 0.35/0.66        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X )
% 0.35/0.66       => ( ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) )
% 0.35/0.66         => ( ( archim3151403230148437115or_rat @ X )
% 0.35/0.66            = Z ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_unique
% 0.35/0.66  thf(fact_8584_floor__eq__iff,axiom,
% 0.35/0.66      ! [X: real,A: int] :
% 0.35/0.66        ( ( ( archim6058952711729229775r_real @ X )
% 0.35/0.66          = A )
% 0.35/0.66        = ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ X )
% 0.35/0.66          & ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_eq_iff
% 0.35/0.66  thf(fact_8585_floor__eq__iff,axiom,
% 0.35/0.66      ! [X: rat,A: int] :
% 0.35/0.66        ( ( ( archim3151403230148437115or_rat @ X )
% 0.35/0.66          = A )
% 0.35/0.66        = ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ X )
% 0.35/0.66          & ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_eq_iff
% 0.35/0.66  thf(fact_8586_floor__split,axiom,
% 0.35/0.66      ! [P: int > $o,T: real] :
% 0.35/0.66        ( ( P @ ( archim6058952711729229775r_real @ T ) )
% 0.35/0.66        = ( ! [I3: int] :
% 0.35/0.66              ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ I3 ) @ T )
% 0.35/0.66                & ( ord_less_real @ T @ ( plus_plus_real @ ( ring_1_of_int_real @ I3 ) @ one_one_real ) ) )
% 0.35/0.66             => ( P @ I3 ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_split
% 0.35/0.66  thf(fact_8587_floor__split,axiom,
% 0.35/0.66      ! [P: int > $o,T: rat] :
% 0.35/0.66        ( ( P @ ( archim3151403230148437115or_rat @ T ) )
% 0.35/0.66        = ( ! [I3: int] :
% 0.35/0.66              ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ I3 ) @ T )
% 0.35/0.66                & ( ord_less_rat @ T @ ( plus_plus_rat @ ( ring_1_of_int_rat @ I3 ) @ one_one_rat ) ) )
% 0.35/0.66             => ( P @ I3 ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_split
% 0.35/0.66  thf(fact_8588_le__mult__floor,axiom,
% 0.35/0.66      ! [A: real,B: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.35/0.66       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.35/0.66         => ( ord_less_eq_int @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B ) ) @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % le_mult_floor
% 0.35/0.66  thf(fact_8589_le__mult__floor,axiom,
% 0.35/0.66      ! [A: rat,B: rat] :
% 0.35/0.66        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.35/0.66       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.35/0.66         => ( ord_less_eq_int @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % le_mult_floor
% 0.35/0.66  thf(fact_8590_less__floor__iff,axiom,
% 0.35/0.66      ! [Z: int,X: real] :
% 0.35/0.66        ( ( ord_less_int @ Z @ ( archim6058952711729229775r_real @ X ) )
% 0.35/0.66        = ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X ) ) ).
% 0.35/0.66  
% 0.35/0.66  % less_floor_iff
% 0.35/0.66  thf(fact_8591_less__floor__iff,axiom,
% 0.35/0.66      ! [Z: int,X: rat] :
% 0.35/0.66        ( ( ord_less_int @ Z @ ( archim3151403230148437115or_rat @ X ) )
% 0.35/0.66        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X ) ) ).
% 0.35/0.66  
% 0.35/0.66  % less_floor_iff
% 0.35/0.66  thf(fact_8592_floor__le__iff,axiom,
% 0.35/0.66      ! [X: real,Z: int] :
% 0.35/0.66        ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ Z )
% 0.35/0.66        = ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_le_iff
% 0.35/0.66  thf(fact_8593_floor__le__iff,axiom,
% 0.35/0.66      ! [X: rat,Z: int] :
% 0.35/0.66        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ Z )
% 0.35/0.66        = ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_le_iff
% 0.35/0.66  thf(fact_8594_floor__correct,axiom,
% 0.35/0.66      ! [X: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) ) @ X )
% 0.35/0.66        & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_correct
% 0.35/0.66  thf(fact_8595_floor__correct,axiom,
% 0.35/0.66      ! [X: rat] :
% 0.35/0.66        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) ) @ X )
% 0.35/0.66        & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_correct
% 0.35/0.66  thf(fact_8596_floor__eq2,axiom,
% 0.35/0.66      ! [N: int,X: real] :
% 0.35/0.66        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ N ) @ X )
% 0.35/0.66       => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 0.35/0.66         => ( ( archim6058952711729229775r_real @ X )
% 0.35/0.66            = N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_eq2
% 0.35/0.66  thf(fact_8597_floor__divide__real__eq__div,axiom,
% 0.35/0.66      ! [B: int,A: real] :
% 0.35/0.66        ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.35/0.66       => ( ( archim6058952711729229775r_real @ ( divide_divide_real @ A @ ( ring_1_of_int_real @ B ) ) )
% 0.35/0.66          = ( divide_divide_int @ ( archim6058952711729229775r_real @ A ) @ B ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_divide_real_eq_div
% 0.35/0.66  thf(fact_8598_or__not__num__neg_Oelims,axiom,
% 0.35/0.66      ! [X: num,Xa2: num,Y2: num] :
% 0.35/0.66        ( ( ( bit_or_not_num_neg @ X @ Xa2 )
% 0.35/0.66          = Y2 )
% 0.35/0.66       => ( ( ( X = one )
% 0.35/0.66           => ( ( Xa2 = one )
% 0.35/0.66             => ( Y2 != one ) ) )
% 0.35/0.66         => ( ( ( X = one )
% 0.35/0.66             => ! [M4: num] :
% 0.35/0.66                  ( ( Xa2
% 0.35/0.66                    = ( bit0 @ M4 ) )
% 0.35/0.66                 => ( Y2
% 0.35/0.66                   != ( bit1 @ M4 ) ) ) )
% 0.35/0.66           => ( ( ( X = one )
% 0.35/0.66               => ! [M4: num] :
% 0.35/0.66                    ( ( Xa2
% 0.35/0.66                      = ( bit1 @ M4 ) )
% 0.35/0.66                   => ( Y2
% 0.35/0.66                     != ( bit1 @ M4 ) ) ) )
% 0.35/0.66             => ( ( ? [N3: num] :
% 0.35/0.66                      ( X
% 0.35/0.66                      = ( bit0 @ N3 ) )
% 0.35/0.66                 => ( ( Xa2 = one )
% 0.35/0.66                   => ( Y2
% 0.35/0.66                     != ( bit0 @ one ) ) ) )
% 0.35/0.66               => ( ! [N3: num] :
% 0.35/0.66                      ( ( X
% 0.35/0.66                        = ( bit0 @ N3 ) )
% 0.35/0.66                     => ! [M4: num] :
% 0.35/0.66                          ( ( Xa2
% 0.35/0.66                            = ( bit0 @ M4 ) )
% 0.35/0.66                         => ( Y2
% 0.35/0.66                           != ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) ) ) )
% 0.35/0.66                 => ( ! [N3: num] :
% 0.35/0.66                        ( ( X
% 0.35/0.66                          = ( bit0 @ N3 ) )
% 0.35/0.66                       => ! [M4: num] :
% 0.35/0.66                            ( ( Xa2
% 0.35/0.66                              = ( bit1 @ M4 ) )
% 0.35/0.66                           => ( Y2
% 0.35/0.66                             != ( bit0 @ ( bit_or_not_num_neg @ N3 @ M4 ) ) ) ) )
% 0.35/0.66                   => ( ( ? [N3: num] :
% 0.35/0.66                            ( X
% 0.35/0.66                            = ( bit1 @ N3 ) )
% 0.35/0.66                       => ( ( Xa2 = one )
% 0.35/0.66                         => ( Y2 != one ) ) )
% 0.35/0.66                     => ( ! [N3: num] :
% 0.35/0.66                            ( ( X
% 0.35/0.66                              = ( bit1 @ N3 ) )
% 0.35/0.66                           => ! [M4: num] :
% 0.35/0.66                                ( ( Xa2
% 0.35/0.66                                  = ( bit0 @ M4 ) )
% 0.35/0.66                               => ( Y2
% 0.35/0.66                                 != ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) ) ) )
% 0.35/0.66                       => ~ ! [N3: num] :
% 0.35/0.66                              ( ( X
% 0.35/0.66                                = ( bit1 @ N3 ) )
% 0.35/0.66                             => ! [M4: num] :
% 0.35/0.66                                  ( ( Xa2
% 0.35/0.66                                    = ( bit1 @ M4 ) )
% 0.35/0.66                                 => ( Y2
% 0.35/0.66                                   != ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % or_not_num_neg.elims
% 0.35/0.66  thf(fact_8599_pochhammer__product,axiom,
% 0.35/0.66      ! [M: nat,N: nat,Z: rat] :
% 0.35/0.66        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.66       => ( ( comm_s4028243227959126397er_rat @ Z @ N )
% 0.35/0.66          = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ M ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_product
% 0.35/0.66  thf(fact_8600_pochhammer__product,axiom,
% 0.35/0.66      ! [M: nat,N: nat,Z: real] :
% 0.35/0.66        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.66       => ( ( comm_s7457072308508201937r_real @ Z @ N )
% 0.35/0.66          = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ M ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_product
% 0.35/0.66  thf(fact_8601_pochhammer__product,axiom,
% 0.35/0.66      ! [M: nat,N: nat,Z: int] :
% 0.35/0.66        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.66       => ( ( comm_s4660882817536571857er_int @ Z @ N )
% 0.35/0.66          = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ M ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_product
% 0.35/0.66  thf(fact_8602_pochhammer__product,axiom,
% 0.35/0.66      ! [M: nat,N: nat,Z: nat] :
% 0.35/0.66        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.66       => ( ( comm_s4663373288045622133er_nat @ Z @ N )
% 0.35/0.66          = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ M ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_product
% 0.35/0.66  thf(fact_8603_pochhammer__product,axiom,
% 0.35/0.66      ! [M: nat,N: nat,Z: complex] :
% 0.35/0.66        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.66       => ( ( comm_s2602460028002588243omplex @ Z @ N )
% 0.35/0.66          = ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ M ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_product
% 0.35/0.66  thf(fact_8604_floor__divide__lower,axiom,
% 0.35/0.66      ! [Q2: real,P6: real] :
% 0.35/0.66        ( ( ord_less_real @ zero_zero_real @ Q2 )
% 0.35/0.66       => ( ord_less_eq_real @ ( times_times_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P6 @ Q2 ) ) ) @ Q2 ) @ P6 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_divide_lower
% 0.35/0.66  thf(fact_8605_floor__divide__lower,axiom,
% 0.35/0.66      ! [Q2: rat,P6: rat] :
% 0.35/0.66        ( ( ord_less_rat @ zero_zero_rat @ Q2 )
% 0.35/0.66       => ( ord_less_eq_rat @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P6 @ Q2 ) ) ) @ Q2 ) @ P6 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_divide_lower
% 0.35/0.66  thf(fact_8606_pochhammer__absorb__comp,axiom,
% 0.35/0.66      ! [R: code_integer,K: nat] :
% 0.35/0.66        ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ R @ ( semiri4939895301339042750nteger @ K ) ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ R ) @ K ) )
% 0.35/0.66        = ( times_3573771949741848930nteger @ R @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ R ) @ one_one_Code_integer ) @ K ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_absorb_comp
% 0.35/0.66  thf(fact_8607_pochhammer__absorb__comp,axiom,
% 0.35/0.66      ! [R: rat,K: nat] :
% 0.35/0.66        ( ( times_times_rat @ ( minus_minus_rat @ R @ ( semiri681578069525770553at_rat @ K ) ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ R ) @ K ) )
% 0.35/0.66        = ( times_times_rat @ R @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ R ) @ one_one_rat ) @ K ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_absorb_comp
% 0.35/0.66  thf(fact_8608_pochhammer__absorb__comp,axiom,
% 0.35/0.66      ! [R: real,K: nat] :
% 0.35/0.66        ( ( times_times_real @ ( minus_minus_real @ R @ ( semiri5074537144036343181t_real @ K ) ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ R ) @ K ) )
% 0.35/0.66        = ( times_times_real @ R @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( uminus_uminus_real @ R ) @ one_one_real ) @ K ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_absorb_comp
% 0.35/0.66  thf(fact_8609_pochhammer__absorb__comp,axiom,
% 0.35/0.66      ! [R: int,K: nat] :
% 0.35/0.66        ( ( times_times_int @ ( minus_minus_int @ R @ ( semiri1314217659103216013at_int @ K ) ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ R ) @ K ) )
% 0.35/0.66        = ( times_times_int @ R @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( uminus_uminus_int @ R ) @ one_one_int ) @ K ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_absorb_comp
% 0.35/0.66  thf(fact_8610_pochhammer__absorb__comp,axiom,
% 0.35/0.66      ! [R: complex,K: nat] :
% 0.35/0.66        ( ( times_times_complex @ ( minus_minus_complex @ R @ ( semiri8010041392384452111omplex @ K ) ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ R ) @ K ) )
% 0.35/0.66        = ( times_times_complex @ R @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ R ) @ one_one_complex ) @ K ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_absorb_comp
% 0.35/0.66  thf(fact_8611_floor__divide__upper,axiom,
% 0.35/0.66      ! [Q2: real,P6: real] :
% 0.35/0.66        ( ( ord_less_real @ zero_zero_real @ Q2 )
% 0.35/0.66       => ( ord_less_real @ P6 @ ( times_times_real @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P6 @ Q2 ) ) ) @ one_one_real ) @ Q2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_divide_upper
% 0.35/0.66  thf(fact_8612_floor__divide__upper,axiom,
% 0.35/0.66      ! [Q2: rat,P6: rat] :
% 0.35/0.66        ( ( ord_less_rat @ zero_zero_rat @ Q2 )
% 0.35/0.66       => ( ord_less_rat @ P6 @ ( times_times_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P6 @ Q2 ) ) ) @ one_one_rat ) @ Q2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_divide_upper
% 0.35/0.66  thf(fact_8613_pochhammer__same,axiom,
% 0.35/0.66      ! [N: nat] :
% 0.35/0.66        ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ N )
% 0.35/0.66        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_same
% 0.35/0.66  thf(fact_8614_pochhammer__same,axiom,
% 0.35/0.66      ! [N: nat] :
% 0.35/0.66        ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ N )
% 0.35/0.66        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_same
% 0.35/0.66  thf(fact_8615_pochhammer__same,axiom,
% 0.35/0.66      ! [N: nat] :
% 0.35/0.66        ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ N )
% 0.35/0.66        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_same
% 0.35/0.66  thf(fact_8616_pochhammer__same,axiom,
% 0.35/0.66      ! [N: nat] :
% 0.35/0.66        ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ N )
% 0.35/0.66        = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( semiri5044797733671781792omplex @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_same
% 0.35/0.66  thf(fact_8617_pochhammer__same,axiom,
% 0.35/0.66      ! [N: nat] :
% 0.35/0.66        ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ N )
% 0.35/0.66        = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_same
% 0.35/0.66  thf(fact_8618_round__def,axiom,
% 0.35/0.66      ( archim8280529875227126926d_real
% 0.35/0.66      = ( ^ [X2: real] : ( archim6058952711729229775r_real @ ( plus_plus_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % round_def
% 0.35/0.66  thf(fact_8619_round__def,axiom,
% 0.35/0.66      ( archim7778729529865785530nd_rat
% 0.35/0.66      = ( ^ [X2: rat] : ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % round_def
% 0.35/0.66  thf(fact_8620_pochhammer__minus_H,axiom,
% 0.35/0.66      ! [B: code_integer,K: nat] :
% 0.35/0.66        ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K )
% 0.35/0.66        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_minus'
% 0.35/0.66  thf(fact_8621_pochhammer__minus_H,axiom,
% 0.35/0.66      ! [B: rat,K: nat] :
% 0.35/0.66        ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K )
% 0.35/0.66        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_minus'
% 0.35/0.66  thf(fact_8622_pochhammer__minus_H,axiom,
% 0.35/0.66      ! [B: real,K: nat] :
% 0.35/0.66        ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K )
% 0.35/0.66        = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_minus'
% 0.35/0.66  thf(fact_8623_pochhammer__minus_H,axiom,
% 0.35/0.66      ! [B: int,K: nat] :
% 0.35/0.66        ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K )
% 0.35/0.66        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_minus'
% 0.35/0.66  thf(fact_8624_pochhammer__minus_H,axiom,
% 0.35/0.66      ! [B: complex,K: nat] :
% 0.35/0.66        ( ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K )
% 0.35/0.66        = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_minus'
% 0.35/0.66  thf(fact_8625_pochhammer__minus,axiom,
% 0.35/0.66      ! [B: code_integer,K: nat] :
% 0.35/0.66        ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K )
% 0.35/0.66        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_minus
% 0.35/0.66  thf(fact_8626_pochhammer__minus,axiom,
% 0.35/0.66      ! [B: rat,K: nat] :
% 0.35/0.66        ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K )
% 0.35/0.66        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_minus
% 0.35/0.66  thf(fact_8627_pochhammer__minus,axiom,
% 0.35/0.66      ! [B: real,K: nat] :
% 0.35/0.66        ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K )
% 0.35/0.66        = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_minus
% 0.35/0.66  thf(fact_8628_pochhammer__minus,axiom,
% 0.35/0.66      ! [B: int,K: nat] :
% 0.35/0.66        ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K )
% 0.35/0.66        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_minus
% 0.35/0.66  thf(fact_8629_pochhammer__minus,axiom,
% 0.35/0.66      ! [B: complex,K: nat] :
% 0.35/0.66        ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K )
% 0.35/0.66        = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_minus
% 0.35/0.66  thf(fact_8630_floor__log__eq__powr__iff,axiom,
% 0.35/0.66      ! [X: real,B: real,K: int] :
% 0.35/0.66        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.66       => ( ( ord_less_real @ one_one_real @ B )
% 0.35/0.66         => ( ( ( archim6058952711729229775r_real @ ( log @ B @ X ) )
% 0.35/0.66              = K )
% 0.35/0.66            = ( ( ord_less_eq_real @ ( powr_real @ B @ ( ring_1_of_int_real @ K ) ) @ X )
% 0.35/0.66              & ( ord_less_real @ X @ ( powr_real @ B @ ( ring_1_of_int_real @ ( plus_plus_int @ K @ one_one_int ) ) ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_log_eq_powr_iff
% 0.35/0.66  thf(fact_8631_floor__log2__div2,axiom,
% 0.35/0.66      ! [N: nat] :
% 0.35/0.66        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.66       => ( ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 0.35/0.66          = ( plus_plus_int @ ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_int ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_log2_div2
% 0.35/0.66  thf(fact_8632_fact__double,axiom,
% 0.35/0.66      ! [N: nat] :
% 0.35/0.66        ( ( semiri5044797733671781792omplex @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.66        = ( times_times_complex @ ( times_times_complex @ ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( comm_s2602460028002588243omplex @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ N ) ) @ ( semiri5044797733671781792omplex @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_double
% 0.35/0.66  thf(fact_8633_fact__double,axiom,
% 0.35/0.66      ! [N: nat] :
% 0.35/0.66        ( ( semiri773545260158071498ct_rat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.66        = ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ N ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_double
% 0.35/0.66  thf(fact_8634_fact__double,axiom,
% 0.35/0.66      ! [N: nat] :
% 0.35/0.66        ( ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.66        = ( times_times_real @ ( times_times_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( comm_s7457072308508201937r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ N ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % fact_double
% 0.35/0.66  thf(fact_8635_floor__log__nat__eq__if,axiom,
% 0.35/0.66      ! [B: nat,N: nat,K: nat] :
% 0.35/0.66        ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 0.35/0.66       => ( ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 0.35/0.66         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.35/0.66           => ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 0.35/0.66              = ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % floor_log_nat_eq_if
% 0.35/0.66  thf(fact_8636_pochhammer__times__pochhammer__half,axiom,
% 0.35/0.66      ! [Z: rat,N: nat] :
% 0.35/0.66        ( ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 0.35/0.66        = ( groups73079841787564623at_rat
% 0.35/0.66          @ ^ [K3: nat] : ( plus_plus_rat @ Z @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ K3 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 0.35/0.66          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_times_pochhammer_half
% 0.35/0.66  thf(fact_8637_pochhammer__times__pochhammer__half,axiom,
% 0.35/0.66      ! [Z: real,N: nat] :
% 0.35/0.66        ( ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ ( suc @ N ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 0.35/0.66        = ( groups129246275422532515t_real
% 0.35/0.66          @ ^ [K3: nat] : ( plus_plus_real @ Z @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ K3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.66          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_times_pochhammer_half
% 0.35/0.66  thf(fact_8638_pochhammer__times__pochhammer__half,axiom,
% 0.35/0.66      ! [Z: complex,N: nat] :
% 0.35/0.66        ( ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ ( suc @ N ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 0.35/0.66        = ( groups6464643781859351333omplex
% 0.35/0.66          @ ^ [K3: nat] : ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ K3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 0.35/0.66          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_times_pochhammer_half
% 0.35/0.66  thf(fact_8639_pochhammer__code,axiom,
% 0.35/0.66      ( comm_s4028243227959126397er_rat
% 0.35/0.66      = ( ^ [A3: rat,N2: nat] :
% 0.35/0.66            ( if_rat @ ( N2 = zero_zero_nat ) @ one_one_rat
% 0.35/0.66            @ ( set_fo1949268297981939178at_rat
% 0.35/0.66              @ ^ [O: nat] : ( times_times_rat @ ( plus_plus_rat @ A3 @ ( semiri681578069525770553at_rat @ O ) ) )
% 0.35/0.66              @ zero_zero_nat
% 0.35/0.66              @ ( minus_minus_nat @ N2 @ one_one_nat )
% 0.35/0.66              @ one_one_rat ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_code
% 0.35/0.66  thf(fact_8640_pochhammer__code,axiom,
% 0.35/0.66      ( comm_s7457072308508201937r_real
% 0.35/0.66      = ( ^ [A3: real,N2: nat] :
% 0.35/0.66            ( if_real @ ( N2 = zero_zero_nat ) @ one_one_real
% 0.35/0.66            @ ( set_fo3111899725591712190t_real
% 0.35/0.66              @ ^ [O: nat] : ( times_times_real @ ( plus_plus_real @ A3 @ ( semiri5074537144036343181t_real @ O ) ) )
% 0.35/0.66              @ zero_zero_nat
% 0.35/0.66              @ ( minus_minus_nat @ N2 @ one_one_nat )
% 0.35/0.66              @ one_one_real ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_code
% 0.35/0.66  thf(fact_8641_pochhammer__code,axiom,
% 0.35/0.66      ( comm_s4660882817536571857er_int
% 0.35/0.66      = ( ^ [A3: int,N2: nat] :
% 0.35/0.66            ( if_int @ ( N2 = zero_zero_nat ) @ one_one_int
% 0.35/0.66            @ ( set_fo2581907887559384638at_int
% 0.35/0.66              @ ^ [O: nat] : ( times_times_int @ ( plus_plus_int @ A3 @ ( semiri1314217659103216013at_int @ O ) ) )
% 0.35/0.66              @ zero_zero_nat
% 0.35/0.66              @ ( minus_minus_nat @ N2 @ one_one_nat )
% 0.35/0.66              @ one_one_int ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_code
% 0.35/0.66  thf(fact_8642_pochhammer__code,axiom,
% 0.35/0.66      ( comm_s2602460028002588243omplex
% 0.35/0.66      = ( ^ [A3: complex,N2: nat] :
% 0.35/0.66            ( if_complex @ ( N2 = zero_zero_nat ) @ one_one_complex
% 0.35/0.66            @ ( set_fo1517530859248394432omplex
% 0.35/0.66              @ ^ [O: nat] : ( times_times_complex @ ( plus_plus_complex @ A3 @ ( semiri8010041392384452111omplex @ O ) ) )
% 0.35/0.66              @ zero_zero_nat
% 0.35/0.66              @ ( minus_minus_nat @ N2 @ one_one_nat )
% 0.35/0.66              @ one_one_complex ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_code
% 0.35/0.66  thf(fact_8643_pochhammer__code,axiom,
% 0.35/0.66      ( comm_s4663373288045622133er_nat
% 0.35/0.66      = ( ^ [A3: nat,N2: nat] :
% 0.35/0.66            ( if_nat @ ( N2 = zero_zero_nat ) @ one_one_nat
% 0.35/0.66            @ ( set_fo2584398358068434914at_nat
% 0.35/0.66              @ ^ [O: nat] : ( times_times_nat @ ( plus_plus_nat @ A3 @ ( semiri1316708129612266289at_nat @ O ) ) )
% 0.35/0.66              @ zero_zero_nat
% 0.35/0.66              @ ( minus_minus_nat @ N2 @ one_one_nat )
% 0.35/0.66              @ one_one_nat ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % pochhammer_code
% 0.35/0.66  thf(fact_8644_round__altdef,axiom,
% 0.35/0.66      ( archim8280529875227126926d_real
% 0.35/0.66      = ( ^ [X2: real] : ( if_int @ ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( archim2898591450579166408c_real @ X2 ) ) @ ( archim7802044766580827645g_real @ X2 ) @ ( archim6058952711729229775r_real @ X2 ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % round_altdef
% 0.35/0.66  thf(fact_8645_round__altdef,axiom,
% 0.35/0.66      ( archim7778729529865785530nd_rat
% 0.35/0.66      = ( ^ [X2: rat] : ( if_int @ ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( archimedean_frac_rat @ X2 ) ) @ ( archim2889992004027027881ng_rat @ X2 ) @ ( archim3151403230148437115or_rat @ X2 ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % round_altdef
% 0.35/0.66  thf(fact_8646_of__nat__code,axiom,
% 0.35/0.66      ( semiri681578069525770553at_rat
% 0.35/0.66      = ( ^ [N2: nat] :
% 0.35/0.66            ( semiri7787848453975740701ux_rat
% 0.35/0.66            @ ^ [I3: rat] : ( plus_plus_rat @ I3 @ one_one_rat )
% 0.35/0.66            @ N2
% 0.35/0.66            @ zero_zero_rat ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % of_nat_code
% 0.35/0.66  thf(fact_8647_of__nat__code,axiom,
% 0.35/0.66      ( semiri5074537144036343181t_real
% 0.35/0.66      = ( ^ [N2: nat] :
% 0.35/0.66            ( semiri7260567687927622513x_real
% 0.35/0.66            @ ^ [I3: real] : ( plus_plus_real @ I3 @ one_one_real )
% 0.35/0.66            @ N2
% 0.35/0.66            @ zero_zero_real ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % of_nat_code
% 0.35/0.66  thf(fact_8648_of__nat__code,axiom,
% 0.35/0.66      ( semiri1314217659103216013at_int
% 0.35/0.66      = ( ^ [N2: nat] :
% 0.35/0.66            ( semiri8420488043553186161ux_int
% 0.35/0.66            @ ^ [I3: int] : ( plus_plus_int @ I3 @ one_one_int )
% 0.35/0.66            @ N2
% 0.35/0.66            @ zero_zero_int ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % of_nat_code
% 0.35/0.66  thf(fact_8649_of__nat__code,axiom,
% 0.35/0.66      ( semiri1316708129612266289at_nat
% 0.35/0.66      = ( ^ [N2: nat] :
% 0.35/0.66            ( semiri8422978514062236437ux_nat
% 0.35/0.66            @ ^ [I3: nat] : ( plus_plus_nat @ I3 @ one_one_nat )
% 0.35/0.66            @ N2
% 0.35/0.66            @ zero_zero_nat ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % of_nat_code
% 0.35/0.66  thf(fact_8650_of__nat__code,axiom,
% 0.35/0.66      ( semiri8010041392384452111omplex
% 0.35/0.66      = ( ^ [N2: nat] :
% 0.35/0.66            ( semiri2816024913162550771omplex
% 0.35/0.66            @ ^ [I3: complex] : ( plus_plus_complex @ I3 @ one_one_complex )
% 0.35/0.66            @ N2
% 0.35/0.66            @ zero_zero_complex ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % of_nat_code
% 0.35/0.66  thf(fact_8651_prod_Oneutral__const,axiom,
% 0.35/0.66      ! [A2: set_nat] :
% 0.35/0.66        ( ( groups708209901874060359at_nat
% 0.35/0.66          @ ^ [Uu3: nat] : one_one_nat
% 0.35/0.66          @ A2 )
% 0.35/0.66        = one_one_nat ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.neutral_const
% 0.35/0.66  thf(fact_8652_prod_Oneutral__const,axiom,
% 0.35/0.66      ! [A2: set_nat] :
% 0.35/0.66        ( ( groups705719431365010083at_int
% 0.35/0.66          @ ^ [Uu3: nat] : one_one_int
% 0.35/0.66          @ A2 )
% 0.35/0.66        = one_one_int ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.neutral_const
% 0.35/0.66  thf(fact_8653_prod_Oneutral__const,axiom,
% 0.35/0.66      ! [A2: set_int] :
% 0.35/0.66        ( ( groups1705073143266064639nt_int
% 0.35/0.66          @ ^ [Uu3: int] : one_one_int
% 0.35/0.66          @ A2 )
% 0.35/0.66        = one_one_int ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.neutral_const
% 0.35/0.66  thf(fact_8654_prod_Oempty,axiom,
% 0.35/0.66      ! [G: nat > complex] :
% 0.35/0.66        ( ( groups6464643781859351333omplex @ G @ bot_bot_set_nat )
% 0.35/0.66        = one_one_complex ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.empty
% 0.35/0.66  thf(fact_8655_prod_Oempty,axiom,
% 0.35/0.66      ! [G: nat > real] :
% 0.35/0.66        ( ( groups129246275422532515t_real @ G @ bot_bot_set_nat )
% 0.35/0.66        = one_one_real ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.empty
% 0.35/0.66  thf(fact_8656_prod_Oempty,axiom,
% 0.35/0.66      ! [G: nat > rat] :
% 0.35/0.66        ( ( groups73079841787564623at_rat @ G @ bot_bot_set_nat )
% 0.35/0.66        = one_one_rat ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.empty
% 0.35/0.66  thf(fact_8657_prod_Oempty,axiom,
% 0.35/0.66      ! [G: int > complex] :
% 0.35/0.66        ( ( groups7440179247065528705omplex @ G @ bot_bot_set_int )
% 0.35/0.66        = one_one_complex ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.empty
% 0.35/0.66  thf(fact_8658_prod_Oempty,axiom,
% 0.35/0.66      ! [G: int > real] :
% 0.35/0.66        ( ( groups2316167850115554303t_real @ G @ bot_bot_set_int )
% 0.35/0.66        = one_one_real ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.empty
% 0.35/0.66  thf(fact_8659_prod_Oempty,axiom,
% 0.35/0.66      ! [G: int > rat] :
% 0.35/0.66        ( ( groups1072433553688619179nt_rat @ G @ bot_bot_set_int )
% 0.35/0.66        = one_one_rat ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.empty
% 0.35/0.66  thf(fact_8660_prod_Oempty,axiom,
% 0.35/0.66      ! [G: int > nat] :
% 0.35/0.66        ( ( groups1707563613775114915nt_nat @ G @ bot_bot_set_int )
% 0.35/0.66        = one_one_nat ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.empty
% 0.35/0.66  thf(fact_8661_prod_Oempty,axiom,
% 0.35/0.66      ! [G: real > complex] :
% 0.35/0.66        ( ( groups713298508707869441omplex @ G @ bot_bot_set_real )
% 0.35/0.66        = one_one_complex ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.empty
% 0.35/0.66  thf(fact_8662_prod_Oempty,axiom,
% 0.35/0.66      ! [G: real > real] :
% 0.35/0.66        ( ( groups1681761925125756287l_real @ G @ bot_bot_set_real )
% 0.35/0.66        = one_one_real ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.empty
% 0.35/0.66  thf(fact_8663_prod_Oempty,axiom,
% 0.35/0.66      ! [G: real > rat] :
% 0.35/0.66        ( ( groups4061424788464935467al_rat @ G @ bot_bot_set_real )
% 0.35/0.66        = one_one_rat ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.empty
% 0.35/0.66  thf(fact_8664_prod_Oinfinite,axiom,
% 0.35/0.66      ! [A2: set_nat,G: nat > complex] :
% 0.35/0.66        ( ~ ( finite_finite_nat @ A2 )
% 0.35/0.66       => ( ( groups6464643781859351333omplex @ G @ A2 )
% 0.35/0.66          = one_one_complex ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.infinite
% 0.35/0.66  thf(fact_8665_prod_Oinfinite,axiom,
% 0.35/0.66      ! [A2: set_complex,G: complex > complex] :
% 0.35/0.66        ( ~ ( finite3207457112153483333omplex @ A2 )
% 0.35/0.66       => ( ( groups3708469109370488835omplex @ G @ A2 )
% 0.35/0.66          = one_one_complex ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.infinite
% 0.35/0.66  thf(fact_8666_prod_Oinfinite,axiom,
% 0.35/0.66      ! [A2: set_nat,G: nat > real] :
% 0.35/0.66        ( ~ ( finite_finite_nat @ A2 )
% 0.35/0.66       => ( ( groups129246275422532515t_real @ G @ A2 )
% 0.35/0.66          = one_one_real ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.infinite
% 0.35/0.66  thf(fact_8667_prod_Oinfinite,axiom,
% 0.35/0.66      ! [A2: set_complex,G: complex > real] :
% 0.35/0.66        ( ~ ( finite3207457112153483333omplex @ A2 )
% 0.35/0.66       => ( ( groups766887009212190081x_real @ G @ A2 )
% 0.35/0.66          = one_one_real ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.infinite
% 0.35/0.66  thf(fact_8668_prod_Oinfinite,axiom,
% 0.35/0.66      ! [A2: set_nat,G: nat > rat] :
% 0.35/0.66        ( ~ ( finite_finite_nat @ A2 )
% 0.35/0.66       => ( ( groups73079841787564623at_rat @ G @ A2 )
% 0.35/0.66          = one_one_rat ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.infinite
% 0.35/0.66  thf(fact_8669_prod_Oinfinite,axiom,
% 0.35/0.66      ! [A2: set_complex,G: complex > rat] :
% 0.35/0.66        ( ~ ( finite3207457112153483333omplex @ A2 )
% 0.35/0.66       => ( ( groups225925009352817453ex_rat @ G @ A2 )
% 0.35/0.66          = one_one_rat ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.infinite
% 0.35/0.66  thf(fact_8670_prod_Oinfinite,axiom,
% 0.35/0.66      ! [A2: set_complex,G: complex > nat] :
% 0.35/0.66        ( ~ ( finite3207457112153483333omplex @ A2 )
% 0.35/0.66       => ( ( groups861055069439313189ex_nat @ G @ A2 )
% 0.35/0.66          = one_one_nat ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.infinite
% 0.35/0.66  thf(fact_8671_prod_Oinfinite,axiom,
% 0.35/0.66      ! [A2: set_complex,G: complex > int] :
% 0.35/0.66        ( ~ ( finite3207457112153483333omplex @ A2 )
% 0.35/0.66       => ( ( groups858564598930262913ex_int @ G @ A2 )
% 0.35/0.66          = one_one_int ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.infinite
% 0.35/0.66  thf(fact_8672_prod_Oinfinite,axiom,
% 0.35/0.66      ! [A2: set_nat,G: nat > nat] :
% 0.35/0.66        ( ~ ( finite_finite_nat @ A2 )
% 0.35/0.66       => ( ( groups708209901874060359at_nat @ G @ A2 )
% 0.35/0.66          = one_one_nat ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.infinite
% 0.35/0.66  thf(fact_8673_prod_Oinfinite,axiom,
% 0.35/0.66      ! [A2: set_nat,G: nat > int] :
% 0.35/0.66        ( ~ ( finite_finite_nat @ A2 )
% 0.35/0.66       => ( ( groups705719431365010083at_int @ G @ A2 )
% 0.35/0.66          = one_one_int ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.infinite
% 0.35/0.66  thf(fact_8674_prod_Odelta_H,axiom,
% 0.35/0.66      ! [S2: set_real,A: real,B: real > complex] :
% 0.35/0.66        ( ( finite_finite_real @ S2 )
% 0.35/0.66       => ( ( ( member_real @ A @ S2 )
% 0.35/0.66           => ( ( groups713298508707869441omplex
% 0.35/0.66                @ ^ [K3: real] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = ( B @ A ) ) )
% 0.35/0.66          & ( ~ ( member_real @ A @ S2 )
% 0.35/0.66           => ( ( groups713298508707869441omplex
% 0.35/0.66                @ ^ [K3: real] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = one_one_complex ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.delta'
% 0.35/0.66  thf(fact_8675_prod_Odelta_H,axiom,
% 0.35/0.66      ! [S2: set_int,A: int,B: int > complex] :
% 0.35/0.66        ( ( finite_finite_int @ S2 )
% 0.35/0.66       => ( ( ( member_int @ A @ S2 )
% 0.35/0.66           => ( ( groups7440179247065528705omplex
% 0.35/0.66                @ ^ [K3: int] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = ( B @ A ) ) )
% 0.35/0.66          & ( ~ ( member_int @ A @ S2 )
% 0.35/0.66           => ( ( groups7440179247065528705omplex
% 0.35/0.66                @ ^ [K3: int] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = one_one_complex ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.delta'
% 0.35/0.66  thf(fact_8676_prod_Odelta_H,axiom,
% 0.35/0.66      ! [S2: set_nat,A: nat,B: nat > complex] :
% 0.35/0.66        ( ( finite_finite_nat @ S2 )
% 0.35/0.66       => ( ( ( member_nat @ A @ S2 )
% 0.35/0.66           => ( ( groups6464643781859351333omplex
% 0.35/0.66                @ ^ [K3: nat] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = ( B @ A ) ) )
% 0.35/0.66          & ( ~ ( member_nat @ A @ S2 )
% 0.35/0.66           => ( ( groups6464643781859351333omplex
% 0.35/0.66                @ ^ [K3: nat] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = one_one_complex ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.delta'
% 0.35/0.66  thf(fact_8677_prod_Odelta_H,axiom,
% 0.35/0.66      ! [S2: set_complex,A: complex,B: complex > complex] :
% 0.35/0.66        ( ( finite3207457112153483333omplex @ S2 )
% 0.35/0.66       => ( ( ( member_complex @ A @ S2 )
% 0.35/0.66           => ( ( groups3708469109370488835omplex
% 0.35/0.66                @ ^ [K3: complex] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = ( B @ A ) ) )
% 0.35/0.66          & ( ~ ( member_complex @ A @ S2 )
% 0.35/0.66           => ( ( groups3708469109370488835omplex
% 0.35/0.66                @ ^ [K3: complex] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = one_one_complex ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.delta'
% 0.35/0.66  thf(fact_8678_prod_Odelta_H,axiom,
% 0.35/0.66      ! [S2: set_real,A: real,B: real > real] :
% 0.35/0.66        ( ( finite_finite_real @ S2 )
% 0.35/0.66       => ( ( ( member_real @ A @ S2 )
% 0.35/0.66           => ( ( groups1681761925125756287l_real
% 0.35/0.66                @ ^ [K3: real] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = ( B @ A ) ) )
% 0.35/0.66          & ( ~ ( member_real @ A @ S2 )
% 0.35/0.66           => ( ( groups1681761925125756287l_real
% 0.35/0.66                @ ^ [K3: real] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = one_one_real ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.delta'
% 0.35/0.66  thf(fact_8679_prod_Odelta_H,axiom,
% 0.35/0.66      ! [S2: set_int,A: int,B: int > real] :
% 0.35/0.66        ( ( finite_finite_int @ S2 )
% 0.35/0.66       => ( ( ( member_int @ A @ S2 )
% 0.35/0.66           => ( ( groups2316167850115554303t_real
% 0.35/0.66                @ ^ [K3: int] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = ( B @ A ) ) )
% 0.35/0.66          & ( ~ ( member_int @ A @ S2 )
% 0.35/0.66           => ( ( groups2316167850115554303t_real
% 0.35/0.66                @ ^ [K3: int] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = one_one_real ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.delta'
% 0.35/0.66  thf(fact_8680_prod_Odelta_H,axiom,
% 0.35/0.66      ! [S2: set_nat,A: nat,B: nat > real] :
% 0.35/0.66        ( ( finite_finite_nat @ S2 )
% 0.35/0.66       => ( ( ( member_nat @ A @ S2 )
% 0.35/0.66           => ( ( groups129246275422532515t_real
% 0.35/0.66                @ ^ [K3: nat] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = ( B @ A ) ) )
% 0.35/0.66          & ( ~ ( member_nat @ A @ S2 )
% 0.35/0.66           => ( ( groups129246275422532515t_real
% 0.35/0.66                @ ^ [K3: nat] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = one_one_real ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.delta'
% 0.35/0.66  thf(fact_8681_prod_Odelta_H,axiom,
% 0.35/0.66      ! [S2: set_complex,A: complex,B: complex > real] :
% 0.35/0.66        ( ( finite3207457112153483333omplex @ S2 )
% 0.35/0.66       => ( ( ( member_complex @ A @ S2 )
% 0.35/0.66           => ( ( groups766887009212190081x_real
% 0.35/0.66                @ ^ [K3: complex] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = ( B @ A ) ) )
% 0.35/0.66          & ( ~ ( member_complex @ A @ S2 )
% 0.35/0.66           => ( ( groups766887009212190081x_real
% 0.35/0.66                @ ^ [K3: complex] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = one_one_real ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.delta'
% 0.35/0.66  thf(fact_8682_prod_Odelta_H,axiom,
% 0.35/0.66      ! [S2: set_real,A: real,B: real > rat] :
% 0.35/0.66        ( ( finite_finite_real @ S2 )
% 0.35/0.66       => ( ( ( member_real @ A @ S2 )
% 0.35/0.66           => ( ( groups4061424788464935467al_rat
% 0.35/0.66                @ ^ [K3: real] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ one_one_rat )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = ( B @ A ) ) )
% 0.35/0.66          & ( ~ ( member_real @ A @ S2 )
% 0.35/0.66           => ( ( groups4061424788464935467al_rat
% 0.35/0.66                @ ^ [K3: real] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ one_one_rat )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = one_one_rat ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.delta'
% 0.35/0.66  thf(fact_8683_prod_Odelta_H,axiom,
% 0.35/0.66      ! [S2: set_int,A: int,B: int > rat] :
% 0.35/0.66        ( ( finite_finite_int @ S2 )
% 0.35/0.66       => ( ( ( member_int @ A @ S2 )
% 0.35/0.66           => ( ( groups1072433553688619179nt_rat
% 0.35/0.66                @ ^ [K3: int] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ one_one_rat )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = ( B @ A ) ) )
% 0.35/0.66          & ( ~ ( member_int @ A @ S2 )
% 0.35/0.66           => ( ( groups1072433553688619179nt_rat
% 0.35/0.66                @ ^ [K3: int] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ one_one_rat )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = one_one_rat ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.delta'
% 0.35/0.66  thf(fact_8684_prod_Odelta,axiom,
% 0.35/0.66      ! [S2: set_real,A: real,B: real > complex] :
% 0.35/0.66        ( ( finite_finite_real @ S2 )
% 0.35/0.66       => ( ( ( member_real @ A @ S2 )
% 0.35/0.66           => ( ( groups713298508707869441omplex
% 0.35/0.66                @ ^ [K3: real] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = ( B @ A ) ) )
% 0.35/0.66          & ( ~ ( member_real @ A @ S2 )
% 0.35/0.66           => ( ( groups713298508707869441omplex
% 0.35/0.66                @ ^ [K3: real] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = one_one_complex ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.delta
% 0.35/0.66  thf(fact_8685_prod_Odelta,axiom,
% 0.35/0.66      ! [S2: set_int,A: int,B: int > complex] :
% 0.35/0.66        ( ( finite_finite_int @ S2 )
% 0.35/0.66       => ( ( ( member_int @ A @ S2 )
% 0.35/0.66           => ( ( groups7440179247065528705omplex
% 0.35/0.66                @ ^ [K3: int] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = ( B @ A ) ) )
% 0.35/0.66          & ( ~ ( member_int @ A @ S2 )
% 0.35/0.66           => ( ( groups7440179247065528705omplex
% 0.35/0.66                @ ^ [K3: int] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = one_one_complex ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.delta
% 0.35/0.66  thf(fact_8686_prod_Odelta,axiom,
% 0.35/0.66      ! [S2: set_nat,A: nat,B: nat > complex] :
% 0.35/0.66        ( ( finite_finite_nat @ S2 )
% 0.35/0.66       => ( ( ( member_nat @ A @ S2 )
% 0.35/0.66           => ( ( groups6464643781859351333omplex
% 0.35/0.66                @ ^ [K3: nat] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = ( B @ A ) ) )
% 0.35/0.66          & ( ~ ( member_nat @ A @ S2 )
% 0.35/0.66           => ( ( groups6464643781859351333omplex
% 0.35/0.66                @ ^ [K3: nat] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = one_one_complex ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.delta
% 0.35/0.66  thf(fact_8687_prod_Odelta,axiom,
% 0.35/0.66      ! [S2: set_complex,A: complex,B: complex > complex] :
% 0.35/0.66        ( ( finite3207457112153483333omplex @ S2 )
% 0.35/0.66       => ( ( ( member_complex @ A @ S2 )
% 0.35/0.66           => ( ( groups3708469109370488835omplex
% 0.35/0.66                @ ^ [K3: complex] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = ( B @ A ) ) )
% 0.35/0.66          & ( ~ ( member_complex @ A @ S2 )
% 0.35/0.66           => ( ( groups3708469109370488835omplex
% 0.35/0.66                @ ^ [K3: complex] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = one_one_complex ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.delta
% 0.35/0.66  thf(fact_8688_prod_Odelta,axiom,
% 0.35/0.66      ! [S2: set_real,A: real,B: real > real] :
% 0.35/0.66        ( ( finite_finite_real @ S2 )
% 0.35/0.66       => ( ( ( member_real @ A @ S2 )
% 0.35/0.66           => ( ( groups1681761925125756287l_real
% 0.35/0.66                @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = ( B @ A ) ) )
% 0.35/0.66          & ( ~ ( member_real @ A @ S2 )
% 0.35/0.66           => ( ( groups1681761925125756287l_real
% 0.35/0.66                @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = one_one_real ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.delta
% 0.35/0.66  thf(fact_8689_prod_Odelta,axiom,
% 0.35/0.66      ! [S2: set_int,A: int,B: int > real] :
% 0.35/0.66        ( ( finite_finite_int @ S2 )
% 0.35/0.66       => ( ( ( member_int @ A @ S2 )
% 0.35/0.66           => ( ( groups2316167850115554303t_real
% 0.35/0.66                @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = ( B @ A ) ) )
% 0.35/0.66          & ( ~ ( member_int @ A @ S2 )
% 0.35/0.66           => ( ( groups2316167850115554303t_real
% 0.35/0.66                @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = one_one_real ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.delta
% 0.35/0.66  thf(fact_8690_prod_Odelta,axiom,
% 0.35/0.66      ! [S2: set_nat,A: nat,B: nat > real] :
% 0.35/0.66        ( ( finite_finite_nat @ S2 )
% 0.35/0.66       => ( ( ( member_nat @ A @ S2 )
% 0.35/0.66           => ( ( groups129246275422532515t_real
% 0.35/0.66                @ ^ [K3: nat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = ( B @ A ) ) )
% 0.35/0.66          & ( ~ ( member_nat @ A @ S2 )
% 0.35/0.66           => ( ( groups129246275422532515t_real
% 0.35/0.66                @ ^ [K3: nat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = one_one_real ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.delta
% 0.35/0.66  thf(fact_8691_prod_Odelta,axiom,
% 0.35/0.66      ! [S2: set_complex,A: complex,B: complex > real] :
% 0.35/0.66        ( ( finite3207457112153483333omplex @ S2 )
% 0.35/0.66       => ( ( ( member_complex @ A @ S2 )
% 0.35/0.66           => ( ( groups766887009212190081x_real
% 0.35/0.66                @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = ( B @ A ) ) )
% 0.35/0.66          & ( ~ ( member_complex @ A @ S2 )
% 0.35/0.66           => ( ( groups766887009212190081x_real
% 0.35/0.66                @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = one_one_real ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.delta
% 0.35/0.66  thf(fact_8692_prod_Odelta,axiom,
% 0.35/0.66      ! [S2: set_real,A: real,B: real > rat] :
% 0.35/0.66        ( ( finite_finite_real @ S2 )
% 0.35/0.66       => ( ( ( member_real @ A @ S2 )
% 0.35/0.66           => ( ( groups4061424788464935467al_rat
% 0.35/0.66                @ ^ [K3: real] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ one_one_rat )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = ( B @ A ) ) )
% 0.35/0.66          & ( ~ ( member_real @ A @ S2 )
% 0.35/0.66           => ( ( groups4061424788464935467al_rat
% 0.35/0.66                @ ^ [K3: real] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ one_one_rat )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = one_one_rat ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.delta
% 0.35/0.66  thf(fact_8693_prod_Odelta,axiom,
% 0.35/0.66      ! [S2: set_int,A: int,B: int > rat] :
% 0.35/0.66        ( ( finite_finite_int @ S2 )
% 0.35/0.66       => ( ( ( member_int @ A @ S2 )
% 0.35/0.66           => ( ( groups1072433553688619179nt_rat
% 0.35/0.66                @ ^ [K3: int] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ one_one_rat )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = ( B @ A ) ) )
% 0.35/0.66          & ( ~ ( member_int @ A @ S2 )
% 0.35/0.66           => ( ( groups1072433553688619179nt_rat
% 0.35/0.66                @ ^ [K3: int] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ one_one_rat )
% 0.35/0.66                @ S2 )
% 0.35/0.66              = one_one_rat ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.delta
% 0.35/0.66  thf(fact_8694_prod_Oinsert,axiom,
% 0.35/0.66      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > complex] :
% 0.35/0.66        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.35/0.66       => ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 0.35/0.66         => ( ( groups127312072573709053omplex @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 0.35/0.66            = ( times_times_complex @ ( G @ X ) @ ( groups127312072573709053omplex @ G @ A2 ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.insert
% 0.35/0.66  thf(fact_8695_prod_Oinsert,axiom,
% 0.35/0.66      ! [A2: set_real,X: real,G: real > complex] :
% 0.35/0.66        ( ( finite_finite_real @ A2 )
% 0.35/0.66       => ( ~ ( member_real @ X @ A2 )
% 0.35/0.66         => ( ( groups713298508707869441omplex @ G @ ( insert_real @ X @ A2 ) )
% 0.35/0.66            = ( times_times_complex @ ( G @ X ) @ ( groups713298508707869441omplex @ G @ A2 ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.insert
% 0.35/0.66  thf(fact_8696_prod_Oinsert,axiom,
% 0.35/0.66      ! [A2: set_int,X: int,G: int > complex] :
% 0.35/0.66        ( ( finite_finite_int @ A2 )
% 0.35/0.66       => ( ~ ( member_int @ X @ A2 )
% 0.35/0.66         => ( ( groups7440179247065528705omplex @ G @ ( insert_int @ X @ A2 ) )
% 0.35/0.66            = ( times_times_complex @ ( G @ X ) @ ( groups7440179247065528705omplex @ G @ A2 ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.insert
% 0.35/0.66  thf(fact_8697_prod_Oinsert,axiom,
% 0.35/0.66      ! [A2: set_nat,X: nat,G: nat > complex] :
% 0.35/0.66        ( ( finite_finite_nat @ A2 )
% 0.35/0.66       => ( ~ ( member_nat @ X @ A2 )
% 0.35/0.66         => ( ( groups6464643781859351333omplex @ G @ ( insert_nat @ X @ A2 ) )
% 0.35/0.66            = ( times_times_complex @ ( G @ X ) @ ( groups6464643781859351333omplex @ G @ A2 ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.insert
% 0.35/0.66  thf(fact_8698_prod_Oinsert,axiom,
% 0.35/0.66      ! [A2: set_complex,X: complex,G: complex > complex] :
% 0.35/0.66        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.66       => ( ~ ( member_complex @ X @ A2 )
% 0.35/0.66         => ( ( groups3708469109370488835omplex @ G @ ( insert_complex @ X @ A2 ) )
% 0.35/0.66            = ( times_times_complex @ ( G @ X ) @ ( groups3708469109370488835omplex @ G @ A2 ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.insert
% 0.35/0.66  thf(fact_8699_prod_Oinsert,axiom,
% 0.35/0.66      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > real] :
% 0.35/0.66        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.35/0.66       => ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 0.35/0.66         => ( ( groups2703838992350267259T_real @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 0.35/0.66            = ( times_times_real @ ( G @ X ) @ ( groups2703838992350267259T_real @ G @ A2 ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.insert
% 0.35/0.66  thf(fact_8700_prod_Oinsert,axiom,
% 0.35/0.66      ! [A2: set_real,X: real,G: real > real] :
% 0.35/0.66        ( ( finite_finite_real @ A2 )
% 0.35/0.66       => ( ~ ( member_real @ X @ A2 )
% 0.35/0.66         => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X @ A2 ) )
% 0.35/0.66            = ( times_times_real @ ( G @ X ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.insert
% 0.35/0.66  thf(fact_8701_prod_Oinsert,axiom,
% 0.35/0.66      ! [A2: set_int,X: int,G: int > real] :
% 0.35/0.66        ( ( finite_finite_int @ A2 )
% 0.35/0.66       => ( ~ ( member_int @ X @ A2 )
% 0.35/0.66         => ( ( groups2316167850115554303t_real @ G @ ( insert_int @ X @ A2 ) )
% 0.35/0.66            = ( times_times_real @ ( G @ X ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.insert
% 0.35/0.66  thf(fact_8702_prod_Oinsert,axiom,
% 0.35/0.66      ! [A2: set_nat,X: nat,G: nat > real] :
% 0.35/0.66        ( ( finite_finite_nat @ A2 )
% 0.35/0.66       => ( ~ ( member_nat @ X @ A2 )
% 0.35/0.66         => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X @ A2 ) )
% 0.35/0.66            = ( times_times_real @ ( G @ X ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.insert
% 0.35/0.66  thf(fact_8703_prod_Oinsert,axiom,
% 0.35/0.66      ! [A2: set_complex,X: complex,G: complex > real] :
% 0.35/0.66        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.66       => ( ~ ( member_complex @ X @ A2 )
% 0.35/0.66         => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X @ A2 ) )
% 0.35/0.66            = ( times_times_real @ ( G @ X ) @ ( groups766887009212190081x_real @ G @ A2 ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.insert
% 0.35/0.66  thf(fact_8704_prod_OlessThan__Suc,axiom,
% 0.35/0.66      ! [G: nat > complex,N: nat] :
% 0.35/0.66        ( ( groups6464643781859351333omplex @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.35/0.66        = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.lessThan_Suc
% 0.35/0.66  thf(fact_8705_prod_OlessThan__Suc,axiom,
% 0.35/0.66      ! [G: nat > real,N: nat] :
% 0.35/0.66        ( ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.35/0.66        = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.lessThan_Suc
% 0.35/0.66  thf(fact_8706_prod_OlessThan__Suc,axiom,
% 0.35/0.66      ! [G: nat > nat,N: nat] :
% 0.35/0.66        ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.35/0.66        = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.lessThan_Suc
% 0.35/0.66  thf(fact_8707_prod_OlessThan__Suc,axiom,
% 0.35/0.66      ! [G: nat > int,N: nat] :
% 0.35/0.66        ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.35/0.66        = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.lessThan_Suc
% 0.35/0.66  thf(fact_8708_prod_Ocl__ivl__Suc,axiom,
% 0.35/0.66      ! [N: nat,M: nat,G: nat > rat] :
% 0.35/0.66        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.35/0.66         => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.35/0.66            = one_one_rat ) )
% 0.35/0.66        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 0.35/0.66         => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.35/0.66            = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.cl_ivl_Suc
% 0.35/0.66  thf(fact_8709_prod_Ocl__ivl__Suc,axiom,
% 0.35/0.66      ! [N: nat,M: nat,G: nat > complex] :
% 0.35/0.66        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.35/0.66         => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.35/0.66            = one_one_complex ) )
% 0.35/0.66        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 0.35/0.66         => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.35/0.66            = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.cl_ivl_Suc
% 0.35/0.66  thf(fact_8710_prod_Ocl__ivl__Suc,axiom,
% 0.35/0.66      ! [N: nat,M: nat,G: nat > real] :
% 0.35/0.66        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.35/0.66         => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.35/0.66            = one_one_real ) )
% 0.35/0.66        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 0.35/0.66         => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.35/0.66            = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.cl_ivl_Suc
% 0.35/0.66  thf(fact_8711_prod_Ocl__ivl__Suc,axiom,
% 0.35/0.66      ! [N: nat,M: nat,G: nat > nat] :
% 0.35/0.66        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.35/0.66         => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.35/0.66            = one_one_nat ) )
% 0.35/0.66        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 0.35/0.66         => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.35/0.66            = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.cl_ivl_Suc
% 0.35/0.66  thf(fact_8712_prod_Ocl__ivl__Suc,axiom,
% 0.35/0.66      ! [N: nat,M: nat,G: nat > int] :
% 0.35/0.66        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.35/0.66         => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.35/0.66            = one_one_int ) )
% 0.35/0.66        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 0.35/0.66         => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.35/0.66            = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.cl_ivl_Suc
% 0.35/0.66  thf(fact_8713_prod_Oneutral,axiom,
% 0.35/0.66      ! [A2: set_nat,G: nat > nat] :
% 0.35/0.66        ( ! [X3: nat] :
% 0.35/0.66            ( ( member_nat @ X3 @ A2 )
% 0.35/0.66           => ( ( G @ X3 )
% 0.35/0.66              = one_one_nat ) )
% 0.35/0.66       => ( ( groups708209901874060359at_nat @ G @ A2 )
% 0.35/0.66          = one_one_nat ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.neutral
% 0.35/0.66  thf(fact_8714_prod_Oneutral,axiom,
% 0.35/0.66      ! [A2: set_nat,G: nat > int] :
% 0.35/0.66        ( ! [X3: nat] :
% 0.35/0.66            ( ( member_nat @ X3 @ A2 )
% 0.35/0.66           => ( ( G @ X3 )
% 0.35/0.66              = one_one_int ) )
% 0.35/0.66       => ( ( groups705719431365010083at_int @ G @ A2 )
% 0.35/0.66          = one_one_int ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.neutral
% 0.35/0.66  thf(fact_8715_prod_Oneutral,axiom,
% 0.35/0.66      ! [A2: set_int,G: int > int] :
% 0.35/0.66        ( ! [X3: int] :
% 0.35/0.66            ( ( member_int @ X3 @ A2 )
% 0.35/0.66           => ( ( G @ X3 )
% 0.35/0.66              = one_one_int ) )
% 0.35/0.66       => ( ( groups1705073143266064639nt_int @ G @ A2 )
% 0.35/0.66          = one_one_int ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.neutral
% 0.35/0.66  thf(fact_8716_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.35/0.66      ! [G: complex > complex,A2: set_complex] :
% 0.35/0.66        ( ( ( groups3708469109370488835omplex @ G @ A2 )
% 0.35/0.66         != one_one_complex )
% 0.35/0.66       => ~ ! [A4: complex] :
% 0.35/0.66              ( ( member_complex @ A4 @ A2 )
% 0.35/0.66             => ( ( G @ A4 )
% 0.35/0.66                = one_one_complex ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.not_neutral_contains_not_neutral
% 0.35/0.66  thf(fact_8717_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.35/0.66      ! [G: real > complex,A2: set_real] :
% 0.35/0.66        ( ( ( groups713298508707869441omplex @ G @ A2 )
% 0.35/0.66         != one_one_complex )
% 0.35/0.66       => ~ ! [A4: real] :
% 0.35/0.66              ( ( member_real @ A4 @ A2 )
% 0.35/0.66             => ( ( G @ A4 )
% 0.35/0.66                = one_one_complex ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.not_neutral_contains_not_neutral
% 0.35/0.66  thf(fact_8718_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.35/0.66      ! [G: nat > complex,A2: set_nat] :
% 0.35/0.66        ( ( ( groups6464643781859351333omplex @ G @ A2 )
% 0.35/0.66         != one_one_complex )
% 0.35/0.66       => ~ ! [A4: nat] :
% 0.35/0.66              ( ( member_nat @ A4 @ A2 )
% 0.35/0.66             => ( ( G @ A4 )
% 0.35/0.66                = one_one_complex ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.not_neutral_contains_not_neutral
% 0.35/0.66  thf(fact_8719_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.35/0.66      ! [G: int > complex,A2: set_int] :
% 0.35/0.66        ( ( ( groups7440179247065528705omplex @ G @ A2 )
% 0.35/0.66         != one_one_complex )
% 0.35/0.66       => ~ ! [A4: int] :
% 0.35/0.66              ( ( member_int @ A4 @ A2 )
% 0.35/0.66             => ( ( G @ A4 )
% 0.35/0.66                = one_one_complex ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.not_neutral_contains_not_neutral
% 0.35/0.66  thf(fact_8720_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.35/0.66      ! [G: complex > real,A2: set_complex] :
% 0.35/0.66        ( ( ( groups766887009212190081x_real @ G @ A2 )
% 0.35/0.66         != one_one_real )
% 0.35/0.66       => ~ ! [A4: complex] :
% 0.35/0.66              ( ( member_complex @ A4 @ A2 )
% 0.35/0.66             => ( ( G @ A4 )
% 0.35/0.66                = one_one_real ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.not_neutral_contains_not_neutral
% 0.35/0.66  thf(fact_8721_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.35/0.66      ! [G: real > real,A2: set_real] :
% 0.35/0.66        ( ( ( groups1681761925125756287l_real @ G @ A2 )
% 0.35/0.66         != one_one_real )
% 0.35/0.66       => ~ ! [A4: real] :
% 0.35/0.66              ( ( member_real @ A4 @ A2 )
% 0.35/0.66             => ( ( G @ A4 )
% 0.35/0.66                = one_one_real ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.not_neutral_contains_not_neutral
% 0.35/0.66  thf(fact_8722_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.35/0.66      ! [G: nat > real,A2: set_nat] :
% 0.35/0.66        ( ( ( groups129246275422532515t_real @ G @ A2 )
% 0.35/0.66         != one_one_real )
% 0.35/0.66       => ~ ! [A4: nat] :
% 0.35/0.66              ( ( member_nat @ A4 @ A2 )
% 0.35/0.66             => ( ( G @ A4 )
% 0.35/0.66                = one_one_real ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.not_neutral_contains_not_neutral
% 0.35/0.66  thf(fact_8723_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.35/0.66      ! [G: int > real,A2: set_int] :
% 0.35/0.66        ( ( ( groups2316167850115554303t_real @ G @ A2 )
% 0.35/0.66         != one_one_real )
% 0.35/0.66       => ~ ! [A4: int] :
% 0.35/0.66              ( ( member_int @ A4 @ A2 )
% 0.35/0.66             => ( ( G @ A4 )
% 0.35/0.66                = one_one_real ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.not_neutral_contains_not_neutral
% 0.35/0.66  thf(fact_8724_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.35/0.66      ! [G: complex > rat,A2: set_complex] :
% 0.35/0.66        ( ( ( groups225925009352817453ex_rat @ G @ A2 )
% 0.35/0.66         != one_one_rat )
% 0.35/0.66       => ~ ! [A4: complex] :
% 0.35/0.66              ( ( member_complex @ A4 @ A2 )
% 0.35/0.66             => ( ( G @ A4 )
% 0.35/0.66                = one_one_rat ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.not_neutral_contains_not_neutral
% 0.35/0.66  thf(fact_8725_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.35/0.66      ! [G: real > rat,A2: set_real] :
% 0.35/0.66        ( ( ( groups4061424788464935467al_rat @ G @ A2 )
% 0.35/0.66         != one_one_rat )
% 0.35/0.66       => ~ ! [A4: real] :
% 0.35/0.66              ( ( member_real @ A4 @ A2 )
% 0.35/0.66             => ( ( G @ A4 )
% 0.35/0.66                = one_one_rat ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.not_neutral_contains_not_neutral
% 0.35/0.66  thf(fact_8726_prod__power__distrib,axiom,
% 0.35/0.66      ! [F: nat > nat,A2: set_nat,N: nat] :
% 0.35/0.66        ( ( power_power_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ N )
% 0.35/0.66        = ( groups708209901874060359at_nat
% 0.35/0.66          @ ^ [X2: nat] : ( power_power_nat @ ( F @ X2 ) @ N )
% 0.35/0.66          @ A2 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_power_distrib
% 0.35/0.66  thf(fact_8727_prod__power__distrib,axiom,
% 0.35/0.66      ! [F: nat > int,A2: set_nat,N: nat] :
% 0.35/0.66        ( ( power_power_int @ ( groups705719431365010083at_int @ F @ A2 ) @ N )
% 0.35/0.66        = ( groups705719431365010083at_int
% 0.35/0.66          @ ^ [X2: nat] : ( power_power_int @ ( F @ X2 ) @ N )
% 0.35/0.66          @ A2 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_power_distrib
% 0.35/0.66  thf(fact_8728_prod__power__distrib,axiom,
% 0.35/0.66      ! [F: int > int,A2: set_int,N: nat] :
% 0.35/0.66        ( ( power_power_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ N )
% 0.35/0.66        = ( groups1705073143266064639nt_int
% 0.35/0.66          @ ^ [X2: int] : ( power_power_int @ ( F @ X2 ) @ N )
% 0.35/0.66          @ A2 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_power_distrib
% 0.35/0.66  thf(fact_8729_prod_Odistrib,axiom,
% 0.35/0.66      ! [G: nat > nat,H2: nat > nat,A2: set_nat] :
% 0.35/0.66        ( ( groups708209901874060359at_nat
% 0.35/0.66          @ ^ [X2: nat] : ( times_times_nat @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 0.35/0.66          @ A2 )
% 0.35/0.66        = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ A2 ) @ ( groups708209901874060359at_nat @ H2 @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.distrib
% 0.35/0.66  thf(fact_8730_prod_Odistrib,axiom,
% 0.35/0.66      ! [G: nat > int,H2: nat > int,A2: set_nat] :
% 0.35/0.66        ( ( groups705719431365010083at_int
% 0.35/0.66          @ ^ [X2: nat] : ( times_times_int @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 0.35/0.66          @ A2 )
% 0.35/0.66        = ( times_times_int @ ( groups705719431365010083at_int @ G @ A2 ) @ ( groups705719431365010083at_int @ H2 @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.distrib
% 0.35/0.66  thf(fact_8731_prod_Odistrib,axiom,
% 0.35/0.66      ! [G: int > int,H2: int > int,A2: set_int] :
% 0.35/0.66        ( ( groups1705073143266064639nt_int
% 0.35/0.66          @ ^ [X2: int] : ( times_times_int @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 0.35/0.66          @ A2 )
% 0.35/0.66        = ( times_times_int @ ( groups1705073143266064639nt_int @ G @ A2 ) @ ( groups1705073143266064639nt_int @ H2 @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.distrib
% 0.35/0.66  thf(fact_8732_mod__prod__eq,axiom,
% 0.35/0.66      ! [F: nat > nat,A: nat,A2: set_nat] :
% 0.35/0.66        ( ( modulo_modulo_nat
% 0.35/0.66          @ ( groups708209901874060359at_nat
% 0.35/0.66            @ ^ [I3: nat] : ( modulo_modulo_nat @ ( F @ I3 ) @ A )
% 0.35/0.66            @ A2 )
% 0.35/0.66          @ A )
% 0.35/0.66        = ( modulo_modulo_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ A ) ) ).
% 0.35/0.66  
% 0.35/0.66  % mod_prod_eq
% 0.35/0.66  thf(fact_8733_mod__prod__eq,axiom,
% 0.35/0.66      ! [F: nat > int,A: int,A2: set_nat] :
% 0.35/0.66        ( ( modulo_modulo_int
% 0.35/0.66          @ ( groups705719431365010083at_int
% 0.35/0.66            @ ^ [I3: nat] : ( modulo_modulo_int @ ( F @ I3 ) @ A )
% 0.35/0.66            @ A2 )
% 0.35/0.66          @ A )
% 0.35/0.66        = ( modulo_modulo_int @ ( groups705719431365010083at_int @ F @ A2 ) @ A ) ) ).
% 0.35/0.66  
% 0.35/0.66  % mod_prod_eq
% 0.35/0.66  thf(fact_8734_mod__prod__eq,axiom,
% 0.35/0.66      ! [F: int > int,A: int,A2: set_int] :
% 0.35/0.66        ( ( modulo_modulo_int
% 0.35/0.66          @ ( groups1705073143266064639nt_int
% 0.35/0.66            @ ^ [I3: int] : ( modulo_modulo_int @ ( F @ I3 ) @ A )
% 0.35/0.66            @ A2 )
% 0.35/0.66          @ A )
% 0.35/0.66        = ( modulo_modulo_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ A ) ) ).
% 0.35/0.66  
% 0.35/0.66  % mod_prod_eq
% 0.35/0.66  thf(fact_8735_prod__nonneg,axiom,
% 0.35/0.66      ! [A2: set_nat,F: nat > nat] :
% 0.35/0.66        ( ! [X3: nat] :
% 0.35/0.66            ( ( member_nat @ X3 @ A2 )
% 0.35/0.66           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 0.35/0.66       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_nonneg
% 0.35/0.66  thf(fact_8736_prod__nonneg,axiom,
% 0.35/0.66      ! [A2: set_nat,F: nat > int] :
% 0.35/0.66        ( ! [X3: nat] :
% 0.35/0.66            ( ( member_nat @ X3 @ A2 )
% 0.35/0.66           => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 0.35/0.66       => ( ord_less_eq_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_nonneg
% 0.35/0.66  thf(fact_8737_prod__nonneg,axiom,
% 0.35/0.66      ! [A2: set_int,F: int > int] :
% 0.35/0.66        ( ! [X3: int] :
% 0.35/0.66            ( ( member_int @ X3 @ A2 )
% 0.35/0.66           => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 0.35/0.66       => ( ord_less_eq_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_nonneg
% 0.35/0.66  thf(fact_8738_prod__mono,axiom,
% 0.35/0.66      ! [A2: set_complex,F: complex > real,G: complex > real] :
% 0.35/0.66        ( ! [I4: complex] :
% 0.35/0.66            ( ( member_complex @ I4 @ A2 )
% 0.35/0.66           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 0.35/0.66              & ( ord_less_eq_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 0.35/0.66       => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ( groups766887009212190081x_real @ G @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_mono
% 0.35/0.66  thf(fact_8739_prod__mono,axiom,
% 0.35/0.66      ! [A2: set_real,F: real > real,G: real > real] :
% 0.35/0.66        ( ! [I4: real] :
% 0.35/0.66            ( ( member_real @ I4 @ A2 )
% 0.35/0.66           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 0.35/0.66              & ( ord_less_eq_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 0.35/0.66       => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_mono
% 0.35/0.66  thf(fact_8740_prod__mono,axiom,
% 0.35/0.66      ! [A2: set_nat,F: nat > real,G: nat > real] :
% 0.35/0.66        ( ! [I4: nat] :
% 0.35/0.66            ( ( member_nat @ I4 @ A2 )
% 0.35/0.66           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 0.35/0.66              & ( ord_less_eq_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 0.35/0.66       => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_mono
% 0.35/0.66  thf(fact_8741_prod__mono,axiom,
% 0.35/0.66      ! [A2: set_int,F: int > real,G: int > real] :
% 0.35/0.66        ( ! [I4: int] :
% 0.35/0.66            ( ( member_int @ I4 @ A2 )
% 0.35/0.66           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 0.35/0.66              & ( ord_less_eq_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 0.35/0.66       => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_mono
% 0.35/0.66  thf(fact_8742_prod__mono,axiom,
% 0.35/0.66      ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 0.35/0.66        ( ! [I4: complex] :
% 0.35/0.66            ( ( member_complex @ I4 @ A2 )
% 0.35/0.66           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) )
% 0.35/0.66              & ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 0.35/0.66       => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ ( groups225925009352817453ex_rat @ G @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_mono
% 0.35/0.66  thf(fact_8743_prod__mono,axiom,
% 0.35/0.66      ! [A2: set_real,F: real > rat,G: real > rat] :
% 0.35/0.66        ( ! [I4: real] :
% 0.35/0.66            ( ( member_real @ I4 @ A2 )
% 0.35/0.66           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) )
% 0.35/0.66              & ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 0.35/0.66       => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ ( groups4061424788464935467al_rat @ G @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_mono
% 0.35/0.66  thf(fact_8744_prod__mono,axiom,
% 0.35/0.66      ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 0.35/0.66        ( ! [I4: nat] :
% 0.35/0.66            ( ( member_nat @ I4 @ A2 )
% 0.35/0.66           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) )
% 0.35/0.66              & ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 0.35/0.66       => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ ( groups73079841787564623at_rat @ G @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_mono
% 0.35/0.66  thf(fact_8745_prod__mono,axiom,
% 0.35/0.66      ! [A2: set_int,F: int > rat,G: int > rat] :
% 0.35/0.66        ( ! [I4: int] :
% 0.35/0.66            ( ( member_int @ I4 @ A2 )
% 0.35/0.66           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) )
% 0.35/0.66              & ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 0.35/0.66       => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ ( groups1072433553688619179nt_rat @ G @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_mono
% 0.35/0.66  thf(fact_8746_prod__mono,axiom,
% 0.35/0.66      ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 0.35/0.66        ( ! [I4: complex] :
% 0.35/0.66            ( ( member_complex @ I4 @ A2 )
% 0.35/0.66           => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) )
% 0.35/0.66              & ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 0.35/0.66       => ( ord_less_eq_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) @ ( groups861055069439313189ex_nat @ G @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_mono
% 0.35/0.66  thf(fact_8747_prod__mono,axiom,
% 0.35/0.66      ! [A2: set_real,F: real > nat,G: real > nat] :
% 0.35/0.66        ( ! [I4: real] :
% 0.35/0.66            ( ( member_real @ I4 @ A2 )
% 0.35/0.66           => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) )
% 0.35/0.66              & ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 0.35/0.66       => ( ord_less_eq_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) @ ( groups4696554848551431203al_nat @ G @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_mono
% 0.35/0.66  thf(fact_8748_prod__pos,axiom,
% 0.35/0.66      ! [A2: set_nat,F: nat > nat] :
% 0.35/0.66        ( ! [X3: nat] :
% 0.35/0.66            ( ( member_nat @ X3 @ A2 )
% 0.35/0.66           => ( ord_less_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 0.35/0.66       => ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_pos
% 0.35/0.66  thf(fact_8749_prod__pos,axiom,
% 0.35/0.66      ! [A2: set_nat,F: nat > int] :
% 0.35/0.66        ( ! [X3: nat] :
% 0.35/0.66            ( ( member_nat @ X3 @ A2 )
% 0.35/0.66           => ( ord_less_int @ zero_zero_int @ ( F @ X3 ) ) )
% 0.35/0.66       => ( ord_less_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_pos
% 0.35/0.66  thf(fact_8750_prod__pos,axiom,
% 0.35/0.66      ! [A2: set_int,F: int > int] :
% 0.35/0.66        ( ! [X3: int] :
% 0.35/0.66            ( ( member_int @ X3 @ A2 )
% 0.35/0.66           => ( ord_less_int @ zero_zero_int @ ( F @ X3 ) ) )
% 0.35/0.66       => ( ord_less_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_pos
% 0.35/0.66  thf(fact_8751_prod__ge__1,axiom,
% 0.35/0.66      ! [A2: set_complex,F: complex > real] :
% 0.35/0.66        ( ! [X3: complex] :
% 0.35/0.66            ( ( member_complex @ X3 @ A2 )
% 0.35/0.66           => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 0.35/0.66       => ( ord_less_eq_real @ one_one_real @ ( groups766887009212190081x_real @ F @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_ge_1
% 0.35/0.66  thf(fact_8752_prod__ge__1,axiom,
% 0.35/0.66      ! [A2: set_real,F: real > real] :
% 0.35/0.66        ( ! [X3: real] :
% 0.35/0.66            ( ( member_real @ X3 @ A2 )
% 0.35/0.66           => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 0.35/0.66       => ( ord_less_eq_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_ge_1
% 0.35/0.66  thf(fact_8753_prod__ge__1,axiom,
% 0.35/0.66      ! [A2: set_nat,F: nat > real] :
% 0.35/0.66        ( ! [X3: nat] :
% 0.35/0.66            ( ( member_nat @ X3 @ A2 )
% 0.35/0.66           => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 0.35/0.66       => ( ord_less_eq_real @ one_one_real @ ( groups129246275422532515t_real @ F @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_ge_1
% 0.35/0.66  thf(fact_8754_prod__ge__1,axiom,
% 0.35/0.66      ! [A2: set_int,F: int > real] :
% 0.35/0.66        ( ! [X3: int] :
% 0.35/0.66            ( ( member_int @ X3 @ A2 )
% 0.35/0.66           => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 0.35/0.66       => ( ord_less_eq_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_ge_1
% 0.35/0.66  thf(fact_8755_prod__ge__1,axiom,
% 0.35/0.66      ! [A2: set_complex,F: complex > rat] :
% 0.35/0.66        ( ! [X3: complex] :
% 0.35/0.66            ( ( member_complex @ X3 @ A2 )
% 0.35/0.66           => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 0.35/0.66       => ( ord_less_eq_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_ge_1
% 0.35/0.66  thf(fact_8756_prod__ge__1,axiom,
% 0.35/0.66      ! [A2: set_real,F: real > rat] :
% 0.35/0.66        ( ! [X3: real] :
% 0.35/0.66            ( ( member_real @ X3 @ A2 )
% 0.35/0.66           => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 0.35/0.66       => ( ord_less_eq_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_ge_1
% 0.35/0.66  thf(fact_8757_prod__ge__1,axiom,
% 0.35/0.66      ! [A2: set_nat,F: nat > rat] :
% 0.35/0.66        ( ! [X3: nat] :
% 0.35/0.66            ( ( member_nat @ X3 @ A2 )
% 0.35/0.66           => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 0.35/0.66       => ( ord_less_eq_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_ge_1
% 0.35/0.66  thf(fact_8758_prod__ge__1,axiom,
% 0.35/0.66      ! [A2: set_int,F: int > rat] :
% 0.35/0.66        ( ! [X3: int] :
% 0.35/0.66            ( ( member_int @ X3 @ A2 )
% 0.35/0.66           => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 0.35/0.66       => ( ord_less_eq_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_ge_1
% 0.35/0.66  thf(fact_8759_prod__ge__1,axiom,
% 0.35/0.66      ! [A2: set_complex,F: complex > nat] :
% 0.35/0.66        ( ! [X3: complex] :
% 0.35/0.66            ( ( member_complex @ X3 @ A2 )
% 0.35/0.66           => ( ord_less_eq_nat @ one_one_nat @ ( F @ X3 ) ) )
% 0.35/0.66       => ( ord_less_eq_nat @ one_one_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_ge_1
% 0.35/0.66  thf(fact_8760_prod__ge__1,axiom,
% 0.35/0.66      ! [A2: set_real,F: real > nat] :
% 0.35/0.66        ( ! [X3: real] :
% 0.35/0.66            ( ( member_real @ X3 @ A2 )
% 0.35/0.66           => ( ord_less_eq_nat @ one_one_nat @ ( F @ X3 ) ) )
% 0.35/0.66       => ( ord_less_eq_nat @ one_one_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_ge_1
% 0.35/0.66  thf(fact_8761_prod__atLeastAtMost__code,axiom,
% 0.35/0.66      ! [F: nat > rat,A: nat,B: nat] :
% 0.35/0.66        ( ( groups73079841787564623at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.35/0.66        = ( set_fo1949268297981939178at_rat
% 0.35/0.66          @ ^ [A3: nat] : ( times_times_rat @ ( F @ A3 ) )
% 0.35/0.66          @ A
% 0.35/0.66          @ B
% 0.35/0.66          @ one_one_rat ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_atLeastAtMost_code
% 0.35/0.66  thf(fact_8762_prod__atLeastAtMost__code,axiom,
% 0.35/0.66      ! [F: nat > complex,A: nat,B: nat] :
% 0.35/0.66        ( ( groups6464643781859351333omplex @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.35/0.66        = ( set_fo1517530859248394432omplex
% 0.35/0.66          @ ^ [A3: nat] : ( times_times_complex @ ( F @ A3 ) )
% 0.35/0.66          @ A
% 0.35/0.66          @ B
% 0.35/0.66          @ one_one_complex ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_atLeastAtMost_code
% 0.35/0.66  thf(fact_8763_prod__atLeastAtMost__code,axiom,
% 0.35/0.66      ! [F: nat > real,A: nat,B: nat] :
% 0.35/0.66        ( ( groups129246275422532515t_real @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.35/0.66        = ( set_fo3111899725591712190t_real
% 0.35/0.66          @ ^ [A3: nat] : ( times_times_real @ ( F @ A3 ) )
% 0.35/0.66          @ A
% 0.35/0.66          @ B
% 0.35/0.66          @ one_one_real ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_atLeastAtMost_code
% 0.35/0.66  thf(fact_8764_prod__atLeastAtMost__code,axiom,
% 0.35/0.66      ! [F: nat > nat,A: nat,B: nat] :
% 0.35/0.66        ( ( groups708209901874060359at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.35/0.66        = ( set_fo2584398358068434914at_nat
% 0.35/0.66          @ ^ [A3: nat] : ( times_times_nat @ ( F @ A3 ) )
% 0.35/0.66          @ A
% 0.35/0.66          @ B
% 0.35/0.66          @ one_one_nat ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_atLeastAtMost_code
% 0.35/0.66  thf(fact_8765_prod__atLeastAtMost__code,axiom,
% 0.35/0.66      ! [F: nat > int,A: nat,B: nat] :
% 0.35/0.66        ( ( groups705719431365010083at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.35/0.66        = ( set_fo2581907887559384638at_int
% 0.35/0.66          @ ^ [A3: nat] : ( times_times_int @ ( F @ A3 ) )
% 0.35/0.66          @ A
% 0.35/0.66          @ B
% 0.35/0.66          @ one_one_int ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_atLeastAtMost_code
% 0.35/0.66  thf(fact_8766_prod_Ointer__filter,axiom,
% 0.35/0.66      ! [A2: set_int,G: int > complex,P: int > $o] :
% 0.35/0.66        ( ( finite_finite_int @ A2 )
% 0.35/0.66       => ( ( groups7440179247065528705omplex @ G
% 0.35/0.66            @ ( collect_int
% 0.35/0.66              @ ^ [X2: int] :
% 0.35/0.66                  ( ( member_int @ X2 @ A2 )
% 0.35/0.66                  & ( P @ X2 ) ) ) )
% 0.35/0.66          = ( groups7440179247065528705omplex
% 0.35/0.66            @ ^ [X2: int] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_complex )
% 0.35/0.66            @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.inter_filter
% 0.35/0.66  thf(fact_8767_prod_Ointer__filter,axiom,
% 0.35/0.66      ! [A2: set_real,G: real > complex,P: real > $o] :
% 0.35/0.66        ( ( finite_finite_real @ A2 )
% 0.35/0.66       => ( ( groups713298508707869441omplex @ G
% 0.35/0.66            @ ( collect_real
% 0.35/0.66              @ ^ [X2: real] :
% 0.35/0.66                  ( ( member_real @ X2 @ A2 )
% 0.35/0.66                  & ( P @ X2 ) ) ) )
% 0.35/0.66          = ( groups713298508707869441omplex
% 0.35/0.66            @ ^ [X2: real] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_complex )
% 0.35/0.66            @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.inter_filter
% 0.35/0.66  thf(fact_8768_prod_Ointer__filter,axiom,
% 0.35/0.66      ! [A2: set_nat,G: nat > complex,P: nat > $o] :
% 0.35/0.66        ( ( finite_finite_nat @ A2 )
% 0.35/0.66       => ( ( groups6464643781859351333omplex @ G
% 0.35/0.66            @ ( collect_nat
% 0.35/0.66              @ ^ [X2: nat] :
% 0.35/0.66                  ( ( member_nat @ X2 @ A2 )
% 0.35/0.66                  & ( P @ X2 ) ) ) )
% 0.35/0.66          = ( groups6464643781859351333omplex
% 0.35/0.66            @ ^ [X2: nat] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_complex )
% 0.35/0.66            @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.inter_filter
% 0.35/0.66  thf(fact_8769_prod_Ointer__filter,axiom,
% 0.35/0.66      ! [A2: set_complex,G: complex > complex,P: complex > $o] :
% 0.35/0.66        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.66       => ( ( groups3708469109370488835omplex @ G
% 0.35/0.66            @ ( collect_complex
% 0.35/0.66              @ ^ [X2: complex] :
% 0.35/0.66                  ( ( member_complex @ X2 @ A2 )
% 0.35/0.66                  & ( P @ X2 ) ) ) )
% 0.35/0.66          = ( groups3708469109370488835omplex
% 0.35/0.66            @ ^ [X2: complex] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_complex )
% 0.35/0.66            @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.inter_filter
% 0.35/0.66  thf(fact_8770_prod_Ointer__filter,axiom,
% 0.35/0.66      ! [A2: set_int,G: int > real,P: int > $o] :
% 0.35/0.66        ( ( finite_finite_int @ A2 )
% 0.35/0.66       => ( ( groups2316167850115554303t_real @ G
% 0.35/0.66            @ ( collect_int
% 0.35/0.66              @ ^ [X2: int] :
% 0.35/0.66                  ( ( member_int @ X2 @ A2 )
% 0.35/0.66                  & ( P @ X2 ) ) ) )
% 0.35/0.66          = ( groups2316167850115554303t_real
% 0.35/0.66            @ ^ [X2: int] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_real )
% 0.35/0.66            @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.inter_filter
% 0.35/0.66  thf(fact_8771_prod_Ointer__filter,axiom,
% 0.35/0.66      ! [A2: set_real,G: real > real,P: real > $o] :
% 0.35/0.66        ( ( finite_finite_real @ A2 )
% 0.35/0.66       => ( ( groups1681761925125756287l_real @ G
% 0.35/0.66            @ ( collect_real
% 0.35/0.66              @ ^ [X2: real] :
% 0.35/0.66                  ( ( member_real @ X2 @ A2 )
% 0.35/0.66                  & ( P @ X2 ) ) ) )
% 0.35/0.66          = ( groups1681761925125756287l_real
% 0.35/0.66            @ ^ [X2: real] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_real )
% 0.35/0.66            @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.inter_filter
% 0.35/0.66  thf(fact_8772_prod_Ointer__filter,axiom,
% 0.35/0.66      ! [A2: set_nat,G: nat > real,P: nat > $o] :
% 0.35/0.66        ( ( finite_finite_nat @ A2 )
% 0.35/0.66       => ( ( groups129246275422532515t_real @ G
% 0.35/0.66            @ ( collect_nat
% 0.35/0.66              @ ^ [X2: nat] :
% 0.35/0.66                  ( ( member_nat @ X2 @ A2 )
% 0.35/0.66                  & ( P @ X2 ) ) ) )
% 0.35/0.66          = ( groups129246275422532515t_real
% 0.35/0.66            @ ^ [X2: nat] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_real )
% 0.35/0.66            @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.inter_filter
% 0.35/0.66  thf(fact_8773_prod_Ointer__filter,axiom,
% 0.35/0.66      ! [A2: set_complex,G: complex > real,P: complex > $o] :
% 0.35/0.66        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.66       => ( ( groups766887009212190081x_real @ G
% 0.35/0.66            @ ( collect_complex
% 0.35/0.66              @ ^ [X2: complex] :
% 0.35/0.66                  ( ( member_complex @ X2 @ A2 )
% 0.35/0.66                  & ( P @ X2 ) ) ) )
% 0.35/0.66          = ( groups766887009212190081x_real
% 0.35/0.66            @ ^ [X2: complex] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_real )
% 0.35/0.66            @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.inter_filter
% 0.35/0.66  thf(fact_8774_prod_Ointer__filter,axiom,
% 0.35/0.66      ! [A2: set_int,G: int > rat,P: int > $o] :
% 0.35/0.66        ( ( finite_finite_int @ A2 )
% 0.35/0.66       => ( ( groups1072433553688619179nt_rat @ G
% 0.35/0.66            @ ( collect_int
% 0.35/0.66              @ ^ [X2: int] :
% 0.35/0.66                  ( ( member_int @ X2 @ A2 )
% 0.35/0.66                  & ( P @ X2 ) ) ) )
% 0.35/0.66          = ( groups1072433553688619179nt_rat
% 0.35/0.66            @ ^ [X2: int] : ( if_rat @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_rat )
% 0.35/0.66            @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.inter_filter
% 0.35/0.66  thf(fact_8775_prod_Ointer__filter,axiom,
% 0.35/0.66      ! [A2: set_real,G: real > rat,P: real > $o] :
% 0.35/0.66        ( ( finite_finite_real @ A2 )
% 0.35/0.66       => ( ( groups4061424788464935467al_rat @ G
% 0.35/0.66            @ ( collect_real
% 0.35/0.66              @ ^ [X2: real] :
% 0.35/0.66                  ( ( member_real @ X2 @ A2 )
% 0.35/0.66                  & ( P @ X2 ) ) ) )
% 0.35/0.66          = ( groups4061424788464935467al_rat
% 0.35/0.66            @ ^ [X2: real] : ( if_rat @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_rat )
% 0.35/0.66            @ A2 ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.inter_filter
% 0.35/0.66  thf(fact_8776_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 0.35/0.66      ! [G: nat > nat,M: nat,N: nat] :
% 0.35/0.66        ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 0.35/0.66        = ( groups708209901874060359at_nat
% 0.35/0.66          @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.35/0.66          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.shift_bounds_cl_Suc_ivl
% 0.35/0.66  thf(fact_8777_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 0.35/0.66      ! [G: nat > int,M: nat,N: nat] :
% 0.35/0.66        ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 0.35/0.66        = ( groups705719431365010083at_int
% 0.35/0.66          @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.35/0.66          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.shift_bounds_cl_Suc_ivl
% 0.35/0.66  thf(fact_8778_power__sum,axiom,
% 0.35/0.66      ! [C: real,F: nat > nat,A2: set_nat] :
% 0.35/0.66        ( ( power_power_real @ C @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 0.35/0.66        = ( groups129246275422532515t_real
% 0.35/0.66          @ ^ [A3: nat] : ( power_power_real @ C @ ( F @ A3 ) )
% 0.35/0.66          @ A2 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % power_sum
% 0.35/0.66  thf(fact_8779_power__sum,axiom,
% 0.35/0.66      ! [C: complex,F: nat > nat,A2: set_nat] :
% 0.35/0.66        ( ( power_power_complex @ C @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 0.35/0.66        = ( groups6464643781859351333omplex
% 0.35/0.66          @ ^ [A3: nat] : ( power_power_complex @ C @ ( F @ A3 ) )
% 0.35/0.66          @ A2 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % power_sum
% 0.35/0.66  thf(fact_8780_power__sum,axiom,
% 0.35/0.66      ! [C: nat,F: nat > nat,A2: set_nat] :
% 0.35/0.66        ( ( power_power_nat @ C @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 0.35/0.66        = ( groups708209901874060359at_nat
% 0.35/0.66          @ ^ [A3: nat] : ( power_power_nat @ C @ ( F @ A3 ) )
% 0.35/0.66          @ A2 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % power_sum
% 0.35/0.66  thf(fact_8781_power__sum,axiom,
% 0.35/0.66      ! [C: int,F: nat > nat,A2: set_nat] :
% 0.35/0.66        ( ( power_power_int @ C @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 0.35/0.66        = ( groups705719431365010083at_int
% 0.35/0.66          @ ^ [A3: nat] : ( power_power_int @ C @ ( F @ A3 ) )
% 0.35/0.66          @ A2 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % power_sum
% 0.35/0.66  thf(fact_8782_power__sum,axiom,
% 0.35/0.66      ! [C: int,F: int > nat,A2: set_int] :
% 0.35/0.66        ( ( power_power_int @ C @ ( groups4541462559716669496nt_nat @ F @ A2 ) )
% 0.35/0.66        = ( groups1705073143266064639nt_int
% 0.35/0.66          @ ^ [A3: int] : ( power_power_int @ C @ ( F @ A3 ) )
% 0.35/0.66          @ A2 ) ) ).
% 0.35/0.66  
% 0.35/0.66  % power_sum
% 0.35/0.66  thf(fact_8783_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 0.35/0.66      ! [G: nat > nat,M: nat,K: nat,N: nat] :
% 0.35/0.66        ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 0.35/0.66        = ( groups708209901874060359at_nat
% 0.35/0.66          @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 0.35/0.66          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.shift_bounds_cl_nat_ivl
% 0.35/0.66  thf(fact_8784_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 0.35/0.66      ! [G: nat > int,M: nat,K: nat,N: nat] :
% 0.35/0.66        ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 0.35/0.66        = ( groups705719431365010083at_int
% 0.35/0.66          @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 0.35/0.66          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.shift_bounds_cl_nat_ivl
% 0.35/0.66  thf(fact_8785_frac__ge__0,axiom,
% 0.35/0.66      ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( archim2898591450579166408c_real @ X ) ) ).
% 0.35/0.66  
% 0.35/0.66  % frac_ge_0
% 0.35/0.66  thf(fact_8786_frac__ge__0,axiom,
% 0.35/0.66      ! [X: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( archimedean_frac_rat @ X ) ) ).
% 0.35/0.66  
% 0.35/0.66  % frac_ge_0
% 0.35/0.66  thf(fact_8787_frac__lt__1,axiom,
% 0.35/0.66      ! [X: real] : ( ord_less_real @ ( archim2898591450579166408c_real @ X ) @ one_one_real ) ).
% 0.35/0.66  
% 0.35/0.66  % frac_lt_1
% 0.35/0.66  thf(fact_8788_frac__lt__1,axiom,
% 0.35/0.66      ! [X: rat] : ( ord_less_rat @ ( archimedean_frac_rat @ X ) @ one_one_rat ) ).
% 0.35/0.66  
% 0.35/0.66  % frac_lt_1
% 0.35/0.66  thf(fact_8789_prod__le__1,axiom,
% 0.35/0.66      ! [A2: set_complex,F: complex > real] :
% 0.35/0.66        ( ! [X3: complex] :
% 0.35/0.66            ( ( member_complex @ X3 @ A2 )
% 0.35/0.66           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 0.35/0.66              & ( ord_less_eq_real @ ( F @ X3 ) @ one_one_real ) ) )
% 0.35/0.66       => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A2 ) @ one_one_real ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_le_1
% 0.35/0.66  thf(fact_8790_prod__le__1,axiom,
% 0.35/0.66      ! [A2: set_real,F: real > real] :
% 0.35/0.66        ( ! [X3: real] :
% 0.35/0.66            ( ( member_real @ X3 @ A2 )
% 0.35/0.66           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 0.35/0.66              & ( ord_less_eq_real @ ( F @ X3 ) @ one_one_real ) ) )
% 0.35/0.66       => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ one_one_real ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_le_1
% 0.35/0.66  thf(fact_8791_prod__le__1,axiom,
% 0.35/0.66      ! [A2: set_nat,F: nat > real] :
% 0.35/0.66        ( ! [X3: nat] :
% 0.35/0.66            ( ( member_nat @ X3 @ A2 )
% 0.35/0.66           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 0.35/0.66              & ( ord_less_eq_real @ ( F @ X3 ) @ one_one_real ) ) )
% 0.35/0.66       => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ one_one_real ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_le_1
% 0.35/0.66  thf(fact_8792_prod__le__1,axiom,
% 0.35/0.66      ! [A2: set_int,F: int > real] :
% 0.35/0.66        ( ! [X3: int] :
% 0.35/0.66            ( ( member_int @ X3 @ A2 )
% 0.35/0.66           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 0.35/0.66              & ( ord_less_eq_real @ ( F @ X3 ) @ one_one_real ) ) )
% 0.35/0.66       => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ one_one_real ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_le_1
% 0.35/0.66  thf(fact_8793_prod__le__1,axiom,
% 0.35/0.66      ! [A2: set_complex,F: complex > rat] :
% 0.35/0.66        ( ! [X3: complex] :
% 0.35/0.66            ( ( member_complex @ X3 @ A2 )
% 0.35/0.66           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 0.35/0.66              & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 0.35/0.66       => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_le_1
% 0.35/0.66  thf(fact_8794_prod__le__1,axiom,
% 0.35/0.66      ! [A2: set_real,F: real > rat] :
% 0.35/0.66        ( ! [X3: real] :
% 0.35/0.66            ( ( member_real @ X3 @ A2 )
% 0.35/0.66           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 0.35/0.66              & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 0.35/0.66       => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_le_1
% 0.35/0.66  thf(fact_8795_prod__le__1,axiom,
% 0.35/0.66      ! [A2: set_nat,F: nat > rat] :
% 0.35/0.66        ( ! [X3: nat] :
% 0.35/0.66            ( ( member_nat @ X3 @ A2 )
% 0.35/0.66           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 0.35/0.66              & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 0.35/0.66       => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_le_1
% 0.35/0.66  thf(fact_8796_prod__le__1,axiom,
% 0.35/0.66      ! [A2: set_int,F: int > rat] :
% 0.35/0.66        ( ! [X3: int] :
% 0.35/0.66            ( ( member_int @ X3 @ A2 )
% 0.35/0.66           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 0.35/0.66              & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 0.35/0.66       => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_le_1
% 0.35/0.66  thf(fact_8797_prod__le__1,axiom,
% 0.35/0.66      ! [A2: set_complex,F: complex > nat] :
% 0.35/0.66        ( ! [X3: complex] :
% 0.35/0.66            ( ( member_complex @ X3 @ A2 )
% 0.35/0.66           => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) )
% 0.35/0.66              & ( ord_less_eq_nat @ ( F @ X3 ) @ one_one_nat ) ) )
% 0.35/0.66       => ( ord_less_eq_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) @ one_one_nat ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_le_1
% 0.35/0.66  thf(fact_8798_prod__le__1,axiom,
% 0.35/0.66      ! [A2: set_real,F: real > nat] :
% 0.35/0.66        ( ! [X3: real] :
% 0.35/0.66            ( ( member_real @ X3 @ A2 )
% 0.35/0.66           => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) )
% 0.35/0.66              & ( ord_less_eq_nat @ ( F @ X3 ) @ one_one_nat ) ) )
% 0.35/0.66       => ( ord_less_eq_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) @ one_one_nat ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod_le_1
% 0.35/0.66  thf(fact_8799_frac__1__eq,axiom,
% 0.35/0.66      ! [X: real] :
% 0.35/0.66        ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X @ one_one_real ) )
% 0.35/0.66        = ( archim2898591450579166408c_real @ X ) ) ).
% 0.35/0.66  
% 0.35/0.66  % frac_1_eq
% 0.35/0.66  thf(fact_8800_frac__1__eq,axiom,
% 0.35/0.66      ! [X: rat] :
% 0.35/0.66        ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ one_one_rat ) )
% 0.35/0.66        = ( archimedean_frac_rat @ X ) ) ).
% 0.35/0.66  
% 0.35/0.66  % frac_1_eq
% 0.35/0.66  thf(fact_8801_prod_Orelated,axiom,
% 0.35/0.66      ! [R2: rat > rat > $o,S2: set_nat,H2: nat > rat,G: nat > rat] :
% 0.35/0.66        ( ( R2 @ one_one_rat @ one_one_rat )
% 0.35/0.66       => ( ! [X15: rat,Y15: rat,X22: rat,Y23: rat] :
% 0.35/0.66              ( ( ( R2 @ X15 @ X22 )
% 0.35/0.66                & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.66             => ( R2 @ ( times_times_rat @ X15 @ Y15 ) @ ( times_times_rat @ X22 @ Y23 ) ) )
% 0.35/0.66         => ( ( finite_finite_nat @ S2 )
% 0.35/0.66           => ( ! [X3: nat] :
% 0.35/0.66                  ( ( member_nat @ X3 @ S2 )
% 0.35/0.66                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.66             => ( R2 @ ( groups73079841787564623at_rat @ H2 @ S2 ) @ ( groups73079841787564623at_rat @ G @ S2 ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.related
% 0.35/0.66  thf(fact_8802_prod_Orelated,axiom,
% 0.35/0.66      ! [R2: rat > rat > $o,S2: set_complex,H2: complex > rat,G: complex > rat] :
% 0.35/0.66        ( ( R2 @ one_one_rat @ one_one_rat )
% 0.35/0.66       => ( ! [X15: rat,Y15: rat,X22: rat,Y23: rat] :
% 0.35/0.66              ( ( ( R2 @ X15 @ X22 )
% 0.35/0.66                & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.66             => ( R2 @ ( times_times_rat @ X15 @ Y15 ) @ ( times_times_rat @ X22 @ Y23 ) ) )
% 0.35/0.66         => ( ( finite3207457112153483333omplex @ S2 )
% 0.35/0.66           => ( ! [X3: complex] :
% 0.35/0.66                  ( ( member_complex @ X3 @ S2 )
% 0.35/0.66                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.66             => ( R2 @ ( groups225925009352817453ex_rat @ H2 @ S2 ) @ ( groups225925009352817453ex_rat @ G @ S2 ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.related
% 0.35/0.66  thf(fact_8803_prod_Orelated,axiom,
% 0.35/0.66      ! [R2: complex > complex > $o,S2: set_nat,H2: nat > complex,G: nat > complex] :
% 0.35/0.66        ( ( R2 @ one_one_complex @ one_one_complex )
% 0.35/0.66       => ( ! [X15: complex,Y15: complex,X22: complex,Y23: complex] :
% 0.35/0.66              ( ( ( R2 @ X15 @ X22 )
% 0.35/0.66                & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.66             => ( R2 @ ( times_times_complex @ X15 @ Y15 ) @ ( times_times_complex @ X22 @ Y23 ) ) )
% 0.35/0.66         => ( ( finite_finite_nat @ S2 )
% 0.35/0.66           => ( ! [X3: nat] :
% 0.35/0.66                  ( ( member_nat @ X3 @ S2 )
% 0.35/0.66                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.66             => ( R2 @ ( groups6464643781859351333omplex @ H2 @ S2 ) @ ( groups6464643781859351333omplex @ G @ S2 ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.related
% 0.35/0.66  thf(fact_8804_prod_Orelated,axiom,
% 0.35/0.66      ! [R2: complex > complex > $o,S2: set_complex,H2: complex > complex,G: complex > complex] :
% 0.35/0.66        ( ( R2 @ one_one_complex @ one_one_complex )
% 0.35/0.66       => ( ! [X15: complex,Y15: complex,X22: complex,Y23: complex] :
% 0.35/0.66              ( ( ( R2 @ X15 @ X22 )
% 0.35/0.66                & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.66             => ( R2 @ ( times_times_complex @ X15 @ Y15 ) @ ( times_times_complex @ X22 @ Y23 ) ) )
% 0.35/0.66         => ( ( finite3207457112153483333omplex @ S2 )
% 0.35/0.66           => ( ! [X3: complex] :
% 0.35/0.66                  ( ( member_complex @ X3 @ S2 )
% 0.35/0.66                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.66             => ( R2 @ ( groups3708469109370488835omplex @ H2 @ S2 ) @ ( groups3708469109370488835omplex @ G @ S2 ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.related
% 0.35/0.66  thf(fact_8805_prod_Orelated,axiom,
% 0.35/0.66      ! [R2: real > real > $o,S2: set_nat,H2: nat > real,G: nat > real] :
% 0.35/0.66        ( ( R2 @ one_one_real @ one_one_real )
% 0.35/0.66       => ( ! [X15: real,Y15: real,X22: real,Y23: real] :
% 0.35/0.66              ( ( ( R2 @ X15 @ X22 )
% 0.35/0.66                & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.66             => ( R2 @ ( times_times_real @ X15 @ Y15 ) @ ( times_times_real @ X22 @ Y23 ) ) )
% 0.35/0.66         => ( ( finite_finite_nat @ S2 )
% 0.35/0.66           => ( ! [X3: nat] :
% 0.35/0.66                  ( ( member_nat @ X3 @ S2 )
% 0.35/0.66                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.66             => ( R2 @ ( groups129246275422532515t_real @ H2 @ S2 ) @ ( groups129246275422532515t_real @ G @ S2 ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.related
% 0.35/0.66  thf(fact_8806_prod_Orelated,axiom,
% 0.35/0.66      ! [R2: real > real > $o,S2: set_complex,H2: complex > real,G: complex > real] :
% 0.35/0.66        ( ( R2 @ one_one_real @ one_one_real )
% 0.35/0.66       => ( ! [X15: real,Y15: real,X22: real,Y23: real] :
% 0.35/0.66              ( ( ( R2 @ X15 @ X22 )
% 0.35/0.66                & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.66             => ( R2 @ ( times_times_real @ X15 @ Y15 ) @ ( times_times_real @ X22 @ Y23 ) ) )
% 0.35/0.66         => ( ( finite3207457112153483333omplex @ S2 )
% 0.35/0.66           => ( ! [X3: complex] :
% 0.35/0.66                  ( ( member_complex @ X3 @ S2 )
% 0.35/0.66                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.66             => ( R2 @ ( groups766887009212190081x_real @ H2 @ S2 ) @ ( groups766887009212190081x_real @ G @ S2 ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.related
% 0.35/0.66  thf(fact_8807_prod_Orelated,axiom,
% 0.35/0.66      ! [R2: nat > nat > $o,S2: set_complex,H2: complex > nat,G: complex > nat] :
% 0.35/0.66        ( ( R2 @ one_one_nat @ one_one_nat )
% 0.35/0.66       => ( ! [X15: nat,Y15: nat,X22: nat,Y23: nat] :
% 0.35/0.66              ( ( ( R2 @ X15 @ X22 )
% 0.35/0.66                & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.66             => ( R2 @ ( times_times_nat @ X15 @ Y15 ) @ ( times_times_nat @ X22 @ Y23 ) ) )
% 0.35/0.66         => ( ( finite3207457112153483333omplex @ S2 )
% 0.35/0.66           => ( ! [X3: complex] :
% 0.35/0.66                  ( ( member_complex @ X3 @ S2 )
% 0.35/0.66                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.66             => ( R2 @ ( groups861055069439313189ex_nat @ H2 @ S2 ) @ ( groups861055069439313189ex_nat @ G @ S2 ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.related
% 0.35/0.66  thf(fact_8808_prod_Orelated,axiom,
% 0.35/0.66      ! [R2: int > int > $o,S2: set_complex,H2: complex > int,G: complex > int] :
% 0.35/0.66        ( ( R2 @ one_one_int @ one_one_int )
% 0.35/0.66       => ( ! [X15: int,Y15: int,X22: int,Y23: int] :
% 0.35/0.66              ( ( ( R2 @ X15 @ X22 )
% 0.35/0.66                & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.66             => ( R2 @ ( times_times_int @ X15 @ Y15 ) @ ( times_times_int @ X22 @ Y23 ) ) )
% 0.35/0.66         => ( ( finite3207457112153483333omplex @ S2 )
% 0.35/0.66           => ( ! [X3: complex] :
% 0.35/0.66                  ( ( member_complex @ X3 @ S2 )
% 0.35/0.66                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.66             => ( R2 @ ( groups858564598930262913ex_int @ H2 @ S2 ) @ ( groups858564598930262913ex_int @ G @ S2 ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.related
% 0.35/0.66  thf(fact_8809_prod_Orelated,axiom,
% 0.35/0.66      ! [R2: nat > nat > $o,S2: set_nat,H2: nat > nat,G: nat > nat] :
% 0.35/0.66        ( ( R2 @ one_one_nat @ one_one_nat )
% 0.35/0.66       => ( ! [X15: nat,Y15: nat,X22: nat,Y23: nat] :
% 0.35/0.66              ( ( ( R2 @ X15 @ X22 )
% 0.35/0.66                & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.66             => ( R2 @ ( times_times_nat @ X15 @ Y15 ) @ ( times_times_nat @ X22 @ Y23 ) ) )
% 0.35/0.66         => ( ( finite_finite_nat @ S2 )
% 0.35/0.66           => ( ! [X3: nat] :
% 0.35/0.66                  ( ( member_nat @ X3 @ S2 )
% 0.35/0.66                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.66             => ( R2 @ ( groups708209901874060359at_nat @ H2 @ S2 ) @ ( groups708209901874060359at_nat @ G @ S2 ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.related
% 0.35/0.66  thf(fact_8810_prod_Orelated,axiom,
% 0.35/0.66      ! [R2: int > int > $o,S2: set_nat,H2: nat > int,G: nat > int] :
% 0.35/0.66        ( ( R2 @ one_one_int @ one_one_int )
% 0.35/0.66       => ( ! [X15: int,Y15: int,X22: int,Y23: int] :
% 0.35/0.66              ( ( ( R2 @ X15 @ X22 )
% 0.35/0.66                & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.66             => ( R2 @ ( times_times_int @ X15 @ Y15 ) @ ( times_times_int @ X22 @ Y23 ) ) )
% 0.35/0.66         => ( ( finite_finite_nat @ S2 )
% 0.35/0.66           => ( ! [X3: nat] :
% 0.35/0.66                  ( ( member_nat @ X3 @ S2 )
% 0.35/0.66                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 0.35/0.66             => ( R2 @ ( groups705719431365010083at_int @ H2 @ S2 ) @ ( groups705719431365010083at_int @ G @ S2 ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.related
% 0.35/0.66  thf(fact_8811_prod_Oinsert__if,axiom,
% 0.35/0.66      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > complex] :
% 0.35/0.66        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.35/0.66       => ( ( ( member_VEBT_VEBT @ X @ A2 )
% 0.35/0.66           => ( ( groups127312072573709053omplex @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 0.35/0.66              = ( groups127312072573709053omplex @ G @ A2 ) ) )
% 0.35/0.66          & ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 0.35/0.66           => ( ( groups127312072573709053omplex @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 0.35/0.66              = ( times_times_complex @ ( G @ X ) @ ( groups127312072573709053omplex @ G @ A2 ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.insert_if
% 0.35/0.66  thf(fact_8812_prod_Oinsert__if,axiom,
% 0.35/0.66      ! [A2: set_real,X: real,G: real > complex] :
% 0.35/0.66        ( ( finite_finite_real @ A2 )
% 0.35/0.66       => ( ( ( member_real @ X @ A2 )
% 0.35/0.66           => ( ( groups713298508707869441omplex @ G @ ( insert_real @ X @ A2 ) )
% 0.35/0.66              = ( groups713298508707869441omplex @ G @ A2 ) ) )
% 0.35/0.66          & ( ~ ( member_real @ X @ A2 )
% 0.35/0.66           => ( ( groups713298508707869441omplex @ G @ ( insert_real @ X @ A2 ) )
% 0.35/0.66              = ( times_times_complex @ ( G @ X ) @ ( groups713298508707869441omplex @ G @ A2 ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.insert_if
% 0.35/0.66  thf(fact_8813_prod_Oinsert__if,axiom,
% 0.35/0.66      ! [A2: set_int,X: int,G: int > complex] :
% 0.35/0.66        ( ( finite_finite_int @ A2 )
% 0.35/0.66       => ( ( ( member_int @ X @ A2 )
% 0.35/0.66           => ( ( groups7440179247065528705omplex @ G @ ( insert_int @ X @ A2 ) )
% 0.35/0.66              = ( groups7440179247065528705omplex @ G @ A2 ) ) )
% 0.35/0.66          & ( ~ ( member_int @ X @ A2 )
% 0.35/0.66           => ( ( groups7440179247065528705omplex @ G @ ( insert_int @ X @ A2 ) )
% 0.35/0.66              = ( times_times_complex @ ( G @ X ) @ ( groups7440179247065528705omplex @ G @ A2 ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.insert_if
% 0.35/0.66  thf(fact_8814_prod_Oinsert__if,axiom,
% 0.35/0.66      ! [A2: set_nat,X: nat,G: nat > complex] :
% 0.35/0.66        ( ( finite_finite_nat @ A2 )
% 0.35/0.66       => ( ( ( member_nat @ X @ A2 )
% 0.35/0.66           => ( ( groups6464643781859351333omplex @ G @ ( insert_nat @ X @ A2 ) )
% 0.35/0.66              = ( groups6464643781859351333omplex @ G @ A2 ) ) )
% 0.35/0.66          & ( ~ ( member_nat @ X @ A2 )
% 0.35/0.66           => ( ( groups6464643781859351333omplex @ G @ ( insert_nat @ X @ A2 ) )
% 0.35/0.66              = ( times_times_complex @ ( G @ X ) @ ( groups6464643781859351333omplex @ G @ A2 ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.insert_if
% 0.35/0.66  thf(fact_8815_prod_Oinsert__if,axiom,
% 0.35/0.66      ! [A2: set_complex,X: complex,G: complex > complex] :
% 0.35/0.66        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.66       => ( ( ( member_complex @ X @ A2 )
% 0.35/0.66           => ( ( groups3708469109370488835omplex @ G @ ( insert_complex @ X @ A2 ) )
% 0.35/0.66              = ( groups3708469109370488835omplex @ G @ A2 ) ) )
% 0.35/0.66          & ( ~ ( member_complex @ X @ A2 )
% 0.35/0.66           => ( ( groups3708469109370488835omplex @ G @ ( insert_complex @ X @ A2 ) )
% 0.35/0.66              = ( times_times_complex @ ( G @ X ) @ ( groups3708469109370488835omplex @ G @ A2 ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.insert_if
% 0.35/0.66  thf(fact_8816_prod_Oinsert__if,axiom,
% 0.35/0.66      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > real] :
% 0.35/0.66        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.35/0.66       => ( ( ( member_VEBT_VEBT @ X @ A2 )
% 0.35/0.66           => ( ( groups2703838992350267259T_real @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 0.35/0.66              = ( groups2703838992350267259T_real @ G @ A2 ) ) )
% 0.35/0.66          & ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 0.35/0.66           => ( ( groups2703838992350267259T_real @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 0.35/0.66              = ( times_times_real @ ( G @ X ) @ ( groups2703838992350267259T_real @ G @ A2 ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.insert_if
% 0.35/0.66  thf(fact_8817_prod_Oinsert__if,axiom,
% 0.35/0.66      ! [A2: set_real,X: real,G: real > real] :
% 0.35/0.66        ( ( finite_finite_real @ A2 )
% 0.35/0.66       => ( ( ( member_real @ X @ A2 )
% 0.35/0.66           => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X @ A2 ) )
% 0.35/0.66              = ( groups1681761925125756287l_real @ G @ A2 ) ) )
% 0.35/0.66          & ( ~ ( member_real @ X @ A2 )
% 0.35/0.66           => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X @ A2 ) )
% 0.35/0.66              = ( times_times_real @ ( G @ X ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.insert_if
% 0.35/0.66  thf(fact_8818_prod_Oinsert__if,axiom,
% 0.35/0.66      ! [A2: set_int,X: int,G: int > real] :
% 0.35/0.66        ( ( finite_finite_int @ A2 )
% 0.35/0.66       => ( ( ( member_int @ X @ A2 )
% 0.35/0.66           => ( ( groups2316167850115554303t_real @ G @ ( insert_int @ X @ A2 ) )
% 0.35/0.66              = ( groups2316167850115554303t_real @ G @ A2 ) ) )
% 0.35/0.66          & ( ~ ( member_int @ X @ A2 )
% 0.35/0.66           => ( ( groups2316167850115554303t_real @ G @ ( insert_int @ X @ A2 ) )
% 0.35/0.66              = ( times_times_real @ ( G @ X ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.insert_if
% 0.35/0.66  thf(fact_8819_prod_Oinsert__if,axiom,
% 0.35/0.66      ! [A2: set_nat,X: nat,G: nat > real] :
% 0.35/0.66        ( ( finite_finite_nat @ A2 )
% 0.35/0.66       => ( ( ( member_nat @ X @ A2 )
% 0.35/0.66           => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X @ A2 ) )
% 0.35/0.66              = ( groups129246275422532515t_real @ G @ A2 ) ) )
% 0.35/0.66          & ( ~ ( member_nat @ X @ A2 )
% 0.35/0.66           => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X @ A2 ) )
% 0.35/0.66              = ( times_times_real @ ( G @ X ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.insert_if
% 0.35/0.66  thf(fact_8820_prod_Oinsert__if,axiom,
% 0.35/0.66      ! [A2: set_complex,X: complex,G: complex > real] :
% 0.35/0.66        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.66       => ( ( ( member_complex @ X @ A2 )
% 0.35/0.66           => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X @ A2 ) )
% 0.35/0.66              = ( groups766887009212190081x_real @ G @ A2 ) ) )
% 0.35/0.66          & ( ~ ( member_complex @ X @ A2 )
% 0.35/0.66           => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X @ A2 ) )
% 0.35/0.66              = ( times_times_real @ ( G @ X ) @ ( groups766887009212190081x_real @ G @ A2 ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.insert_if
% 0.35/0.66  thf(fact_8821_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.35/0.66      ! [S5: set_real,T5: set_real,S2: set_real,I2: real > real,J: real > real,T4: set_real,G: real > complex,H2: real > complex] :
% 0.35/0.66        ( ( finite_finite_real @ S5 )
% 0.35/0.66       => ( ( finite_finite_real @ T5 )
% 0.35/0.66         => ( ! [A4: real] :
% 0.35/0.66                ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 0.35/0.66               => ( ( I2 @ ( J @ A4 ) )
% 0.35/0.66                  = A4 ) )
% 0.35/0.66           => ( ! [A4: real] :
% 0.35/0.66                  ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 0.35/0.66                 => ( member_real @ ( J @ A4 ) @ ( minus_minus_set_real @ T4 @ T5 ) ) )
% 0.35/0.66             => ( ! [B3: real] :
% 0.35/0.66                    ( ( member_real @ B3 @ ( minus_minus_set_real @ T4 @ T5 ) )
% 0.35/0.66                   => ( ( J @ ( I2 @ B3 ) )
% 0.35/0.66                      = B3 ) )
% 0.35/0.66               => ( ! [B3: real] :
% 0.35/0.66                      ( ( member_real @ B3 @ ( minus_minus_set_real @ T4 @ T5 ) )
% 0.35/0.66                     => ( member_real @ ( I2 @ B3 ) @ ( minus_minus_set_real @ S2 @ S5 ) ) )
% 0.35/0.66                 => ( ! [A4: real] :
% 0.35/0.66                        ( ( member_real @ A4 @ S5 )
% 0.35/0.66                       => ( ( G @ A4 )
% 0.35/0.66                          = one_one_complex ) )
% 0.35/0.66                   => ( ! [B3: real] :
% 0.35/0.66                          ( ( member_real @ B3 @ T5 )
% 0.35/0.66                         => ( ( H2 @ B3 )
% 0.35/0.66                            = one_one_complex ) )
% 0.35/0.66                     => ( ! [A4: real] :
% 0.35/0.66                            ( ( member_real @ A4 @ S2 )
% 0.35/0.66                           => ( ( H2 @ ( J @ A4 ) )
% 0.35/0.66                              = ( G @ A4 ) ) )
% 0.35/0.66                       => ( ( groups713298508707869441omplex @ G @ S2 )
% 0.35/0.66                          = ( groups713298508707869441omplex @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.66  
% 0.35/0.66  % prod.reindex_bij_witness_not_neutral
% 0.35/0.66  thf(fact_8822_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.35/0.66      ! [S5: set_real,T5: set_int,S2: set_real,I2: int > real,J: real > int,T4: set_int,G: real > complex,H2: int > complex] :
% 0.35/0.66        ( ( finite_finite_real @ S5 )
% 0.35/0.67       => ( ( finite_finite_int @ T5 )
% 0.35/0.67         => ( ! [A4: real] :
% 0.35/0.67                ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 0.35/0.67               => ( ( I2 @ ( J @ A4 ) )
% 0.35/0.67                  = A4 ) )
% 0.35/0.67           => ( ! [A4: real] :
% 0.35/0.67                  ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 0.35/0.67                 => ( member_int @ ( J @ A4 ) @ ( minus_minus_set_int @ T4 @ T5 ) ) )
% 0.35/0.67             => ( ! [B3: int] :
% 0.35/0.67                    ( ( member_int @ B3 @ ( minus_minus_set_int @ T4 @ T5 ) )
% 0.35/0.67                   => ( ( J @ ( I2 @ B3 ) )
% 0.35/0.67                      = B3 ) )
% 0.35/0.67               => ( ! [B3: int] :
% 0.35/0.67                      ( ( member_int @ B3 @ ( minus_minus_set_int @ T4 @ T5 ) )
% 0.35/0.67                     => ( member_real @ ( I2 @ B3 ) @ ( minus_minus_set_real @ S2 @ S5 ) ) )
% 0.35/0.67                 => ( ! [A4: real] :
% 0.35/0.67                        ( ( member_real @ A4 @ S5 )
% 0.35/0.67                       => ( ( G @ A4 )
% 0.35/0.67                          = one_one_complex ) )
% 0.35/0.67                   => ( ! [B3: int] :
% 0.35/0.67                          ( ( member_int @ B3 @ T5 )
% 0.35/0.67                         => ( ( H2 @ B3 )
% 0.35/0.67                            = one_one_complex ) )
% 0.35/0.67                     => ( ! [A4: real] :
% 0.35/0.67                            ( ( member_real @ A4 @ S2 )
% 0.35/0.67                           => ( ( H2 @ ( J @ A4 ) )
% 0.35/0.67                              = ( G @ A4 ) ) )
% 0.35/0.67                       => ( ( groups713298508707869441omplex @ G @ S2 )
% 0.35/0.67                          = ( groups7440179247065528705omplex @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.reindex_bij_witness_not_neutral
% 0.35/0.67  thf(fact_8823_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.35/0.67      ! [S5: set_int,T5: set_real,S2: set_int,I2: real > int,J: int > real,T4: set_real,G: int > complex,H2: real > complex] :
% 0.35/0.67        ( ( finite_finite_int @ S5 )
% 0.35/0.67       => ( ( finite_finite_real @ T5 )
% 0.35/0.67         => ( ! [A4: int] :
% 0.35/0.67                ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 0.35/0.67               => ( ( I2 @ ( J @ A4 ) )
% 0.35/0.67                  = A4 ) )
% 0.35/0.67           => ( ! [A4: int] :
% 0.35/0.67                  ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 0.35/0.67                 => ( member_real @ ( J @ A4 ) @ ( minus_minus_set_real @ T4 @ T5 ) ) )
% 0.35/0.67             => ( ! [B3: real] :
% 0.35/0.67                    ( ( member_real @ B3 @ ( minus_minus_set_real @ T4 @ T5 ) )
% 0.35/0.67                   => ( ( J @ ( I2 @ B3 ) )
% 0.35/0.67                      = B3 ) )
% 0.35/0.67               => ( ! [B3: real] :
% 0.35/0.67                      ( ( member_real @ B3 @ ( minus_minus_set_real @ T4 @ T5 ) )
% 0.35/0.67                     => ( member_int @ ( I2 @ B3 ) @ ( minus_minus_set_int @ S2 @ S5 ) ) )
% 0.35/0.67                 => ( ! [A4: int] :
% 0.35/0.67                        ( ( member_int @ A4 @ S5 )
% 0.35/0.67                       => ( ( G @ A4 )
% 0.35/0.67                          = one_one_complex ) )
% 0.35/0.67                   => ( ! [B3: real] :
% 0.35/0.67                          ( ( member_real @ B3 @ T5 )
% 0.35/0.67                         => ( ( H2 @ B3 )
% 0.35/0.67                            = one_one_complex ) )
% 0.35/0.67                     => ( ! [A4: int] :
% 0.35/0.67                            ( ( member_int @ A4 @ S2 )
% 0.35/0.67                           => ( ( H2 @ ( J @ A4 ) )
% 0.35/0.67                              = ( G @ A4 ) ) )
% 0.35/0.67                       => ( ( groups7440179247065528705omplex @ G @ S2 )
% 0.35/0.67                          = ( groups713298508707869441omplex @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.reindex_bij_witness_not_neutral
% 0.35/0.67  thf(fact_8824_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.35/0.67      ! [S5: set_int,T5: set_int,S2: set_int,I2: int > int,J: int > int,T4: set_int,G: int > complex,H2: int > complex] :
% 0.35/0.67        ( ( finite_finite_int @ S5 )
% 0.35/0.67       => ( ( finite_finite_int @ T5 )
% 0.35/0.67         => ( ! [A4: int] :
% 0.35/0.67                ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 0.35/0.67               => ( ( I2 @ ( J @ A4 ) )
% 0.35/0.67                  = A4 ) )
% 0.35/0.67           => ( ! [A4: int] :
% 0.35/0.67                  ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 0.35/0.67                 => ( member_int @ ( J @ A4 ) @ ( minus_minus_set_int @ T4 @ T5 ) ) )
% 0.35/0.67             => ( ! [B3: int] :
% 0.35/0.67                    ( ( member_int @ B3 @ ( minus_minus_set_int @ T4 @ T5 ) )
% 0.35/0.67                   => ( ( J @ ( I2 @ B3 ) )
% 0.35/0.67                      = B3 ) )
% 0.35/0.67               => ( ! [B3: int] :
% 0.35/0.67                      ( ( member_int @ B3 @ ( minus_minus_set_int @ T4 @ T5 ) )
% 0.35/0.67                     => ( member_int @ ( I2 @ B3 ) @ ( minus_minus_set_int @ S2 @ S5 ) ) )
% 0.35/0.67                 => ( ! [A4: int] :
% 0.35/0.67                        ( ( member_int @ A4 @ S5 )
% 0.35/0.67                       => ( ( G @ A4 )
% 0.35/0.67                          = one_one_complex ) )
% 0.35/0.67                   => ( ! [B3: int] :
% 0.35/0.67                          ( ( member_int @ B3 @ T5 )
% 0.35/0.67                         => ( ( H2 @ B3 )
% 0.35/0.67                            = one_one_complex ) )
% 0.35/0.67                     => ( ! [A4: int] :
% 0.35/0.67                            ( ( member_int @ A4 @ S2 )
% 0.35/0.67                           => ( ( H2 @ ( J @ A4 ) )
% 0.35/0.67                              = ( G @ A4 ) ) )
% 0.35/0.67                       => ( ( groups7440179247065528705omplex @ G @ S2 )
% 0.35/0.67                          = ( groups7440179247065528705omplex @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.reindex_bij_witness_not_neutral
% 0.35/0.67  thf(fact_8825_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.35/0.67      ! [S5: set_real,T5: set_complex,S2: set_real,I2: complex > real,J: real > complex,T4: set_complex,G: real > complex,H2: complex > complex] :
% 0.35/0.67        ( ( finite_finite_real @ S5 )
% 0.35/0.67       => ( ( finite3207457112153483333omplex @ T5 )
% 0.35/0.67         => ( ! [A4: real] :
% 0.35/0.67                ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 0.35/0.67               => ( ( I2 @ ( J @ A4 ) )
% 0.35/0.67                  = A4 ) )
% 0.35/0.67           => ( ! [A4: real] :
% 0.35/0.67                  ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 0.35/0.67                 => ( member_complex @ ( J @ A4 ) @ ( minus_811609699411566653omplex @ T4 @ T5 ) ) )
% 0.35/0.67             => ( ! [B3: complex] :
% 0.35/0.67                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T4 @ T5 ) )
% 0.35/0.67                   => ( ( J @ ( I2 @ B3 ) )
% 0.35/0.67                      = B3 ) )
% 0.35/0.67               => ( ! [B3: complex] :
% 0.35/0.67                      ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T4 @ T5 ) )
% 0.35/0.67                     => ( member_real @ ( I2 @ B3 ) @ ( minus_minus_set_real @ S2 @ S5 ) ) )
% 0.35/0.67                 => ( ! [A4: real] :
% 0.35/0.67                        ( ( member_real @ A4 @ S5 )
% 0.35/0.67                       => ( ( G @ A4 )
% 0.35/0.67                          = one_one_complex ) )
% 0.35/0.67                   => ( ! [B3: complex] :
% 0.35/0.67                          ( ( member_complex @ B3 @ T5 )
% 0.35/0.67                         => ( ( H2 @ B3 )
% 0.35/0.67                            = one_one_complex ) )
% 0.35/0.67                     => ( ! [A4: real] :
% 0.35/0.67                            ( ( member_real @ A4 @ S2 )
% 0.35/0.67                           => ( ( H2 @ ( J @ A4 ) )
% 0.35/0.67                              = ( G @ A4 ) ) )
% 0.35/0.67                       => ( ( groups713298508707869441omplex @ G @ S2 )
% 0.35/0.67                          = ( groups3708469109370488835omplex @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.reindex_bij_witness_not_neutral
% 0.35/0.67  thf(fact_8826_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.35/0.67      ! [S5: set_int,T5: set_complex,S2: set_int,I2: complex > int,J: int > complex,T4: set_complex,G: int > complex,H2: complex > complex] :
% 0.35/0.67        ( ( finite_finite_int @ S5 )
% 0.35/0.67       => ( ( finite3207457112153483333omplex @ T5 )
% 0.35/0.67         => ( ! [A4: int] :
% 0.35/0.67                ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 0.35/0.67               => ( ( I2 @ ( J @ A4 ) )
% 0.35/0.67                  = A4 ) )
% 0.35/0.67           => ( ! [A4: int] :
% 0.35/0.67                  ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 0.35/0.67                 => ( member_complex @ ( J @ A4 ) @ ( minus_811609699411566653omplex @ T4 @ T5 ) ) )
% 0.35/0.67             => ( ! [B3: complex] :
% 0.35/0.67                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T4 @ T5 ) )
% 0.35/0.67                   => ( ( J @ ( I2 @ B3 ) )
% 0.35/0.67                      = B3 ) )
% 0.35/0.67               => ( ! [B3: complex] :
% 0.35/0.67                      ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T4 @ T5 ) )
% 0.35/0.67                     => ( member_int @ ( I2 @ B3 ) @ ( minus_minus_set_int @ S2 @ S5 ) ) )
% 0.35/0.67                 => ( ! [A4: int] :
% 0.35/0.67                        ( ( member_int @ A4 @ S5 )
% 0.35/0.67                       => ( ( G @ A4 )
% 0.35/0.67                          = one_one_complex ) )
% 0.35/0.67                   => ( ! [B3: complex] :
% 0.35/0.67                          ( ( member_complex @ B3 @ T5 )
% 0.35/0.67                         => ( ( H2 @ B3 )
% 0.35/0.67                            = one_one_complex ) )
% 0.35/0.67                     => ( ! [A4: int] :
% 0.35/0.67                            ( ( member_int @ A4 @ S2 )
% 0.35/0.67                           => ( ( H2 @ ( J @ A4 ) )
% 0.35/0.67                              = ( G @ A4 ) ) )
% 0.35/0.67                       => ( ( groups7440179247065528705omplex @ G @ S2 )
% 0.35/0.67                          = ( groups3708469109370488835omplex @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.reindex_bij_witness_not_neutral
% 0.35/0.67  thf(fact_8827_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.35/0.67      ! [S5: set_complex,T5: set_real,S2: set_complex,I2: real > complex,J: complex > real,T4: set_real,G: complex > complex,H2: real > complex] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ S5 )
% 0.35/0.67       => ( ( finite_finite_real @ T5 )
% 0.35/0.67         => ( ! [A4: complex] :
% 0.35/0.67                ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ S2 @ S5 ) )
% 0.35/0.67               => ( ( I2 @ ( J @ A4 ) )
% 0.35/0.67                  = A4 ) )
% 0.35/0.67           => ( ! [A4: complex] :
% 0.35/0.67                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ S2 @ S5 ) )
% 0.35/0.67                 => ( member_real @ ( J @ A4 ) @ ( minus_minus_set_real @ T4 @ T5 ) ) )
% 0.35/0.67             => ( ! [B3: real] :
% 0.35/0.67                    ( ( member_real @ B3 @ ( minus_minus_set_real @ T4 @ T5 ) )
% 0.35/0.67                   => ( ( J @ ( I2 @ B3 ) )
% 0.35/0.67                      = B3 ) )
% 0.35/0.67               => ( ! [B3: real] :
% 0.35/0.67                      ( ( member_real @ B3 @ ( minus_minus_set_real @ T4 @ T5 ) )
% 0.35/0.67                     => ( member_complex @ ( I2 @ B3 ) @ ( minus_811609699411566653omplex @ S2 @ S5 ) ) )
% 0.35/0.67                 => ( ! [A4: complex] :
% 0.35/0.67                        ( ( member_complex @ A4 @ S5 )
% 0.35/0.67                       => ( ( G @ A4 )
% 0.35/0.67                          = one_one_complex ) )
% 0.35/0.67                   => ( ! [B3: real] :
% 0.35/0.67                          ( ( member_real @ B3 @ T5 )
% 0.35/0.67                         => ( ( H2 @ B3 )
% 0.35/0.67                            = one_one_complex ) )
% 0.35/0.67                     => ( ! [A4: complex] :
% 0.35/0.67                            ( ( member_complex @ A4 @ S2 )
% 0.35/0.67                           => ( ( H2 @ ( J @ A4 ) )
% 0.35/0.67                              = ( G @ A4 ) ) )
% 0.35/0.67                       => ( ( groups3708469109370488835omplex @ G @ S2 )
% 0.35/0.67                          = ( groups713298508707869441omplex @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.reindex_bij_witness_not_neutral
% 0.35/0.67  thf(fact_8828_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.35/0.67      ! [S5: set_complex,T5: set_int,S2: set_complex,I2: int > complex,J: complex > int,T4: set_int,G: complex > complex,H2: int > complex] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ S5 )
% 0.35/0.67       => ( ( finite_finite_int @ T5 )
% 0.35/0.67         => ( ! [A4: complex] :
% 0.35/0.67                ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ S2 @ S5 ) )
% 0.35/0.67               => ( ( I2 @ ( J @ A4 ) )
% 0.35/0.67                  = A4 ) )
% 0.35/0.67           => ( ! [A4: complex] :
% 0.35/0.67                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ S2 @ S5 ) )
% 0.35/0.67                 => ( member_int @ ( J @ A4 ) @ ( minus_minus_set_int @ T4 @ T5 ) ) )
% 0.35/0.67             => ( ! [B3: int] :
% 0.35/0.67                    ( ( member_int @ B3 @ ( minus_minus_set_int @ T4 @ T5 ) )
% 0.35/0.67                   => ( ( J @ ( I2 @ B3 ) )
% 0.35/0.67                      = B3 ) )
% 0.35/0.67               => ( ! [B3: int] :
% 0.35/0.67                      ( ( member_int @ B3 @ ( minus_minus_set_int @ T4 @ T5 ) )
% 0.35/0.67                     => ( member_complex @ ( I2 @ B3 ) @ ( minus_811609699411566653omplex @ S2 @ S5 ) ) )
% 0.35/0.67                 => ( ! [A4: complex] :
% 0.35/0.67                        ( ( member_complex @ A4 @ S5 )
% 0.35/0.67                       => ( ( G @ A4 )
% 0.35/0.67                          = one_one_complex ) )
% 0.35/0.67                   => ( ! [B3: int] :
% 0.35/0.67                          ( ( member_int @ B3 @ T5 )
% 0.35/0.67                         => ( ( H2 @ B3 )
% 0.35/0.67                            = one_one_complex ) )
% 0.35/0.67                     => ( ! [A4: complex] :
% 0.35/0.67                            ( ( member_complex @ A4 @ S2 )
% 0.35/0.67                           => ( ( H2 @ ( J @ A4 ) )
% 0.35/0.67                              = ( G @ A4 ) ) )
% 0.35/0.67                       => ( ( groups3708469109370488835omplex @ G @ S2 )
% 0.35/0.67                          = ( groups7440179247065528705omplex @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.reindex_bij_witness_not_neutral
% 0.35/0.67  thf(fact_8829_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.35/0.67      ! [S5: set_complex,T5: set_complex,S2: set_complex,I2: complex > complex,J: complex > complex,T4: set_complex,G: complex > complex,H2: complex > complex] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ S5 )
% 0.35/0.67       => ( ( finite3207457112153483333omplex @ T5 )
% 0.35/0.67         => ( ! [A4: complex] :
% 0.35/0.67                ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ S2 @ S5 ) )
% 0.35/0.67               => ( ( I2 @ ( J @ A4 ) )
% 0.35/0.67                  = A4 ) )
% 0.35/0.67           => ( ! [A4: complex] :
% 0.35/0.67                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ S2 @ S5 ) )
% 0.35/0.67                 => ( member_complex @ ( J @ A4 ) @ ( minus_811609699411566653omplex @ T4 @ T5 ) ) )
% 0.35/0.67             => ( ! [B3: complex] :
% 0.35/0.67                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T4 @ T5 ) )
% 0.35/0.67                   => ( ( J @ ( I2 @ B3 ) )
% 0.35/0.67                      = B3 ) )
% 0.35/0.67               => ( ! [B3: complex] :
% 0.35/0.67                      ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T4 @ T5 ) )
% 0.35/0.67                     => ( member_complex @ ( I2 @ B3 ) @ ( minus_811609699411566653omplex @ S2 @ S5 ) ) )
% 0.35/0.67                 => ( ! [A4: complex] :
% 0.35/0.67                        ( ( member_complex @ A4 @ S5 )
% 0.35/0.67                       => ( ( G @ A4 )
% 0.35/0.67                          = one_one_complex ) )
% 0.35/0.67                   => ( ! [B3: complex] :
% 0.35/0.67                          ( ( member_complex @ B3 @ T5 )
% 0.35/0.67                         => ( ( H2 @ B3 )
% 0.35/0.67                            = one_one_complex ) )
% 0.35/0.67                     => ( ! [A4: complex] :
% 0.35/0.67                            ( ( member_complex @ A4 @ S2 )
% 0.35/0.67                           => ( ( H2 @ ( J @ A4 ) )
% 0.35/0.67                              = ( G @ A4 ) ) )
% 0.35/0.67                       => ( ( groups3708469109370488835omplex @ G @ S2 )
% 0.35/0.67                          = ( groups3708469109370488835omplex @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.reindex_bij_witness_not_neutral
% 0.35/0.67  thf(fact_8830_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.35/0.67      ! [S5: set_real,T5: set_real,S2: set_real,I2: real > real,J: real > real,T4: set_real,G: real > real,H2: real > real] :
% 0.35/0.67        ( ( finite_finite_real @ S5 )
% 0.35/0.67       => ( ( finite_finite_real @ T5 )
% 0.35/0.67         => ( ! [A4: real] :
% 0.35/0.67                ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 0.35/0.67               => ( ( I2 @ ( J @ A4 ) )
% 0.35/0.67                  = A4 ) )
% 0.35/0.67           => ( ! [A4: real] :
% 0.35/0.67                  ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 0.35/0.67                 => ( member_real @ ( J @ A4 ) @ ( minus_minus_set_real @ T4 @ T5 ) ) )
% 0.35/0.67             => ( ! [B3: real] :
% 0.35/0.67                    ( ( member_real @ B3 @ ( minus_minus_set_real @ T4 @ T5 ) )
% 0.35/0.67                   => ( ( J @ ( I2 @ B3 ) )
% 0.35/0.67                      = B3 ) )
% 0.35/0.67               => ( ! [B3: real] :
% 0.35/0.67                      ( ( member_real @ B3 @ ( minus_minus_set_real @ T4 @ T5 ) )
% 0.35/0.67                     => ( member_real @ ( I2 @ B3 ) @ ( minus_minus_set_real @ S2 @ S5 ) ) )
% 0.35/0.67                 => ( ! [A4: real] :
% 0.35/0.67                        ( ( member_real @ A4 @ S5 )
% 0.35/0.67                       => ( ( G @ A4 )
% 0.35/0.67                          = one_one_real ) )
% 0.35/0.67                   => ( ! [B3: real] :
% 0.35/0.67                          ( ( member_real @ B3 @ T5 )
% 0.35/0.67                         => ( ( H2 @ B3 )
% 0.35/0.67                            = one_one_real ) )
% 0.35/0.67                     => ( ! [A4: real] :
% 0.35/0.67                            ( ( member_real @ A4 @ S2 )
% 0.35/0.67                           => ( ( H2 @ ( J @ A4 ) )
% 0.35/0.67                              = ( G @ A4 ) ) )
% 0.35/0.67                       => ( ( groups1681761925125756287l_real @ G @ S2 )
% 0.35/0.67                          = ( groups1681761925125756287l_real @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.reindex_bij_witness_not_neutral
% 0.35/0.67  thf(fact_8831_prod_Osetdiff__irrelevant,axiom,
% 0.35/0.67      ! [A2: set_real,G: real > complex] :
% 0.35/0.67        ( ( finite_finite_real @ A2 )
% 0.35/0.67       => ( ( groups713298508707869441omplex @ G
% 0.35/0.67            @ ( minus_minus_set_real @ A2
% 0.35/0.67              @ ( collect_real
% 0.35/0.67                @ ^ [X2: real] :
% 0.35/0.67                    ( ( G @ X2 )
% 0.35/0.67                    = one_one_complex ) ) ) )
% 0.35/0.67          = ( groups713298508707869441omplex @ G @ A2 ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.setdiff_irrelevant
% 0.35/0.67  thf(fact_8832_prod_Osetdiff__irrelevant,axiom,
% 0.35/0.67      ! [A2: set_complex,G: complex > complex] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.67       => ( ( groups3708469109370488835omplex @ G
% 0.35/0.67            @ ( minus_811609699411566653omplex @ A2
% 0.35/0.67              @ ( collect_complex
% 0.35/0.67                @ ^ [X2: complex] :
% 0.35/0.67                    ( ( G @ X2 )
% 0.35/0.67                    = one_one_complex ) ) ) )
% 0.35/0.67          = ( groups3708469109370488835omplex @ G @ A2 ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.setdiff_irrelevant
% 0.35/0.67  thf(fact_8833_prod_Osetdiff__irrelevant,axiom,
% 0.35/0.67      ! [A2: set_real,G: real > real] :
% 0.35/0.67        ( ( finite_finite_real @ A2 )
% 0.35/0.67       => ( ( groups1681761925125756287l_real @ G
% 0.35/0.67            @ ( minus_minus_set_real @ A2
% 0.35/0.67              @ ( collect_real
% 0.35/0.67                @ ^ [X2: real] :
% 0.35/0.67                    ( ( G @ X2 )
% 0.35/0.67                    = one_one_real ) ) ) )
% 0.35/0.67          = ( groups1681761925125756287l_real @ G @ A2 ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.setdiff_irrelevant
% 0.35/0.67  thf(fact_8834_prod_Osetdiff__irrelevant,axiom,
% 0.35/0.67      ! [A2: set_complex,G: complex > real] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.67       => ( ( groups766887009212190081x_real @ G
% 0.35/0.67            @ ( minus_811609699411566653omplex @ A2
% 0.35/0.67              @ ( collect_complex
% 0.35/0.67                @ ^ [X2: complex] :
% 0.35/0.67                    ( ( G @ X2 )
% 0.35/0.67                    = one_one_real ) ) ) )
% 0.35/0.67          = ( groups766887009212190081x_real @ G @ A2 ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.setdiff_irrelevant
% 0.35/0.67  thf(fact_8835_prod_Osetdiff__irrelevant,axiom,
% 0.35/0.67      ! [A2: set_real,G: real > rat] :
% 0.35/0.67        ( ( finite_finite_real @ A2 )
% 0.35/0.67       => ( ( groups4061424788464935467al_rat @ G
% 0.35/0.67            @ ( minus_minus_set_real @ A2
% 0.35/0.67              @ ( collect_real
% 0.35/0.67                @ ^ [X2: real] :
% 0.35/0.67                    ( ( G @ X2 )
% 0.35/0.67                    = one_one_rat ) ) ) )
% 0.35/0.67          = ( groups4061424788464935467al_rat @ G @ A2 ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.setdiff_irrelevant
% 0.35/0.67  thf(fact_8836_prod_Osetdiff__irrelevant,axiom,
% 0.35/0.67      ! [A2: set_complex,G: complex > rat] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.67       => ( ( groups225925009352817453ex_rat @ G
% 0.35/0.67            @ ( minus_811609699411566653omplex @ A2
% 0.35/0.67              @ ( collect_complex
% 0.35/0.67                @ ^ [X2: complex] :
% 0.35/0.67                    ( ( G @ X2 )
% 0.35/0.67                    = one_one_rat ) ) ) )
% 0.35/0.67          = ( groups225925009352817453ex_rat @ G @ A2 ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.setdiff_irrelevant
% 0.35/0.67  thf(fact_8837_prod_Osetdiff__irrelevant,axiom,
% 0.35/0.67      ! [A2: set_real,G: real > nat] :
% 0.35/0.67        ( ( finite_finite_real @ A2 )
% 0.35/0.67       => ( ( groups4696554848551431203al_nat @ G
% 0.35/0.67            @ ( minus_minus_set_real @ A2
% 0.35/0.67              @ ( collect_real
% 0.35/0.67                @ ^ [X2: real] :
% 0.35/0.67                    ( ( G @ X2 )
% 0.35/0.67                    = one_one_nat ) ) ) )
% 0.35/0.67          = ( groups4696554848551431203al_nat @ G @ A2 ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.setdiff_irrelevant
% 0.35/0.67  thf(fact_8838_prod_Osetdiff__irrelevant,axiom,
% 0.35/0.67      ! [A2: set_complex,G: complex > nat] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.67       => ( ( groups861055069439313189ex_nat @ G
% 0.35/0.67            @ ( minus_811609699411566653omplex @ A2
% 0.35/0.67              @ ( collect_complex
% 0.35/0.67                @ ^ [X2: complex] :
% 0.35/0.67                    ( ( G @ X2 )
% 0.35/0.67                    = one_one_nat ) ) ) )
% 0.35/0.67          = ( groups861055069439313189ex_nat @ G @ A2 ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.setdiff_irrelevant
% 0.35/0.67  thf(fact_8839_prod_Osetdiff__irrelevant,axiom,
% 0.35/0.67      ! [A2: set_real,G: real > int] :
% 0.35/0.67        ( ( finite_finite_real @ A2 )
% 0.35/0.67       => ( ( groups4694064378042380927al_int @ G
% 0.35/0.67            @ ( minus_minus_set_real @ A2
% 0.35/0.67              @ ( collect_real
% 0.35/0.67                @ ^ [X2: real] :
% 0.35/0.67                    ( ( G @ X2 )
% 0.35/0.67                    = one_one_int ) ) ) )
% 0.35/0.67          = ( groups4694064378042380927al_int @ G @ A2 ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.setdiff_irrelevant
% 0.35/0.67  thf(fact_8840_prod_Osetdiff__irrelevant,axiom,
% 0.35/0.67      ! [A2: set_complex,G: complex > int] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.67       => ( ( groups858564598930262913ex_int @ G
% 0.35/0.67            @ ( minus_811609699411566653omplex @ A2
% 0.35/0.67              @ ( collect_complex
% 0.35/0.67                @ ^ [X2: complex] :
% 0.35/0.67                    ( ( G @ X2 )
% 0.35/0.67                    = one_one_int ) ) ) )
% 0.35/0.67          = ( groups858564598930262913ex_int @ G @ A2 ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.setdiff_irrelevant
% 0.35/0.67  thf(fact_8841_prod_Onat__diff__reindex,axiom,
% 0.35/0.67      ! [G: nat > nat,N: nat] :
% 0.35/0.67        ( ( groups708209901874060359at_nat
% 0.35/0.67          @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 0.35/0.67          @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.67        = ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.nat_diff_reindex
% 0.35/0.67  thf(fact_8842_prod_Onat__diff__reindex,axiom,
% 0.35/0.67      ! [G: nat > int,N: nat] :
% 0.35/0.67        ( ( groups705719431365010083at_int
% 0.35/0.67          @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 0.35/0.67          @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.67        = ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.nat_diff_reindex
% 0.35/0.67  thf(fact_8843_prod_OatLeastAtMost__rev,axiom,
% 0.35/0.67      ! [G: nat > nat,N: nat,M: nat] :
% 0.35/0.67        ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 0.35/0.67        = ( groups708209901874060359at_nat
% 0.35/0.67          @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I3 ) )
% 0.35/0.67          @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.atLeastAtMost_rev
% 0.35/0.67  thf(fact_8844_prod_OatLeastAtMost__rev,axiom,
% 0.35/0.67      ! [G: nat > int,N: nat,M: nat] :
% 0.35/0.67        ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 0.35/0.67        = ( groups705719431365010083at_int
% 0.35/0.67          @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I3 ) )
% 0.35/0.67          @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.atLeastAtMost_rev
% 0.35/0.67  thf(fact_8845_less__1__prod2,axiom,
% 0.35/0.67      ! [I6: set_real,I2: real,F: real > real] :
% 0.35/0.67        ( ( finite_finite_real @ I6 )
% 0.35/0.67       => ( ( member_real @ I2 @ I6 )
% 0.35/0.67         => ( ( ord_less_real @ one_one_real @ ( F @ I2 ) )
% 0.35/0.67           => ( ! [I4: real] :
% 0.35/0.67                  ( ( member_real @ I4 @ I6 )
% 0.35/0.67                 => ( ord_less_eq_real @ one_one_real @ ( F @ I4 ) ) )
% 0.35/0.67             => ( ord_less_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ I6 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % less_1_prod2
% 0.35/0.67  thf(fact_8846_less__1__prod2,axiom,
% 0.35/0.67      ! [I6: set_int,I2: int,F: int > real] :
% 0.35/0.67        ( ( finite_finite_int @ I6 )
% 0.35/0.67       => ( ( member_int @ I2 @ I6 )
% 0.35/0.67         => ( ( ord_less_real @ one_one_real @ ( F @ I2 ) )
% 0.35/0.67           => ( ! [I4: int] :
% 0.35/0.67                  ( ( member_int @ I4 @ I6 )
% 0.35/0.67                 => ( ord_less_eq_real @ one_one_real @ ( F @ I4 ) ) )
% 0.35/0.67             => ( ord_less_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ I6 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % less_1_prod2
% 0.35/0.67  thf(fact_8847_less__1__prod2,axiom,
% 0.35/0.67      ! [I6: set_nat,I2: nat,F: nat > real] :
% 0.35/0.67        ( ( finite_finite_nat @ I6 )
% 0.35/0.67       => ( ( member_nat @ I2 @ I6 )
% 0.35/0.67         => ( ( ord_less_real @ one_one_real @ ( F @ I2 ) )
% 0.35/0.67           => ( ! [I4: nat] :
% 0.35/0.67                  ( ( member_nat @ I4 @ I6 )
% 0.35/0.67                 => ( ord_less_eq_real @ one_one_real @ ( F @ I4 ) ) )
% 0.35/0.67             => ( ord_less_real @ one_one_real @ ( groups129246275422532515t_real @ F @ I6 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % less_1_prod2
% 0.35/0.67  thf(fact_8848_less__1__prod2,axiom,
% 0.35/0.67      ! [I6: set_complex,I2: complex,F: complex > real] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ I6 )
% 0.35/0.67       => ( ( member_complex @ I2 @ I6 )
% 0.35/0.67         => ( ( ord_less_real @ one_one_real @ ( F @ I2 ) )
% 0.35/0.67           => ( ! [I4: complex] :
% 0.35/0.67                  ( ( member_complex @ I4 @ I6 )
% 0.35/0.67                 => ( ord_less_eq_real @ one_one_real @ ( F @ I4 ) ) )
% 0.35/0.67             => ( ord_less_real @ one_one_real @ ( groups766887009212190081x_real @ F @ I6 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % less_1_prod2
% 0.35/0.67  thf(fact_8849_less__1__prod2,axiom,
% 0.35/0.67      ! [I6: set_real,I2: real,F: real > rat] :
% 0.35/0.67        ( ( finite_finite_real @ I6 )
% 0.35/0.67       => ( ( member_real @ I2 @ I6 )
% 0.35/0.67         => ( ( ord_less_rat @ one_one_rat @ ( F @ I2 ) )
% 0.35/0.67           => ( ! [I4: real] :
% 0.35/0.67                  ( ( member_real @ I4 @ I6 )
% 0.35/0.67                 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I4 ) ) )
% 0.35/0.67             => ( ord_less_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ I6 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % less_1_prod2
% 0.35/0.67  thf(fact_8850_less__1__prod2,axiom,
% 0.35/0.67      ! [I6: set_int,I2: int,F: int > rat] :
% 0.35/0.67        ( ( finite_finite_int @ I6 )
% 0.35/0.67       => ( ( member_int @ I2 @ I6 )
% 0.35/0.67         => ( ( ord_less_rat @ one_one_rat @ ( F @ I2 ) )
% 0.35/0.67           => ( ! [I4: int] :
% 0.35/0.67                  ( ( member_int @ I4 @ I6 )
% 0.35/0.67                 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I4 ) ) )
% 0.35/0.67             => ( ord_less_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ I6 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % less_1_prod2
% 0.35/0.67  thf(fact_8851_less__1__prod2,axiom,
% 0.35/0.67      ! [I6: set_nat,I2: nat,F: nat > rat] :
% 0.35/0.67        ( ( finite_finite_nat @ I6 )
% 0.35/0.67       => ( ( member_nat @ I2 @ I6 )
% 0.35/0.67         => ( ( ord_less_rat @ one_one_rat @ ( F @ I2 ) )
% 0.35/0.67           => ( ! [I4: nat] :
% 0.35/0.67                  ( ( member_nat @ I4 @ I6 )
% 0.35/0.67                 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I4 ) ) )
% 0.35/0.67             => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ I6 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % less_1_prod2
% 0.35/0.67  thf(fact_8852_less__1__prod2,axiom,
% 0.35/0.67      ! [I6: set_complex,I2: complex,F: complex > rat] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ I6 )
% 0.35/0.67       => ( ( member_complex @ I2 @ I6 )
% 0.35/0.67         => ( ( ord_less_rat @ one_one_rat @ ( F @ I2 ) )
% 0.35/0.67           => ( ! [I4: complex] :
% 0.35/0.67                  ( ( member_complex @ I4 @ I6 )
% 0.35/0.67                 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I4 ) ) )
% 0.35/0.67             => ( ord_less_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F @ I6 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % less_1_prod2
% 0.35/0.67  thf(fact_8853_less__1__prod2,axiom,
% 0.35/0.67      ! [I6: set_real,I2: real,F: real > int] :
% 0.35/0.67        ( ( finite_finite_real @ I6 )
% 0.35/0.67       => ( ( member_real @ I2 @ I6 )
% 0.35/0.67         => ( ( ord_less_int @ one_one_int @ ( F @ I2 ) )
% 0.35/0.67           => ( ! [I4: real] :
% 0.35/0.67                  ( ( member_real @ I4 @ I6 )
% 0.35/0.67                 => ( ord_less_eq_int @ one_one_int @ ( F @ I4 ) ) )
% 0.35/0.67             => ( ord_less_int @ one_one_int @ ( groups4694064378042380927al_int @ F @ I6 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % less_1_prod2
% 0.35/0.67  thf(fact_8854_less__1__prod2,axiom,
% 0.35/0.67      ! [I6: set_complex,I2: complex,F: complex > int] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ I6 )
% 0.35/0.67       => ( ( member_complex @ I2 @ I6 )
% 0.35/0.67         => ( ( ord_less_int @ one_one_int @ ( F @ I2 ) )
% 0.35/0.67           => ( ! [I4: complex] :
% 0.35/0.67                  ( ( member_complex @ I4 @ I6 )
% 0.35/0.67                 => ( ord_less_eq_int @ one_one_int @ ( F @ I4 ) ) )
% 0.35/0.67             => ( ord_less_int @ one_one_int @ ( groups858564598930262913ex_int @ F @ I6 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % less_1_prod2
% 0.35/0.67  thf(fact_8855_less__1__prod,axiom,
% 0.35/0.67      ! [I6: set_complex,F: complex > real] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ I6 )
% 0.35/0.67       => ( ( I6 != bot_bot_set_complex )
% 0.35/0.67         => ( ! [I4: complex] :
% 0.35/0.67                ( ( member_complex @ I4 @ I6 )
% 0.35/0.67               => ( ord_less_real @ one_one_real @ ( F @ I4 ) ) )
% 0.35/0.67           => ( ord_less_real @ one_one_real @ ( groups766887009212190081x_real @ F @ I6 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % less_1_prod
% 0.35/0.67  thf(fact_8856_less__1__prod,axiom,
% 0.35/0.67      ! [I6: set_nat,F: nat > real] :
% 0.35/0.67        ( ( finite_finite_nat @ I6 )
% 0.35/0.67       => ( ( I6 != bot_bot_set_nat )
% 0.35/0.67         => ( ! [I4: nat] :
% 0.35/0.67                ( ( member_nat @ I4 @ I6 )
% 0.35/0.67               => ( ord_less_real @ one_one_real @ ( F @ I4 ) ) )
% 0.35/0.67           => ( ord_less_real @ one_one_real @ ( groups129246275422532515t_real @ F @ I6 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % less_1_prod
% 0.35/0.67  thf(fact_8857_less__1__prod,axiom,
% 0.35/0.67      ! [I6: set_int,F: int > real] :
% 0.35/0.67        ( ( finite_finite_int @ I6 )
% 0.35/0.67       => ( ( I6 != bot_bot_set_int )
% 0.35/0.67         => ( ! [I4: int] :
% 0.35/0.67                ( ( member_int @ I4 @ I6 )
% 0.35/0.67               => ( ord_less_real @ one_one_real @ ( F @ I4 ) ) )
% 0.35/0.67           => ( ord_less_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ I6 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % less_1_prod
% 0.35/0.67  thf(fact_8858_less__1__prod,axiom,
% 0.35/0.67      ! [I6: set_real,F: real > real] :
% 0.35/0.67        ( ( finite_finite_real @ I6 )
% 0.35/0.67       => ( ( I6 != bot_bot_set_real )
% 0.35/0.67         => ( ! [I4: real] :
% 0.35/0.67                ( ( member_real @ I4 @ I6 )
% 0.35/0.67               => ( ord_less_real @ one_one_real @ ( F @ I4 ) ) )
% 0.35/0.67           => ( ord_less_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ I6 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % less_1_prod
% 0.35/0.67  thf(fact_8859_less__1__prod,axiom,
% 0.35/0.67      ! [I6: set_complex,F: complex > rat] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ I6 )
% 0.35/0.67       => ( ( I6 != bot_bot_set_complex )
% 0.35/0.67         => ( ! [I4: complex] :
% 0.35/0.67                ( ( member_complex @ I4 @ I6 )
% 0.35/0.67               => ( ord_less_rat @ one_one_rat @ ( F @ I4 ) ) )
% 0.35/0.67           => ( ord_less_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F @ I6 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % less_1_prod
% 0.35/0.67  thf(fact_8860_less__1__prod,axiom,
% 0.35/0.67      ! [I6: set_nat,F: nat > rat] :
% 0.35/0.67        ( ( finite_finite_nat @ I6 )
% 0.35/0.67       => ( ( I6 != bot_bot_set_nat )
% 0.35/0.67         => ( ! [I4: nat] :
% 0.35/0.67                ( ( member_nat @ I4 @ I6 )
% 0.35/0.67               => ( ord_less_rat @ one_one_rat @ ( F @ I4 ) ) )
% 0.35/0.67           => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ I6 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % less_1_prod
% 0.35/0.67  thf(fact_8861_less__1__prod,axiom,
% 0.35/0.67      ! [I6: set_int,F: int > rat] :
% 0.35/0.67        ( ( finite_finite_int @ I6 )
% 0.35/0.67       => ( ( I6 != bot_bot_set_int )
% 0.35/0.67         => ( ! [I4: int] :
% 0.35/0.67                ( ( member_int @ I4 @ I6 )
% 0.35/0.67               => ( ord_less_rat @ one_one_rat @ ( F @ I4 ) ) )
% 0.35/0.67           => ( ord_less_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ I6 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % less_1_prod
% 0.35/0.67  thf(fact_8862_less__1__prod,axiom,
% 0.35/0.67      ! [I6: set_real,F: real > rat] :
% 0.35/0.67        ( ( finite_finite_real @ I6 )
% 0.35/0.67       => ( ( I6 != bot_bot_set_real )
% 0.35/0.67         => ( ! [I4: real] :
% 0.35/0.67                ( ( member_real @ I4 @ I6 )
% 0.35/0.67               => ( ord_less_rat @ one_one_rat @ ( F @ I4 ) ) )
% 0.35/0.67           => ( ord_less_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ I6 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % less_1_prod
% 0.35/0.67  thf(fact_8863_less__1__prod,axiom,
% 0.35/0.67      ! [I6: set_complex,F: complex > int] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ I6 )
% 0.35/0.67       => ( ( I6 != bot_bot_set_complex )
% 0.35/0.67         => ( ! [I4: complex] :
% 0.35/0.67                ( ( member_complex @ I4 @ I6 )
% 0.35/0.67               => ( ord_less_int @ one_one_int @ ( F @ I4 ) ) )
% 0.35/0.67           => ( ord_less_int @ one_one_int @ ( groups858564598930262913ex_int @ F @ I6 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % less_1_prod
% 0.35/0.67  thf(fact_8864_less__1__prod,axiom,
% 0.35/0.67      ! [I6: set_real,F: real > int] :
% 0.35/0.67        ( ( finite_finite_real @ I6 )
% 0.35/0.67       => ( ( I6 != bot_bot_set_real )
% 0.35/0.67         => ( ! [I4: real] :
% 0.35/0.67                ( ( member_real @ I4 @ I6 )
% 0.35/0.67               => ( ord_less_int @ one_one_int @ ( F @ I4 ) ) )
% 0.35/0.67           => ( ord_less_int @ one_one_int @ ( groups4694064378042380927al_int @ F @ I6 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % less_1_prod
% 0.35/0.67  thf(fact_8865_prod_Osubset__diff,axiom,
% 0.35/0.67      ! [B2: set_complex,A2: set_complex,G: complex > complex] :
% 0.35/0.67        ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 0.35/0.67       => ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.67         => ( ( groups3708469109370488835omplex @ G @ A2 )
% 0.35/0.67            = ( times_times_complex @ ( groups3708469109370488835omplex @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups3708469109370488835omplex @ G @ B2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.subset_diff
% 0.35/0.67  thf(fact_8866_prod_Osubset__diff,axiom,
% 0.35/0.67      ! [B2: set_complex,A2: set_complex,G: complex > real] :
% 0.35/0.67        ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 0.35/0.67       => ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.67         => ( ( groups766887009212190081x_real @ G @ A2 )
% 0.35/0.67            = ( times_times_real @ ( groups766887009212190081x_real @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups766887009212190081x_real @ G @ B2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.subset_diff
% 0.35/0.67  thf(fact_8867_prod_Osubset__diff,axiom,
% 0.35/0.67      ! [B2: set_complex,A2: set_complex,G: complex > nat] :
% 0.35/0.67        ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 0.35/0.67       => ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.67         => ( ( groups861055069439313189ex_nat @ G @ A2 )
% 0.35/0.67            = ( times_times_nat @ ( groups861055069439313189ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups861055069439313189ex_nat @ G @ B2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.subset_diff
% 0.35/0.67  thf(fact_8868_prod_Osubset__diff,axiom,
% 0.35/0.67      ! [B2: set_complex,A2: set_complex,G: complex > int] :
% 0.35/0.67        ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 0.35/0.67       => ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.67         => ( ( groups858564598930262913ex_int @ G @ A2 )
% 0.35/0.67            = ( times_times_int @ ( groups858564598930262913ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups858564598930262913ex_int @ G @ B2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.subset_diff
% 0.35/0.67  thf(fact_8869_prod_Osubset__diff,axiom,
% 0.35/0.67      ! [B2: set_real,A2: set_real,G: real > complex] :
% 0.35/0.67        ( ( ord_less_eq_set_real @ B2 @ A2 )
% 0.35/0.67       => ( ( finite_finite_real @ A2 )
% 0.35/0.67         => ( ( groups713298508707869441omplex @ G @ A2 )
% 0.35/0.67            = ( times_times_complex @ ( groups713298508707869441omplex @ G @ ( minus_minus_set_real @ A2 @ B2 ) ) @ ( groups713298508707869441omplex @ G @ B2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.subset_diff
% 0.35/0.67  thf(fact_8870_prod_Osubset__diff,axiom,
% 0.35/0.67      ! [B2: set_real,A2: set_real,G: real > real] :
% 0.35/0.67        ( ( ord_less_eq_set_real @ B2 @ A2 )
% 0.35/0.67       => ( ( finite_finite_real @ A2 )
% 0.35/0.67         => ( ( groups1681761925125756287l_real @ G @ A2 )
% 0.35/0.67            = ( times_times_real @ ( groups1681761925125756287l_real @ G @ ( minus_minus_set_real @ A2 @ B2 ) ) @ ( groups1681761925125756287l_real @ G @ B2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.subset_diff
% 0.35/0.67  thf(fact_8871_prod_Osubset__diff,axiom,
% 0.35/0.67      ! [B2: set_real,A2: set_real,G: real > nat] :
% 0.35/0.67        ( ( ord_less_eq_set_real @ B2 @ A2 )
% 0.35/0.67       => ( ( finite_finite_real @ A2 )
% 0.35/0.67         => ( ( groups4696554848551431203al_nat @ G @ A2 )
% 0.35/0.67            = ( times_times_nat @ ( groups4696554848551431203al_nat @ G @ ( minus_minus_set_real @ A2 @ B2 ) ) @ ( groups4696554848551431203al_nat @ G @ B2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.subset_diff
% 0.35/0.67  thf(fact_8872_prod_Osubset__diff,axiom,
% 0.35/0.67      ! [B2: set_real,A2: set_real,G: real > int] :
% 0.35/0.67        ( ( ord_less_eq_set_real @ B2 @ A2 )
% 0.35/0.67       => ( ( finite_finite_real @ A2 )
% 0.35/0.67         => ( ( groups4694064378042380927al_int @ G @ A2 )
% 0.35/0.67            = ( times_times_int @ ( groups4694064378042380927al_int @ G @ ( minus_minus_set_real @ A2 @ B2 ) ) @ ( groups4694064378042380927al_int @ G @ B2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.subset_diff
% 0.35/0.67  thf(fact_8873_prod_Osubset__diff,axiom,
% 0.35/0.67      ! [B2: set_nat,A2: set_nat,G: nat > complex] :
% 0.35/0.67        ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 0.35/0.67       => ( ( finite_finite_nat @ A2 )
% 0.35/0.67         => ( ( groups6464643781859351333omplex @ G @ A2 )
% 0.35/0.67            = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups6464643781859351333omplex @ G @ B2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.subset_diff
% 0.35/0.67  thf(fact_8874_prod_Osubset__diff,axiom,
% 0.35/0.67      ! [B2: set_nat,A2: set_nat,G: nat > real] :
% 0.35/0.67        ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 0.35/0.67       => ( ( finite_finite_nat @ A2 )
% 0.35/0.67         => ( ( groups129246275422532515t_real @ G @ A2 )
% 0.35/0.67            = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups129246275422532515t_real @ G @ B2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.subset_diff
% 0.35/0.67  thf(fact_8875_prod_Omono__neutral__cong__right,axiom,
% 0.35/0.67      ! [T4: set_int,S2: set_int,G: int > complex,H2: int > complex] :
% 0.35/0.67        ( ( finite_finite_int @ T4 )
% 0.35/0.67       => ( ( ord_less_eq_set_int @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: int] :
% 0.35/0.67                ( ( member_int @ X3 @ ( minus_minus_set_int @ T4 @ S2 ) )
% 0.35/0.67               => ( ( G @ X3 )
% 0.35/0.67                  = one_one_complex ) )
% 0.35/0.67           => ( ! [X3: int] :
% 0.35/0.67                  ( ( member_int @ X3 @ S2 )
% 0.35/0.67                 => ( ( G @ X3 )
% 0.35/0.67                    = ( H2 @ X3 ) ) )
% 0.35/0.67             => ( ( groups7440179247065528705omplex @ G @ T4 )
% 0.35/0.67                = ( groups7440179247065528705omplex @ H2 @ S2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_cong_right
% 0.35/0.67  thf(fact_8876_prod_Omono__neutral__cong__right,axiom,
% 0.35/0.67      ! [T4: set_complex,S2: set_complex,G: complex > complex,H2: complex > complex] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.67       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: complex] :
% 0.35/0.67                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 0.35/0.67               => ( ( G @ X3 )
% 0.35/0.67                  = one_one_complex ) )
% 0.35/0.67           => ( ! [X3: complex] :
% 0.35/0.67                  ( ( member_complex @ X3 @ S2 )
% 0.35/0.67                 => ( ( G @ X3 )
% 0.35/0.67                    = ( H2 @ X3 ) ) )
% 0.35/0.67             => ( ( groups3708469109370488835omplex @ G @ T4 )
% 0.35/0.67                = ( groups3708469109370488835omplex @ H2 @ S2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_cong_right
% 0.35/0.67  thf(fact_8877_prod_Omono__neutral__cong__right,axiom,
% 0.35/0.67      ! [T4: set_int,S2: set_int,G: int > real,H2: int > real] :
% 0.35/0.67        ( ( finite_finite_int @ T4 )
% 0.35/0.67       => ( ( ord_less_eq_set_int @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: int] :
% 0.35/0.67                ( ( member_int @ X3 @ ( minus_minus_set_int @ T4 @ S2 ) )
% 0.35/0.67               => ( ( G @ X3 )
% 0.35/0.67                  = one_one_real ) )
% 0.35/0.67           => ( ! [X3: int] :
% 0.35/0.67                  ( ( member_int @ X3 @ S2 )
% 0.35/0.67                 => ( ( G @ X3 )
% 0.35/0.67                    = ( H2 @ X3 ) ) )
% 0.35/0.67             => ( ( groups2316167850115554303t_real @ G @ T4 )
% 0.35/0.67                = ( groups2316167850115554303t_real @ H2 @ S2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_cong_right
% 0.35/0.67  thf(fact_8878_prod_Omono__neutral__cong__right,axiom,
% 0.35/0.67      ! [T4: set_complex,S2: set_complex,G: complex > real,H2: complex > real] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.67       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: complex] :
% 0.35/0.67                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 0.35/0.67               => ( ( G @ X3 )
% 0.35/0.67                  = one_one_real ) )
% 0.35/0.67           => ( ! [X3: complex] :
% 0.35/0.67                  ( ( member_complex @ X3 @ S2 )
% 0.35/0.67                 => ( ( G @ X3 )
% 0.35/0.67                    = ( H2 @ X3 ) ) )
% 0.35/0.67             => ( ( groups766887009212190081x_real @ G @ T4 )
% 0.35/0.67                = ( groups766887009212190081x_real @ H2 @ S2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_cong_right
% 0.35/0.67  thf(fact_8879_prod_Omono__neutral__cong__right,axiom,
% 0.35/0.67      ! [T4: set_int,S2: set_int,G: int > rat,H2: int > rat] :
% 0.35/0.67        ( ( finite_finite_int @ T4 )
% 0.35/0.67       => ( ( ord_less_eq_set_int @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: int] :
% 0.35/0.67                ( ( member_int @ X3 @ ( minus_minus_set_int @ T4 @ S2 ) )
% 0.35/0.67               => ( ( G @ X3 )
% 0.35/0.67                  = one_one_rat ) )
% 0.35/0.67           => ( ! [X3: int] :
% 0.35/0.67                  ( ( member_int @ X3 @ S2 )
% 0.35/0.67                 => ( ( G @ X3 )
% 0.35/0.67                    = ( H2 @ X3 ) ) )
% 0.35/0.67             => ( ( groups1072433553688619179nt_rat @ G @ T4 )
% 0.35/0.67                = ( groups1072433553688619179nt_rat @ H2 @ S2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_cong_right
% 0.35/0.67  thf(fact_8880_prod_Omono__neutral__cong__right,axiom,
% 0.35/0.67      ! [T4: set_complex,S2: set_complex,G: complex > rat,H2: complex > rat] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.67       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: complex] :
% 0.35/0.67                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 0.35/0.67               => ( ( G @ X3 )
% 0.35/0.67                  = one_one_rat ) )
% 0.35/0.67           => ( ! [X3: complex] :
% 0.35/0.67                  ( ( member_complex @ X3 @ S2 )
% 0.35/0.67                 => ( ( G @ X3 )
% 0.35/0.67                    = ( H2 @ X3 ) ) )
% 0.35/0.67             => ( ( groups225925009352817453ex_rat @ G @ T4 )
% 0.35/0.67                = ( groups225925009352817453ex_rat @ H2 @ S2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_cong_right
% 0.35/0.67  thf(fact_8881_prod_Omono__neutral__cong__right,axiom,
% 0.35/0.67      ! [T4: set_int,S2: set_int,G: int > nat,H2: int > nat] :
% 0.35/0.67        ( ( finite_finite_int @ T4 )
% 0.35/0.67       => ( ( ord_less_eq_set_int @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: int] :
% 0.35/0.67                ( ( member_int @ X3 @ ( minus_minus_set_int @ T4 @ S2 ) )
% 0.35/0.67               => ( ( G @ X3 )
% 0.35/0.67                  = one_one_nat ) )
% 0.35/0.67           => ( ! [X3: int] :
% 0.35/0.67                  ( ( member_int @ X3 @ S2 )
% 0.35/0.67                 => ( ( G @ X3 )
% 0.35/0.67                    = ( H2 @ X3 ) ) )
% 0.35/0.67             => ( ( groups1707563613775114915nt_nat @ G @ T4 )
% 0.35/0.67                = ( groups1707563613775114915nt_nat @ H2 @ S2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_cong_right
% 0.35/0.67  thf(fact_8882_prod_Omono__neutral__cong__right,axiom,
% 0.35/0.67      ! [T4: set_complex,S2: set_complex,G: complex > nat,H2: complex > nat] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.67       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: complex] :
% 0.35/0.67                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 0.35/0.67               => ( ( G @ X3 )
% 0.35/0.67                  = one_one_nat ) )
% 0.35/0.67           => ( ! [X3: complex] :
% 0.35/0.67                  ( ( member_complex @ X3 @ S2 )
% 0.35/0.67                 => ( ( G @ X3 )
% 0.35/0.67                    = ( H2 @ X3 ) ) )
% 0.35/0.67             => ( ( groups861055069439313189ex_nat @ G @ T4 )
% 0.35/0.67                = ( groups861055069439313189ex_nat @ H2 @ S2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_cong_right
% 0.35/0.67  thf(fact_8883_prod_Omono__neutral__cong__right,axiom,
% 0.35/0.67      ! [T4: set_complex,S2: set_complex,G: complex > int,H2: complex > int] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.67       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: complex] :
% 0.35/0.67                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 0.35/0.67               => ( ( G @ X3 )
% 0.35/0.67                  = one_one_int ) )
% 0.35/0.67           => ( ! [X3: complex] :
% 0.35/0.67                  ( ( member_complex @ X3 @ S2 )
% 0.35/0.67                 => ( ( G @ X3 )
% 0.35/0.67                    = ( H2 @ X3 ) ) )
% 0.35/0.67             => ( ( groups858564598930262913ex_int @ G @ T4 )
% 0.35/0.67                = ( groups858564598930262913ex_int @ H2 @ S2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_cong_right
% 0.35/0.67  thf(fact_8884_prod_Omono__neutral__cong__right,axiom,
% 0.35/0.67      ! [T4: set_real,S2: set_real,G: real > complex,H2: real > complex] :
% 0.35/0.67        ( ( finite_finite_real @ T4 )
% 0.35/0.67       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: real] :
% 0.35/0.67                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 0.35/0.67               => ( ( G @ X3 )
% 0.35/0.67                  = one_one_complex ) )
% 0.35/0.67           => ( ! [X3: real] :
% 0.35/0.67                  ( ( member_real @ X3 @ S2 )
% 0.35/0.67                 => ( ( G @ X3 )
% 0.35/0.67                    = ( H2 @ X3 ) ) )
% 0.35/0.67             => ( ( groups713298508707869441omplex @ G @ T4 )
% 0.35/0.67                = ( groups713298508707869441omplex @ H2 @ S2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_cong_right
% 0.35/0.67  thf(fact_8885_prod_Omono__neutral__cong__left,axiom,
% 0.35/0.67      ! [T4: set_int,S2: set_int,H2: int > complex,G: int > complex] :
% 0.35/0.67        ( ( finite_finite_int @ T4 )
% 0.35/0.67       => ( ( ord_less_eq_set_int @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: int] :
% 0.35/0.67                ( ( member_int @ X3 @ ( minus_minus_set_int @ T4 @ S2 ) )
% 0.35/0.67               => ( ( H2 @ X3 )
% 0.35/0.67                  = one_one_complex ) )
% 0.35/0.67           => ( ! [X3: int] :
% 0.35/0.67                  ( ( member_int @ X3 @ S2 )
% 0.35/0.67                 => ( ( G @ X3 )
% 0.35/0.67                    = ( H2 @ X3 ) ) )
% 0.35/0.67             => ( ( groups7440179247065528705omplex @ G @ S2 )
% 0.35/0.67                = ( groups7440179247065528705omplex @ H2 @ T4 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_cong_left
% 0.35/0.67  thf(fact_8886_prod_Omono__neutral__cong__left,axiom,
% 0.35/0.67      ! [T4: set_complex,S2: set_complex,H2: complex > complex,G: complex > complex] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.67       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: complex] :
% 0.35/0.67                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 0.35/0.67               => ( ( H2 @ X3 )
% 0.35/0.67                  = one_one_complex ) )
% 0.35/0.67           => ( ! [X3: complex] :
% 0.35/0.67                  ( ( member_complex @ X3 @ S2 )
% 0.35/0.67                 => ( ( G @ X3 )
% 0.35/0.67                    = ( H2 @ X3 ) ) )
% 0.35/0.67             => ( ( groups3708469109370488835omplex @ G @ S2 )
% 0.35/0.67                = ( groups3708469109370488835omplex @ H2 @ T4 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_cong_left
% 0.35/0.67  thf(fact_8887_prod_Omono__neutral__cong__left,axiom,
% 0.35/0.67      ! [T4: set_int,S2: set_int,H2: int > real,G: int > real] :
% 0.35/0.67        ( ( finite_finite_int @ T4 )
% 0.35/0.67       => ( ( ord_less_eq_set_int @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: int] :
% 0.35/0.67                ( ( member_int @ X3 @ ( minus_minus_set_int @ T4 @ S2 ) )
% 0.35/0.67               => ( ( H2 @ X3 )
% 0.35/0.67                  = one_one_real ) )
% 0.35/0.67           => ( ! [X3: int] :
% 0.35/0.67                  ( ( member_int @ X3 @ S2 )
% 0.35/0.67                 => ( ( G @ X3 )
% 0.35/0.67                    = ( H2 @ X3 ) ) )
% 0.35/0.67             => ( ( groups2316167850115554303t_real @ G @ S2 )
% 0.35/0.67                = ( groups2316167850115554303t_real @ H2 @ T4 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_cong_left
% 0.35/0.67  thf(fact_8888_prod_Omono__neutral__cong__left,axiom,
% 0.35/0.67      ! [T4: set_complex,S2: set_complex,H2: complex > real,G: complex > real] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.67       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: complex] :
% 0.35/0.67                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 0.35/0.67               => ( ( H2 @ X3 )
% 0.35/0.67                  = one_one_real ) )
% 0.35/0.67           => ( ! [X3: complex] :
% 0.35/0.67                  ( ( member_complex @ X3 @ S2 )
% 0.35/0.67                 => ( ( G @ X3 )
% 0.35/0.67                    = ( H2 @ X3 ) ) )
% 0.35/0.67             => ( ( groups766887009212190081x_real @ G @ S2 )
% 0.35/0.67                = ( groups766887009212190081x_real @ H2 @ T4 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_cong_left
% 0.35/0.67  thf(fact_8889_prod_Omono__neutral__cong__left,axiom,
% 0.35/0.67      ! [T4: set_int,S2: set_int,H2: int > rat,G: int > rat] :
% 0.35/0.67        ( ( finite_finite_int @ T4 )
% 0.35/0.67       => ( ( ord_less_eq_set_int @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: int] :
% 0.35/0.67                ( ( member_int @ X3 @ ( minus_minus_set_int @ T4 @ S2 ) )
% 0.35/0.67               => ( ( H2 @ X3 )
% 0.35/0.67                  = one_one_rat ) )
% 0.35/0.67           => ( ! [X3: int] :
% 0.35/0.67                  ( ( member_int @ X3 @ S2 )
% 0.35/0.67                 => ( ( G @ X3 )
% 0.35/0.67                    = ( H2 @ X3 ) ) )
% 0.35/0.67             => ( ( groups1072433553688619179nt_rat @ G @ S2 )
% 0.35/0.67                = ( groups1072433553688619179nt_rat @ H2 @ T4 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_cong_left
% 0.35/0.67  thf(fact_8890_prod_Omono__neutral__cong__left,axiom,
% 0.35/0.67      ! [T4: set_complex,S2: set_complex,H2: complex > rat,G: complex > rat] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.67       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: complex] :
% 0.35/0.67                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 0.35/0.67               => ( ( H2 @ X3 )
% 0.35/0.67                  = one_one_rat ) )
% 0.35/0.67           => ( ! [X3: complex] :
% 0.35/0.67                  ( ( member_complex @ X3 @ S2 )
% 0.35/0.67                 => ( ( G @ X3 )
% 0.35/0.67                    = ( H2 @ X3 ) ) )
% 0.35/0.67             => ( ( groups225925009352817453ex_rat @ G @ S2 )
% 0.35/0.67                = ( groups225925009352817453ex_rat @ H2 @ T4 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_cong_left
% 0.35/0.67  thf(fact_8891_prod_Omono__neutral__cong__left,axiom,
% 0.35/0.67      ! [T4: set_int,S2: set_int,H2: int > nat,G: int > nat] :
% 0.35/0.67        ( ( finite_finite_int @ T4 )
% 0.35/0.67       => ( ( ord_less_eq_set_int @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: int] :
% 0.35/0.67                ( ( member_int @ X3 @ ( minus_minus_set_int @ T4 @ S2 ) )
% 0.35/0.67               => ( ( H2 @ X3 )
% 0.35/0.67                  = one_one_nat ) )
% 0.35/0.67           => ( ! [X3: int] :
% 0.35/0.67                  ( ( member_int @ X3 @ S2 )
% 0.35/0.67                 => ( ( G @ X3 )
% 0.35/0.67                    = ( H2 @ X3 ) ) )
% 0.35/0.67             => ( ( groups1707563613775114915nt_nat @ G @ S2 )
% 0.35/0.67                = ( groups1707563613775114915nt_nat @ H2 @ T4 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_cong_left
% 0.35/0.67  thf(fact_8892_prod_Omono__neutral__cong__left,axiom,
% 0.35/0.67      ! [T4: set_complex,S2: set_complex,H2: complex > nat,G: complex > nat] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.67       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: complex] :
% 0.35/0.67                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 0.35/0.67               => ( ( H2 @ X3 )
% 0.35/0.67                  = one_one_nat ) )
% 0.35/0.67           => ( ! [X3: complex] :
% 0.35/0.67                  ( ( member_complex @ X3 @ S2 )
% 0.35/0.67                 => ( ( G @ X3 )
% 0.35/0.67                    = ( H2 @ X3 ) ) )
% 0.35/0.67             => ( ( groups861055069439313189ex_nat @ G @ S2 )
% 0.35/0.67                = ( groups861055069439313189ex_nat @ H2 @ T4 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_cong_left
% 0.35/0.67  thf(fact_8893_prod_Omono__neutral__cong__left,axiom,
% 0.35/0.67      ! [T4: set_complex,S2: set_complex,H2: complex > int,G: complex > int] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.67       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: complex] :
% 0.35/0.67                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 0.35/0.67               => ( ( H2 @ X3 )
% 0.35/0.67                  = one_one_int ) )
% 0.35/0.67           => ( ! [X3: complex] :
% 0.35/0.67                  ( ( member_complex @ X3 @ S2 )
% 0.35/0.67                 => ( ( G @ X3 )
% 0.35/0.67                    = ( H2 @ X3 ) ) )
% 0.35/0.67             => ( ( groups858564598930262913ex_int @ G @ S2 )
% 0.35/0.67                = ( groups858564598930262913ex_int @ H2 @ T4 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_cong_left
% 0.35/0.67  thf(fact_8894_prod_Omono__neutral__cong__left,axiom,
% 0.35/0.67      ! [T4: set_real,S2: set_real,H2: real > complex,G: real > complex] :
% 0.35/0.67        ( ( finite_finite_real @ T4 )
% 0.35/0.67       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: real] :
% 0.35/0.67                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 0.35/0.67               => ( ( H2 @ X3 )
% 0.35/0.67                  = one_one_complex ) )
% 0.35/0.67           => ( ! [X3: real] :
% 0.35/0.67                  ( ( member_real @ X3 @ S2 )
% 0.35/0.67                 => ( ( G @ X3 )
% 0.35/0.67                    = ( H2 @ X3 ) ) )
% 0.35/0.67             => ( ( groups713298508707869441omplex @ G @ S2 )
% 0.35/0.67                = ( groups713298508707869441omplex @ H2 @ T4 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_cong_left
% 0.35/0.67  thf(fact_8895_prod_Omono__neutral__right,axiom,
% 0.35/0.67      ! [T4: set_complex,S2: set_complex,G: complex > complex] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.67       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: complex] :
% 0.35/0.67                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 0.35/0.67               => ( ( G @ X3 )
% 0.35/0.67                  = one_one_complex ) )
% 0.35/0.67           => ( ( groups3708469109370488835omplex @ G @ T4 )
% 0.35/0.67              = ( groups3708469109370488835omplex @ G @ S2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_right
% 0.35/0.67  thf(fact_8896_prod_Omono__neutral__right,axiom,
% 0.35/0.67      ! [T4: set_complex,S2: set_complex,G: complex > real] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.67       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: complex] :
% 0.35/0.67                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 0.35/0.67               => ( ( G @ X3 )
% 0.35/0.67                  = one_one_real ) )
% 0.35/0.67           => ( ( groups766887009212190081x_real @ G @ T4 )
% 0.35/0.67              = ( groups766887009212190081x_real @ G @ S2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_right
% 0.35/0.67  thf(fact_8897_prod_Omono__neutral__right,axiom,
% 0.35/0.67      ! [T4: set_complex,S2: set_complex,G: complex > rat] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.67       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: complex] :
% 0.35/0.67                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 0.35/0.67               => ( ( G @ X3 )
% 0.35/0.67                  = one_one_rat ) )
% 0.35/0.67           => ( ( groups225925009352817453ex_rat @ G @ T4 )
% 0.35/0.67              = ( groups225925009352817453ex_rat @ G @ S2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_right
% 0.35/0.67  thf(fact_8898_prod_Omono__neutral__right,axiom,
% 0.35/0.67      ! [T4: set_complex,S2: set_complex,G: complex > nat] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.67       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: complex] :
% 0.35/0.67                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 0.35/0.67               => ( ( G @ X3 )
% 0.35/0.67                  = one_one_nat ) )
% 0.35/0.67           => ( ( groups861055069439313189ex_nat @ G @ T4 )
% 0.35/0.67              = ( groups861055069439313189ex_nat @ G @ S2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_right
% 0.35/0.67  thf(fact_8899_prod_Omono__neutral__right,axiom,
% 0.35/0.67      ! [T4: set_complex,S2: set_complex,G: complex > int] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.67       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: complex] :
% 0.35/0.67                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 0.35/0.67               => ( ( G @ X3 )
% 0.35/0.67                  = one_one_int ) )
% 0.35/0.67           => ( ( groups858564598930262913ex_int @ G @ T4 )
% 0.35/0.67              = ( groups858564598930262913ex_int @ G @ S2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_right
% 0.35/0.67  thf(fact_8900_prod_Omono__neutral__right,axiom,
% 0.35/0.67      ! [T4: set_real,S2: set_real,G: real > complex] :
% 0.35/0.67        ( ( finite_finite_real @ T4 )
% 0.35/0.67       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: real] :
% 0.35/0.67                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 0.35/0.67               => ( ( G @ X3 )
% 0.35/0.67                  = one_one_complex ) )
% 0.35/0.67           => ( ( groups713298508707869441omplex @ G @ T4 )
% 0.35/0.67              = ( groups713298508707869441omplex @ G @ S2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_right
% 0.35/0.67  thf(fact_8901_prod_Omono__neutral__right,axiom,
% 0.35/0.67      ! [T4: set_real,S2: set_real,G: real > real] :
% 0.35/0.67        ( ( finite_finite_real @ T4 )
% 0.35/0.67       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: real] :
% 0.35/0.67                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 0.35/0.67               => ( ( G @ X3 )
% 0.35/0.67                  = one_one_real ) )
% 0.35/0.67           => ( ( groups1681761925125756287l_real @ G @ T4 )
% 0.35/0.67              = ( groups1681761925125756287l_real @ G @ S2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_right
% 0.35/0.67  thf(fact_8902_prod_Omono__neutral__right,axiom,
% 0.35/0.67      ! [T4: set_real,S2: set_real,G: real > rat] :
% 0.35/0.67        ( ( finite_finite_real @ T4 )
% 0.35/0.67       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: real] :
% 0.35/0.67                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 0.35/0.67               => ( ( G @ X3 )
% 0.35/0.67                  = one_one_rat ) )
% 0.35/0.67           => ( ( groups4061424788464935467al_rat @ G @ T4 )
% 0.35/0.67              = ( groups4061424788464935467al_rat @ G @ S2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_right
% 0.35/0.67  thf(fact_8903_prod_Omono__neutral__right,axiom,
% 0.35/0.67      ! [T4: set_real,S2: set_real,G: real > nat] :
% 0.35/0.67        ( ( finite_finite_real @ T4 )
% 0.35/0.67       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: real] :
% 0.35/0.67                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 0.35/0.67               => ( ( G @ X3 )
% 0.35/0.67                  = one_one_nat ) )
% 0.35/0.67           => ( ( groups4696554848551431203al_nat @ G @ T4 )
% 0.35/0.67              = ( groups4696554848551431203al_nat @ G @ S2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_right
% 0.35/0.67  thf(fact_8904_prod_Omono__neutral__right,axiom,
% 0.35/0.67      ! [T4: set_real,S2: set_real,G: real > int] :
% 0.35/0.67        ( ( finite_finite_real @ T4 )
% 0.35/0.67       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: real] :
% 0.35/0.67                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 0.35/0.67               => ( ( G @ X3 )
% 0.35/0.67                  = one_one_int ) )
% 0.35/0.67           => ( ( groups4694064378042380927al_int @ G @ T4 )
% 0.35/0.67              = ( groups4694064378042380927al_int @ G @ S2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_right
% 0.35/0.67  thf(fact_8905_prod_Omono__neutral__left,axiom,
% 0.35/0.67      ! [T4: set_complex,S2: set_complex,G: complex > complex] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.67       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: complex] :
% 0.35/0.67                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 0.35/0.67               => ( ( G @ X3 )
% 0.35/0.67                  = one_one_complex ) )
% 0.35/0.67           => ( ( groups3708469109370488835omplex @ G @ S2 )
% 0.35/0.67              = ( groups3708469109370488835omplex @ G @ T4 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_left
% 0.35/0.67  thf(fact_8906_prod_Omono__neutral__left,axiom,
% 0.35/0.67      ! [T4: set_complex,S2: set_complex,G: complex > real] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.67       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: complex] :
% 0.35/0.67                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 0.35/0.67               => ( ( G @ X3 )
% 0.35/0.67                  = one_one_real ) )
% 0.35/0.67           => ( ( groups766887009212190081x_real @ G @ S2 )
% 0.35/0.67              = ( groups766887009212190081x_real @ G @ T4 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_left
% 0.35/0.67  thf(fact_8907_prod_Omono__neutral__left,axiom,
% 0.35/0.67      ! [T4: set_complex,S2: set_complex,G: complex > rat] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.67       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: complex] :
% 0.35/0.67                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 0.35/0.67               => ( ( G @ X3 )
% 0.35/0.67                  = one_one_rat ) )
% 0.35/0.67           => ( ( groups225925009352817453ex_rat @ G @ S2 )
% 0.35/0.67              = ( groups225925009352817453ex_rat @ G @ T4 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_left
% 0.35/0.67  thf(fact_8908_prod_Omono__neutral__left,axiom,
% 0.35/0.67      ! [T4: set_complex,S2: set_complex,G: complex > nat] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.67       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: complex] :
% 0.35/0.67                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 0.35/0.67               => ( ( G @ X3 )
% 0.35/0.67                  = one_one_nat ) )
% 0.35/0.67           => ( ( groups861055069439313189ex_nat @ G @ S2 )
% 0.35/0.67              = ( groups861055069439313189ex_nat @ G @ T4 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_left
% 0.35/0.67  thf(fact_8909_prod_Omono__neutral__left,axiom,
% 0.35/0.67      ! [T4: set_complex,S2: set_complex,G: complex > int] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.67       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: complex] :
% 0.35/0.67                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 0.35/0.67               => ( ( G @ X3 )
% 0.35/0.67                  = one_one_int ) )
% 0.35/0.67           => ( ( groups858564598930262913ex_int @ G @ S2 )
% 0.35/0.67              = ( groups858564598930262913ex_int @ G @ T4 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_left
% 0.35/0.67  thf(fact_8910_prod_Omono__neutral__left,axiom,
% 0.35/0.67      ! [T4: set_real,S2: set_real,G: real > complex] :
% 0.35/0.67        ( ( finite_finite_real @ T4 )
% 0.35/0.67       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: real] :
% 0.35/0.67                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 0.35/0.67               => ( ( G @ X3 )
% 0.35/0.67                  = one_one_complex ) )
% 0.35/0.67           => ( ( groups713298508707869441omplex @ G @ S2 )
% 0.35/0.67              = ( groups713298508707869441omplex @ G @ T4 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_left
% 0.35/0.67  thf(fact_8911_prod_Omono__neutral__left,axiom,
% 0.35/0.67      ! [T4: set_real,S2: set_real,G: real > real] :
% 0.35/0.67        ( ( finite_finite_real @ T4 )
% 0.35/0.67       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: real] :
% 0.35/0.67                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 0.35/0.67               => ( ( G @ X3 )
% 0.35/0.67                  = one_one_real ) )
% 0.35/0.67           => ( ( groups1681761925125756287l_real @ G @ S2 )
% 0.35/0.67              = ( groups1681761925125756287l_real @ G @ T4 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_left
% 0.35/0.67  thf(fact_8912_prod_Omono__neutral__left,axiom,
% 0.35/0.67      ! [T4: set_real,S2: set_real,G: real > rat] :
% 0.35/0.67        ( ( finite_finite_real @ T4 )
% 0.35/0.67       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: real] :
% 0.35/0.67                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 0.35/0.67               => ( ( G @ X3 )
% 0.35/0.67                  = one_one_rat ) )
% 0.35/0.67           => ( ( groups4061424788464935467al_rat @ G @ S2 )
% 0.35/0.67              = ( groups4061424788464935467al_rat @ G @ T4 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_left
% 0.35/0.67  thf(fact_8913_prod_Omono__neutral__left,axiom,
% 0.35/0.67      ! [T4: set_real,S2: set_real,G: real > nat] :
% 0.35/0.67        ( ( finite_finite_real @ T4 )
% 0.35/0.67       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: real] :
% 0.35/0.67                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 0.35/0.67               => ( ( G @ X3 )
% 0.35/0.67                  = one_one_nat ) )
% 0.35/0.67           => ( ( groups4696554848551431203al_nat @ G @ S2 )
% 0.35/0.67              = ( groups4696554848551431203al_nat @ G @ T4 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_left
% 0.35/0.67  thf(fact_8914_prod_Omono__neutral__left,axiom,
% 0.35/0.67      ! [T4: set_real,S2: set_real,G: real > int] :
% 0.35/0.67        ( ( finite_finite_real @ T4 )
% 0.35/0.67       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 0.35/0.67         => ( ! [X3: real] :
% 0.35/0.67                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 0.35/0.67               => ( ( G @ X3 )
% 0.35/0.67                  = one_one_int ) )
% 0.35/0.67           => ( ( groups4694064378042380927al_int @ G @ S2 )
% 0.35/0.67              = ( groups4694064378042380927al_int @ G @ T4 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.mono_neutral_left
% 0.35/0.67  thf(fact_8915_prod_Osame__carrierI,axiom,
% 0.35/0.67      ! [C4: set_int,A2: set_int,B2: set_int,G: int > complex,H2: int > complex] :
% 0.35/0.67        ( ( finite_finite_int @ C4 )
% 0.35/0.67       => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 0.35/0.67         => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 0.35/0.67           => ( ! [A4: int] :
% 0.35/0.67                  ( ( member_int @ A4 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 0.35/0.67                 => ( ( G @ A4 )
% 0.35/0.67                    = one_one_complex ) )
% 0.35/0.67             => ( ! [B3: int] :
% 0.35/0.67                    ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 0.35/0.67                   => ( ( H2 @ B3 )
% 0.35/0.67                      = one_one_complex ) )
% 0.35/0.67               => ( ( ( groups7440179247065528705omplex @ G @ C4 )
% 0.35/0.67                    = ( groups7440179247065528705omplex @ H2 @ C4 ) )
% 0.35/0.67                 => ( ( groups7440179247065528705omplex @ G @ A2 )
% 0.35/0.67                    = ( groups7440179247065528705omplex @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.same_carrierI
% 0.35/0.67  thf(fact_8916_prod_Osame__carrierI,axiom,
% 0.35/0.67      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > complex,H2: complex > complex] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ C4 )
% 0.35/0.67       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 0.35/0.67         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 0.35/0.67           => ( ! [A4: complex] :
% 0.35/0.67                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 0.35/0.67                 => ( ( G @ A4 )
% 0.35/0.67                    = one_one_complex ) )
% 0.35/0.67             => ( ! [B3: complex] :
% 0.35/0.67                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 0.35/0.67                   => ( ( H2 @ B3 )
% 0.35/0.67                      = one_one_complex ) )
% 0.35/0.67               => ( ( ( groups3708469109370488835omplex @ G @ C4 )
% 0.35/0.67                    = ( groups3708469109370488835omplex @ H2 @ C4 ) )
% 0.35/0.67                 => ( ( groups3708469109370488835omplex @ G @ A2 )
% 0.35/0.67                    = ( groups3708469109370488835omplex @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.same_carrierI
% 0.35/0.67  thf(fact_8917_prod_Osame__carrierI,axiom,
% 0.35/0.67      ! [C4: set_int,A2: set_int,B2: set_int,G: int > real,H2: int > real] :
% 0.35/0.67        ( ( finite_finite_int @ C4 )
% 0.35/0.67       => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 0.35/0.67         => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 0.35/0.67           => ( ! [A4: int] :
% 0.35/0.67                  ( ( member_int @ A4 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 0.35/0.67                 => ( ( G @ A4 )
% 0.35/0.67                    = one_one_real ) )
% 0.35/0.67             => ( ! [B3: int] :
% 0.35/0.67                    ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 0.35/0.67                   => ( ( H2 @ B3 )
% 0.35/0.67                      = one_one_real ) )
% 0.35/0.67               => ( ( ( groups2316167850115554303t_real @ G @ C4 )
% 0.35/0.67                    = ( groups2316167850115554303t_real @ H2 @ C4 ) )
% 0.35/0.67                 => ( ( groups2316167850115554303t_real @ G @ A2 )
% 0.35/0.67                    = ( groups2316167850115554303t_real @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.same_carrierI
% 0.35/0.67  thf(fact_8918_prod_Osame__carrierI,axiom,
% 0.35/0.67      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > real,H2: complex > real] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ C4 )
% 0.35/0.67       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 0.35/0.67         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 0.35/0.67           => ( ! [A4: complex] :
% 0.35/0.67                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 0.35/0.67                 => ( ( G @ A4 )
% 0.35/0.67                    = one_one_real ) )
% 0.35/0.67             => ( ! [B3: complex] :
% 0.35/0.67                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 0.35/0.67                   => ( ( H2 @ B3 )
% 0.35/0.67                      = one_one_real ) )
% 0.35/0.67               => ( ( ( groups766887009212190081x_real @ G @ C4 )
% 0.35/0.67                    = ( groups766887009212190081x_real @ H2 @ C4 ) )
% 0.35/0.67                 => ( ( groups766887009212190081x_real @ G @ A2 )
% 0.35/0.67                    = ( groups766887009212190081x_real @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.same_carrierI
% 0.35/0.67  thf(fact_8919_prod_Osame__carrierI,axiom,
% 0.35/0.67      ! [C4: set_int,A2: set_int,B2: set_int,G: int > rat,H2: int > rat] :
% 0.35/0.67        ( ( finite_finite_int @ C4 )
% 0.35/0.67       => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 0.35/0.67         => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 0.35/0.67           => ( ! [A4: int] :
% 0.35/0.67                  ( ( member_int @ A4 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 0.35/0.67                 => ( ( G @ A4 )
% 0.35/0.67                    = one_one_rat ) )
% 0.35/0.67             => ( ! [B3: int] :
% 0.35/0.67                    ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 0.35/0.67                   => ( ( H2 @ B3 )
% 0.35/0.67                      = one_one_rat ) )
% 0.35/0.67               => ( ( ( groups1072433553688619179nt_rat @ G @ C4 )
% 0.35/0.67                    = ( groups1072433553688619179nt_rat @ H2 @ C4 ) )
% 0.35/0.67                 => ( ( groups1072433553688619179nt_rat @ G @ A2 )
% 0.35/0.67                    = ( groups1072433553688619179nt_rat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.same_carrierI
% 0.35/0.67  thf(fact_8920_prod_Osame__carrierI,axiom,
% 0.35/0.67      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > rat,H2: complex > rat] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ C4 )
% 0.35/0.67       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 0.35/0.67         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 0.35/0.67           => ( ! [A4: complex] :
% 0.35/0.67                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 0.35/0.67                 => ( ( G @ A4 )
% 0.35/0.67                    = one_one_rat ) )
% 0.35/0.67             => ( ! [B3: complex] :
% 0.35/0.67                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 0.35/0.67                   => ( ( H2 @ B3 )
% 0.35/0.67                      = one_one_rat ) )
% 0.35/0.67               => ( ( ( groups225925009352817453ex_rat @ G @ C4 )
% 0.35/0.67                    = ( groups225925009352817453ex_rat @ H2 @ C4 ) )
% 0.35/0.67                 => ( ( groups225925009352817453ex_rat @ G @ A2 )
% 0.35/0.67                    = ( groups225925009352817453ex_rat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.same_carrierI
% 0.35/0.67  thf(fact_8921_prod_Osame__carrierI,axiom,
% 0.35/0.67      ! [C4: set_int,A2: set_int,B2: set_int,G: int > nat,H2: int > nat] :
% 0.35/0.67        ( ( finite_finite_int @ C4 )
% 0.35/0.67       => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 0.35/0.67         => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 0.35/0.67           => ( ! [A4: int] :
% 0.35/0.67                  ( ( member_int @ A4 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 0.35/0.67                 => ( ( G @ A4 )
% 0.35/0.67                    = one_one_nat ) )
% 0.35/0.67             => ( ! [B3: int] :
% 0.35/0.67                    ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 0.35/0.67                   => ( ( H2 @ B3 )
% 0.35/0.67                      = one_one_nat ) )
% 0.35/0.67               => ( ( ( groups1707563613775114915nt_nat @ G @ C4 )
% 0.35/0.67                    = ( groups1707563613775114915nt_nat @ H2 @ C4 ) )
% 0.35/0.67                 => ( ( groups1707563613775114915nt_nat @ G @ A2 )
% 0.35/0.67                    = ( groups1707563613775114915nt_nat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.same_carrierI
% 0.35/0.67  thf(fact_8922_prod_Osame__carrierI,axiom,
% 0.35/0.67      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > nat,H2: complex > nat] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ C4 )
% 0.35/0.67       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 0.35/0.67         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 0.35/0.67           => ( ! [A4: complex] :
% 0.35/0.67                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 0.35/0.67                 => ( ( G @ A4 )
% 0.35/0.67                    = one_one_nat ) )
% 0.35/0.67             => ( ! [B3: complex] :
% 0.35/0.67                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 0.35/0.67                   => ( ( H2 @ B3 )
% 0.35/0.67                      = one_one_nat ) )
% 0.35/0.67               => ( ( ( groups861055069439313189ex_nat @ G @ C4 )
% 0.35/0.67                    = ( groups861055069439313189ex_nat @ H2 @ C4 ) )
% 0.35/0.67                 => ( ( groups861055069439313189ex_nat @ G @ A2 )
% 0.35/0.67                    = ( groups861055069439313189ex_nat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.same_carrierI
% 0.35/0.67  thf(fact_8923_prod_Osame__carrierI,axiom,
% 0.35/0.67      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > int,H2: complex > int] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ C4 )
% 0.35/0.67       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 0.35/0.67         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 0.35/0.67           => ( ! [A4: complex] :
% 0.35/0.67                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 0.35/0.67                 => ( ( G @ A4 )
% 0.35/0.67                    = one_one_int ) )
% 0.35/0.67             => ( ! [B3: complex] :
% 0.35/0.67                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 0.35/0.67                   => ( ( H2 @ B3 )
% 0.35/0.67                      = one_one_int ) )
% 0.35/0.67               => ( ( ( groups858564598930262913ex_int @ G @ C4 )
% 0.35/0.67                    = ( groups858564598930262913ex_int @ H2 @ C4 ) )
% 0.35/0.67                 => ( ( groups858564598930262913ex_int @ G @ A2 )
% 0.35/0.67                    = ( groups858564598930262913ex_int @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.same_carrierI
% 0.35/0.67  thf(fact_8924_prod_Osame__carrierI,axiom,
% 0.35/0.67      ! [C4: set_real,A2: set_real,B2: set_real,G: real > complex,H2: real > complex] :
% 0.35/0.67        ( ( finite_finite_real @ C4 )
% 0.35/0.67       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 0.35/0.67         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 0.35/0.67           => ( ! [A4: real] :
% 0.35/0.67                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 0.35/0.67                 => ( ( G @ A4 )
% 0.35/0.67                    = one_one_complex ) )
% 0.35/0.67             => ( ! [B3: real] :
% 0.35/0.67                    ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 0.35/0.67                   => ( ( H2 @ B3 )
% 0.35/0.67                      = one_one_complex ) )
% 0.35/0.67               => ( ( ( groups713298508707869441omplex @ G @ C4 )
% 0.35/0.67                    = ( groups713298508707869441omplex @ H2 @ C4 ) )
% 0.35/0.67                 => ( ( groups713298508707869441omplex @ G @ A2 )
% 0.35/0.67                    = ( groups713298508707869441omplex @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.same_carrierI
% 0.35/0.67  thf(fact_8925_prod_Osame__carrier,axiom,
% 0.35/0.67      ! [C4: set_int,A2: set_int,B2: set_int,G: int > complex,H2: int > complex] :
% 0.35/0.67        ( ( finite_finite_int @ C4 )
% 0.35/0.67       => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 0.35/0.67         => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 0.35/0.67           => ( ! [A4: int] :
% 0.35/0.67                  ( ( member_int @ A4 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 0.35/0.67                 => ( ( G @ A4 )
% 0.35/0.67                    = one_one_complex ) )
% 0.35/0.67             => ( ! [B3: int] :
% 0.35/0.67                    ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 0.35/0.67                   => ( ( H2 @ B3 )
% 0.35/0.67                      = one_one_complex ) )
% 0.35/0.67               => ( ( ( groups7440179247065528705omplex @ G @ A2 )
% 0.35/0.67                    = ( groups7440179247065528705omplex @ H2 @ B2 ) )
% 0.35/0.67                  = ( ( groups7440179247065528705omplex @ G @ C4 )
% 0.35/0.67                    = ( groups7440179247065528705omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.same_carrier
% 0.35/0.67  thf(fact_8926_prod_Osame__carrier,axiom,
% 0.35/0.67      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > complex,H2: complex > complex] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ C4 )
% 0.35/0.67       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 0.35/0.67         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 0.35/0.67           => ( ! [A4: complex] :
% 0.35/0.67                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 0.35/0.67                 => ( ( G @ A4 )
% 0.35/0.67                    = one_one_complex ) )
% 0.35/0.67             => ( ! [B3: complex] :
% 0.35/0.67                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 0.35/0.67                   => ( ( H2 @ B3 )
% 0.35/0.67                      = one_one_complex ) )
% 0.35/0.67               => ( ( ( groups3708469109370488835omplex @ G @ A2 )
% 0.35/0.67                    = ( groups3708469109370488835omplex @ H2 @ B2 ) )
% 0.35/0.67                  = ( ( groups3708469109370488835omplex @ G @ C4 )
% 0.35/0.67                    = ( groups3708469109370488835omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.same_carrier
% 0.35/0.67  thf(fact_8927_prod_Osame__carrier,axiom,
% 0.35/0.67      ! [C4: set_int,A2: set_int,B2: set_int,G: int > real,H2: int > real] :
% 0.35/0.67        ( ( finite_finite_int @ C4 )
% 0.35/0.67       => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 0.35/0.67         => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 0.35/0.67           => ( ! [A4: int] :
% 0.35/0.67                  ( ( member_int @ A4 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 0.35/0.67                 => ( ( G @ A4 )
% 0.35/0.67                    = one_one_real ) )
% 0.35/0.67             => ( ! [B3: int] :
% 0.35/0.67                    ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 0.35/0.67                   => ( ( H2 @ B3 )
% 0.35/0.67                      = one_one_real ) )
% 0.35/0.67               => ( ( ( groups2316167850115554303t_real @ G @ A2 )
% 0.35/0.67                    = ( groups2316167850115554303t_real @ H2 @ B2 ) )
% 0.35/0.67                  = ( ( groups2316167850115554303t_real @ G @ C4 )
% 0.35/0.67                    = ( groups2316167850115554303t_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.same_carrier
% 0.35/0.67  thf(fact_8928_prod_Osame__carrier,axiom,
% 0.35/0.67      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > real,H2: complex > real] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ C4 )
% 0.35/0.67       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 0.35/0.67         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 0.35/0.67           => ( ! [A4: complex] :
% 0.35/0.67                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 0.35/0.67                 => ( ( G @ A4 )
% 0.35/0.67                    = one_one_real ) )
% 0.35/0.67             => ( ! [B3: complex] :
% 0.35/0.67                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 0.35/0.67                   => ( ( H2 @ B3 )
% 0.35/0.67                      = one_one_real ) )
% 0.35/0.67               => ( ( ( groups766887009212190081x_real @ G @ A2 )
% 0.35/0.67                    = ( groups766887009212190081x_real @ H2 @ B2 ) )
% 0.35/0.67                  = ( ( groups766887009212190081x_real @ G @ C4 )
% 0.35/0.67                    = ( groups766887009212190081x_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.same_carrier
% 0.35/0.67  thf(fact_8929_prod_Osame__carrier,axiom,
% 0.35/0.67      ! [C4: set_int,A2: set_int,B2: set_int,G: int > rat,H2: int > rat] :
% 0.35/0.67        ( ( finite_finite_int @ C4 )
% 0.35/0.67       => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 0.35/0.67         => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 0.35/0.67           => ( ! [A4: int] :
% 0.35/0.67                  ( ( member_int @ A4 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 0.35/0.67                 => ( ( G @ A4 )
% 0.35/0.67                    = one_one_rat ) )
% 0.35/0.67             => ( ! [B3: int] :
% 0.35/0.67                    ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 0.35/0.67                   => ( ( H2 @ B3 )
% 0.35/0.67                      = one_one_rat ) )
% 0.35/0.67               => ( ( ( groups1072433553688619179nt_rat @ G @ A2 )
% 0.35/0.67                    = ( groups1072433553688619179nt_rat @ H2 @ B2 ) )
% 0.35/0.67                  = ( ( groups1072433553688619179nt_rat @ G @ C4 )
% 0.35/0.67                    = ( groups1072433553688619179nt_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.same_carrier
% 0.35/0.67  thf(fact_8930_prod_Osame__carrier,axiom,
% 0.35/0.67      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > rat,H2: complex > rat] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ C4 )
% 0.35/0.67       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 0.35/0.67         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 0.35/0.67           => ( ! [A4: complex] :
% 0.35/0.67                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 0.35/0.67                 => ( ( G @ A4 )
% 0.35/0.67                    = one_one_rat ) )
% 0.35/0.67             => ( ! [B3: complex] :
% 0.35/0.67                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 0.35/0.67                   => ( ( H2 @ B3 )
% 0.35/0.67                      = one_one_rat ) )
% 0.35/0.67               => ( ( ( groups225925009352817453ex_rat @ G @ A2 )
% 0.35/0.67                    = ( groups225925009352817453ex_rat @ H2 @ B2 ) )
% 0.35/0.67                  = ( ( groups225925009352817453ex_rat @ G @ C4 )
% 0.35/0.67                    = ( groups225925009352817453ex_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.same_carrier
% 0.35/0.67  thf(fact_8931_prod_Osame__carrier,axiom,
% 0.35/0.67      ! [C4: set_int,A2: set_int,B2: set_int,G: int > nat,H2: int > nat] :
% 0.35/0.67        ( ( finite_finite_int @ C4 )
% 0.35/0.67       => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 0.35/0.67         => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 0.35/0.67           => ( ! [A4: int] :
% 0.35/0.67                  ( ( member_int @ A4 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 0.35/0.67                 => ( ( G @ A4 )
% 0.35/0.67                    = one_one_nat ) )
% 0.35/0.67             => ( ! [B3: int] :
% 0.35/0.67                    ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 0.35/0.67                   => ( ( H2 @ B3 )
% 0.35/0.67                      = one_one_nat ) )
% 0.35/0.67               => ( ( ( groups1707563613775114915nt_nat @ G @ A2 )
% 0.35/0.67                    = ( groups1707563613775114915nt_nat @ H2 @ B2 ) )
% 0.35/0.67                  = ( ( groups1707563613775114915nt_nat @ G @ C4 )
% 0.35/0.67                    = ( groups1707563613775114915nt_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.same_carrier
% 0.35/0.67  thf(fact_8932_prod_Osame__carrier,axiom,
% 0.35/0.67      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > nat,H2: complex > nat] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ C4 )
% 0.35/0.67       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 0.35/0.67         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 0.35/0.67           => ( ! [A4: complex] :
% 0.35/0.67                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 0.35/0.67                 => ( ( G @ A4 )
% 0.35/0.67                    = one_one_nat ) )
% 0.35/0.67             => ( ! [B3: complex] :
% 0.35/0.67                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 0.35/0.67                   => ( ( H2 @ B3 )
% 0.35/0.67                      = one_one_nat ) )
% 0.35/0.67               => ( ( ( groups861055069439313189ex_nat @ G @ A2 )
% 0.35/0.67                    = ( groups861055069439313189ex_nat @ H2 @ B2 ) )
% 0.35/0.67                  = ( ( groups861055069439313189ex_nat @ G @ C4 )
% 0.35/0.67                    = ( groups861055069439313189ex_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.same_carrier
% 0.35/0.67  thf(fact_8933_prod_Osame__carrier,axiom,
% 0.35/0.67      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > int,H2: complex > int] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ C4 )
% 0.35/0.67       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 0.35/0.67         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 0.35/0.67           => ( ! [A4: complex] :
% 0.35/0.67                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 0.35/0.67                 => ( ( G @ A4 )
% 0.35/0.67                    = one_one_int ) )
% 0.35/0.67             => ( ! [B3: complex] :
% 0.35/0.67                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 0.35/0.67                   => ( ( H2 @ B3 )
% 0.35/0.67                      = one_one_int ) )
% 0.35/0.67               => ( ( ( groups858564598930262913ex_int @ G @ A2 )
% 0.35/0.67                    = ( groups858564598930262913ex_int @ H2 @ B2 ) )
% 0.35/0.67                  = ( ( groups858564598930262913ex_int @ G @ C4 )
% 0.35/0.67                    = ( groups858564598930262913ex_int @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.same_carrier
% 0.35/0.67  thf(fact_8934_prod_Osame__carrier,axiom,
% 0.35/0.67      ! [C4: set_real,A2: set_real,B2: set_real,G: real > complex,H2: real > complex] :
% 0.35/0.67        ( ( finite_finite_real @ C4 )
% 0.35/0.67       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 0.35/0.67         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 0.35/0.67           => ( ! [A4: real] :
% 0.35/0.67                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 0.35/0.67                 => ( ( G @ A4 )
% 0.35/0.67                    = one_one_complex ) )
% 0.35/0.67             => ( ! [B3: real] :
% 0.35/0.67                    ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 0.35/0.67                   => ( ( H2 @ B3 )
% 0.35/0.67                      = one_one_complex ) )
% 0.35/0.67               => ( ( ( groups713298508707869441omplex @ G @ A2 )
% 0.35/0.67                    = ( groups713298508707869441omplex @ H2 @ B2 ) )
% 0.35/0.67                  = ( ( groups713298508707869441omplex @ G @ C4 )
% 0.35/0.67                    = ( groups713298508707869441omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.same_carrier
% 0.35/0.67  thf(fact_8935_prod_OatLeast0__atMost__Suc,axiom,
% 0.35/0.67      ! [G: nat > complex,N: nat] :
% 0.35/0.67        ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.35/0.67        = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.atLeast0_atMost_Suc
% 0.35/0.67  thf(fact_8936_prod_OatLeast0__atMost__Suc,axiom,
% 0.35/0.67      ! [G: nat > real,N: nat] :
% 0.35/0.67        ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.35/0.67        = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.atLeast0_atMost_Suc
% 0.35/0.67  thf(fact_8937_prod_OatLeast0__atMost__Suc,axiom,
% 0.35/0.67      ! [G: nat > nat,N: nat] :
% 0.35/0.67        ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.35/0.67        = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.atLeast0_atMost_Suc
% 0.35/0.67  thf(fact_8938_prod_OatLeast0__atMost__Suc,axiom,
% 0.35/0.67      ! [G: nat > int,N: nat] :
% 0.35/0.67        ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.35/0.67        = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.atLeast0_atMost_Suc
% 0.35/0.67  thf(fact_8939_prod_OatLeast__Suc__atMost,axiom,
% 0.35/0.67      ! [M: nat,N: nat,G: nat > complex] :
% 0.35/0.67        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.67       => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.35/0.67          = ( times_times_complex @ ( G @ M ) @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.atLeast_Suc_atMost
% 0.35/0.67  thf(fact_8940_prod_OatLeast__Suc__atMost,axiom,
% 0.35/0.67      ! [M: nat,N: nat,G: nat > real] :
% 0.35/0.67        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.67       => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.35/0.67          = ( times_times_real @ ( G @ M ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.atLeast_Suc_atMost
% 0.35/0.67  thf(fact_8941_prod_OatLeast__Suc__atMost,axiom,
% 0.35/0.67      ! [M: nat,N: nat,G: nat > nat] :
% 0.35/0.67        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.67       => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.35/0.67          = ( times_times_nat @ ( G @ M ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.atLeast_Suc_atMost
% 0.35/0.67  thf(fact_8942_prod_OatLeast__Suc__atMost,axiom,
% 0.35/0.67      ! [M: nat,N: nat,G: nat > int] :
% 0.35/0.67        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.67       => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.35/0.67          = ( times_times_int @ ( G @ M ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.atLeast_Suc_atMost
% 0.35/0.67  thf(fact_8943_prod_Onat__ivl__Suc_H,axiom,
% 0.35/0.67      ! [M: nat,N: nat,G: nat > complex] :
% 0.35/0.67        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.35/0.67       => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.35/0.67          = ( times_times_complex @ ( G @ ( suc @ N ) ) @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.nat_ivl_Suc'
% 0.35/0.67  thf(fact_8944_prod_Onat__ivl__Suc_H,axiom,
% 0.35/0.67      ! [M: nat,N: nat,G: nat > real] :
% 0.35/0.67        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.35/0.67       => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.35/0.67          = ( times_times_real @ ( G @ ( suc @ N ) ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.nat_ivl_Suc'
% 0.35/0.67  thf(fact_8945_prod_Onat__ivl__Suc_H,axiom,
% 0.35/0.67      ! [M: nat,N: nat,G: nat > nat] :
% 0.35/0.67        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.35/0.67       => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.35/0.67          = ( times_times_nat @ ( G @ ( suc @ N ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.nat_ivl_Suc'
% 0.35/0.67  thf(fact_8946_prod_Onat__ivl__Suc_H,axiom,
% 0.35/0.67      ! [M: nat,N: nat,G: nat > int] :
% 0.35/0.67        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.35/0.67       => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.35/0.67          = ( times_times_int @ ( G @ ( suc @ N ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.nat_ivl_Suc'
% 0.35/0.67  thf(fact_8947_prod_OlessThan__Suc__shift,axiom,
% 0.35/0.67      ! [G: nat > complex,N: nat] :
% 0.35/0.67        ( ( groups6464643781859351333omplex @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.35/0.67        = ( times_times_complex @ ( G @ zero_zero_nat )
% 0.35/0.67          @ ( groups6464643781859351333omplex
% 0.35/0.67            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.35/0.67            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.lessThan_Suc_shift
% 0.35/0.67  thf(fact_8948_prod_OlessThan__Suc__shift,axiom,
% 0.35/0.67      ! [G: nat > real,N: nat] :
% 0.35/0.67        ( ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.35/0.67        = ( times_times_real @ ( G @ zero_zero_nat )
% 0.35/0.67          @ ( groups129246275422532515t_real
% 0.35/0.67            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.35/0.67            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.lessThan_Suc_shift
% 0.35/0.67  thf(fact_8949_prod_OlessThan__Suc__shift,axiom,
% 0.35/0.67      ! [G: nat > nat,N: nat] :
% 0.35/0.67        ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.35/0.67        = ( times_times_nat @ ( G @ zero_zero_nat )
% 0.35/0.67          @ ( groups708209901874060359at_nat
% 0.35/0.67            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.35/0.67            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.lessThan_Suc_shift
% 0.35/0.67  thf(fact_8950_prod_OlessThan__Suc__shift,axiom,
% 0.35/0.67      ! [G: nat > int,N: nat] :
% 0.35/0.67        ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.35/0.67        = ( times_times_int @ ( G @ zero_zero_nat )
% 0.35/0.67          @ ( groups705719431365010083at_int
% 0.35/0.67            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.35/0.67            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.lessThan_Suc_shift
% 0.35/0.67  thf(fact_8951_prod_OSuc__reindex__ivl,axiom,
% 0.35/0.67      ! [M: nat,N: nat,G: nat > complex] :
% 0.35/0.67        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.67       => ( ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 0.35/0.67          = ( times_times_complex @ ( G @ M )
% 0.35/0.67            @ ( groups6464643781859351333omplex
% 0.35/0.67              @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.35/0.67              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.Suc_reindex_ivl
% 0.35/0.67  thf(fact_8952_prod_OSuc__reindex__ivl,axiom,
% 0.35/0.67      ! [M: nat,N: nat,G: nat > real] :
% 0.35/0.67        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.67       => ( ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 0.35/0.67          = ( times_times_real @ ( G @ M )
% 0.35/0.67            @ ( groups129246275422532515t_real
% 0.35/0.67              @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.35/0.67              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.Suc_reindex_ivl
% 0.35/0.67  thf(fact_8953_prod_OSuc__reindex__ivl,axiom,
% 0.35/0.67      ! [M: nat,N: nat,G: nat > nat] :
% 0.35/0.67        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.67       => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 0.35/0.67          = ( times_times_nat @ ( G @ M )
% 0.35/0.67            @ ( groups708209901874060359at_nat
% 0.35/0.67              @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.35/0.67              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.Suc_reindex_ivl
% 0.35/0.67  thf(fact_8954_prod_OSuc__reindex__ivl,axiom,
% 0.35/0.67      ! [M: nat,N: nat,G: nat > int] :
% 0.35/0.67        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.67       => ( ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 0.35/0.67          = ( times_times_int @ ( G @ M )
% 0.35/0.67            @ ( groups705719431365010083at_int
% 0.35/0.67              @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.35/0.67              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.Suc_reindex_ivl
% 0.35/0.67  thf(fact_8955_frac__def,axiom,
% 0.35/0.67      ( archim2898591450579166408c_real
% 0.35/0.67      = ( ^ [X2: real] : ( minus_minus_real @ X2 @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % frac_def
% 0.35/0.67  thf(fact_8956_frac__def,axiom,
% 0.35/0.67      ( archimedean_frac_rat
% 0.35/0.67      = ( ^ [X2: rat] : ( minus_minus_rat @ X2 @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % frac_def
% 0.35/0.67  thf(fact_8957_prod_OatLeast1__atMost__eq,axiom,
% 0.35/0.67      ! [G: nat > nat,N: nat] :
% 0.35/0.67        ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 0.35/0.67        = ( groups708209901874060359at_nat
% 0.35/0.67          @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 0.35/0.67          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.atLeast1_atMost_eq
% 0.35/0.67  thf(fact_8958_prod_OatLeast1__atMost__eq,axiom,
% 0.35/0.67      ! [G: nat > int,N: nat] :
% 0.35/0.67        ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 0.35/0.67        = ( groups705719431365010083at_int
% 0.35/0.67          @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 0.35/0.67          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.atLeast1_atMost_eq
% 0.35/0.67  thf(fact_8959_fact__prod,axiom,
% 0.35/0.67      ( semiri1406184849735516958ct_int
% 0.35/0.67      = ( ^ [N2: nat] :
% 0.35/0.67            ( semiri1314217659103216013at_int
% 0.35/0.67            @ ( groups708209901874060359at_nat
% 0.35/0.67              @ ^ [X2: nat] : X2
% 0.35/0.67              @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % fact_prod
% 0.35/0.67  thf(fact_8960_fact__prod,axiom,
% 0.35/0.67      ( semiri5044797733671781792omplex
% 0.35/0.67      = ( ^ [N2: nat] :
% 0.35/0.67            ( semiri8010041392384452111omplex
% 0.35/0.67            @ ( groups708209901874060359at_nat
% 0.35/0.67              @ ^ [X2: nat] : X2
% 0.35/0.67              @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % fact_prod
% 0.35/0.67  thf(fact_8961_fact__prod,axiom,
% 0.35/0.67      ( semiri2265585572941072030t_real
% 0.35/0.67      = ( ^ [N2: nat] :
% 0.35/0.67            ( semiri5074537144036343181t_real
% 0.35/0.67            @ ( groups708209901874060359at_nat
% 0.35/0.67              @ ^ [X2: nat] : X2
% 0.35/0.67              @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % fact_prod
% 0.35/0.67  thf(fact_8962_fact__prod,axiom,
% 0.35/0.67      ( semiri1408675320244567234ct_nat
% 0.35/0.67      = ( ^ [N2: nat] :
% 0.35/0.67            ( semiri1316708129612266289at_nat
% 0.35/0.67            @ ( groups708209901874060359at_nat
% 0.35/0.67              @ ^ [X2: nat] : X2
% 0.35/0.67              @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % fact_prod
% 0.35/0.67  thf(fact_8963_prod__mono__strict,axiom,
% 0.35/0.67      ! [A2: set_complex,F: complex > real,G: complex > real] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.67       => ( ! [I4: complex] :
% 0.35/0.67              ( ( member_complex @ I4 @ A2 )
% 0.35/0.67             => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 0.35/0.67                & ( ord_less_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 0.35/0.67         => ( ( A2 != bot_bot_set_complex )
% 0.35/0.67           => ( ord_less_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ( groups766887009212190081x_real @ G @ A2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod_mono_strict
% 0.35/0.67  thf(fact_8964_prod__mono__strict,axiom,
% 0.35/0.67      ! [A2: set_nat,F: nat > real,G: nat > real] :
% 0.35/0.67        ( ( finite_finite_nat @ A2 )
% 0.35/0.67       => ( ! [I4: nat] :
% 0.35/0.67              ( ( member_nat @ I4 @ A2 )
% 0.35/0.67             => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 0.35/0.67                & ( ord_less_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 0.35/0.67         => ( ( A2 != bot_bot_set_nat )
% 0.35/0.67           => ( ord_less_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod_mono_strict
% 0.35/0.67  thf(fact_8965_prod__mono__strict,axiom,
% 0.35/0.67      ! [A2: set_int,F: int > real,G: int > real] :
% 0.35/0.67        ( ( finite_finite_int @ A2 )
% 0.35/0.67       => ( ! [I4: int] :
% 0.35/0.67              ( ( member_int @ I4 @ A2 )
% 0.35/0.67             => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 0.35/0.67                & ( ord_less_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 0.35/0.67         => ( ( A2 != bot_bot_set_int )
% 0.35/0.67           => ( ord_less_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod_mono_strict
% 0.35/0.67  thf(fact_8966_prod__mono__strict,axiom,
% 0.35/0.67      ! [A2: set_real,F: real > real,G: real > real] :
% 0.35/0.67        ( ( finite_finite_real @ A2 )
% 0.35/0.67       => ( ! [I4: real] :
% 0.35/0.67              ( ( member_real @ I4 @ A2 )
% 0.35/0.67             => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 0.35/0.67                & ( ord_less_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 0.35/0.67         => ( ( A2 != bot_bot_set_real )
% 0.35/0.67           => ( ord_less_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod_mono_strict
% 0.35/0.67  thf(fact_8967_prod__mono__strict,axiom,
% 0.35/0.67      ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.67       => ( ! [I4: complex] :
% 0.35/0.67              ( ( member_complex @ I4 @ A2 )
% 0.35/0.67             => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) )
% 0.35/0.67                & ( ord_less_rat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 0.35/0.67         => ( ( A2 != bot_bot_set_complex )
% 0.35/0.67           => ( ord_less_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ ( groups225925009352817453ex_rat @ G @ A2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod_mono_strict
% 0.35/0.67  thf(fact_8968_prod__mono__strict,axiom,
% 0.35/0.67      ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 0.35/0.67        ( ( finite_finite_nat @ A2 )
% 0.35/0.67       => ( ! [I4: nat] :
% 0.35/0.67              ( ( member_nat @ I4 @ A2 )
% 0.35/0.67             => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) )
% 0.35/0.67                & ( ord_less_rat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 0.35/0.67         => ( ( A2 != bot_bot_set_nat )
% 0.35/0.67           => ( ord_less_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ ( groups73079841787564623at_rat @ G @ A2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod_mono_strict
% 0.35/0.67  thf(fact_8969_prod__mono__strict,axiom,
% 0.35/0.67      ! [A2: set_int,F: int > rat,G: int > rat] :
% 0.35/0.67        ( ( finite_finite_int @ A2 )
% 0.35/0.67       => ( ! [I4: int] :
% 0.35/0.67              ( ( member_int @ I4 @ A2 )
% 0.35/0.67             => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) )
% 0.35/0.67                & ( ord_less_rat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 0.35/0.67         => ( ( A2 != bot_bot_set_int )
% 0.35/0.67           => ( ord_less_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ ( groups1072433553688619179nt_rat @ G @ A2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod_mono_strict
% 0.35/0.67  thf(fact_8970_prod__mono__strict,axiom,
% 0.35/0.67      ! [A2: set_real,F: real > rat,G: real > rat] :
% 0.35/0.67        ( ( finite_finite_real @ A2 )
% 0.35/0.67       => ( ! [I4: real] :
% 0.35/0.67              ( ( member_real @ I4 @ A2 )
% 0.35/0.67             => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) )
% 0.35/0.67                & ( ord_less_rat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 0.35/0.67         => ( ( A2 != bot_bot_set_real )
% 0.35/0.67           => ( ord_less_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ ( groups4061424788464935467al_rat @ G @ A2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod_mono_strict
% 0.35/0.67  thf(fact_8971_prod__mono__strict,axiom,
% 0.35/0.67      ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.67       => ( ! [I4: complex] :
% 0.35/0.67              ( ( member_complex @ I4 @ A2 )
% 0.35/0.67             => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) )
% 0.35/0.67                & ( ord_less_nat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 0.35/0.67         => ( ( A2 != bot_bot_set_complex )
% 0.35/0.67           => ( ord_less_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) @ ( groups861055069439313189ex_nat @ G @ A2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod_mono_strict
% 0.35/0.67  thf(fact_8972_prod__mono__strict,axiom,
% 0.35/0.67      ! [A2: set_int,F: int > nat,G: int > nat] :
% 0.35/0.67        ( ( finite_finite_int @ A2 )
% 0.35/0.67       => ( ! [I4: int] :
% 0.35/0.67              ( ( member_int @ I4 @ A2 )
% 0.35/0.67             => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) )
% 0.35/0.67                & ( ord_less_nat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 0.35/0.67         => ( ( A2 != bot_bot_set_int )
% 0.35/0.67           => ( ord_less_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ ( groups1707563613775114915nt_nat @ G @ A2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod_mono_strict
% 0.35/0.67  thf(fact_8973_even__prod__iff,axiom,
% 0.35/0.67      ! [A2: set_nat,F: nat > code_integer] :
% 0.35/0.67        ( ( finite_finite_nat @ A2 )
% 0.35/0.67       => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups3455450783089532116nteger @ F @ A2 ) )
% 0.35/0.67          = ( ? [X2: nat] :
% 0.35/0.67                ( ( member_nat @ X2 @ A2 )
% 0.35/0.67                & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % even_prod_iff
% 0.35/0.67  thf(fact_8974_even__prod__iff,axiom,
% 0.35/0.67      ! [A2: set_complex,F: complex > code_integer] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.67       => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups8682486955453173170nteger @ F @ A2 ) )
% 0.35/0.67          = ( ? [X2: complex] :
% 0.35/0.67                ( ( member_complex @ X2 @ A2 )
% 0.35/0.67                & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % even_prod_iff
% 0.35/0.67  thf(fact_8975_even__prod__iff,axiom,
% 0.35/0.67      ! [A2: set_complex,F: complex > nat] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.67       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups861055069439313189ex_nat @ F @ A2 ) )
% 0.35/0.67          = ( ? [X2: complex] :
% 0.35/0.67                ( ( member_complex @ X2 @ A2 )
% 0.35/0.67                & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % even_prod_iff
% 0.35/0.67  thf(fact_8976_even__prod__iff,axiom,
% 0.35/0.67      ! [A2: set_complex,F: complex > int] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.67       => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups858564598930262913ex_int @ F @ A2 ) )
% 0.35/0.67          = ( ? [X2: complex] :
% 0.35/0.67                ( ( member_complex @ X2 @ A2 )
% 0.35/0.67                & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % even_prod_iff
% 0.35/0.67  thf(fact_8977_even__prod__iff,axiom,
% 0.35/0.67      ! [A2: set_nat,F: nat > nat] :
% 0.35/0.67        ( ( finite_finite_nat @ A2 )
% 0.35/0.67       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 0.35/0.67          = ( ? [X2: nat] :
% 0.35/0.67                ( ( member_nat @ X2 @ A2 )
% 0.35/0.67                & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % even_prod_iff
% 0.35/0.67  thf(fact_8978_even__prod__iff,axiom,
% 0.35/0.67      ! [A2: set_nat,F: nat > int] :
% 0.35/0.67        ( ( finite_finite_nat @ A2 )
% 0.35/0.67       => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups705719431365010083at_int @ F @ A2 ) )
% 0.35/0.67          = ( ? [X2: nat] :
% 0.35/0.67                ( ( member_nat @ X2 @ A2 )
% 0.35/0.67                & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % even_prod_iff
% 0.35/0.67  thf(fact_8979_even__prod__iff,axiom,
% 0.35/0.67      ! [A2: set_int,F: int > int] :
% 0.35/0.67        ( ( finite_finite_int @ A2 )
% 0.35/0.67       => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups1705073143266064639nt_int @ F @ A2 ) )
% 0.35/0.67          = ( ? [X2: int] :
% 0.35/0.67                ( ( member_int @ X2 @ A2 )
% 0.35/0.67                & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % even_prod_iff
% 0.35/0.67  thf(fact_8980_prod_Oremove,axiom,
% 0.35/0.67      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > complex] :
% 0.35/0.67        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.35/0.67       => ( ( member_VEBT_VEBT @ X @ A2 )
% 0.35/0.67         => ( ( groups127312072573709053omplex @ G @ A2 )
% 0.35/0.67            = ( times_times_complex @ ( G @ X ) @ ( groups127312072573709053omplex @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.remove
% 0.35/0.67  thf(fact_8981_prod_Oremove,axiom,
% 0.35/0.67      ! [A2: set_complex,X: complex,G: complex > complex] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.67       => ( ( member_complex @ X @ A2 )
% 0.35/0.67         => ( ( groups3708469109370488835omplex @ G @ A2 )
% 0.35/0.67            = ( times_times_complex @ ( G @ X ) @ ( groups3708469109370488835omplex @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.remove
% 0.35/0.67  thf(fact_8982_prod_Oremove,axiom,
% 0.35/0.67      ! [A2: set_int,X: int,G: int > complex] :
% 0.35/0.67        ( ( finite_finite_int @ A2 )
% 0.35/0.67       => ( ( member_int @ X @ A2 )
% 0.35/0.67         => ( ( groups7440179247065528705omplex @ G @ A2 )
% 0.35/0.67            = ( times_times_complex @ ( G @ X ) @ ( groups7440179247065528705omplex @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.remove
% 0.35/0.67  thf(fact_8983_prod_Oremove,axiom,
% 0.35/0.67      ! [A2: set_real,X: real,G: real > complex] :
% 0.35/0.67        ( ( finite_finite_real @ A2 )
% 0.35/0.67       => ( ( member_real @ X @ A2 )
% 0.35/0.67         => ( ( groups713298508707869441omplex @ G @ A2 )
% 0.35/0.67            = ( times_times_complex @ ( G @ X ) @ ( groups713298508707869441omplex @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.remove
% 0.35/0.67  thf(fact_8984_prod_Oremove,axiom,
% 0.35/0.67      ! [A2: set_nat,X: nat,G: nat > complex] :
% 0.35/0.67        ( ( finite_finite_nat @ A2 )
% 0.35/0.67       => ( ( member_nat @ X @ A2 )
% 0.35/0.67         => ( ( groups6464643781859351333omplex @ G @ A2 )
% 0.35/0.67            = ( times_times_complex @ ( G @ X ) @ ( groups6464643781859351333omplex @ G @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.remove
% 0.35/0.67  thf(fact_8985_prod_Oremove,axiom,
% 0.35/0.67      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > real] :
% 0.35/0.67        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.35/0.67       => ( ( member_VEBT_VEBT @ X @ A2 )
% 0.35/0.67         => ( ( groups2703838992350267259T_real @ G @ A2 )
% 0.35/0.67            = ( times_times_real @ ( G @ X ) @ ( groups2703838992350267259T_real @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.remove
% 0.35/0.67  thf(fact_8986_prod_Oremove,axiom,
% 0.35/0.67      ! [A2: set_complex,X: complex,G: complex > real] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.67       => ( ( member_complex @ X @ A2 )
% 0.35/0.67         => ( ( groups766887009212190081x_real @ G @ A2 )
% 0.35/0.67            = ( times_times_real @ ( G @ X ) @ ( groups766887009212190081x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.remove
% 0.35/0.67  thf(fact_8987_prod_Oremove,axiom,
% 0.35/0.67      ! [A2: set_int,X: int,G: int > real] :
% 0.35/0.67        ( ( finite_finite_int @ A2 )
% 0.35/0.67       => ( ( member_int @ X @ A2 )
% 0.35/0.67         => ( ( groups2316167850115554303t_real @ G @ A2 )
% 0.35/0.67            = ( times_times_real @ ( G @ X ) @ ( groups2316167850115554303t_real @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.remove
% 0.35/0.67  thf(fact_8988_prod_Oremove,axiom,
% 0.35/0.67      ! [A2: set_real,X: real,G: real > real] :
% 0.35/0.67        ( ( finite_finite_real @ A2 )
% 0.35/0.67       => ( ( member_real @ X @ A2 )
% 0.35/0.67         => ( ( groups1681761925125756287l_real @ G @ A2 )
% 0.35/0.67            = ( times_times_real @ ( G @ X ) @ ( groups1681761925125756287l_real @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.remove
% 0.35/0.67  thf(fact_8989_prod_Oremove,axiom,
% 0.35/0.67      ! [A2: set_nat,X: nat,G: nat > real] :
% 0.35/0.67        ( ( finite_finite_nat @ A2 )
% 0.35/0.67       => ( ( member_nat @ X @ A2 )
% 0.35/0.67         => ( ( groups129246275422532515t_real @ G @ A2 )
% 0.35/0.67            = ( times_times_real @ ( G @ X ) @ ( groups129246275422532515t_real @ G @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.remove
% 0.35/0.67  thf(fact_8990_prod_Oinsert__remove,axiom,
% 0.35/0.67      ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > complex,X: vEBT_VEBT] :
% 0.35/0.67        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.35/0.67       => ( ( groups127312072573709053omplex @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 0.35/0.67          = ( times_times_complex @ ( G @ X ) @ ( groups127312072573709053omplex @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.insert_remove
% 0.35/0.67  thf(fact_8991_prod_Oinsert__remove,axiom,
% 0.35/0.67      ! [A2: set_complex,G: complex > complex,X: complex] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.67       => ( ( groups3708469109370488835omplex @ G @ ( insert_complex @ X @ A2 ) )
% 0.35/0.67          = ( times_times_complex @ ( G @ X ) @ ( groups3708469109370488835omplex @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.insert_remove
% 0.35/0.67  thf(fact_8992_prod_Oinsert__remove,axiom,
% 0.35/0.67      ! [A2: set_int,G: int > complex,X: int] :
% 0.35/0.67        ( ( finite_finite_int @ A2 )
% 0.35/0.67       => ( ( groups7440179247065528705omplex @ G @ ( insert_int @ X @ A2 ) )
% 0.35/0.67          = ( times_times_complex @ ( G @ X ) @ ( groups7440179247065528705omplex @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.insert_remove
% 0.35/0.67  thf(fact_8993_prod_Oinsert__remove,axiom,
% 0.35/0.67      ! [A2: set_real,G: real > complex,X: real] :
% 0.35/0.67        ( ( finite_finite_real @ A2 )
% 0.35/0.67       => ( ( groups713298508707869441omplex @ G @ ( insert_real @ X @ A2 ) )
% 0.35/0.67          = ( times_times_complex @ ( G @ X ) @ ( groups713298508707869441omplex @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.insert_remove
% 0.35/0.67  thf(fact_8994_prod_Oinsert__remove,axiom,
% 0.35/0.67      ! [A2: set_nat,G: nat > complex,X: nat] :
% 0.35/0.67        ( ( finite_finite_nat @ A2 )
% 0.35/0.67       => ( ( groups6464643781859351333omplex @ G @ ( insert_nat @ X @ A2 ) )
% 0.35/0.67          = ( times_times_complex @ ( G @ X ) @ ( groups6464643781859351333omplex @ G @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.insert_remove
% 0.35/0.67  thf(fact_8995_prod_Oinsert__remove,axiom,
% 0.35/0.67      ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > real,X: vEBT_VEBT] :
% 0.35/0.67        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.35/0.67       => ( ( groups2703838992350267259T_real @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 0.35/0.67          = ( times_times_real @ ( G @ X ) @ ( groups2703838992350267259T_real @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.insert_remove
% 0.35/0.67  thf(fact_8996_prod_Oinsert__remove,axiom,
% 0.35/0.67      ! [A2: set_complex,G: complex > real,X: complex] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.67       => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X @ A2 ) )
% 0.35/0.67          = ( times_times_real @ ( G @ X ) @ ( groups766887009212190081x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.insert_remove
% 0.35/0.67  thf(fact_8997_prod_Oinsert__remove,axiom,
% 0.35/0.67      ! [A2: set_int,G: int > real,X: int] :
% 0.35/0.67        ( ( finite_finite_int @ A2 )
% 0.35/0.67       => ( ( groups2316167850115554303t_real @ G @ ( insert_int @ X @ A2 ) )
% 0.35/0.67          = ( times_times_real @ ( G @ X ) @ ( groups2316167850115554303t_real @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.insert_remove
% 0.35/0.67  thf(fact_8998_prod_Oinsert__remove,axiom,
% 0.35/0.67      ! [A2: set_real,G: real > real,X: real] :
% 0.35/0.67        ( ( finite_finite_real @ A2 )
% 0.35/0.67       => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X @ A2 ) )
% 0.35/0.67          = ( times_times_real @ ( G @ X ) @ ( groups1681761925125756287l_real @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.insert_remove
% 0.35/0.67  thf(fact_8999_prod_Oinsert__remove,axiom,
% 0.35/0.67      ! [A2: set_nat,G: nat > real,X: nat] :
% 0.35/0.67        ( ( finite_finite_nat @ A2 )
% 0.35/0.67       => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X @ A2 ) )
% 0.35/0.67          = ( times_times_real @ ( G @ X ) @ ( groups129246275422532515t_real @ G @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.insert_remove
% 0.35/0.67  thf(fact_9000_prod_Oub__add__nat,axiom,
% 0.35/0.67      ! [M: nat,N: nat,G: nat > complex,P6: nat] :
% 0.35/0.67        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 0.35/0.67       => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 0.35/0.67          = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.ub_add_nat
% 0.35/0.67  thf(fact_9001_prod_Oub__add__nat,axiom,
% 0.35/0.67      ! [M: nat,N: nat,G: nat > real,P6: nat] :
% 0.35/0.67        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 0.35/0.67       => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 0.35/0.67          = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.ub_add_nat
% 0.35/0.67  thf(fact_9002_prod_Oub__add__nat,axiom,
% 0.35/0.67      ! [M: nat,N: nat,G: nat > nat,P6: nat] :
% 0.35/0.67        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 0.35/0.67       => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 0.35/0.67          = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.ub_add_nat
% 0.35/0.67  thf(fact_9003_prod_Oub__add__nat,axiom,
% 0.35/0.67      ! [M: nat,N: nat,G: nat > int,P6: nat] :
% 0.35/0.67        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 0.35/0.67       => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 0.35/0.67          = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.ub_add_nat
% 0.35/0.67  thf(fact_9004_fold__atLeastAtMost__nat_Osimps,axiom,
% 0.35/0.67      ( set_fo2584398358068434914at_nat
% 0.35/0.67      = ( ^ [F3: nat > nat > nat,A3: nat,B4: nat,Acc2: nat] : ( if_nat @ ( ord_less_nat @ B4 @ A3 ) @ Acc2 @ ( set_fo2584398358068434914at_nat @ F3 @ ( plus_plus_nat @ A3 @ one_one_nat ) @ B4 @ ( F3 @ A3 @ Acc2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % fold_atLeastAtMost_nat.simps
% 0.35/0.67  thf(fact_9005_fold__atLeastAtMost__nat_Oelims,axiom,
% 0.35/0.67      ! [X: nat > nat > nat,Xa2: nat,Xb: nat,Xc: nat,Y2: nat] :
% 0.35/0.67        ( ( ( set_fo2584398358068434914at_nat @ X @ Xa2 @ Xb @ Xc )
% 0.35/0.67          = Y2 )
% 0.35/0.67       => ( ( ( ord_less_nat @ Xb @ Xa2 )
% 0.35/0.67           => ( Y2 = Xc ) )
% 0.35/0.67          & ( ~ ( ord_less_nat @ Xb @ Xa2 )
% 0.35/0.67           => ( Y2
% 0.35/0.67              = ( set_fo2584398358068434914at_nat @ X @ ( plus_plus_nat @ Xa2 @ one_one_nat ) @ Xb @ ( X @ Xa2 @ Xc ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % fold_atLeastAtMost_nat.elims
% 0.35/0.67  thf(fact_9006_prod_Odelta__remove,axiom,
% 0.35/0.67      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > complex,C: vEBT_VEBT > complex] :
% 0.35/0.67        ( ( finite5795047828879050333T_VEBT @ S2 )
% 0.35/0.67       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 0.35/0.67           => ( ( groups127312072573709053omplex
% 0.35/0.67                @ ^ [K3: vEBT_VEBT] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.67                @ S2 )
% 0.35/0.67              = ( times_times_complex @ ( B @ A ) @ ( groups127312072573709053omplex @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 0.35/0.67          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 0.35/0.67           => ( ( groups127312072573709053omplex
% 0.35/0.67                @ ^ [K3: vEBT_VEBT] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.67                @ S2 )
% 0.35/0.67              = ( groups127312072573709053omplex @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.delta_remove
% 0.35/0.67  thf(fact_9007_prod_Odelta__remove,axiom,
% 0.35/0.67      ! [S2: set_complex,A: complex,B: complex > complex,C: complex > complex] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ S2 )
% 0.35/0.67       => ( ( ( member_complex @ A @ S2 )
% 0.35/0.67           => ( ( groups3708469109370488835omplex
% 0.35/0.67                @ ^ [K3: complex] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.67                @ S2 )
% 0.35/0.67              = ( times_times_complex @ ( B @ A ) @ ( groups3708469109370488835omplex @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 0.35/0.67          & ( ~ ( member_complex @ A @ S2 )
% 0.35/0.67           => ( ( groups3708469109370488835omplex
% 0.35/0.67                @ ^ [K3: complex] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.67                @ S2 )
% 0.35/0.67              = ( groups3708469109370488835omplex @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.delta_remove
% 0.35/0.67  thf(fact_9008_prod_Odelta__remove,axiom,
% 0.35/0.67      ! [S2: set_int,A: int,B: int > complex,C: int > complex] :
% 0.35/0.67        ( ( finite_finite_int @ S2 )
% 0.35/0.67       => ( ( ( member_int @ A @ S2 )
% 0.35/0.67           => ( ( groups7440179247065528705omplex
% 0.35/0.67                @ ^ [K3: int] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.67                @ S2 )
% 0.35/0.67              = ( times_times_complex @ ( B @ A ) @ ( groups7440179247065528705omplex @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 0.35/0.67          & ( ~ ( member_int @ A @ S2 )
% 0.35/0.67           => ( ( groups7440179247065528705omplex
% 0.35/0.67                @ ^ [K3: int] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.67                @ S2 )
% 0.35/0.67              = ( groups7440179247065528705omplex @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.delta_remove
% 0.35/0.67  thf(fact_9009_prod_Odelta__remove,axiom,
% 0.35/0.67      ! [S2: set_real,A: real,B: real > complex,C: real > complex] :
% 0.35/0.67        ( ( finite_finite_real @ S2 )
% 0.35/0.67       => ( ( ( member_real @ A @ S2 )
% 0.35/0.67           => ( ( groups713298508707869441omplex
% 0.35/0.67                @ ^ [K3: real] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.67                @ S2 )
% 0.35/0.67              = ( times_times_complex @ ( B @ A ) @ ( groups713298508707869441omplex @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 0.35/0.67          & ( ~ ( member_real @ A @ S2 )
% 0.35/0.67           => ( ( groups713298508707869441omplex
% 0.35/0.67                @ ^ [K3: real] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.67                @ S2 )
% 0.35/0.67              = ( groups713298508707869441omplex @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.delta_remove
% 0.35/0.67  thf(fact_9010_prod_Odelta__remove,axiom,
% 0.35/0.67      ! [S2: set_nat,A: nat,B: nat > complex,C: nat > complex] :
% 0.35/0.67        ( ( finite_finite_nat @ S2 )
% 0.35/0.67       => ( ( ( member_nat @ A @ S2 )
% 0.35/0.67           => ( ( groups6464643781859351333omplex
% 0.35/0.67                @ ^ [K3: nat] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.67                @ S2 )
% 0.35/0.67              = ( times_times_complex @ ( B @ A ) @ ( groups6464643781859351333omplex @ C @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 0.35/0.67          & ( ~ ( member_nat @ A @ S2 )
% 0.35/0.67           => ( ( groups6464643781859351333omplex
% 0.35/0.67                @ ^ [K3: nat] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.67                @ S2 )
% 0.35/0.67              = ( groups6464643781859351333omplex @ C @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.delta_remove
% 0.35/0.67  thf(fact_9011_prod_Odelta__remove,axiom,
% 0.35/0.67      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > real,C: vEBT_VEBT > real] :
% 0.35/0.67        ( ( finite5795047828879050333T_VEBT @ S2 )
% 0.35/0.67       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 0.35/0.67           => ( ( groups2703838992350267259T_real
% 0.35/0.67                @ ^ [K3: vEBT_VEBT] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.67                @ S2 )
% 0.35/0.67              = ( times_times_real @ ( B @ A ) @ ( groups2703838992350267259T_real @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 0.35/0.67          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 0.35/0.67           => ( ( groups2703838992350267259T_real
% 0.35/0.67                @ ^ [K3: vEBT_VEBT] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.67                @ S2 )
% 0.35/0.67              = ( groups2703838992350267259T_real @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.delta_remove
% 0.35/0.67  thf(fact_9012_prod_Odelta__remove,axiom,
% 0.35/0.67      ! [S2: set_complex,A: complex,B: complex > real,C: complex > real] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ S2 )
% 0.35/0.67       => ( ( ( member_complex @ A @ S2 )
% 0.35/0.67           => ( ( groups766887009212190081x_real
% 0.35/0.67                @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.67                @ S2 )
% 0.35/0.67              = ( times_times_real @ ( B @ A ) @ ( groups766887009212190081x_real @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 0.35/0.67          & ( ~ ( member_complex @ A @ S2 )
% 0.35/0.67           => ( ( groups766887009212190081x_real
% 0.35/0.67                @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.67                @ S2 )
% 0.35/0.67              = ( groups766887009212190081x_real @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.delta_remove
% 0.35/0.67  thf(fact_9013_prod_Odelta__remove,axiom,
% 0.35/0.67      ! [S2: set_int,A: int,B: int > real,C: int > real] :
% 0.35/0.67        ( ( finite_finite_int @ S2 )
% 0.35/0.67       => ( ( ( member_int @ A @ S2 )
% 0.35/0.67           => ( ( groups2316167850115554303t_real
% 0.35/0.67                @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.67                @ S2 )
% 0.35/0.67              = ( times_times_real @ ( B @ A ) @ ( groups2316167850115554303t_real @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 0.35/0.67          & ( ~ ( member_int @ A @ S2 )
% 0.35/0.67           => ( ( groups2316167850115554303t_real
% 0.35/0.67                @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.67                @ S2 )
% 0.35/0.67              = ( groups2316167850115554303t_real @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.delta_remove
% 0.35/0.67  thf(fact_9014_prod_Odelta__remove,axiom,
% 0.35/0.67      ! [S2: set_real,A: real,B: real > real,C: real > real] :
% 0.35/0.67        ( ( finite_finite_real @ S2 )
% 0.35/0.67       => ( ( ( member_real @ A @ S2 )
% 0.35/0.67           => ( ( groups1681761925125756287l_real
% 0.35/0.67                @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.67                @ S2 )
% 0.35/0.67              = ( times_times_real @ ( B @ A ) @ ( groups1681761925125756287l_real @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 0.35/0.67          & ( ~ ( member_real @ A @ S2 )
% 0.35/0.67           => ( ( groups1681761925125756287l_real
% 0.35/0.67                @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.67                @ S2 )
% 0.35/0.67              = ( groups1681761925125756287l_real @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.delta_remove
% 0.35/0.67  thf(fact_9015_prod_Odelta__remove,axiom,
% 0.35/0.67      ! [S2: set_nat,A: nat,B: nat > real,C: nat > real] :
% 0.35/0.67        ( ( finite_finite_nat @ S2 )
% 0.35/0.67       => ( ( ( member_nat @ A @ S2 )
% 0.35/0.67           => ( ( groups129246275422532515t_real
% 0.35/0.67                @ ^ [K3: nat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.67                @ S2 )
% 0.35/0.67              = ( times_times_real @ ( B @ A ) @ ( groups129246275422532515t_real @ C @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 0.35/0.67          & ( ~ ( member_nat @ A @ S2 )
% 0.35/0.67           => ( ( groups129246275422532515t_real
% 0.35/0.67                @ ^ [K3: nat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 0.35/0.67                @ S2 )
% 0.35/0.67              = ( groups129246275422532515t_real @ C @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.delta_remove
% 0.35/0.67  thf(fact_9016_frac__eq,axiom,
% 0.35/0.67      ! [X: real] :
% 0.35/0.67        ( ( ( archim2898591450579166408c_real @ X )
% 0.35/0.67          = X )
% 0.35/0.67        = ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.67          & ( ord_less_real @ X @ one_one_real ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % frac_eq
% 0.35/0.67  thf(fact_9017_frac__eq,axiom,
% 0.35/0.67      ! [X: rat] :
% 0.35/0.67        ( ( ( archimedean_frac_rat @ X )
% 0.35/0.67          = X )
% 0.35/0.67        = ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.35/0.67          & ( ord_less_rat @ X @ one_one_rat ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % frac_eq
% 0.35/0.67  thf(fact_9018_norm__prod__diff,axiom,
% 0.35/0.67      ! [I6: set_Pr1261947904930325089at_nat,Z: product_prod_nat_nat > complex,W: product_prod_nat_nat > complex] :
% 0.35/0.67        ( ! [I4: product_prod_nat_nat] :
% 0.35/0.67            ( ( member8440522571783428010at_nat @ I4 @ I6 )
% 0.35/0.67           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I4 ) ) @ one_one_real ) )
% 0.35/0.67       => ( ! [I4: product_prod_nat_nat] :
% 0.35/0.67              ( ( member8440522571783428010at_nat @ I4 @ I6 )
% 0.35/0.67             => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I4 ) ) @ one_one_real ) )
% 0.35/0.67         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups8110221916422527690omplex @ Z @ I6 ) @ ( groups8110221916422527690omplex @ W @ I6 ) ) )
% 0.35/0.67            @ ( groups4567486121110086003t_real
% 0.35/0.67              @ ^ [I3: product_prod_nat_nat] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I3 ) @ ( W @ I3 ) ) )
% 0.35/0.67              @ I6 ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % norm_prod_diff
% 0.35/0.67  thf(fact_9019_norm__prod__diff,axiom,
% 0.35/0.67      ! [I6: set_complex,Z: complex > complex,W: complex > complex] :
% 0.35/0.67        ( ! [I4: complex] :
% 0.35/0.67            ( ( member_complex @ I4 @ I6 )
% 0.35/0.67           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I4 ) ) @ one_one_real ) )
% 0.35/0.67       => ( ! [I4: complex] :
% 0.35/0.67              ( ( member_complex @ I4 @ I6 )
% 0.35/0.67             => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I4 ) ) @ one_one_real ) )
% 0.35/0.67         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups3708469109370488835omplex @ Z @ I6 ) @ ( groups3708469109370488835omplex @ W @ I6 ) ) )
% 0.35/0.67            @ ( groups5808333547571424918x_real
% 0.35/0.67              @ ^ [I3: complex] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I3 ) @ ( W @ I3 ) ) )
% 0.35/0.67              @ I6 ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % norm_prod_diff
% 0.35/0.67  thf(fact_9020_norm__prod__diff,axiom,
% 0.35/0.67      ! [I6: set_real,Z: real > complex,W: real > complex] :
% 0.35/0.67        ( ! [I4: real] :
% 0.35/0.67            ( ( member_real @ I4 @ I6 )
% 0.35/0.67           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I4 ) ) @ one_one_real ) )
% 0.35/0.67       => ( ! [I4: real] :
% 0.35/0.67              ( ( member_real @ I4 @ I6 )
% 0.35/0.67             => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I4 ) ) @ one_one_real ) )
% 0.35/0.67         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups713298508707869441omplex @ Z @ I6 ) @ ( groups713298508707869441omplex @ W @ I6 ) ) )
% 0.35/0.67            @ ( groups8097168146408367636l_real
% 0.35/0.67              @ ^ [I3: real] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I3 ) @ ( W @ I3 ) ) )
% 0.35/0.67              @ I6 ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % norm_prod_diff
% 0.35/0.67  thf(fact_9021_norm__prod__diff,axiom,
% 0.35/0.67      ! [I6: set_int,Z: int > complex,W: int > complex] :
% 0.35/0.67        ( ! [I4: int] :
% 0.35/0.67            ( ( member_int @ I4 @ I6 )
% 0.35/0.67           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I4 ) ) @ one_one_real ) )
% 0.35/0.67       => ( ! [I4: int] :
% 0.35/0.67              ( ( member_int @ I4 @ I6 )
% 0.35/0.67             => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I4 ) ) @ one_one_real ) )
% 0.35/0.67         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups7440179247065528705omplex @ Z @ I6 ) @ ( groups7440179247065528705omplex @ W @ I6 ) ) )
% 0.35/0.67            @ ( groups8778361861064173332t_real
% 0.35/0.67              @ ^ [I3: int] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I3 ) @ ( W @ I3 ) ) )
% 0.35/0.67              @ I6 ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % norm_prod_diff
% 0.35/0.67  thf(fact_9022_norm__prod__diff,axiom,
% 0.35/0.67      ! [I6: set_nat,Z: nat > complex,W: nat > complex] :
% 0.35/0.67        ( ! [I4: nat] :
% 0.35/0.67            ( ( member_nat @ I4 @ I6 )
% 0.35/0.67           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I4 ) ) @ one_one_real ) )
% 0.35/0.67       => ( ! [I4: nat] :
% 0.35/0.67              ( ( member_nat @ I4 @ I6 )
% 0.35/0.67             => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I4 ) ) @ one_one_real ) )
% 0.35/0.67         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups6464643781859351333omplex @ Z @ I6 ) @ ( groups6464643781859351333omplex @ W @ I6 ) ) )
% 0.35/0.67            @ ( groups6591440286371151544t_real
% 0.35/0.67              @ ^ [I3: nat] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I3 ) @ ( W @ I3 ) ) )
% 0.35/0.67              @ I6 ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % norm_prod_diff
% 0.35/0.67  thf(fact_9023_frac__add,axiom,
% 0.35/0.67      ! [X: real,Y2: real] :
% 0.35/0.67        ( ( ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y2 ) ) @ one_one_real )
% 0.35/0.67         => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X @ Y2 ) )
% 0.35/0.67            = ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y2 ) ) ) )
% 0.35/0.67        & ( ~ ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y2 ) ) @ one_one_real )
% 0.35/0.67         => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X @ Y2 ) )
% 0.35/0.67            = ( minus_minus_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y2 ) ) @ one_one_real ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % frac_add
% 0.35/0.67  thf(fact_9024_frac__add,axiom,
% 0.35/0.67      ! [X: rat,Y2: rat] :
% 0.35/0.67        ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y2 ) ) @ one_one_rat )
% 0.35/0.67         => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ Y2 ) )
% 0.35/0.67            = ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y2 ) ) ) )
% 0.35/0.67        & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y2 ) ) @ one_one_rat )
% 0.35/0.67         => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ Y2 ) )
% 0.35/0.67            = ( minus_minus_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y2 ) ) @ one_one_rat ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % frac_add
% 0.35/0.67  thf(fact_9025_fact__eq__fact__times,axiom,
% 0.35/0.67      ! [N: nat,M: nat] :
% 0.35/0.67        ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.67       => ( ( semiri1408675320244567234ct_nat @ M )
% 0.35/0.67          = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N )
% 0.35/0.67            @ ( groups708209901874060359at_nat
% 0.35/0.67              @ ^ [X2: nat] : X2
% 0.35/0.67              @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % fact_eq_fact_times
% 0.35/0.67  thf(fact_9026_prod__mono2,axiom,
% 0.35/0.67      ! [B2: set_int,A2: set_int,F: int > real] :
% 0.35/0.67        ( ( finite_finite_int @ B2 )
% 0.35/0.67       => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 0.35/0.67         => ( ! [B3: int] :
% 0.35/0.67                ( ( member_int @ B3 @ ( minus_minus_set_int @ B2 @ A2 ) )
% 0.35/0.67               => ( ord_less_eq_real @ one_one_real @ ( F @ B3 ) ) )
% 0.35/0.67           => ( ! [A4: int] :
% 0.35/0.67                  ( ( member_int @ A4 @ A2 )
% 0.35/0.67                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A4 ) ) )
% 0.35/0.67             => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ( groups2316167850115554303t_real @ F @ B2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod_mono2
% 0.35/0.67  thf(fact_9027_prod__mono2,axiom,
% 0.35/0.67      ! [B2: set_complex,A2: set_complex,F: complex > real] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ B2 )
% 0.35/0.67       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 0.35/0.67         => ( ! [B3: complex] :
% 0.35/0.67                ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 0.35/0.67               => ( ord_less_eq_real @ one_one_real @ ( F @ B3 ) ) )
% 0.35/0.67           => ( ! [A4: complex] :
% 0.35/0.67                  ( ( member_complex @ A4 @ A2 )
% 0.35/0.67                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A4 ) ) )
% 0.35/0.67             => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ( groups766887009212190081x_real @ F @ B2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod_mono2
% 0.35/0.67  thf(fact_9028_prod__mono2,axiom,
% 0.35/0.67      ! [B2: set_int,A2: set_int,F: int > rat] :
% 0.35/0.67        ( ( finite_finite_int @ B2 )
% 0.35/0.67       => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 0.35/0.67         => ( ! [B3: int] :
% 0.35/0.67                ( ( member_int @ B3 @ ( minus_minus_set_int @ B2 @ A2 ) )
% 0.35/0.67               => ( ord_less_eq_rat @ one_one_rat @ ( F @ B3 ) ) )
% 0.35/0.67           => ( ! [A4: int] :
% 0.35/0.67                  ( ( member_int @ A4 @ A2 )
% 0.35/0.67                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A4 ) ) )
% 0.35/0.67             => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ ( groups1072433553688619179nt_rat @ F @ B2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod_mono2
% 0.35/0.67  thf(fact_9029_prod__mono2,axiom,
% 0.35/0.67      ! [B2: set_complex,A2: set_complex,F: complex > rat] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ B2 )
% 0.35/0.67       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 0.35/0.67         => ( ! [B3: complex] :
% 0.35/0.67                ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 0.35/0.67               => ( ord_less_eq_rat @ one_one_rat @ ( F @ B3 ) ) )
% 0.35/0.67           => ( ! [A4: complex] :
% 0.35/0.67                  ( ( member_complex @ A4 @ A2 )
% 0.35/0.67                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A4 ) ) )
% 0.35/0.67             => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ ( groups225925009352817453ex_rat @ F @ B2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod_mono2
% 0.35/0.67  thf(fact_9030_prod__mono2,axiom,
% 0.35/0.67      ! [B2: set_complex,A2: set_complex,F: complex > int] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ B2 )
% 0.35/0.67       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 0.35/0.67         => ( ! [B3: complex] :
% 0.35/0.67                ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 0.35/0.67               => ( ord_less_eq_int @ one_one_int @ ( F @ B3 ) ) )
% 0.35/0.67           => ( ! [A4: complex] :
% 0.35/0.67                  ( ( member_complex @ A4 @ A2 )
% 0.35/0.67                 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A4 ) ) )
% 0.35/0.67             => ( ord_less_eq_int @ ( groups858564598930262913ex_int @ F @ A2 ) @ ( groups858564598930262913ex_int @ F @ B2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod_mono2
% 0.35/0.67  thf(fact_9031_prod__mono2,axiom,
% 0.35/0.67      ! [B2: set_real,A2: set_real,F: real > real] :
% 0.35/0.67        ( ( finite_finite_real @ B2 )
% 0.35/0.67       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 0.35/0.67         => ( ! [B3: real] :
% 0.35/0.67                ( ( member_real @ B3 @ ( minus_minus_set_real @ B2 @ A2 ) )
% 0.35/0.67               => ( ord_less_eq_real @ one_one_real @ ( F @ B3 ) ) )
% 0.35/0.67           => ( ! [A4: real] :
% 0.35/0.67                  ( ( member_real @ A4 @ A2 )
% 0.35/0.67                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A4 ) ) )
% 0.35/0.67             => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( groups1681761925125756287l_real @ F @ B2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod_mono2
% 0.35/0.67  thf(fact_9032_prod__mono2,axiom,
% 0.35/0.67      ! [B2: set_real,A2: set_real,F: real > rat] :
% 0.35/0.67        ( ( finite_finite_real @ B2 )
% 0.35/0.67       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 0.35/0.67         => ( ! [B3: real] :
% 0.35/0.67                ( ( member_real @ B3 @ ( minus_minus_set_real @ B2 @ A2 ) )
% 0.35/0.67               => ( ord_less_eq_rat @ one_one_rat @ ( F @ B3 ) ) )
% 0.35/0.67           => ( ! [A4: real] :
% 0.35/0.67                  ( ( member_real @ A4 @ A2 )
% 0.35/0.67                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A4 ) ) )
% 0.35/0.67             => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ ( groups4061424788464935467al_rat @ F @ B2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod_mono2
% 0.35/0.67  thf(fact_9033_prod__mono2,axiom,
% 0.35/0.67      ! [B2: set_real,A2: set_real,F: real > int] :
% 0.35/0.67        ( ( finite_finite_real @ B2 )
% 0.35/0.67       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 0.35/0.67         => ( ! [B3: real] :
% 0.35/0.67                ( ( member_real @ B3 @ ( minus_minus_set_real @ B2 @ A2 ) )
% 0.35/0.67               => ( ord_less_eq_int @ one_one_int @ ( F @ B3 ) ) )
% 0.35/0.67           => ( ! [A4: real] :
% 0.35/0.67                  ( ( member_real @ A4 @ A2 )
% 0.35/0.67                 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A4 ) ) )
% 0.35/0.67             => ( ord_less_eq_int @ ( groups4694064378042380927al_int @ F @ A2 ) @ ( groups4694064378042380927al_int @ F @ B2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod_mono2
% 0.35/0.67  thf(fact_9034_prod__mono2,axiom,
% 0.35/0.67      ! [B2: set_nat,A2: set_nat,F: nat > real] :
% 0.35/0.67        ( ( finite_finite_nat @ B2 )
% 0.35/0.67       => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.35/0.67         => ( ! [B3: nat] :
% 0.35/0.67                ( ( member_nat @ B3 @ ( minus_minus_set_nat @ B2 @ A2 ) )
% 0.35/0.67               => ( ord_less_eq_real @ one_one_real @ ( F @ B3 ) ) )
% 0.35/0.67           => ( ! [A4: nat] :
% 0.35/0.67                  ( ( member_nat @ A4 @ A2 )
% 0.35/0.67                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A4 ) ) )
% 0.35/0.67             => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( groups129246275422532515t_real @ F @ B2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod_mono2
% 0.35/0.67  thf(fact_9035_prod__mono2,axiom,
% 0.35/0.67      ! [B2: set_nat,A2: set_nat,F: nat > rat] :
% 0.35/0.67        ( ( finite_finite_nat @ B2 )
% 0.35/0.67       => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.35/0.67         => ( ! [B3: nat] :
% 0.35/0.67                ( ( member_nat @ B3 @ ( minus_minus_set_nat @ B2 @ A2 ) )
% 0.35/0.67               => ( ord_less_eq_rat @ one_one_rat @ ( F @ B3 ) ) )
% 0.35/0.67           => ( ! [A4: nat] :
% 0.35/0.67                  ( ( member_nat @ A4 @ A2 )
% 0.35/0.67                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A4 ) ) )
% 0.35/0.67             => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ ( groups73079841787564623at_rat @ F @ B2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod_mono2
% 0.35/0.67  thf(fact_9036_prod__diff1,axiom,
% 0.35/0.67      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > complex,A: vEBT_VEBT] :
% 0.35/0.67        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.35/0.67       => ( ( ( F @ A )
% 0.35/0.67           != zero_zero_complex )
% 0.35/0.67         => ( ( ( member_VEBT_VEBT @ A @ A2 )
% 0.35/0.67             => ( ( groups127312072573709053omplex @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.35/0.67                = ( divide1717551699836669952omplex @ ( groups127312072573709053omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.35/0.67            & ( ~ ( member_VEBT_VEBT @ A @ A2 )
% 0.35/0.67             => ( ( groups127312072573709053omplex @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.35/0.67                = ( groups127312072573709053omplex @ F @ A2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod_diff1
% 0.35/0.67  thf(fact_9037_prod__diff1,axiom,
% 0.35/0.67      ! [A2: set_complex,F: complex > complex,A: complex] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.67       => ( ( ( F @ A )
% 0.35/0.67           != zero_zero_complex )
% 0.35/0.67         => ( ( ( member_complex @ A @ A2 )
% 0.35/0.67             => ( ( groups3708469109370488835omplex @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.35/0.67                = ( divide1717551699836669952omplex @ ( groups3708469109370488835omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.35/0.67            & ( ~ ( member_complex @ A @ A2 )
% 0.35/0.67             => ( ( groups3708469109370488835omplex @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.35/0.67                = ( groups3708469109370488835omplex @ F @ A2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod_diff1
% 0.35/0.67  thf(fact_9038_prod__diff1,axiom,
% 0.35/0.67      ! [A2: set_int,F: int > complex,A: int] :
% 0.35/0.67        ( ( finite_finite_int @ A2 )
% 0.35/0.67       => ( ( ( F @ A )
% 0.35/0.67           != zero_zero_complex )
% 0.35/0.67         => ( ( ( member_int @ A @ A2 )
% 0.35/0.67             => ( ( groups7440179247065528705omplex @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.35/0.67                = ( divide1717551699836669952omplex @ ( groups7440179247065528705omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.35/0.67            & ( ~ ( member_int @ A @ A2 )
% 0.35/0.67             => ( ( groups7440179247065528705omplex @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.35/0.67                = ( groups7440179247065528705omplex @ F @ A2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod_diff1
% 0.35/0.67  thf(fact_9039_prod__diff1,axiom,
% 0.35/0.67      ! [A2: set_real,F: real > complex,A: real] :
% 0.35/0.67        ( ( finite_finite_real @ A2 )
% 0.35/0.67       => ( ( ( F @ A )
% 0.35/0.67           != zero_zero_complex )
% 0.35/0.67         => ( ( ( member_real @ A @ A2 )
% 0.35/0.67             => ( ( groups713298508707869441omplex @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.35/0.67                = ( divide1717551699836669952omplex @ ( groups713298508707869441omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.35/0.67            & ( ~ ( member_real @ A @ A2 )
% 0.35/0.67             => ( ( groups713298508707869441omplex @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.35/0.67                = ( groups713298508707869441omplex @ F @ A2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod_diff1
% 0.35/0.67  thf(fact_9040_prod__diff1,axiom,
% 0.35/0.67      ! [A2: set_nat,F: nat > complex,A: nat] :
% 0.35/0.67        ( ( finite_finite_nat @ A2 )
% 0.35/0.67       => ( ( ( F @ A )
% 0.35/0.67           != zero_zero_complex )
% 0.35/0.67         => ( ( ( member_nat @ A @ A2 )
% 0.35/0.67             => ( ( groups6464643781859351333omplex @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.35/0.67                = ( divide1717551699836669952omplex @ ( groups6464643781859351333omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.35/0.67            & ( ~ ( member_nat @ A @ A2 )
% 0.35/0.67             => ( ( groups6464643781859351333omplex @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.35/0.67                = ( groups6464643781859351333omplex @ F @ A2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod_diff1
% 0.35/0.67  thf(fact_9041_prod__diff1,axiom,
% 0.35/0.67      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > real,A: vEBT_VEBT] :
% 0.35/0.67        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.35/0.67       => ( ( ( F @ A )
% 0.35/0.67           != zero_zero_real )
% 0.35/0.67         => ( ( ( member_VEBT_VEBT @ A @ A2 )
% 0.35/0.67             => ( ( groups2703838992350267259T_real @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.35/0.67                = ( divide_divide_real @ ( groups2703838992350267259T_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.35/0.67            & ( ~ ( member_VEBT_VEBT @ A @ A2 )
% 0.35/0.67             => ( ( groups2703838992350267259T_real @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.35/0.67                = ( groups2703838992350267259T_real @ F @ A2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod_diff1
% 0.35/0.67  thf(fact_9042_prod__diff1,axiom,
% 0.35/0.67      ! [A2: set_complex,F: complex > real,A: complex] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.67       => ( ( ( F @ A )
% 0.35/0.67           != zero_zero_real )
% 0.35/0.67         => ( ( ( member_complex @ A @ A2 )
% 0.35/0.67             => ( ( groups766887009212190081x_real @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.35/0.67                = ( divide_divide_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.35/0.67            & ( ~ ( member_complex @ A @ A2 )
% 0.35/0.67             => ( ( groups766887009212190081x_real @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.35/0.67                = ( groups766887009212190081x_real @ F @ A2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod_diff1
% 0.35/0.67  thf(fact_9043_prod__diff1,axiom,
% 0.35/0.67      ! [A2: set_int,F: int > real,A: int] :
% 0.35/0.67        ( ( finite_finite_int @ A2 )
% 0.35/0.67       => ( ( ( F @ A )
% 0.35/0.67           != zero_zero_real )
% 0.35/0.67         => ( ( ( member_int @ A @ A2 )
% 0.35/0.67             => ( ( groups2316167850115554303t_real @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.35/0.67                = ( divide_divide_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.35/0.67            & ( ~ ( member_int @ A @ A2 )
% 0.35/0.67             => ( ( groups2316167850115554303t_real @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.35/0.67                = ( groups2316167850115554303t_real @ F @ A2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod_diff1
% 0.35/0.67  thf(fact_9044_prod__diff1,axiom,
% 0.35/0.67      ! [A2: set_real,F: real > real,A: real] :
% 0.35/0.67        ( ( finite_finite_real @ A2 )
% 0.35/0.67       => ( ( ( F @ A )
% 0.35/0.67           != zero_zero_real )
% 0.35/0.67         => ( ( ( member_real @ A @ A2 )
% 0.35/0.67             => ( ( groups1681761925125756287l_real @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.35/0.67                = ( divide_divide_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.35/0.67            & ( ~ ( member_real @ A @ A2 )
% 0.35/0.67             => ( ( groups1681761925125756287l_real @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.35/0.67                = ( groups1681761925125756287l_real @ F @ A2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod_diff1
% 0.35/0.67  thf(fact_9045_prod__diff1,axiom,
% 0.35/0.67      ! [A2: set_nat,F: nat > real,A: nat] :
% 0.35/0.67        ( ( finite_finite_nat @ A2 )
% 0.35/0.67       => ( ( ( F @ A )
% 0.35/0.67           != zero_zero_real )
% 0.35/0.67         => ( ( ( member_nat @ A @ A2 )
% 0.35/0.67             => ( ( groups129246275422532515t_real @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.35/0.67                = ( divide_divide_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.35/0.67            & ( ~ ( member_nat @ A @ A2 )
% 0.35/0.67             => ( ( groups129246275422532515t_real @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.35/0.67                = ( groups129246275422532515t_real @ F @ A2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod_diff1
% 0.35/0.67  thf(fact_9046_pochhammer__Suc__prod,axiom,
% 0.35/0.67      ! [A: rat,N: nat] :
% 0.35/0.67        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 0.35/0.67        = ( groups73079841787564623at_rat
% 0.35/0.67          @ ^ [I3: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ I3 ) )
% 0.35/0.67          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % pochhammer_Suc_prod
% 0.35/0.67  thf(fact_9047_pochhammer__Suc__prod,axiom,
% 0.35/0.67      ! [A: real,N: nat] :
% 0.35/0.67        ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 0.35/0.67        = ( groups129246275422532515t_real
% 0.35/0.67          @ ^ [I3: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ I3 ) )
% 0.35/0.67          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % pochhammer_Suc_prod
% 0.35/0.67  thf(fact_9048_pochhammer__Suc__prod,axiom,
% 0.35/0.67      ! [A: complex,N: nat] :
% 0.35/0.67        ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 0.35/0.67        = ( groups6464643781859351333omplex
% 0.35/0.67          @ ^ [I3: nat] : ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ I3 ) )
% 0.35/0.67          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % pochhammer_Suc_prod
% 0.35/0.67  thf(fact_9049_pochhammer__Suc__prod,axiom,
% 0.35/0.67      ! [A: nat,N: nat] :
% 0.35/0.67        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 0.35/0.67        = ( groups708209901874060359at_nat
% 0.35/0.67          @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ I3 ) )
% 0.35/0.67          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % pochhammer_Suc_prod
% 0.35/0.67  thf(fact_9050_pochhammer__Suc__prod,axiom,
% 0.35/0.67      ! [A: int,N: nat] :
% 0.35/0.67        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 0.35/0.67        = ( groups705719431365010083at_int
% 0.35/0.67          @ ^ [I3: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ I3 ) )
% 0.35/0.67          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % pochhammer_Suc_prod
% 0.35/0.67  thf(fact_9051_pochhammer__prod__rev,axiom,
% 0.35/0.67      ( comm_s4028243227959126397er_rat
% 0.35/0.67      = ( ^ [A3: rat,N2: nat] :
% 0.35/0.67            ( groups73079841787564623at_rat
% 0.35/0.67            @ ^ [I3: nat] : ( plus_plus_rat @ A3 @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 0.35/0.67            @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % pochhammer_prod_rev
% 0.35/0.67  thf(fact_9052_pochhammer__prod__rev,axiom,
% 0.35/0.67      ( comm_s7457072308508201937r_real
% 0.35/0.67      = ( ^ [A3: real,N2: nat] :
% 0.35/0.67            ( groups129246275422532515t_real
% 0.35/0.67            @ ^ [I3: nat] : ( plus_plus_real @ A3 @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 0.35/0.67            @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % pochhammer_prod_rev
% 0.35/0.67  thf(fact_9053_pochhammer__prod__rev,axiom,
% 0.35/0.67      ( comm_s2602460028002588243omplex
% 0.35/0.67      = ( ^ [A3: complex,N2: nat] :
% 0.35/0.67            ( groups6464643781859351333omplex
% 0.35/0.67            @ ^ [I3: nat] : ( plus_plus_complex @ A3 @ ( semiri8010041392384452111omplex @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 0.35/0.67            @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % pochhammer_prod_rev
% 0.35/0.67  thf(fact_9054_pochhammer__prod__rev,axiom,
% 0.35/0.67      ( comm_s4663373288045622133er_nat
% 0.35/0.67      = ( ^ [A3: nat,N2: nat] :
% 0.35/0.67            ( groups708209901874060359at_nat
% 0.35/0.67            @ ^ [I3: nat] : ( plus_plus_nat @ A3 @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 0.35/0.67            @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % pochhammer_prod_rev
% 0.35/0.67  thf(fact_9055_pochhammer__prod__rev,axiom,
% 0.35/0.67      ( comm_s4660882817536571857er_int
% 0.35/0.67      = ( ^ [A3: int,N2: nat] :
% 0.35/0.67            ( groups705719431365010083at_int
% 0.35/0.67            @ ^ [I3: nat] : ( plus_plus_int @ A3 @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 0.35/0.67            @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % pochhammer_prod_rev
% 0.35/0.67  thf(fact_9056_fact__div__fact,axiom,
% 0.35/0.67      ! [N: nat,M: nat] :
% 0.35/0.67        ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.67       => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) )
% 0.35/0.67          = ( groups708209901874060359at_nat
% 0.35/0.67            @ ^ [X2: nat] : X2
% 0.35/0.67            @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % fact_div_fact
% 0.35/0.67  thf(fact_9057_prod_Oin__pairs,axiom,
% 0.35/0.67      ! [G: nat > complex,M: nat,N: nat] :
% 0.35/0.67        ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.35/0.67        = ( groups6464643781859351333omplex
% 0.35/0.67          @ ^ [I3: nat] : ( times_times_complex @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.35/0.67          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.in_pairs
% 0.35/0.67  thf(fact_9058_prod_Oin__pairs,axiom,
% 0.35/0.67      ! [G: nat > real,M: nat,N: nat] :
% 0.35/0.67        ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.35/0.67        = ( groups129246275422532515t_real
% 0.35/0.67          @ ^ [I3: nat] : ( times_times_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.35/0.67          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.in_pairs
% 0.35/0.67  thf(fact_9059_prod_Oin__pairs,axiom,
% 0.35/0.67      ! [G: nat > nat,M: nat,N: nat] :
% 0.35/0.67        ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.35/0.67        = ( groups708209901874060359at_nat
% 0.35/0.67          @ ^ [I3: nat] : ( times_times_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.35/0.67          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.in_pairs
% 0.35/0.67  thf(fact_9060_prod_Oin__pairs,axiom,
% 0.35/0.67      ! [G: nat > int,M: nat,N: nat] :
% 0.35/0.67        ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.35/0.67        = ( groups705719431365010083at_int
% 0.35/0.67          @ ^ [I3: nat] : ( times_times_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.35/0.67          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod.in_pairs
% 0.35/0.67  thf(fact_9061_sum__atLeastAtMost__code,axiom,
% 0.35/0.67      ! [F: nat > complex,A: nat,B: nat] :
% 0.35/0.67        ( ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.35/0.67        = ( set_fo1517530859248394432omplex
% 0.35/0.67          @ ^ [A3: nat] : ( plus_plus_complex @ ( F @ A3 ) )
% 0.35/0.67          @ A
% 0.35/0.67          @ B
% 0.35/0.67          @ zero_zero_complex ) ) ).
% 0.35/0.67  
% 0.35/0.67  % sum_atLeastAtMost_code
% 0.35/0.67  thf(fact_9062_sum__atLeastAtMost__code,axiom,
% 0.35/0.67      ! [F: nat > rat,A: nat,B: nat] :
% 0.35/0.67        ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.35/0.67        = ( set_fo1949268297981939178at_rat
% 0.35/0.67          @ ^ [A3: nat] : ( plus_plus_rat @ ( F @ A3 ) )
% 0.35/0.67          @ A
% 0.35/0.67          @ B
% 0.35/0.67          @ zero_zero_rat ) ) ).
% 0.35/0.67  
% 0.35/0.67  % sum_atLeastAtMost_code
% 0.35/0.67  thf(fact_9063_sum__atLeastAtMost__code,axiom,
% 0.35/0.67      ! [F: nat > int,A: nat,B: nat] :
% 0.35/0.67        ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.35/0.67        = ( set_fo2581907887559384638at_int
% 0.35/0.67          @ ^ [A3: nat] : ( plus_plus_int @ ( F @ A3 ) )
% 0.35/0.67          @ A
% 0.35/0.67          @ B
% 0.35/0.67          @ zero_zero_int ) ) ).
% 0.35/0.67  
% 0.35/0.67  % sum_atLeastAtMost_code
% 0.35/0.67  thf(fact_9064_sum__atLeastAtMost__code,axiom,
% 0.35/0.67      ! [F: nat > nat,A: nat,B: nat] :
% 0.35/0.67        ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.35/0.67        = ( set_fo2584398358068434914at_nat
% 0.35/0.67          @ ^ [A3: nat] : ( plus_plus_nat @ ( F @ A3 ) )
% 0.35/0.67          @ A
% 0.35/0.67          @ B
% 0.35/0.67          @ zero_zero_nat ) ) ).
% 0.35/0.67  
% 0.35/0.67  % sum_atLeastAtMost_code
% 0.35/0.67  thf(fact_9065_sum__atLeastAtMost__code,axiom,
% 0.35/0.67      ! [F: nat > real,A: nat,B: nat] :
% 0.35/0.67        ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.35/0.67        = ( set_fo3111899725591712190t_real
% 0.35/0.67          @ ^ [A3: nat] : ( plus_plus_real @ ( F @ A3 ) )
% 0.35/0.67          @ A
% 0.35/0.67          @ B
% 0.35/0.67          @ zero_zero_real ) ) ).
% 0.35/0.67  
% 0.35/0.67  % sum_atLeastAtMost_code
% 0.35/0.67  thf(fact_9066_pochhammer__Suc__prod__rev,axiom,
% 0.35/0.67      ! [A: rat,N: nat] :
% 0.35/0.67        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 0.35/0.67        = ( groups73079841787564623at_rat
% 0.35/0.67          @ ^ [I3: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N @ I3 ) ) )
% 0.35/0.67          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % pochhammer_Suc_prod_rev
% 0.35/0.67  thf(fact_9067_pochhammer__Suc__prod__rev,axiom,
% 0.35/0.67      ! [A: real,N: nat] :
% 0.35/0.67        ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 0.35/0.67        = ( groups129246275422532515t_real
% 0.35/0.67          @ ^ [I3: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ I3 ) ) )
% 0.35/0.67          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % pochhammer_Suc_prod_rev
% 0.35/0.67  thf(fact_9068_pochhammer__Suc__prod__rev,axiom,
% 0.35/0.67      ! [A: complex,N: nat] :
% 0.35/0.67        ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 0.35/0.67        = ( groups6464643781859351333omplex
% 0.35/0.67          @ ^ [I3: nat] : ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ ( minus_minus_nat @ N @ I3 ) ) )
% 0.35/0.67          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % pochhammer_Suc_prod_rev
% 0.35/0.67  thf(fact_9069_pochhammer__Suc__prod__rev,axiom,
% 0.35/0.67      ! [A: nat,N: nat] :
% 0.35/0.67        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 0.35/0.67        = ( groups708209901874060359at_nat
% 0.35/0.67          @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N @ I3 ) ) )
% 0.35/0.67          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % pochhammer_Suc_prod_rev
% 0.35/0.67  thf(fact_9070_pochhammer__Suc__prod__rev,axiom,
% 0.35/0.67      ! [A: int,N: nat] :
% 0.35/0.67        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 0.35/0.67        = ( groups705719431365010083at_int
% 0.35/0.67          @ ^ [I3: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ I3 ) ) )
% 0.35/0.67          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % pochhammer_Suc_prod_rev
% 0.35/0.67  thf(fact_9071_floor__add,axiom,
% 0.35/0.67      ! [X: real,Y2: real] :
% 0.35/0.67        ( ( ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y2 ) ) @ one_one_real )
% 0.35/0.67         => ( ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ Y2 ) )
% 0.35/0.67            = ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y2 ) ) ) )
% 0.35/0.67        & ( ~ ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y2 ) ) @ one_one_real )
% 0.35/0.67         => ( ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ Y2 ) )
% 0.35/0.67            = ( plus_plus_int @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y2 ) ) @ one_one_int ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % floor_add
% 0.35/0.67  thf(fact_9072_floor__add,axiom,
% 0.35/0.67      ! [X: rat,Y2: rat] :
% 0.35/0.67        ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y2 ) ) @ one_one_rat )
% 0.35/0.67         => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ Y2 ) )
% 0.35/0.67            = ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y2 ) ) ) )
% 0.35/0.67        & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y2 ) ) @ one_one_rat )
% 0.35/0.67         => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ Y2 ) )
% 0.35/0.67            = ( plus_plus_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y2 ) ) @ one_one_int ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % floor_add
% 0.35/0.67  thf(fact_9073_fact__code,axiom,
% 0.35/0.67      ( semiri1406184849735516958ct_int
% 0.35/0.67      = ( ^ [N2: nat] : ( semiri1314217659103216013at_int @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 @ one_one_nat ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % fact_code
% 0.35/0.67  thf(fact_9074_fact__code,axiom,
% 0.35/0.67      ( semiri5044797733671781792omplex
% 0.35/0.67      = ( ^ [N2: nat] : ( semiri8010041392384452111omplex @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 @ one_one_nat ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % fact_code
% 0.35/0.67  thf(fact_9075_fact__code,axiom,
% 0.35/0.67      ( semiri2265585572941072030t_real
% 0.35/0.67      = ( ^ [N2: nat] : ( semiri5074537144036343181t_real @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 @ one_one_nat ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % fact_code
% 0.35/0.67  thf(fact_9076_fact__code,axiom,
% 0.35/0.67      ( semiri1408675320244567234ct_nat
% 0.35/0.67      = ( ^ [N2: nat] : ( semiri1316708129612266289at_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 @ one_one_nat ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % fact_code
% 0.35/0.67  thf(fact_9077_gchoose__row__sum__weighted,axiom,
% 0.35/0.67      ! [R: rat,M: nat] :
% 0.35/0.67        ( ( groups2906978787729119204at_rat
% 0.35/0.67          @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ R @ K3 ) @ ( minus_minus_rat @ ( divide_divide_rat @ R @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K3 ) ) )
% 0.35/0.67          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 0.35/0.67        = ( times_times_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ ( suc @ M ) ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ R @ ( suc @ M ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % gchoose_row_sum_weighted
% 0.35/0.67  thf(fact_9078_gchoose__row__sum__weighted,axiom,
% 0.35/0.67      ! [R: complex,M: nat] :
% 0.35/0.67        ( ( groups2073611262835488442omplex
% 0.35/0.67          @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ R @ K3 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ R @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K3 ) ) )
% 0.35/0.67          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 0.35/0.67        = ( times_times_complex @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ ( suc @ M ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( gbinomial_complex @ R @ ( suc @ M ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % gchoose_row_sum_weighted
% 0.35/0.67  thf(fact_9079_gchoose__row__sum__weighted,axiom,
% 0.35/0.67      ! [R: real,M: nat] :
% 0.35/0.67        ( ( groups6591440286371151544t_real
% 0.35/0.67          @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ R @ K3 ) @ ( minus_minus_real @ ( divide_divide_real @ R @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K3 ) ) )
% 0.35/0.67          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 0.35/0.67        = ( times_times_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( gbinomial_real @ R @ ( suc @ M ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % gchoose_row_sum_weighted
% 0.35/0.67  thf(fact_9080_Maclaurin__sin__bound,axiom,
% 0.35/0.67      ! [X: real,N: nat] :
% 0.35/0.67        ( ord_less_eq_real
% 0.35/0.67        @ ( abs_abs_real
% 0.35/0.67          @ ( minus_minus_real @ ( sin_real @ X )
% 0.35/0.67            @ ( groups6591440286371151544t_real
% 0.35/0.67              @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 0.35/0.67              @ ( set_ord_lessThan_nat @ N ) ) ) )
% 0.35/0.67        @ ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( abs_abs_real @ X ) @ N ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % Maclaurin_sin_bound
% 0.35/0.67  thf(fact_9081_central__binomial__lower__bound,axiom,
% 0.35/0.67      ! [N: nat] :
% 0.35/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.67       => ( ord_less_eq_real @ ( divide_divide_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ N ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % central_binomial_lower_bound
% 0.35/0.67  thf(fact_9082_exp__two__pi__i,axiom,
% 0.35/0.67      ( ( exp_complex @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( real_V4546457046886955230omplex @ pi ) ) @ imaginary_unit ) )
% 0.35/0.67      = one_one_complex ) ).
% 0.35/0.67  
% 0.35/0.67  % exp_two_pi_i
% 0.35/0.67  thf(fact_9083_inverse__mult__distrib,axiom,
% 0.35/0.67      ! [A: real,B: real] :
% 0.35/0.67        ( ( inverse_inverse_real @ ( times_times_real @ A @ B ) )
% 0.35/0.67        = ( times_times_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_mult_distrib
% 0.35/0.67  thf(fact_9084_inverse__mult__distrib,axiom,
% 0.35/0.67      ! [A: complex,B: complex] :
% 0.35/0.67        ( ( invers8013647133539491842omplex @ ( times_times_complex @ A @ B ) )
% 0.35/0.67        = ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_mult_distrib
% 0.35/0.67  thf(fact_9085_inverse__1,axiom,
% 0.35/0.67      ( ( inverse_inverse_rat @ one_one_rat )
% 0.35/0.67      = one_one_rat ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_1
% 0.35/0.67  thf(fact_9086_inverse__1,axiom,
% 0.35/0.67      ( ( inverse_inverse_real @ one_one_real )
% 0.35/0.67      = one_one_real ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_1
% 0.35/0.67  thf(fact_9087_inverse__1,axiom,
% 0.35/0.67      ( ( invers8013647133539491842omplex @ one_one_complex )
% 0.35/0.67      = one_one_complex ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_1
% 0.35/0.67  thf(fact_9088_inverse__eq__1__iff,axiom,
% 0.35/0.67      ! [X: rat] :
% 0.35/0.67        ( ( ( inverse_inverse_rat @ X )
% 0.35/0.67          = one_one_rat )
% 0.35/0.67        = ( X = one_one_rat ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_eq_1_iff
% 0.35/0.67  thf(fact_9089_inverse__eq__1__iff,axiom,
% 0.35/0.67      ! [X: real] :
% 0.35/0.67        ( ( ( inverse_inverse_real @ X )
% 0.35/0.67          = one_one_real )
% 0.35/0.67        = ( X = one_one_real ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_eq_1_iff
% 0.35/0.67  thf(fact_9090_inverse__eq__1__iff,axiom,
% 0.35/0.67      ! [X: complex] :
% 0.35/0.67        ( ( ( invers8013647133539491842omplex @ X )
% 0.35/0.67          = one_one_complex )
% 0.35/0.67        = ( X = one_one_complex ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_eq_1_iff
% 0.35/0.67  thf(fact_9091_inverse__divide,axiom,
% 0.35/0.67      ! [A: rat,B: rat] :
% 0.35/0.67        ( ( inverse_inverse_rat @ ( divide_divide_rat @ A @ B ) )
% 0.35/0.67        = ( divide_divide_rat @ B @ A ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_divide
% 0.35/0.67  thf(fact_9092_inverse__divide,axiom,
% 0.35/0.67      ! [A: real,B: real] :
% 0.35/0.67        ( ( inverse_inverse_real @ ( divide_divide_real @ A @ B ) )
% 0.35/0.67        = ( divide_divide_real @ B @ A ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_divide
% 0.35/0.67  thf(fact_9093_inverse__divide,axiom,
% 0.35/0.67      ! [A: complex,B: complex] :
% 0.35/0.67        ( ( invers8013647133539491842omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.35/0.67        = ( divide1717551699836669952omplex @ B @ A ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_divide
% 0.35/0.67  thf(fact_9094_binomial__Suc__n,axiom,
% 0.35/0.67      ! [N: nat] :
% 0.35/0.67        ( ( binomial @ ( suc @ N ) @ N )
% 0.35/0.67        = ( suc @ N ) ) ).
% 0.35/0.67  
% 0.35/0.67  % binomial_Suc_n
% 0.35/0.67  thf(fact_9095_binomial__n__n,axiom,
% 0.35/0.67      ! [N: nat] :
% 0.35/0.67        ( ( binomial @ N @ N )
% 0.35/0.67        = one_one_nat ) ).
% 0.35/0.67  
% 0.35/0.67  % binomial_n_n
% 0.35/0.67  thf(fact_9096_inverse__nonnegative__iff__nonnegative,axiom,
% 0.35/0.67      ! [A: rat] :
% 0.35/0.67        ( ( ord_less_eq_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 0.35/0.67        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_nonnegative_iff_nonnegative
% 0.35/0.67  thf(fact_9097_inverse__nonnegative__iff__nonnegative,axiom,
% 0.35/0.67      ! [A: real] :
% 0.35/0.67        ( ( ord_less_eq_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 0.35/0.67        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_nonnegative_iff_nonnegative
% 0.35/0.67  thf(fact_9098_inverse__nonpositive__iff__nonpositive,axiom,
% 0.35/0.67      ! [A: rat] :
% 0.35/0.67        ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 0.35/0.67        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_nonpositive_iff_nonpositive
% 0.35/0.67  thf(fact_9099_inverse__nonpositive__iff__nonpositive,axiom,
% 0.35/0.67      ! [A: real] :
% 0.35/0.67        ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 0.35/0.67        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_nonpositive_iff_nonpositive
% 0.35/0.67  thf(fact_9100_inverse__less__iff__less,axiom,
% 0.35/0.67      ! [A: rat,B: rat] :
% 0.35/0.67        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.35/0.67       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.35/0.67         => ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 0.35/0.67            = ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_less_iff_less
% 0.35/0.67  thf(fact_9101_inverse__less__iff__less,axiom,
% 0.35/0.67      ! [A: real,B: real] :
% 0.35/0.67        ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.67       => ( ( ord_less_real @ zero_zero_real @ B )
% 0.35/0.67         => ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 0.35/0.67            = ( ord_less_real @ B @ A ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_less_iff_less
% 0.35/0.67  thf(fact_9102_inverse__less__iff__less__neg,axiom,
% 0.35/0.67      ! [A: rat,B: rat] :
% 0.35/0.67        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.35/0.67       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.35/0.67         => ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 0.35/0.67            = ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_less_iff_less_neg
% 0.35/0.67  thf(fact_9103_inverse__less__iff__less__neg,axiom,
% 0.35/0.67      ! [A: real,B: real] :
% 0.35/0.67        ( ( ord_less_real @ A @ zero_zero_real )
% 0.35/0.67       => ( ( ord_less_real @ B @ zero_zero_real )
% 0.35/0.67         => ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 0.35/0.67            = ( ord_less_real @ B @ A ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_less_iff_less_neg
% 0.35/0.67  thf(fact_9104_inverse__negative__iff__negative,axiom,
% 0.35/0.67      ! [A: rat] :
% 0.35/0.67        ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 0.35/0.67        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_negative_iff_negative
% 0.35/0.67  thf(fact_9105_inverse__negative__iff__negative,axiom,
% 0.35/0.67      ! [A: real] :
% 0.35/0.67        ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 0.35/0.67        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_negative_iff_negative
% 0.35/0.67  thf(fact_9106_inverse__positive__iff__positive,axiom,
% 0.35/0.67      ! [A: rat] :
% 0.35/0.67        ( ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 0.35/0.67        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_positive_iff_positive
% 0.35/0.67  thf(fact_9107_inverse__positive__iff__positive,axiom,
% 0.35/0.67      ! [A: real] :
% 0.35/0.67        ( ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 0.35/0.67        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_positive_iff_positive
% 0.35/0.67  thf(fact_9108_gbinomial__0_I2_J,axiom,
% 0.35/0.67      ! [K: nat] :
% 0.35/0.67        ( ( gbinomial_complex @ zero_zero_complex @ ( suc @ K ) )
% 0.35/0.67        = zero_zero_complex ) ).
% 0.35/0.67  
% 0.35/0.67  % gbinomial_0(2)
% 0.35/0.67  thf(fact_9109_gbinomial__0_I2_J,axiom,
% 0.35/0.67      ! [K: nat] :
% 0.35/0.67        ( ( gbinomial_real @ zero_zero_real @ ( suc @ K ) )
% 0.35/0.67        = zero_zero_real ) ).
% 0.35/0.67  
% 0.35/0.67  % gbinomial_0(2)
% 0.35/0.67  thf(fact_9110_gbinomial__0_I2_J,axiom,
% 0.35/0.67      ! [K: nat] :
% 0.35/0.67        ( ( gbinomial_rat @ zero_zero_rat @ ( suc @ K ) )
% 0.35/0.67        = zero_zero_rat ) ).
% 0.35/0.67  
% 0.35/0.67  % gbinomial_0(2)
% 0.35/0.67  thf(fact_9111_gbinomial__0_I2_J,axiom,
% 0.35/0.67      ! [K: nat] :
% 0.35/0.67        ( ( gbinomial_nat @ zero_zero_nat @ ( suc @ K ) )
% 0.35/0.67        = zero_zero_nat ) ).
% 0.35/0.67  
% 0.35/0.67  % gbinomial_0(2)
% 0.35/0.67  thf(fact_9112_gbinomial__0_I2_J,axiom,
% 0.35/0.67      ! [K: nat] :
% 0.35/0.67        ( ( gbinomial_int @ zero_zero_int @ ( suc @ K ) )
% 0.35/0.67        = zero_zero_int ) ).
% 0.35/0.67  
% 0.35/0.67  % gbinomial_0(2)
% 0.35/0.67  thf(fact_9113_binomial__1,axiom,
% 0.35/0.67      ! [N: nat] :
% 0.35/0.67        ( ( binomial @ N @ ( suc @ zero_zero_nat ) )
% 0.35/0.67        = N ) ).
% 0.35/0.67  
% 0.35/0.67  % binomial_1
% 0.35/0.67  thf(fact_9114_binomial__0__Suc,axiom,
% 0.35/0.67      ! [K: nat] :
% 0.35/0.67        ( ( binomial @ zero_zero_nat @ ( suc @ K ) )
% 0.35/0.67        = zero_zero_nat ) ).
% 0.35/0.67  
% 0.35/0.67  % binomial_0_Suc
% 0.35/0.67  thf(fact_9115_binomial__Suc__Suc,axiom,
% 0.35/0.67      ! [N: nat,K: nat] :
% 0.35/0.67        ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 0.35/0.67        = ( plus_plus_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % binomial_Suc_Suc
% 0.35/0.67  thf(fact_9116_binomial__eq__0__iff,axiom,
% 0.35/0.67      ! [N: nat,K: nat] :
% 0.35/0.67        ( ( ( binomial @ N @ K )
% 0.35/0.67          = zero_zero_nat )
% 0.35/0.67        = ( ord_less_nat @ N @ K ) ) ).
% 0.35/0.67  
% 0.35/0.67  % binomial_eq_0_iff
% 0.35/0.67  thf(fact_9117_gbinomial__0_I1_J,axiom,
% 0.35/0.67      ! [A: complex] :
% 0.35/0.67        ( ( gbinomial_complex @ A @ zero_zero_nat )
% 0.35/0.67        = one_one_complex ) ).
% 0.35/0.67  
% 0.35/0.67  % gbinomial_0(1)
% 0.35/0.67  thf(fact_9118_gbinomial__0_I1_J,axiom,
% 0.35/0.67      ! [A: real] :
% 0.35/0.67        ( ( gbinomial_real @ A @ zero_zero_nat )
% 0.35/0.67        = one_one_real ) ).
% 0.35/0.67  
% 0.35/0.67  % gbinomial_0(1)
% 0.35/0.67  thf(fact_9119_gbinomial__0_I1_J,axiom,
% 0.35/0.67      ! [A: rat] :
% 0.35/0.67        ( ( gbinomial_rat @ A @ zero_zero_nat )
% 0.35/0.67        = one_one_rat ) ).
% 0.35/0.67  
% 0.35/0.67  % gbinomial_0(1)
% 0.35/0.67  thf(fact_9120_gbinomial__0_I1_J,axiom,
% 0.35/0.67      ! [A: nat] :
% 0.35/0.67        ( ( gbinomial_nat @ A @ zero_zero_nat )
% 0.35/0.67        = one_one_nat ) ).
% 0.35/0.67  
% 0.35/0.67  % gbinomial_0(1)
% 0.35/0.67  thf(fact_9121_gbinomial__0_I1_J,axiom,
% 0.35/0.67      ! [A: int] :
% 0.35/0.67        ( ( gbinomial_int @ A @ zero_zero_nat )
% 0.35/0.67        = one_one_int ) ).
% 0.35/0.67  
% 0.35/0.67  % gbinomial_0(1)
% 0.35/0.67  thf(fact_9122_binomial__n__0,axiom,
% 0.35/0.67      ! [N: nat] :
% 0.35/0.67        ( ( binomial @ N @ zero_zero_nat )
% 0.35/0.67        = one_one_nat ) ).
% 0.35/0.67  
% 0.35/0.67  % binomial_n_0
% 0.35/0.67  thf(fact_9123_norm__ii,axiom,
% 0.35/0.67      ( ( real_V1022390504157884413omplex @ imaginary_unit )
% 0.35/0.67      = one_one_real ) ).
% 0.35/0.67  
% 0.35/0.67  % norm_ii
% 0.35/0.67  thf(fact_9124_prod__eq__1__iff,axiom,
% 0.35/0.67      ! [A2: set_complex,F: complex > nat] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.67       => ( ( ( groups861055069439313189ex_nat @ F @ A2 )
% 0.35/0.67            = one_one_nat )
% 0.35/0.67          = ( ! [X2: complex] :
% 0.35/0.67                ( ( member_complex @ X2 @ A2 )
% 0.35/0.67               => ( ( F @ X2 )
% 0.35/0.67                  = one_one_nat ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod_eq_1_iff
% 0.35/0.67  thf(fact_9125_prod__eq__1__iff,axiom,
% 0.35/0.67      ! [A2: set_nat,F: nat > nat] :
% 0.35/0.67        ( ( finite_finite_nat @ A2 )
% 0.35/0.67       => ( ( ( groups708209901874060359at_nat @ F @ A2 )
% 0.35/0.67            = one_one_nat )
% 0.35/0.67          = ( ! [X2: nat] :
% 0.35/0.67                ( ( member_nat @ X2 @ A2 )
% 0.35/0.67               => ( ( F @ X2 )
% 0.35/0.67                  = one_one_nat ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod_eq_1_iff
% 0.35/0.67  thf(fact_9126_inverse__le__iff__le__neg,axiom,
% 0.35/0.67      ! [A: rat,B: rat] :
% 0.35/0.67        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.35/0.67       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.35/0.67         => ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 0.35/0.67            = ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_le_iff_le_neg
% 0.35/0.67  thf(fact_9127_inverse__le__iff__le__neg,axiom,
% 0.35/0.67      ! [A: real,B: real] :
% 0.35/0.67        ( ( ord_less_real @ A @ zero_zero_real )
% 0.35/0.67       => ( ( ord_less_real @ B @ zero_zero_real )
% 0.35/0.67         => ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 0.35/0.67            = ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_le_iff_le_neg
% 0.35/0.67  thf(fact_9128_inverse__le__iff__le,axiom,
% 0.35/0.67      ! [A: rat,B: rat] :
% 0.35/0.67        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.35/0.67       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.35/0.67         => ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 0.35/0.67            = ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_le_iff_le
% 0.35/0.67  thf(fact_9129_inverse__le__iff__le,axiom,
% 0.35/0.67      ! [A: real,B: real] :
% 0.35/0.67        ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.67       => ( ( ord_less_real @ zero_zero_real @ B )
% 0.35/0.67         => ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 0.35/0.67            = ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_le_iff_le
% 0.35/0.67  thf(fact_9130_right__inverse,axiom,
% 0.35/0.67      ! [A: rat] :
% 0.35/0.67        ( ( A != zero_zero_rat )
% 0.35/0.67       => ( ( times_times_rat @ A @ ( inverse_inverse_rat @ A ) )
% 0.35/0.67          = one_one_rat ) ) ).
% 0.35/0.67  
% 0.35/0.67  % right_inverse
% 0.35/0.67  thf(fact_9131_right__inverse,axiom,
% 0.35/0.67      ! [A: real] :
% 0.35/0.67        ( ( A != zero_zero_real )
% 0.35/0.67       => ( ( times_times_real @ A @ ( inverse_inverse_real @ A ) )
% 0.35/0.67          = one_one_real ) ) ).
% 0.35/0.67  
% 0.35/0.67  % right_inverse
% 0.35/0.67  thf(fact_9132_right__inverse,axiom,
% 0.35/0.67      ! [A: complex] :
% 0.35/0.67        ( ( A != zero_zero_complex )
% 0.35/0.67       => ( ( times_times_complex @ A @ ( invers8013647133539491842omplex @ A ) )
% 0.35/0.67          = one_one_complex ) ) ).
% 0.35/0.67  
% 0.35/0.67  % right_inverse
% 0.35/0.67  thf(fact_9133_left__inverse,axiom,
% 0.35/0.67      ! [A: rat] :
% 0.35/0.67        ( ( A != zero_zero_rat )
% 0.35/0.67       => ( ( times_times_rat @ ( inverse_inverse_rat @ A ) @ A )
% 0.35/0.67          = one_one_rat ) ) ).
% 0.35/0.67  
% 0.35/0.67  % left_inverse
% 0.35/0.67  thf(fact_9134_left__inverse,axiom,
% 0.35/0.67      ! [A: real] :
% 0.35/0.67        ( ( A != zero_zero_real )
% 0.35/0.67       => ( ( times_times_real @ ( inverse_inverse_real @ A ) @ A )
% 0.35/0.67          = one_one_real ) ) ).
% 0.35/0.67  
% 0.35/0.67  % left_inverse
% 0.35/0.67  thf(fact_9135_left__inverse,axiom,
% 0.35/0.67      ! [A: complex] :
% 0.35/0.67        ( ( A != zero_zero_complex )
% 0.35/0.67       => ( ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ A )
% 0.35/0.67          = one_one_complex ) ) ).
% 0.35/0.67  
% 0.35/0.67  % left_inverse
% 0.35/0.67  thf(fact_9136_inverse__eq__divide__numeral,axiom,
% 0.35/0.67      ! [W: num] :
% 0.35/0.67        ( ( inverse_inverse_rat @ ( numeral_numeral_rat @ W ) )
% 0.35/0.67        = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ W ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_eq_divide_numeral
% 0.35/0.67  thf(fact_9137_inverse__eq__divide__numeral,axiom,
% 0.35/0.67      ! [W: num] :
% 0.35/0.67        ( ( inverse_inverse_real @ ( numeral_numeral_real @ W ) )
% 0.35/0.67        = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ W ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_eq_divide_numeral
% 0.35/0.67  thf(fact_9138_inverse__eq__divide__numeral,axiom,
% 0.35/0.67      ! [W: num] :
% 0.35/0.67        ( ( invers8013647133539491842omplex @ ( numera6690914467698888265omplex @ W ) )
% 0.35/0.67        = ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_eq_divide_numeral
% 0.35/0.67  thf(fact_9139_zero__less__binomial__iff,axiom,
% 0.35/0.67      ! [N: nat,K: nat] :
% 0.35/0.67        ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) )
% 0.35/0.67        = ( ord_less_eq_nat @ K @ N ) ) ).
% 0.35/0.67  
% 0.35/0.67  % zero_less_binomial_iff
% 0.35/0.67  thf(fact_9140_prod__pos__nat__iff,axiom,
% 0.35/0.67      ! [A2: set_complex,F: complex > nat] :
% 0.35/0.67        ( ( finite3207457112153483333omplex @ A2 )
% 0.35/0.67       => ( ( ord_less_nat @ zero_zero_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) )
% 0.35/0.67          = ( ! [X2: complex] :
% 0.35/0.67                ( ( member_complex @ X2 @ A2 )
% 0.35/0.67               => ( ord_less_nat @ zero_zero_nat @ ( F @ X2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod_pos_nat_iff
% 0.35/0.67  thf(fact_9141_prod__pos__nat__iff,axiom,
% 0.35/0.67      ! [A2: set_nat,F: nat > nat] :
% 0.35/0.67        ( ( finite_finite_nat @ A2 )
% 0.35/0.67       => ( ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 0.35/0.67          = ( ! [X2: nat] :
% 0.35/0.67                ( ( member_nat @ X2 @ A2 )
% 0.35/0.67               => ( ord_less_nat @ zero_zero_nat @ ( F @ X2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod_pos_nat_iff
% 0.35/0.67  thf(fact_9142_inverse__eq__divide__neg__numeral,axiom,
% 0.35/0.67      ! [W: num] :
% 0.35/0.67        ( ( inverse_inverse_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 0.35/0.67        = ( divide_divide_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_eq_divide_neg_numeral
% 0.35/0.67  thf(fact_9143_inverse__eq__divide__neg__numeral,axiom,
% 0.35/0.67      ! [W: num] :
% 0.35/0.67        ( ( inverse_inverse_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 0.35/0.67        = ( divide_divide_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_eq_divide_neg_numeral
% 0.35/0.67  thf(fact_9144_inverse__eq__divide__neg__numeral,axiom,
% 0.35/0.67      ! [W: num] :
% 0.35/0.67        ( ( invers8013647133539491842omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 0.35/0.67        = ( divide1717551699836669952omplex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_eq_divide_neg_numeral
% 0.35/0.67  thf(fact_9145_power2__i,axiom,
% 0.35/0.67      ( ( power_power_complex @ imaginary_unit @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.67      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.35/0.67  
% 0.35/0.67  % power2_i
% 0.35/0.67  thf(fact_9146_i__even__power,axiom,
% 0.35/0.67      ! [N: nat] :
% 0.35/0.67        ( ( power_power_complex @ imaginary_unit @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.67        = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) ) ).
% 0.35/0.67  
% 0.35/0.67  % i_even_power
% 0.35/0.67  thf(fact_9147_exp__two__pi__i_H,axiom,
% 0.35/0.67      ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) )
% 0.35/0.67      = one_one_complex ) ).
% 0.35/0.67  
% 0.35/0.67  % exp_two_pi_i'
% 0.35/0.67  thf(fact_9148_mult__commute__imp__mult__inverse__commute,axiom,
% 0.35/0.67      ! [Y2: real,X: real] :
% 0.35/0.67        ( ( ( times_times_real @ Y2 @ X )
% 0.35/0.67          = ( times_times_real @ X @ Y2 ) )
% 0.35/0.67       => ( ( times_times_real @ ( inverse_inverse_real @ Y2 ) @ X )
% 0.35/0.67          = ( times_times_real @ X @ ( inverse_inverse_real @ Y2 ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % mult_commute_imp_mult_inverse_commute
% 0.35/0.67  thf(fact_9149_mult__commute__imp__mult__inverse__commute,axiom,
% 0.35/0.67      ! [Y2: complex,X: complex] :
% 0.35/0.67        ( ( ( times_times_complex @ Y2 @ X )
% 0.35/0.67          = ( times_times_complex @ X @ Y2 ) )
% 0.35/0.67       => ( ( times_times_complex @ ( invers8013647133539491842omplex @ Y2 ) @ X )
% 0.35/0.67          = ( times_times_complex @ X @ ( invers8013647133539491842omplex @ Y2 ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % mult_commute_imp_mult_inverse_commute
% 0.35/0.67  thf(fact_9150_choose__one,axiom,
% 0.35/0.67      ! [N: nat] :
% 0.35/0.67        ( ( binomial @ N @ one_one_nat )
% 0.35/0.67        = N ) ).
% 0.35/0.67  
% 0.35/0.67  % choose_one
% 0.35/0.67  thf(fact_9151_power__inverse,axiom,
% 0.35/0.67      ! [A: real,N: nat] :
% 0.35/0.67        ( ( power_power_real @ ( inverse_inverse_real @ A ) @ N )
% 0.35/0.67        = ( inverse_inverse_real @ ( power_power_real @ A @ N ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % power_inverse
% 0.35/0.67  thf(fact_9152_power__inverse,axiom,
% 0.35/0.67      ! [A: complex,N: nat] :
% 0.35/0.67        ( ( power_power_complex @ ( invers8013647133539491842omplex @ A ) @ N )
% 0.35/0.67        = ( invers8013647133539491842omplex @ ( power_power_complex @ A @ N ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % power_inverse
% 0.35/0.67  thf(fact_9153_real__sqrt__inverse,axiom,
% 0.35/0.67      ! [X: real] :
% 0.35/0.67        ( ( sqrt @ ( inverse_inverse_real @ X ) )
% 0.35/0.67        = ( inverse_inverse_real @ ( sqrt @ X ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % real_sqrt_inverse
% 0.35/0.67  thf(fact_9154_norm__inverse__le__norm,axiom,
% 0.35/0.67      ! [R: real,X: real] :
% 0.35/0.67        ( ( ord_less_eq_real @ R @ ( real_V7735802525324610683m_real @ X ) )
% 0.35/0.67       => ( ( ord_less_real @ zero_zero_real @ R )
% 0.35/0.67         => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( inverse_inverse_real @ X ) ) @ ( inverse_inverse_real @ R ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % norm_inverse_le_norm
% 0.35/0.67  thf(fact_9155_norm__inverse__le__norm,axiom,
% 0.35/0.67      ! [R: real,X: complex] :
% 0.35/0.67        ( ( ord_less_eq_real @ R @ ( real_V1022390504157884413omplex @ X ) )
% 0.35/0.67       => ( ( ord_less_real @ zero_zero_real @ R )
% 0.35/0.67         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( invers8013647133539491842omplex @ X ) ) @ ( inverse_inverse_real @ R ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % norm_inverse_le_norm
% 0.35/0.67  thf(fact_9156_binomial__eq__0,axiom,
% 0.35/0.67      ! [N: nat,K: nat] :
% 0.35/0.67        ( ( ord_less_nat @ N @ K )
% 0.35/0.67       => ( ( binomial @ N @ K )
% 0.35/0.67          = zero_zero_nat ) ) ).
% 0.35/0.67  
% 0.35/0.67  % binomial_eq_0
% 0.35/0.67  thf(fact_9157_positive__imp__inverse__positive,axiom,
% 0.35/0.67      ! [A: rat] :
% 0.35/0.67        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.35/0.67       => ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % positive_imp_inverse_positive
% 0.35/0.67  thf(fact_9158_positive__imp__inverse__positive,axiom,
% 0.35/0.67      ! [A: real] :
% 0.35/0.67        ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.67       => ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % positive_imp_inverse_positive
% 0.35/0.67  thf(fact_9159_negative__imp__inverse__negative,axiom,
% 0.35/0.67      ! [A: rat] :
% 0.35/0.67        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.35/0.67       => ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat ) ) ).
% 0.35/0.67  
% 0.35/0.67  % negative_imp_inverse_negative
% 0.35/0.67  thf(fact_9160_negative__imp__inverse__negative,axiom,
% 0.35/0.67      ! [A: real] :
% 0.35/0.67        ( ( ord_less_real @ A @ zero_zero_real )
% 0.35/0.67       => ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real ) ) ).
% 0.35/0.67  
% 0.35/0.67  % negative_imp_inverse_negative
% 0.35/0.67  thf(fact_9161_inverse__positive__imp__positive,axiom,
% 0.35/0.67      ! [A: rat] :
% 0.35/0.67        ( ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 0.35/0.67       => ( ( A != zero_zero_rat )
% 0.35/0.67         => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_positive_imp_positive
% 0.35/0.67  thf(fact_9162_inverse__positive__imp__positive,axiom,
% 0.35/0.67      ! [A: real] :
% 0.35/0.67        ( ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 0.35/0.67       => ( ( A != zero_zero_real )
% 0.35/0.67         => ( ord_less_real @ zero_zero_real @ A ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_positive_imp_positive
% 0.35/0.67  thf(fact_9163_inverse__negative__imp__negative,axiom,
% 0.35/0.67      ! [A: rat] :
% 0.35/0.67        ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 0.35/0.67       => ( ( A != zero_zero_rat )
% 0.35/0.67         => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_negative_imp_negative
% 0.35/0.67  thf(fact_9164_inverse__negative__imp__negative,axiom,
% 0.35/0.67      ! [A: real] :
% 0.35/0.67        ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 0.35/0.67       => ( ( A != zero_zero_real )
% 0.35/0.67         => ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_negative_imp_negative
% 0.35/0.67  thf(fact_9165_less__imp__inverse__less__neg,axiom,
% 0.35/0.67      ! [A: rat,B: rat] :
% 0.35/0.67        ( ( ord_less_rat @ A @ B )
% 0.35/0.67       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.35/0.67         => ( ord_less_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % less_imp_inverse_less_neg
% 0.35/0.67  thf(fact_9166_less__imp__inverse__less__neg,axiom,
% 0.35/0.67      ! [A: real,B: real] :
% 0.35/0.67        ( ( ord_less_real @ A @ B )
% 0.35/0.67       => ( ( ord_less_real @ B @ zero_zero_real )
% 0.35/0.67         => ( ord_less_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % less_imp_inverse_less_neg
% 0.35/0.67  thf(fact_9167_inverse__less__imp__less__neg,axiom,
% 0.35/0.67      ! [A: rat,B: rat] :
% 0.35/0.67        ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 0.35/0.67       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.35/0.67         => ( ord_less_rat @ B @ A ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_less_imp_less_neg
% 0.35/0.67  thf(fact_9168_inverse__less__imp__less__neg,axiom,
% 0.35/0.67      ! [A: real,B: real] :
% 0.35/0.67        ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 0.35/0.67       => ( ( ord_less_real @ B @ zero_zero_real )
% 0.35/0.67         => ( ord_less_real @ B @ A ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_less_imp_less_neg
% 0.35/0.67  thf(fact_9169_less__imp__inverse__less,axiom,
% 0.35/0.67      ! [A: rat,B: rat] :
% 0.35/0.67        ( ( ord_less_rat @ A @ B )
% 0.35/0.67       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.35/0.67         => ( ord_less_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % less_imp_inverse_less
% 0.35/0.67  thf(fact_9170_less__imp__inverse__less,axiom,
% 0.35/0.67      ! [A: real,B: real] :
% 0.35/0.67        ( ( ord_less_real @ A @ B )
% 0.35/0.67       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.67         => ( ord_less_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % less_imp_inverse_less
% 0.35/0.67  thf(fact_9171_inverse__less__imp__less,axiom,
% 0.35/0.67      ! [A: rat,B: rat] :
% 0.35/0.67        ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 0.35/0.67       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.35/0.67         => ( ord_less_rat @ B @ A ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_less_imp_less
% 0.35/0.67  thf(fact_9172_inverse__less__imp__less,axiom,
% 0.35/0.67      ! [A: real,B: real] :
% 0.35/0.67        ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 0.35/0.67       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.67         => ( ord_less_real @ B @ A ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_less_imp_less
% 0.35/0.67  thf(fact_9173_nonzero__inverse__mult__distrib,axiom,
% 0.35/0.67      ! [A: rat,B: rat] :
% 0.35/0.67        ( ( A != zero_zero_rat )
% 0.35/0.67       => ( ( B != zero_zero_rat )
% 0.35/0.67         => ( ( inverse_inverse_rat @ ( times_times_rat @ A @ B ) )
% 0.35/0.67            = ( times_times_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % nonzero_inverse_mult_distrib
% 0.35/0.67  thf(fact_9174_nonzero__inverse__mult__distrib,axiom,
% 0.35/0.67      ! [A: real,B: real] :
% 0.35/0.67        ( ( A != zero_zero_real )
% 0.35/0.67       => ( ( B != zero_zero_real )
% 0.35/0.67         => ( ( inverse_inverse_real @ ( times_times_real @ A @ B ) )
% 0.35/0.67            = ( times_times_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % nonzero_inverse_mult_distrib
% 0.35/0.67  thf(fact_9175_nonzero__inverse__mult__distrib,axiom,
% 0.35/0.67      ! [A: complex,B: complex] :
% 0.35/0.67        ( ( A != zero_zero_complex )
% 0.35/0.67       => ( ( B != zero_zero_complex )
% 0.35/0.67         => ( ( invers8013647133539491842omplex @ ( times_times_complex @ A @ B ) )
% 0.35/0.67            = ( times_times_complex @ ( invers8013647133539491842omplex @ B ) @ ( invers8013647133539491842omplex @ A ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % nonzero_inverse_mult_distrib
% 0.35/0.67  thf(fact_9176_Suc__times__binomial__eq,axiom,
% 0.35/0.67      ! [N: nat,K: nat] :
% 0.35/0.67        ( ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) )
% 0.35/0.67        = ( times_times_nat @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) @ ( suc @ K ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % Suc_times_binomial_eq
% 0.35/0.67  thf(fact_9177_Suc__times__binomial,axiom,
% 0.35/0.67      ! [K: nat,N: nat] :
% 0.35/0.67        ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) )
% 0.35/0.67        = ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % Suc_times_binomial
% 0.35/0.67  thf(fact_9178_inverse__numeral__1,axiom,
% 0.35/0.67      ( ( inverse_inverse_rat @ ( numeral_numeral_rat @ one ) )
% 0.35/0.67      = ( numeral_numeral_rat @ one ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_numeral_1
% 0.35/0.67  thf(fact_9179_inverse__numeral__1,axiom,
% 0.35/0.67      ( ( inverse_inverse_real @ ( numeral_numeral_real @ one ) )
% 0.35/0.67      = ( numeral_numeral_real @ one ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_numeral_1
% 0.35/0.67  thf(fact_9180_inverse__numeral__1,axiom,
% 0.35/0.67      ( ( invers8013647133539491842omplex @ ( numera6690914467698888265omplex @ one ) )
% 0.35/0.67      = ( numera6690914467698888265omplex @ one ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_numeral_1
% 0.35/0.67  thf(fact_9181_inverse__unique,axiom,
% 0.35/0.67      ! [A: rat,B: rat] :
% 0.35/0.67        ( ( ( times_times_rat @ A @ B )
% 0.35/0.67          = one_one_rat )
% 0.35/0.67       => ( ( inverse_inverse_rat @ A )
% 0.35/0.67          = B ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_unique
% 0.35/0.67  thf(fact_9182_inverse__unique,axiom,
% 0.35/0.67      ! [A: real,B: real] :
% 0.35/0.67        ( ( ( times_times_real @ A @ B )
% 0.35/0.67          = one_one_real )
% 0.35/0.67       => ( ( inverse_inverse_real @ A )
% 0.35/0.67          = B ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_unique
% 0.35/0.67  thf(fact_9183_inverse__unique,axiom,
% 0.35/0.67      ! [A: complex,B: complex] :
% 0.35/0.67        ( ( ( times_times_complex @ A @ B )
% 0.35/0.67          = one_one_complex )
% 0.35/0.67       => ( ( invers8013647133539491842omplex @ A )
% 0.35/0.67          = B ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_unique
% 0.35/0.67  thf(fact_9184_choose__mult__lemma,axiom,
% 0.35/0.67      ! [M: nat,R: nat,K: nat] :
% 0.35/0.67        ( ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R ) @ K ) @ ( plus_plus_nat @ M @ K ) ) @ ( binomial @ ( plus_plus_nat @ M @ K ) @ K ) )
% 0.35/0.67        = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R ) @ K ) @ K ) @ ( binomial @ ( plus_plus_nat @ M @ R ) @ M ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % choose_mult_lemma
% 0.35/0.67  thf(fact_9185_divide__inverse__commute,axiom,
% 0.35/0.67      ( divide1717551699836669952omplex
% 0.35/0.67      = ( ^ [A3: complex,B4: complex] : ( times_times_complex @ ( invers8013647133539491842omplex @ B4 ) @ A3 ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % divide_inverse_commute
% 0.35/0.67  thf(fact_9186_binomial__symmetric,axiom,
% 0.35/0.67      ! [K: nat,N: nat] :
% 0.35/0.67        ( ( ord_less_eq_nat @ K @ N )
% 0.35/0.67       => ( ( binomial @ N @ K )
% 0.35/0.67          = ( binomial @ N @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % binomial_symmetric
% 0.35/0.67  thf(fact_9187_binomial__le__pow,axiom,
% 0.35/0.67      ! [R: nat,N: nat] :
% 0.35/0.67        ( ( ord_less_eq_nat @ R @ N )
% 0.35/0.67       => ( ord_less_eq_nat @ ( binomial @ N @ R ) @ ( power_power_nat @ N @ R ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % binomial_le_pow
% 0.35/0.67  thf(fact_9188_divide__real__def,axiom,
% 0.35/0.67      ( divide_divide_real
% 0.35/0.67      = ( ^ [X2: real,Y: real] : ( times_times_real @ X2 @ ( inverse_inverse_real @ Y ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % divide_real_def
% 0.35/0.67  thf(fact_9189_zero__less__binomial,axiom,
% 0.35/0.67      ! [K: nat,N: nat] :
% 0.35/0.67        ( ( ord_less_eq_nat @ K @ N )
% 0.35/0.67       => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % zero_less_binomial
% 0.35/0.67  thf(fact_9190_Suc__times__binomial__add,axiom,
% 0.35/0.67      ! [A: nat,B: nat] :
% 0.35/0.67        ( ( times_times_nat @ ( suc @ A ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ ( suc @ A ) ) )
% 0.35/0.67        = ( times_times_nat @ ( suc @ B ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ A ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % Suc_times_binomial_add
% 0.35/0.67  thf(fact_9191_binomial__Suc__Suc__eq__times,axiom,
% 0.35/0.67      ! [N: nat,K: nat] :
% 0.35/0.67        ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 0.35/0.67        = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) @ ( suc @ K ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % binomial_Suc_Suc_eq_times
% 0.35/0.67  thf(fact_9192_choose__mult,axiom,
% 0.35/0.67      ! [K: nat,M: nat,N: nat] :
% 0.35/0.67        ( ( ord_less_eq_nat @ K @ M )
% 0.35/0.67       => ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.67         => ( ( times_times_nat @ ( binomial @ N @ M ) @ ( binomial @ M @ K ) )
% 0.35/0.67            = ( times_times_nat @ ( binomial @ N @ K ) @ ( binomial @ ( minus_minus_nat @ N @ K ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % choose_mult
% 0.35/0.67  thf(fact_9193_binomial__absorb__comp,axiom,
% 0.35/0.67      ! [N: nat,K: nat] :
% 0.35/0.67        ( ( times_times_nat @ ( minus_minus_nat @ N @ K ) @ ( binomial @ N @ K ) )
% 0.35/0.67        = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % binomial_absorb_comp
% 0.35/0.67  thf(fact_9194_inverse__powr,axiom,
% 0.35/0.67      ! [Y2: real,A: real] :
% 0.35/0.67        ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 0.35/0.67       => ( ( powr_real @ ( inverse_inverse_real @ Y2 ) @ A )
% 0.35/0.67          = ( inverse_inverse_real @ ( powr_real @ Y2 @ A ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % inverse_powr
% 0.35/0.67  thf(fact_9195_imaginary__unit_Ocode,axiom,
% 0.35/0.67      ( imaginary_unit
% 0.35/0.67      = ( complex2 @ zero_zero_real @ one_one_real ) ) ).
% 0.35/0.67  
% 0.35/0.67  % imaginary_unit.code
% 0.35/0.67  thf(fact_9196_Complex__eq__i,axiom,
% 0.35/0.67      ! [X: real,Y2: real] :
% 0.35/0.67        ( ( ( complex2 @ X @ Y2 )
% 0.35/0.67          = imaginary_unit )
% 0.35/0.67        = ( ( X = zero_zero_real )
% 0.35/0.67          & ( Y2 = one_one_real ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % Complex_eq_i
% 0.35/0.67  thf(fact_9197_binomial__absorption,axiom,
% 0.35/0.67      ! [K: nat,N: nat] :
% 0.35/0.67        ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ N @ ( suc @ K ) ) )
% 0.35/0.67        = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % binomial_absorption
% 0.35/0.67  thf(fact_9198_forall__pos__mono__1,axiom,
% 0.35/0.67      ! [P: real > $o,E: real] :
% 0.35/0.67        ( ! [D3: real,E2: real] :
% 0.35/0.67            ( ( ord_less_real @ D3 @ E2 )
% 0.35/0.67           => ( ( P @ D3 )
% 0.35/0.67             => ( P @ E2 ) ) )
% 0.35/0.67       => ( ! [N3: nat] : ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) )
% 0.35/0.67         => ( ( ord_less_real @ zero_zero_real @ E )
% 0.35/0.67           => ( P @ E ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % forall_pos_mono_1
% 0.35/0.67  thf(fact_9199_binomial__fact__lemma,axiom,
% 0.35/0.67      ! [K: nat,N: nat] :
% 0.35/0.67        ( ( ord_less_eq_nat @ K @ N )
% 0.35/0.67       => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( binomial @ N @ K ) )
% 0.35/0.67          = ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % binomial_fact_lemma
% 0.35/0.67  thf(fact_9200_real__arch__inverse,axiom,
% 0.35/0.67      ! [E: real] :
% 0.35/0.67        ( ( ord_less_real @ zero_zero_real @ E )
% 0.35/0.67        = ( ? [N2: nat] :
% 0.35/0.67              ( ( N2 != zero_zero_nat )
% 0.35/0.67              & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 0.35/0.67              & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ E ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % real_arch_inverse
% 0.35/0.67  thf(fact_9201_forall__pos__mono,axiom,
% 0.35/0.67      ! [P: real > $o,E: real] :
% 0.35/0.67        ( ! [D3: real,E2: real] :
% 0.35/0.67            ( ( ord_less_real @ D3 @ E2 )
% 0.35/0.67           => ( ( P @ D3 )
% 0.35/0.67             => ( P @ E2 ) ) )
% 0.35/0.67       => ( ! [N3: nat] :
% 0.35/0.67              ( ( N3 != zero_zero_nat )
% 0.35/0.67             => ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) ) )
% 0.35/0.67         => ( ( ord_less_real @ zero_zero_real @ E )
% 0.35/0.67           => ( P @ E ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % forall_pos_mono
% 0.35/0.67  thf(fact_9202_sqrt__divide__self__eq,axiom,
% 0.35/0.67      ! [X: real] :
% 0.35/0.67        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.67       => ( ( divide_divide_real @ ( sqrt @ X ) @ X )
% 0.35/0.67          = ( inverse_inverse_real @ ( sqrt @ X ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % sqrt_divide_self_eq
% 0.35/0.67  thf(fact_9203_ln__inverse,axiom,
% 0.35/0.67      ! [X: real] :
% 0.35/0.67        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.67       => ( ( ln_ln_real @ ( inverse_inverse_real @ X ) )
% 0.35/0.67          = ( uminus_uminus_real @ ( ln_ln_real @ X ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % ln_inverse
% 0.35/0.67  thf(fact_9204_prod__int__plus__eq,axiom,
% 0.35/0.67      ! [I2: nat,J: nat] :
% 0.35/0.67        ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I2 @ ( plus_plus_nat @ I2 @ J ) ) )
% 0.35/0.67        = ( groups1705073143266064639nt_int
% 0.35/0.67          @ ^ [X2: int] : X2
% 0.35/0.67          @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I2 @ J ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % prod_int_plus_eq
% 0.35/0.67  thf(fact_9205_binomial__maximum,axiom,
% 0.35/0.67      ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % binomial_maximum
% 0.35/0.67  thf(fact_9206_binomial__antimono,axiom,
% 0.35/0.67      ! [K: nat,K6: nat,N: nat] :
% 0.35/0.67        ( ( ord_less_eq_nat @ K @ K6 )
% 0.35/0.67       => ( ( ord_less_eq_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ K )
% 0.35/0.67         => ( ( ord_less_eq_nat @ K6 @ N )
% 0.35/0.67           => ( ord_less_eq_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % binomial_antimono
% 0.35/0.67  thf(fact_9207_binomial__mono,axiom,
% 0.35/0.67      ! [K: nat,K6: nat,N: nat] :
% 0.35/0.67        ( ( ord_less_eq_nat @ K @ K6 )
% 0.35/0.67       => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 0.35/0.67         => ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % binomial_mono
% 0.35/0.67  thf(fact_9208_binomial__maximum_H,axiom,
% 0.35/0.67      ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ K ) @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 0.35/0.67  
% 0.35/0.67  % binomial_maximum'
% 0.35/0.67  thf(fact_9209_binomial__le__pow2,axiom,
% 0.35/0.67      ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.35/0.67  
% 0.35/0.67  % binomial_le_pow2
% 0.35/0.67  thf(fact_9210_choose__reduce__nat,axiom,
% 0.35/0.67      ! [N: nat,K: nat] :
% 0.35/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.67       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.35/0.67         => ( ( binomial @ N @ K )
% 0.35/0.67            = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % choose_reduce_nat
% 0.35/0.67  thf(fact_9211_times__binomial__minus1__eq,axiom,
% 0.35/0.67      ! [K: nat,N: nat] :
% 0.35/0.67        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.35/0.67       => ( ( times_times_nat @ K @ ( binomial @ N @ K ) )
% 0.35/0.67          = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % times_binomial_minus1_eq
% 0.35/0.67  thf(fact_9212_binomial__altdef__nat,axiom,
% 0.35/0.67      ! [K: nat,N: nat] :
% 0.35/0.67        ( ( ord_less_eq_nat @ K @ N )
% 0.35/0.67       => ( ( binomial @ N @ K )
% 0.35/0.67          = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % binomial_altdef_nat
% 0.35/0.67  thf(fact_9213_log__inverse,axiom,
% 0.35/0.67      ! [A: real,X: real] :
% 0.35/0.67        ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.67       => ( ( A != one_one_real )
% 0.35/0.67         => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.67           => ( ( log @ A @ ( inverse_inverse_real @ X ) )
% 0.35/0.67              = ( uminus_uminus_real @ ( log @ A @ X ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % log_inverse
% 0.35/0.67  thf(fact_9214_binomial__less__binomial__Suc,axiom,
% 0.35/0.67      ! [K: nat,N: nat] :
% 0.35/0.67        ( ( ord_less_nat @ K @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.67       => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % binomial_less_binomial_Suc
% 0.35/0.67  thf(fact_9215_binomial__strict__mono,axiom,
% 0.35/0.67      ! [K: nat,K6: nat,N: nat] :
% 0.35/0.67        ( ( ord_less_nat @ K @ K6 )
% 0.35/0.67       => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 0.35/0.67         => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % binomial_strict_mono
% 0.35/0.67  thf(fact_9216_binomial__strict__antimono,axiom,
% 0.35/0.67      ! [K: nat,K6: nat,N: nat] :
% 0.35/0.67        ( ( ord_less_nat @ K @ K6 )
% 0.35/0.67       => ( ( ord_less_eq_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) )
% 0.35/0.67         => ( ( ord_less_eq_nat @ K6 @ N )
% 0.35/0.67           => ( ord_less_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % binomial_strict_antimono
% 0.35/0.67  thf(fact_9217_central__binomial__odd,axiom,
% 0.35/0.67      ! [N: nat] :
% 0.35/0.67        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.67       => ( ( binomial @ N @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.67          = ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % central_binomial_odd
% 0.35/0.67  thf(fact_9218_binomial__addition__formula,axiom,
% 0.35/0.67      ! [N: nat,K: nat] :
% 0.35/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.67       => ( ( binomial @ N @ ( suc @ K ) )
% 0.35/0.67          = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % binomial_addition_formula
% 0.35/0.67  thf(fact_9219_exp__plus__inverse__exp,axiom,
% 0.35/0.67      ! [X: real] : ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % exp_plus_inverse_exp
% 0.35/0.67  thf(fact_9220_choose__two,axiom,
% 0.35/0.67      ! [N: nat] :
% 0.35/0.67        ( ( binomial @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.67        = ( divide_divide_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % choose_two
% 0.35/0.67  thf(fact_9221_plus__inverse__ge__2,axiom,
% 0.35/0.67      ! [X: real] :
% 0.35/0.67        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.67       => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ X @ ( inverse_inverse_real @ X ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % plus_inverse_ge_2
% 0.35/0.67  thf(fact_9222_real__inv__sqrt__pow2,axiom,
% 0.35/0.67      ! [X: real] :
% 0.35/0.67        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.67       => ( ( power_power_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.67          = ( inverse_inverse_real @ X ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % real_inv_sqrt_pow2
% 0.35/0.67  thf(fact_9223_tan__cot,axiom,
% 0.35/0.67      ! [X: real] :
% 0.35/0.67        ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) )
% 0.35/0.67        = ( inverse_inverse_real @ ( tan_real @ X ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % tan_cot
% 0.35/0.67  thf(fact_9224_real__le__x__sinh,axiom,
% 0.35/0.67      ! [X: real] :
% 0.35/0.67        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.67       => ( ord_less_eq_real @ X @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % real_le_x_sinh
% 0.35/0.67  thf(fact_9225_real__le__abs__sinh,axiom,
% 0.35/0.67      ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % real_le_abs_sinh
% 0.35/0.67  thf(fact_9226_cmod__unit__one,axiom,
% 0.35/0.67      ! [A: real] :
% 0.35/0.67        ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A ) ) ) ) )
% 0.35/0.67        = one_one_real ) ).
% 0.35/0.67  
% 0.35/0.67  % cmod_unit_one
% 0.35/0.67  thf(fact_9227_binomial__code,axiom,
% 0.35/0.67      ( binomial
% 0.35/0.67      = ( ^ [N2: nat,K3: nat] : ( if_nat @ ( ord_less_nat @ N2 @ K3 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K3 ) ) @ ( binomial @ N2 @ ( minus_minus_nat @ N2 @ K3 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N2 @ K3 ) @ one_one_nat ) @ N2 @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K3 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % binomial_code
% 0.35/0.67  thf(fact_9228_Arg__minus__ii,axiom,
% 0.35/0.67      ( ( arg @ ( uminus1482373934393186551omplex @ imaginary_unit ) )
% 0.35/0.67      = ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % Arg_minus_ii
% 0.35/0.67  thf(fact_9229_csqrt__ii,axiom,
% 0.35/0.67      ( ( csqrt @ imaginary_unit )
% 0.35/0.67      = ( divide1717551699836669952omplex @ ( plus_plus_complex @ one_one_complex @ imaginary_unit ) @ ( real_V4546457046886955230omplex @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % csqrt_ii
% 0.35/0.67  thf(fact_9230_Arg__ii,axiom,
% 0.35/0.67      ( ( arg @ imaginary_unit )
% 0.35/0.67      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % Arg_ii
% 0.35/0.67  thf(fact_9231_power2__csqrt,axiom,
% 0.35/0.67      ! [Z: complex] :
% 0.35/0.67        ( ( power_power_complex @ ( csqrt @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.67        = Z ) ).
% 0.35/0.67  
% 0.35/0.67  % power2_csqrt
% 0.35/0.67  thf(fact_9232_lessThan__Suc__atMost,axiom,
% 0.35/0.67      ! [K: nat] :
% 0.35/0.67        ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 0.35/0.67        = ( set_ord_atMost_nat @ K ) ) ).
% 0.35/0.67  
% 0.35/0.67  % lessThan_Suc_atMost
% 0.35/0.67  thf(fact_9233_atMost__Suc,axiom,
% 0.35/0.67      ! [K: nat] :
% 0.35/0.67        ( ( set_ord_atMost_nat @ ( suc @ K ) )
% 0.35/0.67        = ( insert_nat @ ( suc @ K ) @ ( set_ord_atMost_nat @ K ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % atMost_Suc
% 0.35/0.67  thf(fact_9234_atMost__nat__numeral,axiom,
% 0.35/0.67      ! [K: num] :
% 0.35/0.67        ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K ) )
% 0.35/0.67        = ( insert_nat @ ( numeral_numeral_nat @ K ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % atMost_nat_numeral
% 0.35/0.67  thf(fact_9235_sum__choose__upper,axiom,
% 0.35/0.67      ! [M: nat,N: nat] :
% 0.35/0.67        ( ( groups3542108847815614940at_nat
% 0.35/0.67          @ ^ [K3: nat] : ( binomial @ K3 @ M )
% 0.35/0.67          @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.67        = ( binomial @ ( suc @ N ) @ ( suc @ M ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % sum_choose_upper
% 0.35/0.67  thf(fact_9236_sum__choose__lower,axiom,
% 0.35/0.67      ! [R: nat,N: nat] :
% 0.35/0.67        ( ( groups3542108847815614940at_nat
% 0.35/0.67          @ ^ [K3: nat] : ( binomial @ ( plus_plus_nat @ R @ K3 ) @ K3 )
% 0.35/0.67          @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.67        = ( binomial @ ( suc @ ( plus_plus_nat @ R @ N ) ) @ N ) ) ).
% 0.35/0.67  
% 0.35/0.67  % sum_choose_lower
% 0.35/0.67  thf(fact_9237_choose__rising__sum_I1_J,axiom,
% 0.35/0.67      ! [N: nat,M: nat] :
% 0.35/0.67        ( ( groups3542108847815614940at_nat
% 0.35/0.67          @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 0.35/0.67          @ ( set_ord_atMost_nat @ M ) )
% 0.35/0.67        = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % choose_rising_sum(1)
% 0.35/0.67  thf(fact_9238_choose__rising__sum_I2_J,axiom,
% 0.35/0.67      ! [N: nat,M: nat] :
% 0.35/0.67        ( ( groups3542108847815614940at_nat
% 0.35/0.67          @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 0.35/0.67          @ ( set_ord_atMost_nat @ M ) )
% 0.35/0.67        = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ M ) ) ).
% 0.35/0.67  
% 0.35/0.67  % choose_rising_sum(2)
% 0.35/0.67  thf(fact_9239_sum__choose__diagonal,axiom,
% 0.35/0.67      ! [M: nat,N: nat] :
% 0.35/0.67        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.67       => ( ( groups3542108847815614940at_nat
% 0.35/0.67            @ ^ [K3: nat] : ( binomial @ ( minus_minus_nat @ N @ K3 ) @ ( minus_minus_nat @ M @ K3 ) )
% 0.35/0.67            @ ( set_ord_atMost_nat @ M ) )
% 0.35/0.67          = ( binomial @ ( suc @ N ) @ M ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % sum_choose_diagonal
% 0.35/0.67  thf(fact_9240_vandermonde,axiom,
% 0.35/0.67      ! [M: nat,N: nat,R: nat] :
% 0.35/0.67        ( ( groups3542108847815614940at_nat
% 0.35/0.67          @ ^ [K3: nat] : ( times_times_nat @ ( binomial @ M @ K3 ) @ ( binomial @ N @ ( minus_minus_nat @ R @ K3 ) ) )
% 0.35/0.67          @ ( set_ord_atMost_nat @ R ) )
% 0.35/0.67        = ( binomial @ ( plus_plus_nat @ M @ N ) @ R ) ) ).
% 0.35/0.67  
% 0.35/0.67  % vandermonde
% 0.35/0.67  thf(fact_9241_of__real__sqrt,axiom,
% 0.35/0.67      ! [X: real] :
% 0.35/0.67        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.67       => ( ( real_V4546457046886955230omplex @ ( sqrt @ X ) )
% 0.35/0.67          = ( csqrt @ ( real_V4546457046886955230omplex @ X ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % of_real_sqrt
% 0.35/0.67  thf(fact_9242_choose__row__sum,axiom,
% 0.35/0.67      ! [N: nat] :
% 0.35/0.67        ( ( groups3542108847815614940at_nat @ ( binomial @ N ) @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.67        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.35/0.67  
% 0.35/0.67  % choose_row_sum
% 0.35/0.67  thf(fact_9243_Arg__bounded,axiom,
% 0.35/0.67      ! [Z: complex] :
% 0.35/0.67        ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 0.35/0.67        & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ).
% 0.35/0.67  
% 0.35/0.67  % Arg_bounded
% 0.35/0.67  thf(fact_9244_binomial,axiom,
% 0.35/0.67      ! [A: nat,B: nat,N: nat] :
% 0.35/0.67        ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 0.35/0.67        = ( groups3542108847815614940at_nat
% 0.35/0.67          @ ^ [K3: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N @ K3 ) ) @ ( power_power_nat @ A @ K3 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 0.35/0.67          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % binomial
% 0.35/0.67  thf(fact_9245_atLeast1__atMost__eq__remove0,axiom,
% 0.35/0.67      ! [N: nat] :
% 0.35/0.67        ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.35/0.67        = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % atLeast1_atMost_eq_remove0
% 0.35/0.67  thf(fact_9246_polynomial__product__nat,axiom,
% 0.35/0.67      ! [M: nat,A: nat > nat,N: nat,B: nat > nat,X: nat] :
% 0.35/0.67        ( ! [I4: nat] :
% 0.35/0.67            ( ( ord_less_nat @ M @ I4 )
% 0.35/0.67           => ( ( A @ I4 )
% 0.35/0.67              = zero_zero_nat ) )
% 0.35/0.67       => ( ! [J2: nat] :
% 0.35/0.67              ( ( ord_less_nat @ N @ J2 )
% 0.35/0.67             => ( ( B @ J2 )
% 0.35/0.67                = zero_zero_nat ) )
% 0.35/0.67         => ( ( times_times_nat
% 0.35/0.67              @ ( groups3542108847815614940at_nat
% 0.35/0.67                @ ^ [I3: nat] : ( times_times_nat @ ( A @ I3 ) @ ( power_power_nat @ X @ I3 ) )
% 0.35/0.67                @ ( set_ord_atMost_nat @ M ) )
% 0.35/0.67              @ ( groups3542108847815614940at_nat
% 0.35/0.67                @ ^ [J3: nat] : ( times_times_nat @ ( B @ J3 ) @ ( power_power_nat @ X @ J3 ) )
% 0.35/0.67                @ ( set_ord_atMost_nat @ N ) ) )
% 0.35/0.67            = ( groups3542108847815614940at_nat
% 0.35/0.67              @ ^ [R5: nat] :
% 0.35/0.67                  ( times_times_nat
% 0.35/0.67                  @ ( groups3542108847815614940at_nat
% 0.35/0.67                    @ ^ [K3: nat] : ( times_times_nat @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 0.35/0.67                    @ ( set_ord_atMost_nat @ R5 ) )
% 0.35/0.67                  @ ( power_power_nat @ X @ R5 ) )
% 0.35/0.67              @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % polynomial_product_nat
% 0.35/0.67  thf(fact_9247_choose__square__sum,axiom,
% 0.35/0.67      ! [N: nat] :
% 0.35/0.67        ( ( groups3542108847815614940at_nat
% 0.35/0.67          @ ^ [K3: nat] : ( power_power_nat @ ( binomial @ N @ K3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.67          @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.67        = ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 0.35/0.67  
% 0.35/0.67  % choose_square_sum
% 0.35/0.67  thf(fact_9248_complex__inverse,axiom,
% 0.35/0.67      ! [A: real,B: real] :
% 0.35/0.67        ( ( invers8013647133539491842omplex @ ( complex2 @ A @ B ) )
% 0.35/0.67        = ( complex2 @ ( divide_divide_real @ A @ ( plus_plus_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( uminus_uminus_real @ B ) @ ( plus_plus_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % complex_inverse
% 0.35/0.67  thf(fact_9249_binomial__r__part__sum,axiom,
% 0.35/0.67      ! [M: nat] :
% 0.35/0.67        ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M ) )
% 0.35/0.67        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % binomial_r_part_sum
% 0.35/0.67  thf(fact_9250_choose__linear__sum,axiom,
% 0.35/0.67      ! [N: nat] :
% 0.35/0.67        ( ( groups3542108847815614940at_nat
% 0.35/0.67          @ ^ [I3: nat] : ( times_times_nat @ I3 @ ( binomial @ N @ I3 ) )
% 0.35/0.67          @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.67        = ( times_times_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % choose_linear_sum
% 0.35/0.67  thf(fact_9251_cis__minus__pi__half,axiom,
% 0.35/0.67      ( ( cis @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.35/0.67      = ( uminus1482373934393186551omplex @ imaginary_unit ) ) ).
% 0.35/0.67  
% 0.35/0.67  % cis_minus_pi_half
% 0.35/0.67  thf(fact_9252_of__nat__id,axiom,
% 0.35/0.67      ( semiri1316708129612266289at_nat
% 0.35/0.67      = ( ^ [N2: nat] : N2 ) ) ).
% 0.35/0.67  
% 0.35/0.67  % of_nat_id
% 0.35/0.67  thf(fact_9253_norm__cis,axiom,
% 0.35/0.67      ! [A: real] :
% 0.35/0.67        ( ( real_V1022390504157884413omplex @ ( cis @ A ) )
% 0.35/0.67        = one_one_real ) ).
% 0.35/0.67  
% 0.35/0.67  % norm_cis
% 0.35/0.67  thf(fact_9254_cis__pi__half,axiom,
% 0.35/0.67      ( ( cis @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.67      = imaginary_unit ) ).
% 0.35/0.67  
% 0.35/0.67  % cis_pi_half
% 0.35/0.67  thf(fact_9255_cis__2pi,axiom,
% 0.35/0.67      ( ( cis @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.35/0.67      = one_one_complex ) ).
% 0.35/0.67  
% 0.35/0.67  % cis_2pi
% 0.35/0.67  thf(fact_9256_real__scaleR__def,axiom,
% 0.35/0.67      real_V1485227260804924795R_real = times_times_real ).
% 0.35/0.67  
% 0.35/0.67  % real_scaleR_def
% 0.35/0.67  thf(fact_9257_complex__scaleR,axiom,
% 0.35/0.67      ! [R: real,A: real,B: real] :
% 0.35/0.67        ( ( real_V2046097035970521341omplex @ R @ ( complex2 @ A @ B ) )
% 0.35/0.67        = ( complex2 @ ( times_times_real @ R @ A ) @ ( times_times_real @ R @ B ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % complex_scaleR
% 0.35/0.67  thf(fact_9258_cis__mult,axiom,
% 0.35/0.67      ! [A: real,B: real] :
% 0.35/0.67        ( ( times_times_complex @ ( cis @ A ) @ ( cis @ B ) )
% 0.35/0.67        = ( cis @ ( plus_plus_real @ A @ B ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % cis_mult
% 0.35/0.67  thf(fact_9259_cis__divide,axiom,
% 0.35/0.67      ! [A: real,B: real] :
% 0.35/0.67        ( ( divide1717551699836669952omplex @ ( cis @ A ) @ ( cis @ B ) )
% 0.35/0.67        = ( cis @ ( minus_minus_real @ A @ B ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % cis_divide
% 0.35/0.67  thf(fact_9260_DeMoivre,axiom,
% 0.35/0.67      ! [A: real,N: nat] :
% 0.35/0.67        ( ( power_power_complex @ ( cis @ A ) @ N )
% 0.35/0.67        = ( cis @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % DeMoivre
% 0.35/0.67  thf(fact_9261_bij__betw__roots__unity,axiom,
% 0.35/0.67      ! [N: nat] :
% 0.35/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.67       => ( bij_betw_nat_complex
% 0.35/0.67          @ ^ [K3: nat] : ( cis @ ( divide_divide_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( semiri5074537144036343181t_real @ K3 ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 0.35/0.67          @ ( set_ord_lessThan_nat @ N )
% 0.35/0.67          @ ( collect_complex
% 0.35/0.67            @ ^ [Z4: complex] :
% 0.35/0.67                ( ( power_power_complex @ Z4 @ N )
% 0.35/0.67                = one_one_complex ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % bij_betw_roots_unity
% 0.35/0.67  thf(fact_9262_cot__less__zero,axiom,
% 0.35/0.67      ! [X: real] :
% 0.35/0.67        ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 0.35/0.67       => ( ( ord_less_real @ X @ zero_zero_real )
% 0.35/0.67         => ( ord_less_real @ ( cot_real @ X ) @ zero_zero_real ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % cot_less_zero
% 0.35/0.67  thf(fact_9263_sinh__real__less__iff,axiom,
% 0.35/0.67      ! [X: real,Y2: real] :
% 0.35/0.67        ( ( ord_less_real @ ( sinh_real @ X ) @ ( sinh_real @ Y2 ) )
% 0.35/0.67        = ( ord_less_real @ X @ Y2 ) ) ).
% 0.35/0.67  
% 0.35/0.67  % sinh_real_less_iff
% 0.35/0.67  thf(fact_9264_sinh__real__le__iff,axiom,
% 0.35/0.67      ! [X: real,Y2: real] :
% 0.35/0.67        ( ( ord_less_eq_real @ ( sinh_real @ X ) @ ( sinh_real @ Y2 ) )
% 0.35/0.67        = ( ord_less_eq_real @ X @ Y2 ) ) ).
% 0.35/0.67  
% 0.35/0.67  % sinh_real_le_iff
% 0.35/0.67  thf(fact_9265_sinh__real__neg__iff,axiom,
% 0.35/0.67      ! [X: real] :
% 0.35/0.67        ( ( ord_less_real @ ( sinh_real @ X ) @ zero_zero_real )
% 0.35/0.67        = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 0.35/0.67  
% 0.35/0.67  % sinh_real_neg_iff
% 0.35/0.67  thf(fact_9266_sinh__real__pos__iff,axiom,
% 0.35/0.67      ! [X: real] :
% 0.35/0.67        ( ( ord_less_real @ zero_zero_real @ ( sinh_real @ X ) )
% 0.35/0.67        = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 0.35/0.67  
% 0.35/0.67  % sinh_real_pos_iff
% 0.35/0.67  thf(fact_9267_sinh__real__nonneg__iff,axiom,
% 0.35/0.67      ! [X: real] :
% 0.35/0.67        ( ( ord_less_eq_real @ zero_zero_real @ ( sinh_real @ X ) )
% 0.35/0.67        = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 0.35/0.67  
% 0.35/0.67  % sinh_real_nonneg_iff
% 0.35/0.67  thf(fact_9268_sinh__real__nonpos__iff,axiom,
% 0.35/0.67      ! [X: real] :
% 0.35/0.67        ( ( ord_less_eq_real @ ( sinh_real @ X ) @ zero_zero_real )
% 0.35/0.67        = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 0.35/0.67  
% 0.35/0.67  % sinh_real_nonpos_iff
% 0.35/0.67  thf(fact_9269_cot__npi,axiom,
% 0.35/0.67      ! [N: nat] :
% 0.35/0.67        ( ( cot_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 0.35/0.67        = zero_zero_real ) ).
% 0.35/0.67  
% 0.35/0.67  % cot_npi
% 0.35/0.67  thf(fact_9270_cot__periodic,axiom,
% 0.35/0.67      ! [X: real] :
% 0.35/0.67        ( ( cot_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 0.35/0.67        = ( cot_real @ X ) ) ).
% 0.35/0.67  
% 0.35/0.67  % cot_periodic
% 0.35/0.67  thf(fact_9271_sinh__le__cosh__real,axiom,
% 0.35/0.67      ! [X: real] : ( ord_less_eq_real @ ( sinh_real @ X ) @ ( cosh_real @ X ) ) ).
% 0.35/0.67  
% 0.35/0.67  % sinh_le_cosh_real
% 0.35/0.67  thf(fact_9272_sinh__less__cosh__real,axiom,
% 0.35/0.67      ! [X: real] : ( ord_less_real @ ( sinh_real @ X ) @ ( cosh_real @ X ) ) ).
% 0.35/0.67  
% 0.35/0.67  % sinh_less_cosh_real
% 0.35/0.67  thf(fact_9273_cosh__real__pos,axiom,
% 0.35/0.67      ! [X: real] : ( ord_less_real @ zero_zero_real @ ( cosh_real @ X ) ) ).
% 0.35/0.67  
% 0.35/0.67  % cosh_real_pos
% 0.35/0.67  thf(fact_9274_cosh__real__nonpos__le__iff,axiom,
% 0.35/0.67      ! [X: real,Y2: real] :
% 0.35/0.67        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.35/0.67       => ( ( ord_less_eq_real @ Y2 @ zero_zero_real )
% 0.35/0.67         => ( ( ord_less_eq_real @ ( cosh_real @ X ) @ ( cosh_real @ Y2 ) )
% 0.35/0.67            = ( ord_less_eq_real @ Y2 @ X ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % cosh_real_nonpos_le_iff
% 0.35/0.67  thf(fact_9275_cosh__real__nonneg__le__iff,axiom,
% 0.35/0.67      ! [X: real,Y2: real] :
% 0.35/0.67        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.67       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 0.35/0.67         => ( ( ord_less_eq_real @ ( cosh_real @ X ) @ ( cosh_real @ Y2 ) )
% 0.35/0.67            = ( ord_less_eq_real @ X @ Y2 ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % cosh_real_nonneg_le_iff
% 0.35/0.67  thf(fact_9276_cosh__real__nonneg,axiom,
% 0.35/0.67      ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( cosh_real @ X ) ) ).
% 0.35/0.67  
% 0.35/0.67  % cosh_real_nonneg
% 0.35/0.67  thf(fact_9277_cosh__real__ge__1,axiom,
% 0.35/0.67      ! [X: real] : ( ord_less_eq_real @ one_one_real @ ( cosh_real @ X ) ) ).
% 0.35/0.67  
% 0.35/0.67  % cosh_real_ge_1
% 0.35/0.67  thf(fact_9278_cosh__real__nonpos__less__iff,axiom,
% 0.35/0.67      ! [X: real,Y2: real] :
% 0.35/0.67        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.35/0.67       => ( ( ord_less_eq_real @ Y2 @ zero_zero_real )
% 0.35/0.67         => ( ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y2 ) )
% 0.35/0.67            = ( ord_less_real @ Y2 @ X ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % cosh_real_nonpos_less_iff
% 0.35/0.67  thf(fact_9279_cosh__real__nonneg__less__iff,axiom,
% 0.35/0.67      ! [X: real,Y2: real] :
% 0.35/0.67        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.67       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 0.35/0.67         => ( ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y2 ) )
% 0.35/0.67            = ( ord_less_real @ X @ Y2 ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % cosh_real_nonneg_less_iff
% 0.35/0.67  thf(fact_9280_cosh__real__strict__mono,axiom,
% 0.35/0.67      ! [X: real,Y2: real] :
% 0.35/0.67        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.67       => ( ( ord_less_real @ X @ Y2 )
% 0.35/0.67         => ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y2 ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % cosh_real_strict_mono
% 0.35/0.67  thf(fact_9281_arcosh__cosh__real,axiom,
% 0.35/0.67      ! [X: real] :
% 0.35/0.67        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.67       => ( ( arcosh_real @ ( cosh_real @ X ) )
% 0.35/0.67          = X ) ) ).
% 0.35/0.67  
% 0.35/0.67  % arcosh_cosh_real
% 0.35/0.67  thf(fact_9282_cosh__ln__real,axiom,
% 0.35/0.67      ! [X: real] :
% 0.35/0.67        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.67       => ( ( cosh_real @ ( ln_ln_real @ X ) )
% 0.35/0.67          = ( divide_divide_real @ ( plus_plus_real @ X @ ( inverse_inverse_real @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % cosh_ln_real
% 0.35/0.67  thf(fact_9283_cot__gt__zero,axiom,
% 0.35/0.67      ! [X: real] :
% 0.35/0.67        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.67       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.67         => ( ord_less_real @ zero_zero_real @ ( cot_real @ X ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % cot_gt_zero
% 0.35/0.67  thf(fact_9284_sinh__ln__real,axiom,
% 0.35/0.67      ! [X: real] :
% 0.35/0.67        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.67       => ( ( sinh_real @ ( ln_ln_real @ X ) )
% 0.35/0.67          = ( divide_divide_real @ ( minus_minus_real @ X @ ( inverse_inverse_real @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % sinh_ln_real
% 0.35/0.67  thf(fact_9285_tan__cot_H,axiom,
% 0.35/0.67      ! [X: real] :
% 0.35/0.67        ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) )
% 0.35/0.67        = ( cot_real @ X ) ) ).
% 0.35/0.67  
% 0.35/0.67  % tan_cot'
% 0.35/0.67  thf(fact_9286_arctan__def,axiom,
% 0.35/0.67      ( arctan
% 0.35/0.67      = ( ^ [Y: real] :
% 0.35/0.67            ( the_real
% 0.35/0.67            @ ^ [X2: real] :
% 0.35/0.67                ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 0.35/0.67                & ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.67                & ( ( tan_real @ X2 )
% 0.35/0.67                  = Y ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % arctan_def
% 0.35/0.67  thf(fact_9287_arcsin__def,axiom,
% 0.35/0.67      ( arcsin
% 0.35/0.67      = ( ^ [Y: real] :
% 0.35/0.67            ( the_real
% 0.35/0.67            @ ^ [X2: real] :
% 0.35/0.67                ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 0.35/0.67                & ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.67                & ( ( sin_real @ X2 )
% 0.35/0.67                  = Y ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % arcsin_def
% 0.35/0.67  thf(fact_9288_signed__take__bit__eq__take__bit__minus,axiom,
% 0.35/0.67      ( bit_ri631733984087533419it_int
% 0.35/0.67      = ( ^ [N2: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ K3 ) @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % signed_take_bit_eq_take_bit_minus
% 0.35/0.67  thf(fact_9289_signed__take__bit__nonnegative__iff,axiom,
% 0.35/0.67      ! [N: nat,K: int] :
% 0.35/0.67        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 0.35/0.67        = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % signed_take_bit_nonnegative_iff
% 0.35/0.67  thf(fact_9290_signed__take__bit__negative__iff,axiom,
% 0.35/0.67      ! [N: nat,K: int] :
% 0.35/0.67        ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ zero_zero_int )
% 0.35/0.67        = ( bit_se1146084159140164899it_int @ K @ N ) ) ).
% 0.35/0.67  
% 0.35/0.67  % signed_take_bit_negative_iff
% 0.35/0.67  thf(fact_9291_bit__minus__numeral__Bit0__Suc__iff,axiom,
% 0.35/0.67      ! [W: num,N: nat] :
% 0.35/0.67        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( suc @ N ) )
% 0.35/0.67        = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ N ) ) ).
% 0.35/0.67  
% 0.35/0.67  % bit_minus_numeral_Bit0_Suc_iff
% 0.35/0.67  thf(fact_9292_bit__minus__numeral__Bit1__Suc__iff,axiom,
% 0.35/0.67      ! [W: num,N: nat] :
% 0.35/0.67        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( suc @ N ) )
% 0.35/0.67        = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ N ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % bit_minus_numeral_Bit1_Suc_iff
% 0.35/0.67  thf(fact_9293_bit__minus__numeral__int_I1_J,axiom,
% 0.35/0.67      ! [W: num,N: num] :
% 0.35/0.67        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 0.35/0.67        = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ ( pred_numeral @ N ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % bit_minus_numeral_int(1)
% 0.35/0.67  thf(fact_9294_bit__minus__numeral__int_I2_J,axiom,
% 0.35/0.67      ! [W: num,N: num] :
% 0.35/0.67        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 0.35/0.67        = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % bit_minus_numeral_int(2)
% 0.35/0.67  thf(fact_9295_bit__and__int__iff,axiom,
% 0.35/0.67      ! [K: int,L2: int,N: nat] :
% 0.35/0.67        ( ( bit_se1146084159140164899it_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) @ N )
% 0.35/0.67        = ( ( bit_se1146084159140164899it_int @ K @ N )
% 0.35/0.67          & ( bit_se1146084159140164899it_int @ L2 @ N ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % bit_and_int_iff
% 0.35/0.67  thf(fact_9296_bit__or__int__iff,axiom,
% 0.35/0.67      ! [K: int,L2: int,N: nat] :
% 0.35/0.67        ( ( bit_se1146084159140164899it_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) @ N )
% 0.35/0.67        = ( ( bit_se1146084159140164899it_int @ K @ N )
% 0.35/0.67          | ( bit_se1146084159140164899it_int @ L2 @ N ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % bit_or_int_iff
% 0.35/0.67  thf(fact_9297_bit__not__int__iff_H,axiom,
% 0.35/0.67      ! [K: int,N: nat] :
% 0.35/0.67        ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ ( uminus_uminus_int @ K ) @ one_one_int ) @ N )
% 0.35/0.67        = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % bit_not_int_iff'
% 0.35/0.67  thf(fact_9298_ln__neg__is__const,axiom,
% 0.35/0.67      ! [X: real] :
% 0.35/0.67        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.35/0.67       => ( ( ln_ln_real @ X )
% 0.35/0.67          = ( the_real
% 0.35/0.67            @ ^ [X2: real] : $false ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % ln_neg_is_const
% 0.35/0.67  thf(fact_9299_bit__imp__take__bit__positive,axiom,
% 0.35/0.67      ! [N: nat,M: nat,K: int] :
% 0.35/0.67        ( ( ord_less_nat @ N @ M )
% 0.35/0.67       => ( ( bit_se1146084159140164899it_int @ K @ N )
% 0.35/0.67         => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M @ K ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % bit_imp_take_bit_positive
% 0.35/0.67  thf(fact_9300_bit__concat__bit__iff,axiom,
% 0.35/0.67      ! [M: nat,K: int,L2: int,N: nat] :
% 0.35/0.67        ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M @ K @ L2 ) @ N )
% 0.35/0.67        = ( ( ( ord_less_nat @ N @ M )
% 0.35/0.67            & ( bit_se1146084159140164899it_int @ K @ N ) )
% 0.35/0.67          | ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.67            & ( bit_se1146084159140164899it_int @ L2 @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % bit_concat_bit_iff
% 0.35/0.67  thf(fact_9301_signed__take__bit__eq__concat__bit,axiom,
% 0.35/0.67      ( bit_ri631733984087533419it_int
% 0.35/0.67      = ( ^ [N2: nat,K3: int] : ( bit_concat_bit @ N2 @ K3 @ ( uminus_uminus_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N2 ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % signed_take_bit_eq_concat_bit
% 0.35/0.67  thf(fact_9302_int__bit__bound,axiom,
% 0.35/0.67      ! [K: int] :
% 0.35/0.67        ~ ! [N3: nat] :
% 0.35/0.67            ( ! [M5: nat] :
% 0.35/0.67                ( ( ord_less_eq_nat @ N3 @ M5 )
% 0.35/0.67               => ( ( bit_se1146084159140164899it_int @ K @ M5 )
% 0.35/0.67                  = ( bit_se1146084159140164899it_int @ K @ N3 ) ) )
% 0.35/0.67           => ~ ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.35/0.67               => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N3 @ one_one_nat ) )
% 0.35/0.67                  = ( ~ ( bit_se1146084159140164899it_int @ K @ N3 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % int_bit_bound
% 0.35/0.67  thf(fact_9303_bit__int__def,axiom,
% 0.35/0.67      ( bit_se1146084159140164899it_int
% 0.35/0.67      = ( ^ [K3: int,N2: nat] :
% 0.35/0.67            ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % bit_int_def
% 0.35/0.67  thf(fact_9304_arccos__def,axiom,
% 0.35/0.67      ( arccos
% 0.35/0.67      = ( ^ [Y: real] :
% 0.35/0.67            ( the_real
% 0.35/0.67            @ ^ [X2: real] :
% 0.35/0.67                ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 0.35/0.67                & ( ord_less_eq_real @ X2 @ pi )
% 0.35/0.67                & ( ( cos_real @ X2 )
% 0.35/0.67                  = Y ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % arccos_def
% 0.35/0.67  thf(fact_9305_set__bit__eq,axiom,
% 0.35/0.67      ( bit_se7879613467334960850it_int
% 0.35/0.67      = ( ^ [N2: nat,K3: int] :
% 0.35/0.67            ( plus_plus_int @ K3
% 0.35/0.67            @ ( times_times_int
% 0.35/0.67              @ ( zero_n2684676970156552555ol_int
% 0.35/0.67                @ ~ ( bit_se1146084159140164899it_int @ K3 @ N2 ) )
% 0.35/0.67              @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % set_bit_eq
% 0.35/0.67  thf(fact_9306_unset__bit__eq,axiom,
% 0.35/0.67      ( bit_se4203085406695923979it_int
% 0.35/0.67      = ( ^ [N2: nat,K3: int] : ( minus_minus_int @ K3 @ ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % unset_bit_eq
% 0.35/0.67  thf(fact_9307_pi__half,axiom,
% 0.35/0.67      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.35/0.67      = ( the_real
% 0.35/0.67        @ ^ [X2: real] :
% 0.35/0.67            ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 0.35/0.67            & ( ord_less_eq_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.35/0.67            & ( ( cos_real @ X2 )
% 0.35/0.67              = zero_zero_real ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % pi_half
% 0.35/0.67  thf(fact_9308_pi__def,axiom,
% 0.35/0.67      ( pi
% 0.35/0.67      = ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 0.35/0.67        @ ( the_real
% 0.35/0.67          @ ^ [X2: real] :
% 0.35/0.67              ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 0.35/0.67              & ( ord_less_eq_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.35/0.67              & ( ( cos_real @ X2 )
% 0.35/0.67                = zero_zero_real ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % pi_def
% 0.35/0.67  thf(fact_9309_take__bit__Suc__from__most,axiom,
% 0.35/0.67      ! [N: nat,K: int] :
% 0.35/0.67        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ K )
% 0.35/0.67        = ( plus_plus_int @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K @ N ) ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % take_bit_Suc_from_most
% 0.35/0.67  thf(fact_9310_bij__betw__nth__root__unity,axiom,
% 0.35/0.67      ! [C: complex,N: nat] :
% 0.35/0.67        ( ( C != zero_zero_complex )
% 0.35/0.67       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.67         => ( bij_be1856998921033663316omplex @ ( times_times_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ ( root @ N @ ( real_V1022390504157884413omplex @ C ) ) ) @ ( cis @ ( divide_divide_real @ ( arg @ C ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) )
% 0.35/0.67            @ ( collect_complex
% 0.35/0.67              @ ^ [Z4: complex] :
% 0.35/0.67                  ( ( power_power_complex @ Z4 @ N )
% 0.35/0.67                  = one_one_complex ) )
% 0.35/0.67            @ ( collect_complex
% 0.35/0.67              @ ^ [Z4: complex] :
% 0.35/0.67                  ( ( power_power_complex @ Z4 @ N )
% 0.35/0.67                  = C ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % bij_betw_nth_root_unity
% 0.35/0.67  thf(fact_9311_modulo__int__unfold,axiom,
% 0.35/0.67      ! [L2: int,K: int,N: nat,M: nat] :
% 0.35/0.67        ( ( ( ( ( sgn_sgn_int @ L2 )
% 0.35/0.67              = zero_zero_int )
% 0.35/0.67            | ( ( sgn_sgn_int @ K )
% 0.35/0.67              = zero_zero_int )
% 0.35/0.67            | ( N = zero_zero_nat ) )
% 0.35/0.67         => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.35/0.67            = ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) ) )
% 0.35/0.67        & ( ~ ( ( ( sgn_sgn_int @ L2 )
% 0.35/0.67                = zero_zero_int )
% 0.35/0.67              | ( ( sgn_sgn_int @ K )
% 0.35/0.67                = zero_zero_int )
% 0.35/0.67              | ( N = zero_zero_nat ) )
% 0.35/0.67         => ( ( ( ( sgn_sgn_int @ K )
% 0.35/0.67                = ( sgn_sgn_int @ L2 ) )
% 0.35/0.67             => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.35/0.67                = ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) )
% 0.35/0.67            & ( ( ( sgn_sgn_int @ K )
% 0.35/0.67               != ( sgn_sgn_int @ L2 ) )
% 0.35/0.67             => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.35/0.67                = ( times_times_int @ ( sgn_sgn_int @ L2 )
% 0.35/0.67                  @ ( minus_minus_int
% 0.35/0.67                    @ ( semiri1314217659103216013at_int
% 0.35/0.67                      @ ( times_times_nat @ N
% 0.35/0.67                        @ ( zero_n2687167440665602831ol_nat
% 0.35/0.67                          @ ~ ( dvd_dvd_nat @ N @ M ) ) ) )
% 0.35/0.67                    @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % modulo_int_unfold
% 0.35/0.67  thf(fact_9312_powr__int,axiom,
% 0.35/0.67      ! [X: real,I2: int] :
% 0.35/0.67        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.67       => ( ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 0.35/0.67           => ( ( powr_real @ X @ ( ring_1_of_int_real @ I2 ) )
% 0.35/0.67              = ( power_power_real @ X @ ( nat2 @ I2 ) ) ) )
% 0.35/0.67          & ( ~ ( ord_less_eq_int @ zero_zero_int @ I2 )
% 0.35/0.67           => ( ( powr_real @ X @ ( ring_1_of_int_real @ I2 ) )
% 0.35/0.67              = ( divide_divide_real @ one_one_real @ ( power_power_real @ X @ ( nat2 @ ( uminus_uminus_int @ I2 ) ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % powr_int
% 0.35/0.67  thf(fact_9313_divide__int__unfold,axiom,
% 0.35/0.67      ! [L2: int,K: int,N: nat,M: nat] :
% 0.35/0.67        ( ( ( ( ( sgn_sgn_int @ L2 )
% 0.35/0.67              = zero_zero_int )
% 0.35/0.67            | ( ( sgn_sgn_int @ K )
% 0.35/0.67              = zero_zero_int )
% 0.35/0.67            | ( N = zero_zero_nat ) )
% 0.35/0.67         => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.35/0.67            = zero_zero_int ) )
% 0.35/0.67        & ( ~ ( ( ( sgn_sgn_int @ L2 )
% 0.35/0.67                = zero_zero_int )
% 0.35/0.67              | ( ( sgn_sgn_int @ K )
% 0.35/0.67                = zero_zero_int )
% 0.35/0.67              | ( N = zero_zero_nat ) )
% 0.35/0.67         => ( ( ( ( sgn_sgn_int @ K )
% 0.35/0.67                = ( sgn_sgn_int @ L2 ) )
% 0.35/0.67             => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.35/0.67                = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) )
% 0.35/0.67            & ( ( ( sgn_sgn_int @ K )
% 0.35/0.67               != ( sgn_sgn_int @ L2 ) )
% 0.35/0.67             => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.35/0.67                = ( uminus_uminus_int
% 0.35/0.67                  @ ( semiri1314217659103216013at_int
% 0.35/0.67                    @ ( plus_plus_nat @ ( divide_divide_nat @ M @ N )
% 0.35/0.67                      @ ( zero_n2687167440665602831ol_nat
% 0.35/0.67                        @ ~ ( dvd_dvd_nat @ N @ M ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % divide_int_unfold
% 0.35/0.67  thf(fact_9314_real__root__zero,axiom,
% 0.35/0.67      ! [N: nat] :
% 0.35/0.67        ( ( root @ N @ zero_zero_real )
% 0.35/0.67        = zero_zero_real ) ).
% 0.35/0.67  
% 0.35/0.67  % real_root_zero
% 0.35/0.67  thf(fact_9315_nat__numeral,axiom,
% 0.35/0.67      ! [K: num] :
% 0.35/0.67        ( ( nat2 @ ( numeral_numeral_int @ K ) )
% 0.35/0.67        = ( numeral_numeral_nat @ K ) ) ).
% 0.35/0.67  
% 0.35/0.67  % nat_numeral
% 0.35/0.67  thf(fact_9316_real__root__Suc__0,axiom,
% 0.35/0.67      ! [X: real] :
% 0.35/0.67        ( ( root @ ( suc @ zero_zero_nat ) @ X )
% 0.35/0.67        = X ) ).
% 0.35/0.67  
% 0.35/0.67  % real_root_Suc_0
% 0.35/0.67  thf(fact_9317_real__root__eq__iff,axiom,
% 0.35/0.67      ! [N: nat,X: real,Y2: real] :
% 0.35/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.67       => ( ( ( root @ N @ X )
% 0.35/0.67            = ( root @ N @ Y2 ) )
% 0.35/0.67          = ( X = Y2 ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % real_root_eq_iff
% 0.35/0.67  thf(fact_9318_root__0,axiom,
% 0.35/0.67      ! [X: real] :
% 0.35/0.67        ( ( root @ zero_zero_nat @ X )
% 0.35/0.67        = zero_zero_real ) ).
% 0.35/0.67  
% 0.35/0.67  % root_0
% 0.35/0.67  thf(fact_9319_nat__1,axiom,
% 0.35/0.67      ( ( nat2 @ one_one_int )
% 0.35/0.67      = ( suc @ zero_zero_nat ) ) ).
% 0.35/0.67  
% 0.35/0.67  % nat_1
% 0.35/0.67  thf(fact_9320_real__root__eq__0__iff,axiom,
% 0.35/0.67      ! [N: nat,X: real] :
% 0.35/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.67       => ( ( ( root @ N @ X )
% 0.35/0.67            = zero_zero_real )
% 0.35/0.67          = ( X = zero_zero_real ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % real_root_eq_0_iff
% 0.35/0.67  thf(fact_9321_real__root__less__iff,axiom,
% 0.35/0.67      ! [N: nat,X: real,Y2: real] :
% 0.35/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.67       => ( ( ord_less_real @ ( root @ N @ X ) @ ( root @ N @ Y2 ) )
% 0.35/0.67          = ( ord_less_real @ X @ Y2 ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % real_root_less_iff
% 0.35/0.67  thf(fact_9322_real__root__le__iff,axiom,
% 0.35/0.67      ! [N: nat,X: real,Y2: real] :
% 0.35/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.67       => ( ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N @ Y2 ) )
% 0.35/0.67          = ( ord_less_eq_real @ X @ Y2 ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % real_root_le_iff
% 0.35/0.67  thf(fact_9323_zless__nat__conj,axiom,
% 0.35/0.67      ! [W: int,Z: int] :
% 0.35/0.67        ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 0.35/0.67        = ( ( ord_less_int @ zero_zero_int @ Z )
% 0.35/0.67          & ( ord_less_int @ W @ Z ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % zless_nat_conj
% 0.35/0.67  thf(fact_9324_real__root__eq__1__iff,axiom,
% 0.35/0.67      ! [N: nat,X: real] :
% 0.35/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.67       => ( ( ( root @ N @ X )
% 0.35/0.67            = one_one_real )
% 0.35/0.67          = ( X = one_one_real ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % real_root_eq_1_iff
% 0.35/0.67  thf(fact_9325_real__root__one,axiom,
% 0.35/0.67      ! [N: nat] :
% 0.35/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.67       => ( ( root @ N @ one_one_real )
% 0.35/0.67          = one_one_real ) ) ).
% 0.35/0.67  
% 0.35/0.67  % real_root_one
% 0.35/0.67  thf(fact_9326_nat__neg__numeral,axiom,
% 0.35/0.67      ! [K: num] :
% 0.35/0.67        ( ( nat2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.35/0.67        = zero_zero_nat ) ).
% 0.35/0.67  
% 0.35/0.67  % nat_neg_numeral
% 0.35/0.67  thf(fact_9327_real__root__gt__0__iff,axiom,
% 0.35/0.67      ! [N: nat,Y2: real] :
% 0.35/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.67       => ( ( ord_less_real @ zero_zero_real @ ( root @ N @ Y2 ) )
% 0.35/0.67          = ( ord_less_real @ zero_zero_real @ Y2 ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % real_root_gt_0_iff
% 0.35/0.67  thf(fact_9328_real__root__lt__0__iff,axiom,
% 0.35/0.67      ! [N: nat,X: real] :
% 0.35/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.67       => ( ( ord_less_real @ ( root @ N @ X ) @ zero_zero_real )
% 0.35/0.67          = ( ord_less_real @ X @ zero_zero_real ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % real_root_lt_0_iff
% 0.35/0.67  thf(fact_9329_real__root__ge__0__iff,axiom,
% 0.35/0.67      ! [N: nat,Y2: real] :
% 0.35/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.67       => ( ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ Y2 ) )
% 0.35/0.67          = ( ord_less_eq_real @ zero_zero_real @ Y2 ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % real_root_ge_0_iff
% 0.35/0.67  thf(fact_9330_real__root__le__0__iff,axiom,
% 0.35/0.67      ! [N: nat,X: real] :
% 0.35/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.67       => ( ( ord_less_eq_real @ ( root @ N @ X ) @ zero_zero_real )
% 0.35/0.67          = ( ord_less_eq_real @ X @ zero_zero_real ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % real_root_le_0_iff
% 0.35/0.67  thf(fact_9331_zero__less__nat__eq,axiom,
% 0.35/0.67      ! [Z: int] :
% 0.35/0.67        ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z ) )
% 0.35/0.67        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 0.35/0.67  
% 0.35/0.67  % zero_less_nat_eq
% 0.35/0.67  thf(fact_9332_real__root__lt__1__iff,axiom,
% 0.35/0.67      ! [N: nat,X: real] :
% 0.35/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.67       => ( ( ord_less_real @ ( root @ N @ X ) @ one_one_real )
% 0.35/0.67          = ( ord_less_real @ X @ one_one_real ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % real_root_lt_1_iff
% 0.35/0.67  thf(fact_9333_real__root__gt__1__iff,axiom,
% 0.35/0.67      ! [N: nat,Y2: real] :
% 0.35/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.67       => ( ( ord_less_real @ one_one_real @ ( root @ N @ Y2 ) )
% 0.35/0.67          = ( ord_less_real @ one_one_real @ Y2 ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % real_root_gt_1_iff
% 0.35/0.67  thf(fact_9334_real__root__le__1__iff,axiom,
% 0.35/0.67      ! [N: nat,X: real] :
% 0.35/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.67       => ( ( ord_less_eq_real @ ( root @ N @ X ) @ one_one_real )
% 0.35/0.67          = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % real_root_le_1_iff
% 0.35/0.67  thf(fact_9335_real__root__ge__1__iff,axiom,
% 0.35/0.67      ! [N: nat,Y2: real] :
% 0.35/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.67       => ( ( ord_less_eq_real @ one_one_real @ ( root @ N @ Y2 ) )
% 0.35/0.67          = ( ord_less_eq_real @ one_one_real @ Y2 ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % real_root_ge_1_iff
% 0.35/0.67  thf(fact_9336_diff__nat__numeral,axiom,
% 0.35/0.67      ! [V: num,V3: num] :
% 0.35/0.67        ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ ( numeral_numeral_nat @ V3 ) )
% 0.35/0.67        = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ V3 ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % diff_nat_numeral
% 0.35/0.67  thf(fact_9337_nat__eq__numeral__power__cancel__iff,axiom,
% 0.35/0.67      ! [Y2: int,X: num,N: nat] :
% 0.35/0.67        ( ( ( nat2 @ Y2 )
% 0.35/0.67          = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 0.35/0.67        = ( Y2
% 0.35/0.67          = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % nat_eq_numeral_power_cancel_iff
% 0.35/0.67  thf(fact_9338_numeral__power__eq__nat__cancel__iff,axiom,
% 0.35/0.67      ! [X: num,N: nat,Y2: int] :
% 0.35/0.67        ( ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 0.35/0.67          = ( nat2 @ Y2 ) )
% 0.35/0.67        = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 0.35/0.67          = Y2 ) ) ).
% 0.35/0.67  
% 0.35/0.67  % numeral_power_eq_nat_cancel_iff
% 0.35/0.67  thf(fact_9339_nat__ceiling__le__eq,axiom,
% 0.35/0.67      ! [X: real,A: nat] :
% 0.35/0.67        ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) @ A )
% 0.35/0.67        = ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ A ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % nat_ceiling_le_eq
% 0.35/0.67  thf(fact_9340_one__less__nat__eq,axiom,
% 0.35/0.67      ! [Z: int] :
% 0.35/0.67        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z ) )
% 0.35/0.67        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 0.35/0.67  
% 0.35/0.67  % one_less_nat_eq
% 0.35/0.67  thf(fact_9341_real__root__pow__pos2,axiom,
% 0.35/0.67      ! [N: nat,X: real] :
% 0.35/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.67       => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.67         => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 0.35/0.67            = X ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % real_root_pow_pos2
% 0.35/0.67  thf(fact_9342_nat__numeral__diff__1,axiom,
% 0.35/0.67      ! [V: num] :
% 0.35/0.67        ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat )
% 0.35/0.67        = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ one_one_int ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % nat_numeral_diff_1
% 0.35/0.67  thf(fact_9343_nat__less__numeral__power__cancel__iff,axiom,
% 0.35/0.67      ! [A: int,X: num,N: nat] :
% 0.35/0.67        ( ( ord_less_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 0.35/0.67        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % nat_less_numeral_power_cancel_iff
% 0.35/0.67  thf(fact_9344_numeral__power__less__nat__cancel__iff,axiom,
% 0.35/0.67      ! [X: num,N: nat,A: int] :
% 0.35/0.67        ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) @ ( nat2 @ A ) )
% 0.35/0.67        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 0.35/0.67  
% 0.35/0.67  % numeral_power_less_nat_cancel_iff
% 0.35/0.67  thf(fact_9345_nat__le__numeral__power__cancel__iff,axiom,
% 0.35/0.67      ! [A: int,X: num,N: nat] :
% 0.35/0.67        ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 0.35/0.67        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % nat_le_numeral_power_cancel_iff
% 0.35/0.67  thf(fact_9346_numeral__power__le__nat__cancel__iff,axiom,
% 0.35/0.67      ! [X: num,N: nat,A: int] :
% 0.35/0.67        ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) @ ( nat2 @ A ) )
% 0.35/0.67        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 0.35/0.67  
% 0.35/0.67  % numeral_power_le_nat_cancel_iff
% 0.35/0.67  thf(fact_9347_bit__nat__iff,axiom,
% 0.35/0.67      ! [K: int,N: nat] :
% 0.35/0.67        ( ( bit_se1148574629649215175it_nat @ ( nat2 @ K ) @ N )
% 0.35/0.67        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.35/0.67          & ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % bit_nat_iff
% 0.35/0.67  thf(fact_9348_real__root__inverse,axiom,
% 0.35/0.67      ! [N: nat,X: real] :
% 0.35/0.67        ( ( root @ N @ ( inverse_inverse_real @ X ) )
% 0.35/0.67        = ( inverse_inverse_real @ ( root @ N @ X ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % real_root_inverse
% 0.35/0.67  thf(fact_9349_real__root__commute,axiom,
% 0.35/0.67      ! [M: nat,N: nat,X: real] :
% 0.35/0.67        ( ( root @ M @ ( root @ N @ X ) )
% 0.35/0.67        = ( root @ N @ ( root @ M @ X ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % real_root_commute
% 0.35/0.67  thf(fact_9350_real__root__minus,axiom,
% 0.35/0.67      ! [N: nat,X: real] :
% 0.35/0.67        ( ( root @ N @ ( uminus_uminus_real @ X ) )
% 0.35/0.67        = ( uminus_uminus_real @ ( root @ N @ X ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % real_root_minus
% 0.35/0.67  thf(fact_9351_real__root__mult__exp,axiom,
% 0.35/0.67      ! [M: nat,N: nat,X: real] :
% 0.35/0.67        ( ( root @ ( times_times_nat @ M @ N ) @ X )
% 0.35/0.67        = ( root @ M @ ( root @ N @ X ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % real_root_mult_exp
% 0.35/0.67  thf(fact_9352_real__root__mult,axiom,
% 0.35/0.67      ! [N: nat,X: real,Y2: real] :
% 0.35/0.67        ( ( root @ N @ ( times_times_real @ X @ Y2 ) )
% 0.35/0.67        = ( times_times_real @ ( root @ N @ X ) @ ( root @ N @ Y2 ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % real_root_mult
% 0.35/0.67  thf(fact_9353_real__root__divide,axiom,
% 0.35/0.67      ! [N: nat,X: real,Y2: real] :
% 0.35/0.67        ( ( root @ N @ ( divide_divide_real @ X @ Y2 ) )
% 0.35/0.67        = ( divide_divide_real @ ( root @ N @ X ) @ ( root @ N @ Y2 ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % real_root_divide
% 0.35/0.67  thf(fact_9354_not__bit__Suc__0__Suc,axiom,
% 0.35/0.67      ! [N: nat] :
% 0.35/0.67        ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N ) ) ).
% 0.35/0.67  
% 0.35/0.67  % not_bit_Suc_0_Suc
% 0.35/0.67  thf(fact_9355_bit__Suc__0__iff,axiom,
% 0.35/0.67      ! [N: nat] :
% 0.35/0.67        ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.35/0.67        = ( N = zero_zero_nat ) ) ).
% 0.35/0.67  
% 0.35/0.67  % bit_Suc_0_iff
% 0.35/0.67  thf(fact_9356_real__root__pos__pos__le,axiom,
% 0.35/0.67      ! [X: real,N: nat] :
% 0.35/0.67        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.67       => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % real_root_pos_pos_le
% 0.35/0.67  thf(fact_9357_nat__numeral__as__int,axiom,
% 0.35/0.67      ( numeral_numeral_nat
% 0.35/0.67      = ( ^ [I3: num] : ( nat2 @ ( numeral_numeral_int @ I3 ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % nat_numeral_as_int
% 0.35/0.67  thf(fact_9358_nat__mono,axiom,
% 0.35/0.67      ! [X: int,Y2: int] :
% 0.35/0.67        ( ( ord_less_eq_int @ X @ Y2 )
% 0.35/0.67       => ( ord_less_eq_nat @ ( nat2 @ X ) @ ( nat2 @ Y2 ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % nat_mono
% 0.35/0.67  thf(fact_9359_nat__one__as__int,axiom,
% 0.35/0.67      ( one_one_nat
% 0.35/0.67      = ( nat2 @ one_one_int ) ) ).
% 0.35/0.67  
% 0.35/0.67  % nat_one_as_int
% 0.35/0.67  thf(fact_9360_div__eq__sgn__abs,axiom,
% 0.35/0.67      ! [K: int,L2: int] :
% 0.35/0.67        ( ( ( sgn_sgn_int @ K )
% 0.35/0.67          = ( sgn_sgn_int @ L2 ) )
% 0.35/0.67       => ( ( divide_divide_int @ K @ L2 )
% 0.35/0.67          = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % div_eq_sgn_abs
% 0.35/0.67  thf(fact_9361_unset__bit__nat__def,axiom,
% 0.35/0.67      ( bit_se4205575877204974255it_nat
% 0.35/0.67      = ( ^ [M6: nat,N2: nat] : ( nat2 @ ( bit_se4203085406695923979it_int @ M6 @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % unset_bit_nat_def
% 0.35/0.67  thf(fact_9362_nat__mask__eq,axiom,
% 0.35/0.67      ! [N: nat] :
% 0.35/0.67        ( ( nat2 @ ( bit_se2000444600071755411sk_int @ N ) )
% 0.35/0.67        = ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 0.35/0.67  
% 0.35/0.67  % nat_mask_eq
% 0.35/0.67  thf(fact_9363_not__bit__Suc__0__numeral,axiom,
% 0.35/0.67      ! [N: num] :
% 0.35/0.67        ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N ) ) ).
% 0.35/0.67  
% 0.35/0.67  % not_bit_Suc_0_numeral
% 0.35/0.67  thf(fact_9364_real__root__less__mono,axiom,
% 0.35/0.67      ! [N: nat,X: real,Y2: real] :
% 0.35/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.67       => ( ( ord_less_real @ X @ Y2 )
% 0.35/0.67         => ( ord_less_real @ ( root @ N @ X ) @ ( root @ N @ Y2 ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % real_root_less_mono
% 0.35/0.67  thf(fact_9365_real__root__le__mono,axiom,
% 0.35/0.67      ! [N: nat,X: real,Y2: real] :
% 0.35/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.67       => ( ( ord_less_eq_real @ X @ Y2 )
% 0.35/0.67         => ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N @ Y2 ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % real_root_le_mono
% 0.35/0.67  thf(fact_9366_real__root__power,axiom,
% 0.35/0.67      ! [N: nat,X: real,K: nat] :
% 0.35/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.67       => ( ( root @ N @ ( power_power_real @ X @ K ) )
% 0.35/0.67          = ( power_power_real @ ( root @ N @ X ) @ K ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % real_root_power
% 0.35/0.67  thf(fact_9367_real__root__abs,axiom,
% 0.35/0.67      ! [N: nat,X: real] :
% 0.35/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.67       => ( ( root @ N @ ( abs_abs_real @ X ) )
% 0.35/0.67          = ( abs_abs_real @ ( root @ N @ X ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % real_root_abs
% 0.35/0.67  thf(fact_9368_nat__mono__iff,axiom,
% 0.35/0.67      ! [Z: int,W: int] :
% 0.35/0.67        ( ( ord_less_int @ zero_zero_int @ Z )
% 0.35/0.67       => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 0.35/0.67          = ( ord_less_int @ W @ Z ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % nat_mono_iff
% 0.35/0.67  thf(fact_9369_zless__nat__eq__int__zless,axiom,
% 0.35/0.67      ! [M: nat,Z: int] :
% 0.35/0.67        ( ( ord_less_nat @ M @ ( nat2 @ Z ) )
% 0.35/0.67        = ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ Z ) ) ).
% 0.35/0.67  
% 0.35/0.67  % zless_nat_eq_int_zless
% 0.35/0.67  thf(fact_9370_nat__le__iff,axiom,
% 0.35/0.67      ! [X: int,N: nat] :
% 0.35/0.67        ( ( ord_less_eq_nat @ ( nat2 @ X ) @ N )
% 0.35/0.67        = ( ord_less_eq_int @ X @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % nat_le_iff
% 0.35/0.67  thf(fact_9371_nat__int__add,axiom,
% 0.35/0.67      ! [A: nat,B: nat] :
% 0.35/0.67        ( ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) )
% 0.35/0.67        = ( plus_plus_nat @ A @ B ) ) ).
% 0.35/0.67  
% 0.35/0.67  % nat_int_add
% 0.35/0.67  thf(fact_9372_sgn__mod,axiom,
% 0.35/0.67      ! [L2: int,K: int] :
% 0.35/0.67        ( ( L2 != zero_zero_int )
% 0.35/0.67       => ( ~ ( dvd_dvd_int @ L2 @ K )
% 0.35/0.67         => ( ( sgn_sgn_int @ ( modulo_modulo_int @ K @ L2 ) )
% 0.35/0.67            = ( sgn_sgn_int @ L2 ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % sgn_mod
% 0.35/0.67  thf(fact_9373_int__minus,axiom,
% 0.35/0.67      ! [N: nat,M: nat] :
% 0.35/0.67        ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ M ) )
% 0.35/0.67        = ( semiri1314217659103216013at_int @ ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % int_minus
% 0.35/0.67  thf(fact_9374_nat__abs__mult__distrib,axiom,
% 0.35/0.67      ! [W: int,Z: int] :
% 0.35/0.67        ( ( nat2 @ ( abs_abs_int @ ( times_times_int @ W @ Z ) ) )
% 0.35/0.67        = ( times_times_nat @ ( nat2 @ ( abs_abs_int @ W ) ) @ ( nat2 @ ( abs_abs_int @ Z ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % nat_abs_mult_distrib
% 0.35/0.67  thf(fact_9375_real__nat__ceiling__ge,axiom,
% 0.35/0.67      ! [X: real] : ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % real_nat_ceiling_ge
% 0.35/0.67  thf(fact_9376_nat__plus__as__int,axiom,
% 0.35/0.67      ( plus_plus_nat
% 0.35/0.67      = ( ^ [A3: nat,B4: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % nat_plus_as_int
% 0.35/0.67  thf(fact_9377_and__nat__def,axiom,
% 0.35/0.67      ( bit_se727722235901077358nd_nat
% 0.35/0.67      = ( ^ [M6: nat,N2: nat] : ( nat2 @ ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % and_nat_def
% 0.35/0.67  thf(fact_9378_nat__times__as__int,axiom,
% 0.35/0.67      ( times_times_nat
% 0.35/0.67      = ( ^ [A3: nat,B4: nat] : ( nat2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % nat_times_as_int
% 0.35/0.67  thf(fact_9379_or__nat__def,axiom,
% 0.35/0.67      ( bit_se1412395901928357646or_nat
% 0.35/0.67      = ( ^ [M6: nat,N2: nat] : ( nat2 @ ( bit_se1409905431419307370or_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % or_nat_def
% 0.35/0.67  thf(fact_9380_nat__minus__as__int,axiom,
% 0.35/0.67      ( minus_minus_nat
% 0.35/0.67      = ( ^ [A3: nat,B4: nat] : ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % nat_minus_as_int
% 0.35/0.67  thf(fact_9381_nat__div__as__int,axiom,
% 0.35/0.67      ( divide_divide_nat
% 0.35/0.67      = ( ^ [A3: nat,B4: nat] : ( nat2 @ ( divide_divide_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % nat_div_as_int
% 0.35/0.67  thf(fact_9382_real__root__gt__zero,axiom,
% 0.35/0.67      ! [N: nat,X: real] :
% 0.35/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.67       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.67         => ( ord_less_real @ zero_zero_real @ ( root @ N @ X ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % real_root_gt_zero
% 0.35/0.67  thf(fact_9383_real__root__strict__decreasing,axiom,
% 0.35/0.67      ! [N: nat,N4: nat,X: real] :
% 0.35/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.67       => ( ( ord_less_nat @ N @ N4 )
% 0.35/0.67         => ( ( ord_less_real @ one_one_real @ X )
% 0.35/0.67           => ( ord_less_real @ ( root @ N4 @ X ) @ ( root @ N @ X ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % real_root_strict_decreasing
% 0.35/0.67  thf(fact_9384_sqrt__def,axiom,
% 0.35/0.67      ( sqrt
% 0.35/0.67      = ( root @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % sqrt_def
% 0.35/0.67  thf(fact_9385_root__abs__power,axiom,
% 0.35/0.67      ! [N: nat,Y2: real] :
% 0.35/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.67       => ( ( abs_abs_real @ ( root @ N @ ( power_power_real @ Y2 @ N ) ) )
% 0.35/0.67          = ( abs_abs_real @ Y2 ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % root_abs_power
% 0.35/0.67  thf(fact_9386_nat__less__eq__zless,axiom,
% 0.35/0.67      ! [W: int,Z: int] :
% 0.35/0.67        ( ( ord_less_eq_int @ zero_zero_int @ W )
% 0.35/0.67       => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 0.35/0.67          = ( ord_less_int @ W @ Z ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % nat_less_eq_zless
% 0.35/0.67  thf(fact_9387_nat__le__eq__zle,axiom,
% 0.35/0.67      ! [W: int,Z: int] :
% 0.35/0.67        ( ( ( ord_less_int @ zero_zero_int @ W )
% 0.35/0.67          | ( ord_less_eq_int @ zero_zero_int @ Z ) )
% 0.35/0.67       => ( ( ord_less_eq_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 0.35/0.67          = ( ord_less_eq_int @ W @ Z ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % nat_le_eq_zle
% 0.35/0.67  thf(fact_9388_nat__add__distrib,axiom,
% 0.35/0.67      ! [Z: int,Z6: int] :
% 0.35/0.67        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.35/0.67       => ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 0.35/0.67         => ( ( nat2 @ ( plus_plus_int @ Z @ Z6 ) )
% 0.35/0.67            = ( plus_plus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % nat_add_distrib
% 0.35/0.67  thf(fact_9389_le__nat__iff,axiom,
% 0.35/0.67      ! [K: int,N: nat] :
% 0.35/0.67        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.35/0.67       => ( ( ord_less_eq_nat @ N @ ( nat2 @ K ) )
% 0.35/0.67          = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % le_nat_iff
% 0.35/0.67  thf(fact_9390_div__sgn__abs__cancel,axiom,
% 0.35/0.67      ! [V: int,K: int,L2: int] :
% 0.35/0.67        ( ( V != zero_zero_int )
% 0.35/0.67       => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ K ) ) @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ L2 ) ) )
% 0.35/0.67          = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % div_sgn_abs_cancel
% 0.35/0.67  thf(fact_9391_Suc__as__int,axiom,
% 0.35/0.67      ( suc
% 0.35/0.67      = ( ^ [A3: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ one_one_int ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % Suc_as_int
% 0.35/0.67  thf(fact_9392_nat__mult__distrib,axiom,
% 0.35/0.67      ! [Z: int,Z6: int] :
% 0.35/0.67        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.35/0.67       => ( ( nat2 @ ( times_times_int @ Z @ Z6 ) )
% 0.35/0.67          = ( times_times_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % nat_mult_distrib
% 0.35/0.67  thf(fact_9393_nat__abs__triangle__ineq,axiom,
% 0.35/0.67      ! [K: int,L2: int] : ( ord_less_eq_nat @ ( nat2 @ ( abs_abs_int @ ( plus_plus_int @ K @ L2 ) ) ) @ ( plus_plus_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % nat_abs_triangle_ineq
% 0.35/0.67  thf(fact_9394_nat__diff__distrib,axiom,
% 0.35/0.67      ! [Z6: int,Z: int] :
% 0.35/0.67        ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 0.35/0.67       => ( ( ord_less_eq_int @ Z6 @ Z )
% 0.35/0.67         => ( ( nat2 @ ( minus_minus_int @ Z @ Z6 ) )
% 0.35/0.67            = ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % nat_diff_distrib
% 0.35/0.67  thf(fact_9395_nat__diff__distrib_H,axiom,
% 0.35/0.67      ! [X: int,Y2: int] :
% 0.35/0.67        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.35/0.67       => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 0.35/0.67         => ( ( nat2 @ ( minus_minus_int @ X @ Y2 ) )
% 0.35/0.67            = ( minus_minus_nat @ ( nat2 @ X ) @ ( nat2 @ Y2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % nat_diff_distrib'
% 0.35/0.67  thf(fact_9396_nat__div__distrib_H,axiom,
% 0.35/0.67      ! [Y2: int,X: int] :
% 0.35/0.67        ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 0.35/0.67       => ( ( nat2 @ ( divide_divide_int @ X @ Y2 ) )
% 0.35/0.67          = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y2 ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % nat_div_distrib'
% 0.35/0.67  thf(fact_9397_nat__div__distrib,axiom,
% 0.35/0.67      ! [X: int,Y2: int] :
% 0.35/0.67        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.35/0.67       => ( ( nat2 @ ( divide_divide_int @ X @ Y2 ) )
% 0.35/0.67          = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y2 ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % nat_div_distrib
% 0.35/0.67  thf(fact_9398_div__dvd__sgn__abs,axiom,
% 0.35/0.67      ! [L2: int,K: int] :
% 0.35/0.67        ( ( dvd_dvd_int @ L2 @ K )
% 0.35/0.67       => ( ( divide_divide_int @ K @ L2 )
% 0.35/0.67          = ( times_times_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( sgn_sgn_int @ L2 ) ) @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % div_dvd_sgn_abs
% 0.35/0.67  thf(fact_9399_nat__power__eq,axiom,
% 0.35/0.67      ! [Z: int,N: nat] :
% 0.35/0.67        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.35/0.67       => ( ( nat2 @ ( power_power_int @ Z @ N ) )
% 0.35/0.67          = ( power_power_nat @ ( nat2 @ Z ) @ N ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % nat_power_eq
% 0.35/0.67  thf(fact_9400_nat__floor__neg,axiom,
% 0.35/0.67      ! [X: real] :
% 0.35/0.67        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.35/0.67       => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 0.35/0.67          = zero_zero_nat ) ) ).
% 0.35/0.67  
% 0.35/0.67  % nat_floor_neg
% 0.35/0.67  thf(fact_9401_div__abs__eq__div__nat,axiom,
% 0.35/0.67      ! [K: int,L2: int] :
% 0.35/0.67        ( ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) )
% 0.35/0.67        = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % div_abs_eq_div_nat
% 0.35/0.67  thf(fact_9402_nat__mod__distrib,axiom,
% 0.35/0.67      ! [X: int,Y2: int] :
% 0.35/0.67        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.35/0.67       => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 0.35/0.67         => ( ( nat2 @ ( modulo_modulo_int @ X @ Y2 ) )
% 0.35/0.67            = ( modulo_modulo_nat @ ( nat2 @ X ) @ ( nat2 @ Y2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % nat_mod_distrib
% 0.35/0.67  thf(fact_9403_floor__eq3,axiom,
% 0.35/0.67      ! [N: nat,X: real] :
% 0.35/0.67        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ X )
% 0.35/0.67       => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 0.35/0.67         => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 0.35/0.67            = N ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % floor_eq3
% 0.35/0.67  thf(fact_9404_le__nat__floor,axiom,
% 0.35/0.67      ! [X: nat,A: real] :
% 0.35/0.67        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ A )
% 0.35/0.67       => ( ord_less_eq_nat @ X @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % le_nat_floor
% 0.35/0.67  thf(fact_9405_mod__abs__eq__div__nat,axiom,
% 0.35/0.67      ! [K: int,L2: int] :
% 0.35/0.67        ( ( modulo_modulo_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) )
% 0.35/0.67        = ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ).
% 0.35/0.67  
% 0.35/0.67  % mod_abs_eq_div_nat
% 0.35/0.67  thf(fact_9406_nat__take__bit__eq,axiom,
% 0.35/0.67      ! [K: int,N: nat] :
% 0.35/0.67        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.35/0.67       => ( ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 0.35/0.68          = ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % nat_take_bit_eq
% 0.35/0.68  thf(fact_9407_take__bit__nat__eq,axiom,
% 0.35/0.68      ! [K: int,N: nat] :
% 0.35/0.68        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.35/0.68       => ( ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) )
% 0.35/0.68          = ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % take_bit_nat_eq
% 0.35/0.68  thf(fact_9408_divide__int__def,axiom,
% 0.35/0.68      ( divide_divide_int
% 0.35/0.68      = ( ^ [K3: int,L: int] :
% 0.35/0.68            ( if_int @ ( L = zero_zero_int ) @ zero_zero_int
% 0.35/0.68            @ ( if_int
% 0.35/0.68              @ ( ( sgn_sgn_int @ K3 )
% 0.35/0.68                = ( sgn_sgn_int @ L ) )
% 0.35/0.68              @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) )
% 0.35/0.68              @ ( uminus_uminus_int
% 0.35/0.68                @ ( semiri1314217659103216013at_int
% 0.35/0.68                  @ ( plus_plus_nat @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) )
% 0.35/0.68                    @ ( zero_n2687167440665602831ol_nat
% 0.35/0.68                      @ ~ ( dvd_dvd_int @ L @ K3 ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % divide_int_def
% 0.35/0.68  thf(fact_9409_modulo__int__def,axiom,
% 0.35/0.68      ( modulo_modulo_int
% 0.35/0.68      = ( ^ [K3: int,L: int] :
% 0.35/0.68            ( if_int @ ( L = zero_zero_int ) @ K3
% 0.35/0.68            @ ( if_int
% 0.35/0.68              @ ( ( sgn_sgn_int @ K3 )
% 0.35/0.68                = ( sgn_sgn_int @ L ) )
% 0.35/0.68              @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) )
% 0.35/0.68              @ ( times_times_int @ ( sgn_sgn_int @ L )
% 0.35/0.68                @ ( minus_minus_int
% 0.35/0.68                  @ ( times_times_int @ ( abs_abs_int @ L )
% 0.35/0.68                    @ ( zero_n2684676970156552555ol_int
% 0.35/0.68                      @ ~ ( dvd_dvd_int @ L @ K3 ) ) )
% 0.35/0.68                  @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % modulo_int_def
% 0.35/0.68  thf(fact_9410_real__root__pos__pos,axiom,
% 0.35/0.68      ! [N: nat,X: real] :
% 0.35/0.68        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.68         => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % real_root_pos_pos
% 0.35/0.68  thf(fact_9411_real__root__strict__increasing,axiom,
% 0.35/0.68      ! [N: nat,N4: nat,X: real] :
% 0.35/0.68        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68       => ( ( ord_less_nat @ N @ N4 )
% 0.35/0.68         => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.68           => ( ( ord_less_real @ X @ one_one_real )
% 0.35/0.68             => ( ord_less_real @ ( root @ N @ X ) @ ( root @ N4 @ X ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % real_root_strict_increasing
% 0.35/0.68  thf(fact_9412_real__root__decreasing,axiom,
% 0.35/0.68      ! [N: nat,N4: nat,X: real] :
% 0.35/0.68        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68       => ( ( ord_less_eq_nat @ N @ N4 )
% 0.35/0.68         => ( ( ord_less_eq_real @ one_one_real @ X )
% 0.35/0.68           => ( ord_less_eq_real @ ( root @ N4 @ X ) @ ( root @ N @ X ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % real_root_decreasing
% 0.35/0.68  thf(fact_9413_odd__real__root__power__cancel,axiom,
% 0.35/0.68      ! [N: nat,X: real] :
% 0.35/0.68        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.68       => ( ( root @ N @ ( power_power_real @ X @ N ) )
% 0.35/0.68          = X ) ) ).
% 0.35/0.68  
% 0.35/0.68  % odd_real_root_power_cancel
% 0.35/0.68  thf(fact_9414_odd__real__root__unique,axiom,
% 0.35/0.68      ! [N: nat,Y2: real,X: real] :
% 0.35/0.68        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.68       => ( ( ( power_power_real @ Y2 @ N )
% 0.35/0.68            = X )
% 0.35/0.68         => ( ( root @ N @ X )
% 0.35/0.68            = Y2 ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % odd_real_root_unique
% 0.35/0.68  thf(fact_9415_odd__real__root__pow,axiom,
% 0.35/0.68      ! [N: nat,X: real] :
% 0.35/0.68        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.68       => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 0.35/0.68          = X ) ) ).
% 0.35/0.68  
% 0.35/0.68  % odd_real_root_pow
% 0.35/0.68  thf(fact_9416_real__root__pow__pos,axiom,
% 0.35/0.68      ! [N: nat,X: real] :
% 0.35/0.68        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.68         => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 0.35/0.68            = X ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % real_root_pow_pos
% 0.35/0.68  thf(fact_9417_real__root__pos__unique,axiom,
% 0.35/0.68      ! [N: nat,Y2: real,X: real] :
% 0.35/0.68        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 0.35/0.68         => ( ( ( power_power_real @ Y2 @ N )
% 0.35/0.68              = X )
% 0.35/0.68           => ( ( root @ N @ X )
% 0.35/0.68              = Y2 ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % real_root_pos_unique
% 0.35/0.68  thf(fact_9418_real__root__power__cancel,axiom,
% 0.35/0.68      ! [N: nat,X: real] :
% 0.35/0.68        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68       => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.68         => ( ( root @ N @ ( power_power_real @ X @ N ) )
% 0.35/0.68            = X ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % real_root_power_cancel
% 0.35/0.68  thf(fact_9419_nat__2,axiom,
% 0.35/0.68      ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.68      = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % nat_2
% 0.35/0.68  thf(fact_9420_Suc__nat__eq__nat__zadd1,axiom,
% 0.35/0.68      ! [Z: int] :
% 0.35/0.68        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.35/0.68       => ( ( suc @ ( nat2 @ Z ) )
% 0.35/0.68          = ( nat2 @ ( plus_plus_int @ one_one_int @ Z ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Suc_nat_eq_nat_zadd1
% 0.35/0.68  thf(fact_9421_nat__less__iff,axiom,
% 0.35/0.68      ! [W: int,M: nat] :
% 0.35/0.68        ( ( ord_less_eq_int @ zero_zero_int @ W )
% 0.35/0.68       => ( ( ord_less_nat @ ( nat2 @ W ) @ M )
% 0.35/0.68          = ( ord_less_int @ W @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % nat_less_iff
% 0.35/0.68  thf(fact_9422_nat__mult__distrib__neg,axiom,
% 0.35/0.68      ! [Z: int,Z6: int] :
% 0.35/0.68        ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 0.35/0.68       => ( ( nat2 @ ( times_times_int @ Z @ Z6 ) )
% 0.35/0.68          = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z ) ) @ ( nat2 @ ( uminus_uminus_int @ Z6 ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % nat_mult_distrib_neg
% 0.35/0.68  thf(fact_9423_nat__abs__int__diff,axiom,
% 0.35/0.68      ! [A: nat,B: nat] :
% 0.35/0.68        ( ( ( ord_less_eq_nat @ A @ B )
% 0.35/0.68         => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 0.35/0.68            = ( minus_minus_nat @ B @ A ) ) )
% 0.35/0.68        & ( ~ ( ord_less_eq_nat @ A @ B )
% 0.35/0.68         => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 0.35/0.68            = ( minus_minus_nat @ A @ B ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % nat_abs_int_diff
% 0.35/0.68  thf(fact_9424_floor__eq4,axiom,
% 0.35/0.68      ! [N: nat,X: real] :
% 0.35/0.68        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ X )
% 0.35/0.68       => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 0.35/0.68         => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 0.35/0.68            = N ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % floor_eq4
% 0.35/0.68  thf(fact_9425_diff__nat__eq__if,axiom,
% 0.35/0.68      ! [Z6: int,Z: int] :
% 0.35/0.68        ( ( ( ord_less_int @ Z6 @ zero_zero_int )
% 0.35/0.68         => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) )
% 0.35/0.68            = ( nat2 @ Z ) ) )
% 0.35/0.68        & ( ~ ( ord_less_int @ Z6 @ zero_zero_int )
% 0.35/0.68         => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) )
% 0.35/0.68            = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z @ Z6 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z @ Z6 ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % diff_nat_eq_if
% 0.35/0.68  thf(fact_9426_real__root__increasing,axiom,
% 0.35/0.68      ! [N: nat,N4: nat,X: real] :
% 0.35/0.68        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68       => ( ( ord_less_eq_nat @ N @ N4 )
% 0.35/0.68         => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.68           => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.35/0.68             => ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N4 @ X ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % real_root_increasing
% 0.35/0.68  thf(fact_9427_bit__nat__def,axiom,
% 0.35/0.68      ( bit_se1148574629649215175it_nat
% 0.35/0.68      = ( ^ [M6: nat,N2: nat] :
% 0.35/0.68            ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % bit_nat_def
% 0.35/0.68  thf(fact_9428_eucl__rel__int__remainderI,axiom,
% 0.35/0.68      ! [R: int,L2: int,K: int,Q2: int] :
% 0.35/0.68        ( ( ( sgn_sgn_int @ R )
% 0.35/0.68          = ( sgn_sgn_int @ L2 ) )
% 0.35/0.68       => ( ( ord_less_int @ ( abs_abs_int @ R ) @ ( abs_abs_int @ L2 ) )
% 0.35/0.68         => ( ( K
% 0.35/0.68              = ( plus_plus_int @ ( times_times_int @ Q2 @ L2 ) @ R ) )
% 0.35/0.68           => ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % eucl_rel_int_remainderI
% 0.35/0.68  thf(fact_9429_log__root,axiom,
% 0.35/0.68      ! [N: nat,A: real,B: real] :
% 0.35/0.68        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.68         => ( ( log @ B @ ( root @ N @ A ) )
% 0.35/0.68            = ( divide_divide_real @ ( log @ B @ A ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % log_root
% 0.35/0.68  thf(fact_9430_log__base__root,axiom,
% 0.35/0.68      ! [N: nat,B: real,X: real] :
% 0.35/0.68        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68       => ( ( ord_less_real @ zero_zero_real @ B )
% 0.35/0.68         => ( ( log @ ( root @ N @ B ) @ X )
% 0.35/0.68            = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % log_base_root
% 0.35/0.68  thf(fact_9431_ln__root,axiom,
% 0.35/0.68      ! [N: nat,B: real] :
% 0.35/0.68        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68       => ( ( ord_less_real @ zero_zero_real @ B )
% 0.35/0.68         => ( ( ln_ln_real @ ( root @ N @ B ) )
% 0.35/0.68            = ( divide_divide_real @ ( ln_ln_real @ B ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % ln_root
% 0.35/0.68  thf(fact_9432_eucl__rel__int_Osimps,axiom,
% 0.35/0.68      ( eucl_rel_int
% 0.35/0.68      = ( ^ [A1: int,A22: int,A32: product_prod_int_int] :
% 0.35/0.68            ( ? [K3: int] :
% 0.35/0.68                ( ( A1 = K3 )
% 0.35/0.68                & ( A22 = zero_zero_int )
% 0.35/0.68                & ( A32
% 0.35/0.68                  = ( product_Pair_int_int @ zero_zero_int @ K3 ) ) )
% 0.35/0.68            | ? [L: int,K3: int,Q4: int] :
% 0.35/0.68                ( ( A1 = K3 )
% 0.35/0.68                & ( A22 = L )
% 0.35/0.68                & ( A32
% 0.35/0.68                  = ( product_Pair_int_int @ Q4 @ zero_zero_int ) )
% 0.35/0.68                & ( L != zero_zero_int )
% 0.35/0.68                & ( K3
% 0.35/0.68                  = ( times_times_int @ Q4 @ L ) ) )
% 0.35/0.68            | ? [R5: int,L: int,K3: int,Q4: int] :
% 0.35/0.68                ( ( A1 = K3 )
% 0.35/0.68                & ( A22 = L )
% 0.35/0.68                & ( A32
% 0.35/0.68                  = ( product_Pair_int_int @ Q4 @ R5 ) )
% 0.35/0.68                & ( ( sgn_sgn_int @ R5 )
% 0.35/0.68                  = ( sgn_sgn_int @ L ) )
% 0.35/0.68                & ( ord_less_int @ ( abs_abs_int @ R5 ) @ ( abs_abs_int @ L ) )
% 0.35/0.68                & ( K3
% 0.35/0.68                  = ( plus_plus_int @ ( times_times_int @ Q4 @ L ) @ R5 ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % eucl_rel_int.simps
% 0.35/0.68  thf(fact_9433_eucl__rel__int_Ocases,axiom,
% 0.35/0.68      ! [A12: int,A23: int,A33: product_prod_int_int] :
% 0.35/0.68        ( ( eucl_rel_int @ A12 @ A23 @ A33 )
% 0.35/0.68       => ( ( ( A23 = zero_zero_int )
% 0.35/0.68           => ( A33
% 0.35/0.68             != ( product_Pair_int_int @ zero_zero_int @ A12 ) ) )
% 0.35/0.68         => ( ! [Q3: int] :
% 0.35/0.68                ( ( A33
% 0.35/0.68                  = ( product_Pair_int_int @ Q3 @ zero_zero_int ) )
% 0.35/0.68               => ( ( A23 != zero_zero_int )
% 0.35/0.68                 => ( A12
% 0.35/0.68                   != ( times_times_int @ Q3 @ A23 ) ) ) )
% 0.35/0.68           => ~ ! [R3: int,Q3: int] :
% 0.35/0.68                  ( ( A33
% 0.35/0.68                    = ( product_Pair_int_int @ Q3 @ R3 ) )
% 0.35/0.68                 => ( ( ( sgn_sgn_int @ R3 )
% 0.35/0.68                      = ( sgn_sgn_int @ A23 ) )
% 0.35/0.68                   => ( ( ord_less_int @ ( abs_abs_int @ R3 ) @ ( abs_abs_int @ A23 ) )
% 0.35/0.68                     => ( A12
% 0.35/0.68                       != ( plus_plus_int @ ( times_times_int @ Q3 @ A23 ) @ R3 ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % eucl_rel_int.cases
% 0.35/0.68  thf(fact_9434_div__noneq__sgn__abs,axiom,
% 0.35/0.68      ! [L2: int,K: int] :
% 0.35/0.68        ( ( L2 != zero_zero_int )
% 0.35/0.68       => ( ( ( sgn_sgn_int @ K )
% 0.35/0.68           != ( sgn_sgn_int @ L2 ) )
% 0.35/0.68         => ( ( divide_divide_int @ K @ L2 )
% 0.35/0.68            = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) ) )
% 0.35/0.68              @ ( zero_n2684676970156552555ol_int
% 0.35/0.68                @ ~ ( dvd_dvd_int @ L2 @ K ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % div_noneq_sgn_abs
% 0.35/0.68  thf(fact_9435_root__powr__inverse,axiom,
% 0.35/0.68      ! [N: nat,X: real] :
% 0.35/0.68        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.68         => ( ( root @ N @ X )
% 0.35/0.68            = ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % root_powr_inverse
% 0.35/0.68  thf(fact_9436_even__nat__iff,axiom,
% 0.35/0.68      ! [K: int] :
% 0.35/0.68        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.35/0.68       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat2 @ K ) )
% 0.35/0.68          = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % even_nat_iff
% 0.35/0.68  thf(fact_9437_powr__real__of__int,axiom,
% 0.35/0.68      ! [X: real,N: int] :
% 0.35/0.68        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.68       => ( ( ( ord_less_eq_int @ zero_zero_int @ N )
% 0.35/0.68           => ( ( powr_real @ X @ ( ring_1_of_int_real @ N ) )
% 0.35/0.68              = ( power_power_real @ X @ ( nat2 @ N ) ) ) )
% 0.35/0.68          & ( ~ ( ord_less_eq_int @ zero_zero_int @ N )
% 0.35/0.68           => ( ( powr_real @ X @ ( ring_1_of_int_real @ N ) )
% 0.35/0.68              = ( inverse_inverse_real @ ( power_power_real @ X @ ( nat2 @ ( uminus_uminus_int @ N ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % powr_real_of_int
% 0.35/0.68  thf(fact_9438_arctan__inverse,axiom,
% 0.35/0.68      ! [X: real] :
% 0.35/0.68        ( ( X != zero_zero_real )
% 0.35/0.68       => ( ( arctan @ ( divide_divide_real @ one_one_real @ X ) )
% 0.35/0.68          = ( minus_minus_real @ ( divide_divide_real @ ( times_times_real @ ( sgn_sgn_real @ X ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( arctan @ X ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % arctan_inverse
% 0.35/0.68  thf(fact_9439_cis__multiple__2pi,axiom,
% 0.35/0.68      ! [N: real] :
% 0.35/0.68        ( ( member_real @ N @ ring_1_Ints_real )
% 0.35/0.68       => ( ( cis @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 0.35/0.68          = one_one_complex ) ) ).
% 0.35/0.68  
% 0.35/0.68  % cis_multiple_2pi
% 0.35/0.68  thf(fact_9440_setceilmax,axiom,
% 0.35/0.68      ! [S3: vEBT_VEBT,M: nat,Listy: list_VEBT_VEBT,N: nat] :
% 0.35/0.68        ( ( vEBT_invar_vebt @ S3 @ M )
% 0.35/0.68       => ( ! [X3: vEBT_VEBT] :
% 0.35/0.68              ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Listy ) )
% 0.35/0.68             => ( vEBT_invar_vebt @ X3 @ N ) )
% 0.35/0.68         => ( ( M
% 0.35/0.68              = ( suc @ N ) )
% 0.35/0.68           => ( ! [X3: vEBT_VEBT] :
% 0.35/0.68                  ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Listy ) )
% 0.35/0.68                 => ( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ X3 ) )
% 0.35/0.68                    = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) )
% 0.35/0.68             => ( ( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ S3 ) )
% 0.35/0.68                  = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) )
% 0.35/0.68               => ( ( semiri1314217659103216013at_int @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ S3 @ ( set_VEBT_VEBT2 @ Listy ) ) ) ) )
% 0.35/0.68                  = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % setceilmax
% 0.35/0.68  thf(fact_9441_height__compose__list,axiom,
% 0.35/0.68      ! [T: vEBT_VEBT,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.35/0.68        ( ( member_VEBT_VEBT @ T @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.35/0.68       => ( ord_less_eq_nat @ ( vEBT_VEBT_height @ T ) @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary @ ( set_VEBT_VEBT2 @ TreeList ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % height_compose_list
% 0.35/0.68  thf(fact_9442_max__ins__scaled,axiom,
% 0.35/0.68      ! [N: nat,X14: vEBT_VEBT,M: nat,X13: list_VEBT_VEBT] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( vEBT_VEBT_height @ X14 ) ) @ ( plus_plus_nat @ M @ ( times_times_nat @ N @ ( lattic8265883725875713057ax_nat @ ( insert_nat @ ( vEBT_VEBT_height @ X14 ) @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( set_VEBT_VEBT2 @ X13 ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % max_ins_scaled
% 0.35/0.68  thf(fact_9443_height__i__max,axiom,
% 0.35/0.68      ! [I2: nat,X13: list_VEBT_VEBT,Foo: nat] :
% 0.35/0.68        ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ X13 ) )
% 0.35/0.68       => ( ord_less_eq_nat @ ( vEBT_VEBT_height @ ( nth_VEBT_VEBT @ X13 @ I2 ) ) @ ( ord_max_nat @ Foo @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( set_VEBT_VEBT2 @ X13 ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % height_i_max
% 0.35/0.68  thf(fact_9444_max__idx__list,axiom,
% 0.35/0.68      ! [I2: nat,X13: list_VEBT_VEBT,N: nat,X14: vEBT_VEBT] :
% 0.35/0.68        ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ X13 ) )
% 0.35/0.68       => ( ord_less_eq_nat @ ( times_times_nat @ N @ ( vEBT_VEBT_height @ ( nth_VEBT_VEBT @ X13 @ I2 ) ) ) @ ( suc @ ( suc @ ( times_times_nat @ N @ ( ord_max_nat @ ( vEBT_VEBT_height @ X14 ) @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( set_VEBT_VEBT2 @ X13 ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % max_idx_list
% 0.35/0.68  thf(fact_9445_sgn__le__0__iff,axiom,
% 0.35/0.68      ! [X: real] :
% 0.35/0.68        ( ( ord_less_eq_real @ ( sgn_sgn_real @ X ) @ zero_zero_real )
% 0.35/0.68        = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 0.35/0.68  
% 0.35/0.68  % sgn_le_0_iff
% 0.35/0.68  thf(fact_9446_zero__le__sgn__iff,axiom,
% 0.35/0.68      ! [X: real] :
% 0.35/0.68        ( ( ord_less_eq_real @ zero_zero_real @ ( sgn_sgn_real @ X ) )
% 0.35/0.68        = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 0.35/0.68  
% 0.35/0.68  % zero_le_sgn_iff
% 0.35/0.68  thf(fact_9447_real__sgn__eq,axiom,
% 0.35/0.68      ( sgn_sgn_real
% 0.35/0.68      = ( ^ [X2: real] : ( divide_divide_real @ X2 @ ( abs_abs_real @ X2 ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % real_sgn_eq
% 0.35/0.68  thf(fact_9448_sgn__root,axiom,
% 0.35/0.68      ! [N: nat,X: real] :
% 0.35/0.68        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68       => ( ( sgn_sgn_real @ ( root @ N @ X ) )
% 0.35/0.68          = ( sgn_sgn_real @ X ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % sgn_root
% 0.35/0.68  thf(fact_9449_VEBT__internal_Oheight_Osimps_I2_J,axiom,
% 0.35/0.68      ! [Uu: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.35/0.68        ( ( vEBT_VEBT_height @ ( vEBT_Node @ Uu @ Deg @ TreeList @ Summary ) )
% 0.35/0.68        = ( plus_plus_nat @ one_one_nat @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary @ ( set_VEBT_VEBT2 @ TreeList ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % VEBT_internal.height.simps(2)
% 0.35/0.68  thf(fact_9450_sgn__real__def,axiom,
% 0.35/0.68      ( sgn_sgn_real
% 0.35/0.68      = ( ^ [A3: real] : ( if_real @ ( A3 = zero_zero_real ) @ zero_zero_real @ ( if_real @ ( ord_less_real @ zero_zero_real @ A3 ) @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % sgn_real_def
% 0.35/0.68  thf(fact_9451_VEBT__internal_Oheight_Oelims,axiom,
% 0.35/0.68      ! [X: vEBT_VEBT,Y2: nat] :
% 0.35/0.68        ( ( ( vEBT_VEBT_height @ X )
% 0.35/0.68          = Y2 )
% 0.35/0.68       => ( ( ? [A4: $o,B3: $o] :
% 0.35/0.68                ( X
% 0.35/0.68                = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.68           => ( Y2 != zero_zero_nat ) )
% 0.35/0.68         => ~ ! [Uu2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.68                ( ( X
% 0.35/0.68                  = ( vEBT_Node @ Uu2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.35/0.68               => ( Y2
% 0.35/0.68                 != ( plus_plus_nat @ one_one_nat @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary2 @ ( set_VEBT_VEBT2 @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % VEBT_internal.height.elims
% 0.35/0.68  thf(fact_9452_sin__times__pi__eq__0,axiom,
% 0.35/0.68      ! [X: real] :
% 0.35/0.68        ( ( ( sin_real @ ( times_times_real @ X @ pi ) )
% 0.35/0.68          = zero_zero_real )
% 0.35/0.68        = ( member_real @ X @ ring_1_Ints_real ) ) ).
% 0.35/0.68  
% 0.35/0.68  % sin_times_pi_eq_0
% 0.35/0.68  thf(fact_9453_divide__nat__def,axiom,
% 0.35/0.68      ( divide_divide_nat
% 0.35/0.68      = ( ^ [M6: nat,N2: nat] :
% 0.35/0.68            ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat
% 0.35/0.68            @ ( lattic8265883725875713057ax_nat
% 0.35/0.68              @ ( collect_nat
% 0.35/0.68                @ ^ [K3: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K3 @ N2 ) @ M6 ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % divide_nat_def
% 0.35/0.68  thf(fact_9454_sgn__power__injE,axiom,
% 0.35/0.68      ! [A: real,N: nat,X: real,B: real] :
% 0.35/0.68        ( ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 0.35/0.68          = X )
% 0.35/0.68       => ( ( X
% 0.35/0.68            = ( times_times_real @ ( sgn_sgn_real @ B ) @ ( power_power_real @ ( abs_abs_real @ B ) @ N ) ) )
% 0.35/0.68         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68           => ( A = B ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % sgn_power_injE
% 0.35/0.68  thf(fact_9455_sgn__power__root,axiom,
% 0.35/0.68      ! [N: nat,X: real] :
% 0.35/0.68        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68       => ( ( times_times_real @ ( sgn_sgn_real @ ( root @ N @ X ) ) @ ( power_power_real @ ( abs_abs_real @ ( root @ N @ X ) ) @ N ) )
% 0.35/0.68          = X ) ) ).
% 0.35/0.68  
% 0.35/0.68  % sgn_power_root
% 0.35/0.68  thf(fact_9456_root__sgn__power,axiom,
% 0.35/0.68      ! [N: nat,Y2: real] :
% 0.35/0.68        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68       => ( ( root @ N @ ( times_times_real @ ( sgn_sgn_real @ Y2 ) @ ( power_power_real @ ( abs_abs_real @ Y2 ) @ N ) ) )
% 0.35/0.68          = Y2 ) ) ).
% 0.35/0.68  
% 0.35/0.68  % root_sgn_power
% 0.35/0.68  thf(fact_9457_cis__Arg__unique,axiom,
% 0.35/0.68      ! [Z: complex,X: real] :
% 0.35/0.68        ( ( ( sgn_sgn_complex @ Z )
% 0.35/0.68          = ( cis @ X ) )
% 0.35/0.68       => ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X )
% 0.35/0.68         => ( ( ord_less_eq_real @ X @ pi )
% 0.35/0.68           => ( ( arg @ Z )
% 0.35/0.68              = X ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % cis_Arg_unique
% 0.35/0.68  thf(fact_9458_split__root,axiom,
% 0.35/0.68      ! [P: real > $o,N: nat,X: real] :
% 0.35/0.68        ( ( P @ ( root @ N @ X ) )
% 0.35/0.68        = ( ( ( N = zero_zero_nat )
% 0.35/0.68           => ( P @ zero_zero_real ) )
% 0.35/0.68          & ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68           => ! [Y: real] :
% 0.35/0.68                ( ( ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N ) )
% 0.35/0.68                  = X )
% 0.35/0.68               => ( P @ Y ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % split_root
% 0.35/0.68  thf(fact_9459_sin__integer__2pi,axiom,
% 0.35/0.68      ! [N: real] :
% 0.35/0.68        ( ( member_real @ N @ ring_1_Ints_real )
% 0.35/0.68       => ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 0.35/0.68          = zero_zero_real ) ) ).
% 0.35/0.68  
% 0.35/0.68  % sin_integer_2pi
% 0.35/0.68  thf(fact_9460_cos__integer__2pi,axiom,
% 0.35/0.68      ! [N: real] :
% 0.35/0.68        ( ( member_real @ N @ ring_1_Ints_real )
% 0.35/0.68       => ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 0.35/0.68          = one_one_real ) ) ).
% 0.35/0.68  
% 0.35/0.68  % cos_integer_2pi
% 0.35/0.68  thf(fact_9461_Arg__correct,axiom,
% 0.35/0.68      ! [Z: complex] :
% 0.35/0.68        ( ( Z != zero_zero_complex )
% 0.35/0.68       => ( ( ( sgn_sgn_complex @ Z )
% 0.35/0.68            = ( cis @ ( arg @ Z ) ) )
% 0.35/0.68          & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 0.35/0.68          & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Arg_correct
% 0.35/0.68  thf(fact_9462_bij__betw__Suc,axiom,
% 0.35/0.68      ! [M7: set_nat,N4: set_nat] :
% 0.35/0.68        ( ( bij_betw_nat_nat @ suc @ M7 @ N4 )
% 0.35/0.68        = ( ( image_nat_nat @ suc @ M7 )
% 0.35/0.68          = N4 ) ) ).
% 0.35/0.68  
% 0.35/0.68  % bij_betw_Suc
% 0.35/0.68  thf(fact_9463_image__Suc__atLeastAtMost,axiom,
% 0.35/0.68      ! [I2: nat,J: nat] :
% 0.35/0.68        ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I2 @ J ) )
% 0.35/0.68        = ( set_or1269000886237332187st_nat @ ( suc @ I2 ) @ ( suc @ J ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % image_Suc_atLeastAtMost
% 0.35/0.68  thf(fact_9464_zero__notin__Suc__image,axiom,
% 0.35/0.68      ! [A2: set_nat] :
% 0.35/0.68        ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A2 ) ) ).
% 0.35/0.68  
% 0.35/0.68  % zero_notin_Suc_image
% 0.35/0.68  thf(fact_9465_image__Suc__lessThan,axiom,
% 0.35/0.68      ! [N: nat] :
% 0.35/0.68        ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.68        = ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ).
% 0.35/0.68  
% 0.35/0.68  % image_Suc_lessThan
% 0.35/0.68  thf(fact_9466_image__Suc__atMost,axiom,
% 0.35/0.68      ! [N: nat] :
% 0.35/0.68        ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.68        = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % image_Suc_atMost
% 0.35/0.68  thf(fact_9467_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 0.35/0.68      ! [N: nat] :
% 0.35/0.68        ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 0.35/0.68        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % atLeast0_atMost_Suc_eq_insert_0
% 0.35/0.68  thf(fact_9468_lessThan__Suc__eq__insert__0,axiom,
% 0.35/0.68      ! [N: nat] :
% 0.35/0.68        ( ( set_ord_lessThan_nat @ ( suc @ N ) )
% 0.35/0.68        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % lessThan_Suc_eq_insert_0
% 0.35/0.68  thf(fact_9469_atMost__Suc__eq__insert__0,axiom,
% 0.35/0.68      ! [N: nat] :
% 0.35/0.68        ( ( set_ord_atMost_nat @ ( suc @ N ) )
% 0.35/0.68        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % atMost_Suc_eq_insert_0
% 0.35/0.68  thf(fact_9470_Arg__def,axiom,
% 0.35/0.68      ( arg
% 0.35/0.68      = ( ^ [Z4: complex] :
% 0.35/0.68            ( if_real @ ( Z4 = zero_zero_complex ) @ zero_zero_real
% 0.35/0.68            @ ( fChoice_real
% 0.35/0.68              @ ^ [A3: real] :
% 0.35/0.68                  ( ( ( sgn_sgn_complex @ Z4 )
% 0.35/0.68                    = ( cis @ A3 ) )
% 0.35/0.68                  & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ A3 )
% 0.35/0.68                  & ( ord_less_eq_real @ A3 @ pi ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Arg_def
% 0.35/0.68  thf(fact_9471_horner__sum__of__bool__2__less,axiom,
% 0.35/0.68      ! [Bs: list_o] : ( ord_less_int @ ( groups9116527308978886569_o_int @ zero_n2684676970156552555ol_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Bs ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( size_size_list_o @ Bs ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % horner_sum_of_bool_2_less
% 0.35/0.68  thf(fact_9472_xor__Suc__0__eq,axiom,
% 0.35/0.68      ! [N: nat] :
% 0.35/0.68        ( ( bit_se6528837805403552850or_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.35/0.68        = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.68          @ ( zero_n2687167440665602831ol_nat
% 0.35/0.68            @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % xor_Suc_0_eq
% 0.35/0.68  thf(fact_9473_xor__nat__numerals_I4_J,axiom,
% 0.35/0.68      ! [X: num] :
% 0.35/0.68        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 0.35/0.68        = ( numeral_numeral_nat @ ( bit0 @ X ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % xor_nat_numerals(4)
% 0.35/0.68  thf(fact_9474_xor__nat__numerals_I3_J,axiom,
% 0.35/0.68      ! [X: num] :
% 0.35/0.68        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 0.35/0.68        = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % xor_nat_numerals(3)
% 0.35/0.68  thf(fact_9475_xor__nat__numerals_I2_J,axiom,
% 0.35/0.68      ! [Y2: num] :
% 0.35/0.68        ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) )
% 0.35/0.68        = ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % xor_nat_numerals(2)
% 0.35/0.68  thf(fact_9476_xor__nat__numerals_I1_J,axiom,
% 0.35/0.68      ! [Y2: num] :
% 0.35/0.68        ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) )
% 0.35/0.68        = ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % xor_nat_numerals(1)
% 0.35/0.68  thf(fact_9477_xor__nat__unfold,axiom,
% 0.35/0.68      ( bit_se6528837805403552850or_nat
% 0.35/0.68      = ( ^ [M6: nat,N2: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N2 @ ( if_nat @ ( N2 = zero_zero_nat ) @ M6 @ ( plus_plus_nat @ ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % xor_nat_unfold
% 0.35/0.68  thf(fact_9478_xor__nat__rec,axiom,
% 0.35/0.68      ( bit_se6528837805403552850or_nat
% 0.35/0.68      = ( ^ [M6: nat,N2: nat] :
% 0.35/0.68            ( plus_plus_nat
% 0.35/0.68            @ ( zero_n2687167440665602831ol_nat
% 0.35/0.68              @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 ) )
% 0.35/0.68               != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.35/0.68            @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % xor_nat_rec
% 0.35/0.68  thf(fact_9479_Suc__0__xor__eq,axiom,
% 0.35/0.68      ! [N: nat] :
% 0.35/0.68        ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.35/0.68        = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.68          @ ( zero_n2687167440665602831ol_nat
% 0.35/0.68            @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Suc_0_xor_eq
% 0.35/0.68  thf(fact_9480_push__bit__nonnegative__int__iff,axiom,
% 0.35/0.68      ! [N: nat,K: int] :
% 0.35/0.68        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se545348938243370406it_int @ N @ K ) )
% 0.35/0.68        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.35/0.68  
% 0.35/0.68  % push_bit_nonnegative_int_iff
% 0.35/0.68  thf(fact_9481_push__bit__negative__int__iff,axiom,
% 0.35/0.68      ! [N: nat,K: int] :
% 0.35/0.68        ( ( ord_less_int @ ( bit_se545348938243370406it_int @ N @ K ) @ zero_zero_int )
% 0.35/0.68        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.35/0.68  
% 0.35/0.68  % push_bit_negative_int_iff
% 0.35/0.68  thf(fact_9482_concat__bit__of__zero__1,axiom,
% 0.35/0.68      ! [N: nat,L2: int] :
% 0.35/0.68        ( ( bit_concat_bit @ N @ zero_zero_int @ L2 )
% 0.35/0.68        = ( bit_se545348938243370406it_int @ N @ L2 ) ) ).
% 0.35/0.68  
% 0.35/0.68  % concat_bit_of_zero_1
% 0.35/0.68  thf(fact_9483_xor__nonnegative__int__iff,axiom,
% 0.35/0.68      ! [K: int,L2: int] :
% 0.35/0.68        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ K @ L2 ) )
% 0.35/0.68        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.35/0.68          = ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % xor_nonnegative_int_iff
% 0.35/0.68  thf(fact_9484_xor__negative__int__iff,axiom,
% 0.35/0.68      ! [K: int,L2: int] :
% 0.35/0.68        ( ( ord_less_int @ ( bit_se6526347334894502574or_int @ K @ L2 ) @ zero_zero_int )
% 0.35/0.68        = ( ( ord_less_int @ K @ zero_zero_int )
% 0.35/0.68         != ( ord_less_int @ L2 @ zero_zero_int ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % xor_negative_int_iff
% 0.35/0.68  thf(fact_9485_push__bit__of__Suc__0,axiom,
% 0.35/0.68      ! [N: nat] :
% 0.35/0.68        ( ( bit_se547839408752420682it_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.35/0.68        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.35/0.68  
% 0.35/0.68  % push_bit_of_Suc_0
% 0.35/0.68  thf(fact_9486_bit__xor__int__iff,axiom,
% 0.35/0.68      ! [K: int,L2: int,N: nat] :
% 0.35/0.68        ( ( bit_se1146084159140164899it_int @ ( bit_se6526347334894502574or_int @ K @ L2 ) @ N )
% 0.35/0.68        = ( ( bit_se1146084159140164899it_int @ K @ N )
% 0.35/0.68         != ( bit_se1146084159140164899it_int @ L2 @ N ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % bit_xor_int_iff
% 0.35/0.68  thf(fact_9487_flip__bit__int__def,axiom,
% 0.35/0.68      ( bit_se2159334234014336723it_int
% 0.35/0.68      = ( ^ [N2: nat,K3: int] : ( bit_se6526347334894502574or_int @ K3 @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % flip_bit_int_def
% 0.35/0.68  thf(fact_9488_push__bit__nat__eq,axiom,
% 0.35/0.68      ! [N: nat,K: int] :
% 0.35/0.68        ( ( bit_se547839408752420682it_nat @ N @ ( nat2 @ K ) )
% 0.35/0.68        = ( nat2 @ ( bit_se545348938243370406it_int @ N @ K ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % push_bit_nat_eq
% 0.35/0.68  thf(fact_9489_XOR__lower,axiom,
% 0.35/0.68      ! [X: int,Y2: int] :
% 0.35/0.68        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.35/0.68       => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 0.35/0.68         => ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ X @ Y2 ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % XOR_lower
% 0.35/0.68  thf(fact_9490_set__bit__nat__def,axiom,
% 0.35/0.68      ( bit_se7882103937844011126it_nat
% 0.35/0.68      = ( ^ [M6: nat,N2: nat] : ( bit_se1412395901928357646or_nat @ N2 @ ( bit_se547839408752420682it_nat @ M6 @ one_one_nat ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % set_bit_nat_def
% 0.35/0.68  thf(fact_9491_flip__bit__nat__def,axiom,
% 0.35/0.68      ( bit_se2161824704523386999it_nat
% 0.35/0.68      = ( ^ [M6: nat,N2: nat] : ( bit_se6528837805403552850or_nat @ N2 @ ( bit_se547839408752420682it_nat @ M6 @ one_one_nat ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % flip_bit_nat_def
% 0.35/0.68  thf(fact_9492_bit__push__bit__iff__int,axiom,
% 0.35/0.68      ! [M: nat,K: int,N: nat] :
% 0.35/0.68        ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M @ K ) @ N )
% 0.35/0.68        = ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.68          & ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % bit_push_bit_iff_int
% 0.35/0.68  thf(fact_9493_xor__nat__def,axiom,
% 0.35/0.68      ( bit_se6528837805403552850or_nat
% 0.35/0.68      = ( ^ [M6: nat,N2: nat] : ( nat2 @ ( bit_se6526347334894502574or_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % xor_nat_def
% 0.35/0.68  thf(fact_9494_bit__push__bit__iff__nat,axiom,
% 0.35/0.68      ! [M: nat,Q2: nat,N: nat] :
% 0.35/0.68        ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M @ Q2 ) @ N )
% 0.35/0.68        = ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.68          & ( bit_se1148574629649215175it_nat @ Q2 @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % bit_push_bit_iff_nat
% 0.35/0.68  thf(fact_9495_concat__bit__eq,axiom,
% 0.35/0.68      ( bit_concat_bit
% 0.35/0.68      = ( ^ [N2: nat,K3: int,L: int] : ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N2 @ K3 ) @ ( bit_se545348938243370406it_int @ N2 @ L ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % concat_bit_eq
% 0.35/0.68  thf(fact_9496_concat__bit__def,axiom,
% 0.35/0.68      ( bit_concat_bit
% 0.35/0.68      = ( ^ [N2: nat,K3: int,L: int] : ( bit_se1409905431419307370or_int @ ( bit_se2923211474154528505it_int @ N2 @ K3 ) @ ( bit_se545348938243370406it_int @ N2 @ L ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % concat_bit_def
% 0.35/0.68  thf(fact_9497_set__bit__int__def,axiom,
% 0.35/0.68      ( bit_se7879613467334960850it_int
% 0.35/0.68      = ( ^ [N2: nat,K3: int] : ( bit_se1409905431419307370or_int @ K3 @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % set_bit_int_def
% 0.35/0.68  thf(fact_9498_push__bit__nat__def,axiom,
% 0.35/0.68      ( bit_se547839408752420682it_nat
% 0.35/0.68      = ( ^ [N2: nat,M6: nat] : ( times_times_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % push_bit_nat_def
% 0.35/0.68  thf(fact_9499_push__bit__int__def,axiom,
% 0.35/0.68      ( bit_se545348938243370406it_int
% 0.35/0.68      = ( ^ [N2: nat,K3: int] : ( times_times_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % push_bit_int_def
% 0.35/0.68  thf(fact_9500_push__bit__minus__one,axiom,
% 0.35/0.68      ! [N: nat] :
% 0.35/0.68        ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.68        = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % push_bit_minus_one
% 0.35/0.68  thf(fact_9501_XOR__upper,axiom,
% 0.35/0.68      ! [X: int,N: nat,Y2: int] :
% 0.35/0.68        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.35/0.68       => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.68         => ( ( ord_less_int @ Y2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.68           => ( ord_less_int @ ( bit_se6526347334894502574or_int @ X @ Y2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % XOR_upper
% 0.35/0.68  thf(fact_9502_xor__int__rec,axiom,
% 0.35/0.68      ( bit_se6526347334894502574or_int
% 0.35/0.68      = ( ^ [K3: int,L: int] :
% 0.35/0.68            ( plus_plus_int
% 0.35/0.68            @ ( zero_n2684676970156552555ol_int
% 0.35/0.68              @ ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) )
% 0.35/0.68               != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) )
% 0.35/0.68            @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % xor_int_rec
% 0.35/0.68  thf(fact_9503_xor__int__unfold,axiom,
% 0.35/0.68      ( bit_se6526347334894502574or_int
% 0.35/0.68      = ( ^ [K3: int,L: int] :
% 0.35/0.68            ( if_int
% 0.35/0.68            @ ( K3
% 0.35/0.68              = ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.68            @ ( bit_ri7919022796975470100ot_int @ L )
% 0.35/0.68            @ ( if_int
% 0.35/0.68              @ ( L
% 0.35/0.68                = ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.68              @ ( bit_ri7919022796975470100ot_int @ K3 )
% 0.35/0.68              @ ( if_int @ ( K3 = zero_zero_int ) @ L @ ( if_int @ ( L = zero_zero_int ) @ K3 @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % xor_int_unfold
% 0.35/0.68  thf(fact_9504_VEBT__internal_Oheight_Opelims,axiom,
% 0.35/0.68      ! [X: vEBT_VEBT,Y2: nat] :
% 0.35/0.68        ( ( ( vEBT_VEBT_height @ X )
% 0.35/0.68          = Y2 )
% 0.35/0.68       => ( ( accp_VEBT_VEBT @ vEBT_VEBT_height_rel @ X )
% 0.35/0.68         => ( ! [A4: $o,B3: $o] :
% 0.35/0.68                ( ( X
% 0.35/0.68                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.68               => ( ( Y2 = zero_zero_nat )
% 0.35/0.68                 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_height_rel @ ( vEBT_Leaf @ A4 @ B3 ) ) ) )
% 0.35/0.68           => ~ ! [Uu2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.68                  ( ( X
% 0.35/0.68                    = ( vEBT_Node @ Uu2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.35/0.68                 => ( ( Y2
% 0.35/0.68                      = ( plus_plus_nat @ one_one_nat @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary2 @ ( set_VEBT_VEBT2 @ TreeList2 ) ) ) ) ) )
% 0.35/0.68                   => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_height_rel @ ( vEBT_Node @ Uu2 @ Deg2 @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % VEBT_internal.height.pelims
% 0.35/0.68  thf(fact_9505_Cauchy__iff2,axiom,
% 0.35/0.68      ( topolo4055970368930404560y_real
% 0.35/0.68      = ( ^ [X4: nat > real] :
% 0.35/0.68          ! [J3: nat] :
% 0.35/0.68          ? [M8: nat] :
% 0.35/0.68          ! [M6: nat] :
% 0.35/0.68            ( ( ord_less_eq_nat @ M8 @ M6 )
% 0.35/0.68           => ! [N2: nat] :
% 0.35/0.68                ( ( ord_less_eq_nat @ M8 @ N2 )
% 0.35/0.68               => ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ ( X4 @ M6 ) @ ( X4 @ N2 ) ) ) @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ J3 ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Cauchy_iff2
% 0.35/0.68  thf(fact_9506_not__negative__int__iff,axiom,
% 0.35/0.68      ! [K: int] :
% 0.35/0.68        ( ( ord_less_int @ ( bit_ri7919022796975470100ot_int @ K ) @ zero_zero_int )
% 0.35/0.68        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.35/0.68  
% 0.35/0.68  % not_negative_int_iff
% 0.35/0.68  thf(fact_9507_not__nonnegative__int__iff,axiom,
% 0.35/0.68      ! [K: int] :
% 0.35/0.68        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 0.35/0.68        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.35/0.68  
% 0.35/0.68  % not_nonnegative_int_iff
% 0.35/0.68  thf(fact_9508_or__minus__minus__numerals,axiom,
% 0.35/0.68      ! [M: num,N: num] :
% 0.35/0.68        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.68        = ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % or_minus_minus_numerals
% 0.35/0.68  thf(fact_9509_and__minus__minus__numerals,axiom,
% 0.35/0.68      ! [M: num,N: num] :
% 0.35/0.68        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.68        = ( bit_ri7919022796975470100ot_int @ ( bit_se1409905431419307370or_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % and_minus_minus_numerals
% 0.35/0.68  thf(fact_9510_bit__not__int__iff,axiom,
% 0.35/0.68      ! [K: int,N: nat] :
% 0.35/0.68        ( ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ K ) @ N )
% 0.35/0.68        = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % bit_not_int_iff
% 0.35/0.68  thf(fact_9511_or__int__def,axiom,
% 0.35/0.68      ( bit_se1409905431419307370or_int
% 0.35/0.68      = ( ^ [K3: int,L: int] : ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K3 ) @ ( bit_ri7919022796975470100ot_int @ L ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % or_int_def
% 0.35/0.68  thf(fact_9512_not__int__def,axiom,
% 0.35/0.68      ( bit_ri7919022796975470100ot_int
% 0.35/0.68      = ( ^ [K3: int] : ( minus_minus_int @ ( uminus_uminus_int @ K3 ) @ one_one_int ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % not_int_def
% 0.35/0.68  thf(fact_9513_and__not__numerals_I1_J,axiom,
% 0.35/0.68      ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 0.35/0.68      = zero_zero_int ) ).
% 0.35/0.68  
% 0.35/0.68  % and_not_numerals(1)
% 0.35/0.68  thf(fact_9514_or__not__numerals_I1_J,axiom,
% 0.35/0.68      ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 0.35/0.68      = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 0.35/0.68  
% 0.35/0.68  % or_not_numerals(1)
% 0.35/0.68  thf(fact_9515_unset__bit__int__def,axiom,
% 0.35/0.68      ( bit_se4203085406695923979it_int
% 0.35/0.68      = ( ^ [N2: nat,K3: int] : ( bit_se725231765392027082nd_int @ K3 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % unset_bit_int_def
% 0.35/0.68  thf(fact_9516_xor__int__def,axiom,
% 0.35/0.68      ( bit_se6526347334894502574or_int
% 0.35/0.68      = ( ^ [K3: int,L: int] : ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ K3 @ ( bit_ri7919022796975470100ot_int @ L ) ) @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K3 ) @ L ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % xor_int_def
% 0.35/0.68  thf(fact_9517_not__int__div__2,axiom,
% 0.35/0.68      ! [K: int] :
% 0.35/0.68        ( ( divide_divide_int @ ( bit_ri7919022796975470100ot_int @ K ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.68        = ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % not_int_div_2
% 0.35/0.68  thf(fact_9518_even__not__iff__int,axiom,
% 0.35/0.68      ! [K: int] :
% 0.35/0.68        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ K ) )
% 0.35/0.68        = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % even_not_iff_int
% 0.35/0.68  thf(fact_9519_and__not__numerals_I4_J,axiom,
% 0.35/0.68      ! [M: num] :
% 0.35/0.68        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 0.35/0.68        = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % and_not_numerals(4)
% 0.35/0.68  thf(fact_9520_and__not__numerals_I2_J,axiom,
% 0.35/0.68      ! [N: num] :
% 0.35/0.68        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.35/0.68        = one_one_int ) ).
% 0.35/0.68  
% 0.35/0.68  % and_not_numerals(2)
% 0.35/0.68  thf(fact_9521_or__not__numerals_I4_J,axiom,
% 0.35/0.68      ! [M: num] :
% 0.35/0.68        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 0.35/0.68        = ( bit_ri7919022796975470100ot_int @ one_one_int ) ) ).
% 0.35/0.68  
% 0.35/0.68  % or_not_numerals(4)
% 0.35/0.68  thf(fact_9522_or__not__numerals_I2_J,axiom,
% 0.35/0.68      ! [N: num] :
% 0.35/0.68        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.35/0.68        = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % or_not_numerals(2)
% 0.35/0.68  thf(fact_9523_bit__minus__int__iff,axiom,
% 0.35/0.68      ! [K: int,N: nat] :
% 0.35/0.68        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ K ) @ N )
% 0.35/0.68        = ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ K @ one_one_int ) ) @ N ) ) ).
% 0.35/0.68  
% 0.35/0.68  % bit_minus_int_iff
% 0.35/0.68  thf(fact_9524_numeral__or__not__num__eq,axiom,
% 0.35/0.68      ! [M: num,N: num] :
% 0.35/0.68        ( ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N ) )
% 0.35/0.68        = ( uminus_uminus_int @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % numeral_or_not_num_eq
% 0.35/0.68  thf(fact_9525_int__numeral__not__or__num__neg,axiom,
% 0.35/0.68      ! [M: num,N: num] :
% 0.35/0.68        ( ( bit_se1409905431419307370or_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.35/0.68        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ N @ M ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % int_numeral_not_or_num_neg
% 0.35/0.68  thf(fact_9526_int__numeral__or__not__num__neg,axiom,
% 0.35/0.68      ! [M: num,N: num] :
% 0.35/0.68        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.68        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % int_numeral_or_not_num_neg
% 0.35/0.68  thf(fact_9527_and__not__numerals_I5_J,axiom,
% 0.35/0.68      ! [M: num,N: num] :
% 0.35/0.68        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.35/0.68        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % and_not_numerals(5)
% 0.35/0.68  thf(fact_9528_and__not__numerals_I7_J,axiom,
% 0.35/0.68      ! [M: num] :
% 0.35/0.68        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 0.35/0.68        = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % and_not_numerals(7)
% 0.35/0.68  thf(fact_9529_or__not__numerals_I3_J,axiom,
% 0.35/0.68      ! [N: num] :
% 0.35/0.68        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.35/0.68        = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % or_not_numerals(3)
% 0.35/0.68  thf(fact_9530_and__not__numerals_I3_J,axiom,
% 0.35/0.68      ! [N: num] :
% 0.35/0.68        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.35/0.68        = zero_zero_int ) ).
% 0.35/0.68  
% 0.35/0.68  % and_not_numerals(3)
% 0.35/0.68  thf(fact_9531_or__not__numerals_I7_J,axiom,
% 0.35/0.68      ! [M: num] :
% 0.35/0.68        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 0.35/0.68        = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 0.35/0.68  
% 0.35/0.68  % or_not_numerals(7)
% 0.35/0.68  thf(fact_9532_and__not__numerals_I9_J,axiom,
% 0.35/0.68      ! [M: num,N: num] :
% 0.35/0.68        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.35/0.68        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % and_not_numerals(9)
% 0.35/0.68  thf(fact_9533_and__not__numerals_I6_J,axiom,
% 0.35/0.68      ! [M: num,N: num] :
% 0.35/0.68        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.35/0.68        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % and_not_numerals(6)
% 0.35/0.68  thf(fact_9534_or__not__numerals_I6_J,axiom,
% 0.35/0.68      ! [M: num,N: num] :
% 0.35/0.68        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.35/0.68        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % or_not_numerals(6)
% 0.35/0.68  thf(fact_9535_or__not__numerals_I5_J,axiom,
% 0.35/0.68      ! [M: num,N: num] :
% 0.35/0.68        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.35/0.68        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % or_not_numerals(5)
% 0.35/0.68  thf(fact_9536_and__not__numerals_I8_J,axiom,
% 0.35/0.68      ! [M: num,N: num] :
% 0.35/0.68        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.35/0.68        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % and_not_numerals(8)
% 0.35/0.68  thf(fact_9537_or__not__numerals_I8_J,axiom,
% 0.35/0.68      ! [M: num,N: num] :
% 0.35/0.68        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.35/0.68        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % or_not_numerals(8)
% 0.35/0.68  thf(fact_9538_or__not__numerals_I9_J,axiom,
% 0.35/0.68      ! [M: num,N: num] :
% 0.35/0.68        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.35/0.68        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % or_not_numerals(9)
% 0.35/0.68  thf(fact_9539_not__int__rec,axiom,
% 0.35/0.68      ( bit_ri7919022796975470100ot_int
% 0.35/0.68      = ( ^ [K3: int] : ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % not_int_rec
% 0.35/0.68  thf(fact_9540_vebt__maxt_Opelims,axiom,
% 0.35/0.68      ! [X: vEBT_VEBT,Y2: option_nat] :
% 0.35/0.68        ( ( ( vEBT_vebt_maxt @ X )
% 0.35/0.68          = Y2 )
% 0.35/0.68       => ( ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ X )
% 0.35/0.68         => ( ! [A4: $o,B3: $o] :
% 0.35/0.68                ( ( X
% 0.35/0.68                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.68               => ( ( ( B3
% 0.35/0.68                     => ( Y2
% 0.35/0.68                        = ( some_nat @ one_one_nat ) ) )
% 0.35/0.68                    & ( ~ B3
% 0.35/0.68                     => ( ( A4
% 0.35/0.68                         => ( Y2
% 0.35/0.68                            = ( some_nat @ zero_zero_nat ) ) )
% 0.35/0.68                        & ( ~ A4
% 0.35/0.68                         => ( Y2 = none_nat ) ) ) ) )
% 0.35/0.68                 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Leaf @ A4 @ B3 ) ) ) )
% 0.35/0.68           => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.35/0.68                  ( ( X
% 0.35/0.68                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.35/0.68                 => ( ( Y2 = none_nat )
% 0.35/0.68                   => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 0.35/0.68             => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.35/0.68                    ( ( X
% 0.35/0.68                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 0.35/0.68                   => ( ( Y2
% 0.35/0.68                        = ( some_nat @ Ma2 ) )
% 0.35/0.68                     => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % vebt_maxt.pelims
% 0.35/0.68  thf(fact_9541_vebt__mint_Opelims,axiom,
% 0.35/0.68      ! [X: vEBT_VEBT,Y2: option_nat] :
% 0.35/0.68        ( ( ( vEBT_vebt_mint @ X )
% 0.35/0.68          = Y2 )
% 0.35/0.68       => ( ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ X )
% 0.35/0.68         => ( ! [A4: $o,B3: $o] :
% 0.35/0.68                ( ( X
% 0.35/0.68                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.68               => ( ( ( A4
% 0.35/0.68                     => ( Y2
% 0.35/0.68                        = ( some_nat @ zero_zero_nat ) ) )
% 0.35/0.68                    & ( ~ A4
% 0.35/0.68                     => ( ( B3
% 0.35/0.68                         => ( Y2
% 0.35/0.68                            = ( some_nat @ one_one_nat ) ) )
% 0.35/0.68                        & ( ~ B3
% 0.35/0.68                         => ( Y2 = none_nat ) ) ) ) )
% 0.35/0.68                 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Leaf @ A4 @ B3 ) ) ) )
% 0.35/0.68           => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.35/0.68                  ( ( X
% 0.35/0.68                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.35/0.68                 => ( ( Y2 = none_nat )
% 0.35/0.68                   => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 0.35/0.68             => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.35/0.68                    ( ( X
% 0.35/0.68                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 0.35/0.68                   => ( ( Y2
% 0.35/0.68                        = ( some_nat @ Mi2 ) )
% 0.35/0.68                     => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % vebt_mint.pelims
% 0.35/0.68  thf(fact_9542_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Opelims,axiom,
% 0.35/0.68      ! [X: vEBT_VEBT,Y2: nat] :
% 0.35/0.68        ( ( ( vEBT_T_m_i_n_t @ X )
% 0.35/0.68          = Y2 )
% 0.35/0.68       => ( ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ X )
% 0.35/0.68         => ( ! [A4: $o,B3: $o] :
% 0.35/0.68                ( ( X
% 0.35/0.68                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.68               => ( ( Y2
% 0.35/0.68                    = ( plus_plus_nat @ one_one_nat @ ( if_nat @ A4 @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 0.35/0.68                 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ ( vEBT_Leaf @ A4 @ B3 ) ) ) )
% 0.35/0.68           => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.35/0.68                  ( ( X
% 0.35/0.68                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.35/0.68                 => ( ( Y2 = one_one_nat )
% 0.35/0.68                   => ~ ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 0.35/0.68             => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.35/0.68                    ( ( X
% 0.35/0.68                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 0.35/0.68                   => ( ( Y2 = one_one_nat )
% 0.35/0.68                     => ~ ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.pelims
% 0.35/0.68  thf(fact_9543_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Opelims,axiom,
% 0.35/0.68      ! [X: vEBT_VEBT,Y2: nat] :
% 0.35/0.68        ( ( ( vEBT_T_m_a_x_t @ X )
% 0.35/0.68          = Y2 )
% 0.35/0.68       => ( ( accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ X )
% 0.35/0.68         => ( ! [A4: $o,B3: $o] :
% 0.35/0.68                ( ( X
% 0.35/0.68                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 0.35/0.68               => ( ( Y2
% 0.35/0.68                    = ( plus_plus_nat @ one_one_nat @ ( if_nat @ B3 @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 0.35/0.68                 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ ( vEBT_Leaf @ A4 @ B3 ) ) ) )
% 0.35/0.68           => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.35/0.68                  ( ( X
% 0.35/0.68                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.35/0.68                 => ( ( Y2 = one_one_nat )
% 0.35/0.68                   => ~ ( accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 0.35/0.68             => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.35/0.68                    ( ( X
% 0.35/0.68                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 0.35/0.68                   => ( ( Y2 = one_one_nat )
% 0.35/0.68                     => ~ ( accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % T\<^sub>m\<^sub>a\<^sub>x\<^sub>t.pelims
% 0.35/0.68  thf(fact_9544_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Opelims,axiom,
% 0.35/0.68      ! [X: vEBT_VEBT,Y2: nat] :
% 0.35/0.68        ( ( ( vEBT_T_m_i_n_N_u_l_l @ X )
% 0.35/0.68          = Y2 )
% 0.35/0.68       => ( ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ X )
% 0.35/0.68         => ( ( ( X
% 0.35/0.68                = ( vEBT_Leaf @ $false @ $false ) )
% 0.35/0.68             => ( ( Y2 = one_one_nat )
% 0.35/0.68               => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Leaf @ $false @ $false ) ) ) )
% 0.35/0.68           => ( ! [Uv2: $o] :
% 0.35/0.68                  ( ( X
% 0.35/0.68                    = ( vEBT_Leaf @ $true @ Uv2 ) )
% 0.35/0.68                 => ( ( Y2 = one_one_nat )
% 0.35/0.68                   => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) ) )
% 0.35/0.68             => ( ! [Uu2: $o] :
% 0.35/0.68                    ( ( X
% 0.35/0.68                      = ( vEBT_Leaf @ Uu2 @ $true ) )
% 0.35/0.68                   => ( ( Y2 = one_one_nat )
% 0.35/0.68                     => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) ) )
% 0.35/0.68               => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 0.35/0.68                      ( ( X
% 0.35/0.68                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 0.35/0.68                     => ( ( Y2 = one_one_nat )
% 0.35/0.68                       => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) )
% 0.35/0.68                 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.35/0.68                        ( ( X
% 0.35/0.68                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 0.35/0.68                       => ( ( Y2 = one_one_nat )
% 0.35/0.68                         => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.pelims
% 0.35/0.68  thf(fact_9545_VEBT__internal_OminNull_Opelims_I1_J,axiom,
% 0.35/0.68      ! [X: vEBT_VEBT,Y2: $o] :
% 0.35/0.68        ( ( ( vEBT_VEBT_minNull @ X )
% 0.35/0.68          = Y2 )
% 0.35/0.68       => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 0.35/0.68         => ( ( ( X
% 0.35/0.68                = ( vEBT_Leaf @ $false @ $false ) )
% 0.35/0.68             => ( Y2
% 0.35/0.68               => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) ) )
% 0.35/0.68           => ( ! [Uv2: $o] :
% 0.35/0.68                  ( ( X
% 0.35/0.68                    = ( vEBT_Leaf @ $true @ Uv2 ) )
% 0.35/0.68                 => ( ~ Y2
% 0.35/0.68                   => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) ) )
% 0.35/0.68             => ( ! [Uu2: $o] :
% 0.35/0.68                    ( ( X
% 0.35/0.68                      = ( vEBT_Leaf @ Uu2 @ $true ) )
% 0.35/0.68                   => ( ~ Y2
% 0.35/0.68                     => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) ) )
% 0.35/0.68               => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 0.35/0.68                      ( ( X
% 0.35/0.68                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 0.35/0.68                     => ( Y2
% 0.35/0.68                       => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) )
% 0.35/0.68                 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.35/0.68                        ( ( X
% 0.35/0.68                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 0.35/0.68                       => ( ~ Y2
% 0.35/0.68                         => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % VEBT_internal.minNull.pelims(1)
% 0.35/0.68  thf(fact_9546_VEBT__internal_OminNull_Opelims_I3_J,axiom,
% 0.35/0.68      ! [X: vEBT_VEBT] :
% 0.35/0.68        ( ~ ( vEBT_VEBT_minNull @ X )
% 0.35/0.68       => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 0.35/0.68         => ( ! [Uv2: $o] :
% 0.35/0.68                ( ( X
% 0.35/0.68                  = ( vEBT_Leaf @ $true @ Uv2 ) )
% 0.35/0.68               => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) )
% 0.35/0.68           => ( ! [Uu2: $o] :
% 0.35/0.68                  ( ( X
% 0.35/0.68                    = ( vEBT_Leaf @ Uu2 @ $true ) )
% 0.35/0.68                 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) )
% 0.35/0.68             => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.35/0.68                    ( ( X
% 0.35/0.68                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 0.35/0.68                   => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % VEBT_internal.minNull.pelims(3)
% 0.35/0.68  thf(fact_9547_VEBT__internal_OminNull_Opelims_I2_J,axiom,
% 0.35/0.68      ! [X: vEBT_VEBT] :
% 0.35/0.68        ( ( vEBT_VEBT_minNull @ X )
% 0.35/0.68       => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 0.35/0.68         => ( ( ( X
% 0.35/0.68                = ( vEBT_Leaf @ $false @ $false ) )
% 0.35/0.68             => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) )
% 0.35/0.68           => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 0.35/0.68                  ( ( X
% 0.35/0.68                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 0.35/0.68                 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % VEBT_internal.minNull.pelims(2)
% 0.35/0.68  thf(fact_9548_Sum__Ico__nat,axiom,
% 0.35/0.68      ! [M: nat,N: nat] :
% 0.35/0.68        ( ( groups3542108847815614940at_nat
% 0.35/0.68          @ ^ [X2: nat] : X2
% 0.35/0.68          @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 0.35/0.68        = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Sum_Ico_nat
% 0.35/0.68  thf(fact_9549_sum__power2,axiom,
% 0.35/0.68      ! [K: nat] :
% 0.35/0.68        ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 0.35/0.68        = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 0.35/0.68  
% 0.35/0.68  % sum_power2
% 0.35/0.68  thf(fact_9550_VEBT_Osize_I3_J,axiom,
% 0.35/0.68      ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 0.35/0.68        ( ( size_size_VEBT_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 0.35/0.68        = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ size_size_VEBT_VEBT @ X13 ) @ ( size_size_VEBT_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % VEBT.size(3)
% 0.35/0.68  thf(fact_9551_image__Suc__atLeastLessThan,axiom,
% 0.35/0.68      ! [I2: nat,J: nat] :
% 0.35/0.68        ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I2 @ J ) )
% 0.35/0.68        = ( set_or4665077453230672383an_nat @ ( suc @ I2 ) @ ( suc @ J ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % image_Suc_atLeastLessThan
% 0.35/0.68  thf(fact_9552_atLeastLessThan__singleton,axiom,
% 0.35/0.68      ! [M: nat] :
% 0.35/0.68        ( ( set_or4665077453230672383an_nat @ M @ ( suc @ M ) )
% 0.35/0.68        = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 0.35/0.68  
% 0.35/0.68  % atLeastLessThan_singleton
% 0.35/0.68  thf(fact_9553_all__nat__less__eq,axiom,
% 0.35/0.68      ! [N: nat,P: nat > $o] :
% 0.35/0.68        ( ( ! [M6: nat] :
% 0.35/0.68              ( ( ord_less_nat @ M6 @ N )
% 0.35/0.68             => ( P @ M6 ) ) )
% 0.35/0.68        = ( ! [X2: nat] :
% 0.35/0.68              ( ( member_nat @ X2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 0.35/0.68             => ( P @ X2 ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % all_nat_less_eq
% 0.35/0.68  thf(fact_9554_ex__nat__less__eq,axiom,
% 0.35/0.68      ! [N: nat,P: nat > $o] :
% 0.35/0.68        ( ( ? [M6: nat] :
% 0.35/0.68              ( ( ord_less_nat @ M6 @ N )
% 0.35/0.68              & ( P @ M6 ) ) )
% 0.35/0.68        = ( ? [X2: nat] :
% 0.35/0.68              ( ( member_nat @ X2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 0.35/0.68              & ( P @ X2 ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % ex_nat_less_eq
% 0.35/0.68  thf(fact_9555_atLeastLessThanSuc__atLeastAtMost,axiom,
% 0.35/0.68      ! [L2: nat,U: nat] :
% 0.35/0.68        ( ( set_or4665077453230672383an_nat @ L2 @ ( suc @ U ) )
% 0.35/0.68        = ( set_or1269000886237332187st_nat @ L2 @ U ) ) ).
% 0.35/0.68  
% 0.35/0.68  % atLeastLessThanSuc_atLeastAtMost
% 0.35/0.68  thf(fact_9556_atLeast0__lessThan__Suc,axiom,
% 0.35/0.68      ! [N: nat] :
% 0.35/0.68        ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 0.35/0.68        = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % atLeast0_lessThan_Suc
% 0.35/0.68  thf(fact_9557_atLeastLessThanSuc,axiom,
% 0.35/0.68      ! [M: nat,N: nat] :
% 0.35/0.68        ( ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.68         => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 0.35/0.68            = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) )
% 0.35/0.68        & ( ~ ( ord_less_eq_nat @ M @ N )
% 0.35/0.68         => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 0.35/0.68            = bot_bot_set_nat ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % atLeastLessThanSuc
% 0.35/0.68  thf(fact_9558_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 0.35/0.68      ! [N: nat] :
% 0.35/0.68        ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 0.35/0.68        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % atLeast0_lessThan_Suc_eq_insert_0
% 0.35/0.68  thf(fact_9559_prod__Suc__Suc__fact,axiom,
% 0.35/0.68      ! [N: nat] :
% 0.35/0.68        ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 0.35/0.68        = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 0.35/0.68  
% 0.35/0.68  % prod_Suc_Suc_fact
% 0.35/0.68  thf(fact_9560_prod__Suc__fact,axiom,
% 0.35/0.68      ! [N: nat] :
% 0.35/0.68        ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 0.35/0.68        = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 0.35/0.68  
% 0.35/0.68  % prod_Suc_fact
% 0.35/0.68  thf(fact_9561_atLeastLessThan__nat__numeral,axiom,
% 0.35/0.68      ! [M: nat,K: num] :
% 0.35/0.68        ( ( ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 0.35/0.68         => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 0.35/0.68            = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M @ ( pred_numeral @ K ) ) ) ) )
% 0.35/0.68        & ( ~ ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 0.35/0.68         => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 0.35/0.68            = bot_bot_set_nat ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % atLeastLessThan_nat_numeral
% 0.35/0.68  thf(fact_9562_atLeast1__lessThan__eq__remove0,axiom,
% 0.35/0.68      ! [N: nat] :
% 0.35/0.68        ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.35/0.68        = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % atLeast1_lessThan_eq_remove0
% 0.35/0.68  thf(fact_9563_image__minus__const__atLeastLessThan__nat,axiom,
% 0.35/0.68      ! [C: nat,Y2: nat,X: nat] :
% 0.35/0.68        ( ( ( ord_less_nat @ C @ Y2 )
% 0.35/0.68         => ( ( image_nat_nat
% 0.35/0.68              @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 0.35/0.68              @ ( set_or4665077453230672383an_nat @ X @ Y2 ) )
% 0.35/0.68            = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X @ C ) @ ( minus_minus_nat @ Y2 @ C ) ) ) )
% 0.35/0.68        & ( ~ ( ord_less_nat @ C @ Y2 )
% 0.35/0.68         => ( ( ( ord_less_nat @ X @ Y2 )
% 0.35/0.68             => ( ( image_nat_nat
% 0.35/0.68                  @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 0.35/0.68                  @ ( set_or4665077453230672383an_nat @ X @ Y2 ) )
% 0.35/0.68                = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 0.35/0.68            & ( ~ ( ord_less_nat @ X @ Y2 )
% 0.35/0.68             => ( ( image_nat_nat
% 0.35/0.68                  @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 0.35/0.68                  @ ( set_or4665077453230672383an_nat @ X @ Y2 ) )
% 0.35/0.68                = bot_bot_set_nat ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % image_minus_const_atLeastLessThan_nat
% 0.35/0.68  thf(fact_9564_Chebyshev__sum__upper__nat,axiom,
% 0.35/0.68      ! [N: nat,A: nat > nat,B: nat > nat] :
% 0.35/0.68        ( ! [I4: nat,J2: nat] :
% 0.35/0.68            ( ( ord_less_eq_nat @ I4 @ J2 )
% 0.35/0.68           => ( ( ord_less_nat @ J2 @ N )
% 0.35/0.68             => ( ord_less_eq_nat @ ( A @ I4 ) @ ( A @ J2 ) ) ) )
% 0.35/0.68       => ( ! [I4: nat,J2: nat] :
% 0.35/0.68              ( ( ord_less_eq_nat @ I4 @ J2 )
% 0.35/0.68             => ( ( ord_less_nat @ J2 @ N )
% 0.35/0.68               => ( ord_less_eq_nat @ ( B @ J2 ) @ ( B @ I4 ) ) ) )
% 0.35/0.68         => ( ord_less_eq_nat
% 0.35/0.68            @ ( times_times_nat @ N
% 0.35/0.68              @ ( groups3542108847815614940at_nat
% 0.35/0.68                @ ^ [I3: nat] : ( times_times_nat @ ( A @ I3 ) @ ( B @ I3 ) )
% 0.35/0.68                @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 0.35/0.68            @ ( times_times_nat @ ( groups3542108847815614940at_nat @ A @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( groups3542108847815614940at_nat @ B @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Chebyshev_sum_upper_nat
% 0.35/0.68  thf(fact_9565_image__add__int__atLeastLessThan,axiom,
% 0.35/0.68      ! [L2: int,U: int] :
% 0.35/0.68        ( ( image_int_int
% 0.35/0.68          @ ^ [X2: int] : ( plus_plus_int @ X2 @ L2 )
% 0.35/0.68          @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L2 ) ) )
% 0.35/0.68        = ( set_or4662586982721622107an_int @ L2 @ U ) ) ).
% 0.35/0.68  
% 0.35/0.68  % image_add_int_atLeastLessThan
% 0.35/0.68  thf(fact_9566_VEBT_Osize__gen_I1_J,axiom,
% 0.35/0.68      ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 0.35/0.68        ( ( vEBT_size_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 0.35/0.68        = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ vEBT_size_VEBT @ X13 ) @ ( vEBT_size_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % VEBT.size_gen(1)
% 0.35/0.68  thf(fact_9567_valid__eq,axiom,
% 0.35/0.68      vEBT_VEBT_valid = vEBT_invar_vebt ).
% 0.35/0.68  
% 0.35/0.68  % valid_eq
% 0.35/0.68  thf(fact_9568_valid__eq1,axiom,
% 0.35/0.68      ! [T: vEBT_VEBT,D2: nat] :
% 0.35/0.68        ( ( vEBT_invar_vebt @ T @ D2 )
% 0.35/0.68       => ( vEBT_VEBT_valid @ T @ D2 ) ) ).
% 0.35/0.68  
% 0.35/0.68  % valid_eq1
% 0.35/0.68  thf(fact_9569_valid__eq2,axiom,
% 0.35/0.68      ! [T: vEBT_VEBT,D2: nat] :
% 0.35/0.68        ( ( vEBT_VEBT_valid @ T @ D2 )
% 0.35/0.68       => ( vEBT_invar_vebt @ T @ D2 ) ) ).
% 0.35/0.68  
% 0.35/0.68  % valid_eq2
% 0.35/0.68  thf(fact_9570_VEBT__internal_Ovalid_H_Osimps_I1_J,axiom,
% 0.35/0.68      ! [Uu: $o,Uv: $o,D2: nat] :
% 0.35/0.68        ( ( vEBT_VEBT_valid @ ( vEBT_Leaf @ Uu @ Uv ) @ D2 )
% 0.35/0.68        = ( D2 = one_one_nat ) ) ).
% 0.35/0.68  
% 0.35/0.68  % VEBT_internal.valid'.simps(1)
% 0.35/0.68  thf(fact_9571_VEBT_Osize__gen_I2_J,axiom,
% 0.35/0.68      ! [X21: $o,X222: $o] :
% 0.35/0.68        ( ( vEBT_size_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 0.35/0.68        = zero_zero_nat ) ).
% 0.35/0.68  
% 0.35/0.68  % VEBT.size_gen(2)
% 0.35/0.68  thf(fact_9572_Code__Target__Int_Opositive__def,axiom,
% 0.35/0.68      code_Target_positive = numeral_numeral_int ).
% 0.35/0.68  
% 0.35/0.68  % Code_Target_Int.positive_def
% 0.35/0.68  thf(fact_9573_csqrt_Osimps_I1_J,axiom,
% 0.35/0.68      ! [Z: complex] :
% 0.35/0.68        ( ( re @ ( csqrt @ Z ) )
% 0.35/0.68        = ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % csqrt.simps(1)
% 0.35/0.68  thf(fact_9574_complex__Re__numeral,axiom,
% 0.35/0.68      ! [V: num] :
% 0.35/0.68        ( ( re @ ( numera6690914467698888265omplex @ V ) )
% 0.35/0.68        = ( numeral_numeral_real @ V ) ) ).
% 0.35/0.68  
% 0.35/0.68  % complex_Re_numeral
% 0.35/0.68  thf(fact_9575_Re__divide__of__nat,axiom,
% 0.35/0.68      ! [Z: complex,N: nat] :
% 0.35/0.68        ( ( re @ ( divide1717551699836669952omplex @ Z @ ( semiri8010041392384452111omplex @ N ) ) )
% 0.35/0.68        = ( divide_divide_real @ ( re @ Z ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Re_divide_of_nat
% 0.35/0.68  thf(fact_9576_Re__divide__of__real,axiom,
% 0.35/0.68      ! [Z: complex,R: real] :
% 0.35/0.68        ( ( re @ ( divide1717551699836669952omplex @ Z @ ( real_V4546457046886955230omplex @ R ) ) )
% 0.35/0.68        = ( divide_divide_real @ ( re @ Z ) @ R ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Re_divide_of_real
% 0.35/0.68  thf(fact_9577_Re__sgn,axiom,
% 0.35/0.68      ! [Z: complex] :
% 0.35/0.68        ( ( re @ ( sgn_sgn_complex @ Z ) )
% 0.35/0.68        = ( divide_divide_real @ ( re @ Z ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Re_sgn
% 0.35/0.68  thf(fact_9578_Re__divide__numeral,axiom,
% 0.35/0.68      ! [Z: complex,W: num] :
% 0.35/0.68        ( ( re @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 0.35/0.68        = ( divide_divide_real @ ( re @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Re_divide_numeral
% 0.35/0.68  thf(fact_9579_complex__Re__le__cmod,axiom,
% 0.35/0.68      ! [X: complex] : ( ord_less_eq_real @ ( re @ X ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 0.35/0.68  
% 0.35/0.68  % complex_Re_le_cmod
% 0.35/0.68  thf(fact_9580_one__complex_Osimps_I1_J,axiom,
% 0.35/0.68      ( ( re @ one_one_complex )
% 0.35/0.68      = one_one_real ) ).
% 0.35/0.68  
% 0.35/0.68  % one_complex.simps(1)
% 0.35/0.68  thf(fact_9581_plus__complex_Osimps_I1_J,axiom,
% 0.35/0.68      ! [X: complex,Y2: complex] :
% 0.35/0.68        ( ( re @ ( plus_plus_complex @ X @ Y2 ) )
% 0.35/0.68        = ( plus_plus_real @ ( re @ X ) @ ( re @ Y2 ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % plus_complex.simps(1)
% 0.35/0.68  thf(fact_9582_scaleR__complex_Osimps_I1_J,axiom,
% 0.35/0.68      ! [R: real,X: complex] :
% 0.35/0.68        ( ( re @ ( real_V2046097035970521341omplex @ R @ X ) )
% 0.35/0.68        = ( times_times_real @ R @ ( re @ X ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % scaleR_complex.simps(1)
% 0.35/0.68  thf(fact_9583_minus__complex_Osimps_I1_J,axiom,
% 0.35/0.68      ! [X: complex,Y2: complex] :
% 0.35/0.68        ( ( re @ ( minus_minus_complex @ X @ Y2 ) )
% 0.35/0.68        = ( minus_minus_real @ ( re @ X ) @ ( re @ Y2 ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % minus_complex.simps(1)
% 0.35/0.68  thf(fact_9584_abs__Re__le__cmod,axiom,
% 0.35/0.68      ! [X: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 0.35/0.68  
% 0.35/0.68  % abs_Re_le_cmod
% 0.35/0.68  thf(fact_9585_Re__csqrt,axiom,
% 0.35/0.68      ! [Z: complex] : ( ord_less_eq_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Re_csqrt
% 0.35/0.68  thf(fact_9586_cmod__plus__Re__le__0__iff,axiom,
% 0.35/0.68      ! [Z: complex] :
% 0.35/0.68        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ zero_zero_real )
% 0.35/0.68        = ( ( re @ Z )
% 0.35/0.68          = ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % cmod_plus_Re_le_0_iff
% 0.35/0.68  thf(fact_9587_cos__n__Re__cis__pow__n,axiom,
% 0.35/0.68      ! [N: nat,A: real] :
% 0.35/0.68        ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 0.35/0.68        = ( re @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % cos_n_Re_cis_pow_n
% 0.35/0.68  thf(fact_9588_csqrt_Ocode,axiom,
% 0.35/0.68      ( csqrt
% 0.35/0.68      = ( ^ [Z4: complex] :
% 0.35/0.68            ( complex2 @ ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z4 ) @ ( re @ Z4 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.68            @ ( times_times_real
% 0.35/0.68              @ ( if_real
% 0.35/0.68                @ ( ( im @ Z4 )
% 0.35/0.68                  = zero_zero_real )
% 0.35/0.68                @ one_one_real
% 0.35/0.68                @ ( sgn_sgn_real @ ( im @ Z4 ) ) )
% 0.35/0.68              @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z4 ) @ ( re @ Z4 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % csqrt.code
% 0.35/0.68  thf(fact_9589_csqrt_Osimps_I2_J,axiom,
% 0.35/0.68      ! [Z: complex] :
% 0.35/0.68        ( ( im @ ( csqrt @ Z ) )
% 0.35/0.68        = ( times_times_real
% 0.35/0.68          @ ( if_real
% 0.35/0.68            @ ( ( im @ Z )
% 0.35/0.68              = zero_zero_real )
% 0.35/0.68            @ one_one_real
% 0.35/0.68            @ ( sgn_sgn_real @ ( im @ Z ) ) )
% 0.35/0.68          @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % csqrt.simps(2)
% 0.35/0.68  thf(fact_9590_csqrt__of__real__nonpos,axiom,
% 0.35/0.68      ! [X: complex] :
% 0.35/0.68        ( ( ( im @ X )
% 0.35/0.68          = zero_zero_real )
% 0.35/0.68       => ( ( ord_less_eq_real @ ( re @ X ) @ zero_zero_real )
% 0.35/0.68         => ( ( csqrt @ X )
% 0.35/0.68            = ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sqrt @ ( abs_abs_real @ ( re @ X ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % csqrt_of_real_nonpos
% 0.35/0.68  thf(fact_9591_Im__divide__of__real,axiom,
% 0.35/0.68      ! [Z: complex,R: real] :
% 0.35/0.68        ( ( im @ ( divide1717551699836669952omplex @ Z @ ( real_V4546457046886955230omplex @ R ) ) )
% 0.35/0.68        = ( divide_divide_real @ ( im @ Z ) @ R ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Im_divide_of_real
% 0.35/0.68  thf(fact_9592_Im__sgn,axiom,
% 0.35/0.68      ! [Z: complex] :
% 0.35/0.68        ( ( im @ ( sgn_sgn_complex @ Z ) )
% 0.35/0.68        = ( divide_divide_real @ ( im @ Z ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Im_sgn
% 0.35/0.68  thf(fact_9593_Re__power__real,axiom,
% 0.35/0.68      ! [X: complex,N: nat] :
% 0.35/0.68        ( ( ( im @ X )
% 0.35/0.68          = zero_zero_real )
% 0.35/0.68       => ( ( re @ ( power_power_complex @ X @ N ) )
% 0.35/0.68          = ( power_power_real @ ( re @ X ) @ N ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Re_power_real
% 0.35/0.68  thf(fact_9594_Im__divide__numeral,axiom,
% 0.35/0.68      ! [Z: complex,W: num] :
% 0.35/0.68        ( ( im @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 0.35/0.68        = ( divide_divide_real @ ( im @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Im_divide_numeral
% 0.35/0.68  thf(fact_9595_Im__divide__of__nat,axiom,
% 0.35/0.68      ! [Z: complex,N: nat] :
% 0.35/0.68        ( ( im @ ( divide1717551699836669952omplex @ Z @ ( semiri8010041392384452111omplex @ N ) ) )
% 0.35/0.68        = ( divide_divide_real @ ( im @ Z ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Im_divide_of_nat
% 0.35/0.68  thf(fact_9596_csqrt__of__real__nonneg,axiom,
% 0.35/0.68      ! [X: complex] :
% 0.35/0.68        ( ( ( im @ X )
% 0.35/0.68          = zero_zero_real )
% 0.35/0.68       => ( ( ord_less_eq_real @ zero_zero_real @ ( re @ X ) )
% 0.35/0.68         => ( ( csqrt @ X )
% 0.35/0.68            = ( real_V4546457046886955230omplex @ ( sqrt @ ( re @ X ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % csqrt_of_real_nonneg
% 0.35/0.68  thf(fact_9597_csqrt__minus,axiom,
% 0.35/0.68      ! [X: complex] :
% 0.35/0.68        ( ( ( ord_less_real @ ( im @ X ) @ zero_zero_real )
% 0.35/0.68          | ( ( ( im @ X )
% 0.35/0.68              = zero_zero_real )
% 0.35/0.68            & ( ord_less_eq_real @ zero_zero_real @ ( re @ X ) ) ) )
% 0.35/0.68       => ( ( csqrt @ ( uminus1482373934393186551omplex @ X ) )
% 0.35/0.68          = ( times_times_complex @ imaginary_unit @ ( csqrt @ X ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % csqrt_minus
% 0.35/0.68  thf(fact_9598_imaginary__unit_Osimps_I2_J,axiom,
% 0.35/0.68      ( ( im @ imaginary_unit )
% 0.35/0.68      = one_one_real ) ).
% 0.35/0.68  
% 0.35/0.68  % imaginary_unit.simps(2)
% 0.35/0.68  thf(fact_9599_plus__complex_Osimps_I2_J,axiom,
% 0.35/0.68      ! [X: complex,Y2: complex] :
% 0.35/0.68        ( ( im @ ( plus_plus_complex @ X @ Y2 ) )
% 0.35/0.68        = ( plus_plus_real @ ( im @ X ) @ ( im @ Y2 ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % plus_complex.simps(2)
% 0.35/0.68  thf(fact_9600_scaleR__complex_Osimps_I2_J,axiom,
% 0.35/0.68      ! [R: real,X: complex] :
% 0.35/0.68        ( ( im @ ( real_V2046097035970521341omplex @ R @ X ) )
% 0.35/0.68        = ( times_times_real @ R @ ( im @ X ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % scaleR_complex.simps(2)
% 0.35/0.68  thf(fact_9601_minus__complex_Osimps_I2_J,axiom,
% 0.35/0.68      ! [X: complex,Y2: complex] :
% 0.35/0.68        ( ( im @ ( minus_minus_complex @ X @ Y2 ) )
% 0.35/0.68        = ( minus_minus_real @ ( im @ X ) @ ( im @ Y2 ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % minus_complex.simps(2)
% 0.35/0.68  thf(fact_9602_abs__Im__le__cmod,axiom,
% 0.35/0.68      ! [X: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 0.35/0.68  
% 0.35/0.68  % abs_Im_le_cmod
% 0.35/0.68  thf(fact_9603_times__complex_Osimps_I2_J,axiom,
% 0.35/0.68      ! [X: complex,Y2: complex] :
% 0.35/0.68        ( ( im @ ( times_times_complex @ X @ Y2 ) )
% 0.35/0.68        = ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( im @ Y2 ) ) @ ( times_times_real @ ( im @ X ) @ ( re @ Y2 ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % times_complex.simps(2)
% 0.35/0.68  thf(fact_9604_cmod__Re__le__iff,axiom,
% 0.35/0.68      ! [X: complex,Y2: complex] :
% 0.35/0.68        ( ( ( im @ X )
% 0.35/0.68          = ( im @ Y2 ) )
% 0.35/0.68       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y2 ) )
% 0.35/0.68          = ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X ) ) @ ( abs_abs_real @ ( re @ Y2 ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % cmod_Re_le_iff
% 0.35/0.68  thf(fact_9605_cmod__Im__le__iff,axiom,
% 0.35/0.68      ! [X: complex,Y2: complex] :
% 0.35/0.68        ( ( ( re @ X )
% 0.35/0.68          = ( re @ Y2 ) )
% 0.35/0.68       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y2 ) )
% 0.35/0.68          = ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X ) ) @ ( abs_abs_real @ ( im @ Y2 ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % cmod_Im_le_iff
% 0.35/0.68  thf(fact_9606_times__complex_Osimps_I1_J,axiom,
% 0.35/0.68      ! [X: complex,Y2: complex] :
% 0.35/0.68        ( ( re @ ( times_times_complex @ X @ Y2 ) )
% 0.35/0.68        = ( minus_minus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y2 ) ) @ ( times_times_real @ ( im @ X ) @ ( im @ Y2 ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % times_complex.simps(1)
% 0.35/0.68  thf(fact_9607_plus__complex_Ocode,axiom,
% 0.35/0.68      ( plus_plus_complex
% 0.35/0.68      = ( ^ [X2: complex,Y: complex] : ( complex2 @ ( plus_plus_real @ ( re @ X2 ) @ ( re @ Y ) ) @ ( plus_plus_real @ ( im @ X2 ) @ ( im @ Y ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % plus_complex.code
% 0.35/0.68  thf(fact_9608_scaleR__complex_Ocode,axiom,
% 0.35/0.68      ( real_V2046097035970521341omplex
% 0.35/0.68      = ( ^ [R5: real,X2: complex] : ( complex2 @ ( times_times_real @ R5 @ ( re @ X2 ) ) @ ( times_times_real @ R5 @ ( im @ X2 ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % scaleR_complex.code
% 0.35/0.68  thf(fact_9609_minus__complex_Ocode,axiom,
% 0.35/0.68      ( minus_minus_complex
% 0.35/0.68      = ( ^ [X2: complex,Y: complex] : ( complex2 @ ( minus_minus_real @ ( re @ X2 ) @ ( re @ Y ) ) @ ( minus_minus_real @ ( im @ X2 ) @ ( im @ Y ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % minus_complex.code
% 0.35/0.68  thf(fact_9610_csqrt__principal,axiom,
% 0.35/0.68      ! [Z: complex] :
% 0.35/0.68        ( ( ord_less_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) )
% 0.35/0.68        | ( ( ( re @ ( csqrt @ Z ) )
% 0.35/0.68            = zero_zero_real )
% 0.35/0.68          & ( ord_less_eq_real @ zero_zero_real @ ( im @ ( csqrt @ Z ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % csqrt_principal
% 0.35/0.68  thf(fact_9611_cmod__le,axiom,
% 0.35/0.68      ! [Z: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( plus_plus_real @ ( abs_abs_real @ ( re @ Z ) ) @ ( abs_abs_real @ ( im @ Z ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % cmod_le
% 0.35/0.68  thf(fact_9612_sin__n__Im__cis__pow__n,axiom,
% 0.35/0.68      ! [N: nat,A: real] :
% 0.35/0.68        ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 0.35/0.68        = ( im @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % sin_n_Im_cis_pow_n
% 0.35/0.68  thf(fact_9613_Re__exp,axiom,
% 0.35/0.68      ! [Z: complex] :
% 0.35/0.68        ( ( re @ ( exp_complex @ Z ) )
% 0.35/0.68        = ( times_times_real @ ( exp_real @ ( re @ Z ) ) @ ( cos_real @ ( im @ Z ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Re_exp
% 0.35/0.68  thf(fact_9614_Im__exp,axiom,
% 0.35/0.68      ! [Z: complex] :
% 0.35/0.68        ( ( im @ ( exp_complex @ Z ) )
% 0.35/0.68        = ( times_times_real @ ( exp_real @ ( re @ Z ) ) @ ( sin_real @ ( im @ Z ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Im_exp
% 0.35/0.68  thf(fact_9615_times__complex_Ocode,axiom,
% 0.35/0.68      ( times_times_complex
% 0.35/0.68      = ( ^ [X2: complex,Y: complex] : ( complex2 @ ( minus_minus_real @ ( times_times_real @ ( re @ X2 ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X2 ) @ ( im @ Y ) ) ) @ ( plus_plus_real @ ( times_times_real @ ( re @ X2 ) @ ( im @ Y ) ) @ ( times_times_real @ ( im @ X2 ) @ ( re @ Y ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % times_complex.code
% 0.35/0.68  thf(fact_9616_cmod__power2,axiom,
% 0.35/0.68      ! [Z: complex] :
% 0.35/0.68        ( ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.68        = ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % cmod_power2
% 0.35/0.68  thf(fact_9617_Im__power2,axiom,
% 0.35/0.68      ! [X: complex] :
% 0.35/0.68        ( ( im @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.68        = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ X ) ) @ ( im @ X ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Im_power2
% 0.35/0.68  thf(fact_9618_Re__power2,axiom,
% 0.35/0.68      ! [X: complex] :
% 0.35/0.68        ( ( re @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.68        = ( minus_minus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Re_power2
% 0.35/0.68  thf(fact_9619_complex__eq__0,axiom,
% 0.35/0.68      ! [Z: complex] :
% 0.35/0.68        ( ( Z = zero_zero_complex )
% 0.35/0.68        = ( ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.68          = zero_zero_real ) ) ).
% 0.35/0.68  
% 0.35/0.68  % complex_eq_0
% 0.35/0.68  thf(fact_9620_norm__complex__def,axiom,
% 0.35/0.68      ( real_V1022390504157884413omplex
% 0.35/0.68      = ( ^ [Z4: complex] : ( sqrt @ ( plus_plus_real @ ( power_power_real @ ( re @ Z4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % norm_complex_def
% 0.35/0.68  thf(fact_9621_inverse__complex_Osimps_I1_J,axiom,
% 0.35/0.68      ! [X: complex] :
% 0.35/0.68        ( ( re @ ( invers8013647133539491842omplex @ X ) )
% 0.35/0.68        = ( divide_divide_real @ ( re @ X ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % inverse_complex.simps(1)
% 0.35/0.68  thf(fact_9622_complex__neq__0,axiom,
% 0.35/0.68      ! [Z: complex] :
% 0.35/0.68        ( ( Z != zero_zero_complex )
% 0.35/0.68        = ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % complex_neq_0
% 0.35/0.68  thf(fact_9623_Re__divide,axiom,
% 0.35/0.68      ! [X: complex,Y2: complex] :
% 0.35/0.68        ( ( re @ ( divide1717551699836669952omplex @ X @ Y2 ) )
% 0.35/0.68        = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y2 ) ) @ ( times_times_real @ ( im @ X ) @ ( im @ Y2 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Re_divide
% 0.35/0.68  thf(fact_9624_csqrt__square,axiom,
% 0.35/0.68      ! [B: complex] :
% 0.35/0.68        ( ( ( ord_less_real @ zero_zero_real @ ( re @ B ) )
% 0.35/0.68          | ( ( ( re @ B )
% 0.35/0.68              = zero_zero_real )
% 0.35/0.68            & ( ord_less_eq_real @ zero_zero_real @ ( im @ B ) ) ) )
% 0.35/0.68       => ( ( csqrt @ ( power_power_complex @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.68          = B ) ) ).
% 0.35/0.68  
% 0.35/0.68  % csqrt_square
% 0.35/0.68  thf(fact_9625_csqrt__unique,axiom,
% 0.35/0.68      ! [W: complex,Z: complex] :
% 0.35/0.68        ( ( ( power_power_complex @ W @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.68          = Z )
% 0.35/0.68       => ( ( ( ord_less_real @ zero_zero_real @ ( re @ W ) )
% 0.35/0.68            | ( ( ( re @ W )
% 0.35/0.68                = zero_zero_real )
% 0.35/0.68              & ( ord_less_eq_real @ zero_zero_real @ ( im @ W ) ) ) )
% 0.35/0.68         => ( ( csqrt @ Z )
% 0.35/0.68            = W ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % csqrt_unique
% 0.35/0.68  thf(fact_9626_inverse__complex_Osimps_I2_J,axiom,
% 0.35/0.68      ! [X: complex] :
% 0.35/0.68        ( ( im @ ( invers8013647133539491842omplex @ X ) )
% 0.35/0.68        = ( divide_divide_real @ ( uminus_uminus_real @ ( im @ X ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % inverse_complex.simps(2)
% 0.35/0.68  thf(fact_9627_Im__divide,axiom,
% 0.35/0.68      ! [X: complex,Y2: complex] :
% 0.35/0.68        ( ( im @ ( divide1717551699836669952omplex @ X @ Y2 ) )
% 0.35/0.68        = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X ) @ ( re @ Y2 ) ) @ ( times_times_real @ ( re @ X ) @ ( im @ Y2 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Im_divide
% 0.35/0.68  thf(fact_9628_complex__abs__le__norm,axiom,
% 0.35/0.68      ! [Z: complex] : ( ord_less_eq_real @ ( plus_plus_real @ ( abs_abs_real @ ( re @ Z ) ) @ ( abs_abs_real @ ( im @ Z ) ) ) @ ( times_times_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % complex_abs_le_norm
% 0.35/0.68  thf(fact_9629_complex__unit__circle,axiom,
% 0.35/0.68      ! [Z: complex] :
% 0.35/0.68        ( ( Z != zero_zero_complex )
% 0.35/0.68       => ( ( plus_plus_real @ ( power_power_real @ ( divide_divide_real @ ( re @ Z ) @ ( real_V1022390504157884413omplex @ Z ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( divide_divide_real @ ( im @ Z ) @ ( real_V1022390504157884413omplex @ Z ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.68          = one_one_real ) ) ).
% 0.35/0.68  
% 0.35/0.68  % complex_unit_circle
% 0.35/0.68  thf(fact_9630_inverse__complex_Ocode,axiom,
% 0.35/0.68      ( invers8013647133539491842omplex
% 0.35/0.68      = ( ^ [X2: complex] : ( complex2 @ ( divide_divide_real @ ( re @ X2 ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( uminus_uminus_real @ ( im @ X2 ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % inverse_complex.code
% 0.35/0.68  thf(fact_9631_Complex__divide,axiom,
% 0.35/0.68      ( divide1717551699836669952omplex
% 0.35/0.68      = ( ^ [X2: complex,Y: complex] : ( complex2 @ ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X2 ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X2 ) @ ( im @ Y ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X2 ) @ ( re @ Y ) ) @ ( times_times_real @ ( re @ X2 ) @ ( im @ Y ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Complex_divide
% 0.35/0.68  thf(fact_9632_Im__Reals__divide,axiom,
% 0.35/0.68      ! [R: complex,Z: complex] :
% 0.35/0.68        ( ( member_complex @ R @ real_V2521375963428798218omplex )
% 0.35/0.68       => ( ( im @ ( divide1717551699836669952omplex @ R @ Z ) )
% 0.35/0.68          = ( divide_divide_real @ ( times_times_real @ ( uminus_uminus_real @ ( re @ R ) ) @ ( im @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Im_Reals_divide
% 0.35/0.68  thf(fact_9633_Re__Reals__divide,axiom,
% 0.35/0.68      ! [R: complex,Z: complex] :
% 0.35/0.68        ( ( member_complex @ R @ real_V2521375963428798218omplex )
% 0.35/0.68       => ( ( re @ ( divide1717551699836669952omplex @ R @ Z ) )
% 0.35/0.68          = ( divide_divide_real @ ( times_times_real @ ( re @ R ) @ ( re @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Re_Reals_divide
% 0.35/0.68  thf(fact_9634_Re__divide__Reals,axiom,
% 0.35/0.68      ! [R: complex,Z: complex] :
% 0.35/0.68        ( ( member_complex @ R @ real_V2521375963428798218omplex )
% 0.35/0.68       => ( ( re @ ( divide1717551699836669952omplex @ Z @ R ) )
% 0.35/0.68          = ( divide_divide_real @ ( re @ Z ) @ ( re @ R ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Re_divide_Reals
% 0.35/0.68  thf(fact_9635_Im__divide__Reals,axiom,
% 0.35/0.68      ! [R: complex,Z: complex] :
% 0.35/0.68        ( ( member_complex @ R @ real_V2521375963428798218omplex )
% 0.35/0.68       => ( ( im @ ( divide1717551699836669952omplex @ Z @ R ) )
% 0.35/0.68          = ( divide_divide_real @ ( im @ Z ) @ ( re @ R ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Im_divide_Reals
% 0.35/0.68  thf(fact_9636_complex__diff__cnj,axiom,
% 0.35/0.68      ! [Z: complex] :
% 0.35/0.68        ( ( minus_minus_complex @ Z @ ( cnj @ Z ) )
% 0.35/0.68        = ( times_times_complex @ ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( im @ Z ) ) ) @ imaginary_unit ) ) ).
% 0.35/0.68  
% 0.35/0.68  % complex_diff_cnj
% 0.35/0.68  thf(fact_9637_complex__mult__cnj,axiom,
% 0.35/0.68      ! [Z: complex] :
% 0.35/0.68        ( ( times_times_complex @ Z @ ( cnj @ Z ) )
% 0.35/0.68        = ( real_V4546457046886955230omplex @ ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % complex_mult_cnj
% 0.35/0.68  thf(fact_9638_complex__cnj__diff,axiom,
% 0.35/0.68      ! [X: complex,Y2: complex] :
% 0.35/0.68        ( ( cnj @ ( minus_minus_complex @ X @ Y2 ) )
% 0.35/0.68        = ( minus_minus_complex @ ( cnj @ X ) @ ( cnj @ Y2 ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % complex_cnj_diff
% 0.35/0.68  thf(fact_9639_Re__complex__div__gt__0,axiom,
% 0.35/0.68      ! [A: complex,B: complex] :
% 0.35/0.68        ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 0.35/0.68        = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Re_complex_div_gt_0
% 0.35/0.68  thf(fact_9640_Re__complex__div__lt__0,axiom,
% 0.35/0.68      ! [A: complex,B: complex] :
% 0.35/0.68        ( ( ord_less_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 0.35/0.68        = ( ord_less_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Re_complex_div_lt_0
% 0.35/0.68  thf(fact_9641_Re__complex__div__ge__0,axiom,
% 0.35/0.68      ! [A: complex,B: complex] :
% 0.35/0.68        ( ( ord_less_eq_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 0.35/0.68        = ( ord_less_eq_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Re_complex_div_ge_0
% 0.35/0.68  thf(fact_9642_Re__complex__div__le__0,axiom,
% 0.35/0.68      ! [A: complex,B: complex] :
% 0.35/0.68        ( ( ord_less_eq_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 0.35/0.68        = ( ord_less_eq_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Re_complex_div_le_0
% 0.35/0.68  thf(fact_9643_Im__complex__div__gt__0,axiom,
% 0.35/0.68      ! [A: complex,B: complex] :
% 0.35/0.68        ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 0.35/0.68        = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Im_complex_div_gt_0
% 0.35/0.68  thf(fact_9644_Im__complex__div__lt__0,axiom,
% 0.35/0.68      ! [A: complex,B: complex] :
% 0.35/0.68        ( ( ord_less_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 0.35/0.68        = ( ord_less_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Im_complex_div_lt_0
% 0.35/0.68  thf(fact_9645_Im__complex__div__ge__0,axiom,
% 0.35/0.68      ! [A: complex,B: complex] :
% 0.35/0.68        ( ( ord_less_eq_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 0.35/0.68        = ( ord_less_eq_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Im_complex_div_ge_0
% 0.35/0.68  thf(fact_9646_Im__complex__div__le__0,axiom,
% 0.35/0.68      ! [A: complex,B: complex] :
% 0.35/0.68        ( ( ord_less_eq_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 0.35/0.68        = ( ord_less_eq_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Im_complex_div_le_0
% 0.35/0.68  thf(fact_9647_complex__mod__mult__cnj,axiom,
% 0.35/0.68      ! [Z: complex] :
% 0.35/0.68        ( ( real_V1022390504157884413omplex @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 0.35/0.68        = ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % complex_mod_mult_cnj
% 0.35/0.68  thf(fact_9648_complex__div__gt__0,axiom,
% 0.35/0.68      ! [A: complex,B: complex] :
% 0.35/0.68        ( ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 0.35/0.68          = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) )
% 0.35/0.68        & ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 0.35/0.68          = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % complex_div_gt_0
% 0.35/0.68  thf(fact_9649_complex__norm__square,axiom,
% 0.35/0.68      ! [Z: complex] :
% 0.35/0.68        ( ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.68        = ( times_times_complex @ Z @ ( cnj @ Z ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % complex_norm_square
% 0.35/0.68  thf(fact_9650_complex__add__cnj,axiom,
% 0.35/0.68      ! [Z: complex] :
% 0.35/0.68        ( ( plus_plus_complex @ Z @ ( cnj @ Z ) )
% 0.35/0.68        = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ Z ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % complex_add_cnj
% 0.35/0.68  thf(fact_9651_complex__div__cnj,axiom,
% 0.35/0.68      ( divide1717551699836669952omplex
% 0.35/0.68      = ( ^ [A3: complex,B4: complex] : ( divide1717551699836669952omplex @ ( times_times_complex @ A3 @ ( cnj @ B4 ) ) @ ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ B4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % complex_div_cnj
% 0.35/0.68  thf(fact_9652_cnj__add__mult__eq__Re,axiom,
% 0.35/0.68      ! [Z: complex,W: complex] :
% 0.35/0.68        ( ( plus_plus_complex @ ( times_times_complex @ Z @ ( cnj @ W ) ) @ ( times_times_complex @ ( cnj @ Z ) @ W ) )
% 0.35/0.68        = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ ( times_times_complex @ Z @ ( cnj @ W ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % cnj_add_mult_eq_Re
% 0.35/0.68  thf(fact_9653_divmod__step__integer__def,axiom,
% 0.35/0.68      ( unique4921790084139445826nteger
% 0.35/0.68      = ( ^ [L: num] :
% 0.35/0.68            ( produc6916734918728496179nteger
% 0.35/0.68            @ ^ [Q4: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % divmod_step_integer_def
% 0.35/0.68  thf(fact_9654_card__Collect__less__nat,axiom,
% 0.35/0.68      ! [N: nat] :
% 0.35/0.68        ( ( finite_card_nat
% 0.35/0.68          @ ( collect_nat
% 0.35/0.68            @ ^ [I3: nat] : ( ord_less_nat @ I3 @ N ) ) )
% 0.35/0.68        = N ) ).
% 0.35/0.68  
% 0.35/0.68  % card_Collect_less_nat
% 0.35/0.68  thf(fact_9655_card__atMost,axiom,
% 0.35/0.68      ! [U: nat] :
% 0.35/0.68        ( ( finite_card_nat @ ( set_ord_atMost_nat @ U ) )
% 0.35/0.68        = ( suc @ U ) ) ).
% 0.35/0.68  
% 0.35/0.68  % card_atMost
% 0.35/0.68  thf(fact_9656_card__atLeastLessThan,axiom,
% 0.35/0.68      ! [L2: nat,U: nat] :
% 0.35/0.68        ( ( finite_card_nat @ ( set_or4665077453230672383an_nat @ L2 @ U ) )
% 0.35/0.68        = ( minus_minus_nat @ U @ L2 ) ) ).
% 0.35/0.68  
% 0.35/0.68  % card_atLeastLessThan
% 0.35/0.68  thf(fact_9657_card__Collect__le__nat,axiom,
% 0.35/0.68      ! [N: nat] :
% 0.35/0.68        ( ( finite_card_nat
% 0.35/0.68          @ ( collect_nat
% 0.35/0.68            @ ^ [I3: nat] : ( ord_less_eq_nat @ I3 @ N ) ) )
% 0.35/0.68        = ( suc @ N ) ) ).
% 0.35/0.68  
% 0.35/0.68  % card_Collect_le_nat
% 0.35/0.68  thf(fact_9658_card__atLeastAtMost,axiom,
% 0.35/0.68      ! [L2: nat,U: nat] :
% 0.35/0.68        ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L2 @ U ) )
% 0.35/0.68        = ( minus_minus_nat @ ( suc @ U ) @ L2 ) ) ).
% 0.35/0.68  
% 0.35/0.68  % card_atLeastAtMost
% 0.35/0.68  thf(fact_9659_card__atLeastLessThan__int,axiom,
% 0.35/0.68      ! [L2: int,U: int] :
% 0.35/0.68        ( ( finite_card_int @ ( set_or4662586982721622107an_int @ L2 @ U ) )
% 0.35/0.68        = ( nat2 @ ( minus_minus_int @ U @ L2 ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % card_atLeastLessThan_int
% 0.35/0.68  thf(fact_9660_card__atLeastAtMost__int,axiom,
% 0.35/0.68      ! [L2: int,U: int] :
% 0.35/0.68        ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L2 @ U ) )
% 0.35/0.68        = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L2 ) @ one_one_int ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % card_atLeastAtMost_int
% 0.35/0.68  thf(fact_9661_minus__integer__code_I2_J,axiom,
% 0.35/0.68      ! [L2: code_integer] :
% 0.35/0.68        ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ L2 )
% 0.35/0.68        = ( uminus1351360451143612070nteger @ L2 ) ) ).
% 0.35/0.68  
% 0.35/0.68  % minus_integer_code(2)
% 0.35/0.68  thf(fact_9662_minus__integer__code_I1_J,axiom,
% 0.35/0.68      ! [K: code_integer] :
% 0.35/0.68        ( ( minus_8373710615458151222nteger @ K @ zero_z3403309356797280102nteger )
% 0.35/0.68        = K ) ).
% 0.35/0.68  
% 0.35/0.68  % minus_integer_code(1)
% 0.35/0.68  thf(fact_9663_card__less,axiom,
% 0.35/0.68      ! [M7: set_nat,I2: nat] :
% 0.35/0.68        ( ( member_nat @ zero_zero_nat @ M7 )
% 0.35/0.68       => ( ( finite_card_nat
% 0.35/0.68            @ ( collect_nat
% 0.35/0.68              @ ^ [K3: nat] :
% 0.35/0.68                  ( ( member_nat @ K3 @ M7 )
% 0.35/0.68                  & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) )
% 0.35/0.68         != zero_zero_nat ) ) ).
% 0.35/0.68  
% 0.35/0.68  % card_less
% 0.35/0.68  thf(fact_9664_card__less__Suc,axiom,
% 0.35/0.68      ! [M7: set_nat,I2: nat] :
% 0.35/0.68        ( ( member_nat @ zero_zero_nat @ M7 )
% 0.35/0.68       => ( ( suc
% 0.35/0.68            @ ( finite_card_nat
% 0.35/0.68              @ ( collect_nat
% 0.35/0.68                @ ^ [K3: nat] :
% 0.35/0.68                    ( ( member_nat @ ( suc @ K3 ) @ M7 )
% 0.35/0.68                    & ( ord_less_nat @ K3 @ I2 ) ) ) ) )
% 0.35/0.68          = ( finite_card_nat
% 0.35/0.68            @ ( collect_nat
% 0.35/0.68              @ ^ [K3: nat] :
% 0.35/0.68                  ( ( member_nat @ K3 @ M7 )
% 0.35/0.68                  & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % card_less_Suc
% 0.35/0.68  thf(fact_9665_card__less__Suc2,axiom,
% 0.35/0.68      ! [M7: set_nat,I2: nat] :
% 0.35/0.68        ( ~ ( member_nat @ zero_zero_nat @ M7 )
% 0.35/0.68       => ( ( finite_card_nat
% 0.35/0.68            @ ( collect_nat
% 0.35/0.68              @ ^ [K3: nat] :
% 0.35/0.68                  ( ( member_nat @ ( suc @ K3 ) @ M7 )
% 0.35/0.68                  & ( ord_less_nat @ K3 @ I2 ) ) ) )
% 0.35/0.68          = ( finite_card_nat
% 0.35/0.68            @ ( collect_nat
% 0.35/0.68              @ ^ [K3: nat] :
% 0.35/0.68                  ( ( member_nat @ K3 @ M7 )
% 0.35/0.68                  & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % card_less_Suc2
% 0.35/0.68  thf(fact_9666_one__natural_Orsp,axiom,
% 0.35/0.68      one_one_nat = one_one_nat ).
% 0.35/0.68  
% 0.35/0.68  % one_natural.rsp
% 0.35/0.68  thf(fact_9667_subset__card__intvl__is__intvl,axiom,
% 0.35/0.68      ! [A2: set_nat,K: nat] :
% 0.35/0.68        ( ( ord_less_eq_set_nat @ A2 @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) )
% 0.35/0.68       => ( A2
% 0.35/0.68          = ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % subset_card_intvl_is_intvl
% 0.35/0.68  thf(fact_9668_card__le__Suc__Max,axiom,
% 0.35/0.68      ! [S2: set_nat] :
% 0.35/0.68        ( ( finite_finite_nat @ S2 )
% 0.35/0.68       => ( ord_less_eq_nat @ ( finite_card_nat @ S2 ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S2 ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % card_le_Suc_Max
% 0.35/0.68  thf(fact_9669_subset__eq__atLeast0__lessThan__card,axiom,
% 0.35/0.68      ! [N4: set_nat,N: nat] :
% 0.35/0.68        ( ( ord_less_eq_set_nat @ N4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 0.35/0.68       => ( ord_less_eq_nat @ ( finite_card_nat @ N4 ) @ N ) ) ).
% 0.35/0.68  
% 0.35/0.68  % subset_eq_atLeast0_lessThan_card
% 0.35/0.68  thf(fact_9670_card__sum__le__nat__sum,axiom,
% 0.35/0.68      ! [S2: set_nat] :
% 0.35/0.68        ( ord_less_eq_nat
% 0.35/0.68        @ ( groups3542108847815614940at_nat
% 0.35/0.68          @ ^ [X2: nat] : X2
% 0.35/0.68          @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S2 ) ) )
% 0.35/0.68        @ ( groups3542108847815614940at_nat
% 0.35/0.68          @ ^ [X2: nat] : X2
% 0.35/0.68          @ S2 ) ) ).
% 0.35/0.68  
% 0.35/0.68  % card_sum_le_nat_sum
% 0.35/0.68  thf(fact_9671_card__nth__roots,axiom,
% 0.35/0.68      ! [C: complex,N: nat] :
% 0.35/0.68        ( ( C != zero_zero_complex )
% 0.35/0.68       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68         => ( ( finite_card_complex
% 0.35/0.68              @ ( collect_complex
% 0.35/0.68                @ ^ [Z4: complex] :
% 0.35/0.68                    ( ( power_power_complex @ Z4 @ N )
% 0.35/0.68                    = C ) ) )
% 0.35/0.68            = N ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % card_nth_roots
% 0.35/0.68  thf(fact_9672_card__roots__unity__eq,axiom,
% 0.35/0.68      ! [N: nat] :
% 0.35/0.68        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68       => ( ( finite_card_complex
% 0.35/0.68            @ ( collect_complex
% 0.35/0.68              @ ^ [Z4: complex] :
% 0.35/0.68                  ( ( power_power_complex @ Z4 @ N )
% 0.35/0.68                  = one_one_complex ) ) )
% 0.35/0.68          = N ) ) ).
% 0.35/0.68  
% 0.35/0.68  % card_roots_unity_eq
% 0.35/0.68  thf(fact_9673_integer__of__int__code,axiom,
% 0.35/0.68      ( code_integer_of_int
% 0.35/0.68      = ( ^ [K3: int] :
% 0.35/0.68            ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K3 ) ) )
% 0.35/0.68            @ ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 0.35/0.68              @ ( if_Code_integer
% 0.35/0.68                @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.68                  = zero_zero_int )
% 0.35/0.68                @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.35/0.68                @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % integer_of_int_code
% 0.35/0.68  thf(fact_9674_divide__integer_Oabs__eq,axiom,
% 0.35/0.68      ! [Xa2: int,X: int] :
% 0.35/0.68        ( ( divide6298287555418463151nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 0.35/0.68        = ( code_integer_of_int @ ( divide_divide_int @ Xa2 @ X ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % divide_integer.abs_eq
% 0.35/0.68  thf(fact_9675_minus__integer_Oabs__eq,axiom,
% 0.35/0.68      ! [Xa2: int,X: int] :
% 0.35/0.68        ( ( minus_8373710615458151222nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 0.35/0.68        = ( code_integer_of_int @ ( minus_minus_int @ Xa2 @ X ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % minus_integer.abs_eq
% 0.35/0.68  thf(fact_9676_integer__of__num_I3_J,axiom,
% 0.35/0.68      ! [N: num] :
% 0.35/0.68        ( ( code_integer_of_num @ ( bit1 @ N ) )
% 0.35/0.68        = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) @ one_one_Code_integer ) ) ).
% 0.35/0.68  
% 0.35/0.68  % integer_of_num(3)
% 0.35/0.68  thf(fact_9677_num__of__integer__code,axiom,
% 0.35/0.68      ( code_num_of_integer
% 0.35/0.68      = ( ^ [K3: code_integer] :
% 0.35/0.68            ( if_num @ ( ord_le3102999989581377725nteger @ K3 @ one_one_Code_integer ) @ one
% 0.35/0.68            @ ( produc7336495610019696514er_num
% 0.35/0.68              @ ^ [L: code_integer,J3: code_integer] : ( if_num @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_num @ ( code_num_of_integer @ L ) @ ( code_num_of_integer @ L ) ) @ ( plus_plus_num @ ( plus_plus_num @ ( code_num_of_integer @ L ) @ ( code_num_of_integer @ L ) ) @ one ) )
% 0.35/0.68              @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % num_of_integer_code
% 0.35/0.68  thf(fact_9678_integer__of__num__triv_I1_J,axiom,
% 0.35/0.68      ( ( code_integer_of_num @ one )
% 0.35/0.68      = one_one_Code_integer ) ).
% 0.35/0.68  
% 0.35/0.68  % integer_of_num_triv(1)
% 0.35/0.68  thf(fact_9679_integer__of__num_I2_J,axiom,
% 0.35/0.68      ! [N: num] :
% 0.35/0.68        ( ( code_integer_of_num @ ( bit0 @ N ) )
% 0.35/0.68        = ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % integer_of_num(2)
% 0.35/0.68  thf(fact_9680_integer__of__num__triv_I2_J,axiom,
% 0.35/0.68      ( ( code_integer_of_num @ ( bit0 @ one ) )
% 0.35/0.68      = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % integer_of_num_triv(2)
% 0.35/0.68  thf(fact_9681_nat__of__integer__code,axiom,
% 0.35/0.68      ( code_nat_of_integer
% 0.35/0.68      = ( ^ [K3: code_integer] :
% 0.35/0.68            ( if_nat @ ( ord_le3102999989581377725nteger @ K3 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 0.35/0.68            @ ( produc1555791787009142072er_nat
% 0.35/0.68              @ ^ [L: code_integer,J3: code_integer] : ( if_nat @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_nat @ ( code_nat_of_integer @ L ) @ ( code_nat_of_integer @ L ) ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( code_nat_of_integer @ L ) @ ( code_nat_of_integer @ L ) ) @ one_one_nat ) )
% 0.35/0.68              @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % nat_of_integer_code
% 0.35/0.68  thf(fact_9682_int__of__integer__code,axiom,
% 0.35/0.68      ( code_int_of_integer
% 0.35/0.68      = ( ^ [K3: code_integer] :
% 0.35/0.68            ( if_int @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K3 ) ) )
% 0.35/0.68            @ ( if_int @ ( K3 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 0.35/0.68              @ ( produc1553301316500091796er_int
% 0.35/0.68                @ ^ [L: code_integer,J3: code_integer] : ( if_int @ ( J3 = zero_z3403309356797280102nteger ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L ) ) @ one_one_int ) )
% 0.35/0.68                @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % int_of_integer_code
% 0.35/0.68  thf(fact_9683_int__of__integer__numeral,axiom,
% 0.35/0.68      ! [K: num] :
% 0.35/0.68        ( ( code_int_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 0.35/0.68        = ( numeral_numeral_int @ K ) ) ).
% 0.35/0.68  
% 0.35/0.68  % int_of_integer_numeral
% 0.35/0.68  thf(fact_9684_minus__integer_Orep__eq,axiom,
% 0.35/0.68      ! [X: code_integer,Xa2: code_integer] :
% 0.35/0.68        ( ( code_int_of_integer @ ( minus_8373710615458151222nteger @ X @ Xa2 ) )
% 0.35/0.68        = ( minus_minus_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % minus_integer.rep_eq
% 0.35/0.68  thf(fact_9685_divide__integer_Orep__eq,axiom,
% 0.35/0.68      ! [X: code_integer,Xa2: code_integer] :
% 0.35/0.68        ( ( code_int_of_integer @ ( divide6298287555418463151nteger @ X @ Xa2 ) )
% 0.35/0.68        = ( divide_divide_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % divide_integer.rep_eq
% 0.35/0.68  thf(fact_9686_nat__of__integer__code__post_I3_J,axiom,
% 0.35/0.68      ! [K: num] :
% 0.35/0.68        ( ( code_nat_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 0.35/0.68        = ( numeral_numeral_nat @ K ) ) ).
% 0.35/0.68  
% 0.35/0.68  % nat_of_integer_code_post(3)
% 0.35/0.68  thf(fact_9687_nat__of__integer__code__post_I2_J,axiom,
% 0.35/0.68      ( ( code_nat_of_integer @ one_one_Code_integer )
% 0.35/0.68      = one_one_nat ) ).
% 0.35/0.68  
% 0.35/0.68  % nat_of_integer_code_post(2)
% 0.35/0.68  thf(fact_9688_floor__real__def,axiom,
% 0.35/0.68      ( archim6058952711729229775r_real
% 0.35/0.68      = ( ^ [X2: real] :
% 0.35/0.68            ( the_int
% 0.35/0.68            @ ^ [Z4: int] :
% 0.35/0.68                ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z4 ) @ X2 )
% 0.35/0.68                & ( ord_less_real @ X2 @ ( ring_1_of_int_real @ ( plus_plus_int @ Z4 @ one_one_int ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % floor_real_def
% 0.35/0.68  thf(fact_9689_bit__cut__integer__def,axiom,
% 0.35/0.68      ( code_bit_cut_integer
% 0.35/0.68      = ( ^ [K3: code_integer] :
% 0.35/0.68            ( produc6677183202524767010eger_o @ ( divide6298287555418463151nteger @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.35/0.68            @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ K3 ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % bit_cut_integer_def
% 0.35/0.68  thf(fact_9690_nat_Odisc__eq__case_I2_J,axiom,
% 0.35/0.68      ! [Nat: nat] :
% 0.35/0.68        ( ( Nat != zero_zero_nat )
% 0.35/0.68        = ( case_nat_o @ $false
% 0.35/0.68          @ ^ [Uu3: nat] : $true
% 0.35/0.68          @ Nat ) ) ).
% 0.35/0.68  
% 0.35/0.68  % nat.disc_eq_case(2)
% 0.35/0.68  thf(fact_9691_nat_Odisc__eq__case_I1_J,axiom,
% 0.35/0.68      ! [Nat: nat] :
% 0.35/0.68        ( ( Nat = zero_zero_nat )
% 0.35/0.68        = ( case_nat_o @ $true
% 0.35/0.68          @ ^ [Uu3: nat] : $false
% 0.35/0.68          @ Nat ) ) ).
% 0.35/0.68  
% 0.35/0.68  % nat.disc_eq_case(1)
% 0.35/0.68  thf(fact_9692_less__eq__nat_Osimps_I2_J,axiom,
% 0.35/0.68      ! [M: nat,N: nat] :
% 0.35/0.68        ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.35/0.68        = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M ) @ N ) ) ).
% 0.35/0.68  
% 0.35/0.68  % less_eq_nat.simps(2)
% 0.35/0.68  thf(fact_9693_max__Suc2,axiom,
% 0.35/0.68      ! [M: nat,N: nat] :
% 0.35/0.68        ( ( ord_max_nat @ M @ ( suc @ N ) )
% 0.35/0.68        = ( case_nat_nat @ ( suc @ N )
% 0.35/0.68          @ ^ [M2: nat] : ( suc @ ( ord_max_nat @ M2 @ N ) )
% 0.35/0.68          @ M ) ) ).
% 0.35/0.68  
% 0.35/0.68  % max_Suc2
% 0.35/0.68  thf(fact_9694_max__Suc1,axiom,
% 0.35/0.68      ! [N: nat,M: nat] :
% 0.35/0.68        ( ( ord_max_nat @ ( suc @ N ) @ M )
% 0.35/0.68        = ( case_nat_nat @ ( suc @ N )
% 0.35/0.68          @ ^ [M2: nat] : ( suc @ ( ord_max_nat @ N @ M2 ) )
% 0.35/0.68          @ M ) ) ).
% 0.35/0.68  
% 0.35/0.68  % max_Suc1
% 0.35/0.68  thf(fact_9695_diff__Suc,axiom,
% 0.35/0.68      ! [M: nat,N: nat] :
% 0.35/0.68        ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 0.35/0.68        = ( case_nat_nat @ zero_zero_nat
% 0.35/0.68          @ ^ [K3: nat] : K3
% 0.35/0.68          @ ( minus_minus_nat @ M @ N ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % diff_Suc
% 0.35/0.68  thf(fact_9696_bit__cut__integer__code,axiom,
% 0.35/0.68      ( code_bit_cut_integer
% 0.35/0.68      = ( ^ [K3: code_integer] :
% 0.35/0.68            ( if_Pro5737122678794959658eger_o @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 0.35/0.68            @ ( produc9125791028180074456eger_o
% 0.35/0.68              @ ^ [R5: code_integer,S6: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ R5 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ S6 ) ) @ ( S6 = one_one_Code_integer ) )
% 0.35/0.68              @ ( code_divmod_abs @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % bit_cut_integer_code
% 0.35/0.68  thf(fact_9697_pred__def,axiom,
% 0.35/0.68      ( pred
% 0.35/0.68      = ( case_nat_nat @ zero_zero_nat
% 0.35/0.68        @ ^ [X24: nat] : X24 ) ) ).
% 0.35/0.68  
% 0.35/0.68  % pred_def
% 0.35/0.68  thf(fact_9698_divmod__integer__code,axiom,
% 0.35/0.68      ( code_divmod_integer
% 0.35/0.68      = ( ^ [K3: code_integer,L: code_integer] :
% 0.35/0.68            ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 0.35/0.68            @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L )
% 0.35/0.68              @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ ( code_divmod_abs @ K3 @ L )
% 0.35/0.68                @ ( produc6916734918728496179nteger
% 0.35/0.68                  @ ^ [R5: code_integer,S6: code_integer] : ( if_Pro6119634080678213985nteger @ ( S6 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L @ S6 ) ) )
% 0.35/0.68                  @ ( code_divmod_abs @ K3 @ L ) ) )
% 0.35/0.68              @ ( if_Pro6119634080678213985nteger @ ( L = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 0.35/0.68                @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 0.35/0.68                  @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K3 @ L )
% 0.35/0.68                    @ ( produc6916734918728496179nteger
% 0.35/0.68                      @ ^ [R5: code_integer,S6: code_integer] : ( if_Pro6119634080678213985nteger @ ( S6 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L ) @ S6 ) ) )
% 0.35/0.68                      @ ( code_divmod_abs @ K3 @ L ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % divmod_integer_code
% 0.35/0.68  thf(fact_9699_drop__bit__numeral__minus__bit1,axiom,
% 0.35/0.68      ! [L2: num,K: num] :
% 0.35/0.68        ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.35/0.68        = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % drop_bit_numeral_minus_bit1
% 0.35/0.68  thf(fact_9700_Suc__0__mod__numeral,axiom,
% 0.35/0.68      ! [K: num] :
% 0.35/0.68        ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 0.35/0.68        = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Suc_0_mod_numeral
% 0.35/0.68  thf(fact_9701_drop__bit__nonnegative__int__iff,axiom,
% 0.35/0.68      ! [N: nat,K: int] :
% 0.35/0.68        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se8568078237143864401it_int @ N @ K ) )
% 0.35/0.68        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.35/0.68  
% 0.35/0.68  % drop_bit_nonnegative_int_iff
% 0.35/0.68  thf(fact_9702_drop__bit__negative__int__iff,axiom,
% 0.35/0.68      ! [N: nat,K: int] :
% 0.35/0.68        ( ( ord_less_int @ ( bit_se8568078237143864401it_int @ N @ K ) @ zero_zero_int )
% 0.35/0.68        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.35/0.68  
% 0.35/0.68  % drop_bit_negative_int_iff
% 0.35/0.68  thf(fact_9703_drop__bit__minus__one,axiom,
% 0.35/0.68      ! [N: nat] :
% 0.35/0.68        ( ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.68        = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.35/0.68  
% 0.35/0.68  % drop_bit_minus_one
% 0.35/0.68  thf(fact_9704_snd__divmod__nat,axiom,
% 0.35/0.68      ! [M: nat,N: nat] :
% 0.35/0.68        ( ( product_snd_nat_nat @ ( divmod_nat @ M @ N ) )
% 0.35/0.68        = ( modulo_modulo_nat @ M @ N ) ) ).
% 0.35/0.68  
% 0.35/0.68  % snd_divmod_nat
% 0.35/0.68  thf(fact_9705_drop__bit__Suc__minus__bit0,axiom,
% 0.35/0.68      ! [N: nat,K: num] :
% 0.35/0.68        ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 0.35/0.68        = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % drop_bit_Suc_minus_bit0
% 0.35/0.68  thf(fact_9706_drop__bit__numeral__minus__bit0,axiom,
% 0.35/0.68      ! [L2: num,K: num] :
% 0.35/0.68        ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 0.35/0.68        = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % drop_bit_numeral_minus_bit0
% 0.35/0.68  thf(fact_9707_drop__bit__Suc__minus__bit1,axiom,
% 0.35/0.68      ! [N: nat,K: num] :
% 0.35/0.68        ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.35/0.68        = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % drop_bit_Suc_minus_bit1
% 0.35/0.68  thf(fact_9708_drop__bit__push__bit__int,axiom,
% 0.35/0.68      ! [M: nat,N: nat,K: int] :
% 0.35/0.68        ( ( bit_se8568078237143864401it_int @ M @ ( bit_se545348938243370406it_int @ N @ K ) )
% 0.35/0.68        = ( bit_se8568078237143864401it_int @ ( minus_minus_nat @ M @ N ) @ ( bit_se545348938243370406it_int @ ( minus_minus_nat @ N @ M ) @ K ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % drop_bit_push_bit_int
% 0.35/0.68  thf(fact_9709_drop__bit__int__def,axiom,
% 0.35/0.68      ( bit_se8568078237143864401it_int
% 0.35/0.68      = ( ^ [N2: nat,K3: int] : ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % drop_bit_int_def
% 0.35/0.68  thf(fact_9710_Suc__0__div__numeral,axiom,
% 0.35/0.68      ! [K: num] :
% 0.35/0.68        ( ( divide_divide_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 0.35/0.68        = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Suc_0_div_numeral
% 0.35/0.68  thf(fact_9711_prod__decode__aux_Oelims,axiom,
% 0.35/0.68      ! [X: nat,Xa2: nat,Y2: product_prod_nat_nat] :
% 0.35/0.68        ( ( ( nat_prod_decode_aux @ X @ Xa2 )
% 0.35/0.68          = Y2 )
% 0.35/0.68       => ( ( ( ord_less_eq_nat @ Xa2 @ X )
% 0.35/0.68           => ( Y2
% 0.35/0.68              = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X @ Xa2 ) ) ) )
% 0.35/0.68          & ( ~ ( ord_less_eq_nat @ Xa2 @ X )
% 0.35/0.68           => ( Y2
% 0.35/0.68              = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % prod_decode_aux.elims
% 0.35/0.68  thf(fact_9712_prod__decode__aux_Osimps,axiom,
% 0.35/0.68      ( nat_prod_decode_aux
% 0.35/0.68      = ( ^ [K3: nat,M6: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M6 @ K3 ) @ ( product_Pair_nat_nat @ M6 @ ( minus_minus_nat @ K3 @ M6 ) ) @ ( nat_prod_decode_aux @ ( suc @ K3 ) @ ( minus_minus_nat @ M6 @ ( suc @ K3 ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % prod_decode_aux.simps
% 0.35/0.68  thf(fact_9713_drop__bit__of__Suc__0,axiom,
% 0.35/0.68      ! [N: nat] :
% 0.35/0.68        ( ( bit_se8570568707652914677it_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.35/0.68        = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % drop_bit_of_Suc_0
% 0.35/0.68  thf(fact_9714_fst__divmod__nat,axiom,
% 0.35/0.68      ! [M: nat,N: nat] :
% 0.35/0.68        ( ( product_fst_nat_nat @ ( divmod_nat @ M @ N ) )
% 0.35/0.68        = ( divide_divide_nat @ M @ N ) ) ).
% 0.35/0.68  
% 0.35/0.68  % fst_divmod_nat
% 0.35/0.68  thf(fact_9715_drop__bit__nat__eq,axiom,
% 0.35/0.68      ! [N: nat,K: int] :
% 0.35/0.68        ( ( bit_se8570568707652914677it_nat @ N @ ( nat2 @ K ) )
% 0.35/0.68        = ( nat2 @ ( bit_se8568078237143864401it_int @ N @ K ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % drop_bit_nat_eq
% 0.35/0.68  thf(fact_9716_drop__bit__nat__def,axiom,
% 0.35/0.68      ( bit_se8570568707652914677it_nat
% 0.35/0.68      = ( ^ [N2: nat,M6: nat] : ( divide_divide_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % drop_bit_nat_def
% 0.35/0.68  thf(fact_9717_minus__one__mod__numeral,axiom,
% 0.35/0.68      ! [N: num] :
% 0.35/0.68        ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 0.35/0.68        = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % minus_one_mod_numeral
% 0.35/0.68  thf(fact_9718_one__mod__minus__numeral,axiom,
% 0.35/0.68      ! [N: num] :
% 0.35/0.68        ( ( modulo_modulo_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.68        = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % one_mod_minus_numeral
% 0.35/0.68  thf(fact_9719_minus__numeral__mod__numeral,axiom,
% 0.35/0.68      ! [M: num,N: num] :
% 0.35/0.68        ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.35/0.68        = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % minus_numeral_mod_numeral
% 0.35/0.68  thf(fact_9720_numeral__mod__minus__numeral,axiom,
% 0.35/0.68      ! [M: num,N: num] :
% 0.35/0.68        ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.68        = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % numeral_mod_minus_numeral
% 0.35/0.68  thf(fact_9721_Divides_Oadjust__mod__def,axiom,
% 0.35/0.68      ( adjust_mod
% 0.35/0.68      = ( ^ [L: int,R5: int] : ( if_int @ ( R5 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ L @ R5 ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Divides.adjust_mod_def
% 0.35/0.68  thf(fact_9722_bezw_Oelims,axiom,
% 0.35/0.68      ! [X: nat,Xa2: nat,Y2: product_prod_int_int] :
% 0.35/0.68        ( ( ( bezw @ X @ Xa2 )
% 0.35/0.68          = Y2 )
% 0.35/0.68       => ( ( ( Xa2 = zero_zero_nat )
% 0.35/0.68           => ( Y2
% 0.35/0.68              = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 0.35/0.68          & ( ( Xa2 != zero_zero_nat )
% 0.35/0.68           => ( Y2
% 0.35/0.68              = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa2 ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % bezw.elims
% 0.35/0.68  thf(fact_9723_bezw_Osimps,axiom,
% 0.35/0.68      ( bezw
% 0.35/0.68      = ( ^ [X2: nat,Y: nat] : ( if_Pro3027730157355071871nt_int @ ( Y = zero_zero_nat ) @ ( product_Pair_int_int @ one_one_int @ zero_zero_int ) @ ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X2 @ Y ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X2 @ Y ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X2 @ Y ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X2 @ Y ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % bezw.simps
% 0.35/0.68  thf(fact_9724_bezw__non__0,axiom,
% 0.35/0.68      ! [Y2: nat,X: nat] :
% 0.35/0.68        ( ( ord_less_nat @ zero_zero_nat @ Y2 )
% 0.35/0.68       => ( ( bezw @ X @ Y2 )
% 0.35/0.68          = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y2 @ ( modulo_modulo_nat @ X @ Y2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y2 @ ( modulo_modulo_nat @ X @ Y2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y2 @ ( modulo_modulo_nat @ X @ Y2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Y2 ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % bezw_non_0
% 0.35/0.68  thf(fact_9725_bezw_Opelims,axiom,
% 0.35/0.68      ! [X: nat,Xa2: nat,Y2: product_prod_int_int] :
% 0.35/0.68        ( ( ( bezw @ X @ Xa2 )
% 0.35/0.68          = Y2 )
% 0.35/0.68       => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 0.35/0.68         => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 0.35/0.68                 => ( Y2
% 0.35/0.68                    = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 0.35/0.68                & ( ( Xa2 != zero_zero_nat )
% 0.35/0.68                 => ( Y2
% 0.35/0.68                    = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa2 ) ) ) ) ) ) ) )
% 0.35/0.68             => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % bezw.pelims
% 0.35/0.68  thf(fact_9726_prod__decode__aux_Opelims,axiom,
% 0.35/0.68      ! [X: nat,Xa2: nat,Y2: product_prod_nat_nat] :
% 0.35/0.68        ( ( ( nat_prod_decode_aux @ X @ Xa2 )
% 0.35/0.68          = Y2 )
% 0.35/0.68       => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 0.35/0.68         => ~ ( ( ( ( ord_less_eq_nat @ Xa2 @ X )
% 0.35/0.68                 => ( Y2
% 0.35/0.68                    = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X @ Xa2 ) ) ) )
% 0.35/0.68                & ( ~ ( ord_less_eq_nat @ Xa2 @ X )
% 0.35/0.68                 => ( Y2
% 0.35/0.68                    = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X ) ) ) ) ) )
% 0.35/0.68             => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % prod_decode_aux.pelims
% 0.35/0.68  thf(fact_9727_nat__descend__induct,axiom,
% 0.35/0.68      ! [N: nat,P: nat > $o,M: nat] :
% 0.35/0.68        ( ! [K2: nat] :
% 0.35/0.68            ( ( ord_less_nat @ N @ K2 )
% 0.35/0.68           => ( P @ K2 ) )
% 0.35/0.68       => ( ! [K2: nat] :
% 0.35/0.68              ( ( ord_less_eq_nat @ K2 @ N )
% 0.35/0.68             => ( ! [I: nat] :
% 0.35/0.68                    ( ( ord_less_nat @ K2 @ I )
% 0.35/0.68                   => ( P @ I ) )
% 0.35/0.68               => ( P @ K2 ) ) )
% 0.35/0.68         => ( P @ M ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % nat_descend_induct
% 0.35/0.68  thf(fact_9728_card__greaterThanLessThan__int,axiom,
% 0.35/0.68      ! [L2: int,U: int] :
% 0.35/0.68        ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L2 @ U ) )
% 0.35/0.68        = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L2 @ one_one_int ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % card_greaterThanLessThan_int
% 0.35/0.68  thf(fact_9729_infinite__nat__iff__unbounded__le,axiom,
% 0.35/0.68      ! [S2: set_nat] :
% 0.35/0.68        ( ( ~ ( finite_finite_nat @ S2 ) )
% 0.35/0.68        = ( ! [M6: nat] :
% 0.35/0.68            ? [N2: nat] :
% 0.35/0.68              ( ( ord_less_eq_nat @ M6 @ N2 )
% 0.35/0.68              & ( member_nat @ N2 @ S2 ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % infinite_nat_iff_unbounded_le
% 0.35/0.68  thf(fact_9730_infinite__nat__iff__unbounded,axiom,
% 0.35/0.68      ! [S2: set_nat] :
% 0.35/0.68        ( ( ~ ( finite_finite_nat @ S2 ) )
% 0.35/0.68        = ( ! [M6: nat] :
% 0.35/0.68            ? [N2: nat] :
% 0.35/0.68              ( ( ord_less_nat @ M6 @ N2 )
% 0.35/0.68              & ( member_nat @ N2 @ S2 ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % infinite_nat_iff_unbounded
% 0.35/0.68  thf(fact_9731_unbounded__k__infinite,axiom,
% 0.35/0.68      ! [K: nat,S2: set_nat] :
% 0.35/0.68        ( ! [M4: nat] :
% 0.35/0.68            ( ( ord_less_nat @ K @ M4 )
% 0.35/0.68           => ? [N9: nat] :
% 0.35/0.68                ( ( ord_less_nat @ M4 @ N9 )
% 0.35/0.68                & ( member_nat @ N9 @ S2 ) ) )
% 0.35/0.68       => ~ ( finite_finite_nat @ S2 ) ) ).
% 0.35/0.68  
% 0.35/0.68  % unbounded_k_infinite
% 0.35/0.68  thf(fact_9732_finite__enumerate,axiom,
% 0.35/0.68      ! [S2: set_nat] :
% 0.35/0.68        ( ( finite_finite_nat @ S2 )
% 0.35/0.68       => ? [R3: nat > nat] :
% 0.35/0.68            ( ( strict1292158309912662752at_nat @ R3 @ ( set_ord_lessThan_nat @ ( finite_card_nat @ S2 ) ) )
% 0.35/0.68            & ! [N9: nat] :
% 0.35/0.68                ( ( ord_less_nat @ N9 @ ( finite_card_nat @ S2 ) )
% 0.35/0.68               => ( member_nat @ ( R3 @ N9 ) @ S2 ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % finite_enumerate
% 0.35/0.68  thf(fact_9733_xor__minus__numerals_I1_J,axiom,
% 0.35/0.68      ! [N: num,K: int] :
% 0.35/0.68        ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ K )
% 0.35/0.68        = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ ( neg_numeral_sub_int @ N @ one ) @ K ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % xor_minus_numerals(1)
% 0.35/0.68  thf(fact_9734_xor__minus__numerals_I2_J,axiom,
% 0.35/0.68      ! [K: int,N: num] :
% 0.35/0.68        ( ( bit_se6526347334894502574or_int @ K @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.68        = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ K @ ( neg_numeral_sub_int @ N @ one ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % xor_minus_numerals(2)
% 0.35/0.68  thf(fact_9735_card__greaterThanLessThan,axiom,
% 0.35/0.68      ! [L2: nat,U: nat] :
% 0.35/0.68        ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L2 @ U ) )
% 0.35/0.68        = ( minus_minus_nat @ U @ ( suc @ L2 ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % card_greaterThanLessThan
% 0.35/0.68  thf(fact_9736_atLeastSucLessThan__greaterThanLessThan,axiom,
% 0.35/0.68      ! [L2: nat,U: nat] :
% 0.35/0.68        ( ( set_or4665077453230672383an_nat @ ( suc @ L2 ) @ U )
% 0.35/0.68        = ( set_or5834768355832116004an_nat @ L2 @ U ) ) ).
% 0.35/0.68  
% 0.35/0.68  % atLeastSucLessThan_greaterThanLessThan
% 0.35/0.68  thf(fact_9737_tanh__real__bounds,axiom,
% 0.35/0.68      ! [X: real] : ( member_real @ ( tanh_real @ X ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) ).
% 0.35/0.68  
% 0.35/0.68  % tanh_real_bounds
% 0.35/0.68  thf(fact_9738_sub__BitM__One__eq,axiom,
% 0.35/0.68      ! [N: num] :
% 0.35/0.68        ( ( neg_numeral_sub_int @ ( bitM @ N ) @ one )
% 0.35/0.68        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( neg_numeral_sub_int @ N @ one ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % sub_BitM_One_eq
% 0.35/0.68  thf(fact_9739_Suc__funpow,axiom,
% 0.35/0.68      ! [N: nat] :
% 0.35/0.68        ( ( compow_nat_nat @ N @ suc )
% 0.35/0.68        = ( plus_plus_nat @ N ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Suc_funpow
% 0.35/0.68  thf(fact_9740_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 0.35/0.68      ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 0.35/0.68      @ ^ [X2: nat,Y: nat] : ( ord_less_eq_nat @ Y @ X2 )
% 0.35/0.68      @ ^ [X2: nat,Y: nat] : ( ord_less_nat @ Y @ X2 ) ) ).
% 0.35/0.68  
% 0.35/0.68  % max_nat.semilattice_neutr_order_axioms
% 0.35/0.68  thf(fact_9741_times__int_Oabs__eq,axiom,
% 0.35/0.68      ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 0.35/0.68        ( ( times_times_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 0.35/0.68        = ( abs_Integ
% 0.35/0.68          @ ( produc27273713700761075at_nat
% 0.35/0.68            @ ^ [X2: nat,Y: nat] :
% 0.35/0.68                ( produc2626176000494625587at_nat
% 0.35/0.68                @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U2 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y @ U2 ) ) ) )
% 0.35/0.68            @ Xa2
% 0.35/0.68            @ X ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % times_int.abs_eq
% 0.35/0.68  thf(fact_9742_eq__Abs__Integ,axiom,
% 0.35/0.68      ! [Z: int] :
% 0.35/0.68        ~ ! [X3: nat,Y3: nat] :
% 0.35/0.68            ( Z
% 0.35/0.68           != ( abs_Integ @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % eq_Abs_Integ
% 0.35/0.68  thf(fact_9743_nat_Oabs__eq,axiom,
% 0.35/0.68      ! [X: product_prod_nat_nat] :
% 0.35/0.68        ( ( nat2 @ ( abs_Integ @ X ) )
% 0.35/0.68        = ( produc6842872674320459806at_nat @ minus_minus_nat @ X ) ) ).
% 0.35/0.68  
% 0.35/0.68  % nat.abs_eq
% 0.35/0.68  thf(fact_9744_zero__int__def,axiom,
% 0.35/0.68      ( zero_zero_int
% 0.35/0.68      = ( abs_Integ @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % zero_int_def
% 0.35/0.68  thf(fact_9745_int__def,axiom,
% 0.35/0.68      ( semiri1314217659103216013at_int
% 0.35/0.68      = ( ^ [N2: nat] : ( abs_Integ @ ( product_Pair_nat_nat @ N2 @ zero_zero_nat ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % int_def
% 0.35/0.68  thf(fact_9746_uminus__int_Oabs__eq,axiom,
% 0.35/0.68      ! [X: product_prod_nat_nat] :
% 0.35/0.68        ( ( uminus_uminus_int @ ( abs_Integ @ X ) )
% 0.35/0.68        = ( abs_Integ
% 0.35/0.68          @ ( produc2626176000494625587at_nat
% 0.35/0.68            @ ^ [X2: nat,Y: nat] : ( product_Pair_nat_nat @ Y @ X2 )
% 0.35/0.68            @ X ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % uminus_int.abs_eq
% 0.35/0.68  thf(fact_9747_one__int__def,axiom,
% 0.35/0.68      ( one_one_int
% 0.35/0.68      = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % one_int_def
% 0.35/0.68  thf(fact_9748_less__int_Oabs__eq,axiom,
% 0.35/0.68      ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 0.35/0.68        ( ( ord_less_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 0.35/0.68        = ( produc8739625826339149834_nat_o
% 0.35/0.68          @ ^ [X2: nat,Y: nat] :
% 0.35/0.68              ( produc6081775807080527818_nat_o
% 0.35/0.68              @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) )
% 0.35/0.68          @ Xa2
% 0.35/0.68          @ X ) ) ).
% 0.35/0.68  
% 0.35/0.68  % less_int.abs_eq
% 0.35/0.68  thf(fact_9749_less__eq__int_Oabs__eq,axiom,
% 0.35/0.68      ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 0.35/0.68        ( ( ord_less_eq_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 0.35/0.68        = ( produc8739625826339149834_nat_o
% 0.35/0.68          @ ^ [X2: nat,Y: nat] :
% 0.35/0.68              ( produc6081775807080527818_nat_o
% 0.35/0.68              @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) )
% 0.35/0.68          @ Xa2
% 0.35/0.68          @ X ) ) ).
% 0.35/0.68  
% 0.35/0.68  % less_eq_int.abs_eq
% 0.35/0.68  thf(fact_9750_plus__int_Oabs__eq,axiom,
% 0.35/0.68      ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 0.35/0.68        ( ( plus_plus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 0.35/0.68        = ( abs_Integ
% 0.35/0.68          @ ( produc27273713700761075at_nat
% 0.35/0.68            @ ^ [X2: nat,Y: nat] :
% 0.35/0.68                ( produc2626176000494625587at_nat
% 0.35/0.68                @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ U2 ) @ ( plus_plus_nat @ Y @ V4 ) ) )
% 0.35/0.68            @ Xa2
% 0.35/0.68            @ X ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % plus_int.abs_eq
% 0.35/0.68  thf(fact_9751_minus__int_Oabs__eq,axiom,
% 0.35/0.68      ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 0.35/0.68        ( ( minus_minus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 0.35/0.68        = ( abs_Integ
% 0.35/0.68          @ ( produc27273713700761075at_nat
% 0.35/0.68            @ ^ [X2: nat,Y: nat] :
% 0.35/0.68                ( produc2626176000494625587at_nat
% 0.35/0.68                @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ Y @ U2 ) ) )
% 0.35/0.68            @ Xa2
% 0.35/0.68            @ X ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % minus_int.abs_eq
% 0.35/0.68  thf(fact_9752_num__of__nat_Osimps_I2_J,axiom,
% 0.35/0.68      ! [N: nat] :
% 0.35/0.68        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68         => ( ( num_of_nat @ ( suc @ N ) )
% 0.35/0.68            = ( inc @ ( num_of_nat @ N ) ) ) )
% 0.35/0.68        & ( ~ ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68         => ( ( num_of_nat @ ( suc @ N ) )
% 0.35/0.68            = one ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % num_of_nat.simps(2)
% 0.35/0.68  thf(fact_9753_num__of__nat__numeral__eq,axiom,
% 0.35/0.68      ! [Q2: num] :
% 0.35/0.68        ( ( num_of_nat @ ( numeral_numeral_nat @ Q2 ) )
% 0.35/0.68        = Q2 ) ).
% 0.35/0.68  
% 0.35/0.68  % num_of_nat_numeral_eq
% 0.35/0.68  thf(fact_9754_num__of__nat_Osimps_I1_J,axiom,
% 0.35/0.68      ( ( num_of_nat @ zero_zero_nat )
% 0.35/0.68      = one ) ).
% 0.35/0.68  
% 0.35/0.68  % num_of_nat.simps(1)
% 0.35/0.68  thf(fact_9755_numeral__num__of__nat,axiom,
% 0.35/0.68      ! [N: nat] :
% 0.35/0.68        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68       => ( ( numeral_numeral_nat @ ( num_of_nat @ N ) )
% 0.35/0.68          = N ) ) ).
% 0.35/0.68  
% 0.35/0.68  % numeral_num_of_nat
% 0.35/0.68  thf(fact_9756_num__of__nat__One,axiom,
% 0.35/0.68      ! [N: nat] :
% 0.35/0.68        ( ( ord_less_eq_nat @ N @ one_one_nat )
% 0.35/0.68       => ( ( num_of_nat @ N )
% 0.35/0.68          = one ) ) ).
% 0.35/0.68  
% 0.35/0.68  % num_of_nat_One
% 0.35/0.68  thf(fact_9757_num__of__nat__double,axiom,
% 0.35/0.68      ! [N: nat] :
% 0.35/0.68        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68       => ( ( num_of_nat @ ( plus_plus_nat @ N @ N ) )
% 0.35/0.68          = ( bit0 @ ( num_of_nat @ N ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % num_of_nat_double
% 0.35/0.68  thf(fact_9758_num__of__nat__plus__distrib,axiom,
% 0.35/0.68      ! [M: nat,N: nat] :
% 0.35/0.68        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.35/0.68       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68         => ( ( num_of_nat @ ( plus_plus_nat @ M @ N ) )
% 0.35/0.68            = ( plus_plus_num @ ( num_of_nat @ M ) @ ( num_of_nat @ N ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % num_of_nat_plus_distrib
% 0.35/0.68  thf(fact_9759_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 0.35/0.68      ! [N: nat,J: nat,I2: nat] :
% 0.35/0.68        ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ ( suc @ I2 ) ) )
% 0.35/0.68       => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I2 @ J ) ) @ N )
% 0.35/0.68          = ( suc @ ( plus_plus_nat @ I2 @ N ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % nth_sorted_list_of_set_greaterThanLessThan
% 0.35/0.68  thf(fact_9760_less__eq__int_Orep__eq,axiom,
% 0.35/0.68      ( ord_less_eq_int
% 0.35/0.68      = ( ^ [X2: int,Xa4: int] :
% 0.35/0.68            ( produc8739625826339149834_nat_o
% 0.35/0.68            @ ^ [Y: nat,Z4: nat] :
% 0.35/0.68                ( produc6081775807080527818_nat_o
% 0.35/0.68                @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y @ V4 ) @ ( plus_plus_nat @ U2 @ Z4 ) ) )
% 0.35/0.68            @ ( rep_Integ @ X2 )
% 0.35/0.68            @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % less_eq_int.rep_eq
% 0.35/0.68  thf(fact_9761_less__int_Orep__eq,axiom,
% 0.35/0.68      ( ord_less_int
% 0.35/0.68      = ( ^ [X2: int,Xa4: int] :
% 0.35/0.68            ( produc8739625826339149834_nat_o
% 0.35/0.68            @ ^ [Y: nat,Z4: nat] :
% 0.35/0.68                ( produc6081775807080527818_nat_o
% 0.35/0.68                @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y @ V4 ) @ ( plus_plus_nat @ U2 @ Z4 ) ) )
% 0.35/0.68            @ ( rep_Integ @ X2 )
% 0.35/0.68            @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % less_int.rep_eq
% 0.35/0.68  thf(fact_9762_nat_Orep__eq,axiom,
% 0.35/0.68      ( nat2
% 0.35/0.68      = ( ^ [X2: int] : ( produc6842872674320459806at_nat @ minus_minus_nat @ ( rep_Integ @ X2 ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % nat.rep_eq
% 0.35/0.68  thf(fact_9763_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 0.35/0.68      ! [N: nat,J: nat,I2: nat] :
% 0.35/0.68        ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ I2 ) )
% 0.35/0.68       => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I2 @ J ) ) @ N )
% 0.35/0.68          = ( suc @ ( plus_plus_nat @ I2 @ N ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % nth_sorted_list_of_set_greaterThanAtMost
% 0.35/0.68  thf(fact_9764_prod__encode__def,axiom,
% 0.35/0.68      ( nat_prod_encode
% 0.35/0.68      = ( produc6842872674320459806at_nat
% 0.35/0.68        @ ^ [M6: nat,N2: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M6 @ N2 ) ) @ M6 ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % prod_encode_def
% 0.35/0.68  thf(fact_9765_uminus__int__def,axiom,
% 0.35/0.68      ( uminus_uminus_int
% 0.35/0.68      = ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ
% 0.35/0.68        @ ( produc2626176000494625587at_nat
% 0.35/0.68          @ ^ [X2: nat,Y: nat] : ( product_Pair_nat_nat @ Y @ X2 ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % uminus_int_def
% 0.35/0.68  thf(fact_9766_card__greaterThanAtMost,axiom,
% 0.35/0.68      ! [L2: nat,U: nat] :
% 0.35/0.68        ( ( finite_card_nat @ ( set_or6659071591806873216st_nat @ L2 @ U ) )
% 0.35/0.68        = ( minus_minus_nat @ U @ L2 ) ) ).
% 0.35/0.68  
% 0.35/0.68  % card_greaterThanAtMost
% 0.35/0.68  thf(fact_9767_atLeastSucAtMost__greaterThanAtMost,axiom,
% 0.35/0.68      ! [L2: nat,U: nat] :
% 0.35/0.68        ( ( set_or1269000886237332187st_nat @ ( suc @ L2 ) @ U )
% 0.35/0.68        = ( set_or6659071591806873216st_nat @ L2 @ U ) ) ).
% 0.35/0.68  
% 0.35/0.68  % atLeastSucAtMost_greaterThanAtMost
% 0.35/0.68  thf(fact_9768_le__prod__encode__2,axiom,
% 0.35/0.68      ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % le_prod_encode_2
% 0.35/0.68  thf(fact_9769_le__prod__encode__1,axiom,
% 0.35/0.68      ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % le_prod_encode_1
% 0.35/0.68  thf(fact_9770_prod__encode__prod__decode__aux,axiom,
% 0.35/0.68      ! [K: nat,M: nat] :
% 0.35/0.68        ( ( nat_prod_encode @ ( nat_prod_decode_aux @ K @ M ) )
% 0.35/0.68        = ( plus_plus_nat @ ( nat_triangle @ K ) @ M ) ) ).
% 0.35/0.68  
% 0.35/0.68  % prod_encode_prod_decode_aux
% 0.35/0.68  thf(fact_9771_times__int__def,axiom,
% 0.35/0.68      ( times_times_int
% 0.35/0.68      = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 0.35/0.68        @ ( produc27273713700761075at_nat
% 0.35/0.68          @ ^ [X2: nat,Y: nat] :
% 0.35/0.68              ( produc2626176000494625587at_nat
% 0.35/0.68              @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U2 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y @ U2 ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % times_int_def
% 0.35/0.68  thf(fact_9772_minus__int__def,axiom,
% 0.35/0.68      ( minus_minus_int
% 0.35/0.68      = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 0.35/0.68        @ ( produc27273713700761075at_nat
% 0.35/0.68          @ ^ [X2: nat,Y: nat] :
% 0.35/0.68              ( produc2626176000494625587at_nat
% 0.35/0.68              @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ Y @ U2 ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % minus_int_def
% 0.35/0.68  thf(fact_9773_plus__int__def,axiom,
% 0.35/0.68      ( plus_plus_int
% 0.35/0.68      = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 0.35/0.68        @ ( produc27273713700761075at_nat
% 0.35/0.68          @ ^ [X2: nat,Y: nat] :
% 0.35/0.68              ( produc2626176000494625587at_nat
% 0.35/0.68              @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ U2 ) @ ( plus_plus_nat @ Y @ V4 ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % plus_int_def
% 0.35/0.68  thf(fact_9774_card__greaterThanAtMost__int,axiom,
% 0.35/0.68      ! [L2: int,U: int] :
% 0.35/0.68        ( ( finite_card_int @ ( set_or6656581121297822940st_int @ L2 @ U ) )
% 0.35/0.68        = ( nat2 @ ( minus_minus_int @ U @ L2 ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % card_greaterThanAtMost_int
% 0.35/0.68  thf(fact_9775_Gcd__remove0__nat,axiom,
% 0.35/0.68      ! [M7: set_nat] :
% 0.35/0.68        ( ( finite_finite_nat @ M7 )
% 0.35/0.68       => ( ( gcd_Gcd_nat @ M7 )
% 0.35/0.68          = ( gcd_Gcd_nat @ ( minus_minus_set_nat @ M7 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Gcd_remove0_nat
% 0.35/0.68  thf(fact_9776_pow_Osimps_I3_J,axiom,
% 0.35/0.68      ! [X: num,Y2: num] :
% 0.35/0.68        ( ( pow @ X @ ( bit1 @ Y2 ) )
% 0.35/0.68        = ( times_times_num @ ( sqr @ ( pow @ X @ Y2 ) ) @ X ) ) ).
% 0.35/0.68  
% 0.35/0.68  % pow.simps(3)
% 0.35/0.68  thf(fact_9777_Gcd__nat__eq__one,axiom,
% 0.35/0.68      ! [N4: set_nat] :
% 0.35/0.68        ( ( member_nat @ one_one_nat @ N4 )
% 0.35/0.68       => ( ( gcd_Gcd_nat @ N4 )
% 0.35/0.68          = one_one_nat ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Gcd_nat_eq_one
% 0.35/0.68  thf(fact_9778_sqr_Osimps_I2_J,axiom,
% 0.35/0.68      ! [N: num] :
% 0.35/0.68        ( ( sqr @ ( bit0 @ N ) )
% 0.35/0.68        = ( bit0 @ ( bit0 @ ( sqr @ N ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % sqr.simps(2)
% 0.35/0.68  thf(fact_9779_sqr_Osimps_I1_J,axiom,
% 0.35/0.68      ( ( sqr @ one )
% 0.35/0.68      = one ) ).
% 0.35/0.68  
% 0.35/0.68  % sqr.simps(1)
% 0.35/0.68  thf(fact_9780_sqr__conv__mult,axiom,
% 0.35/0.68      ( sqr
% 0.35/0.68      = ( ^ [X2: num] : ( times_times_num @ X2 @ X2 ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % sqr_conv_mult
% 0.35/0.68  thf(fact_9781_pow_Osimps_I2_J,axiom,
% 0.35/0.68      ! [X: num,Y2: num] :
% 0.35/0.68        ( ( pow @ X @ ( bit0 @ Y2 ) )
% 0.35/0.68        = ( sqr @ ( pow @ X @ Y2 ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % pow.simps(2)
% 0.35/0.68  thf(fact_9782_sqr_Osimps_I3_J,axiom,
% 0.35/0.68      ! [N: num] :
% 0.35/0.68        ( ( sqr @ ( bit1 @ N ) )
% 0.35/0.68        = ( bit1 @ ( bit0 @ ( plus_plus_num @ ( sqr @ N ) @ N ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % sqr.simps(3)
% 0.35/0.68  thf(fact_9783_take__bit__numeral__minus__numeral__int,axiom,
% 0.35/0.68      ! [M: num,N: num] :
% 0.35/0.68        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.68        = ( case_option_int_num @ zero_zero_int
% 0.35/0.68          @ ^ [Q4: num] : ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_int @ Q4 ) ) )
% 0.35/0.68          @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % take_bit_numeral_minus_numeral_int
% 0.35/0.68  thf(fact_9784_of__nat__eq__id,axiom,
% 0.35/0.68      semiri1316708129612266289at_nat = id_nat ).
% 0.35/0.68  
% 0.35/0.68  % of_nat_eq_id
% 0.35/0.68  thf(fact_9785_take__bit__num__simps_I1_J,axiom,
% 0.35/0.68      ! [M: num] :
% 0.35/0.68        ( ( bit_take_bit_num @ zero_zero_nat @ M )
% 0.35/0.68        = none_num ) ).
% 0.35/0.68  
% 0.35/0.68  % take_bit_num_simps(1)
% 0.35/0.68  thf(fact_9786_take__bit__num__simps_I2_J,axiom,
% 0.35/0.68      ! [N: nat] :
% 0.35/0.68        ( ( bit_take_bit_num @ ( suc @ N ) @ one )
% 0.35/0.68        = ( some_num @ one ) ) ).
% 0.35/0.68  
% 0.35/0.68  % take_bit_num_simps(2)
% 0.35/0.68  thf(fact_9787_take__bit__num__simps_I5_J,axiom,
% 0.35/0.68      ! [R: num] :
% 0.35/0.68        ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R ) @ one )
% 0.35/0.68        = ( some_num @ one ) ) ).
% 0.35/0.68  
% 0.35/0.68  % take_bit_num_simps(5)
% 0.35/0.68  thf(fact_9788_Code__Abstract__Nat_Otake__bit__num__code_I1_J,axiom,
% 0.35/0.68      ! [N: nat] :
% 0.35/0.68        ( ( bit_take_bit_num @ N @ one )
% 0.35/0.68        = ( case_nat_option_num @ none_num
% 0.35/0.68          @ ^ [N2: nat] : ( some_num @ one )
% 0.35/0.68          @ N ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Code_Abstract_Nat.take_bit_num_code(1)
% 0.35/0.68  thf(fact_9789_less__int__def,axiom,
% 0.35/0.68      ( ord_less_int
% 0.35/0.68      = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 0.35/0.68        @ ( produc8739625826339149834_nat_o
% 0.35/0.68          @ ^ [X2: nat,Y: nat] :
% 0.35/0.68              ( produc6081775807080527818_nat_o
% 0.35/0.68              @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % less_int_def
% 0.35/0.68  thf(fact_9790_less__eq__int__def,axiom,
% 0.35/0.68      ( ord_less_eq_int
% 0.35/0.68      = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 0.35/0.68        @ ( produc8739625826339149834_nat_o
% 0.35/0.68          @ ^ [X2: nat,Y: nat] :
% 0.35/0.68              ( produc6081775807080527818_nat_o
% 0.35/0.68              @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % less_eq_int_def
% 0.35/0.68  thf(fact_9791_nat__def,axiom,
% 0.35/0.68      ( nat2
% 0.35/0.68      = ( map_fu2345160673673942751at_nat @ rep_Integ @ id_nat @ ( produc6842872674320459806at_nat @ minus_minus_nat ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % nat_def
% 0.35/0.68  thf(fact_9792_take__bit__num__def,axiom,
% 0.35/0.68      ( bit_take_bit_num
% 0.35/0.68      = ( ^ [N2: nat,M6: num] :
% 0.35/0.68            ( if_option_num
% 0.35/0.68            @ ( ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ M6 ) )
% 0.35/0.68              = zero_zero_nat )
% 0.35/0.68            @ none_num
% 0.35/0.68            @ ( some_num @ ( num_of_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ M6 ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % take_bit_num_def
% 0.35/0.68  thf(fact_9793_and__minus__numerals_I3_J,axiom,
% 0.35/0.68      ! [M: num,N: num] :
% 0.35/0.68        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.35/0.68        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % and_minus_numerals(3)
% 0.35/0.68  thf(fact_9794_and__minus__numerals_I7_J,axiom,
% 0.35/0.68      ! [N: num,M: num] :
% 0.35/0.68        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 0.35/0.68        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % and_minus_numerals(7)
% 0.35/0.68  thf(fact_9795_and__minus__numerals_I4_J,axiom,
% 0.35/0.68      ! [M: num,N: num] :
% 0.35/0.68        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.35/0.68        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % and_minus_numerals(4)
% 0.35/0.68  thf(fact_9796_take__bit__num__simps_I4_J,axiom,
% 0.35/0.68      ! [N: nat,M: num] :
% 0.35/0.68        ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit1 @ M ) )
% 0.35/0.68        = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N @ M ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % take_bit_num_simps(4)
% 0.35/0.68  thf(fact_9797_take__bit__num__simps_I3_J,axiom,
% 0.35/0.68      ! [N: nat,M: num] :
% 0.35/0.68        ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit0 @ M ) )
% 0.35/0.68        = ( case_o6005452278849405969um_num @ none_num
% 0.35/0.68          @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 0.35/0.68          @ ( bit_take_bit_num @ N @ M ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % take_bit_num_simps(3)
% 0.35/0.68  thf(fact_9798_take__bit__num__simps_I7_J,axiom,
% 0.35/0.68      ! [R: num,M: num] :
% 0.35/0.68        ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R ) @ ( bit1 @ M ) )
% 0.35/0.68        = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ ( pred_numeral @ R ) @ M ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % take_bit_num_simps(7)
% 0.35/0.68  thf(fact_9799_take__bit__num__simps_I6_J,axiom,
% 0.35/0.68      ! [R: num,M: num] :
% 0.35/0.68        ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R ) @ ( bit0 @ M ) )
% 0.35/0.68        = ( case_o6005452278849405969um_num @ none_num
% 0.35/0.68          @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 0.35/0.68          @ ( bit_take_bit_num @ ( pred_numeral @ R ) @ M ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % take_bit_num_simps(6)
% 0.35/0.68  thf(fact_9800_and__minus__numerals_I8_J,axiom,
% 0.35/0.68      ! [N: num,M: num] :
% 0.35/0.68        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 0.35/0.68        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % and_minus_numerals(8)
% 0.35/0.68  thf(fact_9801_and__not__num_Osimps_I8_J,axiom,
% 0.35/0.68      ! [M: num,N: num] :
% 0.35/0.68        ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.35/0.68        = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 0.35/0.68          @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 0.35/0.68          @ ( bit_and_not_num @ M @ N ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % and_not_num.simps(8)
% 0.35/0.68  thf(fact_9802_and__not__num_Osimps_I1_J,axiom,
% 0.35/0.68      ( ( bit_and_not_num @ one @ one )
% 0.35/0.68      = none_num ) ).
% 0.35/0.68  
% 0.35/0.68  % and_not_num.simps(1)
% 0.35/0.68  thf(fact_9803_and__not__num_Osimps_I4_J,axiom,
% 0.35/0.68      ! [M: num] :
% 0.35/0.68        ( ( bit_and_not_num @ ( bit0 @ M ) @ one )
% 0.35/0.68        = ( some_num @ ( bit0 @ M ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % and_not_num.simps(4)
% 0.35/0.68  thf(fact_9804_and__not__num_Osimps_I2_J,axiom,
% 0.35/0.68      ! [N: num] :
% 0.35/0.68        ( ( bit_and_not_num @ one @ ( bit0 @ N ) )
% 0.35/0.68        = ( some_num @ one ) ) ).
% 0.35/0.68  
% 0.35/0.68  % and_not_num.simps(2)
% 0.35/0.68  thf(fact_9805_and__not__num_Osimps_I3_J,axiom,
% 0.35/0.68      ! [N: num] :
% 0.35/0.68        ( ( bit_and_not_num @ one @ ( bit1 @ N ) )
% 0.35/0.68        = none_num ) ).
% 0.35/0.68  
% 0.35/0.68  % and_not_num.simps(3)
% 0.35/0.68  thf(fact_9806_Code__Abstract__Nat_Otake__bit__num__code_I2_J,axiom,
% 0.35/0.68      ! [N: nat,M: num] :
% 0.35/0.68        ( ( bit_take_bit_num @ N @ ( bit0 @ M ) )
% 0.35/0.68        = ( case_nat_option_num @ none_num
% 0.35/0.68          @ ^ [N2: nat] :
% 0.35/0.68              ( case_o6005452278849405969um_num @ none_num
% 0.35/0.68              @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 0.35/0.68              @ ( bit_take_bit_num @ N2 @ M ) )
% 0.35/0.68          @ N ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Code_Abstract_Nat.take_bit_num_code(2)
% 0.35/0.68  thf(fact_9807_and__not__num_Osimps_I7_J,axiom,
% 0.35/0.68      ! [M: num] :
% 0.35/0.68        ( ( bit_and_not_num @ ( bit1 @ M ) @ one )
% 0.35/0.68        = ( some_num @ ( bit0 @ M ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % and_not_num.simps(7)
% 0.35/0.68  thf(fact_9808_and__not__num__eq__Some__iff,axiom,
% 0.35/0.68      ! [M: num,N: num,Q2: num] :
% 0.35/0.68        ( ( ( bit_and_not_num @ M @ N )
% 0.35/0.68          = ( some_num @ Q2 ) )
% 0.35/0.68        = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.68          = ( numeral_numeral_int @ Q2 ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % and_not_num_eq_Some_iff
% 0.35/0.68  thf(fact_9809_Code__Abstract__Nat_Otake__bit__num__code_I3_J,axiom,
% 0.35/0.68      ! [N: nat,M: num] :
% 0.35/0.68        ( ( bit_take_bit_num @ N @ ( bit1 @ M ) )
% 0.35/0.68        = ( case_nat_option_num @ none_num
% 0.35/0.68          @ ^ [N2: nat] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N2 @ M ) ) )
% 0.35/0.68          @ N ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Code_Abstract_Nat.take_bit_num_code(3)
% 0.35/0.68  thf(fact_9810_and__not__num__eq__None__iff,axiom,
% 0.35/0.68      ! [M: num,N: num] :
% 0.35/0.68        ( ( ( bit_and_not_num @ M @ N )
% 0.35/0.68          = none_num )
% 0.35/0.68        = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.68          = zero_zero_int ) ) ).
% 0.35/0.68  
% 0.35/0.68  % and_not_num_eq_None_iff
% 0.35/0.68  thf(fact_9811_int__numeral__and__not__num,axiom,
% 0.35/0.68      ! [M: num,N: num] :
% 0.35/0.68        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.68        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ N ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % int_numeral_and_not_num
% 0.35/0.68  thf(fact_9812_int__numeral__not__and__num,axiom,
% 0.35/0.68      ! [M: num,N: num] :
% 0.35/0.68        ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.35/0.68        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ N @ M ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % int_numeral_not_and_num
% 0.35/0.68  thf(fact_9813_Bit__Operations_Otake__bit__num__code,axiom,
% 0.35/0.68      ( bit_take_bit_num
% 0.35/0.68      = ( ^ [N2: nat,M6: num] :
% 0.35/0.68            ( produc478579273971653890on_num
% 0.35/0.68            @ ^ [A3: nat,X2: num] :
% 0.35/0.68                ( case_nat_option_num @ none_num
% 0.35/0.68                @ ^ [O: nat] :
% 0.35/0.68                    ( case_num_option_num @ ( some_num @ one )
% 0.35/0.68                    @ ^ [P4: num] :
% 0.35/0.68                        ( case_o6005452278849405969um_num @ none_num
% 0.35/0.68                        @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 0.35/0.68                        @ ( bit_take_bit_num @ O @ P4 ) )
% 0.35/0.68                    @ ^ [P4: num] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ O @ P4 ) ) )
% 0.35/0.68                    @ X2 )
% 0.35/0.68                @ A3 )
% 0.35/0.68            @ ( product_Pair_nat_num @ N2 @ M6 ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Bit_Operations.take_bit_num_code
% 0.35/0.68  thf(fact_9814_and__not__num_Oelims,axiom,
% 0.35/0.68      ! [X: num,Xa2: num,Y2: option_num] :
% 0.35/0.68        ( ( ( bit_and_not_num @ X @ Xa2 )
% 0.35/0.68          = Y2 )
% 0.35/0.68       => ( ( ( X = one )
% 0.35/0.68           => ( ( Xa2 = one )
% 0.35/0.68             => ( Y2 != none_num ) ) )
% 0.35/0.68         => ( ( ( X = one )
% 0.35/0.68             => ( ? [N3: num] :
% 0.35/0.68                    ( Xa2
% 0.35/0.68                    = ( bit0 @ N3 ) )
% 0.35/0.68               => ( Y2
% 0.35/0.68                 != ( some_num @ one ) ) ) )
% 0.35/0.68           => ( ( ( X = one )
% 0.35/0.68               => ( ? [N3: num] :
% 0.35/0.68                      ( Xa2
% 0.35/0.68                      = ( bit1 @ N3 ) )
% 0.35/0.68                 => ( Y2 != none_num ) ) )
% 0.35/0.68             => ( ! [M4: num] :
% 0.35/0.68                    ( ( X
% 0.35/0.68                      = ( bit0 @ M4 ) )
% 0.35/0.68                   => ( ( Xa2 = one )
% 0.35/0.68                     => ( Y2
% 0.35/0.68                       != ( some_num @ ( bit0 @ M4 ) ) ) ) )
% 0.35/0.68               => ( ! [M4: num] :
% 0.35/0.68                      ( ( X
% 0.35/0.68                        = ( bit0 @ M4 ) )
% 0.35/0.68                     => ! [N3: num] :
% 0.35/0.68                          ( ( Xa2
% 0.35/0.68                            = ( bit0 @ N3 ) )
% 0.35/0.68                         => ( Y2
% 0.35/0.68                           != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N3 ) ) ) ) )
% 0.35/0.68                 => ( ! [M4: num] :
% 0.35/0.68                        ( ( X
% 0.35/0.68                          = ( bit0 @ M4 ) )
% 0.35/0.68                       => ! [N3: num] :
% 0.35/0.68                            ( ( Xa2
% 0.35/0.68                              = ( bit1 @ N3 ) )
% 0.35/0.68                           => ( Y2
% 0.35/0.68                             != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N3 ) ) ) ) )
% 0.35/0.68                   => ( ! [M4: num] :
% 0.35/0.68                          ( ( X
% 0.35/0.68                            = ( bit1 @ M4 ) )
% 0.35/0.68                         => ( ( Xa2 = one )
% 0.35/0.68                           => ( Y2
% 0.35/0.68                             != ( some_num @ ( bit0 @ M4 ) ) ) ) )
% 0.35/0.68                     => ( ! [M4: num] :
% 0.35/0.68                            ( ( X
% 0.35/0.68                              = ( bit1 @ M4 ) )
% 0.35/0.68                           => ! [N3: num] :
% 0.35/0.68                                ( ( Xa2
% 0.35/0.68                                  = ( bit0 @ N3 ) )
% 0.35/0.68                               => ( Y2
% 0.35/0.68                                 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 0.35/0.68                                    @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 0.35/0.68                                    @ ( bit_and_not_num @ M4 @ N3 ) ) ) ) )
% 0.35/0.68                       => ~ ! [M4: num] :
% 0.35/0.68                              ( ( X
% 0.35/0.68                                = ( bit1 @ M4 ) )
% 0.35/0.68                             => ! [N3: num] :
% 0.35/0.68                                  ( ( Xa2
% 0.35/0.68                                    = ( bit1 @ N3 ) )
% 0.35/0.68                                 => ( Y2
% 0.35/0.68                                   != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % and_not_num.elims
% 0.35/0.68  thf(fact_9815_and__not__num_Osimps_I5_J,axiom,
% 0.35/0.68      ! [M: num,N: num] :
% 0.35/0.68        ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.35/0.68        = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % and_not_num.simps(5)
% 0.35/0.68  thf(fact_9816_and__not__num_Osimps_I6_J,axiom,
% 0.35/0.68      ! [M: num,N: num] :
% 0.35/0.68        ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.35/0.68        = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % and_not_num.simps(6)
% 0.35/0.68  thf(fact_9817_and__not__num_Osimps_I9_J,axiom,
% 0.35/0.68      ! [M: num,N: num] :
% 0.35/0.68        ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.35/0.68        = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % and_not_num.simps(9)
% 0.35/0.68  thf(fact_9818_and__num_Oelims,axiom,
% 0.35/0.68      ! [X: num,Xa2: num,Y2: option_num] :
% 0.35/0.68        ( ( ( bit_un7362597486090784418nd_num @ X @ Xa2 )
% 0.35/0.68          = Y2 )
% 0.35/0.68       => ( ( ( X = one )
% 0.35/0.68           => ( ( Xa2 = one )
% 0.35/0.68             => ( Y2
% 0.35/0.68               != ( some_num @ one ) ) ) )
% 0.35/0.68         => ( ( ( X = one )
% 0.35/0.68             => ( ? [N3: num] :
% 0.35/0.68                    ( Xa2
% 0.35/0.68                    = ( bit0 @ N3 ) )
% 0.35/0.68               => ( Y2 != none_num ) ) )
% 0.35/0.68           => ( ( ( X = one )
% 0.35/0.68               => ( ? [N3: num] :
% 0.35/0.68                      ( Xa2
% 0.35/0.68                      = ( bit1 @ N3 ) )
% 0.35/0.68                 => ( Y2
% 0.35/0.68                   != ( some_num @ one ) ) ) )
% 0.35/0.68             => ( ( ? [M4: num] :
% 0.35/0.68                      ( X
% 0.35/0.68                      = ( bit0 @ M4 ) )
% 0.35/0.68                 => ( ( Xa2 = one )
% 0.35/0.68                   => ( Y2 != none_num ) ) )
% 0.35/0.68               => ( ! [M4: num] :
% 0.35/0.68                      ( ( X
% 0.35/0.68                        = ( bit0 @ M4 ) )
% 0.35/0.68                     => ! [N3: num] :
% 0.35/0.68                          ( ( Xa2
% 0.35/0.68                            = ( bit0 @ N3 ) )
% 0.35/0.68                         => ( Y2
% 0.35/0.68                           != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) ) ) )
% 0.35/0.68                 => ( ! [M4: num] :
% 0.35/0.68                        ( ( X
% 0.35/0.68                          = ( bit0 @ M4 ) )
% 0.35/0.68                       => ! [N3: num] :
% 0.35/0.68                            ( ( Xa2
% 0.35/0.68                              = ( bit1 @ N3 ) )
% 0.35/0.68                           => ( Y2
% 0.35/0.68                             != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) ) ) )
% 0.35/0.68                   => ( ( ? [M4: num] :
% 0.35/0.68                            ( X
% 0.35/0.68                            = ( bit1 @ M4 ) )
% 0.35/0.68                       => ( ( Xa2 = one )
% 0.35/0.68                         => ( Y2
% 0.35/0.68                           != ( some_num @ one ) ) ) )
% 0.35/0.68                     => ( ! [M4: num] :
% 0.35/0.68                            ( ( X
% 0.35/0.68                              = ( bit1 @ M4 ) )
% 0.35/0.68                           => ! [N3: num] :
% 0.35/0.68                                ( ( Xa2
% 0.35/0.68                                  = ( bit0 @ N3 ) )
% 0.35/0.68                               => ( Y2
% 0.35/0.68                                 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) ) ) )
% 0.35/0.68                       => ~ ! [M4: num] :
% 0.35/0.68                              ( ( X
% 0.35/0.68                                = ( bit1 @ M4 ) )
% 0.35/0.68                             => ! [N3: num] :
% 0.35/0.68                                  ( ( Xa2
% 0.35/0.68                                    = ( bit1 @ N3 ) )
% 0.35/0.68                                 => ( Y2
% 0.35/0.68                                   != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 0.35/0.68                                      @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 0.35/0.68                                      @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % and_num.elims
% 0.35/0.68  thf(fact_9819_xor__num_Oelims,axiom,
% 0.35/0.68      ! [X: num,Xa2: num,Y2: option_num] :
% 0.35/0.68        ( ( ( bit_un2480387367778600638or_num @ X @ Xa2 )
% 0.35/0.68          = Y2 )
% 0.35/0.68       => ( ( ( X = one )
% 0.35/0.68           => ( ( Xa2 = one )
% 0.35/0.68             => ( Y2 != none_num ) ) )
% 0.35/0.68         => ( ( ( X = one )
% 0.35/0.68             => ! [N3: num] :
% 0.35/0.68                  ( ( Xa2
% 0.35/0.68                    = ( bit0 @ N3 ) )
% 0.35/0.68                 => ( Y2
% 0.35/0.68                   != ( some_num @ ( bit1 @ N3 ) ) ) ) )
% 0.35/0.68           => ( ( ( X = one )
% 0.35/0.68               => ! [N3: num] :
% 0.35/0.68                    ( ( Xa2
% 0.35/0.68                      = ( bit1 @ N3 ) )
% 0.35/0.68                   => ( Y2
% 0.35/0.68                     != ( some_num @ ( bit0 @ N3 ) ) ) ) )
% 0.35/0.68             => ( ! [M4: num] :
% 0.35/0.68                    ( ( X
% 0.35/0.68                      = ( bit0 @ M4 ) )
% 0.35/0.68                   => ( ( Xa2 = one )
% 0.35/0.68                     => ( Y2
% 0.35/0.68                       != ( some_num @ ( bit1 @ M4 ) ) ) ) )
% 0.35/0.68               => ( ! [M4: num] :
% 0.35/0.68                      ( ( X
% 0.35/0.68                        = ( bit0 @ M4 ) )
% 0.35/0.68                     => ! [N3: num] :
% 0.35/0.68                          ( ( Xa2
% 0.35/0.68                            = ( bit0 @ N3 ) )
% 0.35/0.68                         => ( Y2
% 0.35/0.68                           != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) ) ) )
% 0.35/0.68                 => ( ! [M4: num] :
% 0.35/0.68                        ( ( X
% 0.35/0.68                          = ( bit0 @ M4 ) )
% 0.35/0.68                       => ! [N3: num] :
% 0.35/0.68                            ( ( Xa2
% 0.35/0.68                              = ( bit1 @ N3 ) )
% 0.35/0.68                           => ( Y2
% 0.35/0.68                             != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) ) ) ) )
% 0.35/0.68                   => ( ! [M4: num] :
% 0.35/0.68                          ( ( X
% 0.35/0.68                            = ( bit1 @ M4 ) )
% 0.35/0.68                         => ( ( Xa2 = one )
% 0.35/0.68                           => ( Y2
% 0.35/0.68                             != ( some_num @ ( bit0 @ M4 ) ) ) ) )
% 0.35/0.68                     => ( ! [M4: num] :
% 0.35/0.68                            ( ( X
% 0.35/0.68                              = ( bit1 @ M4 ) )
% 0.35/0.68                           => ! [N3: num] :
% 0.35/0.68                                ( ( Xa2
% 0.35/0.68                                  = ( bit0 @ N3 ) )
% 0.35/0.68                               => ( Y2
% 0.35/0.68                                 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) ) ) ) )
% 0.35/0.68                       => ~ ! [M4: num] :
% 0.35/0.68                              ( ( X
% 0.35/0.68                                = ( bit1 @ M4 ) )
% 0.35/0.68                             => ! [N3: num] :
% 0.35/0.68                                  ( ( Xa2
% 0.35/0.68                                    = ( bit1 @ N3 ) )
% 0.35/0.68                                 => ( Y2
% 0.35/0.68                                   != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % xor_num.elims
% 0.35/0.68  thf(fact_9820_xor__num_Osimps_I8_J,axiom,
% 0.35/0.68      ! [M: num,N: num] :
% 0.35/0.68        ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.35/0.68        = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % xor_num.simps(8)
% 0.35/0.68  thf(fact_9821_and__num_Osimps_I1_J,axiom,
% 0.35/0.68      ( ( bit_un7362597486090784418nd_num @ one @ one )
% 0.35/0.68      = ( some_num @ one ) ) ).
% 0.35/0.68  
% 0.35/0.68  % and_num.simps(1)
% 0.35/0.68  thf(fact_9822_xor__num_Osimps_I1_J,axiom,
% 0.35/0.68      ( ( bit_un2480387367778600638or_num @ one @ one )
% 0.35/0.68      = none_num ) ).
% 0.35/0.68  
% 0.35/0.68  % xor_num.simps(1)
% 0.35/0.68  thf(fact_9823_xor__num_Osimps_I5_J,axiom,
% 0.35/0.68      ! [M: num,N: num] :
% 0.35/0.68        ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.35/0.68        = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % xor_num.simps(5)
% 0.35/0.68  thf(fact_9824_and__num_Osimps_I5_J,axiom,
% 0.35/0.68      ! [M: num,N: num] :
% 0.35/0.68        ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.35/0.68        = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % and_num.simps(5)
% 0.35/0.68  thf(fact_9825_and__num_Osimps_I3_J,axiom,
% 0.35/0.68      ! [N: num] :
% 0.35/0.68        ( ( bit_un7362597486090784418nd_num @ one @ ( bit1 @ N ) )
% 0.35/0.68        = ( some_num @ one ) ) ).
% 0.35/0.68  
% 0.35/0.68  % and_num.simps(3)
% 0.35/0.68  thf(fact_9826_and__num_Osimps_I7_J,axiom,
% 0.35/0.68      ! [M: num] :
% 0.35/0.68        ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ one )
% 0.35/0.68        = ( some_num @ one ) ) ).
% 0.35/0.68  
% 0.35/0.68  % and_num.simps(7)
% 0.35/0.68  thf(fact_9827_and__num_Osimps_I2_J,axiom,
% 0.35/0.68      ! [N: num] :
% 0.35/0.68        ( ( bit_un7362597486090784418nd_num @ one @ ( bit0 @ N ) )
% 0.35/0.68        = none_num ) ).
% 0.35/0.68  
% 0.35/0.68  % and_num.simps(2)
% 0.35/0.68  thf(fact_9828_and__num_Osimps_I4_J,axiom,
% 0.35/0.68      ! [M: num] :
% 0.35/0.68        ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ one )
% 0.35/0.68        = none_num ) ).
% 0.35/0.68  
% 0.35/0.68  % and_num.simps(4)
% 0.35/0.68  thf(fact_9829_and__num_Osimps_I8_J,axiom,
% 0.35/0.68      ! [M: num,N: num] :
% 0.35/0.68        ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.35/0.68        = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % and_num.simps(8)
% 0.35/0.68  thf(fact_9830_and__num_Osimps_I6_J,axiom,
% 0.35/0.68      ! [M: num,N: num] :
% 0.35/0.68        ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.35/0.68        = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % and_num.simps(6)
% 0.35/0.68  thf(fact_9831_xor__num_Osimps_I9_J,axiom,
% 0.35/0.68      ! [M: num,N: num] :
% 0.35/0.68        ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.35/0.68        = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % xor_num.simps(9)
% 0.35/0.68  thf(fact_9832_xor__num_Osimps_I2_J,axiom,
% 0.35/0.68      ! [N: num] :
% 0.35/0.68        ( ( bit_un2480387367778600638or_num @ one @ ( bit0 @ N ) )
% 0.35/0.68        = ( some_num @ ( bit1 @ N ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % xor_num.simps(2)
% 0.35/0.68  thf(fact_9833_xor__num_Osimps_I3_J,axiom,
% 0.35/0.68      ! [N: num] :
% 0.35/0.68        ( ( bit_un2480387367778600638or_num @ one @ ( bit1 @ N ) )
% 0.35/0.68        = ( some_num @ ( bit0 @ N ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % xor_num.simps(3)
% 0.35/0.68  thf(fact_9834_xor__num_Osimps_I4_J,axiom,
% 0.35/0.68      ! [M: num] :
% 0.35/0.68        ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ one )
% 0.35/0.68        = ( some_num @ ( bit1 @ M ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % xor_num.simps(4)
% 0.35/0.68  thf(fact_9835_xor__num_Osimps_I7_J,axiom,
% 0.35/0.68      ! [M: num] :
% 0.35/0.68        ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ one )
% 0.35/0.68        = ( some_num @ ( bit0 @ M ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % xor_num.simps(7)
% 0.35/0.68  thf(fact_9836_and__num_Osimps_I9_J,axiom,
% 0.35/0.68      ! [M: num,N: num] :
% 0.35/0.68        ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.35/0.68        = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 0.35/0.68          @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 0.35/0.68          @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % and_num.simps(9)
% 0.35/0.68  thf(fact_9837_xor__num_Osimps_I6_J,axiom,
% 0.35/0.68      ! [M: num,N: num] :
% 0.35/0.68        ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.35/0.68        = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % xor_num.simps(6)
% 0.35/0.68  thf(fact_9838_xor__num__dict,axiom,
% 0.35/0.68      bit_un2480387367778600638or_num = bit_un6178654185764691216or_num ).
% 0.35/0.68  
% 0.35/0.68  % xor_num_dict
% 0.35/0.68  thf(fact_9839_and__num__dict,axiom,
% 0.35/0.68      bit_un7362597486090784418nd_num = bit_un1837492267222099188nd_num ).
% 0.35/0.68  
% 0.35/0.68  % and_num_dict
% 0.35/0.68  thf(fact_9840_min__Suc__Suc,axiom,
% 0.35/0.68      ! [M: nat,N: nat] :
% 0.35/0.68        ( ( ord_min_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.35/0.68        = ( suc @ ( ord_min_nat @ M @ N ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % min_Suc_Suc
% 0.35/0.68  thf(fact_9841_min__0R,axiom,
% 0.35/0.68      ! [N: nat] :
% 0.35/0.68        ( ( ord_min_nat @ N @ zero_zero_nat )
% 0.35/0.68        = zero_zero_nat ) ).
% 0.35/0.68  
% 0.35/0.68  % min_0R
% 0.35/0.68  thf(fact_9842_min__0L,axiom,
% 0.35/0.68      ! [N: nat] :
% 0.35/0.68        ( ( ord_min_nat @ zero_zero_nat @ N )
% 0.35/0.68        = zero_zero_nat ) ).
% 0.35/0.68  
% 0.35/0.68  % min_0L
% 0.35/0.68  thf(fact_9843_min__numeral__Suc,axiom,
% 0.35/0.68      ! [K: num,N: nat] :
% 0.35/0.68        ( ( ord_min_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 0.35/0.68        = ( suc @ ( ord_min_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % min_numeral_Suc
% 0.35/0.68  thf(fact_9844_min__Suc__numeral,axiom,
% 0.35/0.68      ! [N: nat,K: num] :
% 0.35/0.68        ( ( ord_min_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 0.35/0.68        = ( suc @ ( ord_min_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % min_Suc_numeral
% 0.35/0.68  thf(fact_9845_min__diff,axiom,
% 0.35/0.68      ! [M: nat,I2: nat,N: nat] :
% 0.35/0.68        ( ( ord_min_nat @ ( minus_minus_nat @ M @ I2 ) @ ( minus_minus_nat @ N @ I2 ) )
% 0.35/0.68        = ( minus_minus_nat @ ( ord_min_nat @ M @ N ) @ I2 ) ) ).
% 0.35/0.68  
% 0.35/0.68  % min_diff
% 0.35/0.68  thf(fact_9846_nat__mult__min__right,axiom,
% 0.35/0.68      ! [M: nat,N: nat,Q2: nat] :
% 0.35/0.68        ( ( times_times_nat @ M @ ( ord_min_nat @ N @ Q2 ) )
% 0.35/0.68        = ( ord_min_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q2 ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % nat_mult_min_right
% 0.35/0.68  thf(fact_9847_nat__mult__min__left,axiom,
% 0.35/0.68      ! [M: nat,N: nat,Q2: nat] :
% 0.35/0.68        ( ( times_times_nat @ ( ord_min_nat @ M @ N ) @ Q2 )
% 0.35/0.68        = ( ord_min_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N @ Q2 ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % nat_mult_min_left
% 0.35/0.68  thf(fact_9848_concat__bit__assoc__sym,axiom,
% 0.35/0.68      ! [M: nat,N: nat,K: int,L2: int,R: int] :
% 0.35/0.68        ( ( bit_concat_bit @ M @ ( bit_concat_bit @ N @ K @ L2 ) @ R )
% 0.35/0.68        = ( bit_concat_bit @ ( ord_min_nat @ M @ N ) @ K @ ( bit_concat_bit @ ( minus_minus_nat @ M @ N ) @ L2 @ R ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % concat_bit_assoc_sym
% 0.35/0.68  thf(fact_9849_take__bit__concat__bit__eq,axiom,
% 0.35/0.68      ! [M: nat,N: nat,K: int,L2: int] :
% 0.35/0.68        ( ( bit_se2923211474154528505it_int @ M @ ( bit_concat_bit @ N @ K @ L2 ) )
% 0.35/0.68        = ( bit_concat_bit @ ( ord_min_nat @ M @ N ) @ K @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ M @ N ) @ L2 ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % take_bit_concat_bit_eq
% 0.35/0.68  thf(fact_9850_min__Suc2,axiom,
% 0.35/0.68      ! [M: nat,N: nat] :
% 0.35/0.68        ( ( ord_min_nat @ M @ ( suc @ N ) )
% 0.35/0.68        = ( case_nat_nat @ zero_zero_nat
% 0.35/0.68          @ ^ [M2: nat] : ( suc @ ( ord_min_nat @ M2 @ N ) )
% 0.35/0.68          @ M ) ) ).
% 0.35/0.68  
% 0.35/0.68  % min_Suc2
% 0.35/0.68  thf(fact_9851_min__Suc1,axiom,
% 0.35/0.68      ! [N: nat,M: nat] :
% 0.35/0.68        ( ( ord_min_nat @ ( suc @ N ) @ M )
% 0.35/0.68        = ( case_nat_nat @ zero_zero_nat
% 0.35/0.68          @ ^ [M2: nat] : ( suc @ ( ord_min_nat @ N @ M2 ) )
% 0.35/0.68          @ M ) ) ).
% 0.35/0.68  
% 0.35/0.68  % min_Suc1
% 0.35/0.68  thf(fact_9852_min__enat__simps_I2_J,axiom,
% 0.35/0.68      ! [Q2: extended_enat] :
% 0.35/0.68        ( ( ord_mi8085742599997312461d_enat @ Q2 @ zero_z5237406670263579293d_enat )
% 0.35/0.68        = zero_z5237406670263579293d_enat ) ).
% 0.35/0.68  
% 0.35/0.68  % min_enat_simps(2)
% 0.35/0.68  thf(fact_9853_min__enat__simps_I3_J,axiom,
% 0.35/0.68      ! [Q2: extended_enat] :
% 0.35/0.68        ( ( ord_mi8085742599997312461d_enat @ zero_z5237406670263579293d_enat @ Q2 )
% 0.35/0.68        = zero_z5237406670263579293d_enat ) ).
% 0.35/0.68  
% 0.35/0.68  % min_enat_simps(3)
% 0.35/0.68  thf(fact_9854_divmod__integer__eq__cases,axiom,
% 0.35/0.68      ( code_divmod_integer
% 0.35/0.68      = ( ^ [K3: code_integer,L: code_integer] :
% 0.35/0.68            ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 0.35/0.68            @ ( if_Pro6119634080678213985nteger @ ( L = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 0.35/0.68              @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L
% 0.35/0.68                @ ( if_Pro6119634080678213985nteger
% 0.35/0.68                  @ ( ( sgn_sgn_Code_integer @ K3 )
% 0.35/0.68                    = ( sgn_sgn_Code_integer @ L ) )
% 0.35/0.68                  @ ( code_divmod_abs @ K3 @ L )
% 0.35/0.68                  @ ( produc6916734918728496179nteger
% 0.35/0.68                    @ ^ [R5: code_integer,S6: code_integer] : ( if_Pro6119634080678213985nteger @ ( S6 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ L ) @ S6 ) ) )
% 0.35/0.68                    @ ( code_divmod_abs @ K3 @ L ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % divmod_integer_eq_cases
% 0.35/0.68  thf(fact_9855_sorted__list__of__set__greaterThanAtMost,axiom,
% 0.35/0.68      ! [I2: nat,J: nat] :
% 0.35/0.68        ( ( ord_less_eq_nat @ ( suc @ I2 ) @ J )
% 0.35/0.68       => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I2 @ J ) )
% 0.35/0.68          = ( cons_nat @ ( suc @ I2 ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I2 ) @ J ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % sorted_list_of_set_greaterThanAtMost
% 0.35/0.68  thf(fact_9856_sorted__list__of__set__greaterThanLessThan,axiom,
% 0.35/0.68      ! [I2: nat,J: nat] :
% 0.35/0.68        ( ( ord_less_nat @ ( suc @ I2 ) @ J )
% 0.35/0.68       => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I2 @ J ) )
% 0.35/0.68          = ( cons_nat @ ( suc @ I2 ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I2 ) @ J ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % sorted_list_of_set_greaterThanLessThan
% 0.35/0.68  thf(fact_9857_card_Ocomp__fun__commute__on,axiom,
% 0.35/0.68      ( ( comp_nat_nat_nat @ suc @ suc )
% 0.35/0.68      = ( comp_nat_nat_nat @ suc @ suc ) ) ).
% 0.35/0.68  
% 0.35/0.68  % card.comp_fun_commute_on
% 0.35/0.68  thf(fact_9858_Code__Target__Int_Onegative__def,axiom,
% 0.35/0.68      ( code_Target_negative
% 0.35/0.68      = ( comp_int_int_num @ uminus_uminus_int @ numeral_numeral_int ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Code_Target_Int.negative_def
% 0.35/0.68  thf(fact_9859_upto__aux__rec,axiom,
% 0.35/0.68      ( upto_aux
% 0.35/0.68      = ( ^ [I3: int,J3: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J3 @ I3 ) @ Js @ ( upto_aux @ I3 @ ( minus_minus_int @ J3 @ one_one_int ) @ ( cons_int @ J3 @ Js ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % upto_aux_rec
% 0.35/0.68  thf(fact_9860_Inf__real__def,axiom,
% 0.35/0.68      ( comple4887499456419720421f_real
% 0.35/0.68      = ( ^ [X4: set_real] : ( uminus_uminus_real @ ( comple1385675409528146559p_real @ ( image_real_real @ uminus_uminus_real @ X4 ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Inf_real_def
% 0.35/0.68  thf(fact_9861_range__mod,axiom,
% 0.35/0.68      ! [N: nat] :
% 0.35/0.68        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68       => ( ( image_nat_nat
% 0.35/0.68            @ ^ [M6: nat] : ( modulo_modulo_nat @ M6 @ N )
% 0.35/0.68            @ top_top_set_nat )
% 0.35/0.68          = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % range_mod
% 0.35/0.68  thf(fact_9862_suminf__eq__SUP__real,axiom,
% 0.35/0.68      ! [X8: nat > real] :
% 0.35/0.68        ( ( summable_real @ X8 )
% 0.35/0.68       => ( ! [I4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( X8 @ I4 ) )
% 0.35/0.68         => ( ( suminf_real @ X8 )
% 0.35/0.68            = ( comple1385675409528146559p_real
% 0.35/0.68              @ ( image_nat_real
% 0.35/0.68                @ ^ [I3: nat] : ( groups6591440286371151544t_real @ X8 @ ( set_ord_lessThan_nat @ I3 ) )
% 0.35/0.68                @ top_top_set_nat ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % suminf_eq_SUP_real
% 0.35/0.68  thf(fact_9863_UNIV__nat__eq,axiom,
% 0.35/0.68      ( top_top_set_nat
% 0.35/0.68      = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ top_top_set_nat ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % UNIV_nat_eq
% 0.35/0.68  thf(fact_9864_card__UNIV__unit,axiom,
% 0.35/0.68      ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 0.35/0.68      = one_one_nat ) ).
% 0.35/0.68  
% 0.35/0.68  % card_UNIV_unit
% 0.35/0.68  thf(fact_9865_card__UNIV__bool,axiom,
% 0.35/0.68      ( ( finite_card_o @ top_top_set_o )
% 0.35/0.68      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % card_UNIV_bool
% 0.35/0.68  thf(fact_9866_range__mult,axiom,
% 0.35/0.68      ! [A: real] :
% 0.35/0.68        ( ( ( A = zero_zero_real )
% 0.35/0.68         => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 0.35/0.68            = ( insert_real @ zero_zero_real @ bot_bot_set_real ) ) )
% 0.35/0.68        & ( ( A != zero_zero_real )
% 0.35/0.68         => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 0.35/0.68            = top_top_set_real ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % range_mult
% 0.35/0.68  thf(fact_9867_root__def,axiom,
% 0.35/0.68      ( root
% 0.35/0.68      = ( ^ [N2: nat,X2: real] :
% 0.35/0.68            ( if_real @ ( N2 = zero_zero_nat ) @ zero_zero_real
% 0.35/0.68            @ ( the_in5290026491893676941l_real @ top_top_set_real
% 0.35/0.68              @ ^ [Y: real] : ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N2 ) )
% 0.35/0.68              @ X2 ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % root_def
% 0.35/0.68  thf(fact_9868_inf__enat__def,axiom,
% 0.35/0.68      inf_in1870772243966228564d_enat = ord_mi8085742599997312461d_enat ).
% 0.35/0.68  
% 0.35/0.68  % inf_enat_def
% 0.35/0.68  thf(fact_9869_inf__nat__def,axiom,
% 0.35/0.68      inf_inf_nat = ord_min_nat ).
% 0.35/0.68  
% 0.35/0.68  % inf_nat_def
% 0.35/0.68  thf(fact_9870_card__UNIV__char,axiom,
% 0.35/0.68      ( ( finite_card_char @ top_top_set_char )
% 0.35/0.68      = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % card_UNIV_char
% 0.35/0.68  thf(fact_9871_UNIV__char__of__nat,axiom,
% 0.35/0.68      ( top_top_set_char
% 0.35/0.68      = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % UNIV_char_of_nat
% 0.35/0.68  thf(fact_9872_sorted__list__of__set__lessThan__Suc,axiom,
% 0.35/0.68      ! [K: nat] :
% 0.35/0.68        ( ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ ( suc @ K ) ) )
% 0.35/0.68        = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ K ) ) @ ( cons_nat @ K @ nil_nat ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % sorted_list_of_set_lessThan_Suc
% 0.35/0.68  thf(fact_9873_sorted__list__of__set__atMost__Suc,axiom,
% 0.35/0.68      ! [K: nat] :
% 0.35/0.68        ( ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ ( suc @ K ) ) )
% 0.35/0.68        = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ K ) ) @ ( cons_nat @ ( suc @ K ) @ nil_nat ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % sorted_list_of_set_atMost_Suc
% 0.35/0.68  thf(fact_9874_nat__of__char__less__256,axiom,
% 0.35/0.68      ! [C: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % nat_of_char_less_256
% 0.35/0.68  thf(fact_9875_range__nat__of__char,axiom,
% 0.35/0.68      ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 0.35/0.68      = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % range_nat_of_char
% 0.35/0.68  thf(fact_9876_integer__of__char__code,axiom,
% 0.35/0.68      ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B72: $o] :
% 0.35/0.68        ( ( integer_of_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B72 ) )
% 0.35/0.68        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ B72 ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B62 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B52 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B42 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B32 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B22 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B1 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B0 ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % integer_of_char_code
% 0.35/0.68  thf(fact_9877_list__encode_Oelims,axiom,
% 0.35/0.68      ! [X: list_nat,Y2: nat] :
% 0.35/0.68        ( ( ( nat_list_encode @ X )
% 0.35/0.68          = Y2 )
% 0.35/0.68       => ( ( ( X = nil_nat )
% 0.35/0.68           => ( Y2 != zero_zero_nat ) )
% 0.35/0.68         => ~ ! [X3: nat,Xs3: list_nat] :
% 0.35/0.68                ( ( X
% 0.35/0.68                  = ( cons_nat @ X3 @ Xs3 ) )
% 0.35/0.68               => ( Y2
% 0.35/0.68                 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X3 @ ( nat_list_encode @ Xs3 ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % list_encode.elims
% 0.35/0.68  thf(fact_9878_list__encode_Osimps_I2_J,axiom,
% 0.35/0.68      ! [X: nat,Xs2: list_nat] :
% 0.35/0.68        ( ( nat_list_encode @ ( cons_nat @ X @ Xs2 ) )
% 0.35/0.68        = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X @ ( nat_list_encode @ Xs2 ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % list_encode.simps(2)
% 0.35/0.68  thf(fact_9879_String_Ochar__of__ascii__of,axiom,
% 0.35/0.68      ! [C: char] :
% 0.35/0.68        ( ( comm_s629917340098488124ar_nat @ ( ascii_of @ C ) )
% 0.35/0.68        = ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( comm_s629917340098488124ar_nat @ C ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % String.char_of_ascii_of
% 0.35/0.68  thf(fact_9880_upto__rec__numeral_I4_J,axiom,
% 0.35/0.68      ! [M: num,N: num] :
% 0.35/0.68        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.68         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.68            = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 0.35/0.68        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.68         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.68            = nil_int ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % upto_rec_numeral(4)
% 0.35/0.68  thf(fact_9881_length__upto,axiom,
% 0.35/0.68      ! [I2: int,J: int] :
% 0.35/0.68        ( ( size_size_list_int @ ( upto @ I2 @ J ) )
% 0.35/0.68        = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J @ I2 ) @ one_one_int ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % length_upto
% 0.35/0.68  thf(fact_9882_upto__rec__numeral_I1_J,axiom,
% 0.35/0.68      ! [M: num,N: num] :
% 0.35/0.68        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.35/0.68         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.35/0.68            = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 0.35/0.68        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.35/0.68         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.35/0.68            = nil_int ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % upto_rec_numeral(1)
% 0.35/0.68  thf(fact_9883_upto__rec__numeral_I2_J,axiom,
% 0.35/0.68      ! [M: num,N: num] :
% 0.35/0.68        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.68         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.68            = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 0.35/0.68        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.68         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.68            = nil_int ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % upto_rec_numeral(2)
% 0.35/0.68  thf(fact_9884_upto__rec__numeral_I3_J,axiom,
% 0.35/0.68      ! [M: num,N: num] :
% 0.35/0.68        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.35/0.68         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.35/0.68            = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 0.35/0.68        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.35/0.68         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.35/0.68            = nil_int ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % upto_rec_numeral(3)
% 0.35/0.68  thf(fact_9885_upto__split1,axiom,
% 0.35/0.68      ! [I2: int,J: int,K: int] :
% 0.35/0.68        ( ( ord_less_eq_int @ I2 @ J )
% 0.35/0.68       => ( ( ord_less_eq_int @ J @ K )
% 0.35/0.68         => ( ( upto @ I2 @ K )
% 0.35/0.68            = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % upto_split1
% 0.35/0.68  thf(fact_9886_atLeastLessThan__upto,axiom,
% 0.35/0.68      ( set_or4662586982721622107an_int
% 0.35/0.68      = ( ^ [I3: int,J3: int] : ( set_int2 @ ( upto @ I3 @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % atLeastLessThan_upto
% 0.35/0.68  thf(fact_9887_upto__rec2,axiom,
% 0.35/0.68      ! [I2: int,J: int] :
% 0.35/0.68        ( ( ord_less_eq_int @ I2 @ J )
% 0.35/0.68       => ( ( upto @ I2 @ J )
% 0.35/0.68          = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % upto_rec2
% 0.35/0.68  thf(fact_9888_greaterThanLessThan__upto,axiom,
% 0.35/0.68      ( set_or5832277885323065728an_int
% 0.35/0.68      = ( ^ [I3: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % greaterThanLessThan_upto
% 0.35/0.68  thf(fact_9889_upto__split3,axiom,
% 0.35/0.68      ! [I2: int,J: int,K: int] :
% 0.35/0.68        ( ( ord_less_eq_int @ I2 @ J )
% 0.35/0.68       => ( ( ord_less_eq_int @ J @ K )
% 0.35/0.68         => ( ( upto @ I2 @ K )
% 0.35/0.68            = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % upto_split3
% 0.35/0.68  thf(fact_9890_DERIV__real__root__generic,axiom,
% 0.35/0.68      ! [N: nat,X: real,D4: real] :
% 0.35/0.68        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68       => ( ( X != zero_zero_real )
% 0.35/0.68         => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.68             => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.68               => ( D4
% 0.35/0.68                  = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) )
% 0.35/0.68           => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.68               => ( ( ord_less_real @ X @ zero_zero_real )
% 0.35/0.68                 => ( D4
% 0.35/0.68                    = ( uminus_uminus_real @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ) )
% 0.35/0.68             => ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.68                 => ( D4
% 0.35/0.68                    = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) )
% 0.35/0.68               => ( has_fi5821293074295781190e_real @ ( root @ N ) @ D4 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % DERIV_real_root_generic
% 0.35/0.68  thf(fact_9891_DERIV__pos__imp__increasing,axiom,
% 0.35/0.68      ! [A: real,B: real,F: real > real] :
% 0.35/0.68        ( ( ord_less_real @ A @ B )
% 0.35/0.68       => ( ! [X3: real] :
% 0.35/0.68              ( ( ord_less_eq_real @ A @ X3 )
% 0.35/0.68             => ( ( ord_less_eq_real @ X3 @ B )
% 0.35/0.68               => ? [Y4: real] :
% 0.35/0.68                    ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.35/0.68                    & ( ord_less_real @ zero_zero_real @ Y4 ) ) ) )
% 0.35/0.68         => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % DERIV_pos_imp_increasing
% 0.35/0.68  thf(fact_9892_DERIV__neg__imp__decreasing,axiom,
% 0.35/0.68      ! [A: real,B: real,F: real > real] :
% 0.35/0.68        ( ( ord_less_real @ A @ B )
% 0.35/0.68       => ( ! [X3: real] :
% 0.35/0.68              ( ( ord_less_eq_real @ A @ X3 )
% 0.35/0.68             => ( ( ord_less_eq_real @ X3 @ B )
% 0.35/0.68               => ? [Y4: real] :
% 0.35/0.68                    ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.35/0.68                    & ( ord_less_real @ Y4 @ zero_zero_real ) ) ) )
% 0.35/0.68         => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % DERIV_neg_imp_decreasing
% 0.35/0.68  thf(fact_9893_deriv__nonneg__imp__mono,axiom,
% 0.35/0.68      ! [A: real,B: real,G: real > real,G2: real > real] :
% 0.35/0.68        ( ! [X3: real] :
% 0.35/0.68            ( ( member_real @ X3 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 0.35/0.68           => ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 0.35/0.68       => ( ! [X3: real] :
% 0.35/0.68              ( ( member_real @ X3 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 0.35/0.68             => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X3 ) ) )
% 0.35/0.68         => ( ( ord_less_eq_real @ A @ B )
% 0.35/0.68           => ( ord_less_eq_real @ ( G @ A ) @ ( G @ B ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % deriv_nonneg_imp_mono
% 0.35/0.68  thf(fact_9894_DERIV__nonneg__imp__nondecreasing,axiom,
% 0.35/0.68      ! [A: real,B: real,F: real > real] :
% 0.35/0.68        ( ( ord_less_eq_real @ A @ B )
% 0.35/0.68       => ( ! [X3: real] :
% 0.35/0.68              ( ( ord_less_eq_real @ A @ X3 )
% 0.35/0.68             => ( ( ord_less_eq_real @ X3 @ B )
% 0.35/0.68               => ? [Y4: real] :
% 0.35/0.68                    ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.35/0.68                    & ( ord_less_eq_real @ zero_zero_real @ Y4 ) ) ) )
% 0.35/0.68         => ( ord_less_eq_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % DERIV_nonneg_imp_nondecreasing
% 0.35/0.68  thf(fact_9895_DERIV__nonpos__imp__nonincreasing,axiom,
% 0.35/0.68      ! [A: real,B: real,F: real > real] :
% 0.35/0.68        ( ( ord_less_eq_real @ A @ B )
% 0.35/0.68       => ( ! [X3: real] :
% 0.35/0.68              ( ( ord_less_eq_real @ A @ X3 )
% 0.35/0.68             => ( ( ord_less_eq_real @ X3 @ B )
% 0.35/0.68               => ? [Y4: real] :
% 0.35/0.68                    ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.35/0.68                    & ( ord_less_eq_real @ Y4 @ zero_zero_real ) ) ) )
% 0.35/0.68         => ( ord_less_eq_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % DERIV_nonpos_imp_nonincreasing
% 0.35/0.68  thf(fact_9896_DERIV__pos__inc__left,axiom,
% 0.35/0.68      ! [F: real > real,L2: real,X: real] :
% 0.35/0.68        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.35/0.68       => ( ( ord_less_real @ zero_zero_real @ L2 )
% 0.35/0.68         => ? [D3: real] :
% 0.35/0.68              ( ( ord_less_real @ zero_zero_real @ D3 )
% 0.35/0.68              & ! [H4: real] :
% 0.35/0.68                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.35/0.68                 => ( ( ord_less_real @ H4 @ D3 )
% 0.35/0.68                   => ( ord_less_real @ ( F @ ( minus_minus_real @ X @ H4 ) ) @ ( F @ X ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % DERIV_pos_inc_left
% 0.35/0.68  thf(fact_9897_DERIV__neg__dec__left,axiom,
% 0.35/0.68      ! [F: real > real,L2: real,X: real] :
% 0.35/0.68        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.35/0.68       => ( ( ord_less_real @ L2 @ zero_zero_real )
% 0.35/0.68         => ? [D3: real] :
% 0.35/0.68              ( ( ord_less_real @ zero_zero_real @ D3 )
% 0.35/0.68              & ! [H4: real] :
% 0.35/0.68                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.35/0.68                 => ( ( ord_less_real @ H4 @ D3 )
% 0.35/0.68                   => ( ord_less_real @ ( F @ X ) @ ( F @ ( minus_minus_real @ X @ H4 ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % DERIV_neg_dec_left
% 0.35/0.68  thf(fact_9898_DERIV__pos__inc__right,axiom,
% 0.35/0.68      ! [F: real > real,L2: real,X: real] :
% 0.35/0.68        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.35/0.68       => ( ( ord_less_real @ zero_zero_real @ L2 )
% 0.35/0.68         => ? [D3: real] :
% 0.35/0.68              ( ( ord_less_real @ zero_zero_real @ D3 )
% 0.35/0.68              & ! [H4: real] :
% 0.35/0.68                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.35/0.68                 => ( ( ord_less_real @ H4 @ D3 )
% 0.35/0.68                   => ( ord_less_real @ ( F @ X ) @ ( F @ ( plus_plus_real @ X @ H4 ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % DERIV_pos_inc_right
% 0.35/0.68  thf(fact_9899_DERIV__neg__dec__right,axiom,
% 0.35/0.68      ! [F: real > real,L2: real,X: real] :
% 0.35/0.68        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.35/0.68       => ( ( ord_less_real @ L2 @ zero_zero_real )
% 0.35/0.68         => ? [D3: real] :
% 0.35/0.68              ( ( ord_less_real @ zero_zero_real @ D3 )
% 0.35/0.68              & ! [H4: real] :
% 0.35/0.68                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.35/0.68                 => ( ( ord_less_real @ H4 @ D3 )
% 0.35/0.68                   => ( ord_less_real @ ( F @ ( plus_plus_real @ X @ H4 ) ) @ ( F @ X ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % DERIV_neg_dec_right
% 0.35/0.68  thf(fact_9900_DERIV__const__ratio__const,axiom,
% 0.35/0.68      ! [A: real,B: real,F: real > real,K: real] :
% 0.35/0.68        ( ( A != B )
% 0.35/0.68       => ( ! [X3: real] : ( has_fi5821293074295781190e_real @ F @ K @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.35/0.68         => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 0.35/0.68            = ( times_times_real @ ( minus_minus_real @ B @ A ) @ K ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % DERIV_const_ratio_const
% 0.35/0.68  thf(fact_9901_DERIV__const__ratio__const2,axiom,
% 0.35/0.68      ! [A: real,B: real,F: real > real,K: real] :
% 0.35/0.68        ( ( A != B )
% 0.35/0.68       => ( ! [X3: real] : ( has_fi5821293074295781190e_real @ F @ K @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.35/0.68         => ( ( divide_divide_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( minus_minus_real @ B @ A ) )
% 0.35/0.68            = K ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % DERIV_const_ratio_const2
% 0.35/0.68  thf(fact_9902_DERIV__isconst3,axiom,
% 0.35/0.68      ! [A: real,B: real,X: real,Y2: real,F: real > real] :
% 0.35/0.68        ( ( ord_less_real @ A @ B )
% 0.35/0.68       => ( ( member_real @ X @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.35/0.68         => ( ( member_real @ Y2 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.35/0.68           => ( ! [X3: real] :
% 0.35/0.68                  ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.35/0.68                 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 0.35/0.68             => ( ( F @ X )
% 0.35/0.68                = ( F @ Y2 ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % DERIV_isconst3
% 0.35/0.68  thf(fact_9903_has__real__derivative__pos__inc__left,axiom,
% 0.35/0.68      ! [F: real > real,L2: real,X: real,S2: set_real] :
% 0.35/0.68        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ S2 ) )
% 0.35/0.68       => ( ( ord_less_real @ zero_zero_real @ L2 )
% 0.35/0.68         => ? [D3: real] :
% 0.35/0.68              ( ( ord_less_real @ zero_zero_real @ D3 )
% 0.35/0.68              & ! [H4: real] :
% 0.35/0.68                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.35/0.68                 => ( ( member_real @ ( minus_minus_real @ X @ H4 ) @ S2 )
% 0.35/0.68                   => ( ( ord_less_real @ H4 @ D3 )
% 0.35/0.68                     => ( ord_less_real @ ( F @ ( minus_minus_real @ X @ H4 ) ) @ ( F @ X ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % has_real_derivative_pos_inc_left
% 0.35/0.68  thf(fact_9904_has__real__derivative__neg__dec__left,axiom,
% 0.35/0.68      ! [F: real > real,L2: real,X: real,S2: set_real] :
% 0.35/0.68        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ S2 ) )
% 0.35/0.68       => ( ( ord_less_real @ L2 @ zero_zero_real )
% 0.35/0.68         => ? [D3: real] :
% 0.35/0.68              ( ( ord_less_real @ zero_zero_real @ D3 )
% 0.35/0.68              & ! [H4: real] :
% 0.35/0.68                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.35/0.68                 => ( ( member_real @ ( minus_minus_real @ X @ H4 ) @ S2 )
% 0.35/0.68                   => ( ( ord_less_real @ H4 @ D3 )
% 0.35/0.68                     => ( ord_less_real @ ( F @ X ) @ ( F @ ( minus_minus_real @ X @ H4 ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % has_real_derivative_neg_dec_left
% 0.35/0.68  thf(fact_9905_has__real__derivative__neg__dec__right,axiom,
% 0.35/0.68      ! [F: real > real,L2: real,X: real,S2: set_real] :
% 0.35/0.68        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ S2 ) )
% 0.35/0.68       => ( ( ord_less_real @ L2 @ zero_zero_real )
% 0.35/0.68         => ? [D3: real] :
% 0.35/0.68              ( ( ord_less_real @ zero_zero_real @ D3 )
% 0.35/0.68              & ! [H4: real] :
% 0.35/0.68                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.35/0.68                 => ( ( member_real @ ( plus_plus_real @ X @ H4 ) @ S2 )
% 0.35/0.68                   => ( ( ord_less_real @ H4 @ D3 )
% 0.35/0.68                     => ( ord_less_real @ ( F @ ( plus_plus_real @ X @ H4 ) ) @ ( F @ X ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % has_real_derivative_neg_dec_right
% 0.35/0.68  thf(fact_9906_has__real__derivative__pos__inc__right,axiom,
% 0.35/0.68      ! [F: real > real,L2: real,X: real,S2: set_real] :
% 0.35/0.68        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ S2 ) )
% 0.35/0.68       => ( ( ord_less_real @ zero_zero_real @ L2 )
% 0.35/0.68         => ? [D3: real] :
% 0.35/0.68              ( ( ord_less_real @ zero_zero_real @ D3 )
% 0.35/0.68              & ! [H4: real] :
% 0.35/0.68                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.35/0.68                 => ( ( member_real @ ( plus_plus_real @ X @ H4 ) @ S2 )
% 0.35/0.68                   => ( ( ord_less_real @ H4 @ D3 )
% 0.35/0.68                     => ( ord_less_real @ ( F @ X ) @ ( F @ ( plus_plus_real @ X @ H4 ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % has_real_derivative_pos_inc_right
% 0.35/0.68  thf(fact_9907_MVT2,axiom,
% 0.35/0.68      ! [A: real,B: real,F: real > real,F4: real > real] :
% 0.35/0.68        ( ( ord_less_real @ A @ B )
% 0.35/0.68       => ( ! [X3: real] :
% 0.35/0.68              ( ( ord_less_eq_real @ A @ X3 )
% 0.35/0.68             => ( ( ord_less_eq_real @ X3 @ B )
% 0.35/0.68               => ( has_fi5821293074295781190e_real @ F @ ( F4 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 0.35/0.68         => ? [Z3: real] :
% 0.35/0.68              ( ( ord_less_real @ A @ Z3 )
% 0.35/0.68              & ( ord_less_real @ Z3 @ B )
% 0.35/0.68              & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 0.35/0.68                = ( times_times_real @ ( minus_minus_real @ B @ A ) @ ( F4 @ Z3 ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % MVT2
% 0.35/0.68  thf(fact_9908_DERIV__local__const,axiom,
% 0.35/0.68      ! [F: real > real,L2: real,X: real,D2: real] :
% 0.35/0.68        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.35/0.68       => ( ( ord_less_real @ zero_zero_real @ D2 )
% 0.35/0.68         => ( ! [Y3: real] :
% 0.35/0.68                ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y3 ) ) @ D2 )
% 0.35/0.68               => ( ( F @ X )
% 0.35/0.68                  = ( F @ Y3 ) ) )
% 0.35/0.68           => ( L2 = zero_zero_real ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % DERIV_local_const
% 0.35/0.68  thf(fact_9909_DERIV__ln,axiom,
% 0.35/0.68      ! [X: real] :
% 0.35/0.68        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.68       => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( inverse_inverse_real @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % DERIV_ln
% 0.35/0.68  thf(fact_9910_DERIV__const__average,axiom,
% 0.35/0.68      ! [A: real,B: real,V: real > real,K: real] :
% 0.35/0.68        ( ( A != B )
% 0.35/0.68       => ( ! [X3: real] : ( has_fi5821293074295781190e_real @ V @ K @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.35/0.68         => ( ( V @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.68            = ( divide_divide_real @ ( plus_plus_real @ ( V @ A ) @ ( V @ B ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % DERIV_const_average
% 0.35/0.68  thf(fact_9911_DERIV__local__min,axiom,
% 0.35/0.68      ! [F: real > real,L2: real,X: real,D2: real] :
% 0.35/0.68        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.35/0.68       => ( ( ord_less_real @ zero_zero_real @ D2 )
% 0.35/0.68         => ( ! [Y3: real] :
% 0.35/0.68                ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y3 ) ) @ D2 )
% 0.35/0.68               => ( ord_less_eq_real @ ( F @ X ) @ ( F @ Y3 ) ) )
% 0.35/0.68           => ( L2 = zero_zero_real ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % DERIV_local_min
% 0.35/0.68  thf(fact_9912_DERIV__local__max,axiom,
% 0.35/0.68      ! [F: real > real,L2: real,X: real,D2: real] :
% 0.35/0.68        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.35/0.68       => ( ( ord_less_real @ zero_zero_real @ D2 )
% 0.35/0.68         => ( ! [Y3: real] :
% 0.35/0.68                ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y3 ) ) @ D2 )
% 0.35/0.68               => ( ord_less_eq_real @ ( F @ Y3 ) @ ( F @ X ) ) )
% 0.35/0.68           => ( L2 = zero_zero_real ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % DERIV_local_max
% 0.35/0.68  thf(fact_9913_DERIV__ln__divide,axiom,
% 0.35/0.68      ! [X: real] :
% 0.35/0.68        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.68       => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( divide_divide_real @ one_one_real @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % DERIV_ln_divide
% 0.35/0.68  thf(fact_9914_DERIV__pow,axiom,
% 0.35/0.68      ! [N: nat,X: real,S3: set_real] :
% 0.35/0.68        ( has_fi5821293074295781190e_real
% 0.35/0.68        @ ^ [X2: real] : ( power_power_real @ X2 @ N )
% 0.35/0.68        @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ X @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 0.35/0.68        @ ( topolo2177554685111907308n_real @ X @ S3 ) ) ).
% 0.35/0.68  
% 0.35/0.68  % DERIV_pow
% 0.35/0.68  thf(fact_9915_DERIV__fun__pow,axiom,
% 0.35/0.68      ! [G: real > real,M: real,X: real,N: nat] :
% 0.35/0.68        ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.35/0.68       => ( has_fi5821293074295781190e_real
% 0.35/0.68          @ ^ [X2: real] : ( power_power_real @ ( G @ X2 ) @ N )
% 0.35/0.68          @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( G @ X ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) @ M )
% 0.35/0.68          @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % DERIV_fun_pow
% 0.35/0.68  thf(fact_9916_has__real__derivative__powr,axiom,
% 0.35/0.68      ! [Z: real,R: real] :
% 0.35/0.68        ( ( ord_less_real @ zero_zero_real @ Z )
% 0.35/0.68       => ( has_fi5821293074295781190e_real
% 0.35/0.68          @ ^ [Z4: real] : ( powr_real @ Z4 @ R )
% 0.35/0.68          @ ( times_times_real @ R @ ( powr_real @ Z @ ( minus_minus_real @ R @ one_one_real ) ) )
% 0.35/0.68          @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % has_real_derivative_powr
% 0.35/0.68  thf(fact_9917_DERIV__fun__powr,axiom,
% 0.35/0.68      ! [G: real > real,M: real,X: real,R: real] :
% 0.35/0.68        ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.35/0.68       => ( ( ord_less_real @ zero_zero_real @ ( G @ X ) )
% 0.35/0.68         => ( has_fi5821293074295781190e_real
% 0.35/0.68            @ ^ [X2: real] : ( powr_real @ ( G @ X2 ) @ R )
% 0.35/0.68            @ ( times_times_real @ ( times_times_real @ R @ ( powr_real @ ( G @ X ) @ ( minus_minus_real @ R @ ( semiri5074537144036343181t_real @ one_one_nat ) ) ) ) @ M )
% 0.35/0.68            @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % DERIV_fun_powr
% 0.35/0.68  thf(fact_9918_DERIV__log,axiom,
% 0.35/0.68      ! [X: real,B: real] :
% 0.35/0.68        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.68       => ( has_fi5821293074295781190e_real @ ( log @ B ) @ ( divide_divide_real @ one_one_real @ ( times_times_real @ ( ln_ln_real @ B ) @ X ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % DERIV_log
% 0.35/0.68  thf(fact_9919_DERIV__powr,axiom,
% 0.35/0.68      ! [G: real > real,M: real,X: real,F: real > real,R: real] :
% 0.35/0.68        ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.35/0.68       => ( ( ord_less_real @ zero_zero_real @ ( G @ X ) )
% 0.35/0.68         => ( ( has_fi5821293074295781190e_real @ F @ R @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.35/0.68           => ( has_fi5821293074295781190e_real
% 0.35/0.68              @ ^ [X2: real] : ( powr_real @ ( G @ X2 ) @ ( F @ X2 ) )
% 0.35/0.68              @ ( times_times_real @ ( powr_real @ ( G @ X ) @ ( F @ X ) ) @ ( plus_plus_real @ ( times_times_real @ R @ ( ln_ln_real @ ( G @ X ) ) ) @ ( divide_divide_real @ ( times_times_real @ M @ ( F @ X ) ) @ ( G @ X ) ) ) )
% 0.35/0.68              @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % DERIV_powr
% 0.35/0.68  thf(fact_9920_DERIV__real__sqrt,axiom,
% 0.35/0.68      ! [X: real] :
% 0.35/0.68        ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.68       => ( has_fi5821293074295781190e_real @ sqrt @ ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % DERIV_real_sqrt
% 0.35/0.68  thf(fact_9921_DERIV__arctan,axiom,
% 0.35/0.68      ! [X: real] : ( has_fi5821293074295781190e_real @ arctan @ ( inverse_inverse_real @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ).
% 0.35/0.68  
% 0.35/0.68  % DERIV_arctan
% 0.35/0.68  thf(fact_9922_DERIV__series_H,axiom,
% 0.35/0.68      ! [F: real > nat > real,F4: real > nat > real,X0: real,A: real,B: real,L5: nat > real] :
% 0.35/0.68        ( ! [N3: nat] :
% 0.35/0.68            ( has_fi5821293074295781190e_real
% 0.35/0.68            @ ^ [X2: real] : ( F @ X2 @ N3 )
% 0.35/0.68            @ ( F4 @ X0 @ N3 )
% 0.35/0.68            @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) )
% 0.35/0.68       => ( ! [X3: real] :
% 0.35/0.68              ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.35/0.68             => ( summable_real @ ( F @ X3 ) ) )
% 0.35/0.68         => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.35/0.68           => ( ( summable_real @ ( F4 @ X0 ) )
% 0.35/0.68             => ( ( summable_real @ L5 )
% 0.35/0.68               => ( ! [N3: nat,X3: real,Y3: real] :
% 0.35/0.68                      ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.35/0.68                     => ( ( member_real @ Y3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.35/0.68                       => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( F @ X3 @ N3 ) @ ( F @ Y3 @ N3 ) ) ) @ ( times_times_real @ ( L5 @ N3 ) @ ( abs_abs_real @ ( minus_minus_real @ X3 @ Y3 ) ) ) ) ) )
% 0.35/0.68                 => ( has_fi5821293074295781190e_real
% 0.35/0.68                    @ ^ [X2: real] : ( suminf_real @ ( F @ X2 ) )
% 0.35/0.68                    @ ( suminf_real @ ( F4 @ X0 ) )
% 0.35/0.68                    @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % DERIV_series'
% 0.35/0.68  thf(fact_9923_arsinh__real__has__field__derivative,axiom,
% 0.35/0.68      ! [X: real,A2: set_real] : ( has_fi5821293074295781190e_real @ arsinh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X @ A2 ) ) ).
% 0.35/0.68  
% 0.35/0.68  % arsinh_real_has_field_derivative
% 0.35/0.68  thf(fact_9924_DERIV__real__sqrt__generic,axiom,
% 0.35/0.68      ! [X: real,D4: real] :
% 0.35/0.68        ( ( X != zero_zero_real )
% 0.35/0.68       => ( ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.68           => ( D4
% 0.35/0.68              = ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.35/0.68         => ( ( ( ord_less_real @ X @ zero_zero_real )
% 0.35/0.68             => ( D4
% 0.35/0.68                = ( divide_divide_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.35/0.68           => ( has_fi5821293074295781190e_real @ sqrt @ D4 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % DERIV_real_sqrt_generic
% 0.35/0.68  thf(fact_9925_arcosh__real__has__field__derivative,axiom,
% 0.35/0.68      ! [X: real,A2: set_real] :
% 0.35/0.68        ( ( ord_less_real @ one_one_real @ X )
% 0.35/0.68       => ( has_fi5821293074295781190e_real @ arcosh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X @ A2 ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % arcosh_real_has_field_derivative
% 0.35/0.68  thf(fact_9926_artanh__real__has__field__derivative,axiom,
% 0.35/0.68      ! [X: real,A2: set_real] :
% 0.35/0.68        ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.35/0.68       => ( has_fi5821293074295781190e_real @ artanh_real @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ A2 ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % artanh_real_has_field_derivative
% 0.35/0.68  thf(fact_9927_DERIV__power__series_H,axiom,
% 0.35/0.68      ! [R2: real,F: nat > real,X0: real] :
% 0.35/0.68        ( ! [X3: real] :
% 0.35/0.68            ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R2 ) @ R2 ) )
% 0.35/0.68           => ( summable_real
% 0.35/0.68              @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( F @ N2 ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) @ ( power_power_real @ X3 @ N2 ) ) ) )
% 0.35/0.68       => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R2 ) @ R2 ) )
% 0.35/0.68         => ( ( ord_less_real @ zero_zero_real @ R2 )
% 0.35/0.68           => ( has_fi5821293074295781190e_real
% 0.35/0.68              @ ^ [X2: real] :
% 0.35/0.68                  ( suminf_real
% 0.35/0.68                  @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ X2 @ ( suc @ N2 ) ) ) )
% 0.35/0.68              @ ( suminf_real
% 0.35/0.68                @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( F @ N2 ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) @ ( power_power_real @ X0 @ N2 ) ) )
% 0.35/0.68              @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % DERIV_power_series'
% 0.35/0.68  thf(fact_9928_DERIV__real__root,axiom,
% 0.35/0.68      ! [N: nat,X: real] :
% 0.35/0.68        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.68         => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % DERIV_real_root
% 0.35/0.68  thf(fact_9929_DERIV__arccos,axiom,
% 0.35/0.68      ! [X: real] :
% 0.35/0.68        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.35/0.68       => ( ( ord_less_real @ X @ one_one_real )
% 0.35/0.68         => ( has_fi5821293074295781190e_real @ arccos @ ( inverse_inverse_real @ ( uminus_uminus_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % DERIV_arccos
% 0.35/0.68  thf(fact_9930_DERIV__arcsin,axiom,
% 0.35/0.68      ! [X: real] :
% 0.35/0.68        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.35/0.68       => ( ( ord_less_real @ X @ one_one_real )
% 0.35/0.68         => ( has_fi5821293074295781190e_real @ arcsin @ ( inverse_inverse_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % DERIV_arcsin
% 0.35/0.68  thf(fact_9931_Maclaurin__all__le,axiom,
% 0.35/0.68      ! [Diff: nat > real > real,F: real > real,X: real,N: nat] :
% 0.35/0.68        ( ( ( Diff @ zero_zero_nat )
% 0.35/0.68          = F )
% 0.35/0.68       => ( ! [M4: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.35/0.68         => ? [T6: real] :
% 0.35/0.68              ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 0.35/0.68              & ( ( F @ X )
% 0.35/0.68                = ( plus_plus_real
% 0.35/0.68                  @ ( groups6591440286371151544t_real
% 0.35/0.68                    @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 0.35/0.68                    @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.68                  @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Maclaurin_all_le
% 0.35/0.68  thf(fact_9932_Maclaurin__all__le__objl,axiom,
% 0.35/0.68      ! [Diff: nat > real > real,F: real > real,X: real,N: nat] :
% 0.35/0.68        ( ( ( ( Diff @ zero_zero_nat )
% 0.35/0.68            = F )
% 0.35/0.68          & ! [M4: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 0.35/0.68       => ? [T6: real] :
% 0.35/0.68            ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 0.35/0.68            & ( ( F @ X )
% 0.35/0.68              = ( plus_plus_real
% 0.35/0.68                @ ( groups6591440286371151544t_real
% 0.35/0.68                  @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 0.35/0.68                  @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.68                @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Maclaurin_all_le_objl
% 0.35/0.68  thf(fact_9933_DERIV__odd__real__root,axiom,
% 0.35/0.68      ! [N: nat,X: real] :
% 0.35/0.68        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.68       => ( ( X != zero_zero_real )
% 0.35/0.68         => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % DERIV_odd_real_root
% 0.35/0.68  thf(fact_9934_Maclaurin__minus,axiom,
% 0.35/0.68      ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 0.35/0.68        ( ( ord_less_real @ H2 @ zero_zero_real )
% 0.35/0.68       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68         => ( ( ( Diff @ zero_zero_nat )
% 0.35/0.68              = F )
% 0.35/0.68           => ( ! [M4: nat,T6: real] :
% 0.35/0.68                  ( ( ( ord_less_nat @ M4 @ N )
% 0.35/0.68                    & ( ord_less_eq_real @ H2 @ T6 )
% 0.35/0.68                    & ( ord_less_eq_real @ T6 @ zero_zero_real ) )
% 0.35/0.68                 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.35/0.68             => ? [T6: real] :
% 0.35/0.68                  ( ( ord_less_real @ H2 @ T6 )
% 0.35/0.68                  & ( ord_less_real @ T6 @ zero_zero_real )
% 0.35/0.68                  & ( ( F @ H2 )
% 0.35/0.68                    = ( plus_plus_real
% 0.35/0.68                      @ ( groups6591440286371151544t_real
% 0.35/0.68                        @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 0.35/0.68                        @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.68                      @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Maclaurin_minus
% 0.35/0.68  thf(fact_9935_Maclaurin2,axiom,
% 0.35/0.68      ! [H2: real,Diff: nat > real > real,F: real > real,N: nat] :
% 0.35/0.68        ( ( ord_less_real @ zero_zero_real @ H2 )
% 0.35/0.68       => ( ( ( Diff @ zero_zero_nat )
% 0.35/0.68            = F )
% 0.35/0.68         => ( ! [M4: nat,T6: real] :
% 0.35/0.68                ( ( ( ord_less_nat @ M4 @ N )
% 0.35/0.68                  & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 0.35/0.68                  & ( ord_less_eq_real @ T6 @ H2 ) )
% 0.35/0.68               => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.35/0.68           => ? [T6: real] :
% 0.35/0.68                ( ( ord_less_real @ zero_zero_real @ T6 )
% 0.35/0.68                & ( ord_less_eq_real @ T6 @ H2 )
% 0.35/0.68                & ( ( F @ H2 )
% 0.35/0.68                  = ( plus_plus_real
% 0.35/0.68                    @ ( groups6591440286371151544t_real
% 0.35/0.68                      @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 0.35/0.68                      @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.68                    @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Maclaurin2
% 0.35/0.68  thf(fact_9936_Maclaurin,axiom,
% 0.35/0.68      ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 0.35/0.68        ( ( ord_less_real @ zero_zero_real @ H2 )
% 0.35/0.68       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68         => ( ( ( Diff @ zero_zero_nat )
% 0.35/0.68              = F )
% 0.35/0.68           => ( ! [M4: nat,T6: real] :
% 0.35/0.68                  ( ( ( ord_less_nat @ M4 @ N )
% 0.35/0.68                    & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 0.35/0.68                    & ( ord_less_eq_real @ T6 @ H2 ) )
% 0.35/0.68                 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.35/0.68             => ? [T6: real] :
% 0.35/0.68                  ( ( ord_less_real @ zero_zero_real @ T6 )
% 0.35/0.68                  & ( ord_less_real @ T6 @ H2 )
% 0.35/0.68                  & ( ( F @ H2 )
% 0.35/0.68                    = ( plus_plus_real
% 0.35/0.68                      @ ( groups6591440286371151544t_real
% 0.35/0.68                        @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 0.35/0.68                        @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.68                      @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Maclaurin
% 0.35/0.68  thf(fact_9937_Maclaurin__all__lt,axiom,
% 0.35/0.68      ! [Diff: nat > real > real,F: real > real,N: nat,X: real] :
% 0.35/0.68        ( ( ( Diff @ zero_zero_nat )
% 0.35/0.68          = F )
% 0.35/0.68       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68         => ( ( X != zero_zero_real )
% 0.35/0.68           => ( ! [M4: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.35/0.68             => ? [T6: real] :
% 0.35/0.68                  ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T6 ) )
% 0.35/0.68                  & ( ord_less_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 0.35/0.68                  & ( ( F @ X )
% 0.35/0.68                    = ( plus_plus_real
% 0.35/0.68                      @ ( groups6591440286371151544t_real
% 0.35/0.68                        @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 0.35/0.68                        @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.68                      @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Maclaurin_all_lt
% 0.35/0.68  thf(fact_9938_Maclaurin__bi__le,axiom,
% 0.35/0.68      ! [Diff: nat > real > real,F: real > real,N: nat,X: real] :
% 0.35/0.68        ( ( ( Diff @ zero_zero_nat )
% 0.35/0.68          = F )
% 0.35/0.68       => ( ! [M4: nat,T6: real] :
% 0.35/0.68              ( ( ( ord_less_nat @ M4 @ N )
% 0.35/0.68                & ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) ) )
% 0.35/0.68             => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.35/0.68         => ? [T6: real] :
% 0.35/0.68              ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 0.35/0.68              & ( ( F @ X )
% 0.35/0.68                = ( plus_plus_real
% 0.35/0.68                  @ ( groups6591440286371151544t_real
% 0.35/0.68                    @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 0.35/0.68                    @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.68                  @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Maclaurin_bi_le
% 0.35/0.68  thf(fact_9939_Taylor__down,axiom,
% 0.35/0.68      ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 0.35/0.68        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68       => ( ( ( Diff @ zero_zero_nat )
% 0.35/0.68            = F )
% 0.35/0.68         => ( ! [M4: nat,T6: real] :
% 0.35/0.68                ( ( ( ord_less_nat @ M4 @ N )
% 0.35/0.68                  & ( ord_less_eq_real @ A @ T6 )
% 0.35/0.68                  & ( ord_less_eq_real @ T6 @ B ) )
% 0.35/0.68               => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.35/0.68           => ( ( ord_less_real @ A @ C )
% 0.35/0.68             => ( ( ord_less_eq_real @ C @ B )
% 0.35/0.68               => ? [T6: real] :
% 0.35/0.68                    ( ( ord_less_real @ A @ T6 )
% 0.35/0.68                    & ( ord_less_real @ T6 @ C )
% 0.35/0.68                    & ( ( F @ A )
% 0.35/0.68                      = ( plus_plus_real
% 0.35/0.68                        @ ( groups6591440286371151544t_real
% 0.35/0.68                          @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ M6 ) )
% 0.35/0.68                          @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.68                        @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Taylor_down
% 0.35/0.68  thf(fact_9940_Taylor__up,axiom,
% 0.35/0.68      ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 0.35/0.68        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68       => ( ( ( Diff @ zero_zero_nat )
% 0.35/0.68            = F )
% 0.35/0.68         => ( ! [M4: nat,T6: real] :
% 0.35/0.68                ( ( ( ord_less_nat @ M4 @ N )
% 0.35/0.68                  & ( ord_less_eq_real @ A @ T6 )
% 0.35/0.68                  & ( ord_less_eq_real @ T6 @ B ) )
% 0.35/0.68               => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.35/0.68           => ( ( ord_less_eq_real @ A @ C )
% 0.35/0.68             => ( ( ord_less_real @ C @ B )
% 0.35/0.68               => ? [T6: real] :
% 0.35/0.68                    ( ( ord_less_real @ C @ T6 )
% 0.35/0.68                    & ( ord_less_real @ T6 @ B )
% 0.35/0.68                    & ( ( F @ B )
% 0.35/0.68                      = ( plus_plus_real
% 0.35/0.68                        @ ( groups6591440286371151544t_real
% 0.35/0.68                          @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ M6 ) )
% 0.35/0.68                          @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.68                        @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Taylor_up
% 0.35/0.68  thf(fact_9941_Taylor,axiom,
% 0.35/0.68      ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real,X: real] :
% 0.35/0.68        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68       => ( ( ( Diff @ zero_zero_nat )
% 0.35/0.68            = F )
% 0.35/0.68         => ( ! [M4: nat,T6: real] :
% 0.35/0.68                ( ( ( ord_less_nat @ M4 @ N )
% 0.35/0.68                  & ( ord_less_eq_real @ A @ T6 )
% 0.35/0.68                  & ( ord_less_eq_real @ T6 @ B ) )
% 0.35/0.68               => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.35/0.68           => ( ( ord_less_eq_real @ A @ C )
% 0.35/0.68             => ( ( ord_less_eq_real @ C @ B )
% 0.35/0.68               => ( ( ord_less_eq_real @ A @ X )
% 0.35/0.68                 => ( ( ord_less_eq_real @ X @ B )
% 0.35/0.68                   => ( ( X != C )
% 0.35/0.68                     => ? [T6: real] :
% 0.35/0.68                          ( ( ( ord_less_real @ X @ C )
% 0.35/0.68                           => ( ( ord_less_real @ X @ T6 )
% 0.35/0.68                              & ( ord_less_real @ T6 @ C ) ) )
% 0.35/0.68                          & ( ~ ( ord_less_real @ X @ C )
% 0.35/0.68                           => ( ( ord_less_real @ C @ T6 )
% 0.35/0.68                              & ( ord_less_real @ T6 @ X ) ) )
% 0.35/0.68                          & ( ( F @ X )
% 0.35/0.68                            = ( plus_plus_real
% 0.35/0.68                              @ ( groups6591440286371151544t_real
% 0.35/0.68                                @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C ) @ M6 ) )
% 0.35/0.68                                @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.68                              @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C ) @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Taylor
% 0.35/0.68  thf(fact_9942_Maclaurin__lemma2,axiom,
% 0.35/0.68      ! [N: nat,H2: real,Diff: nat > real > real,K: nat,B2: real] :
% 0.35/0.68        ( ! [M4: nat,T6: real] :
% 0.35/0.68            ( ( ( ord_less_nat @ M4 @ N )
% 0.35/0.68              & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 0.35/0.68              & ( ord_less_eq_real @ T6 @ H2 ) )
% 0.35/0.68           => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.35/0.68       => ( ( N
% 0.35/0.68            = ( suc @ K ) )
% 0.35/0.68         => ! [M5: nat,T7: real] :
% 0.35/0.68              ( ( ( ord_less_nat @ M5 @ N )
% 0.35/0.68                & ( ord_less_eq_real @ zero_zero_real @ T7 )
% 0.35/0.68                & ( ord_less_eq_real @ T7 @ H2 ) )
% 0.35/0.68             => ( has_fi5821293074295781190e_real
% 0.35/0.68                @ ^ [U2: real] :
% 0.35/0.68                    ( minus_minus_real @ ( Diff @ M5 @ U2 )
% 0.35/0.68                    @ ( plus_plus_real
% 0.35/0.68                      @ ( groups6591440286371151544t_real
% 0.35/0.68                        @ ^ [P4: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ M5 @ P4 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P4 ) ) @ ( power_power_real @ U2 @ P4 ) )
% 0.35/0.68                        @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ M5 ) ) )
% 0.35/0.68                      @ ( times_times_real @ B2 @ ( divide_divide_real @ ( power_power_real @ U2 @ ( minus_minus_nat @ N @ M5 ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ M5 ) ) ) ) ) )
% 0.35/0.68                @ ( minus_minus_real @ ( Diff @ ( suc @ M5 ) @ T7 )
% 0.35/0.68                  @ ( plus_plus_real
% 0.35/0.68                    @ ( groups6591440286371151544t_real
% 0.35/0.68                      @ ^ [P4: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ ( suc @ M5 ) @ P4 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P4 ) ) @ ( power_power_real @ T7 @ P4 ) )
% 0.35/0.68                      @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ M5 ) ) ) )
% 0.35/0.68                    @ ( times_times_real @ B2 @ ( divide_divide_real @ ( power_power_real @ T7 @ ( minus_minus_nat @ N @ ( suc @ M5 ) ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ ( suc @ M5 ) ) ) ) ) ) )
% 0.35/0.68                @ ( topolo2177554685111907308n_real @ T7 @ top_top_set_real ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % Maclaurin_lemma2
% 0.35/0.68  thf(fact_9943_DERIV__arctan__series,axiom,
% 0.35/0.68      ! [X: real] :
% 0.35/0.68        ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.35/0.68       => ( has_fi5821293074295781190e_real
% 0.35/0.68          @ ^ [X9: real] :
% 0.35/0.68              ( suminf_real
% 0.35/0.68              @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X9 @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) )
% 0.35/0.68          @ ( suminf_real
% 0.35/0.68            @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( power_power_real @ X @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.68          @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % DERIV_arctan_series
% 0.35/0.68  thf(fact_9944_DERIV__even__real__root,axiom,
% 0.35/0.68      ! [N: nat,X: real] :
% 0.35/0.68        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.68         => ( ( ord_less_real @ X @ zero_zero_real )
% 0.35/0.68           => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % DERIV_even_real_root
% 0.35/0.68  thf(fact_9945_isCont__Lb__Ub,axiom,
% 0.35/0.68      ! [A: real,B: real,F: real > real] :
% 0.35/0.68        ( ( ord_less_eq_real @ A @ B )
% 0.35/0.68       => ( ! [X3: real] :
% 0.35/0.68              ( ( ( ord_less_eq_real @ A @ X3 )
% 0.35/0.68                & ( ord_less_eq_real @ X3 @ B ) )
% 0.35/0.68             => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ F ) )
% 0.35/0.68         => ? [L6: real,M9: real] :
% 0.35/0.68              ( ! [X5: real] :
% 0.35/0.68                  ( ( ( ord_less_eq_real @ A @ X5 )
% 0.35/0.68                    & ( ord_less_eq_real @ X5 @ B ) )
% 0.35/0.68                 => ( ( ord_less_eq_real @ L6 @ ( F @ X5 ) )
% 0.35/0.68                    & ( ord_less_eq_real @ ( F @ X5 ) @ M9 ) ) )
% 0.35/0.68              & ! [Y4: real] :
% 0.35/0.68                  ( ( ( ord_less_eq_real @ L6 @ Y4 )
% 0.35/0.68                    & ( ord_less_eq_real @ Y4 @ M9 ) )
% 0.35/0.68                 => ? [X3: real] :
% 0.35/0.68                      ( ( ord_less_eq_real @ A @ X3 )
% 0.35/0.68                      & ( ord_less_eq_real @ X3 @ B )
% 0.35/0.68                      & ( ( F @ X3 )
% 0.35/0.68                        = Y4 ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % isCont_Lb_Ub
% 0.35/0.68  thf(fact_9946_LIM__fun__less__zero,axiom,
% 0.35/0.68      ! [F: real > real,L2: real,C: real] :
% 0.35/0.68        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 0.35/0.68       => ( ( ord_less_real @ L2 @ zero_zero_real )
% 0.35/0.68         => ? [R3: real] :
% 0.35/0.68              ( ( ord_less_real @ zero_zero_real @ R3 )
% 0.35/0.68              & ! [X5: real] :
% 0.35/0.68                  ( ( ( X5 != C )
% 0.35/0.68                    & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X5 ) ) @ R3 ) )
% 0.35/0.68                 => ( ord_less_real @ ( F @ X5 ) @ zero_zero_real ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % LIM_fun_less_zero
% 0.35/0.68  thf(fact_9947_LIM__fun__not__zero,axiom,
% 0.35/0.68      ! [F: real > real,L2: real,C: real] :
% 0.35/0.68        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 0.35/0.68       => ( ( L2 != zero_zero_real )
% 0.35/0.68         => ? [R3: real] :
% 0.35/0.68              ( ( ord_less_real @ zero_zero_real @ R3 )
% 0.35/0.68              & ! [X5: real] :
% 0.35/0.68                  ( ( ( X5 != C )
% 0.35/0.68                    & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X5 ) ) @ R3 ) )
% 0.35/0.68                 => ( ( F @ X5 )
% 0.35/0.68                   != zero_zero_real ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % LIM_fun_not_zero
% 0.35/0.68  thf(fact_9948_LIM__fun__gt__zero,axiom,
% 0.35/0.68      ! [F: real > real,L2: real,C: real] :
% 0.35/0.68        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 0.35/0.68       => ( ( ord_less_real @ zero_zero_real @ L2 )
% 0.35/0.68         => ? [R3: real] :
% 0.35/0.68              ( ( ord_less_real @ zero_zero_real @ R3 )
% 0.35/0.68              & ! [X5: real] :
% 0.35/0.68                  ( ( ( X5 != C )
% 0.35/0.68                    & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X5 ) ) @ R3 ) )
% 0.35/0.68                 => ( ord_less_real @ zero_zero_real @ ( F @ X5 ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % LIM_fun_gt_zero
% 0.35/0.68  thf(fact_9949_isCont__real__sqrt,axiom,
% 0.35/0.68      ! [X: real] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ sqrt ) ).
% 0.35/0.68  
% 0.35/0.68  % isCont_real_sqrt
% 0.35/0.68  thf(fact_9950_isCont__real__root,axiom,
% 0.35/0.68      ! [X: real,N: nat] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ ( root @ N ) ) ).
% 0.35/0.68  
% 0.35/0.68  % isCont_real_root
% 0.35/0.68  thf(fact_9951_isCont__inverse__function2,axiom,
% 0.35/0.68      ! [A: real,X: real,B: real,G: real > real,F: real > real] :
% 0.35/0.68        ( ( ord_less_real @ A @ X )
% 0.35/0.68       => ( ( ord_less_real @ X @ B )
% 0.35/0.68         => ( ! [Z3: real] :
% 0.35/0.68                ( ( ord_less_eq_real @ A @ Z3 )
% 0.35/0.68               => ( ( ord_less_eq_real @ Z3 @ B )
% 0.35/0.68                 => ( ( G @ ( F @ Z3 ) )
% 0.35/0.68                    = Z3 ) ) )
% 0.35/0.68           => ( ! [Z3: real] :
% 0.35/0.68                  ( ( ord_less_eq_real @ A @ Z3 )
% 0.35/0.68                 => ( ( ord_less_eq_real @ Z3 @ B )
% 0.35/0.68                   => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) ) )
% 0.35/0.68             => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X ) @ top_top_set_real ) @ G ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % isCont_inverse_function2
% 0.35/0.68  thf(fact_9952_isCont__arcosh,axiom,
% 0.35/0.68      ! [X: real] :
% 0.35/0.68        ( ( ord_less_real @ one_one_real @ X )
% 0.35/0.68       => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ arcosh_real ) ) ).
% 0.35/0.68  
% 0.35/0.68  % isCont_arcosh
% 0.35/0.68  thf(fact_9953_LIM__cos__div__sin,axiom,
% 0.35/0.68      ( filterlim_real_real
% 0.35/0.68      @ ^ [X2: real] : ( divide_divide_real @ ( cos_real @ X2 ) @ ( sin_real @ X2 ) )
% 0.35/0.68      @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.35/0.68      @ ( topolo2177554685111907308n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ top_top_set_real ) ) ).
% 0.35/0.68  
% 0.35/0.68  % LIM_cos_div_sin
% 0.35/0.68  thf(fact_9954_DERIV__inverse__function,axiom,
% 0.35/0.68      ! [F: real > real,D4: real,G: real > real,X: real,A: real,B: real] :
% 0.35/0.68        ( ( has_fi5821293074295781190e_real @ F @ D4 @ ( topolo2177554685111907308n_real @ ( G @ X ) @ top_top_set_real ) )
% 0.35/0.68       => ( ( D4 != zero_zero_real )
% 0.35/0.68         => ( ( ord_less_real @ A @ X )
% 0.35/0.68           => ( ( ord_less_real @ X @ B )
% 0.35/0.68             => ( ! [Y3: real] :
% 0.35/0.68                    ( ( ord_less_real @ A @ Y3 )
% 0.35/0.68                   => ( ( ord_less_real @ Y3 @ B )
% 0.35/0.68                     => ( ( F @ ( G @ Y3 ) )
% 0.35/0.68                        = Y3 ) ) )
% 0.35/0.68               => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ G )
% 0.35/0.68                 => ( has_fi5821293074295781190e_real @ G @ ( inverse_inverse_real @ D4 ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % DERIV_inverse_function
% 0.35/0.68  thf(fact_9955_isCont__arccos,axiom,
% 0.35/0.68      ! [X: real] :
% 0.35/0.68        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.35/0.68       => ( ( ord_less_real @ X @ one_one_real )
% 0.35/0.68         => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ arccos ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % isCont_arccos
% 0.35/0.68  thf(fact_9956_isCont__arcsin,axiom,
% 0.35/0.68      ! [X: real] :
% 0.35/0.68        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.35/0.68       => ( ( ord_less_real @ X @ one_one_real )
% 0.35/0.68         => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ arcsin ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % isCont_arcsin
% 0.35/0.68  thf(fact_9957_LIM__less__bound,axiom,
% 0.35/0.68      ! [B: real,X: real,F: real > real] :
% 0.35/0.68        ( ( ord_less_real @ B @ X )
% 0.35/0.68       => ( ! [X3: real] :
% 0.35/0.68              ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ B @ X ) )
% 0.35/0.68             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 0.35/0.68         => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ F )
% 0.35/0.68           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % LIM_less_bound
% 0.35/0.68  thf(fact_9958_isCont__artanh,axiom,
% 0.35/0.68      ! [X: real] :
% 0.35/0.68        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.35/0.68       => ( ( ord_less_real @ X @ one_one_real )
% 0.35/0.68         => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ artanh_real ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % isCont_artanh
% 0.35/0.68  thf(fact_9959_isCont__inverse__function,axiom,
% 0.35/0.68      ! [D2: real,X: real,G: real > real,F: real > real] :
% 0.35/0.68        ( ( ord_less_real @ zero_zero_real @ D2 )
% 0.35/0.68       => ( ! [Z3: real] :
% 0.35/0.68              ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z3 @ X ) ) @ D2 )
% 0.35/0.68             => ( ( G @ ( F @ Z3 ) )
% 0.35/0.68                = Z3 ) )
% 0.35/0.68         => ( ! [Z3: real] :
% 0.35/0.68                ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z3 @ X ) ) @ D2 )
% 0.35/0.68               => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) )
% 0.35/0.68           => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X ) @ top_top_set_real ) @ G ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % isCont_inverse_function
% 0.35/0.68  thf(fact_9960_GMVT_H,axiom,
% 0.35/0.68      ! [A: real,B: real,F: real > real,G: real > real,G2: real > real,F4: real > real] :
% 0.35/0.68        ( ( ord_less_real @ A @ B )
% 0.35/0.68       => ( ! [Z3: real] :
% 0.35/0.68              ( ( ord_less_eq_real @ A @ Z3 )
% 0.35/0.68             => ( ( ord_less_eq_real @ Z3 @ B )
% 0.35/0.68               => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) ) )
% 0.35/0.68         => ( ! [Z3: real] :
% 0.35/0.68                ( ( ord_less_eq_real @ A @ Z3 )
% 0.35/0.68               => ( ( ord_less_eq_real @ Z3 @ B )
% 0.35/0.68                 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ G ) ) )
% 0.35/0.68           => ( ! [Z3: real] :
% 0.35/0.68                  ( ( ord_less_real @ A @ Z3 )
% 0.35/0.68                 => ( ( ord_less_real @ Z3 @ B )
% 0.35/0.68                   => ( has_fi5821293074295781190e_real @ G @ ( G2 @ Z3 ) @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) )
% 0.35/0.68             => ( ! [Z3: real] :
% 0.35/0.68                    ( ( ord_less_real @ A @ Z3 )
% 0.35/0.68                   => ( ( ord_less_real @ Z3 @ B )
% 0.35/0.68                     => ( has_fi5821293074295781190e_real @ F @ ( F4 @ Z3 ) @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) )
% 0.35/0.68               => ? [C2: real] :
% 0.35/0.68                    ( ( ord_less_real @ A @ C2 )
% 0.35/0.68                    & ( ord_less_real @ C2 @ B )
% 0.35/0.68                    & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( G2 @ C2 ) )
% 0.35/0.68                      = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ ( F4 @ C2 ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % GMVT'
% 0.35/0.68  thf(fact_9961_summable__Leibniz_I2_J,axiom,
% 0.35/0.68      ! [A: nat > real] :
% 0.35/0.68        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.35/0.68       => ( ( topolo6980174941875973593q_real @ A )
% 0.35/0.68         => ( ( ord_less_real @ zero_zero_real @ ( A @ zero_zero_nat ) )
% 0.35/0.68           => ! [N9: nat] :
% 0.35/0.68                ( member_real
% 0.35/0.68                @ ( suminf_real
% 0.35/0.68                  @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) )
% 0.35/0.68                @ ( set_or1222579329274155063t_real
% 0.35/0.68                  @ ( groups6591440286371151544t_real
% 0.35/0.68                    @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.35/0.68                    @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) ) )
% 0.35/0.68                  @ ( groups6591440286371151544t_real
% 0.35/0.68                    @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.35/0.68                    @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) @ one_one_nat ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % summable_Leibniz(2)
% 0.35/0.68  thf(fact_9962_summable__Leibniz_I3_J,axiom,
% 0.35/0.68      ! [A: nat > real] :
% 0.35/0.68        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.35/0.68       => ( ( topolo6980174941875973593q_real @ A )
% 0.35/0.68         => ( ( ord_less_real @ ( A @ zero_zero_nat ) @ zero_zero_real )
% 0.35/0.68           => ! [N9: nat] :
% 0.35/0.68                ( member_real
% 0.35/0.68                @ ( suminf_real
% 0.35/0.68                  @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) )
% 0.35/0.68                @ ( set_or1222579329274155063t_real
% 0.35/0.68                  @ ( groups6591440286371151544t_real
% 0.35/0.68                    @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.35/0.68                    @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) @ one_one_nat ) ) )
% 0.35/0.68                  @ ( groups6591440286371151544t_real
% 0.35/0.68                    @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.35/0.68                    @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % summable_Leibniz(3)
% 0.35/0.68  thf(fact_9963_mult__nat__right__at__top,axiom,
% 0.35/0.68      ! [C: nat] :
% 0.35/0.68        ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.35/0.68       => ( filterlim_nat_nat
% 0.35/0.68          @ ^ [X2: nat] : ( times_times_nat @ X2 @ C )
% 0.35/0.68          @ at_top_nat
% 0.35/0.68          @ at_top_nat ) ) ).
% 0.35/0.68  
% 0.35/0.68  % mult_nat_right_at_top
% 0.35/0.68  thf(fact_9964_mult__nat__left__at__top,axiom,
% 0.35/0.68      ! [C: nat] :
% 0.35/0.68        ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.35/0.68       => ( filterlim_nat_nat @ ( times_times_nat @ C ) @ at_top_nat @ at_top_nat ) ) ).
% 0.35/0.68  
% 0.35/0.68  % mult_nat_left_at_top
% 0.35/0.68  thf(fact_9965_monoseq__convergent,axiom,
% 0.35/0.68      ! [X8: nat > real,B2: real] :
% 0.35/0.68        ( ( topolo6980174941875973593q_real @ X8 )
% 0.35/0.68       => ( ! [I4: nat] : ( ord_less_eq_real @ ( abs_abs_real @ ( X8 @ I4 ) ) @ B2 )
% 0.35/0.68         => ~ ! [L6: real] :
% 0.35/0.68                ~ ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % monoseq_convergent
% 0.35/0.68  thf(fact_9966_LIMSEQ__root,axiom,
% 0.35/0.68      ( filterlim_nat_real
% 0.35/0.68      @ ^ [N2: nat] : ( root @ N2 @ ( semiri5074537144036343181t_real @ N2 ) )
% 0.35/0.68      @ ( topolo2815343760600316023s_real @ one_one_real )
% 0.35/0.68      @ at_top_nat ) ).
% 0.35/0.68  
% 0.35/0.68  % LIMSEQ_root
% 0.35/0.68  thf(fact_9967_nested__sequence__unique,axiom,
% 0.35/0.68      ! [F: nat > real,G: nat > real] :
% 0.35/0.68        ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.35/0.68       => ( ! [N3: nat] : ( ord_less_eq_real @ ( G @ ( suc @ N3 ) ) @ ( G @ N3 ) )
% 0.35/0.68         => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 0.35/0.68           => ( ( filterlim_nat_real
% 0.35/0.68                @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 0.35/0.68                @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.35/0.68                @ at_top_nat )
% 0.35/0.68             => ? [L4: real] :
% 0.35/0.68                  ( ! [N9: nat] : ( ord_less_eq_real @ ( F @ N9 ) @ L4 )
% 0.35/0.68                  & ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat )
% 0.35/0.68                  & ! [N9: nat] : ( ord_less_eq_real @ L4 @ ( G @ N9 ) )
% 0.35/0.68                  & ( filterlim_nat_real @ G @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % nested_sequence_unique
% 0.35/0.68  thf(fact_9968_LIMSEQ__inverse__zero,axiom,
% 0.35/0.68      ! [X8: nat > real] :
% 0.35/0.68        ( ! [R3: real] :
% 0.35/0.68          ? [N7: nat] :
% 0.35/0.68          ! [N3: nat] :
% 0.35/0.68            ( ( ord_less_eq_nat @ N7 @ N3 )
% 0.35/0.68           => ( ord_less_real @ R3 @ ( X8 @ N3 ) ) )
% 0.35/0.68       => ( filterlim_nat_real
% 0.35/0.68          @ ^ [N2: nat] : ( inverse_inverse_real @ ( X8 @ N2 ) )
% 0.35/0.68          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.35/0.68          @ at_top_nat ) ) ).
% 0.35/0.68  
% 0.35/0.68  % LIMSEQ_inverse_zero
% 0.35/0.68  thf(fact_9969_lim__inverse__n_H,axiom,
% 0.35/0.68      ( filterlim_nat_real
% 0.35/0.68      @ ^ [N2: nat] : ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N2 ) )
% 0.35/0.68      @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.35/0.68      @ at_top_nat ) ).
% 0.35/0.68  
% 0.35/0.68  % lim_inverse_n'
% 0.35/0.68  thf(fact_9970_LIMSEQ__root__const,axiom,
% 0.35/0.68      ! [C: real] :
% 0.35/0.68        ( ( ord_less_real @ zero_zero_real @ C )
% 0.35/0.68       => ( filterlim_nat_real
% 0.35/0.68          @ ^ [N2: nat] : ( root @ N2 @ C )
% 0.35/0.68          @ ( topolo2815343760600316023s_real @ one_one_real )
% 0.35/0.68          @ at_top_nat ) ) ).
% 0.35/0.68  
% 0.35/0.68  % LIMSEQ_root_const
% 0.35/0.68  thf(fact_9971_LIMSEQ__inverse__real__of__nat,axiom,
% 0.35/0.68      ( filterlim_nat_real
% 0.35/0.68      @ ^ [N2: nat] : ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) )
% 0.35/0.68      @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.35/0.68      @ at_top_nat ) ).
% 0.35/0.68  
% 0.35/0.68  % LIMSEQ_inverse_real_of_nat
% 0.35/0.68  thf(fact_9972_LIMSEQ__inverse__real__of__nat__add,axiom,
% 0.35/0.68      ! [R: real] :
% 0.35/0.68        ( filterlim_nat_real
% 0.35/0.68        @ ^ [N2: nat] : ( plus_plus_real @ R @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) )
% 0.35/0.68        @ ( topolo2815343760600316023s_real @ R )
% 0.35/0.68        @ at_top_nat ) ).
% 0.35/0.68  
% 0.35/0.68  % LIMSEQ_inverse_real_of_nat_add
% 0.35/0.68  thf(fact_9973_increasing__LIMSEQ,axiom,
% 0.35/0.68      ! [F: nat > real,L2: real] :
% 0.35/0.68        ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.35/0.68       => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ L2 )
% 0.35/0.68         => ( ! [E2: real] :
% 0.35/0.68                ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.35/0.68               => ? [N9: nat] : ( ord_less_eq_real @ L2 @ ( plus_plus_real @ ( F @ N9 ) @ E2 ) ) )
% 0.35/0.68           => ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ at_top_nat ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % increasing_LIMSEQ
% 0.35/0.68  thf(fact_9974_LIMSEQ__realpow__zero,axiom,
% 0.35/0.68      ! [X: real] :
% 0.35/0.68        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.68       => ( ( ord_less_real @ X @ one_one_real )
% 0.35/0.68         => ( filterlim_nat_real @ ( power_power_real @ X ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % LIMSEQ_realpow_zero
% 0.35/0.68  thf(fact_9975_LIMSEQ__divide__realpow__zero,axiom,
% 0.35/0.68      ! [X: real,A: real] :
% 0.35/0.68        ( ( ord_less_real @ one_one_real @ X )
% 0.35/0.68       => ( filterlim_nat_real
% 0.35/0.68          @ ^ [N2: nat] : ( divide_divide_real @ A @ ( power_power_real @ X @ N2 ) )
% 0.35/0.68          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.35/0.68          @ at_top_nat ) ) ).
% 0.35/0.68  
% 0.35/0.68  % LIMSEQ_divide_realpow_zero
% 0.35/0.68  thf(fact_9976_LIMSEQ__abs__realpow__zero,axiom,
% 0.35/0.68      ! [C: real] :
% 0.35/0.68        ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 0.35/0.68       => ( filterlim_nat_real @ ( power_power_real @ ( abs_abs_real @ C ) ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 0.35/0.68  
% 0.35/0.68  % LIMSEQ_abs_realpow_zero
% 0.35/0.68  thf(fact_9977_LIMSEQ__abs__realpow__zero2,axiom,
% 0.35/0.68      ! [C: real] :
% 0.35/0.68        ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 0.35/0.68       => ( filterlim_nat_real @ ( power_power_real @ C ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 0.35/0.68  
% 0.35/0.68  % LIMSEQ_abs_realpow_zero2
% 0.35/0.68  thf(fact_9978_LIMSEQ__inverse__realpow__zero,axiom,
% 0.35/0.68      ! [X: real] :
% 0.35/0.68        ( ( ord_less_real @ one_one_real @ X )
% 0.35/0.68       => ( filterlim_nat_real
% 0.35/0.68          @ ^ [N2: nat] : ( inverse_inverse_real @ ( power_power_real @ X @ N2 ) )
% 0.35/0.68          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.35/0.68          @ at_top_nat ) ) ).
% 0.35/0.68  
% 0.35/0.68  % LIMSEQ_inverse_realpow_zero
% 0.35/0.68  thf(fact_9979_LIMSEQ__inverse__real__of__nat__add__minus,axiom,
% 0.35/0.68      ! [R: real] :
% 0.35/0.68        ( filterlim_nat_real
% 0.35/0.68        @ ^ [N2: nat] : ( plus_plus_real @ R @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) )
% 0.35/0.68        @ ( topolo2815343760600316023s_real @ R )
% 0.35/0.68        @ at_top_nat ) ).
% 0.35/0.68  
% 0.35/0.68  % LIMSEQ_inverse_real_of_nat_add_minus
% 0.35/0.68  thf(fact_9980_tendsto__exp__limit__sequentially,axiom,
% 0.35/0.68      ! [X: real] :
% 0.35/0.68        ( filterlim_nat_real
% 0.35/0.68        @ ^ [N2: nat] : ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 )
% 0.35/0.68        @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 0.35/0.68        @ at_top_nat ) ).
% 0.35/0.68  
% 0.35/0.68  % tendsto_exp_limit_sequentially
% 0.35/0.68  thf(fact_9981_LIMSEQ__inverse__real__of__nat__add__minus__mult,axiom,
% 0.35/0.68      ! [R: real] :
% 0.35/0.68        ( filterlim_nat_real
% 0.35/0.68        @ ^ [N2: nat] : ( times_times_real @ R @ ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) ) )
% 0.35/0.68        @ ( topolo2815343760600316023s_real @ R )
% 0.35/0.68        @ at_top_nat ) ).
% 0.35/0.68  
% 0.35/0.68  % LIMSEQ_inverse_real_of_nat_add_minus_mult
% 0.35/0.68  thf(fact_9982_summable__Leibniz_I1_J,axiom,
% 0.35/0.68      ! [A: nat > real] :
% 0.35/0.68        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.35/0.68       => ( ( topolo6980174941875973593q_real @ A )
% 0.35/0.68         => ( summable_real
% 0.35/0.68            @ ^ [N2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( A @ N2 ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % summable_Leibniz(1)
% 0.35/0.68  thf(fact_9983_summable,axiom,
% 0.35/0.68      ! [A: nat > real] :
% 0.35/0.68        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.35/0.68       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 0.35/0.68         => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 0.35/0.68           => ( summable_real
% 0.35/0.68              @ ^ [N2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( A @ N2 ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % summable
% 0.35/0.68  thf(fact_9984_cos__diff__limit__1,axiom,
% 0.35/0.68      ! [Theta: nat > real,Theta2: real] :
% 0.35/0.68        ( ( filterlim_nat_real
% 0.35/0.68          @ ^ [J3: nat] : ( cos_real @ ( minus_minus_real @ ( Theta @ J3 ) @ Theta2 ) )
% 0.35/0.68          @ ( topolo2815343760600316023s_real @ one_one_real )
% 0.35/0.68          @ at_top_nat )
% 0.35/0.68       => ~ ! [K2: nat > int] :
% 0.35/0.68              ~ ( filterlim_nat_real
% 0.35/0.68                @ ^ [J3: nat] : ( minus_minus_real @ ( Theta @ J3 ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K2 @ J3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 0.35/0.68                @ ( topolo2815343760600316023s_real @ Theta2 )
% 0.35/0.68                @ at_top_nat ) ) ).
% 0.35/0.68  
% 0.35/0.68  % cos_diff_limit_1
% 0.35/0.68  thf(fact_9985_cos__limit__1,axiom,
% 0.35/0.68      ! [Theta: nat > real] :
% 0.35/0.68        ( ( filterlim_nat_real
% 0.35/0.68          @ ^ [J3: nat] : ( cos_real @ ( Theta @ J3 ) )
% 0.35/0.68          @ ( topolo2815343760600316023s_real @ one_one_real )
% 0.35/0.68          @ at_top_nat )
% 0.35/0.68       => ? [K2: nat > int] :
% 0.35/0.68            ( filterlim_nat_real
% 0.35/0.68            @ ^ [J3: nat] : ( minus_minus_real @ ( Theta @ J3 ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K2 @ J3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 0.35/0.68            @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.35/0.68            @ at_top_nat ) ) ).
% 0.35/0.68  
% 0.35/0.68  % cos_limit_1
% 0.35/0.68  thf(fact_9986_summable__Leibniz_I4_J,axiom,
% 0.35/0.68      ! [A: nat > real] :
% 0.35/0.68        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.35/0.68       => ( ( topolo6980174941875973593q_real @ A )
% 0.35/0.68         => ( filterlim_nat_real
% 0.35/0.68            @ ^ [N2: nat] :
% 0.35/0.68                ( groups6591440286371151544t_real
% 0.35/0.68                @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.35/0.68                @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.35/0.68            @ ( topolo2815343760600316023s_real
% 0.35/0.68              @ ( suminf_real
% 0.35/0.68                @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 0.35/0.68            @ at_top_nat ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % summable_Leibniz(4)
% 0.35/0.68  thf(fact_9987_zeroseq__arctan__series,axiom,
% 0.35/0.68      ! [X: real] :
% 0.35/0.68        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.35/0.68       => ( filterlim_nat_real
% 0.35/0.68          @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) )
% 0.35/0.68          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.35/0.68          @ at_top_nat ) ) ).
% 0.35/0.68  
% 0.35/0.68  % zeroseq_arctan_series
% 0.35/0.68  thf(fact_9988_summable__Leibniz_H_I2_J,axiom,
% 0.35/0.68      ! [A: nat > real,N: nat] :
% 0.35/0.68        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.35/0.68       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 0.35/0.68         => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 0.35/0.68           => ( ord_less_eq_real
% 0.35/0.68              @ ( groups6591440286371151544t_real
% 0.35/0.68                @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.35/0.68                @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.68              @ ( suminf_real
% 0.35/0.68                @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % summable_Leibniz'(2)
% 0.35/0.68  thf(fact_9989_summable__Leibniz_H_I3_J,axiom,
% 0.35/0.68      ! [A: nat > real] :
% 0.35/0.68        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.35/0.68       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 0.35/0.68         => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 0.35/0.68           => ( filterlim_nat_real
% 0.35/0.68              @ ^ [N2: nat] :
% 0.35/0.68                  ( groups6591440286371151544t_real
% 0.35/0.68                  @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.35/0.68                  @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.35/0.68              @ ( topolo2815343760600316023s_real
% 0.35/0.68                @ ( suminf_real
% 0.35/0.68                  @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 0.35/0.68              @ at_top_nat ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % summable_Leibniz'(3)
% 0.35/0.68  thf(fact_9990_sums__alternating__upper__lower,axiom,
% 0.35/0.68      ! [A: nat > real] :
% 0.35/0.68        ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 0.35/0.68       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 0.35/0.68         => ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.35/0.68           => ? [L4: real] :
% 0.35/0.68                ( ! [N9: nat] :
% 0.35/0.68                    ( ord_less_eq_real
% 0.35/0.68                    @ ( groups6591440286371151544t_real
% 0.35/0.68                      @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.35/0.68                      @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) ) )
% 0.35/0.68                    @ L4 )
% 0.35/0.68                & ( filterlim_nat_real
% 0.35/0.68                  @ ^ [N2: nat] :
% 0.35/0.68                      ( groups6591440286371151544t_real
% 0.35/0.68                      @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.35/0.68                      @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.35/0.68                  @ ( topolo2815343760600316023s_real @ L4 )
% 0.35/0.68                  @ at_top_nat )
% 0.35/0.68                & ! [N9: nat] :
% 0.35/0.68                    ( ord_less_eq_real @ L4
% 0.35/0.68                    @ ( groups6591440286371151544t_real
% 0.35/0.68                      @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.35/0.68                      @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) @ one_one_nat ) ) ) )
% 0.35/0.68                & ( filterlim_nat_real
% 0.35/0.68                  @ ^ [N2: nat] :
% 0.35/0.68                      ( groups6591440286371151544t_real
% 0.35/0.68                      @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.35/0.68                      @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 0.35/0.68                  @ ( topolo2815343760600316023s_real @ L4 )
% 0.35/0.68                  @ at_top_nat ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % sums_alternating_upper_lower
% 0.35/0.68  thf(fact_9991_summable__Leibniz_I5_J,axiom,
% 0.35/0.68      ! [A: nat > real] :
% 0.35/0.68        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.35/0.68       => ( ( topolo6980174941875973593q_real @ A )
% 0.35/0.68         => ( filterlim_nat_real
% 0.35/0.68            @ ^ [N2: nat] :
% 0.35/0.68                ( groups6591440286371151544t_real
% 0.35/0.68                @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.35/0.68                @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 0.35/0.68            @ ( topolo2815343760600316023s_real
% 0.35/0.68              @ ( suminf_real
% 0.35/0.68                @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 0.35/0.68            @ at_top_nat ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % summable_Leibniz(5)
% 0.35/0.68  thf(fact_9992_summable__Leibniz_H_I4_J,axiom,
% 0.35/0.68      ! [A: nat > real,N: nat] :
% 0.35/0.68        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.35/0.68       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 0.35/0.68         => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 0.35/0.68           => ( ord_less_eq_real
% 0.35/0.68              @ ( suminf_real
% 0.35/0.68                @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) )
% 0.35/0.68              @ ( groups6591440286371151544t_real
% 0.35/0.68                @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.35/0.68                @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % summable_Leibniz'(4)
% 0.35/0.68  thf(fact_9993_summable__Leibniz_H_I5_J,axiom,
% 0.35/0.68      ! [A: nat > real] :
% 0.35/0.68        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.35/0.68       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 0.35/0.68         => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 0.35/0.68           => ( filterlim_nat_real
% 0.35/0.68              @ ^ [N2: nat] :
% 0.35/0.68                  ( groups6591440286371151544t_real
% 0.35/0.68                  @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.35/0.68                  @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 0.35/0.68              @ ( topolo2815343760600316023s_real
% 0.35/0.68                @ ( suminf_real
% 0.35/0.68                  @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 0.35/0.68              @ at_top_nat ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % summable_Leibniz'(5)
% 0.35/0.68  thf(fact_9994_real__bounded__linear,axiom,
% 0.35/0.68      ( real_V5970128139526366754l_real
% 0.35/0.68      = ( ^ [F3: real > real] :
% 0.35/0.68          ? [C3: real] :
% 0.35/0.68            ( F3
% 0.35/0.68            = ( ^ [X2: real] : ( times_times_real @ X2 @ C3 ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % real_bounded_linear
% 0.35/0.68  thf(fact_9995_filterlim__Suc,axiom,
% 0.35/0.68      filterlim_nat_nat @ suc @ at_top_nat @ at_top_nat ).
% 0.35/0.68  
% 0.35/0.68  % filterlim_Suc
% 0.35/0.68  thf(fact_9996_dist__complex__def,axiom,
% 0.35/0.68      ( real_V3694042436643373181omplex
% 0.35/0.68      = ( ^ [X2: complex,Y: complex] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Y ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % dist_complex_def
% 0.35/0.68  thf(fact_9997_dist__real__def,axiom,
% 0.35/0.68      ( real_V975177566351809787t_real
% 0.35/0.68      = ( ^ [X2: real,Y: real] : ( abs_abs_real @ ( minus_minus_real @ X2 @ Y ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % dist_real_def
% 0.35/0.68  thf(fact_9998_tendsto__exp__limit__at__right,axiom,
% 0.35/0.68      ! [X: real] :
% 0.35/0.68        ( filterlim_real_real
% 0.35/0.68        @ ^ [Y: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ X @ Y ) ) @ ( divide_divide_real @ one_one_real @ Y ) )
% 0.35/0.68        @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 0.35/0.68        @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % tendsto_exp_limit_at_right
% 0.35/0.68  thf(fact_9999_tendsto__arcosh__at__left__1,axiom,
% 0.35/0.68      filterlim_real_real @ arcosh_real @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5849166863359141190n_real @ one_one_real ) ) ).
% 0.35/0.68  
% 0.35/0.68  % tendsto_arcosh_at_left_1
% 0.35/0.68  thf(fact_10000_filterlim__tan__at__right,axiom,
% 0.35/0.68      filterlim_real_real @ tan_real @ at_bot_real @ ( topolo2177554685111907308n_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( set_or5849166863359141190n_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % filterlim_tan_at_right
% 0.35/0.68  thf(fact_10001_atLeast__Suc__greaterThan,axiom,
% 0.35/0.68      ! [K: nat] :
% 0.35/0.68        ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 0.35/0.68        = ( set_or1210151606488870762an_nat @ K ) ) ).
% 0.35/0.68  
% 0.35/0.68  % atLeast_Suc_greaterThan
% 0.35/0.68  thf(fact_10002_greaterThan__0,axiom,
% 0.35/0.68      ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 0.35/0.68      = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 0.35/0.68  
% 0.35/0.68  % greaterThan_0
% 0.35/0.68  thf(fact_10003_greaterThan__Suc,axiom,
% 0.35/0.68      ! [K: nat] :
% 0.35/0.68        ( ( set_or1210151606488870762an_nat @ ( suc @ K ) )
% 0.35/0.68        = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K ) @ ( insert_nat @ ( suc @ K ) @ bot_bot_set_nat ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % greaterThan_Suc
% 0.35/0.68  thf(fact_10004_atLeast__Suc,axiom,
% 0.35/0.68      ! [K: nat] :
% 0.35/0.68        ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 0.35/0.68        = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K ) @ ( insert_nat @ K @ bot_bot_set_nat ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % atLeast_Suc
% 0.35/0.68  thf(fact_10005_tanh__real__at__bot,axiom,
% 0.35/0.68      filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ one_one_real ) ) @ at_bot_real ).
% 0.35/0.68  
% 0.35/0.68  % tanh_real_at_bot
% 0.35/0.68  thf(fact_10006_artanh__real__at__right__1,axiom,
% 0.35/0.68      filterlim_real_real @ artanh_real @ at_bot_real @ ( topolo2177554685111907308n_real @ ( uminus_uminus_real @ one_one_real ) @ ( set_or5849166863359141190n_real @ ( uminus_uminus_real @ one_one_real ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % artanh_real_at_right_1
% 0.35/0.68  thf(fact_10007_DERIV__pos__imp__increasing__at__bot,axiom,
% 0.35/0.68      ! [B: real,F: real > real,Flim: real] :
% 0.35/0.68        ( ! [X3: real] :
% 0.35/0.68            ( ( ord_less_eq_real @ X3 @ B )
% 0.35/0.68           => ? [Y4: real] :
% 0.35/0.68                ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.35/0.68                & ( ord_less_real @ zero_zero_real @ Y4 ) ) )
% 0.35/0.68       => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_bot_real )
% 0.35/0.68         => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % DERIV_pos_imp_increasing_at_bot
% 0.35/0.68  thf(fact_10008_filterlim__pow__at__bot__odd,axiom,
% 0.35/0.68      ! [N: nat,F: real > real,F5: filter_real] :
% 0.35/0.68        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68       => ( ( filterlim_real_real @ F @ at_bot_real @ F5 )
% 0.35/0.68         => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.68           => ( filterlim_real_real
% 0.35/0.68              @ ^ [X2: real] : ( power_power_real @ ( F @ X2 ) @ N )
% 0.35/0.68              @ at_bot_real
% 0.35/0.68              @ F5 ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % filterlim_pow_at_bot_odd
% 0.35/0.68  thf(fact_10009_tendsto__arctan__at__bot,axiom,
% 0.35/0.68      filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ at_bot_real ).
% 0.35/0.68  
% 0.35/0.68  % tendsto_arctan_at_bot
% 0.35/0.68  thf(fact_10010_filterlim__pow__at__bot__even,axiom,
% 0.35/0.68      ! [N: nat,F: real > real,F5: filter_real] :
% 0.35/0.68        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68       => ( ( filterlim_real_real @ F @ at_bot_real @ F5 )
% 0.35/0.68         => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.68           => ( filterlim_real_real
% 0.35/0.68              @ ^ [X2: real] : ( power_power_real @ ( F @ X2 ) @ N )
% 0.35/0.68              @ at_top_real
% 0.35/0.68              @ F5 ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % filterlim_pow_at_bot_even
% 0.35/0.68  thf(fact_10011_sqrt__at__top,axiom,
% 0.35/0.68      filterlim_real_real @ sqrt @ at_top_real @ at_top_real ).
% 0.35/0.68  
% 0.35/0.68  % sqrt_at_top
% 0.35/0.68  thf(fact_10012_tanh__real__at__top,axiom,
% 0.35/0.68      filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ one_one_real ) @ at_top_real ).
% 0.35/0.68  
% 0.35/0.68  % tanh_real_at_top
% 0.35/0.68  thf(fact_10013_artanh__real__at__left__1,axiom,
% 0.35/0.68      filterlim_real_real @ artanh_real @ at_top_real @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5984915006950818249n_real @ one_one_real ) ) ).
% 0.35/0.68  
% 0.35/0.68  % artanh_real_at_left_1
% 0.35/0.68  thf(fact_10014_ln__x__over__x__tendsto__0,axiom,
% 0.35/0.68      ( filterlim_real_real
% 0.35/0.68      @ ^ [X2: real] : ( divide_divide_real @ ( ln_ln_real @ X2 ) @ X2 )
% 0.35/0.68      @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.35/0.68      @ at_top_real ) ).
% 0.35/0.68  
% 0.35/0.68  % ln_x_over_x_tendsto_0
% 0.35/0.68  thf(fact_10015_tendsto__power__div__exp__0,axiom,
% 0.35/0.68      ! [K: nat] :
% 0.35/0.68        ( filterlim_real_real
% 0.35/0.68        @ ^ [X2: real] : ( divide_divide_real @ ( power_power_real @ X2 @ K ) @ ( exp_real @ X2 ) )
% 0.35/0.68        @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.35/0.68        @ at_top_real ) ).
% 0.35/0.68  
% 0.35/0.68  % tendsto_power_div_exp_0
% 0.35/0.68  thf(fact_10016_tendsto__exp__limit__at__top,axiom,
% 0.35/0.68      ! [X: real] :
% 0.35/0.68        ( filterlim_real_real
% 0.35/0.68        @ ^ [Y: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ Y ) ) @ Y )
% 0.35/0.68        @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 0.35/0.68        @ at_top_real ) ).
% 0.35/0.68  
% 0.35/0.68  % tendsto_exp_limit_at_top
% 0.35/0.68  thf(fact_10017_filterlim__tan__at__left,axiom,
% 0.35/0.68      filterlim_real_real @ tan_real @ at_top_real @ ( topolo2177554685111907308n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( set_or5984915006950818249n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % filterlim_tan_at_left
% 0.35/0.68  thf(fact_10018_tendsto__arctan__at__top,axiom,
% 0.35/0.68      filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ at_top_real ).
% 0.35/0.68  
% 0.35/0.68  % tendsto_arctan_at_top
% 0.35/0.68  thf(fact_10019_DERIV__neg__imp__decreasing__at__top,axiom,
% 0.35/0.68      ! [B: real,F: real > real,Flim: real] :
% 0.35/0.68        ( ! [X3: real] :
% 0.35/0.68            ( ( ord_less_eq_real @ B @ X3 )
% 0.35/0.68           => ? [Y4: real] :
% 0.35/0.68                ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.35/0.68                & ( ord_less_real @ Y4 @ zero_zero_real ) ) )
% 0.35/0.68       => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_top_real )
% 0.35/0.68         => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % DERIV_neg_imp_decreasing_at_top
% 0.35/0.68  thf(fact_10020_lhopital__right__at__top,axiom,
% 0.35/0.68      ! [G: real > real,X: real,G2: real > real,F: real > real,F4: real > real,Y2: real] :
% 0.35/0.68        ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 0.35/0.68       => ( ( eventually_real
% 0.35/0.68            @ ^ [X2: real] :
% 0.35/0.68                ( ( G2 @ X2 )
% 0.35/0.68               != zero_zero_real )
% 0.35/0.68            @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 0.35/0.68         => ( ( eventually_real
% 0.35/0.68              @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 0.35/0.68              @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 0.35/0.68           => ( ( eventually_real
% 0.35/0.68                @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 0.35/0.68                @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 0.35/0.68             => ( ( filterlim_real_real
% 0.35/0.68                  @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 0.35/0.68                  @ ( topolo2815343760600316023s_real @ Y2 )
% 0.35/0.68                  @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 0.35/0.68               => ( filterlim_real_real
% 0.35/0.68                  @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 0.35/0.68                  @ ( topolo2815343760600316023s_real @ Y2 )
% 0.35/0.68                  @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % lhopital_right_at_top
% 0.35/0.68  thf(fact_10021_eventually__sequentially__Suc,axiom,
% 0.35/0.68      ! [P: nat > $o] :
% 0.35/0.68        ( ( eventually_nat
% 0.35/0.68          @ ^ [I3: nat] : ( P @ ( suc @ I3 ) )
% 0.35/0.68          @ at_top_nat )
% 0.35/0.68        = ( eventually_nat @ P @ at_top_nat ) ) ).
% 0.35/0.68  
% 0.35/0.68  % eventually_sequentially_Suc
% 0.35/0.68  thf(fact_10022_eventually__sequentially__seg,axiom,
% 0.35/0.68      ! [P: nat > $o,K: nat] :
% 0.35/0.68        ( ( eventually_nat
% 0.35/0.68          @ ^ [N2: nat] : ( P @ ( plus_plus_nat @ N2 @ K ) )
% 0.35/0.68          @ at_top_nat )
% 0.35/0.68        = ( eventually_nat @ P @ at_top_nat ) ) ).
% 0.35/0.68  
% 0.35/0.68  % eventually_sequentially_seg
% 0.35/0.68  thf(fact_10023_eventually__sequentially,axiom,
% 0.35/0.68      ! [P: nat > $o] :
% 0.35/0.68        ( ( eventually_nat @ P @ at_top_nat )
% 0.35/0.68        = ( ? [N6: nat] :
% 0.35/0.68            ! [N2: nat] :
% 0.35/0.68              ( ( ord_less_eq_nat @ N6 @ N2 )
% 0.35/0.68             => ( P @ N2 ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % eventually_sequentially
% 0.35/0.68  thf(fact_10024_eventually__sequentiallyI,axiom,
% 0.35/0.68      ! [C: nat,P: nat > $o] :
% 0.35/0.68        ( ! [X3: nat] :
% 0.35/0.68            ( ( ord_less_eq_nat @ C @ X3 )
% 0.35/0.68           => ( P @ X3 ) )
% 0.35/0.68       => ( eventually_nat @ P @ at_top_nat ) ) ).
% 0.35/0.68  
% 0.35/0.68  % eventually_sequentiallyI
% 0.35/0.68  thf(fact_10025_le__sequentially,axiom,
% 0.35/0.68      ! [F5: filter_nat] :
% 0.35/0.68        ( ( ord_le2510731241096832064er_nat @ F5 @ at_top_nat )
% 0.35/0.68        = ( ! [N6: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N6 ) @ F5 ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % le_sequentially
% 0.35/0.68  thf(fact_10026_sequentially__offset,axiom,
% 0.35/0.68      ! [P: nat > $o,K: nat] :
% 0.35/0.68        ( ( eventually_nat @ P @ at_top_nat )
% 0.35/0.68       => ( eventually_nat
% 0.35/0.68          @ ^ [I3: nat] : ( P @ ( plus_plus_nat @ I3 @ K ) )
% 0.35/0.68          @ at_top_nat ) ) ).
% 0.35/0.68  
% 0.35/0.68  % sequentially_offset
% 0.35/0.68  thf(fact_10027_eventually__at__left__real,axiom,
% 0.35/0.68      ! [B: real,A: real] :
% 0.35/0.68        ( ( ord_less_real @ B @ A )
% 0.35/0.68       => ( eventually_real
% 0.35/0.68          @ ^ [X2: real] : ( member_real @ X2 @ ( set_or1633881224788618240n_real @ B @ A ) )
% 0.35/0.68          @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % eventually_at_left_real
% 0.35/0.68  thf(fact_10028_eventually__at__right__to__0,axiom,
% 0.35/0.68      ! [P: real > $o,A: real] :
% 0.35/0.68        ( ( eventually_real @ P @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 0.35/0.68        = ( eventually_real
% 0.35/0.68          @ ^ [X2: real] : ( P @ ( plus_plus_real @ X2 @ A ) )
% 0.35/0.68          @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % eventually_at_right_to_0
% 0.35/0.68  thf(fact_10029_eventually__at__right__real,axiom,
% 0.35/0.68      ! [A: real,B: real] :
% 0.35/0.68        ( ( ord_less_real @ A @ B )
% 0.35/0.68       => ( eventually_real
% 0.35/0.68          @ ^ [X2: real] : ( member_real @ X2 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.35/0.68          @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % eventually_at_right_real
% 0.35/0.68  thf(fact_10030_lhopital__left__at__top__at__top,axiom,
% 0.35/0.68      ! [F: real > real,A: real,G: real > real,F4: real > real,G2: real > real] :
% 0.35/0.68        ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 0.35/0.68       => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 0.35/0.68         => ( ( eventually_real
% 0.35/0.68              @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 0.35/0.68              @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 0.35/0.68           => ( ( eventually_real
% 0.35/0.68                @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 0.35/0.68                @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 0.35/0.68             => ( ( filterlim_real_real
% 0.35/0.68                  @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 0.35/0.68                  @ at_top_real
% 0.35/0.68                  @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 0.35/0.68               => ( filterlim_real_real
% 0.35/0.68                  @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 0.35/0.68                  @ at_top_real
% 0.35/0.68                  @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ) ) ) ) ).
% 0.35/0.68  
% 0.35/0.68  % lhopital_left_at_top_at_top
% 0.35/0.68  thf(fact_10031_lhopital__at__top__at__top,axiom,
% 0.35/0.68      ! [F: real > real,A: real,G: real > real,F4: real > real,G2: real > real] :
% 0.35/0.68        ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 0.35/0.68       => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 0.35/0.68         => ( ( eventually_real
% 0.35/0.68              @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 0.35/0.69              @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 0.35/0.69           => ( ( eventually_real
% 0.35/0.69                @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 0.35/0.69                @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 0.35/0.69             => ( ( filterlim_real_real
% 0.35/0.69                  @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 0.35/0.69                  @ at_top_real
% 0.35/0.69                  @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 0.35/0.69               => ( filterlim_real_real
% 0.35/0.69                  @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 0.35/0.69                  @ at_top_real
% 0.35/0.69                  @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) ) ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % lhopital_at_top_at_top
% 0.35/0.69  thf(fact_10032_lhopital__left,axiom,
% 0.35/0.69      ! [F: real > real,X: real,G: real > real,G2: real > real,F4: real > real,F5: filter_real] :
% 0.35/0.69        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 0.35/0.69       => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 0.35/0.69         => ( ( eventually_real
% 0.35/0.69              @ ^ [X2: real] :
% 0.35/0.69                  ( ( G @ X2 )
% 0.35/0.69                 != zero_zero_real )
% 0.35/0.69              @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 0.35/0.69           => ( ( eventually_real
% 0.35/0.69                @ ^ [X2: real] :
% 0.35/0.69                    ( ( G2 @ X2 )
% 0.35/0.69                   != zero_zero_real )
% 0.35/0.69                @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 0.35/0.69             => ( ( eventually_real
% 0.35/0.69                  @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 0.35/0.69                  @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 0.35/0.69               => ( ( eventually_real
% 0.35/0.69                    @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 0.35/0.69                    @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 0.35/0.69                 => ( ( filterlim_real_real
% 0.35/0.69                      @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 0.35/0.69                      @ F5
% 0.35/0.69                      @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 0.35/0.69                   => ( filterlim_real_real
% 0.35/0.69                      @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 0.35/0.69                      @ F5
% 0.35/0.69                      @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % lhopital_left
% 0.35/0.69  thf(fact_10033_lhopital,axiom,
% 0.35/0.69      ! [F: real > real,X: real,G: real > real,G2: real > real,F4: real > real,F5: filter_real] :
% 0.35/0.69        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.35/0.69       => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.35/0.69         => ( ( eventually_real
% 0.35/0.69              @ ^ [X2: real] :
% 0.35/0.69                  ( ( G @ X2 )
% 0.35/0.69                 != zero_zero_real )
% 0.35/0.69              @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.35/0.69           => ( ( eventually_real
% 0.35/0.69                @ ^ [X2: real] :
% 0.35/0.69                    ( ( G2 @ X2 )
% 0.35/0.69                   != zero_zero_real )
% 0.35/0.69                @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.35/0.69             => ( ( eventually_real
% 0.35/0.69                  @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 0.35/0.69                  @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.35/0.69               => ( ( eventually_real
% 0.35/0.69                    @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 0.35/0.69                    @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.35/0.69                 => ( ( filterlim_real_real
% 0.35/0.69                      @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 0.35/0.69                      @ F5
% 0.35/0.69                      @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.35/0.69                   => ( filterlim_real_real
% 0.35/0.69                      @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 0.35/0.69                      @ F5
% 0.35/0.69                      @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % lhopital
% 0.35/0.69  thf(fact_10034_lhopital__right__at__top__at__top,axiom,
% 0.35/0.69      ! [F: real > real,A: real,G: real > real,F4: real > real,G2: real > real] :
% 0.35/0.69        ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 0.35/0.69       => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 0.35/0.69         => ( ( eventually_real
% 0.35/0.69              @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 0.35/0.69              @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 0.35/0.69           => ( ( eventually_real
% 0.35/0.69                @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 0.35/0.69                @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 0.35/0.69             => ( ( filterlim_real_real
% 0.35/0.69                  @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 0.35/0.69                  @ at_top_real
% 0.35/0.69                  @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 0.35/0.69               => ( filterlim_real_real
% 0.35/0.69                  @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 0.35/0.69                  @ at_top_real
% 0.35/0.69                  @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % lhopital_right_at_top_at_top
% 0.35/0.69  thf(fact_10035_lhopital__left__at__top__at__bot,axiom,
% 0.35/0.69      ! [F: real > real,A: real,G: real > real,F4: real > real,G2: real > real] :
% 0.35/0.69        ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 0.35/0.69       => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 0.35/0.69         => ( ( eventually_real
% 0.35/0.69              @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 0.35/0.69              @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 0.35/0.69           => ( ( eventually_real
% 0.35/0.69                @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 0.35/0.69                @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 0.35/0.69             => ( ( filterlim_real_real
% 0.35/0.69                  @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 0.35/0.69                  @ at_bot_real
% 0.35/0.69                  @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 0.35/0.69               => ( filterlim_real_real
% 0.35/0.69                  @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 0.35/0.69                  @ at_bot_real
% 0.35/0.69                  @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % lhopital_left_at_top_at_bot
% 0.35/0.69  thf(fact_10036_lhopital__at__top__at__bot,axiom,
% 0.35/0.69      ! [F: real > real,A: real,G: real > real,F4: real > real,G2: real > real] :
% 0.35/0.69        ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 0.35/0.69       => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 0.35/0.69         => ( ( eventually_real
% 0.35/0.69              @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 0.35/0.69              @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 0.35/0.69           => ( ( eventually_real
% 0.35/0.69                @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 0.35/0.69                @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 0.35/0.69             => ( ( filterlim_real_real
% 0.35/0.69                  @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 0.35/0.69                  @ at_bot_real
% 0.35/0.69                  @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 0.35/0.69               => ( filterlim_real_real
% 0.35/0.69                  @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 0.35/0.69                  @ at_bot_real
% 0.35/0.69                  @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) ) ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % lhopital_at_top_at_bot
% 0.35/0.69  thf(fact_10037_lhopital__left__at__top,axiom,
% 0.35/0.69      ! [G: real > real,X: real,G2: real > real,F: real > real,F4: real > real,Y2: real] :
% 0.35/0.69        ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 0.35/0.69       => ( ( eventually_real
% 0.35/0.69            @ ^ [X2: real] :
% 0.35/0.69                ( ( G2 @ X2 )
% 0.35/0.69               != zero_zero_real )
% 0.35/0.69            @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 0.35/0.69         => ( ( eventually_real
% 0.35/0.69              @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 0.35/0.69              @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 0.35/0.69           => ( ( eventually_real
% 0.35/0.69                @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 0.35/0.69                @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 0.35/0.69             => ( ( filterlim_real_real
% 0.35/0.69                  @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 0.35/0.69                  @ ( topolo2815343760600316023s_real @ Y2 )
% 0.35/0.69                  @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 0.35/0.69               => ( filterlim_real_real
% 0.35/0.69                  @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 0.35/0.69                  @ ( topolo2815343760600316023s_real @ Y2 )
% 0.35/0.69                  @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) ) ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % lhopital_left_at_top
% 0.35/0.69  thf(fact_10038_lhopital__at__top,axiom,
% 0.35/0.69      ! [G: real > real,X: real,G2: real > real,F: real > real,F4: real > real,Y2: real] :
% 0.35/0.69        ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.35/0.69       => ( ( eventually_real
% 0.35/0.69            @ ^ [X2: real] :
% 0.35/0.69                ( ( G2 @ X2 )
% 0.35/0.69               != zero_zero_real )
% 0.35/0.69            @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.35/0.69         => ( ( eventually_real
% 0.35/0.69              @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 0.35/0.69              @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.35/0.69           => ( ( eventually_real
% 0.35/0.69                @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 0.35/0.69                @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.35/0.69             => ( ( filterlim_real_real
% 0.35/0.69                  @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 0.35/0.69                  @ ( topolo2815343760600316023s_real @ Y2 )
% 0.35/0.69                  @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.35/0.69               => ( filterlim_real_real
% 0.35/0.69                  @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 0.35/0.69                  @ ( topolo2815343760600316023s_real @ Y2 )
% 0.35/0.69                  @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % lhopital_at_top
% 0.35/0.69  thf(fact_10039_lhospital__at__top__at__top,axiom,
% 0.35/0.69      ! [G: real > real,G2: real > real,F: real > real,F4: real > real,X: real] :
% 0.35/0.69        ( ( filterlim_real_real @ G @ at_top_real @ at_top_real )
% 0.35/0.69       => ( ( eventually_real
% 0.35/0.69            @ ^ [X2: real] :
% 0.35/0.69                ( ( G2 @ X2 )
% 0.35/0.69               != zero_zero_real )
% 0.35/0.69            @ at_top_real )
% 0.35/0.69         => ( ( eventually_real
% 0.35/0.69              @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 0.35/0.69              @ at_top_real )
% 0.35/0.69           => ( ( eventually_real
% 0.35/0.69                @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 0.35/0.69                @ at_top_real )
% 0.35/0.69             => ( ( filterlim_real_real
% 0.35/0.69                  @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 0.35/0.69                  @ ( topolo2815343760600316023s_real @ X )
% 0.35/0.69                  @ at_top_real )
% 0.35/0.69               => ( filterlim_real_real
% 0.35/0.69                  @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 0.35/0.69                  @ ( topolo2815343760600316023s_real @ X )
% 0.35/0.69                  @ at_top_real ) ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % lhospital_at_top_at_top
% 0.35/0.69  thf(fact_10040_lhopital__right,axiom,
% 0.35/0.69      ! [F: real > real,X: real,G: real > real,G2: real > real,F4: real > real,F5: filter_real] :
% 0.35/0.69        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 0.35/0.69       => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 0.35/0.69         => ( ( eventually_real
% 0.35/0.69              @ ^ [X2: real] :
% 0.35/0.69                  ( ( G @ X2 )
% 0.35/0.69                 != zero_zero_real )
% 0.35/0.69              @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 0.35/0.69           => ( ( eventually_real
% 0.35/0.69                @ ^ [X2: real] :
% 0.35/0.69                    ( ( G2 @ X2 )
% 0.35/0.69                   != zero_zero_real )
% 0.35/0.69                @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 0.35/0.69             => ( ( eventually_real
% 0.35/0.69                  @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 0.35/0.69                  @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 0.35/0.69               => ( ( eventually_real
% 0.35/0.69                    @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 0.35/0.69                    @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 0.35/0.69                 => ( ( filterlim_real_real
% 0.35/0.69                      @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 0.35/0.69                      @ F5
% 0.35/0.69                      @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 0.35/0.69                   => ( filterlim_real_real
% 0.35/0.69                      @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 0.35/0.69                      @ F5
% 0.35/0.69                      @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % lhopital_right
% 0.35/0.69  thf(fact_10041_lhopital__right__0,axiom,
% 0.35/0.69      ! [F0: real > real,G0: real > real,G2: real > real,F4: real > real,F5: filter_real] :
% 0.35/0.69        ( ( filterlim_real_real @ F0 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.35/0.69       => ( ( filterlim_real_real @ G0 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.35/0.69         => ( ( eventually_real
% 0.35/0.69              @ ^ [X2: real] :
% 0.35/0.69                  ( ( G0 @ X2 )
% 0.35/0.69                 != zero_zero_real )
% 0.35/0.69              @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.35/0.69           => ( ( eventually_real
% 0.35/0.69                @ ^ [X2: real] :
% 0.35/0.69                    ( ( G2 @ X2 )
% 0.35/0.69                   != zero_zero_real )
% 0.35/0.69                @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.35/0.69             => ( ( eventually_real
% 0.35/0.69                  @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F0 @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 0.35/0.69                  @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.35/0.69               => ( ( eventually_real
% 0.35/0.69                    @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G0 @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 0.35/0.69                    @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.35/0.69                 => ( ( filterlim_real_real
% 0.35/0.69                      @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 0.35/0.69                      @ F5
% 0.35/0.69                      @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.35/0.69                   => ( filterlim_real_real
% 0.35/0.69                      @ ^ [X2: real] : ( divide_divide_real @ ( F0 @ X2 ) @ ( G0 @ X2 ) )
% 0.35/0.69                      @ F5
% 0.35/0.69                      @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % lhopital_right_0
% 0.35/0.69  thf(fact_10042_lhopital__right__at__top__at__bot,axiom,
% 0.35/0.69      ! [F: real > real,A: real,G: real > real,F4: real > real,G2: real > real] :
% 0.35/0.69        ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 0.35/0.69       => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 0.35/0.69         => ( ( eventually_real
% 0.35/0.69              @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 0.35/0.69              @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 0.35/0.69           => ( ( eventually_real
% 0.35/0.69                @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 0.35/0.69                @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 0.35/0.69             => ( ( filterlim_real_real
% 0.35/0.69                  @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 0.35/0.69                  @ at_bot_real
% 0.35/0.69                  @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 0.35/0.69               => ( filterlim_real_real
% 0.35/0.69                  @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 0.35/0.69                  @ at_bot_real
% 0.35/0.69                  @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % lhopital_right_at_top_at_bot
% 0.35/0.69  thf(fact_10043_lhopital__right__0__at__top,axiom,
% 0.35/0.69      ! [G: real > real,G2: real > real,F: real > real,F4: real > real,X: real] :
% 0.35/0.69        ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.35/0.69       => ( ( eventually_real
% 0.35/0.69            @ ^ [X2: real] :
% 0.35/0.69                ( ( G2 @ X2 )
% 0.35/0.69               != zero_zero_real )
% 0.35/0.69            @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.35/0.69         => ( ( eventually_real
% 0.35/0.69              @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 0.35/0.69              @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.35/0.69           => ( ( eventually_real
% 0.35/0.69                @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 0.35/0.69                @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.35/0.69             => ( ( filterlim_real_real
% 0.35/0.69                  @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 0.35/0.69                  @ ( topolo2815343760600316023s_real @ X )
% 0.35/0.69                  @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.35/0.69               => ( filterlim_real_real
% 0.35/0.69                  @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 0.35/0.69                  @ ( topolo2815343760600316023s_real @ X )
% 0.35/0.69                  @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % lhopital_right_0_at_top
% 0.35/0.69  thf(fact_10044_GreatestI__nat,axiom,
% 0.35/0.69      ! [P: nat > $o,K: nat,B: nat] :
% 0.35/0.69        ( ( P @ K )
% 0.35/0.69       => ( ! [Y3: nat] :
% 0.35/0.69              ( ( P @ Y3 )
% 0.35/0.69             => ( ord_less_eq_nat @ Y3 @ B ) )
% 0.35/0.69         => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % GreatestI_nat
% 0.35/0.69  thf(fact_10045_Greatest__le__nat,axiom,
% 0.35/0.69      ! [P: nat > $o,K: nat,B: nat] :
% 0.35/0.69        ( ( P @ K )
% 0.35/0.69       => ( ! [Y3: nat] :
% 0.35/0.69              ( ( P @ Y3 )
% 0.35/0.69             => ( ord_less_eq_nat @ Y3 @ B ) )
% 0.35/0.69         => ( ord_less_eq_nat @ K @ ( order_Greatest_nat @ P ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % Greatest_le_nat
% 0.35/0.69  thf(fact_10046_GreatestI__ex__nat,axiom,
% 0.35/0.69      ! [P: nat > $o,B: nat] :
% 0.35/0.69        ( ? [X_1: nat] : ( P @ X_1 )
% 0.35/0.69       => ( ! [Y3: nat] :
% 0.35/0.69              ( ( P @ Y3 )
% 0.35/0.69             => ( ord_less_eq_nat @ Y3 @ B ) )
% 0.35/0.69         => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % GreatestI_ex_nat
% 0.35/0.69  thf(fact_10047_Bseq__realpow,axiom,
% 0.35/0.69      ! [X: real] :
% 0.35/0.69        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.69       => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.35/0.69         => ( bfun_nat_real @ ( power_power_real @ X ) @ at_top_nat ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % Bseq_realpow
% 0.35/0.69  thf(fact_10048_VEBT__internal_Ovalid_H_Oelims_I1_J,axiom,
% 0.35/0.69      ! [X: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 0.35/0.69        ( ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 0.35/0.69          = Y2 )
% 0.35/0.69       => ( ( ? [Uu2: $o,Uv2: $o] :
% 0.35/0.69                ( X
% 0.35/0.69                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.35/0.69           => ( Y2
% 0.35/0.69              = ( Xa2 != one_one_nat ) ) )
% 0.35/0.69         => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.69                ( ( X
% 0.35/0.69                  = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.35/0.69               => ( Y2
% 0.35/0.69                  = ( ~ ( ( Deg2 = Xa2 )
% 0.35/0.69                        & ! [X2: vEBT_VEBT] :
% 0.35/0.69                            ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.35/0.69                           => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.69                        & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.69                        & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.35/0.69                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.69                        & ( case_o184042715313410164at_nat
% 0.35/0.69                          @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 0.35/0.69                            & ! [X2: vEBT_VEBT] :
% 0.35/0.69                                ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.35/0.69                               => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 0.35/0.69                          @ ( produc6081775807080527818_nat_o
% 0.35/0.69                            @ ^ [Mi3: nat,Ma3: nat] :
% 0.35/0.69                                ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.35/0.69                                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.35/0.69                                & ! [I3: nat] :
% 0.35/0.69                                    ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.69                                   => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X4 ) )
% 0.35/0.69                                      = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 0.35/0.69                                & ( ( Mi3 = Ma3 )
% 0.35/0.69                                 => ! [X2: vEBT_VEBT] :
% 0.35/0.69                                      ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.35/0.69                                     => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 0.35/0.69                                & ( ( Mi3 != Ma3 )
% 0.35/0.69                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 0.35/0.69                                    & ! [X2: nat] :
% 0.35/0.69                                        ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.35/0.69                                       => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X2 )
% 0.35/0.69                                         => ( ( ord_less_nat @ Mi3 @ X2 )
% 0.35/0.69                                            & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 0.35/0.69                          @ Mima ) ) ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % VEBT_internal.valid'.elims(1)
% 0.35/0.69  thf(fact_10049_decseq__bounded,axiom,
% 0.35/0.69      ! [X8: nat > real,B2: real] :
% 0.35/0.69        ( ( order_9091379641038594480t_real @ X8 )
% 0.35/0.69       => ( ! [I4: nat] : ( ord_less_eq_real @ B2 @ ( X8 @ I4 ) )
% 0.35/0.69         => ( bfun_nat_real @ X8 @ at_top_nat ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % decseq_bounded
% 0.35/0.69  thf(fact_10050_decseq__convergent,axiom,
% 0.35/0.69      ! [X8: nat > real,B2: real] :
% 0.35/0.69        ( ( order_9091379641038594480t_real @ X8 )
% 0.35/0.69       => ( ! [I4: nat] : ( ord_less_eq_real @ B2 @ ( X8 @ I4 ) )
% 0.35/0.69         => ~ ! [L6: real] :
% 0.35/0.69                ( ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 0.35/0.69               => ~ ! [I: nat] : ( ord_less_eq_real @ L6 @ ( X8 @ I ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % decseq_convergent
% 0.35/0.69  thf(fact_10051_VEBT__internal_Ovalid_H_Osimps_I2_J,axiom,
% 0.35/0.69      ! [Mima2: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Deg4: nat] :
% 0.35/0.69        ( ( vEBT_VEBT_valid @ ( vEBT_Node @ Mima2 @ Deg @ TreeList @ Summary ) @ Deg4 )
% 0.35/0.69        = ( ( Deg = Deg4 )
% 0.35/0.69          & ! [X2: vEBT_VEBT] :
% 0.35/0.69              ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.35/0.69             => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.69          & ( vEBT_VEBT_valid @ Summary @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.69          & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.35/0.69            = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.69          & ( case_o184042715313410164at_nat
% 0.35/0.69            @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X4 )
% 0.35/0.69              & ! [X2: vEBT_VEBT] :
% 0.35/0.69                  ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.35/0.69                 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 0.35/0.69            @ ( produc6081775807080527818_nat_o
% 0.35/0.69              @ ^ [Mi3: nat,Ma3: nat] :
% 0.35/0.69                  ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.35/0.69                  & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 0.35/0.69                  & ! [I3: nat] :
% 0.35/0.69                      ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.69                     => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ X4 ) )
% 0.35/0.69                        = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 0.35/0.69                  & ( ( Mi3 = Ma3 )
% 0.35/0.69                   => ! [X2: vEBT_VEBT] :
% 0.35/0.69                        ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.35/0.69                       => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 0.35/0.69                  & ( ( Mi3 != Ma3 )
% 0.35/0.69                   => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 0.35/0.69                      & ! [X2: nat] :
% 0.35/0.69                          ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 0.35/0.69                         => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X2 )
% 0.35/0.69                           => ( ( ord_less_nat @ Mi3 @ X2 )
% 0.35/0.69                              & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 0.35/0.69            @ Mima2 ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % VEBT_internal.valid'.simps(2)
% 0.35/0.69  thf(fact_10052_VEBT__internal_Ovalid_H_Oelims_I3_J,axiom,
% 0.35/0.69      ! [X: vEBT_VEBT,Xa2: nat] :
% 0.35/0.69        ( ~ ( vEBT_VEBT_valid @ X @ Xa2 )
% 0.35/0.69       => ( ( ? [Uu2: $o,Uv2: $o] :
% 0.35/0.69                ( X
% 0.35/0.69                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.35/0.69           => ( Xa2 = one_one_nat ) )
% 0.35/0.69         => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.69                ( ( X
% 0.35/0.69                  = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.35/0.69               => ( ( Deg2 = Xa2 )
% 0.35/0.69                  & ! [X3: vEBT_VEBT] :
% 0.35/0.69                      ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.35/0.69                     => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.69                  & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.69                  & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.35/0.69                    = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.69                  & ( case_o184042715313410164at_nat
% 0.35/0.69                    @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 0.35/0.69                      & ! [X2: vEBT_VEBT] :
% 0.35/0.69                          ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.35/0.69                         => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 0.35/0.69                    @ ( produc6081775807080527818_nat_o
% 0.35/0.69                      @ ^ [Mi3: nat,Ma3: nat] :
% 0.35/0.69                          ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.35/0.69                          & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.35/0.69                          & ! [I3: nat] :
% 0.35/0.69                              ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.69                             => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X4 ) )
% 0.35/0.69                                = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 0.35/0.69                          & ( ( Mi3 = Ma3 )
% 0.35/0.69                           => ! [X2: vEBT_VEBT] :
% 0.35/0.69                                ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.35/0.69                               => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 0.35/0.69                          & ( ( Mi3 != Ma3 )
% 0.35/0.69                           => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 0.35/0.69                              & ! [X2: nat] :
% 0.35/0.69                                  ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.35/0.69                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X2 )
% 0.35/0.69                                   => ( ( ord_less_nat @ Mi3 @ X2 )
% 0.35/0.69                                      & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 0.35/0.69                    @ Mima ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % VEBT_internal.valid'.elims(3)
% 0.35/0.69  thf(fact_10053_VEBT__internal_Ovalid_H_Oelims_I2_J,axiom,
% 0.35/0.69      ! [X: vEBT_VEBT,Xa2: nat] :
% 0.35/0.69        ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 0.35/0.69       => ( ( ? [Uu2: $o,Uv2: $o] :
% 0.35/0.69                ( X
% 0.35/0.69                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.35/0.69           => ( Xa2 != one_one_nat ) )
% 0.35/0.69         => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.69                ( ( X
% 0.35/0.69                  = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.35/0.69               => ~ ( ( Deg2 = Xa2 )
% 0.35/0.69                    & ! [X5: vEBT_VEBT] :
% 0.35/0.69                        ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.35/0.69                       => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.69                    & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.69                    & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.35/0.69                      = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.69                    & ( case_o184042715313410164at_nat
% 0.35/0.69                      @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 0.35/0.69                        & ! [X2: vEBT_VEBT] :
% 0.35/0.69                            ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.35/0.69                           => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 0.35/0.69                      @ ( produc6081775807080527818_nat_o
% 0.35/0.69                        @ ^ [Mi3: nat,Ma3: nat] :
% 0.35/0.69                            ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.35/0.69                            & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.35/0.69                            & ! [I3: nat] :
% 0.35/0.69                                ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.69                               => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X4 ) )
% 0.35/0.69                                  = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 0.35/0.69                            & ( ( Mi3 = Ma3 )
% 0.35/0.69                             => ! [X2: vEBT_VEBT] :
% 0.35/0.69                                  ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.35/0.69                                 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 0.35/0.69                            & ( ( Mi3 != Ma3 )
% 0.35/0.69                             => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 0.35/0.69                                & ! [X2: nat] :
% 0.35/0.69                                    ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.35/0.69                                   => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X2 )
% 0.35/0.69                                     => ( ( ord_less_nat @ Mi3 @ X2 )
% 0.35/0.69                                        & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 0.35/0.69                      @ Mima ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % VEBT_internal.valid'.elims(2)
% 0.35/0.69  thf(fact_10054_VEBT__internal_Ovalid_H_Opelims_I3_J,axiom,
% 0.35/0.69      ! [X: vEBT_VEBT,Xa2: nat] :
% 0.35/0.69        ( ~ ( vEBT_VEBT_valid @ X @ Xa2 )
% 0.35/0.69       => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.69         => ( ! [Uu2: $o,Uv2: $o] :
% 0.35/0.69                ( ( X
% 0.35/0.69                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.35/0.69               => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 0.35/0.69                 => ( Xa2 = one_one_nat ) ) )
% 0.35/0.69           => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.69                  ( ( X
% 0.35/0.69                    = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.35/0.69                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) )
% 0.35/0.69                   => ( ( Deg2 = Xa2 )
% 0.35/0.69                      & ! [X3: vEBT_VEBT] :
% 0.35/0.69                          ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.35/0.69                         => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.69                      & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.69                      & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.35/0.69                        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.69                      & ( case_o184042715313410164at_nat
% 0.35/0.69                        @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 0.35/0.69                          & ! [X2: vEBT_VEBT] :
% 0.35/0.69                              ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.35/0.69                             => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 0.35/0.69                        @ ( produc6081775807080527818_nat_o
% 0.35/0.69                          @ ^ [Mi3: nat,Ma3: nat] :
% 0.35/0.69                              ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.35/0.69                              & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.35/0.69                              & ! [I3: nat] :
% 0.35/0.69                                  ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.69                                 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X4 ) )
% 0.35/0.69                                    = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 0.35/0.69                              & ( ( Mi3 = Ma3 )
% 0.35/0.69                               => ! [X2: vEBT_VEBT] :
% 0.35/0.69                                    ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.35/0.69                                   => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 0.35/0.69                              & ( ( Mi3 != Ma3 )
% 0.35/0.69                               => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 0.35/0.69                                  & ! [X2: nat] :
% 0.35/0.69                                      ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.35/0.69                                     => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X2 )
% 0.35/0.69                                       => ( ( ord_less_nat @ Mi3 @ X2 )
% 0.35/0.69                                          & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 0.35/0.69                        @ Mima ) ) ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % VEBT_internal.valid'.pelims(3)
% 0.35/0.69  thf(fact_10055_VEBT__internal_Ovalid_H_Opelims_I2_J,axiom,
% 0.35/0.69      ! [X: vEBT_VEBT,Xa2: nat] :
% 0.35/0.69        ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 0.35/0.69       => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.69         => ( ! [Uu2: $o,Uv2: $o] :
% 0.35/0.69                ( ( X
% 0.35/0.69                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.35/0.69               => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 0.35/0.69                 => ( Xa2 != one_one_nat ) ) )
% 0.35/0.69           => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.69                  ( ( X
% 0.35/0.69                    = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.35/0.69                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) )
% 0.35/0.69                   => ~ ( ( Deg2 = Xa2 )
% 0.35/0.69                        & ! [X5: vEBT_VEBT] :
% 0.35/0.69                            ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.35/0.69                           => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.69                        & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.69                        & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.35/0.69                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.69                        & ( case_o184042715313410164at_nat
% 0.35/0.69                          @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 0.35/0.69                            & ! [X2: vEBT_VEBT] :
% 0.35/0.69                                ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.35/0.69                               => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 0.35/0.69                          @ ( produc6081775807080527818_nat_o
% 0.35/0.69                            @ ^ [Mi3: nat,Ma3: nat] :
% 0.35/0.69                                ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.35/0.69                                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.35/0.69                                & ! [I3: nat] :
% 0.35/0.69                                    ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.69                                   => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X4 ) )
% 0.35/0.69                                      = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 0.35/0.69                                & ( ( Mi3 = Ma3 )
% 0.35/0.69                                 => ! [X2: vEBT_VEBT] :
% 0.35/0.69                                      ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.35/0.69                                     => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 0.35/0.69                                & ( ( Mi3 != Ma3 )
% 0.35/0.69                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 0.35/0.69                                    & ! [X2: nat] :
% 0.35/0.69                                        ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.35/0.69                                       => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X2 )
% 0.35/0.69                                         => ( ( ord_less_nat @ Mi3 @ X2 )
% 0.35/0.69                                            & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 0.35/0.69                          @ Mima ) ) ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % VEBT_internal.valid'.pelims(2)
% 0.35/0.69  thf(fact_10056_VEBT__internal_Ovalid_H_Opelims_I1_J,axiom,
% 0.35/0.69      ! [X: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 0.35/0.69        ( ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 0.35/0.69          = Y2 )
% 0.35/0.69       => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.69         => ( ! [Uu2: $o,Uv2: $o] :
% 0.35/0.69                ( ( X
% 0.35/0.69                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.35/0.69               => ( ( Y2
% 0.35/0.69                    = ( Xa2 = one_one_nat ) )
% 0.35/0.69                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 0.35/0.69           => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.69                  ( ( X
% 0.35/0.69                    = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.35/0.69                 => ( ( Y2
% 0.35/0.69                      = ( ( Deg2 = Xa2 )
% 0.35/0.69                        & ! [X2: vEBT_VEBT] :
% 0.35/0.69                            ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.35/0.69                           => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.69                        & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.69                        & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.35/0.69                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.69                        & ( case_o184042715313410164at_nat
% 0.35/0.69                          @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 0.35/0.69                            & ! [X2: vEBT_VEBT] :
% 0.35/0.69                                ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.35/0.69                               => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 0.35/0.69                          @ ( produc6081775807080527818_nat_o
% 0.35/0.69                            @ ^ [Mi3: nat,Ma3: nat] :
% 0.35/0.69                                ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.35/0.69                                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.35/0.69                                & ! [I3: nat] :
% 0.35/0.69                                    ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.69                                   => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X4 ) )
% 0.35/0.69                                      = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 0.35/0.69                                & ( ( Mi3 = Ma3 )
% 0.35/0.69                                 => ! [X2: vEBT_VEBT] :
% 0.35/0.69                                      ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.35/0.69                                     => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 0.35/0.69                                & ( ( Mi3 != Ma3 )
% 0.35/0.69                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 0.35/0.69                                    & ! [X2: nat] :
% 0.35/0.69                                        ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.35/0.69                                       => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X2 )
% 0.35/0.69                                         => ( ( ord_less_nat @ Mi3 @ X2 )
% 0.35/0.69                                            & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 0.35/0.69                          @ Mima ) ) )
% 0.35/0.69                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % VEBT_internal.valid'.pelims(1)
% 0.35/0.69  thf(fact_10057_GMVT,axiom,
% 0.35/0.69      ! [A: real,B: real,F: real > real,G: real > real] :
% 0.35/0.69        ( ( ord_less_real @ A @ B )
% 0.35/0.69       => ( ! [X3: real] :
% 0.35/0.69              ( ( ( ord_less_eq_real @ A @ X3 )
% 0.35/0.69                & ( ord_less_eq_real @ X3 @ B ) )
% 0.35/0.69             => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ F ) )
% 0.35/0.69         => ( ! [X3: real] :
% 0.35/0.69                ( ( ( ord_less_real @ A @ X3 )
% 0.35/0.69                  & ( ord_less_real @ X3 @ B ) )
% 0.35/0.69               => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 0.35/0.69           => ( ! [X3: real] :
% 0.35/0.69                  ( ( ( ord_less_eq_real @ A @ X3 )
% 0.35/0.69                    & ( ord_less_eq_real @ X3 @ B ) )
% 0.35/0.69                 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ G ) )
% 0.35/0.69             => ( ! [X3: real] :
% 0.35/0.69                    ( ( ( ord_less_real @ A @ X3 )
% 0.35/0.69                      & ( ord_less_real @ X3 @ B ) )
% 0.35/0.69                   => ( differ6690327859849518006l_real @ G @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 0.35/0.69               => ? [G_c: real,F_c: real,C2: real] :
% 0.35/0.69                    ( ( has_fi5821293074295781190e_real @ G @ G_c @ ( topolo2177554685111907308n_real @ C2 @ top_top_set_real ) )
% 0.35/0.69                    & ( has_fi5821293074295781190e_real @ F @ F_c @ ( topolo2177554685111907308n_real @ C2 @ top_top_set_real ) )
% 0.35/0.69                    & ( ord_less_real @ A @ C2 )
% 0.35/0.69                    & ( ord_less_real @ C2 @ B )
% 0.35/0.69                    & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ G_c )
% 0.35/0.69                      = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ F_c ) ) ) ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % GMVT
% 0.35/0.69  thf(fact_10058_MVT,axiom,
% 0.35/0.69      ! [A: real,B: real,F: real > real] :
% 0.35/0.69        ( ( ord_less_real @ A @ B )
% 0.35/0.69       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.35/0.69         => ( ! [X3: real] :
% 0.35/0.69                ( ( ord_less_real @ A @ X3 )
% 0.35/0.69               => ( ( ord_less_real @ X3 @ B )
% 0.35/0.69                 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 0.35/0.69           => ? [L4: real,Z3: real] :
% 0.35/0.69                ( ( ord_less_real @ A @ Z3 )
% 0.35/0.69                & ( ord_less_real @ Z3 @ B )
% 0.35/0.69                & ( has_fi5821293074295781190e_real @ F @ L4 @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) )
% 0.35/0.69                & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 0.35/0.69                  = ( times_times_real @ ( minus_minus_real @ B @ A ) @ L4 ) ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % MVT
% 0.35/0.69  thf(fact_10059_continuous__on__arcosh,axiom,
% 0.35/0.69      ! [A2: set_real] :
% 0.35/0.69        ( ( ord_less_eq_set_real @ A2 @ ( set_ord_atLeast_real @ one_one_real ) )
% 0.35/0.69       => ( topolo5044208981011980120l_real @ A2 @ arcosh_real ) ) ).
% 0.35/0.69  
% 0.35/0.69  % continuous_on_arcosh
% 0.35/0.69  thf(fact_10060_continuous__on__arcosh_H,axiom,
% 0.35/0.69      ! [A2: set_real,F: real > real] :
% 0.35/0.69        ( ( topolo5044208981011980120l_real @ A2 @ F )
% 0.35/0.69       => ( ! [X3: real] :
% 0.35/0.69              ( ( member_real @ X3 @ A2 )
% 0.35/0.69             => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 0.35/0.69         => ( topolo5044208981011980120l_real @ A2
% 0.35/0.69            @ ^ [X2: real] : ( arcosh_real @ ( F @ X2 ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % continuous_on_arcosh'
% 0.35/0.69  thf(fact_10061_continuous__image__closed__interval,axiom,
% 0.35/0.69      ! [A: real,B: real,F: real > real] :
% 0.35/0.69        ( ( ord_less_eq_real @ A @ B )
% 0.35/0.69       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.35/0.69         => ? [C2: real,D3: real] :
% 0.35/0.69              ( ( ( image_real_real @ F @ ( set_or1222579329274155063t_real @ A @ B ) )
% 0.35/0.69                = ( set_or1222579329274155063t_real @ C2 @ D3 ) )
% 0.35/0.69              & ( ord_less_eq_real @ C2 @ D3 ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % continuous_image_closed_interval
% 0.35/0.69  thf(fact_10062_continuous__on__arccos_H,axiom,
% 0.35/0.69      topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arccos ).
% 0.35/0.69  
% 0.35/0.69  % continuous_on_arccos'
% 0.35/0.69  thf(fact_10063_continuous__on__arcsin_H,axiom,
% 0.35/0.69      topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arcsin ).
% 0.35/0.69  
% 0.35/0.69  % continuous_on_arcsin'
% 0.35/0.69  thf(fact_10064_continuous__on__artanh,axiom,
% 0.35/0.69      ! [A2: set_real] :
% 0.35/0.69        ( ( ord_less_eq_set_real @ A2 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) )
% 0.35/0.69       => ( topolo5044208981011980120l_real @ A2 @ artanh_real ) ) ).
% 0.35/0.69  
% 0.35/0.69  % continuous_on_artanh
% 0.35/0.69  thf(fact_10065_continuous__on__artanh_H,axiom,
% 0.35/0.69      ! [A2: set_real,F: real > real] :
% 0.35/0.69        ( ( topolo5044208981011980120l_real @ A2 @ F )
% 0.35/0.69       => ( ! [X3: real] :
% 0.35/0.69              ( ( member_real @ X3 @ A2 )
% 0.35/0.69             => ( member_real @ ( F @ X3 ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) )
% 0.35/0.69         => ( topolo5044208981011980120l_real @ A2
% 0.35/0.69            @ ^ [X2: real] : ( artanh_real @ ( F @ X2 ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % continuous_on_artanh'
% 0.35/0.69  thf(fact_10066_Rolle__deriv,axiom,
% 0.35/0.69      ! [A: real,B: real,F: real > real,F4: real > real > real] :
% 0.35/0.69        ( ( ord_less_real @ A @ B )
% 0.35/0.69       => ( ( ( F @ A )
% 0.35/0.69            = ( F @ B ) )
% 0.35/0.69         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.35/0.69           => ( ! [X3: real] :
% 0.35/0.69                  ( ( ord_less_real @ A @ X3 )
% 0.35/0.69                 => ( ( ord_less_real @ X3 @ B )
% 0.35/0.69                   => ( has_de1759254742604945161l_real @ F @ ( F4 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 0.35/0.69             => ? [Z3: real] :
% 0.35/0.69                  ( ( ord_less_real @ A @ Z3 )
% 0.35/0.69                  & ( ord_less_real @ Z3 @ B )
% 0.35/0.69                  & ( ( F4 @ Z3 )
% 0.35/0.69                    = ( ^ [V4: real] : zero_zero_real ) ) ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % Rolle_deriv
% 0.35/0.69  thf(fact_10067_mvt,axiom,
% 0.35/0.69      ! [A: real,B: real,F: real > real,F4: real > real > real] :
% 0.35/0.69        ( ( ord_less_real @ A @ B )
% 0.35/0.69       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.35/0.69         => ( ! [X3: real] :
% 0.35/0.69                ( ( ord_less_real @ A @ X3 )
% 0.35/0.69               => ( ( ord_less_real @ X3 @ B )
% 0.35/0.69                 => ( has_de1759254742604945161l_real @ F @ ( F4 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 0.35/0.69           => ~ ! [Xi: real] :
% 0.35/0.69                  ( ( ord_less_real @ A @ Xi )
% 0.35/0.69                 => ( ( ord_less_real @ Xi @ B )
% 0.35/0.69                   => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 0.35/0.69                     != ( F4 @ Xi @ ( minus_minus_real @ B @ A ) ) ) ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % mvt
% 0.35/0.69  thf(fact_10068_DERIV__isconst__end,axiom,
% 0.35/0.69      ! [A: real,B: real,F: real > real] :
% 0.35/0.69        ( ( ord_less_real @ A @ B )
% 0.35/0.69       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.35/0.69         => ( ! [X3: real] :
% 0.35/0.69                ( ( ord_less_real @ A @ X3 )
% 0.35/0.69               => ( ( ord_less_real @ X3 @ B )
% 0.35/0.69                 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 0.35/0.69           => ( ( F @ B )
% 0.35/0.69              = ( F @ A ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % DERIV_isconst_end
% 0.35/0.69  thf(fact_10069_DERIV__neg__imp__decreasing__open,axiom,
% 0.35/0.69      ! [A: real,B: real,F: real > real] :
% 0.35/0.69        ( ( ord_less_real @ A @ B )
% 0.35/0.69       => ( ! [X3: real] :
% 0.35/0.69              ( ( ord_less_real @ A @ X3 )
% 0.35/0.69             => ( ( ord_less_real @ X3 @ B )
% 0.35/0.69               => ? [Y4: real] :
% 0.35/0.69                    ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.35/0.69                    & ( ord_less_real @ Y4 @ zero_zero_real ) ) ) )
% 0.35/0.69         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.35/0.69           => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % DERIV_neg_imp_decreasing_open
% 0.35/0.69  thf(fact_10070_DERIV__pos__imp__increasing__open,axiom,
% 0.35/0.69      ! [A: real,B: real,F: real > real] :
% 0.35/0.69        ( ( ord_less_real @ A @ B )
% 0.35/0.69       => ( ! [X3: real] :
% 0.35/0.69              ( ( ord_less_real @ A @ X3 )
% 0.35/0.69             => ( ( ord_less_real @ X3 @ B )
% 0.35/0.69               => ? [Y4: real] :
% 0.35/0.69                    ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.35/0.69                    & ( ord_less_real @ zero_zero_real @ Y4 ) ) ) )
% 0.35/0.69         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.35/0.69           => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % DERIV_pos_imp_increasing_open
% 0.35/0.69  thf(fact_10071_DERIV__isconst2,axiom,
% 0.35/0.69      ! [A: real,B: real,F: real > real,X: real] :
% 0.35/0.69        ( ( ord_less_real @ A @ B )
% 0.35/0.69       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.35/0.69         => ( ! [X3: real] :
% 0.35/0.69                ( ( ord_less_real @ A @ X3 )
% 0.35/0.69               => ( ( ord_less_real @ X3 @ B )
% 0.35/0.69                 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 0.35/0.69           => ( ( ord_less_eq_real @ A @ X )
% 0.35/0.69             => ( ( ord_less_eq_real @ X @ B )
% 0.35/0.69               => ( ( F @ X )
% 0.35/0.69                  = ( F @ A ) ) ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % DERIV_isconst2
% 0.35/0.69  thf(fact_10072_Rolle,axiom,
% 0.35/0.69      ! [A: real,B: real,F: real > real] :
% 0.35/0.69        ( ( ord_less_real @ A @ B )
% 0.35/0.69       => ( ( ( F @ A )
% 0.35/0.69            = ( F @ B ) )
% 0.35/0.69         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.35/0.69           => ( ! [X3: real] :
% 0.35/0.69                  ( ( ord_less_real @ A @ X3 )
% 0.35/0.69                 => ( ( ord_less_real @ X3 @ B )
% 0.35/0.69                   => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 0.35/0.69             => ? [Z3: real] :
% 0.35/0.69                  ( ( ord_less_real @ A @ Z3 )
% 0.35/0.69                  & ( ord_less_real @ Z3 @ B )
% 0.35/0.69                  & ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % Rolle
% 0.35/0.69  thf(fact_10073_uniformity__real__def,axiom,
% 0.35/0.69      ( topolo1511823702728130853y_real
% 0.35/0.69      = ( comple2936214249959783750l_real
% 0.35/0.69        @ ( image_2178119161166701260l_real
% 0.35/0.69          @ ^ [E3: real] :
% 0.35/0.69              ( princi6114159922880469582l_real
% 0.35/0.69              @ ( collec3799799289383736868l_real
% 0.35/0.69                @ ( produc5414030515140494994real_o
% 0.35/0.69                  @ ^ [X2: real,Y: real] : ( ord_less_real @ ( real_V975177566351809787t_real @ X2 @ Y ) @ E3 ) ) ) )
% 0.35/0.69          @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % uniformity_real_def
% 0.35/0.69  thf(fact_10074_uniformity__complex__def,axiom,
% 0.35/0.69      ( topolo896644834953643431omplex
% 0.35/0.69      = ( comple8358262395181532106omplex
% 0.35/0.69        @ ( image_5971271580939081552omplex
% 0.35/0.69          @ ^ [E3: real] :
% 0.35/0.69              ( princi3496590319149328850omplex
% 0.35/0.69              @ ( collec8663557070575231912omplex
% 0.35/0.69                @ ( produc6771430404735790350plex_o
% 0.35/0.69                  @ ^ [X2: complex,Y: complex] : ( ord_less_real @ ( real_V3694042436643373181omplex @ X2 @ Y ) @ E3 ) ) ) )
% 0.35/0.69          @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % uniformity_complex_def
% 0.35/0.69  thf(fact_10075_mono__Suc,axiom,
% 0.35/0.69      order_mono_nat_nat @ suc ).
% 0.35/0.69  
% 0.35/0.69  % mono_Suc
% 0.35/0.69  thf(fact_10076_mono__times__nat,axiom,
% 0.35/0.69      ! [N: nat] :
% 0.35/0.69        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.69       => ( order_mono_nat_nat @ ( times_times_nat @ N ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % mono_times_nat
% 0.35/0.69  thf(fact_10077_incseq__bounded,axiom,
% 0.35/0.69      ! [X8: nat > real,B2: real] :
% 0.35/0.69        ( ( order_mono_nat_real @ X8 )
% 0.35/0.69       => ( ! [I4: nat] : ( ord_less_eq_real @ ( X8 @ I4 ) @ B2 )
% 0.35/0.69         => ( bfun_nat_real @ X8 @ at_top_nat ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % incseq_bounded
% 0.35/0.69  thf(fact_10078_incseq__convergent,axiom,
% 0.35/0.69      ! [X8: nat > real,B2: real] :
% 0.35/0.69        ( ( order_mono_nat_real @ X8 )
% 0.35/0.69       => ( ! [I4: nat] : ( ord_less_eq_real @ ( X8 @ I4 ) @ B2 )
% 0.35/0.69         => ~ ! [L6: real] :
% 0.35/0.69                ( ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 0.35/0.69               => ~ ! [I: nat] : ( ord_less_eq_real @ ( X8 @ I ) @ L6 ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % incseq_convergent
% 0.35/0.69  thf(fact_10079_mono__ge2__power__minus__self,axiom,
% 0.35/0.69      ! [K: nat] :
% 0.35/0.69        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 0.35/0.69       => ( order_mono_nat_nat
% 0.35/0.69          @ ^ [M6: nat] : ( minus_minus_nat @ ( power_power_nat @ K @ M6 ) @ M6 ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % mono_ge2_power_minus_self
% 0.35/0.69  thf(fact_10080_eventually__prod__sequentially,axiom,
% 0.35/0.69      ! [P: product_prod_nat_nat > $o] :
% 0.35/0.69        ( ( eventu1038000079068216329at_nat @ P @ ( prod_filter_nat_nat @ at_top_nat @ at_top_nat ) )
% 0.35/0.69        = ( ? [N6: nat] :
% 0.35/0.69            ! [M6: nat] :
% 0.35/0.69              ( ( ord_less_eq_nat @ N6 @ M6 )
% 0.35/0.69             => ! [N2: nat] :
% 0.35/0.69                  ( ( ord_less_eq_nat @ N6 @ N2 )
% 0.35/0.69                 => ( P @ ( product_Pair_nat_nat @ N2 @ M6 ) ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % eventually_prod_sequentially
% 0.35/0.69  thf(fact_10081_filtermap__at__right__shift,axiom,
% 0.35/0.69      ! [D2: real,A: real] :
% 0.35/0.69        ( ( filtermap_real_real
% 0.35/0.69          @ ^ [X2: real] : ( minus_minus_real @ X2 @ D2 )
% 0.35/0.69          @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 0.35/0.69        = ( topolo2177554685111907308n_real @ ( minus_minus_real @ A @ D2 ) @ ( set_or5849166863359141190n_real @ ( minus_minus_real @ A @ D2 ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % filtermap_at_right_shift
% 0.35/0.69  thf(fact_10082_at__right__to__0,axiom,
% 0.35/0.69      ! [A: real] :
% 0.35/0.69        ( ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) )
% 0.35/0.69        = ( filtermap_real_real
% 0.35/0.69          @ ^ [X2: real] : ( plus_plus_real @ X2 @ A )
% 0.35/0.69          @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % at_right_to_0
% 0.35/0.69  thf(fact_10083_nonneg__incseq__Bseq__subseq__iff,axiom,
% 0.35/0.69      ! [F: nat > real,G: nat > nat] :
% 0.35/0.69        ( ! [X3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 0.35/0.69       => ( ( order_mono_nat_real @ F )
% 0.35/0.69         => ( ( order_5726023648592871131at_nat @ G )
% 0.35/0.69           => ( ( bfun_nat_real
% 0.35/0.69                @ ^ [X2: nat] : ( F @ ( G @ X2 ) )
% 0.35/0.69                @ at_top_nat )
% 0.35/0.69              = ( bfun_nat_real @ F @ at_top_nat ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % nonneg_incseq_Bseq_subseq_iff
% 0.35/0.69  thf(fact_10084_inj__sgn__power,axiom,
% 0.35/0.69      ! [N: nat] :
% 0.35/0.69        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.69       => ( inj_on_real_real
% 0.35/0.69          @ ^ [Y: real] : ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N ) )
% 0.35/0.69          @ top_top_set_real ) ) ).
% 0.35/0.69  
% 0.35/0.69  % inj_sgn_power
% 0.35/0.69  thf(fact_10085_strict__mono__imp__increasing,axiom,
% 0.35/0.69      ! [F: nat > nat,N: nat] :
% 0.35/0.69        ( ( order_5726023648592871131at_nat @ F )
% 0.35/0.69       => ( ord_less_eq_nat @ N @ ( F @ N ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % strict_mono_imp_increasing
% 0.35/0.69  thf(fact_10086_log__inj,axiom,
% 0.35/0.69      ! [B: real] :
% 0.35/0.69        ( ( ord_less_real @ one_one_real @ B )
% 0.35/0.69       => ( inj_on_real_real @ ( log @ B ) @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % log_inj
% 0.35/0.69  thf(fact_10087_inj__on__diff__nat,axiom,
% 0.35/0.69      ! [N4: set_nat,K: nat] :
% 0.35/0.69        ( ! [N3: nat] :
% 0.35/0.69            ( ( member_nat @ N3 @ N4 )
% 0.35/0.69           => ( ord_less_eq_nat @ K @ N3 ) )
% 0.35/0.69       => ( inj_on_nat_nat
% 0.35/0.69          @ ^ [N2: nat] : ( minus_minus_nat @ N2 @ K )
% 0.35/0.69          @ N4 ) ) ).
% 0.35/0.69  
% 0.35/0.69  % inj_on_diff_nat
% 0.35/0.69  thf(fact_10088_inj__Suc,axiom,
% 0.35/0.69      ! [N4: set_nat] : ( inj_on_nat_nat @ suc @ N4 ) ).
% 0.35/0.69  
% 0.35/0.69  % inj_Suc
% 0.35/0.69  thf(fact_10089_summable__reindex,axiom,
% 0.35/0.69      ! [F: nat > real,G: nat > nat] :
% 0.35/0.69        ( ( summable_real @ F )
% 0.35/0.69       => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 0.35/0.69         => ( ! [X3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 0.35/0.69           => ( summable_real @ ( comp_nat_real_nat @ F @ G ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % summable_reindex
% 0.35/0.69  thf(fact_10090_suminf__reindex__mono,axiom,
% 0.35/0.69      ! [F: nat > real,G: nat > nat] :
% 0.35/0.69        ( ( summable_real @ F )
% 0.35/0.69       => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 0.35/0.69         => ( ! [X3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 0.35/0.69           => ( ord_less_eq_real @ ( suminf_real @ ( comp_nat_real_nat @ F @ G ) ) @ ( suminf_real @ F ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % suminf_reindex_mono
% 0.35/0.69  thf(fact_10091_inj__on__char__of__nat,axiom,
% 0.35/0.69      inj_on_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % inj_on_char_of_nat
% 0.35/0.69  thf(fact_10092_suminf__reindex,axiom,
% 0.35/0.69      ! [F: nat > real,G: nat > nat] :
% 0.35/0.69        ( ( summable_real @ F )
% 0.35/0.69       => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 0.35/0.69         => ( ! [X3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 0.35/0.69           => ( ! [X3: nat] :
% 0.35/0.69                  ( ~ ( member_nat @ X3 @ ( image_nat_nat @ G @ top_top_set_nat ) )
% 0.35/0.69                 => ( ( F @ X3 )
% 0.35/0.69                    = zero_zero_real ) )
% 0.35/0.69             => ( ( suminf_real @ ( comp_nat_real_nat @ F @ G ) )
% 0.35/0.69                = ( suminf_real @ F ) ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % suminf_reindex
% 0.35/0.69  thf(fact_10093_pos__deriv__imp__strict__mono,axiom,
% 0.35/0.69      ! [F: real > real,F4: real > real] :
% 0.35/0.69        ( ! [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.35/0.69       => ( ! [X3: real] : ( ord_less_real @ zero_zero_real @ ( F4 @ X3 ) )
% 0.35/0.69         => ( order_7092887310737990675l_real @ F ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % pos_deriv_imp_strict_mono
% 0.35/0.69  thf(fact_10094_powr__real__of__int_H,axiom,
% 0.35/0.69      ! [X: real,N: int] :
% 0.35/0.69        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.69       => ( ( ( X != zero_zero_real )
% 0.35/0.69            | ( ord_less_int @ zero_zero_int @ N ) )
% 0.35/0.69         => ( ( powr_real @ X @ ( ring_1_of_int_real @ N ) )
% 0.35/0.69            = ( power_int_real @ X @ N ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % powr_real_of_int'
% 0.35/0.69  thf(fact_10095_pred__nat__def,axiom,
% 0.35/0.69      ( pred_nat
% 0.35/0.69      = ( collec3392354462482085612at_nat
% 0.35/0.69        @ ( produc6081775807080527818_nat_o
% 0.35/0.69          @ ^ [M6: nat,N2: nat] :
% 0.35/0.69              ( N2
% 0.35/0.69              = ( suc @ M6 ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % pred_nat_def
% 0.35/0.69  thf(fact_10096_atLeastLessThan__add__Un,axiom,
% 0.35/0.69      ! [I2: nat,J: nat,K: nat] :
% 0.35/0.69        ( ( ord_less_eq_nat @ I2 @ J )
% 0.35/0.69       => ( ( set_or4665077453230672383an_nat @ I2 @ ( plus_plus_nat @ J @ K ) )
% 0.35/0.69          = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I2 @ J ) @ ( set_or4665077453230672383an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % atLeastLessThan_add_Un
% 0.35/0.69  thf(fact_10097_sup__enat__def,axiom,
% 0.35/0.69      sup_su3973961784419623482d_enat = ord_ma741700101516333627d_enat ).
% 0.35/0.69  
% 0.35/0.69  % sup_enat_def
% 0.35/0.69  thf(fact_10098_sup__nat__def,axiom,
% 0.35/0.69      sup_sup_nat = ord_max_nat ).
% 0.35/0.69  
% 0.35/0.69  % sup_nat_def
% 0.35/0.69  thf(fact_10099_Rats__eq__int__div__nat,axiom,
% 0.35/0.69      ( field_5140801741446780682s_real
% 0.35/0.69      = ( collect_real
% 0.35/0.69        @ ^ [Uu3: real] :
% 0.35/0.69          ? [I3: int,N2: nat] :
% 0.35/0.69            ( ( Uu3
% 0.35/0.69              = ( divide_divide_real @ ( ring_1_of_int_real @ I3 ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 0.35/0.69            & ( N2 != zero_zero_nat ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % Rats_eq_int_div_nat
% 0.35/0.69  thf(fact_10100_Rats__abs__iff,axiom,
% 0.35/0.69      ! [X: real] :
% 0.35/0.69        ( ( member_real @ ( abs_abs_real @ X ) @ field_5140801741446780682s_real )
% 0.35/0.69        = ( member_real @ X @ field_5140801741446780682s_real ) ) ).
% 0.35/0.69  
% 0.35/0.69  % Rats_abs_iff
% 0.35/0.69  thf(fact_10101_Rats__dense__in__real,axiom,
% 0.35/0.69      ! [X: real,Y2: real] :
% 0.35/0.69        ( ( ord_less_real @ X @ Y2 )
% 0.35/0.69       => ? [X3: real] :
% 0.35/0.69            ( ( member_real @ X3 @ field_5140801741446780682s_real )
% 0.35/0.69            & ( ord_less_real @ X @ X3 )
% 0.35/0.69            & ( ord_less_real @ X3 @ Y2 ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % Rats_dense_in_real
% 0.35/0.69  thf(fact_10102_Rats__no__bot__less,axiom,
% 0.35/0.69      ! [X: real] :
% 0.35/0.69      ? [X3: real] :
% 0.35/0.69        ( ( member_real @ X3 @ field_5140801741446780682s_real )
% 0.35/0.69        & ( ord_less_real @ X3 @ X ) ) ).
% 0.35/0.69  
% 0.35/0.69  % Rats_no_bot_less
% 0.35/0.69  thf(fact_10103_Rats__no__top__le,axiom,
% 0.35/0.69      ! [X: real] :
% 0.35/0.69      ? [X3: real] :
% 0.35/0.69        ( ( member_real @ X3 @ field_5140801741446780682s_real )
% 0.35/0.69        & ( ord_less_eq_real @ X @ X3 ) ) ).
% 0.35/0.69  
% 0.35/0.69  % Rats_no_top_le
% 0.35/0.69  thf(fact_10104_Rats__eq__int__div__int,axiom,
% 0.35/0.69      ( field_5140801741446780682s_real
% 0.35/0.69      = ( collect_real
% 0.35/0.69        @ ^ [Uu3: real] :
% 0.35/0.69          ? [I3: int,J3: int] :
% 0.35/0.69            ( ( Uu3
% 0.35/0.69              = ( divide_divide_real @ ( ring_1_of_int_real @ I3 ) @ ( ring_1_of_int_real @ J3 ) ) )
% 0.35/0.69            & ( J3 != zero_zero_int ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % Rats_eq_int_div_int
% 0.35/0.69  thf(fact_10105_less__eq,axiom,
% 0.35/0.69      ! [M: nat,N: nat] :
% 0.35/0.69        ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N ) @ ( transi6264000038957366511cl_nat @ pred_nat ) )
% 0.35/0.69        = ( ord_less_nat @ M @ N ) ) ).
% 0.35/0.69  
% 0.35/0.69  % less_eq
% 0.35/0.69  thf(fact_10106_pred__nat__trancl__eq__le,axiom,
% 0.35/0.69      ! [M: nat,N: nat] :
% 0.35/0.69        ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N ) @ ( transi2905341329935302413cl_nat @ pred_nat ) )
% 0.35/0.69        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.35/0.69  
% 0.35/0.69  % pred_nat_trancl_eq_le
% 0.35/0.69  thf(fact_10107_tl__upt,axiom,
% 0.35/0.69      ! [M: nat,N: nat] :
% 0.35/0.69        ( ( tl_nat @ ( upt @ M @ N ) )
% 0.35/0.69        = ( upt @ ( suc @ M ) @ N ) ) ).
% 0.35/0.69  
% 0.35/0.69  % tl_upt
% 0.35/0.69  thf(fact_10108_hd__upt,axiom,
% 0.35/0.69      ! [I2: nat,J: nat] :
% 0.35/0.69        ( ( ord_less_nat @ I2 @ J )
% 0.35/0.69       => ( ( hd_nat @ ( upt @ I2 @ J ) )
% 0.35/0.69          = I2 ) ) ).
% 0.35/0.69  
% 0.35/0.69  % hd_upt
% 0.35/0.69  thf(fact_10109_drop__upt,axiom,
% 0.35/0.69      ! [M: nat,I2: nat,J: nat] :
% 0.35/0.69        ( ( drop_nat @ M @ ( upt @ I2 @ J ) )
% 0.35/0.69        = ( upt @ ( plus_plus_nat @ I2 @ M ) @ J ) ) ).
% 0.35/0.69  
% 0.35/0.69  % drop_upt
% 0.35/0.69  thf(fact_10110_length__upt,axiom,
% 0.35/0.69      ! [I2: nat,J: nat] :
% 0.35/0.69        ( ( size_size_list_nat @ ( upt @ I2 @ J ) )
% 0.35/0.69        = ( minus_minus_nat @ J @ I2 ) ) ).
% 0.35/0.69  
% 0.35/0.69  % length_upt
% 0.35/0.69  thf(fact_10111_take__upt,axiom,
% 0.35/0.69      ! [I2: nat,M: nat,N: nat] :
% 0.35/0.69        ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ M ) @ N )
% 0.35/0.69       => ( ( take_nat @ M @ ( upt @ I2 @ N ) )
% 0.35/0.69          = ( upt @ I2 @ ( plus_plus_nat @ I2 @ M ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % take_upt
% 0.35/0.69  thf(fact_10112_upt__conv__Nil,axiom,
% 0.35/0.69      ! [J: nat,I2: nat] :
% 0.35/0.69        ( ( ord_less_eq_nat @ J @ I2 )
% 0.35/0.69       => ( ( upt @ I2 @ J )
% 0.35/0.69          = nil_nat ) ) ).
% 0.35/0.69  
% 0.35/0.69  % upt_conv_Nil
% 0.35/0.69  thf(fact_10113_upt__eq__Nil__conv,axiom,
% 0.35/0.69      ! [I2: nat,J: nat] :
% 0.35/0.69        ( ( ( upt @ I2 @ J )
% 0.35/0.69          = nil_nat )
% 0.35/0.69        = ( ( J = zero_zero_nat )
% 0.35/0.69          | ( ord_less_eq_nat @ J @ I2 ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % upt_eq_Nil_conv
% 0.35/0.69  thf(fact_10114_nth__upt,axiom,
% 0.35/0.69      ! [I2: nat,K: nat,J: nat] :
% 0.35/0.69        ( ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ J )
% 0.35/0.69       => ( ( nth_nat @ ( upt @ I2 @ J ) @ K )
% 0.35/0.69          = ( plus_plus_nat @ I2 @ K ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % nth_upt
% 0.35/0.69  thf(fact_10115_upt__rec__numeral,axiom,
% 0.35/0.69      ! [M: num,N: num] :
% 0.35/0.69        ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.35/0.69         => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.35/0.69            = ( cons_nat @ ( numeral_numeral_nat @ M ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) ) ) ) )
% 0.35/0.69        & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.35/0.69         => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.35/0.69            = nil_nat ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % upt_rec_numeral
% 0.35/0.69  thf(fact_10116_map__Suc__upt,axiom,
% 0.35/0.69      ! [M: nat,N: nat] :
% 0.35/0.69        ( ( map_nat_nat @ suc @ ( upt @ M @ N ) )
% 0.35/0.69        = ( upt @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % map_Suc_upt
% 0.35/0.69  thf(fact_10117_map__add__upt,axiom,
% 0.35/0.69      ! [N: nat,M: nat] :
% 0.35/0.69        ( ( map_nat_nat
% 0.35/0.69          @ ^ [I3: nat] : ( plus_plus_nat @ I3 @ N )
% 0.35/0.69          @ ( upt @ zero_zero_nat @ M ) )
% 0.35/0.69        = ( upt @ N @ ( plus_plus_nat @ M @ N ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % map_add_upt
% 0.35/0.69  thf(fact_10118_upt__conv__Cons__Cons,axiom,
% 0.35/0.69      ! [M: nat,N: nat,Ns: list_nat,Q2: nat] :
% 0.35/0.69        ( ( ( cons_nat @ M @ ( cons_nat @ N @ Ns ) )
% 0.35/0.69          = ( upt @ M @ Q2 ) )
% 0.35/0.69        = ( ( cons_nat @ N @ Ns )
% 0.35/0.69          = ( upt @ ( suc @ M ) @ Q2 ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % upt_conv_Cons_Cons
% 0.35/0.69  thf(fact_10119_greaterThanLessThan__upt,axiom,
% 0.35/0.69      ( set_or5834768355832116004an_nat
% 0.35/0.69      = ( ^ [N2: nat,M6: nat] : ( set_nat2 @ ( upt @ ( suc @ N2 ) @ M6 ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % greaterThanLessThan_upt
% 0.35/0.69  thf(fact_10120_greaterThanAtMost__upt,axiom,
% 0.35/0.69      ( set_or6659071591806873216st_nat
% 0.35/0.69      = ( ^ [N2: nat,M6: nat] : ( set_nat2 @ ( upt @ ( suc @ N2 ) @ ( suc @ M6 ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % greaterThanAtMost_upt
% 0.35/0.69  thf(fact_10121_atLeastAtMost__upt,axiom,
% 0.35/0.69      ( set_or1269000886237332187st_nat
% 0.35/0.69      = ( ^ [N2: nat,M6: nat] : ( set_nat2 @ ( upt @ N2 @ ( suc @ M6 ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % atLeastAtMost_upt
% 0.35/0.69  thf(fact_10122_atMost__upto,axiom,
% 0.35/0.69      ( set_ord_atMost_nat
% 0.35/0.69      = ( ^ [N2: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ ( suc @ N2 ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % atMost_upto
% 0.35/0.69  thf(fact_10123_upt__conv__Cons,axiom,
% 0.35/0.69      ! [I2: nat,J: nat] :
% 0.35/0.69        ( ( ord_less_nat @ I2 @ J )
% 0.35/0.69       => ( ( upt @ I2 @ J )
% 0.35/0.69          = ( cons_nat @ I2 @ ( upt @ ( suc @ I2 ) @ J ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % upt_conv_Cons
% 0.35/0.69  thf(fact_10124_map__decr__upt,axiom,
% 0.35/0.69      ! [M: nat,N: nat] :
% 0.35/0.69        ( ( map_nat_nat
% 0.35/0.69          @ ^ [N2: nat] : ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 0.35/0.69          @ ( upt @ ( suc @ M ) @ ( suc @ N ) ) )
% 0.35/0.69        = ( upt @ M @ N ) ) ).
% 0.35/0.69  
% 0.35/0.69  % map_decr_upt
% 0.35/0.69  thf(fact_10125_upt__add__eq__append,axiom,
% 0.35/0.69      ! [I2: nat,J: nat,K: nat] :
% 0.35/0.69        ( ( ord_less_eq_nat @ I2 @ J )
% 0.35/0.69       => ( ( upt @ I2 @ ( plus_plus_nat @ J @ K ) )
% 0.35/0.69          = ( append_nat @ ( upt @ I2 @ J ) @ ( upt @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % upt_add_eq_append
% 0.35/0.69  thf(fact_10126_upt__eq__Cons__conv,axiom,
% 0.35/0.69      ! [I2: nat,J: nat,X: nat,Xs2: list_nat] :
% 0.35/0.69        ( ( ( upt @ I2 @ J )
% 0.35/0.69          = ( cons_nat @ X @ Xs2 ) )
% 0.35/0.69        = ( ( ord_less_nat @ I2 @ J )
% 0.35/0.69          & ( I2 = X )
% 0.35/0.69          & ( ( upt @ ( plus_plus_nat @ I2 @ one_one_nat ) @ J )
% 0.35/0.69            = Xs2 ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % upt_eq_Cons_conv
% 0.35/0.69  thf(fact_10127_upt__rec,axiom,
% 0.35/0.69      ( upt
% 0.35/0.69      = ( ^ [I3: nat,J3: nat] : ( if_list_nat @ ( ord_less_nat @ I3 @ J3 ) @ ( cons_nat @ I3 @ ( upt @ ( suc @ I3 ) @ J3 ) ) @ nil_nat ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % upt_rec
% 0.35/0.69  thf(fact_10128_upt__Suc__append,axiom,
% 0.35/0.69      ! [I2: nat,J: nat] :
% 0.35/0.69        ( ( ord_less_eq_nat @ I2 @ J )
% 0.35/0.69       => ( ( upt @ I2 @ ( suc @ J ) )
% 0.35/0.69          = ( append_nat @ ( upt @ I2 @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % upt_Suc_append
% 0.35/0.69  thf(fact_10129_upt__Suc,axiom,
% 0.35/0.69      ! [I2: nat,J: nat] :
% 0.35/0.69        ( ( ( ord_less_eq_nat @ I2 @ J )
% 0.35/0.69         => ( ( upt @ I2 @ ( suc @ J ) )
% 0.35/0.69            = ( append_nat @ ( upt @ I2 @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) )
% 0.35/0.69        & ( ~ ( ord_less_eq_nat @ I2 @ J )
% 0.35/0.69         => ( ( upt @ I2 @ ( suc @ J ) )
% 0.35/0.69            = nil_nat ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % upt_Suc
% 0.35/0.69  thf(fact_10130_sum__list__upt,axiom,
% 0.35/0.69      ! [M: nat,N: nat] :
% 0.35/0.69        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.69       => ( ( groups4561878855575611511st_nat @ ( upt @ M @ N ) )
% 0.35/0.69          = ( groups3542108847815614940at_nat
% 0.35/0.69            @ ^ [X2: nat] : X2
% 0.35/0.69            @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % sum_list_upt
% 0.35/0.69  thf(fact_10131_card__length__sum__list__rec,axiom,
% 0.35/0.69      ! [M: nat,N4: nat] :
% 0.35/0.69        ( ( ord_less_eq_nat @ one_one_nat @ M )
% 0.35/0.69       => ( ( finite_card_list_nat
% 0.35/0.69            @ ( collect_list_nat
% 0.35/0.69              @ ^ [L: list_nat] :
% 0.35/0.69                  ( ( ( size_size_list_nat @ L )
% 0.35/0.69                    = M )
% 0.35/0.69                  & ( ( groups4561878855575611511st_nat @ L )
% 0.35/0.69                    = N4 ) ) ) )
% 0.35/0.69          = ( plus_plus_nat
% 0.35/0.69            @ ( finite_card_list_nat
% 0.35/0.69              @ ( collect_list_nat
% 0.35/0.69                @ ^ [L: list_nat] :
% 0.35/0.69                    ( ( ( size_size_list_nat @ L )
% 0.35/0.69                      = ( minus_minus_nat @ M @ one_one_nat ) )
% 0.35/0.69                    & ( ( groups4561878855575611511st_nat @ L )
% 0.35/0.69                      = N4 ) ) ) )
% 0.35/0.69            @ ( finite_card_list_nat
% 0.35/0.69              @ ( collect_list_nat
% 0.35/0.69                @ ^ [L: list_nat] :
% 0.35/0.69                    ( ( ( size_size_list_nat @ L )
% 0.35/0.69                      = M )
% 0.35/0.69                    & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L ) @ one_one_nat )
% 0.35/0.69                      = N4 ) ) ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % card_length_sum_list_rec
% 0.35/0.69  thf(fact_10132_card__length__sum__list,axiom,
% 0.35/0.69      ! [M: nat,N4: nat] :
% 0.35/0.69        ( ( finite_card_list_nat
% 0.35/0.69          @ ( collect_list_nat
% 0.35/0.69            @ ^ [L: list_nat] :
% 0.35/0.69                ( ( ( size_size_list_nat @ L )
% 0.35/0.69                  = M )
% 0.35/0.69                & ( ( groups4561878855575611511st_nat @ L )
% 0.35/0.69                  = N4 ) ) ) )
% 0.35/0.69        = ( binomial @ ( minus_minus_nat @ ( plus_plus_nat @ N4 @ M ) @ one_one_nat ) @ N4 ) ) ).
% 0.35/0.69  
% 0.35/0.69  % card_length_sum_list
% 0.35/0.69  thf(fact_10133_sorted__wrt__upt,axiom,
% 0.35/0.69      ! [M: nat,N: nat] : ( sorted_wrt_nat @ ord_less_nat @ ( upt @ M @ N ) ) ).
% 0.35/0.69  
% 0.35/0.69  % sorted_wrt_upt
% 0.35/0.69  thf(fact_10134_sorted__upt,axiom,
% 0.35/0.69      ! [M: nat,N: nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( upt @ M @ N ) ) ).
% 0.35/0.69  
% 0.35/0.69  % sorted_upt
% 0.35/0.69  thf(fact_10135_sorted__wrt__less__idx,axiom,
% 0.35/0.69      ! [Ns: list_nat,I2: nat] :
% 0.35/0.69        ( ( sorted_wrt_nat @ ord_less_nat @ Ns )
% 0.35/0.69       => ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Ns ) )
% 0.35/0.69         => ( ord_less_eq_nat @ I2 @ ( nth_nat @ Ns @ I2 ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % sorted_wrt_less_idx
% 0.35/0.69  thf(fact_10136_list__encode_Opelims,axiom,
% 0.35/0.69      ! [X: list_nat,Y2: nat] :
% 0.35/0.69        ( ( ( nat_list_encode @ X )
% 0.35/0.69          = Y2 )
% 0.35/0.69       => ( ( accp_list_nat @ nat_list_encode_rel @ X )
% 0.35/0.69         => ( ( ( X = nil_nat )
% 0.35/0.69             => ( ( Y2 = zero_zero_nat )
% 0.35/0.69               => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 0.35/0.69           => ~ ! [X3: nat,Xs3: list_nat] :
% 0.35/0.69                  ( ( X
% 0.35/0.69                    = ( cons_nat @ X3 @ Xs3 ) )
% 0.35/0.69                 => ( ( Y2
% 0.35/0.69                      = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X3 @ ( nat_list_encode @ Xs3 ) ) ) ) )
% 0.35/0.69                   => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X3 @ Xs3 ) ) ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % list_encode.pelims
% 0.35/0.69  thf(fact_10137_and__not__num_Opelims,axiom,
% 0.35/0.69      ! [X: num,Xa2: num,Y2: option_num] :
% 0.35/0.69        ( ( ( bit_and_not_num @ X @ Xa2 )
% 0.35/0.69          = Y2 )
% 0.35/0.69       => ( ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ X @ Xa2 ) )
% 0.35/0.69         => ( ( ( X = one )
% 0.35/0.69             => ( ( Xa2 = one )
% 0.35/0.69               => ( ( Y2 = none_num )
% 0.35/0.69                 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 0.35/0.69           => ( ( ( X = one )
% 0.35/0.69               => ! [N3: num] :
% 0.35/0.69                    ( ( Xa2
% 0.35/0.69                      = ( bit0 @ N3 ) )
% 0.35/0.69                   => ( ( Y2
% 0.35/0.69                        = ( some_num @ one ) )
% 0.35/0.69                     => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 0.35/0.69             => ( ( ( X = one )
% 0.35/0.69                 => ! [N3: num] :
% 0.35/0.69                      ( ( Xa2
% 0.35/0.69                        = ( bit1 @ N3 ) )
% 0.35/0.69                     => ( ( Y2 = none_num )
% 0.35/0.69                       => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 0.35/0.69               => ( ! [M4: num] :
% 0.35/0.69                      ( ( X
% 0.35/0.69                        = ( bit0 @ M4 ) )
% 0.35/0.69                     => ( ( Xa2 = one )
% 0.35/0.69                       => ( ( Y2
% 0.35/0.69                            = ( some_num @ ( bit0 @ M4 ) ) )
% 0.35/0.69                         => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) ) ) ) )
% 0.35/0.69                 => ( ! [M4: num] :
% 0.35/0.69                        ( ( X
% 0.35/0.69                          = ( bit0 @ M4 ) )
% 0.35/0.69                       => ! [N3: num] :
% 0.35/0.69                            ( ( Xa2
% 0.35/0.69                              = ( bit0 @ N3 ) )
% 0.35/0.69                           => ( ( Y2
% 0.35/0.69                                = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N3 ) ) )
% 0.35/0.69                             => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 0.35/0.69                   => ( ! [M4: num] :
% 0.35/0.69                          ( ( X
% 0.35/0.69                            = ( bit0 @ M4 ) )
% 0.35/0.69                         => ! [N3: num] :
% 0.35/0.69                              ( ( Xa2
% 0.35/0.69                                = ( bit1 @ N3 ) )
% 0.35/0.69                             => ( ( Y2
% 0.35/0.69                                  = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N3 ) ) )
% 0.35/0.69                               => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 0.35/0.69                     => ( ! [M4: num] :
% 0.35/0.69                            ( ( X
% 0.35/0.69                              = ( bit1 @ M4 ) )
% 0.35/0.69                           => ( ( Xa2 = one )
% 0.35/0.69                             => ( ( Y2
% 0.35/0.69                                  = ( some_num @ ( bit0 @ M4 ) ) )
% 0.35/0.69                               => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) ) ) ) )
% 0.35/0.69                       => ( ! [M4: num] :
% 0.35/0.69                              ( ( X
% 0.35/0.69                                = ( bit1 @ M4 ) )
% 0.35/0.69                             => ! [N3: num] :
% 0.35/0.69                                  ( ( Xa2
% 0.35/0.69                                    = ( bit0 @ N3 ) )
% 0.35/0.69                                 => ( ( Y2
% 0.35/0.69                                      = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 0.35/0.69                                        @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 0.35/0.69                                        @ ( bit_and_not_num @ M4 @ N3 ) ) )
% 0.35/0.69                                   => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 0.35/0.69                         => ~ ! [M4: num] :
% 0.35/0.69                                ( ( X
% 0.35/0.69                                  = ( bit1 @ M4 ) )
% 0.35/0.69                               => ! [N3: num] :
% 0.35/0.69                                    ( ( Xa2
% 0.35/0.69                                      = ( bit1 @ N3 ) )
% 0.35/0.69                                   => ( ( Y2
% 0.35/0.69                                        = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N3 ) ) )
% 0.35/0.69                                     => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % and_not_num.pelims
% 0.35/0.69  thf(fact_10138_and__num_Opelims,axiom,
% 0.35/0.69      ! [X: num,Xa2: num,Y2: option_num] :
% 0.35/0.69        ( ( ( bit_un7362597486090784418nd_num @ X @ Xa2 )
% 0.35/0.69          = Y2 )
% 0.35/0.69       => ( ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ X @ Xa2 ) )
% 0.35/0.69         => ( ( ( X = one )
% 0.35/0.69             => ( ( Xa2 = one )
% 0.35/0.69               => ( ( Y2
% 0.35/0.69                    = ( some_num @ one ) )
% 0.35/0.69                 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 0.35/0.69           => ( ( ( X = one )
% 0.35/0.69               => ! [N3: num] :
% 0.35/0.69                    ( ( Xa2
% 0.35/0.69                      = ( bit0 @ N3 ) )
% 0.35/0.69                   => ( ( Y2 = none_num )
% 0.35/0.69                     => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 0.35/0.69             => ( ( ( X = one )
% 0.35/0.69                 => ! [N3: num] :
% 0.35/0.69                      ( ( Xa2
% 0.35/0.69                        = ( bit1 @ N3 ) )
% 0.35/0.69                     => ( ( Y2
% 0.35/0.69                          = ( some_num @ one ) )
% 0.35/0.69                       => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 0.35/0.69               => ( ! [M4: num] :
% 0.35/0.69                      ( ( X
% 0.35/0.69                        = ( bit0 @ M4 ) )
% 0.35/0.69                     => ( ( Xa2 = one )
% 0.35/0.69                       => ( ( Y2 = none_num )
% 0.35/0.69                         => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) ) ) ) )
% 0.35/0.69                 => ( ! [M4: num] :
% 0.35/0.69                        ( ( X
% 0.35/0.69                          = ( bit0 @ M4 ) )
% 0.35/0.69                       => ! [N3: num] :
% 0.35/0.69                            ( ( Xa2
% 0.35/0.69                              = ( bit0 @ N3 ) )
% 0.35/0.69                           => ( ( Y2
% 0.35/0.69                                = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) )
% 0.35/0.69                             => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 0.35/0.69                   => ( ! [M4: num] :
% 0.35/0.69                          ( ( X
% 0.35/0.69                            = ( bit0 @ M4 ) )
% 0.35/0.69                         => ! [N3: num] :
% 0.35/0.69                              ( ( Xa2
% 0.35/0.69                                = ( bit1 @ N3 ) )
% 0.35/0.69                             => ( ( Y2
% 0.35/0.69                                  = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) )
% 0.35/0.69                               => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 0.35/0.69                     => ( ! [M4: num] :
% 0.35/0.69                            ( ( X
% 0.35/0.69                              = ( bit1 @ M4 ) )
% 0.35/0.69                           => ( ( Xa2 = one )
% 0.35/0.69                             => ( ( Y2
% 0.35/0.69                                  = ( some_num @ one ) )
% 0.35/0.69                               => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) ) ) ) )
% 0.35/0.69                       => ( ! [M4: num] :
% 0.35/0.69                              ( ( X
% 0.35/0.69                                = ( bit1 @ M4 ) )
% 0.35/0.69                             => ! [N3: num] :
% 0.35/0.69                                  ( ( Xa2
% 0.35/0.69                                    = ( bit0 @ N3 ) )
% 0.35/0.69                                 => ( ( Y2
% 0.35/0.69                                      = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) )
% 0.35/0.69                                   => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 0.35/0.69                         => ~ ! [M4: num] :
% 0.35/0.69                                ( ( X
% 0.35/0.69                                  = ( bit1 @ M4 ) )
% 0.35/0.69                               => ! [N3: num] :
% 0.35/0.69                                    ( ( Xa2
% 0.35/0.69                                      = ( bit1 @ N3 ) )
% 0.35/0.69                                   => ( ( Y2
% 0.35/0.69                                        = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 0.35/0.69                                          @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 0.35/0.69                                          @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) )
% 0.35/0.69                                     => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % and_num.pelims
% 0.35/0.69  thf(fact_10139_xor__num_Opelims,axiom,
% 0.35/0.69      ! [X: num,Xa2: num,Y2: option_num] :
% 0.35/0.69        ( ( ( bit_un2480387367778600638or_num @ X @ Xa2 )
% 0.35/0.69          = Y2 )
% 0.35/0.69       => ( ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ X @ Xa2 ) )
% 0.35/0.69         => ( ( ( X = one )
% 0.35/0.69             => ( ( Xa2 = one )
% 0.35/0.69               => ( ( Y2 = none_num )
% 0.35/0.69                 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 0.35/0.69           => ( ( ( X = one )
% 0.35/0.69               => ! [N3: num] :
% 0.35/0.69                    ( ( Xa2
% 0.35/0.69                      = ( bit0 @ N3 ) )
% 0.35/0.69                   => ( ( Y2
% 0.35/0.69                        = ( some_num @ ( bit1 @ N3 ) ) )
% 0.35/0.69                     => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 0.35/0.69             => ( ( ( X = one )
% 0.35/0.69                 => ! [N3: num] :
% 0.35/0.69                      ( ( Xa2
% 0.35/0.69                        = ( bit1 @ N3 ) )
% 0.35/0.69                     => ( ( Y2
% 0.35/0.69                          = ( some_num @ ( bit0 @ N3 ) ) )
% 0.35/0.69                       => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 0.35/0.69               => ( ! [M4: num] :
% 0.35/0.69                      ( ( X
% 0.35/0.69                        = ( bit0 @ M4 ) )
% 0.35/0.69                     => ( ( Xa2 = one )
% 0.35/0.69                       => ( ( Y2
% 0.35/0.69                            = ( some_num @ ( bit1 @ M4 ) ) )
% 0.35/0.69                         => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) ) ) ) )
% 0.35/0.69                 => ( ! [M4: num] :
% 0.35/0.69                        ( ( X
% 0.35/0.69                          = ( bit0 @ M4 ) )
% 0.35/0.69                       => ! [N3: num] :
% 0.35/0.69                            ( ( Xa2
% 0.35/0.69                              = ( bit0 @ N3 ) )
% 0.35/0.69                           => ( ( Y2
% 0.35/0.69                                = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) )
% 0.35/0.69                             => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 0.35/0.69                   => ( ! [M4: num] :
% 0.35/0.69                          ( ( X
% 0.35/0.69                            = ( bit0 @ M4 ) )
% 0.35/0.69                         => ! [N3: num] :
% 0.35/0.69                              ( ( Xa2
% 0.35/0.69                                = ( bit1 @ N3 ) )
% 0.35/0.69                             => ( ( Y2
% 0.35/0.69                                  = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) ) )
% 0.35/0.69                               => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 0.35/0.69                     => ( ! [M4: num] :
% 0.35/0.69                            ( ( X
% 0.35/0.69                              = ( bit1 @ M4 ) )
% 0.35/0.69                           => ( ( Xa2 = one )
% 0.35/0.69                             => ( ( Y2
% 0.35/0.69                                  = ( some_num @ ( bit0 @ M4 ) ) )
% 0.35/0.69                               => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) ) ) ) )
% 0.35/0.69                       => ( ! [M4: num] :
% 0.35/0.69                              ( ( X
% 0.35/0.69                                = ( bit1 @ M4 ) )
% 0.35/0.69                             => ! [N3: num] :
% 0.35/0.69                                  ( ( Xa2
% 0.35/0.69                                    = ( bit0 @ N3 ) )
% 0.35/0.69                                 => ( ( Y2
% 0.35/0.69                                      = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) ) )
% 0.35/0.69                                   => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 0.35/0.69                         => ~ ! [M4: num] :
% 0.35/0.69                                ( ( X
% 0.35/0.69                                  = ( bit1 @ M4 ) )
% 0.35/0.69                               => ! [N3: num] :
% 0.35/0.69                                    ( ( Xa2
% 0.35/0.69                                      = ( bit1 @ N3 ) )
% 0.35/0.69                                   => ( ( Y2
% 0.35/0.69                                        = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) )
% 0.35/0.69                                     => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % xor_num.pelims
% 0.35/0.69  thf(fact_10140_or__not__num__neg_Opelims,axiom,
% 0.35/0.69      ! [X: num,Xa2: num,Y2: num] :
% 0.35/0.69        ( ( ( bit_or_not_num_neg @ X @ Xa2 )
% 0.35/0.69          = Y2 )
% 0.35/0.69       => ( ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ X @ Xa2 ) )
% 0.35/0.69         => ( ( ( X = one )
% 0.35/0.69             => ( ( Xa2 = one )
% 0.35/0.69               => ( ( Y2 = one )
% 0.35/0.69                 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 0.35/0.69           => ( ( ( X = one )
% 0.35/0.69               => ! [M4: num] :
% 0.35/0.69                    ( ( Xa2
% 0.35/0.69                      = ( bit0 @ M4 ) )
% 0.35/0.69                   => ( ( Y2
% 0.35/0.69                        = ( bit1 @ M4 ) )
% 0.35/0.69                     => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit0 @ M4 ) ) ) ) ) )
% 0.35/0.69             => ( ( ( X = one )
% 0.35/0.69                 => ! [M4: num] :
% 0.35/0.69                      ( ( Xa2
% 0.35/0.69                        = ( bit1 @ M4 ) )
% 0.35/0.69                     => ( ( Y2
% 0.35/0.69                          = ( bit1 @ M4 ) )
% 0.35/0.69                       => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit1 @ M4 ) ) ) ) ) )
% 0.35/0.69               => ( ! [N3: num] :
% 0.35/0.69                      ( ( X
% 0.35/0.69                        = ( bit0 @ N3 ) )
% 0.35/0.69                     => ( ( Xa2 = one )
% 0.35/0.69                       => ( ( Y2
% 0.35/0.69                            = ( bit0 @ one ) )
% 0.35/0.69                         => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ one ) ) ) ) )
% 0.35/0.69                 => ( ! [N3: num] :
% 0.35/0.69                        ( ( X
% 0.35/0.69                          = ( bit0 @ N3 ) )
% 0.35/0.69                       => ! [M4: num] :
% 0.35/0.69                            ( ( Xa2
% 0.35/0.69                              = ( bit0 @ M4 ) )
% 0.35/0.69                           => ( ( Y2
% 0.35/0.69                                = ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) )
% 0.35/0.69                             => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ ( bit0 @ M4 ) ) ) ) ) )
% 0.35/0.69                   => ( ! [N3: num] :
% 0.35/0.69                          ( ( X
% 0.35/0.69                            = ( bit0 @ N3 ) )
% 0.35/0.69                         => ! [M4: num] :
% 0.35/0.69                              ( ( Xa2
% 0.35/0.69                                = ( bit1 @ M4 ) )
% 0.35/0.69                             => ( ( Y2
% 0.35/0.69                                  = ( bit0 @ ( bit_or_not_num_neg @ N3 @ M4 ) ) )
% 0.35/0.69                               => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ ( bit1 @ M4 ) ) ) ) ) )
% 0.35/0.69                     => ( ! [N3: num] :
% 0.35/0.69                            ( ( X
% 0.35/0.69                              = ( bit1 @ N3 ) )
% 0.35/0.69                           => ( ( Xa2 = one )
% 0.35/0.69                             => ( ( Y2 = one )
% 0.35/0.69                               => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ one ) ) ) ) )
% 0.35/0.69                       => ( ! [N3: num] :
% 0.35/0.69                              ( ( X
% 0.35/0.69                                = ( bit1 @ N3 ) )
% 0.35/0.69                             => ! [M4: num] :
% 0.35/0.69                                  ( ( Xa2
% 0.35/0.69                                    = ( bit0 @ M4 ) )
% 0.35/0.69                                 => ( ( Y2
% 0.35/0.69                                      = ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) )
% 0.35/0.69                                   => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ ( bit0 @ M4 ) ) ) ) ) )
% 0.35/0.69                         => ~ ! [N3: num] :
% 0.35/0.69                                ( ( X
% 0.35/0.69                                  = ( bit1 @ N3 ) )
% 0.35/0.69                               => ! [M4: num] :
% 0.35/0.69                                    ( ( Xa2
% 0.35/0.69                                      = ( bit1 @ M4 ) )
% 0.35/0.69                                   => ( ( Y2
% 0.35/0.69                                        = ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) )
% 0.35/0.69                                     => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ ( bit1 @ M4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % or_not_num_neg.pelims
% 0.35/0.69  thf(fact_10141_and__num__rel__dict,axiom,
% 0.35/0.69      bit_un4731106466462545111um_rel = bit_un5425074673868309765um_rel ).
% 0.35/0.69  
% 0.35/0.69  % and_num_rel_dict
% 0.35/0.69  thf(fact_10142_xor__num__rel__dict,axiom,
% 0.35/0.69      bit_un2901131394128224187um_rel = bit_un3595099601533988841um_rel ).
% 0.35/0.69  
% 0.35/0.69  % xor_num_rel_dict
% 0.35/0.69  thf(fact_10143_rcis__inverse,axiom,
% 0.35/0.69      ! [R: real,A: real] :
% 0.35/0.69        ( ( invers8013647133539491842omplex @ ( rcis @ R @ A ) )
% 0.35/0.69        = ( rcis @ ( divide_divide_real @ one_one_real @ R ) @ ( uminus_uminus_real @ A ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % rcis_inverse
% 0.35/0.69  thf(fact_10144_Re__rcis,axiom,
% 0.35/0.69      ! [R: real,A: real] :
% 0.35/0.69        ( ( re @ ( rcis @ R @ A ) )
% 0.35/0.69        = ( times_times_real @ R @ ( cos_real @ A ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % Re_rcis
% 0.35/0.69  thf(fact_10145_Im__rcis,axiom,
% 0.35/0.69      ! [R: real,A: real] :
% 0.35/0.69        ( ( im @ ( rcis @ R @ A ) )
% 0.35/0.69        = ( times_times_real @ R @ ( sin_real @ A ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % Im_rcis
% 0.35/0.69  thf(fact_10146_cis__rcis__eq,axiom,
% 0.35/0.69      ( cis
% 0.35/0.69      = ( rcis @ one_one_real ) ) ).
% 0.35/0.69  
% 0.35/0.69  % cis_rcis_eq
% 0.35/0.69  thf(fact_10147_rcis__mult,axiom,
% 0.35/0.69      ! [R1: real,A: real,R22: real,B: real] :
% 0.35/0.69        ( ( times_times_complex @ ( rcis @ R1 @ A ) @ ( rcis @ R22 @ B ) )
% 0.35/0.69        = ( rcis @ ( times_times_real @ R1 @ R22 ) @ ( plus_plus_real @ A @ B ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % rcis_mult
% 0.35/0.69  thf(fact_10148_rcis__divide,axiom,
% 0.35/0.69      ! [R1: real,A: real,R22: real,B: real] :
% 0.35/0.69        ( ( divide1717551699836669952omplex @ ( rcis @ R1 @ A ) @ ( rcis @ R22 @ B ) )
% 0.35/0.69        = ( rcis @ ( divide_divide_real @ R1 @ R22 ) @ ( minus_minus_real @ A @ B ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % rcis_divide
% 0.35/0.69  thf(fact_10149_DeMoivre2,axiom,
% 0.35/0.69      ! [R: real,A: real,N: nat] :
% 0.35/0.69        ( ( power_power_complex @ ( rcis @ R @ A ) @ N )
% 0.35/0.69        = ( rcis @ ( power_power_real @ R @ N ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % DeMoivre2
% 0.35/0.69  thf(fact_10150_Field__natLeq__on,axiom,
% 0.35/0.69      ! [N: nat] :
% 0.35/0.69        ( ( field_nat
% 0.35/0.69          @ ( collec3392354462482085612at_nat
% 0.35/0.69            @ ( produc6081775807080527818_nat_o
% 0.35/0.69              @ ^ [X2: nat,Y: nat] :
% 0.35/0.69                  ( ( ord_less_nat @ X2 @ N )
% 0.35/0.69                  & ( ord_less_nat @ Y @ N )
% 0.35/0.69                  & ( ord_less_eq_nat @ X2 @ Y ) ) ) ) )
% 0.35/0.69        = ( collect_nat
% 0.35/0.69          @ ^ [X2: nat] : ( ord_less_nat @ X2 @ N ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % Field_natLeq_on
% 0.35/0.69  thf(fact_10151_natLess__def,axiom,
% 0.35/0.69      ( bNF_Ca8459412986667044542atLess
% 0.35/0.69      = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % natLess_def
% 0.35/0.69  thf(fact_10152_wf__less,axiom,
% 0.35/0.69      wf_nat @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ).
% 0.35/0.69  
% 0.35/0.69  % wf_less
% 0.35/0.69  thf(fact_10153_product__atMost__eq__Un,axiom,
% 0.35/0.69      ! [A2: set_nat,M: nat] :
% 0.35/0.69        ( ( produc457027306803732586at_nat @ A2
% 0.35/0.69          @ ^ [Uu3: nat] : ( set_ord_atMost_nat @ M ) )
% 0.35/0.69        = ( sup_su6327502436637775413at_nat
% 0.35/0.69          @ ( produc457027306803732586at_nat @ A2
% 0.35/0.69            @ ^ [I3: nat] : ( set_ord_atMost_nat @ ( minus_minus_nat @ M @ I3 ) ) )
% 0.35/0.69          @ ( produc457027306803732586at_nat @ A2
% 0.35/0.69            @ ^ [I3: nat] : ( set_or6659071591806873216st_nat @ ( minus_minus_nat @ M @ I3 ) @ M ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % product_atMost_eq_Un
% 0.35/0.69  thf(fact_10154_pairs__le__eq__Sigma,axiom,
% 0.35/0.69      ! [M: nat] :
% 0.35/0.69        ( ( collec3392354462482085612at_nat
% 0.35/0.69          @ ( produc6081775807080527818_nat_o
% 0.35/0.69            @ ^ [I3: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ J3 ) @ M ) ) )
% 0.35/0.69        = ( produc457027306803732586at_nat @ ( set_ord_atMost_nat @ M )
% 0.35/0.69          @ ^ [R5: nat] : ( set_ord_atMost_nat @ ( minus_minus_nat @ M @ R5 ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % pairs_le_eq_Sigma
% 0.35/0.69  thf(fact_10155_finite__vimage__Suc__iff,axiom,
% 0.35/0.69      ! [F5: set_nat] :
% 0.35/0.69        ( ( finite_finite_nat @ ( vimage_nat_nat @ suc @ F5 ) )
% 0.35/0.69        = ( finite_finite_nat @ F5 ) ) ).
% 0.35/0.69  
% 0.35/0.69  % finite_vimage_Suc_iff
% 0.35/0.69  thf(fact_10156_le__enumerate,axiom,
% 0.35/0.69      ! [S2: set_nat,N: nat] :
% 0.35/0.69        ( ~ ( finite_finite_nat @ S2 )
% 0.35/0.69       => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S2 @ N ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % le_enumerate
% 0.35/0.69  thf(fact_10157_vimage__Suc__insert__Suc,axiom,
% 0.35/0.69      ! [N: nat,A2: set_nat] :
% 0.35/0.69        ( ( vimage_nat_nat @ suc @ ( insert_nat @ ( suc @ N ) @ A2 ) )
% 0.35/0.69        = ( insert_nat @ N @ ( vimage_nat_nat @ suc @ A2 ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % vimage_Suc_insert_Suc
% 0.35/0.69  thf(fact_10158_vimage__Suc__insert__0,axiom,
% 0.35/0.69      ! [A2: set_nat] :
% 0.35/0.69        ( ( vimage_nat_nat @ suc @ ( insert_nat @ zero_zero_nat @ A2 ) )
% 0.35/0.69        = ( vimage_nat_nat @ suc @ A2 ) ) ).
% 0.35/0.69  
% 0.35/0.69  % vimage_Suc_insert_0
% 0.35/0.69  thf(fact_10159_finite__le__enumerate,axiom,
% 0.35/0.69      ! [S2: set_nat,N: nat] :
% 0.35/0.69        ( ( finite_finite_nat @ S2 )
% 0.35/0.69       => ( ( ord_less_nat @ N @ ( finite_card_nat @ S2 ) )
% 0.35/0.69         => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S2 @ N ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % finite_le_enumerate
% 0.35/0.69  thf(fact_10160_set__decode__div__2,axiom,
% 0.35/0.69      ! [X: nat] :
% 0.35/0.69        ( ( nat_set_decode @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.69        = ( vimage_nat_nat @ suc @ ( nat_set_decode @ X ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % set_decode_div_2
% 0.35/0.69  thf(fact_10161_set__encode__vimage__Suc,axiom,
% 0.35/0.69      ! [A2: set_nat] :
% 0.35/0.69        ( ( nat_set_encode @ ( vimage_nat_nat @ suc @ A2 ) )
% 0.35/0.69        = ( divide_divide_nat @ ( nat_set_encode @ A2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % set_encode_vimage_Suc
% 0.35/0.69  thf(fact_10162_Least__eq__0,axiom,
% 0.35/0.69      ! [P: nat > $o] :
% 0.35/0.69        ( ( P @ zero_zero_nat )
% 0.35/0.69       => ( ( ord_Least_nat @ P )
% 0.35/0.69          = zero_zero_nat ) ) ).
% 0.35/0.69  
% 0.35/0.69  % Least_eq_0
% 0.35/0.69  thf(fact_10163_Least__Suc,axiom,
% 0.35/0.69      ! [P: nat > $o,N: nat] :
% 0.35/0.69        ( ( P @ N )
% 0.35/0.69       => ( ~ ( P @ zero_zero_nat )
% 0.35/0.69         => ( ( ord_Least_nat @ P )
% 0.35/0.69            = ( suc
% 0.35/0.69              @ ( ord_Least_nat
% 0.35/0.69                @ ^ [M6: nat] : ( P @ ( suc @ M6 ) ) ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % Least_Suc
% 0.35/0.69  thf(fact_10164_Least__Suc2,axiom,
% 0.35/0.69      ! [P: nat > $o,N: nat,Q: nat > $o,M: nat] :
% 0.35/0.69        ( ( P @ N )
% 0.35/0.69       => ( ( Q @ M )
% 0.35/0.69         => ( ~ ( P @ zero_zero_nat )
% 0.35/0.69           => ( ! [K2: nat] :
% 0.35/0.69                  ( ( P @ ( suc @ K2 ) )
% 0.35/0.69                  = ( Q @ K2 ) )
% 0.35/0.69             => ( ( ord_Least_nat @ P )
% 0.35/0.69                = ( suc @ ( ord_Least_nat @ Q ) ) ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % Least_Suc2
% 0.35/0.69  thf(fact_10165_Sup__real__def,axiom,
% 0.35/0.69      ( comple1385675409528146559p_real
% 0.35/0.69      = ( ^ [X4: set_real] :
% 0.35/0.69            ( ord_Least_real
% 0.35/0.69            @ ^ [Z4: real] :
% 0.35/0.69              ! [X2: real] :
% 0.35/0.69                ( ( member_real @ X2 @ X4 )
% 0.35/0.69               => ( ord_less_eq_real @ X2 @ Z4 ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % Sup_real_def
% 0.35/0.69  thf(fact_10166_Restr__natLeq,axiom,
% 0.35/0.69      ! [N: nat] :
% 0.35/0.69        ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 0.35/0.69          @ ( produc457027306803732586at_nat
% 0.35/0.69            @ ( collect_nat
% 0.35/0.69              @ ^ [X2: nat] : ( ord_less_nat @ X2 @ N ) )
% 0.35/0.69            @ ^ [Uu3: nat] :
% 0.35/0.69                ( collect_nat
% 0.35/0.69                @ ^ [X2: nat] : ( ord_less_nat @ X2 @ N ) ) ) )
% 0.35/0.69        = ( collec3392354462482085612at_nat
% 0.35/0.69          @ ( produc6081775807080527818_nat_o
% 0.35/0.69            @ ^ [X2: nat,Y: nat] :
% 0.35/0.69                ( ( ord_less_nat @ X2 @ N )
% 0.35/0.69                & ( ord_less_nat @ Y @ N )
% 0.35/0.69                & ( ord_less_eq_nat @ X2 @ Y ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % Restr_natLeq
% 0.35/0.69  thf(fact_10167_natLeq__natLess__Id,axiom,
% 0.35/0.69      ( bNF_Ca8459412986667044542atLess
% 0.35/0.69      = ( minus_1356011639430497352at_nat @ bNF_Ca8665028551170535155natLeq @ id_nat2 ) ) ).
% 0.35/0.69  
% 0.35/0.69  % natLeq_natLess_Id
% 0.35/0.69  thf(fact_10168_natLeq__def,axiom,
% 0.35/0.69      ( bNF_Ca8665028551170535155natLeq
% 0.35/0.69      = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_eq_nat ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % natLeq_def
% 0.35/0.69  thf(fact_10169_Restr__natLeq2,axiom,
% 0.35/0.69      ! [N: nat] :
% 0.35/0.69        ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 0.35/0.69          @ ( produc457027306803732586at_nat @ ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N )
% 0.35/0.69            @ ^ [Uu3: nat] : ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N ) ) )
% 0.35/0.69        = ( collec3392354462482085612at_nat
% 0.35/0.69          @ ( produc6081775807080527818_nat_o
% 0.35/0.69            @ ^ [X2: nat,Y: nat] :
% 0.35/0.69                ( ( ord_less_nat @ X2 @ N )
% 0.35/0.69                & ( ord_less_nat @ Y @ N )
% 0.35/0.69                & ( ord_less_eq_nat @ X2 @ Y ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % Restr_natLeq2
% 0.35/0.69  thf(fact_10170_natLeq__underS__less,axiom,
% 0.35/0.69      ! [N: nat] :
% 0.35/0.69        ( ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N )
% 0.35/0.69        = ( collect_nat
% 0.35/0.69          @ ^ [X2: nat] : ( ord_less_nat @ X2 @ N ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % natLeq_underS_less
% 0.35/0.69  thf(fact_10171_quotient__of__number_I5_J,axiom,
% 0.35/0.69      ! [K: num] :
% 0.35/0.69        ( ( quotient_of @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 0.35/0.69        = ( product_Pair_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 0.35/0.69  
% 0.35/0.69  % quotient_of_number(5)
% 0.35/0.69  thf(fact_10172_quotient__of__number_I3_J,axiom,
% 0.35/0.69      ! [K: num] :
% 0.35/0.69        ( ( quotient_of @ ( numeral_numeral_rat @ K ) )
% 0.35/0.69        = ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) ) ).
% 0.35/0.69  
% 0.35/0.69  % quotient_of_number(3)
% 0.35/0.69  thf(fact_10173_diff__rat__def,axiom,
% 0.35/0.69      ( minus_minus_rat
% 0.35/0.69      = ( ^ [Q4: rat,R5: rat] : ( plus_plus_rat @ Q4 @ ( uminus_uminus_rat @ R5 ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % diff_rat_def
% 0.35/0.69  thf(fact_10174_rat__floor__code,axiom,
% 0.35/0.69      ( archim3151403230148437115or_rat
% 0.35/0.69      = ( ^ [P4: rat] : ( produc8211389475949308722nt_int @ divide_divide_int @ ( quotient_of @ P4 ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % rat_floor_code
% 0.35/0.69  thf(fact_10175_rat__minus__code,axiom,
% 0.35/0.69      ! [P6: rat,Q2: rat] :
% 0.35/0.69        ( ( quotient_of @ ( minus_minus_rat @ P6 @ Q2 ) )
% 0.35/0.69        = ( produc4245557441103728435nt_int
% 0.35/0.69          @ ^ [A3: int,C3: int] :
% 0.35/0.69              ( produc4245557441103728435nt_int
% 0.35/0.69              @ ^ [B4: int,D: int] : ( normalize @ ( product_Pair_int_int @ ( minus_minus_int @ ( times_times_int @ A3 @ D ) @ ( times_times_int @ B4 @ C3 ) ) @ ( times_times_int @ C3 @ D ) ) )
% 0.35/0.69              @ ( quotient_of @ Q2 ) )
% 0.35/0.69          @ ( quotient_of @ P6 ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % rat_minus_code
% 0.35/0.69  thf(fact_10176_Frct__code__post_I4_J,axiom,
% 0.35/0.69      ! [K: num] :
% 0.35/0.69        ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) )
% 0.35/0.69        = ( numeral_numeral_rat @ K ) ) ).
% 0.35/0.69  
% 0.35/0.69  % Frct_code_post(4)
% 0.35/0.69  thf(fact_10177_obtain__pos__sum,axiom,
% 0.35/0.69      ! [R: rat] :
% 0.35/0.69        ( ( ord_less_rat @ zero_zero_rat @ R )
% 0.35/0.69       => ~ ! [S: rat] :
% 0.35/0.69              ( ( ord_less_rat @ zero_zero_rat @ S )
% 0.35/0.69             => ! [T6: rat] :
% 0.35/0.69                  ( ( ord_less_rat @ zero_zero_rat @ T6 )
% 0.35/0.69                 => ( R
% 0.35/0.69                   != ( plus_plus_rat @ S @ T6 ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % obtain_pos_sum
% 0.35/0.69  thf(fact_10178_Frct__code__post_I6_J,axiom,
% 0.35/0.69      ! [K: num,L2: num] :
% 0.35/0.69        ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_int @ L2 ) ) )
% 0.35/0.69        = ( divide_divide_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_rat @ L2 ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % Frct_code_post(6)
% 0.35/0.69  thf(fact_10179_Frct__code__post_I5_J,axiom,
% 0.35/0.69      ! [K: num] :
% 0.35/0.69        ( ( frct @ ( product_Pair_int_int @ one_one_int @ ( numeral_numeral_int @ K ) ) )
% 0.35/0.69        = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % Frct_code_post(5)
% 0.35/0.69  thf(fact_10180_normalize__def,axiom,
% 0.35/0.69      ( normalize
% 0.35/0.69      = ( ^ [P4: product_prod_int_int] :
% 0.35/0.69            ( if_Pro3027730157355071871nt_int @ ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ P4 ) ) @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P4 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P4 ) @ ( product_snd_int_int @ P4 ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P4 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P4 ) @ ( product_snd_int_int @ P4 ) ) ) )
% 0.35/0.69            @ ( if_Pro3027730157355071871nt_int
% 0.35/0.69              @ ( ( product_snd_int_int @ P4 )
% 0.35/0.69                = zero_zero_int )
% 0.35/0.69              @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 0.35/0.69              @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P4 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P4 ) @ ( product_snd_int_int @ P4 ) ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P4 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P4 ) @ ( product_snd_int_int @ P4 ) ) ) ) ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % normalize_def
% 0.35/0.69  thf(fact_10181_gcd__neg__numeral__2__int,axiom,
% 0.35/0.69      ! [X: int,N: num] :
% 0.35/0.69        ( ( gcd_gcd_int @ X @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.69        = ( gcd_gcd_int @ X @ ( numeral_numeral_int @ N ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % gcd_neg_numeral_2_int
% 0.35/0.69  thf(fact_10182_gcd__neg__numeral__1__int,axiom,
% 0.35/0.69      ! [N: num,X: int] :
% 0.35/0.69        ( ( gcd_gcd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ X )
% 0.35/0.69        = ( gcd_gcd_int @ ( numeral_numeral_int @ N ) @ X ) ) ).
% 0.35/0.69  
% 0.35/0.69  % gcd_neg_numeral_1_int
% 0.35/0.69  thf(fact_10183_gcd__1__nat,axiom,
% 0.35/0.69      ! [M: nat] :
% 0.35/0.69        ( ( gcd_gcd_nat @ M @ one_one_nat )
% 0.35/0.69        = one_one_nat ) ).
% 0.35/0.69  
% 0.35/0.69  % gcd_1_nat
% 0.35/0.69  thf(fact_10184_gcd__Suc__0,axiom,
% 0.35/0.69      ! [M: nat] :
% 0.35/0.69        ( ( gcd_gcd_nat @ M @ ( suc @ zero_zero_nat ) )
% 0.35/0.69        = ( suc @ zero_zero_nat ) ) ).
% 0.35/0.69  
% 0.35/0.69  % gcd_Suc_0
% 0.35/0.69  thf(fact_10185_gcd__pos__nat,axiom,
% 0.35/0.69      ! [M: nat,N: nat] :
% 0.35/0.69        ( ( ord_less_nat @ zero_zero_nat @ ( gcd_gcd_nat @ M @ N ) )
% 0.35/0.69        = ( ( M != zero_zero_nat )
% 0.35/0.69          | ( N != zero_zero_nat ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % gcd_pos_nat
% 0.35/0.69  thf(fact_10186_last__upt,axiom,
% 0.35/0.69      ! [I2: nat,J: nat] :
% 0.35/0.69        ( ( ord_less_nat @ I2 @ J )
% 0.35/0.69       => ( ( last_nat @ ( upt @ I2 @ J ) )
% 0.35/0.69          = ( minus_minus_nat @ J @ one_one_nat ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % last_upt
% 0.35/0.69  thf(fact_10187_bezout__nat,axiom,
% 0.35/0.69      ! [A: nat,B: nat] :
% 0.35/0.69        ( ( A != zero_zero_nat )
% 0.35/0.69       => ? [X3: nat,Y3: nat] :
% 0.35/0.69            ( ( times_times_nat @ A @ X3 )
% 0.35/0.69            = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % bezout_nat
% 0.35/0.69  thf(fact_10188_bezout__gcd__nat_H,axiom,
% 0.35/0.69      ! [B: nat,A: nat] :
% 0.35/0.69      ? [X3: nat,Y3: nat] :
% 0.35/0.69        ( ( ( ord_less_eq_nat @ ( times_times_nat @ B @ Y3 ) @ ( times_times_nat @ A @ X3 ) )
% 0.35/0.69          & ( ( minus_minus_nat @ ( times_times_nat @ A @ X3 ) @ ( times_times_nat @ B @ Y3 ) )
% 0.35/0.69            = ( gcd_gcd_nat @ A @ B ) ) )
% 0.35/0.69        | ( ( ord_less_eq_nat @ ( times_times_nat @ A @ Y3 ) @ ( times_times_nat @ B @ X3 ) )
% 0.35/0.69          & ( ( minus_minus_nat @ ( times_times_nat @ B @ X3 ) @ ( times_times_nat @ A @ Y3 ) )
% 0.35/0.69            = ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % bezout_gcd_nat'
% 0.35/0.69  thf(fact_10189_gcd__diff1__nat,axiom,
% 0.35/0.69      ! [N: nat,M: nat] :
% 0.35/0.69        ( ( ord_less_eq_nat @ N @ M )
% 0.35/0.69       => ( ( gcd_gcd_nat @ ( minus_minus_nat @ M @ N ) @ N )
% 0.35/0.69          = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % gcd_diff1_nat
% 0.35/0.69  thf(fact_10190_gcd__diff2__nat,axiom,
% 0.35/0.69      ! [M: nat,N: nat] :
% 0.35/0.69        ( ( ord_less_eq_nat @ M @ N )
% 0.35/0.69       => ( ( gcd_gcd_nat @ ( minus_minus_nat @ N @ M ) @ N )
% 0.35/0.69          = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % gcd_diff2_nat
% 0.35/0.69  thf(fact_10191_gcd__le2__nat,axiom,
% 0.35/0.69      ! [B: nat,A: nat] :
% 0.35/0.69        ( ( B != zero_zero_nat )
% 0.35/0.69       => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ B ) ) ).
% 0.35/0.69  
% 0.35/0.69  % gcd_le2_nat
% 0.35/0.69  thf(fact_10192_gcd__le1__nat,axiom,
% 0.35/0.69      ! [A: nat,B: nat] :
% 0.35/0.69        ( ( A != zero_zero_nat )
% 0.35/0.69       => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ A ) ) ).
% 0.35/0.69  
% 0.35/0.69  % gcd_le1_nat
% 0.35/0.69  thf(fact_10193_gcd__mult__distrib__nat,axiom,
% 0.35/0.69      ! [K: nat,M: nat,N: nat] :
% 0.35/0.69        ( ( times_times_nat @ K @ ( gcd_gcd_nat @ M @ N ) )
% 0.35/0.69        = ( gcd_gcd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % gcd_mult_distrib_nat
% 0.35/0.69  thf(fact_10194_gcd__is__Max__divisors__nat,axiom,
% 0.35/0.69      ! [N: nat,M: nat] :
% 0.35/0.69        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.69       => ( ( gcd_gcd_nat @ M @ N )
% 0.35/0.69          = ( lattic8265883725875713057ax_nat
% 0.35/0.69            @ ( collect_nat
% 0.35/0.69              @ ^ [D: nat] :
% 0.35/0.69                  ( ( dvd_dvd_nat @ D @ M )
% 0.35/0.69                  & ( dvd_dvd_nat @ D @ N ) ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % gcd_is_Max_divisors_nat
% 0.35/0.69  thf(fact_10195_gcd__nat_Opelims,axiom,
% 0.35/0.69      ! [X: nat,Xa2: nat,Y2: nat] :
% 0.35/0.69        ( ( ( gcd_gcd_nat @ X @ Xa2 )
% 0.35/0.69          = Y2 )
% 0.35/0.69       => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 0.35/0.69         => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 0.35/0.69                 => ( Y2 = X ) )
% 0.35/0.69                & ( ( Xa2 != zero_zero_nat )
% 0.35/0.69                 => ( Y2
% 0.35/0.69                    = ( gcd_gcd_nat @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) ) )
% 0.35/0.69             => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % gcd_nat.pelims
% 0.35/0.69  thf(fact_10196_natLeq__on__wo__rel,axiom,
% 0.35/0.69      ! [N: nat] :
% 0.35/0.69        ( bNF_We3818239936649020644el_nat
% 0.35/0.69        @ ( collec3392354462482085612at_nat
% 0.35/0.69          @ ( produc6081775807080527818_nat_o
% 0.35/0.69            @ ^ [X2: nat,Y: nat] :
% 0.35/0.69                ( ( ord_less_nat @ X2 @ N )
% 0.35/0.69                & ( ord_less_nat @ Y @ N )
% 0.35/0.69                & ( ord_less_eq_nat @ X2 @ Y ) ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % natLeq_on_wo_rel
% 0.35/0.69  thf(fact_10197_Bseq__monoseq__convergent_H__inc,axiom,
% 0.35/0.69      ! [F: nat > real,M7: nat] :
% 0.35/0.69        ( ( bfun_nat_real
% 0.35/0.69          @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ M7 ) )
% 0.35/0.69          @ at_top_nat )
% 0.35/0.69       => ( ! [M4: nat,N3: nat] :
% 0.35/0.69              ( ( ord_less_eq_nat @ M7 @ M4 )
% 0.35/0.69             => ( ( ord_less_eq_nat @ M4 @ N3 )
% 0.35/0.69               => ( ord_less_eq_real @ ( F @ M4 ) @ ( F @ N3 ) ) ) )
% 0.35/0.69         => ( topolo7531315842566124627t_real @ F ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % Bseq_monoseq_convergent'_inc
% 0.35/0.69  thf(fact_10198_Bseq__monoseq__convergent_H__dec,axiom,
% 0.35/0.69      ! [F: nat > real,M7: nat] :
% 0.35/0.69        ( ( bfun_nat_real
% 0.35/0.69          @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ M7 ) )
% 0.35/0.69          @ at_top_nat )
% 0.35/0.69       => ( ! [M4: nat,N3: nat] :
% 0.35/0.69              ( ( ord_less_eq_nat @ M7 @ M4 )
% 0.35/0.69             => ( ( ord_less_eq_nat @ M4 @ N3 )
% 0.35/0.69               => ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ M4 ) ) ) )
% 0.35/0.69         => ( topolo7531315842566124627t_real @ F ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % Bseq_monoseq_convergent'_dec
% 0.35/0.69  thf(fact_10199_Bseq__mono__convergent,axiom,
% 0.35/0.69      ! [X8: nat > real] :
% 0.35/0.69        ( ( bfun_nat_real @ X8 @ at_top_nat )
% 0.35/0.69       => ( ! [M4: nat,N3: nat] :
% 0.35/0.69              ( ( ord_less_eq_nat @ M4 @ N3 )
% 0.35/0.69             => ( ord_less_eq_real @ ( X8 @ M4 ) @ ( X8 @ N3 ) ) )
% 0.35/0.69         => ( topolo7531315842566124627t_real @ X8 ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % Bseq_mono_convergent
% 0.35/0.69  thf(fact_10200_convergent__realpow,axiom,
% 0.35/0.69      ! [X: real] :
% 0.35/0.69        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.69       => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.35/0.69         => ( topolo7531315842566124627t_real @ ( power_power_real @ X ) ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % convergent_realpow
% 0.35/0.69  thf(fact_10201_bot__nat__0_Oordering__top__axioms,axiom,
% 0.35/0.69      ( ordering_top_nat
% 0.35/0.69      @ ^ [X2: nat,Y: nat] : ( ord_less_eq_nat @ Y @ X2 )
% 0.35/0.69      @ ^ [X2: nat,Y: nat] : ( ord_less_nat @ Y @ X2 )
% 0.35/0.69      @ zero_zero_nat ) ).
% 0.35/0.69  
% 0.35/0.69  % bot_nat_0.ordering_top_axioms
% 0.35/0.69  thf(fact_10202_pair__lessI2,axiom,
% 0.35/0.69      ! [A: nat,B: nat,S3: nat,T: nat] :
% 0.35/0.69        ( ( ord_less_eq_nat @ A @ B )
% 0.35/0.69       => ( ( ord_less_nat @ S3 @ T )
% 0.35/0.69         => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S3 ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_less ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % pair_lessI2
% 0.35/0.69  thf(fact_10203_pair__less__iff1,axiom,
% 0.35/0.69      ! [X: nat,Y2: nat,Z: nat] :
% 0.35/0.69        ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ X @ Y2 ) @ ( product_Pair_nat_nat @ X @ Z ) ) @ fun_pair_less )
% 0.35/0.69        = ( ord_less_nat @ Y2 @ Z ) ) ).
% 0.35/0.69  
% 0.35/0.69  % pair_less_iff1
% 0.35/0.69  thf(fact_10204_pair__lessI1,axiom,
% 0.35/0.69      ! [A: nat,B: nat,S3: nat,T: nat] :
% 0.35/0.69        ( ( ord_less_nat @ A @ B )
% 0.35/0.69       => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S3 ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_less ) ) ).
% 0.35/0.69  
% 0.35/0.69  % pair_lessI1
% 0.35/0.69  thf(fact_10205_pair__leqI2,axiom,
% 0.35/0.69      ! [A: nat,B: nat,S3: nat,T: nat] :
% 0.35/0.69        ( ( ord_less_eq_nat @ A @ B )
% 0.35/0.69       => ( ( ord_less_eq_nat @ S3 @ T )
% 0.35/0.69         => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S3 ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_leq ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % pair_leqI2
% 0.35/0.69  thf(fact_10206_pair__leqI1,axiom,
% 0.35/0.69      ! [A: nat,B: nat,S3: nat,T: nat] :
% 0.35/0.69        ( ( ord_less_nat @ A @ B )
% 0.35/0.69       => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S3 ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_leq ) ) ).
% 0.35/0.69  
% 0.35/0.69  % pair_leqI1
% 0.35/0.69  thf(fact_10207_of__rat__dense,axiom,
% 0.35/0.69      ! [X: real,Y2: real] :
% 0.35/0.69        ( ( ord_less_real @ X @ Y2 )
% 0.35/0.69       => ? [Q3: rat] :
% 0.35/0.69            ( ( ord_less_real @ X @ ( field_7254667332652039916t_real @ Q3 ) )
% 0.35/0.69            & ( ord_less_real @ ( field_7254667332652039916t_real @ Q3 ) @ Y2 ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  % of_rat_dense
% 0.35/0.69  thf(fact_10208_euclidean__size__int__def,axiom,
% 0.35/0.69      ( euclid4774559944035922753ze_int
% 0.35/0.69      = ( comp_int_nat_int @ nat2 @ abs_abs_int ) ) ).
% 0.35/0.69  
% 0.35/0.69  % euclidean_size_int_def
% 0.35/0.69  thf(fact_10209_euclidean__size__nat__def,axiom,
% 0.35/0.69      euclid4777050414544973029ze_nat = id_nat ).
% 0.35/0.69  
% 0.35/0.69  % euclidean_size_nat_def
% 0.35/0.69  thf(fact_10210_abs__division__segment,axiom,
% 0.35/0.69      ! [K: int] :
% 0.35/0.69        ( ( abs_abs_int @ ( euclid3395696857347342551nt_int @ K ) )
% 0.35/0.69        = one_one_int ) ).
% 0.35/0.69  
% 0.35/0.69  % abs_division_segment
% 0.35/0.69  
% 0.35/0.69  % Helper facts (42)
% 0.35/0.69  thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 0.35/0.69      ! [X: int,Y2: int] :
% 0.35/0.69        ( ( if_int @ $false @ X @ Y2 )
% 0.35/0.69        = Y2 ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 0.35/0.69      ! [X: int,Y2: int] :
% 0.35/0.69        ( ( if_int @ $true @ X @ Y2 )
% 0.35/0.69        = X ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 0.35/0.69      ! [X: nat,Y2: nat] :
% 0.35/0.69        ( ( if_nat @ $false @ X @ Y2 )
% 0.35/0.69        = Y2 ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 0.35/0.69      ! [X: nat,Y2: nat] :
% 0.35/0.69        ( ( if_nat @ $true @ X @ Y2 )
% 0.35/0.69        = X ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 0.35/0.69      ! [X: num,Y2: num] :
% 0.35/0.69        ( ( if_num @ $false @ X @ Y2 )
% 0.35/0.69        = Y2 ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 0.35/0.69      ! [X: num,Y2: num] :
% 0.35/0.69        ( ( if_num @ $true @ X @ Y2 )
% 0.35/0.69        = X ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 0.35/0.69      ! [X: rat,Y2: rat] :
% 0.35/0.69        ( ( if_rat @ $false @ X @ Y2 )
% 0.35/0.69        = Y2 ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 0.35/0.69      ! [X: rat,Y2: rat] :
% 0.35/0.69        ( ( if_rat @ $true @ X @ Y2 )
% 0.35/0.69        = X ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 0.35/0.69      ! [X: real,Y2: real] :
% 0.35/0.69        ( ( if_real @ $false @ X @ Y2 )
% 0.35/0.69        = Y2 ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 0.35/0.69      ! [X: real,Y2: real] :
% 0.35/0.69        ( ( if_real @ $true @ X @ Y2 )
% 0.35/0.69        = X ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_fChoice_1_1_fChoice_001t__Real__Oreal_T,axiom,
% 0.35/0.69      ! [P: real > $o] :
% 0.35/0.69        ( ( P @ ( fChoice_real @ P ) )
% 0.35/0.69        = ( ? [X4: real] : ( P @ X4 ) ) ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_2_1_If_001t__Complex__Ocomplex_T,axiom,
% 0.35/0.69      ! [X: complex,Y2: complex] :
% 0.35/0.69        ( ( if_complex @ $false @ X @ Y2 )
% 0.35/0.69        = Y2 ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_1_1_If_001t__Complex__Ocomplex_T,axiom,
% 0.35/0.69      ! [X: complex,Y2: complex] :
% 0.35/0.69        ( ( if_complex @ $true @ X @ Y2 )
% 0.35/0.69        = X ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_2_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 0.35/0.69      ! [X: extended_enat,Y2: extended_enat] :
% 0.35/0.69        ( ( if_Extended_enat @ $false @ X @ Y2 )
% 0.35/0.69        = Y2 ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_1_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 0.35/0.69      ! [X: extended_enat,Y2: extended_enat] :
% 0.35/0.69        ( ( if_Extended_enat @ $true @ X @ Y2 )
% 0.35/0.69        = X ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 0.35/0.69      ! [X: code_integer,Y2: code_integer] :
% 0.35/0.69        ( ( if_Code_integer @ $false @ X @ Y2 )
% 0.35/0.69        = Y2 ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 0.35/0.69      ! [X: code_integer,Y2: code_integer] :
% 0.35/0.69        ( ( if_Code_integer @ $true @ X @ Y2 )
% 0.35/0.69        = X ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_2_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 0.35/0.69      ! [X: set_nat,Y2: set_nat] :
% 0.35/0.69        ( ( if_set_nat @ $false @ X @ Y2 )
% 0.35/0.69        = Y2 ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_1_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 0.35/0.69      ! [X: set_nat,Y2: set_nat] :
% 0.35/0.69        ( ( if_set_nat @ $true @ X @ Y2 )
% 0.35/0.69        = X ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_2_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 0.35/0.69      ! [X: vEBT_VEBT,Y2: vEBT_VEBT] :
% 0.35/0.69        ( ( if_VEBT_VEBT @ $false @ X @ Y2 )
% 0.35/0.69        = Y2 ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_1_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 0.35/0.69      ! [X: vEBT_VEBT,Y2: vEBT_VEBT] :
% 0.35/0.69        ( ( if_VEBT_VEBT @ $true @ X @ Y2 )
% 0.35/0.69        = X ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 0.35/0.69      ! [X: list_int,Y2: list_int] :
% 0.35/0.69        ( ( if_list_int @ $false @ X @ Y2 )
% 0.35/0.69        = Y2 ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 0.35/0.69      ! [X: list_int,Y2: list_int] :
% 0.35/0.69        ( ( if_list_int @ $true @ X @ Y2 )
% 0.35/0.69        = X ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 0.35/0.69      ! [X: list_nat,Y2: list_nat] :
% 0.35/0.69        ( ( if_list_nat @ $false @ X @ Y2 )
% 0.35/0.69        = Y2 ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 0.35/0.69      ! [X: list_nat,Y2: list_nat] :
% 0.35/0.69        ( ( if_list_nat @ $true @ X @ Y2 )
% 0.35/0.69        = X ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_2_1_If_001t__Set__Oset_It__Real__Oreal_J_T,axiom,
% 0.35/0.69      ! [X: set_real,Y2: set_real] :
% 0.35/0.69        ( ( if_set_real @ $false @ X @ Y2 )
% 0.35/0.69        = Y2 ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_1_1_If_001t__Set__Oset_It__Real__Oreal_J_T,axiom,
% 0.35/0.69      ! [X: set_real,Y2: set_real] :
% 0.35/0.69        ( ( if_set_real @ $true @ X @ Y2 )
% 0.35/0.69        = X ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_2_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 0.35/0.69      ! [X: int > int,Y2: int > int] :
% 0.35/0.69        ( ( if_int_int @ $false @ X @ Y2 )
% 0.35/0.69        = Y2 ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_1_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 0.35/0.69      ! [X: int > int,Y2: int > int] :
% 0.35/0.69        ( ( if_int_int @ $true @ X @ Y2 )
% 0.35/0.69        = X ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_2_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 0.35/0.69      ! [X: option_nat,Y2: option_nat] :
% 0.35/0.69        ( ( if_option_nat @ $false @ X @ Y2 )
% 0.35/0.69        = Y2 ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_1_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 0.35/0.69      ! [X: option_nat,Y2: option_nat] :
% 0.35/0.69        ( ( if_option_nat @ $true @ X @ Y2 )
% 0.35/0.69        = X ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 0.35/0.69      ! [X: option_num,Y2: option_num] :
% 0.35/0.69        ( ( if_option_num @ $false @ X @ Y2 )
% 0.35/0.69        = Y2 ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 0.35/0.69      ! [X: option_num,Y2: option_num] :
% 0.35/0.69        ( ( if_option_num @ $true @ X @ Y2 )
% 0.35/0.69        = X ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 0.35/0.69      ! [X: product_prod_int_int,Y2: product_prod_int_int] :
% 0.35/0.69        ( ( if_Pro3027730157355071871nt_int @ $false @ X @ Y2 )
% 0.35/0.69        = Y2 ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 0.35/0.69      ! [X: product_prod_int_int,Y2: product_prod_int_int] :
% 0.35/0.69        ( ( if_Pro3027730157355071871nt_int @ $true @ X @ Y2 )
% 0.35/0.69        = X ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 0.35/0.69      ! [X: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 0.35/0.69        ( ( if_Pro6206227464963214023at_nat @ $false @ X @ Y2 )
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% 0.35/0.69  
% 0.35/0.69  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 0.35/0.69      ! [X: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 0.35/0.69        ( ( if_Pro6206227464963214023at_nat @ $true @ X @ Y2 )
% 0.35/0.69        = X ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 0.35/0.69      ! [X: produc6271795597528267376eger_o,Y2: produc6271795597528267376eger_o] :
% 0.35/0.69        ( ( if_Pro5737122678794959658eger_o @ $false @ X @ Y2 )
% 0.35/0.69        = Y2 ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 0.35/0.69      ! [X: produc6271795597528267376eger_o,Y2: produc6271795597528267376eger_o] :
% 0.35/0.69        ( ( if_Pro5737122678794959658eger_o @ $true @ X @ Y2 )
% 0.35/0.69        = X ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 0.35/0.69      ! [P: $o] :
% 0.35/0.69        ( ( P = $true )
% 0.35/0.69        | ( P = $false ) ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 0.35/0.69      ! [X: produc8923325533196201883nteger,Y2: produc8923325533196201883nteger] :
% 0.35/0.69        ( ( if_Pro6119634080678213985nteger @ $false @ X @ Y2 )
% 0.35/0.69        = Y2 ) ).
% 0.35/0.69  
% 0.35/0.69  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 0.35/0.69      ! [X: produc8923325533196201883nteger,Y2: produc8923325533196201883nteger] :
% 0.35/0.69        ( ( if_Pro6119634080678213985nteger @ $true @ X @ Y2 )
% 0.35/0.69        = X ) ).
% 0.35/0.69  
% 0.35/0.69  % Conjectures (1)
% 0.35/0.69  thf(conj_0,conjecture,
% 0.35/0.69      ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 0.35/0.69      = ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_t @ summary ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat ) @ one_one_nat ) ) ).
% 0.35/0.69  
% 0.35/0.69  %------------------------------------------------------------------------------
% 0.35/0.69  ------------------------
% 6.84/2.63  ---- Embedded in THF ---
% 6.84/2.63  %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 6.84/2.63  %%% Generated on Fri Feb 27 11:07:22 EST 2026
% 6.84/2.63  %%% using '$$dhol' embedding, version 1.3.0.
% 6.84/2.63  %%% Logic specification used:
% 6.84/2.63  %%% thf(spec, logic, $$dhol).
% 6.84/2.63  
% 6.84/2.63  % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.T5XVM49IAI/DTF2DTF21656.p
% See solution above
% 6.84/2.66  ------------------------
% 9.49/5.22  ---- Cleaned THF ---
% 9.49/5.23  thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
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% 9.49/5.23  thf(sy_c_Code__Numeral_Ointeger_Oint__of__integer,type,
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% 9.49/5.23  thf(sy_c_Code__Numeral_Ointeger_Ointeger__of__int,type,
% 9.49/5.23      code_integer_of_int: int > code_integer ).
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% 9.49/5.23  thf(sy_c_Code__Numeral_Ointeger__of__num,type,
% 9.49/5.23      code_integer_of_num: num > code_integer ).
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% 9.49/5.23  thf(sy_c_Code__Numeral_Onat__of__integer,type,
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% 9.49/5.23  thf(sy_c_Code__Target__Int_Onegative,type,
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% 9.49/5.23  thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Real__Oreal,type,
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% 9.49/5.23  
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% 9.49/5.23      re: complex > real ).
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% 9.49/5.23      csqrt: complex > complex ).
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% 9.49/5.23      imaginary_unit: complex ).
% 9.49/5.23  
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% 9.49/5.23  
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% 9.49/5.23  thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Nat__Onat,type,
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% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Real__Oreal,type,
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% 9.49/5.23  
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% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Filter_Ofiltermap_001t__Real__Oreal_001t__Real__Oreal,type,
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% 9.49/5.23  
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% 9.49/5.23      bij_betw_nat_complex: ( nat > complex ) > set_nat > set_complex > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Fun_Obij__betw_001t__Nat__Onat_001t__Nat__Onat,type,
% 9.49/5.23      bij_betw_nat_nat: ( nat > nat ) > set_nat > set_nat > $o ).
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% 9.49/5.23  thf(sy_c_Fun_Ocomp_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
% 9.49/5.23      comp_C8797469213163452608nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
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% 9.49/5.23  thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
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% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Int__Oint_001t__Num__Onum,type,
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% 9.49/5.23  thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint,type,
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% 9.49/5.23  thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
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% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Real__Oreal_001t__Nat__Onat,type,
% 9.49/5.23      comp_nat_real_nat: ( nat > real ) > ( nat > nat ) > nat > real ).
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% 9.49/5.23  thf(sy_c_Fun_Oid_001_Eo,type,
% 9.49/5.23      id_o: $o > $o ).
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% 9.49/5.23  thf(sy_c_Fun_Oid_001t__Nat__Onat,type,
% 9.49/5.23      id_nat: nat > nat ).
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% 9.49/5.23  thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 9.49/5.23      inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).
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% 9.49/5.23  thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__String__Ochar,type,
% 9.49/5.23      inj_on_nat_char: ( nat > char ) > set_nat > $o ).
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% 9.49/5.23  thf(sy_c_Fun_Oinj__on_001t__Real__Oreal_001t__Real__Oreal,type,
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% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Fun_Ostrict__mono__on_001t__Nat__Onat_001t__Nat__Onat,type,
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% 9.49/5.23  thf(sy_c_Fun_Othe__inv__into_001t__Real__Oreal_001t__Real__Oreal,type,
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% 9.49/5.23  thf(sy_c_Fun__Def_Opair__leq,type,
% 9.49/5.23      fun_pair_leq: set_Pr8693737435421807431at_nat ).
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% 9.49/5.23  thf(sy_c_Fun__Def_Opair__less,type,
% 9.49/5.23      fun_pair_less: set_Pr8693737435421807431at_nat ).
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% 9.49/5.23  thf(sy_c_GCD_OGcd__class_OGcd_001t__Nat__Onat,type,
% 9.49/5.23      gcd_Gcd_nat: set_nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_GCD_Obezw,type,
% 9.49/5.23      bezw: nat > nat > product_prod_int_int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_GCD_Obezw__rel,type,
% 9.49/5.23      bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Int__Oint,type,
% 9.49/5.23      gcd_gcd_int: int > int > int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Nat__Onat,type,
% 9.49/5.23      gcd_gcd_nat: nat > nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_GCD_Ogcd__nat__rel,type,
% 9.49/5.23      gcd_nat_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
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% 9.49/5.23  
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% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Groups_Oabs__class_Oabs_001t__Rat__Orat,type,
% 9.49/5.23      abs_abs_rat: rat > rat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Groups_Oabs__class_Oabs_001t__Real__Oreal,type,
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% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__List__Olist_It__Nat__Onat_J_M_Eo_J,type,
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% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Nat__Onat_M_Eo_J,type,
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% 9.49/5.23  thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Real__Oreal_M_Eo_J,type,
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% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Groups_Ominus__class_Ominus_001t__Int__Oint,type,
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% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
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% 9.49/5.23  thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Real__Oreal_J,type,
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% 9.49/5.23  thf(sy_c_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 9.49/5.23      if_Pro6119634080678213985nteger: $o > produc8923325533196201883nteger > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 9.49/5.23      if_Pro3027730157355071871nt_int: $o > product_prod_int_int > product_prod_int_int > product_prod_int_int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 9.49/5.23      if_Pro6206227464963214023at_nat: $o > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_If_001t__Rat__Orat,type,
% 9.49/5.23      if_rat: $o > rat > rat > rat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_If_001t__Real__Oreal,type,
% 9.49/5.23      if_real: $o > real > real > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_If_001t__Set__Oset_It__Nat__Onat_J,type,
% 9.49/5.23      if_set_nat: $o > set_nat > set_nat > set_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_If_001t__Set__Oset_It__Real__Oreal_J,type,
% 9.49/5.23      if_set_real: $o > set_real > set_real > set_real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_If_001t__VEBT____Definitions__OVEBT,type,
% 9.49/5.23      if_VEBT_VEBT: $o > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Infinite__Set_Owellorder__class_Oenumerate_001t__Nat__Onat,type,
% 9.49/5.23      infini8530281810654367211te_nat: set_nat > nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Int_OAbs__Integ,type,
% 9.49/5.23      abs_Integ: product_prod_nat_nat > int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Int_ORep__Integ,type,
% 9.49/5.23      rep_Integ: int > product_prod_nat_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Int_Onat,type,
% 9.49/5.23      nat2: int > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Int_Opower__int_001t__Real__Oreal,type,
% 9.49/5.23      power_int_real: real > int > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Int_Oring__1__class_OInts_001t__Real__Oreal,type,
% 9.49/5.23      ring_1_Ints_real: set_real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Int_Oring__1__class_Oof__int_001t__Code____Numeral__Ointeger,type,
% 9.49/5.23      ring_18347121197199848620nteger: int > code_integer ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Int_Oring__1__class_Oof__int_001t__Complex__Ocomplex,type,
% 9.49/5.23      ring_17405671764205052669omplex: int > complex ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Int_Oring__1__class_Oof__int_001t__Int__Oint,type,
% 9.49/5.23      ring_1_of_int_int: int > int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Int_Oring__1__class_Oof__int_001t__Rat__Orat,type,
% 9.49/5.23      ring_1_of_int_rat: int > rat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Int_Oring__1__class_Oof__int_001t__Real__Oreal,type,
% 9.49/5.23      ring_1_of_int_real: int > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Extended____Nat__Oenat,type,
% 9.49/5.23      inf_in1870772243966228564d_enat: extended_enat > extended_enat > extended_enat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Nat__Onat,type,
% 9.49/5.23      inf_inf_nat: nat > nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 9.49/5.23      inf_in2572325071724192079at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Nat__Onat,type,
% 9.49/5.23      semila1623282765462674594er_nat: ( nat > nat > nat ) > nat > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Lattices_Osup__class_Osup_001t__Extended____Nat__Oenat,type,
% 9.49/5.23      sup_su3973961784419623482d_enat: extended_enat > extended_enat > extended_enat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Lattices_Osup__class_Osup_001t__Nat__Onat,type,
% 9.49/5.23      sup_sup_nat: nat > nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J,type,
% 9.49/5.23      sup_sup_set_nat: set_nat > set_nat > set_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 9.49/5.23      sup_su6327502436637775413at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Nat__Onat,type,
% 9.49/5.23      lattic8265883725875713057ax_nat: set_nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Limits_OBfun_001t__Nat__Onat_001t__Real__Oreal,type,
% 9.49/5.23      bfun_nat_real: ( nat > real ) > filter_nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Oappend_001t__Int__Oint,type,
% 9.49/5.23      append_int: list_int > list_int > list_int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Oappend_001t__Nat__Onat,type,
% 9.49/5.23      append_nat: list_nat > list_nat > list_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Odrop_001t__Nat__Onat,type,
% 9.49/5.23      drop_nat: nat > list_nat > list_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Olast_001t__Nat__Onat,type,
% 9.49/5.23      last_nat: list_nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Nat__Onat,type,
% 9.49/5.23      linord2614967742042102400et_nat: set_nat > list_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
% 9.49/5.23      cons_int: int > list_int > list_int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 9.49/5.23      cons_nat: nat > list_nat > list_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Olist_ONil_001t__Int__Oint,type,
% 9.49/5.23      nil_int: list_int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 9.49/5.23      nil_nat: list_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Olist_Ohd_001t__Nat__Onat,type,
% 9.49/5.23      hd_nat: list_nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat,type,
% 9.49/5.23      map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Olist_Oset_001_Eo,type,
% 9.49/5.23      set_o2: list_o > set_o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Olist_Oset_001t__Complex__Ocomplex,type,
% 9.49/5.23      set_complex2: list_complex > set_complex ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Olist_Oset_001t__Int__Oint,type,
% 9.49/5.23      set_int2: list_int > set_int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 9.49/5.23      set_nat2: list_nat > set_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 9.49/5.23      set_Pr5648618587558075414at_nat: list_P6011104703257516679at_nat > set_Pr1261947904930325089at_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Olist_Oset_001t__Real__Oreal,type,
% 9.49/5.23      set_real2: list_real > set_real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Olist_Oset_001t__VEBT____Definitions__OVEBT,type,
% 9.49/5.23      set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Olist_Osize__list_001t__VEBT____Definitions__OVEBT,type,
% 9.49/5.23      size_list_VEBT_VEBT: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Olist_Otl_001t__Nat__Onat,type,
% 9.49/5.23      tl_nat: list_nat > list_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Olist__update_001_Eo,type,
% 9.49/5.23      list_update_o: list_o > nat > $o > list_o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Olist__update_001t__Complex__Ocomplex,type,
% 9.49/5.23      list_update_complex: list_complex > nat > complex > list_complex ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Olist__update_001t__Int__Oint,type,
% 9.49/5.23      list_update_int: list_int > nat > int > list_int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Olist__update_001t__Nat__Onat,type,
% 9.49/5.23      list_update_nat: list_nat > nat > nat > list_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Olist__update_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 9.49/5.23      list_u6180841689913720943at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat > list_P6011104703257516679at_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Olist__update_001t__Real__Oreal,type,
% 9.49/5.23      list_update_real: list_real > nat > real > list_real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Olist__update_001t__VEBT____Definitions__OVEBT,type,
% 9.49/5.23      list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Onth_001_Eo,type,
% 9.49/5.23      nth_o: list_o > nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Onth_001t__Complex__Ocomplex,type,
% 9.49/5.23      nth_complex: list_complex > nat > complex ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Onth_001t__Int__Oint,type,
% 9.49/5.23      nth_int: list_int > nat > int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 9.49/5.23      nth_nat: list_nat > nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Onth_001t__Num__Onum,type,
% 9.49/5.23      nth_num: list_num > nat > num ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
% 9.49/5.23      nth_Product_prod_o_o: list_P4002435161011370285od_o_o > nat > product_prod_o_o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
% 9.49/5.23      nth_Pr1649062631805364268_o_int: list_P3795440434834930179_o_int > nat > product_prod_o_int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
% 9.49/5.23      nth_Pr5826913651314560976_o_nat: list_P6285523579766656935_o_nat > nat > product_prod_o_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J,type,
% 9.49/5.23      nth_Pr6777367263587873994T_VEBT: list_P7495141550334521929T_VEBT > nat > produc2504756804600209347T_VEBT ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 9.49/5.23      nth_Pr7617993195940197384at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J,type,
% 9.49/5.23      nth_Pr8326237132889035090at_num: list_P1726324292696863441at_num > nat > product_prod_nat_num ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 9.49/5.23      nth_Pr6456567536196504476um_num: list_P3744719386663036955um_num > nat > product_prod_num_num ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J,type,
% 9.49/5.23      nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J,type,
% 9.49/5.23      nth_Pr6837108013167703752BT_int: list_P4547456442757143711BT_int > nat > produc4894624898956917775BT_int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 9.49/5.23      nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 9.49/5.23      nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Onth_001t__Real__Oreal,type,
% 9.49/5.23      nth_real: list_real > nat > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Onth_001t__VEBT____Definitions__OVEBT,type,
% 9.49/5.23      nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Oproduct_001_Eo_001_Eo,type,
% 9.49/5.23      product_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Oproduct_001_Eo_001t__Int__Oint,type,
% 9.49/5.23      product_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Oproduct_001_Eo_001t__Nat__Onat,type,
% 9.49/5.23      product_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Oproduct_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 9.49/5.23      product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Oproduct_001t__Nat__Onat_001_Eo,type,
% 9.49/5.23      product_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__Num__Onum,type,
% 9.49/5.23      product_nat_num: list_nat > list_num > list_P1726324292696863441at_num ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 9.49/5.23      produc7156399406898700509T_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Oproduct_001t__Num__Onum_001t__Num__Onum,type,
% 9.49/5.23      product_num_num: list_num > list_num > list_P3744719386663036955um_num ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 9.49/5.23      product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 9.49/5.23      produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 9.49/5.23      produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 9.49/5.23      produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Oreplicate_001_Eo,type,
% 9.49/5.23      replicate_o: nat > $o > list_o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Oreplicate_001t__Complex__Ocomplex,type,
% 9.49/5.23      replicate_complex: nat > complex > list_complex ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Oreplicate_001t__Int__Oint,type,
% 9.49/5.23      replicate_int: nat > int > list_int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Oreplicate_001t__Nat__Onat,type,
% 9.49/5.23      replicate_nat: nat > nat > list_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Oreplicate_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 9.49/5.23      replic4235873036481779905at_nat: nat > product_prod_nat_nat > list_P6011104703257516679at_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Oreplicate_001t__Real__Oreal,type,
% 9.49/5.23      replicate_real: nat > real > list_real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Oreplicate_001t__VEBT____Definitions__OVEBT,type,
% 9.49/5.23      replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Osorted__wrt_001t__Nat__Onat,type,
% 9.49/5.23      sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Otake_001t__Nat__Onat,type,
% 9.49/5.23      take_nat: nat > list_nat > list_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Oupt,type,
% 9.49/5.23      upt: nat > nat > list_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Oupto,type,
% 9.49/5.23      upto: int > int > list_int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_List_Oupto__aux,type,
% 9.49/5.23      upto_aux: int > int > list_int > list_int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_OSuc,type,
% 9.49/5.23      suc: nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Ocompow_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 9.49/5.23      compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Onat_Ocase__nat_001_Eo,type,
% 9.49/5.23      case_nat_o: $o > ( nat > $o ) > nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Onat_Ocase__nat_001t__Nat__Onat,type,
% 9.49/5.23      case_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Onat_Ocase__nat_001t__Option__Ooption_It__Num__Onum_J,type,
% 9.49/5.23      case_nat_option_num: option_num > ( nat > option_num ) > nat > option_num ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Onat_Opred,type,
% 9.49/5.23      pred: nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Ointeger,type,
% 9.49/5.23      semiri4939895301339042750nteger: nat > code_integer ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Complex__Ocomplex,type,
% 9.49/5.23      semiri8010041392384452111omplex: nat > complex ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Extended____Nat__Oenat,type,
% 9.49/5.23      semiri4216267220026989637d_enat: nat > extended_enat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 9.49/5.23      semiri1314217659103216013at_int: nat > int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 9.49/5.23      semiri1316708129612266289at_nat: nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
% 9.49/5.23      semiri681578069525770553at_rat: nat > rat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
% 9.49/5.23      semiri5074537144036343181t_real: nat > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Complex__Ocomplex,type,
% 9.49/5.23      semiri2816024913162550771omplex: ( complex > complex ) > nat > complex > complex ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Int__Oint,type,
% 9.49/5.23      semiri8420488043553186161ux_int: ( int > int ) > nat > int > int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Nat__Onat,type,
% 9.49/5.23      semiri8422978514062236437ux_nat: ( nat > nat ) > nat > nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Rat__Orat,type,
% 9.49/5.23      semiri7787848453975740701ux_rat: ( rat > rat ) > nat > rat > rat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Real__Oreal,type,
% 9.49/5.23      semiri7260567687927622513x_real: ( real > real ) > nat > real > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_I_Eo_J,type,
% 9.49/5.23      size_size_list_o: list_o > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 9.49/5.23      size_s3451745648224563538omplex: list_complex > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Int__Oint_J,type,
% 9.49/5.23      size_size_list_int: list_int > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 9.49/5.23      size_size_list_nat: list_nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Num__Onum_J,type,
% 9.49/5.23      size_size_list_num: list_num > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
% 9.49/5.23      size_s1515746228057227161od_o_o: list_P4002435161011370285od_o_o > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J_J,type,
% 9.49/5.23      size_s2953683556165314199_o_int: list_P3795440434834930179_o_int > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J,type,
% 9.49/5.23      size_s5443766701097040955_o_nat: list_P6285523579766656935_o_nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 9.49/5.23      size_s4313452262239582901T_VEBT: list_P7495141550334521929T_VEBT > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J,type,
% 9.49/5.23      size_s6491369823275344609_nat_o: list_P7333126701944960589_nat_o > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 9.49/5.23      size_s5460976970255530739at_nat: list_P6011104703257516679at_nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 9.49/5.23      size_s4762443039079500285T_VEBT: list_P5647936690300460905T_VEBT > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J_J,type,
% 9.49/5.23      size_s9168528473962070013VEBT_o: list_P3126845725202233233VEBT_o > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J_J,type,
% 9.49/5.23      size_s3661962791536183091BT_int: list_P4547456442757143711BT_int > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J_J,type,
% 9.49/5.23      size_s6152045936467909847BT_nat: list_P7037539587688870467BT_nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 9.49/5.23      size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Real__Oreal_J,type,
% 9.49/5.23      size_size_list_real: list_real > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 9.49/5.23      size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Osize__class_Osize_001t__Num__Onum,type,
% 9.49/5.23      size_size_num: num > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Nat__Onat_J,type,
% 9.49/5.23      size_size_option_nat: option_nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Num__Onum_J,type,
% 9.49/5.23      size_size_option_num: option_num > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 9.49/5.23      size_s170228958280169651at_nat: option4927543243414619207at_nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat_Osize__class_Osize_001t__VEBT____Definitions__OVEBT,type,
% 9.49/5.23      size_size_VEBT_VEBT: vEBT_VEBT > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat__Bijection_Olist__encode,type,
% 9.49/5.23      nat_list_encode: list_nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat__Bijection_Olist__encode__rel,type,
% 9.49/5.23      nat_list_encode_rel: list_nat > list_nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat__Bijection_Oprod__decode__aux,type,
% 9.49/5.23      nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat__Bijection_Oprod__decode__aux__rel,type,
% 9.49/5.23      nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat__Bijection_Oprod__encode,type,
% 9.49/5.23      nat_prod_encode: product_prod_nat_nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat__Bijection_Oset__decode,type,
% 9.49/5.23      nat_set_decode: nat > set_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat__Bijection_Oset__encode,type,
% 9.49/5.23      nat_set_encode: set_nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Nat__Bijection_Otriangle,type,
% 9.49/5.23      nat_triangle: nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_NthRoot_Oroot,type,
% 9.49/5.23      root: nat > real > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_NthRoot_Osqrt,type,
% 9.49/5.23      sqrt: real > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Num_OBitM,type,
% 9.49/5.23      bitM: num > num ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Num_Oinc,type,
% 9.49/5.23      inc: num > num ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Code____Numeral__Ointeger,type,
% 9.49/5.23      neg_nu8804712462038260780nteger: code_integer > code_integer ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Complex__Ocomplex,type,
% 9.49/5.23      neg_nu7009210354673126013omplex: complex > complex ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Int__Oint,type,
% 9.49/5.23      neg_numeral_dbl_int: int > int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Rat__Orat,type,
% 9.49/5.23      neg_numeral_dbl_rat: rat > rat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Real__Oreal,type,
% 9.49/5.23      neg_numeral_dbl_real: real > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Code____Numeral__Ointeger,type,
% 9.49/5.23      neg_nu7757733837767384882nteger: code_integer > code_integer ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Complex__Ocomplex,type,
% 9.49/5.23      neg_nu6511756317524482435omplex: complex > complex ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Int__Oint,type,
% 9.49/5.23      neg_nu3811975205180677377ec_int: int > int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Rat__Orat,type,
% 9.49/5.23      neg_nu3179335615603231917ec_rat: rat > rat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Real__Oreal,type,
% 9.49/5.23      neg_nu6075765906172075777c_real: real > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Code____Numeral__Ointeger,type,
% 9.49/5.23      neg_nu5831290666863070958nteger: code_integer > code_integer ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Complex__Ocomplex,type,
% 9.49/5.23      neg_nu8557863876264182079omplex: complex > complex ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Int__Oint,type,
% 9.49/5.23      neg_nu5851722552734809277nc_int: int > int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Rat__Orat,type,
% 9.49/5.23      neg_nu5219082963157363817nc_rat: rat > rat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Real__Oreal,type,
% 9.49/5.23      neg_nu8295874005876285629c_real: real > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Num_Oneg__numeral__class_Osub_001t__Int__Oint,type,
% 9.49/5.23      neg_numeral_sub_int: num > num > int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Num_Onum_OBit0,type,
% 9.49/5.23      bit0: num > num ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Num_Onum_OBit1,type,
% 9.49/5.23      bit1: num > num ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Num_Onum_OOne,type,
% 9.49/5.23      one: num ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Num_Onum_Ocase__num_001t__Option__Ooption_It__Num__Onum_J,type,
% 9.49/5.23      case_num_option_num: option_num > ( num > option_num ) > ( num > option_num ) > num > option_num ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Num_Onum_Osize__num,type,
% 9.49/5.23      size_num: num > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Num_Onum__of__nat,type,
% 9.49/5.23      num_of_nat: nat > num ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Code____Numeral__Ointeger,type,
% 9.49/5.23      numera6620942414471956472nteger: num > code_integer ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Complex__Ocomplex,type,
% 9.49/5.23      numera6690914467698888265omplex: num > complex ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Extended____Nat__Oenat,type,
% 9.49/5.23      numera1916890842035813515d_enat: num > extended_enat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Int__Oint,type,
% 9.49/5.23      numeral_numeral_int: num > int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat,type,
% 9.49/5.23      numeral_numeral_nat: num > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Rat__Orat,type,
% 9.49/5.23      numeral_numeral_rat: num > rat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Real__Oreal,type,
% 9.49/5.23      numeral_numeral_real: num > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Num_Opow,type,
% 9.49/5.23      pow: num > num > num ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Num_Opred__numeral,type,
% 9.49/5.23      pred_numeral: num > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Num_Osqr,type,
% 9.49/5.23      sqr: num > num ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Option_Ooption_ONone_001t__Nat__Onat,type,
% 9.49/5.23      none_nat: option_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Option_Ooption_ONone_001t__Num__Onum,type,
% 9.49/5.23      none_num: option_num ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 9.49/5.23      none_P5556105721700978146at_nat: option4927543243414619207at_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Option_Ooption_OSome_001t__Nat__Onat,type,
% 9.49/5.23      some_nat: nat > option_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Option_Ooption_OSome_001t__Num__Onum,type,
% 9.49/5.23      some_num: num > option_num ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 9.49/5.23      some_P7363390416028606310at_nat: product_prod_nat_nat > option4927543243414619207at_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 9.49/5.23  thf(sy_c_Product__Type_OPair_001_Eo_001_Eo,type,
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% 9.49/5.23  thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Nat__Onat,type,
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% 9.49/5.23  thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Nat__Onat_J_001t__Option__Ooption_It__Nat__Onat_J,type,
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% 9.49/5.23  thf(sy_c_Product__Type_OSigma_001t__Nat__Onat_001t__Nat__Onat,type,
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% 9.49/5.23  thf(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001t__Nat__Onat,type,
% 9.49/5.23      product_fst_nat_nat: product_prod_nat_nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Product__Type_Oprod_Osnd_001t__Int__Oint_001t__Int__Oint,type,
% 9.49/5.23      product_snd_int_int: product_prod_int_int > int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Product__Type_Oprod_Osnd_001t__Nat__Onat_001t__Nat__Onat,type,
% 9.49/5.23      product_snd_nat_nat: product_prod_nat_nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Rat_OFrct,type,
% 9.49/5.23      frct: product_prod_int_int > rat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Rat_Ofield__char__0__class_ORats_001t__Real__Oreal,type,
% 9.49/5.23      field_5140801741446780682s_real: set_real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Rat_Ofield__char__0__class_Oof__rat_001t__Real__Oreal,type,
% 9.49/5.23      field_7254667332652039916t_real: rat > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Rat_Onormalize,type,
% 9.49/5.23      normalize: product_prod_int_int > product_prod_int_int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Rat_Oquotient__of,type,
% 9.49/5.23      quotient_of: rat > product_prod_int_int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Real__Vector__Spaces_OReals_001t__Complex__Ocomplex,type,
% 9.49/5.23      real_V2521375963428798218omplex: set_complex ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Real__Vector__Spaces_Obounded__linear_001t__Real__Oreal_001t__Real__Oreal,type,
% 9.49/5.23      real_V5970128139526366754l_real: ( real > real ) > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Real__Vector__Spaces_Odist__class_Odist_001t__Complex__Ocomplex,type,
% 9.49/5.23      real_V3694042436643373181omplex: complex > complex > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Real__Vector__Spaces_Odist__class_Odist_001t__Real__Oreal,type,
% 9.49/5.23      real_V975177566351809787t_real: real > real > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex,type,
% 9.49/5.23      real_V1022390504157884413omplex: complex > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Real__Oreal,type,
% 9.49/5.23      real_V7735802525324610683m_real: real > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Complex__Ocomplex,type,
% 9.49/5.23      real_V4546457046886955230omplex: real > complex ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Real__Oreal,type,
% 9.49/5.23      real_V1803761363581548252l_real: real > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Complex__Ocomplex,type,
% 9.49/5.23      real_V2046097035970521341omplex: real > complex > complex ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Real__Oreal,type,
% 9.49/5.23      real_V1485227260804924795R_real: real > real > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Relation_OField_001t__Nat__Onat,type,
% 9.49/5.23      field_nat: set_Pr1261947904930325089at_nat > set_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Relation_OId_001t__Nat__Onat,type,
% 9.49/5.23      id_nat2: set_Pr1261947904930325089at_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Rings_Odivide__class_Odivide_001t__Code____Numeral__Ointeger,type,
% 9.49/5.23      divide6298287555418463151nteger: code_integer > code_integer > code_integer ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Rings_Odivide__class_Odivide_001t__Complex__Ocomplex,type,
% 9.49/5.23      divide1717551699836669952omplex: complex > complex > complex ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Rings_Odivide__class_Odivide_001t__Int__Oint,type,
% 9.49/5.23      divide_divide_int: int > int > int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat,type,
% 9.49/5.23      divide_divide_nat: nat > nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Rings_Odivide__class_Odivide_001t__Rat__Orat,type,
% 9.49/5.23      divide_divide_rat: rat > rat > rat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Rings_Odivide__class_Odivide_001t__Real__Oreal,type,
% 9.49/5.23      divide_divide_real: real > real > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Rings_Odvd__class_Odvd_001t__Code____Numeral__Ointeger,type,
% 9.49/5.23      dvd_dvd_Code_integer: code_integer > code_integer > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Rings_Odvd__class_Odvd_001t__Complex__Ocomplex,type,
% 9.49/5.23      dvd_dvd_complex: complex > complex > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Rings_Odvd__class_Odvd_001t__Int__Oint,type,
% 9.49/5.23      dvd_dvd_int: int > int > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Rings_Odvd__class_Odvd_001t__Nat__Onat,type,
% 9.49/5.23      dvd_dvd_nat: nat > nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Rings_Odvd__class_Odvd_001t__Rat__Orat,type,
% 9.49/5.23      dvd_dvd_rat: rat > rat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Rings_Odvd__class_Odvd_001t__Real__Oreal,type,
% 9.49/5.23      dvd_dvd_real: real > real > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Code____Numeral__Ointeger,type,
% 9.49/5.23      modulo364778990260209775nteger: code_integer > code_integer > code_integer ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Int__Oint,type,
% 9.49/5.23      modulo_modulo_int: int > int > int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Nat__Onat,type,
% 9.49/5.23      modulo_modulo_nat: nat > nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Code____Numeral__Ointeger,type,
% 9.49/5.23      zero_n356916108424825756nteger: $o > code_integer ).
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% 9.49/5.23  thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Complex__Ocomplex,type,
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% 9.49/5.23  thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Int__Oint,type,
% 9.49/5.23      zero_n2684676970156552555ol_int: $o > int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Nat__Onat,type,
% 9.49/5.23      zero_n2687167440665602831ol_nat: $o > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Rat__Orat,type,
% 9.49/5.23      zero_n2052037380579107095ol_rat: $o > rat ).
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% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Series_Osuminf_001t__Complex__Ocomplex,type,
% 9.49/5.23      suminf_complex: ( nat > complex ) > complex ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Series_Osuminf_001t__Int__Oint,type,
% 9.49/5.23      suminf_int: ( nat > int ) > int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Series_Osuminf_001t__Nat__Onat,type,
% 9.49/5.23      suminf_nat: ( nat > nat ) > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Series_Osuminf_001t__Real__Oreal,type,
% 9.49/5.23      suminf_real: ( nat > real ) > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Series_Osummable_001t__Complex__Ocomplex,type,
% 9.49/5.23      summable_complex: ( nat > complex ) > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Series_Osummable_001t__Int__Oint,type,
% 9.49/5.23      summable_int: ( nat > int ) > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Series_Osummable_001t__Nat__Onat,type,
% 9.49/5.23      summable_nat: ( nat > nat ) > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Series_Osummable_001t__Real__Oreal,type,
% 9.49/5.23      summable_real: ( nat > real ) > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Series_Osums_001t__Complex__Ocomplex,type,
% 9.49/5.23      sums_complex: ( nat > complex ) > complex > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Series_Osums_001t__Int__Oint,type,
% 9.49/5.23      sums_int: ( nat > int ) > int > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Series_Osums_001t__Nat__Onat,type,
% 9.49/5.23      sums_nat: ( nat > nat ) > nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Series_Osums_001t__Real__Oreal,type,
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% 9.49/5.23  thf(sy_c_Set_OCollect_001t__List__Olist_I_Eo_J,type,
% 9.49/5.23      collect_list_o: ( list_o > $o ) > set_list_o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Set_OCollect_001t__List__Olist_It__Complex__Ocomplex_J,type,
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% 9.49/5.23  thf(sy_c_Set_OCollect_001t__List__Olist_It__Int__Oint_J,type,
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% 9.49/5.23  thf(sy_c_Set_OCollect_001t__List__Olist_It__Real__Oreal_J,type,
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% 9.49/5.23  thf(sy_c_Set_OCollect_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
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% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Set_OCollect_001t__Num__Onum,type,
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% 9.49/5.23  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J,type,
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% 9.49/5.23  thf(sy_c_Set_Oimage_001t__Int__Oint_001t__Int__Oint,type,
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% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 9.49/5.23      image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Real__Oreal,type,
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% 9.49/5.23  thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__String__Ochar,type,
% 9.49/5.23      image_nat_char: ( nat > char ) > set_nat > set_char ).
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% 9.49/5.23  thf(sy_c_Set_Oimage_001t__String__Ochar_001t__Nat__Onat,type,
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% 9.49/5.23  thf(sy_c_Set_Oimage_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
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% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Set_Oinsert_001t__Complex__Ocomplex,type,
% 9.49/5.23      insert_complex: complex > set_complex > set_complex ).
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% 9.49/5.23  thf(sy_c_Set_Oinsert_001t__Int__Oint,type,
% 9.49/5.23      insert_int: int > set_int > set_int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Set_Oinsert_001t__Nat__Onat,type,
% 9.49/5.23      insert_nat: nat > set_nat > set_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Set_Oinsert_001t__Num__Onum,type,
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% 9.49/5.23  thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Set_Oinsert_001t__Rat__Orat,type,
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% 9.49/5.23  thf(sy_c_Set_Oinsert_001t__Real__Oreal,type,
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% 9.49/5.23  thf(sy_c_Set_Oinsert_001t__VEBT____Definitions__OVEBT,type,
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% 9.49/5.23  thf(sy_c_Set_Ovimage_001t__Nat__Onat_001t__Nat__Onat,type,
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% 9.49/5.23  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Rat__Orat,type,
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% 9.49/5.23      set_or4548717258645045905et_nat: set_nat > set_nat > set_set_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__Real__Oreal_J,type,
% 9.49/5.23      set_or7743017856606604397t_real: set_real > set_real > set_set_real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Int__Oint,type,
% 9.49/5.23      set_or4662586982721622107an_int: int > int > set_int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Nat__Onat,type,
% 9.49/5.23      set_or4665077453230672383an_nat: nat > nat > set_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Nat__Onat,type,
% 9.49/5.23      set_ord_atLeast_nat: nat > set_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Real__Oreal,type,
% 9.49/5.23      set_ord_atLeast_real: real > set_real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Nat__Onat,type,
% 9.49/5.23      set_ord_atMost_nat: nat > set_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Int__Oint,type,
% 9.49/5.23      set_or6656581121297822940st_int: int > int > set_int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Nat__Onat,type,
% 9.49/5.23      set_or6659071591806873216st_nat: nat > nat > set_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Int__Oint,type,
% 9.49/5.23      set_or5832277885323065728an_int: int > int > set_int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Nat__Onat,type,
% 9.49/5.23      set_or5834768355832116004an_nat: nat > nat > set_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Real__Oreal,type,
% 9.49/5.23      set_or1633881224788618240n_real: real > real > set_real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Nat__Onat,type,
% 9.49/5.23      set_or1210151606488870762an_nat: nat > set_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Real__Oreal,type,
% 9.49/5.23      set_or5849166863359141190n_real: real > set_real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Int__Oint,type,
% 9.49/5.23      set_ord_lessThan_int: int > set_int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Nat__Onat,type,
% 9.49/5.23      set_ord_lessThan_nat: nat > set_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Num__Onum,type,
% 9.49/5.23      set_ord_lessThan_num: num > set_num ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Rat__Orat,type,
% 9.49/5.23      set_ord_lessThan_rat: rat > set_rat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Real__Oreal,type,
% 9.49/5.23      set_or5984915006950818249n_real: real > set_real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_String_Oascii__of,type,
% 9.49/5.23      ascii_of: char > char ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_String_Ochar_OChar,type,
% 9.49/5.23      char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_String_Ocomm__semiring__1__class_Oof__char_001t__Nat__Onat,type,
% 9.49/5.23      comm_s629917340098488124ar_nat: char > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_String_Ointeger__of__char,type,
% 9.49/5.23      integer_of_char: char > code_integer ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_String_Ounique__euclidean__semiring__with__bit__operations__class_Ochar__of_001t__Nat__Onat,type,
% 9.49/5.23      unique3096191561947761185of_nat: nat > char ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Topological__Spaces_Ocontinuous_001t__Real__Oreal_001t__Real__Oreal,type,
% 9.49/5.23      topolo4422821103128117721l_real: filter_real > ( real > real ) > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Topological__Spaces_Ocontinuous__on_001t__Real__Oreal_001t__Real__Oreal,type,
% 9.49/5.23      topolo5044208981011980120l_real: set_real > ( real > real ) > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Topological__Spaces_Omonoseq_001t__Int__Oint,type,
% 9.49/5.23      topolo4899668324122417113eq_int: ( nat > int ) > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Topological__Spaces_Omonoseq_001t__Nat__Onat,type,
% 9.49/5.23      topolo4902158794631467389eq_nat: ( nat > nat ) > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Topological__Spaces_Omonoseq_001t__Num__Onum,type,
% 9.49/5.23      topolo1459490580787246023eq_num: ( nat > num ) > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Topological__Spaces_Omonoseq_001t__Real__Oreal,type,
% 9.49/5.23      topolo6980174941875973593q_real: ( nat > real ) > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Topological__Spaces_Omonoseq_001t__Set__Oset_It__Nat__Onat_J,type,
% 9.49/5.23      topolo7278393974255667507et_nat: ( nat > set_nat ) > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Topological__Spaces_Omonoseq_001t__Set__Oset_It__Real__Oreal_J,type,
% 9.49/5.23      topolo2489691266198938127t_real: ( nat > set_real ) > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Topological__Spaces_Otopological__space__class_Oat__within_001t__Real__Oreal,type,
% 9.49/5.23      topolo2177554685111907308n_real: real > set_real > filter_real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Topological__Spaces_Otopological__space__class_Oconvergent_001t__Real__Oreal,type,
% 9.49/5.23      topolo7531315842566124627t_real: ( nat > real ) > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Topological__Spaces_Otopological__space__class_Onhds_001t__Real__Oreal,type,
% 9.49/5.23      topolo2815343760600316023s_real: real > filter_real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Topological__Spaces_Ouniform__space__class_OCauchy_001t__Real__Oreal,type,
% 9.49/5.23      topolo4055970368930404560y_real: ( nat > real ) > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Topological__Spaces_Ouniformity__class_Ouniformity_001t__Complex__Ocomplex,type,
% 9.49/5.23      topolo896644834953643431omplex: filter6041513312241820739omplex ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Topological__Spaces_Ouniformity__class_Ouniformity_001t__Real__Oreal,type,
% 9.49/5.23      topolo1511823702728130853y_real: filter2146258269922977983l_real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Transcendental_Oarccos,type,
% 9.49/5.23      arccos: real > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Transcendental_Oarcosh_001t__Real__Oreal,type,
% 9.49/5.23      arcosh_real: real > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Transcendental_Oarcsin,type,
% 9.49/5.23      arcsin: real > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Transcendental_Oarctan,type,
% 9.49/5.23      arctan: real > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Transcendental_Oarsinh_001t__Real__Oreal,type,
% 9.49/5.23      arsinh_real: real > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Transcendental_Oartanh_001t__Real__Oreal,type,
% 9.49/5.23      artanh_real: real > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Transcendental_Ocos_001t__Complex__Ocomplex,type,
% 9.49/5.23      cos_complex: complex > complex ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Transcendental_Ocos_001t__Real__Oreal,type,
% 9.49/5.23      cos_real: real > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Transcendental_Ocos__coeff,type,
% 9.49/5.23      cos_coeff: nat > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Transcendental_Ocosh_001t__Real__Oreal,type,
% 9.49/5.23      cosh_real: real > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Transcendental_Ocot_001t__Real__Oreal,type,
% 9.49/5.23      cot_real: real > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Transcendental_Odiffs_001t__Complex__Ocomplex,type,
% 9.49/5.23      diffs_complex: ( nat > complex ) > nat > complex ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Transcendental_Odiffs_001t__Int__Oint,type,
% 9.49/5.23      diffs_int: ( nat > int ) > nat > int ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Transcendental_Odiffs_001t__Real__Oreal,type,
% 9.49/5.23      diffs_real: ( nat > real ) > nat > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Transcendental_Oexp_001t__Complex__Ocomplex,type,
% 9.49/5.23      exp_complex: complex > complex ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Transcendental_Oexp_001t__Real__Oreal,type,
% 9.49/5.23      exp_real: real > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Transcendental_Oln__class_Oln_001t__Real__Oreal,type,
% 9.49/5.23      ln_ln_real: real > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Transcendental_Olog,type,
% 9.49/5.23      log: real > real > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Transcendental_Opi,type,
% 9.49/5.23      pi: real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Transcendental_Opowr_001t__Real__Oreal,type,
% 9.49/5.23      powr_real: real > real > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Transcendental_Osin_001t__Complex__Ocomplex,type,
% 9.49/5.23      sin_complex: complex > complex ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Transcendental_Osin_001t__Real__Oreal,type,
% 9.49/5.23      sin_real: real > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Transcendental_Osin__coeff,type,
% 9.49/5.23      sin_coeff: nat > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Transcendental_Osinh_001t__Real__Oreal,type,
% 9.49/5.23      sinh_real: real > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Transcendental_Otan_001t__Complex__Ocomplex,type,
% 9.49/5.23      tan_complex: complex > complex ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Transcendental_Otan_001t__Real__Oreal,type,
% 9.49/5.23      tan_real: real > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Transcendental_Otanh_001t__Complex__Ocomplex,type,
% 9.49/5.23      tanh_complex: complex > complex ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Transcendental_Otanh_001t__Real__Oreal,type,
% 9.49/5.23      tanh_real: real > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Transitive__Closure_Ortrancl_001t__Nat__Onat,type,
% 9.49/5.23      transi2905341329935302413cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Transitive__Closure_Otrancl_001t__Nat__Onat,type,
% 9.49/5.23      transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t,type,
% 9.49/5.23      vEBT_T_i_n_s_e_r_t: vEBT_VEBT > nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H,type,
% 9.49/5.23      vEBT_T_i_n_s_e_r_t2: vEBT_VEBT > nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H__rel,type,
% 9.49/5.23      vEBT_T5076183648494686801_t_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t__rel,type,
% 9.49/5.23      vEBT_T9217963907923527482_t_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t,type,
% 9.49/5.23      vEBT_T_m_a_x_t: vEBT_VEBT > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t__rel,type,
% 9.49/5.23      vEBT_T_m_a_x_t_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r,type,
% 9.49/5.23      vEBT_T_m_e_m_b_e_r: vEBT_VEBT > nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H,type,
% 9.49/5.23      vEBT_T_m_e_m_b_e_r2: vEBT_VEBT > nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H__rel,type,
% 9.49/5.23      vEBT_T8099345112685741742_r_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r__rel,type,
% 9.49/5.23      vEBT_T5837161174952499735_r_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l,type,
% 9.49/5.23      vEBT_T_m_i_n_N_u_l_l: vEBT_VEBT > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l__rel,type,
% 9.49/5.23      vEBT_T5462971552011256508_l_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t,type,
% 9.49/5.23      vEBT_T_m_i_n_t: vEBT_VEBT > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t__rel,type,
% 9.49/5.23      vEBT_T_m_i_n_t_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d,type,
% 9.49/5.23      vEBT_T_p_r_e_d: vEBT_VEBT > nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H,type,
% 9.49/5.23      vEBT_T_p_r_e_d2: vEBT_VEBT > nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H__rel,type,
% 9.49/5.23      vEBT_T_p_r_e_d_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d__rel,type,
% 9.49/5.23      vEBT_T_p_r_e_d_rel2: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c,type,
% 9.49/5.23      vEBT_T_s_u_c_c: vEBT_VEBT > nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H,type,
% 9.49/5.23      vEBT_T_s_u_c_c2: vEBT_VEBT > nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H__rel,type,
% 9.49/5.23      vEBT_T_s_u_c_c_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c__rel,type,
% 9.49/5.23      vEBT_T_s_u_c_c_rel2: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Definitions_OVEBT_OLeaf,type,
% 9.49/5.23      vEBT_Leaf: $o > $o > vEBT_VEBT ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Definitions_OVEBT_ONode,type,
% 9.49/5.23      vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Definitions_OVEBT_Osize__VEBT,type,
% 9.49/5.23      vEBT_size_VEBT: vEBT_VEBT > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Definitions_OVEBT__internal_Oboth__member__options,type,
% 9.49/5.23      vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Definitions_OVEBT__internal_Ohigh,type,
% 9.49/5.23      vEBT_VEBT_high: nat > nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Definitions_OVEBT__internal_Oin__children,type,
% 9.49/5.23      vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Definitions_OVEBT__internal_Olow,type,
% 9.49/5.23      vEBT_VEBT_low: nat > nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima,type,
% 9.49/5.23      vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima__rel,type,
% 9.49/5.23      vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member,type,
% 9.49/5.23      vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member__rel,type,
% 9.49/5.23      vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H,type,
% 9.49/5.23      vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H__rel,type,
% 9.49/5.23      vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Definitions_Oinvar__vebt,type,
% 9.49/5.23      vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Definitions_Oset__vebt,type,
% 9.49/5.23      vEBT_set_vebt: vEBT_VEBT > set_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Definitions_Ovebt__buildup,type,
% 9.49/5.23      vEBT_vebt_buildup: nat > vEBT_VEBT ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Definitions_Ovebt__buildup__rel,type,
% 9.49/5.23      vEBT_v4011308405150292612up_rel: nat > nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__DeleteBounds_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e,type,
% 9.49/5.23      vEBT_T_d_e_l_e_t_e: vEBT_VEBT > nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__DeleteBounds_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e__rel,type,
% 9.49/5.23      vEBT_T8441311223069195367_e_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Delete_Ovebt__delete,type,
% 9.49/5.23      vEBT_vebt_delete: vEBT_VEBT > nat > vEBT_VEBT ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Delete_Ovebt__delete__rel,type,
% 9.49/5.23      vEBT_vebt_delete_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Height_OVEBT__internal_Oheight,type,
% 9.49/5.23      vEBT_VEBT_height: vEBT_VEBT > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Height_OVEBT__internal_Oheight__rel,type,
% 9.49/5.23      vEBT_VEBT_height_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Insert_Ovebt__insert,type,
% 9.49/5.23      vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Insert_Ovebt__insert__rel,type,
% 9.49/5.23      vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Member_OVEBT__internal_Obit__concat,type,
% 9.49/5.23      vEBT_VEBT_bit_concat: nat > nat > nat > nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Member_OVEBT__internal_OminNull,type,
% 9.49/5.23      vEBT_VEBT_minNull: vEBT_VEBT > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Member_OVEBT__internal_OminNull__rel,type,
% 9.49/5.23      vEBT_V6963167321098673237ll_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Member_OVEBT__internal_Oset__vebt_H,type,
% 9.49/5.23      vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Member_Ovebt__member,type,
% 9.49/5.23      vEBT_vebt_member: vEBT_VEBT > nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Member_Ovebt__member__rel,type,
% 9.49/5.23      vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__MinMax_OVEBT__internal_Oadd,type,
% 9.49/5.23      vEBT_VEBT_add: option_nat > option_nat > option_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__MinMax_OVEBT__internal_Ogreater,type,
% 9.49/5.23      vEBT_VEBT_greater: option_nat > option_nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__MinMax_OVEBT__internal_Oless,type,
% 9.49/5.23      vEBT_VEBT_less: option_nat > option_nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__MinMax_OVEBT__internal_Olesseq,type,
% 9.49/5.23      vEBT_VEBT_lesseq: option_nat > option_nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__MinMax_OVEBT__internal_Omax__in__set,type,
% 9.49/5.23      vEBT_VEBT_max_in_set: set_nat > nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__MinMax_OVEBT__internal_Omin__in__set,type,
% 9.49/5.23      vEBT_VEBT_min_in_set: set_nat > nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__MinMax_OVEBT__internal_Omul,type,
% 9.49/5.23      vEBT_VEBT_mul: option_nat > option_nat > option_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Nat__Onat,type,
% 9.49/5.23      vEBT_V4262088993061758097ft_nat: ( nat > nat > nat ) > option_nat > option_nat > option_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Num__Onum,type,
% 9.49/5.23      vEBT_V819420779217536731ft_num: ( num > num > num ) > option_num > option_num > option_num ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 9.49/5.23      vEBT_V1502963449132264192at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > option4927543243414619207at_nat > option4927543243414619207at_nat > option4927543243414619207at_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__MinMax_OVEBT__internal_Opower,type,
% 9.49/5.23      vEBT_VEBT_power: option_nat > option_nat > option_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__MinMax_Ovebt__maxt,type,
% 9.49/5.23      vEBT_vebt_maxt: vEBT_VEBT > option_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__MinMax_Ovebt__maxt__rel,type,
% 9.49/5.23      vEBT_vebt_maxt_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__MinMax_Ovebt__mint,type,
% 9.49/5.23      vEBT_vebt_mint: vEBT_VEBT > option_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__MinMax_Ovebt__mint__rel,type,
% 9.49/5.23      vEBT_vebt_mint_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Pred_Ois__pred__in__set,type,
% 9.49/5.23      vEBT_is_pred_in_set: set_nat > nat > nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Pred_Ovebt__pred,type,
% 9.49/5.23      vEBT_vebt_pred: vEBT_VEBT > nat > option_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Pred_Ovebt__pred__rel,type,
% 9.49/5.23      vEBT_vebt_pred_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Succ_Ois__succ__in__set,type,
% 9.49/5.23      vEBT_is_succ_in_set: set_nat > nat > nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Succ_Ovebt__succ,type,
% 9.49/5.23      vEBT_vebt_succ: vEBT_VEBT > nat > option_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_VEBT__Succ_Ovebt__succ__rel,type,
% 9.49/5.23      vEBT_vebt_succ_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Wellfounded_Oaccp_001t__List__Olist_It__Nat__Onat_J,type,
% 9.49/5.23      accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Wellfounded_Oaccp_001t__Nat__Onat,type,
% 9.49/5.23      accp_nat: ( nat > nat > $o ) > nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 9.49/5.23      accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 9.49/5.23      accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 9.49/5.23      accp_P3113834385874906142um_num: ( product_prod_num_num > product_prod_num_num > $o ) > product_prod_num_num > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 9.49/5.23      accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Wellfounded_Oaccp_001t__VEBT____Definitions__OVEBT,type,
% 9.49/5.23      accp_VEBT_VEBT: ( vEBT_VEBT > vEBT_VEBT > $o ) > vEBT_VEBT > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Wellfounded_Opred__nat,type,
% 9.49/5.23      pred_nat: set_Pr1261947904930325089at_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_Wellfounded_Owf_001t__Nat__Onat,type,
% 9.49/5.23      wf_nat: set_Pr1261947904930325089at_nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_fChoice_001t__Real__Oreal,type,
% 9.49/5.23      fChoice_real: ( real > $o ) > real ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_member_001_Eo,type,
% 9.49/5.23      member_o: $o > set_o > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_member_001t__Complex__Ocomplex,type,
% 9.49/5.23      member_complex: complex > set_complex > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_member_001t__Int__Oint,type,
% 9.49/5.23      member_int: int > set_int > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_member_001t__List__Olist_I_Eo_J,type,
% 9.49/5.23      member_list_o: list_o > set_list_o > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_member_001t__List__Olist_It__Int__Oint_J,type,
% 9.49/5.23      member_list_int: list_int > set_list_int > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 9.49/5.23      member_list_nat: list_nat > set_list_nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_member_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 9.49/5.23      member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_member_001t__Nat__Onat,type,
% 9.49/5.23      member_nat: nat > set_nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_member_001t__Num__Onum,type,
% 9.49/5.23      member_num: num > set_num > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 9.49/5.23      member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 9.49/5.23      member8206827879206165904at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_member_001t__Rat__Orat,type,
% 9.49/5.23      member_rat: rat > set_rat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_member_001t__Real__Oreal,type,
% 9.49/5.23      member_real: real > set_real > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 9.49/5.23      member_set_nat: set_nat > set_set_nat > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_member_001t__Set__Oset_It__Real__Oreal_J,type,
% 9.49/5.23      member_set_real: set_real > set_set_real > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_c_member_001t__VEBT____Definitions__OVEBT,type,
% 9.49/5.23      member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_v_deg____,type,
% 9.49/5.23      deg: nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_v_m____,type,
% 9.49/5.23      m: nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_v_ma____,type,
% 9.49/5.23      ma: nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_v_mi____,type,
% 9.49/5.23      mi: nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_v_na____,type,
% 9.49/5.23      na: nat ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_v_summary____,type,
% 9.49/5.23      summary: vEBT_VEBT ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_v_treeList____,type,
% 9.49/5.23      treeList: list_VEBT_VEBT ).
% 9.49/5.23  
% 9.49/5.23  thf(sy_v_xa____,type,
% 9.49/5.23      xa: nat ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_0_True,axiom,
% 9.49/5.23      xa = mi ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_1__C4_Ohyps_C_I8_J,axiom,
% 9.49/5.23      ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_2__C4_Ohyps_C_I7_J,axiom,
% 9.49/5.23      ord_less_eq_nat @ mi @ ma ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_3_pow__sum,axiom,
% 9.49/5.23      ! [A: nat,B: nat] :
% 9.49/5.23        ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 9.49/5.23        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_4_False,axiom,
% 9.49/5.23      ~ ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_5__C4_Ohyps_C_I2_J,axiom,
% 9.49/5.23      ( ( size_s6755466524823107622T_VEBT @ treeList )
% 9.49/5.23      = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_6_one__add__one,axiom,
% 9.49/5.23      ( ( plus_plus_complex @ one_one_complex @ one_one_complex )
% 9.49/5.23      = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_7_one__add__one,axiom,
% 9.49/5.23      ( ( plus_plus_real @ one_one_real @ one_one_real )
% 9.49/5.23      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_8_one__add__one,axiom,
% 9.49/5.23      ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 9.49/5.23      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_9_one__add__one,axiom,
% 9.49/5.23      ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 9.49/5.23      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_10_one__add__one,axiom,
% 9.49/5.23      ( ( plus_plus_int @ one_one_int @ one_one_int )
% 9.49/5.23      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_11_numeral__plus__one,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ one_one_complex )
% 9.49/5.23        = ( numera6690914467698888265omplex @ ( plus_plus_num @ N @ one ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_12_numeral__plus__one,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( plus_plus_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 9.49/5.23        = ( numeral_numeral_real @ ( plus_plus_num @ N @ one ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_13_numeral__plus__one,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 9.49/5.23        = ( numeral_numeral_rat @ ( plus_plus_num @ N @ one ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_14_numeral__plus__one,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 9.49/5.23        = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_15_numeral__plus__one,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( plus_plus_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 9.49/5.23        = ( numeral_numeral_int @ ( plus_plus_num @ N @ one ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_16_one__plus__numeral,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ N ) )
% 9.49/5.23        = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_17_one__plus__numeral,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 9.49/5.23        = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_18_one__plus__numeral,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 9.49/5.23        = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_19_one__plus__numeral,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 9.49/5.23        = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_20_one__plus__numeral,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 9.49/5.23        = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_21_bit__concat__def,axiom,
% 9.49/5.23      ( vEBT_VEBT_bit_concat
% 9.49/5.23      = ( ^ [H: nat,L: nat,D: nat] : ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ D ) ) @ L ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_22_high__bound__aux,axiom,
% 9.49/5.23      ! [Ma: nat,N: nat,M: nat] :
% 9.49/5.23        ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 9.49/5.23       => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_23_numeral__eq__one__iff,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( ( numera6690914467698888265omplex @ N )
% 9.49/5.23          = one_one_complex )
% 9.49/5.23        = ( N = one ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_24_numeral__eq__one__iff,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( ( numeral_numeral_real @ N )
% 9.49/5.23          = one_one_real )
% 9.49/5.23        = ( N = one ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_25_numeral__eq__one__iff,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( ( numeral_numeral_rat @ N )
% 9.49/5.23          = one_one_rat )
% 9.49/5.23        = ( N = one ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_26_numeral__eq__one__iff,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( ( numeral_numeral_nat @ N )
% 9.49/5.23          = one_one_nat )
% 9.49/5.23        = ( N = one ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_27_numeral__eq__one__iff,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( ( numeral_numeral_int @ N )
% 9.49/5.23          = one_one_int )
% 9.49/5.23        = ( N = one ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_28_one__eq__numeral__iff,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( one_one_complex
% 9.49/5.23          = ( numera6690914467698888265omplex @ N ) )
% 9.49/5.23        = ( one = N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_29_one__eq__numeral__iff,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( one_one_real
% 9.49/5.23          = ( numeral_numeral_real @ N ) )
% 9.49/5.23        = ( one = N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_30_one__eq__numeral__iff,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( one_one_rat
% 9.49/5.23          = ( numeral_numeral_rat @ N ) )
% 9.49/5.23        = ( one = N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_31_one__eq__numeral__iff,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( one_one_nat
% 9.49/5.23          = ( numeral_numeral_nat @ N ) )
% 9.49/5.23        = ( one = N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_32_one__eq__numeral__iff,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( one_one_int
% 9.49/5.23          = ( numeral_numeral_int @ N ) )
% 9.49/5.23        = ( one = N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_33_tdeletemimi,axiom,
% 9.49/5.23      ! [Deg: nat,Mi: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 9.49/5.23        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 9.49/5.23       => ( ord_less_eq_nat @ ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Mi ) ) @ Deg @ TreeList @ Summary ) @ X ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_34_high__def,axiom,
% 9.49/5.23      ( vEBT_VEBT_high
% 9.49/5.23      = ( ^ [X2: nat,N2: nat] : ( divide_divide_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_35_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Osimps_I3_J,axiom,
% 9.49/5.23      ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 9.49/5.23        ( ( vEBT_T_m_i_n_t @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 9.49/5.23        = one_one_nat ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_36_semiring__norm_I86_J,axiom,
% 9.49/5.23      ! [M: num] :
% 9.49/5.23        ( ( bit1 @ M )
% 9.49/5.23       != one ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_37__C4_Ohyps_C_I3_J,axiom,
% 9.49/5.23      m = na ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_38_max__in__set__def,axiom,
% 9.49/5.23      ( vEBT_VEBT_max_in_set
% 9.49/5.23      = ( ^ [Xs: set_nat,X2: nat] :
% 9.49/5.23            ( ( member_nat @ X2 @ Xs )
% 9.49/5.23            & ! [Y: nat] :
% 9.49/5.23                ( ( member_nat @ Y @ Xs )
% 9.49/5.23               => ( ord_less_eq_nat @ Y @ X2 ) ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_39_min__in__set__def,axiom,
% 9.49/5.23      ( vEBT_VEBT_min_in_set
% 9.49/5.23      = ( ^ [Xs: set_nat,X2: nat] :
% 9.49/5.23            ( ( member_nat @ X2 @ Xs )
% 9.49/5.23            & ! [Y: nat] :
% 9.49/5.23                ( ( member_nat @ Y @ Xs )
% 9.49/5.23               => ( ord_less_eq_nat @ X2 @ Y ) ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_40_numeral__eq__iff,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( ( numera6690914467698888265omplex @ M )
% 9.49/5.23          = ( numera6690914467698888265omplex @ N ) )
% 9.49/5.23        = ( M = N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_41_numeral__eq__iff,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( ( numeral_numeral_real @ M )
% 9.49/5.23          = ( numeral_numeral_real @ N ) )
% 9.49/5.23        = ( M = N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_42_numeral__eq__iff,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( ( numeral_numeral_rat @ M )
% 9.49/5.23          = ( numeral_numeral_rat @ N ) )
% 9.49/5.23        = ( M = N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_43_numeral__eq__iff,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( ( numeral_numeral_nat @ M )
% 9.49/5.23          = ( numeral_numeral_nat @ N ) )
% 9.49/5.23        = ( M = N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_44_numeral__eq__iff,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( ( numeral_numeral_int @ M )
% 9.49/5.23          = ( numeral_numeral_int @ N ) )
% 9.49/5.23        = ( M = N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_45_semiring__norm_I87_J,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( ( bit0 @ M )
% 9.49/5.23          = ( bit0 @ N ) )
% 9.49/5.23        = ( M = N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_46_semiring__norm_I90_J,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( ( bit1 @ M )
% 9.49/5.23          = ( bit1 @ N ) )
% 9.49/5.23        = ( M = N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_47_deggy,axiom,
% 9.49/5.23      ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_48__092_060open_062mi_A_092_060le_062_Ax_A_092_060and_062_Ax_A_092_060le_062_Ama_092_060close_062,axiom,
% 9.49/5.23      ( ( ord_less_eq_nat @ mi @ xa )
% 9.49/5.23      & ( ord_less_eq_nat @ xa @ ma ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_49__C4_Ohyps_C_I4_J,axiom,
% 9.49/5.23      ( deg
% 9.49/5.23      = ( plus_plus_nat @ na @ m ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_50_numeral__le__iff,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 9.49/5.23        = ( ord_less_eq_num @ M @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_51_numeral__le__iff,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 9.49/5.23        = ( ord_less_eq_num @ M @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_52_numeral__le__iff,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 9.49/5.23        = ( ord_less_eq_num @ M @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_53_numeral__le__iff,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 9.49/5.23        = ( ord_less_eq_num @ M @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_54_high__inv,axiom,
% 9.49/5.23      ! [X: nat,N: nat,Y2: nat] :
% 9.49/5.23        ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.23       => ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ Y2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X ) @ N )
% 9.49/5.23          = Y2 ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_55_numeral__less__iff,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 9.49/5.23        = ( ord_less_num @ M @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_56_numeral__less__iff,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 9.49/5.23        = ( ord_less_num @ M @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_57_numeral__less__iff,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 9.49/5.23        = ( ord_less_num @ M @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_58_numeral__less__iff,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 9.49/5.23        = ( ord_less_num @ M @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_59_mult__numeral__left__semiring__numeral,axiom,
% 9.49/5.23      ! [V: num,W: num,Z: complex] :
% 9.49/5.23        ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 9.49/5.23        = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_60_mult__numeral__left__semiring__numeral,axiom,
% 9.49/5.23      ! [V: num,W: num,Z: real] :
% 9.49/5.23        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 9.49/5.23        = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_61_mult__numeral__left__semiring__numeral,axiom,
% 9.49/5.23      ! [V: num,W: num,Z: rat] :
% 9.49/5.23        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 9.49/5.23        = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_62_mult__numeral__left__semiring__numeral,axiom,
% 9.49/5.23      ! [V: num,W: num,Z: nat] :
% 9.49/5.23        ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 9.49/5.23        = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_63_mult__numeral__left__semiring__numeral,axiom,
% 9.49/5.23      ! [V: num,W: num,Z: int] :
% 9.49/5.23        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 9.49/5.23        = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_64_numeral__times__numeral,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) )
% 9.49/5.23        = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_65_numeral__times__numeral,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 9.49/5.23        = ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_66_numeral__times__numeral,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 9.49/5.23        = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_67_numeral__times__numeral,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( times_times_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 9.49/5.23        = ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_68_numeral__times__numeral,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 9.49/5.23        = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_69_semiring__norm_I83_J,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( one
% 9.49/5.23       != ( bit0 @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_70_semiring__norm_I85_J,axiom,
% 9.49/5.23      ! [M: num] :
% 9.49/5.23        ( ( bit0 @ M )
% 9.49/5.23       != one ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_71_semiring__norm_I88_J,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( bit0 @ M )
% 9.49/5.23       != ( bit1 @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_72_semiring__norm_I89_J,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( bit1 @ M )
% 9.49/5.23       != ( bit0 @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_73_semiring__norm_I84_J,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( one
% 9.49/5.23       != ( bit1 @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_74_semiring__norm_I6_J,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 9.49/5.23        = ( bit0 @ ( plus_plus_num @ M @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_75_distrib__right__numeral,axiom,
% 9.49/5.23      ! [A: complex,B: complex,V: num] :
% 9.49/5.23        ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 9.49/5.23        = ( plus_plus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_76_distrib__right__numeral,axiom,
% 9.49/5.23      ! [A: real,B: real,V: num] :
% 9.49/5.23        ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 9.49/5.23        = ( plus_plus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_77_distrib__right__numeral,axiom,
% 9.49/5.23      ! [A: rat,B: rat,V: num] :
% 9.49/5.23        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 9.49/5.23        = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_78_distrib__right__numeral,axiom,
% 9.49/5.23      ! [A: nat,B: nat,V: num] :
% 9.49/5.23        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
% 9.49/5.23        = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_79_distrib__right__numeral,axiom,
% 9.49/5.23      ! [A: int,B: int,V: num] :
% 9.49/5.23        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 9.49/5.23        = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_80_distrib__left__numeral,axiom,
% 9.49/5.23      ! [V: num,B: complex,C: complex] :
% 9.49/5.23        ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ B @ C ) )
% 9.49/5.23        = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_81_distrib__left__numeral,axiom,
% 9.49/5.23      ! [V: num,B: real,C: real] :
% 9.49/5.23        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ B @ C ) )
% 9.49/5.23        = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_82_distrib__left__numeral,axiom,
% 9.49/5.23      ! [V: num,B: rat,C: rat] :
% 9.49/5.23        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ B @ C ) )
% 9.49/5.23        = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_83_distrib__left__numeral,axiom,
% 9.49/5.23      ! [V: num,B: nat,C: nat] :
% 9.49/5.23        ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
% 9.49/5.23        = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_84_distrib__left__numeral,axiom,
% 9.49/5.23      ! [V: num,B: int,C: int] :
% 9.49/5.23        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B @ C ) )
% 9.49/5.23        = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_85_add__numeral__left,axiom,
% 9.49/5.23      ! [V: num,W: num,Z: complex] :
% 9.49/5.23        ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 9.49/5.23        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_86_add__numeral__left,axiom,
% 9.49/5.23      ! [V: num,W: num,Z: real] :
% 9.49/5.23        ( ( plus_plus_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 9.49/5.23        = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_87_add__numeral__left,axiom,
% 9.49/5.23      ! [V: num,W: num,Z: rat] :
% 9.49/5.23        ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 9.49/5.23        = ( plus_plus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_88_add__numeral__left,axiom,
% 9.49/5.23      ! [V: num,W: num,Z: nat] :
% 9.49/5.23        ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 9.49/5.23        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_89_add__numeral__left,axiom,
% 9.49/5.23      ! [V: num,W: num,Z: int] :
% 9.49/5.23        ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 9.49/5.23        = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_90_numeral__plus__numeral,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) )
% 9.49/5.23        = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_91_numeral__plus__numeral,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 9.49/5.23        = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_92_numeral__plus__numeral,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 9.49/5.23        = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_93_numeral__plus__numeral,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( plus_plus_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 9.49/5.23        = ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_94_numeral__plus__numeral,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 9.49/5.23        = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_95_semiring__norm_I2_J,axiom,
% 9.49/5.23      ( ( plus_plus_num @ one @ one )
% 9.49/5.23      = ( bit0 @ one ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_96_semiring__norm_I7_J,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 9.49/5.23        = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_97_semiring__norm_I9_J,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 9.49/5.23        = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_98_mem__Collect__eq,axiom,
% 9.49/5.23      ! [A: int,P: int > $o] :
% 9.49/5.23        ( ( member_int @ A @ ( collect_int @ P ) )
% 9.49/5.23        = ( P @ A ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_99_mem__Collect__eq,axiom,
% 9.49/5.23      ! [A: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 9.49/5.23        ( ( member8440522571783428010at_nat @ A @ ( collec3392354462482085612at_nat @ P ) )
% 9.49/5.23        = ( P @ A ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_100_mem__Collect__eq,axiom,
% 9.49/5.23      ! [A: complex,P: complex > $o] :
% 9.49/5.23        ( ( member_complex @ A @ ( collect_complex @ P ) )
% 9.49/5.23        = ( P @ A ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_101_mem__Collect__eq,axiom,
% 9.49/5.23      ! [A: real,P: real > $o] :
% 9.49/5.23        ( ( member_real @ A @ ( collect_real @ P ) )
% 9.49/5.23        = ( P @ A ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_102_mem__Collect__eq,axiom,
% 9.49/5.23      ! [A: list_nat,P: list_nat > $o] :
% 9.49/5.23        ( ( member_list_nat @ A @ ( collect_list_nat @ P ) )
% 9.49/5.23        = ( P @ A ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_103_mem__Collect__eq,axiom,
% 9.49/5.23      ! [A: nat,P: nat > $o] :
% 9.49/5.23        ( ( member_nat @ A @ ( collect_nat @ P ) )
% 9.49/5.23        = ( P @ A ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_104_Collect__mem__eq,axiom,
% 9.49/5.23      ! [A2: set_int] :
% 9.49/5.23        ( ( collect_int
% 9.49/5.23          @ ^ [X2: int] : ( member_int @ X2 @ A2 ) )
% 9.49/5.23        = A2 ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_105_Collect__mem__eq,axiom,
% 9.49/5.23      ! [A2: set_Pr1261947904930325089at_nat] :
% 9.49/5.23        ( ( collec3392354462482085612at_nat
% 9.49/5.23          @ ^ [X2: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X2 @ A2 ) )
% 9.49/5.23        = A2 ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_106_Collect__mem__eq,axiom,
% 9.49/5.23      ! [A2: set_complex] :
% 9.49/5.23        ( ( collect_complex
% 9.49/5.23          @ ^ [X2: complex] : ( member_complex @ X2 @ A2 ) )
% 9.49/5.23        = A2 ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_107_Collect__mem__eq,axiom,
% 9.49/5.23      ! [A2: set_real] :
% 9.49/5.23        ( ( collect_real
% 9.49/5.23          @ ^ [X2: real] : ( member_real @ X2 @ A2 ) )
% 9.49/5.23        = A2 ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_108_Collect__mem__eq,axiom,
% 9.49/5.23      ! [A2: set_list_nat] :
% 9.49/5.23        ( ( collect_list_nat
% 9.49/5.23          @ ^ [X2: list_nat] : ( member_list_nat @ X2 @ A2 ) )
% 9.49/5.23        = A2 ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_109_Collect__mem__eq,axiom,
% 9.49/5.23      ! [A2: set_nat] :
% 9.49/5.23        ( ( collect_nat
% 9.49/5.23          @ ^ [X2: nat] : ( member_nat @ X2 @ A2 ) )
% 9.49/5.23        = A2 ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_110_Collect__cong,axiom,
% 9.49/5.23      ! [P: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
% 9.49/5.23        ( ! [X3: product_prod_nat_nat] :
% 9.49/5.23            ( ( P @ X3 )
% 9.49/5.23            = ( Q @ X3 ) )
% 9.49/5.23       => ( ( collec3392354462482085612at_nat @ P )
% 9.49/5.23          = ( collec3392354462482085612at_nat @ Q ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_111_Collect__cong,axiom,
% 9.49/5.23      ! [P: complex > $o,Q: complex > $o] :
% 9.49/5.23        ( ! [X3: complex] :
% 9.49/5.23            ( ( P @ X3 )
% 9.49/5.23            = ( Q @ X3 ) )
% 9.49/5.23       => ( ( collect_complex @ P )
% 9.49/5.23          = ( collect_complex @ Q ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_112_Collect__cong,axiom,
% 9.49/5.23      ! [P: real > $o,Q: real > $o] :
% 9.49/5.23        ( ! [X3: real] :
% 9.49/5.23            ( ( P @ X3 )
% 9.49/5.23            = ( Q @ X3 ) )
% 9.49/5.23       => ( ( collect_real @ P )
% 9.49/5.23          = ( collect_real @ Q ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_113_Collect__cong,axiom,
% 9.49/5.23      ! [P: list_nat > $o,Q: list_nat > $o] :
% 9.49/5.23        ( ! [X3: list_nat] :
% 9.49/5.23            ( ( P @ X3 )
% 9.49/5.23            = ( Q @ X3 ) )
% 9.49/5.23       => ( ( collect_list_nat @ P )
% 9.49/5.23          = ( collect_list_nat @ Q ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_114_Collect__cong,axiom,
% 9.49/5.23      ! [P: nat > $o,Q: nat > $o] :
% 9.49/5.23        ( ! [X3: nat] :
% 9.49/5.23            ( ( P @ X3 )
% 9.49/5.23            = ( Q @ X3 ) )
% 9.49/5.23       => ( ( collect_nat @ P )
% 9.49/5.23          = ( collect_nat @ Q ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_115_numeral__le__one__iff,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 9.49/5.23        = ( ord_less_eq_num @ N @ one ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_116_numeral__le__one__iff,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 9.49/5.23        = ( ord_less_eq_num @ N @ one ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_117_numeral__le__one__iff,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 9.49/5.23        = ( ord_less_eq_num @ N @ one ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_118_numeral__le__one__iff,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 9.49/5.23        = ( ord_less_eq_num @ N @ one ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_119_one__less__numeral__iff,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( ord_less_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 9.49/5.23        = ( ord_less_num @ one @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_120_one__less__numeral__iff,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 9.49/5.23        = ( ord_less_num @ one @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_121_one__less__numeral__iff,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 9.49/5.23        = ( ord_less_num @ one @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_122_one__less__numeral__iff,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 9.49/5.23        = ( ord_less_num @ one @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_123_le__divide__eq__numeral1_I1_J,axiom,
% 9.49/5.23      ! [A: real,B: real,W: num] :
% 9.49/5.23        ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 9.49/5.23        = ( ord_less_eq_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_124_le__divide__eq__numeral1_I1_J,axiom,
% 9.49/5.23      ! [A: rat,B: rat,W: num] :
% 9.49/5.23        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 9.49/5.23        = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_125_divide__le__eq__numeral1_I1_J,axiom,
% 9.49/5.23      ! [B: real,W: num,A: real] :
% 9.49/5.23        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 9.49/5.23        = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_126_divide__le__eq__numeral1_I1_J,axiom,
% 9.49/5.23      ! [B: rat,W: num,A: rat] :
% 9.49/5.23        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 9.49/5.23        = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_127_less__divide__eq__numeral1_I1_J,axiom,
% 9.49/5.23      ! [A: real,B: real,W: num] :
% 9.49/5.23        ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 9.49/5.23        = ( ord_less_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_128_less__divide__eq__numeral1_I1_J,axiom,
% 9.49/5.23      ! [A: rat,B: rat,W: num] :
% 9.49/5.23        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 9.49/5.23        = ( ord_less_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_129_divide__less__eq__numeral1_I1_J,axiom,
% 9.49/5.23      ! [B: real,W: num,A: real] :
% 9.49/5.23        ( ( ord_less_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 9.49/5.23        = ( ord_less_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_130_divide__less__eq__numeral1_I1_J,axiom,
% 9.49/5.23      ! [B: rat,W: num,A: rat] :
% 9.49/5.23        ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 9.49/5.23        = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_131_semiring__norm_I3_J,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( plus_plus_num @ one @ ( bit0 @ N ) )
% 9.49/5.23        = ( bit1 @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_132_semiring__norm_I4_J,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( plus_plus_num @ one @ ( bit1 @ N ) )
% 9.49/5.23        = ( bit0 @ ( plus_plus_num @ N @ one ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_133_semiring__norm_I5_J,axiom,
% 9.49/5.23      ! [M: num] :
% 9.49/5.23        ( ( plus_plus_num @ ( bit0 @ M ) @ one )
% 9.49/5.23        = ( bit1 @ M ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_134_semiring__norm_I8_J,axiom,
% 9.49/5.23      ! [M: num] :
% 9.49/5.23        ( ( plus_plus_num @ ( bit1 @ M ) @ one )
% 9.49/5.23        = ( bit0 @ ( plus_plus_num @ M @ one ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_135_semiring__norm_I10_J,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 9.49/5.23        = ( bit0 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ one ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_136__C4_Ohyps_C_I1_J,axiom,
% 9.49/5.23      vEBT_invar_vebt @ summary @ m ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_137__C4_Ohyps_C_I5_J,axiom,
% 9.49/5.23      ! [I: nat] :
% 9.49/5.23        ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 9.49/5.23       => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ X4 ) )
% 9.49/5.23          = ( vEBT_V8194947554948674370ptions @ summary @ I ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_138_add__One__commute,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( plus_plus_num @ one @ N )
% 9.49/5.23        = ( plus_plus_num @ N @ one ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_139_le__numeral__extra_I4_J,axiom,
% 9.49/5.23      ord_less_eq_real @ one_one_real @ one_one_real ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_140_le__numeral__extra_I4_J,axiom,
% 9.49/5.23      ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_141_le__numeral__extra_I4_J,axiom,
% 9.49/5.23      ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_142_le__numeral__extra_I4_J,axiom,
% 9.49/5.23      ord_less_eq_int @ one_one_int @ one_one_int ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_143_one__le__numeral,axiom,
% 9.49/5.23      ! [N: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_144_one__le__numeral,axiom,
% 9.49/5.23      ! [N: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_145_one__le__numeral,axiom,
% 9.49/5.23      ! [N: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_146_one__le__numeral,axiom,
% 9.49/5.23      ! [N: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_147_less__numeral__extra_I4_J,axiom,
% 9.49/5.23      ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_148_less__numeral__extra_I4_J,axiom,
% 9.49/5.23      ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_149_less__numeral__extra_I4_J,axiom,
% 9.49/5.23      ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_150_less__numeral__extra_I4_J,axiom,
% 9.49/5.23      ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_151_left__add__mult__distrib,axiom,
% 9.49/5.23      ! [I2: nat,U: nat,J: nat,K: nat] :
% 9.49/5.23        ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
% 9.49/5.23        = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I2 @ J ) @ U ) @ K ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_152_mint__bound,axiom,
% 9.49/5.23      ! [T: vEBT_VEBT] : ( ord_less_eq_nat @ ( vEBT_T_m_i_n_t @ T ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_153_is__num__normalize_I1_J,axiom,
% 9.49/5.23      ! [A: real,B: real,C: real] :
% 9.49/5.23        ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 9.49/5.23        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_154_is__num__normalize_I1_J,axiom,
% 9.49/5.23      ! [A: rat,B: rat,C: rat] :
% 9.49/5.23        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 9.49/5.23        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_155_is__num__normalize_I1_J,axiom,
% 9.49/5.23      ! [A: int,B: int,C: int] :
% 9.49/5.23        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 9.49/5.23        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_156_is__num__normalize_I1_J,axiom,
% 9.49/5.23      ! [A: complex,B: complex,C: complex] :
% 9.49/5.23        ( ( plus_plus_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 9.49/5.23        = ( plus_plus_complex @ A @ ( plus_plus_complex @ B @ C ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_157_divide__numeral__1,axiom,
% 9.49/5.23      ! [A: complex] :
% 9.49/5.23        ( ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ one ) )
% 9.49/5.23        = A ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_158_divide__numeral__1,axiom,
% 9.49/5.23      ! [A: real] :
% 9.49/5.23        ( ( divide_divide_real @ A @ ( numeral_numeral_real @ one ) )
% 9.49/5.23        = A ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_159_divide__numeral__1,axiom,
% 9.49/5.23      ! [A: rat] :
% 9.49/5.23        ( ( divide_divide_rat @ A @ ( numeral_numeral_rat @ one ) )
% 9.49/5.23        = A ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_160_not__numeral__less__one,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ one_one_real ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_161_not__numeral__less__one,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_162_not__numeral__less__one,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_163_not__numeral__less__one,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_164_mult__numeral__1__right,axiom,
% 9.49/5.23      ! [A: complex] :
% 9.49/5.23        ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ one ) )
% 9.49/5.23        = A ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_165_mult__numeral__1__right,axiom,
% 9.49/5.23      ! [A: real] :
% 9.49/5.23        ( ( times_times_real @ A @ ( numeral_numeral_real @ one ) )
% 9.49/5.23        = A ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_166_mult__numeral__1__right,axiom,
% 9.49/5.23      ! [A: rat] :
% 9.49/5.23        ( ( times_times_rat @ A @ ( numeral_numeral_rat @ one ) )
% 9.49/5.23        = A ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_167_mult__numeral__1__right,axiom,
% 9.49/5.23      ! [A: nat] :
% 9.49/5.23        ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
% 9.49/5.23        = A ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_168_mult__numeral__1__right,axiom,
% 9.49/5.23      ! [A: int] :
% 9.49/5.23        ( ( times_times_int @ A @ ( numeral_numeral_int @ one ) )
% 9.49/5.23        = A ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_169_mult__numeral__1,axiom,
% 9.49/5.23      ! [A: complex] :
% 9.49/5.23        ( ( times_times_complex @ ( numera6690914467698888265omplex @ one ) @ A )
% 9.49/5.23        = A ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_170_mult__numeral__1,axiom,
% 9.49/5.23      ! [A: real] :
% 9.49/5.23        ( ( times_times_real @ ( numeral_numeral_real @ one ) @ A )
% 9.49/5.23        = A ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_171_mult__numeral__1,axiom,
% 9.49/5.23      ! [A: rat] :
% 9.49/5.23        ( ( times_times_rat @ ( numeral_numeral_rat @ one ) @ A )
% 9.49/5.23        = A ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_172_mult__numeral__1,axiom,
% 9.49/5.23      ! [A: nat] :
% 9.49/5.23        ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
% 9.49/5.23        = A ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_173_mult__numeral__1,axiom,
% 9.49/5.23      ! [A: int] :
% 9.49/5.23        ( ( times_times_int @ ( numeral_numeral_int @ one ) @ A )
% 9.49/5.23        = A ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_174_left__add__twice,axiom,
% 9.49/5.23      ! [A: complex,B: complex] :
% 9.49/5.23        ( ( plus_plus_complex @ A @ ( plus_plus_complex @ A @ B ) )
% 9.49/5.23        = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_175_left__add__twice,axiom,
% 9.49/5.23      ! [A: real,B: real] :
% 9.49/5.23        ( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B ) )
% 9.49/5.23        = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_176_left__add__twice,axiom,
% 9.49/5.23      ! [A: rat,B: rat] :
% 9.49/5.23        ( ( plus_plus_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 9.49/5.23        = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_177_left__add__twice,axiom,
% 9.49/5.23      ! [A: nat,B: nat] :
% 9.49/5.23        ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 9.49/5.23        = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_178_left__add__twice,axiom,
% 9.49/5.23      ! [A: int,B: int] :
% 9.49/5.23        ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B ) )
% 9.49/5.23        = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_179_mult__2__right,axiom,
% 9.49/5.23      ! [Z: complex] :
% 9.49/5.23        ( ( times_times_complex @ Z @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) )
% 9.49/5.23        = ( plus_plus_complex @ Z @ Z ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_180_mult__2__right,axiom,
% 9.49/5.23      ! [Z: real] :
% 9.49/5.23        ( ( times_times_real @ Z @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 9.49/5.23        = ( plus_plus_real @ Z @ Z ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_181_mult__2__right,axiom,
% 9.49/5.23      ! [Z: rat] :
% 9.49/5.23        ( ( times_times_rat @ Z @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 9.49/5.23        = ( plus_plus_rat @ Z @ Z ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_182_mult__2__right,axiom,
% 9.49/5.23      ! [Z: nat] :
% 9.49/5.23        ( ( times_times_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.23        = ( plus_plus_nat @ Z @ Z ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_183_mult__2__right,axiom,
% 9.49/5.23      ! [Z: int] :
% 9.49/5.23        ( ( times_times_int @ Z @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.49/5.23        = ( plus_plus_int @ Z @ Z ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_184_mult__2,axiom,
% 9.49/5.23      ! [Z: complex] :
% 9.49/5.23        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z )
% 9.49/5.23        = ( plus_plus_complex @ Z @ Z ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_185_mult__2,axiom,
% 9.49/5.23      ! [Z: real] :
% 9.49/5.23        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z )
% 9.49/5.23        = ( plus_plus_real @ Z @ Z ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_186_mult__2,axiom,
% 9.49/5.23      ! [Z: rat] :
% 9.49/5.23        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z )
% 9.49/5.23        = ( plus_plus_rat @ Z @ Z ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_187_mult__2,axiom,
% 9.49/5.23      ! [Z: nat] :
% 9.49/5.23        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z )
% 9.49/5.23        = ( plus_plus_nat @ Z @ Z ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_188_mult__2,axiom,
% 9.49/5.23      ! [Z: int] :
% 9.49/5.23        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z )
% 9.49/5.23        = ( plus_plus_int @ Z @ Z ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_189_numeral__Bit0,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 9.49/5.23        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_190_numeral__Bit0,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 9.49/5.23        = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_191_numeral__Bit0,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 9.49/5.23        = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_192_numeral__Bit0,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 9.49/5.23        = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_193_numeral__Bit0,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 9.49/5.23        = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_194_one__plus__numeral__commute,axiom,
% 9.49/5.23      ! [X: num] :
% 9.49/5.23        ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ X ) )
% 9.49/5.23        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X ) @ one_one_complex ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_195_one__plus__numeral__commute,axiom,
% 9.49/5.23      ! [X: num] :
% 9.49/5.23        ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ X ) )
% 9.49/5.23        = ( plus_plus_real @ ( numeral_numeral_real @ X ) @ one_one_real ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_196_one__plus__numeral__commute,axiom,
% 9.49/5.23      ! [X: num] :
% 9.49/5.23        ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 9.49/5.23        = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_197_one__plus__numeral__commute,axiom,
% 9.49/5.23      ! [X: num] :
% 9.49/5.23        ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 9.49/5.23        = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_198_one__plus__numeral__commute,axiom,
% 9.49/5.23      ! [X: num] :
% 9.49/5.23        ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 9.49/5.23        = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_199_numeral__One,axiom,
% 9.49/5.23      ( ( numera6690914467698888265omplex @ one )
% 9.49/5.23      = one_one_complex ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_200_numeral__One,axiom,
% 9.49/5.23      ( ( numeral_numeral_real @ one )
% 9.49/5.23      = one_one_real ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_201_numeral__One,axiom,
% 9.49/5.23      ( ( numeral_numeral_rat @ one )
% 9.49/5.23      = one_one_rat ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_202_numeral__One,axiom,
% 9.49/5.23      ( ( numeral_numeral_nat @ one )
% 9.49/5.23      = one_one_nat ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_203_numeral__One,axiom,
% 9.49/5.23      ( ( numeral_numeral_int @ one )
% 9.49/5.23      = one_one_int ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_204_num_Oexhaust,axiom,
% 9.49/5.23      ! [Y2: num] :
% 9.49/5.23        ( ( Y2 != one )
% 9.49/5.23       => ( ! [X22: num] :
% 9.49/5.23              ( Y2
% 9.49/5.23             != ( bit0 @ X22 ) )
% 9.49/5.23         => ~ ! [X32: num] :
% 9.49/5.23                ( Y2
% 9.49/5.23               != ( bit1 @ X32 ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_205_numerals_I1_J,axiom,
% 9.49/5.23      ( ( numeral_numeral_nat @ one )
% 9.49/5.23      = one_one_nat ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_206_numeral__Bit1,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 9.49/5.23        = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_207_numeral__Bit1,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 9.49/5.23        = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_208_numeral__Bit1,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 9.49/5.23        = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_209_numeral__Bit1,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 9.49/5.23        = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_210_numeral__Bit1,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 9.49/5.23        = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_211_nat__1__add__1,axiom,
% 9.49/5.23      ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 9.49/5.23      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_212_insert__simp__mima,axiom,
% 9.49/5.23      ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 9.49/5.23        ( ( ( X = Mi )
% 9.49/5.23          | ( X = Ma ) )
% 9.49/5.23       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 9.49/5.23         => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 9.49/5.23            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_213_add__self__div__2,axiom,
% 9.49/5.23      ! [M: nat] :
% 9.49/5.23        ( ( divide_divide_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.23        = M ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_214_power__increasing__iff,axiom,
% 9.49/5.23      ! [B: real,X: nat,Y2: nat] :
% 9.49/5.23        ( ( ord_less_real @ one_one_real @ B )
% 9.49/5.23       => ( ( ord_less_eq_real @ ( power_power_real @ B @ X ) @ ( power_power_real @ B @ Y2 ) )
% 9.49/5.23          = ( ord_less_eq_nat @ X @ Y2 ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_215_power__increasing__iff,axiom,
% 9.49/5.23      ! [B: rat,X: nat,Y2: nat] :
% 9.49/5.23        ( ( ord_less_rat @ one_one_rat @ B )
% 9.49/5.23       => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y2 ) )
% 9.49/5.23          = ( ord_less_eq_nat @ X @ Y2 ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_216_power__increasing__iff,axiom,
% 9.49/5.23      ! [B: nat,X: nat,Y2: nat] :
% 9.49/5.23        ( ( ord_less_nat @ one_one_nat @ B )
% 9.49/5.23       => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y2 ) )
% 9.49/5.23          = ( ord_less_eq_nat @ X @ Y2 ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_217_power__increasing__iff,axiom,
% 9.49/5.23      ! [B: int,X: nat,Y2: nat] :
% 9.49/5.23        ( ( ord_less_int @ one_one_int @ B )
% 9.49/5.23       => ( ( ord_less_eq_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y2 ) )
% 9.49/5.23          = ( ord_less_eq_nat @ X @ Y2 ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_218__C4_OIH_C_I2_J,axiom,
% 9.49/5.23      ! [X: nat] : ( ord_less_eq_nat @ ( vEBT_T_d_e_l_e_t_e @ summary @ X ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ summary ) ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_219_power__add__numeral2,axiom,
% 9.49/5.23      ! [A: complex,M: num,N: num,B: complex] :
% 9.49/5.23        ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 9.49/5.23        = ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_220_power__add__numeral2,axiom,
% 9.49/5.23      ! [A: real,M: num,N: num,B: real] :
% 9.49/5.23        ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 9.49/5.23        = ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_221_power__add__numeral2,axiom,
% 9.49/5.23      ! [A: nat,M: num,N: num,B: nat] :
% 9.49/5.23        ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 9.49/5.23        = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_222_power__add__numeral2,axiom,
% 9.49/5.23      ! [A: int,M: num,N: num,B: int] :
% 9.49/5.23        ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 9.49/5.23        = ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_223_power__add__numeral,axiom,
% 9.49/5.23      ! [A: complex,M: num,N: num] :
% 9.49/5.23        ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) )
% 9.49/5.23        = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_224_power__add__numeral,axiom,
% 9.49/5.23      ! [A: real,M: num,N: num] :
% 9.49/5.23        ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) )
% 9.49/5.23        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_225_power__add__numeral,axiom,
% 9.49/5.23      ! [A: nat,M: num,N: num] :
% 9.49/5.23        ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) )
% 9.49/5.23        = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_226_power__add__numeral,axiom,
% 9.49/5.23      ! [A: int,M: num,N: num] :
% 9.49/5.23        ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) )
% 9.49/5.23        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_227_power__strict__increasing__iff,axiom,
% 9.49/5.23      ! [B: real,X: nat,Y2: nat] :
% 9.49/5.23        ( ( ord_less_real @ one_one_real @ B )
% 9.49/5.23       => ( ( ord_less_real @ ( power_power_real @ B @ X ) @ ( power_power_real @ B @ Y2 ) )
% 9.49/5.23          = ( ord_less_nat @ X @ Y2 ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_228_power__strict__increasing__iff,axiom,
% 9.49/5.23      ! [B: rat,X: nat,Y2: nat] :
% 9.49/5.23        ( ( ord_less_rat @ one_one_rat @ B )
% 9.49/5.23       => ( ( ord_less_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y2 ) )
% 9.49/5.23          = ( ord_less_nat @ X @ Y2 ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_229_power__strict__increasing__iff,axiom,
% 9.49/5.23      ! [B: nat,X: nat,Y2: nat] :
% 9.49/5.23        ( ( ord_less_nat @ one_one_nat @ B )
% 9.49/5.23       => ( ( ord_less_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y2 ) )
% 9.49/5.23          = ( ord_less_nat @ X @ Y2 ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_230_power__strict__increasing__iff,axiom,
% 9.49/5.23      ! [B: int,X: nat,Y2: nat] :
% 9.49/5.23        ( ( ord_less_int @ one_one_int @ B )
% 9.49/5.23       => ( ( ord_less_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y2 ) )
% 9.49/5.23          = ( ord_less_nat @ X @ Y2 ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_231_ex__power__ivl2,axiom,
% 9.49/5.23      ! [B: nat,K: nat] :
% 9.49/5.23        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 9.49/5.23       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 9.49/5.23         => ? [N3: nat] :
% 9.49/5.23              ( ( ord_less_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 9.49/5.23              & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_232_ex__power__ivl1,axiom,
% 9.49/5.23      ! [B: nat,K: nat] :
% 9.49/5.23        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 9.49/5.23       => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 9.49/5.23         => ? [N3: nat] :
% 9.49/5.23              ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 9.49/5.23              & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_233_sum__squares__bound,axiom,
% 9.49/5.23      ! [X: real,Y2: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y2 ) @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_234_sum__squares__bound,axiom,
% 9.49/5.23      ! [X: rat,Y2: rat] : ( ord_less_eq_rat @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y2 ) @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_235_power__inject__exp,axiom,
% 9.49/5.23      ! [A: real,M: nat,N: nat] :
% 9.49/5.23        ( ( ord_less_real @ one_one_real @ A )
% 9.49/5.23       => ( ( ( power_power_real @ A @ M )
% 9.49/5.23            = ( power_power_real @ A @ N ) )
% 9.49/5.23          = ( M = N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_236_power__inject__exp,axiom,
% 9.49/5.23      ! [A: rat,M: nat,N: nat] :
% 9.49/5.23        ( ( ord_less_rat @ one_one_rat @ A )
% 9.49/5.23       => ( ( ( power_power_rat @ A @ M )
% 9.49/5.23            = ( power_power_rat @ A @ N ) )
% 9.49/5.23          = ( M = N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_237_power__inject__exp,axiom,
% 9.49/5.23      ! [A: nat,M: nat,N: nat] :
% 9.49/5.23        ( ( ord_less_nat @ one_one_nat @ A )
% 9.49/5.23       => ( ( ( power_power_nat @ A @ M )
% 9.49/5.23            = ( power_power_nat @ A @ N ) )
% 9.49/5.23          = ( M = N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_238_power__inject__exp,axiom,
% 9.49/5.23      ! [A: int,M: nat,N: nat] :
% 9.49/5.23        ( ( ord_less_int @ one_one_int @ A )
% 9.49/5.23       => ( ( ( power_power_int @ A @ M )
% 9.49/5.23            = ( power_power_int @ A @ N ) )
% 9.49/5.23          = ( M = N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_239_power2__sum,axiom,
% 9.49/5.23      ! [X: complex,Y2: complex] :
% 9.49/5.23        ( ( power_power_complex @ ( plus_plus_complex @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.23        = ( plus_plus_complex @ ( plus_plus_complex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) @ Y2 ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_240_power2__sum,axiom,
% 9.49/5.23      ! [X: real,Y2: real] :
% 9.49/5.23        ( ( power_power_real @ ( plus_plus_real @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.23        = ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y2 ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_241_power2__sum,axiom,
% 9.49/5.23      ! [X: rat,Y2: rat] :
% 9.49/5.23        ( ( power_power_rat @ ( plus_plus_rat @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.23        = ( plus_plus_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y2 ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_242_power2__sum,axiom,
% 9.49/5.23      ! [X: nat,Y2: nat] :
% 9.49/5.23        ( ( power_power_nat @ ( plus_plus_nat @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.23        = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) @ Y2 ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_243_power2__sum,axiom,
% 9.49/5.23      ! [X: int,Y2: int] :
% 9.49/5.23        ( ( power_power_int @ ( plus_plus_int @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.23        = ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X ) @ Y2 ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_244_deg__deg__n,axiom,
% 9.49/5.23      ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 9.49/5.23        ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N )
% 9.49/5.23       => ( Deg = N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_245_height__compose__summary,axiom,
% 9.49/5.23      ! [Summary: vEBT_VEBT,Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT] : ( ord_less_eq_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ Summary ) ) @ ( vEBT_VEBT_height @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_246_power__one,axiom,
% 9.49/5.23      ! [N: nat] :
% 9.49/5.23        ( ( power_power_rat @ one_one_rat @ N )
% 9.49/5.23        = one_one_rat ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_247_power__one,axiom,
% 9.49/5.23      ! [N: nat] :
% 9.49/5.23        ( ( power_power_nat @ one_one_nat @ N )
% 9.49/5.23        = one_one_nat ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_248_power__one,axiom,
% 9.49/5.23      ! [N: nat] :
% 9.49/5.23        ( ( power_power_real @ one_one_real @ N )
% 9.49/5.23        = one_one_real ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_249_power__one,axiom,
% 9.49/5.23      ! [N: nat] :
% 9.49/5.23        ( ( power_power_int @ one_one_int @ N )
% 9.49/5.23        = one_one_int ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_250_power__one,axiom,
% 9.49/5.23      ! [N: nat] :
% 9.49/5.23        ( ( power_power_complex @ one_one_complex @ N )
% 9.49/5.23        = one_one_complex ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_251_two__powr__height__bound__deg,axiom,
% 9.49/5.23      ! [T: vEBT_VEBT,N: nat] :
% 9.49/5.23        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.23       => ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( vEBT_VEBT_height @ T ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_252_power__one__right,axiom,
% 9.49/5.23      ! [A: nat] :
% 9.49/5.23        ( ( power_power_nat @ A @ one_one_nat )
% 9.49/5.23        = A ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_253_power__one__right,axiom,
% 9.49/5.23      ! [A: real] :
% 9.49/5.23        ( ( power_power_real @ A @ one_one_nat )
% 9.49/5.23        = A ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_254_power__one__right,axiom,
% 9.49/5.23      ! [A: int] :
% 9.49/5.23        ( ( power_power_int @ A @ one_one_nat )
% 9.49/5.23        = A ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_255_power__one__right,axiom,
% 9.49/5.23      ! [A: complex] :
% 9.49/5.23        ( ( power_power_complex @ A @ one_one_nat )
% 9.49/5.23        = A ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_256_valid__insert__both__member__options__add,axiom,
% 9.49/5.23      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 9.49/5.23        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.23       => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.23         => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ X ) @ X ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_257_valid__insert__both__member__options__pres,axiom,
% 9.49/5.23      ! [T: vEBT_VEBT,N: nat,X: nat,Y2: nat] :
% 9.49/5.23        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.23       => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.23         => ( ( ord_less_nat @ Y2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.23           => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 9.49/5.23             => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ Y2 ) @ X ) ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_258_semiring__norm_I13_J,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( times_times_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 9.49/5.23        = ( bit0 @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_259_semiring__norm_I12_J,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( times_times_num @ one @ N )
% 9.49/5.23        = N ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_260_semiring__norm_I11_J,axiom,
% 9.49/5.23      ! [M: num] :
% 9.49/5.23        ( ( times_times_num @ M @ one )
% 9.49/5.23        = M ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_261_semiring__norm_I78_J,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( ord_less_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 9.49/5.23        = ( ord_less_num @ M @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_262_semiring__norm_I71_J,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 9.49/5.23        = ( ord_less_eq_num @ M @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_263_semiring__norm_I75_J,axiom,
% 9.49/5.23      ! [M: num] :
% 9.49/5.23        ~ ( ord_less_num @ M @ one ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_264_semiring__norm_I68_J,axiom,
% 9.49/5.23      ! [N: num] : ( ord_less_eq_num @ one @ N ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_265_semiring__norm_I80_J,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( ord_less_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 9.49/5.23        = ( ord_less_num @ M @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_266_semiring__norm_I73_J,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 9.49/5.23        = ( ord_less_eq_num @ M @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_267_mi__ma__2__deg,axiom,
% 9.49/5.23      ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 9.49/5.23        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 9.49/5.23       => ( ( ord_less_eq_nat @ Mi @ Ma )
% 9.49/5.23          & ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_268_num__double,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( times_times_num @ ( bit0 @ one ) @ N )
% 9.49/5.23        = ( bit0 @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_269_power__mult__numeral,axiom,
% 9.49/5.23      ! [A: nat,M: num,N: num] :
% 9.49/5.23        ( ( power_power_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 9.49/5.23        = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_270_power__mult__numeral,axiom,
% 9.49/5.23      ! [A: real,M: num,N: num] :
% 9.49/5.23        ( ( power_power_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 9.49/5.23        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_271_power__mult__numeral,axiom,
% 9.49/5.23      ! [A: int,M: num,N: num] :
% 9.49/5.23        ( ( power_power_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 9.49/5.23        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_272_power__mult__numeral,axiom,
% 9.49/5.23      ! [A: complex,M: num,N: num] :
% 9.49/5.23        ( ( power_power_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 9.49/5.23        = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_273_semiring__norm_I15_J,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( times_times_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 9.49/5.23        = ( bit0 @ ( times_times_num @ ( bit1 @ M ) @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_274_semiring__norm_I14_J,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( times_times_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 9.49/5.23        = ( bit0 @ ( times_times_num @ M @ ( bit1 @ N ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_275_semiring__norm_I76_J,axiom,
% 9.49/5.23      ! [N: num] : ( ord_less_num @ one @ ( bit0 @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_276_semiring__norm_I69_J,axiom,
% 9.49/5.23      ! [M: num] :
% 9.49/5.23        ~ ( ord_less_eq_num @ ( bit0 @ M ) @ one ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_277_semiring__norm_I81_J,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( ord_less_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 9.49/5.23        = ( ord_less_num @ M @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_278_semiring__norm_I72_J,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 9.49/5.23        = ( ord_less_eq_num @ M @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_279_semiring__norm_I77_J,axiom,
% 9.49/5.23      ! [N: num] : ( ord_less_num @ one @ ( bit1 @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_280_semiring__norm_I70_J,axiom,
% 9.49/5.23      ! [M: num] :
% 9.49/5.23        ~ ( ord_less_eq_num @ ( bit1 @ M ) @ one ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_281_semiring__norm_I16_J,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( times_times_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 9.49/5.23        = ( bit1 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_282_semiring__norm_I79_J,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( ord_less_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 9.49/5.23        = ( ord_less_eq_num @ M @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_283_semiring__norm_I74_J,axiom,
% 9.49/5.23      ! [M: num,N: num] :
% 9.49/5.23        ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 9.49/5.23        = ( ord_less_num @ M @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_284__C4_Ohyps_C_I6_J,axiom,
% 9.49/5.23      ( ( mi = ma )
% 9.49/5.23     => ! [X5: vEBT_VEBT] :
% 9.49/5.23          ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ treeList ) )
% 9.49/5.23         => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_285__C4_OIH_C_I1_J,axiom,
% 9.49/5.23      ! [X5: vEBT_VEBT] :
% 9.49/5.23        ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ treeList ) )
% 9.49/5.23       => ( ( vEBT_invar_vebt @ X5 @ na )
% 9.49/5.23          & ! [Xa: nat] : ( ord_less_eq_nat @ ( vEBT_T_d_e_l_e_t_e @ X5 @ Xa ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ X5 ) ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_286__C4_Ohyps_C_I9_J,axiom,
% 9.49/5.23      ( ( mi != ma )
% 9.49/5.23     => ! [I: nat] :
% 9.49/5.23          ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 9.49/5.23         => ( ( ( ( vEBT_VEBT_high @ ma @ na )
% 9.49/5.23                = I )
% 9.49/5.23             => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
% 9.49/5.23            & ! [X5: nat] :
% 9.49/5.23                ( ( ( ( vEBT_VEBT_high @ X5 @ na )
% 9.49/5.23                    = I )
% 9.49/5.23                  & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ ( vEBT_VEBT_low @ X5 @ na ) ) )
% 9.49/5.23               => ( ( ord_less_nat @ mi @ X5 )
% 9.49/5.23                  & ( ord_less_eq_nat @ X5 @ ma ) ) ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_287_L2__set__mult__ineq__lemma,axiom,
% 9.49/5.23      ! [A: real,C: real,B: real,D2: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_real @ A @ C ) ) @ ( times_times_real @ B @ D2 ) ) @ ( plus_plus_real @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ D2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ C @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_288_four__x__squared,axiom,
% 9.49/5.23      ! [X: real] :
% 9.49/5.23        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.23        = ( power_power_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_289_le__num__One__iff,axiom,
% 9.49/5.23      ! [X: num] :
% 9.49/5.23        ( ( ord_less_eq_num @ X @ one )
% 9.49/5.23        = ( X = one ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_290_div__mult2__numeral__eq,axiom,
% 9.49/5.23      ! [A: nat,K: num,L2: num] :
% 9.49/5.23        ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ L2 ) )
% 9.49/5.23        = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ K @ L2 ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_291_div__mult2__numeral__eq,axiom,
% 9.49/5.23      ! [A: int,K: num,L2: num] :
% 9.49/5.23        ( ( divide_divide_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ L2 ) )
% 9.49/5.23        = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( times_times_num @ K @ L2 ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_292_height__node,axiom,
% 9.49/5.23      ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 9.49/5.23        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 9.49/5.23       => ( ord_less_eq_nat @ one_one_nat @ ( vEBT_VEBT_height @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_293_power__commuting__commutes,axiom,
% 9.49/5.23      ! [X: complex,Y2: complex,N: nat] :
% 9.49/5.23        ( ( ( times_times_complex @ X @ Y2 )
% 9.49/5.23          = ( times_times_complex @ Y2 @ X ) )
% 9.49/5.23       => ( ( times_times_complex @ ( power_power_complex @ X @ N ) @ Y2 )
% 9.49/5.23          = ( times_times_complex @ Y2 @ ( power_power_complex @ X @ N ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_294_power__commuting__commutes,axiom,
% 9.49/5.23      ! [X: real,Y2: real,N: nat] :
% 9.49/5.23        ( ( ( times_times_real @ X @ Y2 )
% 9.49/5.23          = ( times_times_real @ Y2 @ X ) )
% 9.49/5.23       => ( ( times_times_real @ ( power_power_real @ X @ N ) @ Y2 )
% 9.49/5.23          = ( times_times_real @ Y2 @ ( power_power_real @ X @ N ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_295_power__commuting__commutes,axiom,
% 9.49/5.23      ! [X: nat,Y2: nat,N: nat] :
% 9.49/5.23        ( ( ( times_times_nat @ X @ Y2 )
% 9.49/5.23          = ( times_times_nat @ Y2 @ X ) )
% 9.49/5.23       => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ Y2 )
% 9.49/5.23          = ( times_times_nat @ Y2 @ ( power_power_nat @ X @ N ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_296_power__commuting__commutes,axiom,
% 9.49/5.23      ! [X: int,Y2: int,N: nat] :
% 9.49/5.23        ( ( ( times_times_int @ X @ Y2 )
% 9.49/5.23          = ( times_times_int @ Y2 @ X ) )
% 9.49/5.23       => ( ( times_times_int @ ( power_power_int @ X @ N ) @ Y2 )
% 9.49/5.23          = ( times_times_int @ Y2 @ ( power_power_int @ X @ N ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_297_power__mult__distrib,axiom,
% 9.49/5.23      ! [A: complex,B: complex,N: nat] :
% 9.49/5.23        ( ( power_power_complex @ ( times_times_complex @ A @ B ) @ N )
% 9.49/5.23        = ( times_times_complex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_298_power__mult__distrib,axiom,
% 9.49/5.23      ! [A: real,B: real,N: nat] :
% 9.49/5.23        ( ( power_power_real @ ( times_times_real @ A @ B ) @ N )
% 9.49/5.23        = ( times_times_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_299_power__mult__distrib,axiom,
% 9.49/5.23      ! [A: nat,B: nat,N: nat] :
% 9.49/5.23        ( ( power_power_nat @ ( times_times_nat @ A @ B ) @ N )
% 9.49/5.23        = ( times_times_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_300_power__mult__distrib,axiom,
% 9.49/5.23      ! [A: int,B: int,N: nat] :
% 9.49/5.23        ( ( power_power_int @ ( times_times_int @ A @ B ) @ N )
% 9.49/5.23        = ( times_times_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_301_power__commutes,axiom,
% 9.49/5.23      ! [A: complex,N: nat] :
% 9.49/5.23        ( ( times_times_complex @ ( power_power_complex @ A @ N ) @ A )
% 9.49/5.23        = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_302_power__commutes,axiom,
% 9.49/5.23      ! [A: real,N: nat] :
% 9.49/5.23        ( ( times_times_real @ ( power_power_real @ A @ N ) @ A )
% 9.49/5.23        = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_303_power__commutes,axiom,
% 9.49/5.23      ! [A: nat,N: nat] :
% 9.49/5.23        ( ( times_times_nat @ ( power_power_nat @ A @ N ) @ A )
% 9.49/5.23        = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_304_power__commutes,axiom,
% 9.49/5.23      ! [A: int,N: nat] :
% 9.49/5.23        ( ( times_times_int @ ( power_power_int @ A @ N ) @ A )
% 9.49/5.23        = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_305_power__divide,axiom,
% 9.49/5.23      ! [A: complex,B: complex,N: nat] :
% 9.49/5.23        ( ( power_power_complex @ ( divide1717551699836669952omplex @ A @ B ) @ N )
% 9.49/5.23        = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_306_power__divide,axiom,
% 9.49/5.23      ! [A: real,B: real,N: nat] :
% 9.49/5.23        ( ( power_power_real @ ( divide_divide_real @ A @ B ) @ N )
% 9.49/5.23        = ( divide_divide_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_307_power__divide,axiom,
% 9.49/5.23      ! [A: rat,B: rat,N: nat] :
% 9.49/5.23        ( ( power_power_rat @ ( divide_divide_rat @ A @ B ) @ N )
% 9.49/5.23        = ( divide_divide_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_308_power__mult,axiom,
% 9.49/5.23      ! [A: nat,M: nat,N: nat] :
% 9.49/5.23        ( ( power_power_nat @ A @ ( times_times_nat @ M @ N ) )
% 9.49/5.23        = ( power_power_nat @ ( power_power_nat @ A @ M ) @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_309_power__mult,axiom,
% 9.49/5.23      ! [A: real,M: nat,N: nat] :
% 9.49/5.23        ( ( power_power_real @ A @ ( times_times_nat @ M @ N ) )
% 9.49/5.23        = ( power_power_real @ ( power_power_real @ A @ M ) @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_310_power__mult,axiom,
% 9.49/5.23      ! [A: int,M: nat,N: nat] :
% 9.49/5.23        ( ( power_power_int @ A @ ( times_times_nat @ M @ N ) )
% 9.49/5.23        = ( power_power_int @ ( power_power_int @ A @ M ) @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_311_power__mult,axiom,
% 9.49/5.23      ! [A: complex,M: nat,N: nat] :
% 9.49/5.23        ( ( power_power_complex @ A @ ( times_times_nat @ M @ N ) )
% 9.49/5.23        = ( power_power_complex @ ( power_power_complex @ A @ M ) @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_312_div__le__dividend,axiom,
% 9.49/5.23      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ M ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_313_div__le__mono,axiom,
% 9.49/5.23      ! [M: nat,N: nat,K: nat] :
% 9.49/5.23        ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.23       => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N @ K ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_314_div__mult2__eq,axiom,
% 9.49/5.23      ! [M: nat,N: nat,Q2: nat] :
% 9.49/5.23        ( ( divide_divide_nat @ M @ ( times_times_nat @ N @ Q2 ) )
% 9.49/5.23        = ( divide_divide_nat @ ( divide_divide_nat @ M @ N ) @ Q2 ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_315_one__le__power,axiom,
% 9.49/5.23      ! [A: rat,N: nat] :
% 9.49/5.23        ( ( ord_less_eq_rat @ one_one_rat @ A )
% 9.49/5.23       => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_316_one__le__power,axiom,
% 9.49/5.23      ! [A: real,N: nat] :
% 9.49/5.23        ( ( ord_less_eq_real @ one_one_real @ A )
% 9.49/5.23       => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_317_one__le__power,axiom,
% 9.49/5.23      ! [A: nat,N: nat] :
% 9.49/5.23        ( ( ord_less_eq_nat @ one_one_nat @ A )
% 9.49/5.23       => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_318_one__le__power,axiom,
% 9.49/5.23      ! [A: int,N: nat] :
% 9.49/5.23        ( ( ord_less_eq_int @ one_one_int @ A )
% 9.49/5.23       => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_319_left__right__inverse__power,axiom,
% 9.49/5.23      ! [X: rat,Y2: rat,N: nat] :
% 9.49/5.23        ( ( ( times_times_rat @ X @ Y2 )
% 9.49/5.23          = one_one_rat )
% 9.49/5.23       => ( ( times_times_rat @ ( power_power_rat @ X @ N ) @ ( power_power_rat @ Y2 @ N ) )
% 9.49/5.23          = one_one_rat ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_320_left__right__inverse__power,axiom,
% 9.49/5.23      ! [X: complex,Y2: complex,N: nat] :
% 9.49/5.23        ( ( ( times_times_complex @ X @ Y2 )
% 9.49/5.23          = one_one_complex )
% 9.49/5.23       => ( ( times_times_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y2 @ N ) )
% 9.49/5.23          = one_one_complex ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_321_left__right__inverse__power,axiom,
% 9.49/5.23      ! [X: real,Y2: real,N: nat] :
% 9.49/5.23        ( ( ( times_times_real @ X @ Y2 )
% 9.49/5.23          = one_one_real )
% 9.49/5.23       => ( ( times_times_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y2 @ N ) )
% 9.49/5.23          = one_one_real ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_322_left__right__inverse__power,axiom,
% 9.49/5.23      ! [X: nat,Y2: nat,N: nat] :
% 9.49/5.23        ( ( ( times_times_nat @ X @ Y2 )
% 9.49/5.23          = one_one_nat )
% 9.49/5.23       => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y2 @ N ) )
% 9.49/5.23          = one_one_nat ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_323_left__right__inverse__power,axiom,
% 9.49/5.23      ! [X: int,Y2: int,N: nat] :
% 9.49/5.23        ( ( ( times_times_int @ X @ Y2 )
% 9.49/5.23          = one_one_int )
% 9.49/5.23       => ( ( times_times_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y2 @ N ) )
% 9.49/5.23          = one_one_int ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_324_power__one__over,axiom,
% 9.49/5.23      ! [A: complex,N: nat] :
% 9.49/5.23        ( ( power_power_complex @ ( divide1717551699836669952omplex @ one_one_complex @ A ) @ N )
% 9.49/5.23        = ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ A @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_325_power__one__over,axiom,
% 9.49/5.23      ! [A: real,N: nat] :
% 9.49/5.23        ( ( power_power_real @ ( divide_divide_real @ one_one_real @ A ) @ N )
% 9.49/5.23        = ( divide_divide_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_326_power__one__over,axiom,
% 9.49/5.23      ! [A: rat,N: nat] :
% 9.49/5.23        ( ( power_power_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ N )
% 9.49/5.23        = ( divide_divide_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_327_power__add,axiom,
% 9.49/5.23      ! [A: complex,M: nat,N: nat] :
% 9.49/5.23        ( ( power_power_complex @ A @ ( plus_plus_nat @ M @ N ) )
% 9.49/5.23        = ( times_times_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_328_power__add,axiom,
% 9.49/5.23      ! [A: real,M: nat,N: nat] :
% 9.49/5.23        ( ( power_power_real @ A @ ( plus_plus_nat @ M @ N ) )
% 9.49/5.23        = ( times_times_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_329_power__add,axiom,
% 9.49/5.23      ! [A: nat,M: nat,N: nat] :
% 9.49/5.23        ( ( power_power_nat @ A @ ( plus_plus_nat @ M @ N ) )
% 9.49/5.23        = ( times_times_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_330_power__add,axiom,
% 9.49/5.23      ! [A: int,M: nat,N: nat] :
% 9.49/5.23        ( ( power_power_int @ A @ ( plus_plus_nat @ M @ N ) )
% 9.49/5.23        = ( times_times_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_331_less__mult__imp__div__less,axiom,
% 9.49/5.23      ! [M: nat,I2: nat,N: nat] :
% 9.49/5.23        ( ( ord_less_nat @ M @ ( times_times_nat @ I2 @ N ) )
% 9.49/5.23       => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ I2 ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_332_times__div__less__eq__dividend,axiom,
% 9.49/5.23      ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) @ M ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_333_div__times__less__eq__dividend,axiom,
% 9.49/5.23      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) @ M ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_334_numeral__Bit0__div__2,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.23        = ( numeral_numeral_nat @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_335_numeral__Bit0__div__2,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.49/5.23        = ( numeral_numeral_int @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_336_power__gt1__lemma,axiom,
% 9.49/5.23      ! [A: real,N: nat] :
% 9.49/5.23        ( ( ord_less_real @ one_one_real @ A )
% 9.49/5.23       => ( ord_less_real @ one_one_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_337_power__gt1__lemma,axiom,
% 9.49/5.23      ! [A: rat,N: nat] :
% 9.49/5.23        ( ( ord_less_rat @ one_one_rat @ A )
% 9.49/5.23       => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_338_power__gt1__lemma,axiom,
% 9.49/5.23      ! [A: nat,N: nat] :
% 9.49/5.23        ( ( ord_less_nat @ one_one_nat @ A )
% 9.49/5.23       => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_339_power__gt1__lemma,axiom,
% 9.49/5.23      ! [A: int,N: nat] :
% 9.49/5.23        ( ( ord_less_int @ one_one_int @ A )
% 9.49/5.23       => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_340_power__less__power__Suc,axiom,
% 9.49/5.23      ! [A: real,N: nat] :
% 9.49/5.23        ( ( ord_less_real @ one_one_real @ A )
% 9.49/5.23       => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_341_power__less__power__Suc,axiom,
% 9.49/5.23      ! [A: rat,N: nat] :
% 9.49/5.23        ( ( ord_less_rat @ one_one_rat @ A )
% 9.49/5.23       => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_342_power__less__power__Suc,axiom,
% 9.49/5.23      ! [A: nat,N: nat] :
% 9.49/5.23        ( ( ord_less_nat @ one_one_nat @ A )
% 9.49/5.23       => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_343_power__less__power__Suc,axiom,
% 9.49/5.23      ! [A: int,N: nat] :
% 9.49/5.23        ( ( ord_less_int @ one_one_int @ A )
% 9.49/5.23       => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_344_power__less__imp__less__exp,axiom,
% 9.49/5.23      ! [A: real,M: nat,N: nat] :
% 9.49/5.23        ( ( ord_less_real @ one_one_real @ A )
% 9.49/5.23       => ( ( ord_less_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 9.49/5.23         => ( ord_less_nat @ M @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_345_power__less__imp__less__exp,axiom,
% 9.49/5.23      ! [A: rat,M: nat,N: nat] :
% 9.49/5.23        ( ( ord_less_rat @ one_one_rat @ A )
% 9.49/5.23       => ( ( ord_less_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 9.49/5.23         => ( ord_less_nat @ M @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_346_power__less__imp__less__exp,axiom,
% 9.49/5.23      ! [A: nat,M: nat,N: nat] :
% 9.49/5.23        ( ( ord_less_nat @ one_one_nat @ A )
% 9.49/5.23       => ( ( ord_less_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 9.49/5.23         => ( ord_less_nat @ M @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_347_power__less__imp__less__exp,axiom,
% 9.49/5.23      ! [A: int,M: nat,N: nat] :
% 9.49/5.23        ( ( ord_less_int @ one_one_int @ A )
% 9.49/5.23       => ( ( ord_less_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 9.49/5.23         => ( ord_less_nat @ M @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_348_power__strict__increasing,axiom,
% 9.49/5.23      ! [N: nat,N4: nat,A: real] :
% 9.49/5.23        ( ( ord_less_nat @ N @ N4 )
% 9.49/5.23       => ( ( ord_less_real @ one_one_real @ A )
% 9.49/5.23         => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N4 ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_349_power__strict__increasing,axiom,
% 9.49/5.23      ! [N: nat,N4: nat,A: rat] :
% 9.49/5.23        ( ( ord_less_nat @ N @ N4 )
% 9.49/5.23       => ( ( ord_less_rat @ one_one_rat @ A )
% 9.49/5.23         => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_350_power__strict__increasing,axiom,
% 9.49/5.23      ! [N: nat,N4: nat,A: nat] :
% 9.49/5.23        ( ( ord_less_nat @ N @ N4 )
% 9.49/5.23       => ( ( ord_less_nat @ one_one_nat @ A )
% 9.49/5.23         => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_351_power__strict__increasing,axiom,
% 9.49/5.23      ! [N: nat,N4: nat,A: int] :
% 9.49/5.23        ( ( ord_less_nat @ N @ N4 )
% 9.49/5.23       => ( ( ord_less_int @ one_one_int @ A )
% 9.49/5.23         => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_352_power__increasing,axiom,
% 9.49/5.23      ! [N: nat,N4: nat,A: rat] :
% 9.49/5.23        ( ( ord_less_eq_nat @ N @ N4 )
% 9.49/5.23       => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 9.49/5.23         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_353_power__increasing,axiom,
% 9.49/5.23      ! [N: nat,N4: nat,A: real] :
% 9.49/5.23        ( ( ord_less_eq_nat @ N @ N4 )
% 9.49/5.23       => ( ( ord_less_eq_real @ one_one_real @ A )
% 9.49/5.23         => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N4 ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_354_power__increasing,axiom,
% 9.49/5.23      ! [N: nat,N4: nat,A: nat] :
% 9.49/5.23        ( ( ord_less_eq_nat @ N @ N4 )
% 9.49/5.23       => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 9.49/5.23         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_355_power__increasing,axiom,
% 9.49/5.23      ! [N: nat,N4: nat,A: int] :
% 9.49/5.23        ( ( ord_less_eq_nat @ N @ N4 )
% 9.49/5.23       => ( ( ord_less_eq_int @ one_one_int @ A )
% 9.49/5.23         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_356_power__le__imp__le__exp,axiom,
% 9.49/5.23      ! [A: real,M: nat,N: nat] :
% 9.49/5.23        ( ( ord_less_real @ one_one_real @ A )
% 9.49/5.23       => ( ( ord_less_eq_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 9.49/5.23         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_357_power__le__imp__le__exp,axiom,
% 9.49/5.23      ! [A: rat,M: nat,N: nat] :
% 9.49/5.23        ( ( ord_less_rat @ one_one_rat @ A )
% 9.49/5.23       => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 9.49/5.23         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_358_power__le__imp__le__exp,axiom,
% 9.49/5.23      ! [A: nat,M: nat,N: nat] :
% 9.49/5.23        ( ( ord_less_nat @ one_one_nat @ A )
% 9.49/5.23       => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 9.49/5.23         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_359_power__le__imp__le__exp,axiom,
% 9.49/5.23      ! [A: int,M: nat,N: nat] :
% 9.49/5.23        ( ( ord_less_int @ one_one_int @ A )
% 9.49/5.23       => ( ( ord_less_eq_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 9.49/5.23         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_360_power4__eq__xxxx,axiom,
% 9.49/5.23      ! [X: complex] :
% 9.49/5.23        ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 9.49/5.23        = ( times_times_complex @ ( times_times_complex @ ( times_times_complex @ X @ X ) @ X ) @ X ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_361_power4__eq__xxxx,axiom,
% 9.49/5.23      ! [X: real] :
% 9.49/5.23        ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 9.49/5.23        = ( times_times_real @ ( times_times_real @ ( times_times_real @ X @ X ) @ X ) @ X ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_362_power4__eq__xxxx,axiom,
% 9.49/5.23      ! [X: nat] :
% 9.49/5.23        ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 9.49/5.23        = ( times_times_nat @ ( times_times_nat @ ( times_times_nat @ X @ X ) @ X ) @ X ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_363_power4__eq__xxxx,axiom,
% 9.49/5.23      ! [X: int] :
% 9.49/5.23        ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 9.49/5.23        = ( times_times_int @ ( times_times_int @ ( times_times_int @ X @ X ) @ X ) @ X ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_364_power2__eq__square,axiom,
% 9.49/5.23      ! [A: complex] :
% 9.49/5.23        ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.23        = ( times_times_complex @ A @ A ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_365_power2__eq__square,axiom,
% 9.49/5.23      ! [A: real] :
% 9.49/5.23        ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.23        = ( times_times_real @ A @ A ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_366_power2__eq__square,axiom,
% 9.49/5.23      ! [A: nat] :
% 9.49/5.23        ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.23        = ( times_times_nat @ A @ A ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_367_power2__eq__square,axiom,
% 9.49/5.23      ! [A: int] :
% 9.49/5.23        ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.23        = ( times_times_int @ A @ A ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_368_one__power2,axiom,
% 9.49/5.23      ( ( power_power_rat @ one_one_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.23      = one_one_rat ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_369_one__power2,axiom,
% 9.49/5.23      ( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.23      = one_one_nat ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_370_one__power2,axiom,
% 9.49/5.23      ( ( power_power_real @ one_one_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.23      = one_one_real ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_371_one__power2,axiom,
% 9.49/5.23      ( ( power_power_int @ one_one_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.23      = one_one_int ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_372_one__power2,axiom,
% 9.49/5.23      ( ( power_power_complex @ one_one_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.23      = one_one_complex ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_373_numeral__Bit1__div__2,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.23        = ( numeral_numeral_nat @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_374_numeral__Bit1__div__2,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.49/5.23        = ( numeral_numeral_int @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_375_power3__eq__cube,axiom,
% 9.49/5.23      ! [A: complex] :
% 9.49/5.23        ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 9.49/5.23        = ( times_times_complex @ ( times_times_complex @ A @ A ) @ A ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_376_power3__eq__cube,axiom,
% 9.49/5.23      ! [A: real] :
% 9.49/5.23        ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 9.49/5.23        = ( times_times_real @ ( times_times_real @ A @ A ) @ A ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_377_power3__eq__cube,axiom,
% 9.49/5.23      ! [A: nat] :
% 9.49/5.23        ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 9.49/5.23        = ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_378_power3__eq__cube,axiom,
% 9.49/5.23      ! [A: int] :
% 9.49/5.23        ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 9.49/5.23        = ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_379_power__even__eq,axiom,
% 9.49/5.23      ! [A: nat,N: nat] :
% 9.49/5.23        ( ( power_power_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.23        = ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_380_power__even__eq,axiom,
% 9.49/5.23      ! [A: real,N: nat] :
% 9.49/5.23        ( ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.23        = ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_381_power__even__eq,axiom,
% 9.49/5.23      ! [A: int,N: nat] :
% 9.49/5.23        ( ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.23        = ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_382_power__even__eq,axiom,
% 9.49/5.23      ! [A: complex,N: nat] :
% 9.49/5.23        ( ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.23        = ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_383_less__exp,axiom,
% 9.49/5.23      ! [N: nat] : ( ord_less_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_384_self__le__ge2__pow,axiom,
% 9.49/5.23      ! [K: nat,M: nat] :
% 9.49/5.23        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 9.49/5.23       => ( ord_less_eq_nat @ M @ ( power_power_nat @ K @ M ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_385_power2__nat__le__eq__le,axiom,
% 9.49/5.23      ! [M: nat,N: nat] :
% 9.49/5.23        ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.23        = ( ord_less_eq_nat @ M @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_386_power2__nat__le__imp__le,axiom,
% 9.49/5.23      ! [M: nat,N: nat] :
% 9.49/5.23        ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N )
% 9.49/5.23       => ( ord_less_eq_nat @ M @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_387_nested__mint,axiom,
% 9.49/5.23      ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,Va: nat] :
% 9.49/5.23        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 9.49/5.23       => ( ( N
% 9.49/5.23            = ( suc @ ( suc @ Va ) ) )
% 9.49/5.23         => ( ~ ( ord_less_nat @ Ma @ Mi )
% 9.49/5.23           => ( ( Ma != Mi )
% 9.49/5.23             => ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( suc @ ( divide_divide_nat @ Va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_388_both__member__options__from__chilf__to__complete__tree,axiom,
% 9.49/5.23      ! [X: nat,Deg: nat,TreeList: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 9.49/5.23        ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 9.49/5.23       => ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 9.49/5.23         => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.49/5.23           => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_389_post__member__pre__member,axiom,
% 9.49/5.23      ! [T: vEBT_VEBT,N: nat,X: nat,Y2: nat] :
% 9.49/5.23        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.23       => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.23         => ( ( ord_less_nat @ Y2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.23           => ( ( vEBT_vebt_member @ ( vEBT_vebt_insert @ T @ X ) @ Y2 )
% 9.49/5.23             => ( ( vEBT_vebt_member @ T @ Y2 )
% 9.49/5.23                | ( X = Y2 ) ) ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_390_both__member__options__from__complete__tree__to__child,axiom,
% 9.49/5.23      ! [Deg: nat,Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 9.49/5.23        ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 9.49/5.23       => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 9.49/5.23         => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.49/5.23            | ( X = Mi )
% 9.49/5.23            | ( X = Ma ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_391_summaxma,axiom,
% 9.49/5.23      ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 9.49/5.23        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg )
% 9.49/5.23       => ( ( Mi != Ma )
% 9.49/5.23         => ( ( the_nat @ ( vEBT_vebt_maxt @ Summary ) )
% 9.49/5.23            = ( vEBT_VEBT_high @ Ma @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_392_both__member__options__ding,axiom,
% 9.49/5.23      ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X: nat] :
% 9.49/5.23        ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N )
% 9.49/5.23       => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 9.49/5.23         => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.49/5.23           => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ X ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_393_member__bound,axiom,
% 9.49/5.23      ! [Tree: vEBT_VEBT,X: nat,N: nat] :
% 9.49/5.23        ( ( vEBT_vebt_member @ Tree @ X )
% 9.49/5.23       => ( ( vEBT_invar_vebt @ Tree @ N )
% 9.49/5.23         => ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_394_div__exp__eq,axiom,
% 9.49/5.23      ! [A: nat,M: nat,N: nat] :
% 9.49/5.23        ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.23        = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_395_div__exp__eq,axiom,
% 9.49/5.23      ! [A: int,M: nat,N: nat] :
% 9.49/5.23        ( ( divide_divide_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.23        = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_396_set__n__deg__not__0,axiom,
% 9.49/5.23      ! [TreeList: list_VEBT_VEBT,N: nat,M: nat] :
% 9.49/5.23        ( ! [X3: vEBT_VEBT] :
% 9.49/5.23            ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 9.49/5.23           => ( vEBT_invar_vebt @ X3 @ N ) )
% 9.49/5.23       => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 9.49/5.23            = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 9.49/5.23         => ( ord_less_eq_nat @ one_one_nat @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_397_field__less__half__sum,axiom,
% 9.49/5.23      ! [X: real,Y2: real] :
% 9.49/5.23        ( ( ord_less_real @ X @ Y2 )
% 9.49/5.23       => ( ord_less_real @ X @ ( divide_divide_real @ ( plus_plus_real @ X @ Y2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_398_field__less__half__sum,axiom,
% 9.49/5.23      ! [X: rat,Y2: rat] :
% 9.49/5.23        ( ( ord_less_rat @ X @ Y2 )
% 9.49/5.23       => ( ord_less_rat @ X @ ( divide_divide_rat @ ( plus_plus_rat @ X @ Y2 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_399_delt__out__of__range,axiom,
% 9.49/5.23      ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 9.49/5.23        ( ( ( ord_less_nat @ X @ Mi )
% 9.49/5.23          | ( ord_less_nat @ Ma @ X ) )
% 9.49/5.23       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 9.49/5.23         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 9.49/5.23            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_400_nat__1__eq__mult__iff,axiom,
% 9.49/5.23      ! [M: nat,N: nat] :
% 9.49/5.23        ( ( one_one_nat
% 9.49/5.23          = ( times_times_nat @ M @ N ) )
% 9.49/5.23        = ( ( M = one_one_nat )
% 9.49/5.23          & ( N = one_one_nat ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_401_even__odd__cases,axiom,
% 9.49/5.23      ! [X: nat] :
% 9.49/5.23        ( ! [N3: nat] :
% 9.49/5.23            ( X
% 9.49/5.23           != ( plus_plus_nat @ N3 @ N3 ) )
% 9.49/5.23       => ~ ! [N3: nat] :
% 9.49/5.23              ( X
% 9.49/5.23             != ( plus_plus_nat @ N3 @ ( suc @ N3 ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_402_delete__pres__valid,axiom,
% 9.49/5.23      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 9.49/5.23        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.23       => ( vEBT_invar_vebt @ ( vEBT_vebt_delete @ T @ X ) @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_403_deg__SUcn__Node,axiom,
% 9.49/5.23      ! [Tree: vEBT_VEBT,N: nat] :
% 9.49/5.23        ( ( vEBT_invar_vebt @ Tree @ ( suc @ ( suc @ N ) ) )
% 9.49/5.23       => ? [Info2: option4927543243414619207at_nat,TreeList2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 9.49/5.23            ( Tree
% 9.49/5.23            = ( vEBT_Node @ Info2 @ ( suc @ ( suc @ N ) ) @ TreeList2 @ S ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_404_dele__bmo__cont__corr,axiom,
% 9.49/5.23      ! [T: vEBT_VEBT,N: nat,X: nat,Y2: nat] :
% 9.49/5.23        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.23       => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ T @ X ) @ Y2 )
% 9.49/5.23          = ( ( X != Y2 )
% 9.49/5.23            & ( vEBT_V8194947554948674370ptions @ T @ Y2 ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_405_both__member__options__equiv__member,axiom,
% 9.49/5.23      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 9.49/5.23        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.23       => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 9.49/5.23          = ( vEBT_vebt_member @ T @ X ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_406_valid__member__both__member__options,axiom,
% 9.49/5.23      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 9.49/5.23        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.23       => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 9.49/5.23         => ( vEBT_vebt_member @ T @ X ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_407_dele__member__cont__corr,axiom,
% 9.49/5.23      ! [T: vEBT_VEBT,N: nat,X: nat,Y2: nat] :
% 9.49/5.23        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.23       => ( ( vEBT_vebt_member @ ( vEBT_vebt_delete @ T @ X ) @ Y2 )
% 9.49/5.23          = ( ( X != Y2 )
% 9.49/5.23            & ( vEBT_vebt_member @ T @ Y2 ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_408_inthall,axiom,
% 9.49/5.23      ! [Xs2: list_P6011104703257516679at_nat,P: product_prod_nat_nat > $o,N: nat] :
% 9.49/5.23        ( ! [X3: product_prod_nat_nat] :
% 9.49/5.23            ( ( member8440522571783428010at_nat @ X3 @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 9.49/5.23           => ( P @ X3 ) )
% 9.49/5.23       => ( ( ord_less_nat @ N @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 9.49/5.23         => ( P @ ( nth_Pr7617993195940197384at_nat @ Xs2 @ N ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_409_inthall,axiom,
% 9.49/5.23      ! [Xs2: list_complex,P: complex > $o,N: nat] :
% 9.49/5.23        ( ! [X3: complex] :
% 9.49/5.23            ( ( member_complex @ X3 @ ( set_complex2 @ Xs2 ) )
% 9.49/5.23           => ( P @ X3 ) )
% 9.49/5.23       => ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 9.49/5.23         => ( P @ ( nth_complex @ Xs2 @ N ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_410_inthall,axiom,
% 9.49/5.23      ! [Xs2: list_real,P: real > $o,N: nat] :
% 9.49/5.23        ( ! [X3: real] :
% 9.49/5.23            ( ( member_real @ X3 @ ( set_real2 @ Xs2 ) )
% 9.49/5.23           => ( P @ X3 ) )
% 9.49/5.23       => ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 9.49/5.23         => ( P @ ( nth_real @ Xs2 @ N ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_411_inthall,axiom,
% 9.49/5.23      ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o,N: nat] :
% 9.49/5.23        ( ! [X3: vEBT_VEBT] :
% 9.49/5.23            ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 9.49/5.23           => ( P @ X3 ) )
% 9.49/5.23       => ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 9.49/5.23         => ( P @ ( nth_VEBT_VEBT @ Xs2 @ N ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_412_inthall,axiom,
% 9.49/5.23      ! [Xs2: list_o,P: $o > $o,N: nat] :
% 9.49/5.23        ( ! [X3: $o] :
% 9.49/5.23            ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 9.49/5.23           => ( P @ X3 ) )
% 9.49/5.23       => ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 9.49/5.23         => ( P @ ( nth_o @ Xs2 @ N ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_413_inthall,axiom,
% 9.49/5.23      ! [Xs2: list_nat,P: nat > $o,N: nat] :
% 9.49/5.23        ( ! [X3: nat] :
% 9.49/5.23            ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 9.49/5.23           => ( P @ X3 ) )
% 9.49/5.23       => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 9.49/5.23         => ( P @ ( nth_nat @ Xs2 @ N ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_414_inthall,axiom,
% 9.49/5.23      ! [Xs2: list_int,P: int > $o,N: nat] :
% 9.49/5.23        ( ! [X3: int] :
% 9.49/5.23            ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 9.49/5.23           => ( P @ X3 ) )
% 9.49/5.23       => ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 9.49/5.23         => ( P @ ( nth_int @ Xs2 @ N ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_415_bit__split__inv,axiom,
% 9.49/5.23      ! [X: nat,D2: nat] :
% 9.49/5.23        ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X @ D2 ) @ ( vEBT_VEBT_low @ X @ D2 ) @ D2 )
% 9.49/5.23        = X ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_416_nat_Oinject,axiom,
% 9.49/5.23      ! [X23: nat,Y22: nat] :
% 9.49/5.23        ( ( ( suc @ X23 )
% 9.49/5.23          = ( suc @ Y22 ) )
% 9.49/5.23        = ( X23 = Y22 ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_417_old_Onat_Oinject,axiom,
% 9.49/5.23      ! [Nat: nat,Nat2: nat] :
% 9.49/5.23        ( ( ( suc @ Nat )
% 9.49/5.23          = ( suc @ Nat2 ) )
% 9.49/5.23        = ( Nat = Nat2 ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_418_real__divide__square__eq,axiom,
% 9.49/5.23      ! [R: real,A: real] :
% 9.49/5.23        ( ( divide_divide_real @ ( times_times_real @ R @ A ) @ ( times_times_real @ R @ R ) )
% 9.49/5.23        = ( divide_divide_real @ A @ R ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_419_height__compose__child,axiom,
% 9.49/5.23      ! [T: vEBT_VEBT,TreeList: list_VEBT_VEBT,Info: option4927543243414619207at_nat,Deg: nat,Summary: vEBT_VEBT] :
% 9.49/5.23        ( ( member_VEBT_VEBT @ T @ ( set_VEBT_VEBT2 @ TreeList ) )
% 9.49/5.23       => ( ord_less_eq_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( vEBT_VEBT_height @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_420_mi__eq__ma__no__ch,axiom,
% 9.49/5.23      ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 9.49/5.23        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg )
% 9.49/5.23       => ( ( Mi = Ma )
% 9.49/5.23         => ( ! [X5: vEBT_VEBT] :
% 9.49/5.23                ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 9.49/5.23               => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) )
% 9.49/5.23            & ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_421_low__inv,axiom,
% 9.49/5.23      ! [X: nat,N: nat,Y2: nat] :
% 9.49/5.23        ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.23       => ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ Y2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X ) @ N )
% 9.49/5.23          = X ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_422_bits__div__by__1,axiom,
% 9.49/5.23      ! [A: nat] :
% 9.49/5.23        ( ( divide_divide_nat @ A @ one_one_nat )
% 9.49/5.23        = A ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_423_bits__div__by__1,axiom,
% 9.49/5.23      ! [A: int] :
% 9.49/5.23        ( ( divide_divide_int @ A @ one_one_int )
% 9.49/5.23        = A ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_424_lessI,axiom,
% 9.49/5.23      ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_425_Suc__mono,axiom,
% 9.49/5.23      ! [M: nat,N: nat] :
% 9.49/5.23        ( ( ord_less_nat @ M @ N )
% 9.49/5.23       => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_426_Suc__less__eq,axiom,
% 9.49/5.23      ! [M: nat,N: nat] :
% 9.49/5.23        ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 9.49/5.23        = ( ord_less_nat @ M @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_427_add__Suc__right,axiom,
% 9.49/5.23      ! [M: nat,N: nat] :
% 9.49/5.23        ( ( plus_plus_nat @ M @ ( suc @ N ) )
% 9.49/5.23        = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_428_Suc__le__mono,axiom,
% 9.49/5.23      ! [N: nat,M: nat] :
% 9.49/5.23        ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
% 9.49/5.23        = ( ord_less_eq_nat @ N @ M ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_429_nat__add__left__cancel__less,axiom,
% 9.49/5.23      ! [K: nat,M: nat,N: nat] :
% 9.49/5.23        ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 9.49/5.23        = ( ord_less_nat @ M @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_430_nat__add__left__cancel__le,axiom,
% 9.49/5.23      ! [K: nat,M: nat,N: nat] :
% 9.49/5.23        ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 9.49/5.23        = ( ord_less_eq_nat @ M @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_431_nat__mult__eq__1__iff,axiom,
% 9.49/5.23      ! [M: nat,N: nat] :
% 9.49/5.23        ( ( ( times_times_nat @ M @ N )
% 9.49/5.23          = one_one_nat )
% 9.49/5.23        = ( ( M = one_one_nat )
% 9.49/5.23          & ( N = one_one_nat ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_432_member__correct,axiom,
% 9.49/5.23      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 9.49/5.23        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.23       => ( ( vEBT_vebt_member @ T @ X )
% 9.49/5.23          = ( member_nat @ X @ ( vEBT_set_vebt @ T ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_433_mult__Suc__right,axiom,
% 9.49/5.23      ! [M: nat,N: nat] :
% 9.49/5.23        ( ( times_times_nat @ M @ ( suc @ N ) )
% 9.49/5.23        = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_434_member__inv,axiom,
% 9.49/5.23      ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 9.49/5.23        ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 9.49/5.23       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 9.49/5.23          & ( ( X = Mi )
% 9.49/5.23            | ( X = Ma )
% 9.49/5.23            | ( ( ord_less_nat @ X @ Ma )
% 9.49/5.23              & ( ord_less_nat @ Mi @ X )
% 9.49/5.23              & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 9.49/5.23              & ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_435_Suc__numeral,axiom,
% 9.49/5.23      ! [N: num] :
% 9.49/5.23        ( ( suc @ ( numeral_numeral_nat @ N ) )
% 9.49/5.23        = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_436_add__2__eq__Suc_H,axiom,
% 9.49/5.23      ! [N: nat] :
% 9.49/5.23        ( ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.23        = ( suc @ ( suc @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_437_add__2__eq__Suc,axiom,
% 9.49/5.23      ! [N: nat] :
% 9.49/5.23        ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.23        = ( suc @ ( suc @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_438_Suc__1,axiom,
% 9.49/5.23      ( ( suc @ one_one_nat )
% 9.49/5.23      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_439_div2__Suc__Suc,axiom,
% 9.49/5.23      ! [M: nat] :
% 9.49/5.23        ( ( divide_divide_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.23        = ( suc @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_440_Suc__div__eq__add3__div__numeral,axiom,
% 9.49/5.23      ! [M: nat,V: num] :
% 9.49/5.23        ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 9.49/5.23        = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_441_div__Suc__eq__div__add3,axiom,
% 9.49/5.23      ! [M: nat,N: nat] :
% 9.49/5.23        ( ( divide_divide_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 9.49/5.23        = ( divide_divide_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_442_complete__real,axiom,
% 9.49/5.23      ! [S2: set_real] :
% 9.49/5.23        ( ? [X5: real] : ( member_real @ X5 @ S2 )
% 9.49/5.23       => ( ? [Z2: real] :
% 9.49/5.23            ! [X3: real] :
% 9.49/5.23              ( ( member_real @ X3 @ S2 )
% 9.49/5.23             => ( ord_less_eq_real @ X3 @ Z2 ) )
% 9.49/5.23         => ? [Y3: real] :
% 9.49/5.23              ( ! [X5: real] :
% 9.49/5.23                  ( ( member_real @ X5 @ S2 )
% 9.49/5.23                 => ( ord_less_eq_real @ X5 @ Y3 ) )
% 9.49/5.23              & ! [Z2: real] :
% 9.49/5.23                  ( ! [X3: real] :
% 9.49/5.23                      ( ( member_real @ X3 @ S2 )
% 9.49/5.23                     => ( ord_less_eq_real @ X3 @ Z2 ) )
% 9.49/5.23                 => ( ord_less_eq_real @ Y3 @ Z2 ) ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_443_real__arch__pow,axiom,
% 9.49/5.23      ! [X: real,Y2: real] :
% 9.49/5.23        ( ( ord_less_real @ one_one_real @ X )
% 9.49/5.23       => ? [N3: nat] : ( ord_less_real @ Y2 @ ( power_power_real @ X @ N3 ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_444_less__eq__real__def,axiom,
% 9.49/5.23      ( ord_less_eq_real
% 9.49/5.23      = ( ^ [X2: real,Y: real] :
% 9.49/5.23            ( ( ord_less_real @ X2 @ Y )
% 9.49/5.23            | ( X2 = Y ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_445_Suc__inject,axiom,
% 9.49/5.23      ! [X: nat,Y2: nat] :
% 9.49/5.23        ( ( ( suc @ X )
% 9.49/5.23          = ( suc @ Y2 ) )
% 9.49/5.23       => ( X = Y2 ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_446_n__not__Suc__n,axiom,
% 9.49/5.23      ! [N: nat] :
% 9.49/5.23        ( N
% 9.49/5.23       != ( suc @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_447_Nat_OlessE,axiom,
% 9.49/5.23      ! [I2: nat,K: nat] :
% 9.49/5.23        ( ( ord_less_nat @ I2 @ K )
% 9.49/5.23       => ( ( K
% 9.49/5.23           != ( suc @ I2 ) )
% 9.49/5.23         => ~ ! [J2: nat] :
% 9.49/5.23                ( ( ord_less_nat @ I2 @ J2 )
% 9.49/5.23               => ( K
% 9.49/5.23                 != ( suc @ J2 ) ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_448_Suc__lessD,axiom,
% 9.49/5.23      ! [M: nat,N: nat] :
% 9.49/5.23        ( ( ord_less_nat @ ( suc @ M ) @ N )
% 9.49/5.23       => ( ord_less_nat @ M @ N ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_449_Suc__lessE,axiom,
% 9.49/5.23      ! [I2: nat,K: nat] :
% 9.49/5.23        ( ( ord_less_nat @ ( suc @ I2 ) @ K )
% 9.49/5.23       => ~ ! [J2: nat] :
% 9.49/5.23              ( ( ord_less_nat @ I2 @ J2 )
% 9.49/5.23             => ( K
% 9.49/5.23               != ( suc @ J2 ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_450_Suc__lessI,axiom,
% 9.49/5.23      ! [M: nat,N: nat] :
% 9.49/5.23        ( ( ord_less_nat @ M @ N )
% 9.49/5.23       => ( ( ( suc @ M )
% 9.49/5.23           != N )
% 9.49/5.23         => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_451_less__SucE,axiom,
% 9.49/5.23      ! [M: nat,N: nat] :
% 9.49/5.23        ( ( ord_less_nat @ M @ ( suc @ N ) )
% 9.49/5.23       => ( ~ ( ord_less_nat @ M @ N )
% 9.49/5.23         => ( M = N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_452_less__SucI,axiom,
% 9.49/5.23      ! [M: nat,N: nat] :
% 9.49/5.23        ( ( ord_less_nat @ M @ N )
% 9.49/5.23       => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_453_Ex__less__Suc,axiom,
% 9.49/5.23      ! [N: nat,P: nat > $o] :
% 9.49/5.23        ( ( ? [I3: nat] :
% 9.49/5.23              ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 9.49/5.23              & ( P @ I3 ) ) )
% 9.49/5.23        = ( ( P @ N )
% 9.49/5.23          | ? [I3: nat] :
% 9.49/5.23              ( ( ord_less_nat @ I3 @ N )
% 9.49/5.23              & ( P @ I3 ) ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_454_less__Suc__eq,axiom,
% 9.49/5.23      ! [M: nat,N: nat] :
% 9.49/5.23        ( ( ord_less_nat @ M @ ( suc @ N ) )
% 9.49/5.23        = ( ( ord_less_nat @ M @ N )
% 9.49/5.23          | ( M = N ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_455_not__less__eq,axiom,
% 9.49/5.23      ! [M: nat,N: nat] :
% 9.49/5.23        ( ( ~ ( ord_less_nat @ M @ N ) )
% 9.49/5.23        = ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 9.49/5.23  
% 9.49/5.23  thf(fact_456_All__less__Suc,axiom,
% 9.49/5.23      ! [N: nat,P: nat > $o] :
% 9.49/5.23        ( ( ! [I3: nat] :
% 9.49/5.23              ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 9.49/5.23             => ( P @ I3 ) ) )
% 9.49/5.23        = ( ( P @ N )
% 9.49/5.24          & ! [I3: nat] :
% 9.49/5.24              ( ( ord_less_nat @ I3 @ N )
% 9.49/5.24             => ( P @ I3 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_457_Suc__less__eq2,axiom,
% 9.49/5.24      ! [N: nat,M: nat] :
% 9.49/5.24        ( ( ord_less_nat @ ( suc @ N ) @ M )
% 9.49/5.24        = ( ? [M2: nat] :
% 9.49/5.24              ( ( M
% 9.49/5.24                = ( suc @ M2 ) )
% 9.49/5.24              & ( ord_less_nat @ N @ M2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_458_less__antisym,axiom,
% 9.49/5.24      ! [N: nat,M: nat] :
% 9.49/5.24        ( ~ ( ord_less_nat @ N @ M )
% 9.49/5.24       => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 9.49/5.24         => ( M = N ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_459_Suc__less__SucD,axiom,
% 9.49/5.24      ! [M: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 9.49/5.24       => ( ord_less_nat @ M @ N ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_460_less__trans__Suc,axiom,
% 9.49/5.24      ! [I2: nat,J: nat,K: nat] :
% 9.49/5.24        ( ( ord_less_nat @ I2 @ J )
% 9.49/5.24       => ( ( ord_less_nat @ J @ K )
% 9.49/5.24         => ( ord_less_nat @ ( suc @ I2 ) @ K ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_461_less__Suc__induct,axiom,
% 9.49/5.24      ! [I2: nat,J: nat,P: nat > nat > $o] :
% 9.49/5.24        ( ( ord_less_nat @ I2 @ J )
% 9.49/5.24       => ( ! [I4: nat] : ( P @ I4 @ ( suc @ I4 ) )
% 9.49/5.24         => ( ! [I4: nat,J2: nat,K2: nat] :
% 9.49/5.24                ( ( ord_less_nat @ I4 @ J2 )
% 9.49/5.24               => ( ( ord_less_nat @ J2 @ K2 )
% 9.49/5.24                 => ( ( P @ I4 @ J2 )
% 9.49/5.24                   => ( ( P @ J2 @ K2 )
% 9.49/5.24                     => ( P @ I4 @ K2 ) ) ) ) )
% 9.49/5.24           => ( P @ I2 @ J ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_462_strict__inc__induct,axiom,
% 9.49/5.24      ! [I2: nat,J: nat,P: nat > $o] :
% 9.49/5.24        ( ( ord_less_nat @ I2 @ J )
% 9.49/5.24       => ( ! [I4: nat] :
% 9.49/5.24              ( ( J
% 9.49/5.24                = ( suc @ I4 ) )
% 9.49/5.24             => ( P @ I4 ) )
% 9.49/5.24         => ( ! [I4: nat] :
% 9.49/5.24                ( ( ord_less_nat @ I4 @ J )
% 9.49/5.24               => ( ( P @ ( suc @ I4 ) )
% 9.49/5.24                 => ( P @ I4 ) ) )
% 9.49/5.24           => ( P @ I2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_463_not__less__less__Suc__eq,axiom,
% 9.49/5.24      ! [N: nat,M: nat] :
% 9.49/5.24        ( ~ ( ord_less_nat @ N @ M )
% 9.49/5.24       => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 9.49/5.24          = ( N = M ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_464_add__Suc__shift,axiom,
% 9.49/5.24      ! [M: nat,N: nat] :
% 9.49/5.24        ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 9.49/5.24        = ( plus_plus_nat @ M @ ( suc @ N ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_465_add__Suc,axiom,
% 9.49/5.24      ! [M: nat,N: nat] :
% 9.49/5.24        ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 9.49/5.24        = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_466_nat__arith_Osuc1,axiom,
% 9.49/5.24      ! [A2: nat,K: nat,A: nat] :
% 9.49/5.24        ( ( A2
% 9.49/5.24          = ( plus_plus_nat @ K @ A ) )
% 9.49/5.24       => ( ( suc @ A2 )
% 9.49/5.24          = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_467_Suc__leD,axiom,
% 9.49/5.24      ! [M: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 9.49/5.24       => ( ord_less_eq_nat @ M @ N ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_468_le__SucE,axiom,
% 9.49/5.24      ! [M: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 9.49/5.24       => ( ~ ( ord_less_eq_nat @ M @ N )
% 9.49/5.24         => ( M
% 9.49/5.24            = ( suc @ N ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_469_le__SucI,axiom,
% 9.49/5.24      ! [M: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.24       => ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_470_Suc__le__D,axiom,
% 9.49/5.24      ! [N: nat,M3: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ ( suc @ N ) @ M3 )
% 9.49/5.24       => ? [M4: nat] :
% 9.49/5.24            ( M3
% 9.49/5.24            = ( suc @ M4 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_471_le__Suc__eq,axiom,
% 9.49/5.24      ! [M: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 9.49/5.24        = ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.24          | ( M
% 9.49/5.24            = ( suc @ N ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_472_Suc__n__not__le__n,axiom,
% 9.49/5.24      ! [N: nat] :
% 9.49/5.24        ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_473_not__less__eq__eq,axiom,
% 9.49/5.24      ! [M: nat,N: nat] :
% 9.49/5.24        ( ( ~ ( ord_less_eq_nat @ M @ N ) )
% 9.49/5.24        = ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_474_full__nat__induct,axiom,
% 9.49/5.24      ! [P: nat > $o,N: nat] :
% 9.49/5.24        ( ! [N3: nat] :
% 9.49/5.24            ( ! [M5: nat] :
% 9.49/5.24                ( ( ord_less_eq_nat @ ( suc @ M5 ) @ N3 )
% 9.49/5.24               => ( P @ M5 ) )
% 9.49/5.24           => ( P @ N3 ) )
% 9.49/5.24       => ( P @ N ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_475_nat__induct__at__least,axiom,
% 9.49/5.24      ! [M: nat,N: nat,P: nat > $o] :
% 9.49/5.24        ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.24       => ( ( P @ M )
% 9.49/5.24         => ( ! [N3: nat] :
% 9.49/5.24                ( ( ord_less_eq_nat @ M @ N3 )
% 9.49/5.24               => ( ( P @ N3 )
% 9.49/5.24                 => ( P @ ( suc @ N3 ) ) ) )
% 9.49/5.24           => ( P @ N ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_476_transitive__stepwise__le,axiom,
% 9.49/5.24      ! [M: nat,N: nat,R2: nat > nat > $o] :
% 9.49/5.24        ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.24       => ( ! [X3: nat] : ( R2 @ X3 @ X3 )
% 9.49/5.24         => ( ! [X3: nat,Y3: nat,Z3: nat] :
% 9.49/5.24                ( ( R2 @ X3 @ Y3 )
% 9.49/5.24               => ( ( R2 @ Y3 @ Z3 )
% 9.49/5.24                 => ( R2 @ X3 @ Z3 ) ) )
% 9.49/5.24           => ( ! [N3: nat] : ( R2 @ N3 @ ( suc @ N3 ) )
% 9.49/5.24             => ( R2 @ M @ N ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_477_Suc__mult__cancel1,axiom,
% 9.49/5.24      ! [K: nat,M: nat,N: nat] :
% 9.49/5.24        ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 9.49/5.24          = ( times_times_nat @ ( suc @ K ) @ N ) )
% 9.49/5.24        = ( M = N ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_478_lift__Suc__mono__less,axiom,
% 9.49/5.24      ! [F: nat > real,N: nat,N5: nat] :
% 9.49/5.24        ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 9.49/5.24       => ( ( ord_less_nat @ N @ N5 )
% 9.49/5.24         => ( ord_less_real @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_479_lift__Suc__mono__less,axiom,
% 9.49/5.24      ! [F: nat > rat,N: nat,N5: nat] :
% 9.49/5.24        ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 9.49/5.24       => ( ( ord_less_nat @ N @ N5 )
% 9.49/5.24         => ( ord_less_rat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_480_lift__Suc__mono__less,axiom,
% 9.49/5.24      ! [F: nat > num,N: nat,N5: nat] :
% 9.49/5.24        ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 9.49/5.24       => ( ( ord_less_nat @ N @ N5 )
% 9.49/5.24         => ( ord_less_num @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_481_lift__Suc__mono__less,axiom,
% 9.49/5.24      ! [F: nat > nat,N: nat,N5: nat] :
% 9.49/5.24        ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 9.49/5.24       => ( ( ord_less_nat @ N @ N5 )
% 9.49/5.24         => ( ord_less_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_482_lift__Suc__mono__less,axiom,
% 9.49/5.24      ! [F: nat > int,N: nat,N5: nat] :
% 9.49/5.24        ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 9.49/5.24       => ( ( ord_less_nat @ N @ N5 )
% 9.49/5.24         => ( ord_less_int @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_483_lift__Suc__mono__less__iff,axiom,
% 9.49/5.24      ! [F: nat > real,N: nat,M: nat] :
% 9.49/5.24        ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 9.49/5.24       => ( ( ord_less_real @ ( F @ N ) @ ( F @ M ) )
% 9.49/5.24          = ( ord_less_nat @ N @ M ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_484_lift__Suc__mono__less__iff,axiom,
% 9.49/5.24      ! [F: nat > rat,N: nat,M: nat] :
% 9.49/5.24        ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 9.49/5.24       => ( ( ord_less_rat @ ( F @ N ) @ ( F @ M ) )
% 9.49/5.24          = ( ord_less_nat @ N @ M ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_485_lift__Suc__mono__less__iff,axiom,
% 9.49/5.24      ! [F: nat > num,N: nat,M: nat] :
% 9.49/5.24        ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 9.49/5.24       => ( ( ord_less_num @ ( F @ N ) @ ( F @ M ) )
% 9.49/5.24          = ( ord_less_nat @ N @ M ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_486_lift__Suc__mono__less__iff,axiom,
% 9.49/5.24      ! [F: nat > nat,N: nat,M: nat] :
% 9.49/5.24        ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 9.49/5.24       => ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
% 9.49/5.24          = ( ord_less_nat @ N @ M ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_487_lift__Suc__mono__less__iff,axiom,
% 9.49/5.24      ! [F: nat > int,N: nat,M: nat] :
% 9.49/5.24        ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 9.49/5.24       => ( ( ord_less_int @ ( F @ N ) @ ( F @ M ) )
% 9.49/5.24          = ( ord_less_nat @ N @ M ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_488_lift__Suc__mono__le,axiom,
% 9.49/5.24      ! [F: nat > set_real,N: nat,N5: nat] :
% 9.49/5.24        ( ! [N3: nat] : ( ord_less_eq_set_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 9.49/5.24       => ( ( ord_less_eq_nat @ N @ N5 )
% 9.49/5.24         => ( ord_less_eq_set_real @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_489_lift__Suc__mono__le,axiom,
% 9.49/5.24      ! [F: nat > set_nat,N: nat,N5: nat] :
% 9.49/5.24        ( ! [N3: nat] : ( ord_less_eq_set_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 9.49/5.24       => ( ( ord_less_eq_nat @ N @ N5 )
% 9.49/5.24         => ( ord_less_eq_set_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_490_lift__Suc__mono__le,axiom,
% 9.49/5.24      ! [F: nat > num,N: nat,N5: nat] :
% 9.49/5.24        ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 9.49/5.24       => ( ( ord_less_eq_nat @ N @ N5 )
% 9.49/5.24         => ( ord_less_eq_num @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_491_lift__Suc__mono__le,axiom,
% 9.49/5.24      ! [F: nat > nat,N: nat,N5: nat] :
% 9.49/5.24        ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 9.49/5.24       => ( ( ord_less_eq_nat @ N @ N5 )
% 9.49/5.24         => ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_492_lift__Suc__mono__le,axiom,
% 9.49/5.24      ! [F: nat > int,N: nat,N5: nat] :
% 9.49/5.24        ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 9.49/5.24       => ( ( ord_less_eq_nat @ N @ N5 )
% 9.49/5.24         => ( ord_less_eq_int @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_493_lift__Suc__antimono__le,axiom,
% 9.49/5.24      ! [F: nat > set_real,N: nat,N5: nat] :
% 9.49/5.24        ( ! [N3: nat] : ( ord_less_eq_set_real @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 9.49/5.24       => ( ( ord_less_eq_nat @ N @ N5 )
% 9.49/5.24         => ( ord_less_eq_set_real @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_494_lift__Suc__antimono__le,axiom,
% 9.49/5.24      ! [F: nat > set_nat,N: nat,N5: nat] :
% 9.49/5.24        ( ! [N3: nat] : ( ord_less_eq_set_nat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 9.49/5.24       => ( ( ord_less_eq_nat @ N @ N5 )
% 9.49/5.24         => ( ord_less_eq_set_nat @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_495_lift__Suc__antimono__le,axiom,
% 9.49/5.24      ! [F: nat > num,N: nat,N5: nat] :
% 9.49/5.24        ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 9.49/5.24       => ( ( ord_less_eq_nat @ N @ N5 )
% 9.49/5.24         => ( ord_less_eq_num @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_496_lift__Suc__antimono__le,axiom,
% 9.49/5.24      ! [F: nat > nat,N: nat,N5: nat] :
% 9.49/5.24        ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 9.49/5.24       => ( ( ord_less_eq_nat @ N @ N5 )
% 9.49/5.24         => ( ord_less_eq_nat @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_497_lift__Suc__antimono__le,axiom,
% 9.49/5.24      ! [F: nat > int,N: nat,N5: nat] :
% 9.49/5.24        ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 9.49/5.24       => ( ( ord_less_eq_nat @ N @ N5 )
% 9.49/5.24         => ( ord_less_eq_int @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_498_less__imp__Suc__add,axiom,
% 9.49/5.24      ! [M: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_nat @ M @ N )
% 9.49/5.24       => ? [K2: nat] :
% 9.49/5.24            ( N
% 9.49/5.24            = ( suc @ ( plus_plus_nat @ M @ K2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_499_less__iff__Suc__add,axiom,
% 9.49/5.24      ( ord_less_nat
% 9.49/5.24      = ( ^ [M6: nat,N2: nat] :
% 9.49/5.24          ? [K3: nat] :
% 9.49/5.24            ( N2
% 9.49/5.24            = ( suc @ ( plus_plus_nat @ M6 @ K3 ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_500_less__add__Suc2,axiom,
% 9.49/5.24      ! [I2: nat,M: nat] : ( ord_less_nat @ I2 @ ( suc @ ( plus_plus_nat @ M @ I2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_501_less__add__Suc1,axiom,
% 9.49/5.24      ! [I2: nat,M: nat] : ( ord_less_nat @ I2 @ ( suc @ ( plus_plus_nat @ I2 @ M ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_502_less__natE,axiom,
% 9.49/5.24      ! [M: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_nat @ M @ N )
% 9.49/5.24       => ~ ! [Q3: nat] :
% 9.49/5.24              ( N
% 9.49/5.24             != ( suc @ ( plus_plus_nat @ M @ Q3 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_503_Suc__leI,axiom,
% 9.49/5.24      ! [M: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_nat @ M @ N )
% 9.49/5.24       => ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_504_Suc__le__eq,axiom,
% 9.49/5.24      ! [M: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 9.49/5.24        = ( ord_less_nat @ M @ N ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_505_dec__induct,axiom,
% 9.49/5.24      ! [I2: nat,J: nat,P: nat > $o] :
% 9.49/5.24        ( ( ord_less_eq_nat @ I2 @ J )
% 9.49/5.24       => ( ( P @ I2 )
% 9.49/5.24         => ( ! [N3: nat] :
% 9.49/5.24                ( ( ord_less_eq_nat @ I2 @ N3 )
% 9.49/5.24               => ( ( ord_less_nat @ N3 @ J )
% 9.49/5.24                 => ( ( P @ N3 )
% 9.49/5.24                   => ( P @ ( suc @ N3 ) ) ) ) )
% 9.49/5.24           => ( P @ J ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_506_inc__induct,axiom,
% 9.49/5.24      ! [I2: nat,J: nat,P: nat > $o] :
% 9.49/5.24        ( ( ord_less_eq_nat @ I2 @ J )
% 9.49/5.24       => ( ( P @ J )
% 9.49/5.24         => ( ! [N3: nat] :
% 9.49/5.24                ( ( ord_less_eq_nat @ I2 @ N3 )
% 9.49/5.24               => ( ( ord_less_nat @ N3 @ J )
% 9.49/5.24                 => ( ( P @ ( suc @ N3 ) )
% 9.49/5.24                   => ( P @ N3 ) ) ) )
% 9.49/5.24           => ( P @ I2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_507_Suc__le__lessD,axiom,
% 9.49/5.24      ! [M: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 9.49/5.24       => ( ord_less_nat @ M @ N ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_508_le__less__Suc__eq,axiom,
% 9.49/5.24      ! [M: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.24       => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 9.49/5.24          = ( N = M ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_509_less__Suc__eq__le,axiom,
% 9.49/5.24      ! [M: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_nat @ M @ ( suc @ N ) )
% 9.49/5.24        = ( ord_less_eq_nat @ M @ N ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_510_less__eq__Suc__le,axiom,
% 9.49/5.24      ( ord_less_nat
% 9.49/5.24      = ( ^ [N2: nat] : ( ord_less_eq_nat @ ( suc @ N2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_511_le__imp__less__Suc,axiom,
% 9.49/5.24      ! [M: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.24       => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_512_Suc__eq__plus1__left,axiom,
% 9.49/5.24      ( suc
% 9.49/5.24      = ( plus_plus_nat @ one_one_nat ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_513_plus__1__eq__Suc,axiom,
% 9.49/5.24      ( ( plus_plus_nat @ one_one_nat )
% 9.49/5.24      = suc ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_514_Suc__eq__plus1,axiom,
% 9.49/5.24      ( suc
% 9.49/5.24      = ( ^ [N2: nat] : ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_515_Suc__mult__less__cancel1,axiom,
% 9.49/5.24      ! [K: nat,M: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 9.49/5.24        = ( ord_less_nat @ M @ N ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_516_mult__Suc,axiom,
% 9.49/5.24      ! [M: nat,N: nat] :
% 9.49/5.24        ( ( times_times_nat @ ( suc @ M ) @ N )
% 9.49/5.24        = ( plus_plus_nat @ N @ ( times_times_nat @ M @ N ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_517_Suc__mult__le__cancel1,axiom,
% 9.49/5.24      ! [K: nat,M: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 9.49/5.24        = ( ord_less_eq_nat @ M @ N ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_518_power__Suc,axiom,
% 9.49/5.24      ! [A: complex,N: nat] :
% 9.49/5.24        ( ( power_power_complex @ A @ ( suc @ N ) )
% 9.49/5.24        = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_519_power__Suc,axiom,
% 9.49/5.24      ! [A: real,N: nat] :
% 9.49/5.24        ( ( power_power_real @ A @ ( suc @ N ) )
% 9.49/5.24        = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_520_power__Suc,axiom,
% 9.49/5.24      ! [A: nat,N: nat] :
% 9.49/5.24        ( ( power_power_nat @ A @ ( suc @ N ) )
% 9.49/5.24        = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_521_power__Suc,axiom,
% 9.49/5.24      ! [A: int,N: nat] :
% 9.49/5.24        ( ( power_power_int @ A @ ( suc @ N ) )
% 9.49/5.24        = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_522_power__Suc2,axiom,
% 9.49/5.24      ! [A: complex,N: nat] :
% 9.49/5.24        ( ( power_power_complex @ A @ ( suc @ N ) )
% 9.49/5.24        = ( times_times_complex @ ( power_power_complex @ A @ N ) @ A ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_523_power__Suc2,axiom,
% 9.49/5.24      ! [A: real,N: nat] :
% 9.49/5.24        ( ( power_power_real @ A @ ( suc @ N ) )
% 9.49/5.24        = ( times_times_real @ ( power_power_real @ A @ N ) @ A ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_524_power__Suc2,axiom,
% 9.49/5.24      ! [A: nat,N: nat] :
% 9.49/5.24        ( ( power_power_nat @ A @ ( suc @ N ) )
% 9.49/5.24        = ( times_times_nat @ ( power_power_nat @ A @ N ) @ A ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_525_power__Suc2,axiom,
% 9.49/5.24      ! [A: int,N: nat] :
% 9.49/5.24        ( ( power_power_int @ A @ ( suc @ N ) )
% 9.49/5.24        = ( times_times_int @ ( power_power_int @ A @ N ) @ A ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_526_Suc__div__le__mono,axiom,
% 9.49/5.24      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ ( divide_divide_nat @ ( suc @ M ) @ N ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_527_power__gt1,axiom,
% 9.49/5.24      ! [A: real,N: nat] :
% 9.49/5.24        ( ( ord_less_real @ one_one_real @ A )
% 9.49/5.24       => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ ( suc @ N ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_528_power__gt1,axiom,
% 9.49/5.24      ! [A: rat,N: nat] :
% 9.49/5.24        ( ( ord_less_rat @ one_one_rat @ A )
% 9.49/5.24       => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_529_power__gt1,axiom,
% 9.49/5.24      ! [A: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_nat @ one_one_nat @ A )
% 9.49/5.24       => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_530_power__gt1,axiom,
% 9.49/5.24      ! [A: int,N: nat] :
% 9.49/5.24        ( ( ord_less_int @ one_one_int @ A )
% 9.49/5.24       => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_531_eval__nat__numeral_I3_J,axiom,
% 9.49/5.24      ! [N: num] :
% 9.49/5.24        ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 9.49/5.24        = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_532_nat__neq__iff,axiom,
% 9.49/5.24      ! [M: nat,N: nat] :
% 9.49/5.24        ( ( M != N )
% 9.49/5.24        = ( ( ord_less_nat @ M @ N )
% 9.49/5.24          | ( ord_less_nat @ N @ M ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_533_less__not__refl,axiom,
% 9.49/5.24      ! [N: nat] :
% 9.49/5.24        ~ ( ord_less_nat @ N @ N ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_534_less__not__refl2,axiom,
% 9.49/5.24      ! [N: nat,M: nat] :
% 9.49/5.24        ( ( ord_less_nat @ N @ M )
% 9.49/5.24       => ( M != N ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_535_less__not__refl3,axiom,
% 9.49/5.24      ! [S3: nat,T: nat] :
% 9.49/5.24        ( ( ord_less_nat @ S3 @ T )
% 9.49/5.24       => ( S3 != T ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_536_less__irrefl__nat,axiom,
% 9.49/5.24      ! [N: nat] :
% 9.49/5.24        ~ ( ord_less_nat @ N @ N ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_537_nat__less__induct,axiom,
% 9.49/5.24      ! [P: nat > $o,N: nat] :
% 9.49/5.24        ( ! [N3: nat] :
% 9.49/5.24            ( ! [M5: nat] :
% 9.49/5.24                ( ( ord_less_nat @ M5 @ N3 )
% 9.49/5.24               => ( P @ M5 ) )
% 9.49/5.24           => ( P @ N3 ) )
% 9.49/5.24       => ( P @ N ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_538_infinite__descent,axiom,
% 9.49/5.24      ! [P: nat > $o,N: nat] :
% 9.49/5.24        ( ! [N3: nat] :
% 9.49/5.24            ( ~ ( P @ N3 )
% 9.49/5.24           => ? [M5: nat] :
% 9.49/5.24                ( ( ord_less_nat @ M5 @ N3 )
% 9.49/5.24                & ~ ( P @ M5 ) ) )
% 9.49/5.24       => ( P @ N ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_539_linorder__neqE__nat,axiom,
% 9.49/5.24      ! [X: nat,Y2: nat] :
% 9.49/5.24        ( ( X != Y2 )
% 9.49/5.24       => ( ~ ( ord_less_nat @ X @ Y2 )
% 9.49/5.24         => ( ord_less_nat @ Y2 @ X ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_540_le__refl,axiom,
% 9.49/5.24      ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_541_le__trans,axiom,
% 9.49/5.24      ! [I2: nat,J: nat,K: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ I2 @ J )
% 9.49/5.24       => ( ( ord_less_eq_nat @ J @ K )
% 9.49/5.24         => ( ord_less_eq_nat @ I2 @ K ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_542_eq__imp__le,axiom,
% 9.49/5.24      ! [M: nat,N: nat] :
% 9.49/5.24        ( ( M = N )
% 9.49/5.24       => ( ord_less_eq_nat @ M @ N ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_543_le__antisym,axiom,
% 9.49/5.24      ! [M: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.24       => ( ( ord_less_eq_nat @ N @ M )
% 9.49/5.24         => ( M = N ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_544_nat__le__linear,axiom,
% 9.49/5.24      ! [M: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.24        | ( ord_less_eq_nat @ N @ M ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_545_Nat_Oex__has__greatest__nat,axiom,
% 9.49/5.24      ! [P: nat > $o,K: nat,B: nat] :
% 9.49/5.24        ( ( P @ K )
% 9.49/5.24       => ( ! [Y3: nat] :
% 9.49/5.24              ( ( P @ Y3 )
% 9.49/5.24             => ( ord_less_eq_nat @ Y3 @ B ) )
% 9.49/5.24         => ? [X3: nat] :
% 9.49/5.24              ( ( P @ X3 )
% 9.49/5.24              & ! [Y4: nat] :
% 9.49/5.24                  ( ( P @ Y4 )
% 9.49/5.24                 => ( ord_less_eq_nat @ Y4 @ X3 ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_546_size__neq__size__imp__neq,axiom,
% 9.49/5.24      ! [X: list_VEBT_VEBT,Y2: list_VEBT_VEBT] :
% 9.49/5.24        ( ( ( size_s6755466524823107622T_VEBT @ X )
% 9.49/5.24         != ( size_s6755466524823107622T_VEBT @ Y2 ) )
% 9.49/5.24       => ( X != Y2 ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_547_size__neq__size__imp__neq,axiom,
% 9.49/5.24      ! [X: list_o,Y2: list_o] :
% 9.49/5.24        ( ( ( size_size_list_o @ X )
% 9.49/5.24         != ( size_size_list_o @ Y2 ) )
% 9.49/5.24       => ( X != Y2 ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_548_size__neq__size__imp__neq,axiom,
% 9.49/5.24      ! [X: list_nat,Y2: list_nat] :
% 9.49/5.24        ( ( ( size_size_list_nat @ X )
% 9.49/5.24         != ( size_size_list_nat @ Y2 ) )
% 9.49/5.24       => ( X != Y2 ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_549_size__neq__size__imp__neq,axiom,
% 9.49/5.24      ! [X: list_int,Y2: list_int] :
% 9.49/5.24        ( ( ( size_size_list_int @ X )
% 9.49/5.24         != ( size_size_list_int @ Y2 ) )
% 9.49/5.24       => ( X != Y2 ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_550_size__neq__size__imp__neq,axiom,
% 9.49/5.24      ! [X: num,Y2: num] :
% 9.49/5.24        ( ( ( size_size_num @ X )
% 9.49/5.24         != ( size_size_num @ Y2 ) )
% 9.49/5.24       => ( X != Y2 ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_551_Suc3__eq__add__3,axiom,
% 9.49/5.24      ! [N: nat] :
% 9.49/5.24        ( ( suc @ ( suc @ ( suc @ N ) ) )
% 9.49/5.24        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_552_div__nat__eqI,axiom,
% 9.49/5.24      ! [N: nat,Q2: nat,M: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q2 ) @ M )
% 9.49/5.24       => ( ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q2 ) ) )
% 9.49/5.24         => ( ( divide_divide_nat @ M @ N )
% 9.49/5.24            = Q2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_553_Suc__nat__number__of__add,axiom,
% 9.49/5.24      ! [V: num,N: nat] :
% 9.49/5.24        ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N ) )
% 9.49/5.24        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ one ) ) @ N ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_554_Suc__div__eq__add3__div,axiom,
% 9.49/5.24      ! [M: nat,N: nat] :
% 9.49/5.24        ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 9.49/5.24        = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_555_power__odd__eq,axiom,
% 9.49/5.24      ! [A: complex,N: nat] :
% 9.49/5.24        ( ( power_power_complex @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 9.49/5.24        = ( times_times_complex @ A @ ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_556_power__odd__eq,axiom,
% 9.49/5.24      ! [A: real,N: nat] :
% 9.49/5.24        ( ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 9.49/5.24        = ( times_times_real @ A @ ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_557_power__odd__eq,axiom,
% 9.49/5.24      ! [A: nat,N: nat] :
% 9.49/5.24        ( ( power_power_nat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 9.49/5.24        = ( times_times_nat @ A @ ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_558_power__odd__eq,axiom,
% 9.49/5.24      ! [A: int,N: nat] :
% 9.49/5.24        ( ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 9.49/5.24        = ( times_times_int @ A @ ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_559_two__realpow__ge__one,axiom,
% 9.49/5.24      ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_560_less__add__eq__less,axiom,
% 9.49/5.24      ! [K: nat,L2: nat,M: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_nat @ K @ L2 )
% 9.49/5.24       => ( ( ( plus_plus_nat @ M @ L2 )
% 9.49/5.24            = ( plus_plus_nat @ K @ N ) )
% 9.49/5.24         => ( ord_less_nat @ M @ N ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_561_trans__less__add2,axiom,
% 9.49/5.24      ! [I2: nat,J: nat,M: nat] :
% 9.49/5.24        ( ( ord_less_nat @ I2 @ J )
% 9.49/5.24       => ( ord_less_nat @ I2 @ ( plus_plus_nat @ M @ J ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_562_trans__less__add1,axiom,
% 9.49/5.24      ! [I2: nat,J: nat,M: nat] :
% 9.49/5.24        ( ( ord_less_nat @ I2 @ J )
% 9.49/5.24       => ( ord_less_nat @ I2 @ ( plus_plus_nat @ J @ M ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_563_add__less__mono1,axiom,
% 9.49/5.24      ! [I2: nat,J: nat,K: nat] :
% 9.49/5.24        ( ( ord_less_nat @ I2 @ J )
% 9.49/5.24       => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_564_not__add__less2,axiom,
% 9.49/5.24      ! [J: nat,I2: nat] :
% 9.49/5.24        ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I2 ) @ I2 ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_565_not__add__less1,axiom,
% 9.49/5.24      ! [I2: nat,J: nat] :
% 9.49/5.24        ~ ( ord_less_nat @ ( plus_plus_nat @ I2 @ J ) @ I2 ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_566_add__less__mono,axiom,
% 9.49/5.24      ! [I2: nat,J: nat,K: nat,L2: nat] :
% 9.49/5.24        ( ( ord_less_nat @ I2 @ J )
% 9.49/5.24       => ( ( ord_less_nat @ K @ L2 )
% 9.49/5.24         => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_567_add__lessD1,axiom,
% 9.49/5.24      ! [I2: nat,J: nat,K: nat] :
% 9.49/5.24        ( ( ord_less_nat @ ( plus_plus_nat @ I2 @ J ) @ K )
% 9.49/5.24       => ( ord_less_nat @ I2 @ K ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_568_nat__less__le,axiom,
% 9.49/5.24      ( ord_less_nat
% 9.49/5.24      = ( ^ [M6: nat,N2: nat] :
% 9.49/5.24            ( ( ord_less_eq_nat @ M6 @ N2 )
% 9.49/5.24            & ( M6 != N2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_569_less__imp__le__nat,axiom,
% 9.49/5.24      ! [M: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_nat @ M @ N )
% 9.49/5.24       => ( ord_less_eq_nat @ M @ N ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_570_le__eq__less__or__eq,axiom,
% 9.49/5.24      ( ord_less_eq_nat
% 9.49/5.24      = ( ^ [M6: nat,N2: nat] :
% 9.49/5.24            ( ( ord_less_nat @ M6 @ N2 )
% 9.49/5.24            | ( M6 = N2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_571_less__or__eq__imp__le,axiom,
% 9.49/5.24      ! [M: nat,N: nat] :
% 9.49/5.24        ( ( ( ord_less_nat @ M @ N )
% 9.49/5.24          | ( M = N ) )
% 9.49/5.24       => ( ord_less_eq_nat @ M @ N ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_572_le__neq__implies__less,axiom,
% 9.49/5.24      ! [M: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.24       => ( ( M != N )
% 9.49/5.24         => ( ord_less_nat @ M @ N ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_573_less__mono__imp__le__mono,axiom,
% 9.49/5.24      ! [F: nat > nat,I2: nat,J: nat] :
% 9.49/5.24        ( ! [I4: nat,J2: nat] :
% 9.49/5.24            ( ( ord_less_nat @ I4 @ J2 )
% 9.49/5.24           => ( ord_less_nat @ ( F @ I4 ) @ ( F @ J2 ) ) )
% 9.49/5.24       => ( ( ord_less_eq_nat @ I2 @ J )
% 9.49/5.24         => ( ord_less_eq_nat @ ( F @ I2 ) @ ( F @ J ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_574_nat__le__iff__add,axiom,
% 9.49/5.24      ( ord_less_eq_nat
% 9.49/5.24      = ( ^ [M6: nat,N2: nat] :
% 9.49/5.24          ? [K3: nat] :
% 9.49/5.24            ( N2
% 9.49/5.24            = ( plus_plus_nat @ M6 @ K3 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_575_trans__le__add2,axiom,
% 9.49/5.24      ! [I2: nat,J: nat,M: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ I2 @ J )
% 9.49/5.24       => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ M @ J ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_576_trans__le__add1,axiom,
% 9.49/5.24      ! [I2: nat,J: nat,M: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ I2 @ J )
% 9.49/5.24       => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ J @ M ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_577_add__le__mono1,axiom,
% 9.49/5.24      ! [I2: nat,J: nat,K: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ I2 @ J )
% 9.49/5.24       => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_578_add__le__mono,axiom,
% 9.49/5.24      ! [I2: nat,J: nat,K: nat,L2: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ I2 @ J )
% 9.49/5.24       => ( ( ord_less_eq_nat @ K @ L2 )
% 9.49/5.24         => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_579_le__Suc__ex,axiom,
% 9.49/5.24      ! [K: nat,L2: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ K @ L2 )
% 9.49/5.24       => ? [N3: nat] :
% 9.49/5.24            ( L2
% 9.49/5.24            = ( plus_plus_nat @ K @ N3 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_580_add__leD2,axiom,
% 9.49/5.24      ! [M: nat,K: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 9.49/5.24       => ( ord_less_eq_nat @ K @ N ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_581_add__leD1,axiom,
% 9.49/5.24      ! [M: nat,K: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 9.49/5.24       => ( ord_less_eq_nat @ M @ N ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_582_le__add2,axiom,
% 9.49/5.24      ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_583_le__add1,axiom,
% 9.49/5.24      ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_584_add__leE,axiom,
% 9.49/5.24      ! [M: nat,K: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 9.49/5.24       => ~ ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.24           => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_585_add__mult__distrib2,axiom,
% 9.49/5.24      ! [K: nat,M: nat,N: nat] :
% 9.49/5.24        ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N ) )
% 9.49/5.24        = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_586_add__mult__distrib,axiom,
% 9.49/5.24      ! [M: nat,N: nat,K: nat] :
% 9.49/5.24        ( ( times_times_nat @ ( plus_plus_nat @ M @ N ) @ K )
% 9.49/5.24        = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_587_le__cube,axiom,
% 9.49/5.24      ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_588_le__square,axiom,
% 9.49/5.24      ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_589_mult__le__mono,axiom,
% 9.49/5.24      ! [I2: nat,J: nat,K: nat,L2: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ I2 @ J )
% 9.49/5.24       => ( ( ord_less_eq_nat @ K @ L2 )
% 9.49/5.24         => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ L2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_590_mult__le__mono1,axiom,
% 9.49/5.24      ! [I2: nat,J: nat,K: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ I2 @ J )
% 9.49/5.24       => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_591_mult__le__mono2,axiom,
% 9.49/5.24      ! [I2: nat,J: nat,K: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ I2 @ J )
% 9.49/5.24       => ( ord_less_eq_nat @ ( times_times_nat @ K @ I2 ) @ ( times_times_nat @ K @ J ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_592_nat__mult__1__right,axiom,
% 9.49/5.24      ! [N: nat] :
% 9.49/5.24        ( ( times_times_nat @ N @ one_one_nat )
% 9.49/5.24        = N ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_593_nat__mult__1,axiom,
% 9.49/5.24      ! [N: nat] :
% 9.49/5.24        ( ( times_times_nat @ one_one_nat @ N )
% 9.49/5.24        = N ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_594_mono__nat__linear__lb,axiom,
% 9.49/5.24      ! [F: nat > nat,M: nat,K: nat] :
% 9.49/5.24        ( ! [M4: nat,N3: nat] :
% 9.49/5.24            ( ( ord_less_nat @ M4 @ N3 )
% 9.49/5.24           => ( ord_less_nat @ ( F @ M4 ) @ ( F @ N3 ) ) )
% 9.49/5.24       => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_595_field__sum__of__halves,axiom,
% 9.49/5.24      ! [X: real] :
% 9.49/5.24        ( ( plus_plus_real @ ( divide_divide_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.49/5.24        = X ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_596_field__sum__of__halves,axiom,
% 9.49/5.24      ! [X: rat] :
% 9.49/5.24        ( ( plus_plus_rat @ ( divide_divide_rat @ X @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( divide_divide_rat @ X @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 9.49/5.24        = X ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_597_in__children__def,axiom,
% 9.49/5.24      ( vEBT_V5917875025757280293ildren
% 9.49/5.24      = ( ^ [N2: nat,TreeList3: list_VEBT_VEBT,X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ X2 @ N2 ) ) @ ( vEBT_VEBT_low @ X2 @ N2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_598_invar__vebt_Ointros_I5_J,axiom,
% 9.49/5.24      ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 9.49/5.24        ( ! [X3: vEBT_VEBT] :
% 9.49/5.24            ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 9.49/5.24           => ( vEBT_invar_vebt @ X3 @ N ) )
% 9.49/5.24       => ( ( vEBT_invar_vebt @ Summary @ M )
% 9.49/5.24         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 9.49/5.24              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 9.49/5.24           => ( ( M
% 9.49/5.24                = ( suc @ N ) )
% 9.49/5.24             => ( ( Deg
% 9.49/5.24                  = ( plus_plus_nat @ N @ M ) )
% 9.49/5.24               => ( ! [I4: nat] :
% 9.49/5.24                      ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 9.49/5.24                     => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ X4 ) )
% 9.49/5.24                        = ( vEBT_V8194947554948674370ptions @ Summary @ I4 ) ) )
% 9.49/5.24                 => ( ( ( Mi = Ma )
% 9.49/5.24                     => ! [X3: vEBT_VEBT] :
% 9.49/5.24                          ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 9.49/5.24                         => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_12 ) ) )
% 9.49/5.24                   => ( ( ord_less_eq_nat @ Mi @ Ma )
% 9.49/5.24                     => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 9.49/5.24                       => ( ( ( Mi != Ma )
% 9.49/5.24                           => ! [I4: nat] :
% 9.49/5.24                                ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 9.49/5.24                               => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 9.49/5.24                                      = I4 )
% 9.49/5.24                                   => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 9.49/5.24                                  & ! [X3: nat] :
% 9.49/5.24                                      ( ( ( ( vEBT_VEBT_high @ X3 @ N )
% 9.49/5.24                                          = I4 )
% 9.49/5.24                                        & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ X3 @ N ) ) )
% 9.49/5.24                                     => ( ( ord_less_nat @ Mi @ X3 )
% 9.49/5.24                                        & ( ord_less_eq_nat @ X3 @ Ma ) ) ) ) ) )
% 9.49/5.24                         => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_599_invar__vebt_Ointros_I4_J,axiom,
% 9.49/5.24      ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 9.49/5.24        ( ! [X3: vEBT_VEBT] :
% 9.49/5.24            ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 9.49/5.24           => ( vEBT_invar_vebt @ X3 @ N ) )
% 9.49/5.24       => ( ( vEBT_invar_vebt @ Summary @ M )
% 9.49/5.24         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 9.49/5.24              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 9.49/5.24           => ( ( M = N )
% 9.49/5.24             => ( ( Deg
% 9.49/5.24                  = ( plus_plus_nat @ N @ M ) )
% 9.49/5.24               => ( ! [I4: nat] :
% 9.49/5.24                      ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 9.49/5.24                     => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ X4 ) )
% 9.49/5.24                        = ( vEBT_V8194947554948674370ptions @ Summary @ I4 ) ) )
% 9.49/5.24                 => ( ( ( Mi = Ma )
% 9.49/5.24                     => ! [X3: vEBT_VEBT] :
% 9.49/5.24                          ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 9.49/5.24                         => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_12 ) ) )
% 9.49/5.24                   => ( ( ord_less_eq_nat @ Mi @ Ma )
% 9.49/5.24                     => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 9.49/5.24                       => ( ( ( Mi != Ma )
% 9.49/5.24                           => ! [I4: nat] :
% 9.49/5.24                                ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 9.49/5.24                               => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 9.49/5.24                                      = I4 )
% 9.49/5.24                                   => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 9.49/5.24                                  & ! [X3: nat] :
% 9.49/5.24                                      ( ( ( ( vEBT_VEBT_high @ X3 @ N )
% 9.49/5.24                                          = I4 )
% 9.49/5.24                                        & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ X3 @ N ) ) )
% 9.49/5.24                                     => ( ( ord_less_nat @ Mi @ X3 )
% 9.49/5.24                                        & ( ord_less_eq_nat @ X3 @ Ma ) ) ) ) ) )
% 9.49/5.24                         => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_600_minNull__delete__time__bound,axiom,
% 9.49/5.24      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 9.49/5.24        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.24       => ( ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ T @ X ) )
% 9.49/5.24         => ( ord_less_eq_nat @ ( vEBT_T_d_e_l_e_t_e @ T @ X ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_601_del__single__cont,axiom,
% 9.49/5.24      ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 9.49/5.24        ( ( ( X = Mi )
% 9.49/5.24          & ( X = Ma ) )
% 9.49/5.24       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 9.49/5.24         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 9.49/5.24            = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_602_enat__ord__number_I1_J,axiom,
% 9.49/5.24      ! [M: num,N: num] :
% 9.49/5.24        ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 9.49/5.24        = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_603_enat__ord__number_I2_J,axiom,
% 9.49/5.24      ! [M: num,N: num] :
% 9.49/5.24        ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 9.49/5.24        = ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_604_zdiv__numeral__Bit1,axiom,
% 9.49/5.24      ! [V: num,W: num] :
% 9.49/5.24        ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 9.49/5.24        = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_605_double__not__eq__Suc__double,axiom,
% 9.49/5.24      ! [M: nat,N: nat] :
% 9.49/5.24        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 9.49/5.24       != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_606_Suc__double__not__eq__double,axiom,
% 9.49/5.24      ! [M: nat,N: nat] :
% 9.49/5.24        ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 9.49/5.24       != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_607_misiz,axiom,
% 9.49/5.24      ! [T: vEBT_VEBT,N: nat,M: nat] :
% 9.49/5.24        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.24       => ( ( ( some_nat @ M )
% 9.49/5.24            = ( vEBT_vebt_mint @ T ) )
% 9.49/5.24         => ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_608_not__min__Null__member,axiom,
% 9.49/5.24      ! [T: vEBT_VEBT] :
% 9.49/5.24        ( ~ ( vEBT_VEBT_minNull @ T )
% 9.49/5.24       => ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_12 ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_609_min__Null__member,axiom,
% 9.49/5.24      ! [T: vEBT_VEBT,X: nat] :
% 9.49/5.24        ( ( vEBT_VEBT_minNull @ T )
% 9.49/5.24       => ~ ( vEBT_vebt_member @ T @ X ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_610_maxbmo,axiom,
% 9.49/5.24      ! [T: vEBT_VEBT,X: nat] :
% 9.49/5.24        ( ( ( vEBT_vebt_maxt @ T )
% 9.49/5.24          = ( some_nat @ X ) )
% 9.49/5.24       => ( vEBT_V8194947554948674370ptions @ T @ X ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_611_power__shift,axiom,
% 9.49/5.24      ! [X: nat,Y2: nat,Z: nat] :
% 9.49/5.24        ( ( ( power_power_nat @ X @ Y2 )
% 9.49/5.24          = Z )
% 9.49/5.24        = ( ( vEBT_VEBT_power @ ( some_nat @ X ) @ ( some_nat @ Y2 ) )
% 9.49/5.24          = ( some_nat @ Z ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_612_mint__member,axiom,
% 9.49/5.24      ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 9.49/5.24        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.24       => ( ( ( vEBT_vebt_mint @ T )
% 9.49/5.24            = ( some_nat @ Maxi ) )
% 9.49/5.24         => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_613_maxt__member,axiom,
% 9.49/5.24      ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 9.49/5.24        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.24       => ( ( ( vEBT_vebt_maxt @ T )
% 9.49/5.24            = ( some_nat @ Maxi ) )
% 9.49/5.24         => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_614_VEBT_Oinject_I1_J,axiom,
% 9.49/5.24      ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,Y11: option4927543243414619207at_nat,Y12: nat,Y13: list_VEBT_VEBT,Y14: vEBT_VEBT] :
% 9.49/5.24        ( ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 9.49/5.24          = ( vEBT_Node @ Y11 @ Y12 @ Y13 @ Y14 ) )
% 9.49/5.24        = ( ( X11 = Y11 )
% 9.49/5.24          & ( X12 = Y12 )
% 9.49/5.24          & ( X13 = Y13 )
% 9.49/5.24          & ( X14 = Y14 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_615_mint__corr__help,axiom,
% 9.49/5.24      ! [T: vEBT_VEBT,N: nat,Mini: nat,X: nat] :
% 9.49/5.24        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.24       => ( ( ( vEBT_vebt_mint @ T )
% 9.49/5.24            = ( some_nat @ Mini ) )
% 9.49/5.24         => ( ( vEBT_vebt_member @ T @ X )
% 9.49/5.24           => ( ord_less_eq_nat @ Mini @ X ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_616_maxt__corr__help,axiom,
% 9.49/5.24      ! [T: vEBT_VEBT,N: nat,Maxi: nat,X: nat] :
% 9.49/5.24        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.24       => ( ( ( vEBT_vebt_maxt @ T )
% 9.49/5.24            = ( some_nat @ Maxi ) )
% 9.49/5.24         => ( ( vEBT_vebt_member @ T @ X )
% 9.49/5.24           => ( ord_less_eq_nat @ X @ Maxi ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_617_zdiv__numeral__Bit0,axiom,
% 9.49/5.24      ! [V: num,W: num] :
% 9.49/5.24        ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 9.49/5.24        = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_618_lesseq__shift,axiom,
% 9.49/5.24      ( ord_less_eq_nat
% 9.49/5.24      = ( ^ [X2: nat,Y: nat] : ( vEBT_VEBT_lesseq @ ( some_nat @ X2 ) @ ( some_nat @ Y ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_619_enat__less__induct,axiom,
% 9.49/5.24      ! [P: extended_enat > $o,N: extended_enat] :
% 9.49/5.24        ( ! [N3: extended_enat] :
% 9.49/5.24            ( ! [M5: extended_enat] :
% 9.49/5.24                ( ( ord_le72135733267957522d_enat @ M5 @ N3 )
% 9.49/5.24               => ( P @ M5 ) )
% 9.49/5.24           => ( P @ N3 ) )
% 9.49/5.24       => ( P @ N ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_620_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I4_J,axiom,
% 9.49/5.24      ! [Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Uu: nat] :
% 9.49/5.24        ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Uu )
% 9.49/5.24        = one_one_nat ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_621_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Osimps_I2_J,axiom,
% 9.49/5.24      ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 9.49/5.24        ( ( vEBT_T_m_i_n_t @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 9.49/5.24        = one_one_nat ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_622_invar__vebt_Ointros_I2_J,axiom,
% 9.49/5.24      ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 9.49/5.24        ( ! [X3: vEBT_VEBT] :
% 9.49/5.24            ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 9.49/5.24           => ( vEBT_invar_vebt @ X3 @ N ) )
% 9.49/5.24       => ( ( vEBT_invar_vebt @ Summary @ M )
% 9.49/5.24         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 9.49/5.24              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 9.49/5.24           => ( ( M = N )
% 9.49/5.24             => ( ( Deg
% 9.49/5.24                  = ( plus_plus_nat @ N @ M ) )
% 9.49/5.24               => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 )
% 9.49/5.24                 => ( ! [X3: vEBT_VEBT] :
% 9.49/5.24                        ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 9.49/5.24                       => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_12 ) )
% 9.49/5.24                   => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_623_invar__vebt_Ointros_I3_J,axiom,
% 9.49/5.24      ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 9.49/5.24        ( ! [X3: vEBT_VEBT] :
% 9.49/5.24            ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 9.49/5.24           => ( vEBT_invar_vebt @ X3 @ N ) )
% 9.49/5.24       => ( ( vEBT_invar_vebt @ Summary @ M )
% 9.49/5.24         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 9.49/5.24              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 9.49/5.24           => ( ( M
% 9.49/5.24                = ( suc @ N ) )
% 9.49/5.24             => ( ( Deg
% 9.49/5.24                  = ( plus_plus_nat @ N @ M ) )
% 9.49/5.24               => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 )
% 9.49/5.24                 => ( ! [X3: vEBT_VEBT] :
% 9.49/5.24                        ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 9.49/5.24                       => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_12 ) )
% 9.49/5.24                   => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_624_discrete,axiom,
% 9.49/5.24      ( ord_less_nat
% 9.49/5.24      = ( ^ [A3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A3 @ one_one_nat ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_625_discrete,axiom,
% 9.49/5.24      ( ord_less_int
% 9.49/5.24      = ( ^ [A3: int] : ( ord_less_eq_int @ ( plus_plus_int @ A3 @ one_one_int ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_626_maxt__sound,axiom,
% 9.49/5.24      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 9.49/5.24        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.24       => ( ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X )
% 9.49/5.24         => ( ( vEBT_vebt_maxt @ T )
% 9.49/5.24            = ( some_nat @ X ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_627_maxt__corr,axiom,
% 9.49/5.24      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 9.49/5.24        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.24       => ( ( ( vEBT_vebt_maxt @ T )
% 9.49/5.24            = ( some_nat @ X ) )
% 9.49/5.24         => ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_628_mint__sound,axiom,
% 9.49/5.24      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 9.49/5.24        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.24       => ( ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X )
% 9.49/5.24         => ( ( vEBT_vebt_mint @ T )
% 9.49/5.24            = ( some_nat @ X ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_629_mint__corr,axiom,
% 9.49/5.24      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 9.49/5.24        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.24       => ( ( ( vEBT_vebt_mint @ T )
% 9.49/5.24            = ( some_nat @ X ) )
% 9.49/5.24         => ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_630_del__x__mi__lets__in__not__minNull,axiom,
% 9.49/5.24      ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList: list_VEBT_VEBT,L2: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 9.49/5.24        ( ( ( X = Mi )
% 9.49/5.24          & ( ord_less_nat @ X @ Ma ) )
% 9.49/5.24       => ( ( Mi != Ma )
% 9.49/5.24         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 9.49/5.24           => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.24                = H2 )
% 9.49/5.24             => ( ( Xn
% 9.49/5.24                  = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 9.49/5.24               => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.24                    = L2 )
% 9.49/5.24                 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 9.49/5.24                   => ( ( Newnode
% 9.49/5.24                        = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) )
% 9.49/5.24                     => ( ( Newlist
% 9.49/5.24                          = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 9.49/5.24                       => ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 9.49/5.24                         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 9.49/5.24                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_631_del__x__not__mi__newnode__not__nil,axiom,
% 9.49/5.24      ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L2: nat,Newnode: vEBT_VEBT,TreeList: list_VEBT_VEBT,Newlist: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 9.49/5.24        ( ( ( ord_less_nat @ Mi @ X )
% 9.49/5.24          & ( ord_less_eq_nat @ X @ Ma ) )
% 9.49/5.24       => ( ( Mi != Ma )
% 9.49/5.24         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 9.49/5.24           => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.24                = H2 )
% 9.49/5.24             => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.24                  = L2 )
% 9.49/5.24               => ( ( Newnode
% 9.49/5.24                    = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) )
% 9.49/5.24                 => ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 9.49/5.24                   => ( ( Newlist
% 9.49/5.24                        = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 9.49/5.24                     => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 9.49/5.24                       => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 9.49/5.24                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_632_pred__max,axiom,
% 9.49/5.24      ! [Deg: nat,Ma: nat,X: nat,Mi: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 9.49/5.24        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 9.49/5.24       => ( ( ord_less_nat @ Ma @ X )
% 9.49/5.24         => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 9.49/5.24            = ( some_nat @ Ma ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_633_succ__min,axiom,
% 9.49/5.24      ! [Deg: nat,X: nat,Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 9.49/5.24        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 9.49/5.24       => ( ( ord_less_nat @ X @ Mi )
% 9.49/5.24         => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 9.49/5.24            = ( some_nat @ Mi ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_634_mintlistlength,axiom,
% 9.49/5.24      ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 9.49/5.24        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 9.49/5.24       => ( ( Mi != Ma )
% 9.49/5.24         => ( ( ord_less_nat @ Mi @ Ma )
% 9.49/5.24            & ? [M4: nat] :
% 9.49/5.24                ( ( ( some_nat @ M4 )
% 9.49/5.24                  = ( vEBT_vebt_mint @ Summary ) )
% 9.49/5.24                & ( ord_less_nat @ M4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_635_set__vebt__set__vebt_H__valid,axiom,
% 9.49/5.24      ! [T: vEBT_VEBT,N: nat] :
% 9.49/5.24        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.24       => ( ( vEBT_set_vebt @ T )
% 9.49/5.24          = ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_636_helpyd,axiom,
% 9.49/5.24      ! [T: vEBT_VEBT,N: nat,X: nat,Y2: nat] :
% 9.49/5.24        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.24       => ( ( ( vEBT_vebt_succ @ T @ X )
% 9.49/5.24            = ( some_nat @ Y2 ) )
% 9.49/5.24         => ( ord_less_nat @ Y2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_637_power__minus__is__div,axiom,
% 9.49/5.24      ! [B: nat,A: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ B @ A )
% 9.49/5.24       => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ A @ B ) )
% 9.49/5.24          = ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_638_helpypredd,axiom,
% 9.49/5.24      ! [T: vEBT_VEBT,N: nat,X: nat,Y2: nat] :
% 9.49/5.24        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.24       => ( ( ( vEBT_vebt_pred @ T @ X )
% 9.49/5.24            = ( some_nat @ Y2 ) )
% 9.49/5.24         => ( ord_less_nat @ Y2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_639_diff__Suc__Suc,axiom,
% 9.49/5.24      ! [M: nat,N: nat] :
% 9.49/5.24        ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N ) )
% 9.49/5.24        = ( minus_minus_nat @ M @ N ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_640_Suc__diff__diff,axiom,
% 9.49/5.24      ! [M: nat,N: nat,K: nat] :
% 9.49/5.24        ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 9.49/5.24        = ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_641_diff__diff__left,axiom,
% 9.49/5.24      ! [I2: nat,J: nat,K: nat] :
% 9.49/5.24        ( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J ) @ K )
% 9.49/5.24        = ( minus_minus_nat @ I2 @ ( plus_plus_nat @ J @ K ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_642_diff__diff__cancel,axiom,
% 9.49/5.24      ! [I2: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ I2 @ N )
% 9.49/5.24       => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I2 ) )
% 9.49/5.24          = I2 ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_643_right__diff__distrib__numeral,axiom,
% 9.49/5.24      ! [V: num,B: complex,C: complex] :
% 9.49/5.24        ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( minus_minus_complex @ B @ C ) )
% 9.49/5.24        = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_644_right__diff__distrib__numeral,axiom,
% 9.49/5.24      ! [V: num,B: real,C: real] :
% 9.49/5.24        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( minus_minus_real @ B @ C ) )
% 9.49/5.24        = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_645_right__diff__distrib__numeral,axiom,
% 9.49/5.24      ! [V: num,B: rat,C: rat] :
% 9.49/5.24        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( minus_minus_rat @ B @ C ) )
% 9.49/5.24        = ( minus_minus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_646_right__diff__distrib__numeral,axiom,
% 9.49/5.24      ! [V: num,B: int,C: int] :
% 9.49/5.24        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( minus_minus_int @ B @ C ) )
% 9.49/5.24        = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_647_left__diff__distrib__numeral,axiom,
% 9.49/5.24      ! [A: complex,B: complex,V: num] :
% 9.49/5.24        ( ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 9.49/5.24        = ( minus_minus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_648_left__diff__distrib__numeral,axiom,
% 9.49/5.24      ! [A: real,B: real,V: num] :
% 9.49/5.24        ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 9.49/5.24        = ( minus_minus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_649_left__diff__distrib__numeral,axiom,
% 9.49/5.24      ! [A: rat,B: rat,V: num] :
% 9.49/5.24        ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 9.49/5.24        = ( minus_minus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_650_left__diff__distrib__numeral,axiom,
% 9.49/5.24      ! [A: int,B: int,V: num] :
% 9.49/5.24        ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 9.49/5.24        = ( minus_minus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_651_diff__Suc__1,axiom,
% 9.49/5.24      ! [N: nat] :
% 9.49/5.24        ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 9.49/5.24        = N ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_652_Nat_Oadd__diff__assoc,axiom,
% 9.49/5.24      ! [K: nat,J: nat,I2: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ K @ J )
% 9.49/5.24       => ( ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 9.49/5.24          = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J ) @ K ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_653_Nat_Oadd__diff__assoc2,axiom,
% 9.49/5.24      ! [K: nat,J: nat,I2: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ K @ J )
% 9.49/5.24       => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
% 9.49/5.24          = ( minus_minus_nat @ ( plus_plus_nat @ J @ I2 ) @ K ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_654_Nat_Odiff__diff__right,axiom,
% 9.49/5.24      ! [K: nat,J: nat,I2: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ K @ J )
% 9.49/5.24       => ( ( minus_minus_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 9.49/5.24          = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_655_diff__Suc__diff__eq1,axiom,
% 9.49/5.24      ! [K: nat,J: nat,I2: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ K @ J )
% 9.49/5.24       => ( ( minus_minus_nat @ I2 @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 9.49/5.24          = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ K ) @ ( suc @ J ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_656_diff__Suc__diff__eq2,axiom,
% 9.49/5.24      ! [K: nat,J: nat,I2: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ K @ J )
% 9.49/5.24       => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I2 )
% 9.49/5.24          = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_657_pred__member,axiom,
% 9.49/5.24      ! [T: vEBT_VEBT,X: nat,Y2: nat] :
% 9.49/5.24        ( ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Y2 )
% 9.49/5.24        = ( ( vEBT_vebt_member @ T @ Y2 )
% 9.49/5.24          & ( ord_less_nat @ Y2 @ X )
% 9.49/5.24          & ! [Z4: nat] :
% 9.49/5.24              ( ( ( vEBT_vebt_member @ T @ Z4 )
% 9.49/5.24                & ( ord_less_nat @ Z4 @ X ) )
% 9.49/5.24             => ( ord_less_eq_nat @ Z4 @ Y2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_658_succ__member,axiom,
% 9.49/5.24      ! [T: vEBT_VEBT,X: nat,Y2: nat] :
% 9.49/5.24        ( ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Y2 )
% 9.49/5.24        = ( ( vEBT_vebt_member @ T @ Y2 )
% 9.49/5.24          & ( ord_less_nat @ X @ Y2 )
% 9.49/5.24          & ! [Z4: nat] :
% 9.49/5.24              ( ( ( vEBT_vebt_member @ T @ Z4 )
% 9.49/5.24                & ( ord_less_nat @ X @ Z4 ) )
% 9.49/5.24             => ( ord_less_eq_nat @ Y2 @ Z4 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_659_succ__corr,axiom,
% 9.49/5.24      ! [T: vEBT_VEBT,N: nat,X: nat,Sx: nat] :
% 9.49/5.24        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.24       => ( ( ( vEBT_vebt_succ @ T @ X )
% 9.49/5.24            = ( some_nat @ Sx ) )
% 9.49/5.24          = ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_660_pred__corr,axiom,
% 9.49/5.24      ! [T: vEBT_VEBT,N: nat,X: nat,Px: nat] :
% 9.49/5.24        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.24       => ( ( ( vEBT_vebt_pred @ T @ X )
% 9.49/5.24            = ( some_nat @ Px ) )
% 9.49/5.24          = ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Px ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_661_pred__correct,axiom,
% 9.49/5.24      ! [T: vEBT_VEBT,N: nat,X: nat,Sx: nat] :
% 9.49/5.24        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.24       => ( ( ( vEBT_vebt_pred @ T @ X )
% 9.49/5.24            = ( some_nat @ Sx ) )
% 9.49/5.24          = ( vEBT_is_pred_in_set @ ( vEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_662_succ__correct,axiom,
% 9.49/5.24      ! [T: vEBT_VEBT,N: nat,X: nat,Sx: nat] :
% 9.49/5.24        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.24       => ( ( ( vEBT_vebt_succ @ T @ X )
% 9.49/5.24            = ( some_nat @ Sx ) )
% 9.49/5.24          = ( vEBT_is_succ_in_set @ ( vEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_663_local_Opower__def,axiom,
% 9.49/5.24      ( vEBT_VEBT_power
% 9.49/5.24      = ( vEBT_V4262088993061758097ft_nat @ power_power_nat ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_664_diff__commute,axiom,
% 9.49/5.24      ! [I2: nat,J: nat,K: nat] :
% 9.49/5.24        ( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J ) @ K )
% 9.49/5.24        = ( minus_minus_nat @ ( minus_minus_nat @ I2 @ K ) @ J ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_665_add__diff__add,axiom,
% 9.49/5.24      ! [A: real,C: real,B: real,D2: real] :
% 9.49/5.24        ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D2 ) )
% 9.49/5.24        = ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ ( minus_minus_real @ C @ D2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_666_add__diff__add,axiom,
% 9.49/5.24      ! [A: complex,C: complex,B: complex,D2: complex] :
% 9.49/5.24        ( ( minus_minus_complex @ ( plus_plus_complex @ A @ C ) @ ( plus_plus_complex @ B @ D2 ) )
% 9.49/5.24        = ( plus_plus_complex @ ( minus_minus_complex @ A @ B ) @ ( minus_minus_complex @ C @ D2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_667_add__diff__add,axiom,
% 9.49/5.24      ! [A: rat,C: rat,B: rat,D2: rat] :
% 9.49/5.24        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) )
% 9.49/5.24        = ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ ( minus_minus_rat @ C @ D2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_668_add__diff__add,axiom,
% 9.49/5.24      ! [A: int,C: int,B: int,D2: int] :
% 9.49/5.24        ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) )
% 9.49/5.24        = ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ ( minus_minus_int @ C @ D2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_669_zero__induct__lemma,axiom,
% 9.49/5.24      ! [P: nat > $o,K: nat,I2: nat] :
% 9.49/5.24        ( ( P @ K )
% 9.49/5.24       => ( ! [N3: nat] :
% 9.49/5.24              ( ( P @ ( suc @ N3 ) )
% 9.49/5.24             => ( P @ N3 ) )
% 9.49/5.24         => ( P @ ( minus_minus_nat @ K @ I2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_670_diff__less__mono2,axiom,
% 9.49/5.24      ! [M: nat,N: nat,L2: nat] :
% 9.49/5.24        ( ( ord_less_nat @ M @ N )
% 9.49/5.24       => ( ( ord_less_nat @ M @ L2 )
% 9.49/5.24         => ( ord_less_nat @ ( minus_minus_nat @ L2 @ N ) @ ( minus_minus_nat @ L2 @ M ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_671_less__imp__diff__less,axiom,
% 9.49/5.24      ! [J: nat,K: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_nat @ J @ K )
% 9.49/5.24       => ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_672_diff__add__inverse2,axiom,
% 9.49/5.24      ! [M: nat,N: nat] :
% 9.49/5.24        ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
% 9.49/5.24        = M ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_673_diff__add__inverse,axiom,
% 9.49/5.24      ! [N: nat,M: nat] :
% 9.49/5.24        ( ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ N )
% 9.49/5.24        = M ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_674_diff__cancel2,axiom,
% 9.49/5.24      ! [M: nat,K: nat,N: nat] :
% 9.49/5.24        ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) )
% 9.49/5.24        = ( minus_minus_nat @ M @ N ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_675_Nat_Odiff__cancel,axiom,
% 9.49/5.24      ! [K: nat,M: nat,N: nat] :
% 9.49/5.24        ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 9.49/5.24        = ( minus_minus_nat @ M @ N ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_676_eq__diff__iff,axiom,
% 9.49/5.24      ! [K: nat,M: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ K @ M )
% 9.49/5.24       => ( ( ord_less_eq_nat @ K @ N )
% 9.49/5.24         => ( ( ( minus_minus_nat @ M @ K )
% 9.49/5.24              = ( minus_minus_nat @ N @ K ) )
% 9.49/5.24            = ( M = N ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_677_le__diff__iff,axiom,
% 9.49/5.24      ! [K: nat,M: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ K @ M )
% 9.49/5.24       => ( ( ord_less_eq_nat @ K @ N )
% 9.49/5.24         => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 9.49/5.24            = ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_678_Nat_Odiff__diff__eq,axiom,
% 9.49/5.24      ! [K: nat,M: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ K @ M )
% 9.49/5.24       => ( ( ord_less_eq_nat @ K @ N )
% 9.49/5.24         => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 9.49/5.24            = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_679_diff__le__mono,axiom,
% 9.49/5.24      ! [M: nat,N: nat,L2: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.24       => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L2 ) @ ( minus_minus_nat @ N @ L2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_680_diff__le__self,axiom,
% 9.49/5.24      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_681_le__diff__iff_H,axiom,
% 9.49/5.24      ! [A: nat,C: nat,B: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ A @ C )
% 9.49/5.24       => ( ( ord_less_eq_nat @ B @ C )
% 9.49/5.24         => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 9.49/5.24            = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_682_diff__le__mono2,axiom,
% 9.49/5.24      ! [M: nat,N: nat,L2: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.24       => ( ord_less_eq_nat @ ( minus_minus_nat @ L2 @ N ) @ ( minus_minus_nat @ L2 @ M ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_683_diff__mult__distrib,axiom,
% 9.49/5.24      ! [M: nat,N: nat,K: nat] :
% 9.49/5.24        ( ( times_times_nat @ ( minus_minus_nat @ M @ N ) @ K )
% 9.49/5.24        = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_684_diff__mult__distrib2,axiom,
% 9.49/5.24      ! [K: nat,M: nat,N: nat] :
% 9.49/5.24        ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 9.49/5.24        = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_685_mult__diff__mult,axiom,
% 9.49/5.24      ! [X: rat,Y2: rat,A: rat,B: rat] :
% 9.49/5.24        ( ( minus_minus_rat @ ( times_times_rat @ X @ Y2 ) @ ( times_times_rat @ A @ B ) )
% 9.49/5.24        = ( plus_plus_rat @ ( times_times_rat @ X @ ( minus_minus_rat @ Y2 @ B ) ) @ ( times_times_rat @ ( minus_minus_rat @ X @ A ) @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_686_mult__diff__mult,axiom,
% 9.49/5.24      ! [X: complex,Y2: complex,A: complex,B: complex] :
% 9.49/5.24        ( ( minus_minus_complex @ ( times_times_complex @ X @ Y2 ) @ ( times_times_complex @ A @ B ) )
% 9.49/5.24        = ( plus_plus_complex @ ( times_times_complex @ X @ ( minus_minus_complex @ Y2 @ B ) ) @ ( times_times_complex @ ( minus_minus_complex @ X @ A ) @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_687_mult__diff__mult,axiom,
% 9.49/5.24      ! [X: real,Y2: real,A: real,B: real] :
% 9.49/5.24        ( ( minus_minus_real @ ( times_times_real @ X @ Y2 ) @ ( times_times_real @ A @ B ) )
% 9.49/5.24        = ( plus_plus_real @ ( times_times_real @ X @ ( minus_minus_real @ Y2 @ B ) ) @ ( times_times_real @ ( minus_minus_real @ X @ A ) @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_688_mult__diff__mult,axiom,
% 9.49/5.24      ! [X: int,Y2: int,A: int,B: int] :
% 9.49/5.24        ( ( minus_minus_int @ ( times_times_int @ X @ Y2 ) @ ( times_times_int @ A @ B ) )
% 9.49/5.24        = ( plus_plus_int @ ( times_times_int @ X @ ( minus_minus_int @ Y2 @ B ) ) @ ( times_times_int @ ( minus_minus_int @ X @ A ) @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_689_Suc__diff__Suc,axiom,
% 9.49/5.24      ! [N: nat,M: nat] :
% 9.49/5.24        ( ( ord_less_nat @ N @ M )
% 9.49/5.24       => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N ) ) )
% 9.49/5.24          = ( minus_minus_nat @ M @ N ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_690_diff__less__Suc,axiom,
% 9.49/5.24      ! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_691_Suc__diff__le,axiom,
% 9.49/5.24      ! [N: nat,M: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ N @ M )
% 9.49/5.24       => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 9.49/5.24          = ( suc @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_692_diff__Suc__eq__diff__pred,axiom,
% 9.49/5.24      ! [M: nat,N: nat] :
% 9.49/5.24        ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 9.49/5.24        = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_693_add__diff__inverse__nat,axiom,
% 9.49/5.24      ! [M: nat,N: nat] :
% 9.49/5.24        ( ~ ( ord_less_nat @ M @ N )
% 9.49/5.24       => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
% 9.49/5.24          = M ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_694_less__diff__conv,axiom,
% 9.49/5.24      ! [I2: nat,J: nat,K: nat] :
% 9.49/5.24        ( ( ord_less_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 9.49/5.24        = ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_695_less__diff__iff,axiom,
% 9.49/5.24      ! [K: nat,M: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ K @ M )
% 9.49/5.24       => ( ( ord_less_eq_nat @ K @ N )
% 9.49/5.24         => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 9.49/5.24            = ( ord_less_nat @ M @ N ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_696_diff__less__mono,axiom,
% 9.49/5.24      ! [A: nat,B: nat,C: nat] :
% 9.49/5.24        ( ( ord_less_nat @ A @ B )
% 9.49/5.24       => ( ( ord_less_eq_nat @ C @ A )
% 9.49/5.24         => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_697_le__diff__conv,axiom,
% 9.49/5.24      ! [J: nat,K: nat,I2: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
% 9.49/5.24        = ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I2 @ K ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_698_Nat_Ole__diff__conv2,axiom,
% 9.49/5.24      ! [K: nat,J: nat,I2: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ K @ J )
% 9.49/5.24       => ( ( ord_less_eq_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 9.49/5.24          = ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_699_Nat_Odiff__add__assoc,axiom,
% 9.49/5.24      ! [K: nat,J: nat,I2: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ K @ J )
% 9.49/5.24       => ( ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J ) @ K )
% 9.49/5.24          = ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_700_Nat_Odiff__add__assoc2,axiom,
% 9.49/5.24      ! [K: nat,J: nat,I2: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ K @ J )
% 9.49/5.24       => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I2 ) @ K )
% 9.49/5.24          = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_701_Nat_Ole__imp__diff__is__add,axiom,
% 9.49/5.24      ! [I2: nat,J: nat,K: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ I2 @ J )
% 9.49/5.24       => ( ( ( minus_minus_nat @ J @ I2 )
% 9.49/5.24            = K )
% 9.49/5.24          = ( J
% 9.49/5.24            = ( plus_plus_nat @ K @ I2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_702_less__diff__conv2,axiom,
% 9.49/5.24      ! [K: nat,J: nat,I2: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ K @ J )
% 9.49/5.24       => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
% 9.49/5.24          = ( ord_less_nat @ J @ ( plus_plus_nat @ I2 @ K ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_703_nat__eq__add__iff1,axiom,
% 9.49/5.24      ! [J: nat,I2: nat,U: nat,M: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ J @ I2 )
% 9.49/5.24       => ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M )
% 9.49/5.24            = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 9.49/5.24          = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M )
% 9.49/5.24            = N ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_704_nat__eq__add__iff2,axiom,
% 9.49/5.24      ! [I2: nat,J: nat,U: nat,M: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ I2 @ J )
% 9.49/5.24       => ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M )
% 9.49/5.24            = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 9.49/5.24          = ( M
% 9.49/5.24            = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_705_nat__le__add__iff1,axiom,
% 9.49/5.24      ! [J: nat,I2: nat,U: nat,M: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ J @ I2 )
% 9.49/5.24       => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 9.49/5.24          = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_706_nat__le__add__iff2,axiom,
% 9.49/5.24      ! [I2: nat,J: nat,U: nat,M: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ I2 @ J )
% 9.49/5.24       => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 9.49/5.24          = ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_707_nat__diff__add__eq1,axiom,
% 9.49/5.24      ! [J: nat,I2: nat,U: nat,M: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ J @ I2 )
% 9.49/5.24       => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 9.49/5.24          = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_708_nat__diff__add__eq2,axiom,
% 9.49/5.24      ! [I2: nat,J: nat,U: nat,M: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ I2 @ J )
% 9.49/5.24       => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 9.49/5.24          = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_709_power2__commute,axiom,
% 9.49/5.24      ! [X: real,Y2: real] :
% 9.49/5.24        ( ( power_power_real @ ( minus_minus_real @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.24        = ( power_power_real @ ( minus_minus_real @ Y2 @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_710_power2__commute,axiom,
% 9.49/5.24      ! [X: complex,Y2: complex] :
% 9.49/5.24        ( ( power_power_complex @ ( minus_minus_complex @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.24        = ( power_power_complex @ ( minus_minus_complex @ Y2 @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_711_power2__commute,axiom,
% 9.49/5.24      ! [X: rat,Y2: rat] :
% 9.49/5.24        ( ( power_power_rat @ ( minus_minus_rat @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.24        = ( power_power_rat @ ( minus_minus_rat @ Y2 @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_712_power2__commute,axiom,
% 9.49/5.24      ! [X: int,Y2: int] :
% 9.49/5.24        ( ( power_power_int @ ( minus_minus_int @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.24        = ( power_power_int @ ( minus_minus_int @ Y2 @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_713_nat__less__add__iff1,axiom,
% 9.49/5.24      ! [J: nat,I2: nat,U: nat,M: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ J @ I2 )
% 9.49/5.24       => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 9.49/5.24          = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_714_nat__less__add__iff2,axiom,
% 9.49/5.24      ! [I2: nat,J: nat,U: nat,M: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ I2 @ J )
% 9.49/5.24       => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 9.49/5.24          = ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_715_diff__le__diff__pow,axiom,
% 9.49/5.24      ! [K: nat,M: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 9.49/5.24       => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ ( minus_minus_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_716_power2__diff,axiom,
% 9.49/5.24      ! [X: complex,Y2: complex] :
% 9.49/5.24        ( ( power_power_complex @ ( minus_minus_complex @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.24        = ( minus_minus_complex @ ( plus_plus_complex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) @ Y2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_717_power2__diff,axiom,
% 9.49/5.24      ! [X: real,Y2: real] :
% 9.49/5.24        ( ( power_power_real @ ( minus_minus_real @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.24        = ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_718_power2__diff,axiom,
% 9.49/5.24      ! [X: rat,Y2: rat] :
% 9.49/5.24        ( ( power_power_rat @ ( minus_minus_rat @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.24        = ( minus_minus_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_719_power2__diff,axiom,
% 9.49/5.24      ! [X: int,Y2: int] :
% 9.49/5.24        ( ( power_power_int @ ( minus_minus_int @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.24        = ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X ) @ Y2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_720_set__swap,axiom,
% 9.49/5.24      ! [I2: nat,Xs2: list_VEBT_VEBT,J: nat] :
% 9.49/5.24        ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 9.49/5.24       => ( ( ord_less_nat @ J @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 9.49/5.24         => ( ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ ( nth_VEBT_VEBT @ Xs2 @ J ) ) @ J @ ( nth_VEBT_VEBT @ Xs2 @ I2 ) ) )
% 9.49/5.24            = ( set_VEBT_VEBT2 @ Xs2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_721_set__swap,axiom,
% 9.49/5.24      ! [I2: nat,Xs2: list_o,J: nat] :
% 9.49/5.24        ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 9.49/5.24       => ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs2 ) )
% 9.49/5.24         => ( ( set_o2 @ ( list_update_o @ ( list_update_o @ Xs2 @ I2 @ ( nth_o @ Xs2 @ J ) ) @ J @ ( nth_o @ Xs2 @ I2 ) ) )
% 9.49/5.24            = ( set_o2 @ Xs2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_722_set__swap,axiom,
% 9.49/5.24      ! [I2: nat,Xs2: list_nat,J: nat] :
% 9.49/5.24        ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 9.49/5.24       => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 9.49/5.24         => ( ( set_nat2 @ ( list_update_nat @ ( list_update_nat @ Xs2 @ I2 @ ( nth_nat @ Xs2 @ J ) ) @ J @ ( nth_nat @ Xs2 @ I2 ) ) )
% 9.49/5.24            = ( set_nat2 @ Xs2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_723_set__swap,axiom,
% 9.49/5.24      ! [I2: nat,Xs2: list_int,J: nat] :
% 9.49/5.24        ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 9.49/5.24       => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs2 ) )
% 9.49/5.24         => ( ( set_int2 @ ( list_update_int @ ( list_update_int @ Xs2 @ I2 @ ( nth_int @ Xs2 @ J ) ) @ J @ ( nth_int @ Xs2 @ I2 ) ) )
% 9.49/5.24            = ( set_int2 @ Xs2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_724_insert__simp__norm,axiom,
% 9.49/5.24      ! [X: nat,Deg: nat,TreeList: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 9.49/5.24        ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 9.49/5.24       => ( ( ord_less_nat @ Mi @ X )
% 9.49/5.24         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 9.49/5.24           => ( ( X != Ma )
% 9.49/5.24             => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 9.49/5.24                = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( ord_max_nat @ X @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_725_insert__simp__excp,axiom,
% 9.49/5.24      ! [Mi: nat,Deg: nat,TreeList: list_VEBT_VEBT,X: nat,Ma: nat,Summary: vEBT_VEBT] :
% 9.49/5.24        ( ( ord_less_nat @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 9.49/5.24       => ( ( ord_less_nat @ X @ Mi )
% 9.49/5.24         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 9.49/5.24           => ( ( X != Ma )
% 9.49/5.24             => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 9.49/5.24                = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ ( ord_max_nat @ Mi @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_726_nth__list__update__eq,axiom,
% 9.49/5.24      ! [I2: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 9.49/5.24        ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 9.49/5.24       => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ I2 )
% 9.49/5.24          = X ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_727_nth__list__update__eq,axiom,
% 9.49/5.24      ! [I2: nat,Xs2: list_o,X: $o] :
% 9.49/5.24        ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 9.49/5.24       => ( ( nth_o @ ( list_update_o @ Xs2 @ I2 @ X ) @ I2 )
% 9.49/5.24          = X ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_728_nth__list__update__eq,axiom,
% 9.49/5.24      ! [I2: nat,Xs2: list_nat,X: nat] :
% 9.49/5.24        ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 9.49/5.24       => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) @ I2 )
% 9.49/5.24          = X ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_729_nth__list__update__eq,axiom,
% 9.49/5.24      ! [I2: nat,Xs2: list_int,X: int] :
% 9.49/5.24        ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 9.49/5.24       => ( ( nth_int @ ( list_update_int @ Xs2 @ I2 @ X ) @ I2 )
% 9.49/5.24          = X ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_730_divmod__step__eq,axiom,
% 9.49/5.24      ! [L2: num,R: nat,Q2: nat] :
% 9.49/5.24        ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R )
% 9.49/5.24         => ( ( unique5026877609467782581ep_nat @ L2 @ ( product_Pair_nat_nat @ Q2 @ R ) )
% 9.49/5.24            = ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ one_one_nat ) @ ( minus_minus_nat @ R @ ( numeral_numeral_nat @ L2 ) ) ) ) )
% 9.49/5.24        & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R )
% 9.49/5.24         => ( ( unique5026877609467782581ep_nat @ L2 @ ( product_Pair_nat_nat @ Q2 @ R ) )
% 9.49/5.24            = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ R ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_731_divmod__step__eq,axiom,
% 9.49/5.24      ! [L2: num,R: int,Q2: int] :
% 9.49/5.24        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R )
% 9.49/5.24         => ( ( unique5024387138958732305ep_int @ L2 @ ( product_Pair_int_int @ Q2 @ R ) )
% 9.49/5.24            = ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ one_one_int ) @ ( minus_minus_int @ R @ ( numeral_numeral_int @ L2 ) ) ) ) )
% 9.49/5.24        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R )
% 9.49/5.24         => ( ( unique5024387138958732305ep_int @ L2 @ ( product_Pair_int_int @ Q2 @ R ) )
% 9.49/5.24            = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ R ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_732_divmod__step__eq,axiom,
% 9.49/5.24      ! [L2: num,R: code_integer,Q2: code_integer] :
% 9.49/5.24        ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R )
% 9.49/5.24         => ( ( unique4921790084139445826nteger @ L2 @ ( produc1086072967326762835nteger @ Q2 @ R ) )
% 9.49/5.24            = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R @ ( numera6620942414471956472nteger @ L2 ) ) ) ) )
% 9.49/5.24        & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R )
% 9.49/5.24         => ( ( unique4921790084139445826nteger @ L2 @ ( produc1086072967326762835nteger @ Q2 @ R ) )
% 9.49/5.24            = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ R ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_733_succ__list__to__short,axiom,
% 9.49/5.24      ! [Deg: nat,Mi: nat,X: nat,TreeList: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 9.49/5.24        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 9.49/5.24       => ( ( ord_less_eq_nat @ Mi @ X )
% 9.49/5.24         => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.49/5.24           => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 9.49/5.24              = none_nat ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_734_pred__list__to__short,axiom,
% 9.49/5.24      ! [Deg: nat,X: nat,Ma: nat,TreeList: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 9.49/5.24        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 9.49/5.24       => ( ( ord_less_eq_nat @ X @ Ma )
% 9.49/5.24         => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.49/5.24           => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 9.49/5.24              = none_nat ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_735_list__update__beyond,axiom,
% 9.49/5.24      ! [Xs2: list_VEBT_VEBT,I2: nat,X: vEBT_VEBT] :
% 9.49/5.24        ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ I2 )
% 9.49/5.24       => ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X )
% 9.49/5.24          = Xs2 ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_736_list__update__beyond,axiom,
% 9.49/5.24      ! [Xs2: list_o,I2: nat,X: $o] :
% 9.49/5.24        ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs2 ) @ I2 )
% 9.49/5.24       => ( ( list_update_o @ Xs2 @ I2 @ X )
% 9.49/5.24          = Xs2 ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_737_list__update__beyond,axiom,
% 9.49/5.24      ! [Xs2: list_nat,I2: nat,X: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs2 ) @ I2 )
% 9.49/5.24       => ( ( list_update_nat @ Xs2 @ I2 @ X )
% 9.49/5.24          = Xs2 ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_738_list__update__beyond,axiom,
% 9.49/5.24      ! [Xs2: list_int,I2: nat,X: int] :
% 9.49/5.24        ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs2 ) @ I2 )
% 9.49/5.24       => ( ( list_update_int @ Xs2 @ I2 @ X )
% 9.49/5.24          = Xs2 ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_739_option_Ocollapse,axiom,
% 9.49/5.24      ! [Option: option4927543243414619207at_nat] :
% 9.49/5.24        ( ( Option != none_P5556105721700978146at_nat )
% 9.49/5.24       => ( ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) )
% 9.49/5.24          = Option ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_740_option_Ocollapse,axiom,
% 9.49/5.24      ! [Option: option_nat] :
% 9.49/5.24        ( ( Option != none_nat )
% 9.49/5.24       => ( ( some_nat @ ( the_nat @ Option ) )
% 9.49/5.24          = Option ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_741_option_Ocollapse,axiom,
% 9.49/5.24      ! [Option: option_num] :
% 9.49/5.24        ( ( Option != none_num )
% 9.49/5.24       => ( ( some_num @ ( the_num @ Option ) )
% 9.49/5.24          = Option ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_742_le__add__diff__inverse,axiom,
% 9.49/5.24      ! [B: real,A: real] :
% 9.49/5.24        ( ( ord_less_eq_real @ B @ A )
% 9.49/5.24       => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 9.49/5.24          = A ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_743_le__add__diff__inverse,axiom,
% 9.49/5.24      ! [B: rat,A: rat] :
% 9.49/5.24        ( ( ord_less_eq_rat @ B @ A )
% 9.49/5.24       => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 9.49/5.24          = A ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_744_le__add__diff__inverse,axiom,
% 9.49/5.24      ! [B: nat,A: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ B @ A )
% 9.49/5.24       => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 9.49/5.24          = A ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_745_le__add__diff__inverse,axiom,
% 9.49/5.24      ! [B: int,A: int] :
% 9.49/5.24        ( ( ord_less_eq_int @ B @ A )
% 9.49/5.24       => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 9.49/5.24          = A ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_746_le__add__diff__inverse2,axiom,
% 9.49/5.24      ! [B: real,A: real] :
% 9.49/5.24        ( ( ord_less_eq_real @ B @ A )
% 9.49/5.24       => ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 9.49/5.24          = A ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_747_le__add__diff__inverse2,axiom,
% 9.49/5.24      ! [B: rat,A: rat] :
% 9.49/5.24        ( ( ord_less_eq_rat @ B @ A )
% 9.49/5.24       => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 9.49/5.24          = A ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_748_le__add__diff__inverse2,axiom,
% 9.49/5.24      ! [B: nat,A: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ B @ A )
% 9.49/5.24       => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 9.49/5.24          = A ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_749_le__add__diff__inverse2,axiom,
% 9.49/5.24      ! [B: int,A: int] :
% 9.49/5.24        ( ( ord_less_eq_int @ B @ A )
% 9.49/5.24       => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 9.49/5.24          = A ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_750_minNullmin,axiom,
% 9.49/5.24      ! [T: vEBT_VEBT] :
% 9.49/5.24        ( ( vEBT_VEBT_minNull @ T )
% 9.49/5.24       => ( ( vEBT_vebt_mint @ T )
% 9.49/5.24          = none_nat ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_751_minminNull,axiom,
% 9.49/5.24      ! [T: vEBT_VEBT] :
% 9.49/5.24        ( ( ( vEBT_vebt_mint @ T )
% 9.49/5.24          = none_nat )
% 9.49/5.24       => ( vEBT_VEBT_minNull @ T ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_752_option_Oinject,axiom,
% 9.49/5.24      ! [X23: product_prod_nat_nat,Y22: product_prod_nat_nat] :
% 9.49/5.24        ( ( ( some_P7363390416028606310at_nat @ X23 )
% 9.49/5.24          = ( some_P7363390416028606310at_nat @ Y22 ) )
% 9.49/5.24        = ( X23 = Y22 ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_753_option_Oinject,axiom,
% 9.49/5.24      ! [X23: nat,Y22: nat] :
% 9.49/5.24        ( ( ( some_nat @ X23 )
% 9.49/5.24          = ( some_nat @ Y22 ) )
% 9.49/5.24        = ( X23 = Y22 ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_754_option_Oinject,axiom,
% 9.49/5.24      ! [X23: num,Y22: num] :
% 9.49/5.24        ( ( ( some_num @ X23 )
% 9.49/5.24          = ( some_num @ Y22 ) )
% 9.49/5.24        = ( X23 = Y22 ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_755_list__update__overwrite,axiom,
% 9.49/5.24      ! [Xs2: list_VEBT_VEBT,I2: nat,X: vEBT_VEBT,Y2: vEBT_VEBT] :
% 9.49/5.24        ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ I2 @ Y2 )
% 9.49/5.24        = ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ Y2 ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_756_geqmaxNone,axiom,
% 9.49/5.24      ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X: nat] :
% 9.49/5.24        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 9.49/5.24       => ( ( ord_less_eq_nat @ Ma @ X )
% 9.49/5.24         => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 9.49/5.24            = none_nat ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_757_div__by__1,axiom,
% 9.49/5.24      ! [A: complex] :
% 9.49/5.24        ( ( divide1717551699836669952omplex @ A @ one_one_complex )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_758_div__by__1,axiom,
% 9.49/5.24      ! [A: real] :
% 9.49/5.24        ( ( divide_divide_real @ A @ one_one_real )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_759_div__by__1,axiom,
% 9.49/5.24      ! [A: rat] :
% 9.49/5.24        ( ( divide_divide_rat @ A @ one_one_rat )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_760_div__by__1,axiom,
% 9.49/5.24      ! [A: nat] :
% 9.49/5.24        ( ( divide_divide_nat @ A @ one_one_nat )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_761_div__by__1,axiom,
% 9.49/5.24      ! [A: int] :
% 9.49/5.24        ( ( divide_divide_int @ A @ one_one_int )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_762_not__None__eq,axiom,
% 9.49/5.24      ! [X: option4927543243414619207at_nat] :
% 9.49/5.24        ( ( X != none_P5556105721700978146at_nat )
% 9.49/5.24        = ( ? [Y: product_prod_nat_nat] :
% 9.49/5.24              ( X
% 9.49/5.24              = ( some_P7363390416028606310at_nat @ Y ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_763_not__None__eq,axiom,
% 9.49/5.24      ! [X: option_nat] :
% 9.49/5.24        ( ( X != none_nat )
% 9.49/5.24        = ( ? [Y: nat] :
% 9.49/5.24              ( X
% 9.49/5.24              = ( some_nat @ Y ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_764_not__None__eq,axiom,
% 9.49/5.24      ! [X: option_num] :
% 9.49/5.24        ( ( X != none_num )
% 9.49/5.24        = ( ? [Y: num] :
% 9.49/5.24              ( X
% 9.49/5.24              = ( some_num @ Y ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_765_not__Some__eq,axiom,
% 9.49/5.24      ! [X: option4927543243414619207at_nat] :
% 9.49/5.24        ( ( ! [Y: product_prod_nat_nat] :
% 9.49/5.24              ( X
% 9.49/5.24             != ( some_P7363390416028606310at_nat @ Y ) ) )
% 9.49/5.24        = ( X = none_P5556105721700978146at_nat ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_766_not__Some__eq,axiom,
% 9.49/5.24      ! [X: option_nat] :
% 9.49/5.24        ( ( ! [Y: nat] :
% 9.49/5.24              ( X
% 9.49/5.24             != ( some_nat @ Y ) ) )
% 9.49/5.24        = ( X = none_nat ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_767_not__Some__eq,axiom,
% 9.49/5.24      ! [X: option_num] :
% 9.49/5.24        ( ( ! [Y: num] :
% 9.49/5.24              ( X
% 9.49/5.24             != ( some_num @ Y ) ) )
% 9.49/5.24        = ( X = none_num ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_768_length__list__update,axiom,
% 9.49/5.24      ! [Xs2: list_VEBT_VEBT,I2: nat,X: vEBT_VEBT] :
% 9.49/5.24        ( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) )
% 9.49/5.24        = ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_769_length__list__update,axiom,
% 9.49/5.24      ! [Xs2: list_o,I2: nat,X: $o] :
% 9.49/5.24        ( ( size_size_list_o @ ( list_update_o @ Xs2 @ I2 @ X ) )
% 9.49/5.24        = ( size_size_list_o @ Xs2 ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_770_length__list__update,axiom,
% 9.49/5.24      ! [Xs2: list_nat,I2: nat,X: nat] :
% 9.49/5.24        ( ( size_size_list_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) )
% 9.49/5.24        = ( size_size_list_nat @ Xs2 ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_771_length__list__update,axiom,
% 9.49/5.24      ! [Xs2: list_int,I2: nat,X: int] :
% 9.49/5.24        ( ( size_size_list_int @ ( list_update_int @ Xs2 @ I2 @ X ) )
% 9.49/5.24        = ( size_size_list_int @ Xs2 ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_772_list__update__id,axiom,
% 9.49/5.24      ! [Xs2: list_nat,I2: nat] :
% 9.49/5.24        ( ( list_update_nat @ Xs2 @ I2 @ ( nth_nat @ Xs2 @ I2 ) )
% 9.49/5.24        = Xs2 ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_773_list__update__id,axiom,
% 9.49/5.24      ! [Xs2: list_VEBT_VEBT,I2: nat] :
% 9.49/5.24        ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ ( nth_VEBT_VEBT @ Xs2 @ I2 ) )
% 9.49/5.24        = Xs2 ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_774_nth__list__update__neq,axiom,
% 9.49/5.24      ! [I2: nat,J: nat,Xs2: list_nat,X: nat] :
% 9.49/5.24        ( ( I2 != J )
% 9.49/5.24       => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) @ J )
% 9.49/5.24          = ( nth_nat @ Xs2 @ J ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_775_nth__list__update__neq,axiom,
% 9.49/5.24      ! [I2: nat,J: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 9.49/5.24        ( ( I2 != J )
% 9.49/5.24       => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ J )
% 9.49/5.24          = ( nth_VEBT_VEBT @ Xs2 @ J ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_776_max__Suc__Suc,axiom,
% 9.49/5.24      ! [M: nat,N: nat] :
% 9.49/5.24        ( ( ord_max_nat @ ( suc @ M ) @ ( suc @ N ) )
% 9.49/5.24        = ( suc @ ( ord_max_nat @ M @ N ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_777_max__number__of_I1_J,axiom,
% 9.49/5.24      ! [U: num,V: num] :
% 9.49/5.24        ( ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 9.49/5.24         => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 9.49/5.24            = ( numera1916890842035813515d_enat @ V ) ) )
% 9.49/5.24        & ( ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 9.49/5.24         => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 9.49/5.24            = ( numera1916890842035813515d_enat @ U ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_778_max__number__of_I1_J,axiom,
% 9.49/5.24      ! [U: num,V: num] :
% 9.49/5.24        ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 9.49/5.24         => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 9.49/5.24            = ( numeral_numeral_real @ V ) ) )
% 9.49/5.24        & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 9.49/5.24         => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 9.49/5.24            = ( numeral_numeral_real @ U ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_779_max__number__of_I1_J,axiom,
% 9.49/5.24      ! [U: num,V: num] :
% 9.49/5.24        ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 9.49/5.24         => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 9.49/5.24            = ( numeral_numeral_rat @ V ) ) )
% 9.49/5.24        & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 9.49/5.24         => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 9.49/5.24            = ( numeral_numeral_rat @ U ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_780_max__number__of_I1_J,axiom,
% 9.49/5.24      ! [U: num,V: num] :
% 9.49/5.24        ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 9.49/5.24         => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 9.49/5.24            = ( numeral_numeral_nat @ V ) ) )
% 9.49/5.24        & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 9.49/5.24         => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 9.49/5.24            = ( numeral_numeral_nat @ U ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_781_max__number__of_I1_J,axiom,
% 9.49/5.24      ! [U: num,V: num] :
% 9.49/5.24        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 9.49/5.24         => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 9.49/5.24            = ( numeral_numeral_int @ V ) ) )
% 9.49/5.24        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 9.49/5.24         => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 9.49/5.24            = ( numeral_numeral_int @ U ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_782_max__0__1_I6_J,axiom,
% 9.49/5.24      ! [X: num] :
% 9.49/5.24        ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X ) @ one_on7984719198319812577d_enat )
% 9.49/5.24        = ( numera1916890842035813515d_enat @ X ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_783_max__0__1_I6_J,axiom,
% 9.49/5.24      ! [X: num] :
% 9.49/5.24        ( ( ord_max_real @ ( numeral_numeral_real @ X ) @ one_one_real )
% 9.49/5.24        = ( numeral_numeral_real @ X ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_784_max__0__1_I6_J,axiom,
% 9.49/5.24      ! [X: num] :
% 9.49/5.24        ( ( ord_max_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat )
% 9.49/5.24        = ( numeral_numeral_rat @ X ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_785_max__0__1_I6_J,axiom,
% 9.49/5.24      ! [X: num] :
% 9.49/5.24        ( ( ord_max_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat )
% 9.49/5.24        = ( numeral_numeral_nat @ X ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_786_max__0__1_I6_J,axiom,
% 9.49/5.24      ! [X: num] :
% 9.49/5.24        ( ( ord_max_int @ ( numeral_numeral_int @ X ) @ one_one_int )
% 9.49/5.24        = ( numeral_numeral_int @ X ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_787_max__0__1_I5_J,axiom,
% 9.49/5.24      ! [X: num] :
% 9.49/5.24        ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 9.49/5.24        = ( numera1916890842035813515d_enat @ X ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_788_max__0__1_I5_J,axiom,
% 9.49/5.24      ! [X: num] :
% 9.49/5.24        ( ( ord_max_real @ one_one_real @ ( numeral_numeral_real @ X ) )
% 9.49/5.24        = ( numeral_numeral_real @ X ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_789_max__0__1_I5_J,axiom,
% 9.49/5.24      ! [X: num] :
% 9.49/5.24        ( ( ord_max_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 9.49/5.24        = ( numeral_numeral_rat @ X ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_790_max__0__1_I5_J,axiom,
% 9.49/5.24      ! [X: num] :
% 9.49/5.24        ( ( ord_max_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 9.49/5.24        = ( numeral_numeral_nat @ X ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_791_max__0__1_I5_J,axiom,
% 9.49/5.24      ! [X: num] :
% 9.49/5.24        ( ( ord_max_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 9.49/5.24        = ( numeral_numeral_int @ X ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_792_nat__add__max__left,axiom,
% 9.49/5.24      ! [M: nat,N: nat,Q2: nat] :
% 9.49/5.24        ( ( plus_plus_nat @ ( ord_max_nat @ M @ N ) @ Q2 )
% 9.49/5.24        = ( ord_max_nat @ ( plus_plus_nat @ M @ Q2 ) @ ( plus_plus_nat @ N @ Q2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_793_nat__add__max__right,axiom,
% 9.49/5.24      ! [M: nat,N: nat,Q2: nat] :
% 9.49/5.24        ( ( plus_plus_nat @ M @ ( ord_max_nat @ N @ Q2 ) )
% 9.49/5.24        = ( ord_max_nat @ ( plus_plus_nat @ M @ N ) @ ( plus_plus_nat @ M @ Q2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_794_nat__mult__max__right,axiom,
% 9.49/5.24      ! [M: nat,N: nat,Q2: nat] :
% 9.49/5.24        ( ( times_times_nat @ M @ ( ord_max_nat @ N @ Q2 ) )
% 9.49/5.24        = ( ord_max_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_795_nat__mult__max__left,axiom,
% 9.49/5.24      ! [M: nat,N: nat,Q2: nat] :
% 9.49/5.24        ( ( times_times_nat @ ( ord_max_nat @ M @ N ) @ Q2 )
% 9.49/5.24        = ( ord_max_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N @ Q2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_796_add__diff__assoc__enat,axiom,
% 9.49/5.24      ! [Z: extended_enat,Y2: extended_enat,X: extended_enat] :
% 9.49/5.24        ( ( ord_le2932123472753598470d_enat @ Z @ Y2 )
% 9.49/5.24       => ( ( plus_p3455044024723400733d_enat @ X @ ( minus_3235023915231533773d_enat @ Y2 @ Z ) )
% 9.49/5.24          = ( minus_3235023915231533773d_enat @ ( plus_p3455044024723400733d_enat @ X @ Y2 ) @ Z ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_797_nat__minus__add__max,axiom,
% 9.49/5.24      ! [N: nat,M: nat] :
% 9.49/5.24        ( ( plus_plus_nat @ ( minus_minus_nat @ N @ M ) @ M )
% 9.49/5.24        = ( ord_max_nat @ N @ M ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_798_xor__num_Ocases,axiom,
% 9.49/5.24      ! [X: product_prod_num_num] :
% 9.49/5.24        ( ( X
% 9.49/5.24         != ( product_Pair_num_num @ one @ one ) )
% 9.49/5.24       => ( ! [N3: num] :
% 9.49/5.24              ( X
% 9.49/5.24             != ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) )
% 9.49/5.24         => ( ! [N3: num] :
% 9.49/5.24                ( X
% 9.49/5.24               != ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) )
% 9.49/5.24           => ( ! [M4: num] :
% 9.49/5.24                  ( X
% 9.49/5.24                 != ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) )
% 9.49/5.24             => ( ! [M4: num,N3: num] :
% 9.49/5.24                    ( X
% 9.49/5.24                   != ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N3 ) ) )
% 9.49/5.24               => ( ! [M4: num,N3: num] :
% 9.49/5.24                      ( X
% 9.49/5.24                     != ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N3 ) ) )
% 9.49/5.24                 => ( ! [M4: num] :
% 9.49/5.24                        ( X
% 9.49/5.24                       != ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) )
% 9.49/5.24                   => ( ! [M4: num,N3: num] :
% 9.49/5.24                          ( X
% 9.49/5.24                         != ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N3 ) ) )
% 9.49/5.24                     => ~ ! [M4: num,N3: num] :
% 9.49/5.24                            ( X
% 9.49/5.24                           != ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_799_linorder__neqE__linordered__idom,axiom,
% 9.49/5.24      ! [X: real,Y2: real] :
% 9.49/5.24        ( ( X != Y2 )
% 9.49/5.24       => ( ~ ( ord_less_real @ X @ Y2 )
% 9.49/5.24         => ( ord_less_real @ Y2 @ X ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_800_linorder__neqE__linordered__idom,axiom,
% 9.49/5.24      ! [X: rat,Y2: rat] :
% 9.49/5.24        ( ( X != Y2 )
% 9.49/5.24       => ( ~ ( ord_less_rat @ X @ Y2 )
% 9.49/5.24         => ( ord_less_rat @ Y2 @ X ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_801_linorder__neqE__linordered__idom,axiom,
% 9.49/5.24      ! [X: int,Y2: int] :
% 9.49/5.24        ( ( X != Y2 )
% 9.49/5.24       => ( ~ ( ord_less_int @ X @ Y2 )
% 9.49/5.24         => ( ord_less_int @ Y2 @ X ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_802_subset__code_I1_J,axiom,
% 9.49/5.24      ! [Xs2: list_P6011104703257516679at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.49/5.24        ( ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ Xs2 ) @ B2 )
% 9.49/5.24        = ( ! [X2: product_prod_nat_nat] :
% 9.49/5.24              ( ( member8440522571783428010at_nat @ X2 @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 9.49/5.24             => ( member8440522571783428010at_nat @ X2 @ B2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_803_subset__code_I1_J,axiom,
% 9.49/5.24      ! [Xs2: list_complex,B2: set_complex] :
% 9.49/5.24        ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ B2 )
% 9.49/5.24        = ( ! [X2: complex] :
% 9.49/5.24              ( ( member_complex @ X2 @ ( set_complex2 @ Xs2 ) )
% 9.49/5.24             => ( member_complex @ X2 @ B2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_804_subset__code_I1_J,axiom,
% 9.49/5.24      ! [Xs2: list_VEBT_VEBT,B2: set_VEBT_VEBT] :
% 9.49/5.24        ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ B2 )
% 9.49/5.24        = ( ! [X2: vEBT_VEBT] :
% 9.49/5.24              ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 9.49/5.24             => ( member_VEBT_VEBT @ X2 @ B2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_805_subset__code_I1_J,axiom,
% 9.49/5.24      ! [Xs2: list_int,B2: set_int] :
% 9.49/5.24        ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ B2 )
% 9.49/5.24        = ( ! [X2: int] :
% 9.49/5.24              ( ( member_int @ X2 @ ( set_int2 @ Xs2 ) )
% 9.49/5.24             => ( member_int @ X2 @ B2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_806_subset__code_I1_J,axiom,
% 9.49/5.24      ! [Xs2: list_real,B2: set_real] :
% 9.49/5.24        ( ( ord_less_eq_set_real @ ( set_real2 @ Xs2 ) @ B2 )
% 9.49/5.24        = ( ! [X2: real] :
% 9.49/5.24              ( ( member_real @ X2 @ ( set_real2 @ Xs2 ) )
% 9.49/5.24             => ( member_real @ X2 @ B2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_807_subset__code_I1_J,axiom,
% 9.49/5.24      ! [Xs2: list_nat,B2: set_nat] :
% 9.49/5.24        ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ B2 )
% 9.49/5.24        = ( ! [X2: nat] :
% 9.49/5.24              ( ( member_nat @ X2 @ ( set_nat2 @ Xs2 ) )
% 9.49/5.24             => ( member_nat @ X2 @ B2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_808_neq__if__length__neq,axiom,
% 9.49/5.24      ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 9.49/5.24        ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 9.49/5.24         != ( size_s6755466524823107622T_VEBT @ Ys ) )
% 9.49/5.24       => ( Xs2 != Ys ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_809_neq__if__length__neq,axiom,
% 9.49/5.24      ! [Xs2: list_o,Ys: list_o] :
% 9.49/5.24        ( ( ( size_size_list_o @ Xs2 )
% 9.49/5.24         != ( size_size_list_o @ Ys ) )
% 9.49/5.24       => ( Xs2 != Ys ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_810_neq__if__length__neq,axiom,
% 9.49/5.24      ! [Xs2: list_nat,Ys: list_nat] :
% 9.49/5.24        ( ( ( size_size_list_nat @ Xs2 )
% 9.49/5.24         != ( size_size_list_nat @ Ys ) )
% 9.49/5.24       => ( Xs2 != Ys ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_811_neq__if__length__neq,axiom,
% 9.49/5.24      ! [Xs2: list_int,Ys: list_int] :
% 9.49/5.24        ( ( ( size_size_list_int @ Xs2 )
% 9.49/5.24         != ( size_size_list_int @ Ys ) )
% 9.49/5.24       => ( Xs2 != Ys ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_812_Ex__list__of__length,axiom,
% 9.49/5.24      ! [N: nat] :
% 9.49/5.24      ? [Xs3: list_VEBT_VEBT] :
% 9.49/5.24        ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 9.49/5.24        = N ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_813_Ex__list__of__length,axiom,
% 9.49/5.24      ! [N: nat] :
% 9.49/5.24      ? [Xs3: list_o] :
% 9.49/5.24        ( ( size_size_list_o @ Xs3 )
% 9.49/5.24        = N ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_814_Ex__list__of__length,axiom,
% 9.49/5.24      ! [N: nat] :
% 9.49/5.24      ? [Xs3: list_nat] :
% 9.49/5.24        ( ( size_size_list_nat @ Xs3 )
% 9.49/5.24        = N ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_815_Ex__list__of__length,axiom,
% 9.49/5.24      ! [N: nat] :
% 9.49/5.24      ? [Xs3: list_int] :
% 9.49/5.24        ( ( size_size_list_int @ Xs3 )
% 9.49/5.24        = N ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_816_list__update__swap,axiom,
% 9.49/5.24      ! [I2: nat,I5: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT,X6: vEBT_VEBT] :
% 9.49/5.24        ( ( I2 != I5 )
% 9.49/5.24       => ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ I5 @ X6 )
% 9.49/5.24          = ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I5 @ X6 ) @ I2 @ X ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_817_ring__class_Oring__distribs_I2_J,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat] :
% 9.49/5.24        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 9.49/5.24        = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_818_ring__class_Oring__distribs_I2_J,axiom,
% 9.49/5.24      ! [A: complex,B: complex,C: complex] :
% 9.49/5.24        ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 9.49/5.24        = ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_819_ring__class_Oring__distribs_I2_J,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real] :
% 9.49/5.24        ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 9.49/5.24        = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_820_ring__class_Oring__distribs_I2_J,axiom,
% 9.49/5.24      ! [A: int,B: int,C: int] :
% 9.49/5.24        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 9.49/5.24        = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_821_ring__class_Oring__distribs_I1_J,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat] :
% 9.49/5.24        ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 9.49/5.24        = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_822_ring__class_Oring__distribs_I1_J,axiom,
% 9.49/5.24      ! [A: complex,B: complex,C: complex] :
% 9.49/5.24        ( ( times_times_complex @ A @ ( plus_plus_complex @ B @ C ) )
% 9.49/5.24        = ( plus_plus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_823_ring__class_Oring__distribs_I1_J,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real] :
% 9.49/5.24        ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 9.49/5.24        = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_824_ring__class_Oring__distribs_I1_J,axiom,
% 9.49/5.24      ! [A: int,B: int,C: int] :
% 9.49/5.24        ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 9.49/5.24        = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_825_comm__semiring__class_Odistrib,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat] :
% 9.49/5.24        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 9.49/5.24        = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_826_comm__semiring__class_Odistrib,axiom,
% 9.49/5.24      ! [A: complex,B: complex,C: complex] :
% 9.49/5.24        ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 9.49/5.24        = ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_827_comm__semiring__class_Odistrib,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real] :
% 9.49/5.24        ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 9.49/5.24        = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_828_comm__semiring__class_Odistrib,axiom,
% 9.49/5.24      ! [A: nat,B: nat,C: nat] :
% 9.49/5.24        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 9.49/5.24        = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_829_comm__semiring__class_Odistrib,axiom,
% 9.49/5.24      ! [A: int,B: int,C: int] :
% 9.49/5.24        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 9.49/5.24        = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_830_distrib__left,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat] :
% 9.49/5.24        ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 9.49/5.24        = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_831_distrib__left,axiom,
% 9.49/5.24      ! [A: complex,B: complex,C: complex] :
% 9.49/5.24        ( ( times_times_complex @ A @ ( plus_plus_complex @ B @ C ) )
% 9.49/5.24        = ( plus_plus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_832_distrib__left,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real] :
% 9.49/5.24        ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 9.49/5.24        = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_833_distrib__left,axiom,
% 9.49/5.24      ! [A: nat,B: nat,C: nat] :
% 9.49/5.24        ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 9.49/5.24        = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_834_distrib__left,axiom,
% 9.49/5.24      ! [A: int,B: int,C: int] :
% 9.49/5.24        ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 9.49/5.24        = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_835_distrib__right,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat] :
% 9.49/5.24        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 9.49/5.24        = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_836_distrib__right,axiom,
% 9.49/5.24      ! [A: complex,B: complex,C: complex] :
% 9.49/5.24        ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 9.49/5.24        = ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_837_distrib__right,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real] :
% 9.49/5.24        ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 9.49/5.24        = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_838_distrib__right,axiom,
% 9.49/5.24      ! [A: nat,B: nat,C: nat] :
% 9.49/5.24        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 9.49/5.24        = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_839_distrib__right,axiom,
% 9.49/5.24      ! [A: int,B: int,C: int] :
% 9.49/5.24        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 9.49/5.24        = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_840_combine__common__factor,axiom,
% 9.49/5.24      ! [A: rat,E: rat,B: rat,C: rat] :
% 9.49/5.24        ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ C ) )
% 9.49/5.24        = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ E ) @ C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_841_combine__common__factor,axiom,
% 9.49/5.24      ! [A: complex,E: complex,B: complex,C: complex] :
% 9.49/5.24        ( ( plus_plus_complex @ ( times_times_complex @ A @ E ) @ ( plus_plus_complex @ ( times_times_complex @ B @ E ) @ C ) )
% 9.49/5.24        = ( plus_plus_complex @ ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ E ) @ C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_842_combine__common__factor,axiom,
% 9.49/5.24      ! [A: real,E: real,B: real,C: real] :
% 9.49/5.24        ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ C ) )
% 9.49/5.24        = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ E ) @ C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_843_combine__common__factor,axiom,
% 9.49/5.24      ! [A: nat,E: nat,B: nat,C: nat] :
% 9.49/5.24        ( ( plus_plus_nat @ ( times_times_nat @ A @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E ) @ C ) )
% 9.49/5.24        = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E ) @ C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_844_combine__common__factor,axiom,
% 9.49/5.24      ! [A: int,E: int,B: int,C: int] :
% 9.49/5.24        ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ C ) )
% 9.49/5.24        = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E ) @ C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_845_right__diff__distrib_H,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat] :
% 9.49/5.24        ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 9.49/5.24        = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_846_right__diff__distrib_H,axiom,
% 9.49/5.24      ! [A: complex,B: complex,C: complex] :
% 9.49/5.24        ( ( times_times_complex @ A @ ( minus_minus_complex @ B @ C ) )
% 9.49/5.24        = ( minus_minus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_847_right__diff__distrib_H,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real] :
% 9.49/5.24        ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 9.49/5.24        = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_848_right__diff__distrib_H,axiom,
% 9.49/5.24      ! [A: nat,B: nat,C: nat] :
% 9.49/5.24        ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
% 9.49/5.24        = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_849_right__diff__distrib_H,axiom,
% 9.49/5.24      ! [A: int,B: int,C: int] :
% 9.49/5.24        ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 9.49/5.24        = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_850_left__diff__distrib_H,axiom,
% 9.49/5.24      ! [B: rat,C: rat,A: rat] :
% 9.49/5.24        ( ( times_times_rat @ ( minus_minus_rat @ B @ C ) @ A )
% 9.49/5.24        = ( minus_minus_rat @ ( times_times_rat @ B @ A ) @ ( times_times_rat @ C @ A ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_851_left__diff__distrib_H,axiom,
% 9.49/5.24      ! [B: complex,C: complex,A: complex] :
% 9.49/5.24        ( ( times_times_complex @ ( minus_minus_complex @ B @ C ) @ A )
% 9.49/5.24        = ( minus_minus_complex @ ( times_times_complex @ B @ A ) @ ( times_times_complex @ C @ A ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_852_left__diff__distrib_H,axiom,
% 9.49/5.24      ! [B: real,C: real,A: real] :
% 9.49/5.24        ( ( times_times_real @ ( minus_minus_real @ B @ C ) @ A )
% 9.49/5.24        = ( minus_minus_real @ ( times_times_real @ B @ A ) @ ( times_times_real @ C @ A ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_853_left__diff__distrib_H,axiom,
% 9.49/5.24      ! [B: nat,C: nat,A: nat] :
% 9.49/5.24        ( ( times_times_nat @ ( minus_minus_nat @ B @ C ) @ A )
% 9.49/5.24        = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_854_left__diff__distrib_H,axiom,
% 9.49/5.24      ! [B: int,C: int,A: int] :
% 9.49/5.24        ( ( times_times_int @ ( minus_minus_int @ B @ C ) @ A )
% 9.49/5.24        = ( minus_minus_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_855_right__diff__distrib,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat] :
% 9.49/5.24        ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 9.49/5.24        = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_856_right__diff__distrib,axiom,
% 9.49/5.24      ! [A: complex,B: complex,C: complex] :
% 9.49/5.24        ( ( times_times_complex @ A @ ( minus_minus_complex @ B @ C ) )
% 9.49/5.24        = ( minus_minus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_857_right__diff__distrib,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real] :
% 9.49/5.24        ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 9.49/5.24        = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_858_right__diff__distrib,axiom,
% 9.49/5.24      ! [A: int,B: int,C: int] :
% 9.49/5.24        ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 9.49/5.24        = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_859_left__diff__distrib,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat] :
% 9.49/5.24        ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 9.49/5.24        = ( minus_minus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_860_left__diff__distrib,axiom,
% 9.49/5.24      ! [A: complex,B: complex,C: complex] :
% 9.49/5.24        ( ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ C )
% 9.49/5.24        = ( minus_minus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_861_left__diff__distrib,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real] :
% 9.49/5.24        ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
% 9.49/5.24        = ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_862_left__diff__distrib,axiom,
% 9.49/5.24      ! [A: int,B: int,C: int] :
% 9.49/5.24        ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 9.49/5.24        = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_863_length__induct,axiom,
% 9.49/5.24      ! [P: list_VEBT_VEBT > $o,Xs2: list_VEBT_VEBT] :
% 9.49/5.24        ( ! [Xs3: list_VEBT_VEBT] :
% 9.49/5.24            ( ! [Ys2: list_VEBT_VEBT] :
% 9.49/5.24                ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ys2 ) @ ( size_s6755466524823107622T_VEBT @ Xs3 ) )
% 9.49/5.24               => ( P @ Ys2 ) )
% 9.49/5.24           => ( P @ Xs3 ) )
% 9.49/5.24       => ( P @ Xs2 ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_864_length__induct,axiom,
% 9.49/5.24      ! [P: list_o > $o,Xs2: list_o] :
% 9.49/5.24        ( ! [Xs3: list_o] :
% 9.49/5.24            ( ! [Ys2: list_o] :
% 9.49/5.24                ( ( ord_less_nat @ ( size_size_list_o @ Ys2 ) @ ( size_size_list_o @ Xs3 ) )
% 9.49/5.24               => ( P @ Ys2 ) )
% 9.49/5.24           => ( P @ Xs3 ) )
% 9.49/5.24       => ( P @ Xs2 ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_865_length__induct,axiom,
% 9.49/5.24      ! [P: list_nat > $o,Xs2: list_nat] :
% 9.49/5.24        ( ! [Xs3: list_nat] :
% 9.49/5.24            ( ! [Ys2: list_nat] :
% 9.49/5.24                ( ( ord_less_nat @ ( size_size_list_nat @ Ys2 ) @ ( size_size_list_nat @ Xs3 ) )
% 9.49/5.24               => ( P @ Ys2 ) )
% 9.49/5.24           => ( P @ Xs3 ) )
% 9.49/5.24       => ( P @ Xs2 ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_866_length__induct,axiom,
% 9.49/5.24      ! [P: list_int > $o,Xs2: list_int] :
% 9.49/5.24        ( ! [Xs3: list_int] :
% 9.49/5.24            ( ! [Ys2: list_int] :
% 9.49/5.24                ( ( ord_less_nat @ ( size_size_list_int @ Ys2 ) @ ( size_size_list_int @ Xs3 ) )
% 9.49/5.24               => ( P @ Ys2 ) )
% 9.49/5.24           => ( P @ Xs3 ) )
% 9.49/5.24       => ( P @ Xs2 ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_867_option_Odistinct_I1_J,axiom,
% 9.49/5.24      ! [X23: product_prod_nat_nat] :
% 9.49/5.24        ( none_P5556105721700978146at_nat
% 9.49/5.24       != ( some_P7363390416028606310at_nat @ X23 ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_868_option_Odistinct_I1_J,axiom,
% 9.49/5.24      ! [X23: nat] :
% 9.49/5.24        ( none_nat
% 9.49/5.24       != ( some_nat @ X23 ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_869_option_Odistinct_I1_J,axiom,
% 9.49/5.24      ! [X23: num] :
% 9.49/5.24        ( none_num
% 9.49/5.24       != ( some_num @ X23 ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_870_option_OdiscI,axiom,
% 9.49/5.24      ! [Option: option4927543243414619207at_nat,X23: product_prod_nat_nat] :
% 9.49/5.24        ( ( Option
% 9.49/5.24          = ( some_P7363390416028606310at_nat @ X23 ) )
% 9.49/5.24       => ( Option != none_P5556105721700978146at_nat ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_871_option_OdiscI,axiom,
% 9.49/5.24      ! [Option: option_nat,X23: nat] :
% 9.49/5.24        ( ( Option
% 9.49/5.24          = ( some_nat @ X23 ) )
% 9.49/5.24       => ( Option != none_nat ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_872_option_OdiscI,axiom,
% 9.49/5.24      ! [Option: option_num,X23: num] :
% 9.49/5.24        ( ( Option
% 9.49/5.24          = ( some_num @ X23 ) )
% 9.49/5.24       => ( Option != none_num ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_873_option_Oexhaust,axiom,
% 9.49/5.24      ! [Y2: option4927543243414619207at_nat] :
% 9.49/5.24        ( ( Y2 != none_P5556105721700978146at_nat )
% 9.49/5.24       => ~ ! [X22: product_prod_nat_nat] :
% 9.49/5.24              ( Y2
% 9.49/5.24             != ( some_P7363390416028606310at_nat @ X22 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_874_option_Oexhaust,axiom,
% 9.49/5.24      ! [Y2: option_nat] :
% 9.49/5.24        ( ( Y2 != none_nat )
% 9.49/5.24       => ~ ! [X22: nat] :
% 9.49/5.24              ( Y2
% 9.49/5.24             != ( some_nat @ X22 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_875_option_Oexhaust,axiom,
% 9.49/5.24      ! [Y2: option_num] :
% 9.49/5.24        ( ( Y2 != none_num )
% 9.49/5.24       => ~ ! [X22: num] :
% 9.49/5.24              ( Y2
% 9.49/5.24             != ( some_num @ X22 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_876_split__option__ex,axiom,
% 9.49/5.24      ( ( ^ [P2: option4927543243414619207at_nat > $o] :
% 9.49/5.24          ? [X7: option4927543243414619207at_nat] : ( P2 @ X7 ) )
% 9.49/5.24      = ( ^ [P3: option4927543243414619207at_nat > $o] :
% 9.49/5.24            ( ( P3 @ none_P5556105721700978146at_nat )
% 9.49/5.24            | ? [X2: product_prod_nat_nat] : ( P3 @ ( some_P7363390416028606310at_nat @ X2 ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_877_split__option__ex,axiom,
% 9.49/5.24      ( ( ^ [P2: option_nat > $o] :
% 9.49/5.24          ? [X7: option_nat] : ( P2 @ X7 ) )
% 9.49/5.24      = ( ^ [P3: option_nat > $o] :
% 9.49/5.24            ( ( P3 @ none_nat )
% 9.49/5.24            | ? [X2: nat] : ( P3 @ ( some_nat @ X2 ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_878_split__option__ex,axiom,
% 9.49/5.24      ( ( ^ [P2: option_num > $o] :
% 9.49/5.24          ? [X7: option_num] : ( P2 @ X7 ) )
% 9.49/5.24      = ( ^ [P3: option_num > $o] :
% 9.49/5.24            ( ( P3 @ none_num )
% 9.49/5.24            | ? [X2: num] : ( P3 @ ( some_num @ X2 ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_879_split__option__all,axiom,
% 9.49/5.24      ( ( ^ [P2: option4927543243414619207at_nat > $o] :
% 9.49/5.24          ! [X7: option4927543243414619207at_nat] : ( P2 @ X7 ) )
% 9.49/5.24      = ( ^ [P3: option4927543243414619207at_nat > $o] :
% 9.49/5.24            ( ( P3 @ none_P5556105721700978146at_nat )
% 9.49/5.24            & ! [X2: product_prod_nat_nat] : ( P3 @ ( some_P7363390416028606310at_nat @ X2 ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_880_split__option__all,axiom,
% 9.49/5.24      ( ( ^ [P2: option_nat > $o] :
% 9.49/5.24          ! [X7: option_nat] : ( P2 @ X7 ) )
% 9.49/5.24      = ( ^ [P3: option_nat > $o] :
% 9.49/5.24            ( ( P3 @ none_nat )
% 9.49/5.24            & ! [X2: nat] : ( P3 @ ( some_nat @ X2 ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_881_split__option__all,axiom,
% 9.49/5.24      ( ( ^ [P2: option_num > $o] :
% 9.49/5.24          ! [X7: option_num] : ( P2 @ X7 ) )
% 9.49/5.24      = ( ^ [P3: option_num > $o] :
% 9.49/5.24            ( ( P3 @ none_num )
% 9.49/5.24            & ! [X2: num] : ( P3 @ ( some_num @ X2 ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_882_combine__options__cases,axiom,
% 9.49/5.24      ! [X: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option4927543243414619207at_nat > $o,Y2: option4927543243414619207at_nat] :
% 9.49/5.24        ( ( ( X = none_P5556105721700978146at_nat )
% 9.49/5.24         => ( P @ X @ Y2 ) )
% 9.49/5.24       => ( ( ( Y2 = none_P5556105721700978146at_nat )
% 9.49/5.24           => ( P @ X @ Y2 ) )
% 9.49/5.24         => ( ! [A4: product_prod_nat_nat,B3: product_prod_nat_nat] :
% 9.49/5.24                ( ( X
% 9.49/5.24                  = ( some_P7363390416028606310at_nat @ A4 ) )
% 9.49/5.24               => ( ( Y2
% 9.49/5.24                    = ( some_P7363390416028606310at_nat @ B3 ) )
% 9.49/5.24                 => ( P @ X @ Y2 ) ) )
% 9.49/5.24           => ( P @ X @ Y2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_883_combine__options__cases,axiom,
% 9.49/5.24      ! [X: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_nat > $o,Y2: option_nat] :
% 9.49/5.24        ( ( ( X = none_P5556105721700978146at_nat )
% 9.49/5.24         => ( P @ X @ Y2 ) )
% 9.49/5.24       => ( ( ( Y2 = none_nat )
% 9.49/5.24           => ( P @ X @ Y2 ) )
% 9.49/5.24         => ( ! [A4: product_prod_nat_nat,B3: nat] :
% 9.49/5.24                ( ( X
% 9.49/5.24                  = ( some_P7363390416028606310at_nat @ A4 ) )
% 9.49/5.24               => ( ( Y2
% 9.49/5.24                    = ( some_nat @ B3 ) )
% 9.49/5.24                 => ( P @ X @ Y2 ) ) )
% 9.49/5.24           => ( P @ X @ Y2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_884_combine__options__cases,axiom,
% 9.49/5.24      ! [X: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_num > $o,Y2: option_num] :
% 9.49/5.24        ( ( ( X = none_P5556105721700978146at_nat )
% 9.49/5.24         => ( P @ X @ Y2 ) )
% 9.49/5.24       => ( ( ( Y2 = none_num )
% 9.49/5.24           => ( P @ X @ Y2 ) )
% 9.49/5.24         => ( ! [A4: product_prod_nat_nat,B3: num] :
% 9.49/5.24                ( ( X
% 9.49/5.24                  = ( some_P7363390416028606310at_nat @ A4 ) )
% 9.49/5.24               => ( ( Y2
% 9.49/5.24                    = ( some_num @ B3 ) )
% 9.49/5.24                 => ( P @ X @ Y2 ) ) )
% 9.49/5.24           => ( P @ X @ Y2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_885_combine__options__cases,axiom,
% 9.49/5.24      ! [X: option_nat,P: option_nat > option4927543243414619207at_nat > $o,Y2: option4927543243414619207at_nat] :
% 9.49/5.24        ( ( ( X = none_nat )
% 9.49/5.24         => ( P @ X @ Y2 ) )
% 9.49/5.24       => ( ( ( Y2 = none_P5556105721700978146at_nat )
% 9.49/5.24           => ( P @ X @ Y2 ) )
% 9.49/5.24         => ( ! [A4: nat,B3: product_prod_nat_nat] :
% 9.49/5.24                ( ( X
% 9.49/5.24                  = ( some_nat @ A4 ) )
% 9.49/5.24               => ( ( Y2
% 9.49/5.24                    = ( some_P7363390416028606310at_nat @ B3 ) )
% 9.49/5.24                 => ( P @ X @ Y2 ) ) )
% 9.49/5.24           => ( P @ X @ Y2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_886_combine__options__cases,axiom,
% 9.49/5.24      ! [X: option_nat,P: option_nat > option_nat > $o,Y2: option_nat] :
% 9.49/5.24        ( ( ( X = none_nat )
% 9.49/5.24         => ( P @ X @ Y2 ) )
% 9.49/5.24       => ( ( ( Y2 = none_nat )
% 9.49/5.24           => ( P @ X @ Y2 ) )
% 9.49/5.24         => ( ! [A4: nat,B3: nat] :
% 9.49/5.24                ( ( X
% 9.49/5.24                  = ( some_nat @ A4 ) )
% 9.49/5.24               => ( ( Y2
% 9.49/5.24                    = ( some_nat @ B3 ) )
% 9.49/5.24                 => ( P @ X @ Y2 ) ) )
% 9.49/5.24           => ( P @ X @ Y2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_887_combine__options__cases,axiom,
% 9.49/5.24      ! [X: option_nat,P: option_nat > option_num > $o,Y2: option_num] :
% 9.49/5.24        ( ( ( X = none_nat )
% 9.49/5.24         => ( P @ X @ Y2 ) )
% 9.49/5.24       => ( ( ( Y2 = none_num )
% 9.49/5.24           => ( P @ X @ Y2 ) )
% 9.49/5.24         => ( ! [A4: nat,B3: num] :
% 9.49/5.24                ( ( X
% 9.49/5.24                  = ( some_nat @ A4 ) )
% 9.49/5.24               => ( ( Y2
% 9.49/5.24                    = ( some_num @ B3 ) )
% 9.49/5.24                 => ( P @ X @ Y2 ) ) )
% 9.49/5.24           => ( P @ X @ Y2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_888_combine__options__cases,axiom,
% 9.49/5.24      ! [X: option_num,P: option_num > option4927543243414619207at_nat > $o,Y2: option4927543243414619207at_nat] :
% 9.49/5.24        ( ( ( X = none_num )
% 9.49/5.24         => ( P @ X @ Y2 ) )
% 9.49/5.24       => ( ( ( Y2 = none_P5556105721700978146at_nat )
% 9.49/5.24           => ( P @ X @ Y2 ) )
% 9.49/5.24         => ( ! [A4: num,B3: product_prod_nat_nat] :
% 9.49/5.24                ( ( X
% 9.49/5.24                  = ( some_num @ A4 ) )
% 9.49/5.24               => ( ( Y2
% 9.49/5.24                    = ( some_P7363390416028606310at_nat @ B3 ) )
% 9.49/5.24                 => ( P @ X @ Y2 ) ) )
% 9.49/5.24           => ( P @ X @ Y2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_889_combine__options__cases,axiom,
% 9.49/5.24      ! [X: option_num,P: option_num > option_nat > $o,Y2: option_nat] :
% 9.49/5.24        ( ( ( X = none_num )
% 9.49/5.24         => ( P @ X @ Y2 ) )
% 9.49/5.24       => ( ( ( Y2 = none_nat )
% 9.49/5.24           => ( P @ X @ Y2 ) )
% 9.49/5.24         => ( ! [A4: num,B3: nat] :
% 9.49/5.24                ( ( X
% 9.49/5.24                  = ( some_num @ A4 ) )
% 9.49/5.24               => ( ( Y2
% 9.49/5.24                    = ( some_nat @ B3 ) )
% 9.49/5.24                 => ( P @ X @ Y2 ) ) )
% 9.49/5.24           => ( P @ X @ Y2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_890_combine__options__cases,axiom,
% 9.49/5.24      ! [X: option_num,P: option_num > option_num > $o,Y2: option_num] :
% 9.49/5.24        ( ( ( X = none_num )
% 9.49/5.24         => ( P @ X @ Y2 ) )
% 9.49/5.24       => ( ( ( Y2 = none_num )
% 9.49/5.24           => ( P @ X @ Y2 ) )
% 9.49/5.24         => ( ! [A4: num,B3: num] :
% 9.49/5.24                ( ( X
% 9.49/5.24                  = ( some_num @ A4 ) )
% 9.49/5.24               => ( ( Y2
% 9.49/5.24                    = ( some_num @ B3 ) )
% 9.49/5.24                 => ( P @ X @ Y2 ) ) )
% 9.49/5.24           => ( P @ X @ Y2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_891_option_Osel,axiom,
% 9.49/5.24      ! [X23: product_prod_nat_nat] :
% 9.49/5.24        ( ( the_Pr8591224930841456533at_nat @ ( some_P7363390416028606310at_nat @ X23 ) )
% 9.49/5.24        = X23 ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_892_option_Osel,axiom,
% 9.49/5.24      ! [X23: nat] :
% 9.49/5.24        ( ( the_nat @ ( some_nat @ X23 ) )
% 9.49/5.24        = X23 ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_893_option_Osel,axiom,
% 9.49/5.24      ! [X23: num] :
% 9.49/5.24        ( ( the_num @ ( some_num @ X23 ) )
% 9.49/5.24        = X23 ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_894_option_Oexpand,axiom,
% 9.49/5.24      ! [Option: option4927543243414619207at_nat,Option2: option4927543243414619207at_nat] :
% 9.49/5.24        ( ( ( Option = none_P5556105721700978146at_nat )
% 9.49/5.24          = ( Option2 = none_P5556105721700978146at_nat ) )
% 9.49/5.24       => ( ( ( Option != none_P5556105721700978146at_nat )
% 9.49/5.24           => ( ( Option2 != none_P5556105721700978146at_nat )
% 9.49/5.24             => ( ( the_Pr8591224930841456533at_nat @ Option )
% 9.49/5.24                = ( the_Pr8591224930841456533at_nat @ Option2 ) ) ) )
% 9.49/5.24         => ( Option = Option2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_895_option_Oexpand,axiom,
% 9.49/5.24      ! [Option: option_nat,Option2: option_nat] :
% 9.49/5.24        ( ( ( Option = none_nat )
% 9.49/5.24          = ( Option2 = none_nat ) )
% 9.49/5.24       => ( ( ( Option != none_nat )
% 9.49/5.24           => ( ( Option2 != none_nat )
% 9.49/5.24             => ( ( the_nat @ Option )
% 9.49/5.24                = ( the_nat @ Option2 ) ) ) )
% 9.49/5.24         => ( Option = Option2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_896_option_Oexpand,axiom,
% 9.49/5.24      ! [Option: option_num,Option2: option_num] :
% 9.49/5.24        ( ( ( Option = none_num )
% 9.49/5.24          = ( Option2 = none_num ) )
% 9.49/5.24       => ( ( ( Option != none_num )
% 9.49/5.24           => ( ( Option2 != none_num )
% 9.49/5.24             => ( ( the_num @ Option )
% 9.49/5.24                = ( the_num @ Option2 ) ) ) )
% 9.49/5.24         => ( Option = Option2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_897_set__update__subsetI,axiom,
% 9.49/5.24      ! [Xs2: list_P6011104703257516679at_nat,A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,I2: nat] :
% 9.49/5.24        ( ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ Xs2 ) @ A2 )
% 9.49/5.24       => ( ( member8440522571783428010at_nat @ X @ A2 )
% 9.49/5.24         => ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ ( list_u6180841689913720943at_nat @ Xs2 @ I2 @ X ) ) @ A2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_898_set__update__subsetI,axiom,
% 9.49/5.24      ! [Xs2: list_complex,A2: set_complex,X: complex,I2: nat] :
% 9.49/5.24        ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ A2 )
% 9.49/5.24       => ( ( member_complex @ X @ A2 )
% 9.49/5.24         => ( ord_le211207098394363844omplex @ ( set_complex2 @ ( list_update_complex @ Xs2 @ I2 @ X ) ) @ A2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_899_set__update__subsetI,axiom,
% 9.49/5.24      ! [Xs2: list_int,A2: set_int,X: int,I2: nat] :
% 9.49/5.24        ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ A2 )
% 9.49/5.24       => ( ( member_int @ X @ A2 )
% 9.49/5.24         => ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs2 @ I2 @ X ) ) @ A2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_900_set__update__subsetI,axiom,
% 9.49/5.24      ! [Xs2: list_VEBT_VEBT,A2: set_VEBT_VEBT,X: vEBT_VEBT,I2: nat] :
% 9.49/5.24        ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ A2 )
% 9.49/5.24       => ( ( member_VEBT_VEBT @ X @ A2 )
% 9.49/5.24         => ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) ) @ A2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_901_set__update__subsetI,axiom,
% 9.49/5.24      ! [Xs2: list_real,A2: set_real,X: real,I2: nat] :
% 9.49/5.24        ( ( ord_less_eq_set_real @ ( set_real2 @ Xs2 ) @ A2 )
% 9.49/5.24       => ( ( member_real @ X @ A2 )
% 9.49/5.24         => ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs2 @ I2 @ X ) ) @ A2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_902_set__update__subsetI,axiom,
% 9.49/5.24      ! [Xs2: list_nat,A2: set_nat,X: nat,I2: nat] :
% 9.49/5.24        ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ A2 )
% 9.49/5.24       => ( ( member_nat @ X @ A2 )
% 9.49/5.24         => ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs2 @ I2 @ X ) ) @ A2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_903_less__1__mult,axiom,
% 9.49/5.24      ! [M: real,N: real] :
% 9.49/5.24        ( ( ord_less_real @ one_one_real @ M )
% 9.49/5.24       => ( ( ord_less_real @ one_one_real @ N )
% 9.49/5.24         => ( ord_less_real @ one_one_real @ ( times_times_real @ M @ N ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_904_less__1__mult,axiom,
% 9.49/5.24      ! [M: rat,N: rat] :
% 9.49/5.24        ( ( ord_less_rat @ one_one_rat @ M )
% 9.49/5.24       => ( ( ord_less_rat @ one_one_rat @ N )
% 9.49/5.24         => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M @ N ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_905_less__1__mult,axiom,
% 9.49/5.24      ! [M: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_nat @ one_one_nat @ M )
% 9.49/5.24       => ( ( ord_less_nat @ one_one_nat @ N )
% 9.49/5.24         => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M @ N ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_906_less__1__mult,axiom,
% 9.49/5.24      ! [M: int,N: int] :
% 9.49/5.24        ( ( ord_less_int @ one_one_int @ M )
% 9.49/5.24       => ( ( ord_less_int @ one_one_int @ N )
% 9.49/5.24         => ( ord_less_int @ one_one_int @ ( times_times_int @ M @ N ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_907_less__add__one,axiom,
% 9.49/5.24      ! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_908_less__add__one,axiom,
% 9.49/5.24      ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_909_less__add__one,axiom,
% 9.49/5.24      ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_910_less__add__one,axiom,
% 9.49/5.24      ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_911_add__mono1,axiom,
% 9.49/5.24      ! [A: real,B: real] :
% 9.49/5.24        ( ( ord_less_real @ A @ B )
% 9.49/5.24       => ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B @ one_one_real ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_912_add__mono1,axiom,
% 9.49/5.24      ! [A: rat,B: rat] :
% 9.49/5.24        ( ( ord_less_rat @ A @ B )
% 9.49/5.24       => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_913_add__mono1,axiom,
% 9.49/5.24      ! [A: nat,B: nat] :
% 9.49/5.24        ( ( ord_less_nat @ A @ B )
% 9.49/5.24       => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_914_add__mono1,axiom,
% 9.49/5.24      ! [A: int,B: int] :
% 9.49/5.24        ( ( ord_less_int @ A @ B )
% 9.49/5.24       => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_915_add__le__add__imp__diff__le,axiom,
% 9.49/5.24      ! [I2: real,K: real,N: real,J: real] :
% 9.49/5.24        ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ N )
% 9.49/5.24       => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 9.49/5.24         => ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ N )
% 9.49/5.24           => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 9.49/5.24             => ( ord_less_eq_real @ ( minus_minus_real @ N @ K ) @ J ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_916_add__le__add__imp__diff__le,axiom,
% 9.49/5.24      ! [I2: rat,K: rat,N: rat,J: rat] :
% 9.49/5.24        ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ N )
% 9.49/5.24       => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 9.49/5.24         => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ N )
% 9.49/5.24           => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 9.49/5.24             => ( ord_less_eq_rat @ ( minus_minus_rat @ N @ K ) @ J ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_917_add__le__add__imp__diff__le,axiom,
% 9.49/5.24      ! [I2: nat,K: nat,N: nat,J: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ N )
% 9.49/5.24       => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 9.49/5.24         => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ N )
% 9.49/5.24           => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 9.49/5.24             => ( ord_less_eq_nat @ ( minus_minus_nat @ N @ K ) @ J ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_918_add__le__add__imp__diff__le,axiom,
% 9.49/5.24      ! [I2: int,K: int,N: int,J: int] :
% 9.49/5.24        ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ N )
% 9.49/5.24       => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 9.49/5.24         => ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ N )
% 9.49/5.24           => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 9.49/5.24             => ( ord_less_eq_int @ ( minus_minus_int @ N @ K ) @ J ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_919_add__le__imp__le__diff,axiom,
% 9.49/5.24      ! [I2: real,K: real,N: real] :
% 9.49/5.24        ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ N )
% 9.49/5.24       => ( ord_less_eq_real @ I2 @ ( minus_minus_real @ N @ K ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_920_add__le__imp__le__diff,axiom,
% 9.49/5.24      ! [I2: rat,K: rat,N: rat] :
% 9.49/5.24        ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ N )
% 9.49/5.24       => ( ord_less_eq_rat @ I2 @ ( minus_minus_rat @ N @ K ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_921_add__le__imp__le__diff,axiom,
% 9.49/5.24      ! [I2: nat,K: nat,N: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ N )
% 9.49/5.24       => ( ord_less_eq_nat @ I2 @ ( minus_minus_nat @ N @ K ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_922_add__le__imp__le__diff,axiom,
% 9.49/5.24      ! [I2: int,K: int,N: int] :
% 9.49/5.24        ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ N )
% 9.49/5.24       => ( ord_less_eq_int @ I2 @ ( minus_minus_int @ N @ K ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_923_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 9.49/5.24      ! [A: real,B: real] :
% 9.49/5.24        ( ~ ( ord_less_real @ A @ B )
% 9.49/5.24       => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 9.49/5.24          = A ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_924_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 9.49/5.24      ! [A: rat,B: rat] :
% 9.49/5.24        ( ~ ( ord_less_rat @ A @ B )
% 9.49/5.24       => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 9.49/5.24          = A ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_925_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 9.49/5.24      ! [A: nat,B: nat] :
% 9.49/5.24        ( ~ ( ord_less_nat @ A @ B )
% 9.49/5.24       => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 9.49/5.24          = A ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_926_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 9.49/5.24      ! [A: int,B: int] :
% 9.49/5.24        ( ~ ( ord_less_int @ A @ B )
% 9.49/5.24       => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 9.49/5.24          = A ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_927_eq__add__iff1,axiom,
% 9.49/5.24      ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 9.49/5.24        ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 9.49/5.24          = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 9.49/5.24        = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C )
% 9.49/5.24          = D2 ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_928_eq__add__iff1,axiom,
% 9.49/5.24      ! [A: complex,E: complex,C: complex,B: complex,D2: complex] :
% 9.49/5.24        ( ( ( plus_plus_complex @ ( times_times_complex @ A @ E ) @ C )
% 9.49/5.24          = ( plus_plus_complex @ ( times_times_complex @ B @ E ) @ D2 ) )
% 9.49/5.24        = ( ( plus_plus_complex @ ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ E ) @ C )
% 9.49/5.24          = D2 ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_929_eq__add__iff1,axiom,
% 9.49/5.24      ! [A: real,E: real,C: real,B: real,D2: real] :
% 9.49/5.24        ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 9.49/5.24          = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D2 ) )
% 9.49/5.24        = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C )
% 9.49/5.24          = D2 ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_930_eq__add__iff1,axiom,
% 9.49/5.24      ! [A: int,E: int,C: int,B: int,D2: int] :
% 9.49/5.24        ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 9.49/5.24          = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 9.49/5.24        = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C )
% 9.49/5.24          = D2 ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_931_eq__add__iff2,axiom,
% 9.49/5.24      ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 9.49/5.24        ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 9.49/5.24          = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 9.49/5.24        = ( C
% 9.49/5.24          = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_932_eq__add__iff2,axiom,
% 9.49/5.24      ! [A: complex,E: complex,C: complex,B: complex,D2: complex] :
% 9.49/5.24        ( ( ( plus_plus_complex @ ( times_times_complex @ A @ E ) @ C )
% 9.49/5.24          = ( plus_plus_complex @ ( times_times_complex @ B @ E ) @ D2 ) )
% 9.49/5.24        = ( C
% 9.49/5.24          = ( plus_plus_complex @ ( times_times_complex @ ( minus_minus_complex @ B @ A ) @ E ) @ D2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_933_eq__add__iff2,axiom,
% 9.49/5.24      ! [A: real,E: real,C: real,B: real,D2: real] :
% 9.49/5.24        ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 9.49/5.24          = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D2 ) )
% 9.49/5.24        = ( C
% 9.49/5.24          = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_934_eq__add__iff2,axiom,
% 9.49/5.24      ! [A: int,E: int,C: int,B: int,D2: int] :
% 9.49/5.24        ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 9.49/5.24          = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 9.49/5.24        = ( C
% 9.49/5.24          = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_935_square__diff__square__factored,axiom,
% 9.49/5.24      ! [X: rat,Y2: rat] :
% 9.49/5.24        ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y2 @ Y2 ) )
% 9.49/5.24        = ( times_times_rat @ ( plus_plus_rat @ X @ Y2 ) @ ( minus_minus_rat @ X @ Y2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_936_square__diff__square__factored,axiom,
% 9.49/5.24      ! [X: complex,Y2: complex] :
% 9.49/5.24        ( ( minus_minus_complex @ ( times_times_complex @ X @ X ) @ ( times_times_complex @ Y2 @ Y2 ) )
% 9.49/5.24        = ( times_times_complex @ ( plus_plus_complex @ X @ Y2 ) @ ( minus_minus_complex @ X @ Y2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_937_square__diff__square__factored,axiom,
% 9.49/5.24      ! [X: real,Y2: real] :
% 9.49/5.24        ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y2 @ Y2 ) )
% 9.49/5.24        = ( times_times_real @ ( plus_plus_real @ X @ Y2 ) @ ( minus_minus_real @ X @ Y2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_938_square__diff__square__factored,axiom,
% 9.49/5.24      ! [X: int,Y2: int] :
% 9.49/5.24        ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y2 @ Y2 ) )
% 9.49/5.24        = ( times_times_int @ ( plus_plus_int @ X @ Y2 ) @ ( minus_minus_int @ X @ Y2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_939_nth__equalityI,axiom,
% 9.49/5.24      ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 9.49/5.24        ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 9.49/5.24          = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 9.49/5.24       => ( ! [I4: nat] :
% 9.49/5.24              ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 9.49/5.24             => ( ( nth_VEBT_VEBT @ Xs2 @ I4 )
% 9.49/5.24                = ( nth_VEBT_VEBT @ Ys @ I4 ) ) )
% 9.49/5.24         => ( Xs2 = Ys ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_940_nth__equalityI,axiom,
% 9.49/5.24      ! [Xs2: list_o,Ys: list_o] :
% 9.49/5.24        ( ( ( size_size_list_o @ Xs2 )
% 9.49/5.24          = ( size_size_list_o @ Ys ) )
% 9.49/5.24       => ( ! [I4: nat] :
% 9.49/5.24              ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs2 ) )
% 9.49/5.24             => ( ( nth_o @ Xs2 @ I4 )
% 9.49/5.24                = ( nth_o @ Ys @ I4 ) ) )
% 9.49/5.24         => ( Xs2 = Ys ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_941_nth__equalityI,axiom,
% 9.49/5.24      ! [Xs2: list_nat,Ys: list_nat] :
% 9.49/5.24        ( ( ( size_size_list_nat @ Xs2 )
% 9.49/5.24          = ( size_size_list_nat @ Ys ) )
% 9.49/5.24       => ( ! [I4: nat] :
% 9.49/5.24              ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs2 ) )
% 9.49/5.24             => ( ( nth_nat @ Xs2 @ I4 )
% 9.49/5.24                = ( nth_nat @ Ys @ I4 ) ) )
% 9.49/5.24         => ( Xs2 = Ys ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_942_nth__equalityI,axiom,
% 9.49/5.24      ! [Xs2: list_int,Ys: list_int] :
% 9.49/5.24        ( ( ( size_size_list_int @ Xs2 )
% 9.49/5.24          = ( size_size_list_int @ Ys ) )
% 9.49/5.24       => ( ! [I4: nat] :
% 9.49/5.24              ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs2 ) )
% 9.49/5.24             => ( ( nth_int @ Xs2 @ I4 )
% 9.49/5.24                = ( nth_int @ Ys @ I4 ) ) )
% 9.49/5.24         => ( Xs2 = Ys ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_943_Skolem__list__nth,axiom,
% 9.49/5.24      ! [K: nat,P: nat > vEBT_VEBT > $o] :
% 9.49/5.24        ( ( ! [I3: nat] :
% 9.49/5.24              ( ( ord_less_nat @ I3 @ K )
% 9.49/5.24             => ? [X4: vEBT_VEBT] : ( P @ I3 @ X4 ) ) )
% 9.49/5.24        = ( ? [Xs: list_VEBT_VEBT] :
% 9.49/5.24              ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 9.49/5.24                = K )
% 9.49/5.24              & ! [I3: nat] :
% 9.49/5.24                  ( ( ord_less_nat @ I3 @ K )
% 9.49/5.24                 => ( P @ I3 @ ( nth_VEBT_VEBT @ Xs @ I3 ) ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_944_Skolem__list__nth,axiom,
% 9.49/5.24      ! [K: nat,P: nat > $o > $o] :
% 9.49/5.24        ( ( ! [I3: nat] :
% 9.49/5.24              ( ( ord_less_nat @ I3 @ K )
% 9.49/5.24             => ? [X4: $o] : ( P @ I3 @ X4 ) ) )
% 9.49/5.24        = ( ? [Xs: list_o] :
% 9.49/5.24              ( ( ( size_size_list_o @ Xs )
% 9.49/5.24                = K )
% 9.49/5.24              & ! [I3: nat] :
% 9.49/5.24                  ( ( ord_less_nat @ I3 @ K )
% 9.49/5.24                 => ( P @ I3 @ ( nth_o @ Xs @ I3 ) ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_945_Skolem__list__nth,axiom,
% 9.49/5.24      ! [K: nat,P: nat > nat > $o] :
% 9.49/5.24        ( ( ! [I3: nat] :
% 9.49/5.24              ( ( ord_less_nat @ I3 @ K )
% 9.49/5.24             => ? [X4: nat] : ( P @ I3 @ X4 ) ) )
% 9.49/5.24        = ( ? [Xs: list_nat] :
% 9.49/5.24              ( ( ( size_size_list_nat @ Xs )
% 9.49/5.24                = K )
% 9.49/5.24              & ! [I3: nat] :
% 9.49/5.24                  ( ( ord_less_nat @ I3 @ K )
% 9.49/5.24                 => ( P @ I3 @ ( nth_nat @ Xs @ I3 ) ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_946_Skolem__list__nth,axiom,
% 9.49/5.24      ! [K: nat,P: nat > int > $o] :
% 9.49/5.24        ( ( ! [I3: nat] :
% 9.49/5.24              ( ( ord_less_nat @ I3 @ K )
% 9.49/5.24             => ? [X4: int] : ( P @ I3 @ X4 ) ) )
% 9.49/5.24        = ( ? [Xs: list_int] :
% 9.49/5.24              ( ( ( size_size_list_int @ Xs )
% 9.49/5.24                = K )
% 9.49/5.24              & ! [I3: nat] :
% 9.49/5.24                  ( ( ord_less_nat @ I3 @ K )
% 9.49/5.24                 => ( P @ I3 @ ( nth_int @ Xs @ I3 ) ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_947_list__eq__iff__nth__eq,axiom,
% 9.49/5.24      ( ( ^ [Y5: list_VEBT_VEBT,Z5: list_VEBT_VEBT] : ( Y5 = Z5 ) )
% 9.49/5.24      = ( ^ [Xs: list_VEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 9.49/5.24            ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 9.49/5.24              = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 9.49/5.24            & ! [I3: nat] :
% 9.49/5.24                ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 9.49/5.24               => ( ( nth_VEBT_VEBT @ Xs @ I3 )
% 9.49/5.24                  = ( nth_VEBT_VEBT @ Ys3 @ I3 ) ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_948_list__eq__iff__nth__eq,axiom,
% 9.49/5.24      ( ( ^ [Y5: list_o,Z5: list_o] : ( Y5 = Z5 ) )
% 9.49/5.24      = ( ^ [Xs: list_o,Ys3: list_o] :
% 9.49/5.24            ( ( ( size_size_list_o @ Xs )
% 9.49/5.24              = ( size_size_list_o @ Ys3 ) )
% 9.49/5.24            & ! [I3: nat] :
% 9.49/5.24                ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs ) )
% 9.49/5.24               => ( ( nth_o @ Xs @ I3 )
% 9.49/5.24                  = ( nth_o @ Ys3 @ I3 ) ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_949_list__eq__iff__nth__eq,axiom,
% 9.49/5.24      ( ( ^ [Y5: list_nat,Z5: list_nat] : ( Y5 = Z5 ) )
% 9.49/5.24      = ( ^ [Xs: list_nat,Ys3: list_nat] :
% 9.49/5.24            ( ( ( size_size_list_nat @ Xs )
% 9.49/5.24              = ( size_size_list_nat @ Ys3 ) )
% 9.49/5.24            & ! [I3: nat] :
% 9.49/5.24                ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 9.49/5.24               => ( ( nth_nat @ Xs @ I3 )
% 9.49/5.24                  = ( nth_nat @ Ys3 @ I3 ) ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_950_list__eq__iff__nth__eq,axiom,
% 9.49/5.24      ( ( ^ [Y5: list_int,Z5: list_int] : ( Y5 = Z5 ) )
% 9.49/5.24      = ( ^ [Xs: list_int,Ys3: list_int] :
% 9.49/5.24            ( ( ( size_size_list_int @ Xs )
% 9.49/5.24              = ( size_size_list_int @ Ys3 ) )
% 9.49/5.24            & ! [I3: nat] :
% 9.49/5.24                ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) )
% 9.49/5.24               => ( ( nth_int @ Xs @ I3 )
% 9.49/5.24                  = ( nth_int @ Ys3 @ I3 ) ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_951_option_Oexhaust__sel,axiom,
% 9.49/5.24      ! [Option: option4927543243414619207at_nat] :
% 9.49/5.24        ( ( Option != none_P5556105721700978146at_nat )
% 9.49/5.24       => ( Option
% 9.49/5.24          = ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_952_option_Oexhaust__sel,axiom,
% 9.49/5.24      ! [Option: option_nat] :
% 9.49/5.24        ( ( Option != none_nat )
% 9.49/5.24       => ( Option
% 9.49/5.24          = ( some_nat @ ( the_nat @ Option ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_953_option_Oexhaust__sel,axiom,
% 9.49/5.24      ! [Option: option_num] :
% 9.49/5.24        ( ( Option != none_num )
% 9.49/5.24       => ( Option
% 9.49/5.24          = ( some_num @ ( the_num @ Option ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_954_ordered__ring__class_Ole__add__iff2,axiom,
% 9.49/5.24      ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 9.49/5.24        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 9.49/5.24        = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_955_ordered__ring__class_Ole__add__iff2,axiom,
% 9.49/5.24      ! [A: real,E: real,C: real,B: real,D2: real] :
% 9.49/5.24        ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D2 ) )
% 9.49/5.24        = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_956_ordered__ring__class_Ole__add__iff2,axiom,
% 9.49/5.24      ! [A: int,E: int,C: int,B: int,D2: int] :
% 9.49/5.24        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 9.49/5.24        = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_957_ordered__ring__class_Ole__add__iff1,axiom,
% 9.49/5.24      ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 9.49/5.24        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 9.49/5.24        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_958_ordered__ring__class_Ole__add__iff1,axiom,
% 9.49/5.24      ! [A: real,E: real,C: real,B: real,D2: real] :
% 9.49/5.24        ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D2 ) )
% 9.49/5.24        = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_959_ordered__ring__class_Ole__add__iff1,axiom,
% 9.49/5.24      ! [A: int,E: int,C: int,B: int,D2: int] :
% 9.49/5.24        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 9.49/5.24        = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_960_less__add__iff2,axiom,
% 9.49/5.24      ! [A: real,E: real,C: real,B: real,D2: real] :
% 9.49/5.24        ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D2 ) )
% 9.49/5.24        = ( ord_less_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_961_less__add__iff2,axiom,
% 9.49/5.24      ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 9.49/5.24        ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 9.49/5.24        = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_962_less__add__iff2,axiom,
% 9.49/5.24      ! [A: int,E: int,C: int,B: int,D2: int] :
% 9.49/5.24        ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 9.49/5.24        = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_963_less__add__iff1,axiom,
% 9.49/5.24      ! [A: real,E: real,C: real,B: real,D2: real] :
% 9.49/5.24        ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D2 ) )
% 9.49/5.24        = ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_964_less__add__iff1,axiom,
% 9.49/5.24      ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 9.49/5.24        ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 9.49/5.24        = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_965_less__add__iff1,axiom,
% 9.49/5.24      ! [A: int,E: int,C: int,B: int,D2: int] :
% 9.49/5.24        ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 9.49/5.24        = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_966_square__diff__one__factored,axiom,
% 9.49/5.24      ! [X: rat] :
% 9.49/5.24        ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ one_one_rat )
% 9.49/5.24        = ( times_times_rat @ ( plus_plus_rat @ X @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_967_square__diff__one__factored,axiom,
% 9.49/5.24      ! [X: complex] :
% 9.49/5.24        ( ( minus_minus_complex @ ( times_times_complex @ X @ X ) @ one_one_complex )
% 9.49/5.24        = ( times_times_complex @ ( plus_plus_complex @ X @ one_one_complex ) @ ( minus_minus_complex @ X @ one_one_complex ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_968_square__diff__one__factored,axiom,
% 9.49/5.24      ! [X: real] :
% 9.49/5.24        ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ one_one_real )
% 9.49/5.24        = ( times_times_real @ ( plus_plus_real @ X @ one_one_real ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_969_square__diff__one__factored,axiom,
% 9.49/5.24      ! [X: int] :
% 9.49/5.24        ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ one_one_int )
% 9.49/5.24        = ( times_times_int @ ( plus_plus_int @ X @ one_one_int ) @ ( minus_minus_int @ X @ one_one_int ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_970_all__set__conv__all__nth,axiom,
% 9.49/5.24      ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 9.49/5.24        ( ( ! [X2: vEBT_VEBT] :
% 9.49/5.24              ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 9.49/5.24             => ( P @ X2 ) ) )
% 9.49/5.24        = ( ! [I3: nat] :
% 9.49/5.24              ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 9.49/5.24             => ( P @ ( nth_VEBT_VEBT @ Xs2 @ I3 ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_971_all__set__conv__all__nth,axiom,
% 9.49/5.24      ! [Xs2: list_o,P: $o > $o] :
% 9.49/5.24        ( ( ! [X2: $o] :
% 9.49/5.24              ( ( member_o @ X2 @ ( set_o2 @ Xs2 ) )
% 9.49/5.24             => ( P @ X2 ) ) )
% 9.49/5.24        = ( ! [I3: nat] :
% 9.49/5.24              ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs2 ) )
% 9.49/5.24             => ( P @ ( nth_o @ Xs2 @ I3 ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_972_all__set__conv__all__nth,axiom,
% 9.49/5.24      ! [Xs2: list_nat,P: nat > $o] :
% 9.49/5.24        ( ( ! [X2: nat] :
% 9.49/5.24              ( ( member_nat @ X2 @ ( set_nat2 @ Xs2 ) )
% 9.49/5.24             => ( P @ X2 ) ) )
% 9.49/5.24        = ( ! [I3: nat] :
% 9.49/5.24              ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs2 ) )
% 9.49/5.24             => ( P @ ( nth_nat @ Xs2 @ I3 ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_973_all__set__conv__all__nth,axiom,
% 9.49/5.24      ! [Xs2: list_int,P: int > $o] :
% 9.49/5.24        ( ( ! [X2: int] :
% 9.49/5.24              ( ( member_int @ X2 @ ( set_int2 @ Xs2 ) )
% 9.49/5.24             => ( P @ X2 ) ) )
% 9.49/5.24        = ( ! [I3: nat] :
% 9.49/5.24              ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs2 ) )
% 9.49/5.24             => ( P @ ( nth_int @ Xs2 @ I3 ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_974_all__nth__imp__all__set,axiom,
% 9.49/5.24      ! [Xs2: list_P6011104703257516679at_nat,P: product_prod_nat_nat > $o,X: product_prod_nat_nat] :
% 9.49/5.24        ( ! [I4: nat] :
% 9.49/5.24            ( ( ord_less_nat @ I4 @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 9.49/5.24           => ( P @ ( nth_Pr7617993195940197384at_nat @ Xs2 @ I4 ) ) )
% 9.49/5.24       => ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 9.49/5.24         => ( P @ X ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_975_all__nth__imp__all__set,axiom,
% 9.49/5.24      ! [Xs2: list_complex,P: complex > $o,X: complex] :
% 9.49/5.24        ( ! [I4: nat] :
% 9.49/5.24            ( ( ord_less_nat @ I4 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 9.49/5.24           => ( P @ ( nth_complex @ Xs2 @ I4 ) ) )
% 9.49/5.24       => ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 9.49/5.24         => ( P @ X ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_976_all__nth__imp__all__set,axiom,
% 9.49/5.24      ! [Xs2: list_real,P: real > $o,X: real] :
% 9.49/5.24        ( ! [I4: nat] :
% 9.49/5.24            ( ( ord_less_nat @ I4 @ ( size_size_list_real @ Xs2 ) )
% 9.49/5.24           => ( P @ ( nth_real @ Xs2 @ I4 ) ) )
% 9.49/5.24       => ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 9.49/5.24         => ( P @ X ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_977_all__nth__imp__all__set,axiom,
% 9.49/5.24      ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o,X: vEBT_VEBT] :
% 9.49/5.24        ( ! [I4: nat] :
% 9.49/5.24            ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 9.49/5.24           => ( P @ ( nth_VEBT_VEBT @ Xs2 @ I4 ) ) )
% 9.49/5.24       => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 9.49/5.24         => ( P @ X ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_978_all__nth__imp__all__set,axiom,
% 9.49/5.24      ! [Xs2: list_o,P: $o > $o,X: $o] :
% 9.49/5.24        ( ! [I4: nat] :
% 9.49/5.24            ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs2 ) )
% 9.49/5.24           => ( P @ ( nth_o @ Xs2 @ I4 ) ) )
% 9.49/5.24       => ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 9.49/5.24         => ( P @ X ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_979_all__nth__imp__all__set,axiom,
% 9.49/5.24      ! [Xs2: list_nat,P: nat > $o,X: nat] :
% 9.49/5.24        ( ! [I4: nat] :
% 9.49/5.24            ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs2 ) )
% 9.49/5.24           => ( P @ ( nth_nat @ Xs2 @ I4 ) ) )
% 9.49/5.24       => ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 9.49/5.24         => ( P @ X ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_980_all__nth__imp__all__set,axiom,
% 9.49/5.24      ! [Xs2: list_int,P: int > $o,X: int] :
% 9.49/5.24        ( ! [I4: nat] :
% 9.49/5.24            ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs2 ) )
% 9.49/5.24           => ( P @ ( nth_int @ Xs2 @ I4 ) ) )
% 9.49/5.24       => ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 9.49/5.24         => ( P @ X ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_981_in__set__conv__nth,axiom,
% 9.49/5.24      ! [X: product_prod_nat_nat,Xs2: list_P6011104703257516679at_nat] :
% 9.49/5.24        ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 9.49/5.24        = ( ? [I3: nat] :
% 9.49/5.24              ( ( ord_less_nat @ I3 @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 9.49/5.24              & ( ( nth_Pr7617993195940197384at_nat @ Xs2 @ I3 )
% 9.49/5.24                = X ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_982_in__set__conv__nth,axiom,
% 9.49/5.24      ! [X: complex,Xs2: list_complex] :
% 9.49/5.24        ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 9.49/5.24        = ( ? [I3: nat] :
% 9.49/5.24              ( ( ord_less_nat @ I3 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 9.49/5.24              & ( ( nth_complex @ Xs2 @ I3 )
% 9.49/5.24                = X ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_983_in__set__conv__nth,axiom,
% 9.49/5.24      ! [X: real,Xs2: list_real] :
% 9.49/5.24        ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 9.49/5.24        = ( ? [I3: nat] :
% 9.49/5.24              ( ( ord_less_nat @ I3 @ ( size_size_list_real @ Xs2 ) )
% 9.49/5.24              & ( ( nth_real @ Xs2 @ I3 )
% 9.49/5.24                = X ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_984_in__set__conv__nth,axiom,
% 9.49/5.24      ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 9.49/5.24        ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 9.49/5.24        = ( ? [I3: nat] :
% 9.49/5.24              ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 9.49/5.24              & ( ( nth_VEBT_VEBT @ Xs2 @ I3 )
% 9.49/5.24                = X ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_985_in__set__conv__nth,axiom,
% 9.49/5.24      ! [X: $o,Xs2: list_o] :
% 9.49/5.24        ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 9.49/5.24        = ( ? [I3: nat] :
% 9.49/5.24              ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs2 ) )
% 9.49/5.24              & ( ( nth_o @ Xs2 @ I3 )
% 9.49/5.24                = X ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_986_in__set__conv__nth,axiom,
% 9.49/5.24      ! [X: nat,Xs2: list_nat] :
% 9.49/5.24        ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 9.49/5.24        = ( ? [I3: nat] :
% 9.49/5.24              ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs2 ) )
% 9.49/5.24              & ( ( nth_nat @ Xs2 @ I3 )
% 9.49/5.24                = X ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_987_in__set__conv__nth,axiom,
% 9.49/5.24      ! [X: int,Xs2: list_int] :
% 9.49/5.24        ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 9.49/5.24        = ( ? [I3: nat] :
% 9.49/5.24              ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs2 ) )
% 9.49/5.24              & ( ( nth_int @ Xs2 @ I3 )
% 9.49/5.24                = X ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_988_list__ball__nth,axiom,
% 9.49/5.24      ! [N: nat,Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 9.49/5.24        ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 9.49/5.24       => ( ! [X3: vEBT_VEBT] :
% 9.49/5.24              ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 9.49/5.24             => ( P @ X3 ) )
% 9.49/5.24         => ( P @ ( nth_VEBT_VEBT @ Xs2 @ N ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_989_list__ball__nth,axiom,
% 9.49/5.24      ! [N: nat,Xs2: list_o,P: $o > $o] :
% 9.49/5.24        ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 9.49/5.24       => ( ! [X3: $o] :
% 9.49/5.24              ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 9.49/5.24             => ( P @ X3 ) )
% 9.49/5.24         => ( P @ ( nth_o @ Xs2 @ N ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_990_list__ball__nth,axiom,
% 9.49/5.24      ! [N: nat,Xs2: list_nat,P: nat > $o] :
% 9.49/5.24        ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 9.49/5.24       => ( ! [X3: nat] :
% 9.49/5.24              ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 9.49/5.24             => ( P @ X3 ) )
% 9.49/5.24         => ( P @ ( nth_nat @ Xs2 @ N ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_991_list__ball__nth,axiom,
% 9.49/5.24      ! [N: nat,Xs2: list_int,P: int > $o] :
% 9.49/5.24        ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 9.49/5.24       => ( ! [X3: int] :
% 9.49/5.24              ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 9.49/5.24             => ( P @ X3 ) )
% 9.49/5.24         => ( P @ ( nth_int @ Xs2 @ N ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_992_nth__mem,axiom,
% 9.49/5.24      ! [N: nat,Xs2: list_P6011104703257516679at_nat] :
% 9.49/5.24        ( ( ord_less_nat @ N @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 9.49/5.24       => ( member8440522571783428010at_nat @ ( nth_Pr7617993195940197384at_nat @ Xs2 @ N ) @ ( set_Pr5648618587558075414at_nat @ Xs2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_993_nth__mem,axiom,
% 9.49/5.24      ! [N: nat,Xs2: list_complex] :
% 9.49/5.24        ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 9.49/5.24       => ( member_complex @ ( nth_complex @ Xs2 @ N ) @ ( set_complex2 @ Xs2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_994_nth__mem,axiom,
% 9.49/5.24      ! [N: nat,Xs2: list_real] :
% 9.49/5.24        ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 9.49/5.24       => ( member_real @ ( nth_real @ Xs2 @ N ) @ ( set_real2 @ Xs2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_995_nth__mem,axiom,
% 9.49/5.24      ! [N: nat,Xs2: list_VEBT_VEBT] :
% 9.49/5.24        ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 9.49/5.24       => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ N ) @ ( set_VEBT_VEBT2 @ Xs2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_996_nth__mem,axiom,
% 9.49/5.24      ! [N: nat,Xs2: list_o] :
% 9.49/5.24        ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 9.49/5.24       => ( member_o @ ( nth_o @ Xs2 @ N ) @ ( set_o2 @ Xs2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_997_nth__mem,axiom,
% 9.49/5.24      ! [N: nat,Xs2: list_nat] :
% 9.49/5.24        ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 9.49/5.24       => ( member_nat @ ( nth_nat @ Xs2 @ N ) @ ( set_nat2 @ Xs2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_998_nth__mem,axiom,
% 9.49/5.24      ! [N: nat,Xs2: list_int] :
% 9.49/5.24        ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 9.49/5.24       => ( member_int @ ( nth_int @ Xs2 @ N ) @ ( set_int2 @ Xs2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_999_set__update__memI,axiom,
% 9.49/5.24      ! [N: nat,Xs2: list_P6011104703257516679at_nat,X: product_prod_nat_nat] :
% 9.49/5.24        ( ( ord_less_nat @ N @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 9.49/5.24       => ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ ( list_u6180841689913720943at_nat @ Xs2 @ N @ X ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1000_set__update__memI,axiom,
% 9.49/5.24      ! [N: nat,Xs2: list_complex,X: complex] :
% 9.49/5.24        ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 9.49/5.24       => ( member_complex @ X @ ( set_complex2 @ ( list_update_complex @ Xs2 @ N @ X ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1001_set__update__memI,axiom,
% 9.49/5.24      ! [N: nat,Xs2: list_real,X: real] :
% 9.49/5.24        ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 9.49/5.24       => ( member_real @ X @ ( set_real2 @ ( list_update_real @ Xs2 @ N @ X ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1002_set__update__memI,axiom,
% 9.49/5.24      ! [N: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 9.49/5.24        ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 9.49/5.24       => ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs2 @ N @ X ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1003_set__update__memI,axiom,
% 9.49/5.24      ! [N: nat,Xs2: list_o,X: $o] :
% 9.49/5.24        ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 9.49/5.24       => ( member_o @ X @ ( set_o2 @ ( list_update_o @ Xs2 @ N @ X ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1004_set__update__memI,axiom,
% 9.49/5.24      ! [N: nat,Xs2: list_nat,X: nat] :
% 9.49/5.24        ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 9.49/5.24       => ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ Xs2 @ N @ X ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1005_set__update__memI,axiom,
% 9.49/5.24      ! [N: nat,Xs2: list_int,X: int] :
% 9.49/5.24        ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 9.49/5.24       => ( member_int @ X @ ( set_int2 @ ( list_update_int @ Xs2 @ N @ X ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1006_nth__list__update,axiom,
% 9.49/5.24      ! [I2: nat,Xs2: list_VEBT_VEBT,J: nat,X: vEBT_VEBT] :
% 9.49/5.24        ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 9.49/5.24       => ( ( ( I2 = J )
% 9.49/5.24           => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ J )
% 9.49/5.24              = X ) )
% 9.49/5.24          & ( ( I2 != J )
% 9.49/5.24           => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ J )
% 9.49/5.24              = ( nth_VEBT_VEBT @ Xs2 @ J ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1007_nth__list__update,axiom,
% 9.49/5.24      ! [I2: nat,Xs2: list_o,X: $o,J: nat] :
% 9.49/5.24        ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 9.49/5.24       => ( ( nth_o @ ( list_update_o @ Xs2 @ I2 @ X ) @ J )
% 9.49/5.24          = ( ( ( I2 = J )
% 9.49/5.24             => X )
% 9.49/5.24            & ( ( I2 != J )
% 9.49/5.24             => ( nth_o @ Xs2 @ J ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1008_nth__list__update,axiom,
% 9.49/5.24      ! [I2: nat,Xs2: list_nat,J: nat,X: nat] :
% 9.49/5.24        ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 9.49/5.24       => ( ( ( I2 = J )
% 9.49/5.24           => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) @ J )
% 9.49/5.24              = X ) )
% 9.49/5.24          & ( ( I2 != J )
% 9.49/5.24           => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) @ J )
% 9.49/5.24              = ( nth_nat @ Xs2 @ J ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1009_nth__list__update,axiom,
% 9.49/5.24      ! [I2: nat,Xs2: list_int,J: nat,X: int] :
% 9.49/5.24        ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 9.49/5.24       => ( ( ( I2 = J )
% 9.49/5.24           => ( ( nth_int @ ( list_update_int @ Xs2 @ I2 @ X ) @ J )
% 9.49/5.24              = X ) )
% 9.49/5.24          & ( ( I2 != J )
% 9.49/5.24           => ( ( nth_int @ ( list_update_int @ Xs2 @ I2 @ X ) @ J )
% 9.49/5.24              = ( nth_int @ Xs2 @ J ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1010_list__update__same__conv,axiom,
% 9.49/5.24      ! [I2: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 9.49/5.24        ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 9.49/5.24       => ( ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X )
% 9.49/5.24            = Xs2 )
% 9.49/5.24          = ( ( nth_VEBT_VEBT @ Xs2 @ I2 )
% 9.49/5.24            = X ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1011_list__update__same__conv,axiom,
% 9.49/5.24      ! [I2: nat,Xs2: list_o,X: $o] :
% 9.49/5.24        ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 9.49/5.24       => ( ( ( list_update_o @ Xs2 @ I2 @ X )
% 9.49/5.24            = Xs2 )
% 9.49/5.24          = ( ( nth_o @ Xs2 @ I2 )
% 9.49/5.24            = X ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1012_list__update__same__conv,axiom,
% 9.49/5.24      ! [I2: nat,Xs2: list_nat,X: nat] :
% 9.49/5.24        ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 9.49/5.24       => ( ( ( list_update_nat @ Xs2 @ I2 @ X )
% 9.49/5.24            = Xs2 )
% 9.49/5.24          = ( ( nth_nat @ Xs2 @ I2 )
% 9.49/5.24            = X ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1013_list__update__same__conv,axiom,
% 9.49/5.24      ! [I2: nat,Xs2: list_int,X: int] :
% 9.49/5.24        ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 9.49/5.24       => ( ( ( list_update_int @ Xs2 @ I2 @ X )
% 9.49/5.24            = Xs2 )
% 9.49/5.24          = ( ( nth_int @ Xs2 @ I2 )
% 9.49/5.24            = X ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1014_real__average__minus__second,axiom,
% 9.49/5.24      ! [B: real,A: real] :
% 9.49/5.24        ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 9.49/5.24        = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1015_real__average__minus__first,axiom,
% 9.49/5.24      ! [A: real,B: real] :
% 9.49/5.24        ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 9.49/5.24        = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1016_vebt__insert_Osimps_I4_J,axiom,
% 9.49/5.24      ! [V: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 9.49/5.24        ( ( vEBT_vebt_insert @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) @ X )
% 9.49/5.24        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ X ) ) @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1017_mul__def,axiom,
% 9.49/5.24      ( vEBT_VEBT_mul
% 9.49/5.24      = ( vEBT_V4262088993061758097ft_nat @ times_times_nat ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1018_add__def,axiom,
% 9.49/5.24      ( vEBT_VEBT_add
% 9.49/5.24      = ( vEBT_V4262088993061758097ft_nat @ plus_plus_nat ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1019_vebt__maxt_Osimps_I3_J,axiom,
% 9.49/5.24      ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 9.49/5.24        ( ( vEBT_vebt_maxt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 9.49/5.24        = ( some_nat @ Ma ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1020_vebt__mint_Osimps_I3_J,axiom,
% 9.49/5.24      ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 9.49/5.24        ( ( vEBT_vebt_mint @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 9.49/5.24        = ( some_nat @ Mi ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1021_max__less__iff__conj,axiom,
% 9.49/5.24      ! [X: extended_enat,Y2: extended_enat,Z: extended_enat] :
% 9.49/5.24        ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ X @ Y2 ) @ Z )
% 9.49/5.24        = ( ( ord_le72135733267957522d_enat @ X @ Z )
% 9.49/5.24          & ( ord_le72135733267957522d_enat @ Y2 @ Z ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1022_max__less__iff__conj,axiom,
% 9.49/5.24      ! [X: real,Y2: real,Z: real] :
% 9.49/5.24        ( ( ord_less_real @ ( ord_max_real @ X @ Y2 ) @ Z )
% 9.49/5.24        = ( ( ord_less_real @ X @ Z )
% 9.49/5.24          & ( ord_less_real @ Y2 @ Z ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1023_max__less__iff__conj,axiom,
% 9.49/5.24      ! [X: rat,Y2: rat,Z: rat] :
% 9.49/5.24        ( ( ord_less_rat @ ( ord_max_rat @ X @ Y2 ) @ Z )
% 9.49/5.24        = ( ( ord_less_rat @ X @ Z )
% 9.49/5.24          & ( ord_less_rat @ Y2 @ Z ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1024_max__less__iff__conj,axiom,
% 9.49/5.24      ! [X: num,Y2: num,Z: num] :
% 9.49/5.24        ( ( ord_less_num @ ( ord_max_num @ X @ Y2 ) @ Z )
% 9.49/5.24        = ( ( ord_less_num @ X @ Z )
% 9.49/5.24          & ( ord_less_num @ Y2 @ Z ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1025_max__less__iff__conj,axiom,
% 9.49/5.24      ! [X: nat,Y2: nat,Z: nat] :
% 9.49/5.24        ( ( ord_less_nat @ ( ord_max_nat @ X @ Y2 ) @ Z )
% 9.49/5.24        = ( ( ord_less_nat @ X @ Z )
% 9.49/5.24          & ( ord_less_nat @ Y2 @ Z ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1026_max__less__iff__conj,axiom,
% 9.49/5.24      ! [X: int,Y2: int,Z: int] :
% 9.49/5.24        ( ( ord_less_int @ ( ord_max_int @ X @ Y2 ) @ Z )
% 9.49/5.24        = ( ( ord_less_int @ X @ Z )
% 9.49/5.24          & ( ord_less_int @ Y2 @ Z ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1027_max_Oabsorb4,axiom,
% 9.49/5.24      ! [A: extended_enat,B: extended_enat] :
% 9.49/5.24        ( ( ord_le72135733267957522d_enat @ A @ B )
% 9.49/5.24       => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 9.49/5.24          = B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1028_max_Oabsorb4,axiom,
% 9.49/5.24      ! [A: real,B: real] :
% 9.49/5.24        ( ( ord_less_real @ A @ B )
% 9.49/5.24       => ( ( ord_max_real @ A @ B )
% 9.49/5.24          = B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1029_max_Oabsorb4,axiom,
% 9.49/5.24      ! [A: rat,B: rat] :
% 9.49/5.24        ( ( ord_less_rat @ A @ B )
% 9.49/5.24       => ( ( ord_max_rat @ A @ B )
% 9.49/5.24          = B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1030_max_Oabsorb4,axiom,
% 9.49/5.24      ! [A: num,B: num] :
% 9.49/5.24        ( ( ord_less_num @ A @ B )
% 9.49/5.24       => ( ( ord_max_num @ A @ B )
% 9.49/5.24          = B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1031_max_Oabsorb4,axiom,
% 9.49/5.24      ! [A: nat,B: nat] :
% 9.49/5.24        ( ( ord_less_nat @ A @ B )
% 9.49/5.24       => ( ( ord_max_nat @ A @ B )
% 9.49/5.24          = B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1032_max_Oabsorb4,axiom,
% 9.49/5.24      ! [A: int,B: int] :
% 9.49/5.24        ( ( ord_less_int @ A @ B )
% 9.49/5.24       => ( ( ord_max_int @ A @ B )
% 9.49/5.24          = B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1033_max_Oabsorb3,axiom,
% 9.49/5.24      ! [B: extended_enat,A: extended_enat] :
% 9.49/5.24        ( ( ord_le72135733267957522d_enat @ B @ A )
% 9.49/5.24       => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 9.49/5.24          = A ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1034_max_Oabsorb3,axiom,
% 9.49/5.24      ! [B: real,A: real] :
% 9.49/5.24        ( ( ord_less_real @ B @ A )
% 9.49/5.24       => ( ( ord_max_real @ A @ B )
% 9.49/5.24          = A ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1035_max_Oabsorb3,axiom,
% 9.49/5.24      ! [B: rat,A: rat] :
% 9.49/5.24        ( ( ord_less_rat @ B @ A )
% 9.49/5.24       => ( ( ord_max_rat @ A @ B )
% 9.49/5.24          = A ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1036_max_Oabsorb3,axiom,
% 9.49/5.24      ! [B: num,A: num] :
% 9.49/5.24        ( ( ord_less_num @ B @ A )
% 9.49/5.24       => ( ( ord_max_num @ A @ B )
% 9.49/5.24          = A ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1037_max_Oabsorb3,axiom,
% 9.49/5.24      ! [B: nat,A: nat] :
% 9.49/5.24        ( ( ord_less_nat @ B @ A )
% 9.49/5.24       => ( ( ord_max_nat @ A @ B )
% 9.49/5.24          = A ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1038_max_Oabsorb3,axiom,
% 9.49/5.24      ! [B: int,A: int] :
% 9.49/5.24        ( ( ord_less_int @ B @ A )
% 9.49/5.24       => ( ( ord_max_int @ A @ B )
% 9.49/5.24          = A ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1039_max_Obounded__iff,axiom,
% 9.49/5.24      ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 9.49/5.24        ( ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 9.49/5.24        = ( ( ord_le2932123472753598470d_enat @ B @ A )
% 9.49/5.24          & ( ord_le2932123472753598470d_enat @ C @ A ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1040_max_Obounded__iff,axiom,
% 9.49/5.24      ! [B: num,C: num,A: num] :
% 9.49/5.24        ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 9.49/5.24        = ( ( ord_less_eq_num @ B @ A )
% 9.49/5.24          & ( ord_less_eq_num @ C @ A ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1041_max_Obounded__iff,axiom,
% 9.49/5.24      ! [B: nat,C: nat,A: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 9.49/5.24        = ( ( ord_less_eq_nat @ B @ A )
% 9.49/5.24          & ( ord_less_eq_nat @ C @ A ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1042_max_Obounded__iff,axiom,
% 9.49/5.24      ! [B: int,C: int,A: int] :
% 9.49/5.24        ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 9.49/5.24        = ( ( ord_less_eq_int @ B @ A )
% 9.49/5.24          & ( ord_less_eq_int @ C @ A ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1043_add__shift,axiom,
% 9.49/5.24      ! [X: nat,Y2: nat,Z: nat] :
% 9.49/5.24        ( ( ( plus_plus_nat @ X @ Y2 )
% 9.49/5.24          = Z )
% 9.49/5.24        = ( ( vEBT_VEBT_add @ ( some_nat @ X ) @ ( some_nat @ Y2 ) )
% 9.49/5.24          = ( some_nat @ Z ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1044_mul__shift,axiom,
% 9.49/5.24      ! [X: nat,Y2: nat,Z: nat] :
% 9.49/5.24        ( ( ( times_times_nat @ X @ Y2 )
% 9.49/5.24          = Z )
% 9.49/5.24        = ( ( vEBT_VEBT_mul @ ( some_nat @ X ) @ ( some_nat @ Y2 ) )
% 9.49/5.24          = ( some_nat @ Z ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1045_max_Oabsorb1,axiom,
% 9.49/5.24      ! [B: extended_enat,A: extended_enat] :
% 9.49/5.24        ( ( ord_le2932123472753598470d_enat @ B @ A )
% 9.49/5.24       => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 9.49/5.24          = A ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1046_max_Oabsorb1,axiom,
% 9.49/5.24      ! [B: num,A: num] :
% 9.49/5.24        ( ( ord_less_eq_num @ B @ A )
% 9.49/5.24       => ( ( ord_max_num @ A @ B )
% 9.49/5.24          = A ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1047_max_Oabsorb1,axiom,
% 9.49/5.24      ! [B: nat,A: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ B @ A )
% 9.49/5.24       => ( ( ord_max_nat @ A @ B )
% 9.49/5.24          = A ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1048_max_Oabsorb1,axiom,
% 9.49/5.24      ! [B: int,A: int] :
% 9.49/5.24        ( ( ord_less_eq_int @ B @ A )
% 9.49/5.24       => ( ( ord_max_int @ A @ B )
% 9.49/5.24          = A ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1049_max_Oabsorb2,axiom,
% 9.49/5.24      ! [A: extended_enat,B: extended_enat] :
% 9.49/5.24        ( ( ord_le2932123472753598470d_enat @ A @ B )
% 9.49/5.24       => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 9.49/5.24          = B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1050_max_Oabsorb2,axiom,
% 9.49/5.24      ! [A: num,B: num] :
% 9.49/5.24        ( ( ord_less_eq_num @ A @ B )
% 9.49/5.24       => ( ( ord_max_num @ A @ B )
% 9.49/5.24          = B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1051_max_Oabsorb2,axiom,
% 9.49/5.24      ! [A: nat,B: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ A @ B )
% 9.49/5.24       => ( ( ord_max_nat @ A @ B )
% 9.49/5.24          = B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1052_max_Oabsorb2,axiom,
% 9.49/5.24      ! [A: int,B: int] :
% 9.49/5.24        ( ( ord_less_eq_int @ A @ B )
% 9.49/5.24       => ( ( ord_max_int @ A @ B )
% 9.49/5.24          = B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1053_max_Omono,axiom,
% 9.49/5.24      ! [C: extended_enat,A: extended_enat,D2: extended_enat,B: extended_enat] :
% 9.49/5.24        ( ( ord_le2932123472753598470d_enat @ C @ A )
% 9.49/5.24       => ( ( ord_le2932123472753598470d_enat @ D2 @ B )
% 9.49/5.24         => ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ C @ D2 ) @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1054_max_Omono,axiom,
% 9.49/5.24      ! [C: num,A: num,D2: num,B: num] :
% 9.49/5.24        ( ( ord_less_eq_num @ C @ A )
% 9.49/5.24       => ( ( ord_less_eq_num @ D2 @ B )
% 9.49/5.24         => ( ord_less_eq_num @ ( ord_max_num @ C @ D2 ) @ ( ord_max_num @ A @ B ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1055_max_Omono,axiom,
% 9.49/5.24      ! [C: nat,A: nat,D2: nat,B: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ C @ A )
% 9.49/5.24       => ( ( ord_less_eq_nat @ D2 @ B )
% 9.49/5.24         => ( ord_less_eq_nat @ ( ord_max_nat @ C @ D2 ) @ ( ord_max_nat @ A @ B ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1056_max_Omono,axiom,
% 9.49/5.24      ! [C: int,A: int,D2: int,B: int] :
% 9.49/5.24        ( ( ord_less_eq_int @ C @ A )
% 9.49/5.24       => ( ( ord_less_eq_int @ D2 @ B )
% 9.49/5.24         => ( ord_less_eq_int @ ( ord_max_int @ C @ D2 ) @ ( ord_max_int @ A @ B ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1057_max_OorderE,axiom,
% 9.49/5.24      ! [B: extended_enat,A: extended_enat] :
% 9.49/5.24        ( ( ord_le2932123472753598470d_enat @ B @ A )
% 9.49/5.24       => ( A
% 9.49/5.24          = ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1058_max_OorderE,axiom,
% 9.49/5.24      ! [B: num,A: num] :
% 9.49/5.24        ( ( ord_less_eq_num @ B @ A )
% 9.49/5.24       => ( A
% 9.49/5.24          = ( ord_max_num @ A @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1059_max_OorderE,axiom,
% 9.49/5.24      ! [B: nat,A: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ B @ A )
% 9.49/5.24       => ( A
% 9.49/5.24          = ( ord_max_nat @ A @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1060_max_OorderE,axiom,
% 9.49/5.24      ! [B: int,A: int] :
% 9.49/5.24        ( ( ord_less_eq_int @ B @ A )
% 9.49/5.24       => ( A
% 9.49/5.24          = ( ord_max_int @ A @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1061_max_OorderI,axiom,
% 9.49/5.24      ! [A: extended_enat,B: extended_enat] :
% 9.49/5.24        ( ( A
% 9.49/5.24          = ( ord_ma741700101516333627d_enat @ A @ B ) )
% 9.49/5.24       => ( ord_le2932123472753598470d_enat @ B @ A ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1062_max_OorderI,axiom,
% 9.49/5.24      ! [A: num,B: num] :
% 9.49/5.24        ( ( A
% 9.49/5.24          = ( ord_max_num @ A @ B ) )
% 9.49/5.24       => ( ord_less_eq_num @ B @ A ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1063_max_OorderI,axiom,
% 9.49/5.24      ! [A: nat,B: nat] :
% 9.49/5.24        ( ( A
% 9.49/5.24          = ( ord_max_nat @ A @ B ) )
% 9.49/5.24       => ( ord_less_eq_nat @ B @ A ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1064_max_OorderI,axiom,
% 9.49/5.24      ! [A: int,B: int] :
% 9.49/5.24        ( ( A
% 9.49/5.24          = ( ord_max_int @ A @ B ) )
% 9.49/5.24       => ( ord_less_eq_int @ B @ A ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1065_max_OboundedE,axiom,
% 9.49/5.24      ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 9.49/5.24        ( ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 9.49/5.24       => ~ ( ( ord_le2932123472753598470d_enat @ B @ A )
% 9.49/5.24           => ~ ( ord_le2932123472753598470d_enat @ C @ A ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1066_max_OboundedE,axiom,
% 9.49/5.24      ! [B: num,C: num,A: num] :
% 9.49/5.24        ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 9.49/5.24       => ~ ( ( ord_less_eq_num @ B @ A )
% 9.49/5.24           => ~ ( ord_less_eq_num @ C @ A ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1067_max_OboundedE,axiom,
% 9.49/5.24      ! [B: nat,C: nat,A: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 9.49/5.24       => ~ ( ( ord_less_eq_nat @ B @ A )
% 9.49/5.24           => ~ ( ord_less_eq_nat @ C @ A ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1068_max_OboundedE,axiom,
% 9.49/5.24      ! [B: int,C: int,A: int] :
% 9.49/5.24        ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 9.49/5.24       => ~ ( ( ord_less_eq_int @ B @ A )
% 9.49/5.24           => ~ ( ord_less_eq_int @ C @ A ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1069_max_OboundedI,axiom,
% 9.49/5.24      ! [B: extended_enat,A: extended_enat,C: extended_enat] :
% 9.49/5.24        ( ( ord_le2932123472753598470d_enat @ B @ A )
% 9.49/5.24       => ( ( ord_le2932123472753598470d_enat @ C @ A )
% 9.49/5.24         => ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1070_max_OboundedI,axiom,
% 9.49/5.24      ! [B: num,A: num,C: num] :
% 9.49/5.24        ( ( ord_less_eq_num @ B @ A )
% 9.49/5.24       => ( ( ord_less_eq_num @ C @ A )
% 9.49/5.24         => ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1071_max_OboundedI,axiom,
% 9.49/5.24      ! [B: nat,A: nat,C: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ B @ A )
% 9.49/5.24       => ( ( ord_less_eq_nat @ C @ A )
% 9.49/5.24         => ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1072_max_OboundedI,axiom,
% 9.49/5.24      ! [B: int,A: int,C: int] :
% 9.49/5.24        ( ( ord_less_eq_int @ B @ A )
% 9.49/5.24       => ( ( ord_less_eq_int @ C @ A )
% 9.49/5.24         => ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1073_max_Oorder__iff,axiom,
% 9.49/5.24      ( ord_le2932123472753598470d_enat
% 9.49/5.24      = ( ^ [B4: extended_enat,A3: extended_enat] :
% 9.49/5.24            ( A3
% 9.49/5.24            = ( ord_ma741700101516333627d_enat @ A3 @ B4 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1074_max_Oorder__iff,axiom,
% 9.49/5.24      ( ord_less_eq_num
% 9.49/5.24      = ( ^ [B4: num,A3: num] :
% 9.49/5.24            ( A3
% 9.49/5.24            = ( ord_max_num @ A3 @ B4 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1075_max_Oorder__iff,axiom,
% 9.49/5.24      ( ord_less_eq_nat
% 9.49/5.24      = ( ^ [B4: nat,A3: nat] :
% 9.49/5.24            ( A3
% 9.49/5.24            = ( ord_max_nat @ A3 @ B4 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1076_max_Oorder__iff,axiom,
% 9.49/5.24      ( ord_less_eq_int
% 9.49/5.24      = ( ^ [B4: int,A3: int] :
% 9.49/5.24            ( A3
% 9.49/5.24            = ( ord_max_int @ A3 @ B4 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1077_max_Ocobounded1,axiom,
% 9.49/5.24      ! [A: extended_enat,B: extended_enat] : ( ord_le2932123472753598470d_enat @ A @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1078_max_Ocobounded1,axiom,
% 9.49/5.24      ! [A: num,B: num] : ( ord_less_eq_num @ A @ ( ord_max_num @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1079_max_Ocobounded1,axiom,
% 9.49/5.24      ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( ord_max_nat @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1080_max_Ocobounded1,axiom,
% 9.49/5.24      ! [A: int,B: int] : ( ord_less_eq_int @ A @ ( ord_max_int @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1081_max_Ocobounded2,axiom,
% 9.49/5.24      ! [B: extended_enat,A: extended_enat] : ( ord_le2932123472753598470d_enat @ B @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1082_max_Ocobounded2,axiom,
% 9.49/5.24      ! [B: num,A: num] : ( ord_less_eq_num @ B @ ( ord_max_num @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1083_max_Ocobounded2,axiom,
% 9.49/5.24      ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( ord_max_nat @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1084_max_Ocobounded2,axiom,
% 9.49/5.24      ! [B: int,A: int] : ( ord_less_eq_int @ B @ ( ord_max_int @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1085_le__max__iff__disj,axiom,
% 9.49/5.24      ! [Z: extended_enat,X: extended_enat,Y2: extended_enat] :
% 9.49/5.24        ( ( ord_le2932123472753598470d_enat @ Z @ ( ord_ma741700101516333627d_enat @ X @ Y2 ) )
% 9.49/5.24        = ( ( ord_le2932123472753598470d_enat @ Z @ X )
% 9.49/5.24          | ( ord_le2932123472753598470d_enat @ Z @ Y2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1086_le__max__iff__disj,axiom,
% 9.49/5.24      ! [Z: num,X: num,Y2: num] :
% 9.49/5.24        ( ( ord_less_eq_num @ Z @ ( ord_max_num @ X @ Y2 ) )
% 9.49/5.24        = ( ( ord_less_eq_num @ Z @ X )
% 9.49/5.24          | ( ord_less_eq_num @ Z @ Y2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1087_le__max__iff__disj,axiom,
% 9.49/5.24      ! [Z: nat,X: nat,Y2: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ Z @ ( ord_max_nat @ X @ Y2 ) )
% 9.49/5.24        = ( ( ord_less_eq_nat @ Z @ X )
% 9.49/5.24          | ( ord_less_eq_nat @ Z @ Y2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1088_le__max__iff__disj,axiom,
% 9.49/5.24      ! [Z: int,X: int,Y2: int] :
% 9.49/5.24        ( ( ord_less_eq_int @ Z @ ( ord_max_int @ X @ Y2 ) )
% 9.49/5.24        = ( ( ord_less_eq_int @ Z @ X )
% 9.49/5.24          | ( ord_less_eq_int @ Z @ Y2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1089_max_Oabsorb__iff1,axiom,
% 9.49/5.24      ( ord_le2932123472753598470d_enat
% 9.49/5.24      = ( ^ [B4: extended_enat,A3: extended_enat] :
% 9.49/5.24            ( ( ord_ma741700101516333627d_enat @ A3 @ B4 )
% 9.49/5.24            = A3 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1090_max_Oabsorb__iff1,axiom,
% 9.49/5.24      ( ord_less_eq_num
% 9.49/5.24      = ( ^ [B4: num,A3: num] :
% 9.49/5.24            ( ( ord_max_num @ A3 @ B4 )
% 9.49/5.24            = A3 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1091_max_Oabsorb__iff1,axiom,
% 9.49/5.24      ( ord_less_eq_nat
% 9.49/5.24      = ( ^ [B4: nat,A3: nat] :
% 9.49/5.24            ( ( ord_max_nat @ A3 @ B4 )
% 9.49/5.24            = A3 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1092_max_Oabsorb__iff1,axiom,
% 9.49/5.24      ( ord_less_eq_int
% 9.49/5.24      = ( ^ [B4: int,A3: int] :
% 9.49/5.24            ( ( ord_max_int @ A3 @ B4 )
% 9.49/5.24            = A3 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1093_max_Oabsorb__iff2,axiom,
% 9.49/5.24      ( ord_le2932123472753598470d_enat
% 9.49/5.24      = ( ^ [A3: extended_enat,B4: extended_enat] :
% 9.49/5.24            ( ( ord_ma741700101516333627d_enat @ A3 @ B4 )
% 9.49/5.24            = B4 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1094_max_Oabsorb__iff2,axiom,
% 9.49/5.24      ( ord_less_eq_num
% 9.49/5.24      = ( ^ [A3: num,B4: num] :
% 9.49/5.24            ( ( ord_max_num @ A3 @ B4 )
% 9.49/5.24            = B4 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1095_max_Oabsorb__iff2,axiom,
% 9.49/5.24      ( ord_less_eq_nat
% 9.49/5.24      = ( ^ [A3: nat,B4: nat] :
% 9.49/5.24            ( ( ord_max_nat @ A3 @ B4 )
% 9.49/5.24            = B4 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1096_max_Oabsorb__iff2,axiom,
% 9.49/5.24      ( ord_less_eq_int
% 9.49/5.24      = ( ^ [A3: int,B4: int] :
% 9.49/5.24            ( ( ord_max_int @ A3 @ B4 )
% 9.49/5.24            = B4 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1097_max_OcoboundedI1,axiom,
% 9.49/5.24      ! [C: extended_enat,A: extended_enat,B: extended_enat] :
% 9.49/5.24        ( ( ord_le2932123472753598470d_enat @ C @ A )
% 9.49/5.24       => ( ord_le2932123472753598470d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1098_max_OcoboundedI1,axiom,
% 9.49/5.24      ! [C: num,A: num,B: num] :
% 9.49/5.24        ( ( ord_less_eq_num @ C @ A )
% 9.49/5.24       => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1099_max_OcoboundedI1,axiom,
% 9.49/5.24      ! [C: nat,A: nat,B: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ C @ A )
% 9.49/5.24       => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1100_max_OcoboundedI1,axiom,
% 9.49/5.24      ! [C: int,A: int,B: int] :
% 9.49/5.24        ( ( ord_less_eq_int @ C @ A )
% 9.49/5.24       => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1101_max_OcoboundedI2,axiom,
% 9.49/5.24      ! [C: extended_enat,B: extended_enat,A: extended_enat] :
% 9.49/5.24        ( ( ord_le2932123472753598470d_enat @ C @ B )
% 9.49/5.24       => ( ord_le2932123472753598470d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1102_max_OcoboundedI2,axiom,
% 9.49/5.24      ! [C: num,B: num,A: num] :
% 9.49/5.24        ( ( ord_less_eq_num @ C @ B )
% 9.49/5.24       => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1103_max_OcoboundedI2,axiom,
% 9.49/5.24      ! [C: nat,B: nat,A: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ C @ B )
% 9.49/5.24       => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1104_max_OcoboundedI2,axiom,
% 9.49/5.24      ! [C: int,B: int,A: int] :
% 9.49/5.24        ( ( ord_less_eq_int @ C @ B )
% 9.49/5.24       => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1105_less__max__iff__disj,axiom,
% 9.49/5.24      ! [Z: extended_enat,X: extended_enat,Y2: extended_enat] :
% 9.49/5.24        ( ( ord_le72135733267957522d_enat @ Z @ ( ord_ma741700101516333627d_enat @ X @ Y2 ) )
% 9.49/5.24        = ( ( ord_le72135733267957522d_enat @ Z @ X )
% 9.49/5.24          | ( ord_le72135733267957522d_enat @ Z @ Y2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1106_less__max__iff__disj,axiom,
% 9.49/5.24      ! [Z: real,X: real,Y2: real] :
% 9.49/5.24        ( ( ord_less_real @ Z @ ( ord_max_real @ X @ Y2 ) )
% 9.49/5.24        = ( ( ord_less_real @ Z @ X )
% 9.49/5.24          | ( ord_less_real @ Z @ Y2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1107_less__max__iff__disj,axiom,
% 9.49/5.24      ! [Z: rat,X: rat,Y2: rat] :
% 9.49/5.24        ( ( ord_less_rat @ Z @ ( ord_max_rat @ X @ Y2 ) )
% 9.49/5.24        = ( ( ord_less_rat @ Z @ X )
% 9.49/5.24          | ( ord_less_rat @ Z @ Y2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1108_less__max__iff__disj,axiom,
% 9.49/5.24      ! [Z: num,X: num,Y2: num] :
% 9.49/5.24        ( ( ord_less_num @ Z @ ( ord_max_num @ X @ Y2 ) )
% 9.49/5.24        = ( ( ord_less_num @ Z @ X )
% 9.49/5.24          | ( ord_less_num @ Z @ Y2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1109_less__max__iff__disj,axiom,
% 9.49/5.24      ! [Z: nat,X: nat,Y2: nat] :
% 9.49/5.24        ( ( ord_less_nat @ Z @ ( ord_max_nat @ X @ Y2 ) )
% 9.49/5.24        = ( ( ord_less_nat @ Z @ X )
% 9.49/5.24          | ( ord_less_nat @ Z @ Y2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1110_less__max__iff__disj,axiom,
% 9.49/5.24      ! [Z: int,X: int,Y2: int] :
% 9.49/5.24        ( ( ord_less_int @ Z @ ( ord_max_int @ X @ Y2 ) )
% 9.49/5.24        = ( ( ord_less_int @ Z @ X )
% 9.49/5.24          | ( ord_less_int @ Z @ Y2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1111_max_Ostrict__boundedE,axiom,
% 9.49/5.24      ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 9.49/5.24        ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 9.49/5.24       => ~ ( ( ord_le72135733267957522d_enat @ B @ A )
% 9.49/5.24           => ~ ( ord_le72135733267957522d_enat @ C @ A ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1112_max_Ostrict__boundedE,axiom,
% 9.49/5.24      ! [B: real,C: real,A: real] :
% 9.49/5.24        ( ( ord_less_real @ ( ord_max_real @ B @ C ) @ A )
% 9.49/5.24       => ~ ( ( ord_less_real @ B @ A )
% 9.49/5.24           => ~ ( ord_less_real @ C @ A ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1113_max_Ostrict__boundedE,axiom,
% 9.49/5.24      ! [B: rat,C: rat,A: rat] :
% 9.49/5.24        ( ( ord_less_rat @ ( ord_max_rat @ B @ C ) @ A )
% 9.49/5.24       => ~ ( ( ord_less_rat @ B @ A )
% 9.49/5.24           => ~ ( ord_less_rat @ C @ A ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1114_max_Ostrict__boundedE,axiom,
% 9.49/5.24      ! [B: num,C: num,A: num] :
% 9.49/5.24        ( ( ord_less_num @ ( ord_max_num @ B @ C ) @ A )
% 9.49/5.24       => ~ ( ( ord_less_num @ B @ A )
% 9.49/5.24           => ~ ( ord_less_num @ C @ A ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1115_max_Ostrict__boundedE,axiom,
% 9.49/5.24      ! [B: nat,C: nat,A: nat] :
% 9.49/5.24        ( ( ord_less_nat @ ( ord_max_nat @ B @ C ) @ A )
% 9.49/5.24       => ~ ( ( ord_less_nat @ B @ A )
% 9.49/5.24           => ~ ( ord_less_nat @ C @ A ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1116_max_Ostrict__boundedE,axiom,
% 9.49/5.24      ! [B: int,C: int,A: int] :
% 9.49/5.24        ( ( ord_less_int @ ( ord_max_int @ B @ C ) @ A )
% 9.49/5.24       => ~ ( ( ord_less_int @ B @ A )
% 9.49/5.24           => ~ ( ord_less_int @ C @ A ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1117_max_Ostrict__order__iff,axiom,
% 9.49/5.24      ( ord_le72135733267957522d_enat
% 9.49/5.24      = ( ^ [B4: extended_enat,A3: extended_enat] :
% 9.49/5.24            ( ( A3
% 9.49/5.24              = ( ord_ma741700101516333627d_enat @ A3 @ B4 ) )
% 9.49/5.24            & ( A3 != B4 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1118_max_Ostrict__order__iff,axiom,
% 9.49/5.24      ( ord_less_real
% 9.49/5.24      = ( ^ [B4: real,A3: real] :
% 9.49/5.24            ( ( A3
% 9.49/5.24              = ( ord_max_real @ A3 @ B4 ) )
% 9.49/5.24            & ( A3 != B4 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1119_max_Ostrict__order__iff,axiom,
% 9.49/5.24      ( ord_less_rat
% 9.49/5.24      = ( ^ [B4: rat,A3: rat] :
% 9.49/5.24            ( ( A3
% 9.49/5.24              = ( ord_max_rat @ A3 @ B4 ) )
% 9.49/5.24            & ( A3 != B4 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1120_max_Ostrict__order__iff,axiom,
% 9.49/5.24      ( ord_less_num
% 9.49/5.24      = ( ^ [B4: num,A3: num] :
% 9.49/5.24            ( ( A3
% 9.49/5.24              = ( ord_max_num @ A3 @ B4 ) )
% 9.49/5.24            & ( A3 != B4 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1121_max_Ostrict__order__iff,axiom,
% 9.49/5.24      ( ord_less_nat
% 9.49/5.24      = ( ^ [B4: nat,A3: nat] :
% 9.49/5.24            ( ( A3
% 9.49/5.24              = ( ord_max_nat @ A3 @ B4 ) )
% 9.49/5.24            & ( A3 != B4 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1122_max_Ostrict__order__iff,axiom,
% 9.49/5.24      ( ord_less_int
% 9.49/5.24      = ( ^ [B4: int,A3: int] :
% 9.49/5.24            ( ( A3
% 9.49/5.24              = ( ord_max_int @ A3 @ B4 ) )
% 9.49/5.24            & ( A3 != B4 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1123_max_Ostrict__coboundedI1,axiom,
% 9.49/5.24      ! [C: extended_enat,A: extended_enat,B: extended_enat] :
% 9.49/5.24        ( ( ord_le72135733267957522d_enat @ C @ A )
% 9.49/5.24       => ( ord_le72135733267957522d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1124_max_Ostrict__coboundedI1,axiom,
% 9.49/5.24      ! [C: real,A: real,B: real] :
% 9.49/5.24        ( ( ord_less_real @ C @ A )
% 9.49/5.24       => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1125_max_Ostrict__coboundedI1,axiom,
% 9.49/5.24      ! [C: rat,A: rat,B: rat] :
% 9.49/5.24        ( ( ord_less_rat @ C @ A )
% 9.49/5.24       => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1126_max_Ostrict__coboundedI1,axiom,
% 9.49/5.24      ! [C: num,A: num,B: num] :
% 9.49/5.24        ( ( ord_less_num @ C @ A )
% 9.49/5.24       => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1127_max_Ostrict__coboundedI1,axiom,
% 9.49/5.24      ! [C: nat,A: nat,B: nat] :
% 9.49/5.24        ( ( ord_less_nat @ C @ A )
% 9.49/5.24       => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1128_max_Ostrict__coboundedI1,axiom,
% 9.49/5.24      ! [C: int,A: int,B: int] :
% 9.49/5.24        ( ( ord_less_int @ C @ A )
% 9.49/5.24       => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1129_max_Ostrict__coboundedI2,axiom,
% 9.49/5.24      ! [C: extended_enat,B: extended_enat,A: extended_enat] :
% 9.49/5.24        ( ( ord_le72135733267957522d_enat @ C @ B )
% 9.49/5.24       => ( ord_le72135733267957522d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1130_max_Ostrict__coboundedI2,axiom,
% 9.49/5.24      ! [C: real,B: real,A: real] :
% 9.49/5.24        ( ( ord_less_real @ C @ B )
% 9.49/5.24       => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1131_max_Ostrict__coboundedI2,axiom,
% 9.49/5.24      ! [C: rat,B: rat,A: rat] :
% 9.49/5.24        ( ( ord_less_rat @ C @ B )
% 9.49/5.24       => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1132_max_Ostrict__coboundedI2,axiom,
% 9.49/5.24      ! [C: num,B: num,A: num] :
% 9.49/5.24        ( ( ord_less_num @ C @ B )
% 9.49/5.24       => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1133_max_Ostrict__coboundedI2,axiom,
% 9.49/5.24      ! [C: nat,B: nat,A: nat] :
% 9.49/5.24        ( ( ord_less_nat @ C @ B )
% 9.49/5.24       => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1134_max_Ostrict__coboundedI2,axiom,
% 9.49/5.24      ! [C: int,B: int,A: int] :
% 9.49/5.24        ( ( ord_less_int @ C @ B )
% 9.49/5.24       => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1135_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 9.49/5.24      ! [X: produc5491161045314408544at_nat] :
% 9.49/5.24        ( ! [Uu2: product_prod_nat_nat > product_prod_nat_nat > $o,Uv2: option4927543243414619207at_nat] :
% 9.49/5.24            ( X
% 9.49/5.24           != ( produc3994169339658061776at_nat @ Uu2 @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv2 ) ) )
% 9.49/5.24       => ( ! [Uw2: product_prod_nat_nat > product_prod_nat_nat > $o,V2: product_prod_nat_nat] :
% 9.49/5.24              ( X
% 9.49/5.24             != ( produc3994169339658061776at_nat @ Uw2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V2 ) @ none_P5556105721700978146at_nat ) ) )
% 9.49/5.24         => ~ ! [F2: product_prod_nat_nat > product_prod_nat_nat > $o,X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 9.49/5.24                ( X
% 9.49/5.24               != ( produc3994169339658061776at_nat @ F2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ X3 ) @ ( some_P7363390416028606310at_nat @ Y3 ) ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1136_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 9.49/5.24      ! [X: produc2233624965454879586on_nat] :
% 9.49/5.24        ( ! [Uu2: nat > nat > $o,Uv2: option_nat] :
% 9.49/5.24            ( X
% 9.49/5.24           != ( produc4035269172776083154on_nat @ Uu2 @ ( produc5098337634421038937on_nat @ none_nat @ Uv2 ) ) )
% 9.49/5.24       => ( ! [Uw2: nat > nat > $o,V2: nat] :
% 9.49/5.24              ( X
% 9.49/5.24             != ( produc4035269172776083154on_nat @ Uw2 @ ( produc5098337634421038937on_nat @ ( some_nat @ V2 ) @ none_nat ) ) )
% 9.49/5.24         => ~ ! [F2: nat > nat > $o,X3: nat,Y3: nat] :
% 9.49/5.24                ( X
% 9.49/5.24               != ( produc4035269172776083154on_nat @ F2 @ ( produc5098337634421038937on_nat @ ( some_nat @ X3 ) @ ( some_nat @ Y3 ) ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1137_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 9.49/5.24      ! [X: produc7036089656553540234on_num] :
% 9.49/5.24        ( ! [Uu2: num > num > $o,Uv2: option_num] :
% 9.49/5.24            ( X
% 9.49/5.24           != ( produc3576312749637752826on_num @ Uu2 @ ( produc8585076106096196333on_num @ none_num @ Uv2 ) ) )
% 9.49/5.24       => ( ! [Uw2: num > num > $o,V2: num] :
% 9.49/5.24              ( X
% 9.49/5.24             != ( produc3576312749637752826on_num @ Uw2 @ ( produc8585076106096196333on_num @ ( some_num @ V2 ) @ none_num ) ) )
% 9.49/5.24         => ~ ! [F2: num > num > $o,X3: num,Y3: num] :
% 9.49/5.24                ( X
% 9.49/5.24               != ( produc3576312749637752826on_num @ F2 @ ( produc8585076106096196333on_num @ ( some_num @ X3 ) @ ( some_num @ Y3 ) ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1138_VEBT__internal_Ooption__shift_Ocases,axiom,
% 9.49/5.24      ! [X: produc5542196010084753463at_nat] :
% 9.49/5.24        ( ! [Uu2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Uv2: option4927543243414619207at_nat] :
% 9.49/5.24            ( X
% 9.49/5.24           != ( produc2899441246263362727at_nat @ Uu2 @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv2 ) ) )
% 9.49/5.24       => ( ! [Uw2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V2: product_prod_nat_nat] :
% 9.49/5.24              ( X
% 9.49/5.24             != ( produc2899441246263362727at_nat @ Uw2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V2 ) @ none_P5556105721700978146at_nat ) ) )
% 9.49/5.24         => ~ ! [F2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A4: product_prod_nat_nat,B3: product_prod_nat_nat] :
% 9.49/5.24                ( X
% 9.49/5.24               != ( produc2899441246263362727at_nat @ F2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ A4 ) @ ( some_P7363390416028606310at_nat @ B3 ) ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1139_VEBT__internal_Ooption__shift_Ocases,axiom,
% 9.49/5.24      ! [X: produc8306885398267862888on_nat] :
% 9.49/5.24        ( ! [Uu2: nat > nat > nat,Uv2: option_nat] :
% 9.49/5.24            ( X
% 9.49/5.24           != ( produc8929957630744042906on_nat @ Uu2 @ ( produc5098337634421038937on_nat @ none_nat @ Uv2 ) ) )
% 9.49/5.24       => ( ! [Uw2: nat > nat > nat,V2: nat] :
% 9.49/5.24              ( X
% 9.49/5.24             != ( produc8929957630744042906on_nat @ Uw2 @ ( produc5098337634421038937on_nat @ ( some_nat @ V2 ) @ none_nat ) ) )
% 9.49/5.24         => ~ ! [F2: nat > nat > nat,A4: nat,B3: nat] :
% 9.49/5.24                ( X
% 9.49/5.24               != ( produc8929957630744042906on_nat @ F2 @ ( produc5098337634421038937on_nat @ ( some_nat @ A4 ) @ ( some_nat @ B3 ) ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1140_VEBT__internal_Ooption__shift_Ocases,axiom,
% 9.49/5.24      ! [X: produc1193250871479095198on_num] :
% 9.49/5.24        ( ! [Uu2: num > num > num,Uv2: option_num] :
% 9.49/5.24            ( X
% 9.49/5.24           != ( produc5778274026573060048on_num @ Uu2 @ ( produc8585076106096196333on_num @ none_num @ Uv2 ) ) )
% 9.49/5.24       => ( ! [Uw2: num > num > num,V2: num] :
% 9.49/5.24              ( X
% 9.49/5.24             != ( produc5778274026573060048on_num @ Uw2 @ ( produc8585076106096196333on_num @ ( some_num @ V2 ) @ none_num ) ) )
% 9.49/5.24         => ~ ! [F2: num > num > num,A4: num,B3: num] :
% 9.49/5.24                ( X
% 9.49/5.24               != ( produc5778274026573060048on_num @ F2 @ ( produc8585076106096196333on_num @ ( some_num @ A4 ) @ ( some_num @ B3 ) ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1141_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 9.49/5.24      ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 9.49/5.24        ( ( vEBT_V1502963449132264192at_nat @ F @ ( some_P7363390416028606310at_nat @ A ) @ ( some_P7363390416028606310at_nat @ B ) )
% 9.49/5.24        = ( some_P7363390416028606310at_nat @ ( F @ A @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1142_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 9.49/5.24      ! [F: num > num > num,A: num,B: num] :
% 9.49/5.24        ( ( vEBT_V819420779217536731ft_num @ F @ ( some_num @ A ) @ ( some_num @ B ) )
% 9.49/5.24        = ( some_num @ ( F @ A @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1143_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 9.49/5.24      ! [F: nat > nat > nat,A: nat,B: nat] :
% 9.49/5.24        ( ( vEBT_V4262088993061758097ft_nat @ F @ ( some_nat @ A ) @ ( some_nat @ B ) )
% 9.49/5.24        = ( some_nat @ ( F @ A @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1144_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 9.49/5.24      ! [Uu: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Uv: option4927543243414619207at_nat] :
% 9.49/5.24        ( ( vEBT_V1502963449132264192at_nat @ Uu @ none_P5556105721700978146at_nat @ Uv )
% 9.49/5.24        = none_P5556105721700978146at_nat ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1145_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 9.49/5.24      ! [Uu: num > num > num,Uv: option_num] :
% 9.49/5.24        ( ( vEBT_V819420779217536731ft_num @ Uu @ none_num @ Uv )
% 9.49/5.24        = none_num ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1146_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 9.49/5.24      ! [Uu: nat > nat > nat,Uv: option_nat] :
% 9.49/5.24        ( ( vEBT_V4262088993061758097ft_nat @ Uu @ none_nat @ Uv )
% 9.49/5.24        = none_nat ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1147_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 9.49/5.24      ! [Uw: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V: product_prod_nat_nat] :
% 9.49/5.24        ( ( vEBT_V1502963449132264192at_nat @ Uw @ ( some_P7363390416028606310at_nat @ V ) @ none_P5556105721700978146at_nat )
% 9.49/5.24        = none_P5556105721700978146at_nat ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1148_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 9.49/5.24      ! [Uw: num > num > num,V: num] :
% 9.49/5.24        ( ( vEBT_V819420779217536731ft_num @ Uw @ ( some_num @ V ) @ none_num )
% 9.49/5.24        = none_num ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1149_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 9.49/5.24      ! [Uw: nat > nat > nat,V: nat] :
% 9.49/5.24        ( ( vEBT_V4262088993061758097ft_nat @ Uw @ ( some_nat @ V ) @ none_nat )
% 9.49/5.24        = none_nat ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1150_VEBT__internal_Ooption__shift_Oelims,axiom,
% 9.49/5.24      ! [X: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Xa2: option4927543243414619207at_nat,Xb: option4927543243414619207at_nat,Y2: option4927543243414619207at_nat] :
% 9.49/5.24        ( ( ( vEBT_V1502963449132264192at_nat @ X @ Xa2 @ Xb )
% 9.49/5.24          = Y2 )
% 9.49/5.24       => ( ( ( Xa2 = none_P5556105721700978146at_nat )
% 9.49/5.24           => ( Y2 != none_P5556105721700978146at_nat ) )
% 9.49/5.24         => ( ( ? [V2: product_prod_nat_nat] :
% 9.49/5.24                  ( Xa2
% 9.49/5.24                  = ( some_P7363390416028606310at_nat @ V2 ) )
% 9.49/5.24             => ( ( Xb = none_P5556105721700978146at_nat )
% 9.49/5.24               => ( Y2 != none_P5556105721700978146at_nat ) ) )
% 9.49/5.24           => ~ ! [A4: product_prod_nat_nat] :
% 9.49/5.24                  ( ( Xa2
% 9.49/5.24                    = ( some_P7363390416028606310at_nat @ A4 ) )
% 9.49/5.24                 => ! [B3: product_prod_nat_nat] :
% 9.49/5.24                      ( ( Xb
% 9.49/5.24                        = ( some_P7363390416028606310at_nat @ B3 ) )
% 9.49/5.24                     => ( Y2
% 9.49/5.24                       != ( some_P7363390416028606310at_nat @ ( X @ A4 @ B3 ) ) ) ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1151_VEBT__internal_Ooption__shift_Oelims,axiom,
% 9.49/5.24      ! [X: num > num > num,Xa2: option_num,Xb: option_num,Y2: option_num] :
% 9.49/5.24        ( ( ( vEBT_V819420779217536731ft_num @ X @ Xa2 @ Xb )
% 9.49/5.24          = Y2 )
% 9.49/5.24       => ( ( ( Xa2 = none_num )
% 9.49/5.24           => ( Y2 != none_num ) )
% 9.49/5.24         => ( ( ? [V2: num] :
% 9.49/5.24                  ( Xa2
% 9.49/5.24                  = ( some_num @ V2 ) )
% 9.49/5.24             => ( ( Xb = none_num )
% 9.49/5.24               => ( Y2 != none_num ) ) )
% 9.49/5.24           => ~ ! [A4: num] :
% 9.49/5.24                  ( ( Xa2
% 9.49/5.24                    = ( some_num @ A4 ) )
% 9.49/5.24                 => ! [B3: num] :
% 9.49/5.24                      ( ( Xb
% 9.49/5.24                        = ( some_num @ B3 ) )
% 9.49/5.24                     => ( Y2
% 9.49/5.24                       != ( some_num @ ( X @ A4 @ B3 ) ) ) ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1152_VEBT__internal_Ooption__shift_Oelims,axiom,
% 9.49/5.24      ! [X: nat > nat > nat,Xa2: option_nat,Xb: option_nat,Y2: option_nat] :
% 9.49/5.24        ( ( ( vEBT_V4262088993061758097ft_nat @ X @ Xa2 @ Xb )
% 9.49/5.24          = Y2 )
% 9.49/5.24       => ( ( ( Xa2 = none_nat )
% 9.49/5.24           => ( Y2 != none_nat ) )
% 9.49/5.24         => ( ( ? [V2: nat] :
% 9.49/5.24                  ( Xa2
% 9.49/5.24                  = ( some_nat @ V2 ) )
% 9.49/5.24             => ( ( Xb = none_nat )
% 9.49/5.24               => ( Y2 != none_nat ) ) )
% 9.49/5.24           => ~ ! [A4: nat] :
% 9.49/5.24                  ( ( Xa2
% 9.49/5.24                    = ( some_nat @ A4 ) )
% 9.49/5.24                 => ! [B3: nat] :
% 9.49/5.24                      ( ( Xb
% 9.49/5.24                        = ( some_nat @ B3 ) )
% 9.49/5.24                     => ( Y2
% 9.49/5.24                       != ( some_nat @ ( X @ A4 @ B3 ) ) ) ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1153_vebt__mint_Osimps_I2_J,axiom,
% 9.49/5.24      ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 9.49/5.24        ( ( vEBT_vebt_mint @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 9.49/5.24        = none_nat ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1154_vebt__maxt_Osimps_I2_J,axiom,
% 9.49/5.24      ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 9.49/5.24        ( ( vEBT_vebt_maxt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 9.49/5.24        = none_nat ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1155_add__diff__cancel__right_H,axiom,
% 9.49/5.24      ! [A: real,B: real] :
% 9.49/5.24        ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1156_add__diff__cancel__right_H,axiom,
% 9.49/5.24      ! [A: complex,B: complex] :
% 9.49/5.24        ( ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ B )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1157_add__diff__cancel__right_H,axiom,
% 9.49/5.24      ! [A: rat,B: rat] :
% 9.49/5.24        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1158_add__diff__cancel__right_H,axiom,
% 9.49/5.24      ! [A: nat,B: nat] :
% 9.49/5.24        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1159_add__diff__cancel__right_H,axiom,
% 9.49/5.24      ! [A: int,B: int] :
% 9.49/5.24        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1160_add__diff__cancel__right,axiom,
% 9.49/5.24      ! [A: real,C: real,B: real] :
% 9.49/5.24        ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 9.49/5.24        = ( minus_minus_real @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1161_add__diff__cancel__right,axiom,
% 9.49/5.24      ! [A: complex,C: complex,B: complex] :
% 9.49/5.24        ( ( minus_minus_complex @ ( plus_plus_complex @ A @ C ) @ ( plus_plus_complex @ B @ C ) )
% 9.49/5.24        = ( minus_minus_complex @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1162_add__diff__cancel__right,axiom,
% 9.49/5.24      ! [A: rat,C: rat,B: rat] :
% 9.49/5.24        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 9.49/5.24        = ( minus_minus_rat @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1163_add__diff__cancel__right,axiom,
% 9.49/5.24      ! [A: nat,C: nat,B: nat] :
% 9.49/5.24        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 9.49/5.24        = ( minus_minus_nat @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1164_add__diff__cancel__right,axiom,
% 9.49/5.24      ! [A: int,C: int,B: int] :
% 9.49/5.24        ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 9.49/5.24        = ( minus_minus_int @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1165_add__diff__cancel__left_H,axiom,
% 9.49/5.24      ! [A: real,B: real] :
% 9.49/5.24        ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 9.49/5.24        = B ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1166_add__diff__cancel__left_H,axiom,
% 9.49/5.24      ! [A: complex,B: complex] :
% 9.49/5.24        ( ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ A )
% 9.49/5.24        = B ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1167_add__diff__cancel__left_H,axiom,
% 9.49/5.24      ! [A: rat,B: rat] :
% 9.49/5.24        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 9.49/5.24        = B ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1168_add__diff__cancel__left_H,axiom,
% 9.49/5.24      ! [A: nat,B: nat] :
% 9.49/5.24        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 9.49/5.24        = B ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1169_add__diff__cancel__left_H,axiom,
% 9.49/5.24      ! [A: int,B: int] :
% 9.49/5.24        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 9.49/5.24        = B ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1170_add__diff__cancel__left,axiom,
% 9.49/5.24      ! [C: real,A: real,B: real] :
% 9.49/5.24        ( ( minus_minus_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 9.49/5.24        = ( minus_minus_real @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1171_add__diff__cancel__left,axiom,
% 9.49/5.24      ! [C: complex,A: complex,B: complex] :
% 9.49/5.24        ( ( minus_minus_complex @ ( plus_plus_complex @ C @ A ) @ ( plus_plus_complex @ C @ B ) )
% 9.49/5.24        = ( minus_minus_complex @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1172_add__diff__cancel__left,axiom,
% 9.49/5.24      ! [C: rat,A: rat,B: rat] :
% 9.49/5.24        ( ( minus_minus_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 9.49/5.24        = ( minus_minus_rat @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1173_add__diff__cancel__left,axiom,
% 9.49/5.24      ! [C: nat,A: nat,B: nat] :
% 9.49/5.24        ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 9.49/5.24        = ( minus_minus_nat @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1174_add__diff__cancel__left,axiom,
% 9.49/5.24      ! [C: int,A: int,B: int] :
% 9.49/5.24        ( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 9.49/5.24        = ( minus_minus_int @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1175_diff__add__cancel,axiom,
% 9.49/5.24      ! [A: real,B: real] :
% 9.49/5.24        ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1176_diff__add__cancel,axiom,
% 9.49/5.24      ! [A: complex,B: complex] :
% 9.49/5.24        ( ( plus_plus_complex @ ( minus_minus_complex @ A @ B ) @ B )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1177_diff__add__cancel,axiom,
% 9.49/5.24      ! [A: rat,B: rat] :
% 9.49/5.24        ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1178_diff__add__cancel,axiom,
% 9.49/5.24      ! [A: int,B: int] :
% 9.49/5.24        ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1179_add__diff__cancel,axiom,
% 9.49/5.24      ! [A: real,B: real] :
% 9.49/5.24        ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1180_add__diff__cancel,axiom,
% 9.49/5.24      ! [A: complex,B: complex] :
% 9.49/5.24        ( ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ B )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1181_add__diff__cancel,axiom,
% 9.49/5.24      ! [A: rat,B: rat] :
% 9.49/5.24        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1182_add__diff__cancel,axiom,
% 9.49/5.24      ! [A: int,B: int] :
% 9.49/5.24        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1183_times__divide__eq__left,axiom,
% 9.49/5.24      ! [B: complex,C: complex,A: complex] :
% 9.49/5.24        ( ( times_times_complex @ ( divide1717551699836669952omplex @ B @ C ) @ A )
% 9.49/5.24        = ( divide1717551699836669952omplex @ ( times_times_complex @ B @ A ) @ C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1184_times__divide__eq__left,axiom,
% 9.49/5.24      ! [B: real,C: real,A: real] :
% 9.49/5.24        ( ( times_times_real @ ( divide_divide_real @ B @ C ) @ A )
% 9.49/5.24        = ( divide_divide_real @ ( times_times_real @ B @ A ) @ C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1185_times__divide__eq__left,axiom,
% 9.49/5.24      ! [B: rat,C: rat,A: rat] :
% 9.49/5.24        ( ( times_times_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 9.49/5.24        = ( divide_divide_rat @ ( times_times_rat @ B @ A ) @ C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1186_divide__divide__eq__left,axiom,
% 9.49/5.24      ! [A: complex,B: complex,C: complex] :
% 9.49/5.24        ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 9.49/5.24        = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1187_divide__divide__eq__left,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real] :
% 9.49/5.24        ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 9.49/5.24        = ( divide_divide_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1188_divide__divide__eq__left,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat] :
% 9.49/5.24        ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 9.49/5.24        = ( divide_divide_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1189_divide__divide__eq__right,axiom,
% 9.49/5.24      ! [A: complex,B: complex,C: complex] :
% 9.49/5.24        ( ( divide1717551699836669952omplex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 9.49/5.24        = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1190_divide__divide__eq__right,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real] :
% 9.49/5.24        ( ( divide_divide_real @ A @ ( divide_divide_real @ B @ C ) )
% 9.49/5.24        = ( divide_divide_real @ ( times_times_real @ A @ C ) @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1191_divide__divide__eq__right,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat] :
% 9.49/5.24        ( ( divide_divide_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 9.49/5.24        = ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1192_times__divide__eq__right,axiom,
% 9.49/5.24      ! [A: complex,B: complex,C: complex] :
% 9.49/5.24        ( ( times_times_complex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 9.49/5.24        = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1193_times__divide__eq__right,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real] :
% 9.49/5.24        ( ( times_times_real @ A @ ( divide_divide_real @ B @ C ) )
% 9.49/5.24        = ( divide_divide_real @ ( times_times_real @ A @ B ) @ C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1194_times__divide__eq__right,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat] :
% 9.49/5.24        ( ( times_times_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 9.49/5.24        = ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1195_add__left__cancel,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real] :
% 9.49/5.24        ( ( ( plus_plus_real @ A @ B )
% 9.49/5.24          = ( plus_plus_real @ A @ C ) )
% 9.49/5.24        = ( B = C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1196_add__left__cancel,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat] :
% 9.49/5.24        ( ( ( plus_plus_rat @ A @ B )
% 9.49/5.24          = ( plus_plus_rat @ A @ C ) )
% 9.49/5.24        = ( B = C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1197_add__left__cancel,axiom,
% 9.49/5.24      ! [A: nat,B: nat,C: nat] :
% 9.49/5.24        ( ( ( plus_plus_nat @ A @ B )
% 9.49/5.24          = ( plus_plus_nat @ A @ C ) )
% 9.49/5.24        = ( B = C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1198_add__left__cancel,axiom,
% 9.49/5.24      ! [A: int,B: int,C: int] :
% 9.49/5.24        ( ( ( plus_plus_int @ A @ B )
% 9.49/5.24          = ( plus_plus_int @ A @ C ) )
% 9.49/5.24        = ( B = C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1199_add__left__cancel,axiom,
% 9.49/5.24      ! [A: complex,B: complex,C: complex] :
% 9.49/5.24        ( ( ( plus_plus_complex @ A @ B )
% 9.49/5.24          = ( plus_plus_complex @ A @ C ) )
% 9.49/5.24        = ( B = C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1200_add__right__cancel,axiom,
% 9.49/5.24      ! [B: real,A: real,C: real] :
% 9.49/5.24        ( ( ( plus_plus_real @ B @ A )
% 9.49/5.24          = ( plus_plus_real @ C @ A ) )
% 9.49/5.24        = ( B = C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1201_add__right__cancel,axiom,
% 9.49/5.24      ! [B: rat,A: rat,C: rat] :
% 9.49/5.24        ( ( ( plus_plus_rat @ B @ A )
% 9.49/5.24          = ( plus_plus_rat @ C @ A ) )
% 9.49/5.24        = ( B = C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1202_add__right__cancel,axiom,
% 9.49/5.24      ! [B: nat,A: nat,C: nat] :
% 9.49/5.24        ( ( ( plus_plus_nat @ B @ A )
% 9.49/5.24          = ( plus_plus_nat @ C @ A ) )
% 9.49/5.24        = ( B = C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1203_add__right__cancel,axiom,
% 9.49/5.24      ! [B: int,A: int,C: int] :
% 9.49/5.24        ( ( ( plus_plus_int @ B @ A )
% 9.49/5.24          = ( plus_plus_int @ C @ A ) )
% 9.49/5.24        = ( B = C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1204_add__right__cancel,axiom,
% 9.49/5.24      ! [B: complex,A: complex,C: complex] :
% 9.49/5.24        ( ( ( plus_plus_complex @ B @ A )
% 9.49/5.24          = ( plus_plus_complex @ C @ A ) )
% 9.49/5.24        = ( B = C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1205_add__le__cancel__left,axiom,
% 9.49/5.24      ! [C: real,A: real,B: real] :
% 9.49/5.24        ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 9.49/5.24        = ( ord_less_eq_real @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1206_add__le__cancel__left,axiom,
% 9.49/5.24      ! [C: rat,A: rat,B: rat] :
% 9.49/5.24        ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 9.49/5.24        = ( ord_less_eq_rat @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1207_add__le__cancel__left,axiom,
% 9.49/5.24      ! [C: nat,A: nat,B: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 9.49/5.24        = ( ord_less_eq_nat @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1208_add__le__cancel__left,axiom,
% 9.49/5.24      ! [C: int,A: int,B: int] :
% 9.49/5.24        ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 9.49/5.24        = ( ord_less_eq_int @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1209_add__le__cancel__right,axiom,
% 9.49/5.24      ! [A: real,C: real,B: real] :
% 9.49/5.24        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 9.49/5.24        = ( ord_less_eq_real @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1210_add__le__cancel__right,axiom,
% 9.49/5.24      ! [A: rat,C: rat,B: rat] :
% 9.49/5.24        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 9.49/5.24        = ( ord_less_eq_rat @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1211_add__le__cancel__right,axiom,
% 9.49/5.24      ! [A: nat,C: nat,B: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 9.49/5.24        = ( ord_less_eq_nat @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1212_add__le__cancel__right,axiom,
% 9.49/5.24      ! [A: int,C: int,B: int] :
% 9.49/5.24        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 9.49/5.24        = ( ord_less_eq_int @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1213_add__less__cancel__left,axiom,
% 9.49/5.24      ! [C: real,A: real,B: real] :
% 9.49/5.24        ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 9.49/5.24        = ( ord_less_real @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1214_add__less__cancel__left,axiom,
% 9.49/5.24      ! [C: rat,A: rat,B: rat] :
% 9.49/5.24        ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 9.49/5.24        = ( ord_less_rat @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1215_add__less__cancel__left,axiom,
% 9.49/5.24      ! [C: nat,A: nat,B: nat] :
% 9.49/5.24        ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 9.49/5.24        = ( ord_less_nat @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1216_add__less__cancel__left,axiom,
% 9.49/5.24      ! [C: int,A: int,B: int] :
% 9.49/5.24        ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 9.49/5.24        = ( ord_less_int @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1217_add__less__cancel__right,axiom,
% 9.49/5.24      ! [A: real,C: real,B: real] :
% 9.49/5.24        ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 9.49/5.24        = ( ord_less_real @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1218_add__less__cancel__right,axiom,
% 9.49/5.24      ! [A: rat,C: rat,B: rat] :
% 9.49/5.24        ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 9.49/5.24        = ( ord_less_rat @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1219_add__less__cancel__right,axiom,
% 9.49/5.24      ! [A: nat,C: nat,B: nat] :
% 9.49/5.24        ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 9.49/5.24        = ( ord_less_nat @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1220_add__less__cancel__right,axiom,
% 9.49/5.24      ! [A: int,C: int,B: int] :
% 9.49/5.24        ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 9.49/5.24        = ( ord_less_int @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1221_mult_Oright__neutral,axiom,
% 9.49/5.24      ! [A: rat] :
% 9.49/5.24        ( ( times_times_rat @ A @ one_one_rat )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1222_mult_Oright__neutral,axiom,
% 9.49/5.24      ! [A: complex] :
% 9.49/5.24        ( ( times_times_complex @ A @ one_one_complex )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1223_mult_Oright__neutral,axiom,
% 9.49/5.24      ! [A: real] :
% 9.49/5.24        ( ( times_times_real @ A @ one_one_real )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1224_mult_Oright__neutral,axiom,
% 9.49/5.24      ! [A: nat] :
% 9.49/5.24        ( ( times_times_nat @ A @ one_one_nat )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1225_mult_Oright__neutral,axiom,
% 9.49/5.24      ! [A: int] :
% 9.49/5.24        ( ( times_times_int @ A @ one_one_int )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1226_mult__1,axiom,
% 9.49/5.24      ! [A: rat] :
% 9.49/5.24        ( ( times_times_rat @ one_one_rat @ A )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1227_mult__1,axiom,
% 9.49/5.24      ! [A: complex] :
% 9.49/5.24        ( ( times_times_complex @ one_one_complex @ A )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1228_mult__1,axiom,
% 9.49/5.24      ! [A: real] :
% 9.49/5.24        ( ( times_times_real @ one_one_real @ A )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1229_mult__1,axiom,
% 9.49/5.24      ! [A: nat] :
% 9.49/5.24        ( ( times_times_nat @ one_one_nat @ A )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1230_mult__1,axiom,
% 9.49/5.24      ! [A: int] :
% 9.49/5.24        ( ( times_times_int @ one_one_int @ A )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1231_linordered__field__no__ub,axiom,
% 9.49/5.24      ! [X5: real] :
% 9.49/5.24      ? [X_12: real] : ( ord_less_real @ X5 @ X_12 ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1232_linordered__field__no__ub,axiom,
% 9.49/5.24      ! [X5: rat] :
% 9.49/5.24      ? [X_12: rat] : ( ord_less_rat @ X5 @ X_12 ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1233_linordered__field__no__lb,axiom,
% 9.49/5.24      ! [X5: real] :
% 9.49/5.24      ? [Y3: real] : ( ord_less_real @ Y3 @ X5 ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1234_linordered__field__no__lb,axiom,
% 9.49/5.24      ! [X5: rat] :
% 9.49/5.24      ? [Y3: rat] : ( ord_less_rat @ Y3 @ X5 ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1235_mult_Oleft__commute,axiom,
% 9.49/5.24      ! [B: complex,A: complex,C: complex] :
% 9.49/5.24        ( ( times_times_complex @ B @ ( times_times_complex @ A @ C ) )
% 9.49/5.24        = ( times_times_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1236_mult_Oleft__commute,axiom,
% 9.49/5.24      ! [B: real,A: real,C: real] :
% 9.49/5.24        ( ( times_times_real @ B @ ( times_times_real @ A @ C ) )
% 9.49/5.24        = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1237_mult_Oleft__commute,axiom,
% 9.49/5.24      ! [B: nat,A: nat,C: nat] :
% 9.49/5.24        ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 9.49/5.24        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1238_mult_Oleft__commute,axiom,
% 9.49/5.24      ! [B: int,A: int,C: int] :
% 9.49/5.24        ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
% 9.49/5.24        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1239_mult_Ocommute,axiom,
% 9.49/5.24      ( times_times_complex
% 9.49/5.24      = ( ^ [A3: complex,B4: complex] : ( times_times_complex @ B4 @ A3 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1240_mult_Ocommute,axiom,
% 9.49/5.24      ( times_times_real
% 9.49/5.24      = ( ^ [A3: real,B4: real] : ( times_times_real @ B4 @ A3 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1241_mult_Ocommute,axiom,
% 9.49/5.24      ( times_times_nat
% 9.49/5.24      = ( ^ [A3: nat,B4: nat] : ( times_times_nat @ B4 @ A3 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1242_mult_Ocommute,axiom,
% 9.49/5.24      ( times_times_int
% 9.49/5.24      = ( ^ [A3: int,B4: int] : ( times_times_int @ B4 @ A3 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1243_mult_Oassoc,axiom,
% 9.49/5.24      ! [A: complex,B: complex,C: complex] :
% 9.49/5.24        ( ( times_times_complex @ ( times_times_complex @ A @ B ) @ C )
% 9.49/5.24        = ( times_times_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1244_mult_Oassoc,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real] :
% 9.49/5.24        ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 9.49/5.24        = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1245_mult_Oassoc,axiom,
% 9.49/5.24      ! [A: nat,B: nat,C: nat] :
% 9.49/5.24        ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 9.49/5.24        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1246_mult_Oassoc,axiom,
% 9.49/5.24      ! [A: int,B: int,C: int] :
% 9.49/5.24        ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 9.49/5.24        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1247_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 9.49/5.24      ! [A: complex,B: complex,C: complex] :
% 9.49/5.24        ( ( times_times_complex @ ( times_times_complex @ A @ B ) @ C )
% 9.49/5.24        = ( times_times_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1248_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real] :
% 9.49/5.24        ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 9.49/5.24        = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1249_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 9.49/5.24      ! [A: nat,B: nat,C: nat] :
% 9.49/5.24        ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 9.49/5.24        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1250_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 9.49/5.24      ! [A: int,B: int,C: int] :
% 9.49/5.24        ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 9.49/5.24        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1251_one__reorient,axiom,
% 9.49/5.24      ! [X: complex] :
% 9.49/5.24        ( ( one_one_complex = X )
% 9.49/5.24        = ( X = one_one_complex ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1252_one__reorient,axiom,
% 9.49/5.24      ! [X: real] :
% 9.49/5.24        ( ( one_one_real = X )
% 9.49/5.24        = ( X = one_one_real ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1253_one__reorient,axiom,
% 9.49/5.24      ! [X: rat] :
% 9.49/5.24        ( ( one_one_rat = X )
% 9.49/5.24        = ( X = one_one_rat ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1254_one__reorient,axiom,
% 9.49/5.24      ! [X: nat] :
% 9.49/5.24        ( ( one_one_nat = X )
% 9.49/5.24        = ( X = one_one_nat ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1255_one__reorient,axiom,
% 9.49/5.24      ! [X: int] :
% 9.49/5.24        ( ( one_one_int = X )
% 9.49/5.24        = ( X = one_one_int ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1256_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real] :
% 9.49/5.24        ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 9.49/5.24        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1257_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat] :
% 9.49/5.24        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 9.49/5.24        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1258_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 9.49/5.24      ! [A: nat,B: nat,C: nat] :
% 9.49/5.24        ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 9.49/5.24        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1259_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 9.49/5.24      ! [A: int,B: int,C: int] :
% 9.49/5.24        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 9.49/5.24        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1260_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 9.49/5.24      ! [A: complex,B: complex,C: complex] :
% 9.49/5.24        ( ( plus_plus_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 9.49/5.24        = ( plus_plus_complex @ A @ ( plus_plus_complex @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1261_add__mono__thms__linordered__semiring_I4_J,axiom,
% 9.49/5.24      ! [I2: real,J: real,K: real,L2: real] :
% 9.49/5.24        ( ( ( I2 = J )
% 9.49/5.24          & ( K = L2 ) )
% 9.49/5.24       => ( ( plus_plus_real @ I2 @ K )
% 9.49/5.24          = ( plus_plus_real @ J @ L2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1262_add__mono__thms__linordered__semiring_I4_J,axiom,
% 9.49/5.24      ! [I2: rat,J: rat,K: rat,L2: rat] :
% 9.49/5.24        ( ( ( I2 = J )
% 9.49/5.24          & ( K = L2 ) )
% 9.49/5.24       => ( ( plus_plus_rat @ I2 @ K )
% 9.49/5.24          = ( plus_plus_rat @ J @ L2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1263_add__mono__thms__linordered__semiring_I4_J,axiom,
% 9.49/5.24      ! [I2: nat,J: nat,K: nat,L2: nat] :
% 9.49/5.24        ( ( ( I2 = J )
% 9.49/5.24          & ( K = L2 ) )
% 9.49/5.24       => ( ( plus_plus_nat @ I2 @ K )
% 9.49/5.24          = ( plus_plus_nat @ J @ L2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1264_add__mono__thms__linordered__semiring_I4_J,axiom,
% 9.49/5.24      ! [I2: int,J: int,K: int,L2: int] :
% 9.49/5.24        ( ( ( I2 = J )
% 9.49/5.24          & ( K = L2 ) )
% 9.49/5.24       => ( ( plus_plus_int @ I2 @ K )
% 9.49/5.24          = ( plus_plus_int @ J @ L2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1265_group__cancel_Oadd1,axiom,
% 9.49/5.24      ! [A2: real,K: real,A: real,B: real] :
% 9.49/5.24        ( ( A2
% 9.49/5.24          = ( plus_plus_real @ K @ A ) )
% 9.49/5.24       => ( ( plus_plus_real @ A2 @ B )
% 9.49/5.24          = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1266_group__cancel_Oadd1,axiom,
% 9.49/5.24      ! [A2: rat,K: rat,A: rat,B: rat] :
% 9.49/5.24        ( ( A2
% 9.49/5.24          = ( plus_plus_rat @ K @ A ) )
% 9.49/5.24       => ( ( plus_plus_rat @ A2 @ B )
% 9.49/5.24          = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1267_group__cancel_Oadd1,axiom,
% 9.49/5.24      ! [A2: nat,K: nat,A: nat,B: nat] :
% 9.49/5.24        ( ( A2
% 9.49/5.24          = ( plus_plus_nat @ K @ A ) )
% 9.49/5.24       => ( ( plus_plus_nat @ A2 @ B )
% 9.49/5.24          = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1268_group__cancel_Oadd1,axiom,
% 9.49/5.24      ! [A2: int,K: int,A: int,B: int] :
% 9.49/5.24        ( ( A2
% 9.49/5.24          = ( plus_plus_int @ K @ A ) )
% 9.49/5.24       => ( ( plus_plus_int @ A2 @ B )
% 9.49/5.24          = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1269_group__cancel_Oadd1,axiom,
% 9.49/5.24      ! [A2: complex,K: complex,A: complex,B: complex] :
% 9.49/5.24        ( ( A2
% 9.49/5.24          = ( plus_plus_complex @ K @ A ) )
% 9.49/5.24       => ( ( plus_plus_complex @ A2 @ B )
% 9.49/5.24          = ( plus_plus_complex @ K @ ( plus_plus_complex @ A @ B ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1270_group__cancel_Oadd2,axiom,
% 9.49/5.24      ! [B2: real,K: real,B: real,A: real] :
% 9.49/5.24        ( ( B2
% 9.49/5.24          = ( plus_plus_real @ K @ B ) )
% 9.49/5.24       => ( ( plus_plus_real @ A @ B2 )
% 9.49/5.24          = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1271_group__cancel_Oadd2,axiom,
% 9.49/5.24      ! [B2: rat,K: rat,B: rat,A: rat] :
% 9.49/5.24        ( ( B2
% 9.49/5.24          = ( plus_plus_rat @ K @ B ) )
% 9.49/5.24       => ( ( plus_plus_rat @ A @ B2 )
% 9.49/5.24          = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1272_group__cancel_Oadd2,axiom,
% 9.49/5.24      ! [B2: nat,K: nat,B: nat,A: nat] :
% 9.49/5.24        ( ( B2
% 9.49/5.24          = ( plus_plus_nat @ K @ B ) )
% 9.49/5.24       => ( ( plus_plus_nat @ A @ B2 )
% 9.49/5.24          = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1273_group__cancel_Oadd2,axiom,
% 9.49/5.24      ! [B2: int,K: int,B: int,A: int] :
% 9.49/5.24        ( ( B2
% 9.49/5.24          = ( plus_plus_int @ K @ B ) )
% 9.49/5.24       => ( ( plus_plus_int @ A @ B2 )
% 9.49/5.24          = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1274_group__cancel_Oadd2,axiom,
% 9.49/5.24      ! [B2: complex,K: complex,B: complex,A: complex] :
% 9.49/5.24        ( ( B2
% 9.49/5.24          = ( plus_plus_complex @ K @ B ) )
% 9.49/5.24       => ( ( plus_plus_complex @ A @ B2 )
% 9.49/5.24          = ( plus_plus_complex @ K @ ( plus_plus_complex @ A @ B ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1275_add_Oassoc,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real] :
% 9.49/5.24        ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 9.49/5.24        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1276_add_Oassoc,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat] :
% 9.49/5.24        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 9.49/5.24        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1277_add_Oassoc,axiom,
% 9.49/5.24      ! [A: nat,B: nat,C: nat] :
% 9.49/5.24        ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 9.49/5.24        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1278_add_Oassoc,axiom,
% 9.49/5.24      ! [A: int,B: int,C: int] :
% 9.49/5.24        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 9.49/5.24        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1279_add_Oassoc,axiom,
% 9.49/5.24      ! [A: complex,B: complex,C: complex] :
% 9.49/5.24        ( ( plus_plus_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 9.49/5.24        = ( plus_plus_complex @ A @ ( plus_plus_complex @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1280_add_Oleft__cancel,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real] :
% 9.49/5.24        ( ( ( plus_plus_real @ A @ B )
% 9.49/5.24          = ( plus_plus_real @ A @ C ) )
% 9.49/5.24        = ( B = C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1281_add_Oleft__cancel,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat] :
% 9.49/5.24        ( ( ( plus_plus_rat @ A @ B )
% 9.49/5.24          = ( plus_plus_rat @ A @ C ) )
% 9.49/5.24        = ( B = C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1282_add_Oleft__cancel,axiom,
% 9.49/5.24      ! [A: int,B: int,C: int] :
% 9.49/5.24        ( ( ( plus_plus_int @ A @ B )
% 9.49/5.24          = ( plus_plus_int @ A @ C ) )
% 9.49/5.24        = ( B = C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1283_add_Oleft__cancel,axiom,
% 9.49/5.24      ! [A: complex,B: complex,C: complex] :
% 9.49/5.24        ( ( ( plus_plus_complex @ A @ B )
% 9.49/5.24          = ( plus_plus_complex @ A @ C ) )
% 9.49/5.24        = ( B = C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1284_add_Oright__cancel,axiom,
% 9.49/5.24      ! [B: real,A: real,C: real] :
% 9.49/5.24        ( ( ( plus_plus_real @ B @ A )
% 9.49/5.24          = ( plus_plus_real @ C @ A ) )
% 9.49/5.24        = ( B = C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1285_add_Oright__cancel,axiom,
% 9.49/5.24      ! [B: rat,A: rat,C: rat] :
% 9.49/5.24        ( ( ( plus_plus_rat @ B @ A )
% 9.49/5.24          = ( plus_plus_rat @ C @ A ) )
% 9.49/5.24        = ( B = C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1286_add_Oright__cancel,axiom,
% 9.49/5.24      ! [B: int,A: int,C: int] :
% 9.49/5.24        ( ( ( plus_plus_int @ B @ A )
% 9.49/5.24          = ( plus_plus_int @ C @ A ) )
% 9.49/5.24        = ( B = C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1287_add_Oright__cancel,axiom,
% 9.49/5.24      ! [B: complex,A: complex,C: complex] :
% 9.49/5.24        ( ( ( plus_plus_complex @ B @ A )
% 9.49/5.24          = ( plus_plus_complex @ C @ A ) )
% 9.49/5.24        = ( B = C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1288_add_Ocommute,axiom,
% 9.49/5.24      ( plus_plus_real
% 9.49/5.24      = ( ^ [A3: real,B4: real] : ( plus_plus_real @ B4 @ A3 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1289_add_Ocommute,axiom,
% 9.49/5.24      ( plus_plus_rat
% 9.49/5.24      = ( ^ [A3: rat,B4: rat] : ( plus_plus_rat @ B4 @ A3 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1290_add_Ocommute,axiom,
% 9.49/5.24      ( plus_plus_nat
% 9.49/5.24      = ( ^ [A3: nat,B4: nat] : ( plus_plus_nat @ B4 @ A3 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1291_add_Ocommute,axiom,
% 9.49/5.24      ( plus_plus_int
% 9.49/5.24      = ( ^ [A3: int,B4: int] : ( plus_plus_int @ B4 @ A3 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1292_add_Ocommute,axiom,
% 9.49/5.24      ( plus_plus_complex
% 9.49/5.24      = ( ^ [A3: complex,B4: complex] : ( plus_plus_complex @ B4 @ A3 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1293_add_Oleft__commute,axiom,
% 9.49/5.24      ! [B: real,A: real,C: real] :
% 9.49/5.24        ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) )
% 9.49/5.24        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1294_add_Oleft__commute,axiom,
% 9.49/5.24      ! [B: rat,A: rat,C: rat] :
% 9.49/5.24        ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C ) )
% 9.49/5.24        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1295_add_Oleft__commute,axiom,
% 9.49/5.24      ! [B: nat,A: nat,C: nat] :
% 9.49/5.24        ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 9.49/5.24        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1296_add_Oleft__commute,axiom,
% 9.49/5.24      ! [B: int,A: int,C: int] :
% 9.49/5.24        ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
% 9.49/5.24        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1297_add_Oleft__commute,axiom,
% 9.49/5.24      ! [B: complex,A: complex,C: complex] :
% 9.49/5.24        ( ( plus_plus_complex @ B @ ( plus_plus_complex @ A @ C ) )
% 9.49/5.24        = ( plus_plus_complex @ A @ ( plus_plus_complex @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1298_add__left__imp__eq,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real] :
% 9.49/5.24        ( ( ( plus_plus_real @ A @ B )
% 9.49/5.24          = ( plus_plus_real @ A @ C ) )
% 9.49/5.24       => ( B = C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1299_add__left__imp__eq,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat] :
% 9.49/5.24        ( ( ( plus_plus_rat @ A @ B )
% 9.49/5.24          = ( plus_plus_rat @ A @ C ) )
% 9.49/5.24       => ( B = C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1300_add__left__imp__eq,axiom,
% 9.49/5.24      ! [A: nat,B: nat,C: nat] :
% 9.49/5.24        ( ( ( plus_plus_nat @ A @ B )
% 9.49/5.24          = ( plus_plus_nat @ A @ C ) )
% 9.49/5.24       => ( B = C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1301_add__left__imp__eq,axiom,
% 9.49/5.24      ! [A: int,B: int,C: int] :
% 9.49/5.24        ( ( ( plus_plus_int @ A @ B )
% 9.49/5.24          = ( plus_plus_int @ A @ C ) )
% 9.49/5.24       => ( B = C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1302_add__left__imp__eq,axiom,
% 9.49/5.24      ! [A: complex,B: complex,C: complex] :
% 9.49/5.24        ( ( ( plus_plus_complex @ A @ B )
% 9.49/5.24          = ( plus_plus_complex @ A @ C ) )
% 9.49/5.24       => ( B = C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1303_add__right__imp__eq,axiom,
% 9.49/5.24      ! [B: real,A: real,C: real] :
% 9.49/5.24        ( ( ( plus_plus_real @ B @ A )
% 9.49/5.24          = ( plus_plus_real @ C @ A ) )
% 9.49/5.24       => ( B = C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1304_add__right__imp__eq,axiom,
% 9.49/5.24      ! [B: rat,A: rat,C: rat] :
% 9.49/5.24        ( ( ( plus_plus_rat @ B @ A )
% 9.49/5.24          = ( plus_plus_rat @ C @ A ) )
% 9.49/5.24       => ( B = C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1305_add__right__imp__eq,axiom,
% 9.49/5.24      ! [B: nat,A: nat,C: nat] :
% 9.49/5.24        ( ( ( plus_plus_nat @ B @ A )
% 9.49/5.24          = ( plus_plus_nat @ C @ A ) )
% 9.49/5.24       => ( B = C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1306_add__right__imp__eq,axiom,
% 9.49/5.24      ! [B: int,A: int,C: int] :
% 9.49/5.24        ( ( ( plus_plus_int @ B @ A )
% 9.49/5.24          = ( plus_plus_int @ C @ A ) )
% 9.49/5.24       => ( B = C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1307_add__right__imp__eq,axiom,
% 9.49/5.24      ! [B: complex,A: complex,C: complex] :
% 9.49/5.24        ( ( ( plus_plus_complex @ B @ A )
% 9.49/5.24          = ( plus_plus_complex @ C @ A ) )
% 9.49/5.24       => ( B = C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1308_diff__right__commute,axiom,
% 9.49/5.24      ! [A: rat,C: rat,B: rat] :
% 9.49/5.24        ( ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B )
% 9.49/5.24        = ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1309_diff__right__commute,axiom,
% 9.49/5.24      ! [A: nat,C: nat,B: nat] :
% 9.49/5.24        ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 9.49/5.24        = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1310_diff__right__commute,axiom,
% 9.49/5.24      ! [A: int,C: int,B: int] :
% 9.49/5.24        ( ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B )
% 9.49/5.24        = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1311_diff__eq__diff__eq,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.49/5.24        ( ( ( minus_minus_rat @ A @ B )
% 9.49/5.24          = ( minus_minus_rat @ C @ D2 ) )
% 9.49/5.24       => ( ( A = B )
% 9.49/5.24          = ( C = D2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1312_diff__eq__diff__eq,axiom,
% 9.49/5.24      ! [A: int,B: int,C: int,D2: int] :
% 9.49/5.24        ( ( ( minus_minus_int @ A @ B )
% 9.49/5.24          = ( minus_minus_int @ C @ D2 ) )
% 9.49/5.24       => ( ( A = B )
% 9.49/5.24          = ( C = D2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1313_add__mono__thms__linordered__semiring_I3_J,axiom,
% 9.49/5.24      ! [I2: real,J: real,K: real,L2: real] :
% 9.49/5.24        ( ( ( ord_less_eq_real @ I2 @ J )
% 9.49/5.24          & ( K = L2 ) )
% 9.49/5.24       => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1314_add__mono__thms__linordered__semiring_I3_J,axiom,
% 9.49/5.24      ! [I2: rat,J: rat,K: rat,L2: rat] :
% 9.49/5.24        ( ( ( ord_less_eq_rat @ I2 @ J )
% 9.49/5.24          & ( K = L2 ) )
% 9.49/5.24       => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1315_add__mono__thms__linordered__semiring_I3_J,axiom,
% 9.49/5.24      ! [I2: nat,J: nat,K: nat,L2: nat] :
% 9.49/5.24        ( ( ( ord_less_eq_nat @ I2 @ J )
% 9.49/5.24          & ( K = L2 ) )
% 9.49/5.24       => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1316_add__mono__thms__linordered__semiring_I3_J,axiom,
% 9.49/5.24      ! [I2: int,J: int,K: int,L2: int] :
% 9.49/5.24        ( ( ( ord_less_eq_int @ I2 @ J )
% 9.49/5.24          & ( K = L2 ) )
% 9.49/5.24       => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1317_add__mono__thms__linordered__semiring_I2_J,axiom,
% 9.49/5.24      ! [I2: real,J: real,K: real,L2: real] :
% 9.49/5.24        ( ( ( I2 = J )
% 9.49/5.24          & ( ord_less_eq_real @ K @ L2 ) )
% 9.49/5.24       => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1318_add__mono__thms__linordered__semiring_I2_J,axiom,
% 9.49/5.24      ! [I2: rat,J: rat,K: rat,L2: rat] :
% 9.49/5.24        ( ( ( I2 = J )
% 9.49/5.24          & ( ord_less_eq_rat @ K @ L2 ) )
% 9.49/5.24       => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1319_add__mono__thms__linordered__semiring_I2_J,axiom,
% 9.49/5.24      ! [I2: nat,J: nat,K: nat,L2: nat] :
% 9.49/5.24        ( ( ( I2 = J )
% 9.49/5.24          & ( ord_less_eq_nat @ K @ L2 ) )
% 9.49/5.24       => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1320_add__mono__thms__linordered__semiring_I2_J,axiom,
% 9.49/5.24      ! [I2: int,J: int,K: int,L2: int] :
% 9.49/5.24        ( ( ( I2 = J )
% 9.49/5.24          & ( ord_less_eq_int @ K @ L2 ) )
% 9.49/5.24       => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1321_add__mono__thms__linordered__semiring_I1_J,axiom,
% 9.49/5.24      ! [I2: real,J: real,K: real,L2: real] :
% 9.49/5.24        ( ( ( ord_less_eq_real @ I2 @ J )
% 9.49/5.24          & ( ord_less_eq_real @ K @ L2 ) )
% 9.49/5.24       => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1322_add__mono__thms__linordered__semiring_I1_J,axiom,
% 9.49/5.24      ! [I2: rat,J: rat,K: rat,L2: rat] :
% 9.49/5.24        ( ( ( ord_less_eq_rat @ I2 @ J )
% 9.49/5.24          & ( ord_less_eq_rat @ K @ L2 ) )
% 9.49/5.24       => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1323_add__mono__thms__linordered__semiring_I1_J,axiom,
% 9.49/5.24      ! [I2: nat,J: nat,K: nat,L2: nat] :
% 9.49/5.24        ( ( ( ord_less_eq_nat @ I2 @ J )
% 9.49/5.24          & ( ord_less_eq_nat @ K @ L2 ) )
% 9.49/5.24       => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1324_add__mono__thms__linordered__semiring_I1_J,axiom,
% 9.49/5.24      ! [I2: int,J: int,K: int,L2: int] :
% 9.49/5.24        ( ( ( ord_less_eq_int @ I2 @ J )
% 9.49/5.24          & ( ord_less_eq_int @ K @ L2 ) )
% 9.49/5.24       => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1325_add__mono,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real,D2: real] :
% 9.49/5.24        ( ( ord_less_eq_real @ A @ B )
% 9.49/5.24       => ( ( ord_less_eq_real @ C @ D2 )
% 9.49/5.24         => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1326_add__mono,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.49/5.24        ( ( ord_less_eq_rat @ A @ B )
% 9.49/5.24       => ( ( ord_less_eq_rat @ C @ D2 )
% 9.49/5.24         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1327_add__mono,axiom,
% 9.49/5.24      ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ A @ B )
% 9.49/5.24       => ( ( ord_less_eq_nat @ C @ D2 )
% 9.49/5.24         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1328_add__mono,axiom,
% 9.49/5.24      ! [A: int,B: int,C: int,D2: int] :
% 9.49/5.24        ( ( ord_less_eq_int @ A @ B )
% 9.49/5.24       => ( ( ord_less_eq_int @ C @ D2 )
% 9.49/5.24         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1329_add__left__mono,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real] :
% 9.49/5.24        ( ( ord_less_eq_real @ A @ B )
% 9.49/5.24       => ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1330_add__left__mono,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat] :
% 9.49/5.24        ( ( ord_less_eq_rat @ A @ B )
% 9.49/5.24       => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1331_add__left__mono,axiom,
% 9.49/5.24      ! [A: nat,B: nat,C: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ A @ B )
% 9.49/5.24       => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1332_add__left__mono,axiom,
% 9.49/5.24      ! [A: int,B: int,C: int] :
% 9.49/5.24        ( ( ord_less_eq_int @ A @ B )
% 9.49/5.24       => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1333_less__eqE,axiom,
% 9.49/5.24      ! [A: nat,B: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ A @ B )
% 9.49/5.24       => ~ ! [C2: nat] :
% 9.49/5.24              ( B
% 9.49/5.24             != ( plus_plus_nat @ A @ C2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1334_add__right__mono,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real] :
% 9.49/5.24        ( ( ord_less_eq_real @ A @ B )
% 9.49/5.24       => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1335_add__right__mono,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat] :
% 9.49/5.24        ( ( ord_less_eq_rat @ A @ B )
% 9.49/5.24       => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1336_add__right__mono,axiom,
% 9.49/5.24      ! [A: nat,B: nat,C: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ A @ B )
% 9.49/5.24       => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1337_add__right__mono,axiom,
% 9.49/5.24      ! [A: int,B: int,C: int] :
% 9.49/5.24        ( ( ord_less_eq_int @ A @ B )
% 9.49/5.24       => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1338_le__iff__add,axiom,
% 9.49/5.24      ( ord_less_eq_nat
% 9.49/5.24      = ( ^ [A3: nat,B4: nat] :
% 9.49/5.24          ? [C3: nat] :
% 9.49/5.24            ( B4
% 9.49/5.24            = ( plus_plus_nat @ A3 @ C3 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1339_add__le__imp__le__left,axiom,
% 9.49/5.24      ! [C: real,A: real,B: real] :
% 9.49/5.24        ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 9.49/5.24       => ( ord_less_eq_real @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1340_add__le__imp__le__left,axiom,
% 9.49/5.24      ! [C: rat,A: rat,B: rat] :
% 9.49/5.24        ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 9.49/5.24       => ( ord_less_eq_rat @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1341_add__le__imp__le__left,axiom,
% 9.49/5.24      ! [C: nat,A: nat,B: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 9.49/5.24       => ( ord_less_eq_nat @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1342_add__le__imp__le__left,axiom,
% 9.49/5.24      ! [C: int,A: int,B: int] :
% 9.49/5.24        ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 9.49/5.24       => ( ord_less_eq_int @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1343_add__le__imp__le__right,axiom,
% 9.49/5.24      ! [A: real,C: real,B: real] :
% 9.49/5.24        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 9.49/5.24       => ( ord_less_eq_real @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1344_add__le__imp__le__right,axiom,
% 9.49/5.24      ! [A: rat,C: rat,B: rat] :
% 9.49/5.24        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 9.49/5.24       => ( ord_less_eq_rat @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1345_add__le__imp__le__right,axiom,
% 9.49/5.24      ! [A: nat,C: nat,B: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 9.49/5.24       => ( ord_less_eq_nat @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1346_add__le__imp__le__right,axiom,
% 9.49/5.24      ! [A: int,C: int,B: int] :
% 9.49/5.24        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 9.49/5.24       => ( ord_less_eq_int @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1347_add__mono__thms__linordered__field_I5_J,axiom,
% 9.49/5.24      ! [I2: real,J: real,K: real,L2: real] :
% 9.49/5.24        ( ( ( ord_less_real @ I2 @ J )
% 9.49/5.24          & ( ord_less_real @ K @ L2 ) )
% 9.49/5.24       => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1348_add__mono__thms__linordered__field_I5_J,axiom,
% 9.49/5.24      ! [I2: rat,J: rat,K: rat,L2: rat] :
% 9.49/5.24        ( ( ( ord_less_rat @ I2 @ J )
% 9.49/5.24          & ( ord_less_rat @ K @ L2 ) )
% 9.49/5.24       => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1349_add__mono__thms__linordered__field_I5_J,axiom,
% 9.49/5.24      ! [I2: nat,J: nat,K: nat,L2: nat] :
% 9.49/5.24        ( ( ( ord_less_nat @ I2 @ J )
% 9.49/5.24          & ( ord_less_nat @ K @ L2 ) )
% 9.49/5.24       => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1350_add__mono__thms__linordered__field_I5_J,axiom,
% 9.49/5.24      ! [I2: int,J: int,K: int,L2: int] :
% 9.49/5.24        ( ( ( ord_less_int @ I2 @ J )
% 9.49/5.24          & ( ord_less_int @ K @ L2 ) )
% 9.49/5.24       => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1351_add__mono__thms__linordered__field_I2_J,axiom,
% 9.49/5.24      ! [I2: real,J: real,K: real,L2: real] :
% 9.49/5.24        ( ( ( I2 = J )
% 9.49/5.24          & ( ord_less_real @ K @ L2 ) )
% 9.49/5.24       => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1352_add__mono__thms__linordered__field_I2_J,axiom,
% 9.49/5.24      ! [I2: rat,J: rat,K: rat,L2: rat] :
% 9.49/5.24        ( ( ( I2 = J )
% 9.49/5.24          & ( ord_less_rat @ K @ L2 ) )
% 9.49/5.24       => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1353_add__mono__thms__linordered__field_I2_J,axiom,
% 9.49/5.24      ! [I2: nat,J: nat,K: nat,L2: nat] :
% 9.49/5.24        ( ( ( I2 = J )
% 9.49/5.24          & ( ord_less_nat @ K @ L2 ) )
% 9.49/5.24       => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1354_add__mono__thms__linordered__field_I2_J,axiom,
% 9.49/5.24      ! [I2: int,J: int,K: int,L2: int] :
% 9.49/5.24        ( ( ( I2 = J )
% 9.49/5.24          & ( ord_less_int @ K @ L2 ) )
% 9.49/5.24       => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1355_add__mono__thms__linordered__field_I1_J,axiom,
% 9.49/5.24      ! [I2: real,J: real,K: real,L2: real] :
% 9.49/5.24        ( ( ( ord_less_real @ I2 @ J )
% 9.49/5.24          & ( K = L2 ) )
% 9.49/5.24       => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1356_add__mono__thms__linordered__field_I1_J,axiom,
% 9.49/5.24      ! [I2: rat,J: rat,K: rat,L2: rat] :
% 9.49/5.24        ( ( ( ord_less_rat @ I2 @ J )
% 9.49/5.24          & ( K = L2 ) )
% 9.49/5.24       => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1357_add__mono__thms__linordered__field_I1_J,axiom,
% 9.49/5.24      ! [I2: nat,J: nat,K: nat,L2: nat] :
% 9.49/5.24        ( ( ( ord_less_nat @ I2 @ J )
% 9.49/5.24          & ( K = L2 ) )
% 9.49/5.24       => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1358_add__mono__thms__linordered__field_I1_J,axiom,
% 9.49/5.24      ! [I2: int,J: int,K: int,L2: int] :
% 9.49/5.24        ( ( ( ord_less_int @ I2 @ J )
% 9.49/5.24          & ( K = L2 ) )
% 9.49/5.24       => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1359_add__strict__mono,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real,D2: real] :
% 9.49/5.24        ( ( ord_less_real @ A @ B )
% 9.49/5.24       => ( ( ord_less_real @ C @ D2 )
% 9.49/5.24         => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1360_add__strict__mono,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.49/5.24        ( ( ord_less_rat @ A @ B )
% 9.49/5.24       => ( ( ord_less_rat @ C @ D2 )
% 9.49/5.24         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1361_add__strict__mono,axiom,
% 9.49/5.24      ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.49/5.24        ( ( ord_less_nat @ A @ B )
% 9.49/5.24       => ( ( ord_less_nat @ C @ D2 )
% 9.49/5.24         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1362_add__strict__mono,axiom,
% 9.49/5.24      ! [A: int,B: int,C: int,D2: int] :
% 9.49/5.24        ( ( ord_less_int @ A @ B )
% 9.49/5.24       => ( ( ord_less_int @ C @ D2 )
% 9.49/5.24         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1363_add__strict__left__mono,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real] :
% 9.49/5.24        ( ( ord_less_real @ A @ B )
% 9.49/5.24       => ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1364_add__strict__left__mono,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat] :
% 9.49/5.24        ( ( ord_less_rat @ A @ B )
% 9.49/5.24       => ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1365_add__strict__left__mono,axiom,
% 9.49/5.24      ! [A: nat,B: nat,C: nat] :
% 9.49/5.24        ( ( ord_less_nat @ A @ B )
% 9.49/5.24       => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1366_add__strict__left__mono,axiom,
% 9.49/5.24      ! [A: int,B: int,C: int] :
% 9.49/5.24        ( ( ord_less_int @ A @ B )
% 9.49/5.24       => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1367_add__strict__right__mono,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real] :
% 9.49/5.24        ( ( ord_less_real @ A @ B )
% 9.49/5.24       => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1368_add__strict__right__mono,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat] :
% 9.49/5.24        ( ( ord_less_rat @ A @ B )
% 9.49/5.24       => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1369_add__strict__right__mono,axiom,
% 9.49/5.24      ! [A: nat,B: nat,C: nat] :
% 9.49/5.24        ( ( ord_less_nat @ A @ B )
% 9.49/5.24       => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1370_add__strict__right__mono,axiom,
% 9.49/5.24      ! [A: int,B: int,C: int] :
% 9.49/5.24        ( ( ord_less_int @ A @ B )
% 9.49/5.24       => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1371_add__less__imp__less__left,axiom,
% 9.49/5.24      ! [C: real,A: real,B: real] :
% 9.49/5.24        ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 9.49/5.24       => ( ord_less_real @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1372_add__less__imp__less__left,axiom,
% 9.49/5.24      ! [C: rat,A: rat,B: rat] :
% 9.49/5.24        ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 9.49/5.24       => ( ord_less_rat @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1373_add__less__imp__less__left,axiom,
% 9.49/5.24      ! [C: nat,A: nat,B: nat] :
% 9.49/5.24        ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 9.49/5.24       => ( ord_less_nat @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1374_add__less__imp__less__left,axiom,
% 9.49/5.24      ! [C: int,A: int,B: int] :
% 9.49/5.24        ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 9.49/5.24       => ( ord_less_int @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1375_add__less__imp__less__right,axiom,
% 9.49/5.24      ! [A: real,C: real,B: real] :
% 9.49/5.24        ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 9.49/5.24       => ( ord_less_real @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1376_add__less__imp__less__right,axiom,
% 9.49/5.24      ! [A: rat,C: rat,B: rat] :
% 9.49/5.24        ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 9.49/5.24       => ( ord_less_rat @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1377_add__less__imp__less__right,axiom,
% 9.49/5.24      ! [A: nat,C: nat,B: nat] :
% 9.49/5.24        ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 9.49/5.24       => ( ord_less_nat @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1378_add__less__imp__less__right,axiom,
% 9.49/5.24      ! [A: int,C: int,B: int] :
% 9.49/5.24        ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 9.49/5.24       => ( ord_less_int @ A @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1379_diff__eq__diff__less__eq,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.49/5.24        ( ( ( minus_minus_rat @ A @ B )
% 9.49/5.24          = ( minus_minus_rat @ C @ D2 ) )
% 9.49/5.24       => ( ( ord_less_eq_rat @ A @ B )
% 9.49/5.24          = ( ord_less_eq_rat @ C @ D2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1380_diff__eq__diff__less__eq,axiom,
% 9.49/5.24      ! [A: int,B: int,C: int,D2: int] :
% 9.49/5.24        ( ( ( minus_minus_int @ A @ B )
% 9.49/5.24          = ( minus_minus_int @ C @ D2 ) )
% 9.49/5.24       => ( ( ord_less_eq_int @ A @ B )
% 9.49/5.24          = ( ord_less_eq_int @ C @ D2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1381_diff__right__mono,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat] :
% 9.49/5.24        ( ( ord_less_eq_rat @ A @ B )
% 9.49/5.24       => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1382_diff__right__mono,axiom,
% 9.49/5.24      ! [A: int,B: int,C: int] :
% 9.49/5.24        ( ( ord_less_eq_int @ A @ B )
% 9.49/5.24       => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1383_diff__left__mono,axiom,
% 9.49/5.24      ! [B: rat,A: rat,C: rat] :
% 9.49/5.24        ( ( ord_less_eq_rat @ B @ A )
% 9.49/5.24       => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1384_diff__left__mono,axiom,
% 9.49/5.24      ! [B: int,A: int,C: int] :
% 9.49/5.24        ( ( ord_less_eq_int @ B @ A )
% 9.49/5.24       => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1385_diff__mono,axiom,
% 9.49/5.24      ! [A: rat,B: rat,D2: rat,C: rat] :
% 9.49/5.24        ( ( ord_less_eq_rat @ A @ B )
% 9.49/5.24       => ( ( ord_less_eq_rat @ D2 @ C )
% 9.49/5.24         => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1386_diff__mono,axiom,
% 9.49/5.24      ! [A: int,B: int,D2: int,C: int] :
% 9.49/5.24        ( ( ord_less_eq_int @ A @ B )
% 9.49/5.24       => ( ( ord_less_eq_int @ D2 @ C )
% 9.49/5.24         => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1387_diff__strict__right__mono,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real] :
% 9.49/5.24        ( ( ord_less_real @ A @ B )
% 9.49/5.24       => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1388_diff__strict__right__mono,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat] :
% 9.49/5.24        ( ( ord_less_rat @ A @ B )
% 9.49/5.24       => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1389_diff__strict__right__mono,axiom,
% 9.49/5.24      ! [A: int,B: int,C: int] :
% 9.49/5.24        ( ( ord_less_int @ A @ B )
% 9.49/5.24       => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1390_diff__strict__left__mono,axiom,
% 9.49/5.24      ! [B: real,A: real,C: real] :
% 9.49/5.24        ( ( ord_less_real @ B @ A )
% 9.49/5.24       => ( ord_less_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1391_diff__strict__left__mono,axiom,
% 9.49/5.24      ! [B: rat,A: rat,C: rat] :
% 9.49/5.24        ( ( ord_less_rat @ B @ A )
% 9.49/5.24       => ( ord_less_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1392_diff__strict__left__mono,axiom,
% 9.49/5.24      ! [B: int,A: int,C: int] :
% 9.49/5.24        ( ( ord_less_int @ B @ A )
% 9.49/5.24       => ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1393_diff__eq__diff__less,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real,D2: real] :
% 9.49/5.24        ( ( ( minus_minus_real @ A @ B )
% 9.49/5.24          = ( minus_minus_real @ C @ D2 ) )
% 9.49/5.24       => ( ( ord_less_real @ A @ B )
% 9.49/5.24          = ( ord_less_real @ C @ D2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1394_diff__eq__diff__less,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.49/5.24        ( ( ( minus_minus_rat @ A @ B )
% 9.49/5.24          = ( minus_minus_rat @ C @ D2 ) )
% 9.49/5.24       => ( ( ord_less_rat @ A @ B )
% 9.49/5.24          = ( ord_less_rat @ C @ D2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1395_diff__eq__diff__less,axiom,
% 9.49/5.24      ! [A: int,B: int,C: int,D2: int] :
% 9.49/5.24        ( ( ( minus_minus_int @ A @ B )
% 9.49/5.24          = ( minus_minus_int @ C @ D2 ) )
% 9.49/5.24       => ( ( ord_less_int @ A @ B )
% 9.49/5.24          = ( ord_less_int @ C @ D2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1396_diff__strict__mono,axiom,
% 9.49/5.24      ! [A: real,B: real,D2: real,C: real] :
% 9.49/5.24        ( ( ord_less_real @ A @ B )
% 9.49/5.24       => ( ( ord_less_real @ D2 @ C )
% 9.49/5.24         => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1397_diff__strict__mono,axiom,
% 9.49/5.24      ! [A: rat,B: rat,D2: rat,C: rat] :
% 9.49/5.24        ( ( ord_less_rat @ A @ B )
% 9.49/5.24       => ( ( ord_less_rat @ D2 @ C )
% 9.49/5.24         => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1398_diff__strict__mono,axiom,
% 9.49/5.24      ! [A: int,B: int,D2: int,C: int] :
% 9.49/5.24        ( ( ord_less_int @ A @ B )
% 9.49/5.24       => ( ( ord_less_int @ D2 @ C )
% 9.49/5.24         => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1399_comm__monoid__mult__class_Omult__1,axiom,
% 9.49/5.24      ! [A: rat] :
% 9.49/5.24        ( ( times_times_rat @ one_one_rat @ A )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1400_comm__monoid__mult__class_Omult__1,axiom,
% 9.49/5.24      ! [A: complex] :
% 9.49/5.24        ( ( times_times_complex @ one_one_complex @ A )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1401_comm__monoid__mult__class_Omult__1,axiom,
% 9.49/5.24      ! [A: real] :
% 9.49/5.24        ( ( times_times_real @ one_one_real @ A )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1402_comm__monoid__mult__class_Omult__1,axiom,
% 9.49/5.24      ! [A: nat] :
% 9.49/5.24        ( ( times_times_nat @ one_one_nat @ A )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1403_comm__monoid__mult__class_Omult__1,axiom,
% 9.49/5.24      ! [A: int] :
% 9.49/5.24        ( ( times_times_int @ one_one_int @ A )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1404_mult_Ocomm__neutral,axiom,
% 9.49/5.24      ! [A: rat] :
% 9.49/5.24        ( ( times_times_rat @ A @ one_one_rat )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1405_mult_Ocomm__neutral,axiom,
% 9.49/5.24      ! [A: complex] :
% 9.49/5.24        ( ( times_times_complex @ A @ one_one_complex )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1406_mult_Ocomm__neutral,axiom,
% 9.49/5.24      ! [A: real] :
% 9.49/5.24        ( ( times_times_real @ A @ one_one_real )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1407_mult_Ocomm__neutral,axiom,
% 9.49/5.24      ! [A: nat] :
% 9.49/5.24        ( ( times_times_nat @ A @ one_one_nat )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1408_mult_Ocomm__neutral,axiom,
% 9.49/5.24      ! [A: int] :
% 9.49/5.24        ( ( times_times_int @ A @ one_one_int )
% 9.49/5.24        = A ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1409_divide__divide__eq__left_H,axiom,
% 9.49/5.24      ! [A: complex,B: complex,C: complex] :
% 9.49/5.24        ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 9.49/5.24        = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ C @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1410_divide__divide__eq__left_H,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real] :
% 9.49/5.24        ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 9.49/5.24        = ( divide_divide_real @ A @ ( times_times_real @ C @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1411_divide__divide__eq__left_H,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat] :
% 9.49/5.24        ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 9.49/5.24        = ( divide_divide_rat @ A @ ( times_times_rat @ C @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1412_divide__divide__times__eq,axiom,
% 9.49/5.24      ! [X: complex,Y2: complex,Z: complex,W: complex] :
% 9.49/5.24        ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ X @ Y2 ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 9.49/5.24        = ( divide1717551699836669952omplex @ ( times_times_complex @ X @ W ) @ ( times_times_complex @ Y2 @ Z ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1413_divide__divide__times__eq,axiom,
% 9.49/5.24      ! [X: real,Y2: real,Z: real,W: real] :
% 9.49/5.24        ( ( divide_divide_real @ ( divide_divide_real @ X @ Y2 ) @ ( divide_divide_real @ Z @ W ) )
% 9.49/5.24        = ( divide_divide_real @ ( times_times_real @ X @ W ) @ ( times_times_real @ Y2 @ Z ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1414_divide__divide__times__eq,axiom,
% 9.49/5.24      ! [X: rat,Y2: rat,Z: rat,W: rat] :
% 9.49/5.24        ( ( divide_divide_rat @ ( divide_divide_rat @ X @ Y2 ) @ ( divide_divide_rat @ Z @ W ) )
% 9.49/5.24        = ( divide_divide_rat @ ( times_times_rat @ X @ W ) @ ( times_times_rat @ Y2 @ Z ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1415_times__divide__times__eq,axiom,
% 9.49/5.24      ! [X: complex,Y2: complex,Z: complex,W: complex] :
% 9.49/5.24        ( ( times_times_complex @ ( divide1717551699836669952omplex @ X @ Y2 ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 9.49/5.24        = ( divide1717551699836669952omplex @ ( times_times_complex @ X @ Z ) @ ( times_times_complex @ Y2 @ W ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1416_times__divide__times__eq,axiom,
% 9.49/5.24      ! [X: real,Y2: real,Z: real,W: real] :
% 9.49/5.24        ( ( times_times_real @ ( divide_divide_real @ X @ Y2 ) @ ( divide_divide_real @ Z @ W ) )
% 9.49/5.24        = ( divide_divide_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y2 @ W ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1417_times__divide__times__eq,axiom,
% 9.49/5.24      ! [X: rat,Y2: rat,Z: rat,W: rat] :
% 9.49/5.24        ( ( times_times_rat @ ( divide_divide_rat @ X @ Y2 ) @ ( divide_divide_rat @ Z @ W ) )
% 9.49/5.24        = ( divide_divide_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y2 @ W ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1418_group__cancel_Osub1,axiom,
% 9.49/5.24      ! [A2: real,K: real,A: real,B: real] :
% 9.49/5.24        ( ( A2
% 9.49/5.24          = ( plus_plus_real @ K @ A ) )
% 9.49/5.24       => ( ( minus_minus_real @ A2 @ B )
% 9.49/5.24          = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1419_group__cancel_Osub1,axiom,
% 9.49/5.24      ! [A2: complex,K: complex,A: complex,B: complex] :
% 9.49/5.24        ( ( A2
% 9.49/5.24          = ( plus_plus_complex @ K @ A ) )
% 9.49/5.24       => ( ( minus_minus_complex @ A2 @ B )
% 9.49/5.24          = ( plus_plus_complex @ K @ ( minus_minus_complex @ A @ B ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1420_group__cancel_Osub1,axiom,
% 9.49/5.24      ! [A2: rat,K: rat,A: rat,B: rat] :
% 9.49/5.24        ( ( A2
% 9.49/5.24          = ( plus_plus_rat @ K @ A ) )
% 9.49/5.24       => ( ( minus_minus_rat @ A2 @ B )
% 9.49/5.24          = ( plus_plus_rat @ K @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1421_group__cancel_Osub1,axiom,
% 9.49/5.24      ! [A2: int,K: int,A: int,B: int] :
% 9.49/5.24        ( ( A2
% 9.49/5.24          = ( plus_plus_int @ K @ A ) )
% 9.49/5.24       => ( ( minus_minus_int @ A2 @ B )
% 9.49/5.24          = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1422_diff__eq__eq,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real] :
% 9.49/5.24        ( ( ( minus_minus_real @ A @ B )
% 9.49/5.24          = C )
% 9.49/5.24        = ( A
% 9.49/5.24          = ( plus_plus_real @ C @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1423_diff__eq__eq,axiom,
% 9.49/5.24      ! [A: complex,B: complex,C: complex] :
% 9.49/5.24        ( ( ( minus_minus_complex @ A @ B )
% 9.49/5.24          = C )
% 9.49/5.24        = ( A
% 9.49/5.24          = ( plus_plus_complex @ C @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1424_diff__eq__eq,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat] :
% 9.49/5.24        ( ( ( minus_minus_rat @ A @ B )
% 9.49/5.24          = C )
% 9.49/5.24        = ( A
% 9.49/5.24          = ( plus_plus_rat @ C @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1425_diff__eq__eq,axiom,
% 9.49/5.24      ! [A: int,B: int,C: int] :
% 9.49/5.24        ( ( ( minus_minus_int @ A @ B )
% 9.49/5.24          = C )
% 9.49/5.24        = ( A
% 9.49/5.24          = ( plus_plus_int @ C @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1426_eq__diff__eq,axiom,
% 9.49/5.24      ! [A: real,C: real,B: real] :
% 9.49/5.24        ( ( A
% 9.49/5.24          = ( minus_minus_real @ C @ B ) )
% 9.49/5.24        = ( ( plus_plus_real @ A @ B )
% 9.49/5.24          = C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1427_eq__diff__eq,axiom,
% 9.49/5.24      ! [A: complex,C: complex,B: complex] :
% 9.49/5.24        ( ( A
% 9.49/5.24          = ( minus_minus_complex @ C @ B ) )
% 9.49/5.24        = ( ( plus_plus_complex @ A @ B )
% 9.49/5.24          = C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1428_eq__diff__eq,axiom,
% 9.49/5.24      ! [A: rat,C: rat,B: rat] :
% 9.49/5.24        ( ( A
% 9.49/5.24          = ( minus_minus_rat @ C @ B ) )
% 9.49/5.24        = ( ( plus_plus_rat @ A @ B )
% 9.49/5.24          = C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1429_eq__diff__eq,axiom,
% 9.49/5.24      ! [A: int,C: int,B: int] :
% 9.49/5.24        ( ( A
% 9.49/5.24          = ( minus_minus_int @ C @ B ) )
% 9.49/5.24        = ( ( plus_plus_int @ A @ B )
% 9.49/5.24          = C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1430_add__diff__eq,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real] :
% 9.49/5.24        ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
% 9.49/5.24        = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1431_add__diff__eq,axiom,
% 9.49/5.24      ! [A: complex,B: complex,C: complex] :
% 9.49/5.24        ( ( plus_plus_complex @ A @ ( minus_minus_complex @ B @ C ) )
% 9.49/5.24        = ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1432_add__diff__eq,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat] :
% 9.49/5.24        ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 9.49/5.24        = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1433_add__diff__eq,axiom,
% 9.49/5.24      ! [A: int,B: int,C: int] :
% 9.49/5.24        ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
% 9.49/5.24        = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1434_diff__diff__eq2,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real] :
% 9.49/5.24        ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
% 9.49/5.24        = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1435_diff__diff__eq2,axiom,
% 9.49/5.24      ! [A: complex,B: complex,C: complex] :
% 9.49/5.24        ( ( minus_minus_complex @ A @ ( minus_minus_complex @ B @ C ) )
% 9.49/5.24        = ( minus_minus_complex @ ( plus_plus_complex @ A @ C ) @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1436_diff__diff__eq2,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat] :
% 9.49/5.24        ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 9.49/5.24        = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1437_diff__diff__eq2,axiom,
% 9.49/5.24      ! [A: int,B: int,C: int] :
% 9.49/5.24        ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
% 9.49/5.24        = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1438_diff__add__eq,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real] :
% 9.49/5.24        ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
% 9.49/5.24        = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1439_diff__add__eq,axiom,
% 9.49/5.24      ! [A: complex,B: complex,C: complex] :
% 9.49/5.24        ( ( plus_plus_complex @ ( minus_minus_complex @ A @ B ) @ C )
% 9.49/5.24        = ( minus_minus_complex @ ( plus_plus_complex @ A @ C ) @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1440_diff__add__eq,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat] :
% 9.49/5.24        ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 9.49/5.24        = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1441_diff__add__eq,axiom,
% 9.49/5.24      ! [A: int,B: int,C: int] :
% 9.49/5.24        ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
% 9.49/5.24        = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1442_diff__add__eq__diff__diff__swap,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real] :
% 9.49/5.24        ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
% 9.49/5.24        = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1443_diff__add__eq__diff__diff__swap,axiom,
% 9.49/5.24      ! [A: complex,B: complex,C: complex] :
% 9.49/5.24        ( ( minus_minus_complex @ A @ ( plus_plus_complex @ B @ C ) )
% 9.49/5.24        = ( minus_minus_complex @ ( minus_minus_complex @ A @ C ) @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1444_diff__add__eq__diff__diff__swap,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat] :
% 9.49/5.24        ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 9.49/5.24        = ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1445_diff__add__eq__diff__diff__swap,axiom,
% 9.49/5.24      ! [A: int,B: int,C: int] :
% 9.49/5.24        ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
% 9.49/5.24        = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1446_add__implies__diff,axiom,
% 9.49/5.24      ! [C: real,B: real,A: real] :
% 9.49/5.24        ( ( ( plus_plus_real @ C @ B )
% 9.49/5.24          = A )
% 9.49/5.24       => ( C
% 9.49/5.24          = ( minus_minus_real @ A @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1447_add__implies__diff,axiom,
% 9.49/5.24      ! [C: complex,B: complex,A: complex] :
% 9.49/5.24        ( ( ( plus_plus_complex @ C @ B )
% 9.49/5.24          = A )
% 9.49/5.24       => ( C
% 9.49/5.24          = ( minus_minus_complex @ A @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1448_add__implies__diff,axiom,
% 9.49/5.24      ! [C: rat,B: rat,A: rat] :
% 9.49/5.24        ( ( ( plus_plus_rat @ C @ B )
% 9.49/5.24          = A )
% 9.49/5.24       => ( C
% 9.49/5.24          = ( minus_minus_rat @ A @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1449_add__implies__diff,axiom,
% 9.49/5.24      ! [C: nat,B: nat,A: nat] :
% 9.49/5.24        ( ( ( plus_plus_nat @ C @ B )
% 9.49/5.24          = A )
% 9.49/5.24       => ( C
% 9.49/5.24          = ( minus_minus_nat @ A @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1450_add__implies__diff,axiom,
% 9.49/5.24      ! [C: int,B: int,A: int] :
% 9.49/5.24        ( ( ( plus_plus_int @ C @ B )
% 9.49/5.24          = A )
% 9.49/5.24       => ( C
% 9.49/5.24          = ( minus_minus_int @ A @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1451_diff__diff__eq,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real] :
% 9.49/5.24        ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
% 9.49/5.24        = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1452_diff__diff__eq,axiom,
% 9.49/5.24      ! [A: complex,B: complex,C: complex] :
% 9.49/5.24        ( ( minus_minus_complex @ ( minus_minus_complex @ A @ B ) @ C )
% 9.49/5.24        = ( minus_minus_complex @ A @ ( plus_plus_complex @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1453_diff__diff__eq,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat] :
% 9.49/5.24        ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 9.49/5.24        = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1454_diff__diff__eq,axiom,
% 9.49/5.24      ! [A: nat,B: nat,C: nat] :
% 9.49/5.24        ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
% 9.49/5.24        = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1455_diff__diff__eq,axiom,
% 9.49/5.24      ! [A: int,B: int,C: int] :
% 9.49/5.24        ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
% 9.49/5.24        = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1456_add__divide__distrib,axiom,
% 9.49/5.24      ! [A: complex,B: complex,C: complex] :
% 9.49/5.24        ( ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ B ) @ C )
% 9.49/5.24        = ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1457_add__divide__distrib,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real] :
% 9.49/5.24        ( ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ C )
% 9.49/5.24        = ( plus_plus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1458_add__divide__distrib,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat] :
% 9.49/5.24        ( ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 9.49/5.24        = ( plus_plus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1459_diff__divide__distrib,axiom,
% 9.49/5.24      ! [A: complex,B: complex,C: complex] :
% 9.49/5.24        ( ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ B ) @ C )
% 9.49/5.24        = ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1460_diff__divide__distrib,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real] :
% 9.49/5.24        ( ( divide_divide_real @ ( minus_minus_real @ A @ B ) @ C )
% 9.49/5.24        = ( minus_minus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1461_diff__divide__distrib,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat] :
% 9.49/5.24        ( ( divide_divide_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 9.49/5.24        = ( minus_minus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1462_max__add__distrib__left,axiom,
% 9.49/5.24      ! [X: real,Y2: real,Z: real] :
% 9.49/5.24        ( ( plus_plus_real @ ( ord_max_real @ X @ Y2 ) @ Z )
% 9.49/5.24        = ( ord_max_real @ ( plus_plus_real @ X @ Z ) @ ( plus_plus_real @ Y2 @ Z ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1463_max__add__distrib__left,axiom,
% 9.49/5.24      ! [X: rat,Y2: rat,Z: rat] :
% 9.49/5.24        ( ( plus_plus_rat @ ( ord_max_rat @ X @ Y2 ) @ Z )
% 9.49/5.24        = ( ord_max_rat @ ( plus_plus_rat @ X @ Z ) @ ( plus_plus_rat @ Y2 @ Z ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1464_max__add__distrib__left,axiom,
% 9.49/5.24      ! [X: nat,Y2: nat,Z: nat] :
% 9.49/5.24        ( ( plus_plus_nat @ ( ord_max_nat @ X @ Y2 ) @ Z )
% 9.49/5.24        = ( ord_max_nat @ ( plus_plus_nat @ X @ Z ) @ ( plus_plus_nat @ Y2 @ Z ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1465_max__add__distrib__left,axiom,
% 9.49/5.24      ! [X: int,Y2: int,Z: int] :
% 9.49/5.24        ( ( plus_plus_int @ ( ord_max_int @ X @ Y2 ) @ Z )
% 9.49/5.24        = ( ord_max_int @ ( plus_plus_int @ X @ Z ) @ ( plus_plus_int @ Y2 @ Z ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1466_max__add__distrib__right,axiom,
% 9.49/5.24      ! [X: real,Y2: real,Z: real] :
% 9.49/5.24        ( ( plus_plus_real @ X @ ( ord_max_real @ Y2 @ Z ) )
% 9.49/5.24        = ( ord_max_real @ ( plus_plus_real @ X @ Y2 ) @ ( plus_plus_real @ X @ Z ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1467_max__add__distrib__right,axiom,
% 9.49/5.24      ! [X: rat,Y2: rat,Z: rat] :
% 9.49/5.24        ( ( plus_plus_rat @ X @ ( ord_max_rat @ Y2 @ Z ) )
% 9.49/5.24        = ( ord_max_rat @ ( plus_plus_rat @ X @ Y2 ) @ ( plus_plus_rat @ X @ Z ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1468_max__add__distrib__right,axiom,
% 9.49/5.24      ! [X: nat,Y2: nat,Z: nat] :
% 9.49/5.24        ( ( plus_plus_nat @ X @ ( ord_max_nat @ Y2 @ Z ) )
% 9.49/5.24        = ( ord_max_nat @ ( plus_plus_nat @ X @ Y2 ) @ ( plus_plus_nat @ X @ Z ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1469_max__add__distrib__right,axiom,
% 9.49/5.24      ! [X: int,Y2: int,Z: int] :
% 9.49/5.24        ( ( plus_plus_int @ X @ ( ord_max_int @ Y2 @ Z ) )
% 9.49/5.24        = ( ord_max_int @ ( plus_plus_int @ X @ Y2 ) @ ( plus_plus_int @ X @ Z ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1470_max__diff__distrib__left,axiom,
% 9.49/5.24      ! [X: rat,Y2: rat,Z: rat] :
% 9.49/5.24        ( ( minus_minus_rat @ ( ord_max_rat @ X @ Y2 ) @ Z )
% 9.49/5.24        = ( ord_max_rat @ ( minus_minus_rat @ X @ Z ) @ ( minus_minus_rat @ Y2 @ Z ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1471_max__diff__distrib__left,axiom,
% 9.49/5.24      ! [X: int,Y2: int,Z: int] :
% 9.49/5.24        ( ( minus_minus_int @ ( ord_max_int @ X @ Y2 ) @ Z )
% 9.49/5.24        = ( ord_max_int @ ( minus_minus_int @ X @ Z ) @ ( minus_minus_int @ Y2 @ Z ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1472_add__mono__thms__linordered__field_I4_J,axiom,
% 9.49/5.24      ! [I2: real,J: real,K: real,L2: real] :
% 9.49/5.24        ( ( ( ord_less_eq_real @ I2 @ J )
% 9.49/5.24          & ( ord_less_real @ K @ L2 ) )
% 9.49/5.24       => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1473_add__mono__thms__linordered__field_I4_J,axiom,
% 9.49/5.24      ! [I2: rat,J: rat,K: rat,L2: rat] :
% 9.49/5.24        ( ( ( ord_less_eq_rat @ I2 @ J )
% 9.49/5.24          & ( ord_less_rat @ K @ L2 ) )
% 9.49/5.24       => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1474_add__mono__thms__linordered__field_I4_J,axiom,
% 9.49/5.24      ! [I2: nat,J: nat,K: nat,L2: nat] :
% 9.49/5.24        ( ( ( ord_less_eq_nat @ I2 @ J )
% 9.49/5.24          & ( ord_less_nat @ K @ L2 ) )
% 9.49/5.24       => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1475_add__mono__thms__linordered__field_I4_J,axiom,
% 9.49/5.24      ! [I2: int,J: int,K: int,L2: int] :
% 9.49/5.24        ( ( ( ord_less_eq_int @ I2 @ J )
% 9.49/5.24          & ( ord_less_int @ K @ L2 ) )
% 9.49/5.24       => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1476_add__mono__thms__linordered__field_I3_J,axiom,
% 9.49/5.24      ! [I2: real,J: real,K: real,L2: real] :
% 9.49/5.24        ( ( ( ord_less_real @ I2 @ J )
% 9.49/5.24          & ( ord_less_eq_real @ K @ L2 ) )
% 9.49/5.24       => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1477_add__mono__thms__linordered__field_I3_J,axiom,
% 9.49/5.24      ! [I2: rat,J: rat,K: rat,L2: rat] :
% 9.49/5.24        ( ( ( ord_less_rat @ I2 @ J )
% 9.49/5.24          & ( ord_less_eq_rat @ K @ L2 ) )
% 9.49/5.24       => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1478_add__mono__thms__linordered__field_I3_J,axiom,
% 9.49/5.24      ! [I2: nat,J: nat,K: nat,L2: nat] :
% 9.49/5.24        ( ( ( ord_less_nat @ I2 @ J )
% 9.49/5.24          & ( ord_less_eq_nat @ K @ L2 ) )
% 9.49/5.24       => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1479_add__mono__thms__linordered__field_I3_J,axiom,
% 9.49/5.24      ! [I2: int,J: int,K: int,L2: int] :
% 9.49/5.24        ( ( ( ord_less_int @ I2 @ J )
% 9.49/5.24          & ( ord_less_eq_int @ K @ L2 ) )
% 9.49/5.24       => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1480_add__le__less__mono,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real,D2: real] :
% 9.49/5.24        ( ( ord_less_eq_real @ A @ B )
% 9.49/5.24       => ( ( ord_less_real @ C @ D2 )
% 9.49/5.24         => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1481_add__le__less__mono,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.49/5.24        ( ( ord_less_eq_rat @ A @ B )
% 9.49/5.24       => ( ( ord_less_rat @ C @ D2 )
% 9.49/5.24         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1482_add__le__less__mono,axiom,
% 9.49/5.24      ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ A @ B )
% 9.49/5.24       => ( ( ord_less_nat @ C @ D2 )
% 9.49/5.24         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1483_add__le__less__mono,axiom,
% 9.49/5.24      ! [A: int,B: int,C: int,D2: int] :
% 9.49/5.24        ( ( ord_less_eq_int @ A @ B )
% 9.49/5.24       => ( ( ord_less_int @ C @ D2 )
% 9.49/5.24         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1484_add__less__le__mono,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real,D2: real] :
% 9.49/5.24        ( ( ord_less_real @ A @ B )
% 9.49/5.24       => ( ( ord_less_eq_real @ C @ D2 )
% 9.49/5.24         => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1485_add__less__le__mono,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.49/5.24        ( ( ord_less_rat @ A @ B )
% 9.49/5.24       => ( ( ord_less_eq_rat @ C @ D2 )
% 9.49/5.24         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1486_add__less__le__mono,axiom,
% 9.49/5.24      ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.49/5.24        ( ( ord_less_nat @ A @ B )
% 9.49/5.24       => ( ( ord_less_eq_nat @ C @ D2 )
% 9.49/5.24         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1487_add__less__le__mono,axiom,
% 9.49/5.24      ! [A: int,B: int,C: int,D2: int] :
% 9.49/5.24        ( ( ord_less_int @ A @ B )
% 9.49/5.24       => ( ( ord_less_eq_int @ C @ D2 )
% 9.49/5.24         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1488_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 9.49/5.24      ! [A: nat,B: nat,C: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ A @ B )
% 9.49/5.24       => ( ( ord_less_eq_nat @ A @ B )
% 9.49/5.24         => ( ( ( minus_minus_nat @ B @ A )
% 9.49/5.24              = C )
% 9.49/5.24            = ( B
% 9.49/5.24              = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1489_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 9.49/5.24      ! [A: nat,B: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ A @ B )
% 9.49/5.24       => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 9.49/5.24          = B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1490_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 9.49/5.24      ! [A: nat,B: nat,C: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ A @ B )
% 9.49/5.24       => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 9.49/5.24          = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1491_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 9.49/5.24      ! [A: nat,B: nat,C: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ A @ B )
% 9.49/5.24       => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
% 9.49/5.24          = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1492_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 9.49/5.24      ! [A: nat,B: nat,C: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ A @ B )
% 9.49/5.24       => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
% 9.49/5.24          = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1493_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 9.49/5.24      ! [A: nat,B: nat,C: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ A @ B )
% 9.49/5.24       => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
% 9.49/5.24          = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1494_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 9.49/5.24      ! [A: nat,B: nat,C: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ A @ B )
% 9.49/5.24       => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 9.49/5.24          = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1495_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 9.49/5.24      ! [A: nat,B: nat,C: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ A @ B )
% 9.49/5.24       => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 9.49/5.24          = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1496_le__add__diff,axiom,
% 9.49/5.24      ! [A: nat,B: nat,C: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ A @ B )
% 9.49/5.24       => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1497_diff__add,axiom,
% 9.49/5.24      ! [A: nat,B: nat] :
% 9.49/5.24        ( ( ord_less_eq_nat @ A @ B )
% 9.49/5.24       => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 9.49/5.24          = B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1498_le__diff__eq,axiom,
% 9.49/5.24      ! [A: real,C: real,B: real] :
% 9.49/5.24        ( ( ord_less_eq_real @ A @ ( minus_minus_real @ C @ B ) )
% 9.49/5.24        = ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1499_le__diff__eq,axiom,
% 9.49/5.24      ! [A: rat,C: rat,B: rat] :
% 9.49/5.24        ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 9.49/5.24        = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1500_le__diff__eq,axiom,
% 9.49/5.24      ! [A: int,C: int,B: int] :
% 9.49/5.24        ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
% 9.49/5.24        = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1501_diff__le__eq,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real] :
% 9.49/5.24        ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C )
% 9.49/5.24        = ( ord_less_eq_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1502_diff__le__eq,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat] :
% 9.49/5.24        ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 9.49/5.24        = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1503_diff__le__eq,axiom,
% 9.49/5.24      ! [A: int,B: int,C: int] :
% 9.49/5.24        ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
% 9.49/5.24        = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1504_diff__less__eq,axiom,
% 9.49/5.24      ! [A: real,B: real,C: real] :
% 9.49/5.24        ( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C )
% 9.49/5.24        = ( ord_less_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1505_diff__less__eq,axiom,
% 9.49/5.24      ! [A: rat,B: rat,C: rat] :
% 9.49/5.24        ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 9.49/5.24        = ( ord_less_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1506_diff__less__eq,axiom,
% 9.49/5.24      ! [A: int,B: int,C: int] :
% 9.49/5.24        ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C )
% 9.49/5.24        = ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1507_less__diff__eq,axiom,
% 9.49/5.24      ! [A: real,C: real,B: real] :
% 9.49/5.24        ( ( ord_less_real @ A @ ( minus_minus_real @ C @ B ) )
% 9.49/5.24        = ( ord_less_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1508_less__diff__eq,axiom,
% 9.49/5.24      ! [A: rat,C: rat,B: rat] :
% 9.49/5.24        ( ( ord_less_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 9.49/5.24        = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1509_less__diff__eq,axiom,
% 9.49/5.24      ! [A: int,C: int,B: int] :
% 9.49/5.24        ( ( ord_less_int @ A @ ( minus_minus_int @ C @ B ) )
% 9.49/5.24        = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1510_gt__half__sum,axiom,
% 9.49/5.24      ! [A: real,B: real] :
% 9.49/5.24        ( ( ord_less_real @ A @ B )
% 9.49/5.24       => ( ord_less_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1511_gt__half__sum,axiom,
% 9.49/5.24      ! [A: rat,B: rat] :
% 9.49/5.24        ( ( ord_less_rat @ A @ B )
% 9.49/5.24       => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1512_less__half__sum,axiom,
% 9.49/5.24      ! [A: real,B: real] :
% 9.49/5.24        ( ( ord_less_real @ A @ B )
% 9.49/5.24       => ( ord_less_real @ A @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1513_less__half__sum,axiom,
% 9.49/5.24      ! [A: rat,B: rat] :
% 9.49/5.24        ( ( ord_less_rat @ A @ B )
% 9.49/5.24       => ( ord_less_rat @ A @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1514_less__shift,axiom,
% 9.49/5.24      ( ord_less_nat
% 9.49/5.24      = ( ^ [X2: nat,Y: nat] : ( vEBT_VEBT_less @ ( some_nat @ X2 ) @ ( some_nat @ Y ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1515_greater__shift,axiom,
% 9.49/5.24      ( ord_less_nat
% 9.49/5.24      = ( ^ [Y: nat,X2: nat] : ( vEBT_VEBT_greater @ ( some_nat @ X2 ) @ ( some_nat @ Y ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1516_vebt__succ_Osimps_I3_J,axiom,
% 9.49/5.24      ! [Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,Va: nat] :
% 9.49/5.24        ( ( vEBT_vebt_succ @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz ) @ Va )
% 9.49/5.24        = none_nat ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1517_vebt__pred_Osimps_I4_J,axiom,
% 9.49/5.24      ! [Uy: nat,Uz: list_VEBT_VEBT,Va: vEBT_VEBT,Vb: nat] :
% 9.49/5.24        ( ( vEBT_vebt_pred @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz @ Va ) @ Vb )
% 9.49/5.24        = none_nat ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1518_member__bound__height,axiom,
% 9.49/5.24      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 9.49/5.24        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.24       => ( ord_less_eq_nat @ ( vEBT_T_m_e_m_b_e_r @ T @ X ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1519_succ__bound__height,axiom,
% 9.49/5.24      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 9.49/5.24        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.24       => ( ord_less_eq_nat @ ( vEBT_T_s_u_c_c @ T @ X ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1520_del__in__range,axiom,
% 9.49/5.24      ! [Mi: nat,X: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 9.49/5.24        ( ( ( ord_less_eq_nat @ Mi @ X )
% 9.49/5.24          & ( ord_less_eq_nat @ X @ Ma ) )
% 9.49/5.24       => ( ( Mi != Ma )
% 9.49/5.24         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 9.49/5.24           => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 9.49/5.24              = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 9.49/5.24                @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.24                  @ ( vEBT_Node
% 9.49/5.24                    @ ( some_P7363390416028606310at_nat
% 9.49/5.24                      @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 9.49/5.24                        @ ( if_nat
% 9.49/5.24                          @ ( ( ( X = Mi )
% 9.49/5.24                             => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 9.49/5.24                                = Ma ) )
% 9.49/5.24                            & ( ( X != Mi )
% 9.49/5.24                             => ( X = Ma ) ) )
% 9.49/5.24                          @ ( if_nat
% 9.49/5.24                            @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.24                              = none_nat )
% 9.49/5.24                            @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 9.49/5.24                            @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 9.49/5.24                          @ Ma ) ) )
% 9.49/5.24                    @ Deg
% 9.49/5.24                    @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.24                    @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.24                  @ ( vEBT_Node
% 9.49/5.24                    @ ( some_P7363390416028606310at_nat
% 9.49/5.24                      @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 9.49/5.24                        @ ( if_nat
% 9.49/5.24                          @ ( ( ( X = Mi )
% 9.49/5.24                             => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 9.49/5.24                                = Ma ) )
% 9.49/5.24                            & ( ( X != Mi )
% 9.49/5.24                             => ( X = Ma ) ) )
% 9.49/5.24                          @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 9.49/5.24                          @ Ma ) ) )
% 9.49/5.24                    @ Deg
% 9.49/5.24                    @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.24                    @ Summary ) )
% 9.49/5.24                @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1521_del__x__mi,axiom,
% 9.49/5.24      ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList: list_VEBT_VEBT,L2: nat] :
% 9.49/5.24        ( ( ( X = Mi )
% 9.49/5.24          & ( ord_less_nat @ X @ Ma ) )
% 9.49/5.24       => ( ( Mi != Ma )
% 9.49/5.24         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 9.49/5.24           => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.24                = H2 )
% 9.49/5.24             => ( ( Xn
% 9.49/5.24                  = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 9.49/5.24               => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.24                    = L2 )
% 9.49/5.24                 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 9.49/5.24                   => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 9.49/5.24                      = ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) )
% 9.49/5.24                        @ ( vEBT_Node
% 9.49/5.24                          @ ( some_P7363390416028606310at_nat
% 9.49/5.24                            @ ( product_Pair_nat_nat @ Xn
% 9.49/5.24                              @ ( if_nat @ ( Xn = Ma )
% 9.49/5.24                                @ ( if_nat
% 9.49/5.24                                  @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 9.49/5.24                                    = none_nat )
% 9.49/5.24                                  @ Xn
% 9.49/5.24                                  @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 9.49/5.24                                @ Ma ) ) )
% 9.49/5.24                          @ Deg
% 9.49/5.24                          @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) )
% 9.49/5.24                          @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 9.49/5.24                        @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) ) @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) ) @ Summary ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1522_del__x__mi__lets__in,axiom,
% 9.49/5.24      ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList: list_VEBT_VEBT,L2: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 9.49/5.24        ( ( ( X = Mi )
% 9.49/5.24          & ( ord_less_nat @ X @ Ma ) )
% 9.49/5.24       => ( ( Mi != Ma )
% 9.49/5.24         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 9.49/5.24           => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.24                = H2 )
% 9.49/5.24             => ( ( Xn
% 9.49/5.24                  = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 9.49/5.24               => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.24                    = L2 )
% 9.49/5.24                 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 9.49/5.24                   => ( ( Newnode
% 9.49/5.24                        = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) )
% 9.49/5.24                     => ( ( Newlist
% 9.49/5.24                          = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 9.49/5.24                       => ( ( ( vEBT_VEBT_minNull @ Newnode )
% 9.49/5.24                           => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 9.49/5.24                              = ( vEBT_Node
% 9.49/5.24                                @ ( some_P7363390416028606310at_nat
% 9.49/5.24                                  @ ( product_Pair_nat_nat @ Xn
% 9.49/5.24                                    @ ( if_nat @ ( Xn = Ma )
% 9.49/5.24                                      @ ( if_nat
% 9.49/5.24                                        @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 9.49/5.24                                          = none_nat )
% 9.49/5.24                                        @ Xn
% 9.49/5.24                                        @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 9.49/5.24                                      @ Ma ) ) )
% 9.49/5.24                                @ Deg
% 9.49/5.24                                @ Newlist
% 9.49/5.24                                @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) )
% 9.49/5.24                          & ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 9.49/5.24                           => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 9.49/5.24                              = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1523_del__x__mi__lets__in__minNull,axiom,
% 9.49/5.24      ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList: list_VEBT_VEBT,L2: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT,Sn: vEBT_VEBT] :
% 9.49/5.24        ( ( ( X = Mi )
% 9.49/5.24          & ( ord_less_nat @ X @ Ma ) )
% 9.49/5.24       => ( ( Mi != Ma )
% 9.49/5.24         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 9.49/5.24           => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.24                = H2 )
% 9.49/5.24             => ( ( Xn
% 9.49/5.24                  = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 9.49/5.24               => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.24                    = L2 )
% 9.49/5.24                 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 9.49/5.24                   => ( ( Newnode
% 9.49/5.24                        = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) )
% 9.49/5.24                     => ( ( Newlist
% 9.49/5.24                          = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 9.49/5.24                       => ( ( vEBT_VEBT_minNull @ Newnode )
% 9.49/5.24                         => ( ( Sn
% 9.49/5.24                              = ( vEBT_vebt_delete @ Summary @ H2 ) )
% 9.49/5.24                           => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 9.49/5.24                              = ( vEBT_Node
% 9.49/5.24                                @ ( some_P7363390416028606310at_nat
% 9.49/5.24                                  @ ( product_Pair_nat_nat @ Xn
% 9.49/5.24                                    @ ( if_nat @ ( Xn = Ma )
% 9.49/5.24                                      @ ( if_nat
% 9.49/5.24                                        @ ( ( vEBT_vebt_maxt @ Sn )
% 9.49/5.24                                          = none_nat )
% 9.49/5.24                                        @ Xn
% 9.49/5.24                                        @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) ) ) ) )
% 9.49/5.24                                      @ Ma ) ) )
% 9.49/5.24                                @ Deg
% 9.49/5.24                                @ Newlist
% 9.49/5.24                                @ Sn ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1524_set__vebt_H__def,axiom,
% 9.49/5.24      ( vEBT_VEBT_set_vebt
% 9.49/5.24      = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_vebt_member @ T2 ) ) ) ) ).
% 9.49/5.24  
% 9.49/5.24  thf(fact_1525_del__x__not__mia,axiom,
% 9.49/5.24      ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 9.49/5.24        ( ( ( ord_less_nat @ Mi @ X )
% 9.49/5.24          & ( ord_less_eq_nat @ X @ Ma ) )
% 9.49/5.24       => ( ( Mi != Ma )
% 9.49/5.24         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 9.49/5.24           => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.24                = H2 )
% 9.49/5.24             => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.24                  = L2 )
% 9.49/5.24               => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 9.49/5.25                 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 9.49/5.25                    = ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) )
% 9.49/5.25                      @ ( vEBT_Node
% 9.49/5.25                        @ ( some_P7363390416028606310at_nat
% 9.49/5.25                          @ ( product_Pair_nat_nat @ Mi
% 9.49/5.25                            @ ( if_nat @ ( X = Ma )
% 9.49/5.25                              @ ( if_nat
% 9.49/5.25                                @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 9.49/5.25                                  = none_nat )
% 9.49/5.25                                @ Mi
% 9.49/5.25                                @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 9.49/5.25                              @ Ma ) ) )
% 9.49/5.25                        @ Deg
% 9.49/5.25                        @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) )
% 9.49/5.25                        @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 9.49/5.25                      @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) ) @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) ) @ Summary ) ) ) ) ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1526_del__x__not__mi__new__node__nil,axiom,
% 9.49/5.25      ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L2: nat,Newnode: vEBT_VEBT,TreeList: list_VEBT_VEBT,Sn: vEBT_VEBT,Summary: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 9.49/5.25        ( ( ( ord_less_nat @ Mi @ X )
% 9.49/5.25          & ( ord_less_eq_nat @ X @ Ma ) )
% 9.49/5.25       => ( ( Mi != Ma )
% 9.49/5.25         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 9.49/5.25           => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.25                = H2 )
% 9.49/5.25             => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.25                  = L2 )
% 9.49/5.25               => ( ( Newnode
% 9.49/5.25                    = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) )
% 9.49/5.25                 => ( ( vEBT_VEBT_minNull @ Newnode )
% 9.49/5.25                   => ( ( Sn
% 9.49/5.25                        = ( vEBT_vebt_delete @ Summary @ H2 ) )
% 9.49/5.25                     => ( ( Newlist
% 9.49/5.25                          = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 9.49/5.25                       => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 9.49/5.25                         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 9.49/5.25                            = ( vEBT_Node
% 9.49/5.25                              @ ( some_P7363390416028606310at_nat
% 9.49/5.25                                @ ( product_Pair_nat_nat @ Mi
% 9.49/5.25                                  @ ( if_nat @ ( X = Ma )
% 9.49/5.25                                    @ ( if_nat
% 9.49/5.25                                      @ ( ( vEBT_vebt_maxt @ Sn )
% 9.49/5.25                                        = none_nat )
% 9.49/5.25                                      @ Mi
% 9.49/5.25                                      @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) ) ) ) )
% 9.49/5.25                                    @ Ma ) ) )
% 9.49/5.25                              @ Deg
% 9.49/5.25                              @ Newlist
% 9.49/5.25                              @ Sn ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1527_del__x__not__mi,axiom,
% 9.49/5.25      ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L2: nat,Newnode: vEBT_VEBT,TreeList: list_VEBT_VEBT,Newlist: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 9.49/5.25        ( ( ( ord_less_nat @ Mi @ X )
% 9.49/5.25          & ( ord_less_eq_nat @ X @ Ma ) )
% 9.49/5.25       => ( ( Mi != Ma )
% 9.49/5.25         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 9.49/5.25           => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.25                = H2 )
% 9.49/5.25             => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.25                  = L2 )
% 9.49/5.25               => ( ( Newnode
% 9.49/5.25                    = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) )
% 9.49/5.25                 => ( ( Newlist
% 9.49/5.25                      = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 9.49/5.25                   => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 9.49/5.25                     => ( ( ( vEBT_VEBT_minNull @ Newnode )
% 9.49/5.25                         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 9.49/5.25                            = ( vEBT_Node
% 9.49/5.25                              @ ( some_P7363390416028606310at_nat
% 9.49/5.25                                @ ( product_Pair_nat_nat @ Mi
% 9.49/5.25                                  @ ( if_nat @ ( X = Ma )
% 9.49/5.25                                    @ ( if_nat
% 9.49/5.25                                      @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 9.49/5.25                                        = none_nat )
% 9.49/5.25                                      @ Mi
% 9.49/5.25                                      @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 9.49/5.25                                    @ Ma ) ) )
% 9.49/5.25                              @ Deg
% 9.49/5.25                              @ Newlist
% 9.49/5.25                              @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) )
% 9.49/5.25                        & ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 9.49/5.25                         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 9.49/5.25                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1528_del__x__mia,axiom,
% 9.49/5.25      ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 9.49/5.25        ( ( ( X = Mi )
% 9.49/5.25          & ( ord_less_nat @ X @ Ma ) )
% 9.49/5.25       => ( ( Mi != Ma )
% 9.49/5.25         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 9.49/5.25           => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 9.49/5.25              = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 9.49/5.25                @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                  @ ( vEBT_Node
% 9.49/5.25                    @ ( some_P7363390416028606310at_nat
% 9.49/5.25                      @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 9.49/5.25                        @ ( if_nat
% 9.49/5.25                          @ ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 9.49/5.25                            = Ma )
% 9.49/5.25                          @ ( if_nat
% 9.49/5.25                            @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                              = none_nat )
% 9.49/5.25                            @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 9.49/5.25                            @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 9.49/5.25                          @ Ma ) ) )
% 9.49/5.25                    @ Deg
% 9.49/5.25                    @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                    @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                  @ ( vEBT_Node
% 9.49/5.25                    @ ( some_P7363390416028606310at_nat
% 9.49/5.25                      @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 9.49/5.25                        @ ( if_nat
% 9.49/5.25                          @ ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 9.49/5.25                            = Ma )
% 9.49/5.25                          @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 9.49/5.25                          @ Ma ) ) )
% 9.49/5.25                    @ Deg
% 9.49/5.25                    @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                    @ Summary ) )
% 9.49/5.25                @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1529_succ__less__length__list,axiom,
% 9.49/5.25      ! [Deg: nat,Mi: nat,X: nat,TreeList: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 9.49/5.25        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 9.49/5.25       => ( ( ord_less_eq_nat @ Mi @ X )
% 9.49/5.25         => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 9.49/5.25           => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 9.49/5.25              = ( if_option_nat
% 9.49/5.25                @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                   != none_nat )
% 9.49/5.25                  & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 9.49/5.25                @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                @ ( if_option_nat
% 9.49/5.25                  @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.49/5.25                    = none_nat )
% 9.49/5.25                  @ none_nat
% 9.49/5.25                  @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1530_succ__greatereq__min,axiom,
% 9.49/5.25      ! [Deg: nat,Mi: nat,X: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 9.49/5.25        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 9.49/5.25       => ( ( ord_less_eq_nat @ Mi @ X )
% 9.49/5.25         => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 9.49/5.25            = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 9.49/5.25              @ ( if_option_nat
% 9.49/5.25                @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                   != none_nat )
% 9.49/5.25                  & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 9.49/5.25                @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                @ ( if_option_nat
% 9.49/5.25                  @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.49/5.25                    = none_nat )
% 9.49/5.25                  @ none_nat
% 9.49/5.25                  @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 9.49/5.25              @ none_nat ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1531_pred__lesseq__max,axiom,
% 9.49/5.25      ! [Deg: nat,X: nat,Ma: nat,Mi: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 9.49/5.25        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 9.49/5.25       => ( ( ord_less_eq_nat @ X @ Ma )
% 9.49/5.25         => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 9.49/5.25            = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 9.49/5.25              @ ( if_option_nat
% 9.49/5.25                @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                   != none_nat )
% 9.49/5.25                  & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 9.49/5.25                @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                @ ( if_option_nat
% 9.49/5.25                  @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.49/5.25                    = none_nat )
% 9.49/5.25                  @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 9.49/5.25                  @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 9.49/5.25              @ none_nat ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1532_pred__less__length__list,axiom,
% 9.49/5.25      ! [Deg: nat,X: nat,Ma: nat,TreeList: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 9.49/5.25        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 9.49/5.25       => ( ( ord_less_eq_nat @ X @ Ma )
% 9.49/5.25         => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 9.49/5.25           => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 9.49/5.25              = ( if_option_nat
% 9.49/5.25                @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                   != none_nat )
% 9.49/5.25                  & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 9.49/5.25                @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                @ ( if_option_nat
% 9.49/5.25                  @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.49/5.25                    = none_nat )
% 9.49/5.25                  @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 9.49/5.25                  @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1533_mult__commute__abs,axiom,
% 9.49/5.25      ! [C: complex] :
% 9.49/5.25        ( ( ^ [X2: complex] : ( times_times_complex @ X2 @ C ) )
% 9.49/5.25        = ( times_times_complex @ C ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1534_mult__commute__abs,axiom,
% 9.49/5.25      ! [C: real] :
% 9.49/5.25        ( ( ^ [X2: real] : ( times_times_real @ X2 @ C ) )
% 9.49/5.25        = ( times_times_real @ C ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1535_mult__commute__abs,axiom,
% 9.49/5.25      ! [C: nat] :
% 9.49/5.25        ( ( ^ [X2: nat] : ( times_times_nat @ X2 @ C ) )
% 9.49/5.25        = ( times_times_nat @ C ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1536_mult__commute__abs,axiom,
% 9.49/5.25      ! [C: int] :
% 9.49/5.25        ( ( ^ [X2: int] : ( times_times_int @ X2 @ C ) )
% 9.49/5.25        = ( times_times_int @ C ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1537_lambda__one,axiom,
% 9.49/5.25      ( ( ^ [X2: rat] : X2 )
% 9.49/5.25      = ( times_times_rat @ one_one_rat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1538_lambda__one,axiom,
% 9.49/5.25      ( ( ^ [X2: complex] : X2 )
% 9.49/5.25      = ( times_times_complex @ one_one_complex ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1539_lambda__one,axiom,
% 9.49/5.25      ( ( ^ [X2: real] : X2 )
% 9.49/5.25      = ( times_times_real @ one_one_real ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1540_lambda__one,axiom,
% 9.49/5.25      ( ( ^ [X2: nat] : X2 )
% 9.49/5.25      = ( times_times_nat @ one_one_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1541_lambda__one,axiom,
% 9.49/5.25      ( ( ^ [X2: int] : X2 )
% 9.49/5.25      = ( times_times_int @ one_one_int ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1542_set__vebt__def,axiom,
% 9.49/5.25      ( vEBT_set_vebt
% 9.49/5.25      = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ T2 ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1543_numeral__code_I2_J,axiom,
% 9.49/5.25      ! [N: num] :
% 9.49/5.25        ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 9.49/5.25        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1544_numeral__code_I2_J,axiom,
% 9.49/5.25      ! [N: num] :
% 9.49/5.25        ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 9.49/5.25        = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1545_numeral__code_I2_J,axiom,
% 9.49/5.25      ! [N: num] :
% 9.49/5.25        ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 9.49/5.25        = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1546_numeral__code_I2_J,axiom,
% 9.49/5.25      ! [N: num] :
% 9.49/5.25        ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 9.49/5.25        = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1547_numeral__code_I2_J,axiom,
% 9.49/5.25      ! [N: num] :
% 9.49/5.25        ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 9.49/5.25        = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1548_numeral__code_I3_J,axiom,
% 9.49/5.25      ! [N: num] :
% 9.49/5.25        ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 9.49/5.25        = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1549_numeral__code_I3_J,axiom,
% 9.49/5.25      ! [N: num] :
% 9.49/5.25        ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 9.49/5.25        = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1550_numeral__code_I3_J,axiom,
% 9.49/5.25      ! [N: num] :
% 9.49/5.25        ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 9.49/5.25        = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1551_numeral__code_I3_J,axiom,
% 9.49/5.25      ! [N: num] :
% 9.49/5.25        ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 9.49/5.25        = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1552_numeral__code_I3_J,axiom,
% 9.49/5.25      ! [N: num] :
% 9.49/5.25        ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 9.49/5.25        = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1553_power__numeral__even,axiom,
% 9.49/5.25      ! [Z: complex,W: num] :
% 9.49/5.25        ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 9.49/5.25        = ( times_times_complex @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1554_power__numeral__even,axiom,
% 9.49/5.25      ! [Z: real,W: num] :
% 9.49/5.25        ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 9.49/5.25        = ( times_times_real @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1555_power__numeral__even,axiom,
% 9.49/5.25      ! [Z: nat,W: num] :
% 9.49/5.25        ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 9.49/5.25        = ( times_times_nat @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1556_power__numeral__even,axiom,
% 9.49/5.25      ! [Z: int,W: num] :
% 9.49/5.25        ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 9.49/5.25        = ( times_times_int @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1557_power__numeral__odd,axiom,
% 9.49/5.25      ! [Z: complex,W: num] :
% 9.49/5.25        ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 9.49/5.25        = ( times_times_complex @ ( times_times_complex @ Z @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1558_power__numeral__odd,axiom,
% 9.49/5.25      ! [Z: real,W: num] :
% 9.49/5.25        ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 9.49/5.25        = ( times_times_real @ ( times_times_real @ Z @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1559_power__numeral__odd,axiom,
% 9.49/5.25      ! [Z: nat,W: num] :
% 9.49/5.25        ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 9.49/5.25        = ( times_times_nat @ ( times_times_nat @ Z @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1560_power__numeral__odd,axiom,
% 9.49/5.25      ! [Z: int,W: num] :
% 9.49/5.25        ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 9.49/5.25        = ( times_times_int @ ( times_times_int @ Z @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1561_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I3_J,axiom,
% 9.49/5.25      ! [Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,Va: nat] :
% 9.49/5.25        ( ( vEBT_T_s_u_c_c @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz ) @ Va )
% 9.49/5.25        = one_one_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1562_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I5_J,axiom,
% 9.49/5.25      ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 9.49/5.25        ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 9.49/5.25        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( X = Mi ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( X = Ma ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Ma @ X ) @ one_one_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_e_m_b_e_r @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1563_vebt__succ_Osimps_I6_J,axiom,
% 9.49/5.25      ! [X: nat,Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 9.49/5.25        ( ( ( ord_less_nat @ X @ Mi )
% 9.49/5.25         => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 9.49/5.25            = ( some_nat @ Mi ) ) )
% 9.49/5.25        & ( ~ ( ord_less_nat @ X @ Mi )
% 9.49/5.25         => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 9.49/5.25            = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 9.49/5.25              @ ( if_option_nat
% 9.49/5.25                @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                   != none_nat )
% 9.49/5.25                  & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 9.49/5.25                @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                @ ( if_option_nat
% 9.49/5.25                  @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.49/5.25                    = none_nat )
% 9.49/5.25                  @ none_nat
% 9.49/5.25                  @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 9.49/5.25              @ none_nat ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1564_vebt__pred_Osimps_I7_J,axiom,
% 9.49/5.25      ! [Ma: nat,X: nat,Mi: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 9.49/5.25        ( ( ( ord_less_nat @ Ma @ X )
% 9.49/5.25         => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 9.49/5.25            = ( some_nat @ Ma ) ) )
% 9.49/5.25        & ( ~ ( ord_less_nat @ Ma @ X )
% 9.49/5.25         => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 9.49/5.25            = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 9.49/5.25              @ ( if_option_nat
% 9.49/5.25                @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                   != none_nat )
% 9.49/5.25                  & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 9.49/5.25                @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                @ ( if_option_nat
% 9.49/5.25                  @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.49/5.25                    = none_nat )
% 9.49/5.25                  @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 9.49/5.25                  @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 9.49/5.25              @ none_nat ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1565_vebt__insert_Osimps_I5_J,axiom,
% 9.49/5.25      ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 9.49/5.25        ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 9.49/5.25        = ( if_VEBT_VEBT
% 9.49/5.25          @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 9.49/5.25            & ~ ( ( X = Mi )
% 9.49/5.25                | ( X = Ma ) ) )
% 9.49/5.25          @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ X @ Mi ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ Ma ) ) ) @ ( suc @ ( suc @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) )
% 9.49/5.25          @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1566_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I2_J,axiom,
% 9.49/5.25      ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X: nat] :
% 9.49/5.25        ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X )
% 9.49/5.25        = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1567_is__pred__in__set__def,axiom,
% 9.49/5.25      ( vEBT_is_pred_in_set
% 9.49/5.25      = ( ^ [Xs: set_nat,X2: nat,Y: nat] :
% 9.49/5.25            ( ( member_nat @ Y @ Xs )
% 9.49/5.25            & ( ord_less_nat @ Y @ X2 )
% 9.49/5.25            & ! [Z4: nat] :
% 9.49/5.25                ( ( member_nat @ Z4 @ Xs )
% 9.49/5.25               => ( ( ord_less_nat @ Z4 @ X2 )
% 9.49/5.25                 => ( ord_less_eq_nat @ Z4 @ Y ) ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1568_is__succ__in__set__def,axiom,
% 9.49/5.25      ( vEBT_is_succ_in_set
% 9.49/5.25      = ( ^ [Xs: set_nat,X2: nat,Y: nat] :
% 9.49/5.25            ( ( member_nat @ Y @ Xs )
% 9.49/5.25            & ( ord_less_nat @ X2 @ Y )
% 9.49/5.25            & ! [Z4: nat] :
% 9.49/5.25                ( ( member_nat @ Z4 @ Xs )
% 9.49/5.25               => ( ( ord_less_nat @ X2 @ Z4 )
% 9.49/5.25                 => ( ord_less_eq_nat @ Y @ Z4 ) ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1569_vebt__delete_Osimps_I7_J,axiom,
% 9.49/5.25      ! [X: nat,Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 9.49/5.25        ( ( ( ( ord_less_nat @ X @ Mi )
% 9.49/5.25            | ( ord_less_nat @ Ma @ X ) )
% 9.49/5.25         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 9.49/5.25            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) ) )
% 9.49/5.25        & ( ~ ( ( ord_less_nat @ X @ Mi )
% 9.49/5.25              | ( ord_less_nat @ Ma @ X ) )
% 9.49/5.25         => ( ( ( ( X = Mi )
% 9.49/5.25                & ( X = Ma ) )
% 9.49/5.25             => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 9.49/5.25                = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) ) )
% 9.49/5.25            & ( ~ ( ( X = Mi )
% 9.49/5.25                  & ( X = Ma ) )
% 9.49/5.25             => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 9.49/5.25                = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 9.49/5.25                  @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                    @ ( vEBT_Node
% 9.49/5.25                      @ ( some_P7363390416028606310at_nat
% 9.49/5.25                        @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 9.49/5.25                          @ ( if_nat
% 9.49/5.25                            @ ( ( ( X = Mi )
% 9.49/5.25                               => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 9.49/5.25                                  = Ma ) )
% 9.49/5.25                              & ( ( X != Mi )
% 9.49/5.25                               => ( X = Ma ) ) )
% 9.49/5.25                            @ ( if_nat
% 9.49/5.25                              @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                                = none_nat )
% 9.49/5.25                              @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 9.49/5.25                              @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 9.49/5.25                            @ Ma ) ) )
% 9.49/5.25                      @ ( suc @ ( suc @ Va ) )
% 9.49/5.25                      @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                      @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                    @ ( vEBT_Node
% 9.49/5.25                      @ ( some_P7363390416028606310at_nat
% 9.49/5.25                        @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 9.49/5.25                          @ ( if_nat
% 9.49/5.25                            @ ( ( ( X = Mi )
% 9.49/5.25                               => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 9.49/5.25                                  = Ma ) )
% 9.49/5.25                              & ( ( X != Mi )
% 9.49/5.25                               => ( X = Ma ) ) )
% 9.49/5.25                            @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 9.49/5.25                            @ Ma ) ) )
% 9.49/5.25                      @ ( suc @ ( suc @ Va ) )
% 9.49/5.25                      @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                      @ Summary ) )
% 9.49/5.25                  @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) ) ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1570_vebt__member_Osimps_I5_J,axiom,
% 9.49/5.25      ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 9.49/5.25        ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 9.49/5.25        = ( ( X != Mi )
% 9.49/5.25         => ( ( X != Ma )
% 9.49/5.25           => ( ~ ( ord_less_nat @ X @ Mi )
% 9.49/5.25              & ( ~ ( ord_less_nat @ X @ Mi )
% 9.49/5.25               => ( ~ ( ord_less_nat @ Ma @ X )
% 9.49/5.25                  & ( ~ ( ord_less_nat @ Ma @ X )
% 9.49/5.25                   => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 9.49/5.25                       => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                      & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1571__C3_C,axiom,
% 9.49/5.25      ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 9.49/5.25      = ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_t @ summary ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat )
% 9.49/5.25        @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) )
% 9.49/5.25          @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25            @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 9.49/5.25              @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_d_e_l_e_t_e @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                  @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 9.49/5.25                    @ ( if_nat
% 9.49/5.25                      @ ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) )
% 9.49/5.25                        = ma )
% 9.49/5.25                      @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 9.49/5.25                        @ ( plus_plus_nat @ one_one_nat
% 9.49/5.25                          @ ( if_nat
% 9.49/5.25                            @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                              = none_nat )
% 9.49/5.25                            @ one_one_nat
% 9.49/5.25                            @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 9.49/5.25                      @ one_one_nat ) ) )
% 9.49/5.25                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 9.49/5.25                  @ ( if_nat
% 9.49/5.25                    @ ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) )
% 9.49/5.25                      = ma )
% 9.49/5.25                    @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 9.49/5.25                    @ one_one_nat ) ) ) ) )
% 9.49/5.25          @ one_one_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1572__C2_C,axiom,
% 9.49/5.25      ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 9.49/5.25      = ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_t @ summary ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat )
% 9.49/5.25        @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) )
% 9.49/5.25          @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25            @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 9.49/5.25              @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_d_e_l_e_t_e @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                  @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 9.49/5.25                    @ ( if_nat
% 9.49/5.25                      @ ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) )
% 9.49/5.25                        = ma )
% 9.49/5.25                      @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 9.49/5.25                        @ ( plus_plus_nat @ one_one_nat
% 9.49/5.25                          @ ( if_nat
% 9.49/5.25                            @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                              = none_nat )
% 9.49/5.25                            @ one_one_nat
% 9.49/5.25                            @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 9.49/5.25                      @ one_one_nat ) ) )
% 9.49/5.25                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 9.49/5.25                  @ ( if_nat
% 9.49/5.25                    @ ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) )
% 9.49/5.25                      = ma )
% 9.49/5.25                    @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 9.49/5.25                    @ one_one_nat ) ) ) ) )
% 9.49/5.25          @ one_one_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1573__C1_C,axiom,
% 9.49/5.25      ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 9.49/5.25      = ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ summary ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat ) ) @ one_one_nat )
% 9.49/5.25        @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) )
% 9.49/5.25          @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25            @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 9.49/5.25              @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_d_e_l_e_t_e @ summary @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                  @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 9.49/5.25                    @ ( if_nat
% 9.49/5.25                      @ ( ( ( xa = mi )
% 9.49/5.25                         => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) )
% 9.49/5.25                            = ma ) )
% 9.49/5.25                        & ( ( xa != mi )
% 9.49/5.25                         => ( xa = ma ) ) )
% 9.49/5.25                      @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 9.49/5.25                        @ ( plus_plus_nat @ one_one_nat
% 9.49/5.25                          @ ( if_nat
% 9.49/5.25                            @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                              = none_nat )
% 9.49/5.25                            @ one_one_nat
% 9.49/5.25                            @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 9.49/5.25                      @ one_one_nat ) ) )
% 9.49/5.25                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 9.49/5.25                  @ ( if_nat
% 9.49/5.25                    @ ( ( ( xa = mi )
% 9.49/5.25                       => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) )
% 9.49/5.25                          = ma ) )
% 9.49/5.25                      & ( ( xa != mi )
% 9.49/5.25                       => ( xa = ma ) ) )
% 9.49/5.25                    @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 9.49/5.25                    @ one_one_nat ) ) ) ) )
% 9.49/5.25          @ one_one_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1574__C0_C,axiom,
% 9.49/5.25      ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 9.49/5.25      = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 9.49/5.25        @ ( if_nat
% 9.49/5.25          @ ( ( xa = mi )
% 9.49/5.25            & ( xa = ma ) )
% 9.49/5.25          @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 9.49/5.25          @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ summary ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat ) ) @ one_one_nat )
% 9.49/5.25            @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) )
% 9.49/5.25              @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 9.49/5.25                  @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                    @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_d_e_l_e_t_e @ summary @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                      @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 9.49/5.25                        @ ( if_nat
% 9.49/5.25                          @ ( ( ( xa = mi )
% 9.49/5.25                             => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) )
% 9.49/5.25                                = ma ) )
% 9.49/5.25                            & ( ( xa != mi )
% 9.49/5.25                             => ( xa = ma ) ) )
% 9.49/5.25                          @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 9.49/5.25                            @ ( plus_plus_nat @ one_one_nat
% 9.49/5.25                              @ ( if_nat
% 9.49/5.25                                @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                                  = none_nat )
% 9.49/5.25                                @ one_one_nat
% 9.49/5.25                                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 9.49/5.25                          @ one_one_nat ) ) )
% 9.49/5.25                    @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 9.49/5.25                      @ ( if_nat
% 9.49/5.25                        @ ( ( ( xa = mi )
% 9.49/5.25                           => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) )
% 9.49/5.25                              = ma ) )
% 9.49/5.25                          & ( ( xa != mi )
% 9.49/5.25                           => ( xa = ma ) ) )
% 9.49/5.25                        @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( xa = mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 9.49/5.25                        @ one_one_nat ) ) ) ) )
% 9.49/5.25              @ one_one_nat ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1575_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I6_J,axiom,
% 9.49/5.25      ! [X: nat,Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 9.49/5.25        ( ( ( ord_less_nat @ X @ Mi )
% 9.49/5.25         => ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 9.49/5.25            = one_one_nat ) )
% 9.49/5.25        & ( ~ ( ord_less_nat @ X @ Mi )
% 9.49/5.25         => ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 9.49/5.25            = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 9.49/5.25              @ ( if_nat
% 9.49/5.25                @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                   != none_nat )
% 9.49/5.25                  & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 9.49/5.25                @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c2 @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                @ ( plus_plus_nat @ ( vEBT_T_s_u_c_c2 @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 9.49/5.25              @ one_one_nat ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1576_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I7_J,axiom,
% 9.49/5.25      ! [Ma: nat,X: nat,Mi: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 9.49/5.25        ( ( ( ord_less_nat @ Ma @ X )
% 9.49/5.25         => ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 9.49/5.25            = one_one_nat ) )
% 9.49/5.25        & ( ~ ( ord_less_nat @ Ma @ X )
% 9.49/5.25         => ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 9.49/5.25            = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 9.49/5.25              @ ( if_nat
% 9.49/5.25                @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                   != none_nat )
% 9.49/5.25                  & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 9.49/5.25                @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d2 @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                @ ( plus_plus_nat @ ( vEBT_T_p_r_e_d2 @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 9.49/5.25              @ one_one_nat ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1577_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I6_J,axiom,
% 9.49/5.25      ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 9.49/5.25        ( ( vEBT_T_s_u_c_c @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 9.49/5.25        = ( plus_plus_nat @ one_one_nat
% 9.49/5.25          @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ one_one_nat
% 9.49/5.25            @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) )
% 9.49/5.25              @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 9.49/5.25                @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 9.49/5.25                  @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 9.49/5.25                    @ ( if_nat
% 9.49/5.25                      @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                         != none_nat )
% 9.49/5.25                        & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 9.49/5.25                      @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_s_u_c_c @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                      @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 9.49/5.25                        @ ( if_nat
% 9.49/5.25                          @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.49/5.25                            = none_nat )
% 9.49/5.25                          @ one_one_nat
% 9.49/5.25                          @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 9.49/5.25                @ one_one_nat ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1578_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I5_J,axiom,
% 9.49/5.25      ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 9.49/5.25        ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 9.49/5.25        = ( if_nat
% 9.49/5.25          @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 9.49/5.25            & ~ ( ( X = Mi )
% 9.49/5.25                | ( X = Ma ) ) )
% 9.49/5.25          @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t2 @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t2 @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 9.49/5.25          @ one_one_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1579_minNull__bound,axiom,
% 9.49/5.25      ! [T: vEBT_VEBT] : ( ord_less_eq_nat @ ( vEBT_T_m_i_n_N_u_l_l @ T ) @ one_one_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1580_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Osimps_I2_J,axiom,
% 9.49/5.25      ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 9.49/5.25        ( ( vEBT_T_m_a_x_t @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 9.49/5.25        = one_one_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1581_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I5_J,axiom,
% 9.49/5.25      ! [Uz: product_prod_nat_nat,Va: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 9.49/5.25        ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz ) @ Va @ Vb @ Vc ) )
% 9.49/5.25        = one_one_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1582_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I4_J,axiom,
% 9.49/5.25      ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 9.49/5.25        ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) )
% 9.49/5.25        = one_one_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1583_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I4_J,axiom,
% 9.49/5.25      ! [Uy: nat,Uz: list_VEBT_VEBT,Va: vEBT_VEBT,Vb: nat] :
% 9.49/5.25        ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz @ Va ) @ Vb )
% 9.49/5.25        = one_one_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1584_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I3_J,axiom,
% 9.49/5.25      ! [Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,Va: nat] :
% 9.49/5.25        ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz ) @ Va )
% 9.49/5.25        = one_one_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1585_maxt__bound,axiom,
% 9.49/5.25      ! [T: vEBT_VEBT] : ( ord_less_eq_nat @ ( vEBT_T_m_a_x_t @ T ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1586_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Osimps_I3_J,axiom,
% 9.49/5.25      ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 9.49/5.25        ( ( vEBT_T_m_a_x_t @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 9.49/5.25        = one_one_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1587_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I4_J,axiom,
% 9.49/5.25      ! [V: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 9.49/5.25        ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) @ X )
% 9.49/5.25        = one_one_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1588_insersimp_H,axiom,
% 9.49/5.25      ! [T: vEBT_VEBT,N: nat,Y2: nat] :
% 9.49/5.25        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.25       => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_12 )
% 9.49/5.25         => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t2 @ T @ Y2 ) @ one_one_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1589_insertsimp_H,axiom,
% 9.49/5.25      ! [T: vEBT_VEBT,N: nat,L2: nat] :
% 9.49/5.25        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.25       => ( ( vEBT_VEBT_minNull @ T )
% 9.49/5.25         => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t2 @ T @ L2 ) @ one_one_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1590_pred__bound__height_H,axiom,
% 9.49/5.25      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 9.49/5.25        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.25       => ( ord_less_eq_nat @ ( vEBT_T_p_r_e_d2 @ T @ X ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1591_insert_H__bound__height,axiom,
% 9.49/5.25      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 9.49/5.25        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.25       => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t2 @ T @ X ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1592_succ_H__bound__height,axiom,
% 9.49/5.25      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 9.49/5.25        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.25       => ( ord_less_eq_nat @ ( vEBT_T_s_u_c_c2 @ T @ X ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1593_VEBT__internal_OminNull_Osimps_I5_J,axiom,
% 9.49/5.25      ! [Uz: product_prod_nat_nat,Va: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 9.49/5.25        ~ ( vEBT_VEBT_minNull @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz ) @ Va @ Vb @ Vc ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1594_vebt__delete_Osimps_I4_J,axiom,
% 9.49/5.25      ! [Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Uu: nat] :
% 9.49/5.25        ( ( vEBT_vebt_delete @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Uu )
% 9.49/5.25        = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1595_VEBT__internal_OminNull_Osimps_I4_J,axiom,
% 9.49/5.25      ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] : ( vEBT_VEBT_minNull @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1596_vebt__member_Osimps_I2_J,axiom,
% 9.49/5.25      ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X: nat] :
% 9.49/5.25        ~ ( vEBT_vebt_member @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1597_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I7_J,axiom,
% 9.49/5.25      ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 9.49/5.25        ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 9.49/5.25        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 9.49/5.25          @ ( if_nat
% 9.49/5.25            @ ( ( ord_less_nat @ X @ Mi )
% 9.49/5.25              | ( ord_less_nat @ Ma @ X ) )
% 9.49/5.25            @ one_one_nat
% 9.49/5.25            @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 9.49/5.25              @ ( if_nat
% 9.49/5.25                @ ( ( X = Mi )
% 9.49/5.25                  & ( X = Ma ) )
% 9.49/5.25                @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 9.49/5.25                @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ Summary ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat ) ) @ one_one_nat )
% 9.49/5.25                  @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 9.49/5.25                    @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                      @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 9.49/5.25                        @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                          @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_d_e_l_e_t_e @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                            @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 9.49/5.25                              @ ( if_nat
% 9.49/5.25                                @ ( ( ( X = Mi )
% 9.49/5.25                                   => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 9.49/5.25                                      = Ma ) )
% 9.49/5.25                                  & ( ( X != Mi )
% 9.49/5.25                                   => ( X = Ma ) ) )
% 9.49/5.25                                @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 9.49/5.25                                  @ ( plus_plus_nat @ one_one_nat
% 9.49/5.25                                    @ ( if_nat
% 9.49/5.25                                      @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                                        = none_nat )
% 9.49/5.25                                      @ one_one_nat
% 9.49/5.25                                      @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 9.49/5.25                                @ one_one_nat ) ) )
% 9.49/5.25                          @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 9.49/5.25                            @ ( if_nat
% 9.49/5.25                              @ ( ( ( X = Mi )
% 9.49/5.25                                 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 9.49/5.25                                    = Ma ) )
% 9.49/5.25                                & ( ( X != Mi )
% 9.49/5.25                                 => ( X = Ma ) ) )
% 9.49/5.25                              @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 9.49/5.25                              @ one_one_nat ) ) ) ) )
% 9.49/5.25                    @ one_one_nat ) ) ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1598_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I7_J,axiom,
% 9.49/5.25      ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 9.49/5.25        ( ( vEBT_T_p_r_e_d @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 9.49/5.25        = ( plus_plus_nat @ one_one_nat
% 9.49/5.25          @ ( if_nat @ ( ord_less_nat @ Ma @ X ) @ one_one_nat
% 9.49/5.25            @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 9.49/5.25              @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 9.49/5.25                @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 9.49/5.25                  @ ( if_nat
% 9.49/5.25                    @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                       != none_nat )
% 9.49/5.25                      & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 9.49/5.25                    @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_p_r_e_d @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                    @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 9.49/5.25                      @ ( if_nat
% 9.49/5.25                        @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.49/5.25                          = none_nat )
% 9.49/5.25                        @ ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 9.49/5.25                        @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 9.49/5.25                @ one_one_nat ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1599_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I5_J,axiom,
% 9.49/5.25      ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 9.49/5.25        ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 9.49/5.25        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 9.49/5.25          @ ( if_nat
% 9.49/5.25            @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 9.49/5.25              & ~ ( ( X = Mi )
% 9.49/5.25                  | ( X = Ma ) ) )
% 9.49/5.25            @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 9.49/5.25            @ one_one_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1600_succ__empty,axiom,
% 9.49/5.25      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 9.49/5.25        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.25       => ( ( ( vEBT_vebt_succ @ T @ X )
% 9.49/5.25            = none_nat )
% 9.49/5.25          = ( ( collect_nat
% 9.49/5.25              @ ^ [Y: nat] :
% 9.49/5.25                  ( ( vEBT_vebt_member @ T @ Y )
% 9.49/5.25                  & ( ord_less_nat @ X @ Y ) ) )
% 9.49/5.25            = bot_bot_set_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1601_pred__empty,axiom,
% 9.49/5.25      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 9.49/5.25        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.25       => ( ( ( vEBT_vebt_pred @ T @ X )
% 9.49/5.25            = none_nat )
% 9.49/5.25          = ( ( collect_nat
% 9.49/5.25              @ ^ [Y: nat] :
% 9.49/5.25                  ( ( vEBT_vebt_member @ T @ Y )
% 9.49/5.25                  & ( ord_less_nat @ Y @ X ) ) )
% 9.49/5.25            = bot_bot_set_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1602_VEBT__internal_Omembermima_Osimps_I4_J,axiom,
% 9.49/5.25      ! [Mi: nat,Ma: nat,V: nat,TreeList: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 9.49/5.25        ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ V ) @ TreeList @ Vc ) @ X )
% 9.49/5.25        = ( ( X = Mi )
% 9.49/5.25          | ( X = Ma )
% 9.49/5.25          | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 9.49/5.25             => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25            & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1603_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Oelims,axiom,
% 9.49/5.25      ! [X: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 9.49/5.25        ( ( ( vEBT_T_d_e_l_e_t_e @ X @ Xa2 )
% 9.49/5.25          = Y2 )
% 9.49/5.25       => ( ( ? [A4: $o,B3: $o] :
% 9.49/5.25                ( X
% 9.49/5.25                = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.25           => ( ( Xa2 = zero_zero_nat )
% 9.49/5.25             => ( Y2 != one_one_nat ) ) )
% 9.49/5.25         => ( ( ? [A4: $o,B3: $o] :
% 9.49/5.25                  ( X
% 9.49/5.25                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.25             => ( ( Xa2
% 9.49/5.25                  = ( suc @ zero_zero_nat ) )
% 9.49/5.25               => ( Y2 != one_one_nat ) ) )
% 9.49/5.25           => ( ( ? [A4: $o,B3: $o] :
% 9.49/5.25                    ( X
% 9.49/5.25                    = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.25               => ( ? [N3: nat] :
% 9.49/5.25                      ( Xa2
% 9.49/5.25                      = ( suc @ ( suc @ N3 ) ) )
% 9.49/5.25                 => ( Y2 != one_one_nat ) ) )
% 9.49/5.25             => ( ( ? [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.25                      ( X
% 9.49/5.25                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 9.49/5.25                 => ( Y2 != one_one_nat ) )
% 9.49/5.25               => ( ( ? [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.25                        ( X
% 9.49/5.25                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TreeList2 @ Summary2 ) )
% 9.49/5.25                   => ( Y2 != one_one_nat ) )
% 9.49/5.25                 => ( ( ? [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.25                          ( X
% 9.49/5.25                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary2 ) )
% 9.49/5.25                     => ( Y2 != one_one_nat ) )
% 9.49/5.25                   => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.25                          ( ( X
% 9.49/5.25                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.25                         => ( Y2
% 9.49/5.25                           != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 9.49/5.25                              @ ( if_nat
% 9.49/5.25                                @ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 9.49/5.25                                  | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 9.49/5.25                                @ one_one_nat
% 9.49/5.25                                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 9.49/5.25                                  @ ( if_nat
% 9.49/5.25                                    @ ( ( Xa2 = Mi2 )
% 9.49/5.25                                      & ( Xa2 = Ma2 ) )
% 9.49/5.25                                    @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 9.49/5.25                                    @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ Summary2 ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat ) ) @ one_one_nat )
% 9.49/5.25                                      @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.25                                        @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                                          @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 9.49/5.25                                            @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                                              @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_d_e_l_e_t_e @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                                                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 9.49/5.25                                                  @ ( if_nat
% 9.49/5.25                                                    @ ( ( ( Xa2 = Mi2 )
% 9.49/5.25                                                       => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 9.49/5.25                                                          = Ma2 ) )
% 9.49/5.25                                                      & ( ( Xa2 != Mi2 )
% 9.49/5.25                                                       => ( Xa2 = Ma2 ) ) )
% 9.49/5.25                                                    @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 9.49/5.25                                                      @ ( plus_plus_nat @ one_one_nat
% 9.49/5.25                                                        @ ( if_nat
% 9.49/5.25                                                          @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25                                                            = none_nat )
% 9.49/5.25                                                          @ one_one_nat
% 9.49/5.25                                                          @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 9.49/5.25                                                    @ one_one_nat ) ) )
% 9.49/5.25                                              @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 9.49/5.25                                                @ ( if_nat
% 9.49/5.25                                                  @ ( ( ( Xa2 = Mi2 )
% 9.49/5.25                                                     => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 9.49/5.25                                                        = Ma2 ) )
% 9.49/5.25                                                    & ( ( Xa2 != Mi2 )
% 9.49/5.25                                                     => ( Xa2 = Ma2 ) ) )
% 9.49/5.25                                                  @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 9.49/5.25                                                  @ one_one_nat ) ) ) ) )
% 9.49/5.25                                        @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1604_VEBT__internal_Onaive__member_Osimps_I3_J,axiom,
% 9.49/5.25      ! [Uy: option4927543243414619207at_nat,V: nat,TreeList: list_VEBT_VEBT,S3: vEBT_VEBT,X: nat] :
% 9.49/5.25        ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S3 ) @ X )
% 9.49/5.25        = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 9.49/5.25           => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25          & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1605_VEBT__internal_Omembermima_Osimps_I5_J,axiom,
% 9.49/5.25      ! [V: nat,TreeList: list_VEBT_VEBT,Vd: vEBT_VEBT,X: nat] :
% 9.49/5.25        ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) @ X )
% 9.49/5.25        = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 9.49/5.25           => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.25          & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1606_pred__bound__height,axiom,
% 9.49/5.25      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 9.49/5.25        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.25       => ( ord_less_eq_nat @ ( vEBT_T_p_r_e_d @ T @ X ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1607_insert__bound__height,axiom,
% 9.49/5.25      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 9.49/5.25        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.25       => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ T @ X ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1608_valid__0__not,axiom,
% 9.49/5.25      ! [T: vEBT_VEBT] :
% 9.49/5.25        ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1609_valid__tree__deg__neq__0,axiom,
% 9.49/5.25      ! [T: vEBT_VEBT] :
% 9.49/5.25        ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1610_deg__not__0,axiom,
% 9.49/5.25      ! [T: vEBT_VEBT,N: nat] :
% 9.49/5.25        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.25       => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1611_Leaf__0__not,axiom,
% 9.49/5.25      ! [A: $o,B: $o] :
% 9.49/5.25        ~ ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1612_deg__1__Leafy,axiom,
% 9.49/5.25      ! [T: vEBT_VEBT,N: nat] :
% 9.49/5.25        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.25       => ( ( N = one_one_nat )
% 9.49/5.25         => ? [A4: $o,B3: $o] :
% 9.49/5.25              ( T
% 9.49/5.25              = ( vEBT_Leaf @ A4 @ B3 ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1613_deg__1__Leaf,axiom,
% 9.49/5.25      ! [T: vEBT_VEBT] :
% 9.49/5.25        ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 9.49/5.25       => ? [A4: $o,B3: $o] :
% 9.49/5.25            ( T
% 9.49/5.25            = ( vEBT_Leaf @ A4 @ B3 ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1614_deg1Leaf,axiom,
% 9.49/5.25      ! [T: vEBT_VEBT] :
% 9.49/5.25        ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 9.49/5.25        = ( ? [A3: $o,B4: $o] :
% 9.49/5.25              ( T
% 9.49/5.25              = ( vEBT_Leaf @ A3 @ B4 ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1615_both__member__options__def,axiom,
% 9.49/5.25      ( vEBT_V8194947554948674370ptions
% 9.49/5.25      = ( ^ [T2: vEBT_VEBT,X2: nat] :
% 9.49/5.25            ( ( vEBT_V5719532721284313246member @ T2 @ X2 )
% 9.49/5.25            | ( vEBT_VEBT_membermima @ T2 @ X2 ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1616_member__valid__both__member__options,axiom,
% 9.49/5.25      ! [Tree: vEBT_VEBT,N: nat,X: nat] :
% 9.49/5.25        ( ( vEBT_invar_vebt @ Tree @ N )
% 9.49/5.25       => ( ( vEBT_vebt_member @ Tree @ X )
% 9.49/5.25         => ( ( vEBT_V5719532721284313246member @ Tree @ X )
% 9.49/5.25            | ( vEBT_VEBT_membermima @ Tree @ X ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1617_VEBT_Oinject_I2_J,axiom,
% 9.49/5.25      ! [X21: $o,X222: $o,Y21: $o,Y222: $o] :
% 9.49/5.25        ( ( ( vEBT_Leaf @ X21 @ X222 )
% 9.49/5.25          = ( vEBT_Leaf @ Y21 @ Y222 ) )
% 9.49/5.25        = ( ( X21 = Y21 )
% 9.49/5.25          & ( X222 = Y222 ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1618_mint__corr__help__empty,axiom,
% 9.49/5.25      ! [T: vEBT_VEBT,N: nat] :
% 9.49/5.25        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.25       => ( ( ( vEBT_vebt_mint @ T )
% 9.49/5.25            = none_nat )
% 9.49/5.25         => ( ( vEBT_VEBT_set_vebt @ T )
% 9.49/5.25            = bot_bot_set_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1619_maxt__corr__help__empty,axiom,
% 9.49/5.25      ! [T: vEBT_VEBT,N: nat] :
% 9.49/5.25        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.25       => ( ( ( vEBT_vebt_maxt @ T )
% 9.49/5.25            = none_nat )
% 9.49/5.25         => ( ( vEBT_VEBT_set_vebt @ T )
% 9.49/5.25            = bot_bot_set_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1620_le__zero__eq,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 9.49/5.25        = ( N = zero_zero_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1621_not__gr__zero,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 9.49/5.25        = ( N = zero_zero_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1622_mult__zero__left,axiom,
% 9.49/5.25      ! [A: rat] :
% 9.49/5.25        ( ( times_times_rat @ zero_zero_rat @ A )
% 9.49/5.25        = zero_zero_rat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1623_mult__zero__left,axiom,
% 9.49/5.25      ! [A: complex] :
% 9.49/5.25        ( ( times_times_complex @ zero_zero_complex @ A )
% 9.49/5.25        = zero_zero_complex ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1624_mult__zero__left,axiom,
% 9.49/5.25      ! [A: real] :
% 9.49/5.25        ( ( times_times_real @ zero_zero_real @ A )
% 9.49/5.25        = zero_zero_real ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1625_mult__zero__left,axiom,
% 9.49/5.25      ! [A: nat] :
% 9.49/5.25        ( ( times_times_nat @ zero_zero_nat @ A )
% 9.49/5.25        = zero_zero_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1626_mult__zero__left,axiom,
% 9.49/5.25      ! [A: int] :
% 9.49/5.25        ( ( times_times_int @ zero_zero_int @ A )
% 9.49/5.25        = zero_zero_int ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1627_mult__zero__right,axiom,
% 9.49/5.25      ! [A: rat] :
% 9.49/5.25        ( ( times_times_rat @ A @ zero_zero_rat )
% 9.49/5.25        = zero_zero_rat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1628_mult__zero__right,axiom,
% 9.49/5.25      ! [A: complex] :
% 9.49/5.25        ( ( times_times_complex @ A @ zero_zero_complex )
% 9.49/5.25        = zero_zero_complex ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1629_mult__zero__right,axiom,
% 9.49/5.25      ! [A: real] :
% 9.49/5.25        ( ( times_times_real @ A @ zero_zero_real )
% 9.49/5.25        = zero_zero_real ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1630_mult__zero__right,axiom,
% 9.49/5.25      ! [A: nat] :
% 9.49/5.25        ( ( times_times_nat @ A @ zero_zero_nat )
% 9.49/5.25        = zero_zero_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1631_mult__zero__right,axiom,
% 9.49/5.25      ! [A: int] :
% 9.49/5.25        ( ( times_times_int @ A @ zero_zero_int )
% 9.49/5.25        = zero_zero_int ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1632_mult__eq__0__iff,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ( times_times_rat @ A @ B )
% 9.49/5.25          = zero_zero_rat )
% 9.49/5.25        = ( ( A = zero_zero_rat )
% 9.49/5.25          | ( B = zero_zero_rat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1633_mult__eq__0__iff,axiom,
% 9.49/5.25      ! [A: complex,B: complex] :
% 9.49/5.25        ( ( ( times_times_complex @ A @ B )
% 9.49/5.25          = zero_zero_complex )
% 9.49/5.25        = ( ( A = zero_zero_complex )
% 9.49/5.25          | ( B = zero_zero_complex ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1634_mult__eq__0__iff,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ( times_times_real @ A @ B )
% 9.49/5.25          = zero_zero_real )
% 9.49/5.25        = ( ( A = zero_zero_real )
% 9.49/5.25          | ( B = zero_zero_real ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1635_mult__eq__0__iff,axiom,
% 9.49/5.25      ! [A: nat,B: nat] :
% 9.49/5.25        ( ( ( times_times_nat @ A @ B )
% 9.49/5.25          = zero_zero_nat )
% 9.49/5.25        = ( ( A = zero_zero_nat )
% 9.49/5.25          | ( B = zero_zero_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1636_mult__eq__0__iff,axiom,
% 9.49/5.25      ! [A: int,B: int] :
% 9.49/5.25        ( ( ( times_times_int @ A @ B )
% 9.49/5.25          = zero_zero_int )
% 9.49/5.25        = ( ( A = zero_zero_int )
% 9.49/5.25          | ( B = zero_zero_int ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1637_mult__cancel__left,axiom,
% 9.49/5.25      ! [C: rat,A: rat,B: rat] :
% 9.49/5.25        ( ( ( times_times_rat @ C @ A )
% 9.49/5.25          = ( times_times_rat @ C @ B ) )
% 9.49/5.25        = ( ( C = zero_zero_rat )
% 9.49/5.25          | ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1638_mult__cancel__left,axiom,
% 9.49/5.25      ! [C: complex,A: complex,B: complex] :
% 9.49/5.25        ( ( ( times_times_complex @ C @ A )
% 9.49/5.25          = ( times_times_complex @ C @ B ) )
% 9.49/5.25        = ( ( C = zero_zero_complex )
% 9.49/5.25          | ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1639_mult__cancel__left,axiom,
% 9.49/5.25      ! [C: real,A: real,B: real] :
% 9.49/5.25        ( ( ( times_times_real @ C @ A )
% 9.49/5.25          = ( times_times_real @ C @ B ) )
% 9.49/5.25        = ( ( C = zero_zero_real )
% 9.49/5.25          | ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1640_mult__cancel__left,axiom,
% 9.49/5.25      ! [C: nat,A: nat,B: nat] :
% 9.49/5.25        ( ( ( times_times_nat @ C @ A )
% 9.49/5.25          = ( times_times_nat @ C @ B ) )
% 9.49/5.25        = ( ( C = zero_zero_nat )
% 9.49/5.25          | ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1641_mult__cancel__left,axiom,
% 9.49/5.25      ! [C: int,A: int,B: int] :
% 9.49/5.25        ( ( ( times_times_int @ C @ A )
% 9.49/5.25          = ( times_times_int @ C @ B ) )
% 9.49/5.25        = ( ( C = zero_zero_int )
% 9.49/5.25          | ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1642_mult__cancel__right,axiom,
% 9.49/5.25      ! [A: rat,C: rat,B: rat] :
% 9.49/5.25        ( ( ( times_times_rat @ A @ C )
% 9.49/5.25          = ( times_times_rat @ B @ C ) )
% 9.49/5.25        = ( ( C = zero_zero_rat )
% 9.49/5.25          | ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1643_mult__cancel__right,axiom,
% 9.49/5.25      ! [A: complex,C: complex,B: complex] :
% 9.49/5.25        ( ( ( times_times_complex @ A @ C )
% 9.49/5.25          = ( times_times_complex @ B @ C ) )
% 9.49/5.25        = ( ( C = zero_zero_complex )
% 9.49/5.25          | ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1644_mult__cancel__right,axiom,
% 9.49/5.25      ! [A: real,C: real,B: real] :
% 9.49/5.25        ( ( ( times_times_real @ A @ C )
% 9.49/5.25          = ( times_times_real @ B @ C ) )
% 9.49/5.25        = ( ( C = zero_zero_real )
% 9.49/5.25          | ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1645_mult__cancel__right,axiom,
% 9.49/5.25      ! [A: nat,C: nat,B: nat] :
% 9.49/5.25        ( ( ( times_times_nat @ A @ C )
% 9.49/5.25          = ( times_times_nat @ B @ C ) )
% 9.49/5.25        = ( ( C = zero_zero_nat )
% 9.49/5.25          | ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1646_mult__cancel__right,axiom,
% 9.49/5.25      ! [A: int,C: int,B: int] :
% 9.49/5.25        ( ( ( times_times_int @ A @ C )
% 9.49/5.25          = ( times_times_int @ B @ C ) )
% 9.49/5.25        = ( ( C = zero_zero_int )
% 9.49/5.25          | ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1647_add__0,axiom,
% 9.49/5.25      ! [A: complex] :
% 9.49/5.25        ( ( plus_plus_complex @ zero_zero_complex @ A )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1648_add__0,axiom,
% 9.49/5.25      ! [A: real] :
% 9.49/5.25        ( ( plus_plus_real @ zero_zero_real @ A )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1649_add__0,axiom,
% 9.49/5.25      ! [A: rat] :
% 9.49/5.25        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1650_add__0,axiom,
% 9.49/5.25      ! [A: nat] :
% 9.49/5.25        ( ( plus_plus_nat @ zero_zero_nat @ A )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1651_add__0,axiom,
% 9.49/5.25      ! [A: int] :
% 9.49/5.25        ( ( plus_plus_int @ zero_zero_int @ A )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1652_zero__eq__add__iff__both__eq__0,axiom,
% 9.49/5.25      ! [X: nat,Y2: nat] :
% 9.49/5.25        ( ( zero_zero_nat
% 9.49/5.25          = ( plus_plus_nat @ X @ Y2 ) )
% 9.49/5.25        = ( ( X = zero_zero_nat )
% 9.49/5.25          & ( Y2 = zero_zero_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1653_add__eq__0__iff__both__eq__0,axiom,
% 9.49/5.25      ! [X: nat,Y2: nat] :
% 9.49/5.25        ( ( ( plus_plus_nat @ X @ Y2 )
% 9.49/5.25          = zero_zero_nat )
% 9.49/5.25        = ( ( X = zero_zero_nat )
% 9.49/5.25          & ( Y2 = zero_zero_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1654_add__cancel__right__right,axiom,
% 9.49/5.25      ! [A: complex,B: complex] :
% 9.49/5.25        ( ( A
% 9.49/5.25          = ( plus_plus_complex @ A @ B ) )
% 9.49/5.25        = ( B = zero_zero_complex ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1655_add__cancel__right__right,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( A
% 9.49/5.25          = ( plus_plus_real @ A @ B ) )
% 9.49/5.25        = ( B = zero_zero_real ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1656_add__cancel__right__right,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( A
% 9.49/5.25          = ( plus_plus_rat @ A @ B ) )
% 9.49/5.25        = ( B = zero_zero_rat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1657_add__cancel__right__right,axiom,
% 9.49/5.25      ! [A: nat,B: nat] :
% 9.49/5.25        ( ( A
% 9.49/5.25          = ( plus_plus_nat @ A @ B ) )
% 9.49/5.25        = ( B = zero_zero_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1658_add__cancel__right__right,axiom,
% 9.49/5.25      ! [A: int,B: int] :
% 9.49/5.25        ( ( A
% 9.49/5.25          = ( plus_plus_int @ A @ B ) )
% 9.49/5.25        = ( B = zero_zero_int ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1659_add__cancel__right__left,axiom,
% 9.49/5.25      ! [A: complex,B: complex] :
% 9.49/5.25        ( ( A
% 9.49/5.25          = ( plus_plus_complex @ B @ A ) )
% 9.49/5.25        = ( B = zero_zero_complex ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1660_add__cancel__right__left,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( A
% 9.49/5.25          = ( plus_plus_real @ B @ A ) )
% 9.49/5.25        = ( B = zero_zero_real ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1661_add__cancel__right__left,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( A
% 9.49/5.25          = ( plus_plus_rat @ B @ A ) )
% 9.49/5.25        = ( B = zero_zero_rat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1662_add__cancel__right__left,axiom,
% 9.49/5.25      ! [A: nat,B: nat] :
% 9.49/5.25        ( ( A
% 9.49/5.25          = ( plus_plus_nat @ B @ A ) )
% 9.49/5.25        = ( B = zero_zero_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1663_add__cancel__right__left,axiom,
% 9.49/5.25      ! [A: int,B: int] :
% 9.49/5.25        ( ( A
% 9.49/5.25          = ( plus_plus_int @ B @ A ) )
% 9.49/5.25        = ( B = zero_zero_int ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1664_add__cancel__left__right,axiom,
% 9.49/5.25      ! [A: complex,B: complex] :
% 9.49/5.25        ( ( ( plus_plus_complex @ A @ B )
% 9.49/5.25          = A )
% 9.49/5.25        = ( B = zero_zero_complex ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1665_add__cancel__left__right,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ( plus_plus_real @ A @ B )
% 9.49/5.25          = A )
% 9.49/5.25        = ( B = zero_zero_real ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1666_add__cancel__left__right,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ( plus_plus_rat @ A @ B )
% 9.49/5.25          = A )
% 9.49/5.25        = ( B = zero_zero_rat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1667_add__cancel__left__right,axiom,
% 9.49/5.25      ! [A: nat,B: nat] :
% 9.49/5.25        ( ( ( plus_plus_nat @ A @ B )
% 9.49/5.25          = A )
% 9.49/5.25        = ( B = zero_zero_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1668_add__cancel__left__right,axiom,
% 9.49/5.25      ! [A: int,B: int] :
% 9.49/5.25        ( ( ( plus_plus_int @ A @ B )
% 9.49/5.25          = A )
% 9.49/5.25        = ( B = zero_zero_int ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1669_add__cancel__left__left,axiom,
% 9.49/5.25      ! [B: complex,A: complex] :
% 9.49/5.25        ( ( ( plus_plus_complex @ B @ A )
% 9.49/5.25          = A )
% 9.49/5.25        = ( B = zero_zero_complex ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1670_add__cancel__left__left,axiom,
% 9.49/5.25      ! [B: real,A: real] :
% 9.49/5.25        ( ( ( plus_plus_real @ B @ A )
% 9.49/5.25          = A )
% 9.49/5.25        = ( B = zero_zero_real ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1671_add__cancel__left__left,axiom,
% 9.49/5.25      ! [B: rat,A: rat] :
% 9.49/5.25        ( ( ( plus_plus_rat @ B @ A )
% 9.49/5.25          = A )
% 9.49/5.25        = ( B = zero_zero_rat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1672_add__cancel__left__left,axiom,
% 9.49/5.25      ! [B: nat,A: nat] :
% 9.49/5.25        ( ( ( plus_plus_nat @ B @ A )
% 9.49/5.25          = A )
% 9.49/5.25        = ( B = zero_zero_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1673_add__cancel__left__left,axiom,
% 9.49/5.25      ! [B: int,A: int] :
% 9.49/5.25        ( ( ( plus_plus_int @ B @ A )
% 9.49/5.25          = A )
% 9.49/5.25        = ( B = zero_zero_int ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1674_double__zero__sym,axiom,
% 9.49/5.25      ! [A: real] :
% 9.49/5.25        ( ( zero_zero_real
% 9.49/5.25          = ( plus_plus_real @ A @ A ) )
% 9.49/5.25        = ( A = zero_zero_real ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1675_double__zero__sym,axiom,
% 9.49/5.25      ! [A: rat] :
% 9.49/5.25        ( ( zero_zero_rat
% 9.49/5.25          = ( plus_plus_rat @ A @ A ) )
% 9.49/5.25        = ( A = zero_zero_rat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1676_double__zero__sym,axiom,
% 9.49/5.25      ! [A: int] :
% 9.49/5.25        ( ( zero_zero_int
% 9.49/5.25          = ( plus_plus_int @ A @ A ) )
% 9.49/5.25        = ( A = zero_zero_int ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1677_add_Oright__neutral,axiom,
% 9.49/5.25      ! [A: complex] :
% 9.49/5.25        ( ( plus_plus_complex @ A @ zero_zero_complex )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1678_add_Oright__neutral,axiom,
% 9.49/5.25      ! [A: real] :
% 9.49/5.25        ( ( plus_plus_real @ A @ zero_zero_real )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1679_add_Oright__neutral,axiom,
% 9.49/5.25      ! [A: rat] :
% 9.49/5.25        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1680_add_Oright__neutral,axiom,
% 9.49/5.25      ! [A: nat] :
% 9.49/5.25        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1681_add_Oright__neutral,axiom,
% 9.49/5.25      ! [A: int] :
% 9.49/5.25        ( ( plus_plus_int @ A @ zero_zero_int )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1682_diff__self,axiom,
% 9.49/5.25      ! [A: complex] :
% 9.49/5.25        ( ( minus_minus_complex @ A @ A )
% 9.49/5.25        = zero_zero_complex ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1683_diff__self,axiom,
% 9.49/5.25      ! [A: real] :
% 9.49/5.25        ( ( minus_minus_real @ A @ A )
% 9.49/5.25        = zero_zero_real ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1684_diff__self,axiom,
% 9.49/5.25      ! [A: rat] :
% 9.49/5.25        ( ( minus_minus_rat @ A @ A )
% 9.49/5.25        = zero_zero_rat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1685_diff__self,axiom,
% 9.49/5.25      ! [A: int] :
% 9.49/5.25        ( ( minus_minus_int @ A @ A )
% 9.49/5.25        = zero_zero_int ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1686_diff__0__right,axiom,
% 9.49/5.25      ! [A: complex] :
% 9.49/5.25        ( ( minus_minus_complex @ A @ zero_zero_complex )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1687_diff__0__right,axiom,
% 9.49/5.25      ! [A: real] :
% 9.49/5.25        ( ( minus_minus_real @ A @ zero_zero_real )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1688_diff__0__right,axiom,
% 9.49/5.25      ! [A: rat] :
% 9.49/5.25        ( ( minus_minus_rat @ A @ zero_zero_rat )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1689_diff__0__right,axiom,
% 9.49/5.25      ! [A: int] :
% 9.49/5.25        ( ( minus_minus_int @ A @ zero_zero_int )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1690_zero__diff,axiom,
% 9.49/5.25      ! [A: nat] :
% 9.49/5.25        ( ( minus_minus_nat @ zero_zero_nat @ A )
% 9.49/5.25        = zero_zero_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1691_diff__zero,axiom,
% 9.49/5.25      ! [A: complex] :
% 9.49/5.25        ( ( minus_minus_complex @ A @ zero_zero_complex )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1692_diff__zero,axiom,
% 9.49/5.25      ! [A: real] :
% 9.49/5.25        ( ( minus_minus_real @ A @ zero_zero_real )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1693_diff__zero,axiom,
% 9.49/5.25      ! [A: rat] :
% 9.49/5.25        ( ( minus_minus_rat @ A @ zero_zero_rat )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1694_diff__zero,axiom,
% 9.49/5.25      ! [A: nat] :
% 9.49/5.25        ( ( minus_minus_nat @ A @ zero_zero_nat )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1695_diff__zero,axiom,
% 9.49/5.25      ! [A: int] :
% 9.49/5.25        ( ( minus_minus_int @ A @ zero_zero_int )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1696_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 9.49/5.25      ! [A: complex] :
% 9.49/5.25        ( ( minus_minus_complex @ A @ A )
% 9.49/5.25        = zero_zero_complex ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1697_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 9.49/5.25      ! [A: real] :
% 9.49/5.25        ( ( minus_minus_real @ A @ A )
% 9.49/5.25        = zero_zero_real ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1698_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 9.49/5.25      ! [A: rat] :
% 9.49/5.25        ( ( minus_minus_rat @ A @ A )
% 9.49/5.25        = zero_zero_rat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1699_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 9.49/5.25      ! [A: nat] :
% 9.49/5.25        ( ( minus_minus_nat @ A @ A )
% 9.49/5.25        = zero_zero_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1700_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 9.49/5.25      ! [A: int] :
% 9.49/5.25        ( ( minus_minus_int @ A @ A )
% 9.49/5.25        = zero_zero_int ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1701_bits__div__0,axiom,
% 9.49/5.25      ! [A: nat] :
% 9.49/5.25        ( ( divide_divide_nat @ zero_zero_nat @ A )
% 9.49/5.25        = zero_zero_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1702_bits__div__0,axiom,
% 9.49/5.25      ! [A: int] :
% 9.49/5.25        ( ( divide_divide_int @ zero_zero_int @ A )
% 9.49/5.25        = zero_zero_int ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1703_bits__div__by__0,axiom,
% 9.49/5.25      ! [A: nat] :
% 9.49/5.25        ( ( divide_divide_nat @ A @ zero_zero_nat )
% 9.49/5.25        = zero_zero_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1704_bits__div__by__0,axiom,
% 9.49/5.25      ! [A: int] :
% 9.49/5.25        ( ( divide_divide_int @ A @ zero_zero_int )
% 9.49/5.25        = zero_zero_int ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1705_div__0,axiom,
% 9.49/5.25      ! [A: complex] :
% 9.49/5.25        ( ( divide1717551699836669952omplex @ zero_zero_complex @ A )
% 9.49/5.25        = zero_zero_complex ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1706_div__0,axiom,
% 9.49/5.25      ! [A: real] :
% 9.49/5.25        ( ( divide_divide_real @ zero_zero_real @ A )
% 9.49/5.25        = zero_zero_real ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1707_div__0,axiom,
% 9.49/5.25      ! [A: rat] :
% 9.49/5.25        ( ( divide_divide_rat @ zero_zero_rat @ A )
% 9.49/5.25        = zero_zero_rat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1708_div__0,axiom,
% 9.49/5.25      ! [A: nat] :
% 9.49/5.25        ( ( divide_divide_nat @ zero_zero_nat @ A )
% 9.49/5.25        = zero_zero_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1709_div__0,axiom,
% 9.49/5.25      ! [A: int] :
% 9.49/5.25        ( ( divide_divide_int @ zero_zero_int @ A )
% 9.49/5.25        = zero_zero_int ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1710_div__by__0,axiom,
% 9.49/5.25      ! [A: complex] :
% 9.49/5.25        ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 9.49/5.25        = zero_zero_complex ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1711_div__by__0,axiom,
% 9.49/5.25      ! [A: real] :
% 9.49/5.25        ( ( divide_divide_real @ A @ zero_zero_real )
% 9.49/5.25        = zero_zero_real ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1712_div__by__0,axiom,
% 9.49/5.25      ! [A: rat] :
% 9.49/5.25        ( ( divide_divide_rat @ A @ zero_zero_rat )
% 9.49/5.25        = zero_zero_rat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1713_div__by__0,axiom,
% 9.49/5.25      ! [A: nat] :
% 9.49/5.25        ( ( divide_divide_nat @ A @ zero_zero_nat )
% 9.49/5.25        = zero_zero_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1714_div__by__0,axiom,
% 9.49/5.25      ! [A: int] :
% 9.49/5.25        ( ( divide_divide_int @ A @ zero_zero_int )
% 9.49/5.25        = zero_zero_int ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1715_divide__eq__0__iff,axiom,
% 9.49/5.25      ! [A: complex,B: complex] :
% 9.49/5.25        ( ( ( divide1717551699836669952omplex @ A @ B )
% 9.49/5.25          = zero_zero_complex )
% 9.49/5.25        = ( ( A = zero_zero_complex )
% 9.49/5.25          | ( B = zero_zero_complex ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1716_divide__eq__0__iff,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ( divide_divide_real @ A @ B )
% 9.49/5.25          = zero_zero_real )
% 9.49/5.25        = ( ( A = zero_zero_real )
% 9.49/5.25          | ( B = zero_zero_real ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1717_divide__eq__0__iff,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ( divide_divide_rat @ A @ B )
% 9.49/5.25          = zero_zero_rat )
% 9.49/5.25        = ( ( A = zero_zero_rat )
% 9.49/5.25          | ( B = zero_zero_rat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1718_divide__cancel__left,axiom,
% 9.49/5.25      ! [C: complex,A: complex,B: complex] :
% 9.49/5.25        ( ( ( divide1717551699836669952omplex @ C @ A )
% 9.49/5.25          = ( divide1717551699836669952omplex @ C @ B ) )
% 9.49/5.25        = ( ( C = zero_zero_complex )
% 9.49/5.25          | ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1719_divide__cancel__left,axiom,
% 9.49/5.25      ! [C: real,A: real,B: real] :
% 9.49/5.25        ( ( ( divide_divide_real @ C @ A )
% 9.49/5.25          = ( divide_divide_real @ C @ B ) )
% 9.49/5.25        = ( ( C = zero_zero_real )
% 9.49/5.25          | ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1720_divide__cancel__left,axiom,
% 9.49/5.25      ! [C: rat,A: rat,B: rat] :
% 9.49/5.25        ( ( ( divide_divide_rat @ C @ A )
% 9.49/5.25          = ( divide_divide_rat @ C @ B ) )
% 9.49/5.25        = ( ( C = zero_zero_rat )
% 9.49/5.25          | ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1721_divide__cancel__right,axiom,
% 9.49/5.25      ! [A: complex,C: complex,B: complex] :
% 9.49/5.25        ( ( ( divide1717551699836669952omplex @ A @ C )
% 9.49/5.25          = ( divide1717551699836669952omplex @ B @ C ) )
% 9.49/5.25        = ( ( C = zero_zero_complex )
% 9.49/5.25          | ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1722_divide__cancel__right,axiom,
% 9.49/5.25      ! [A: real,C: real,B: real] :
% 9.49/5.25        ( ( ( divide_divide_real @ A @ C )
% 9.49/5.25          = ( divide_divide_real @ B @ C ) )
% 9.49/5.25        = ( ( C = zero_zero_real )
% 9.49/5.25          | ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1723_divide__cancel__right,axiom,
% 9.49/5.25      ! [A: rat,C: rat,B: rat] :
% 9.49/5.25        ( ( ( divide_divide_rat @ A @ C )
% 9.49/5.25          = ( divide_divide_rat @ B @ C ) )
% 9.49/5.25        = ( ( C = zero_zero_rat )
% 9.49/5.25          | ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1724_division__ring__divide__zero,axiom,
% 9.49/5.25      ! [A: complex] :
% 9.49/5.25        ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 9.49/5.25        = zero_zero_complex ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1725_division__ring__divide__zero,axiom,
% 9.49/5.25      ! [A: real] :
% 9.49/5.25        ( ( divide_divide_real @ A @ zero_zero_real )
% 9.49/5.25        = zero_zero_real ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1726_division__ring__divide__zero,axiom,
% 9.49/5.25      ! [A: rat] :
% 9.49/5.25        ( ( divide_divide_rat @ A @ zero_zero_rat )
% 9.49/5.25        = zero_zero_rat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1727_bot__nat__0_Onot__eq__extremum,axiom,
% 9.49/5.25      ! [A: nat] :
% 9.49/5.25        ( ( A != zero_zero_nat )
% 9.49/5.25        = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1728_neq0__conv,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ( ( N != zero_zero_nat )
% 9.49/5.25        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1729_less__nat__zero__code,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1730_Nat_Oadd__0__right,axiom,
% 9.49/5.25      ! [M: nat] :
% 9.49/5.25        ( ( plus_plus_nat @ M @ zero_zero_nat )
% 9.49/5.25        = M ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1731_add__is__0,axiom,
% 9.49/5.25      ! [M: nat,N: nat] :
% 9.49/5.25        ( ( ( plus_plus_nat @ M @ N )
% 9.49/5.25          = zero_zero_nat )
% 9.49/5.25        = ( ( M = zero_zero_nat )
% 9.49/5.25          & ( N = zero_zero_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1732_bot__nat__0_Oextremum,axiom,
% 9.49/5.25      ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1733_le0,axiom,
% 9.49/5.25      ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1734_mult__is__0,axiom,
% 9.49/5.25      ! [M: nat,N: nat] :
% 9.49/5.25        ( ( ( times_times_nat @ M @ N )
% 9.49/5.25          = zero_zero_nat )
% 9.49/5.25        = ( ( M = zero_zero_nat )
% 9.49/5.25          | ( N = zero_zero_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1735_mult__0__right,axiom,
% 9.49/5.25      ! [M: nat] :
% 9.49/5.25        ( ( times_times_nat @ M @ zero_zero_nat )
% 9.49/5.25        = zero_zero_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1736_mult__cancel1,axiom,
% 9.49/5.25      ! [K: nat,M: nat,N: nat] :
% 9.49/5.25        ( ( ( times_times_nat @ K @ M )
% 9.49/5.25          = ( times_times_nat @ K @ N ) )
% 9.49/5.25        = ( ( M = N )
% 9.49/5.25          | ( K = zero_zero_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1737_mult__cancel2,axiom,
% 9.49/5.25      ! [M: nat,K: nat,N: nat] :
% 9.49/5.25        ( ( ( times_times_nat @ M @ K )
% 9.49/5.25          = ( times_times_nat @ N @ K ) )
% 9.49/5.25        = ( ( M = N )
% 9.49/5.25          | ( K = zero_zero_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1738_diff__self__eq__0,axiom,
% 9.49/5.25      ! [M: nat] :
% 9.49/5.25        ( ( minus_minus_nat @ M @ M )
% 9.49/5.25        = zero_zero_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1739_diff__0__eq__0,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ( ( minus_minus_nat @ zero_zero_nat @ N )
% 9.49/5.25        = zero_zero_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1740_max__0R,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ( ( ord_max_nat @ N @ zero_zero_nat )
% 9.49/5.25        = N ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1741_max__0L,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ( ( ord_max_nat @ zero_zero_nat @ N )
% 9.49/5.25        = N ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1742_max__nat_Oright__neutral,axiom,
% 9.49/5.25      ! [A: nat] :
% 9.49/5.25        ( ( ord_max_nat @ A @ zero_zero_nat )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1743_max__nat_Oneutr__eq__iff,axiom,
% 9.49/5.25      ! [A: nat,B: nat] :
% 9.49/5.25        ( ( zero_zero_nat
% 9.49/5.25          = ( ord_max_nat @ A @ B ) )
% 9.49/5.25        = ( ( A = zero_zero_nat )
% 9.49/5.25          & ( B = zero_zero_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1744_max__nat_Oleft__neutral,axiom,
% 9.49/5.25      ! [A: nat] :
% 9.49/5.25        ( ( ord_max_nat @ zero_zero_nat @ A )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1745_max__nat_Oeq__neutr__iff,axiom,
% 9.49/5.25      ! [A: nat,B: nat] :
% 9.49/5.25        ( ( ( ord_max_nat @ A @ B )
% 9.49/5.25          = zero_zero_nat )
% 9.49/5.25        = ( ( A = zero_zero_nat )
% 9.49/5.25          & ( B = zero_zero_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1746_add__le__same__cancel1,axiom,
% 9.49/5.25      ! [B: real,A: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B )
% 9.49/5.25        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1747_add__le__same__cancel1,axiom,
% 9.49/5.25      ! [B: rat,A: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 9.49/5.25        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1748_add__le__same__cancel1,axiom,
% 9.49/5.25      ! [B: nat,A: nat] :
% 9.49/5.25        ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 9.49/5.25        = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1749_add__le__same__cancel1,axiom,
% 9.49/5.25      ! [B: int,A: int] :
% 9.49/5.25        ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 9.49/5.25        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1750_add__le__same__cancel2,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
% 9.49/5.25        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1751_add__le__same__cancel2,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 9.49/5.25        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1752_add__le__same__cancel2,axiom,
% 9.49/5.25      ! [A: nat,B: nat] :
% 9.49/5.25        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 9.49/5.25        = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1753_add__le__same__cancel2,axiom,
% 9.49/5.25      ! [A: int,B: int] :
% 9.49/5.25        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 9.49/5.25        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1754_le__add__same__cancel1,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
% 9.49/5.25        = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1755_le__add__same__cancel1,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 9.49/5.25        = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1756_le__add__same__cancel1,axiom,
% 9.49/5.25      ! [A: nat,B: nat] :
% 9.49/5.25        ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 9.49/5.25        = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1757_le__add__same__cancel1,axiom,
% 9.49/5.25      ! [A: int,B: int] :
% 9.49/5.25        ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 9.49/5.25        = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1758_le__add__same__cancel2,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
% 9.49/5.25        = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1759_le__add__same__cancel2,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 9.49/5.25        = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1760_le__add__same__cancel2,axiom,
% 9.49/5.25      ! [A: nat,B: nat] :
% 9.49/5.25        ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 9.49/5.25        = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1761_le__add__same__cancel2,axiom,
% 9.49/5.25      ! [A: int,B: int] :
% 9.49/5.25        ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 9.49/5.25        = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1762_double__add__le__zero__iff__single__add__le__zero,axiom,
% 9.49/5.25      ! [A: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 9.49/5.25        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1763_double__add__le__zero__iff__single__add__le__zero,axiom,
% 9.49/5.25      ! [A: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 9.49/5.25        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1764_double__add__le__zero__iff__single__add__le__zero,axiom,
% 9.49/5.25      ! [A: int] :
% 9.49/5.25        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 9.49/5.25        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1765_zero__le__double__add__iff__zero__le__single__add,axiom,
% 9.49/5.25      ! [A: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 9.49/5.25        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1766_zero__le__double__add__iff__zero__le__single__add,axiom,
% 9.49/5.25      ! [A: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 9.49/5.25        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1767_zero__le__double__add__iff__zero__le__single__add,axiom,
% 9.49/5.25      ! [A: int] :
% 9.49/5.25        ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 9.49/5.25        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1768_zero__less__double__add__iff__zero__less__single__add,axiom,
% 9.49/5.25      ! [A: real] :
% 9.49/5.25        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 9.49/5.25        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1769_zero__less__double__add__iff__zero__less__single__add,axiom,
% 9.49/5.25      ! [A: rat] :
% 9.49/5.25        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 9.49/5.25        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1770_zero__less__double__add__iff__zero__less__single__add,axiom,
% 9.49/5.25      ! [A: int] :
% 9.49/5.25        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 9.49/5.25        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1771_double__add__less__zero__iff__single__add__less__zero,axiom,
% 9.49/5.25      ! [A: real] :
% 9.49/5.25        ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 9.49/5.25        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1772_double__add__less__zero__iff__single__add__less__zero,axiom,
% 9.49/5.25      ! [A: rat] :
% 9.49/5.25        ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 9.49/5.25        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1773_double__add__less__zero__iff__single__add__less__zero,axiom,
% 9.49/5.25      ! [A: int] :
% 9.49/5.25        ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 9.49/5.25        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1774_less__add__same__cancel2,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 9.49/5.25        = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1775_less__add__same__cancel2,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 9.49/5.25        = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1776_less__add__same__cancel2,axiom,
% 9.49/5.25      ! [A: nat,B: nat] :
% 9.49/5.25        ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 9.49/5.25        = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1777_less__add__same__cancel2,axiom,
% 9.49/5.25      ! [A: int,B: int] :
% 9.49/5.25        ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 9.49/5.25        = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1778_less__add__same__cancel1,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 9.49/5.25        = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1779_less__add__same__cancel1,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 9.49/5.25        = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1780_less__add__same__cancel1,axiom,
% 9.49/5.25      ! [A: nat,B: nat] :
% 9.49/5.25        ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 9.49/5.25        = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1781_less__add__same__cancel1,axiom,
% 9.49/5.25      ! [A: int,B: int] :
% 9.49/5.25        ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 9.49/5.25        = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1782_add__less__same__cancel2,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 9.49/5.25        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1783_add__less__same__cancel2,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 9.49/5.25        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1784_add__less__same__cancel2,axiom,
% 9.49/5.25      ! [A: nat,B: nat] :
% 9.49/5.25        ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 9.49/5.25        = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1785_add__less__same__cancel2,axiom,
% 9.49/5.25      ! [A: int,B: int] :
% 9.49/5.25        ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 9.49/5.25        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1786_add__less__same__cancel1,axiom,
% 9.49/5.25      ! [B: real,A: real] :
% 9.49/5.25        ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 9.49/5.25        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1787_add__less__same__cancel1,axiom,
% 9.49/5.25      ! [B: rat,A: rat] :
% 9.49/5.25        ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 9.49/5.25        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1788_add__less__same__cancel1,axiom,
% 9.49/5.25      ! [B: nat,A: nat] :
% 9.49/5.25        ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 9.49/5.25        = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1789_add__less__same__cancel1,axiom,
% 9.49/5.25      ! [B: int,A: int] :
% 9.49/5.25        ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 9.49/5.25        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1790_diff__ge__0__iff__ge,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 9.49/5.25        = ( ord_less_eq_real @ B @ A ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1791_diff__ge__0__iff__ge,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 9.49/5.25        = ( ord_less_eq_rat @ B @ A ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1792_diff__ge__0__iff__ge,axiom,
% 9.49/5.25      ! [A: int,B: int] :
% 9.49/5.25        ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 9.49/5.25        = ( ord_less_eq_int @ B @ A ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1793_diff__gt__0__iff__gt,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 9.49/5.25        = ( ord_less_real @ B @ A ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1794_diff__gt__0__iff__gt,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 9.49/5.25        = ( ord_less_rat @ B @ A ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1795_diff__gt__0__iff__gt,axiom,
% 9.49/5.25      ! [A: int,B: int] :
% 9.49/5.25        ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 9.49/5.25        = ( ord_less_int @ B @ A ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1796_mult__cancel__right2,axiom,
% 9.49/5.25      ! [A: rat,C: rat] :
% 9.49/5.25        ( ( ( times_times_rat @ A @ C )
% 9.49/5.25          = C )
% 9.49/5.25        = ( ( C = zero_zero_rat )
% 9.49/5.25          | ( A = one_one_rat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1797_mult__cancel__right2,axiom,
% 9.49/5.25      ! [A: complex,C: complex] :
% 9.49/5.25        ( ( ( times_times_complex @ A @ C )
% 9.49/5.25          = C )
% 9.49/5.25        = ( ( C = zero_zero_complex )
% 9.49/5.25          | ( A = one_one_complex ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1798_mult__cancel__right2,axiom,
% 9.49/5.25      ! [A: real,C: real] :
% 9.49/5.25        ( ( ( times_times_real @ A @ C )
% 9.49/5.25          = C )
% 9.49/5.25        = ( ( C = zero_zero_real )
% 9.49/5.25          | ( A = one_one_real ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1799_mult__cancel__right2,axiom,
% 9.49/5.25      ! [A: int,C: int] :
% 9.49/5.25        ( ( ( times_times_int @ A @ C )
% 9.49/5.25          = C )
% 9.49/5.25        = ( ( C = zero_zero_int )
% 9.49/5.25          | ( A = one_one_int ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1800_mult__cancel__right1,axiom,
% 9.49/5.25      ! [C: rat,B: rat] :
% 9.49/5.25        ( ( C
% 9.49/5.25          = ( times_times_rat @ B @ C ) )
% 9.49/5.25        = ( ( C = zero_zero_rat )
% 9.49/5.25          | ( B = one_one_rat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1801_mult__cancel__right1,axiom,
% 9.49/5.25      ! [C: complex,B: complex] :
% 9.49/5.25        ( ( C
% 9.49/5.25          = ( times_times_complex @ B @ C ) )
% 9.49/5.25        = ( ( C = zero_zero_complex )
% 9.49/5.25          | ( B = one_one_complex ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1802_mult__cancel__right1,axiom,
% 9.49/5.25      ! [C: real,B: real] :
% 9.49/5.25        ( ( C
% 9.49/5.25          = ( times_times_real @ B @ C ) )
% 9.49/5.25        = ( ( C = zero_zero_real )
% 9.49/5.25          | ( B = one_one_real ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1803_mult__cancel__right1,axiom,
% 9.49/5.25      ! [C: int,B: int] :
% 9.49/5.25        ( ( C
% 9.49/5.25          = ( times_times_int @ B @ C ) )
% 9.49/5.25        = ( ( C = zero_zero_int )
% 9.49/5.25          | ( B = one_one_int ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1804_mult__cancel__left2,axiom,
% 9.49/5.25      ! [C: rat,A: rat] :
% 9.49/5.25        ( ( ( times_times_rat @ C @ A )
% 9.49/5.25          = C )
% 9.49/5.25        = ( ( C = zero_zero_rat )
% 9.49/5.25          | ( A = one_one_rat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1805_mult__cancel__left2,axiom,
% 9.49/5.25      ! [C: complex,A: complex] :
% 9.49/5.25        ( ( ( times_times_complex @ C @ A )
% 9.49/5.25          = C )
% 9.49/5.25        = ( ( C = zero_zero_complex )
% 9.49/5.25          | ( A = one_one_complex ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1806_mult__cancel__left2,axiom,
% 9.49/5.25      ! [C: real,A: real] :
% 9.49/5.25        ( ( ( times_times_real @ C @ A )
% 9.49/5.25          = C )
% 9.49/5.25        = ( ( C = zero_zero_real )
% 9.49/5.25          | ( A = one_one_real ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1807_mult__cancel__left2,axiom,
% 9.49/5.25      ! [C: int,A: int] :
% 9.49/5.25        ( ( ( times_times_int @ C @ A )
% 9.49/5.25          = C )
% 9.49/5.25        = ( ( C = zero_zero_int )
% 9.49/5.25          | ( A = one_one_int ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1808_mult__cancel__left1,axiom,
% 9.49/5.25      ! [C: rat,B: rat] :
% 9.49/5.25        ( ( C
% 9.49/5.25          = ( times_times_rat @ C @ B ) )
% 9.49/5.25        = ( ( C = zero_zero_rat )
% 9.49/5.25          | ( B = one_one_rat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1809_mult__cancel__left1,axiom,
% 9.49/5.25      ! [C: complex,B: complex] :
% 9.49/5.25        ( ( C
% 9.49/5.25          = ( times_times_complex @ C @ B ) )
% 9.49/5.25        = ( ( C = zero_zero_complex )
% 9.49/5.25          | ( B = one_one_complex ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1810_mult__cancel__left1,axiom,
% 9.49/5.25      ! [C: real,B: real] :
% 9.49/5.25        ( ( C
% 9.49/5.25          = ( times_times_real @ C @ B ) )
% 9.49/5.25        = ( ( C = zero_zero_real )
% 9.49/5.25          | ( B = one_one_real ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1811_mult__cancel__left1,axiom,
% 9.49/5.25      ! [C: int,B: int] :
% 9.49/5.25        ( ( C
% 9.49/5.25          = ( times_times_int @ C @ B ) )
% 9.49/5.25        = ( ( C = zero_zero_int )
% 9.49/5.25          | ( B = one_one_int ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1812_sum__squares__eq__zero__iff,axiom,
% 9.49/5.25      ! [X: rat,Y2: rat] :
% 9.49/5.25        ( ( ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y2 @ Y2 ) )
% 9.49/5.25          = zero_zero_rat )
% 9.49/5.25        = ( ( X = zero_zero_rat )
% 9.49/5.25          & ( Y2 = zero_zero_rat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1813_sum__squares__eq__zero__iff,axiom,
% 9.49/5.25      ! [X: real,Y2: real] :
% 9.49/5.25        ( ( ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y2 @ Y2 ) )
% 9.49/5.25          = zero_zero_real )
% 9.49/5.25        = ( ( X = zero_zero_real )
% 9.49/5.25          & ( Y2 = zero_zero_real ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1814_sum__squares__eq__zero__iff,axiom,
% 9.49/5.25      ! [X: int,Y2: int] :
% 9.49/5.25        ( ( ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y2 @ Y2 ) )
% 9.49/5.25          = zero_zero_int )
% 9.49/5.25        = ( ( X = zero_zero_int )
% 9.49/5.25          & ( Y2 = zero_zero_int ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1815_diff__numeral__special_I9_J,axiom,
% 9.49/5.25      ( ( minus_minus_complex @ one_one_complex @ one_one_complex )
% 9.49/5.25      = zero_zero_complex ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1816_diff__numeral__special_I9_J,axiom,
% 9.49/5.25      ( ( minus_minus_real @ one_one_real @ one_one_real )
% 9.49/5.25      = zero_zero_real ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1817_diff__numeral__special_I9_J,axiom,
% 9.49/5.25      ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 9.49/5.25      = zero_zero_rat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1818_diff__numeral__special_I9_J,axiom,
% 9.49/5.25      ( ( minus_minus_int @ one_one_int @ one_one_int )
% 9.49/5.25      = zero_zero_int ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1819_div__mult__mult1,axiom,
% 9.49/5.25      ! [C: nat,A: nat,B: nat] :
% 9.49/5.25        ( ( C != zero_zero_nat )
% 9.49/5.25       => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 9.49/5.25          = ( divide_divide_nat @ A @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1820_div__mult__mult1,axiom,
% 9.49/5.25      ! [C: int,A: int,B: int] :
% 9.49/5.25        ( ( C != zero_zero_int )
% 9.49/5.25       => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 9.49/5.25          = ( divide_divide_int @ A @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1821_div__mult__mult2,axiom,
% 9.49/5.25      ! [C: nat,A: nat,B: nat] :
% 9.49/5.25        ( ( C != zero_zero_nat )
% 9.49/5.25       => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 9.49/5.25          = ( divide_divide_nat @ A @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1822_div__mult__mult2,axiom,
% 9.49/5.25      ! [C: int,A: int,B: int] :
% 9.49/5.25        ( ( C != zero_zero_int )
% 9.49/5.25       => ( ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 9.49/5.25          = ( divide_divide_int @ A @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1823_div__mult__mult1__if,axiom,
% 9.49/5.25      ! [C: nat,A: nat,B: nat] :
% 9.49/5.25        ( ( ( C = zero_zero_nat )
% 9.49/5.25         => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 9.49/5.25            = zero_zero_nat ) )
% 9.49/5.25        & ( ( C != zero_zero_nat )
% 9.49/5.25         => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 9.49/5.25            = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1824_div__mult__mult1__if,axiom,
% 9.49/5.25      ! [C: int,A: int,B: int] :
% 9.49/5.25        ( ( ( C = zero_zero_int )
% 9.49/5.25         => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 9.49/5.25            = zero_zero_int ) )
% 9.49/5.25        & ( ( C != zero_zero_int )
% 9.49/5.25         => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 9.49/5.25            = ( divide_divide_int @ A @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1825_nonzero__mult__div__cancel__left,axiom,
% 9.49/5.25      ! [A: complex,B: complex] :
% 9.49/5.25        ( ( A != zero_zero_complex )
% 9.49/5.25       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ A )
% 9.49/5.25          = B ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1826_nonzero__mult__div__cancel__left,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( A != zero_zero_real )
% 9.49/5.25       => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ A )
% 9.49/5.25          = B ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1827_nonzero__mult__div__cancel__left,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( A != zero_zero_rat )
% 9.49/5.25       => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ A )
% 9.49/5.25          = B ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1828_nonzero__mult__div__cancel__left,axiom,
% 9.49/5.25      ! [A: nat,B: nat] :
% 9.49/5.25        ( ( A != zero_zero_nat )
% 9.49/5.25       => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 9.49/5.25          = B ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1829_nonzero__mult__div__cancel__left,axiom,
% 9.49/5.25      ! [A: int,B: int] :
% 9.49/5.25        ( ( A != zero_zero_int )
% 9.49/5.25       => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 9.49/5.25          = B ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1830_nonzero__mult__div__cancel__right,axiom,
% 9.49/5.25      ! [B: complex,A: complex] :
% 9.49/5.25        ( ( B != zero_zero_complex )
% 9.49/5.25       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ B )
% 9.49/5.25          = A ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1831_nonzero__mult__div__cancel__right,axiom,
% 9.49/5.25      ! [B: real,A: real] :
% 9.49/5.25        ( ( B != zero_zero_real )
% 9.49/5.25       => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ B )
% 9.49/5.25          = A ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1832_nonzero__mult__div__cancel__right,axiom,
% 9.49/5.25      ! [B: rat,A: rat] :
% 9.49/5.25        ( ( B != zero_zero_rat )
% 9.49/5.25       => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ B )
% 9.49/5.25          = A ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1833_nonzero__mult__div__cancel__right,axiom,
% 9.49/5.25      ! [B: nat,A: nat] :
% 9.49/5.25        ( ( B != zero_zero_nat )
% 9.49/5.25       => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 9.49/5.25          = A ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1834_nonzero__mult__div__cancel__right,axiom,
% 9.49/5.25      ! [B: int,A: int] :
% 9.49/5.25        ( ( B != zero_zero_int )
% 9.49/5.25       => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 9.49/5.25          = A ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1835_mult__divide__mult__cancel__left__if,axiom,
% 9.49/5.25      ! [C: complex,A: complex,B: complex] :
% 9.49/5.25        ( ( ( C = zero_zero_complex )
% 9.49/5.25         => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 9.49/5.25            = zero_zero_complex ) )
% 9.49/5.25        & ( ( C != zero_zero_complex )
% 9.49/5.25         => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 9.49/5.25            = ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1836_mult__divide__mult__cancel__left__if,axiom,
% 9.49/5.25      ! [C: real,A: real,B: real] :
% 9.49/5.25        ( ( ( C = zero_zero_real )
% 9.49/5.25         => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 9.49/5.25            = zero_zero_real ) )
% 9.49/5.25        & ( ( C != zero_zero_real )
% 9.49/5.25         => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 9.49/5.25            = ( divide_divide_real @ A @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1837_mult__divide__mult__cancel__left__if,axiom,
% 9.49/5.25      ! [C: rat,A: rat,B: rat] :
% 9.49/5.25        ( ( ( C = zero_zero_rat )
% 9.49/5.25         => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 9.49/5.25            = zero_zero_rat ) )
% 9.49/5.25        & ( ( C != zero_zero_rat )
% 9.49/5.25         => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 9.49/5.25            = ( divide_divide_rat @ A @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1838_nonzero__mult__divide__mult__cancel__left,axiom,
% 9.49/5.25      ! [C: complex,A: complex,B: complex] :
% 9.49/5.25        ( ( C != zero_zero_complex )
% 9.49/5.25       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 9.49/5.25          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1839_nonzero__mult__divide__mult__cancel__left,axiom,
% 9.49/5.25      ! [C: real,A: real,B: real] :
% 9.49/5.25        ( ( C != zero_zero_real )
% 9.49/5.25       => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 9.49/5.25          = ( divide_divide_real @ A @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1840_nonzero__mult__divide__mult__cancel__left,axiom,
% 9.49/5.25      ! [C: rat,A: rat,B: rat] :
% 9.49/5.25        ( ( C != zero_zero_rat )
% 9.49/5.25       => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 9.49/5.25          = ( divide_divide_rat @ A @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1841_nonzero__mult__divide__mult__cancel__left2,axiom,
% 9.49/5.25      ! [C: complex,A: complex,B: complex] :
% 9.49/5.25        ( ( C != zero_zero_complex )
% 9.49/5.25       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ B @ C ) )
% 9.49/5.25          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1842_nonzero__mult__divide__mult__cancel__left2,axiom,
% 9.49/5.25      ! [C: real,A: real,B: real] :
% 9.49/5.25        ( ( C != zero_zero_real )
% 9.49/5.25       => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ B @ C ) )
% 9.49/5.25          = ( divide_divide_real @ A @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1843_nonzero__mult__divide__mult__cancel__left2,axiom,
% 9.49/5.25      ! [C: rat,A: rat,B: rat] :
% 9.49/5.25        ( ( C != zero_zero_rat )
% 9.49/5.25       => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ B @ C ) )
% 9.49/5.25          = ( divide_divide_rat @ A @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1844_nonzero__mult__divide__mult__cancel__right,axiom,
% 9.49/5.25      ! [C: complex,A: complex,B: complex] :
% 9.49/5.25        ( ( C != zero_zero_complex )
% 9.49/5.25       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 9.49/5.25          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1845_nonzero__mult__divide__mult__cancel__right,axiom,
% 9.49/5.25      ! [C: real,A: real,B: real] :
% 9.49/5.25        ( ( C != zero_zero_real )
% 9.49/5.25       => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 9.49/5.25          = ( divide_divide_real @ A @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1846_nonzero__mult__divide__mult__cancel__right,axiom,
% 9.49/5.25      ! [C: rat,A: rat,B: rat] :
% 9.49/5.25        ( ( C != zero_zero_rat )
% 9.49/5.25       => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 9.49/5.25          = ( divide_divide_rat @ A @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1847_nonzero__mult__divide__mult__cancel__right2,axiom,
% 9.49/5.25      ! [C: complex,A: complex,B: complex] :
% 9.49/5.25        ( ( C != zero_zero_complex )
% 9.49/5.25       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ C @ B ) )
% 9.49/5.25          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1848_nonzero__mult__divide__mult__cancel__right2,axiom,
% 9.49/5.25      ! [C: real,A: real,B: real] :
% 9.49/5.25        ( ( C != zero_zero_real )
% 9.49/5.25       => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ C @ B ) )
% 9.49/5.25          = ( divide_divide_real @ A @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1849_nonzero__mult__divide__mult__cancel__right2,axiom,
% 9.49/5.25      ! [C: rat,A: rat,B: rat] :
% 9.49/5.25        ( ( C != zero_zero_rat )
% 9.49/5.25       => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ C @ B ) )
% 9.49/5.25          = ( divide_divide_rat @ A @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1850_diff__add__zero,axiom,
% 9.49/5.25      ! [A: nat,B: nat] :
% 9.49/5.25        ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 9.49/5.25        = zero_zero_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1851_div__self,axiom,
% 9.49/5.25      ! [A: complex] :
% 9.49/5.25        ( ( A != zero_zero_complex )
% 9.49/5.25       => ( ( divide1717551699836669952omplex @ A @ A )
% 9.49/5.25          = one_one_complex ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1852_div__self,axiom,
% 9.49/5.25      ! [A: real] :
% 9.49/5.25        ( ( A != zero_zero_real )
% 9.49/5.25       => ( ( divide_divide_real @ A @ A )
% 9.49/5.25          = one_one_real ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1853_div__self,axiom,
% 9.49/5.25      ! [A: rat] :
% 9.49/5.25        ( ( A != zero_zero_rat )
% 9.49/5.25       => ( ( divide_divide_rat @ A @ A )
% 9.49/5.25          = one_one_rat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1854_div__self,axiom,
% 9.49/5.25      ! [A: nat] :
% 9.49/5.25        ( ( A != zero_zero_nat )
% 9.49/5.25       => ( ( divide_divide_nat @ A @ A )
% 9.49/5.25          = one_one_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1855_div__self,axiom,
% 9.49/5.25      ! [A: int] :
% 9.49/5.25        ( ( A != zero_zero_int )
% 9.49/5.25       => ( ( divide_divide_int @ A @ A )
% 9.49/5.25          = one_one_int ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1856_zero__eq__1__divide__iff,axiom,
% 9.49/5.25      ! [A: real] :
% 9.49/5.25        ( ( zero_zero_real
% 9.49/5.25          = ( divide_divide_real @ one_one_real @ A ) )
% 9.49/5.25        = ( A = zero_zero_real ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1857_zero__eq__1__divide__iff,axiom,
% 9.49/5.25      ! [A: rat] :
% 9.49/5.25        ( ( zero_zero_rat
% 9.49/5.25          = ( divide_divide_rat @ one_one_rat @ A ) )
% 9.49/5.25        = ( A = zero_zero_rat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1858_one__divide__eq__0__iff,axiom,
% 9.49/5.25      ! [A: real] :
% 9.49/5.25        ( ( ( divide_divide_real @ one_one_real @ A )
% 9.49/5.25          = zero_zero_real )
% 9.49/5.25        = ( A = zero_zero_real ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1859_one__divide__eq__0__iff,axiom,
% 9.49/5.25      ! [A: rat] :
% 9.49/5.25        ( ( ( divide_divide_rat @ one_one_rat @ A )
% 9.49/5.25          = zero_zero_rat )
% 9.49/5.25        = ( A = zero_zero_rat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1860_eq__divide__eq__1,axiom,
% 9.49/5.25      ! [B: real,A: real] :
% 9.49/5.25        ( ( one_one_real
% 9.49/5.25          = ( divide_divide_real @ B @ A ) )
% 9.49/5.25        = ( ( A != zero_zero_real )
% 9.49/5.25          & ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1861_eq__divide__eq__1,axiom,
% 9.49/5.25      ! [B: rat,A: rat] :
% 9.49/5.25        ( ( one_one_rat
% 9.49/5.25          = ( divide_divide_rat @ B @ A ) )
% 9.49/5.25        = ( ( A != zero_zero_rat )
% 9.49/5.25          & ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1862_divide__eq__eq__1,axiom,
% 9.49/5.25      ! [B: real,A: real] :
% 9.49/5.25        ( ( ( divide_divide_real @ B @ A )
% 9.49/5.25          = one_one_real )
% 9.49/5.25        = ( ( A != zero_zero_real )
% 9.49/5.25          & ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1863_divide__eq__eq__1,axiom,
% 9.49/5.25      ! [B: rat,A: rat] :
% 9.49/5.25        ( ( ( divide_divide_rat @ B @ A )
% 9.49/5.25          = one_one_rat )
% 9.49/5.25        = ( ( A != zero_zero_rat )
% 9.49/5.25          & ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1864_divide__self__if,axiom,
% 9.49/5.25      ! [A: complex] :
% 9.49/5.25        ( ( ( A = zero_zero_complex )
% 9.49/5.25         => ( ( divide1717551699836669952omplex @ A @ A )
% 9.49/5.25            = zero_zero_complex ) )
% 9.49/5.25        & ( ( A != zero_zero_complex )
% 9.49/5.25         => ( ( divide1717551699836669952omplex @ A @ A )
% 9.49/5.25            = one_one_complex ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1865_divide__self__if,axiom,
% 9.49/5.25      ! [A: real] :
% 9.49/5.25        ( ( ( A = zero_zero_real )
% 9.49/5.25         => ( ( divide_divide_real @ A @ A )
% 9.49/5.25            = zero_zero_real ) )
% 9.49/5.25        & ( ( A != zero_zero_real )
% 9.49/5.25         => ( ( divide_divide_real @ A @ A )
% 9.49/5.25            = one_one_real ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1866_divide__self__if,axiom,
% 9.49/5.25      ! [A: rat] :
% 9.49/5.25        ( ( ( A = zero_zero_rat )
% 9.49/5.25         => ( ( divide_divide_rat @ A @ A )
% 9.49/5.25            = zero_zero_rat ) )
% 9.49/5.25        & ( ( A != zero_zero_rat )
% 9.49/5.25         => ( ( divide_divide_rat @ A @ A )
% 9.49/5.25            = one_one_rat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1867_divide__self,axiom,
% 9.49/5.25      ! [A: complex] :
% 9.49/5.25        ( ( A != zero_zero_complex )
% 9.49/5.25       => ( ( divide1717551699836669952omplex @ A @ A )
% 9.49/5.25          = one_one_complex ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1868_divide__self,axiom,
% 9.49/5.25      ! [A: real] :
% 9.49/5.25        ( ( A != zero_zero_real )
% 9.49/5.25       => ( ( divide_divide_real @ A @ A )
% 9.49/5.25          = one_one_real ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1869_divide__self,axiom,
% 9.49/5.25      ! [A: rat] :
% 9.49/5.25        ( ( A != zero_zero_rat )
% 9.49/5.25       => ( ( divide_divide_rat @ A @ A )
% 9.49/5.25          = one_one_rat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1870_one__eq__divide__iff,axiom,
% 9.49/5.25      ! [A: complex,B: complex] :
% 9.49/5.25        ( ( one_one_complex
% 9.49/5.25          = ( divide1717551699836669952omplex @ A @ B ) )
% 9.49/5.25        = ( ( B != zero_zero_complex )
% 9.49/5.25          & ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1871_one__eq__divide__iff,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( one_one_real
% 9.49/5.25          = ( divide_divide_real @ A @ B ) )
% 9.49/5.25        = ( ( B != zero_zero_real )
% 9.49/5.25          & ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1872_one__eq__divide__iff,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( one_one_rat
% 9.49/5.25          = ( divide_divide_rat @ A @ B ) )
% 9.49/5.25        = ( ( B != zero_zero_rat )
% 9.49/5.25          & ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1873_divide__eq__1__iff,axiom,
% 9.49/5.25      ! [A: complex,B: complex] :
% 9.49/5.25        ( ( ( divide1717551699836669952omplex @ A @ B )
% 9.49/5.25          = one_one_complex )
% 9.49/5.25        = ( ( B != zero_zero_complex )
% 9.49/5.25          & ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1874_divide__eq__1__iff,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ( divide_divide_real @ A @ B )
% 9.49/5.25          = one_one_real )
% 9.49/5.25        = ( ( B != zero_zero_real )
% 9.49/5.25          & ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1875_divide__eq__1__iff,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ( divide_divide_rat @ A @ B )
% 9.49/5.25          = one_one_rat )
% 9.49/5.25        = ( ( B != zero_zero_rat )
% 9.49/5.25          & ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1876_power__0__Suc,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ( ( power_power_rat @ zero_zero_rat @ ( suc @ N ) )
% 9.49/5.25        = zero_zero_rat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1877_power__0__Suc,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ( ( power_power_nat @ zero_zero_nat @ ( suc @ N ) )
% 9.49/5.25        = zero_zero_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1878_power__0__Suc,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ( ( power_power_real @ zero_zero_real @ ( suc @ N ) )
% 9.49/5.25        = zero_zero_real ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1879_power__0__Suc,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ( ( power_power_int @ zero_zero_int @ ( suc @ N ) )
% 9.49/5.25        = zero_zero_int ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1880_power__0__Suc,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ( ( power_power_complex @ zero_zero_complex @ ( suc @ N ) )
% 9.49/5.25        = zero_zero_complex ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1881_power__zero__numeral,axiom,
% 9.49/5.25      ! [K: num] :
% 9.49/5.25        ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ K ) )
% 9.49/5.25        = zero_zero_rat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1882_power__zero__numeral,axiom,
% 9.49/5.25      ! [K: num] :
% 9.49/5.25        ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K ) )
% 9.49/5.25        = zero_zero_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1883_power__zero__numeral,axiom,
% 9.49/5.25      ! [K: num] :
% 9.49/5.25        ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ K ) )
% 9.49/5.25        = zero_zero_real ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1884_power__zero__numeral,axiom,
% 9.49/5.25      ! [K: num] :
% 9.49/5.25        ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ K ) )
% 9.49/5.25        = zero_zero_int ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1885_power__zero__numeral,axiom,
% 9.49/5.25      ! [K: num] :
% 9.49/5.25        ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ K ) )
% 9.49/5.25        = zero_zero_complex ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1886_power__Suc0__right,axiom,
% 9.49/5.25      ! [A: nat] :
% 9.49/5.25        ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1887_power__Suc0__right,axiom,
% 9.49/5.25      ! [A: real] :
% 9.49/5.25        ( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1888_power__Suc0__right,axiom,
% 9.49/5.25      ! [A: int] :
% 9.49/5.25        ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1889_power__Suc0__right,axiom,
% 9.49/5.25      ! [A: complex] :
% 9.49/5.25        ( ( power_power_complex @ A @ ( suc @ zero_zero_nat ) )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1890_less__Suc0,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 9.49/5.25        = ( N = zero_zero_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1891_zero__less__Suc,axiom,
% 9.49/5.25      ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1892_add__gr__0,axiom,
% 9.49/5.25      ! [M: nat,N: nat] :
% 9.49/5.25        ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
% 9.49/5.25        = ( ( ord_less_nat @ zero_zero_nat @ M )
% 9.49/5.25          | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1893_max__0__1_I4_J,axiom,
% 9.49/5.25      ! [X: num] :
% 9.49/5.25        ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X ) @ zero_z5237406670263579293d_enat )
% 9.49/5.25        = ( numera1916890842035813515d_enat @ X ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1894_max__0__1_I4_J,axiom,
% 9.49/5.25      ! [X: num] :
% 9.49/5.25        ( ( ord_max_real @ ( numeral_numeral_real @ X ) @ zero_zero_real )
% 9.49/5.25        = ( numeral_numeral_real @ X ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1895_max__0__1_I4_J,axiom,
% 9.49/5.25      ! [X: num] :
% 9.49/5.25        ( ( ord_max_rat @ ( numeral_numeral_rat @ X ) @ zero_zero_rat )
% 9.49/5.25        = ( numeral_numeral_rat @ X ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1896_max__0__1_I4_J,axiom,
% 9.49/5.25      ! [X: num] :
% 9.49/5.25        ( ( ord_max_nat @ ( numeral_numeral_nat @ X ) @ zero_zero_nat )
% 9.49/5.25        = ( numeral_numeral_nat @ X ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1897_max__0__1_I4_J,axiom,
% 9.49/5.25      ! [X: num] :
% 9.49/5.25        ( ( ord_max_int @ ( numeral_numeral_int @ X ) @ zero_zero_int )
% 9.49/5.25        = ( numeral_numeral_int @ X ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1898_max__0__1_I3_J,axiom,
% 9.49/5.25      ! [X: num] :
% 9.49/5.25        ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 9.49/5.25        = ( numera1916890842035813515d_enat @ X ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1899_max__0__1_I3_J,axiom,
% 9.49/5.25      ! [X: num] :
% 9.49/5.25        ( ( ord_max_real @ zero_zero_real @ ( numeral_numeral_real @ X ) )
% 9.49/5.25        = ( numeral_numeral_real @ X ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1900_max__0__1_I3_J,axiom,
% 9.49/5.25      ! [X: num] :
% 9.49/5.25        ( ( ord_max_rat @ zero_zero_rat @ ( numeral_numeral_rat @ X ) )
% 9.49/5.25        = ( numeral_numeral_rat @ X ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1901_max__0__1_I3_J,axiom,
% 9.49/5.25      ! [X: num] :
% 9.49/5.25        ( ( ord_max_nat @ zero_zero_nat @ ( numeral_numeral_nat @ X ) )
% 9.49/5.25        = ( numeral_numeral_nat @ X ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1902_max__0__1_I3_J,axiom,
% 9.49/5.25      ! [X: num] :
% 9.49/5.25        ( ( ord_max_int @ zero_zero_int @ ( numeral_numeral_int @ X ) )
% 9.49/5.25        = ( numeral_numeral_int @ X ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1903_less__one,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ( ( ord_less_nat @ N @ one_one_nat )
% 9.49/5.25        = ( N = zero_zero_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1904_div__by__Suc__0,axiom,
% 9.49/5.25      ! [M: nat] :
% 9.49/5.25        ( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
% 9.49/5.25        = M ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1905_mult__eq__1__iff,axiom,
% 9.49/5.25      ! [M: nat,N: nat] :
% 9.49/5.25        ( ( ( times_times_nat @ M @ N )
% 9.49/5.25          = ( suc @ zero_zero_nat ) )
% 9.49/5.25        = ( ( M
% 9.49/5.25            = ( suc @ zero_zero_nat ) )
% 9.49/5.25          & ( N
% 9.49/5.25            = ( suc @ zero_zero_nat ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1906_one__eq__mult__iff,axiom,
% 9.49/5.25      ! [M: nat,N: nat] :
% 9.49/5.25        ( ( ( suc @ zero_zero_nat )
% 9.49/5.25          = ( times_times_nat @ M @ N ) )
% 9.49/5.25        = ( ( M
% 9.49/5.25            = ( suc @ zero_zero_nat ) )
% 9.49/5.25          & ( N
% 9.49/5.25            = ( suc @ zero_zero_nat ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1907_max__0__1_I2_J,axiom,
% 9.49/5.25      ( ( ord_max_real @ one_one_real @ zero_zero_real )
% 9.49/5.25      = one_one_real ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1908_max__0__1_I2_J,axiom,
% 9.49/5.25      ( ( ord_max_rat @ one_one_rat @ zero_zero_rat )
% 9.49/5.25      = one_one_rat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1909_max__0__1_I2_J,axiom,
% 9.49/5.25      ( ( ord_max_nat @ one_one_nat @ zero_zero_nat )
% 9.49/5.25      = one_one_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1910_max__0__1_I2_J,axiom,
% 9.49/5.25      ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ zero_z5237406670263579293d_enat )
% 9.49/5.25      = one_on7984719198319812577d_enat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1911_max__0__1_I2_J,axiom,
% 9.49/5.25      ( ( ord_max_int @ one_one_int @ zero_zero_int )
% 9.49/5.25      = one_one_int ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1912_max__0__1_I1_J,axiom,
% 9.49/5.25      ( ( ord_max_real @ zero_zero_real @ one_one_real )
% 9.49/5.25      = one_one_real ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1913_max__0__1_I1_J,axiom,
% 9.49/5.25      ( ( ord_max_rat @ zero_zero_rat @ one_one_rat )
% 9.49/5.25      = one_one_rat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1914_max__0__1_I1_J,axiom,
% 9.49/5.25      ( ( ord_max_nat @ zero_zero_nat @ one_one_nat )
% 9.49/5.25      = one_one_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1915_max__0__1_I1_J,axiom,
% 9.49/5.25      ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ one_on7984719198319812577d_enat )
% 9.49/5.25      = one_on7984719198319812577d_enat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1916_max__0__1_I1_J,axiom,
% 9.49/5.25      ( ( ord_max_int @ zero_zero_int @ one_one_int )
% 9.49/5.25      = one_one_int ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1917_div__less,axiom,
% 9.49/5.25      ! [M: nat,N: nat] :
% 9.49/5.25        ( ( ord_less_nat @ M @ N )
% 9.49/5.25       => ( ( divide_divide_nat @ M @ N )
% 9.49/5.25          = zero_zero_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1918_mult__less__cancel2,axiom,
% 9.49/5.25      ! [M: nat,K: nat,N: nat] :
% 9.49/5.25        ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 9.49/5.25        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 9.49/5.25          & ( ord_less_nat @ M @ N ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1919_nat__0__less__mult__iff,axiom,
% 9.49/5.25      ! [M: nat,N: nat] :
% 9.49/5.25        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N ) )
% 9.49/5.25        = ( ( ord_less_nat @ zero_zero_nat @ M )
% 9.49/5.25          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1920_nat__mult__less__cancel__disj,axiom,
% 9.49/5.25      ! [K: nat,M: nat,N: nat] :
% 9.49/5.25        ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 9.49/5.25        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 9.49/5.25          & ( ord_less_nat @ M @ N ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1921_zero__less__diff,axiom,
% 9.49/5.25      ! [N: nat,M: nat] :
% 9.49/5.25        ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
% 9.49/5.25        = ( ord_less_nat @ M @ N ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1922_nat__power__eq__Suc__0__iff,axiom,
% 9.49/5.25      ! [X: nat,M: nat] :
% 9.49/5.25        ( ( ( power_power_nat @ X @ M )
% 9.49/5.25          = ( suc @ zero_zero_nat ) )
% 9.49/5.25        = ( ( M = zero_zero_nat )
% 9.49/5.25          | ( X
% 9.49/5.25            = ( suc @ zero_zero_nat ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1923_power__Suc__0,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N )
% 9.49/5.25        = ( suc @ zero_zero_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1924_diff__is__0__eq,axiom,
% 9.49/5.25      ! [M: nat,N: nat] :
% 9.49/5.25        ( ( ( minus_minus_nat @ M @ N )
% 9.49/5.25          = zero_zero_nat )
% 9.49/5.25        = ( ord_less_eq_nat @ M @ N ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1925_diff__is__0__eq_H,axiom,
% 9.49/5.25      ! [M: nat,N: nat] :
% 9.49/5.25        ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.25       => ( ( minus_minus_nat @ M @ N )
% 9.49/5.25          = zero_zero_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1926_nat__zero__less__power__iff,axiom,
% 9.49/5.25      ! [X: nat,N: nat] :
% 9.49/5.25        ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
% 9.49/5.25        = ( ( ord_less_nat @ zero_zero_nat @ X )
% 9.49/5.25          | ( N = zero_zero_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1927_nat__mult__div__cancel__disj,axiom,
% 9.49/5.25      ! [K: nat,M: nat,N: nat] :
% 9.49/5.25        ( ( ( K = zero_zero_nat )
% 9.49/5.25         => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 9.49/5.25            = zero_zero_nat ) )
% 9.49/5.25        & ( ( K != zero_zero_nat )
% 9.49/5.25         => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 9.49/5.25            = ( divide_divide_nat @ M @ N ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1928_divide__le__0__1__iff,axiom,
% 9.49/5.25      ! [A: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 9.49/5.25        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1929_divide__le__0__1__iff,axiom,
% 9.49/5.25      ! [A: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 9.49/5.25        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1930_zero__le__divide__1__iff,axiom,
% 9.49/5.25      ! [A: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 9.49/5.25        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1931_zero__le__divide__1__iff,axiom,
% 9.49/5.25      ! [A: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 9.49/5.25        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1932_zero__less__divide__1__iff,axiom,
% 9.49/5.25      ! [A: real] :
% 9.49/5.25        ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 9.49/5.25        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1933_zero__less__divide__1__iff,axiom,
% 9.49/5.25      ! [A: rat] :
% 9.49/5.25        ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 9.49/5.25        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1934_less__divide__eq__1__pos,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_real @ zero_zero_real @ A )
% 9.49/5.25       => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 9.49/5.25          = ( ord_less_real @ A @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1935_less__divide__eq__1__pos,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.49/5.25       => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 9.49/5.25          = ( ord_less_rat @ A @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1936_less__divide__eq__1__neg,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_real @ A @ zero_zero_real )
% 9.49/5.25       => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 9.49/5.25          = ( ord_less_real @ B @ A ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1937_less__divide__eq__1__neg,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.49/5.25       => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 9.49/5.25          = ( ord_less_rat @ B @ A ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1938_divide__less__eq__1__pos,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_real @ zero_zero_real @ A )
% 9.49/5.25       => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 9.49/5.25          = ( ord_less_real @ B @ A ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1939_divide__less__eq__1__pos,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.49/5.25       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 9.49/5.25          = ( ord_less_rat @ B @ A ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1940_divide__less__eq__1__neg,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_real @ A @ zero_zero_real )
% 9.49/5.25       => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 9.49/5.25          = ( ord_less_real @ A @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1941_divide__less__eq__1__neg,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.49/5.25       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 9.49/5.25          = ( ord_less_rat @ A @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1942_divide__less__0__1__iff,axiom,
% 9.49/5.25      ! [A: real] :
% 9.49/5.25        ( ( ord_less_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 9.49/5.25        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1943_divide__less__0__1__iff,axiom,
% 9.49/5.25      ! [A: rat] :
% 9.49/5.25        ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 9.49/5.25        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1944_eq__divide__eq__numeral1_I1_J,axiom,
% 9.49/5.25      ! [A: complex,B: complex,W: num] :
% 9.49/5.25        ( ( A
% 9.49/5.25          = ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) ) )
% 9.49/5.25        = ( ( ( ( numera6690914467698888265omplex @ W )
% 9.49/5.25             != zero_zero_complex )
% 9.49/5.25           => ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) )
% 9.49/5.25              = B ) )
% 9.49/5.25          & ( ( ( numera6690914467698888265omplex @ W )
% 9.49/5.25              = zero_zero_complex )
% 9.49/5.25           => ( A = zero_zero_complex ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1945_eq__divide__eq__numeral1_I1_J,axiom,
% 9.49/5.25      ! [A: real,B: real,W: num] :
% 9.49/5.25        ( ( A
% 9.49/5.25          = ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 9.49/5.25        = ( ( ( ( numeral_numeral_real @ W )
% 9.49/5.25             != zero_zero_real )
% 9.49/5.25           => ( ( times_times_real @ A @ ( numeral_numeral_real @ W ) )
% 9.49/5.25              = B ) )
% 9.49/5.25          & ( ( ( numeral_numeral_real @ W )
% 9.49/5.25              = zero_zero_real )
% 9.49/5.25           => ( A = zero_zero_real ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1946_eq__divide__eq__numeral1_I1_J,axiom,
% 9.49/5.25      ! [A: rat,B: rat,W: num] :
% 9.49/5.25        ( ( A
% 9.49/5.25          = ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 9.49/5.25        = ( ( ( ( numeral_numeral_rat @ W )
% 9.49/5.25             != zero_zero_rat )
% 9.49/5.25           => ( ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) )
% 9.49/5.25              = B ) )
% 9.49/5.25          & ( ( ( numeral_numeral_rat @ W )
% 9.49/5.25              = zero_zero_rat )
% 9.49/5.25           => ( A = zero_zero_rat ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1947_divide__eq__eq__numeral1_I1_J,axiom,
% 9.49/5.25      ! [B: complex,W: num,A: complex] :
% 9.49/5.25        ( ( ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) )
% 9.49/5.25          = A )
% 9.49/5.25        = ( ( ( ( numera6690914467698888265omplex @ W )
% 9.49/5.25             != zero_zero_complex )
% 9.49/5.25           => ( B
% 9.49/5.25              = ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) ) )
% 9.49/5.25          & ( ( ( numera6690914467698888265omplex @ W )
% 9.49/5.25              = zero_zero_complex )
% 9.49/5.25           => ( A = zero_zero_complex ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1948_divide__eq__eq__numeral1_I1_J,axiom,
% 9.49/5.25      ! [B: real,W: num,A: real] :
% 9.49/5.25        ( ( ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) )
% 9.49/5.25          = A )
% 9.49/5.25        = ( ( ( ( numeral_numeral_real @ W )
% 9.49/5.25             != zero_zero_real )
% 9.49/5.25           => ( B
% 9.49/5.25              = ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) )
% 9.49/5.25          & ( ( ( numeral_numeral_real @ W )
% 9.49/5.25              = zero_zero_real )
% 9.49/5.25           => ( A = zero_zero_real ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1949_divide__eq__eq__numeral1_I1_J,axiom,
% 9.49/5.25      ! [B: rat,W: num,A: rat] :
% 9.49/5.25        ( ( ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) )
% 9.49/5.25          = A )
% 9.49/5.25        = ( ( ( ( numeral_numeral_rat @ W )
% 9.49/5.25             != zero_zero_rat )
% 9.49/5.25           => ( B
% 9.49/5.25              = ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) )
% 9.49/5.25          & ( ( ( numeral_numeral_rat @ W )
% 9.49/5.25              = zero_zero_rat )
% 9.49/5.25           => ( A = zero_zero_rat ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1950_nonzero__divide__mult__cancel__right,axiom,
% 9.49/5.25      ! [B: complex,A: complex] :
% 9.49/5.25        ( ( B != zero_zero_complex )
% 9.49/5.25       => ( ( divide1717551699836669952omplex @ B @ ( times_times_complex @ A @ B ) )
% 9.49/5.25          = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1951_nonzero__divide__mult__cancel__right,axiom,
% 9.49/5.25      ! [B: real,A: real] :
% 9.49/5.25        ( ( B != zero_zero_real )
% 9.49/5.25       => ( ( divide_divide_real @ B @ ( times_times_real @ A @ B ) )
% 9.49/5.25          = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1952_nonzero__divide__mult__cancel__right,axiom,
% 9.49/5.25      ! [B: rat,A: rat] :
% 9.49/5.25        ( ( B != zero_zero_rat )
% 9.49/5.25       => ( ( divide_divide_rat @ B @ ( times_times_rat @ A @ B ) )
% 9.49/5.25          = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1953_nonzero__divide__mult__cancel__left,axiom,
% 9.49/5.25      ! [A: complex,B: complex] :
% 9.49/5.25        ( ( A != zero_zero_complex )
% 9.49/5.25       => ( ( divide1717551699836669952omplex @ A @ ( times_times_complex @ A @ B ) )
% 9.49/5.25          = ( divide1717551699836669952omplex @ one_one_complex @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1954_nonzero__divide__mult__cancel__left,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( A != zero_zero_real )
% 9.49/5.25       => ( ( divide_divide_real @ A @ ( times_times_real @ A @ B ) )
% 9.49/5.25          = ( divide_divide_real @ one_one_real @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1955_nonzero__divide__mult__cancel__left,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( A != zero_zero_rat )
% 9.49/5.25       => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B ) )
% 9.49/5.25          = ( divide_divide_rat @ one_one_rat @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1956_div__mult__self4,axiom,
% 9.49/5.25      ! [B: nat,C: nat,A: nat] :
% 9.49/5.25        ( ( B != zero_zero_nat )
% 9.49/5.25       => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 9.49/5.25          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1957_div__mult__self4,axiom,
% 9.49/5.25      ! [B: int,C: int,A: int] :
% 9.49/5.25        ( ( B != zero_zero_int )
% 9.49/5.25       => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 9.49/5.25          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1958_div__mult__self3,axiom,
% 9.49/5.25      ! [B: nat,C: nat,A: nat] :
% 9.49/5.25        ( ( B != zero_zero_nat )
% 9.49/5.25       => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 9.49/5.25          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1959_div__mult__self3,axiom,
% 9.49/5.25      ! [B: int,C: int,A: int] :
% 9.49/5.25        ( ( B != zero_zero_int )
% 9.49/5.25       => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 9.49/5.25          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1960_div__mult__self2,axiom,
% 9.49/5.25      ! [B: nat,A: nat,C: nat] :
% 9.49/5.25        ( ( B != zero_zero_nat )
% 9.49/5.25       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 9.49/5.25          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1961_div__mult__self2,axiom,
% 9.49/5.25      ! [B: int,A: int,C: int] :
% 9.49/5.25        ( ( B != zero_zero_int )
% 9.49/5.25       => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 9.49/5.25          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1962_div__mult__self1,axiom,
% 9.49/5.25      ! [B: nat,A: nat,C: nat] :
% 9.49/5.25        ( ( B != zero_zero_nat )
% 9.49/5.25       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 9.49/5.25          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1963_div__mult__self1,axiom,
% 9.49/5.25      ! [B: int,A: int,C: int] :
% 9.49/5.25        ( ( B != zero_zero_int )
% 9.49/5.25       => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 9.49/5.25          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1964_power__eq__0__iff,axiom,
% 9.49/5.25      ! [A: rat,N: nat] :
% 9.49/5.25        ( ( ( power_power_rat @ A @ N )
% 9.49/5.25          = zero_zero_rat )
% 9.49/5.25        = ( ( A = zero_zero_rat )
% 9.49/5.25          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1965_power__eq__0__iff,axiom,
% 9.49/5.25      ! [A: nat,N: nat] :
% 9.49/5.25        ( ( ( power_power_nat @ A @ N )
% 9.49/5.25          = zero_zero_nat )
% 9.49/5.25        = ( ( A = zero_zero_nat )
% 9.49/5.25          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1966_power__eq__0__iff,axiom,
% 9.49/5.25      ! [A: real,N: nat] :
% 9.49/5.25        ( ( ( power_power_real @ A @ N )
% 9.49/5.25          = zero_zero_real )
% 9.49/5.25        = ( ( A = zero_zero_real )
% 9.49/5.25          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1967_power__eq__0__iff,axiom,
% 9.49/5.25      ! [A: int,N: nat] :
% 9.49/5.25        ( ( ( power_power_int @ A @ N )
% 9.49/5.25          = zero_zero_int )
% 9.49/5.25        = ( ( A = zero_zero_int )
% 9.49/5.25          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1968_power__eq__0__iff,axiom,
% 9.49/5.25      ! [A: complex,N: nat] :
% 9.49/5.25        ( ( ( power_power_complex @ A @ N )
% 9.49/5.25          = zero_zero_complex )
% 9.49/5.25        = ( ( A = zero_zero_complex )
% 9.49/5.25          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1969_Suc__pred,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.25       => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 9.49/5.25          = N ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1970_one__le__mult__iff,axiom,
% 9.49/5.25      ! [M: nat,N: nat] :
% 9.49/5.25        ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) )
% 9.49/5.25        = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M )
% 9.49/5.25          & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1971_mult__le__cancel2,axiom,
% 9.49/5.25      ! [M: nat,K: nat,N: nat] :
% 9.49/5.25        ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 9.49/5.25        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 9.49/5.25         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1972_nat__mult__le__cancel__disj,axiom,
% 9.49/5.25      ! [K: nat,M: nat,N: nat] :
% 9.49/5.25        ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 9.49/5.25        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 9.49/5.25         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1973_div__mult__self__is__m,axiom,
% 9.49/5.25      ! [N: nat,M: nat] :
% 9.49/5.25        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.25       => ( ( divide_divide_nat @ ( times_times_nat @ M @ N ) @ N )
% 9.49/5.25          = M ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1974_div__mult__self1__is__m,axiom,
% 9.49/5.25      ! [N: nat,M: nat] :
% 9.49/5.25        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.25       => ( ( divide_divide_nat @ ( times_times_nat @ N @ M ) @ N )
% 9.49/5.25          = M ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1975_divide__le__eq__1__neg,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_real @ A @ zero_zero_real )
% 9.49/5.25       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 9.49/5.25          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1976_divide__le__eq__1__neg,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.49/5.25       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 9.49/5.25          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1977_divide__le__eq__1__pos,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_real @ zero_zero_real @ A )
% 9.49/5.25       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 9.49/5.25          = ( ord_less_eq_real @ B @ A ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1978_divide__le__eq__1__pos,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.49/5.25       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 9.49/5.25          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1979_le__divide__eq__1__neg,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_real @ A @ zero_zero_real )
% 9.49/5.25       => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 9.49/5.25          = ( ord_less_eq_real @ B @ A ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1980_le__divide__eq__1__neg,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.49/5.25       => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 9.49/5.25          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1981_le__divide__eq__1__pos,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_real @ zero_zero_real @ A )
% 9.49/5.25       => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 9.49/5.25          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1982_le__divide__eq__1__pos,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.49/5.25       => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 9.49/5.25          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1983_power__strict__decreasing__iff,axiom,
% 9.49/5.25      ! [B: real,M: nat,N: nat] :
% 9.49/5.25        ( ( ord_less_real @ zero_zero_real @ B )
% 9.49/5.25       => ( ( ord_less_real @ B @ one_one_real )
% 9.49/5.25         => ( ( ord_less_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N ) )
% 9.49/5.25            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1984_power__strict__decreasing__iff,axiom,
% 9.49/5.25      ! [B: rat,M: nat,N: nat] :
% 9.49/5.25        ( ( ord_less_rat @ zero_zero_rat @ B )
% 9.49/5.25       => ( ( ord_less_rat @ B @ one_one_rat )
% 9.49/5.25         => ( ( ord_less_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 9.49/5.25            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1985_power__strict__decreasing__iff,axiom,
% 9.49/5.25      ! [B: nat,M: nat,N: nat] :
% 9.49/5.25        ( ( ord_less_nat @ zero_zero_nat @ B )
% 9.49/5.25       => ( ( ord_less_nat @ B @ one_one_nat )
% 9.49/5.25         => ( ( ord_less_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 9.49/5.25            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1986_power__strict__decreasing__iff,axiom,
% 9.49/5.25      ! [B: int,M: nat,N: nat] :
% 9.49/5.25        ( ( ord_less_int @ zero_zero_int @ B )
% 9.49/5.25       => ( ( ord_less_int @ B @ one_one_int )
% 9.49/5.25         => ( ( ord_less_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 9.49/5.25            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1987_zero__eq__power2,axiom,
% 9.49/5.25      ! [A: rat] :
% 9.49/5.25        ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.25          = zero_zero_rat )
% 9.49/5.25        = ( A = zero_zero_rat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1988_zero__eq__power2,axiom,
% 9.49/5.25      ! [A: nat] :
% 9.49/5.25        ( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.25          = zero_zero_nat )
% 9.49/5.25        = ( A = zero_zero_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1989_zero__eq__power2,axiom,
% 9.49/5.25      ! [A: real] :
% 9.49/5.25        ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.25          = zero_zero_real )
% 9.49/5.25        = ( A = zero_zero_real ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1990_zero__eq__power2,axiom,
% 9.49/5.25      ! [A: int] :
% 9.49/5.25        ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.25          = zero_zero_int )
% 9.49/5.25        = ( A = zero_zero_int ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1991_zero__eq__power2,axiom,
% 9.49/5.25      ! [A: complex] :
% 9.49/5.25        ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.25          = zero_zero_complex )
% 9.49/5.25        = ( A = zero_zero_complex ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1992_power__mono__iff,axiom,
% 9.49/5.25      ! [A: rat,B: rat,N: nat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.49/5.25       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 9.49/5.25         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.25           => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 9.49/5.25              = ( ord_less_eq_rat @ A @ B ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1993_power__mono__iff,axiom,
% 9.49/5.25      ! [A: real,B: real,N: nat] :
% 9.49/5.25        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 9.49/5.25       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 9.49/5.25         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.25           => ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 9.49/5.25              = ( ord_less_eq_real @ A @ B ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1994_power__mono__iff,axiom,
% 9.49/5.25      ! [A: nat,B: nat,N: nat] :
% 9.49/5.25        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.49/5.25       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 9.49/5.25         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.25           => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 9.49/5.25              = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1995_power__mono__iff,axiom,
% 9.49/5.25      ! [A: int,B: int,N: nat] :
% 9.49/5.25        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.25       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 9.49/5.25         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.25           => ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 9.49/5.25              = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1996_Suc__diff__1,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.25       => ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
% 9.49/5.25          = N ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1997_bits__1__div__2,axiom,
% 9.49/5.25      ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.25      = zero_zero_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1998_bits__1__div__2,axiom,
% 9.49/5.25      ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.49/5.25      = zero_zero_int ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_1999_one__div__two__eq__zero,axiom,
% 9.49/5.25      ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.25      = zero_zero_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2000_one__div__two__eq__zero,axiom,
% 9.49/5.25      ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.49/5.25      = zero_zero_int ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2001_power2__eq__iff__nonneg,axiom,
% 9.49/5.25      ! [X: rat,Y2: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 9.49/5.25       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 9.49/5.25         => ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.25              = ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.25            = ( X = Y2 ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2002_power2__eq__iff__nonneg,axiom,
% 9.49/5.25      ! [X: real,Y2: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.49/5.25       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 9.49/5.25         => ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.25              = ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.25            = ( X = Y2 ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2003_power2__eq__iff__nonneg,axiom,
% 9.49/5.25      ! [X: nat,Y2: nat] :
% 9.49/5.25        ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 9.49/5.25       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y2 )
% 9.49/5.25         => ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.25              = ( power_power_nat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.25            = ( X = Y2 ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2004_power2__eq__iff__nonneg,axiom,
% 9.49/5.25      ! [X: int,Y2: int] :
% 9.49/5.25        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 9.49/5.25       => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 9.49/5.25         => ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.25              = ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.25            = ( X = Y2 ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2005_power2__less__eq__zero__iff,axiom,
% 9.49/5.25      ! [A: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat )
% 9.49/5.25        = ( A = zero_zero_rat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2006_power2__less__eq__zero__iff,axiom,
% 9.49/5.25      ! [A: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real )
% 9.49/5.25        = ( A = zero_zero_real ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2007_power2__less__eq__zero__iff,axiom,
% 9.49/5.25      ! [A: int] :
% 9.49/5.25        ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 9.49/5.25        = ( A = zero_zero_int ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2008_zero__less__power2,axiom,
% 9.49/5.25      ! [A: real] :
% 9.49/5.25        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.25        = ( A != zero_zero_real ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2009_zero__less__power2,axiom,
% 9.49/5.25      ! [A: rat] :
% 9.49/5.25        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.25        = ( A != zero_zero_rat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2010_zero__less__power2,axiom,
% 9.49/5.25      ! [A: int] :
% 9.49/5.25        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.25        = ( A != zero_zero_int ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2011_power__decreasing__iff,axiom,
% 9.49/5.25      ! [B: real,M: nat,N: nat] :
% 9.49/5.25        ( ( ord_less_real @ zero_zero_real @ B )
% 9.49/5.25       => ( ( ord_less_real @ B @ one_one_real )
% 9.49/5.25         => ( ( ord_less_eq_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N ) )
% 9.49/5.25            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2012_power__decreasing__iff,axiom,
% 9.49/5.25      ! [B: rat,M: nat,N: nat] :
% 9.49/5.25        ( ( ord_less_rat @ zero_zero_rat @ B )
% 9.49/5.25       => ( ( ord_less_rat @ B @ one_one_rat )
% 9.49/5.25         => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 9.49/5.25            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2013_power__decreasing__iff,axiom,
% 9.49/5.25      ! [B: nat,M: nat,N: nat] :
% 9.49/5.25        ( ( ord_less_nat @ zero_zero_nat @ B )
% 9.49/5.25       => ( ( ord_less_nat @ B @ one_one_nat )
% 9.49/5.25         => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 9.49/5.25            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2014_power__decreasing__iff,axiom,
% 9.49/5.25      ! [B: int,M: nat,N: nat] :
% 9.49/5.25        ( ( ord_less_int @ zero_zero_int @ B )
% 9.49/5.25       => ( ( ord_less_int @ B @ one_one_int )
% 9.49/5.25         => ( ( ord_less_eq_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 9.49/5.25            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2015_sum__power2__eq__zero__iff,axiom,
% 9.49/5.25      ! [X: rat,Y2: rat] :
% 9.49/5.25        ( ( ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.25          = zero_zero_rat )
% 9.49/5.25        = ( ( X = zero_zero_rat )
% 9.49/5.25          & ( Y2 = zero_zero_rat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2016_sum__power2__eq__zero__iff,axiom,
% 9.49/5.25      ! [X: real,Y2: real] :
% 9.49/5.25        ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.25          = zero_zero_real )
% 9.49/5.25        = ( ( X = zero_zero_real )
% 9.49/5.25          & ( Y2 = zero_zero_real ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2017_sum__power2__eq__zero__iff,axiom,
% 9.49/5.25      ! [X: int,Y2: int] :
% 9.49/5.25        ( ( ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.25          = zero_zero_int )
% 9.49/5.25        = ( ( X = zero_zero_int )
% 9.49/5.25          & ( Y2 = zero_zero_int ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2018_VEBT_Osize_I4_J,axiom,
% 9.49/5.25      ! [X21: $o,X222: $o] :
% 9.49/5.25        ( ( size_size_VEBT_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 9.49/5.25        = zero_zero_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2019_VEBT__internal_Onaive__member_Osimps_I1_J,axiom,
% 9.49/5.25      ! [A: $o,B: $o,X: nat] :
% 9.49/5.25        ( ( vEBT_V5719532721284313246member @ ( vEBT_Leaf @ A @ B ) @ X )
% 9.49/5.25        = ( ( ( X = zero_zero_nat )
% 9.49/5.25           => A )
% 9.49/5.25          & ( ( X != zero_zero_nat )
% 9.49/5.25           => ( ( ( X = one_one_nat )
% 9.49/5.25               => B )
% 9.49/5.25              & ( X = one_one_nat ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2020_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I1_J,axiom,
% 9.49/5.25      ! [Uu: $o,Uv: $o] :
% 9.49/5.25        ( ( vEBT_T_p_r_e_d @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat )
% 9.49/5.25        = one_one_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2021_VEBT__internal_Omembermima_Osimps_I1_J,axiom,
% 9.49/5.25      ! [Uu: $o,Uv: $o,Uw: nat] :
% 9.49/5.25        ~ ( vEBT_VEBT_membermima @ ( vEBT_Leaf @ Uu @ Uv ) @ Uw ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2022_vebt__delete_Osimps_I1_J,axiom,
% 9.49/5.25      ! [A: $o,B: $o] :
% 9.49/5.25        ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat )
% 9.49/5.25        = ( vEBT_Leaf @ $false @ B ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2023_VEBT__internal_Onaive__member_Osimps_I2_J,axiom,
% 9.49/5.25      ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,Ux: nat] :
% 9.49/5.25        ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Ux ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2024_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I1_J,axiom,
% 9.49/5.25      ! [A: $o,B: $o,X: nat] :
% 9.49/5.25        ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Leaf @ A @ B ) @ X )
% 9.49/5.25        = ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( X = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2025_VEBT__internal_Onaive__member_Ocases,axiom,
% 9.49/5.25      ! [X: produc9072475918466114483BT_nat] :
% 9.49/5.25        ( ! [A4: $o,B3: $o,X3: nat] :
% 9.49/5.25            ( X
% 9.49/5.25           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ X3 ) )
% 9.49/5.25       => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,Ux2: nat] :
% 9.49/5.25              ( X
% 9.49/5.25             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Ux2 ) )
% 9.49/5.25         => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 9.49/5.25                ( X
% 9.49/5.25               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) @ X3 ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2026_invar__vebt_Ointros_I1_J,axiom,
% 9.49/5.25      ! [A: $o,B: $o] : ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2027_power__0__left,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ( ( ( N = zero_zero_nat )
% 9.49/5.25         => ( ( power_power_rat @ zero_zero_rat @ N )
% 9.49/5.25            = one_one_rat ) )
% 9.49/5.25        & ( ( N != zero_zero_nat )
% 9.49/5.25         => ( ( power_power_rat @ zero_zero_rat @ N )
% 9.49/5.25            = zero_zero_rat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2028_power__0__left,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ( ( ( N = zero_zero_nat )
% 9.49/5.25         => ( ( power_power_nat @ zero_zero_nat @ N )
% 9.49/5.25            = one_one_nat ) )
% 9.49/5.25        & ( ( N != zero_zero_nat )
% 9.49/5.25         => ( ( power_power_nat @ zero_zero_nat @ N )
% 9.49/5.25            = zero_zero_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2029_power__0__left,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ( ( ( N = zero_zero_nat )
% 9.49/5.25         => ( ( power_power_real @ zero_zero_real @ N )
% 9.49/5.25            = one_one_real ) )
% 9.49/5.25        & ( ( N != zero_zero_nat )
% 9.49/5.25         => ( ( power_power_real @ zero_zero_real @ N )
% 9.49/5.25            = zero_zero_real ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2030_power__0__left,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ( ( ( N = zero_zero_nat )
% 9.49/5.25         => ( ( power_power_int @ zero_zero_int @ N )
% 9.49/5.25            = one_one_int ) )
% 9.49/5.25        & ( ( N != zero_zero_nat )
% 9.49/5.25         => ( ( power_power_int @ zero_zero_int @ N )
% 9.49/5.25            = zero_zero_int ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2031_power__0__left,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ( ( ( N = zero_zero_nat )
% 9.49/5.25         => ( ( power_power_complex @ zero_zero_complex @ N )
% 9.49/5.25            = one_one_complex ) )
% 9.49/5.25        & ( ( N != zero_zero_nat )
% 9.49/5.25         => ( ( power_power_complex @ zero_zero_complex @ N )
% 9.49/5.25            = zero_zero_complex ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2032_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I2_J,axiom,
% 9.49/5.25      ! [A: $o,Uw: $o] :
% 9.49/5.25        ( ( vEBT_T_p_r_e_d @ ( vEBT_Leaf @ A @ Uw ) @ ( suc @ zero_zero_nat ) )
% 9.49/5.25        = ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2033_vebt__delete_Osimps_I2_J,axiom,
% 9.49/5.25      ! [A: $o,B: $o] :
% 9.49/5.25        ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) )
% 9.49/5.25        = ( vEBT_Leaf @ A @ $false ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2034_zero__power,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.25       => ( ( power_power_rat @ zero_zero_rat @ N )
% 9.49/5.25          = zero_zero_rat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2035_zero__power,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.25       => ( ( power_power_nat @ zero_zero_nat @ N )
% 9.49/5.25          = zero_zero_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2036_zero__power,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.25       => ( ( power_power_real @ zero_zero_real @ N )
% 9.49/5.25          = zero_zero_real ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2037_zero__power,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.25       => ( ( power_power_int @ zero_zero_int @ N )
% 9.49/5.25          = zero_zero_int ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2038_zero__power,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.25       => ( ( power_power_complex @ zero_zero_complex @ N )
% 9.49/5.25          = zero_zero_complex ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2039_vebt__member_Osimps_I1_J,axiom,
% 9.49/5.25      ! [A: $o,B: $o,X: nat] :
% 9.49/5.25        ( ( vEBT_vebt_member @ ( vEBT_Leaf @ A @ B ) @ X )
% 9.49/5.25        = ( ( ( X = zero_zero_nat )
% 9.49/5.25           => A )
% 9.49/5.25          & ( ( X != zero_zero_nat )
% 9.49/5.25           => ( ( ( X = one_one_nat )
% 9.49/5.25               => B )
% 9.49/5.25              & ( X = one_one_nat ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2040_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I1_J,axiom,
% 9.49/5.25      ! [A: $o,B: $o] :
% 9.49/5.25        ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat )
% 9.49/5.25        = one_one_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2041_VEBT_Oexhaust,axiom,
% 9.49/5.25      ! [Y2: vEBT_VEBT] :
% 9.49/5.25        ( ! [X112: option4927543243414619207at_nat,X122: nat,X132: list_VEBT_VEBT,X142: vEBT_VEBT] :
% 9.49/5.25            ( Y2
% 9.49/5.25           != ( vEBT_Node @ X112 @ X122 @ X132 @ X142 ) )
% 9.49/5.25       => ~ ! [X212: $o,X223: $o] :
% 9.49/5.25              ( Y2
% 9.49/5.25             != ( vEBT_Leaf @ X212 @ X223 ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2042_VEBT_Odistinct_I1_J,axiom,
% 9.49/5.25      ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,X21: $o,X222: $o] :
% 9.49/5.25        ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 9.49/5.25       != ( vEBT_Leaf @ X21 @ X222 ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2043_VEBT__internal_Ovalid_H_Ocases,axiom,
% 9.49/5.25      ! [X: produc9072475918466114483BT_nat] :
% 9.49/5.25        ( ! [Uu2: $o,Uv2: $o,D3: nat] :
% 9.49/5.25            ( X
% 9.49/5.25           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ D3 ) )
% 9.49/5.25       => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,Deg3: nat] :
% 9.49/5.25              ( X
% 9.49/5.25             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Deg3 ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2044_vebt__insert_Osimps_I1_J,axiom,
% 9.49/5.25      ! [X: nat,A: $o,B: $o] :
% 9.49/5.25        ( ( ( X = zero_zero_nat )
% 9.49/5.25         => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 9.49/5.25            = ( vEBT_Leaf @ $true @ B ) ) )
% 9.49/5.25        & ( ( X != zero_zero_nat )
% 9.49/5.25         => ( ( ( X = one_one_nat )
% 9.49/5.25             => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 9.49/5.25                = ( vEBT_Leaf @ A @ $true ) ) )
% 9.49/5.25            & ( ( X != one_one_nat )
% 9.49/5.25             => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 9.49/5.25                = ( vEBT_Leaf @ A @ B ) ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2045_vebt__pred_Osimps_I1_J,axiom,
% 9.49/5.25      ! [Uu: $o,Uv: $o] :
% 9.49/5.25        ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat )
% 9.49/5.25        = none_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2046_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I1_J,axiom,
% 9.49/5.25      ! [Uu: $o,Uv: $o] :
% 9.49/5.25        ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat )
% 9.49/5.25        = one_one_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2047_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I1_J,axiom,
% 9.49/5.25      ! [Uu: $o,B: $o] :
% 9.49/5.25        ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 9.49/5.25        = one_one_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2048_VEBT__internal_Omembermima_Osimps_I2_J,axiom,
% 9.49/5.25      ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT,Uz: nat] :
% 9.49/5.25        ~ ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Uz ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2049_le__numeral__extra_I3_J,axiom,
% 9.49/5.25      ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2050_le__numeral__extra_I3_J,axiom,
% 9.49/5.25      ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2051_le__numeral__extra_I3_J,axiom,
% 9.49/5.25      ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2052_le__numeral__extra_I3_J,axiom,
% 9.49/5.25      ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2053_zero__le,axiom,
% 9.49/5.25      ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2054_field__lbound__gt__zero,axiom,
% 9.49/5.25      ! [D1: real,D22: real] :
% 9.49/5.25        ( ( ord_less_real @ zero_zero_real @ D1 )
% 9.49/5.25       => ( ( ord_less_real @ zero_zero_real @ D22 )
% 9.49/5.25         => ? [E2: real] :
% 9.49/5.25              ( ( ord_less_real @ zero_zero_real @ E2 )
% 9.49/5.25              & ( ord_less_real @ E2 @ D1 )
% 9.49/5.25              & ( ord_less_real @ E2 @ D22 ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2055_field__lbound__gt__zero,axiom,
% 9.49/5.25      ! [D1: rat,D22: rat] :
% 9.49/5.25        ( ( ord_less_rat @ zero_zero_rat @ D1 )
% 9.49/5.25       => ( ( ord_less_rat @ zero_zero_rat @ D22 )
% 9.49/5.25         => ? [E2: rat] :
% 9.49/5.25              ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 9.49/5.25              & ( ord_less_rat @ E2 @ D1 )
% 9.49/5.25              & ( ord_less_rat @ E2 @ D22 ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2056_less__numeral__extra_I3_J,axiom,
% 9.49/5.25      ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2057_less__numeral__extra_I3_J,axiom,
% 9.49/5.25      ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2058_less__numeral__extra_I3_J,axiom,
% 9.49/5.25      ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2059_less__numeral__extra_I3_J,axiom,
% 9.49/5.25      ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2060_gr__zeroI,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ( ( N != zero_zero_nat )
% 9.49/5.25       => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2061_not__less__zero,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2062_gr__implies__not__zero,axiom,
% 9.49/5.25      ! [M: nat,N: nat] :
% 9.49/5.25        ( ( ord_less_nat @ M @ N )
% 9.49/5.25       => ( N != zero_zero_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2063_zero__less__iff__neq__zero,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.25        = ( N != zero_zero_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2064_zero__neq__numeral,axiom,
% 9.49/5.25      ! [N: num] :
% 9.49/5.25        ( zero_zero_complex
% 9.49/5.25       != ( numera6690914467698888265omplex @ N ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2065_zero__neq__numeral,axiom,
% 9.49/5.25      ! [N: num] :
% 9.49/5.25        ( zero_zero_real
% 9.49/5.25       != ( numeral_numeral_real @ N ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2066_zero__neq__numeral,axiom,
% 9.49/5.25      ! [N: num] :
% 9.49/5.25        ( zero_zero_rat
% 9.49/5.25       != ( numeral_numeral_rat @ N ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2067_zero__neq__numeral,axiom,
% 9.49/5.25      ! [N: num] :
% 9.49/5.25        ( zero_zero_nat
% 9.49/5.25       != ( numeral_numeral_nat @ N ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2068_zero__neq__numeral,axiom,
% 9.49/5.25      ! [N: num] :
% 9.49/5.25        ( zero_zero_int
% 9.49/5.25       != ( numeral_numeral_int @ N ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2069_mult__not__zero,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ( times_times_rat @ A @ B )
% 9.49/5.25         != zero_zero_rat )
% 9.49/5.25       => ( ( A != zero_zero_rat )
% 9.49/5.25          & ( B != zero_zero_rat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2070_mult__not__zero,axiom,
% 9.49/5.25      ! [A: complex,B: complex] :
% 9.49/5.25        ( ( ( times_times_complex @ A @ B )
% 9.49/5.25         != zero_zero_complex )
% 9.49/5.25       => ( ( A != zero_zero_complex )
% 9.49/5.25          & ( B != zero_zero_complex ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2071_mult__not__zero,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ( times_times_real @ A @ B )
% 9.49/5.25         != zero_zero_real )
% 9.49/5.25       => ( ( A != zero_zero_real )
% 9.49/5.25          & ( B != zero_zero_real ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2072_mult__not__zero,axiom,
% 9.49/5.25      ! [A: nat,B: nat] :
% 9.49/5.25        ( ( ( times_times_nat @ A @ B )
% 9.49/5.25         != zero_zero_nat )
% 9.49/5.25       => ( ( A != zero_zero_nat )
% 9.49/5.25          & ( B != zero_zero_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2073_mult__not__zero,axiom,
% 9.49/5.25      ! [A: int,B: int] :
% 9.49/5.25        ( ( ( times_times_int @ A @ B )
% 9.49/5.25         != zero_zero_int )
% 9.49/5.25       => ( ( A != zero_zero_int )
% 9.49/5.25          & ( B != zero_zero_int ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2074_divisors__zero,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ( times_times_rat @ A @ B )
% 9.49/5.25          = zero_zero_rat )
% 9.49/5.25       => ( ( A = zero_zero_rat )
% 9.49/5.25          | ( B = zero_zero_rat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2075_divisors__zero,axiom,
% 9.49/5.25      ! [A: complex,B: complex] :
% 9.49/5.25        ( ( ( times_times_complex @ A @ B )
% 9.49/5.25          = zero_zero_complex )
% 9.49/5.25       => ( ( A = zero_zero_complex )
% 9.49/5.25          | ( B = zero_zero_complex ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2076_divisors__zero,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ( times_times_real @ A @ B )
% 9.49/5.25          = zero_zero_real )
% 9.49/5.25       => ( ( A = zero_zero_real )
% 9.49/5.25          | ( B = zero_zero_real ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2077_divisors__zero,axiom,
% 9.49/5.25      ! [A: nat,B: nat] :
% 9.49/5.25        ( ( ( times_times_nat @ A @ B )
% 9.49/5.25          = zero_zero_nat )
% 9.49/5.25       => ( ( A = zero_zero_nat )
% 9.49/5.25          | ( B = zero_zero_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2078_divisors__zero,axiom,
% 9.49/5.25      ! [A: int,B: int] :
% 9.49/5.25        ( ( ( times_times_int @ A @ B )
% 9.49/5.25          = zero_zero_int )
% 9.49/5.25       => ( ( A = zero_zero_int )
% 9.49/5.25          | ( B = zero_zero_int ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2079_no__zero__divisors,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( A != zero_zero_rat )
% 9.49/5.25       => ( ( B != zero_zero_rat )
% 9.49/5.25         => ( ( times_times_rat @ A @ B )
% 9.49/5.25           != zero_zero_rat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2080_no__zero__divisors,axiom,
% 9.49/5.25      ! [A: complex,B: complex] :
% 9.49/5.25        ( ( A != zero_zero_complex )
% 9.49/5.25       => ( ( B != zero_zero_complex )
% 9.49/5.25         => ( ( times_times_complex @ A @ B )
% 9.49/5.25           != zero_zero_complex ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2081_no__zero__divisors,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( A != zero_zero_real )
% 9.49/5.25       => ( ( B != zero_zero_real )
% 9.49/5.25         => ( ( times_times_real @ A @ B )
% 9.49/5.25           != zero_zero_real ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2082_no__zero__divisors,axiom,
% 9.49/5.25      ! [A: nat,B: nat] :
% 9.49/5.25        ( ( A != zero_zero_nat )
% 9.49/5.25       => ( ( B != zero_zero_nat )
% 9.49/5.25         => ( ( times_times_nat @ A @ B )
% 9.49/5.25           != zero_zero_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2083_no__zero__divisors,axiom,
% 9.49/5.25      ! [A: int,B: int] :
% 9.49/5.25        ( ( A != zero_zero_int )
% 9.49/5.25       => ( ( B != zero_zero_int )
% 9.49/5.25         => ( ( times_times_int @ A @ B )
% 9.49/5.25           != zero_zero_int ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2084_mult__left__cancel,axiom,
% 9.49/5.25      ! [C: rat,A: rat,B: rat] :
% 9.49/5.25        ( ( C != zero_zero_rat )
% 9.49/5.25       => ( ( ( times_times_rat @ C @ A )
% 9.49/5.25            = ( times_times_rat @ C @ B ) )
% 9.49/5.25          = ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2085_mult__left__cancel,axiom,
% 9.49/5.25      ! [C: complex,A: complex,B: complex] :
% 9.49/5.25        ( ( C != zero_zero_complex )
% 9.49/5.25       => ( ( ( times_times_complex @ C @ A )
% 9.49/5.25            = ( times_times_complex @ C @ B ) )
% 9.49/5.25          = ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2086_mult__left__cancel,axiom,
% 9.49/5.25      ! [C: real,A: real,B: real] :
% 9.49/5.25        ( ( C != zero_zero_real )
% 9.49/5.25       => ( ( ( times_times_real @ C @ A )
% 9.49/5.25            = ( times_times_real @ C @ B ) )
% 9.49/5.25          = ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2087_mult__left__cancel,axiom,
% 9.49/5.25      ! [C: nat,A: nat,B: nat] :
% 9.49/5.25        ( ( C != zero_zero_nat )
% 9.49/5.25       => ( ( ( times_times_nat @ C @ A )
% 9.49/5.25            = ( times_times_nat @ C @ B ) )
% 9.49/5.25          = ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2088_mult__left__cancel,axiom,
% 9.49/5.25      ! [C: int,A: int,B: int] :
% 9.49/5.25        ( ( C != zero_zero_int )
% 9.49/5.25       => ( ( ( times_times_int @ C @ A )
% 9.49/5.25            = ( times_times_int @ C @ B ) )
% 9.49/5.25          = ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2089_mult__right__cancel,axiom,
% 9.49/5.25      ! [C: rat,A: rat,B: rat] :
% 9.49/5.25        ( ( C != zero_zero_rat )
% 9.49/5.25       => ( ( ( times_times_rat @ A @ C )
% 9.49/5.25            = ( times_times_rat @ B @ C ) )
% 9.49/5.25          = ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2090_mult__right__cancel,axiom,
% 9.49/5.25      ! [C: complex,A: complex,B: complex] :
% 9.49/5.25        ( ( C != zero_zero_complex )
% 9.49/5.25       => ( ( ( times_times_complex @ A @ C )
% 9.49/5.25            = ( times_times_complex @ B @ C ) )
% 9.49/5.25          = ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2091_mult__right__cancel,axiom,
% 9.49/5.25      ! [C: real,A: real,B: real] :
% 9.49/5.25        ( ( C != zero_zero_real )
% 9.49/5.25       => ( ( ( times_times_real @ A @ C )
% 9.49/5.25            = ( times_times_real @ B @ C ) )
% 9.49/5.25          = ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2092_mult__right__cancel,axiom,
% 9.49/5.25      ! [C: nat,A: nat,B: nat] :
% 9.49/5.25        ( ( C != zero_zero_nat )
% 9.49/5.25       => ( ( ( times_times_nat @ A @ C )
% 9.49/5.25            = ( times_times_nat @ B @ C ) )
% 9.49/5.25          = ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2093_mult__right__cancel,axiom,
% 9.49/5.25      ! [C: int,A: int,B: int] :
% 9.49/5.25        ( ( C != zero_zero_int )
% 9.49/5.25       => ( ( ( times_times_int @ A @ C )
% 9.49/5.25            = ( times_times_int @ B @ C ) )
% 9.49/5.25          = ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2094_zero__neq__one,axiom,
% 9.49/5.25      zero_zero_complex != one_one_complex ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2095_zero__neq__one,axiom,
% 9.49/5.25      zero_zero_real != one_one_real ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2096_zero__neq__one,axiom,
% 9.49/5.25      zero_zero_rat != one_one_rat ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2097_zero__neq__one,axiom,
% 9.49/5.25      zero_zero_nat != one_one_nat ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2098_zero__neq__one,axiom,
% 9.49/5.25      zero_zero_int != one_one_int ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2099_add_Ogroup__left__neutral,axiom,
% 9.49/5.25      ! [A: complex] :
% 9.49/5.25        ( ( plus_plus_complex @ zero_zero_complex @ A )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2100_add_Ogroup__left__neutral,axiom,
% 9.49/5.25      ! [A: real] :
% 9.49/5.25        ( ( plus_plus_real @ zero_zero_real @ A )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2101_add_Ogroup__left__neutral,axiom,
% 9.49/5.25      ! [A: rat] :
% 9.49/5.25        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2102_add_Ogroup__left__neutral,axiom,
% 9.49/5.25      ! [A: int] :
% 9.49/5.25        ( ( plus_plus_int @ zero_zero_int @ A )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2103_add_Ocomm__neutral,axiom,
% 9.49/5.25      ! [A: complex] :
% 9.49/5.25        ( ( plus_plus_complex @ A @ zero_zero_complex )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2104_add_Ocomm__neutral,axiom,
% 9.49/5.25      ! [A: real] :
% 9.49/5.25        ( ( plus_plus_real @ A @ zero_zero_real )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2105_add_Ocomm__neutral,axiom,
% 9.49/5.25      ! [A: rat] :
% 9.49/5.25        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2106_add_Ocomm__neutral,axiom,
% 9.49/5.25      ! [A: nat] :
% 9.49/5.25        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2107_add_Ocomm__neutral,axiom,
% 9.49/5.25      ! [A: int] :
% 9.49/5.25        ( ( plus_plus_int @ A @ zero_zero_int )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2108_comm__monoid__add__class_Oadd__0,axiom,
% 9.49/5.25      ! [A: complex] :
% 9.49/5.25        ( ( plus_plus_complex @ zero_zero_complex @ A )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2109_comm__monoid__add__class_Oadd__0,axiom,
% 9.49/5.25      ! [A: real] :
% 9.49/5.25        ( ( plus_plus_real @ zero_zero_real @ A )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2110_comm__monoid__add__class_Oadd__0,axiom,
% 9.49/5.25      ! [A: rat] :
% 9.49/5.25        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2111_comm__monoid__add__class_Oadd__0,axiom,
% 9.49/5.25      ! [A: nat] :
% 9.49/5.25        ( ( plus_plus_nat @ zero_zero_nat @ A )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2112_comm__monoid__add__class_Oadd__0,axiom,
% 9.49/5.25      ! [A: int] :
% 9.49/5.25        ( ( plus_plus_int @ zero_zero_int @ A )
% 9.49/5.25        = A ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2113_eq__iff__diff__eq__0,axiom,
% 9.49/5.25      ( ( ^ [Y5: complex,Z5: complex] : ( Y5 = Z5 ) )
% 9.49/5.25      = ( ^ [A3: complex,B4: complex] :
% 9.49/5.25            ( ( minus_minus_complex @ A3 @ B4 )
% 9.49/5.25            = zero_zero_complex ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2114_eq__iff__diff__eq__0,axiom,
% 9.49/5.25      ( ( ^ [Y5: real,Z5: real] : ( Y5 = Z5 ) )
% 9.49/5.25      = ( ^ [A3: real,B4: real] :
% 9.49/5.25            ( ( minus_minus_real @ A3 @ B4 )
% 9.49/5.25            = zero_zero_real ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2115_eq__iff__diff__eq__0,axiom,
% 9.49/5.25      ( ( ^ [Y5: rat,Z5: rat] : ( Y5 = Z5 ) )
% 9.49/5.25      = ( ^ [A3: rat,B4: rat] :
% 9.49/5.25            ( ( minus_minus_rat @ A3 @ B4 )
% 9.49/5.25            = zero_zero_rat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2116_eq__iff__diff__eq__0,axiom,
% 9.49/5.25      ( ( ^ [Y5: int,Z5: int] : ( Y5 = Z5 ) )
% 9.49/5.25      = ( ^ [A3: int,B4: int] :
% 9.49/5.25            ( ( minus_minus_int @ A3 @ B4 )
% 9.49/5.25            = zero_zero_int ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2117_power__not__zero,axiom,
% 9.49/5.25      ! [A: rat,N: nat] :
% 9.49/5.25        ( ( A != zero_zero_rat )
% 9.49/5.25       => ( ( power_power_rat @ A @ N )
% 9.49/5.25         != zero_zero_rat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2118_power__not__zero,axiom,
% 9.49/5.25      ! [A: nat,N: nat] :
% 9.49/5.25        ( ( A != zero_zero_nat )
% 9.49/5.25       => ( ( power_power_nat @ A @ N )
% 9.49/5.25         != zero_zero_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2119_power__not__zero,axiom,
% 9.49/5.25      ! [A: real,N: nat] :
% 9.49/5.25        ( ( A != zero_zero_real )
% 9.49/5.25       => ( ( power_power_real @ A @ N )
% 9.49/5.25         != zero_zero_real ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2120_power__not__zero,axiom,
% 9.49/5.25      ! [A: int,N: nat] :
% 9.49/5.25        ( ( A != zero_zero_int )
% 9.49/5.25       => ( ( power_power_int @ A @ N )
% 9.49/5.25         != zero_zero_int ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2121_power__not__zero,axiom,
% 9.49/5.25      ! [A: complex,N: nat] :
% 9.49/5.25        ( ( A != zero_zero_complex )
% 9.49/5.25       => ( ( power_power_complex @ A @ N )
% 9.49/5.25         != zero_zero_complex ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2122_num_Osize_I4_J,axiom,
% 9.49/5.25      ( ( size_size_num @ one )
% 9.49/5.25      = zero_zero_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2123_VEBT__internal_OminNull_Osimps_I3_J,axiom,
% 9.49/5.25      ! [Uu: $o] :
% 9.49/5.25        ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ Uu @ $true ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2124_VEBT__internal_OminNull_Osimps_I2_J,axiom,
% 9.49/5.25      ! [Uv: $o] :
% 9.49/5.25        ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ $true @ Uv ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2125_VEBT__internal_OminNull_Osimps_I1_J,axiom,
% 9.49/5.25      vEBT_VEBT_minNull @ ( vEBT_Leaf @ $false @ $false ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2126_nat_Odistinct_I1_J,axiom,
% 9.49/5.25      ! [X23: nat] :
% 9.49/5.25        ( zero_zero_nat
% 9.49/5.25       != ( suc @ X23 ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2127_old_Onat_Odistinct_I2_J,axiom,
% 9.49/5.25      ! [Nat2: nat] :
% 9.49/5.25        ( ( suc @ Nat2 )
% 9.49/5.25       != zero_zero_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2128_old_Onat_Odistinct_I1_J,axiom,
% 9.49/5.25      ! [Nat2: nat] :
% 9.49/5.25        ( zero_zero_nat
% 9.49/5.25       != ( suc @ Nat2 ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2129_nat_OdiscI,axiom,
% 9.49/5.25      ! [Nat: nat,X23: nat] :
% 9.49/5.25        ( ( Nat
% 9.49/5.25          = ( suc @ X23 ) )
% 9.49/5.25       => ( Nat != zero_zero_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2130_old_Onat_Oexhaust,axiom,
% 9.49/5.25      ! [Y2: nat] :
% 9.49/5.25        ( ( Y2 != zero_zero_nat )
% 9.49/5.25       => ~ ! [Nat3: nat] :
% 9.49/5.25              ( Y2
% 9.49/5.25             != ( suc @ Nat3 ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2131_nat__induct,axiom,
% 9.49/5.25      ! [P: nat > $o,N: nat] :
% 9.49/5.25        ( ( P @ zero_zero_nat )
% 9.49/5.25       => ( ! [N3: nat] :
% 9.49/5.25              ( ( P @ N3 )
% 9.49/5.25             => ( P @ ( suc @ N3 ) ) )
% 9.49/5.25         => ( P @ N ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2132_diff__induct,axiom,
% 9.49/5.25      ! [P: nat > nat > $o,M: nat,N: nat] :
% 9.49/5.25        ( ! [X3: nat] : ( P @ X3 @ zero_zero_nat )
% 9.49/5.25       => ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
% 9.49/5.25         => ( ! [X3: nat,Y3: nat] :
% 9.49/5.25                ( ( P @ X3 @ Y3 )
% 9.49/5.25               => ( P @ ( suc @ X3 ) @ ( suc @ Y3 ) ) )
% 9.49/5.25           => ( P @ M @ N ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2133_zero__induct,axiom,
% 9.49/5.25      ! [P: nat > $o,K: nat] :
% 9.49/5.25        ( ( P @ K )
% 9.49/5.25       => ( ! [N3: nat] :
% 9.49/5.25              ( ( P @ ( suc @ N3 ) )
% 9.49/5.25             => ( P @ N3 ) )
% 9.49/5.25         => ( P @ zero_zero_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2134_Suc__neq__Zero,axiom,
% 9.49/5.25      ! [M: nat] :
% 9.49/5.25        ( ( suc @ M )
% 9.49/5.25       != zero_zero_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2135_Zero__neq__Suc,axiom,
% 9.49/5.25      ! [M: nat] :
% 9.49/5.25        ( zero_zero_nat
% 9.49/5.25       != ( suc @ M ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2136_Zero__not__Suc,axiom,
% 9.49/5.25      ! [M: nat] :
% 9.49/5.25        ( zero_zero_nat
% 9.49/5.25       != ( suc @ M ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2137_not0__implies__Suc,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ( ( N != zero_zero_nat )
% 9.49/5.25       => ? [M4: nat] :
% 9.49/5.25            ( N
% 9.49/5.25            = ( suc @ M4 ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2138_vebt__buildup_Ocases,axiom,
% 9.49/5.25      ! [X: nat] :
% 9.49/5.25        ( ( X != zero_zero_nat )
% 9.49/5.25       => ( ( X
% 9.49/5.25           != ( suc @ zero_zero_nat ) )
% 9.49/5.25         => ~ ! [Va2: nat] :
% 9.49/5.25                ( X
% 9.49/5.25               != ( suc @ ( suc @ Va2 ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2139_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I2_J,axiom,
% 9.49/5.25      ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT,X: nat] :
% 9.49/5.25        ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S3 ) @ X )
% 9.49/5.25        = one_one_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2140_bot__nat__0_Oextremum__strict,axiom,
% 9.49/5.25      ! [A: nat] :
% 9.49/5.25        ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2141_gr0I,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ( ( N != zero_zero_nat )
% 9.49/5.25       => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2142_not__gr0,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 9.49/5.25        = ( N = zero_zero_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2143_not__less0,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2144_less__zeroE,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2145_gr__implies__not0,axiom,
% 9.49/5.25      ! [M: nat,N: nat] :
% 9.49/5.25        ( ( ord_less_nat @ M @ N )
% 9.49/5.25       => ( N != zero_zero_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2146_infinite__descent0,axiom,
% 9.49/5.25      ! [P: nat > $o,N: nat] :
% 9.49/5.25        ( ( P @ zero_zero_nat )
% 9.49/5.25       => ( ! [N3: nat] :
% 9.49/5.25              ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 9.49/5.25             => ( ~ ( P @ N3 )
% 9.49/5.25               => ? [M5: nat] :
% 9.49/5.25                    ( ( ord_less_nat @ M5 @ N3 )
% 9.49/5.25                    & ~ ( P @ M5 ) ) ) )
% 9.49/5.25         => ( P @ N ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2147_add__eq__self__zero,axiom,
% 9.49/5.25      ! [M: nat,N: nat] :
% 9.49/5.25        ( ( ( plus_plus_nat @ M @ N )
% 9.49/5.25          = M )
% 9.49/5.25       => ( N = zero_zero_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2148_plus__nat_Oadd__0,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ( ( plus_plus_nat @ zero_zero_nat @ N )
% 9.49/5.25        = N ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2149_less__eq__nat_Osimps_I1_J,axiom,
% 9.49/5.25      ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2150_bot__nat__0_Oextremum__unique,axiom,
% 9.49/5.25      ! [A: nat] :
% 9.49/5.25        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 9.49/5.25        = ( A = zero_zero_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2151_bot__nat__0_Oextremum__uniqueI,axiom,
% 9.49/5.25      ! [A: nat] :
% 9.49/5.25        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 9.49/5.25       => ( A = zero_zero_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2152_le__0__eq,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 9.49/5.25        = ( N = zero_zero_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2153_mult__0,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ( ( times_times_nat @ zero_zero_nat @ N )
% 9.49/5.25        = zero_zero_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2154_nat__mult__eq__cancel__disj,axiom,
% 9.49/5.25      ! [K: nat,M: nat,N: nat] :
% 9.49/5.25        ( ( ( times_times_nat @ K @ M )
% 9.49/5.25          = ( times_times_nat @ K @ N ) )
% 9.49/5.25        = ( ( K = zero_zero_nat )
% 9.49/5.25          | ( M = N ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2155_diffs0__imp__equal,axiom,
% 9.49/5.25      ! [M: nat,N: nat] :
% 9.49/5.25        ( ( ( minus_minus_nat @ M @ N )
% 9.49/5.25          = zero_zero_nat )
% 9.49/5.25       => ( ( ( minus_minus_nat @ N @ M )
% 9.49/5.25            = zero_zero_nat )
% 9.49/5.25         => ( M = N ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2156_minus__nat_Odiff__0,axiom,
% 9.49/5.25      ! [M: nat] :
% 9.49/5.25        ( ( minus_minus_nat @ M @ zero_zero_nat )
% 9.49/5.25        = M ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2157_power__eq__iff__eq__base,axiom,
% 9.49/5.25      ! [N: nat,A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.25       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.49/5.25         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 9.49/5.25           => ( ( ( power_power_rat @ A @ N )
% 9.49/5.25                = ( power_power_rat @ B @ N ) )
% 9.49/5.25              = ( A = B ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2158_power__eq__iff__eq__base,axiom,
% 9.49/5.25      ! [N: nat,A: real,B: real] :
% 9.49/5.25        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.25       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 9.49/5.25         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 9.49/5.25           => ( ( ( power_power_real @ A @ N )
% 9.49/5.25                = ( power_power_real @ B @ N ) )
% 9.49/5.25              = ( A = B ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2159_power__eq__iff__eq__base,axiom,
% 9.49/5.25      ! [N: nat,A: nat,B: nat] :
% 9.49/5.25        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.25       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.49/5.25         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 9.49/5.25           => ( ( ( power_power_nat @ A @ N )
% 9.49/5.25                = ( power_power_nat @ B @ N ) )
% 9.49/5.25              = ( A = B ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2160_power__eq__iff__eq__base,axiom,
% 9.49/5.25      ! [N: nat,A: int,B: int] :
% 9.49/5.25        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.25       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.25         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 9.49/5.25           => ( ( ( power_power_int @ A @ N )
% 9.49/5.25                = ( power_power_int @ B @ N ) )
% 9.49/5.25              = ( A = B ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2161_power__eq__imp__eq__base,axiom,
% 9.49/5.25      ! [A: rat,N: nat,B: rat] :
% 9.49/5.25        ( ( ( power_power_rat @ A @ N )
% 9.49/5.25          = ( power_power_rat @ B @ N ) )
% 9.49/5.25       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.49/5.25         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 9.49/5.25           => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.25             => ( A = B ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2162_power__eq__imp__eq__base,axiom,
% 9.49/5.25      ! [A: real,N: nat,B: real] :
% 9.49/5.25        ( ( ( power_power_real @ A @ N )
% 9.49/5.25          = ( power_power_real @ B @ N ) )
% 9.49/5.25       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 9.49/5.25         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 9.49/5.25           => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.25             => ( A = B ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2163_power__eq__imp__eq__base,axiom,
% 9.49/5.25      ! [A: nat,N: nat,B: nat] :
% 9.49/5.25        ( ( ( power_power_nat @ A @ N )
% 9.49/5.25          = ( power_power_nat @ B @ N ) )
% 9.49/5.25       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.49/5.25         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 9.49/5.25           => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.25             => ( A = B ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2164_power__eq__imp__eq__base,axiom,
% 9.49/5.25      ! [A: int,N: nat,B: int] :
% 9.49/5.25        ( ( ( power_power_int @ A @ N )
% 9.49/5.25          = ( power_power_int @ B @ N ) )
% 9.49/5.25       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.25         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 9.49/5.25           => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.25             => ( A = B ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2165_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I2_J,axiom,
% 9.49/5.25      ! [A: $o,B: $o] :
% 9.49/5.25        ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) )
% 9.49/5.25        = one_one_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2166_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Osimps_I1_J,axiom,
% 9.49/5.25      ! [A: $o,B: $o] :
% 9.49/5.25        ( ( vEBT_T_m_i_n_t @ ( vEBT_Leaf @ A @ B ) )
% 9.49/5.25        = ( plus_plus_nat @ one_one_nat @ ( if_nat @ A @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2167_lambda__zero,axiom,
% 9.49/5.25      ( ( ^ [H: rat] : zero_zero_rat )
% 9.49/5.25      = ( times_times_rat @ zero_zero_rat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2168_lambda__zero,axiom,
% 9.49/5.25      ( ( ^ [H: complex] : zero_zero_complex )
% 9.49/5.25      = ( times_times_complex @ zero_zero_complex ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2169_lambda__zero,axiom,
% 9.49/5.25      ( ( ^ [H: real] : zero_zero_real )
% 9.49/5.25      = ( times_times_real @ zero_zero_real ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2170_lambda__zero,axiom,
% 9.49/5.25      ( ( ^ [H: nat] : zero_zero_nat )
% 9.49/5.25      = ( times_times_nat @ zero_zero_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2171_lambda__zero,axiom,
% 9.49/5.25      ( ( ^ [H: int] : zero_zero_int )
% 9.49/5.25      = ( times_times_int @ zero_zero_int ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2172_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I2_J,axiom,
% 9.49/5.25      ! [A: $o,Uw: $o] :
% 9.49/5.25        ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Leaf @ A @ Uw ) @ ( suc @ zero_zero_nat ) )
% 9.49/5.25        = one_one_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2173_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I1_J,axiom,
% 9.49/5.25      ! [Uu: $o,B: $o] :
% 9.49/5.25        ( ( vEBT_T_s_u_c_c @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 9.49/5.25        = ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2174_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I3_J,axiom,
% 9.49/5.25      ! [A: $o,B: $o,Va: nat] :
% 9.49/5.25        ( ( vEBT_T_p_r_e_d @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 9.49/5.25        = ( plus_plus_nat @ one_one_nat @ ( if_nat @ B @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2175_VEBT__internal_Omembermima_Osimps_I3_J,axiom,
% 9.49/5.25      ! [Mi: nat,Ma: nat,Va: list_VEBT_VEBT,Vb: vEBT_VEBT,X: nat] :
% 9.49/5.25        ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ Va @ Vb ) @ X )
% 9.49/5.25        = ( ( X = Mi )
% 9.49/5.25          | ( X = Ma ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2176_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I3_J,axiom,
% 9.49/5.25      ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT,X: nat] :
% 9.49/5.25        ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) @ X )
% 9.49/5.25        = one_one_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2177_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I5_J,axiom,
% 9.49/5.25      ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT,Vf: nat] :
% 9.49/5.25        ( ( vEBT_T_p_r_e_d @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) @ Vf )
% 9.49/5.25        = one_one_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2178_power__strict__mono,axiom,
% 9.49/5.25      ! [A: real,B: real,N: nat] :
% 9.49/5.25        ( ( ord_less_real @ A @ B )
% 9.49/5.25       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 9.49/5.25         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.25           => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2179_power__strict__mono,axiom,
% 9.49/5.25      ! [A: rat,B: rat,N: nat] :
% 9.49/5.25        ( ( ord_less_rat @ A @ B )
% 9.49/5.25       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.49/5.25         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.25           => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2180_power__strict__mono,axiom,
% 9.49/5.25      ! [A: nat,B: nat,N: nat] :
% 9.49/5.25        ( ( ord_less_nat @ A @ B )
% 9.49/5.25       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.49/5.25         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.25           => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2181_power__strict__mono,axiom,
% 9.49/5.25      ! [A: int,B: int,N: nat] :
% 9.49/5.25        ( ( ord_less_int @ A @ B )
% 9.49/5.25       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.25         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.25           => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2182_vebt__mint_Osimps_I1_J,axiom,
% 9.49/5.25      ! [A: $o,B: $o] :
% 9.49/5.25        ( ( A
% 9.49/5.25         => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 9.49/5.25            = ( some_nat @ zero_zero_nat ) ) )
% 9.49/5.25        & ( ~ A
% 9.49/5.25         => ( ( B
% 9.49/5.25             => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 9.49/5.25                = ( some_nat @ one_one_nat ) ) )
% 9.49/5.25            & ( ~ B
% 9.49/5.25             => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 9.49/5.25                = none_nat ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2183_vebt__maxt_Osimps_I1_J,axiom,
% 9.49/5.25      ! [B: $o,A: $o] :
% 9.49/5.25        ( ( B
% 9.49/5.25         => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 9.49/5.25            = ( some_nat @ one_one_nat ) ) )
% 9.49/5.25        & ( ~ B
% 9.49/5.25         => ( ( A
% 9.49/5.25             => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 9.49/5.25                = ( some_nat @ zero_zero_nat ) ) )
% 9.49/5.25            & ( ~ A
% 9.49/5.25             => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 9.49/5.25                = none_nat ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2184_vebt__delete_Osimps_I3_J,axiom,
% 9.49/5.25      ! [A: $o,B: $o,N: nat] :
% 9.49/5.25        ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ N ) ) )
% 9.49/5.25        = ( vEBT_Leaf @ A @ B ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2185_vebt__pred_Osimps_I2_J,axiom,
% 9.49/5.25      ! [A: $o,Uw: $o] :
% 9.49/5.25        ( ( A
% 9.49/5.25         => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw ) @ ( suc @ zero_zero_nat ) )
% 9.49/5.25            = ( some_nat @ zero_zero_nat ) ) )
% 9.49/5.25        & ( ~ A
% 9.49/5.25         => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw ) @ ( suc @ zero_zero_nat ) )
% 9.49/5.25            = none_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2186_vebt__succ_Osimps_I1_J,axiom,
% 9.49/5.25      ! [B: $o,Uu: $o] :
% 9.49/5.25        ( ( B
% 9.49/5.25         => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 9.49/5.25            = ( some_nat @ one_one_nat ) ) )
% 9.49/5.25        & ( ~ B
% 9.49/5.25         => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 9.49/5.25            = none_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2187_zero__le__numeral,axiom,
% 9.49/5.25      ! [N: num] : ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2188_zero__le__numeral,axiom,
% 9.49/5.25      ! [N: num] : ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2189_zero__le__numeral,axiom,
% 9.49/5.25      ! [N: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2190_zero__le__numeral,axiom,
% 9.49/5.25      ! [N: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2191_not__numeral__le__zero,axiom,
% 9.49/5.25      ! [N: num] :
% 9.49/5.25        ~ ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2192_not__numeral__le__zero,axiom,
% 9.49/5.25      ! [N: num] :
% 9.49/5.25        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2193_not__numeral__le__zero,axiom,
% 9.49/5.25      ! [N: num] :
% 9.49/5.25        ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2194_not__numeral__le__zero,axiom,
% 9.49/5.25      ! [N: num] :
% 9.49/5.25        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2195_not__numeral__less__zero,axiom,
% 9.49/5.25      ! [N: num] :
% 9.49/5.25        ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2196_not__numeral__less__zero,axiom,
% 9.49/5.25      ! [N: num] :
% 9.49/5.25        ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2197_not__numeral__less__zero,axiom,
% 9.49/5.25      ! [N: num] :
% 9.49/5.25        ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2198_not__numeral__less__zero,axiom,
% 9.49/5.25      ! [N: num] :
% 9.49/5.25        ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2199_zero__less__numeral,axiom,
% 9.49/5.25      ! [N: num] : ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2200_zero__less__numeral,axiom,
% 9.49/5.25      ! [N: num] : ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2201_zero__less__numeral,axiom,
% 9.49/5.25      ! [N: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2202_zero__less__numeral,axiom,
% 9.49/5.25      ! [N: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2203_mult__mono,axiom,
% 9.49/5.25      ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ A @ B )
% 9.49/5.25       => ( ( ord_less_eq_rat @ C @ D2 )
% 9.49/5.25         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 9.49/5.25           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.49/5.25             => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2204_mult__mono,axiom,
% 9.49/5.25      ! [A: real,B: real,C: real,D2: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ A @ B )
% 9.49/5.25       => ( ( ord_less_eq_real @ C @ D2 )
% 9.49/5.25         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 9.49/5.25           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 9.49/5.25             => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2205_mult__mono,axiom,
% 9.49/5.25      ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.49/5.25        ( ( ord_less_eq_nat @ A @ B )
% 9.49/5.25       => ( ( ord_less_eq_nat @ C @ D2 )
% 9.49/5.25         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 9.49/5.25           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 9.49/5.25             => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2206_mult__mono,axiom,
% 9.49/5.25      ! [A: int,B: int,C: int,D2: int] :
% 9.49/5.25        ( ( ord_less_eq_int @ A @ B )
% 9.49/5.25       => ( ( ord_less_eq_int @ C @ D2 )
% 9.49/5.25         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 9.49/5.25           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.49/5.25             => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2207_mult__mono_H,axiom,
% 9.49/5.25      ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ A @ B )
% 9.49/5.25       => ( ( ord_less_eq_rat @ C @ D2 )
% 9.49/5.25         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.49/5.25           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.49/5.25             => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2208_mult__mono_H,axiom,
% 9.49/5.25      ! [A: real,B: real,C: real,D2: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ A @ B )
% 9.49/5.25       => ( ( ord_less_eq_real @ C @ D2 )
% 9.49/5.25         => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 9.49/5.25           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 9.49/5.25             => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2209_mult__mono_H,axiom,
% 9.49/5.25      ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.49/5.25        ( ( ord_less_eq_nat @ A @ B )
% 9.49/5.25       => ( ( ord_less_eq_nat @ C @ D2 )
% 9.49/5.25         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.49/5.25           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 9.49/5.25             => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2210_mult__mono_H,axiom,
% 9.49/5.25      ! [A: int,B: int,C: int,D2: int] :
% 9.49/5.25        ( ( ord_less_eq_int @ A @ B )
% 9.49/5.25       => ( ( ord_less_eq_int @ C @ D2 )
% 9.49/5.25         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.25           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.49/5.25             => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2211_zero__le__square,axiom,
% 9.49/5.25      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2212_zero__le__square,axiom,
% 9.49/5.25      ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2213_zero__le__square,axiom,
% 9.49/5.25      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2214_split__mult__pos__le,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.49/5.25            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 9.49/5.25          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 9.49/5.25            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 9.49/5.25       => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2215_split__mult__pos__le,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 9.49/5.25            & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 9.49/5.25          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 9.49/5.25            & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 9.49/5.25       => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2216_split__mult__pos__le,axiom,
% 9.49/5.25      ! [A: int,B: int] :
% 9.49/5.25        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.25            & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 9.49/5.25          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 9.49/5.25            & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 9.49/5.25       => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2217_mult__left__mono__neg,axiom,
% 9.49/5.25      ! [B: rat,A: rat,C: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ B @ A )
% 9.49/5.25       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 9.49/5.25         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2218_mult__left__mono__neg,axiom,
% 9.49/5.25      ! [B: real,A: real,C: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ B @ A )
% 9.49/5.25       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 9.49/5.25         => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2219_mult__left__mono__neg,axiom,
% 9.49/5.25      ! [B: int,A: int,C: int] :
% 9.49/5.25        ( ( ord_less_eq_int @ B @ A )
% 9.49/5.25       => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 9.49/5.25         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2220_mult__nonpos__nonpos,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 9.49/5.25       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 9.49/5.25         => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2221_mult__nonpos__nonpos,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 9.49/5.25       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 9.49/5.25         => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2222_mult__nonpos__nonpos,axiom,
% 9.49/5.25      ! [A: int,B: int] :
% 9.49/5.25        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 9.49/5.25       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 9.49/5.25         => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2223_mult__left__mono,axiom,
% 9.49/5.25      ! [A: rat,B: rat,C: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ A @ B )
% 9.49/5.25       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.49/5.25         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2224_mult__left__mono,axiom,
% 9.49/5.25      ! [A: real,B: real,C: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ A @ B )
% 9.49/5.25       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 9.49/5.25         => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2225_mult__left__mono,axiom,
% 9.49/5.25      ! [A: nat,B: nat,C: nat] :
% 9.49/5.25        ( ( ord_less_eq_nat @ A @ B )
% 9.49/5.25       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 9.49/5.25         => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2226_mult__left__mono,axiom,
% 9.49/5.25      ! [A: int,B: int,C: int] :
% 9.49/5.25        ( ( ord_less_eq_int @ A @ B )
% 9.49/5.25       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.49/5.25         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2227_mult__right__mono__neg,axiom,
% 9.49/5.25      ! [B: rat,A: rat,C: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ B @ A )
% 9.49/5.25       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 9.49/5.25         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2228_mult__right__mono__neg,axiom,
% 9.49/5.25      ! [B: real,A: real,C: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ B @ A )
% 9.49/5.25       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 9.49/5.25         => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2229_mult__right__mono__neg,axiom,
% 9.49/5.25      ! [B: int,A: int,C: int] :
% 9.49/5.25        ( ( ord_less_eq_int @ B @ A )
% 9.49/5.25       => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 9.49/5.25         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2230_mult__right__mono,axiom,
% 9.49/5.25      ! [A: rat,B: rat,C: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ A @ B )
% 9.49/5.25       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.49/5.25         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2231_mult__right__mono,axiom,
% 9.49/5.25      ! [A: real,B: real,C: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ A @ B )
% 9.49/5.25       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 9.49/5.25         => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2232_mult__right__mono,axiom,
% 9.49/5.25      ! [A: nat,B: nat,C: nat] :
% 9.49/5.25        ( ( ord_less_eq_nat @ A @ B )
% 9.49/5.25       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 9.49/5.25         => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2233_mult__right__mono,axiom,
% 9.49/5.25      ! [A: int,B: int,C: int] :
% 9.49/5.25        ( ( ord_less_eq_int @ A @ B )
% 9.49/5.25       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.49/5.25         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2234_mult__le__0__iff,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 9.49/5.25        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.49/5.25            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 9.49/5.25          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 9.49/5.25            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2235_mult__le__0__iff,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 9.49/5.25        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 9.49/5.25            & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 9.49/5.25          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 9.49/5.25            & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2236_mult__le__0__iff,axiom,
% 9.49/5.25      ! [A: int,B: int] :
% 9.49/5.25        ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 9.49/5.25        = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.25            & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 9.49/5.25          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 9.49/5.25            & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2237_split__mult__neg__le,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.49/5.25            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 9.49/5.25          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 9.49/5.25            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 9.49/5.25       => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2238_split__mult__neg__le,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 9.49/5.25            & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 9.49/5.25          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 9.49/5.25            & ( ord_less_eq_real @ zero_zero_real @ B ) ) )
% 9.49/5.25       => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2239_split__mult__neg__le,axiom,
% 9.49/5.25      ! [A: nat,B: nat] :
% 9.49/5.25        ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.49/5.25            & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 9.49/5.25          | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 9.49/5.25            & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 9.49/5.25       => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2240_split__mult__neg__le,axiom,
% 9.49/5.25      ! [A: int,B: int] :
% 9.49/5.25        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.25            & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 9.49/5.25          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 9.49/5.25            & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 9.49/5.25       => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2241_mult__nonneg__nonneg,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.49/5.25       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 9.49/5.25         => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2242_mult__nonneg__nonneg,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 9.49/5.25       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 9.49/5.25         => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2243_mult__nonneg__nonneg,axiom,
% 9.49/5.25      ! [A: nat,B: nat] :
% 9.49/5.25        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.49/5.25       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 9.49/5.25         => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2244_mult__nonneg__nonneg,axiom,
% 9.49/5.25      ! [A: int,B: int] :
% 9.49/5.25        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.25       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 9.49/5.25         => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2245_mult__nonneg__nonpos,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.49/5.25       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 9.49/5.25         => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2246_mult__nonneg__nonpos,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 9.49/5.25       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 9.49/5.25         => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2247_mult__nonneg__nonpos,axiom,
% 9.49/5.25      ! [A: nat,B: nat] :
% 9.49/5.25        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.49/5.25       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 9.49/5.25         => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2248_mult__nonneg__nonpos,axiom,
% 9.49/5.25      ! [A: int,B: int] :
% 9.49/5.25        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.25       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 9.49/5.25         => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2249_mult__nonpos__nonneg,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 9.49/5.25       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 9.49/5.25         => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2250_mult__nonpos__nonneg,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 9.49/5.25       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 9.49/5.25         => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2251_mult__nonpos__nonneg,axiom,
% 9.49/5.25      ! [A: nat,B: nat] :
% 9.49/5.25        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 9.49/5.25       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 9.49/5.25         => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2252_mult__nonpos__nonneg,axiom,
% 9.49/5.25      ! [A: int,B: int] :
% 9.49/5.25        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 9.49/5.25       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 9.49/5.25         => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2253_mult__nonneg__nonpos2,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.49/5.25       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 9.49/5.25         => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2254_mult__nonneg__nonpos2,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 9.49/5.25       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 9.49/5.25         => ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2255_mult__nonneg__nonpos2,axiom,
% 9.49/5.25      ! [A: nat,B: nat] :
% 9.49/5.25        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.49/5.25       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 9.49/5.25         => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2256_mult__nonneg__nonpos2,axiom,
% 9.49/5.25      ! [A: int,B: int] :
% 9.49/5.25        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.25       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 9.49/5.25         => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2257_zero__le__mult__iff,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 9.49/5.25        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.49/5.25            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 9.49/5.25          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 9.49/5.25            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2258_zero__le__mult__iff,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 9.49/5.25        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 9.49/5.25            & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 9.49/5.25          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 9.49/5.25            & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2259_zero__le__mult__iff,axiom,
% 9.49/5.25      ! [A: int,B: int] :
% 9.49/5.25        ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 9.49/5.25        = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.25            & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 9.49/5.25          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 9.49/5.25            & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2260_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 9.49/5.25      ! [A: rat,B: rat,C: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ A @ B )
% 9.49/5.25       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.49/5.25         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2261_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 9.49/5.25      ! [A: real,B: real,C: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ A @ B )
% 9.49/5.25       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 9.49/5.25         => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2262_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 9.49/5.25      ! [A: nat,B: nat,C: nat] :
% 9.49/5.25        ( ( ord_less_eq_nat @ A @ B )
% 9.49/5.25       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 9.49/5.25         => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2263_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 9.49/5.25      ! [A: int,B: int,C: int] :
% 9.49/5.25        ( ( ord_less_eq_int @ A @ B )
% 9.49/5.25       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.49/5.25         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2264_zero__less__one__class_Ozero__le__one,axiom,
% 9.49/5.25      ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2265_zero__less__one__class_Ozero__le__one,axiom,
% 9.49/5.25      ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2266_zero__less__one__class_Ozero__le__one,axiom,
% 9.49/5.25      ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2267_zero__less__one__class_Ozero__le__one,axiom,
% 9.49/5.25      ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2268_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 9.49/5.25      ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2269_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 9.49/5.25      ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2270_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 9.49/5.25      ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2271_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 9.49/5.25      ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2272_not__one__le__zero,axiom,
% 9.49/5.25      ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2273_not__one__le__zero,axiom,
% 9.49/5.25      ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2274_not__one__le__zero,axiom,
% 9.49/5.25      ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2275_not__one__le__zero,axiom,
% 9.49/5.25      ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2276_add__decreasing,axiom,
% 9.49/5.25      ! [A: real,C: real,B: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 9.49/5.25       => ( ( ord_less_eq_real @ C @ B )
% 9.49/5.25         => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2277_add__decreasing,axiom,
% 9.49/5.25      ! [A: rat,C: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 9.49/5.25       => ( ( ord_less_eq_rat @ C @ B )
% 9.49/5.25         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2278_add__decreasing,axiom,
% 9.49/5.25      ! [A: nat,C: nat,B: nat] :
% 9.49/5.25        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 9.49/5.25       => ( ( ord_less_eq_nat @ C @ B )
% 9.49/5.25         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2279_add__decreasing,axiom,
% 9.49/5.25      ! [A: int,C: int,B: int] :
% 9.49/5.25        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 9.49/5.25       => ( ( ord_less_eq_int @ C @ B )
% 9.49/5.25         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2280_add__increasing,axiom,
% 9.49/5.25      ! [A: real,B: real,C: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 9.49/5.25       => ( ( ord_less_eq_real @ B @ C )
% 9.49/5.25         => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2281_add__increasing,axiom,
% 9.49/5.25      ! [A: rat,B: rat,C: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.49/5.25       => ( ( ord_less_eq_rat @ B @ C )
% 9.49/5.25         => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2282_add__increasing,axiom,
% 9.49/5.25      ! [A: nat,B: nat,C: nat] :
% 9.49/5.25        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.49/5.25       => ( ( ord_less_eq_nat @ B @ C )
% 9.49/5.25         => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2283_add__increasing,axiom,
% 9.49/5.25      ! [A: int,B: int,C: int] :
% 9.49/5.25        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.25       => ( ( ord_less_eq_int @ B @ C )
% 9.49/5.25         => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2284_add__decreasing2,axiom,
% 9.49/5.25      ! [C: real,A: real,B: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ C @ zero_zero_real )
% 9.49/5.25       => ( ( ord_less_eq_real @ A @ B )
% 9.49/5.25         => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2285_add__decreasing2,axiom,
% 9.49/5.25      ! [C: rat,A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 9.49/5.25       => ( ( ord_less_eq_rat @ A @ B )
% 9.49/5.25         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2286_add__decreasing2,axiom,
% 9.49/5.25      ! [C: nat,A: nat,B: nat] :
% 9.49/5.25        ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 9.49/5.25       => ( ( ord_less_eq_nat @ A @ B )
% 9.49/5.25         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2287_add__decreasing2,axiom,
% 9.49/5.25      ! [C: int,A: int,B: int] :
% 9.49/5.25        ( ( ord_less_eq_int @ C @ zero_zero_int )
% 9.49/5.25       => ( ( ord_less_eq_int @ A @ B )
% 9.49/5.25         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2288_add__increasing2,axiom,
% 9.49/5.25      ! [C: real,B: real,A: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ zero_zero_real @ C )
% 9.49/5.25       => ( ( ord_less_eq_real @ B @ A )
% 9.49/5.25         => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2289_add__increasing2,axiom,
% 9.49/5.25      ! [C: rat,B: rat,A: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.49/5.25       => ( ( ord_less_eq_rat @ B @ A )
% 9.49/5.25         => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2290_add__increasing2,axiom,
% 9.49/5.25      ! [C: nat,B: nat,A: nat] :
% 9.49/5.25        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 9.49/5.25       => ( ( ord_less_eq_nat @ B @ A )
% 9.49/5.25         => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2291_add__increasing2,axiom,
% 9.49/5.25      ! [C: int,B: int,A: int] :
% 9.49/5.25        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.49/5.25       => ( ( ord_less_eq_int @ B @ A )
% 9.49/5.25         => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2292_add__nonneg__nonneg,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 9.49/5.25       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 9.49/5.25         => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2293_add__nonneg__nonneg,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.49/5.25       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 9.49/5.25         => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2294_add__nonneg__nonneg,axiom,
% 9.49/5.25      ! [A: nat,B: nat] :
% 9.49/5.25        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.49/5.25       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 9.49/5.25         => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2295_add__nonneg__nonneg,axiom,
% 9.49/5.25      ! [A: int,B: int] :
% 9.49/5.25        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.25       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 9.49/5.25         => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2296_add__nonpos__nonpos,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 9.49/5.25       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 9.49/5.25         => ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2297_add__nonpos__nonpos,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 9.49/5.25       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 9.49/5.25         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2298_add__nonpos__nonpos,axiom,
% 9.49/5.25      ! [A: nat,B: nat] :
% 9.49/5.25        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 9.49/5.25       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 9.49/5.25         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2299_add__nonpos__nonpos,axiom,
% 9.49/5.25      ! [A: int,B: int] :
% 9.49/5.25        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 9.49/5.25       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 9.49/5.25         => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2300_add__nonneg__eq__0__iff,axiom,
% 9.49/5.25      ! [X: real,Y2: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.49/5.25       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 9.49/5.25         => ( ( ( plus_plus_real @ X @ Y2 )
% 9.49/5.25              = zero_zero_real )
% 9.49/5.25            = ( ( X = zero_zero_real )
% 9.49/5.25              & ( Y2 = zero_zero_real ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2301_add__nonneg__eq__0__iff,axiom,
% 9.49/5.25      ! [X: rat,Y2: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 9.49/5.25       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 9.49/5.25         => ( ( ( plus_plus_rat @ X @ Y2 )
% 9.49/5.25              = zero_zero_rat )
% 9.49/5.25            = ( ( X = zero_zero_rat )
% 9.49/5.25              & ( Y2 = zero_zero_rat ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2302_add__nonneg__eq__0__iff,axiom,
% 9.49/5.25      ! [X: nat,Y2: nat] :
% 9.49/5.25        ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 9.49/5.25       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y2 )
% 9.49/5.25         => ( ( ( plus_plus_nat @ X @ Y2 )
% 9.49/5.25              = zero_zero_nat )
% 9.49/5.25            = ( ( X = zero_zero_nat )
% 9.49/5.25              & ( Y2 = zero_zero_nat ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2303_add__nonneg__eq__0__iff,axiom,
% 9.49/5.25      ! [X: int,Y2: int] :
% 9.49/5.25        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 9.49/5.25       => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 9.49/5.25         => ( ( ( plus_plus_int @ X @ Y2 )
% 9.49/5.25              = zero_zero_int )
% 9.49/5.25            = ( ( X = zero_zero_int )
% 9.49/5.25              & ( Y2 = zero_zero_int ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2304_add__nonpos__eq__0__iff,axiom,
% 9.49/5.25      ! [X: real,Y2: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 9.49/5.25       => ( ( ord_less_eq_real @ Y2 @ zero_zero_real )
% 9.49/5.25         => ( ( ( plus_plus_real @ X @ Y2 )
% 9.49/5.25              = zero_zero_real )
% 9.49/5.25            = ( ( X = zero_zero_real )
% 9.49/5.25              & ( Y2 = zero_zero_real ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2305_add__nonpos__eq__0__iff,axiom,
% 9.49/5.25      ! [X: rat,Y2: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 9.49/5.25       => ( ( ord_less_eq_rat @ Y2 @ zero_zero_rat )
% 9.49/5.25         => ( ( ( plus_plus_rat @ X @ Y2 )
% 9.49/5.25              = zero_zero_rat )
% 9.49/5.25            = ( ( X = zero_zero_rat )
% 9.49/5.25              & ( Y2 = zero_zero_rat ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2306_add__nonpos__eq__0__iff,axiom,
% 9.49/5.25      ! [X: nat,Y2: nat] :
% 9.49/5.25        ( ( ord_less_eq_nat @ X @ zero_zero_nat )
% 9.49/5.25       => ( ( ord_less_eq_nat @ Y2 @ zero_zero_nat )
% 9.49/5.25         => ( ( ( plus_plus_nat @ X @ Y2 )
% 9.49/5.25              = zero_zero_nat )
% 9.49/5.25            = ( ( X = zero_zero_nat )
% 9.49/5.25              & ( Y2 = zero_zero_nat ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2307_add__nonpos__eq__0__iff,axiom,
% 9.49/5.25      ! [X: int,Y2: int] :
% 9.49/5.25        ( ( ord_less_eq_int @ X @ zero_zero_int )
% 9.49/5.25       => ( ( ord_less_eq_int @ Y2 @ zero_zero_int )
% 9.49/5.25         => ( ( ( plus_plus_int @ X @ Y2 )
% 9.49/5.25              = zero_zero_int )
% 9.49/5.25            = ( ( X = zero_zero_int )
% 9.49/5.25              & ( Y2 = zero_zero_int ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2308_mult__neg__neg,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_real @ A @ zero_zero_real )
% 9.49/5.25       => ( ( ord_less_real @ B @ zero_zero_real )
% 9.49/5.25         => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2309_mult__neg__neg,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.49/5.25       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 9.49/5.25         => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2310_mult__neg__neg,axiom,
% 9.49/5.25      ! [A: int,B: int] :
% 9.49/5.25        ( ( ord_less_int @ A @ zero_zero_int )
% 9.49/5.25       => ( ( ord_less_int @ B @ zero_zero_int )
% 9.49/5.25         => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2311_not__square__less__zero,axiom,
% 9.49/5.25      ! [A: real] :
% 9.49/5.25        ~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2312_not__square__less__zero,axiom,
% 9.49/5.25      ! [A: rat] :
% 9.49/5.25        ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2313_not__square__less__zero,axiom,
% 9.49/5.25      ! [A: int] :
% 9.49/5.25        ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2314_mult__less__0__iff,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 9.49/5.25        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 9.49/5.25            & ( ord_less_real @ B @ zero_zero_real ) )
% 9.49/5.25          | ( ( ord_less_real @ A @ zero_zero_real )
% 9.49/5.25            & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2315_mult__less__0__iff,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 9.49/5.25        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.49/5.25            & ( ord_less_rat @ B @ zero_zero_rat ) )
% 9.49/5.25          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.49/5.25            & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2316_mult__less__0__iff,axiom,
% 9.49/5.25      ! [A: int,B: int] :
% 9.49/5.25        ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 9.49/5.25        = ( ( ( ord_less_int @ zero_zero_int @ A )
% 9.49/5.25            & ( ord_less_int @ B @ zero_zero_int ) )
% 9.49/5.25          | ( ( ord_less_int @ A @ zero_zero_int )
% 9.49/5.25            & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2317_mult__neg__pos,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_real @ A @ zero_zero_real )
% 9.49/5.25       => ( ( ord_less_real @ zero_zero_real @ B )
% 9.49/5.25         => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2318_mult__neg__pos,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.49/5.25       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 9.49/5.25         => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2319_mult__neg__pos,axiom,
% 9.49/5.25      ! [A: nat,B: nat] :
% 9.49/5.25        ( ( ord_less_nat @ A @ zero_zero_nat )
% 9.49/5.25       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 9.49/5.25         => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2320_mult__neg__pos,axiom,
% 9.49/5.25      ! [A: int,B: int] :
% 9.49/5.25        ( ( ord_less_int @ A @ zero_zero_int )
% 9.49/5.25       => ( ( ord_less_int @ zero_zero_int @ B )
% 9.49/5.25         => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2321_mult__pos__neg,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_real @ zero_zero_real @ A )
% 9.49/5.25       => ( ( ord_less_real @ B @ zero_zero_real )
% 9.49/5.25         => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2322_mult__pos__neg,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.49/5.25       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 9.49/5.25         => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2323_mult__pos__neg,axiom,
% 9.49/5.25      ! [A: nat,B: nat] :
% 9.49/5.25        ( ( ord_less_nat @ zero_zero_nat @ A )
% 9.49/5.25       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 9.49/5.25         => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2324_mult__pos__neg,axiom,
% 9.49/5.25      ! [A: int,B: int] :
% 9.49/5.25        ( ( ord_less_int @ zero_zero_int @ A )
% 9.49/5.25       => ( ( ord_less_int @ B @ zero_zero_int )
% 9.49/5.25         => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2325_mult__pos__pos,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_real @ zero_zero_real @ A )
% 9.49/5.25       => ( ( ord_less_real @ zero_zero_real @ B )
% 9.49/5.25         => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2326_mult__pos__pos,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.49/5.25       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 9.49/5.25         => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2327_mult__pos__pos,axiom,
% 9.49/5.25      ! [A: nat,B: nat] :
% 9.49/5.25        ( ( ord_less_nat @ zero_zero_nat @ A )
% 9.49/5.25       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 9.49/5.25         => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2328_mult__pos__pos,axiom,
% 9.49/5.25      ! [A: int,B: int] :
% 9.49/5.25        ( ( ord_less_int @ zero_zero_int @ A )
% 9.49/5.25       => ( ( ord_less_int @ zero_zero_int @ B )
% 9.49/5.25         => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2329_mult__pos__neg2,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_real @ zero_zero_real @ A )
% 9.49/5.25       => ( ( ord_less_real @ B @ zero_zero_real )
% 9.49/5.25         => ( ord_less_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2330_mult__pos__neg2,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.49/5.25       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 9.49/5.25         => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2331_mult__pos__neg2,axiom,
% 9.49/5.25      ! [A: nat,B: nat] :
% 9.49/5.25        ( ( ord_less_nat @ zero_zero_nat @ A )
% 9.49/5.25       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 9.49/5.25         => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2332_mult__pos__neg2,axiom,
% 9.49/5.25      ! [A: int,B: int] :
% 9.49/5.25        ( ( ord_less_int @ zero_zero_int @ A )
% 9.49/5.25       => ( ( ord_less_int @ B @ zero_zero_int )
% 9.49/5.25         => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2333_zero__less__mult__iff,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 9.49/5.25        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 9.49/5.25            & ( ord_less_real @ zero_zero_real @ B ) )
% 9.49/5.25          | ( ( ord_less_real @ A @ zero_zero_real )
% 9.49/5.25            & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2334_zero__less__mult__iff,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 9.49/5.25        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.49/5.25            & ( ord_less_rat @ zero_zero_rat @ B ) )
% 9.49/5.25          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.49/5.25            & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2335_zero__less__mult__iff,axiom,
% 9.49/5.25      ! [A: int,B: int] :
% 9.49/5.25        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 9.49/5.25        = ( ( ( ord_less_int @ zero_zero_int @ A )
% 9.49/5.25            & ( ord_less_int @ zero_zero_int @ B ) )
% 9.49/5.25          | ( ( ord_less_int @ A @ zero_zero_int )
% 9.49/5.25            & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2336_zero__less__mult__pos,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 9.49/5.25       => ( ( ord_less_real @ zero_zero_real @ A )
% 9.49/5.25         => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2337_zero__less__mult__pos,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 9.49/5.25       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.49/5.25         => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2338_zero__less__mult__pos,axiom,
% 9.49/5.25      ! [A: nat,B: nat] :
% 9.49/5.25        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 9.49/5.25       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 9.49/5.25         => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2339_zero__less__mult__pos,axiom,
% 9.49/5.25      ! [A: int,B: int] :
% 9.49/5.25        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 9.49/5.25       => ( ( ord_less_int @ zero_zero_int @ A )
% 9.49/5.25         => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2340_zero__less__mult__pos2,axiom,
% 9.49/5.25      ! [B: real,A: real] :
% 9.49/5.25        ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) )
% 9.49/5.25       => ( ( ord_less_real @ zero_zero_real @ A )
% 9.49/5.25         => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2341_zero__less__mult__pos2,axiom,
% 9.49/5.25      ! [B: rat,A: rat] :
% 9.49/5.25        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 9.49/5.25       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.49/5.25         => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2342_zero__less__mult__pos2,axiom,
% 9.49/5.25      ! [B: nat,A: nat] :
% 9.49/5.25        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 9.49/5.25       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 9.49/5.25         => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2343_zero__less__mult__pos2,axiom,
% 9.49/5.25      ! [B: int,A: int] :
% 9.49/5.25        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 9.49/5.25       => ( ( ord_less_int @ zero_zero_int @ A )
% 9.49/5.25         => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2344_mult__less__cancel__left__neg,axiom,
% 9.49/5.25      ! [C: real,A: real,B: real] :
% 9.49/5.25        ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.25       => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 9.49/5.25          = ( ord_less_real @ B @ A ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2345_mult__less__cancel__left__neg,axiom,
% 9.49/5.25      ! [C: rat,A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.25       => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 9.49/5.25          = ( ord_less_rat @ B @ A ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2346_mult__less__cancel__left__neg,axiom,
% 9.49/5.25      ! [C: int,A: int,B: int] :
% 9.49/5.25        ( ( ord_less_int @ C @ zero_zero_int )
% 9.49/5.25       => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 9.49/5.25          = ( ord_less_int @ B @ A ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2347_mult__less__cancel__left__pos,axiom,
% 9.49/5.25      ! [C: real,A: real,B: real] :
% 9.49/5.25        ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.25       => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 9.49/5.25          = ( ord_less_real @ A @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2348_mult__less__cancel__left__pos,axiom,
% 9.49/5.25      ! [C: rat,A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.25       => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 9.49/5.25          = ( ord_less_rat @ A @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2349_mult__less__cancel__left__pos,axiom,
% 9.49/5.25      ! [C: int,A: int,B: int] :
% 9.49/5.25        ( ( ord_less_int @ zero_zero_int @ C )
% 9.49/5.25       => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 9.49/5.25          = ( ord_less_int @ A @ B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2350_mult__strict__left__mono__neg,axiom,
% 9.49/5.25      ! [B: real,A: real,C: real] :
% 9.49/5.25        ( ( ord_less_real @ B @ A )
% 9.49/5.25       => ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.25         => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2351_mult__strict__left__mono__neg,axiom,
% 9.49/5.25      ! [B: rat,A: rat,C: rat] :
% 9.49/5.25        ( ( ord_less_rat @ B @ A )
% 9.49/5.25       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.25         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2352_mult__strict__left__mono__neg,axiom,
% 9.49/5.25      ! [B: int,A: int,C: int] :
% 9.49/5.25        ( ( ord_less_int @ B @ A )
% 9.49/5.25       => ( ( ord_less_int @ C @ zero_zero_int )
% 9.49/5.25         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2353_mult__strict__left__mono,axiom,
% 9.49/5.25      ! [A: real,B: real,C: real] :
% 9.49/5.25        ( ( ord_less_real @ A @ B )
% 9.49/5.25       => ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.25         => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2354_mult__strict__left__mono,axiom,
% 9.49/5.25      ! [A: rat,B: rat,C: rat] :
% 9.49/5.25        ( ( ord_less_rat @ A @ B )
% 9.49/5.25       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.25         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2355_mult__strict__left__mono,axiom,
% 9.49/5.25      ! [A: nat,B: nat,C: nat] :
% 9.49/5.25        ( ( ord_less_nat @ A @ B )
% 9.49/5.25       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 9.49/5.25         => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2356_mult__strict__left__mono,axiom,
% 9.49/5.25      ! [A: int,B: int,C: int] :
% 9.49/5.25        ( ( ord_less_int @ A @ B )
% 9.49/5.25       => ( ( ord_less_int @ zero_zero_int @ C )
% 9.49/5.25         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2357_mult__less__cancel__left__disj,axiom,
% 9.49/5.25      ! [C: real,A: real,B: real] :
% 9.49/5.25        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 9.49/5.25        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.25            & ( ord_less_real @ A @ B ) )
% 9.49/5.25          | ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.25            & ( ord_less_real @ B @ A ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2358_mult__less__cancel__left__disj,axiom,
% 9.49/5.25      ! [C: rat,A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 9.49/5.25        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.25            & ( ord_less_rat @ A @ B ) )
% 9.49/5.25          | ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.25            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2359_mult__less__cancel__left__disj,axiom,
% 9.49/5.25      ! [C: int,A: int,B: int] :
% 9.49/5.25        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 9.49/5.25        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 9.49/5.25            & ( ord_less_int @ A @ B ) )
% 9.49/5.25          | ( ( ord_less_int @ C @ zero_zero_int )
% 9.49/5.25            & ( ord_less_int @ B @ A ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2360_mult__strict__right__mono__neg,axiom,
% 9.49/5.25      ! [B: real,A: real,C: real] :
% 9.49/5.25        ( ( ord_less_real @ B @ A )
% 9.49/5.25       => ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.25         => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2361_mult__strict__right__mono__neg,axiom,
% 9.49/5.25      ! [B: rat,A: rat,C: rat] :
% 9.49/5.25        ( ( ord_less_rat @ B @ A )
% 9.49/5.25       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.25         => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2362_mult__strict__right__mono__neg,axiom,
% 9.49/5.25      ! [B: int,A: int,C: int] :
% 9.49/5.25        ( ( ord_less_int @ B @ A )
% 9.49/5.25       => ( ( ord_less_int @ C @ zero_zero_int )
% 9.49/5.25         => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2363_mult__strict__right__mono,axiom,
% 9.49/5.25      ! [A: real,B: real,C: real] :
% 9.49/5.25        ( ( ord_less_real @ A @ B )
% 9.49/5.25       => ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.25         => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2364_mult__strict__right__mono,axiom,
% 9.49/5.25      ! [A: rat,B: rat,C: rat] :
% 9.49/5.25        ( ( ord_less_rat @ A @ B )
% 9.49/5.25       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.25         => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2365_mult__strict__right__mono,axiom,
% 9.49/5.25      ! [A: nat,B: nat,C: nat] :
% 9.49/5.25        ( ( ord_less_nat @ A @ B )
% 9.49/5.25       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 9.49/5.25         => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2366_mult__strict__right__mono,axiom,
% 9.49/5.25      ! [A: int,B: int,C: int] :
% 9.49/5.25        ( ( ord_less_int @ A @ B )
% 9.49/5.25       => ( ( ord_less_int @ zero_zero_int @ C )
% 9.49/5.25         => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2367_mult__less__cancel__right__disj,axiom,
% 9.49/5.25      ! [A: real,C: real,B: real] :
% 9.49/5.25        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 9.49/5.25        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.25            & ( ord_less_real @ A @ B ) )
% 9.49/5.25          | ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.25            & ( ord_less_real @ B @ A ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2368_mult__less__cancel__right__disj,axiom,
% 9.49/5.25      ! [A: rat,C: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 9.49/5.25        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.25            & ( ord_less_rat @ A @ B ) )
% 9.49/5.25          | ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.25            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2369_mult__less__cancel__right__disj,axiom,
% 9.49/5.25      ! [A: int,C: int,B: int] :
% 9.49/5.25        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 9.49/5.25        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 9.49/5.25            & ( ord_less_int @ A @ B ) )
% 9.49/5.25          | ( ( ord_less_int @ C @ zero_zero_int )
% 9.49/5.25            & ( ord_less_int @ B @ A ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2370_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 9.49/5.25      ! [A: real,B: real,C: real] :
% 9.49/5.25        ( ( ord_less_real @ A @ B )
% 9.49/5.25       => ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.25         => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2371_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 9.49/5.25      ! [A: rat,B: rat,C: rat] :
% 9.49/5.25        ( ( ord_less_rat @ A @ B )
% 9.49/5.25       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.25         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2372_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 9.49/5.25      ! [A: nat,B: nat,C: nat] :
% 9.49/5.25        ( ( ord_less_nat @ A @ B )
% 9.49/5.25       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 9.49/5.25         => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2373_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 9.49/5.25      ! [A: int,B: int,C: int] :
% 9.49/5.25        ( ( ord_less_int @ A @ B )
% 9.49/5.25       => ( ( ord_less_int @ zero_zero_int @ C )
% 9.49/5.25         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2374_less__numeral__extra_I1_J,axiom,
% 9.49/5.25      ord_less_real @ zero_zero_real @ one_one_real ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2375_less__numeral__extra_I1_J,axiom,
% 9.49/5.25      ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2376_less__numeral__extra_I1_J,axiom,
% 9.49/5.25      ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2377_less__numeral__extra_I1_J,axiom,
% 9.49/5.25      ord_less_int @ zero_zero_int @ one_one_int ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2378_not__one__less__zero,axiom,
% 9.49/5.25      ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2379_not__one__less__zero,axiom,
% 9.49/5.25      ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2380_not__one__less__zero,axiom,
% 9.49/5.25      ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2381_not__one__less__zero,axiom,
% 9.49/5.25      ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2382_zero__less__one,axiom,
% 9.49/5.25      ord_less_real @ zero_zero_real @ one_one_real ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2383_zero__less__one,axiom,
% 9.49/5.25      ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2384_zero__less__one,axiom,
% 9.49/5.25      ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2385_zero__less__one,axiom,
% 9.49/5.25      ord_less_int @ zero_zero_int @ one_one_int ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2386_add__less__zeroD,axiom,
% 9.49/5.25      ! [X: real,Y2: real] :
% 9.49/5.25        ( ( ord_less_real @ ( plus_plus_real @ X @ Y2 ) @ zero_zero_real )
% 9.49/5.25       => ( ( ord_less_real @ X @ zero_zero_real )
% 9.49/5.25          | ( ord_less_real @ Y2 @ zero_zero_real ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2387_add__less__zeroD,axiom,
% 9.49/5.25      ! [X: rat,Y2: rat] :
% 9.49/5.25        ( ( ord_less_rat @ ( plus_plus_rat @ X @ Y2 ) @ zero_zero_rat )
% 9.49/5.25       => ( ( ord_less_rat @ X @ zero_zero_rat )
% 9.49/5.25          | ( ord_less_rat @ Y2 @ zero_zero_rat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2388_add__less__zeroD,axiom,
% 9.49/5.25      ! [X: int,Y2: int] :
% 9.49/5.25        ( ( ord_less_int @ ( plus_plus_int @ X @ Y2 ) @ zero_zero_int )
% 9.49/5.25       => ( ( ord_less_int @ X @ zero_zero_int )
% 9.49/5.25          | ( ord_less_int @ Y2 @ zero_zero_int ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2389_pos__add__strict,axiom,
% 9.49/5.25      ! [A: real,B: real,C: real] :
% 9.49/5.25        ( ( ord_less_real @ zero_zero_real @ A )
% 9.49/5.25       => ( ( ord_less_real @ B @ C )
% 9.49/5.25         => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2390_pos__add__strict,axiom,
% 9.49/5.25      ! [A: rat,B: rat,C: rat] :
% 9.49/5.25        ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.49/5.25       => ( ( ord_less_rat @ B @ C )
% 9.49/5.25         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2391_pos__add__strict,axiom,
% 9.49/5.25      ! [A: nat,B: nat,C: nat] :
% 9.49/5.25        ( ( ord_less_nat @ zero_zero_nat @ A )
% 9.49/5.25       => ( ( ord_less_nat @ B @ C )
% 9.49/5.25         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2392_pos__add__strict,axiom,
% 9.49/5.25      ! [A: int,B: int,C: int] :
% 9.49/5.25        ( ( ord_less_int @ zero_zero_int @ A )
% 9.49/5.25       => ( ( ord_less_int @ B @ C )
% 9.49/5.25         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2393_canonically__ordered__monoid__add__class_OlessE,axiom,
% 9.49/5.25      ! [A: nat,B: nat] :
% 9.49/5.25        ( ( ord_less_nat @ A @ B )
% 9.49/5.25       => ~ ! [C2: nat] :
% 9.49/5.25              ( ( B
% 9.49/5.25                = ( plus_plus_nat @ A @ C2 ) )
% 9.49/5.25             => ( C2 = zero_zero_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2394_add__pos__pos,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_real @ zero_zero_real @ A )
% 9.49/5.25       => ( ( ord_less_real @ zero_zero_real @ B )
% 9.49/5.25         => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2395_add__pos__pos,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.49/5.25       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 9.49/5.25         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2396_add__pos__pos,axiom,
% 9.49/5.25      ! [A: nat,B: nat] :
% 9.49/5.25        ( ( ord_less_nat @ zero_zero_nat @ A )
% 9.49/5.25       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 9.49/5.25         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2397_add__pos__pos,axiom,
% 9.49/5.25      ! [A: int,B: int] :
% 9.49/5.25        ( ( ord_less_int @ zero_zero_int @ A )
% 9.49/5.25       => ( ( ord_less_int @ zero_zero_int @ B )
% 9.49/5.25         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2398_add__neg__neg,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_real @ A @ zero_zero_real )
% 9.49/5.25       => ( ( ord_less_real @ B @ zero_zero_real )
% 9.49/5.25         => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2399_add__neg__neg,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.49/5.25       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 9.49/5.25         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2400_add__neg__neg,axiom,
% 9.49/5.25      ! [A: nat,B: nat] :
% 9.49/5.25        ( ( ord_less_nat @ A @ zero_zero_nat )
% 9.49/5.25       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 9.49/5.25         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2401_add__neg__neg,axiom,
% 9.49/5.25      ! [A: int,B: int] :
% 9.49/5.25        ( ( ord_less_int @ A @ zero_zero_int )
% 9.49/5.25       => ( ( ord_less_int @ B @ zero_zero_int )
% 9.49/5.25         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2402_le__iff__diff__le__0,axiom,
% 9.49/5.25      ( ord_less_eq_real
% 9.49/5.25      = ( ^ [A3: real,B4: real] : ( ord_less_eq_real @ ( minus_minus_real @ A3 @ B4 ) @ zero_zero_real ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2403_le__iff__diff__le__0,axiom,
% 9.49/5.25      ( ord_less_eq_rat
% 9.49/5.25      = ( ^ [A3: rat,B4: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A3 @ B4 ) @ zero_zero_rat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2404_le__iff__diff__le__0,axiom,
% 9.49/5.25      ( ord_less_eq_int
% 9.49/5.25      = ( ^ [A3: int,B4: int] : ( ord_less_eq_int @ ( minus_minus_int @ A3 @ B4 ) @ zero_zero_int ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2405_divide__le__0__iff,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 9.49/5.25        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 9.49/5.25            & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 9.49/5.25          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 9.49/5.25            & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2406_divide__le__0__iff,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 9.49/5.25        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.49/5.25            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 9.49/5.25          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 9.49/5.25            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2407_divide__right__mono,axiom,
% 9.49/5.25      ! [A: real,B: real,C: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ A @ B )
% 9.49/5.25       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 9.49/5.25         => ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2408_divide__right__mono,axiom,
% 9.49/5.25      ! [A: rat,B: rat,C: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ A @ B )
% 9.49/5.25       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.49/5.25         => ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2409_zero__le__divide__iff,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 9.49/5.25        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 9.49/5.25            & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 9.49/5.25          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 9.49/5.25            & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2410_zero__le__divide__iff,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 9.49/5.25        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.49/5.25            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 9.49/5.25          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 9.49/5.25            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2411_divide__nonneg__nonneg,axiom,
% 9.49/5.25      ! [X: real,Y2: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.49/5.25       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 9.49/5.25         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y2 ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2412_divide__nonneg__nonneg,axiom,
% 9.49/5.25      ! [X: rat,Y2: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 9.49/5.25       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 9.49/5.25         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y2 ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2413_divide__nonneg__nonpos,axiom,
% 9.49/5.25      ! [X: real,Y2: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.49/5.25       => ( ( ord_less_eq_real @ Y2 @ zero_zero_real )
% 9.49/5.25         => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y2 ) @ zero_zero_real ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2414_divide__nonneg__nonpos,axiom,
% 9.49/5.25      ! [X: rat,Y2: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 9.49/5.25       => ( ( ord_less_eq_rat @ Y2 @ zero_zero_rat )
% 9.49/5.25         => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y2 ) @ zero_zero_rat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2415_divide__nonpos__nonneg,axiom,
% 9.49/5.25      ! [X: real,Y2: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 9.49/5.25       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 9.49/5.25         => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y2 ) @ zero_zero_real ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2416_divide__nonpos__nonneg,axiom,
% 9.49/5.25      ! [X: rat,Y2: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 9.49/5.25       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 9.49/5.25         => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y2 ) @ zero_zero_rat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2417_divide__nonpos__nonpos,axiom,
% 9.49/5.25      ! [X: real,Y2: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 9.49/5.25       => ( ( ord_less_eq_real @ Y2 @ zero_zero_real )
% 9.49/5.25         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y2 ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2418_divide__nonpos__nonpos,axiom,
% 9.49/5.25      ! [X: rat,Y2: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 9.49/5.25       => ( ( ord_less_eq_rat @ Y2 @ zero_zero_rat )
% 9.49/5.25         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y2 ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2419_divide__right__mono__neg,axiom,
% 9.49/5.25      ! [A: real,B: real,C: real] :
% 9.49/5.25        ( ( ord_less_eq_real @ A @ B )
% 9.49/5.25       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 9.49/5.25         => ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2420_divide__right__mono__neg,axiom,
% 9.49/5.25      ! [A: rat,B: rat,C: rat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ A @ B )
% 9.49/5.25       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 9.49/5.25         => ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( divide_divide_rat @ A @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2421_less__iff__diff__less__0,axiom,
% 9.49/5.25      ( ord_less_real
% 9.49/5.25      = ( ^ [A3: real,B4: real] : ( ord_less_real @ ( minus_minus_real @ A3 @ B4 ) @ zero_zero_real ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2422_less__iff__diff__less__0,axiom,
% 9.49/5.25      ( ord_less_rat
% 9.49/5.25      = ( ^ [A3: rat,B4: rat] : ( ord_less_rat @ ( minus_minus_rat @ A3 @ B4 ) @ zero_zero_rat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2423_less__iff__diff__less__0,axiom,
% 9.49/5.25      ( ord_less_int
% 9.49/5.25      = ( ^ [A3: int,B4: int] : ( ord_less_int @ ( minus_minus_int @ A3 @ B4 ) @ zero_zero_int ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2424_divide__neg__neg,axiom,
% 9.49/5.25      ! [X: real,Y2: real] :
% 9.49/5.25        ( ( ord_less_real @ X @ zero_zero_real )
% 9.49/5.25       => ( ( ord_less_real @ Y2 @ zero_zero_real )
% 9.49/5.25         => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y2 ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2425_divide__neg__neg,axiom,
% 9.49/5.25      ! [X: rat,Y2: rat] :
% 9.49/5.25        ( ( ord_less_rat @ X @ zero_zero_rat )
% 9.49/5.25       => ( ( ord_less_rat @ Y2 @ zero_zero_rat )
% 9.49/5.25         => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y2 ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2426_divide__neg__pos,axiom,
% 9.49/5.25      ! [X: real,Y2: real] :
% 9.49/5.25        ( ( ord_less_real @ X @ zero_zero_real )
% 9.49/5.25       => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 9.49/5.25         => ( ord_less_real @ ( divide_divide_real @ X @ Y2 ) @ zero_zero_real ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2427_divide__neg__pos,axiom,
% 9.49/5.25      ! [X: rat,Y2: rat] :
% 9.49/5.25        ( ( ord_less_rat @ X @ zero_zero_rat )
% 9.49/5.25       => ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 9.49/5.25         => ( ord_less_rat @ ( divide_divide_rat @ X @ Y2 ) @ zero_zero_rat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2428_divide__pos__neg,axiom,
% 9.49/5.25      ! [X: real,Y2: real] :
% 9.49/5.25        ( ( ord_less_real @ zero_zero_real @ X )
% 9.49/5.25       => ( ( ord_less_real @ Y2 @ zero_zero_real )
% 9.49/5.25         => ( ord_less_real @ ( divide_divide_real @ X @ Y2 ) @ zero_zero_real ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2429_divide__pos__neg,axiom,
% 9.49/5.25      ! [X: rat,Y2: rat] :
% 9.49/5.25        ( ( ord_less_rat @ zero_zero_rat @ X )
% 9.49/5.25       => ( ( ord_less_rat @ Y2 @ zero_zero_rat )
% 9.49/5.25         => ( ord_less_rat @ ( divide_divide_rat @ X @ Y2 ) @ zero_zero_rat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2430_divide__pos__pos,axiom,
% 9.49/5.25      ! [X: real,Y2: real] :
% 9.49/5.25        ( ( ord_less_real @ zero_zero_real @ X )
% 9.49/5.25       => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 9.49/5.25         => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y2 ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2431_divide__pos__pos,axiom,
% 9.49/5.25      ! [X: rat,Y2: rat] :
% 9.49/5.25        ( ( ord_less_rat @ zero_zero_rat @ X )
% 9.49/5.25       => ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 9.49/5.25         => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y2 ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2432_divide__less__0__iff,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 9.49/5.25        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 9.49/5.25            & ( ord_less_real @ B @ zero_zero_real ) )
% 9.49/5.25          | ( ( ord_less_real @ A @ zero_zero_real )
% 9.49/5.25            & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2433_divide__less__0__iff,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 9.49/5.25        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.49/5.25            & ( ord_less_rat @ B @ zero_zero_rat ) )
% 9.49/5.25          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.49/5.25            & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2434_divide__less__cancel,axiom,
% 9.49/5.25      ! [A: real,C: real,B: real] :
% 9.49/5.25        ( ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 9.49/5.25        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.25           => ( ord_less_real @ A @ B ) )
% 9.49/5.25          & ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.25           => ( ord_less_real @ B @ A ) )
% 9.49/5.25          & ( C != zero_zero_real ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2435_divide__less__cancel,axiom,
% 9.49/5.25      ! [A: rat,C: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 9.49/5.25        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.25           => ( ord_less_rat @ A @ B ) )
% 9.49/5.25          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.25           => ( ord_less_rat @ B @ A ) )
% 9.49/5.25          & ( C != zero_zero_rat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2436_zero__less__divide__iff,axiom,
% 9.49/5.25      ! [A: real,B: real] :
% 9.49/5.25        ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 9.49/5.25        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 9.49/5.25            & ( ord_less_real @ zero_zero_real @ B ) )
% 9.49/5.25          | ( ( ord_less_real @ A @ zero_zero_real )
% 9.49/5.25            & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2437_zero__less__divide__iff,axiom,
% 9.49/5.25      ! [A: rat,B: rat] :
% 9.49/5.25        ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 9.49/5.25        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.49/5.25            & ( ord_less_rat @ zero_zero_rat @ B ) )
% 9.49/5.25          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.49/5.25            & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2438_divide__strict__right__mono,axiom,
% 9.49/5.25      ! [A: real,B: real,C: real] :
% 9.49/5.25        ( ( ord_less_real @ A @ B )
% 9.49/5.25       => ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.25         => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2439_divide__strict__right__mono,axiom,
% 9.49/5.25      ! [A: rat,B: rat,C: rat] :
% 9.49/5.25        ( ( ord_less_rat @ A @ B )
% 9.49/5.25       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.25         => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2440_divide__strict__right__mono__neg,axiom,
% 9.49/5.25      ! [B: real,A: real,C: real] :
% 9.49/5.25        ( ( ord_less_real @ B @ A )
% 9.49/5.25       => ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.25         => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2441_divide__strict__right__mono__neg,axiom,
% 9.49/5.25      ! [B: rat,A: rat,C: rat] :
% 9.49/5.25        ( ( ord_less_rat @ B @ A )
% 9.49/5.25       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.25         => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2442_power__mono,axiom,
% 9.49/5.25      ! [A: rat,B: rat,N: nat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ A @ B )
% 9.49/5.25       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.49/5.25         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2443_power__mono,axiom,
% 9.49/5.25      ! [A: real,B: real,N: nat] :
% 9.49/5.25        ( ( ord_less_eq_real @ A @ B )
% 9.49/5.25       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 9.49/5.25         => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2444_power__mono,axiom,
% 9.49/5.25      ! [A: nat,B: nat,N: nat] :
% 9.49/5.25        ( ( ord_less_eq_nat @ A @ B )
% 9.49/5.25       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.49/5.25         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2445_power__mono,axiom,
% 9.49/5.25      ! [A: int,B: int,N: nat] :
% 9.49/5.25        ( ( ord_less_eq_int @ A @ B )
% 9.49/5.25       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.25         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2446_zero__le__power,axiom,
% 9.49/5.25      ! [A: rat,N: nat] :
% 9.49/5.25        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.49/5.25       => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2447_zero__le__power,axiom,
% 9.49/5.25      ! [A: real,N: nat] :
% 9.49/5.25        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 9.49/5.25       => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2448_zero__le__power,axiom,
% 9.49/5.25      ! [A: nat,N: nat] :
% 9.49/5.25        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.49/5.25       => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2449_zero__le__power,axiom,
% 9.49/5.25      ! [A: int,N: nat] :
% 9.49/5.25        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.25       => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2450_zero__less__power,axiom,
% 9.49/5.25      ! [A: real,N: nat] :
% 9.49/5.25        ( ( ord_less_real @ zero_zero_real @ A )
% 9.49/5.25       => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2451_zero__less__power,axiom,
% 9.49/5.25      ! [A: rat,N: nat] :
% 9.49/5.25        ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.49/5.25       => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2452_zero__less__power,axiom,
% 9.49/5.25      ! [A: nat,N: nat] :
% 9.49/5.25        ( ( ord_less_nat @ zero_zero_nat @ A )
% 9.49/5.25       => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2453_zero__less__power,axiom,
% 9.49/5.25      ! [A: int,N: nat] :
% 9.49/5.25        ( ( ord_less_int @ zero_zero_int @ A )
% 9.49/5.25       => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2454_frac__eq__eq,axiom,
% 9.49/5.25      ! [Y2: complex,Z: complex,X: complex,W: complex] :
% 9.49/5.25        ( ( Y2 != zero_zero_complex )
% 9.49/5.25       => ( ( Z != zero_zero_complex )
% 9.49/5.25         => ( ( ( divide1717551699836669952omplex @ X @ Y2 )
% 9.49/5.25              = ( divide1717551699836669952omplex @ W @ Z ) )
% 9.49/5.25            = ( ( times_times_complex @ X @ Z )
% 9.49/5.25              = ( times_times_complex @ W @ Y2 ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2455_frac__eq__eq,axiom,
% 9.49/5.25      ! [Y2: real,Z: real,X: real,W: real] :
% 9.49/5.25        ( ( Y2 != zero_zero_real )
% 9.49/5.25       => ( ( Z != zero_zero_real )
% 9.49/5.25         => ( ( ( divide_divide_real @ X @ Y2 )
% 9.49/5.25              = ( divide_divide_real @ W @ Z ) )
% 9.49/5.25            = ( ( times_times_real @ X @ Z )
% 9.49/5.25              = ( times_times_real @ W @ Y2 ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2456_frac__eq__eq,axiom,
% 9.49/5.25      ! [Y2: rat,Z: rat,X: rat,W: rat] :
% 9.49/5.25        ( ( Y2 != zero_zero_rat )
% 9.49/5.25       => ( ( Z != zero_zero_rat )
% 9.49/5.25         => ( ( ( divide_divide_rat @ X @ Y2 )
% 9.49/5.25              = ( divide_divide_rat @ W @ Z ) )
% 9.49/5.25            = ( ( times_times_rat @ X @ Z )
% 9.49/5.25              = ( times_times_rat @ W @ Y2 ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2457_divide__eq__eq,axiom,
% 9.49/5.25      ! [B: complex,C: complex,A: complex] :
% 9.49/5.25        ( ( ( divide1717551699836669952omplex @ B @ C )
% 9.49/5.25          = A )
% 9.49/5.25        = ( ( ( C != zero_zero_complex )
% 9.49/5.25           => ( B
% 9.49/5.25              = ( times_times_complex @ A @ C ) ) )
% 9.49/5.25          & ( ( C = zero_zero_complex )
% 9.49/5.25           => ( A = zero_zero_complex ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2458_divide__eq__eq,axiom,
% 9.49/5.25      ! [B: real,C: real,A: real] :
% 9.49/5.25        ( ( ( divide_divide_real @ B @ C )
% 9.49/5.25          = A )
% 9.49/5.25        = ( ( ( C != zero_zero_real )
% 9.49/5.25           => ( B
% 9.49/5.25              = ( times_times_real @ A @ C ) ) )
% 9.49/5.25          & ( ( C = zero_zero_real )
% 9.49/5.25           => ( A = zero_zero_real ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2459_divide__eq__eq,axiom,
% 9.49/5.25      ! [B: rat,C: rat,A: rat] :
% 9.49/5.25        ( ( ( divide_divide_rat @ B @ C )
% 9.49/5.25          = A )
% 9.49/5.25        = ( ( ( C != zero_zero_rat )
% 9.49/5.25           => ( B
% 9.49/5.25              = ( times_times_rat @ A @ C ) ) )
% 9.49/5.25          & ( ( C = zero_zero_rat )
% 9.49/5.25           => ( A = zero_zero_rat ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2460_eq__divide__eq,axiom,
% 9.49/5.25      ! [A: complex,B: complex,C: complex] :
% 9.49/5.25        ( ( A
% 9.49/5.25          = ( divide1717551699836669952omplex @ B @ C ) )
% 9.49/5.25        = ( ( ( C != zero_zero_complex )
% 9.49/5.25           => ( ( times_times_complex @ A @ C )
% 9.49/5.25              = B ) )
% 9.49/5.25          & ( ( C = zero_zero_complex )
% 9.49/5.25           => ( A = zero_zero_complex ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2461_eq__divide__eq,axiom,
% 9.49/5.25      ! [A: real,B: real,C: real] :
% 9.49/5.25        ( ( A
% 9.49/5.25          = ( divide_divide_real @ B @ C ) )
% 9.49/5.25        = ( ( ( C != zero_zero_real )
% 9.49/5.25           => ( ( times_times_real @ A @ C )
% 9.49/5.25              = B ) )
% 9.49/5.25          & ( ( C = zero_zero_real )
% 9.49/5.25           => ( A = zero_zero_real ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2462_eq__divide__eq,axiom,
% 9.49/5.25      ! [A: rat,B: rat,C: rat] :
% 9.49/5.25        ( ( A
% 9.49/5.25          = ( divide_divide_rat @ B @ C ) )
% 9.49/5.25        = ( ( ( C != zero_zero_rat )
% 9.49/5.25           => ( ( times_times_rat @ A @ C )
% 9.49/5.25              = B ) )
% 9.49/5.25          & ( ( C = zero_zero_rat )
% 9.49/5.25           => ( A = zero_zero_rat ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2463_divide__eq__imp,axiom,
% 9.49/5.25      ! [C: complex,B: complex,A: complex] :
% 9.49/5.25        ( ( C != zero_zero_complex )
% 9.49/5.25       => ( ( B
% 9.49/5.25            = ( times_times_complex @ A @ C ) )
% 9.49/5.25         => ( ( divide1717551699836669952omplex @ B @ C )
% 9.49/5.25            = A ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2464_divide__eq__imp,axiom,
% 9.49/5.25      ! [C: real,B: real,A: real] :
% 9.49/5.25        ( ( C != zero_zero_real )
% 9.49/5.25       => ( ( B
% 9.49/5.25            = ( times_times_real @ A @ C ) )
% 9.49/5.25         => ( ( divide_divide_real @ B @ C )
% 9.49/5.25            = A ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2465_divide__eq__imp,axiom,
% 9.49/5.25      ! [C: rat,B: rat,A: rat] :
% 9.49/5.25        ( ( C != zero_zero_rat )
% 9.49/5.25       => ( ( B
% 9.49/5.25            = ( times_times_rat @ A @ C ) )
% 9.49/5.25         => ( ( divide_divide_rat @ B @ C )
% 9.49/5.25            = A ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2466_eq__divide__imp,axiom,
% 9.49/5.25      ! [C: complex,A: complex,B: complex] :
% 9.49/5.25        ( ( C != zero_zero_complex )
% 9.49/5.25       => ( ( ( times_times_complex @ A @ C )
% 9.49/5.25            = B )
% 9.49/5.25         => ( A
% 9.49/5.25            = ( divide1717551699836669952omplex @ B @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2467_eq__divide__imp,axiom,
% 9.49/5.25      ! [C: real,A: real,B: real] :
% 9.49/5.25        ( ( C != zero_zero_real )
% 9.49/5.25       => ( ( ( times_times_real @ A @ C )
% 9.49/5.25            = B )
% 9.49/5.25         => ( A
% 9.49/5.25            = ( divide_divide_real @ B @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2468_eq__divide__imp,axiom,
% 9.49/5.25      ! [C: rat,A: rat,B: rat] :
% 9.49/5.25        ( ( C != zero_zero_rat )
% 9.49/5.25       => ( ( ( times_times_rat @ A @ C )
% 9.49/5.25            = B )
% 9.49/5.25         => ( A
% 9.49/5.25            = ( divide_divide_rat @ B @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2469_nonzero__divide__eq__eq,axiom,
% 9.49/5.25      ! [C: complex,B: complex,A: complex] :
% 9.49/5.25        ( ( C != zero_zero_complex )
% 9.49/5.25       => ( ( ( divide1717551699836669952omplex @ B @ C )
% 9.49/5.25            = A )
% 9.49/5.25          = ( B
% 9.49/5.25            = ( times_times_complex @ A @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2470_nonzero__divide__eq__eq,axiom,
% 9.49/5.25      ! [C: real,B: real,A: real] :
% 9.49/5.25        ( ( C != zero_zero_real )
% 9.49/5.25       => ( ( ( divide_divide_real @ B @ C )
% 9.49/5.25            = A )
% 9.49/5.25          = ( B
% 9.49/5.25            = ( times_times_real @ A @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2471_nonzero__divide__eq__eq,axiom,
% 9.49/5.25      ! [C: rat,B: rat,A: rat] :
% 9.49/5.25        ( ( C != zero_zero_rat )
% 9.49/5.25       => ( ( ( divide_divide_rat @ B @ C )
% 9.49/5.25            = A )
% 9.49/5.25          = ( B
% 9.49/5.25            = ( times_times_rat @ A @ C ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2472_nonzero__eq__divide__eq,axiom,
% 9.49/5.25      ! [C: complex,A: complex,B: complex] :
% 9.49/5.25        ( ( C != zero_zero_complex )
% 9.49/5.25       => ( ( A
% 9.49/5.25            = ( divide1717551699836669952omplex @ B @ C ) )
% 9.49/5.25          = ( ( times_times_complex @ A @ C )
% 9.49/5.25            = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2473_nonzero__eq__divide__eq,axiom,
% 9.49/5.25      ! [C: real,A: real,B: real] :
% 9.49/5.25        ( ( C != zero_zero_real )
% 9.49/5.25       => ( ( A
% 9.49/5.25            = ( divide_divide_real @ B @ C ) )
% 9.49/5.25          = ( ( times_times_real @ A @ C )
% 9.49/5.25            = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2474_nonzero__eq__divide__eq,axiom,
% 9.49/5.25      ! [C: rat,A: rat,B: rat] :
% 9.49/5.25        ( ( C != zero_zero_rat )
% 9.49/5.25       => ( ( A
% 9.49/5.25            = ( divide_divide_rat @ B @ C ) )
% 9.49/5.25          = ( ( times_times_rat @ A @ C )
% 9.49/5.25            = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2475_right__inverse__eq,axiom,
% 9.49/5.25      ! [B: complex,A: complex] :
% 9.49/5.25        ( ( B != zero_zero_complex )
% 9.49/5.25       => ( ( ( divide1717551699836669952omplex @ A @ B )
% 9.49/5.25            = one_one_complex )
% 9.49/5.25          = ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2476_right__inverse__eq,axiom,
% 9.49/5.25      ! [B: real,A: real] :
% 9.49/5.25        ( ( B != zero_zero_real )
% 9.49/5.25       => ( ( ( divide_divide_real @ A @ B )
% 9.49/5.25            = one_one_real )
% 9.49/5.25          = ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2477_right__inverse__eq,axiom,
% 9.49/5.25      ! [B: rat,A: rat] :
% 9.49/5.25        ( ( B != zero_zero_rat )
% 9.49/5.25       => ( ( ( divide_divide_rat @ A @ B )
% 9.49/5.25            = one_one_rat )
% 9.49/5.25          = ( A = B ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2478_power__0,axiom,
% 9.49/5.25      ! [A: rat] :
% 9.49/5.25        ( ( power_power_rat @ A @ zero_zero_nat )
% 9.49/5.25        = one_one_rat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2479_power__0,axiom,
% 9.49/5.25      ! [A: nat] :
% 9.49/5.25        ( ( power_power_nat @ A @ zero_zero_nat )
% 9.49/5.25        = one_one_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2480_power__0,axiom,
% 9.49/5.25      ! [A: real] :
% 9.49/5.25        ( ( power_power_real @ A @ zero_zero_nat )
% 9.49/5.25        = one_one_real ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2481_power__0,axiom,
% 9.49/5.25      ! [A: int] :
% 9.49/5.25        ( ( power_power_int @ A @ zero_zero_nat )
% 9.49/5.25        = one_one_int ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2482_power__0,axiom,
% 9.49/5.25      ! [A: complex] :
% 9.49/5.25        ( ( power_power_complex @ A @ zero_zero_nat )
% 9.49/5.25        = one_one_complex ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2483_Ex__less__Suc2,axiom,
% 9.49/5.25      ! [N: nat,P: nat > $o] :
% 9.49/5.25        ( ( ? [I3: nat] :
% 9.49/5.25              ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 9.49/5.25              & ( P @ I3 ) ) )
% 9.49/5.25        = ( ( P @ zero_zero_nat )
% 9.49/5.25          | ? [I3: nat] :
% 9.49/5.25              ( ( ord_less_nat @ I3 @ N )
% 9.49/5.25              & ( P @ ( suc @ I3 ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2484_gr0__conv__Suc,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.25        = ( ? [M6: nat] :
% 9.49/5.25              ( N
% 9.49/5.25              = ( suc @ M6 ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2485_All__less__Suc2,axiom,
% 9.49/5.25      ! [N: nat,P: nat > $o] :
% 9.49/5.25        ( ( ! [I3: nat] :
% 9.49/5.25              ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 9.49/5.25             => ( P @ I3 ) ) )
% 9.49/5.25        = ( ( P @ zero_zero_nat )
% 9.49/5.25          & ! [I3: nat] :
% 9.49/5.25              ( ( ord_less_nat @ I3 @ N )
% 9.49/5.25             => ( P @ ( suc @ I3 ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2486_gr0__implies__Suc,axiom,
% 9.49/5.25      ! [N: nat] :
% 9.49/5.25        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.25       => ? [M4: nat] :
% 9.49/5.25            ( N
% 9.49/5.25            = ( suc @ M4 ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2487_less__Suc__eq__0__disj,axiom,
% 9.49/5.25      ! [M: nat,N: nat] :
% 9.49/5.25        ( ( ord_less_nat @ M @ ( suc @ N ) )
% 9.49/5.25        = ( ( M = zero_zero_nat )
% 9.49/5.25          | ? [J3: nat] :
% 9.49/5.25              ( ( M
% 9.49/5.25                = ( suc @ J3 ) )
% 9.49/5.25              & ( ord_less_nat @ J3 @ N ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2488_one__is__add,axiom,
% 9.49/5.25      ! [M: nat,N: nat] :
% 9.49/5.25        ( ( ( suc @ zero_zero_nat )
% 9.49/5.25          = ( plus_plus_nat @ M @ N ) )
% 9.49/5.25        = ( ( ( M
% 9.49/5.25              = ( suc @ zero_zero_nat ) )
% 9.49/5.25            & ( N = zero_zero_nat ) )
% 9.49/5.25          | ( ( M = zero_zero_nat )
% 9.49/5.25            & ( N
% 9.49/5.25              = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2489_add__is__1,axiom,
% 9.49/5.25      ! [M: nat,N: nat] :
% 9.49/5.25        ( ( ( plus_plus_nat @ M @ N )
% 9.49/5.25          = ( suc @ zero_zero_nat ) )
% 9.49/5.25        = ( ( ( M
% 9.49/5.25              = ( suc @ zero_zero_nat ) )
% 9.49/5.25            & ( N = zero_zero_nat ) )
% 9.49/5.25          | ( ( M = zero_zero_nat )
% 9.49/5.25            & ( N
% 9.49/5.25              = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2490_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I3_J,axiom,
% 9.49/5.25      ! [Uu: $o] :
% 9.49/5.25        ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Leaf @ Uu @ $true ) )
% 9.49/5.25        = one_one_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2491_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I2_J,axiom,
% 9.49/5.25      ! [Uv: $o] :
% 9.49/5.25        ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Leaf @ $true @ Uv ) )
% 9.49/5.25        = one_one_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2492_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I1_J,axiom,
% 9.49/5.25      ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Leaf @ $false @ $false ) )
% 9.49/5.25      = one_one_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2493_option_Osize_I4_J,axiom,
% 9.49/5.25      ! [X23: product_prod_nat_nat] :
% 9.49/5.25        ( ( size_s170228958280169651at_nat @ ( some_P7363390416028606310at_nat @ X23 ) )
% 9.49/5.25        = ( suc @ zero_zero_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2494_option_Osize_I4_J,axiom,
% 9.49/5.25      ! [X23: nat] :
% 9.49/5.25        ( ( size_size_option_nat @ ( some_nat @ X23 ) )
% 9.49/5.25        = ( suc @ zero_zero_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2495_option_Osize_I4_J,axiom,
% 9.49/5.25      ! [X23: num] :
% 9.49/5.25        ( ( size_size_option_num @ ( some_num @ X23 ) )
% 9.49/5.25        = ( suc @ zero_zero_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2496_One__nat__def,axiom,
% 9.49/5.25      ( one_one_nat
% 9.49/5.25      = ( suc @ zero_zero_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2497_less__imp__add__positive,axiom,
% 9.49/5.25      ! [I2: nat,J: nat] :
% 9.49/5.25        ( ( ord_less_nat @ I2 @ J )
% 9.49/5.25       => ? [K2: nat] :
% 9.49/5.25            ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 9.49/5.25            & ( ( plus_plus_nat @ I2 @ K2 )
% 9.49/5.25              = J ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2498_ex__least__nat__le,axiom,
% 9.49/5.25      ! [P: nat > $o,N: nat] :
% 9.49/5.25        ( ( P @ N )
% 9.49/5.25       => ( ~ ( P @ zero_zero_nat )
% 9.49/5.25         => ? [K2: nat] :
% 9.49/5.25              ( ( ord_less_eq_nat @ K2 @ N )
% 9.49/5.25              & ! [I: nat] :
% 9.49/5.25                  ( ( ord_less_nat @ I @ K2 )
% 9.49/5.25                 => ~ ( P @ I ) )
% 9.49/5.25              & ( P @ K2 ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2499_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I1_J,axiom,
% 9.49/5.25      ! [A: $o,B: $o,X: nat] :
% 9.49/5.25        ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Leaf @ A @ B ) @ X )
% 9.49/5.25        = one_one_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2500_option_Osize_I3_J,axiom,
% 9.49/5.25      ( ( size_s170228958280169651at_nat @ none_P5556105721700978146at_nat )
% 9.49/5.25      = ( suc @ zero_zero_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2501_option_Osize_I3_J,axiom,
% 9.49/5.25      ( ( size_size_option_nat @ none_nat )
% 9.49/5.25      = ( suc @ zero_zero_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2502_option_Osize_I3_J,axiom,
% 9.49/5.25      ( ( size_size_option_num @ none_num )
% 9.49/5.25      = ( suc @ zero_zero_nat ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2503_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 9.49/5.25      ! [M: nat,N: nat] :
% 9.49/5.25        ( ( ( divide_divide_nat @ M @ N )
% 9.49/5.25          = zero_zero_nat )
% 9.49/5.25        = ( ( ord_less_nat @ M @ N )
% 9.49/5.25          | ( N = zero_zero_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2504_mult__less__mono1,axiom,
% 9.49/5.25      ! [I2: nat,J: nat,K: nat] :
% 9.49/5.25        ( ( ord_less_nat @ I2 @ J )
% 9.49/5.25       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 9.49/5.25         => ( ord_less_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2505_mult__less__mono2,axiom,
% 9.49/5.25      ! [I2: nat,J: nat,K: nat] :
% 9.49/5.25        ( ( ord_less_nat @ I2 @ J )
% 9.49/5.25       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 9.49/5.25         => ( ord_less_nat @ ( times_times_nat @ K @ I2 ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2506_nat__mult__eq__cancel1,axiom,
% 9.49/5.25      ! [K: nat,M: nat,N: nat] :
% 9.49/5.25        ( ( ord_less_nat @ zero_zero_nat @ K )
% 9.49/5.25       => ( ( ( times_times_nat @ K @ M )
% 9.49/5.25            = ( times_times_nat @ K @ N ) )
% 9.49/5.25          = ( M = N ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2507_nat__mult__less__cancel1,axiom,
% 9.49/5.25      ! [K: nat,M: nat,N: nat] :
% 9.49/5.25        ( ( ord_less_nat @ zero_zero_nat @ K )
% 9.49/5.25       => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 9.49/5.25          = ( ord_less_nat @ M @ N ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2508_diff__less,axiom,
% 9.49/5.25      ! [N: nat,M: nat] :
% 9.49/5.25        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.25       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 9.49/5.25         => ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ M ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2509_diff__add__0,axiom,
% 9.49/5.25      ! [N: nat,M: nat] :
% 9.49/5.25        ( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M ) )
% 9.49/5.25        = zero_zero_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2510_mult__eq__self__implies__10,axiom,
% 9.49/5.25      ! [M: nat,N: nat] :
% 9.49/5.25        ( ( M
% 9.49/5.25          = ( times_times_nat @ M @ N ) )
% 9.49/5.25       => ( ( N = one_one_nat )
% 9.49/5.25          | ( M = zero_zero_nat ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2511_nat__power__less__imp__less,axiom,
% 9.49/5.25      ! [I2: nat,M: nat,N: nat] :
% 9.49/5.25        ( ( ord_less_nat @ zero_zero_nat @ I2 )
% 9.49/5.25       => ( ( ord_less_nat @ ( power_power_nat @ I2 @ M ) @ ( power_power_nat @ I2 @ N ) )
% 9.49/5.25         => ( ord_less_nat @ M @ N ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2512_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I6_J,axiom,
% 9.49/5.25      ! [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT,Vj: nat] :
% 9.49/5.25        ( ( vEBT_T_p_r_e_d @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Vj )
% 9.49/5.25        = one_one_nat ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2513_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Ocases,axiom,
% 9.49/5.25      ! [X: produc9072475918466114483BT_nat] :
% 9.49/5.25        ( ! [A4: $o,B3: $o,X3: nat] :
% 9.49/5.25            ( X
% 9.49/5.25           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ X3 ) )
% 9.49/5.25       => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,X3: nat] :
% 9.49/5.25              ( X
% 9.49/5.25             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ X3 ) )
% 9.49/5.25         => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,X3: nat] :
% 9.49/5.25                ( X
% 9.49/5.25               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ X3 ) )
% 9.49/5.25           => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X3: nat] :
% 9.49/5.25                  ( X
% 9.49/5.25                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ X3 ) )
% 9.49/5.25             => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 9.49/5.25                    ( X
% 9.49/5.25                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ X3 ) ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2514_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Ocases,axiom,
% 9.49/5.25      ! [X: produc9072475918466114483BT_nat] :
% 9.49/5.25        ( ! [A4: $o,B3: $o,X3: nat] :
% 9.49/5.25            ( X
% 9.49/5.25           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ X3 ) )
% 9.49/5.25       => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 9.49/5.25              ( X
% 9.49/5.25             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S ) @ X3 ) )
% 9.49/5.25         => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 9.49/5.25                ( X
% 9.49/5.25               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) @ X3 ) )
% 9.49/5.25           => ( ! [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 9.49/5.25                  ( X
% 9.49/5.25                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) @ X3 ) )
% 9.49/5.25             => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 9.49/5.25                    ( X
% 9.49/5.25                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ X3 ) ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2515_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Ocases,axiom,
% 9.49/5.25      ! [X: produc9072475918466114483BT_nat] :
% 9.49/5.25        ( ! [Uu2: $o,B3: $o] :
% 9.49/5.25            ( X
% 9.49/5.25           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B3 ) @ zero_zero_nat ) )
% 9.49/5.25       => ( ! [Uv2: $o,Uw2: $o,N3: nat] :
% 9.49/5.25              ( X
% 9.49/5.25             != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N3 ) ) )
% 9.49/5.25         => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,Va3: nat] :
% 9.49/5.25                ( X
% 9.49/5.25               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Va3 ) )
% 9.49/5.25           => ( ! [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT,Ve2: nat] :
% 9.49/5.25                  ( X
% 9.49/5.25                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Ve2 ) )
% 9.49/5.25             => ( ! [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh2: vEBT_VEBT,Vi2: nat] :
% 9.49/5.25                    ( X
% 9.49/5.25                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh2 ) @ Vi2 ) )
% 9.49/5.25               => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 9.49/5.25                      ( X
% 9.49/5.25                     != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ X3 ) ) ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2516_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Ocases,axiom,
% 9.49/5.25      ! [X: produc9072475918466114483BT_nat] :
% 9.49/5.25        ( ! [Uu2: $o,Uv2: $o] :
% 9.49/5.25            ( X
% 9.49/5.25           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) )
% 9.49/5.25       => ( ! [A4: $o,Uw2: $o] :
% 9.49/5.25              ( X
% 9.49/5.25             != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) )
% 9.49/5.25         => ( ! [A4: $o,B3: $o,Va2: nat] :
% 9.49/5.25                ( X
% 9.49/5.25               != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ ( suc @ ( suc @ Va2 ) ) ) )
% 9.49/5.25           => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT,Vb2: nat] :
% 9.49/5.25                  ( X
% 9.49/5.25                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) @ Vb2 ) )
% 9.49/5.25             => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT,Vf2: nat] :
% 9.49/5.25                    ( X
% 9.49/5.25                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Vf2 ) )
% 9.49/5.25               => ( ! [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT,Vj2: nat] :
% 9.49/5.25                      ( X
% 9.49/5.25                     != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Vj2 ) )
% 9.49/5.25                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 9.49/5.25                        ( X
% 9.49/5.25                       != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ X3 ) ) ) ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2517_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Ocases,axiom,
% 9.49/5.25      ! [X: produc9072475918466114483BT_nat] :
% 9.49/5.25        ( ! [A4: $o,B3: $o] :
% 9.49/5.25            ( X
% 9.49/5.25           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ zero_zero_nat ) )
% 9.49/5.25       => ( ! [A4: $o,B3: $o] :
% 9.49/5.25              ( X
% 9.49/5.25             != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ ( suc @ zero_zero_nat ) ) )
% 9.49/5.25         => ( ! [A4: $o,B3: $o,N3: nat] :
% 9.49/5.25                ( X
% 9.49/5.25               != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ ( suc @ ( suc @ N3 ) ) ) )
% 9.49/5.25           => ( ! [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,Uu2: nat] :
% 9.49/5.25                  ( X
% 9.49/5.25                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) @ Uu2 ) )
% 9.49/5.25             => ( ! [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 9.49/5.25                    ( X
% 9.49/5.25                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TreeList2 @ Summary2 ) @ X3 ) )
% 9.49/5.25               => ( ! [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 9.49/5.25                      ( X
% 9.49/5.25                     != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary2 ) @ X3 ) )
% 9.49/5.25                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 9.49/5.25                        ( X
% 9.49/5.25                       != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ X3 ) ) ) ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2518_VEBT__internal_Omembermima_Ocases,axiom,
% 9.49/5.25      ! [X: produc9072475918466114483BT_nat] :
% 9.49/5.25        ( ! [Uu2: $o,Uv2: $o,Uw2: nat] :
% 9.49/5.25            ( X
% 9.49/5.25           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Uw2 ) )
% 9.49/5.25       => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT,Uz2: nat] :
% 9.49/5.25              ( X
% 9.49/5.25             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Uz2 ) )
% 9.49/5.25         => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT,X3: nat] :
% 9.49/5.25                ( X
% 9.49/5.25               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ X3 ) )
% 9.49/5.25           => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X3: nat] :
% 9.49/5.25                  ( X
% 9.49/5.25                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) @ X3 ) )
% 9.49/5.25             => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT,X3: nat] :
% 9.49/5.25                    ( X
% 9.49/5.25                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) @ X3 ) ) ) ) ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2519_vebt__insert_Osimps_I2_J,axiom,
% 9.49/5.25      ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT,X: nat] :
% 9.49/5.25        ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S3 ) @ X )
% 9.49/5.25        = ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S3 ) ) ).
% 9.49/5.25  
% 9.49/5.25  thf(fact_2520_vebt__pred_Osimps_I3_J,axiom,
% 9.49/5.25      ! [B: $o,A: $o,Va: nat] :
% 9.49/5.25        ( ( B
% 9.49/5.25         => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 9.49/5.26            = ( some_nat @ one_one_nat ) ) )
% 9.49/5.26        & ( ~ B
% 9.49/5.26         => ( ( A
% 9.49/5.26             => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 9.49/5.26                = ( some_nat @ zero_zero_nat ) ) )
% 9.49/5.26            & ( ~ A
% 9.49/5.26             => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 9.49/5.26                = none_nat ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2521_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Ocases,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT] :
% 9.49/5.26        ( ( X
% 9.49/5.26         != ( vEBT_Leaf @ $false @ $false ) )
% 9.49/5.26       => ( ! [Uv2: $o] :
% 9.49/5.26              ( X
% 9.49/5.26             != ( vEBT_Leaf @ $true @ Uv2 ) )
% 9.49/5.26         => ( ! [Uu2: $o] :
% 9.49/5.26                ( X
% 9.49/5.26               != ( vEBT_Leaf @ Uu2 @ $true ) )
% 9.49/5.26           => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 9.49/5.26                  ( X
% 9.49/5.26                 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 9.49/5.26             => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 9.49/5.26                    ( X
% 9.49/5.26                   != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2522_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I1_J,axiom,
% 9.49/5.26      ! [A: $o,B: $o,X: nat] :
% 9.49/5.26        ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Leaf @ A @ B ) @ X )
% 9.49/5.26        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( X = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2523_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I3_J,axiom,
% 9.49/5.26      ! [A: $o,B: $o,N: nat] :
% 9.49/5.26        ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ N ) ) )
% 9.49/5.26        = one_one_nat ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2524_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Osimps_I1_J,axiom,
% 9.49/5.26      ! [A: $o,B: $o] :
% 9.49/5.26        ( ( vEBT_T_m_a_x_t @ ( vEBT_Leaf @ A @ B ) )
% 9.49/5.26        = ( plus_plus_nat @ one_one_nat @ ( if_nat @ B @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2525_VEBT__internal_OminNull_Oelims_I3_J,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT] :
% 9.49/5.26        ( ~ ( vEBT_VEBT_minNull @ X )
% 9.49/5.26       => ( ! [Uv2: $o] :
% 9.49/5.26              ( X
% 9.49/5.26             != ( vEBT_Leaf @ $true @ Uv2 ) )
% 9.49/5.26         => ( ! [Uu2: $o] :
% 9.49/5.26                ( X
% 9.49/5.26               != ( vEBT_Leaf @ Uu2 @ $true ) )
% 9.49/5.26           => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 9.49/5.26                  ( X
% 9.49/5.26                 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2526_VEBT__internal_OminNull_Oelims_I2_J,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT] :
% 9.49/5.26        ( ( vEBT_VEBT_minNull @ X )
% 9.49/5.26       => ( ( X
% 9.49/5.26           != ( vEBT_Leaf @ $false @ $false ) )
% 9.49/5.26         => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 9.49/5.26                ( X
% 9.49/5.26               != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2527_vebt__succ_Osimps_I2_J,axiom,
% 9.49/5.26      ! [Uv: $o,Uw: $o,N: nat] :
% 9.49/5.26        ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N ) )
% 9.49/5.26        = none_nat ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2528_mult__le__cancel__left,axiom,
% 9.49/5.26      ! [C: real,A: real,B: real] :
% 9.49/5.26        ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 9.49/5.26        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.26           => ( ord_less_eq_real @ A @ B ) )
% 9.49/5.26          & ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.26           => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2529_mult__le__cancel__left,axiom,
% 9.49/5.26      ! [C: rat,A: rat,B: rat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 9.49/5.26        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.26           => ( ord_less_eq_rat @ A @ B ) )
% 9.49/5.26          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.26           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2530_mult__le__cancel__left,axiom,
% 9.49/5.26      ! [C: int,A: int,B: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 9.49/5.26        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 9.49/5.26           => ( ord_less_eq_int @ A @ B ) )
% 9.49/5.26          & ( ( ord_less_int @ C @ zero_zero_int )
% 9.49/5.26           => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2531_mult__le__cancel__right,axiom,
% 9.49/5.26      ! [A: real,C: real,B: real] :
% 9.49/5.26        ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 9.49/5.26        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.26           => ( ord_less_eq_real @ A @ B ) )
% 9.49/5.26          & ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.26           => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2532_mult__le__cancel__right,axiom,
% 9.49/5.26      ! [A: rat,C: rat,B: rat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 9.49/5.26        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.26           => ( ord_less_eq_rat @ A @ B ) )
% 9.49/5.26          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.26           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2533_mult__le__cancel__right,axiom,
% 9.49/5.26      ! [A: int,C: int,B: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 9.49/5.26        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 9.49/5.26           => ( ord_less_eq_int @ A @ B ) )
% 9.49/5.26          & ( ( ord_less_int @ C @ zero_zero_int )
% 9.49/5.26           => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2534_mult__left__less__imp__less,axiom,
% 9.49/5.26      ! [C: real,A: real,B: real] :
% 9.49/5.26        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 9.49/5.26       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 9.49/5.26         => ( ord_less_real @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2535_mult__left__less__imp__less,axiom,
% 9.49/5.26      ! [C: rat,A: rat,B: rat] :
% 9.49/5.26        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 9.49/5.26       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.49/5.26         => ( ord_less_rat @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2536_mult__left__less__imp__less,axiom,
% 9.49/5.26      ! [C: nat,A: nat,B: nat] :
% 9.49/5.26        ( ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 9.49/5.26       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 9.49/5.26         => ( ord_less_nat @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2537_mult__left__less__imp__less,axiom,
% 9.49/5.26      ! [C: int,A: int,B: int] :
% 9.49/5.26        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 9.49/5.26       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.49/5.26         => ( ord_less_int @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2538_mult__strict__mono,axiom,
% 9.49/5.26      ! [A: real,B: real,C: real,D2: real] :
% 9.49/5.26        ( ( ord_less_real @ A @ B )
% 9.49/5.26       => ( ( ord_less_real @ C @ D2 )
% 9.49/5.26         => ( ( ord_less_real @ zero_zero_real @ B )
% 9.49/5.26           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 9.49/5.26             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2539_mult__strict__mono,axiom,
% 9.49/5.26      ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.49/5.26        ( ( ord_less_rat @ A @ B )
% 9.49/5.26       => ( ( ord_less_rat @ C @ D2 )
% 9.49/5.26         => ( ( ord_less_rat @ zero_zero_rat @ B )
% 9.49/5.26           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.49/5.26             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2540_mult__strict__mono,axiom,
% 9.49/5.26      ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.49/5.26        ( ( ord_less_nat @ A @ B )
% 9.49/5.26       => ( ( ord_less_nat @ C @ D2 )
% 9.49/5.26         => ( ( ord_less_nat @ zero_zero_nat @ B )
% 9.49/5.26           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 9.49/5.26             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2541_mult__strict__mono,axiom,
% 9.49/5.26      ! [A: int,B: int,C: int,D2: int] :
% 9.49/5.26        ( ( ord_less_int @ A @ B )
% 9.49/5.26       => ( ( ord_less_int @ C @ D2 )
% 9.49/5.26         => ( ( ord_less_int @ zero_zero_int @ B )
% 9.49/5.26           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.49/5.26             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2542_mult__less__cancel__left,axiom,
% 9.49/5.26      ! [C: real,A: real,B: real] :
% 9.49/5.26        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 9.49/5.26        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 9.49/5.26           => ( ord_less_real @ A @ B ) )
% 9.49/5.26          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 9.49/5.26           => ( ord_less_real @ B @ A ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2543_mult__less__cancel__left,axiom,
% 9.49/5.26      ! [C: rat,A: rat,B: rat] :
% 9.49/5.26        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 9.49/5.26        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.49/5.26           => ( ord_less_rat @ A @ B ) )
% 9.49/5.26          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 9.49/5.26           => ( ord_less_rat @ B @ A ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2544_mult__less__cancel__left,axiom,
% 9.49/5.26      ! [C: int,A: int,B: int] :
% 9.49/5.26        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 9.49/5.26        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.49/5.26           => ( ord_less_int @ A @ B ) )
% 9.49/5.26          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 9.49/5.26           => ( ord_less_int @ B @ A ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2545_mult__right__less__imp__less,axiom,
% 9.49/5.26      ! [A: real,C: real,B: real] :
% 9.49/5.26        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 9.49/5.26       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 9.49/5.26         => ( ord_less_real @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2546_mult__right__less__imp__less,axiom,
% 9.49/5.26      ! [A: rat,C: rat,B: rat] :
% 9.49/5.26        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 9.49/5.26       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.49/5.26         => ( ord_less_rat @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2547_mult__right__less__imp__less,axiom,
% 9.49/5.26      ! [A: nat,C: nat,B: nat] :
% 9.49/5.26        ( ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 9.49/5.26       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 9.49/5.26         => ( ord_less_nat @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2548_mult__right__less__imp__less,axiom,
% 9.49/5.26      ! [A: int,C: int,B: int] :
% 9.49/5.26        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 9.49/5.26       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.49/5.26         => ( ord_less_int @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2549_mult__strict__mono_H,axiom,
% 9.49/5.26      ! [A: real,B: real,C: real,D2: real] :
% 9.49/5.26        ( ( ord_less_real @ A @ B )
% 9.49/5.26       => ( ( ord_less_real @ C @ D2 )
% 9.49/5.26         => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 9.49/5.26           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 9.49/5.26             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2550_mult__strict__mono_H,axiom,
% 9.49/5.26      ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.49/5.26        ( ( ord_less_rat @ A @ B )
% 9.49/5.26       => ( ( ord_less_rat @ C @ D2 )
% 9.49/5.26         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.49/5.26           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.49/5.26             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2551_mult__strict__mono_H,axiom,
% 9.49/5.26      ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.49/5.26        ( ( ord_less_nat @ A @ B )
% 9.49/5.26       => ( ( ord_less_nat @ C @ D2 )
% 9.49/5.26         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.49/5.26           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 9.49/5.26             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2552_mult__strict__mono_H,axiom,
% 9.49/5.26      ! [A: int,B: int,C: int,D2: int] :
% 9.49/5.26        ( ( ord_less_int @ A @ B )
% 9.49/5.26       => ( ( ord_less_int @ C @ D2 )
% 9.49/5.26         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.26           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.49/5.26             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2553_mult__less__cancel__right,axiom,
% 9.49/5.26      ! [A: real,C: real,B: real] :
% 9.49/5.26        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 9.49/5.26        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 9.49/5.26           => ( ord_less_real @ A @ B ) )
% 9.49/5.26          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 9.49/5.26           => ( ord_less_real @ B @ A ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2554_mult__less__cancel__right,axiom,
% 9.49/5.26      ! [A: rat,C: rat,B: rat] :
% 9.49/5.26        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 9.49/5.26        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.49/5.26           => ( ord_less_rat @ A @ B ) )
% 9.49/5.26          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 9.49/5.26           => ( ord_less_rat @ B @ A ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2555_mult__less__cancel__right,axiom,
% 9.49/5.26      ! [A: int,C: int,B: int] :
% 9.49/5.26        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 9.49/5.26        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.49/5.26           => ( ord_less_int @ A @ B ) )
% 9.49/5.26          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 9.49/5.26           => ( ord_less_int @ B @ A ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2556_mult__le__cancel__left__neg,axiom,
% 9.49/5.26      ! [C: real,A: real,B: real] :
% 9.49/5.26        ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.26       => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 9.49/5.26          = ( ord_less_eq_real @ B @ A ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2557_mult__le__cancel__left__neg,axiom,
% 9.49/5.26      ! [C: rat,A: rat,B: rat] :
% 9.49/5.26        ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.26       => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 9.49/5.26          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2558_mult__le__cancel__left__neg,axiom,
% 9.49/5.26      ! [C: int,A: int,B: int] :
% 9.49/5.26        ( ( ord_less_int @ C @ zero_zero_int )
% 9.49/5.26       => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 9.49/5.26          = ( ord_less_eq_int @ B @ A ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2559_mult__le__cancel__left__pos,axiom,
% 9.49/5.26      ! [C: real,A: real,B: real] :
% 9.49/5.26        ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.26       => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 9.49/5.26          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2560_mult__le__cancel__left__pos,axiom,
% 9.49/5.26      ! [C: rat,A: rat,B: rat] :
% 9.49/5.26        ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.26       => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 9.49/5.26          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2561_mult__le__cancel__left__pos,axiom,
% 9.49/5.26      ! [C: int,A: int,B: int] :
% 9.49/5.26        ( ( ord_less_int @ zero_zero_int @ C )
% 9.49/5.26       => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 9.49/5.26          = ( ord_less_eq_int @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2562_mult__left__le__imp__le,axiom,
% 9.49/5.26      ! [C: real,A: real,B: real] :
% 9.49/5.26        ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 9.49/5.26       => ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.26         => ( ord_less_eq_real @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2563_mult__left__le__imp__le,axiom,
% 9.49/5.26      ! [C: rat,A: rat,B: rat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 9.49/5.26       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.26         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2564_mult__left__le__imp__le,axiom,
% 9.49/5.26      ! [C: nat,A: nat,B: nat] :
% 9.49/5.26        ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 9.49/5.26       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 9.49/5.26         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2565_mult__left__le__imp__le,axiom,
% 9.49/5.26      ! [C: int,A: int,B: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 9.49/5.26       => ( ( ord_less_int @ zero_zero_int @ C )
% 9.49/5.26         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2566_mult__right__le__imp__le,axiom,
% 9.49/5.26      ! [A: real,C: real,B: real] :
% 9.49/5.26        ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 9.49/5.26       => ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.26         => ( ord_less_eq_real @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2567_mult__right__le__imp__le,axiom,
% 9.49/5.26      ! [A: rat,C: rat,B: rat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 9.49/5.26       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.26         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2568_mult__right__le__imp__le,axiom,
% 9.49/5.26      ! [A: nat,C: nat,B: nat] :
% 9.49/5.26        ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 9.49/5.26       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 9.49/5.26         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2569_mult__right__le__imp__le,axiom,
% 9.49/5.26      ! [A: int,C: int,B: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 9.49/5.26       => ( ( ord_less_int @ zero_zero_int @ C )
% 9.49/5.26         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2570_mult__le__less__imp__less,axiom,
% 9.49/5.26      ! [A: real,B: real,C: real,D2: real] :
% 9.49/5.26        ( ( ord_less_eq_real @ A @ B )
% 9.49/5.26       => ( ( ord_less_real @ C @ D2 )
% 9.49/5.26         => ( ( ord_less_real @ zero_zero_real @ A )
% 9.49/5.26           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 9.49/5.26             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2571_mult__le__less__imp__less,axiom,
% 9.49/5.26      ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ A @ B )
% 9.49/5.26       => ( ( ord_less_rat @ C @ D2 )
% 9.49/5.26         => ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.49/5.26           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.49/5.26             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2572_mult__le__less__imp__less,axiom,
% 9.49/5.26      ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.49/5.26        ( ( ord_less_eq_nat @ A @ B )
% 9.49/5.26       => ( ( ord_less_nat @ C @ D2 )
% 9.49/5.26         => ( ( ord_less_nat @ zero_zero_nat @ A )
% 9.49/5.26           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 9.49/5.26             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2573_mult__le__less__imp__less,axiom,
% 9.49/5.26      ! [A: int,B: int,C: int,D2: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ A @ B )
% 9.49/5.26       => ( ( ord_less_int @ C @ D2 )
% 9.49/5.26         => ( ( ord_less_int @ zero_zero_int @ A )
% 9.49/5.26           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.49/5.26             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2574_mult__less__le__imp__less,axiom,
% 9.49/5.26      ! [A: real,B: real,C: real,D2: real] :
% 9.49/5.26        ( ( ord_less_real @ A @ B )
% 9.49/5.26       => ( ( ord_less_eq_real @ C @ D2 )
% 9.49/5.26         => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 9.49/5.26           => ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.26             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2575_mult__less__le__imp__less,axiom,
% 9.49/5.26      ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.49/5.26        ( ( ord_less_rat @ A @ B )
% 9.49/5.26       => ( ( ord_less_eq_rat @ C @ D2 )
% 9.49/5.26         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.49/5.26           => ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.26             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2576_mult__less__le__imp__less,axiom,
% 9.49/5.26      ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.49/5.26        ( ( ord_less_nat @ A @ B )
% 9.49/5.26       => ( ( ord_less_eq_nat @ C @ D2 )
% 9.49/5.26         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.49/5.26           => ( ( ord_less_nat @ zero_zero_nat @ C )
% 9.49/5.26             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2577_mult__less__le__imp__less,axiom,
% 9.49/5.26      ! [A: int,B: int,C: int,D2: int] :
% 9.49/5.26        ( ( ord_less_int @ A @ B )
% 9.49/5.26       => ( ( ord_less_eq_int @ C @ D2 )
% 9.49/5.26         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.26           => ( ( ord_less_int @ zero_zero_int @ C )
% 9.49/5.26             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2578_field__le__epsilon,axiom,
% 9.49/5.26      ! [X: real,Y2: real] :
% 9.49/5.26        ( ! [E2: real] :
% 9.49/5.26            ( ( ord_less_real @ zero_zero_real @ E2 )
% 9.49/5.26           => ( ord_less_eq_real @ X @ ( plus_plus_real @ Y2 @ E2 ) ) )
% 9.49/5.26       => ( ord_less_eq_real @ X @ Y2 ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2579_field__le__epsilon,axiom,
% 9.49/5.26      ! [X: rat,Y2: rat] :
% 9.49/5.26        ( ! [E2: rat] :
% 9.49/5.26            ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 9.49/5.26           => ( ord_less_eq_rat @ X @ ( plus_plus_rat @ Y2 @ E2 ) ) )
% 9.49/5.26       => ( ord_less_eq_rat @ X @ Y2 ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2580_add__neg__nonpos,axiom,
% 9.49/5.26      ! [A: real,B: real] :
% 9.49/5.26        ( ( ord_less_real @ A @ zero_zero_real )
% 9.49/5.26       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 9.49/5.26         => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2581_add__neg__nonpos,axiom,
% 9.49/5.26      ! [A: rat,B: rat] :
% 9.49/5.26        ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.49/5.26       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 9.49/5.26         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2582_add__neg__nonpos,axiom,
% 9.49/5.26      ! [A: nat,B: nat] :
% 9.49/5.26        ( ( ord_less_nat @ A @ zero_zero_nat )
% 9.49/5.26       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 9.49/5.26         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2583_add__neg__nonpos,axiom,
% 9.49/5.26      ! [A: int,B: int] :
% 9.49/5.26        ( ( ord_less_int @ A @ zero_zero_int )
% 9.49/5.26       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 9.49/5.26         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2584_add__nonneg__pos,axiom,
% 9.49/5.26      ! [A: real,B: real] :
% 9.49/5.26        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 9.49/5.26       => ( ( ord_less_real @ zero_zero_real @ B )
% 9.49/5.26         => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2585_add__nonneg__pos,axiom,
% 9.49/5.26      ! [A: rat,B: rat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.49/5.26       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 9.49/5.26         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2586_add__nonneg__pos,axiom,
% 9.49/5.26      ! [A: nat,B: nat] :
% 9.49/5.26        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.49/5.26       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 9.49/5.26         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2587_add__nonneg__pos,axiom,
% 9.49/5.26      ! [A: int,B: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.26       => ( ( ord_less_int @ zero_zero_int @ B )
% 9.49/5.26         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2588_add__nonpos__neg,axiom,
% 9.49/5.26      ! [A: real,B: real] :
% 9.49/5.26        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 9.49/5.26       => ( ( ord_less_real @ B @ zero_zero_real )
% 9.49/5.26         => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2589_add__nonpos__neg,axiom,
% 9.49/5.26      ! [A: rat,B: rat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 9.49/5.26       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 9.49/5.26         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2590_add__nonpos__neg,axiom,
% 9.49/5.26      ! [A: nat,B: nat] :
% 9.49/5.26        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 9.49/5.26       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 9.49/5.26         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2591_add__nonpos__neg,axiom,
% 9.49/5.26      ! [A: int,B: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 9.49/5.26       => ( ( ord_less_int @ B @ zero_zero_int )
% 9.49/5.26         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2592_add__pos__nonneg,axiom,
% 9.49/5.26      ! [A: real,B: real] :
% 9.49/5.26        ( ( ord_less_real @ zero_zero_real @ A )
% 9.49/5.26       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 9.49/5.26         => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2593_add__pos__nonneg,axiom,
% 9.49/5.26      ! [A: rat,B: rat] :
% 9.49/5.26        ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.49/5.26       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 9.49/5.26         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2594_add__pos__nonneg,axiom,
% 9.49/5.26      ! [A: nat,B: nat] :
% 9.49/5.26        ( ( ord_less_nat @ zero_zero_nat @ A )
% 9.49/5.26       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 9.49/5.26         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2595_add__pos__nonneg,axiom,
% 9.49/5.26      ! [A: int,B: int] :
% 9.49/5.26        ( ( ord_less_int @ zero_zero_int @ A )
% 9.49/5.26       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 9.49/5.26         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2596_add__strict__increasing,axiom,
% 9.49/5.26      ! [A: real,B: real,C: real] :
% 9.49/5.26        ( ( ord_less_real @ zero_zero_real @ A )
% 9.49/5.26       => ( ( ord_less_eq_real @ B @ C )
% 9.49/5.26         => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2597_add__strict__increasing,axiom,
% 9.49/5.26      ! [A: rat,B: rat,C: rat] :
% 9.49/5.26        ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.49/5.26       => ( ( ord_less_eq_rat @ B @ C )
% 9.49/5.26         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2598_add__strict__increasing,axiom,
% 9.49/5.26      ! [A: nat,B: nat,C: nat] :
% 9.49/5.26        ( ( ord_less_nat @ zero_zero_nat @ A )
% 9.49/5.26       => ( ( ord_less_eq_nat @ B @ C )
% 9.49/5.26         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2599_add__strict__increasing,axiom,
% 9.49/5.26      ! [A: int,B: int,C: int] :
% 9.49/5.26        ( ( ord_less_int @ zero_zero_int @ A )
% 9.49/5.26       => ( ( ord_less_eq_int @ B @ C )
% 9.49/5.26         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2600_add__strict__increasing2,axiom,
% 9.49/5.26      ! [A: real,B: real,C: real] :
% 9.49/5.26        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 9.49/5.26       => ( ( ord_less_real @ B @ C )
% 9.49/5.26         => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2601_add__strict__increasing2,axiom,
% 9.49/5.26      ! [A: rat,B: rat,C: rat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.49/5.26       => ( ( ord_less_rat @ B @ C )
% 9.49/5.26         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2602_add__strict__increasing2,axiom,
% 9.49/5.26      ! [A: nat,B: nat,C: nat] :
% 9.49/5.26        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.49/5.26       => ( ( ord_less_nat @ B @ C )
% 9.49/5.26         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2603_add__strict__increasing2,axiom,
% 9.49/5.26      ! [A: int,B: int,C: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.26       => ( ( ord_less_int @ B @ C )
% 9.49/5.26         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2604_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I3_J,axiom,
% 9.49/5.26      ! [A: $o,B: $o,Va: nat] :
% 9.49/5.26        ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 9.49/5.26        = one_one_nat ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2605_mult__left__le__one__le,axiom,
% 9.49/5.26      ! [X: rat,Y2: rat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 9.49/5.26       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 9.49/5.26         => ( ( ord_less_eq_rat @ Y2 @ one_one_rat )
% 9.49/5.26           => ( ord_less_eq_rat @ ( times_times_rat @ Y2 @ X ) @ X ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2606_mult__left__le__one__le,axiom,
% 9.49/5.26      ! [X: real,Y2: real] :
% 9.49/5.26        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.49/5.26       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 9.49/5.26         => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 9.49/5.26           => ( ord_less_eq_real @ ( times_times_real @ Y2 @ X ) @ X ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2607_mult__left__le__one__le,axiom,
% 9.49/5.26      ! [X: int,Y2: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 9.49/5.26       => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 9.49/5.26         => ( ( ord_less_eq_int @ Y2 @ one_one_int )
% 9.49/5.26           => ( ord_less_eq_int @ ( times_times_int @ Y2 @ X ) @ X ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2608_mult__right__le__one__le,axiom,
% 9.49/5.26      ! [X: rat,Y2: rat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 9.49/5.26       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 9.49/5.26         => ( ( ord_less_eq_rat @ Y2 @ one_one_rat )
% 9.49/5.26           => ( ord_less_eq_rat @ ( times_times_rat @ X @ Y2 ) @ X ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2609_mult__right__le__one__le,axiom,
% 9.49/5.26      ! [X: real,Y2: real] :
% 9.49/5.26        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.49/5.26       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 9.49/5.26         => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 9.49/5.26           => ( ord_less_eq_real @ ( times_times_real @ X @ Y2 ) @ X ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2610_mult__right__le__one__le,axiom,
% 9.49/5.26      ! [X: int,Y2: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 9.49/5.26       => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 9.49/5.26         => ( ( ord_less_eq_int @ Y2 @ one_one_int )
% 9.49/5.26           => ( ord_less_eq_int @ ( times_times_int @ X @ Y2 ) @ X ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2611_mult__le__one,axiom,
% 9.49/5.26      ! [A: rat,B: rat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ A @ one_one_rat )
% 9.49/5.26       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 9.49/5.26         => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 9.49/5.26           => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2612_mult__le__one,axiom,
% 9.49/5.26      ! [A: real,B: real] :
% 9.49/5.26        ( ( ord_less_eq_real @ A @ one_one_real )
% 9.49/5.26       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 9.49/5.26         => ( ( ord_less_eq_real @ B @ one_one_real )
% 9.49/5.26           => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ one_one_real ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2613_mult__le__one,axiom,
% 9.49/5.26      ! [A: nat,B: nat] :
% 9.49/5.26        ( ( ord_less_eq_nat @ A @ one_one_nat )
% 9.49/5.26       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 9.49/5.26         => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 9.49/5.26           => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2614_mult__le__one,axiom,
% 9.49/5.26      ! [A: int,B: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ A @ one_one_int )
% 9.49/5.26       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 9.49/5.26         => ( ( ord_less_eq_int @ B @ one_one_int )
% 9.49/5.26           => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2615_mult__left__le,axiom,
% 9.49/5.26      ! [C: rat,A: rat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ C @ one_one_rat )
% 9.49/5.26       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.49/5.26         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ A ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2616_mult__left__le,axiom,
% 9.49/5.26      ! [C: real,A: real] :
% 9.49/5.26        ( ( ord_less_eq_real @ C @ one_one_real )
% 9.49/5.26       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 9.49/5.26         => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ A ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2617_mult__left__le,axiom,
% 9.49/5.26      ! [C: nat,A: nat] :
% 9.49/5.26        ( ( ord_less_eq_nat @ C @ one_one_nat )
% 9.49/5.26       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.49/5.26         => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2618_mult__left__le,axiom,
% 9.49/5.26      ! [C: int,A: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ C @ one_one_int )
% 9.49/5.26       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.26         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2619_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 9.49/5.26      ! [A: nat,B: nat] :
% 9.49/5.26        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.49/5.26       => ( ( ord_less_nat @ A @ B )
% 9.49/5.26         => ( ( divide_divide_nat @ A @ B )
% 9.49/5.26            = zero_zero_nat ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2620_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 9.49/5.26      ! [A: int,B: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.26       => ( ( ord_less_int @ A @ B )
% 9.49/5.26         => ( ( divide_divide_int @ A @ B )
% 9.49/5.26            = zero_zero_int ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2621_div__positive,axiom,
% 9.49/5.26      ! [B: nat,A: nat] :
% 9.49/5.26        ( ( ord_less_nat @ zero_zero_nat @ B )
% 9.49/5.26       => ( ( ord_less_eq_nat @ B @ A )
% 9.49/5.26         => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2622_div__positive,axiom,
% 9.49/5.26      ! [B: int,A: int] :
% 9.49/5.26        ( ( ord_less_int @ zero_zero_int @ B )
% 9.49/5.26       => ( ( ord_less_eq_int @ B @ A )
% 9.49/5.26         => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2623_frac__le,axiom,
% 9.49/5.26      ! [Y2: real,X: real,W: real,Z: real] :
% 9.49/5.26        ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 9.49/5.26       => ( ( ord_less_eq_real @ X @ Y2 )
% 9.49/5.26         => ( ( ord_less_real @ zero_zero_real @ W )
% 9.49/5.26           => ( ( ord_less_eq_real @ W @ Z )
% 9.49/5.26             => ( ord_less_eq_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y2 @ W ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2624_frac__le,axiom,
% 9.49/5.26      ! [Y2: rat,X: rat,W: rat,Z: rat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 9.49/5.26       => ( ( ord_less_eq_rat @ X @ Y2 )
% 9.49/5.26         => ( ( ord_less_rat @ zero_zero_rat @ W )
% 9.49/5.26           => ( ( ord_less_eq_rat @ W @ Z )
% 9.49/5.26             => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Z ) @ ( divide_divide_rat @ Y2 @ W ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2625_frac__less,axiom,
% 9.49/5.26      ! [X: real,Y2: real,W: real,Z: real] :
% 9.49/5.26        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.49/5.26       => ( ( ord_less_real @ X @ Y2 )
% 9.49/5.26         => ( ( ord_less_real @ zero_zero_real @ W )
% 9.49/5.26           => ( ( ord_less_eq_real @ W @ Z )
% 9.49/5.26             => ( ord_less_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y2 @ W ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2626_frac__less,axiom,
% 9.49/5.26      ! [X: rat,Y2: rat,W: rat,Z: rat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 9.49/5.26       => ( ( ord_less_rat @ X @ Y2 )
% 9.49/5.26         => ( ( ord_less_rat @ zero_zero_rat @ W )
% 9.49/5.26           => ( ( ord_less_eq_rat @ W @ Z )
% 9.49/5.26             => ( ord_less_rat @ ( divide_divide_rat @ X @ Z ) @ ( divide_divide_rat @ Y2 @ W ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2627_frac__less2,axiom,
% 9.49/5.26      ! [X: real,Y2: real,W: real,Z: real] :
% 9.49/5.26        ( ( ord_less_real @ zero_zero_real @ X )
% 9.49/5.26       => ( ( ord_less_eq_real @ X @ Y2 )
% 9.49/5.26         => ( ( ord_less_real @ zero_zero_real @ W )
% 9.49/5.26           => ( ( ord_less_real @ W @ Z )
% 9.49/5.26             => ( ord_less_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y2 @ W ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2628_frac__less2,axiom,
% 9.49/5.26      ! [X: rat,Y2: rat,W: rat,Z: rat] :
% 9.49/5.26        ( ( ord_less_rat @ zero_zero_rat @ X )
% 9.49/5.26       => ( ( ord_less_eq_rat @ X @ Y2 )
% 9.49/5.26         => ( ( ord_less_rat @ zero_zero_rat @ W )
% 9.49/5.26           => ( ( ord_less_rat @ W @ Z )
% 9.49/5.26             => ( ord_less_rat @ ( divide_divide_rat @ X @ Z ) @ ( divide_divide_rat @ Y2 @ W ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2629_divide__le__cancel,axiom,
% 9.49/5.26      ! [A: real,C: real,B: real] :
% 9.49/5.26        ( ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 9.49/5.26        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.26           => ( ord_less_eq_real @ A @ B ) )
% 9.49/5.26          & ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.26           => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2630_divide__le__cancel,axiom,
% 9.49/5.26      ! [A: rat,C: rat,B: rat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 9.49/5.26        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.26           => ( ord_less_eq_rat @ A @ B ) )
% 9.49/5.26          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.26           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2631_divide__nonneg__neg,axiom,
% 9.49/5.26      ! [X: real,Y2: real] :
% 9.49/5.26        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.49/5.26       => ( ( ord_less_real @ Y2 @ zero_zero_real )
% 9.49/5.26         => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y2 ) @ zero_zero_real ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2632_divide__nonneg__neg,axiom,
% 9.49/5.26      ! [X: rat,Y2: rat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 9.49/5.26       => ( ( ord_less_rat @ Y2 @ zero_zero_rat )
% 9.49/5.26         => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y2 ) @ zero_zero_rat ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2633_divide__nonneg__pos,axiom,
% 9.49/5.26      ! [X: real,Y2: real] :
% 9.49/5.26        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.49/5.26       => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 9.49/5.26         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y2 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2634_divide__nonneg__pos,axiom,
% 9.49/5.26      ! [X: rat,Y2: rat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 9.49/5.26       => ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 9.49/5.26         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y2 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2635_divide__nonpos__neg,axiom,
% 9.49/5.26      ! [X: real,Y2: real] :
% 9.49/5.26        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 9.49/5.26       => ( ( ord_less_real @ Y2 @ zero_zero_real )
% 9.49/5.26         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y2 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2636_divide__nonpos__neg,axiom,
% 9.49/5.26      ! [X: rat,Y2: rat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 9.49/5.26       => ( ( ord_less_rat @ Y2 @ zero_zero_rat )
% 9.49/5.26         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y2 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2637_divide__nonpos__pos,axiom,
% 9.49/5.26      ! [X: real,Y2: real] :
% 9.49/5.26        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 9.49/5.26       => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 9.49/5.26         => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y2 ) @ zero_zero_real ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2638_divide__nonpos__pos,axiom,
% 9.49/5.26      ! [X: rat,Y2: rat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 9.49/5.26       => ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 9.49/5.26         => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y2 ) @ zero_zero_rat ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2639_sum__squares__le__zero__iff,axiom,
% 9.49/5.26      ! [X: rat,Y2: rat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y2 @ Y2 ) ) @ zero_zero_rat )
% 9.49/5.26        = ( ( X = zero_zero_rat )
% 9.49/5.26          & ( Y2 = zero_zero_rat ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2640_sum__squares__le__zero__iff,axiom,
% 9.49/5.26      ! [X: real,Y2: real] :
% 9.49/5.26        ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y2 @ Y2 ) ) @ zero_zero_real )
% 9.49/5.26        = ( ( X = zero_zero_real )
% 9.49/5.26          & ( Y2 = zero_zero_real ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2641_sum__squares__le__zero__iff,axiom,
% 9.49/5.26      ! [X: int,Y2: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y2 @ Y2 ) ) @ zero_zero_int )
% 9.49/5.26        = ( ( X = zero_zero_int )
% 9.49/5.26          & ( Y2 = zero_zero_int ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2642_sum__squares__ge__zero,axiom,
% 9.49/5.26      ! [X: rat,Y2: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y2 @ Y2 ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2643_sum__squares__ge__zero,axiom,
% 9.49/5.26      ! [X: real,Y2: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y2 @ Y2 ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2644_sum__squares__ge__zero,axiom,
% 9.49/5.26      ! [X: int,Y2: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y2 @ Y2 ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2645_sum__squares__gt__zero__iff,axiom,
% 9.49/5.26      ! [X: real,Y2: real] :
% 9.49/5.26        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y2 @ Y2 ) ) )
% 9.49/5.26        = ( ( X != zero_zero_real )
% 9.49/5.26          | ( Y2 != zero_zero_real ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2646_sum__squares__gt__zero__iff,axiom,
% 9.49/5.26      ! [X: rat,Y2: rat] :
% 9.49/5.26        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y2 @ Y2 ) ) )
% 9.49/5.26        = ( ( X != zero_zero_rat )
% 9.49/5.26          | ( Y2 != zero_zero_rat ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2647_sum__squares__gt__zero__iff,axiom,
% 9.49/5.26      ! [X: int,Y2: int] :
% 9.49/5.26        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y2 @ Y2 ) ) )
% 9.49/5.26        = ( ( X != zero_zero_int )
% 9.49/5.26          | ( Y2 != zero_zero_int ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2648_not__sum__squares__lt__zero,axiom,
% 9.49/5.26      ! [X: real,Y2: real] :
% 9.49/5.26        ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y2 @ Y2 ) ) @ zero_zero_real ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2649_not__sum__squares__lt__zero,axiom,
% 9.49/5.26      ! [X: rat,Y2: rat] :
% 9.49/5.26        ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y2 @ Y2 ) ) @ zero_zero_rat ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2650_not__sum__squares__lt__zero,axiom,
% 9.49/5.26      ! [X: int,Y2: int] :
% 9.49/5.26        ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y2 @ Y2 ) ) @ zero_zero_int ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2651_zero__less__two,axiom,
% 9.49/5.26      ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2652_zero__less__two,axiom,
% 9.49/5.26      ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2653_zero__less__two,axiom,
% 9.49/5.26      ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2654_zero__less__two,axiom,
% 9.49/5.26      ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2655_power__less__imp__less__base,axiom,
% 9.49/5.26      ! [A: real,N: nat,B: real] :
% 9.49/5.26        ( ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 9.49/5.26       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 9.49/5.26         => ( ord_less_real @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2656_power__less__imp__less__base,axiom,
% 9.49/5.26      ! [A: rat,N: nat,B: rat] :
% 9.49/5.26        ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 9.49/5.26       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 9.49/5.26         => ( ord_less_rat @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2657_power__less__imp__less__base,axiom,
% 9.49/5.26      ! [A: nat,N: nat,B: nat] :
% 9.49/5.26        ( ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 9.49/5.26       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 9.49/5.26         => ( ord_less_nat @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2658_power__less__imp__less__base,axiom,
% 9.49/5.26      ! [A: int,N: nat,B: int] :
% 9.49/5.26        ( ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 9.49/5.26       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 9.49/5.26         => ( ord_less_int @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2659_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I2_J,axiom,
% 9.49/5.26      ! [Uv: $o,Uw: $o,N: nat] :
% 9.49/5.26        ( ( vEBT_T_s_u_c_c @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N ) )
% 9.49/5.26        = one_one_nat ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2660_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I2_J,axiom,
% 9.49/5.26      ! [Uv: $o,Uw: $o,N: nat] :
% 9.49/5.26        ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N ) )
% 9.49/5.26        = one_one_nat ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2661_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 9.49/5.26      ! [C: nat,A: nat,B: nat] :
% 9.49/5.26        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 9.49/5.26       => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 9.49/5.26          = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2662_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 9.49/5.26      ! [C: int,A: int,B: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.49/5.26       => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 9.49/5.26          = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2663_divide__less__eq,axiom,
% 9.49/5.26      ! [B: real,C: real,A: real] :
% 9.49/5.26        ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 9.49/5.26        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.26           => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 9.49/5.26          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.26           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.26               => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 9.49/5.26              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.26               => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2664_divide__less__eq,axiom,
% 9.49/5.26      ! [B: rat,C: rat,A: rat] :
% 9.49/5.26        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 9.49/5.26        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.26           => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 9.49/5.26          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.26           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.26               => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 9.49/5.26              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.26               => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2665_less__divide__eq,axiom,
% 9.49/5.26      ! [A: real,B: real,C: real] :
% 9.49/5.26        ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 9.49/5.26        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.26           => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 9.49/5.26          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.26           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.26               => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 9.49/5.26              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.26               => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2666_less__divide__eq,axiom,
% 9.49/5.26      ! [A: rat,B: rat,C: rat] :
% 9.49/5.26        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 9.49/5.26        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.26           => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 9.49/5.26          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.26           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.26               => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 9.49/5.26              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.26               => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2667_neg__divide__less__eq,axiom,
% 9.49/5.26      ! [C: real,B: real,A: real] :
% 9.49/5.26        ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.26       => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 9.49/5.26          = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2668_neg__divide__less__eq,axiom,
% 9.49/5.26      ! [C: rat,B: rat,A: rat] :
% 9.49/5.26        ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.26       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 9.49/5.26          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2669_neg__less__divide__eq,axiom,
% 9.49/5.26      ! [C: real,A: real,B: real] :
% 9.49/5.26        ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.26       => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 9.49/5.26          = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2670_neg__less__divide__eq,axiom,
% 9.49/5.26      ! [C: rat,A: rat,B: rat] :
% 9.49/5.26        ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.26       => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 9.49/5.26          = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2671_pos__divide__less__eq,axiom,
% 9.49/5.26      ! [C: real,B: real,A: real] :
% 9.49/5.26        ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.26       => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 9.49/5.26          = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2672_pos__divide__less__eq,axiom,
% 9.49/5.26      ! [C: rat,B: rat,A: rat] :
% 9.49/5.26        ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.26       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 9.49/5.26          = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2673_pos__less__divide__eq,axiom,
% 9.49/5.26      ! [C: real,A: real,B: real] :
% 9.49/5.26        ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.26       => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 9.49/5.26          = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2674_pos__less__divide__eq,axiom,
% 9.49/5.26      ! [C: rat,A: rat,B: rat] :
% 9.49/5.26        ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.26       => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 9.49/5.26          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2675_mult__imp__div__pos__less,axiom,
% 9.49/5.26      ! [Y2: real,X: real,Z: real] :
% 9.49/5.26        ( ( ord_less_real @ zero_zero_real @ Y2 )
% 9.49/5.26       => ( ( ord_less_real @ X @ ( times_times_real @ Z @ Y2 ) )
% 9.49/5.26         => ( ord_less_real @ ( divide_divide_real @ X @ Y2 ) @ Z ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2676_mult__imp__div__pos__less,axiom,
% 9.49/5.26      ! [Y2: rat,X: rat,Z: rat] :
% 9.49/5.26        ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 9.49/5.26       => ( ( ord_less_rat @ X @ ( times_times_rat @ Z @ Y2 ) )
% 9.49/5.26         => ( ord_less_rat @ ( divide_divide_rat @ X @ Y2 ) @ Z ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2677_mult__imp__less__div__pos,axiom,
% 9.49/5.26      ! [Y2: real,Z: real,X: real] :
% 9.49/5.26        ( ( ord_less_real @ zero_zero_real @ Y2 )
% 9.49/5.26       => ( ( ord_less_real @ ( times_times_real @ Z @ Y2 ) @ X )
% 9.49/5.26         => ( ord_less_real @ Z @ ( divide_divide_real @ X @ Y2 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2678_mult__imp__less__div__pos,axiom,
% 9.49/5.26      ! [Y2: rat,Z: rat,X: rat] :
% 9.49/5.26        ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 9.49/5.26       => ( ( ord_less_rat @ ( times_times_rat @ Z @ Y2 ) @ X )
% 9.49/5.26         => ( ord_less_rat @ Z @ ( divide_divide_rat @ X @ Y2 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2679_divide__strict__left__mono,axiom,
% 9.49/5.26      ! [B: real,A: real,C: real] :
% 9.49/5.26        ( ( ord_less_real @ B @ A )
% 9.49/5.26       => ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.26         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 9.49/5.26           => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2680_divide__strict__left__mono,axiom,
% 9.49/5.26      ! [B: rat,A: rat,C: rat] :
% 9.49/5.26        ( ( ord_less_rat @ B @ A )
% 9.49/5.26       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.26         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 9.49/5.26           => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2681_divide__strict__left__mono__neg,axiom,
% 9.49/5.26      ! [A: real,B: real,C: real] :
% 9.49/5.26        ( ( ord_less_real @ A @ B )
% 9.49/5.26       => ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.26         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 9.49/5.26           => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2682_divide__strict__left__mono__neg,axiom,
% 9.49/5.26      ! [A: rat,B: rat,C: rat] :
% 9.49/5.26        ( ( ord_less_rat @ A @ B )
% 9.49/5.26       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.26         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 9.49/5.26           => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2683_divide__less__eq__1,axiom,
% 9.49/5.26      ! [B: real,A: real] :
% 9.49/5.26        ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 9.49/5.26        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 9.49/5.26            & ( ord_less_real @ B @ A ) )
% 9.49/5.26          | ( ( ord_less_real @ A @ zero_zero_real )
% 9.49/5.26            & ( ord_less_real @ A @ B ) )
% 9.49/5.26          | ( A = zero_zero_real ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2684_divide__less__eq__1,axiom,
% 9.49/5.26      ! [B: rat,A: rat] :
% 9.49/5.26        ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 9.49/5.26        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.49/5.26            & ( ord_less_rat @ B @ A ) )
% 9.49/5.26          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.49/5.26            & ( ord_less_rat @ A @ B ) )
% 9.49/5.26          | ( A = zero_zero_rat ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2685_less__divide__eq__1,axiom,
% 9.49/5.26      ! [B: real,A: real] :
% 9.49/5.26        ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 9.49/5.26        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 9.49/5.26            & ( ord_less_real @ A @ B ) )
% 9.49/5.26          | ( ( ord_less_real @ A @ zero_zero_real )
% 9.49/5.26            & ( ord_less_real @ B @ A ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2686_less__divide__eq__1,axiom,
% 9.49/5.26      ! [B: rat,A: rat] :
% 9.49/5.26        ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 9.49/5.26        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.49/5.26            & ( ord_less_rat @ A @ B ) )
% 9.49/5.26          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.49/5.26            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2687_power__le__one,axiom,
% 9.49/5.26      ! [A: rat,N: nat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.49/5.26       => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 9.49/5.26         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ one_one_rat ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2688_power__le__one,axiom,
% 9.49/5.26      ! [A: real,N: nat] :
% 9.49/5.26        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 9.49/5.26       => ( ( ord_less_eq_real @ A @ one_one_real )
% 9.49/5.26         => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ one_one_real ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2689_power__le__one,axiom,
% 9.49/5.26      ! [A: nat,N: nat] :
% 9.49/5.26        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.49/5.26       => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 9.49/5.26         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ one_one_nat ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2690_power__le__one,axiom,
% 9.49/5.26      ! [A: int,N: nat] :
% 9.49/5.26        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.26       => ( ( ord_less_eq_int @ A @ one_one_int )
% 9.49/5.26         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ one_one_int ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2691_divide__eq__eq__numeral_I1_J,axiom,
% 9.49/5.26      ! [B: complex,C: complex,W: num] :
% 9.49/5.26        ( ( ( divide1717551699836669952omplex @ B @ C )
% 9.49/5.26          = ( numera6690914467698888265omplex @ W ) )
% 9.49/5.26        = ( ( ( C != zero_zero_complex )
% 9.49/5.26           => ( B
% 9.49/5.26              = ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C ) ) )
% 9.49/5.26          & ( ( C = zero_zero_complex )
% 9.49/5.26           => ( ( numera6690914467698888265omplex @ W )
% 9.49/5.26              = zero_zero_complex ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2692_divide__eq__eq__numeral_I1_J,axiom,
% 9.49/5.26      ! [B: real,C: real,W: num] :
% 9.49/5.26        ( ( ( divide_divide_real @ B @ C )
% 9.49/5.26          = ( numeral_numeral_real @ W ) )
% 9.49/5.26        = ( ( ( C != zero_zero_real )
% 9.49/5.26           => ( B
% 9.49/5.26              = ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 9.49/5.26          & ( ( C = zero_zero_real )
% 9.49/5.26           => ( ( numeral_numeral_real @ W )
% 9.49/5.26              = zero_zero_real ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2693_divide__eq__eq__numeral_I1_J,axiom,
% 9.49/5.26      ! [B: rat,C: rat,W: num] :
% 9.49/5.26        ( ( ( divide_divide_rat @ B @ C )
% 9.49/5.26          = ( numeral_numeral_rat @ W ) )
% 9.49/5.26        = ( ( ( C != zero_zero_rat )
% 9.49/5.26           => ( B
% 9.49/5.26              = ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 9.49/5.26          & ( ( C = zero_zero_rat )
% 9.49/5.26           => ( ( numeral_numeral_rat @ W )
% 9.49/5.26              = zero_zero_rat ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2694_eq__divide__eq__numeral_I1_J,axiom,
% 9.49/5.26      ! [W: num,B: complex,C: complex] :
% 9.49/5.26        ( ( ( numera6690914467698888265omplex @ W )
% 9.49/5.26          = ( divide1717551699836669952omplex @ B @ C ) )
% 9.49/5.26        = ( ( ( C != zero_zero_complex )
% 9.49/5.26           => ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C )
% 9.49/5.26              = B ) )
% 9.49/5.26          & ( ( C = zero_zero_complex )
% 9.49/5.26           => ( ( numera6690914467698888265omplex @ W )
% 9.49/5.26              = zero_zero_complex ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2695_eq__divide__eq__numeral_I1_J,axiom,
% 9.49/5.26      ! [W: num,B: real,C: real] :
% 9.49/5.26        ( ( ( numeral_numeral_real @ W )
% 9.49/5.26          = ( divide_divide_real @ B @ C ) )
% 9.49/5.26        = ( ( ( C != zero_zero_real )
% 9.49/5.26           => ( ( times_times_real @ ( numeral_numeral_real @ W ) @ C )
% 9.49/5.26              = B ) )
% 9.49/5.26          & ( ( C = zero_zero_real )
% 9.49/5.26           => ( ( numeral_numeral_real @ W )
% 9.49/5.26              = zero_zero_real ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2696_eq__divide__eq__numeral_I1_J,axiom,
% 9.49/5.26      ! [W: num,B: rat,C: rat] :
% 9.49/5.26        ( ( ( numeral_numeral_rat @ W )
% 9.49/5.26          = ( divide_divide_rat @ B @ C ) )
% 9.49/5.26        = ( ( ( C != zero_zero_rat )
% 9.49/5.26           => ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C )
% 9.49/5.26              = B ) )
% 9.49/5.26          & ( ( C = zero_zero_rat )
% 9.49/5.26           => ( ( numeral_numeral_rat @ W )
% 9.49/5.26              = zero_zero_rat ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2697_add__divide__eq__if__simps_I2_J,axiom,
% 9.49/5.26      ! [Z: complex,A: complex,B: complex] :
% 9.49/5.26        ( ( ( Z = zero_zero_complex )
% 9.49/5.26         => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 9.49/5.26            = B ) )
% 9.49/5.26        & ( ( Z != zero_zero_complex )
% 9.49/5.26         => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 9.49/5.26            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2698_add__divide__eq__if__simps_I2_J,axiom,
% 9.49/5.26      ! [Z: real,A: real,B: real] :
% 9.49/5.26        ( ( ( Z = zero_zero_real )
% 9.49/5.26         => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 9.49/5.26            = B ) )
% 9.49/5.26        & ( ( Z != zero_zero_real )
% 9.49/5.26         => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 9.49/5.26            = ( divide_divide_real @ ( plus_plus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2699_add__divide__eq__if__simps_I2_J,axiom,
% 9.49/5.26      ! [Z: rat,A: rat,B: rat] :
% 9.49/5.26        ( ( ( Z = zero_zero_rat )
% 9.49/5.26         => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 9.49/5.26            = B ) )
% 9.49/5.26        & ( ( Z != zero_zero_rat )
% 9.49/5.26         => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 9.49/5.26            = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2700_add__divide__eq__if__simps_I1_J,axiom,
% 9.49/5.26      ! [Z: complex,A: complex,B: complex] :
% 9.49/5.26        ( ( ( Z = zero_zero_complex )
% 9.49/5.26         => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 9.49/5.26            = A ) )
% 9.49/5.26        & ( ( Z != zero_zero_complex )
% 9.49/5.26         => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 9.49/5.26            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2701_add__divide__eq__if__simps_I1_J,axiom,
% 9.49/5.26      ! [Z: real,A: real,B: real] :
% 9.49/5.26        ( ( ( Z = zero_zero_real )
% 9.49/5.26         => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 9.49/5.26            = A ) )
% 9.49/5.26        & ( ( Z != zero_zero_real )
% 9.49/5.26         => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 9.49/5.26            = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2702_add__divide__eq__if__simps_I1_J,axiom,
% 9.49/5.26      ! [Z: rat,A: rat,B: rat] :
% 9.49/5.26        ( ( ( Z = zero_zero_rat )
% 9.49/5.26         => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 9.49/5.26            = A ) )
% 9.49/5.26        & ( ( Z != zero_zero_rat )
% 9.49/5.26         => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 9.49/5.26            = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2703_add__frac__eq,axiom,
% 9.49/5.26      ! [Y2: complex,Z: complex,X: complex,W: complex] :
% 9.49/5.26        ( ( Y2 != zero_zero_complex )
% 9.49/5.26       => ( ( Z != zero_zero_complex )
% 9.49/5.26         => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Y2 ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 9.49/5.26            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X @ Z ) @ ( times_times_complex @ W @ Y2 ) ) @ ( times_times_complex @ Y2 @ Z ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2704_add__frac__eq,axiom,
% 9.49/5.26      ! [Y2: real,Z: real,X: real,W: real] :
% 9.49/5.26        ( ( Y2 != zero_zero_real )
% 9.49/5.26       => ( ( Z != zero_zero_real )
% 9.49/5.26         => ( ( plus_plus_real @ ( divide_divide_real @ X @ Y2 ) @ ( divide_divide_real @ W @ Z ) )
% 9.49/5.26            = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y2 ) ) @ ( times_times_real @ Y2 @ Z ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2705_add__frac__eq,axiom,
% 9.49/5.26      ! [Y2: rat,Z: rat,X: rat,W: rat] :
% 9.49/5.26        ( ( Y2 != zero_zero_rat )
% 9.49/5.26       => ( ( Z != zero_zero_rat )
% 9.49/5.26         => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y2 ) @ ( divide_divide_rat @ W @ Z ) )
% 9.49/5.26            = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y2 ) ) @ ( times_times_rat @ Y2 @ Z ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2706_add__frac__num,axiom,
% 9.49/5.26      ! [Y2: complex,X: complex,Z: complex] :
% 9.49/5.26        ( ( Y2 != zero_zero_complex )
% 9.49/5.26       => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Y2 ) @ Z )
% 9.49/5.26          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Z @ Y2 ) ) @ Y2 ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2707_add__frac__num,axiom,
% 9.49/5.26      ! [Y2: real,X: real,Z: real] :
% 9.49/5.26        ( ( Y2 != zero_zero_real )
% 9.49/5.26       => ( ( plus_plus_real @ ( divide_divide_real @ X @ Y2 ) @ Z )
% 9.49/5.26          = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Z @ Y2 ) ) @ Y2 ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2708_add__frac__num,axiom,
% 9.49/5.26      ! [Y2: rat,X: rat,Z: rat] :
% 9.49/5.26        ( ( Y2 != zero_zero_rat )
% 9.49/5.26       => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y2 ) @ Z )
% 9.49/5.26          = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z @ Y2 ) ) @ Y2 ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2709_add__num__frac,axiom,
% 9.49/5.26      ! [Y2: complex,Z: complex,X: complex] :
% 9.49/5.26        ( ( Y2 != zero_zero_complex )
% 9.49/5.26       => ( ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ X @ Y2 ) )
% 9.49/5.26          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Z @ Y2 ) ) @ Y2 ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2710_add__num__frac,axiom,
% 9.49/5.26      ! [Y2: real,Z: real,X: real] :
% 9.49/5.26        ( ( Y2 != zero_zero_real )
% 9.49/5.26       => ( ( plus_plus_real @ Z @ ( divide_divide_real @ X @ Y2 ) )
% 9.49/5.26          = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Z @ Y2 ) ) @ Y2 ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2711_add__num__frac,axiom,
% 9.49/5.26      ! [Y2: rat,Z: rat,X: rat] :
% 9.49/5.26        ( ( Y2 != zero_zero_rat )
% 9.49/5.26       => ( ( plus_plus_rat @ Z @ ( divide_divide_rat @ X @ Y2 ) )
% 9.49/5.26          = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z @ Y2 ) ) @ Y2 ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2712_add__divide__eq__iff,axiom,
% 9.49/5.26      ! [Z: complex,X: complex,Y2: complex] :
% 9.49/5.26        ( ( Z != zero_zero_complex )
% 9.49/5.26       => ( ( plus_plus_complex @ X @ ( divide1717551699836669952omplex @ Y2 @ Z ) )
% 9.49/5.26          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X @ Z ) @ Y2 ) @ Z ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2713_add__divide__eq__iff,axiom,
% 9.49/5.26      ! [Z: real,X: real,Y2: real] :
% 9.49/5.26        ( ( Z != zero_zero_real )
% 9.49/5.26       => ( ( plus_plus_real @ X @ ( divide_divide_real @ Y2 @ Z ) )
% 9.49/5.26          = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X @ Z ) @ Y2 ) @ Z ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2714_add__divide__eq__iff,axiom,
% 9.49/5.26      ! [Z: rat,X: rat,Y2: rat] :
% 9.49/5.26        ( ( Z != zero_zero_rat )
% 9.49/5.26       => ( ( plus_plus_rat @ X @ ( divide_divide_rat @ Y2 @ Z ) )
% 9.49/5.26          = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z ) @ Y2 ) @ Z ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2715_divide__add__eq__iff,axiom,
% 9.49/5.26      ! [Z: complex,X: complex,Y2: complex] :
% 9.49/5.26        ( ( Z != zero_zero_complex )
% 9.49/5.26       => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Z ) @ Y2 )
% 9.49/5.26          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Y2 @ Z ) ) @ Z ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2716_divide__add__eq__iff,axiom,
% 9.49/5.26      ! [Z: real,X: real,Y2: real] :
% 9.49/5.26        ( ( Z != zero_zero_real )
% 9.49/5.26       => ( ( plus_plus_real @ ( divide_divide_real @ X @ Z ) @ Y2 )
% 9.49/5.26          = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Y2 @ Z ) ) @ Z ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2717_divide__add__eq__iff,axiom,
% 9.49/5.26      ! [Z: rat,X: rat,Y2: rat] :
% 9.49/5.26        ( ( Z != zero_zero_rat )
% 9.49/5.26       => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Z ) @ Y2 )
% 9.49/5.26          = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Y2 @ Z ) ) @ Z ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2718_div__add__self2,axiom,
% 9.49/5.26      ! [B: nat,A: nat] :
% 9.49/5.26        ( ( B != zero_zero_nat )
% 9.49/5.26       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 9.49/5.26          = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2719_div__add__self2,axiom,
% 9.49/5.26      ! [B: int,A: int] :
% 9.49/5.26        ( ( B != zero_zero_int )
% 9.49/5.26       => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 9.49/5.26          = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2720_div__add__self1,axiom,
% 9.49/5.26      ! [B: nat,A: nat] :
% 9.49/5.26        ( ( B != zero_zero_nat )
% 9.49/5.26       => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 9.49/5.26          = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2721_div__add__self1,axiom,
% 9.49/5.26      ! [B: int,A: int] :
% 9.49/5.26        ( ( B != zero_zero_int )
% 9.49/5.26       => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 9.49/5.26          = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2722_power__inject__base,axiom,
% 9.49/5.26      ! [A: rat,N: nat,B: rat] :
% 9.49/5.26        ( ( ( power_power_rat @ A @ ( suc @ N ) )
% 9.49/5.26          = ( power_power_rat @ B @ ( suc @ N ) ) )
% 9.49/5.26       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.49/5.26         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 9.49/5.26           => ( A = B ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2723_power__inject__base,axiom,
% 9.49/5.26      ! [A: real,N: nat,B: real] :
% 9.49/5.26        ( ( ( power_power_real @ A @ ( suc @ N ) )
% 9.49/5.26          = ( power_power_real @ B @ ( suc @ N ) ) )
% 9.49/5.26       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 9.49/5.26         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 9.49/5.26           => ( A = B ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2724_power__inject__base,axiom,
% 9.49/5.26      ! [A: nat,N: nat,B: nat] :
% 9.49/5.26        ( ( ( power_power_nat @ A @ ( suc @ N ) )
% 9.49/5.26          = ( power_power_nat @ B @ ( suc @ N ) ) )
% 9.49/5.26       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.49/5.26         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 9.49/5.26           => ( A = B ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2725_power__inject__base,axiom,
% 9.49/5.26      ! [A: int,N: nat,B: int] :
% 9.49/5.26        ( ( ( power_power_int @ A @ ( suc @ N ) )
% 9.49/5.26          = ( power_power_int @ B @ ( suc @ N ) ) )
% 9.49/5.26       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.26         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 9.49/5.26           => ( A = B ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2726_power__le__imp__le__base,axiom,
% 9.49/5.26      ! [A: rat,N: nat,B: rat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ ( power_power_rat @ B @ ( suc @ N ) ) )
% 9.49/5.26       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 9.49/5.26         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2727_power__le__imp__le__base,axiom,
% 9.49/5.26      ! [A: real,N: nat,B: real] :
% 9.49/5.26        ( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ ( power_power_real @ B @ ( suc @ N ) ) )
% 9.49/5.26       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 9.49/5.26         => ( ord_less_eq_real @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2728_power__le__imp__le__base,axiom,
% 9.49/5.26      ! [A: nat,N: nat,B: nat] :
% 9.49/5.26        ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ ( power_power_nat @ B @ ( suc @ N ) ) )
% 9.49/5.26       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 9.49/5.26         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2729_power__le__imp__le__base,axiom,
% 9.49/5.26      ! [A: int,N: nat,B: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ ( power_power_int @ B @ ( suc @ N ) ) )
% 9.49/5.26       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 9.49/5.26         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2730_add__divide__eq__if__simps_I4_J,axiom,
% 9.49/5.26      ! [Z: complex,A: complex,B: complex] :
% 9.49/5.26        ( ( ( Z = zero_zero_complex )
% 9.49/5.26         => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 9.49/5.26            = A ) )
% 9.49/5.26        & ( ( Z != zero_zero_complex )
% 9.49/5.26         => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 9.49/5.26            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2731_add__divide__eq__if__simps_I4_J,axiom,
% 9.49/5.26      ! [Z: real,A: real,B: real] :
% 9.49/5.26        ( ( ( Z = zero_zero_real )
% 9.49/5.26         => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 9.49/5.26            = A ) )
% 9.49/5.26        & ( ( Z != zero_zero_real )
% 9.49/5.26         => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 9.49/5.26            = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2732_add__divide__eq__if__simps_I4_J,axiom,
% 9.49/5.26      ! [Z: rat,A: rat,B: rat] :
% 9.49/5.26        ( ( ( Z = zero_zero_rat )
% 9.49/5.26         => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 9.49/5.26            = A ) )
% 9.49/5.26        & ( ( Z != zero_zero_rat )
% 9.49/5.26         => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 9.49/5.26            = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2733_diff__frac__eq,axiom,
% 9.49/5.26      ! [Y2: complex,Z: complex,X: complex,W: complex] :
% 9.49/5.26        ( ( Y2 != zero_zero_complex )
% 9.49/5.26       => ( ( Z != zero_zero_complex )
% 9.49/5.26         => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X @ Y2 ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 9.49/5.26            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X @ Z ) @ ( times_times_complex @ W @ Y2 ) ) @ ( times_times_complex @ Y2 @ Z ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2734_diff__frac__eq,axiom,
% 9.49/5.26      ! [Y2: real,Z: real,X: real,W: real] :
% 9.49/5.26        ( ( Y2 != zero_zero_real )
% 9.49/5.26       => ( ( Z != zero_zero_real )
% 9.49/5.26         => ( ( minus_minus_real @ ( divide_divide_real @ X @ Y2 ) @ ( divide_divide_real @ W @ Z ) )
% 9.49/5.26            = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y2 ) ) @ ( times_times_real @ Y2 @ Z ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2735_diff__frac__eq,axiom,
% 9.49/5.26      ! [Y2: rat,Z: rat,X: rat,W: rat] :
% 9.49/5.26        ( ( Y2 != zero_zero_rat )
% 9.49/5.26       => ( ( Z != zero_zero_rat )
% 9.49/5.26         => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Y2 ) @ ( divide_divide_rat @ W @ Z ) )
% 9.49/5.26            = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y2 ) ) @ ( times_times_rat @ Y2 @ Z ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2736_diff__divide__eq__iff,axiom,
% 9.49/5.26      ! [Z: complex,X: complex,Y2: complex] :
% 9.49/5.26        ( ( Z != zero_zero_complex )
% 9.49/5.26       => ( ( minus_minus_complex @ X @ ( divide1717551699836669952omplex @ Y2 @ Z ) )
% 9.49/5.26          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X @ Z ) @ Y2 ) @ Z ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2737_diff__divide__eq__iff,axiom,
% 9.49/5.26      ! [Z: real,X: real,Y2: real] :
% 9.49/5.26        ( ( Z != zero_zero_real )
% 9.49/5.26       => ( ( minus_minus_real @ X @ ( divide_divide_real @ Y2 @ Z ) )
% 9.49/5.26          = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ Y2 ) @ Z ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2738_diff__divide__eq__iff,axiom,
% 9.49/5.26      ! [Z: rat,X: rat,Y2: rat] :
% 9.49/5.26        ( ( Z != zero_zero_rat )
% 9.49/5.26       => ( ( minus_minus_rat @ X @ ( divide_divide_rat @ Y2 @ Z ) )
% 9.49/5.26          = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ Y2 ) @ Z ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2739_divide__diff__eq__iff,axiom,
% 9.49/5.26      ! [Z: complex,X: complex,Y2: complex] :
% 9.49/5.26        ( ( Z != zero_zero_complex )
% 9.49/5.26       => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X @ Z ) @ Y2 )
% 9.49/5.26          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ X @ ( times_times_complex @ Y2 @ Z ) ) @ Z ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2740_divide__diff__eq__iff,axiom,
% 9.49/5.26      ! [Z: real,X: real,Y2: real] :
% 9.49/5.26        ( ( Z != zero_zero_real )
% 9.49/5.26       => ( ( minus_minus_real @ ( divide_divide_real @ X @ Z ) @ Y2 )
% 9.49/5.26          = ( divide_divide_real @ ( minus_minus_real @ X @ ( times_times_real @ Y2 @ Z ) ) @ Z ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2741_divide__diff__eq__iff,axiom,
% 9.49/5.26      ! [Z: rat,X: rat,Y2: rat] :
% 9.49/5.26        ( ( Z != zero_zero_rat )
% 9.49/5.26       => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Z ) @ Y2 )
% 9.49/5.26          = ( divide_divide_rat @ ( minus_minus_rat @ X @ ( times_times_rat @ Y2 @ Z ) ) @ Z ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2742_numeral__1__eq__Suc__0,axiom,
% 9.49/5.26      ( ( numeral_numeral_nat @ one )
% 9.49/5.26      = ( suc @ zero_zero_nat ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2743_num_Osize_I5_J,axiom,
% 9.49/5.26      ! [X23: num] :
% 9.49/5.26        ( ( size_size_num @ ( bit0 @ X23 ) )
% 9.49/5.26        = ( plus_plus_nat @ ( size_size_num @ X23 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2744_ex__least__nat__less,axiom,
% 9.49/5.26      ! [P: nat > $o,N: nat] :
% 9.49/5.26        ( ( P @ N )
% 9.49/5.26       => ( ~ ( P @ zero_zero_nat )
% 9.49/5.26         => ? [K2: nat] :
% 9.49/5.26              ( ( ord_less_nat @ K2 @ N )
% 9.49/5.26              & ! [I: nat] :
% 9.49/5.26                  ( ( ord_less_eq_nat @ I @ K2 )
% 9.49/5.26                 => ~ ( P @ I ) )
% 9.49/5.26              & ( P @ ( suc @ K2 ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2745_nat__induct__non__zero,axiom,
% 9.49/5.26      ! [N: nat,P: nat > $o] :
% 9.49/5.26        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.26       => ( ( P @ one_one_nat )
% 9.49/5.26         => ( ! [N3: nat] :
% 9.49/5.26                ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 9.49/5.26               => ( ( P @ N3 )
% 9.49/5.26                 => ( P @ ( suc @ N3 ) ) ) )
% 9.49/5.26           => ( P @ N ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2746_num_Osize_I6_J,axiom,
% 9.49/5.26      ! [X33: num] :
% 9.49/5.26        ( ( size_size_num @ ( bit1 @ X33 ) )
% 9.49/5.26        = ( plus_plus_nat @ ( size_size_num @ X33 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2747_one__less__mult,axiom,
% 9.49/5.26      ! [N: nat,M: nat] :
% 9.49/5.26        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 9.49/5.26       => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 9.49/5.26         => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2748_n__less__m__mult__n,axiom,
% 9.49/5.26      ! [N: nat,M: nat] :
% 9.49/5.26        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.26       => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 9.49/5.26         => ( ord_less_nat @ N @ ( times_times_nat @ M @ N ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2749_n__less__n__mult__m,axiom,
% 9.49/5.26      ! [N: nat,M: nat] :
% 9.49/5.26        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.26       => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 9.49/5.26         => ( ord_less_nat @ N @ ( times_times_nat @ N @ M ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2750_diff__Suc__less,axiom,
% 9.49/5.26      ! [N: nat,I2: nat] :
% 9.49/5.26        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.26       => ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I2 ) ) @ N ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2751_length__pos__if__in__set,axiom,
% 9.49/5.26      ! [X: product_prod_nat_nat,Xs2: list_P6011104703257516679at_nat] :
% 9.49/5.26        ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 9.49/5.26       => ( ord_less_nat @ zero_zero_nat @ ( size_s5460976970255530739at_nat @ Xs2 ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2752_length__pos__if__in__set,axiom,
% 9.49/5.26      ! [X: complex,Xs2: list_complex] :
% 9.49/5.26        ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 9.49/5.26       => ( ord_less_nat @ zero_zero_nat @ ( size_s3451745648224563538omplex @ Xs2 ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2753_length__pos__if__in__set,axiom,
% 9.49/5.26      ! [X: real,Xs2: list_real] :
% 9.49/5.26        ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 9.49/5.26       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_real @ Xs2 ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2754_length__pos__if__in__set,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 9.49/5.26        ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 9.49/5.26       => ( ord_less_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2755_length__pos__if__in__set,axiom,
% 9.49/5.26      ! [X: $o,Xs2: list_o] :
% 9.49/5.26        ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 9.49/5.26       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_o @ Xs2 ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2756_length__pos__if__in__set,axiom,
% 9.49/5.26      ! [X: nat,Xs2: list_nat] :
% 9.49/5.26        ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 9.49/5.26       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs2 ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2757_length__pos__if__in__set,axiom,
% 9.49/5.26      ! [X: int,Xs2: list_int] :
% 9.49/5.26        ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 9.49/5.26       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs2 ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2758_power__gt__expt,axiom,
% 9.49/5.26      ! [N: nat,K: nat] :
% 9.49/5.26        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 9.49/5.26       => ( ord_less_nat @ K @ ( power_power_nat @ N @ K ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2759_div__le__mono2,axiom,
% 9.49/5.26      ! [M: nat,N: nat,K: nat] :
% 9.49/5.26        ( ( ord_less_nat @ zero_zero_nat @ M )
% 9.49/5.26       => ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.26         => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N ) @ ( divide_divide_nat @ K @ M ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2760_div__greater__zero__iff,axiom,
% 9.49/5.26      ! [M: nat,N: nat] :
% 9.49/5.26        ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M @ N ) )
% 9.49/5.26        = ( ( ord_less_eq_nat @ N @ M )
% 9.49/5.26          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2761_nat__diff__split,axiom,
% 9.49/5.26      ! [P: nat > $o,A: nat,B: nat] :
% 9.49/5.26        ( ( P @ ( minus_minus_nat @ A @ B ) )
% 9.49/5.26        = ( ( ( ord_less_nat @ A @ B )
% 9.49/5.26           => ( P @ zero_zero_nat ) )
% 9.49/5.26          & ! [D: nat] :
% 9.49/5.26              ( ( A
% 9.49/5.26                = ( plus_plus_nat @ B @ D ) )
% 9.49/5.26             => ( P @ D ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2762_nat__diff__split__asm,axiom,
% 9.49/5.26      ! [P: nat > $o,A: nat,B: nat] :
% 9.49/5.26        ( ( P @ ( minus_minus_nat @ A @ B ) )
% 9.49/5.26        = ( ~ ( ( ( ord_less_nat @ A @ B )
% 9.49/5.26                & ~ ( P @ zero_zero_nat ) )
% 9.49/5.26              | ? [D: nat] :
% 9.49/5.26                  ( ( A
% 9.49/5.26                    = ( plus_plus_nat @ B @ D ) )
% 9.49/5.26                  & ~ ( P @ D ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2763_nat__mult__le__cancel1,axiom,
% 9.49/5.26      ! [K: nat,M: nat,N: nat] :
% 9.49/5.26        ( ( ord_less_nat @ zero_zero_nat @ K )
% 9.49/5.26       => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 9.49/5.26          = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2764_div__eq__dividend__iff,axiom,
% 9.49/5.26      ! [M: nat,N: nat] :
% 9.49/5.26        ( ( ord_less_nat @ zero_zero_nat @ M )
% 9.49/5.26       => ( ( ( divide_divide_nat @ M @ N )
% 9.49/5.26            = M )
% 9.49/5.26          = ( N = one_one_nat ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2765_div__less__dividend,axiom,
% 9.49/5.26      ! [N: nat,M: nat] :
% 9.49/5.26        ( ( ord_less_nat @ one_one_nat @ N )
% 9.49/5.26       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 9.49/5.26         => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ M ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2766_nat__one__le__power,axiom,
% 9.49/5.26      ! [I2: nat,N: nat] :
% 9.49/5.26        ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I2 )
% 9.49/5.26       => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I2 @ N ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2767_nat__mult__div__cancel1,axiom,
% 9.49/5.26      ! [K: nat,M: nat,N: nat] :
% 9.49/5.26        ( ( ord_less_nat @ zero_zero_nat @ K )
% 9.49/5.26       => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 9.49/5.26          = ( divide_divide_nat @ M @ N ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2768_div__less__iff__less__mult,axiom,
% 9.49/5.26      ! [Q2: nat,M: nat,N: nat] :
% 9.49/5.26        ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 9.49/5.26       => ( ( ord_less_nat @ ( divide_divide_nat @ M @ Q2 ) @ N )
% 9.49/5.26          = ( ord_less_nat @ M @ ( times_times_nat @ N @ Q2 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2769_vebt__member_Osimps_I3_J,axiom,
% 9.49/5.26      ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X: nat] :
% 9.49/5.26        ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2770_vebt__insert_Osimps_I3_J,axiom,
% 9.49/5.26      ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT,X: nat] :
% 9.49/5.26        ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) @ X )
% 9.49/5.26        = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2771_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Oelims,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Y2: nat] :
% 9.49/5.26        ( ( ( vEBT_T_m_i_n_t @ X )
% 9.49/5.26          = Y2 )
% 9.49/5.26       => ( ! [A4: $o] :
% 9.49/5.26              ( ? [B3: $o] :
% 9.49/5.26                  ( X
% 9.49/5.26                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26             => ( Y2
% 9.49/5.26               != ( plus_plus_nat @ one_one_nat @ ( if_nat @ A4 @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 9.49/5.26         => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 9.49/5.26                  ( X
% 9.49/5.26                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 9.49/5.26             => ( Y2 != one_one_nat ) )
% 9.49/5.26           => ~ ( ? [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 9.49/5.26                    ( X
% 9.49/5.26                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 9.49/5.26               => ( Y2 != one_one_nat ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2772_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I2_J,axiom,
% 9.49/5.26      ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT,X: nat] :
% 9.49/5.26        ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S3 ) @ X )
% 9.49/5.26        = one_one_nat ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2773_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Ocases,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT] :
% 9.49/5.26        ( ! [A4: $o,B3: $o] :
% 9.49/5.26            ( X
% 9.49/5.26           != ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26       => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 9.49/5.26              ( X
% 9.49/5.26             != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 9.49/5.26         => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 9.49/5.26                ( X
% 9.49/5.26               != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2774_VEBT__internal_OminNull_Oelims_I1_J,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Y2: $o] :
% 9.49/5.26        ( ( ( vEBT_VEBT_minNull @ X )
% 9.49/5.26          = Y2 )
% 9.49/5.26       => ( ( ( X
% 9.49/5.26              = ( vEBT_Leaf @ $false @ $false ) )
% 9.49/5.26           => ~ Y2 )
% 9.49/5.26         => ( ( ? [Uv2: $o] :
% 9.49/5.26                  ( X
% 9.49/5.26                  = ( vEBT_Leaf @ $true @ Uv2 ) )
% 9.49/5.26             => Y2 )
% 9.49/5.26           => ( ( ? [Uu2: $o] :
% 9.49/5.26                    ( X
% 9.49/5.26                    = ( vEBT_Leaf @ Uu2 @ $true ) )
% 9.49/5.26               => Y2 )
% 9.49/5.26             => ( ( ? [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 9.49/5.26                      ( X
% 9.49/5.26                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 9.49/5.26                 => ~ Y2 )
% 9.49/5.26               => ~ ( ? [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 9.49/5.26                        ( X
% 9.49/5.26                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 9.49/5.26                   => Y2 ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2775_vebt__mint_Oelims,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Y2: option_nat] :
% 9.49/5.26        ( ( ( vEBT_vebt_mint @ X )
% 9.49/5.26          = Y2 )
% 9.49/5.26       => ( ! [A4: $o,B3: $o] :
% 9.49/5.26              ( ( X
% 9.49/5.26                = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26             => ~ ( ( A4
% 9.49/5.26                   => ( Y2
% 9.49/5.26                      = ( some_nat @ zero_zero_nat ) ) )
% 9.49/5.26                  & ( ~ A4
% 9.49/5.26                   => ( ( B3
% 9.49/5.26                       => ( Y2
% 9.49/5.26                          = ( some_nat @ one_one_nat ) ) )
% 9.49/5.26                      & ( ~ B3
% 9.49/5.26                       => ( Y2 = none_nat ) ) ) ) ) )
% 9.49/5.26         => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 9.49/5.26                  ( X
% 9.49/5.26                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 9.49/5.26             => ( Y2 != none_nat ) )
% 9.49/5.26           => ~ ! [Mi2: nat] :
% 9.49/5.26                  ( ? [Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 9.49/5.26                      ( X
% 9.49/5.26                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 9.49/5.26                 => ( Y2
% 9.49/5.26                   != ( some_nat @ Mi2 ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2776_vebt__maxt_Oelims,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Y2: option_nat] :
% 9.49/5.26        ( ( ( vEBT_vebt_maxt @ X )
% 9.49/5.26          = Y2 )
% 9.49/5.26       => ( ! [A4: $o,B3: $o] :
% 9.49/5.26              ( ( X
% 9.49/5.26                = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26             => ~ ( ( B3
% 9.49/5.26                   => ( Y2
% 9.49/5.26                      = ( some_nat @ one_one_nat ) ) )
% 9.49/5.26                  & ( ~ B3
% 9.49/5.26                   => ( ( A4
% 9.49/5.26                       => ( Y2
% 9.49/5.26                          = ( some_nat @ zero_zero_nat ) ) )
% 9.49/5.26                      & ( ~ A4
% 9.49/5.26                       => ( Y2 = none_nat ) ) ) ) ) )
% 9.49/5.26         => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 9.49/5.26                  ( X
% 9.49/5.26                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 9.49/5.26             => ( Y2 != none_nat ) )
% 9.49/5.26           => ~ ! [Mi2: nat,Ma2: nat] :
% 9.49/5.26                  ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 9.49/5.26                      ( X
% 9.49/5.26                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 9.49/5.26                 => ( Y2
% 9.49/5.26                   != ( some_nat @ Ma2 ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2777_mult__le__cancel__left1,axiom,
% 9.49/5.26      ! [C: real,B: real] :
% 9.49/5.26        ( ( ord_less_eq_real @ C @ ( times_times_real @ C @ B ) )
% 9.49/5.26        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.26           => ( ord_less_eq_real @ one_one_real @ B ) )
% 9.49/5.26          & ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.26           => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2778_mult__le__cancel__left1,axiom,
% 9.49/5.26      ! [C: rat,B: rat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B ) )
% 9.49/5.26        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.26           => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 9.49/5.26          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.26           => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2779_mult__le__cancel__left1,axiom,
% 9.49/5.26      ! [C: int,B: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B ) )
% 9.49/5.26        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 9.49/5.26           => ( ord_less_eq_int @ one_one_int @ B ) )
% 9.49/5.26          & ( ( ord_less_int @ C @ zero_zero_int )
% 9.49/5.26           => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2780_mult__le__cancel__left2,axiom,
% 9.49/5.26      ! [C: real,A: real] :
% 9.49/5.26        ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ C )
% 9.49/5.26        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.26           => ( ord_less_eq_real @ A @ one_one_real ) )
% 9.49/5.26          & ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.26           => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2781_mult__le__cancel__left2,axiom,
% 9.49/5.26      ! [C: rat,A: rat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ C )
% 9.49/5.26        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.26           => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 9.49/5.26          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.26           => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2782_mult__le__cancel__left2,axiom,
% 9.49/5.26      ! [C: int,A: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ C )
% 9.49/5.26        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 9.49/5.26           => ( ord_less_eq_int @ A @ one_one_int ) )
% 9.49/5.26          & ( ( ord_less_int @ C @ zero_zero_int )
% 9.49/5.26           => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2783_mult__le__cancel__right1,axiom,
% 9.49/5.26      ! [C: real,B: real] :
% 9.49/5.26        ( ( ord_less_eq_real @ C @ ( times_times_real @ B @ C ) )
% 9.49/5.26        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.26           => ( ord_less_eq_real @ one_one_real @ B ) )
% 9.49/5.26          & ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.26           => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2784_mult__le__cancel__right1,axiom,
% 9.49/5.26      ! [C: rat,B: rat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ C @ ( times_times_rat @ B @ C ) )
% 9.49/5.26        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.26           => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 9.49/5.26          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.26           => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2785_mult__le__cancel__right1,axiom,
% 9.49/5.26      ! [C: int,B: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ C @ ( times_times_int @ B @ C ) )
% 9.49/5.26        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 9.49/5.26           => ( ord_less_eq_int @ one_one_int @ B ) )
% 9.49/5.26          & ( ( ord_less_int @ C @ zero_zero_int )
% 9.49/5.26           => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2786_mult__le__cancel__right2,axiom,
% 9.49/5.26      ! [A: real,C: real] :
% 9.49/5.26        ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ C )
% 9.49/5.26        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.26           => ( ord_less_eq_real @ A @ one_one_real ) )
% 9.49/5.26          & ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.26           => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2787_mult__le__cancel__right2,axiom,
% 9.49/5.26      ! [A: rat,C: rat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ C )
% 9.49/5.26        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.26           => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 9.49/5.26          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.26           => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2788_mult__le__cancel__right2,axiom,
% 9.49/5.26      ! [A: int,C: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ C )
% 9.49/5.26        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 9.49/5.26           => ( ord_less_eq_int @ A @ one_one_int ) )
% 9.49/5.26          & ( ( ord_less_int @ C @ zero_zero_int )
% 9.49/5.26           => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2789_mult__less__cancel__left1,axiom,
% 9.49/5.26      ! [C: real,B: real] :
% 9.49/5.26        ( ( ord_less_real @ C @ ( times_times_real @ C @ B ) )
% 9.49/5.26        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 9.49/5.26           => ( ord_less_real @ one_one_real @ B ) )
% 9.49/5.26          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 9.49/5.26           => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2790_mult__less__cancel__left1,axiom,
% 9.49/5.26      ! [C: rat,B: rat] :
% 9.49/5.26        ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B ) )
% 9.49/5.26        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.49/5.26           => ( ord_less_rat @ one_one_rat @ B ) )
% 9.49/5.26          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 9.49/5.26           => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2791_mult__less__cancel__left1,axiom,
% 9.49/5.26      ! [C: int,B: int] :
% 9.49/5.26        ( ( ord_less_int @ C @ ( times_times_int @ C @ B ) )
% 9.49/5.26        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.49/5.26           => ( ord_less_int @ one_one_int @ B ) )
% 9.49/5.26          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 9.49/5.26           => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2792_mult__less__cancel__left2,axiom,
% 9.49/5.26      ! [C: real,A: real] :
% 9.49/5.26        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ C )
% 9.49/5.26        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 9.49/5.26           => ( ord_less_real @ A @ one_one_real ) )
% 9.49/5.26          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 9.49/5.26           => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2793_mult__less__cancel__left2,axiom,
% 9.49/5.26      ! [C: rat,A: rat] :
% 9.49/5.26        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ C )
% 9.49/5.26        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.49/5.26           => ( ord_less_rat @ A @ one_one_rat ) )
% 9.49/5.26          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 9.49/5.26           => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2794_mult__less__cancel__left2,axiom,
% 9.49/5.26      ! [C: int,A: int] :
% 9.49/5.26        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ C )
% 9.49/5.26        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.49/5.26           => ( ord_less_int @ A @ one_one_int ) )
% 9.49/5.26          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 9.49/5.26           => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2795_mult__less__cancel__right1,axiom,
% 9.49/5.26      ! [C: real,B: real] :
% 9.49/5.26        ( ( ord_less_real @ C @ ( times_times_real @ B @ C ) )
% 9.49/5.26        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 9.49/5.26           => ( ord_less_real @ one_one_real @ B ) )
% 9.49/5.26          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 9.49/5.26           => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2796_mult__less__cancel__right1,axiom,
% 9.49/5.26      ! [C: rat,B: rat] :
% 9.49/5.26        ( ( ord_less_rat @ C @ ( times_times_rat @ B @ C ) )
% 9.49/5.26        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.49/5.26           => ( ord_less_rat @ one_one_rat @ B ) )
% 9.49/5.26          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 9.49/5.26           => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2797_mult__less__cancel__right1,axiom,
% 9.49/5.26      ! [C: int,B: int] :
% 9.49/5.26        ( ( ord_less_int @ C @ ( times_times_int @ B @ C ) )
% 9.49/5.26        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.49/5.26           => ( ord_less_int @ one_one_int @ B ) )
% 9.49/5.26          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 9.49/5.26           => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2798_mult__less__cancel__right2,axiom,
% 9.49/5.26      ! [A: real,C: real] :
% 9.49/5.26        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ C )
% 9.49/5.26        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 9.49/5.26           => ( ord_less_real @ A @ one_one_real ) )
% 9.49/5.26          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 9.49/5.26           => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2799_mult__less__cancel__right2,axiom,
% 9.49/5.26      ! [A: rat,C: rat] :
% 9.49/5.26        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ C )
% 9.49/5.26        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.49/5.26           => ( ord_less_rat @ A @ one_one_rat ) )
% 9.49/5.26          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 9.49/5.26           => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2800_mult__less__cancel__right2,axiom,
% 9.49/5.26      ! [A: int,C: int] :
% 9.49/5.26        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ C )
% 9.49/5.26        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.49/5.26           => ( ord_less_int @ A @ one_one_int ) )
% 9.49/5.26          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 9.49/5.26           => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2801_field__le__mult__one__interval,axiom,
% 9.49/5.26      ! [X: real,Y2: real] :
% 9.49/5.26        ( ! [Z3: real] :
% 9.49/5.26            ( ( ord_less_real @ zero_zero_real @ Z3 )
% 9.49/5.26           => ( ( ord_less_real @ Z3 @ one_one_real )
% 9.49/5.26             => ( ord_less_eq_real @ ( times_times_real @ Z3 @ X ) @ Y2 ) ) )
% 9.49/5.26       => ( ord_less_eq_real @ X @ Y2 ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2802_field__le__mult__one__interval,axiom,
% 9.49/5.26      ! [X: rat,Y2: rat] :
% 9.49/5.26        ( ! [Z3: rat] :
% 9.49/5.26            ( ( ord_less_rat @ zero_zero_rat @ Z3 )
% 9.49/5.26           => ( ( ord_less_rat @ Z3 @ one_one_rat )
% 9.49/5.26             => ( ord_less_eq_rat @ ( times_times_rat @ Z3 @ X ) @ Y2 ) ) )
% 9.49/5.26       => ( ord_less_eq_rat @ X @ Y2 ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2803_divide__le__eq,axiom,
% 9.49/5.26      ! [B: real,C: real,A: real] :
% 9.49/5.26        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 9.49/5.26        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.26           => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 9.49/5.26          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.26           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.26               => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 9.49/5.26              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.26               => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2804_divide__le__eq,axiom,
% 9.49/5.26      ! [B: rat,C: rat,A: rat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 9.49/5.26        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.26           => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 9.49/5.26          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.26           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.26               => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 9.49/5.26              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.26               => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2805_le__divide__eq,axiom,
% 9.49/5.26      ! [A: real,B: real,C: real] :
% 9.49/5.26        ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 9.49/5.26        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.26           => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 9.49/5.26          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.26           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.26               => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 9.49/5.26              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.26               => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2806_le__divide__eq,axiom,
% 9.49/5.26      ! [A: rat,B: rat,C: rat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 9.49/5.26        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.26           => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 9.49/5.26          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.26           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.26               => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 9.49/5.26              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.26               => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2807_divide__left__mono,axiom,
% 9.49/5.26      ! [B: real,A: real,C: real] :
% 9.49/5.26        ( ( ord_less_eq_real @ B @ A )
% 9.49/5.26       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 9.49/5.26         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 9.49/5.26           => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2808_divide__left__mono,axiom,
% 9.49/5.26      ! [B: rat,A: rat,C: rat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ B @ A )
% 9.49/5.26       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.49/5.26         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 9.49/5.26           => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2809_neg__divide__le__eq,axiom,
% 9.49/5.26      ! [C: real,B: real,A: real] :
% 9.49/5.26        ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.26       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 9.49/5.26          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2810_neg__divide__le__eq,axiom,
% 9.49/5.26      ! [C: rat,B: rat,A: rat] :
% 9.49/5.26        ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.26       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 9.49/5.26          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2811_neg__le__divide__eq,axiom,
% 9.49/5.26      ! [C: real,A: real,B: real] :
% 9.49/5.26        ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.26       => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 9.49/5.26          = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2812_neg__le__divide__eq,axiom,
% 9.49/5.26      ! [C: rat,A: rat,B: rat] :
% 9.49/5.26        ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.26       => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 9.49/5.26          = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2813_pos__divide__le__eq,axiom,
% 9.49/5.26      ! [C: real,B: real,A: real] :
% 9.49/5.26        ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.26       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 9.49/5.26          = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2814_pos__divide__le__eq,axiom,
% 9.49/5.26      ! [C: rat,B: rat,A: rat] :
% 9.49/5.26        ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.26       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 9.49/5.26          = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2815_pos__le__divide__eq,axiom,
% 9.49/5.26      ! [C: real,A: real,B: real] :
% 9.49/5.26        ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.26       => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 9.49/5.26          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2816_pos__le__divide__eq,axiom,
% 9.49/5.26      ! [C: rat,A: rat,B: rat] :
% 9.49/5.26        ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.26       => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 9.49/5.26          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2817_mult__imp__div__pos__le,axiom,
% 9.49/5.26      ! [Y2: real,X: real,Z: real] :
% 9.49/5.26        ( ( ord_less_real @ zero_zero_real @ Y2 )
% 9.49/5.26       => ( ( ord_less_eq_real @ X @ ( times_times_real @ Z @ Y2 ) )
% 9.49/5.26         => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y2 ) @ Z ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2818_mult__imp__div__pos__le,axiom,
% 9.49/5.26      ! [Y2: rat,X: rat,Z: rat] :
% 9.49/5.26        ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 9.49/5.26       => ( ( ord_less_eq_rat @ X @ ( times_times_rat @ Z @ Y2 ) )
% 9.49/5.26         => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y2 ) @ Z ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2819_mult__imp__le__div__pos,axiom,
% 9.49/5.26      ! [Y2: real,Z: real,X: real] :
% 9.49/5.26        ( ( ord_less_real @ zero_zero_real @ Y2 )
% 9.49/5.26       => ( ( ord_less_eq_real @ ( times_times_real @ Z @ Y2 ) @ X )
% 9.49/5.26         => ( ord_less_eq_real @ Z @ ( divide_divide_real @ X @ Y2 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2820_mult__imp__le__div__pos,axiom,
% 9.49/5.26      ! [Y2: rat,Z: rat,X: rat] :
% 9.49/5.26        ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 9.49/5.26       => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ Y2 ) @ X )
% 9.49/5.26         => ( ord_less_eq_rat @ Z @ ( divide_divide_rat @ X @ Y2 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2821_divide__left__mono__neg,axiom,
% 9.49/5.26      ! [A: real,B: real,C: real] :
% 9.49/5.26        ( ( ord_less_eq_real @ A @ B )
% 9.49/5.26       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 9.49/5.26         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 9.49/5.26           => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2822_divide__left__mono__neg,axiom,
% 9.49/5.26      ! [A: rat,B: rat,C: rat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ A @ B )
% 9.49/5.26       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 9.49/5.26         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 9.49/5.26           => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2823_divide__le__eq__1,axiom,
% 9.49/5.26      ! [B: real,A: real] :
% 9.49/5.26        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 9.49/5.26        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 9.49/5.26            & ( ord_less_eq_real @ B @ A ) )
% 9.49/5.26          | ( ( ord_less_real @ A @ zero_zero_real )
% 9.49/5.26            & ( ord_less_eq_real @ A @ B ) )
% 9.49/5.26          | ( A = zero_zero_real ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2824_divide__le__eq__1,axiom,
% 9.49/5.26      ! [B: rat,A: rat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 9.49/5.26        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.49/5.26            & ( ord_less_eq_rat @ B @ A ) )
% 9.49/5.26          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.49/5.26            & ( ord_less_eq_rat @ A @ B ) )
% 9.49/5.26          | ( A = zero_zero_rat ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2825_le__divide__eq__1,axiom,
% 9.49/5.26      ! [B: real,A: real] :
% 9.49/5.26        ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 9.49/5.26        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 9.49/5.26            & ( ord_less_eq_real @ A @ B ) )
% 9.49/5.26          | ( ( ord_less_real @ A @ zero_zero_real )
% 9.49/5.26            & ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2826_le__divide__eq__1,axiom,
% 9.49/5.26      ! [B: rat,A: rat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 9.49/5.26        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.49/5.26            & ( ord_less_eq_rat @ A @ B ) )
% 9.49/5.26          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.49/5.26            & ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2827_convex__bound__le,axiom,
% 9.49/5.26      ! [X: rat,A: rat,Y2: rat,U: rat,V: rat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ X @ A )
% 9.49/5.26       => ( ( ord_less_eq_rat @ Y2 @ A )
% 9.49/5.26         => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 9.49/5.26           => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 9.49/5.26             => ( ( ( plus_plus_rat @ U @ V )
% 9.49/5.26                  = one_one_rat )
% 9.49/5.26               => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y2 ) ) @ A ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2828_convex__bound__le,axiom,
% 9.49/5.26      ! [X: real,A: real,Y2: real,U: real,V: real] :
% 9.49/5.26        ( ( ord_less_eq_real @ X @ A )
% 9.49/5.26       => ( ( ord_less_eq_real @ Y2 @ A )
% 9.49/5.26         => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 9.49/5.26           => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 9.49/5.26             => ( ( ( plus_plus_real @ U @ V )
% 9.49/5.26                  = one_one_real )
% 9.49/5.26               => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V @ Y2 ) ) @ A ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2829_convex__bound__le,axiom,
% 9.49/5.26      ! [X: int,A: int,Y2: int,U: int,V: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ X @ A )
% 9.49/5.26       => ( ( ord_less_eq_int @ Y2 @ A )
% 9.49/5.26         => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 9.49/5.26           => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 9.49/5.26             => ( ( ( plus_plus_int @ U @ V )
% 9.49/5.26                  = one_one_int )
% 9.49/5.26               => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y2 ) ) @ A ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2830_divide__less__eq__numeral_I1_J,axiom,
% 9.49/5.26      ! [B: real,C: real,W: num] :
% 9.49/5.26        ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 9.49/5.26        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.26           => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 9.49/5.26          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.26           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.26               => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 9.49/5.26              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.26               => ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2831_divide__less__eq__numeral_I1_J,axiom,
% 9.49/5.26      ! [B: rat,C: rat,W: num] :
% 9.49/5.26        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 9.49/5.26        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.26           => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 9.49/5.26          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.26           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.26               => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 9.49/5.26              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.26               => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2832_less__divide__eq__numeral_I1_J,axiom,
% 9.49/5.26      ! [W: num,B: real,C: real] :
% 9.49/5.26        ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 9.49/5.26        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.26           => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 9.49/5.26          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.26           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.26               => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 9.49/5.26              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.26               => ( ord_less_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2833_less__divide__eq__numeral_I1_J,axiom,
% 9.49/5.26      ! [W: num,B: rat,C: rat] :
% 9.49/5.26        ( ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 9.49/5.26        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.26           => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 9.49/5.26          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.26           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.26               => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 9.49/5.26              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.26               => ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2834_frac__le__eq,axiom,
% 9.49/5.26      ! [Y2: real,Z: real,X: real,W: real] :
% 9.49/5.26        ( ( Y2 != zero_zero_real )
% 9.49/5.26       => ( ( Z != zero_zero_real )
% 9.49/5.26         => ( ( ord_less_eq_real @ ( divide_divide_real @ X @ Y2 ) @ ( divide_divide_real @ W @ Z ) )
% 9.49/5.26            = ( ord_less_eq_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y2 ) ) @ ( times_times_real @ Y2 @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2835_frac__le__eq,axiom,
% 9.49/5.26      ! [Y2: rat,Z: rat,X: rat,W: rat] :
% 9.49/5.26        ( ( Y2 != zero_zero_rat )
% 9.49/5.26       => ( ( Z != zero_zero_rat )
% 9.49/5.26         => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y2 ) @ ( divide_divide_rat @ W @ Z ) )
% 9.49/5.26            = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y2 ) ) @ ( times_times_rat @ Y2 @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2836_power__Suc__less,axiom,
% 9.49/5.26      ! [A: real,N: nat] :
% 9.49/5.26        ( ( ord_less_real @ zero_zero_real @ A )
% 9.49/5.26       => ( ( ord_less_real @ A @ one_one_real )
% 9.49/5.26         => ( ord_less_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) @ ( power_power_real @ A @ N ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2837_power__Suc__less,axiom,
% 9.49/5.26      ! [A: rat,N: nat] :
% 9.49/5.26        ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.49/5.26       => ( ( ord_less_rat @ A @ one_one_rat )
% 9.49/5.26         => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) @ ( power_power_rat @ A @ N ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2838_power__Suc__less,axiom,
% 9.49/5.26      ! [A: nat,N: nat] :
% 9.49/5.26        ( ( ord_less_nat @ zero_zero_nat @ A )
% 9.49/5.26       => ( ( ord_less_nat @ A @ one_one_nat )
% 9.49/5.26         => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) @ ( power_power_nat @ A @ N ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2839_power__Suc__less,axiom,
% 9.49/5.26      ! [A: int,N: nat] :
% 9.49/5.26        ( ( ord_less_int @ zero_zero_int @ A )
% 9.49/5.26       => ( ( ord_less_int @ A @ one_one_int )
% 9.49/5.26         => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) @ ( power_power_int @ A @ N ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2840_frac__less__eq,axiom,
% 9.49/5.26      ! [Y2: real,Z: real,X: real,W: real] :
% 9.49/5.26        ( ( Y2 != zero_zero_real )
% 9.49/5.26       => ( ( Z != zero_zero_real )
% 9.49/5.26         => ( ( ord_less_real @ ( divide_divide_real @ X @ Y2 ) @ ( divide_divide_real @ W @ Z ) )
% 9.49/5.26            = ( ord_less_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y2 ) ) @ ( times_times_real @ Y2 @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2841_frac__less__eq,axiom,
% 9.49/5.26      ! [Y2: rat,Z: rat,X: rat,W: rat] :
% 9.49/5.26        ( ( Y2 != zero_zero_rat )
% 9.49/5.26       => ( ( Z != zero_zero_rat )
% 9.49/5.26         => ( ( ord_less_rat @ ( divide_divide_rat @ X @ Y2 ) @ ( divide_divide_rat @ W @ Z ) )
% 9.49/5.26            = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y2 ) ) @ ( times_times_rat @ Y2 @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2842_power__Suc__le__self,axiom,
% 9.49/5.26      ! [A: rat,N: nat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.49/5.26       => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 9.49/5.26         => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2843_power__Suc__le__self,axiom,
% 9.49/5.26      ! [A: real,N: nat] :
% 9.49/5.26        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 9.49/5.26       => ( ( ord_less_eq_real @ A @ one_one_real )
% 9.49/5.26         => ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2844_power__Suc__le__self,axiom,
% 9.49/5.26      ! [A: nat,N: nat] :
% 9.49/5.26        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.49/5.26       => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 9.49/5.26         => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2845_power__Suc__le__self,axiom,
% 9.49/5.26      ! [A: int,N: nat] :
% 9.49/5.26        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.26       => ( ( ord_less_eq_int @ A @ one_one_int )
% 9.49/5.26         => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2846_power__Suc__less__one,axiom,
% 9.49/5.26      ! [A: real,N: nat] :
% 9.49/5.26        ( ( ord_less_real @ zero_zero_real @ A )
% 9.49/5.26       => ( ( ord_less_real @ A @ one_one_real )
% 9.49/5.26         => ( ord_less_real @ ( power_power_real @ A @ ( suc @ N ) ) @ one_one_real ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2847_power__Suc__less__one,axiom,
% 9.49/5.26      ! [A: rat,N: nat] :
% 9.49/5.26        ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.49/5.26       => ( ( ord_less_rat @ A @ one_one_rat )
% 9.49/5.26         => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ one_one_rat ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2848_power__Suc__less__one,axiom,
% 9.49/5.26      ! [A: nat,N: nat] :
% 9.49/5.26        ( ( ord_less_nat @ zero_zero_nat @ A )
% 9.49/5.26       => ( ( ord_less_nat @ A @ one_one_nat )
% 9.49/5.26         => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ one_one_nat ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2849_power__Suc__less__one,axiom,
% 9.49/5.26      ! [A: int,N: nat] :
% 9.49/5.26        ( ( ord_less_int @ zero_zero_int @ A )
% 9.49/5.26       => ( ( ord_less_int @ A @ one_one_int )
% 9.49/5.26         => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N ) ) @ one_one_int ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2850_power__strict__decreasing,axiom,
% 9.49/5.26      ! [N: nat,N4: nat,A: real] :
% 9.49/5.26        ( ( ord_less_nat @ N @ N4 )
% 9.49/5.26       => ( ( ord_less_real @ zero_zero_real @ A )
% 9.49/5.26         => ( ( ord_less_real @ A @ one_one_real )
% 9.49/5.26           => ( ord_less_real @ ( power_power_real @ A @ N4 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2851_power__strict__decreasing,axiom,
% 9.49/5.26      ! [N: nat,N4: nat,A: rat] :
% 9.49/5.26        ( ( ord_less_nat @ N @ N4 )
% 9.49/5.26       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.49/5.26         => ( ( ord_less_rat @ A @ one_one_rat )
% 9.49/5.26           => ( ord_less_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2852_power__strict__decreasing,axiom,
% 9.49/5.26      ! [N: nat,N4: nat,A: nat] :
% 9.49/5.26        ( ( ord_less_nat @ N @ N4 )
% 9.49/5.26       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 9.49/5.26         => ( ( ord_less_nat @ A @ one_one_nat )
% 9.49/5.26           => ( ord_less_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2853_power__strict__decreasing,axiom,
% 9.49/5.26      ! [N: nat,N4: nat,A: int] :
% 9.49/5.26        ( ( ord_less_nat @ N @ N4 )
% 9.49/5.26       => ( ( ord_less_int @ zero_zero_int @ A )
% 9.49/5.26         => ( ( ord_less_int @ A @ one_one_int )
% 9.49/5.26           => ( ord_less_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2854_zero__power2,axiom,
% 9.49/5.26      ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.26      = zero_zero_rat ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2855_zero__power2,axiom,
% 9.49/5.26      ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.26      = zero_zero_nat ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2856_zero__power2,axiom,
% 9.49/5.26      ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.26      = zero_zero_real ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2857_zero__power2,axiom,
% 9.49/5.26      ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.26      = zero_zero_int ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2858_zero__power2,axiom,
% 9.49/5.26      ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.26      = zero_zero_complex ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2859_power__decreasing,axiom,
% 9.49/5.26      ! [N: nat,N4: nat,A: rat] :
% 9.49/5.26        ( ( ord_less_eq_nat @ N @ N4 )
% 9.49/5.26       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.49/5.26         => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 9.49/5.26           => ( ord_less_eq_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2860_power__decreasing,axiom,
% 9.49/5.26      ! [N: nat,N4: nat,A: real] :
% 9.49/5.26        ( ( ord_less_eq_nat @ N @ N4 )
% 9.49/5.26       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 9.49/5.26         => ( ( ord_less_eq_real @ A @ one_one_real )
% 9.49/5.26           => ( ord_less_eq_real @ ( power_power_real @ A @ N4 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2861_power__decreasing,axiom,
% 9.49/5.26      ! [N: nat,N4: nat,A: nat] :
% 9.49/5.26        ( ( ord_less_eq_nat @ N @ N4 )
% 9.49/5.26       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.49/5.26         => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 9.49/5.26           => ( ord_less_eq_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2862_power__decreasing,axiom,
% 9.49/5.26      ! [N: nat,N4: nat,A: int] :
% 9.49/5.26        ( ( ord_less_eq_nat @ N @ N4 )
% 9.49/5.26       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.26         => ( ( ord_less_eq_int @ A @ one_one_int )
% 9.49/5.26           => ( ord_less_eq_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2863_numeral__2__eq__2,axiom,
% 9.49/5.26      ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 9.49/5.26      = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2864_self__le__power,axiom,
% 9.49/5.26      ! [A: rat,N: nat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ one_one_rat @ A )
% 9.49/5.26       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.26         => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2865_self__le__power,axiom,
% 9.49/5.26      ! [A: real,N: nat] :
% 9.49/5.26        ( ( ord_less_eq_real @ one_one_real @ A )
% 9.49/5.26       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.26         => ( ord_less_eq_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2866_self__le__power,axiom,
% 9.49/5.26      ! [A: nat,N: nat] :
% 9.49/5.26        ( ( ord_less_eq_nat @ one_one_nat @ A )
% 9.49/5.26       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.26         => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2867_self__le__power,axiom,
% 9.49/5.26      ! [A: int,N: nat] :
% 9.49/5.26        ( ( ord_less_eq_int @ one_one_int @ A )
% 9.49/5.26       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.26         => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2868_one__less__power,axiom,
% 9.49/5.26      ! [A: real,N: nat] :
% 9.49/5.26        ( ( ord_less_real @ one_one_real @ A )
% 9.49/5.26       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.26         => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2869_one__less__power,axiom,
% 9.49/5.26      ! [A: rat,N: nat] :
% 9.49/5.26        ( ( ord_less_rat @ one_one_rat @ A )
% 9.49/5.26       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.26         => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2870_one__less__power,axiom,
% 9.49/5.26      ! [A: nat,N: nat] :
% 9.49/5.26        ( ( ord_less_nat @ one_one_nat @ A )
% 9.49/5.26       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.26         => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2871_one__less__power,axiom,
% 9.49/5.26      ! [A: int,N: nat] :
% 9.49/5.26        ( ( ord_less_int @ one_one_int @ A )
% 9.49/5.26       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.26         => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2872_pos2,axiom,
% 9.49/5.26      ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2873_power__diff,axiom,
% 9.49/5.26      ! [A: complex,N: nat,M: nat] :
% 9.49/5.26        ( ( A != zero_zero_complex )
% 9.49/5.26       => ( ( ord_less_eq_nat @ N @ M )
% 9.49/5.26         => ( ( power_power_complex @ A @ ( minus_minus_nat @ M @ N ) )
% 9.49/5.26            = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2874_power__diff,axiom,
% 9.49/5.26      ! [A: real,N: nat,M: nat] :
% 9.49/5.26        ( ( A != zero_zero_real )
% 9.49/5.26       => ( ( ord_less_eq_nat @ N @ M )
% 9.49/5.26         => ( ( power_power_real @ A @ ( minus_minus_nat @ M @ N ) )
% 9.49/5.26            = ( divide_divide_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2875_power__diff,axiom,
% 9.49/5.26      ! [A: rat,N: nat,M: nat] :
% 9.49/5.26        ( ( A != zero_zero_rat )
% 9.49/5.26       => ( ( ord_less_eq_nat @ N @ M )
% 9.49/5.26         => ( ( power_power_rat @ A @ ( minus_minus_nat @ M @ N ) )
% 9.49/5.26            = ( divide_divide_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2876_power__diff,axiom,
% 9.49/5.26      ! [A: nat,N: nat,M: nat] :
% 9.49/5.26        ( ( A != zero_zero_nat )
% 9.49/5.26       => ( ( ord_less_eq_nat @ N @ M )
% 9.49/5.26         => ( ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) )
% 9.49/5.26            = ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2877_power__diff,axiom,
% 9.49/5.26      ! [A: int,N: nat,M: nat] :
% 9.49/5.26        ( ( A != zero_zero_int )
% 9.49/5.26       => ( ( ord_less_eq_nat @ N @ M )
% 9.49/5.26         => ( ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) )
% 9.49/5.26            = ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2878_numeral__3__eq__3,axiom,
% 9.49/5.26      ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 9.49/5.26      = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2879_Suc__pred_H,axiom,
% 9.49/5.26      ! [N: nat] :
% 9.49/5.26        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.26       => ( N
% 9.49/5.26          = ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2880_Suc__diff__eq__diff__pred,axiom,
% 9.49/5.26      ! [N: nat,M: nat] :
% 9.49/5.26        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.26       => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 9.49/5.26          = ( minus_minus_nat @ M @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2881_add__eq__if,axiom,
% 9.49/5.26      ( plus_plus_nat
% 9.49/5.26      = ( ^ [M6: nat,N2: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N2 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) @ N2 ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2882_div__if,axiom,
% 9.49/5.26      ( divide_divide_nat
% 9.49/5.26      = ( ^ [M6: nat,N2: nat] :
% 9.49/5.26            ( if_nat
% 9.49/5.26            @ ( ( ord_less_nat @ M6 @ N2 )
% 9.49/5.26              | ( N2 = zero_zero_nat ) )
% 9.49/5.26            @ zero_zero_nat
% 9.49/5.26            @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M6 @ N2 ) @ N2 ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2883_div__geq,axiom,
% 9.49/5.26      ! [N: nat,M: nat] :
% 9.49/5.26        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.26       => ( ~ ( ord_less_nat @ M @ N )
% 9.49/5.26         => ( ( divide_divide_nat @ M @ N )
% 9.49/5.26            = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2884_split__div,axiom,
% 9.49/5.26      ! [P: nat > $o,M: nat,N: nat] :
% 9.49/5.26        ( ( P @ ( divide_divide_nat @ M @ N ) )
% 9.49/5.26        = ( ( ( N = zero_zero_nat )
% 9.49/5.26           => ( P @ zero_zero_nat ) )
% 9.49/5.26          & ( ( N != zero_zero_nat )
% 9.49/5.26           => ! [I3: nat,J3: nat] :
% 9.49/5.26                ( ( ord_less_nat @ J3 @ N )
% 9.49/5.26               => ( ( M
% 9.49/5.26                    = ( plus_plus_nat @ ( times_times_nat @ N @ I3 ) @ J3 ) )
% 9.49/5.26                 => ( P @ I3 ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2885_dividend__less__div__times,axiom,
% 9.49/5.26      ! [N: nat,M: nat] :
% 9.49/5.26        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.26       => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2886_dividend__less__times__div,axiom,
% 9.49/5.26      ! [N: nat,M: nat] :
% 9.49/5.26        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.26       => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2887_less__eq__div__iff__mult__less__eq,axiom,
% 9.49/5.26      ! [Q2: nat,M: nat,N: nat] :
% 9.49/5.26        ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 9.49/5.26       => ( ( ord_less_eq_nat @ M @ ( divide_divide_nat @ N @ Q2 ) )
% 9.49/5.26          = ( ord_less_eq_nat @ ( times_times_nat @ M @ Q2 ) @ N ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2888_mult__eq__if,axiom,
% 9.49/5.26      ( times_times_nat
% 9.49/5.26      = ( ^ [M6: nat,N2: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N2 @ ( times_times_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) @ N2 ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2889_VEBT__internal_Onaive__member_Oelims_I1_J,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 9.49/5.26        ( ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 9.49/5.26          = Y2 )
% 9.49/5.26       => ( ! [A4: $o,B3: $o] :
% 9.49/5.26              ( ( X
% 9.49/5.26                = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26             => ( Y2
% 9.49/5.26                = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 9.49/5.26                       => A4 )
% 9.49/5.26                      & ( ( Xa2 != zero_zero_nat )
% 9.49/5.26                       => ( ( ( Xa2 = one_one_nat )
% 9.49/5.26                           => B3 )
% 9.49/5.26                          & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 9.49/5.26         => ( ( ? [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 9.49/5.26                  ( X
% 9.49/5.26                  = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 9.49/5.26             => Y2 )
% 9.49/5.26           => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 9.49/5.26                  ( ? [S: vEBT_VEBT] :
% 9.49/5.26                      ( X
% 9.49/5.26                      = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) )
% 9.49/5.26                 => ( Y2
% 9.49/5.26                    = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                           => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2890_VEBT__internal_Onaive__member_Oelims_I2_J,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat] :
% 9.49/5.26        ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 9.49/5.26       => ( ! [A4: $o,B3: $o] :
% 9.49/5.26              ( ( X
% 9.49/5.26                = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26             => ~ ( ( ( Xa2 = zero_zero_nat )
% 9.49/5.26                   => A4 )
% 9.49/5.26                  & ( ( Xa2 != zero_zero_nat )
% 9.49/5.26                   => ( ( ( Xa2 = one_one_nat )
% 9.49/5.26                       => B3 )
% 9.49/5.26                      & ( Xa2 = one_one_nat ) ) ) ) )
% 9.49/5.26         => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 9.49/5.26                ( ? [S: vEBT_VEBT] :
% 9.49/5.26                    ( X
% 9.49/5.26                    = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) )
% 9.49/5.26               => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                     => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                    & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2891_VEBT__internal_Onaive__member_Oelims_I3_J,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat] :
% 9.49/5.26        ( ~ ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 9.49/5.26       => ( ! [A4: $o,B3: $o] :
% 9.49/5.26              ( ( X
% 9.49/5.26                = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26             => ( ( ( Xa2 = zero_zero_nat )
% 9.49/5.26                 => A4 )
% 9.49/5.26                & ( ( Xa2 != zero_zero_nat )
% 9.49/5.26                 => ( ( ( Xa2 = one_one_nat )
% 9.49/5.26                     => B3 )
% 9.49/5.26                    & ( Xa2 = one_one_nat ) ) ) ) )
% 9.49/5.26         => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 9.49/5.26                ( X
% 9.49/5.26               != ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 9.49/5.26           => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 9.49/5.26                  ( ? [S: vEBT_VEBT] :
% 9.49/5.26                      ( X
% 9.49/5.26                      = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) )
% 9.49/5.26                 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                     => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                    & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2892_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I4_J,axiom,
% 9.49/5.26      ! [Uy: nat,Uz: list_VEBT_VEBT,Va: vEBT_VEBT,Vb: nat] :
% 9.49/5.26        ( ( vEBT_T_p_r_e_d @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz @ Va ) @ Vb )
% 9.49/5.26        = one_one_nat ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2893_vebt__member_Osimps_I4_J,axiom,
% 9.49/5.26      ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 9.49/5.26        ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2894_vebt__delete_Osimps_I5_J,axiom,
% 9.49/5.26      ! [Mi: nat,Ma: nat,TrLst: list_VEBT_VEBT,Smry: vEBT_VEBT,X: nat] :
% 9.49/5.26        ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TrLst @ Smry ) @ X )
% 9.49/5.26        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TrLst @ Smry ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2895_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I3_J,axiom,
% 9.49/5.26      ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT,X: nat] :
% 9.49/5.26        ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) @ X )
% 9.49/5.26        = one_one_nat ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2896_vebt__succ_Osimps_I4_J,axiom,
% 9.49/5.26      ! [V: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd: vEBT_VEBT,Ve: nat] :
% 9.49/5.26        ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc @ Vd ) @ Ve )
% 9.49/5.26        = none_nat ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2897_vebt__pred_Osimps_I5_J,axiom,
% 9.49/5.26      ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT,Vf: nat] :
% 9.49/5.26        ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) @ Vf )
% 9.49/5.26        = none_nat ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2898_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I5_J,axiom,
% 9.49/5.26      ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT,Vf: nat] :
% 9.49/5.26        ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) @ Vf )
% 9.49/5.26        = one_one_nat ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2899_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I4_J,axiom,
% 9.49/5.26      ! [V: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd: vEBT_VEBT,Ve: nat] :
% 9.49/5.26        ( ( vEBT_T_s_u_c_c @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc @ Vd ) @ Ve )
% 9.49/5.26        = one_one_nat ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2900_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I4_J,axiom,
% 9.49/5.26      ! [V: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd: vEBT_VEBT,Ve: nat] :
% 9.49/5.26        ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc @ Vd ) @ Ve )
% 9.49/5.26        = one_one_nat ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2901_VEBT__internal_Omembermima_Oelims_I1_J,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 9.49/5.26        ( ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 9.49/5.26          = Y2 )
% 9.49/5.26       => ( ( ? [Uu2: $o,Uv2: $o] :
% 9.49/5.26                ( X
% 9.49/5.26                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 9.49/5.26           => Y2 )
% 9.49/5.26         => ( ( ? [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 9.49/5.26                  ( X
% 9.49/5.26                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 9.49/5.26             => Y2 )
% 9.49/5.26           => ( ! [Mi2: nat,Ma2: nat] :
% 9.49/5.26                  ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 9.49/5.26                      ( X
% 9.49/5.26                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 9.49/5.26                 => ( Y2
% 9.49/5.26                    = ( ~ ( ( Xa2 = Mi2 )
% 9.49/5.26                          | ( Xa2 = Ma2 ) ) ) ) )
% 9.49/5.26             => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 9.49/5.26                    ( ? [Vc2: vEBT_VEBT] :
% 9.49/5.26                        ( X
% 9.49/5.26                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 9.49/5.26                   => ( Y2
% 9.49/5.26                      = ( ~ ( ( Xa2 = Mi2 )
% 9.49/5.26                            | ( Xa2 = Ma2 )
% 9.49/5.26                            | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) )
% 9.49/5.26               => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT] :
% 9.49/5.26                      ( ? [Vd2: vEBT_VEBT] :
% 9.49/5.26                          ( X
% 9.49/5.26                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 9.49/5.26                     => ( Y2
% 9.49/5.26                        = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2902_VEBT__internal_Omembermima_Oelims_I3_J,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat] :
% 9.49/5.26        ( ~ ( vEBT_VEBT_membermima @ X @ Xa2 )
% 9.49/5.26       => ( ! [Uu2: $o,Uv2: $o] :
% 9.49/5.26              ( X
% 9.49/5.26             != ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 9.49/5.26         => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 9.49/5.26                ( X
% 9.49/5.26               != ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 9.49/5.26           => ( ! [Mi2: nat,Ma2: nat] :
% 9.49/5.26                  ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 9.49/5.26                      ( X
% 9.49/5.26                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 9.49/5.26                 => ( ( Xa2 = Mi2 )
% 9.49/5.26                    | ( Xa2 = Ma2 ) ) )
% 9.49/5.26             => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 9.49/5.26                    ( ? [Vc2: vEBT_VEBT] :
% 9.49/5.26                        ( X
% 9.49/5.26                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 9.49/5.26                   => ( ( Xa2 = Mi2 )
% 9.49/5.26                      | ( Xa2 = Ma2 )
% 9.49/5.26                      | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                         => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 9.49/5.26               => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT] :
% 9.49/5.26                      ( ? [Vd2: vEBT_VEBT] :
% 9.49/5.26                          ( X
% 9.49/5.26                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 9.49/5.26                     => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                         => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2903_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Oelims,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Y2: nat] :
% 9.49/5.26        ( ( ( vEBT_T_m_i_n_N_u_l_l @ X )
% 9.49/5.26          = Y2 )
% 9.49/5.26       => ( ( ( X
% 9.49/5.26              = ( vEBT_Leaf @ $false @ $false ) )
% 9.49/5.26           => ( Y2 != one_one_nat ) )
% 9.49/5.26         => ( ( ? [Uv2: $o] :
% 9.49/5.26                  ( X
% 9.49/5.26                  = ( vEBT_Leaf @ $true @ Uv2 ) )
% 9.49/5.26             => ( Y2 != one_one_nat ) )
% 9.49/5.26           => ( ( ? [Uu2: $o] :
% 9.49/5.26                    ( X
% 9.49/5.26                    = ( vEBT_Leaf @ Uu2 @ $true ) )
% 9.49/5.26               => ( Y2 != one_one_nat ) )
% 9.49/5.26             => ( ( ? [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 9.49/5.26                      ( X
% 9.49/5.26                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 9.49/5.26                 => ( Y2 != one_one_nat ) )
% 9.49/5.26               => ~ ( ? [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 9.49/5.26                        ( X
% 9.49/5.26                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 9.49/5.26                   => ( Y2 != one_one_nat ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2904_convex__bound__lt,axiom,
% 9.49/5.26      ! [X: real,A: real,Y2: real,U: real,V: real] :
% 9.49/5.26        ( ( ord_less_real @ X @ A )
% 9.49/5.26       => ( ( ord_less_real @ Y2 @ A )
% 9.49/5.26         => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 9.49/5.26           => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 9.49/5.26             => ( ( ( plus_plus_real @ U @ V )
% 9.49/5.26                  = one_one_real )
% 9.49/5.26               => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V @ Y2 ) ) @ A ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2905_convex__bound__lt,axiom,
% 9.49/5.26      ! [X: rat,A: rat,Y2: rat,U: rat,V: rat] :
% 9.49/5.26        ( ( ord_less_rat @ X @ A )
% 9.49/5.26       => ( ( ord_less_rat @ Y2 @ A )
% 9.49/5.26         => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 9.49/5.26           => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 9.49/5.26             => ( ( ( plus_plus_rat @ U @ V )
% 9.49/5.26                  = one_one_rat )
% 9.49/5.26               => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y2 ) ) @ A ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2906_convex__bound__lt,axiom,
% 9.49/5.26      ! [X: int,A: int,Y2: int,U: int,V: int] :
% 9.49/5.26        ( ( ord_less_int @ X @ A )
% 9.49/5.26       => ( ( ord_less_int @ Y2 @ A )
% 9.49/5.26         => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 9.49/5.26           => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 9.49/5.26             => ( ( ( plus_plus_int @ U @ V )
% 9.49/5.26                  = one_one_int )
% 9.49/5.26               => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y2 ) ) @ A ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2907_divide__le__eq__numeral_I1_J,axiom,
% 9.49/5.26      ! [B: real,C: real,W: num] :
% 9.49/5.26        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 9.49/5.26        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.26           => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 9.49/5.26          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.26           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.26               => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 9.49/5.26              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.26               => ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2908_divide__le__eq__numeral_I1_J,axiom,
% 9.49/5.26      ! [B: rat,C: rat,W: num] :
% 9.49/5.26        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 9.49/5.26        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.26           => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 9.49/5.26          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.26           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.26               => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 9.49/5.26              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.26               => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2909_le__divide__eq__numeral_I1_J,axiom,
% 9.49/5.26      ! [W: num,B: real,C: real] :
% 9.49/5.26        ( ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 9.49/5.26        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.26           => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 9.49/5.26          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.26           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.26               => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 9.49/5.26              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.26               => ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2910_le__divide__eq__numeral_I1_J,axiom,
% 9.49/5.26      ! [W: num,B: rat,C: rat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 9.49/5.26        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.26           => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 9.49/5.26          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.26           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.26               => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 9.49/5.26              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.26               => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2911_half__gt__zero__iff,axiom,
% 9.49/5.26      ! [A: real] :
% 9.49/5.26        ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.49/5.26        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2912_half__gt__zero__iff,axiom,
% 9.49/5.26      ! [A: rat] :
% 9.49/5.26        ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 9.49/5.26        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2913_half__gt__zero,axiom,
% 9.49/5.26      ! [A: real] :
% 9.49/5.26        ( ( ord_less_real @ zero_zero_real @ A )
% 9.49/5.26       => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2914_half__gt__zero,axiom,
% 9.49/5.26      ! [A: rat] :
% 9.49/5.26        ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.49/5.26       => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2915_scaling__mono,axiom,
% 9.49/5.26      ! [U: real,V: real,R: real,S3: real] :
% 9.49/5.26        ( ( ord_less_eq_real @ U @ V )
% 9.49/5.26       => ( ( ord_less_eq_real @ zero_zero_real @ R )
% 9.49/5.26         => ( ( ord_less_eq_real @ R @ S3 )
% 9.49/5.26           => ( ord_less_eq_real @ ( plus_plus_real @ U @ ( divide_divide_real @ ( times_times_real @ R @ ( minus_minus_real @ V @ U ) ) @ S3 ) ) @ V ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2916_scaling__mono,axiom,
% 9.49/5.26      ! [U: rat,V: rat,R: rat,S3: rat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ U @ V )
% 9.49/5.26       => ( ( ord_less_eq_rat @ zero_zero_rat @ R )
% 9.49/5.26         => ( ( ord_less_eq_rat @ R @ S3 )
% 9.49/5.26           => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R @ ( minus_minus_rat @ V @ U ) ) @ S3 ) ) @ V ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2917_power2__le__imp__le,axiom,
% 9.49/5.26      ! [X: rat,Y2: rat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.26       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 9.49/5.26         => ( ord_less_eq_rat @ X @ Y2 ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2918_power2__le__imp__le,axiom,
% 9.49/5.26      ! [X: real,Y2: real] :
% 9.49/5.26        ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.26       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 9.49/5.26         => ( ord_less_eq_real @ X @ Y2 ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2919_power2__le__imp__le,axiom,
% 9.49/5.26      ! [X: nat,Y2: nat] :
% 9.49/5.26        ( ( ord_less_eq_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.26       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y2 )
% 9.49/5.26         => ( ord_less_eq_nat @ X @ Y2 ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2920_power2__le__imp__le,axiom,
% 9.49/5.26      ! [X: int,Y2: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.26       => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 9.49/5.26         => ( ord_less_eq_int @ X @ Y2 ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2921_power2__eq__imp__eq,axiom,
% 9.49/5.26      ! [X: rat,Y2: rat] :
% 9.49/5.26        ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.26          = ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.26       => ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 9.49/5.26         => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 9.49/5.26           => ( X = Y2 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2922_power2__eq__imp__eq,axiom,
% 9.49/5.26      ! [X: real,Y2: real] :
% 9.49/5.26        ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.26          = ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.26       => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.49/5.26         => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 9.49/5.26           => ( X = Y2 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2923_power2__eq__imp__eq,axiom,
% 9.49/5.26      ! [X: nat,Y2: nat] :
% 9.49/5.26        ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.26          = ( power_power_nat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.26       => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 9.49/5.26         => ( ( ord_less_eq_nat @ zero_zero_nat @ Y2 )
% 9.49/5.26           => ( X = Y2 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2924_power2__eq__imp__eq,axiom,
% 9.49/5.26      ! [X: int,Y2: int] :
% 9.49/5.26        ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.26          = ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.26       => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 9.49/5.26         => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 9.49/5.26           => ( X = Y2 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2925_zero__le__power2,axiom,
% 9.49/5.26      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2926_zero__le__power2,axiom,
% 9.49/5.26      ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2927_zero__le__power2,axiom,
% 9.49/5.26      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2928_power2__less__0,axiom,
% 9.49/5.26      ! [A: real] :
% 9.49/5.26        ~ ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2929_power2__less__0,axiom,
% 9.49/5.26      ! [A: rat] :
% 9.49/5.26        ~ ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2930_power2__less__0,axiom,
% 9.49/5.26      ! [A: int] :
% 9.49/5.26        ~ ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2931_exp__add__not__zero__imp__right,axiom,
% 9.49/5.26      ! [M: nat,N: nat] :
% 9.49/5.26        ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 9.49/5.26         != zero_zero_nat )
% 9.49/5.26       => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.26         != zero_zero_nat ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2932_exp__add__not__zero__imp__right,axiom,
% 9.49/5.26      ! [M: nat,N: nat] :
% 9.49/5.26        ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 9.49/5.26         != zero_zero_int )
% 9.49/5.26       => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 9.49/5.26         != zero_zero_int ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2933_exp__add__not__zero__imp__left,axiom,
% 9.49/5.26      ! [M: nat,N: nat] :
% 9.49/5.26        ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 9.49/5.26         != zero_zero_nat )
% 9.49/5.26       => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 9.49/5.26         != zero_zero_nat ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2934_exp__add__not__zero__imp__left,axiom,
% 9.49/5.26      ! [M: nat,N: nat] :
% 9.49/5.26        ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 9.49/5.26         != zero_zero_int )
% 9.49/5.26       => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 9.49/5.26         != zero_zero_int ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2935_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 9.49/5.26      ! [N: nat,M: nat] :
% 9.49/5.26        ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.26         != zero_zero_nat )
% 9.49/5.26       => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 9.49/5.26         != zero_zero_nat ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2936_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 9.49/5.26      ! [N: nat,M: nat] :
% 9.49/5.26        ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 9.49/5.26         != zero_zero_int )
% 9.49/5.26       => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 9.49/5.26         != zero_zero_int ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2937_power__diff__power__eq,axiom,
% 9.49/5.26      ! [A: nat,N: nat,M: nat] :
% 9.49/5.26        ( ( A != zero_zero_nat )
% 9.49/5.26       => ( ( ( ord_less_eq_nat @ N @ M )
% 9.49/5.26           => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 9.49/5.26              = ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 9.49/5.26          & ( ~ ( ord_less_eq_nat @ N @ M )
% 9.49/5.26           => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 9.49/5.26              = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2938_power__diff__power__eq,axiom,
% 9.49/5.26      ! [A: int,N: nat,M: nat] :
% 9.49/5.26        ( ( A != zero_zero_int )
% 9.49/5.26       => ( ( ( ord_less_eq_nat @ N @ M )
% 9.49/5.26           => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 9.49/5.26              = ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 9.49/5.26          & ( ~ ( ord_less_eq_nat @ N @ M )
% 9.49/5.26           => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 9.49/5.26              = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2939_less__2__cases__iff,axiom,
% 9.49/5.26      ! [N: nat] :
% 9.49/5.26        ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.26        = ( ( N = zero_zero_nat )
% 9.49/5.26          | ( N
% 9.49/5.26            = ( suc @ zero_zero_nat ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2940_less__2__cases,axiom,
% 9.49/5.26      ! [N: nat] :
% 9.49/5.26        ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.26       => ( ( N = zero_zero_nat )
% 9.49/5.26          | ( N
% 9.49/5.26            = ( suc @ zero_zero_nat ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2941_nat__induct2,axiom,
% 9.49/5.26      ! [P: nat > $o,N: nat] :
% 9.49/5.26        ( ( P @ zero_zero_nat )
% 9.49/5.26       => ( ( P @ one_one_nat )
% 9.49/5.26         => ( ! [N3: nat] :
% 9.49/5.26                ( ( P @ N3 )
% 9.49/5.26               => ( P @ ( plus_plus_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.49/5.26           => ( P @ N ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2942_power__eq__if,axiom,
% 9.49/5.26      ( power_power_rat
% 9.49/5.26      = ( ^ [P4: rat,M6: nat] : ( if_rat @ ( M6 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P4 @ ( power_power_rat @ P4 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2943_power__eq__if,axiom,
% 9.49/5.26      ( power_power_complex
% 9.49/5.26      = ( ^ [P4: complex,M6: nat] : ( if_complex @ ( M6 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ P4 @ ( power_power_complex @ P4 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2944_power__eq__if,axiom,
% 9.49/5.26      ( power_power_real
% 9.49/5.26      = ( ^ [P4: real,M6: nat] : ( if_real @ ( M6 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ P4 @ ( power_power_real @ P4 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2945_power__eq__if,axiom,
% 9.49/5.26      ( power_power_nat
% 9.49/5.26      = ( ^ [P4: nat,M6: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P4 @ ( power_power_nat @ P4 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2946_power__eq__if,axiom,
% 9.49/5.26      ( power_power_int
% 9.49/5.26      = ( ^ [P4: int,M6: nat] : ( if_int @ ( M6 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P4 @ ( power_power_int @ P4 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2947_power__minus__mult,axiom,
% 9.49/5.26      ! [N: nat,A: complex] :
% 9.49/5.26        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.26       => ( ( times_times_complex @ ( power_power_complex @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 9.49/5.26          = ( power_power_complex @ A @ N ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2948_power__minus__mult,axiom,
% 9.49/5.26      ! [N: nat,A: real] :
% 9.49/5.26        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.26       => ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 9.49/5.26          = ( power_power_real @ A @ N ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2949_power__minus__mult,axiom,
% 9.49/5.26      ! [N: nat,A: nat] :
% 9.49/5.26        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.26       => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 9.49/5.26          = ( power_power_nat @ A @ N ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2950_power__minus__mult,axiom,
% 9.49/5.26      ! [N: nat,A: int] :
% 9.49/5.26        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.26       => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 9.49/5.26          = ( power_power_int @ A @ N ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2951_split__div_H,axiom,
% 9.49/5.26      ! [P: nat > $o,M: nat,N: nat] :
% 9.49/5.26        ( ( P @ ( divide_divide_nat @ M @ N ) )
% 9.49/5.26        = ( ( ( N = zero_zero_nat )
% 9.49/5.26            & ( P @ zero_zero_nat ) )
% 9.49/5.26          | ? [Q4: nat] :
% 9.49/5.26              ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q4 ) @ M )
% 9.49/5.26              & ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q4 ) ) )
% 9.49/5.26              & ( P @ Q4 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2952_le__div__geq,axiom,
% 9.49/5.26      ! [N: nat,M: nat] :
% 9.49/5.26        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.26       => ( ( ord_less_eq_nat @ N @ M )
% 9.49/5.26         => ( ( divide_divide_nat @ M @ N )
% 9.49/5.26            = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2953_vebt__delete_Osimps_I6_J,axiom,
% 9.49/5.26      ! [Mi: nat,Ma: nat,Tr: list_VEBT_VEBT,Sm: vEBT_VEBT,X: nat] :
% 9.49/5.26        ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) @ X )
% 9.49/5.26        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2954_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I5_J,axiom,
% 9.49/5.26      ! [Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 9.49/5.26        ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TreeList @ Summary ) @ X )
% 9.49/5.26        = one_one_nat ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2955_vebt__pred_Osimps_I6_J,axiom,
% 9.49/5.26      ! [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT,Vj: nat] :
% 9.49/5.26        ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Vj )
% 9.49/5.26        = none_nat ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2956_vebt__succ_Osimps_I5_J,axiom,
% 9.49/5.26      ! [V: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh: vEBT_VEBT,Vi: nat] :
% 9.49/5.26        ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh ) @ Vi )
% 9.49/5.26        = none_nat ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2957_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I6_J,axiom,
% 9.49/5.26      ! [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT,Vj: nat] :
% 9.49/5.26        ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Vj )
% 9.49/5.26        = one_one_nat ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2958_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I5_J,axiom,
% 9.49/5.26      ! [V: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh: vEBT_VEBT,Vi: nat] :
% 9.49/5.26        ( ( vEBT_T_s_u_c_c @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh ) @ Vi )
% 9.49/5.26        = one_one_nat ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2959_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I5_J,axiom,
% 9.49/5.26      ! [V: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh: vEBT_VEBT,Vi: nat] :
% 9.49/5.26        ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh ) @ Vi )
% 9.49/5.26        = one_one_nat ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2960_power2__less__imp__less,axiom,
% 9.49/5.26      ! [X: real,Y2: real] :
% 9.49/5.26        ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.26       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 9.49/5.26         => ( ord_less_real @ X @ Y2 ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2961_power2__less__imp__less,axiom,
% 9.49/5.26      ! [X: rat,Y2: rat] :
% 9.49/5.26        ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.26       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 9.49/5.26         => ( ord_less_rat @ X @ Y2 ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2962_power2__less__imp__less,axiom,
% 9.49/5.26      ! [X: nat,Y2: nat] :
% 9.49/5.26        ( ( ord_less_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.26       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y2 )
% 9.49/5.26         => ( ord_less_nat @ X @ Y2 ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2963_power2__less__imp__less,axiom,
% 9.49/5.26      ! [X: int,Y2: int] :
% 9.49/5.26        ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.26       => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 9.49/5.26         => ( ord_less_int @ X @ Y2 ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2964_sum__power2__le__zero__iff,axiom,
% 9.49/5.26      ! [X: rat,Y2: rat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat )
% 9.49/5.26        = ( ( X = zero_zero_rat )
% 9.49/5.26          & ( Y2 = zero_zero_rat ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2965_sum__power2__le__zero__iff,axiom,
% 9.49/5.26      ! [X: real,Y2: real] :
% 9.49/5.26        ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real )
% 9.49/5.26        = ( ( X = zero_zero_real )
% 9.49/5.26          & ( Y2 = zero_zero_real ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2966_sum__power2__le__zero__iff,axiom,
% 9.49/5.26      ! [X: int,Y2: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int )
% 9.49/5.26        = ( ( X = zero_zero_int )
% 9.49/5.26          & ( Y2 = zero_zero_int ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2967_sum__power2__ge__zero,axiom,
% 9.49/5.26      ! [X: rat,Y2: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2968_sum__power2__ge__zero,axiom,
% 9.49/5.26      ! [X: real,Y2: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2969_sum__power2__ge__zero,axiom,
% 9.49/5.26      ! [X: int,Y2: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2970_sum__power2__gt__zero__iff,axiom,
% 9.49/5.26      ! [X: real,Y2: real] :
% 9.49/5.26        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.49/5.26        = ( ( X != zero_zero_real )
% 9.49/5.26          | ( Y2 != zero_zero_real ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2971_sum__power2__gt__zero__iff,axiom,
% 9.49/5.26      ! [X: rat,Y2: rat] :
% 9.49/5.26        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.49/5.26        = ( ( X != zero_zero_rat )
% 9.49/5.26          | ( Y2 != zero_zero_rat ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2972_sum__power2__gt__zero__iff,axiom,
% 9.49/5.26      ! [X: int,Y2: int] :
% 9.49/5.26        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.49/5.26        = ( ( X != zero_zero_int )
% 9.49/5.26          | ( Y2 != zero_zero_int ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2973_not__sum__power2__lt__zero,axiom,
% 9.49/5.26      ! [X: real,Y2: real] :
% 9.49/5.26        ~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2974_not__sum__power2__lt__zero,axiom,
% 9.49/5.26      ! [X: rat,Y2: rat] :
% 9.49/5.26        ~ ( ord_less_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2975_not__sum__power2__lt__zero,axiom,
% 9.49/5.26      ! [X: int,Y2: int] :
% 9.49/5.26        ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2976_zero__le__even__power_H,axiom,
% 9.49/5.26      ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2977_zero__le__even__power_H,axiom,
% 9.49/5.26      ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2978_zero__le__even__power_H,axiom,
% 9.49/5.26      ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2979_Suc__n__div__2__gt__zero,axiom,
% 9.49/5.26      ! [N: nat] :
% 9.49/5.26        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.26       => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2980_div__2__gt__zero,axiom,
% 9.49/5.26      ! [N: nat] :
% 9.49/5.26        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 9.49/5.26       => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2981_nat__bit__induct,axiom,
% 9.49/5.26      ! [P: nat > $o,N: nat] :
% 9.49/5.26        ( ( P @ zero_zero_nat )
% 9.49/5.26       => ( ! [N3: nat] :
% 9.49/5.26              ( ( P @ N3 )
% 9.49/5.26             => ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 9.49/5.26               => ( P @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 9.49/5.26         => ( ! [N3: nat] :
% 9.49/5.26                ( ( P @ N3 )
% 9.49/5.26               => ( P @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 9.49/5.26           => ( P @ N ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2982_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I6_J,axiom,
% 9.49/5.26      ! [Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 9.49/5.26        ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ TreeList @ Summary ) @ X )
% 9.49/5.26        = one_one_nat ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2983_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I3_J,axiom,
% 9.49/5.26      ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X: nat] :
% 9.49/5.26        ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X )
% 9.49/5.26        = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2984_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Oelims,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Y2: nat] :
% 9.49/5.26        ( ( ( vEBT_T_m_a_x_t @ X )
% 9.49/5.26          = Y2 )
% 9.49/5.26       => ( ! [A4: $o,B3: $o] :
% 9.49/5.26              ( ( X
% 9.49/5.26                = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26             => ( Y2
% 9.49/5.26               != ( plus_plus_nat @ one_one_nat @ ( if_nat @ B3 @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 9.49/5.26         => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 9.49/5.26                  ( X
% 9.49/5.26                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 9.49/5.26             => ( Y2 != one_one_nat ) )
% 9.49/5.26           => ~ ( ? [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 9.49/5.26                    ( X
% 9.49/5.26                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 9.49/5.26               => ( Y2 != one_one_nat ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2985_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Oelims,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 9.49/5.26        ( ( ( vEBT_T_i_n_s_e_r_t @ X @ Xa2 )
% 9.49/5.26          = Y2 )
% 9.49/5.26       => ( ( ? [A4: $o,B3: $o] :
% 9.49/5.26                ( X
% 9.49/5.26                = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26           => ( Y2
% 9.49/5.26             != ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa2 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 9.49/5.26         => ( ( ? [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 9.49/5.26                  ( X
% 9.49/5.26                  = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S ) )
% 9.49/5.26             => ( Y2 != one_one_nat ) )
% 9.49/5.26           => ( ( ? [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 9.49/5.26                    ( X
% 9.49/5.26                    = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) )
% 9.49/5.26               => ( Y2 != one_one_nat ) )
% 9.49/5.26             => ( ( ? [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.26                      ( X
% 9.49/5.26                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                 => ( Y2
% 9.49/5.26                   != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.26               => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.26                      ( ( X
% 9.49/5.26                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                     => ( Y2
% 9.49/5.26                       != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 9.49/5.26                          @ ( if_nat
% 9.49/5.26                            @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                              & ~ ( ( Xa2 = Mi2 )
% 9.49/5.26                                  | ( Xa2 = Ma2 ) ) )
% 9.49/5.26                            @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 9.49/5.26                            @ one_one_nat ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2986_odd__0__le__power__imp__0__le,axiom,
% 9.49/5.26      ! [A: rat,N: nat] :
% 9.49/5.26        ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 9.49/5.26       => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2987_odd__0__le__power__imp__0__le,axiom,
% 9.49/5.26      ! [A: real,N: nat] :
% 9.49/5.26        ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 9.49/5.26       => ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2988_odd__0__le__power__imp__0__le,axiom,
% 9.49/5.26      ! [A: int,N: nat] :
% 9.49/5.26        ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 9.49/5.26       => ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2989_odd__power__less__zero,axiom,
% 9.49/5.26      ! [A: real,N: nat] :
% 9.49/5.26        ( ( ord_less_real @ A @ zero_zero_real )
% 9.49/5.26       => ( ord_less_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_real ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2990_odd__power__less__zero,axiom,
% 9.49/5.26      ! [A: rat,N: nat] :
% 9.49/5.26        ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.49/5.26       => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_rat ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2991_odd__power__less__zero,axiom,
% 9.49/5.26      ! [A: int,N: nat] :
% 9.49/5.26        ( ( ord_less_int @ A @ zero_zero_int )
% 9.49/5.26       => ( ord_less_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_int ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2992_VEBT__internal_Oexp__split__high__low_I1_J,axiom,
% 9.49/5.26      ! [X: nat,N: nat,M: nat] :
% 9.49/5.26        ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 9.49/5.26       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.26         => ( ( ord_less_nat @ zero_zero_nat @ M )
% 9.49/5.26           => ( ord_less_nat @ ( vEBT_VEBT_high @ X @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2993_VEBT__internal_Oexp__split__high__low_I2_J,axiom,
% 9.49/5.26      ! [X: nat,N: nat,M: nat] :
% 9.49/5.26        ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 9.49/5.26       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.26         => ( ( ord_less_nat @ zero_zero_nat @ M )
% 9.49/5.26           => ( ord_less_nat @ ( vEBT_VEBT_low @ X @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2994_vebt__member_Oelims_I2_J,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat] :
% 9.49/5.26        ( ( vEBT_vebt_member @ X @ Xa2 )
% 9.49/5.26       => ( ! [A4: $o,B3: $o] :
% 9.49/5.26              ( ( X
% 9.49/5.26                = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26             => ~ ( ( ( Xa2 = zero_zero_nat )
% 9.49/5.26                   => A4 )
% 9.49/5.26                  & ( ( Xa2 != zero_zero_nat )
% 9.49/5.26                   => ( ( ( Xa2 = one_one_nat )
% 9.49/5.26                       => B3 )
% 9.49/5.26                      & ( Xa2 = one_one_nat ) ) ) ) )
% 9.49/5.26         => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT] :
% 9.49/5.26                ( ? [Summary2: vEBT_VEBT] :
% 9.49/5.26                    ( X
% 9.49/5.26                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26               => ~ ( ( Xa2 != Mi2 )
% 9.49/5.26                   => ( ( Xa2 != Ma2 )
% 9.49/5.26                     => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 9.49/5.26                        & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 9.49/5.26                         => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 9.49/5.26                            & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 9.49/5.26                             => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                                 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2995_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I4_J,axiom,
% 9.49/5.26      ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 9.49/5.26        ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X )
% 9.49/5.26        = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2996_VEBT__internal_Omembermima_Oelims_I2_J,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat] :
% 9.49/5.26        ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 9.49/5.26       => ( ! [Mi2: nat,Ma2: nat] :
% 9.49/5.26              ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 9.49/5.26                  ( X
% 9.49/5.26                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 9.49/5.26             => ~ ( ( Xa2 = Mi2 )
% 9.49/5.26                  | ( Xa2 = Ma2 ) ) )
% 9.49/5.26         => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 9.49/5.26                ( ? [Vc2: vEBT_VEBT] :
% 9.49/5.26                    ( X
% 9.49/5.26                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 9.49/5.26               => ~ ( ( Xa2 = Mi2 )
% 9.49/5.26                    | ( Xa2 = Ma2 )
% 9.49/5.26                    | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                       => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                      & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 9.49/5.26           => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT] :
% 9.49/5.26                  ( ? [Vd2: vEBT_VEBT] :
% 9.49/5.26                      ( X
% 9.49/5.26                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 9.49/5.26                 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                       => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                      & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2997_vebt__member_Oelims_I1_J,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 9.49/5.26        ( ( ( vEBT_vebt_member @ X @ Xa2 )
% 9.49/5.26          = Y2 )
% 9.49/5.26       => ( ! [A4: $o,B3: $o] :
% 9.49/5.26              ( ( X
% 9.49/5.26                = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26             => ( Y2
% 9.49/5.26                = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 9.49/5.26                       => A4 )
% 9.49/5.26                      & ( ( Xa2 != zero_zero_nat )
% 9.49/5.26                       => ( ( ( Xa2 = one_one_nat )
% 9.49/5.26                           => B3 )
% 9.49/5.26                          & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 9.49/5.26         => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 9.49/5.26                  ( X
% 9.49/5.26                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 9.49/5.26             => Y2 )
% 9.49/5.26           => ( ( ? [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 9.49/5.26                    ( X
% 9.49/5.26                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 9.49/5.26               => Y2 )
% 9.49/5.26             => ( ( ? [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 9.49/5.26                      ( X
% 9.49/5.26                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 9.49/5.26                 => Y2 )
% 9.49/5.26               => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT] :
% 9.49/5.26                      ( ? [Summary2: vEBT_VEBT] :
% 9.49/5.26                          ( X
% 9.49/5.26                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                     => ( Y2
% 9.49/5.26                        = ( ~ ( ( Xa2 != Mi2 )
% 9.49/5.26                             => ( ( Xa2 != Ma2 )
% 9.49/5.26                               => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 9.49/5.26                                  & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 9.49/5.26                                   => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 9.49/5.26                                      & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 9.49/5.26                                       => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                                           => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2998_vebt__member_Oelims_I3_J,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat] :
% 9.49/5.26        ( ~ ( vEBT_vebt_member @ X @ Xa2 )
% 9.49/5.26       => ( ! [A4: $o,B3: $o] :
% 9.49/5.26              ( ( X
% 9.49/5.26                = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26             => ( ( ( Xa2 = zero_zero_nat )
% 9.49/5.26                 => A4 )
% 9.49/5.26                & ( ( Xa2 != zero_zero_nat )
% 9.49/5.26                 => ( ( ( Xa2 = one_one_nat )
% 9.49/5.26                     => B3 )
% 9.49/5.26                    & ( Xa2 = one_one_nat ) ) ) ) )
% 9.49/5.26         => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 9.49/5.26                ( X
% 9.49/5.26               != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 9.49/5.26           => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 9.49/5.26                  ( X
% 9.49/5.26                 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 9.49/5.26             => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 9.49/5.26                    ( X
% 9.49/5.26                   != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 9.49/5.26               => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT] :
% 9.49/5.26                      ( ? [Summary2: vEBT_VEBT] :
% 9.49/5.26                          ( X
% 9.49/5.26                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                     => ( ( Xa2 != Mi2 )
% 9.49/5.26                       => ( ( Xa2 != Ma2 )
% 9.49/5.26                         => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 9.49/5.26                            & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 9.49/5.26                             => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 9.49/5.26                                & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 9.49/5.26                                 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                                     => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                    & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_2999_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I4_J,axiom,
% 9.49/5.26      ! [V: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 9.49/5.26        ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) @ X )
% 9.49/5.26        = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3000_insersimp,axiom,
% 9.49/5.26      ! [T: vEBT_VEBT,N: nat,Y2: nat] :
% 9.49/5.26        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.26       => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_12 )
% 9.49/5.26         => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ T @ Y2 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3001_insertsimp,axiom,
% 9.49/5.26      ! [T: vEBT_VEBT,N: nat,L2: nat] :
% 9.49/5.26        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.26       => ( ( vEBT_VEBT_minNull @ T )
% 9.49/5.26         => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ T @ L2 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3002_arith__geo__mean,axiom,
% 9.49/5.26      ! [U: real,X: real,Y2: real] :
% 9.49/5.26        ( ( ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.26          = ( times_times_real @ X @ Y2 ) )
% 9.49/5.26       => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.49/5.26         => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 9.49/5.26           => ( ord_less_eq_real @ U @ ( divide_divide_real @ ( plus_plus_real @ X @ Y2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3003_arith__geo__mean,axiom,
% 9.49/5.26      ! [U: rat,X: rat,Y2: rat] :
% 9.49/5.26        ( ( ( power_power_rat @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.26          = ( times_times_rat @ X @ Y2 ) )
% 9.49/5.26       => ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 9.49/5.26         => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 9.49/5.26           => ( ord_less_eq_rat @ U @ ( divide_divide_rat @ ( plus_plus_rat @ X @ Y2 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3004_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Oelims,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 9.49/5.26        ( ( ( vEBT_T_m_e_m_b_e_r @ X @ Xa2 )
% 9.49/5.26          = Y2 )
% 9.49/5.26       => ( ( ? [A4: $o,B3: $o] :
% 9.49/5.26                ( X
% 9.49/5.26                = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26           => ( Y2
% 9.49/5.26             != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa2 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 9.49/5.26         => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 9.49/5.26                  ( X
% 9.49/5.26                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 9.49/5.26             => ( Y2
% 9.49/5.26               != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.26           => ( ( ? [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 9.49/5.26                    ( X
% 9.49/5.26                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 9.49/5.26               => ( Y2
% 9.49/5.26                 != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.26             => ( ( ? [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 9.49/5.26                      ( X
% 9.49/5.26                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 9.49/5.26                 => ( Y2
% 9.49/5.26                   != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.26               => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT] :
% 9.49/5.26                      ( ? [Summary2: vEBT_VEBT] :
% 9.49/5.26                          ( X
% 9.49/5.26                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                     => ( Y2
% 9.49/5.26                       != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa2 = Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa2 = Ma2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ one_one_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_e_m_b_e_r @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3005_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Oelims,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 9.49/5.26        ( ( ( vEBT_T_i_n_s_e_r_t2 @ X @ Xa2 )
% 9.49/5.26          = Y2 )
% 9.49/5.26       => ( ( ? [A4: $o,B3: $o] :
% 9.49/5.26                ( X
% 9.49/5.26                = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26           => ( Y2 != one_one_nat ) )
% 9.49/5.26         => ( ( ? [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 9.49/5.26                  ( X
% 9.49/5.26                  = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S ) )
% 9.49/5.26             => ( Y2 != one_one_nat ) )
% 9.49/5.26           => ( ( ? [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 9.49/5.26                    ( X
% 9.49/5.26                    = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) )
% 9.49/5.26               => ( Y2 != one_one_nat ) )
% 9.49/5.26             => ( ( ? [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.26                      ( X
% 9.49/5.26                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                 => ( Y2 != one_one_nat ) )
% 9.49/5.26               => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.26                      ( ( X
% 9.49/5.26                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                     => ( Y2
% 9.49/5.26                       != ( if_nat
% 9.49/5.26                          @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                            & ~ ( ( Xa2 = Mi2 )
% 9.49/5.26                                | ( Xa2 = Ma2 ) ) )
% 9.49/5.26                          @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t2 @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 9.49/5.26                          @ one_one_nat ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3006_invar__vebt_Osimps,axiom,
% 9.49/5.26      ( vEBT_invar_vebt
% 9.49/5.26      = ( ^ [A1: vEBT_VEBT,A22: nat] :
% 9.49/5.26            ( ( ? [A3: $o,B4: $o] :
% 9.49/5.26                  ( A1
% 9.49/5.26                  = ( vEBT_Leaf @ A3 @ B4 ) )
% 9.49/5.26              & ( A22
% 9.49/5.26                = ( suc @ zero_zero_nat ) ) )
% 9.49/5.26            | ? [TreeList3: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT] :
% 9.49/5.26                ( ( A1
% 9.49/5.26                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ A22 @ TreeList3 @ Summary3 ) )
% 9.49/5.26                & ! [X2: vEBT_VEBT] :
% 9.49/5.26                    ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 9.49/5.26                   => ( vEBT_invar_vebt @ X2 @ N2 ) )
% 9.49/5.26                & ( vEBT_invar_vebt @ Summary3 @ N2 )
% 9.49/5.26                & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 9.49/5.26                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 9.49/5.26                & ( A22
% 9.49/5.26                  = ( plus_plus_nat @ N2 @ N2 ) )
% 9.49/5.26                & ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X4 )
% 9.49/5.26                & ! [X2: vEBT_VEBT] :
% 9.49/5.26                    ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 9.49/5.26                   => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 9.49/5.26            | ? [TreeList3: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT] :
% 9.49/5.26                ( ( A1
% 9.49/5.26                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ A22 @ TreeList3 @ Summary3 ) )
% 9.49/5.26                & ! [X2: vEBT_VEBT] :
% 9.49/5.26                    ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 9.49/5.26                   => ( vEBT_invar_vebt @ X2 @ N2 ) )
% 9.49/5.26                & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N2 ) )
% 9.49/5.26                & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 9.49/5.26                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 9.49/5.26                & ( A22
% 9.49/5.26                  = ( plus_plus_nat @ N2 @ ( suc @ N2 ) ) )
% 9.49/5.26                & ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X4 )
% 9.49/5.26                & ! [X2: vEBT_VEBT] :
% 9.49/5.26                    ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 9.49/5.26                   => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 9.49/5.26            | ? [TreeList3: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 9.49/5.26                ( ( A1
% 9.49/5.26                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A22 @ TreeList3 @ Summary3 ) )
% 9.49/5.26                & ! [X2: vEBT_VEBT] :
% 9.49/5.26                    ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 9.49/5.26                   => ( vEBT_invar_vebt @ X2 @ N2 ) )
% 9.49/5.26                & ( vEBT_invar_vebt @ Summary3 @ N2 )
% 9.49/5.26                & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 9.49/5.26                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 9.49/5.26                & ( A22
% 9.49/5.26                  = ( plus_plus_nat @ N2 @ N2 ) )
% 9.49/5.26                & ! [I3: nat] :
% 9.49/5.26                    ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 9.49/5.26                   => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X4 ) )
% 9.49/5.26                      = ( vEBT_V8194947554948674370ptions @ Summary3 @ I3 ) ) )
% 9.49/5.26                & ( ( Mi3 = Ma3 )
% 9.49/5.26                 => ! [X2: vEBT_VEBT] :
% 9.49/5.26                      ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 9.49/5.26                     => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 9.49/5.26                & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 9.49/5.26                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A22 ) )
% 9.49/5.26                & ( ( Mi3 != Ma3 )
% 9.49/5.26                 => ! [I3: nat] :
% 9.49/5.26                      ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 9.49/5.26                     => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N2 )
% 9.49/5.26                            = I3 )
% 9.49/5.26                         => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ ( vEBT_VEBT_low @ Ma3 @ N2 ) ) )
% 9.49/5.26                        & ! [X2: nat] :
% 9.49/5.26                            ( ( ( ( vEBT_VEBT_high @ X2 @ N2 )
% 9.49/5.26                                = I3 )
% 9.49/5.26                              & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ ( vEBT_VEBT_low @ X2 @ N2 ) ) )
% 9.49/5.26                           => ( ( ord_less_nat @ Mi3 @ X2 )
% 9.49/5.26                              & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) )
% 9.49/5.26            | ? [TreeList3: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 9.49/5.26                ( ( A1
% 9.49/5.26                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A22 @ TreeList3 @ Summary3 ) )
% 9.49/5.26                & ! [X2: vEBT_VEBT] :
% 9.49/5.26                    ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 9.49/5.26                   => ( vEBT_invar_vebt @ X2 @ N2 ) )
% 9.49/5.26                & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N2 ) )
% 9.49/5.26                & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 9.49/5.26                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 9.49/5.26                & ( A22
% 9.49/5.26                  = ( plus_plus_nat @ N2 @ ( suc @ N2 ) ) )
% 9.49/5.26                & ! [I3: nat] :
% 9.49/5.26                    ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 9.49/5.26                   => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X4 ) )
% 9.49/5.26                      = ( vEBT_V8194947554948674370ptions @ Summary3 @ I3 ) ) )
% 9.49/5.26                & ( ( Mi3 = Ma3 )
% 9.49/5.26                 => ! [X2: vEBT_VEBT] :
% 9.49/5.26                      ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 9.49/5.26                     => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 9.49/5.26                & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 9.49/5.26                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A22 ) )
% 9.49/5.26                & ( ( Mi3 != Ma3 )
% 9.49/5.26                 => ! [I3: nat] :
% 9.49/5.26                      ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 9.49/5.26                     => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N2 )
% 9.49/5.26                            = I3 )
% 9.49/5.26                         => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ ( vEBT_VEBT_low @ Ma3 @ N2 ) ) )
% 9.49/5.26                        & ! [X2: nat] :
% 9.49/5.26                            ( ( ( ( vEBT_VEBT_high @ X2 @ N2 )
% 9.49/5.26                                = I3 )
% 9.49/5.26                              & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ ( vEBT_VEBT_low @ X2 @ N2 ) ) )
% 9.49/5.26                           => ( ( ord_less_nat @ Mi3 @ X2 )
% 9.49/5.26                              & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3007_invar__vebt_Ocases,axiom,
% 9.49/5.26      ! [A12: vEBT_VEBT,A23: nat] :
% 9.49/5.26        ( ( vEBT_invar_vebt @ A12 @ A23 )
% 9.49/5.26       => ( ( ? [A4: $o,B3: $o] :
% 9.49/5.26                ( A12
% 9.49/5.26                = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26           => ( A23
% 9.49/5.26             != ( suc @ zero_zero_nat ) ) )
% 9.49/5.26         => ( ! [TreeList2: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat] :
% 9.49/5.26                ( ( A12
% 9.49/5.26                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 9.49/5.26               => ( ( A23 = Deg2 )
% 9.49/5.26                 => ( ! [X5: vEBT_VEBT] :
% 9.49/5.26                        ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 9.49/5.26                       => ( vEBT_invar_vebt @ X5 @ N3 ) )
% 9.49/5.26                   => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 9.49/5.26                     => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 9.49/5.26                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 9.49/5.26                       => ( ( M4 = N3 )
% 9.49/5.26                         => ( ( Deg2
% 9.49/5.26                              = ( plus_plus_nat @ N3 @ M4 ) )
% 9.49/5.26                           => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_1 )
% 9.49/5.26                             => ~ ! [X5: vEBT_VEBT] :
% 9.49/5.26                                    ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 9.49/5.26                                   => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) ) ) ) ) ) ) ) ) )
% 9.49/5.26           => ( ! [TreeList2: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat] :
% 9.49/5.26                  ( ( A12
% 9.49/5.26                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 9.49/5.26                 => ( ( A23 = Deg2 )
% 9.49/5.26                   => ( ! [X5: vEBT_VEBT] :
% 9.49/5.26                          ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 9.49/5.26                         => ( vEBT_invar_vebt @ X5 @ N3 ) )
% 9.49/5.26                     => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 9.49/5.26                       => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 9.49/5.26                            = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 9.49/5.26                         => ( ( M4
% 9.49/5.26                              = ( suc @ N3 ) )
% 9.49/5.26                           => ( ( Deg2
% 9.49/5.26                                = ( plus_plus_nat @ N3 @ M4 ) )
% 9.49/5.26                             => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_1 )
% 9.49/5.26                               => ~ ! [X5: vEBT_VEBT] :
% 9.49/5.26                                      ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 9.49/5.26                                     => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) ) ) ) ) ) ) ) ) )
% 9.49/5.26             => ( ! [TreeList2: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 9.49/5.26                    ( ( A12
% 9.49/5.26                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList2 @ Summary2 ) )
% 9.49/5.26                   => ( ( A23 = Deg2 )
% 9.49/5.26                     => ( ! [X5: vEBT_VEBT] :
% 9.49/5.26                            ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 9.49/5.26                           => ( vEBT_invar_vebt @ X5 @ N3 ) )
% 9.49/5.26                       => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 9.49/5.26                         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 9.49/5.26                              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 9.49/5.26                           => ( ( M4 = N3 )
% 9.49/5.26                             => ( ( Deg2
% 9.49/5.26                                  = ( plus_plus_nat @ N3 @ M4 ) )
% 9.49/5.26                               => ( ! [I: nat] :
% 9.49/5.26                                      ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 9.49/5.26                                     => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I ) @ X4 ) )
% 9.49/5.26                                        = ( vEBT_V8194947554948674370ptions @ Summary2 @ I ) ) )
% 9.49/5.26                                 => ( ( ( Mi2 = Ma2 )
% 9.49/5.26                                     => ! [X5: vEBT_VEBT] :
% 9.49/5.26                                          ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 9.49/5.26                                         => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) ) )
% 9.49/5.26                                   => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 9.49/5.26                                     => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 9.49/5.26                                       => ~ ( ( Mi2 != Ma2 )
% 9.49/5.26                                           => ! [I: nat] :
% 9.49/5.26                                                ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 9.49/5.26                                               => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 9.49/5.26                                                      = I )
% 9.49/5.26                                                   => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 9.49/5.26                                                  & ! [X5: nat] :
% 9.49/5.26                                                      ( ( ( ( vEBT_VEBT_high @ X5 @ N3 )
% 9.49/5.26                                                          = I )
% 9.49/5.26                                                        & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I ) @ ( vEBT_VEBT_low @ X5 @ N3 ) ) )
% 9.49/5.26                                                     => ( ( ord_less_nat @ Mi2 @ X5 )
% 9.49/5.26                                                        & ( ord_less_eq_nat @ X5 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 9.49/5.26               => ~ ! [TreeList2: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 9.49/5.26                      ( ( A12
% 9.49/5.26                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList2 @ Summary2 ) )
% 9.49/5.26                     => ( ( A23 = Deg2 )
% 9.49/5.26                       => ( ! [X5: vEBT_VEBT] :
% 9.49/5.26                              ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 9.49/5.26                             => ( vEBT_invar_vebt @ X5 @ N3 ) )
% 9.49/5.26                         => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 9.49/5.26                           => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 9.49/5.26                                = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 9.49/5.26                             => ( ( M4
% 9.49/5.26                                  = ( suc @ N3 ) )
% 9.49/5.26                               => ( ( Deg2
% 9.49/5.26                                    = ( plus_plus_nat @ N3 @ M4 ) )
% 9.49/5.26                                 => ( ! [I: nat] :
% 9.49/5.26                                        ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 9.49/5.26                                       => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I ) @ X4 ) )
% 9.49/5.26                                          = ( vEBT_V8194947554948674370ptions @ Summary2 @ I ) ) )
% 9.49/5.26                                   => ( ( ( Mi2 = Ma2 )
% 9.49/5.26                                       => ! [X5: vEBT_VEBT] :
% 9.49/5.26                                            ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 9.49/5.26                                           => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) ) )
% 9.49/5.26                                     => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 9.49/5.26                                       => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 9.49/5.26                                         => ~ ( ( Mi2 != Ma2 )
% 9.49/5.26                                             => ! [I: nat] :
% 9.49/5.26                                                  ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 9.49/5.26                                                 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 9.49/5.26                                                        = I )
% 9.49/5.26                                                     => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 9.49/5.26                                                    & ! [X5: nat] :
% 9.49/5.26                                                        ( ( ( ( vEBT_VEBT_high @ X5 @ N3 )
% 9.49/5.26                                                            = I )
% 9.49/5.26                                                          & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I ) @ ( vEBT_VEBT_low @ X5 @ N3 ) ) )
% 9.49/5.26                                                       => ( ( ord_less_nat @ Mi2 @ X5 )
% 9.49/5.26                                                          & ( ord_less_eq_nat @ X5 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3008_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Oelims,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 9.49/5.26        ( ( ( vEBT_T_p_r_e_d @ X @ Xa2 )
% 9.49/5.26          = Y2 )
% 9.49/5.26       => ( ( ? [Uu2: $o,Uv2: $o] :
% 9.49/5.26                ( X
% 9.49/5.26                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 9.49/5.26           => ( ( Xa2 = zero_zero_nat )
% 9.49/5.26             => ( Y2 != one_one_nat ) ) )
% 9.49/5.26         => ( ( ? [A4: $o,Uw2: $o] :
% 9.49/5.26                  ( X
% 9.49/5.26                  = ( vEBT_Leaf @ A4 @ Uw2 ) )
% 9.49/5.26             => ( ( Xa2
% 9.49/5.26                  = ( suc @ zero_zero_nat ) )
% 9.49/5.26               => ( Y2
% 9.49/5.26                 != ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 9.49/5.26           => ( ! [A4: $o,B3: $o] :
% 9.49/5.26                  ( ( X
% 9.49/5.26                    = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26                 => ( ? [Va2: nat] :
% 9.49/5.26                        ( Xa2
% 9.49/5.26                        = ( suc @ ( suc @ Va2 ) ) )
% 9.49/5.26                   => ( Y2
% 9.49/5.26                     != ( plus_plus_nat @ one_one_nat @ ( if_nat @ B3 @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ) )
% 9.49/5.26             => ( ( ? [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 9.49/5.26                      ( X
% 9.49/5.26                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 9.49/5.26                 => ( Y2 != one_one_nat ) )
% 9.49/5.26               => ( ( ? [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 9.49/5.26                        ( X
% 9.49/5.26                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 9.49/5.26                   => ( Y2 != one_one_nat ) )
% 9.49/5.26                 => ( ( ? [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 9.49/5.26                          ( X
% 9.49/5.26                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 9.49/5.26                     => ( Y2 != one_one_nat ) )
% 9.49/5.26                   => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.26                          ( ( X
% 9.49/5.26                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                         => ( Y2
% 9.49/5.26                           != ( plus_plus_nat @ one_one_nat
% 9.49/5.26                              @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ one_one_nat
% 9.49/5.26                                @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 9.49/5.26                                  @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                                    @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 9.49/5.26                                      @ ( if_nat
% 9.49/5.26                                        @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                           != none_nat )
% 9.49/5.26                                          & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 9.49/5.26                                        @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_p_r_e_d @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                        @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 9.49/5.26                                          @ ( if_nat
% 9.49/5.26                                            @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.49/5.26                                              = none_nat )
% 9.49/5.26                                            @ ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 9.49/5.26                                            @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 9.49/5.26                                    @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3009_vebt__insert_Oelims,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat,Y2: vEBT_VEBT] :
% 9.49/5.26        ( ( ( vEBT_vebt_insert @ X @ Xa2 )
% 9.49/5.26          = Y2 )
% 9.49/5.26       => ( ! [A4: $o,B3: $o] :
% 9.49/5.26              ( ( X
% 9.49/5.26                = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26             => ~ ( ( ( Xa2 = zero_zero_nat )
% 9.49/5.26                   => ( Y2
% 9.49/5.26                      = ( vEBT_Leaf @ $true @ B3 ) ) )
% 9.49/5.26                  & ( ( Xa2 != zero_zero_nat )
% 9.49/5.26                   => ( ( ( Xa2 = one_one_nat )
% 9.49/5.26                       => ( Y2
% 9.49/5.26                          = ( vEBT_Leaf @ A4 @ $true ) ) )
% 9.49/5.26                      & ( ( Xa2 != one_one_nat )
% 9.49/5.26                       => ( Y2
% 9.49/5.26                          = ( vEBT_Leaf @ A4 @ B3 ) ) ) ) ) ) )
% 9.49/5.26         => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 9.49/5.26                ( ( X
% 9.49/5.26                  = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S ) )
% 9.49/5.26               => ( Y2
% 9.49/5.26                 != ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S ) ) )
% 9.49/5.26           => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 9.49/5.26                  ( ( X
% 9.49/5.26                    = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) )
% 9.49/5.26                 => ( Y2
% 9.49/5.26                   != ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) ) )
% 9.49/5.26             => ( ! [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.26                    ( ( X
% 9.49/5.26                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                   => ( Y2
% 9.49/5.26                     != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) ) )
% 9.49/5.26               => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.26                      ( ( X
% 9.49/5.26                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                     => ( Y2
% 9.49/5.26                       != ( if_VEBT_VEBT
% 9.49/5.26                          @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                            & ~ ( ( Xa2 = Mi2 )
% 9.49/5.26                                | ( Xa2 = Ma2 ) ) )
% 9.49/5.26                          @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va2 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 9.49/5.26                          @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3010_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Oelims,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 9.49/5.26        ( ( ( vEBT_T_p_r_e_d2 @ X @ Xa2 )
% 9.49/5.26          = Y2 )
% 9.49/5.26       => ( ( ? [Uu2: $o,Uv2: $o] :
% 9.49/5.26                ( X
% 9.49/5.26                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 9.49/5.26           => ( ( Xa2 = zero_zero_nat )
% 9.49/5.26             => ( Y2 != one_one_nat ) ) )
% 9.49/5.26         => ( ( ? [A4: $o,Uw2: $o] :
% 9.49/5.26                  ( X
% 9.49/5.26                  = ( vEBT_Leaf @ A4 @ Uw2 ) )
% 9.49/5.26             => ( ( Xa2
% 9.49/5.26                  = ( suc @ zero_zero_nat ) )
% 9.49/5.26               => ( Y2 != one_one_nat ) ) )
% 9.49/5.26           => ( ( ? [A4: $o,B3: $o] :
% 9.49/5.26                    ( X
% 9.49/5.26                    = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26               => ( ? [Va2: nat] :
% 9.49/5.26                      ( Xa2
% 9.49/5.26                      = ( suc @ ( suc @ Va2 ) ) )
% 9.49/5.26                 => ( Y2 != one_one_nat ) ) )
% 9.49/5.26             => ( ( ? [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 9.49/5.26                      ( X
% 9.49/5.26                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 9.49/5.26                 => ( Y2 != one_one_nat ) )
% 9.49/5.26               => ( ( ? [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 9.49/5.26                        ( X
% 9.49/5.26                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 9.49/5.26                   => ( Y2 != one_one_nat ) )
% 9.49/5.26                 => ( ( ? [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 9.49/5.26                          ( X
% 9.49/5.26                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 9.49/5.26                     => ( Y2 != one_one_nat ) )
% 9.49/5.26                   => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.26                          ( ( X
% 9.49/5.26                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                         => ~ ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 9.49/5.26                               => ( Y2 = one_one_nat ) )
% 9.49/5.26                              & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 9.49/5.26                               => ( Y2
% 9.49/5.26                                  = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                                    @ ( if_nat
% 9.49/5.26                                      @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                         != none_nat )
% 9.49/5.26                                        & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 9.49/5.26                                      @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                      @ ( plus_plus_nat @ ( vEBT_T_p_r_e_d2 @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 9.49/5.26                                    @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3011_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Oelims,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 9.49/5.26        ( ( ( vEBT_T_s_u_c_c2 @ X @ Xa2 )
% 9.49/5.26          = Y2 )
% 9.49/5.26       => ( ( ? [Uu2: $o,B3: $o] :
% 9.49/5.26                ( X
% 9.49/5.26                = ( vEBT_Leaf @ Uu2 @ B3 ) )
% 9.49/5.26           => ( ( Xa2 = zero_zero_nat )
% 9.49/5.26             => ( Y2 != one_one_nat ) ) )
% 9.49/5.26         => ( ( ? [Uv2: $o,Uw2: $o] :
% 9.49/5.26                  ( X
% 9.49/5.26                  = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 9.49/5.26             => ( ? [N3: nat] :
% 9.49/5.26                    ( Xa2
% 9.49/5.26                    = ( suc @ N3 ) )
% 9.49/5.26               => ( Y2 != one_one_nat ) ) )
% 9.49/5.26           => ( ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 9.49/5.26                    ( X
% 9.49/5.26                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 9.49/5.26               => ( Y2 != one_one_nat ) )
% 9.49/5.26             => ( ( ? [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 9.49/5.26                      ( X
% 9.49/5.26                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 9.49/5.26                 => ( Y2 != one_one_nat ) )
% 9.49/5.26               => ( ( ? [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 9.49/5.26                        ( X
% 9.49/5.26                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh2 ) )
% 9.49/5.26                   => ( Y2 != one_one_nat ) )
% 9.49/5.26                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.26                        ( ( X
% 9.49/5.26                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                       => ~ ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 9.49/5.26                             => ( Y2 = one_one_nat ) )
% 9.49/5.26                            & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 9.49/5.26                             => ( Y2
% 9.49/5.26                                = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                                  @ ( if_nat
% 9.49/5.26                                    @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                       != none_nat )
% 9.49/5.26                                      & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 9.49/5.26                                    @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                    @ ( plus_plus_nat @ ( vEBT_T_s_u_c_c2 @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 9.49/5.26                                  @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3012_vebt__delete_Oelims,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat,Y2: vEBT_VEBT] :
% 9.49/5.26        ( ( ( vEBT_vebt_delete @ X @ Xa2 )
% 9.49/5.26          = Y2 )
% 9.49/5.26       => ( ! [A4: $o,B3: $o] :
% 9.49/5.26              ( ( X
% 9.49/5.26                = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26             => ( ( Xa2 = zero_zero_nat )
% 9.49/5.26               => ( Y2
% 9.49/5.26                 != ( vEBT_Leaf @ $false @ B3 ) ) ) )
% 9.49/5.26         => ( ! [A4: $o] :
% 9.49/5.26                ( ? [B3: $o] :
% 9.49/5.26                    ( X
% 9.49/5.26                    = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26               => ( ( Xa2
% 9.49/5.26                    = ( suc @ zero_zero_nat ) )
% 9.49/5.26                 => ( Y2
% 9.49/5.26                   != ( vEBT_Leaf @ A4 @ $false ) ) ) )
% 9.49/5.26           => ( ! [A4: $o,B3: $o] :
% 9.49/5.26                  ( ( X
% 9.49/5.26                    = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26                 => ( ? [N3: nat] :
% 9.49/5.26                        ( Xa2
% 9.49/5.26                        = ( suc @ ( suc @ N3 ) ) )
% 9.49/5.26                   => ( Y2
% 9.49/5.26                     != ( vEBT_Leaf @ A4 @ B3 ) ) ) )
% 9.49/5.26             => ( ! [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.26                    ( ( X
% 9.49/5.26                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 9.49/5.26                   => ( Y2
% 9.49/5.26                     != ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) ) )
% 9.49/5.26               => ( ! [Mi2: nat,Ma2: nat,TrLst2: list_VEBT_VEBT,Smry2: vEBT_VEBT] :
% 9.49/5.26                      ( ( X
% 9.49/5.26                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 9.49/5.26                     => ( Y2
% 9.49/5.26                       != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) ) )
% 9.49/5.26                 => ( ! [Mi2: nat,Ma2: nat,Tr2: list_VEBT_VEBT,Sm2: vEBT_VEBT] :
% 9.49/5.26                        ( ( X
% 9.49/5.26                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 9.49/5.26                       => ( Y2
% 9.49/5.26                         != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) ) )
% 9.49/5.26                   => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.26                          ( ( X
% 9.49/5.26                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                         => ~ ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 9.49/5.26                                  | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 9.49/5.26                               => ( Y2
% 9.49/5.26                                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) ) )
% 9.49/5.26                              & ( ~ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 9.49/5.26                                    | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 9.49/5.26                               => ( ( ( ( Xa2 = Mi2 )
% 9.49/5.26                                      & ( Xa2 = Ma2 ) )
% 9.49/5.26                                   => ( Y2
% 9.49/5.26                                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) ) )
% 9.49/5.26                                  & ( ~ ( ( Xa2 = Mi2 )
% 9.49/5.26                                        & ( Xa2 = Ma2 ) )
% 9.49/5.26                                   => ( Y2
% 9.49/5.26                                      = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                                        @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                          @ ( vEBT_Node
% 9.49/5.26                                            @ ( some_P7363390416028606310at_nat
% 9.49/5.26                                              @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 9.49/5.26                                                @ ( if_nat
% 9.49/5.26                                                  @ ( ( ( Xa2 = Mi2 )
% 9.49/5.26                                                     => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 9.49/5.26                                                        = Ma2 ) )
% 9.49/5.26                                                    & ( ( Xa2 != Mi2 )
% 9.49/5.26                                                     => ( Xa2 = Ma2 ) ) )
% 9.49/5.26                                                  @ ( if_nat
% 9.49/5.26                                                    @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                                      = none_nat )
% 9.49/5.26                                                    @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 9.49/5.26                                                    @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 9.49/5.26                                                  @ Ma2 ) ) )
% 9.49/5.26                                            @ ( suc @ ( suc @ Va2 ) )
% 9.49/5.26                                            @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                            @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                          @ ( vEBT_Node
% 9.49/5.26                                            @ ( some_P7363390416028606310at_nat
% 9.49/5.26                                              @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 9.49/5.26                                                @ ( if_nat
% 9.49/5.26                                                  @ ( ( ( Xa2 = Mi2 )
% 9.49/5.26                                                     => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 9.49/5.26                                                        = Ma2 ) )
% 9.49/5.26                                                    & ( ( Xa2 != Mi2 )
% 9.49/5.26                                                     => ( Xa2 = Ma2 ) ) )
% 9.49/5.26                                                  @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 9.49/5.26                                                  @ Ma2 ) ) )
% 9.49/5.26                                            @ ( suc @ ( suc @ Va2 ) )
% 9.49/5.26                                            @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                            @ Summary2 ) )
% 9.49/5.26                                        @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3013_vebt__succ_Oelims,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat,Y2: option_nat] :
% 9.49/5.26        ( ( ( vEBT_vebt_succ @ X @ Xa2 )
% 9.49/5.26          = Y2 )
% 9.49/5.26       => ( ! [Uu2: $o,B3: $o] :
% 9.49/5.26              ( ( X
% 9.49/5.26                = ( vEBT_Leaf @ Uu2 @ B3 ) )
% 9.49/5.26             => ( ( Xa2 = zero_zero_nat )
% 9.49/5.26               => ~ ( ( B3
% 9.49/5.26                     => ( Y2
% 9.49/5.26                        = ( some_nat @ one_one_nat ) ) )
% 9.49/5.26                    & ( ~ B3
% 9.49/5.26                     => ( Y2 = none_nat ) ) ) ) )
% 9.49/5.26         => ( ( ? [Uv2: $o,Uw2: $o] :
% 9.49/5.26                  ( X
% 9.49/5.26                  = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 9.49/5.26             => ( ? [N3: nat] :
% 9.49/5.26                    ( Xa2
% 9.49/5.26                    = ( suc @ N3 ) )
% 9.49/5.26               => ( Y2 != none_nat ) ) )
% 9.49/5.26           => ( ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 9.49/5.26                    ( X
% 9.49/5.26                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 9.49/5.26               => ( Y2 != none_nat ) )
% 9.49/5.26             => ( ( ? [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 9.49/5.26                      ( X
% 9.49/5.26                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 9.49/5.26                 => ( Y2 != none_nat ) )
% 9.49/5.26               => ( ( ? [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 9.49/5.26                        ( X
% 9.49/5.26                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh2 ) )
% 9.49/5.26                   => ( Y2 != none_nat ) )
% 9.49/5.26                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.26                        ( ( X
% 9.49/5.26                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                       => ~ ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 9.49/5.26                             => ( Y2
% 9.49/5.26                                = ( some_nat @ Mi2 ) ) )
% 9.49/5.26                            & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 9.49/5.26                             => ( Y2
% 9.49/5.26                                = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                                  @ ( if_option_nat
% 9.49/5.26                                    @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                       != none_nat )
% 9.49/5.26                                      & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 9.49/5.26                                    @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                    @ ( if_option_nat
% 9.49/5.26                                      @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.49/5.26                                        = none_nat )
% 9.49/5.26                                      @ none_nat
% 9.49/5.26                                      @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 9.49/5.26                                  @ none_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3014_vebt__pred_Oelims,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat,Y2: option_nat] :
% 9.49/5.26        ( ( ( vEBT_vebt_pred @ X @ Xa2 )
% 9.49/5.26          = Y2 )
% 9.49/5.26       => ( ( ? [Uu2: $o,Uv2: $o] :
% 9.49/5.26                ( X
% 9.49/5.26                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 9.49/5.26           => ( ( Xa2 = zero_zero_nat )
% 9.49/5.26             => ( Y2 != none_nat ) ) )
% 9.49/5.26         => ( ! [A4: $o] :
% 9.49/5.26                ( ? [Uw2: $o] :
% 9.49/5.26                    ( X
% 9.49/5.26                    = ( vEBT_Leaf @ A4 @ Uw2 ) )
% 9.49/5.26               => ( ( Xa2
% 9.49/5.26                    = ( suc @ zero_zero_nat ) )
% 9.49/5.26                 => ~ ( ( A4
% 9.49/5.26                       => ( Y2
% 9.49/5.26                          = ( some_nat @ zero_zero_nat ) ) )
% 9.49/5.26                      & ( ~ A4
% 9.49/5.26                       => ( Y2 = none_nat ) ) ) ) )
% 9.49/5.26           => ( ! [A4: $o,B3: $o] :
% 9.49/5.26                  ( ( X
% 9.49/5.26                    = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26                 => ( ? [Va2: nat] :
% 9.49/5.26                        ( Xa2
% 9.49/5.26                        = ( suc @ ( suc @ Va2 ) ) )
% 9.49/5.26                   => ~ ( ( B3
% 9.49/5.26                         => ( Y2
% 9.49/5.26                            = ( some_nat @ one_one_nat ) ) )
% 9.49/5.26                        & ( ~ B3
% 9.49/5.26                         => ( ( A4
% 9.49/5.26                             => ( Y2
% 9.49/5.26                                = ( some_nat @ zero_zero_nat ) ) )
% 9.49/5.26                            & ( ~ A4
% 9.49/5.26                             => ( Y2 = none_nat ) ) ) ) ) ) )
% 9.49/5.26             => ( ( ? [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 9.49/5.26                      ( X
% 9.49/5.26                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 9.49/5.26                 => ( Y2 != none_nat ) )
% 9.49/5.26               => ( ( ? [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 9.49/5.26                        ( X
% 9.49/5.26                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 9.49/5.26                   => ( Y2 != none_nat ) )
% 9.49/5.26                 => ( ( ? [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 9.49/5.26                          ( X
% 9.49/5.26                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 9.49/5.26                     => ( Y2 != none_nat ) )
% 9.49/5.26                   => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.26                          ( ( X
% 9.49/5.26                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                         => ~ ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 9.49/5.26                               => ( Y2
% 9.49/5.26                                  = ( some_nat @ Ma2 ) ) )
% 9.49/5.26                              & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 9.49/5.26                               => ( Y2
% 9.49/5.26                                  = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                                    @ ( if_option_nat
% 9.49/5.26                                      @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                         != none_nat )
% 9.49/5.26                                        & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 9.49/5.26                                      @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                      @ ( if_option_nat
% 9.49/5.26                                        @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.49/5.26                                          = none_nat )
% 9.49/5.26                                        @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 9.49/5.26                                        @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 9.49/5.26                                    @ none_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3015_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Oelims,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 9.49/5.26        ( ( ( vEBT_T_s_u_c_c @ X @ Xa2 )
% 9.49/5.26          = Y2 )
% 9.49/5.26       => ( ( ? [Uu2: $o,B3: $o] :
% 9.49/5.26                ( X
% 9.49/5.26                = ( vEBT_Leaf @ Uu2 @ B3 ) )
% 9.49/5.26           => ( ( Xa2 = zero_zero_nat )
% 9.49/5.26             => ( Y2
% 9.49/5.26               != ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 9.49/5.26         => ( ( ? [Uv2: $o,Uw2: $o] :
% 9.49/5.26                  ( X
% 9.49/5.26                  = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 9.49/5.26             => ( ? [N3: nat] :
% 9.49/5.26                    ( Xa2
% 9.49/5.26                    = ( suc @ N3 ) )
% 9.49/5.26               => ( Y2 != one_one_nat ) ) )
% 9.49/5.26           => ( ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 9.49/5.26                    ( X
% 9.49/5.26                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 9.49/5.26               => ( Y2 != one_one_nat ) )
% 9.49/5.26             => ( ( ? [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 9.49/5.26                      ( X
% 9.49/5.26                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 9.49/5.26                 => ( Y2 != one_one_nat ) )
% 9.49/5.26               => ( ( ? [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 9.49/5.26                        ( X
% 9.49/5.26                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh2 ) )
% 9.49/5.26                   => ( Y2 != one_one_nat ) )
% 9.49/5.26                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.26                        ( ( X
% 9.49/5.26                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                       => ( Y2
% 9.49/5.26                         != ( plus_plus_nat @ one_one_nat
% 9.49/5.26                            @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ one_one_nat
% 9.49/5.26                              @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) )
% 9.49/5.26                                @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                                  @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 9.49/5.26                                    @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 9.49/5.26                                      @ ( if_nat
% 9.49/5.26                                        @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                           != none_nat )
% 9.49/5.26                                          & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 9.49/5.26                                        @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_s_u_c_c @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                        @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 9.49/5.26                                          @ ( if_nat
% 9.49/5.26                                            @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.49/5.26                                              = none_nat )
% 9.49/5.26                                            @ one_one_nat
% 9.49/5.26                                            @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 9.49/5.26                                  @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3016_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Oelims,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 9.49/5.26        ( ( ( vEBT_T_m_e_m_b_e_r2 @ X @ Xa2 )
% 9.49/5.26          = Y2 )
% 9.49/5.26       => ( ( ? [A4: $o,B3: $o] :
% 9.49/5.26                ( X
% 9.49/5.26                = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26           => ( Y2 != one_one_nat ) )
% 9.49/5.26         => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 9.49/5.26                  ( X
% 9.49/5.26                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 9.49/5.26             => ( Y2 != one_one_nat ) )
% 9.49/5.26           => ( ( ? [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 9.49/5.26                    ( X
% 9.49/5.26                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 9.49/5.26               => ( Y2 != one_one_nat ) )
% 9.49/5.26             => ( ( ? [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 9.49/5.26                      ( X
% 9.49/5.26                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 9.49/5.26                 => ( Y2 != one_one_nat ) )
% 9.49/5.26               => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT] :
% 9.49/5.26                      ( ? [Summary2: vEBT_VEBT] :
% 9.49/5.26                          ( X
% 9.49/5.26                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                     => ( Y2
% 9.49/5.26                       != ( plus_plus_nat @ one_one_nat
% 9.49/5.26                          @ ( if_nat @ ( Xa2 = Mi2 ) @ zero_zero_nat
% 9.49/5.26                            @ ( if_nat @ ( Xa2 = Ma2 ) @ zero_zero_nat
% 9.49/5.26                              @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ zero_zero_nat
% 9.49/5.26                                @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ zero_zero_nat
% 9.49/5.26                                  @ ( if_nat
% 9.49/5.26                                    @ ( ( ord_less_nat @ Mi2 @ Xa2 )
% 9.49/5.26                                      & ( ord_less_nat @ Xa2 @ Ma2 ) )
% 9.49/5.26                                    @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( vEBT_T_m_e_m_b_e_r2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ zero_zero_nat )
% 9.49/5.26                                    @ zero_zero_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3017_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I5_J,axiom,
% 9.49/5.26      ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 9.49/5.26        ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 9.49/5.26        = ( plus_plus_nat @ one_one_nat
% 9.49/5.26          @ ( if_nat @ ( X = Mi ) @ zero_zero_nat
% 9.49/5.26            @ ( if_nat @ ( X = Ma ) @ zero_zero_nat
% 9.49/5.26              @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ zero_zero_nat
% 9.49/5.26                @ ( if_nat @ ( ord_less_nat @ Ma @ X ) @ zero_zero_nat
% 9.49/5.26                  @ ( if_nat
% 9.49/5.26                    @ ( ( ord_less_nat @ Mi @ X )
% 9.49/5.26                      & ( ord_less_nat @ X @ Ma ) )
% 9.49/5.26                    @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( vEBT_T_m_e_m_b_e_r2 @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ zero_zero_nat )
% 9.49/5.26                    @ zero_zero_nat ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3018_buildup__gives__valid,axiom,
% 9.49/5.26      ! [N: nat] :
% 9.49/5.26        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.26       => ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N ) @ N ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3019_inrange,axiom,
% 9.49/5.26      ! [T: vEBT_VEBT,N: nat] :
% 9.49/5.26        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.26       => ( ord_less_eq_set_nat @ ( vEBT_VEBT_set_vebt @ T ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3020_buildup__gives__empty,axiom,
% 9.49/5.26      ! [N: nat] :
% 9.49/5.26        ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_buildup @ N ) )
% 9.49/5.26        = bot_bot_set_nat ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3021_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Opelims,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 9.49/5.26        ( ( ( vEBT_T_d_e_l_e_t_e @ X @ Xa2 )
% 9.49/5.26          = Y2 )
% 9.49/5.26       => ( ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 9.49/5.26         => ( ! [A4: $o,B3: $o] :
% 9.49/5.26                ( ( X
% 9.49/5.26                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26               => ( ( Xa2 = zero_zero_nat )
% 9.49/5.26                 => ( ( Y2 = one_one_nat )
% 9.49/5.26                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ zero_zero_nat ) ) ) ) )
% 9.49/5.26           => ( ! [A4: $o,B3: $o] :
% 9.49/5.26                  ( ( X
% 9.49/5.26                    = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26                 => ( ( Xa2
% 9.49/5.26                      = ( suc @ zero_zero_nat ) )
% 9.49/5.26                   => ( ( Y2 = one_one_nat )
% 9.49/5.26                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 9.49/5.26             => ( ! [A4: $o,B3: $o] :
% 9.49/5.26                    ( ( X
% 9.49/5.26                      = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26                   => ! [N3: nat] :
% 9.49/5.26                        ( ( Xa2
% 9.49/5.26                          = ( suc @ ( suc @ N3 ) ) )
% 9.49/5.26                       => ( ( Y2 = one_one_nat )
% 9.49/5.26                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ ( suc @ ( suc @ N3 ) ) ) ) ) ) )
% 9.49/5.26               => ( ! [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.26                      ( ( X
% 9.49/5.26                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 9.49/5.26                     => ( ( Y2 = one_one_nat )
% 9.49/5.26                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 9.49/5.26                 => ( ! [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.26                        ( ( X
% 9.49/5.26                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TreeList2 @ Summary2 ) )
% 9.49/5.26                       => ( ( Y2 = one_one_nat )
% 9.49/5.26                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 9.49/5.26                   => ( ! [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.26                          ( ( X
% 9.49/5.26                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                         => ( ( Y2 = one_one_nat )
% 9.49/5.26                           => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 9.49/5.26                     => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.26                            ( ( X
% 9.49/5.26                              = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                           => ( ( Y2
% 9.49/5.26                                = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 9.49/5.26                                  @ ( if_nat
% 9.49/5.26                                    @ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 9.49/5.26                                      | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 9.49/5.26                                    @ one_one_nat
% 9.49/5.26                                    @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 9.49/5.26                                      @ ( if_nat
% 9.49/5.26                                        @ ( ( Xa2 = Mi2 )
% 9.49/5.26                                          & ( Xa2 = Ma2 ) )
% 9.49/5.26                                        @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 9.49/5.26                                        @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ Summary2 ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat ) ) @ one_one_nat )
% 9.49/5.26                                          @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                                            @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                              @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 9.49/5.26                                                @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                                  @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_d_e_l_e_t_e @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                                    @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 9.49/5.26                                                      @ ( if_nat
% 9.49/5.26                                                        @ ( ( ( Xa2 = Mi2 )
% 9.49/5.26                                                           => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 9.49/5.26                                                              = Ma2 ) )
% 9.49/5.26                                                          & ( ( Xa2 != Mi2 )
% 9.49/5.26                                                           => ( Xa2 = Ma2 ) ) )
% 9.49/5.26                                                        @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 9.49/5.26                                                          @ ( plus_plus_nat @ one_one_nat
% 9.49/5.26                                                            @ ( if_nat
% 9.49/5.26                                                              @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                                                = none_nat )
% 9.49/5.26                                                              @ one_one_nat
% 9.49/5.26                                                              @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 9.49/5.26                                                        @ one_one_nat ) ) )
% 9.49/5.26                                                  @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 9.49/5.26                                                    @ ( if_nat
% 9.49/5.26                                                      @ ( ( ( Xa2 = Mi2 )
% 9.49/5.26                                                         => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 9.49/5.26                                                            = Ma2 ) )
% 9.49/5.26                                                        & ( ( Xa2 != Mi2 )
% 9.49/5.26                                                         => ( Xa2 = Ma2 ) ) )
% 9.49/5.26                                                      @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 9.49/5.26                                                      @ one_one_nat ) ) ) ) )
% 9.49/5.26                                            @ one_one_nat ) ) ) ) ) ) )
% 9.49/5.26                             => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3022_set__bit__0,axiom,
% 9.49/5.26      ! [A: int] :
% 9.49/5.26        ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 9.49/5.26        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3023_set__bit__0,axiom,
% 9.49/5.26      ! [A: nat] :
% 9.49/5.26        ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 9.49/5.26        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3024_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Opelims,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 9.49/5.26        ( ( ( vEBT_T_s_u_c_c @ X @ Xa2 )
% 9.49/5.26          = Y2 )
% 9.49/5.26       => ( ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 9.49/5.26         => ( ! [Uu2: $o,B3: $o] :
% 9.49/5.26                ( ( X
% 9.49/5.26                  = ( vEBT_Leaf @ Uu2 @ B3 ) )
% 9.49/5.26               => ( ( Xa2 = zero_zero_nat )
% 9.49/5.26                 => ( ( Y2
% 9.49/5.26                      = ( plus_plus_nat @ one_one_nat @ one_one_nat ) )
% 9.49/5.26                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B3 ) @ zero_zero_nat ) ) ) ) )
% 9.49/5.26           => ( ! [Uv2: $o,Uw2: $o] :
% 9.49/5.26                  ( ( X
% 9.49/5.26                    = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 9.49/5.26                 => ! [N3: nat] :
% 9.49/5.26                      ( ( Xa2
% 9.49/5.26                        = ( suc @ N3 ) )
% 9.49/5.26                     => ( ( Y2 = one_one_nat )
% 9.49/5.26                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N3 ) ) ) ) ) )
% 9.49/5.26             => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 9.49/5.26                    ( ( X
% 9.49/5.26                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 9.49/5.26                   => ( ( Y2 = one_one_nat )
% 9.49/5.26                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 9.49/5.26               => ( ! [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 9.49/5.26                      ( ( X
% 9.49/5.26                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 9.49/5.26                     => ( ( Y2 = one_one_nat )
% 9.49/5.26                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Xa2 ) ) ) )
% 9.49/5.26                 => ( ! [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 9.49/5.26                        ( ( X
% 9.49/5.26                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh2 ) )
% 9.49/5.26                       => ( ( Y2 = one_one_nat )
% 9.49/5.26                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh2 ) @ Xa2 ) ) ) )
% 9.49/5.26                   => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.26                          ( ( X
% 9.49/5.26                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                         => ( ( Y2
% 9.49/5.26                              = ( plus_plus_nat @ one_one_nat
% 9.49/5.26                                @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ one_one_nat
% 9.49/5.26                                  @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) )
% 9.49/5.26                                    @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                                      @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 9.49/5.26                                        @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 9.49/5.26                                          @ ( if_nat
% 9.49/5.26                                            @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                               != none_nat )
% 9.49/5.26                                              & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 9.49/5.26                                            @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_s_u_c_c @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                            @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 9.49/5.26                                              @ ( if_nat
% 9.49/5.26                                                @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.49/5.26                                                  = none_nat )
% 9.49/5.26                                                @ one_one_nat
% 9.49/5.26                                                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 9.49/5.26                                      @ one_one_nat ) ) ) ) )
% 9.49/5.26                           => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3025_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Opelims,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 9.49/5.26        ( ( ( vEBT_T_p_r_e_d @ X @ Xa2 )
% 9.49/5.26          = Y2 )
% 9.49/5.26       => ( ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 9.49/5.26         => ( ! [Uu2: $o,Uv2: $o] :
% 9.49/5.26                ( ( X
% 9.49/5.26                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 9.49/5.26               => ( ( Xa2 = zero_zero_nat )
% 9.49/5.26                 => ( ( Y2 = one_one_nat )
% 9.49/5.26                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) ) ) ) )
% 9.49/5.26           => ( ! [A4: $o,Uw2: $o] :
% 9.49/5.26                  ( ( X
% 9.49/5.26                    = ( vEBT_Leaf @ A4 @ Uw2 ) )
% 9.49/5.26                 => ( ( Xa2
% 9.49/5.26                      = ( suc @ zero_zero_nat ) )
% 9.49/5.26                   => ( ( Y2
% 9.49/5.26                        = ( plus_plus_nat @ one_one_nat @ one_one_nat ) )
% 9.49/5.26                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 9.49/5.26             => ( ! [A4: $o,B3: $o] :
% 9.49/5.26                    ( ( X
% 9.49/5.26                      = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26                   => ! [Va2: nat] :
% 9.49/5.26                        ( ( Xa2
% 9.49/5.26                          = ( suc @ ( suc @ Va2 ) ) )
% 9.49/5.26                       => ( ( Y2
% 9.49/5.26                            = ( plus_plus_nat @ one_one_nat @ ( if_nat @ B3 @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 9.49/5.26                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ ( suc @ ( suc @ Va2 ) ) ) ) ) ) )
% 9.49/5.26               => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 9.49/5.26                      ( ( X
% 9.49/5.26                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 9.49/5.26                     => ( ( Y2 = one_one_nat )
% 9.49/5.26                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) @ Xa2 ) ) ) )
% 9.49/5.26                 => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 9.49/5.26                        ( ( X
% 9.49/5.26                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 9.49/5.26                       => ( ( Y2 = one_one_nat )
% 9.49/5.26                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Xa2 ) ) ) )
% 9.49/5.26                   => ( ! [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 9.49/5.26                          ( ( X
% 9.49/5.26                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 9.49/5.26                         => ( ( Y2 = one_one_nat )
% 9.49/5.26                           => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Xa2 ) ) ) )
% 9.49/5.26                     => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.26                            ( ( X
% 9.49/5.26                              = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                           => ( ( Y2
% 9.49/5.26                                = ( plus_plus_nat @ one_one_nat
% 9.49/5.26                                  @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ one_one_nat
% 9.49/5.26                                    @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 9.49/5.26                                      @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                                        @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 9.49/5.26                                          @ ( if_nat
% 9.49/5.26                                            @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                               != none_nat )
% 9.49/5.26                                              & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 9.49/5.26                                            @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_p_r_e_d @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                            @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 9.49/5.26                                              @ ( if_nat
% 9.49/5.26                                                @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.49/5.26                                                  = none_nat )
% 9.49/5.26                                                @ ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 9.49/5.26                                                @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 9.49/5.26                                        @ one_one_nat ) ) ) ) )
% 9.49/5.26                             => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3026_vebt__succ_Opelims,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat,Y2: option_nat] :
% 9.49/5.26        ( ( ( vEBT_vebt_succ @ X @ Xa2 )
% 9.49/5.26          = Y2 )
% 9.49/5.26       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 9.49/5.26         => ( ! [Uu2: $o,B3: $o] :
% 9.49/5.26                ( ( X
% 9.49/5.26                  = ( vEBT_Leaf @ Uu2 @ B3 ) )
% 9.49/5.26               => ( ( Xa2 = zero_zero_nat )
% 9.49/5.26                 => ( ( ( B3
% 9.49/5.26                       => ( Y2
% 9.49/5.26                          = ( some_nat @ one_one_nat ) ) )
% 9.49/5.26                      & ( ~ B3
% 9.49/5.26                       => ( Y2 = none_nat ) ) )
% 9.49/5.26                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B3 ) @ zero_zero_nat ) ) ) ) )
% 9.49/5.26           => ( ! [Uv2: $o,Uw2: $o] :
% 9.49/5.26                  ( ( X
% 9.49/5.26                    = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 9.49/5.26                 => ! [N3: nat] :
% 9.49/5.26                      ( ( Xa2
% 9.49/5.26                        = ( suc @ N3 ) )
% 9.49/5.26                     => ( ( Y2 = none_nat )
% 9.49/5.26                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N3 ) ) ) ) ) )
% 9.49/5.26             => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 9.49/5.26                    ( ( X
% 9.49/5.26                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 9.49/5.26                   => ( ( Y2 = none_nat )
% 9.49/5.26                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 9.49/5.26               => ( ! [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 9.49/5.26                      ( ( X
% 9.49/5.26                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 9.49/5.26                     => ( ( Y2 = none_nat )
% 9.49/5.26                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Xa2 ) ) ) )
% 9.49/5.26                 => ( ! [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 9.49/5.26                        ( ( X
% 9.49/5.26                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh2 ) )
% 9.49/5.26                       => ( ( Y2 = none_nat )
% 9.49/5.26                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh2 ) @ Xa2 ) ) ) )
% 9.49/5.26                   => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.26                          ( ( X
% 9.49/5.26                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                         => ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 9.49/5.26                               => ( Y2
% 9.49/5.26                                  = ( some_nat @ Mi2 ) ) )
% 9.49/5.26                              & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 9.49/5.26                               => ( Y2
% 9.49/5.26                                  = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                                    @ ( if_option_nat
% 9.49/5.26                                      @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                         != none_nat )
% 9.49/5.26                                        & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 9.49/5.26                                      @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                      @ ( if_option_nat
% 9.49/5.26                                        @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.49/5.26                                          = none_nat )
% 9.49/5.26                                        @ none_nat
% 9.49/5.26                                        @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 9.49/5.26                                    @ none_nat ) ) ) )
% 9.49/5.26                           => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3027_buildup__nothing__in__min__max,axiom,
% 9.49/5.26      ! [N: nat,X: nat] :
% 9.49/5.26        ~ ( vEBT_VEBT_membermima @ ( vEBT_vebt_buildup @ N ) @ X ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3028_buildup__nothing__in__leaf,axiom,
% 9.49/5.26      ! [N: nat,X: nat] :
% 9.49/5.26        ~ ( vEBT_V5719532721284313246member @ ( vEBT_vebt_buildup @ N ) @ X ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3029_div__neg__neg__trivial,axiom,
% 9.49/5.26      ! [K: int,L2: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ K @ zero_zero_int )
% 9.49/5.26       => ( ( ord_less_int @ L2 @ K )
% 9.49/5.26         => ( ( divide_divide_int @ K @ L2 )
% 9.49/5.26            = zero_zero_int ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3030_div__pos__pos__trivial,axiom,
% 9.49/5.26      ! [K: int,L2: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 9.49/5.26       => ( ( ord_less_int @ K @ L2 )
% 9.49/5.26         => ( ( divide_divide_int @ K @ L2 )
% 9.49/5.26            = zero_zero_int ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3031_i0__less,axiom,
% 9.49/5.26      ! [N: extended_enat] :
% 9.49/5.26        ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 9.49/5.26        = ( N != zero_z5237406670263579293d_enat ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3032_idiff__0,axiom,
% 9.49/5.26      ! [N: extended_enat] :
% 9.49/5.26        ( ( minus_3235023915231533773d_enat @ zero_z5237406670263579293d_enat @ N )
% 9.49/5.26        = zero_z5237406670263579293d_enat ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3033_idiff__0__right,axiom,
% 9.49/5.26      ! [N: extended_enat] :
% 9.49/5.26        ( ( minus_3235023915231533773d_enat @ N @ zero_z5237406670263579293d_enat )
% 9.49/5.26        = N ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3034_not__real__square__gt__zero,axiom,
% 9.49/5.26      ! [X: real] :
% 9.49/5.26        ( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X @ X ) ) )
% 9.49/5.26        = ( X = zero_zero_real ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3035_half__negative__int__iff,axiom,
% 9.49/5.26      ! [K: int] :
% 9.49/5.26        ( ( ord_less_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 9.49/5.26        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3036_half__nonnegative__int__iff,axiom,
% 9.49/5.26      ! [K: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 9.49/5.26        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3037_div__pos__geq,axiom,
% 9.49/5.26      ! [L2: int,K: int] :
% 9.49/5.26        ( ( ord_less_int @ zero_zero_int @ L2 )
% 9.49/5.26       => ( ( ord_less_eq_int @ L2 @ K )
% 9.49/5.26         => ( ( divide_divide_int @ K @ L2 )
% 9.49/5.26            = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L2 ) @ L2 ) @ one_one_int ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3038_split__zdiv,axiom,
% 9.49/5.26      ! [P: int > $o,N: int,K: int] :
% 9.49/5.26        ( ( P @ ( divide_divide_int @ N @ K ) )
% 9.49/5.26        = ( ( ( K = zero_zero_int )
% 9.49/5.26           => ( P @ zero_zero_int ) )
% 9.49/5.26          & ( ( ord_less_int @ zero_zero_int @ K )
% 9.49/5.26           => ! [I3: int,J3: int] :
% 9.49/5.26                ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 9.49/5.26                  & ( ord_less_int @ J3 @ K )
% 9.49/5.26                  & ( N
% 9.49/5.26                    = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 9.49/5.26               => ( P @ I3 ) ) )
% 9.49/5.26          & ( ( ord_less_int @ K @ zero_zero_int )
% 9.49/5.26           => ! [I3: int,J3: int] :
% 9.49/5.26                ( ( ( ord_less_int @ K @ J3 )
% 9.49/5.26                  & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 9.49/5.26                  & ( N
% 9.49/5.26                    = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 9.49/5.26               => ( P @ I3 ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3039_zdiv__mono1,axiom,
% 9.49/5.26      ! [A: int,A5: int,B: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ A @ A5 )
% 9.49/5.26       => ( ( ord_less_int @ zero_zero_int @ B )
% 9.49/5.26         => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A5 @ B ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3040_zdiv__mono2,axiom,
% 9.49/5.26      ! [A: int,B5: int,B: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.26       => ( ( ord_less_int @ zero_zero_int @ B5 )
% 9.49/5.26         => ( ( ord_less_eq_int @ B5 @ B )
% 9.49/5.26           => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B5 ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3041_zdiv__eq__0__iff,axiom,
% 9.49/5.26      ! [I2: int,K: int] :
% 9.49/5.26        ( ( ( divide_divide_int @ I2 @ K )
% 9.49/5.26          = zero_zero_int )
% 9.49/5.26        = ( ( K = zero_zero_int )
% 9.49/5.26          | ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 9.49/5.26            & ( ord_less_int @ I2 @ K ) )
% 9.49/5.26          | ( ( ord_less_eq_int @ I2 @ zero_zero_int )
% 9.49/5.26            & ( ord_less_int @ K @ I2 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3042_int__div__neg__eq,axiom,
% 9.49/5.26      ! [A: int,B: int,Q2: int,R: int] :
% 9.49/5.26        ( ( A
% 9.49/5.26          = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 9.49/5.26       => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 9.49/5.26         => ( ( ord_less_int @ B @ R )
% 9.49/5.26           => ( ( divide_divide_int @ A @ B )
% 9.49/5.26              = Q2 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3043_int__div__pos__eq,axiom,
% 9.49/5.26      ! [A: int,B: int,Q2: int,R: int] :
% 9.49/5.26        ( ( A
% 9.49/5.26          = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 9.49/5.26       => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 9.49/5.26         => ( ( ord_less_int @ R @ B )
% 9.49/5.26           => ( ( divide_divide_int @ A @ B )
% 9.49/5.26              = Q2 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3044_zdiv__mono1__neg,axiom,
% 9.49/5.26      ! [A: int,A5: int,B: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ A @ A5 )
% 9.49/5.26       => ( ( ord_less_int @ B @ zero_zero_int )
% 9.49/5.26         => ( ord_less_eq_int @ ( divide_divide_int @ A5 @ B ) @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3045_zdiv__mono2__neg,axiom,
% 9.49/5.26      ! [A: int,B5: int,B: int] :
% 9.49/5.26        ( ( ord_less_int @ A @ zero_zero_int )
% 9.49/5.26       => ( ( ord_less_int @ zero_zero_int @ B5 )
% 9.49/5.26         => ( ( ord_less_eq_int @ B5 @ B )
% 9.49/5.26           => ( ord_less_eq_int @ ( divide_divide_int @ A @ B5 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3046_div__int__pos__iff,axiom,
% 9.49/5.26      ! [K: int,L2: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ L2 ) )
% 9.49/5.26        = ( ( K = zero_zero_int )
% 9.49/5.26          | ( L2 = zero_zero_int )
% 9.49/5.26          | ( ( ord_less_eq_int @ zero_zero_int @ K )
% 9.49/5.26            & ( ord_less_eq_int @ zero_zero_int @ L2 ) )
% 9.49/5.26          | ( ( ord_less_int @ K @ zero_zero_int )
% 9.49/5.26            & ( ord_less_int @ L2 @ zero_zero_int ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3047_div__positive__int,axiom,
% 9.49/5.26      ! [L2: int,K: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ L2 @ K )
% 9.49/5.26       => ( ( ord_less_int @ zero_zero_int @ L2 )
% 9.49/5.26         => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K @ L2 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3048_div__nonneg__neg__le0,axiom,
% 9.49/5.26      ! [A: int,B: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.26       => ( ( ord_less_int @ B @ zero_zero_int )
% 9.49/5.26         => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3049_div__nonpos__pos__le0,axiom,
% 9.49/5.26      ! [A: int,B: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 9.49/5.26       => ( ( ord_less_int @ zero_zero_int @ B )
% 9.49/5.26         => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3050_pos__imp__zdiv__pos__iff,axiom,
% 9.49/5.26      ! [K: int,I2: int] :
% 9.49/5.26        ( ( ord_less_int @ zero_zero_int @ K )
% 9.49/5.26       => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I2 @ K ) )
% 9.49/5.26          = ( ord_less_eq_int @ K @ I2 ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3051_neg__imp__zdiv__nonneg__iff,axiom,
% 9.49/5.26      ! [B: int,A: int] :
% 9.49/5.26        ( ( ord_less_int @ B @ zero_zero_int )
% 9.49/5.26       => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 9.49/5.26          = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3052_pos__imp__zdiv__nonneg__iff,axiom,
% 9.49/5.26      ! [B: int,A: int] :
% 9.49/5.26        ( ( ord_less_int @ zero_zero_int @ B )
% 9.49/5.26       => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 9.49/5.26          = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3053_nonneg1__imp__zdiv__pos__iff,axiom,
% 9.49/5.26      ! [A: int,B: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.26       => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 9.49/5.26          = ( ( ord_less_eq_int @ B @ A )
% 9.49/5.26            & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3054_zdiv__zmult2__eq,axiom,
% 9.49/5.26      ! [C: int,A: int,B: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.49/5.26       => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 9.49/5.26          = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3055_pos__imp__zdiv__neg__iff,axiom,
% 9.49/5.26      ! [B: int,A: int] :
% 9.49/5.26        ( ( ord_less_int @ zero_zero_int @ B )
% 9.49/5.26       => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 9.49/5.26          = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3056_neg__imp__zdiv__neg__iff,axiom,
% 9.49/5.26      ! [B: int,A: int] :
% 9.49/5.26        ( ( ord_less_int @ B @ zero_zero_int )
% 9.49/5.26       => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 9.49/5.26          = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3057_int__div__less__self,axiom,
% 9.49/5.26      ! [X: int,K: int] :
% 9.49/5.26        ( ( ord_less_int @ zero_zero_int @ X )
% 9.49/5.26       => ( ( ord_less_int @ one_one_int @ K )
% 9.49/5.26         => ( ord_less_int @ ( divide_divide_int @ X @ K ) @ X ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3058_div__neg__pos__less0,axiom,
% 9.49/5.26      ! [A: int,B: int] :
% 9.49/5.26        ( ( ord_less_int @ A @ zero_zero_int )
% 9.49/5.26       => ( ( ord_less_int @ zero_zero_int @ B )
% 9.49/5.26         => ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3059_enat__0__less__mult__iff,axiom,
% 9.49/5.26      ! [M: extended_enat,N: extended_enat] :
% 9.49/5.26        ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( times_7803423173614009249d_enat @ M @ N ) )
% 9.49/5.26        = ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ M )
% 9.49/5.26          & ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3060_not__iless0,axiom,
% 9.49/5.26      ! [N: extended_enat] :
% 9.49/5.26        ~ ( ord_le72135733267957522d_enat @ N @ zero_z5237406670263579293d_enat ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3061_iadd__is__0,axiom,
% 9.49/5.26      ! [M: extended_enat,N: extended_enat] :
% 9.49/5.26        ( ( ( plus_p3455044024723400733d_enat @ M @ N )
% 9.49/5.26          = zero_z5237406670263579293d_enat )
% 9.49/5.26        = ( ( M = zero_z5237406670263579293d_enat )
% 9.49/5.26          & ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3062_i0__lb,axiom,
% 9.49/5.26      ! [N: extended_enat] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ N ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3063_ile0__eq,axiom,
% 9.49/5.26      ! [N: extended_enat] :
% 9.49/5.26        ( ( ord_le2932123472753598470d_enat @ N @ zero_z5237406670263579293d_enat )
% 9.49/5.26        = ( N = zero_z5237406670263579293d_enat ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3064_ex__nat__less,axiom,
% 9.49/5.26      ! [N: nat,P: nat > $o] :
% 9.49/5.26        ( ( ? [M6: nat] :
% 9.49/5.26              ( ( ord_less_eq_nat @ M6 @ N )
% 9.49/5.26              & ( P @ M6 ) ) )
% 9.49/5.26        = ( ? [X2: nat] :
% 9.49/5.26              ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 9.49/5.26              & ( P @ X2 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3065_all__nat__less,axiom,
% 9.49/5.26      ! [N: nat,P: nat > $o] :
% 9.49/5.26        ( ( ! [M6: nat] :
% 9.49/5.26              ( ( ord_less_eq_nat @ M6 @ N )
% 9.49/5.26             => ( P @ M6 ) ) )
% 9.49/5.26        = ( ! [X2: nat] :
% 9.49/5.26              ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 9.49/5.26             => ( P @ X2 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3066_vebt__buildup_Osimps_I1_J,axiom,
% 9.49/5.26      ( ( vEBT_vebt_buildup @ zero_zero_nat )
% 9.49/5.26      = ( vEBT_Leaf @ $false @ $false ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3067_not__exp__less__eq__0__int,axiom,
% 9.49/5.26      ! [N: nat] :
% 9.49/5.26        ~ ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ zero_zero_int ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3068_realpow__pos__nth2,axiom,
% 9.49/5.26      ! [A: real,N: nat] :
% 9.49/5.26        ( ( ord_less_real @ zero_zero_real @ A )
% 9.49/5.26       => ? [R3: real] :
% 9.49/5.26            ( ( ord_less_real @ zero_zero_real @ R3 )
% 9.49/5.26            & ( ( power_power_real @ R3 @ ( suc @ N ) )
% 9.49/5.26              = A ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3069_real__arch__pow__inv,axiom,
% 9.49/5.26      ! [Y2: real,X: real] :
% 9.49/5.26        ( ( ord_less_real @ zero_zero_real @ Y2 )
% 9.49/5.26       => ( ( ord_less_real @ X @ one_one_real )
% 9.49/5.26         => ? [N3: nat] : ( ord_less_real @ ( power_power_real @ X @ N3 ) @ Y2 ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3070_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I1_J,axiom,
% 9.49/5.26      ! [A: $o,B: $o,X: nat] :
% 9.49/5.26        ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Leaf @ A @ B ) @ X )
% 9.49/5.26        = one_one_nat ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3071_vebt__buildup_Osimps_I2_J,axiom,
% 9.49/5.26      ( ( vEBT_vebt_buildup @ ( suc @ zero_zero_nat ) )
% 9.49/5.26      = ( vEBT_Leaf @ $false @ $false ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3072_realpow__pos__nth,axiom,
% 9.49/5.26      ! [N: nat,A: real] :
% 9.49/5.26        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.26       => ( ( ord_less_real @ zero_zero_real @ A )
% 9.49/5.26         => ? [R3: real] :
% 9.49/5.26              ( ( ord_less_real @ zero_zero_real @ R3 )
% 9.49/5.26              & ( ( power_power_real @ R3 @ N )
% 9.49/5.26                = A ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3073_realpow__pos__nth__unique,axiom,
% 9.49/5.26      ! [N: nat,A: real] :
% 9.49/5.26        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.26       => ( ( ord_less_real @ zero_zero_real @ A )
% 9.49/5.26         => ? [X3: real] :
% 9.49/5.26              ( ( ord_less_real @ zero_zero_real @ X3 )
% 9.49/5.26              & ( ( power_power_real @ X3 @ N )
% 9.49/5.26                = A )
% 9.49/5.26              & ! [Y4: real] :
% 9.49/5.26                  ( ( ( ord_less_real @ zero_zero_real @ Y4 )
% 9.49/5.26                    & ( ( power_power_real @ Y4 @ N )
% 9.49/5.26                      = A ) )
% 9.49/5.26                 => ( Y4 = X3 ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3074_neg__zdiv__mult__2,axiom,
% 9.49/5.26      ! [A: int,B: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 9.49/5.26       => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 9.49/5.26          = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3075_pos__zdiv__mult__2,axiom,
% 9.49/5.26      ! [A: int,B: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.26       => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 9.49/5.26          = ( divide_divide_int @ B @ A ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3076_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I2_J,axiom,
% 9.49/5.26      ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X: nat] :
% 9.49/5.26        ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X )
% 9.49/5.26        = one_one_nat ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3077_int__power__div__base,axiom,
% 9.49/5.26      ! [M: nat,K: int] :
% 9.49/5.26        ( ( ord_less_nat @ zero_zero_nat @ M )
% 9.49/5.26       => ( ( ord_less_int @ zero_zero_int @ K )
% 9.49/5.26         => ( ( divide_divide_int @ ( power_power_int @ K @ M ) @ K )
% 9.49/5.26            = ( power_power_int @ K @ ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3078_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I3_J,axiom,
% 9.49/5.26      ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X: nat] :
% 9.49/5.26        ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X )
% 9.49/5.26        = one_one_nat ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3079_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I4_J,axiom,
% 9.49/5.26      ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 9.49/5.26        ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X )
% 9.49/5.26        = one_one_nat ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3080_member__bound__height_H,axiom,
% 9.49/5.26      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 9.49/5.26        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.26       => ( ord_less_eq_nat @ ( vEBT_T_m_e_m_b_e_r2 @ T @ X ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3081_vebt__pred_Opelims,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat,Y2: option_nat] :
% 9.49/5.26        ( ( ( vEBT_vebt_pred @ X @ Xa2 )
% 9.49/5.26          = Y2 )
% 9.49/5.26       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 9.49/5.26         => ( ! [Uu2: $o,Uv2: $o] :
% 9.49/5.26                ( ( X
% 9.49/5.26                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 9.49/5.26               => ( ( Xa2 = zero_zero_nat )
% 9.49/5.26                 => ( ( Y2 = none_nat )
% 9.49/5.26                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) ) ) ) )
% 9.49/5.26           => ( ! [A4: $o,Uw2: $o] :
% 9.49/5.26                  ( ( X
% 9.49/5.26                    = ( vEBT_Leaf @ A4 @ Uw2 ) )
% 9.49/5.26                 => ( ( Xa2
% 9.49/5.26                      = ( suc @ zero_zero_nat ) )
% 9.49/5.26                   => ( ( ( A4
% 9.49/5.26                         => ( Y2
% 9.49/5.26                            = ( some_nat @ zero_zero_nat ) ) )
% 9.49/5.26                        & ( ~ A4
% 9.49/5.26                         => ( Y2 = none_nat ) ) )
% 9.49/5.26                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 9.49/5.26             => ( ! [A4: $o,B3: $o] :
% 9.49/5.26                    ( ( X
% 9.49/5.26                      = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26                   => ! [Va2: nat] :
% 9.49/5.26                        ( ( Xa2
% 9.49/5.26                          = ( suc @ ( suc @ Va2 ) ) )
% 9.49/5.26                       => ( ( ( B3
% 9.49/5.26                             => ( Y2
% 9.49/5.26                                = ( some_nat @ one_one_nat ) ) )
% 9.49/5.26                            & ( ~ B3
% 9.49/5.26                             => ( ( A4
% 9.49/5.26                                 => ( Y2
% 9.49/5.26                                    = ( some_nat @ zero_zero_nat ) ) )
% 9.49/5.26                                & ( ~ A4
% 9.49/5.26                                 => ( Y2 = none_nat ) ) ) ) )
% 9.49/5.26                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ ( suc @ ( suc @ Va2 ) ) ) ) ) ) )
% 9.49/5.26               => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 9.49/5.26                      ( ( X
% 9.49/5.26                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 9.49/5.26                     => ( ( Y2 = none_nat )
% 9.49/5.26                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) @ Xa2 ) ) ) )
% 9.49/5.26                 => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 9.49/5.26                        ( ( X
% 9.49/5.26                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 9.49/5.26                       => ( ( Y2 = none_nat )
% 9.49/5.26                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Xa2 ) ) ) )
% 9.49/5.26                   => ( ! [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 9.49/5.26                          ( ( X
% 9.49/5.26                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 9.49/5.26                         => ( ( Y2 = none_nat )
% 9.49/5.26                           => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Xa2 ) ) ) )
% 9.49/5.26                     => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.26                            ( ( X
% 9.49/5.26                              = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                           => ( ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 9.49/5.26                                 => ( Y2
% 9.49/5.26                                    = ( some_nat @ Ma2 ) ) )
% 9.49/5.26                                & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 9.49/5.26                                 => ( Y2
% 9.49/5.26                                    = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                                      @ ( if_option_nat
% 9.49/5.26                                        @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                           != none_nat )
% 9.49/5.26                                          & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 9.49/5.26                                        @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                        @ ( if_option_nat
% 9.49/5.26                                          @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.49/5.26                                            = none_nat )
% 9.49/5.26                                          @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 9.49/5.26                                          @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 9.49/5.26                                      @ none_nat ) ) ) )
% 9.49/5.26                             => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3082_vebt__delete_Opelims,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat,Y2: vEBT_VEBT] :
% 9.49/5.26        ( ( ( vEBT_vebt_delete @ X @ Xa2 )
% 9.49/5.26          = Y2 )
% 9.49/5.26       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 9.49/5.26         => ( ! [A4: $o,B3: $o] :
% 9.49/5.26                ( ( X
% 9.49/5.26                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26               => ( ( Xa2 = zero_zero_nat )
% 9.49/5.26                 => ( ( Y2
% 9.49/5.26                      = ( vEBT_Leaf @ $false @ B3 ) )
% 9.49/5.26                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ zero_zero_nat ) ) ) ) )
% 9.49/5.26           => ( ! [A4: $o,B3: $o] :
% 9.49/5.26                  ( ( X
% 9.49/5.26                    = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26                 => ( ( Xa2
% 9.49/5.26                      = ( suc @ zero_zero_nat ) )
% 9.49/5.26                   => ( ( Y2
% 9.49/5.26                        = ( vEBT_Leaf @ A4 @ $false ) )
% 9.49/5.26                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 9.49/5.26             => ( ! [A4: $o,B3: $o] :
% 9.49/5.26                    ( ( X
% 9.49/5.26                      = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26                   => ! [N3: nat] :
% 9.49/5.26                        ( ( Xa2
% 9.49/5.26                          = ( suc @ ( suc @ N3 ) ) )
% 9.49/5.26                       => ( ( Y2
% 9.49/5.26                            = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ ( suc @ ( suc @ N3 ) ) ) ) ) ) )
% 9.49/5.26               => ( ! [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.26                      ( ( X
% 9.49/5.26                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 9.49/5.26                     => ( ( Y2
% 9.49/5.26                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 9.49/5.26                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 9.49/5.26                 => ( ! [Mi2: nat,Ma2: nat,TrLst2: list_VEBT_VEBT,Smry2: vEBT_VEBT] :
% 9.49/5.26                        ( ( X
% 9.49/5.26                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 9.49/5.26                       => ( ( Y2
% 9.49/5.26                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 9.49/5.26                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) @ Xa2 ) ) ) )
% 9.49/5.26                   => ( ! [Mi2: nat,Ma2: nat,Tr2: list_VEBT_VEBT,Sm2: vEBT_VEBT] :
% 9.49/5.26                          ( ( X
% 9.49/5.26                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 9.49/5.26                         => ( ( Y2
% 9.49/5.26                              = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 9.49/5.26                           => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) @ Xa2 ) ) ) )
% 9.49/5.26                     => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.26                            ( ( X
% 9.49/5.26                              = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                           => ( ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 9.49/5.26                                    | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 9.49/5.26                                 => ( Y2
% 9.49/5.26                                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) ) )
% 9.49/5.26                                & ( ~ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 9.49/5.26                                      | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 9.49/5.26                                 => ( ( ( ( Xa2 = Mi2 )
% 9.49/5.26                                        & ( Xa2 = Ma2 ) )
% 9.49/5.26                                     => ( Y2
% 9.49/5.26                                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) ) )
% 9.49/5.26                                    & ( ~ ( ( Xa2 = Mi2 )
% 9.49/5.26                                          & ( Xa2 = Ma2 ) )
% 9.49/5.26                                     => ( Y2
% 9.49/5.26                                        = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                                          @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                            @ ( vEBT_Node
% 9.49/5.26                                              @ ( some_P7363390416028606310at_nat
% 9.49/5.26                                                @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 9.49/5.26                                                  @ ( if_nat
% 9.49/5.26                                                    @ ( ( ( Xa2 = Mi2 )
% 9.49/5.26                                                       => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 9.49/5.26                                                          = Ma2 ) )
% 9.49/5.26                                                      & ( ( Xa2 != Mi2 )
% 9.49/5.26                                                       => ( Xa2 = Ma2 ) ) )
% 9.49/5.26                                                    @ ( if_nat
% 9.49/5.26                                                      @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                                        = none_nat )
% 9.49/5.26                                                      @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 9.49/5.26                                                      @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 9.49/5.26                                                    @ Ma2 ) ) )
% 9.49/5.26                                              @ ( suc @ ( suc @ Va2 ) )
% 9.49/5.26                                              @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                              @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                            @ ( vEBT_Node
% 9.49/5.26                                              @ ( some_P7363390416028606310at_nat
% 9.49/5.26                                                @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 9.49/5.26                                                  @ ( if_nat
% 9.49/5.26                                                    @ ( ( ( Xa2 = Mi2 )
% 9.49/5.26                                                       => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 9.49/5.26                                                          = Ma2 ) )
% 9.49/5.26                                                      & ( ( Xa2 != Mi2 )
% 9.49/5.26                                                       => ( Xa2 = Ma2 ) ) )
% 9.49/5.26                                                    @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 9.49/5.26                                                    @ Ma2 ) ) )
% 9.49/5.26                                              @ ( suc @ ( suc @ Va2 ) )
% 9.49/5.26                                              @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                              @ Summary2 ) )
% 9.49/5.26                                          @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) ) ) ) ) ) )
% 9.49/5.26                             => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3083_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Opelims,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 9.49/5.26        ( ( ( vEBT_T_s_u_c_c2 @ X @ Xa2 )
% 9.49/5.26          = Y2 )
% 9.49/5.26       => ( ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 9.49/5.26         => ( ! [Uu2: $o,B3: $o] :
% 9.49/5.26                ( ( X
% 9.49/5.26                  = ( vEBT_Leaf @ Uu2 @ B3 ) )
% 9.49/5.26               => ( ( Xa2 = zero_zero_nat )
% 9.49/5.26                 => ( ( Y2 = one_one_nat )
% 9.49/5.26                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B3 ) @ zero_zero_nat ) ) ) ) )
% 9.49/5.26           => ( ! [Uv2: $o,Uw2: $o] :
% 9.49/5.26                  ( ( X
% 9.49/5.26                    = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 9.49/5.26                 => ! [N3: nat] :
% 9.49/5.26                      ( ( Xa2
% 9.49/5.26                        = ( suc @ N3 ) )
% 9.49/5.26                     => ( ( Y2 = one_one_nat )
% 9.49/5.26                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N3 ) ) ) ) ) )
% 9.49/5.26             => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 9.49/5.26                    ( ( X
% 9.49/5.26                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 9.49/5.26                   => ( ( Y2 = one_one_nat )
% 9.49/5.26                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 9.49/5.26               => ( ! [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 9.49/5.26                      ( ( X
% 9.49/5.26                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 9.49/5.26                     => ( ( Y2 = one_one_nat )
% 9.49/5.26                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Xa2 ) ) ) )
% 9.49/5.26                 => ( ! [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 9.49/5.26                        ( ( X
% 9.49/5.26                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh2 ) )
% 9.49/5.26                       => ( ( Y2 = one_one_nat )
% 9.49/5.26                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh2 ) @ Xa2 ) ) ) )
% 9.49/5.26                   => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.26                          ( ( X
% 9.49/5.26                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                         => ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 9.49/5.26                               => ( Y2 = one_one_nat ) )
% 9.49/5.26                              & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 9.49/5.26                               => ( Y2
% 9.49/5.26                                  = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                                    @ ( if_nat
% 9.49/5.26                                      @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                         != none_nat )
% 9.49/5.26                                        & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 9.49/5.26                                      @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                      @ ( plus_plus_nat @ ( vEBT_T_s_u_c_c2 @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 9.49/5.26                                    @ one_one_nat ) ) ) )
% 9.49/5.26                           => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3084_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Opelims,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 9.49/5.26        ( ( ( vEBT_T_i_n_s_e_r_t @ X @ Xa2 )
% 9.49/5.26          = Y2 )
% 9.49/5.26       => ( ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 9.49/5.26         => ( ! [A4: $o,B3: $o] :
% 9.49/5.26                ( ( X
% 9.49/5.26                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26               => ( ( Y2
% 9.49/5.26                    = ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa2 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 9.49/5.26                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa2 ) ) ) )
% 9.49/5.26           => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 9.49/5.26                  ( ( X
% 9.49/5.26                    = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S ) )
% 9.49/5.26                 => ( ( Y2 = one_one_nat )
% 9.49/5.26                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S ) @ Xa2 ) ) ) )
% 9.49/5.26             => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 9.49/5.26                    ( ( X
% 9.49/5.26                      = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) )
% 9.49/5.26                   => ( ( Y2 = one_one_nat )
% 9.49/5.26                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) @ Xa2 ) ) ) )
% 9.49/5.26               => ( ! [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.26                      ( ( X
% 9.49/5.26                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                     => ( ( Y2
% 9.49/5.26                          = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.26                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 9.49/5.26                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.26                        ( ( X
% 9.49/5.26                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                       => ( ( Y2
% 9.49/5.26                            = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 9.49/5.26                              @ ( if_nat
% 9.49/5.26                                @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                                  & ~ ( ( Xa2 = Mi2 )
% 9.49/5.26                                      | ( Xa2 = Ma2 ) ) )
% 9.49/5.26                                @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 9.49/5.26                                @ one_one_nat ) ) )
% 9.49/5.26                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3085_vebt__insert_Opelims,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat,Y2: vEBT_VEBT] :
% 9.49/5.26        ( ( ( vEBT_vebt_insert @ X @ Xa2 )
% 9.49/5.26          = Y2 )
% 9.49/5.26       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 9.49/5.26         => ( ! [A4: $o,B3: $o] :
% 9.49/5.26                ( ( X
% 9.49/5.26                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26               => ( ( ( ( Xa2 = zero_zero_nat )
% 9.49/5.26                     => ( Y2
% 9.49/5.26                        = ( vEBT_Leaf @ $true @ B3 ) ) )
% 9.49/5.26                    & ( ( Xa2 != zero_zero_nat )
% 9.49/5.26                     => ( ( ( Xa2 = one_one_nat )
% 9.49/5.26                         => ( Y2
% 9.49/5.26                            = ( vEBT_Leaf @ A4 @ $true ) ) )
% 9.49/5.26                        & ( ( Xa2 != one_one_nat )
% 9.49/5.26                         => ( Y2
% 9.49/5.26                            = ( vEBT_Leaf @ A4 @ B3 ) ) ) ) ) )
% 9.49/5.26                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa2 ) ) ) )
% 9.49/5.26           => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 9.49/5.26                  ( ( X
% 9.49/5.26                    = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S ) )
% 9.49/5.26                 => ( ( Y2
% 9.49/5.26                      = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S ) )
% 9.49/5.26                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S ) @ Xa2 ) ) ) )
% 9.49/5.26             => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 9.49/5.26                    ( ( X
% 9.49/5.26                      = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) )
% 9.49/5.26                   => ( ( Y2
% 9.49/5.26                        = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) )
% 9.49/5.26                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) @ Xa2 ) ) ) )
% 9.49/5.26               => ( ! [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.26                      ( ( X
% 9.49/5.26                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                     => ( ( Y2
% 9.49/5.26                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 9.49/5.26                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.26                        ( ( X
% 9.49/5.26                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                       => ( ( Y2
% 9.49/5.26                            = ( if_VEBT_VEBT
% 9.49/5.26                              @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                                & ~ ( ( Xa2 = Mi2 )
% 9.49/5.26                                    | ( Xa2 = Ma2 ) ) )
% 9.49/5.26                              @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va2 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 9.49/5.26                              @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) ) )
% 9.49/5.26                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3086_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Opelims,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 9.49/5.26        ( ( ( vEBT_T_p_r_e_d2 @ X @ Xa2 )
% 9.49/5.26          = Y2 )
% 9.49/5.26       => ( ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 9.49/5.26         => ( ! [Uu2: $o,Uv2: $o] :
% 9.49/5.26                ( ( X
% 9.49/5.26                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 9.49/5.26               => ( ( Xa2 = zero_zero_nat )
% 9.49/5.26                 => ( ( Y2 = one_one_nat )
% 9.49/5.26                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) ) ) ) )
% 9.49/5.26           => ( ! [A4: $o,Uw2: $o] :
% 9.49/5.26                  ( ( X
% 9.49/5.26                    = ( vEBT_Leaf @ A4 @ Uw2 ) )
% 9.49/5.26                 => ( ( Xa2
% 9.49/5.26                      = ( suc @ zero_zero_nat ) )
% 9.49/5.26                   => ( ( Y2 = one_one_nat )
% 9.49/5.26                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 9.49/5.26             => ( ! [A4: $o,B3: $o] :
% 9.49/5.26                    ( ( X
% 9.49/5.26                      = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26                   => ! [Va2: nat] :
% 9.49/5.26                        ( ( Xa2
% 9.49/5.26                          = ( suc @ ( suc @ Va2 ) ) )
% 9.49/5.26                       => ( ( Y2 = one_one_nat )
% 9.49/5.26                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ ( suc @ ( suc @ Va2 ) ) ) ) ) ) )
% 9.49/5.26               => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 9.49/5.26                      ( ( X
% 9.49/5.26                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 9.49/5.26                     => ( ( Y2 = one_one_nat )
% 9.49/5.26                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) @ Xa2 ) ) ) )
% 9.49/5.26                 => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 9.49/5.26                        ( ( X
% 9.49/5.26                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 9.49/5.26                       => ( ( Y2 = one_one_nat )
% 9.49/5.26                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Xa2 ) ) ) )
% 9.49/5.26                   => ( ! [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 9.49/5.26                          ( ( X
% 9.49/5.26                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 9.49/5.26                         => ( ( Y2 = one_one_nat )
% 9.49/5.26                           => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Xa2 ) ) ) )
% 9.49/5.26                     => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.26                            ( ( X
% 9.49/5.26                              = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                           => ( ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 9.49/5.26                                 => ( Y2 = one_one_nat ) )
% 9.49/5.26                                & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 9.49/5.26                                 => ( Y2
% 9.49/5.26                                    = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                                      @ ( if_nat
% 9.49/5.26                                        @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                           != none_nat )
% 9.49/5.26                                          & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 9.49/5.26                                        @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                        @ ( plus_plus_nat @ ( vEBT_T_p_r_e_d2 @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 9.49/5.26                                      @ one_one_nat ) ) ) )
% 9.49/5.26                             => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3087_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Opelims,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 9.49/5.26        ( ( ( vEBT_T_i_n_s_e_r_t2 @ X @ Xa2 )
% 9.49/5.26          = Y2 )
% 9.49/5.26       => ( ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 9.49/5.26         => ( ! [A4: $o,B3: $o] :
% 9.49/5.26                ( ( X
% 9.49/5.26                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26               => ( ( Y2 = one_one_nat )
% 9.49/5.26                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa2 ) ) ) )
% 9.49/5.26           => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 9.49/5.26                  ( ( X
% 9.49/5.26                    = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S ) )
% 9.49/5.26                 => ( ( Y2 = one_one_nat )
% 9.49/5.26                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S ) @ Xa2 ) ) ) )
% 9.49/5.26             => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 9.49/5.26                    ( ( X
% 9.49/5.26                      = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) )
% 9.49/5.26                   => ( ( Y2 = one_one_nat )
% 9.49/5.26                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) @ Xa2 ) ) ) )
% 9.49/5.26               => ( ! [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.26                      ( ( X
% 9.49/5.26                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                     => ( ( Y2 = one_one_nat )
% 9.49/5.26                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 9.49/5.26                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.26                        ( ( X
% 9.49/5.26                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                       => ( ( Y2
% 9.49/5.26                            = ( if_nat
% 9.49/5.26                              @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                                & ~ ( ( Xa2 = Mi2 )
% 9.49/5.26                                    | ( Xa2 = Ma2 ) ) )
% 9.49/5.26                              @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t2 @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 9.49/5.26                              @ one_one_nat ) )
% 9.49/5.26                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3088_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Opelims,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 9.49/5.26        ( ( ( vEBT_T_m_e_m_b_e_r @ X @ Xa2 )
% 9.49/5.26          = Y2 )
% 9.49/5.26       => ( ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 9.49/5.26         => ( ! [A4: $o,B3: $o] :
% 9.49/5.26                ( ( X
% 9.49/5.26                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26               => ( ( Y2
% 9.49/5.26                    = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa2 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 9.49/5.26                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa2 ) ) ) )
% 9.49/5.26           => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 9.49/5.26                  ( ( X
% 9.49/5.26                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 9.49/5.26                 => ( ( Y2
% 9.49/5.26                      = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.26                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 9.49/5.26             => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 9.49/5.26                    ( ( X
% 9.49/5.26                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 9.49/5.26                   => ( ( Y2
% 9.49/5.26                        = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.26                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 9.49/5.26               => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 9.49/5.26                      ( ( X
% 9.49/5.26                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 9.49/5.26                     => ( ( Y2
% 9.49/5.26                          = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.26                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 9.49/5.26                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.26                        ( ( X
% 9.49/5.26                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                       => ( ( Y2
% 9.49/5.26                            = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa2 = Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa2 = Ma2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ one_one_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_e_m_b_e_r @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) )
% 9.49/5.26                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3089_max__enat__simps_I2_J,axiom,
% 9.49/5.26      ! [Q2: extended_enat] :
% 9.49/5.26        ( ( ord_ma741700101516333627d_enat @ Q2 @ zero_z5237406670263579293d_enat )
% 9.49/5.26        = Q2 ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3090_max__enat__simps_I3_J,axiom,
% 9.49/5.26      ! [Q2: extended_enat] :
% 9.49/5.26        ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ Q2 )
% 9.49/5.26        = Q2 ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3091_set__bit__nonnegative__int__iff,axiom,
% 9.49/5.26      ! [N: nat,K: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se7879613467334960850it_int @ N @ K ) )
% 9.49/5.26        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3092_set__bit__negative__int__iff,axiom,
% 9.49/5.26      ! [N: nat,K: int] :
% 9.49/5.26        ( ( ord_less_int @ ( bit_se7879613467334960850it_int @ N @ K ) @ zero_zero_int )
% 9.49/5.26        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3093_imult__is__0,axiom,
% 9.49/5.26      ! [M: extended_enat,N: extended_enat] :
% 9.49/5.26        ( ( ( times_7803423173614009249d_enat @ M @ N )
% 9.49/5.26          = zero_z5237406670263579293d_enat )
% 9.49/5.26        = ( ( M = zero_z5237406670263579293d_enat )
% 9.49/5.26          | ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3094_zero__one__enat__neq_I1_J,axiom,
% 9.49/5.26      zero_z5237406670263579293d_enat != one_on7984719198319812577d_enat ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3095_unique__quotient__lemma__neg,axiom,
% 9.49/5.26      ! [B: int,Q5: int,R4: int,Q2: int,R: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 9.49/5.26       => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 9.49/5.26         => ( ( ord_less_int @ B @ R )
% 9.49/5.26           => ( ( ord_less_int @ B @ R4 )
% 9.49/5.26             => ( ord_less_eq_int @ Q2 @ Q5 ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3096_unique__quotient__lemma,axiom,
% 9.49/5.26      ! [B: int,Q5: int,R4: int,Q2: int,R: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 9.49/5.26       => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 9.49/5.26         => ( ( ord_less_int @ R4 @ B )
% 9.49/5.26           => ( ( ord_less_int @ R @ B )
% 9.49/5.26             => ( ord_less_eq_int @ Q5 @ Q2 ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3097_zdiv__mono2__neg__lemma,axiom,
% 9.49/5.26      ! [B: int,Q2: int,R: int,B5: int,Q5: int,R4: int] :
% 9.49/5.26        ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R )
% 9.49/5.26          = ( plus_plus_int @ ( times_times_int @ B5 @ Q5 ) @ R4 ) )
% 9.49/5.26       => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B5 @ Q5 ) @ R4 ) @ zero_zero_int )
% 9.49/5.26         => ( ( ord_less_int @ R @ B )
% 9.49/5.26           => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 9.49/5.26             => ( ( ord_less_int @ zero_zero_int @ B5 )
% 9.49/5.26               => ( ( ord_less_eq_int @ B5 @ B )
% 9.49/5.26                 => ( ord_less_eq_int @ Q5 @ Q2 ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3098_zdiv__mono2__lemma,axiom,
% 9.49/5.26      ! [B: int,Q2: int,R: int,B5: int,Q5: int,R4: int] :
% 9.49/5.26        ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R )
% 9.49/5.26          = ( plus_plus_int @ ( times_times_int @ B5 @ Q5 ) @ R4 ) )
% 9.49/5.26       => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B5 @ Q5 ) @ R4 ) )
% 9.49/5.26         => ( ( ord_less_int @ R4 @ B5 )
% 9.49/5.26           => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 9.49/5.26             => ( ( ord_less_int @ zero_zero_int @ B5 )
% 9.49/5.26               => ( ( ord_less_eq_int @ B5 @ B )
% 9.49/5.26                 => ( ord_less_eq_int @ Q2 @ Q5 ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3099_q__pos__lemma,axiom,
% 9.49/5.26      ! [B5: int,Q5: int,R4: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B5 @ Q5 ) @ R4 ) )
% 9.49/5.26       => ( ( ord_less_int @ R4 @ B5 )
% 9.49/5.26         => ( ( ord_less_int @ zero_zero_int @ B5 )
% 9.49/5.26           => ( ord_less_eq_int @ zero_zero_int @ Q5 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3100_set__bit__greater__eq,axiom,
% 9.49/5.26      ! [K: int,N: nat] : ( ord_less_eq_int @ K @ ( bit_se7879613467334960850it_int @ N @ K ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3101_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Opelims,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 9.49/5.26        ( ( ( vEBT_T_m_e_m_b_e_r2 @ X @ Xa2 )
% 9.49/5.26          = Y2 )
% 9.49/5.26       => ( ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 9.49/5.26         => ( ! [A4: $o,B3: $o] :
% 9.49/5.26                ( ( X
% 9.49/5.26                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26               => ( ( Y2 = one_one_nat )
% 9.49/5.26                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa2 ) ) ) )
% 9.49/5.26           => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 9.49/5.26                  ( ( X
% 9.49/5.26                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 9.49/5.26                 => ( ( Y2 = one_one_nat )
% 9.49/5.26                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 9.49/5.26             => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 9.49/5.26                    ( ( X
% 9.49/5.26                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 9.49/5.26                   => ( ( Y2 = one_one_nat )
% 9.49/5.26                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 9.49/5.26               => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 9.49/5.26                      ( ( X
% 9.49/5.26                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 9.49/5.26                     => ( ( Y2 = one_one_nat )
% 9.49/5.26                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 9.49/5.26                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.26                        ( ( X
% 9.49/5.26                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                       => ( ( Y2
% 9.49/5.26                            = ( plus_plus_nat @ one_one_nat
% 9.49/5.26                              @ ( if_nat @ ( Xa2 = Mi2 ) @ zero_zero_nat
% 9.49/5.26                                @ ( if_nat @ ( Xa2 = Ma2 ) @ zero_zero_nat
% 9.49/5.26                                  @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ zero_zero_nat
% 9.49/5.26                                    @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ zero_zero_nat
% 9.49/5.26                                      @ ( if_nat
% 9.49/5.26                                        @ ( ( ord_less_nat @ Mi2 @ Xa2 )
% 9.49/5.26                                          & ( ord_less_nat @ Xa2 @ Ma2 ) )
% 9.49/5.26                                        @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( vEBT_T_m_e_m_b_e_r2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ zero_zero_nat )
% 9.49/5.26                                        @ zero_zero_nat ) ) ) ) ) ) )
% 9.49/5.26                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3102_zle__diff1__eq,axiom,
% 9.49/5.26      ! [W: int,Z: int] :
% 9.49/5.26        ( ( ord_less_eq_int @ W @ ( minus_minus_int @ Z @ one_one_int ) )
% 9.49/5.26        = ( ord_less_int @ W @ Z ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3103_vebt__member_Opelims_I1_J,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 9.49/5.26        ( ( ( vEBT_vebt_member @ X @ Xa2 )
% 9.49/5.26          = Y2 )
% 9.49/5.26       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 9.49/5.26         => ( ! [A4: $o,B3: $o] :
% 9.49/5.26                ( ( X
% 9.49/5.26                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26               => ( ( Y2
% 9.49/5.26                    = ( ( ( Xa2 = zero_zero_nat )
% 9.49/5.26                       => A4 )
% 9.49/5.26                      & ( ( Xa2 != zero_zero_nat )
% 9.49/5.26                       => ( ( ( Xa2 = one_one_nat )
% 9.49/5.26                           => B3 )
% 9.49/5.26                          & ( Xa2 = one_one_nat ) ) ) ) )
% 9.49/5.26                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa2 ) ) ) )
% 9.49/5.26           => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 9.49/5.26                  ( ( X
% 9.49/5.26                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 9.49/5.26                 => ( ~ Y2
% 9.49/5.26                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 9.49/5.26             => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 9.49/5.26                    ( ( X
% 9.49/5.26                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 9.49/5.26                   => ( ~ Y2
% 9.49/5.26                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 9.49/5.26               => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 9.49/5.26                      ( ( X
% 9.49/5.26                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 9.49/5.26                     => ( ~ Y2
% 9.49/5.26                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 9.49/5.26                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.26                        ( ( X
% 9.49/5.26                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                       => ( ( Y2
% 9.49/5.26                            = ( ( Xa2 != Mi2 )
% 9.49/5.26                             => ( ( Xa2 != Ma2 )
% 9.49/5.26                               => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 9.49/5.26                                  & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 9.49/5.26                                   => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 9.49/5.26                                      & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 9.49/5.26                                       => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                                           => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) )
% 9.49/5.26                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3104_vebt__member_Opelims_I3_J,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat] :
% 9.49/5.26        ( ~ ( vEBT_vebt_member @ X @ Xa2 )
% 9.49/5.26       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 9.49/5.26         => ( ! [A4: $o,B3: $o] :
% 9.49/5.26                ( ( X
% 9.49/5.26                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26               => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa2 ) )
% 9.49/5.26                 => ( ( ( Xa2 = zero_zero_nat )
% 9.49/5.26                     => A4 )
% 9.49/5.26                    & ( ( Xa2 != zero_zero_nat )
% 9.49/5.26                     => ( ( ( Xa2 = one_one_nat )
% 9.49/5.26                         => B3 )
% 9.49/5.26                        & ( Xa2 = one_one_nat ) ) ) ) ) )
% 9.49/5.26           => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 9.49/5.26                  ( ( X
% 9.49/5.26                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 9.49/5.26                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) )
% 9.49/5.26             => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 9.49/5.26                    ( ( X
% 9.49/5.26                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 9.49/5.26                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) )
% 9.49/5.26               => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 9.49/5.26                      ( ( X
% 9.49/5.26                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 9.49/5.26                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) )
% 9.49/5.26                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.26                        ( ( X
% 9.49/5.26                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) )
% 9.49/5.26                         => ( ( Xa2 != Mi2 )
% 9.49/5.26                           => ( ( Xa2 != Ma2 )
% 9.49/5.26                             => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 9.49/5.26                                & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 9.49/5.26                                 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 9.49/5.26                                    & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 9.49/5.26                                     => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                                         => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3105_VEBT__internal_Onaive__member_Opelims_I3_J,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat] :
% 9.49/5.26        ( ~ ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 9.49/5.26       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 9.49/5.26         => ( ! [A4: $o,B3: $o] :
% 9.49/5.26                ( ( X
% 9.49/5.26                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26               => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa2 ) )
% 9.49/5.26                 => ( ( ( Xa2 = zero_zero_nat )
% 9.49/5.26                     => A4 )
% 9.49/5.26                    & ( ( Xa2 != zero_zero_nat )
% 9.49/5.26                     => ( ( ( Xa2 = one_one_nat )
% 9.49/5.26                         => B3 )
% 9.49/5.26                        & ( Xa2 = one_one_nat ) ) ) ) ) )
% 9.49/5.26           => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 9.49/5.26                  ( ( X
% 9.49/5.26                    = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 9.49/5.26                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa2 ) ) )
% 9.49/5.26             => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 9.49/5.26                    ( ( X
% 9.49/5.26                      = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) )
% 9.49/5.26                   => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) @ Xa2 ) )
% 9.49/5.26                     => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                         => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3106_VEBT__internal_Onaive__member_Opelims_I2_J,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat] :
% 9.49/5.26        ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 9.49/5.26       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 9.49/5.26         => ( ! [A4: $o,B3: $o] :
% 9.49/5.26                ( ( X
% 9.49/5.26                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26               => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa2 ) )
% 9.49/5.26                 => ~ ( ( ( Xa2 = zero_zero_nat )
% 9.49/5.26                       => A4 )
% 9.49/5.26                      & ( ( Xa2 != zero_zero_nat )
% 9.49/5.26                       => ( ( ( Xa2 = one_one_nat )
% 9.49/5.26                           => B3 )
% 9.49/5.26                          & ( Xa2 = one_one_nat ) ) ) ) ) )
% 9.49/5.26           => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 9.49/5.26                  ( ( X
% 9.49/5.26                    = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) )
% 9.49/5.26                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) @ Xa2 ) )
% 9.49/5.26                   => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                         => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3107_VEBT__internal_Onaive__member_Opelims_I1_J,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 9.49/5.26        ( ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 9.49/5.26          = Y2 )
% 9.49/5.26       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 9.49/5.26         => ( ! [A4: $o,B3: $o] :
% 9.49/5.26                ( ( X
% 9.49/5.26                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26               => ( ( Y2
% 9.49/5.26                    = ( ( ( Xa2 = zero_zero_nat )
% 9.49/5.26                       => A4 )
% 9.49/5.26                      & ( ( Xa2 != zero_zero_nat )
% 9.49/5.26                       => ( ( ( Xa2 = one_one_nat )
% 9.49/5.26                           => B3 )
% 9.49/5.26                          & ( Xa2 = one_one_nat ) ) ) ) )
% 9.49/5.26                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa2 ) ) ) )
% 9.49/5.26           => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 9.49/5.26                  ( ( X
% 9.49/5.26                    = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 9.49/5.26                 => ( ~ Y2
% 9.49/5.26                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 9.49/5.26             => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 9.49/5.26                    ( ( X
% 9.49/5.26                      = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) )
% 9.49/5.26                   => ( ( Y2
% 9.49/5.26                        = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                           => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) )
% 9.49/5.26                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) @ Xa2 ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3108_vebt__member_Opelims_I2_J,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat] :
% 9.49/5.26        ( ( vEBT_vebt_member @ X @ Xa2 )
% 9.49/5.26       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 9.49/5.26         => ( ! [A4: $o,B3: $o] :
% 9.49/5.26                ( ( X
% 9.49/5.26                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.26               => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa2 ) )
% 9.49/5.26                 => ~ ( ( ( Xa2 = zero_zero_nat )
% 9.49/5.26                       => A4 )
% 9.49/5.26                      & ( ( Xa2 != zero_zero_nat )
% 9.49/5.26                       => ( ( ( Xa2 = one_one_nat )
% 9.49/5.26                           => B3 )
% 9.49/5.26                          & ( Xa2 = one_one_nat ) ) ) ) ) )
% 9.49/5.26           => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.26                  ( ( X
% 9.49/5.26                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 9.49/5.26                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) )
% 9.49/5.26                   => ~ ( ( Xa2 != Mi2 )
% 9.49/5.26                       => ( ( Xa2 != Ma2 )
% 9.49/5.26                         => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 9.49/5.26                            & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 9.49/5.26                             => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 9.49/5.26                                & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 9.49/5.26                                 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                                     => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                                    & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3109_double__eq__0__iff,axiom,
% 9.49/5.26      ! [A: real] :
% 9.49/5.26        ( ( ( plus_plus_real @ A @ A )
% 9.49/5.26          = zero_zero_real )
% 9.49/5.26        = ( A = zero_zero_real ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3110_double__eq__0__iff,axiom,
% 9.49/5.26      ! [A: rat] :
% 9.49/5.26        ( ( ( plus_plus_rat @ A @ A )
% 9.49/5.26          = zero_zero_rat )
% 9.49/5.26        = ( A = zero_zero_rat ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3111_double__eq__0__iff,axiom,
% 9.49/5.26      ! [A: int] :
% 9.49/5.26        ( ( ( plus_plus_int @ A @ A )
% 9.49/5.26          = zero_zero_int )
% 9.49/5.26        = ( A = zero_zero_int ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3112_minus__int__code_I1_J,axiom,
% 9.49/5.26      ! [K: int] :
% 9.49/5.26        ( ( minus_minus_int @ K @ zero_zero_int )
% 9.49/5.26        = K ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3113_int__distrib_I4_J,axiom,
% 9.49/5.26      ! [W: int,Z1: int,Z22: int] :
% 9.49/5.26        ( ( times_times_int @ W @ ( minus_minus_int @ Z1 @ Z22 ) )
% 9.49/5.26        = ( minus_minus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3114_int__distrib_I3_J,axiom,
% 9.49/5.26      ! [Z1: int,Z22: int,W: int] :
% 9.49/5.26        ( ( times_times_int @ ( minus_minus_int @ Z1 @ Z22 ) @ W )
% 9.49/5.26        = ( minus_minus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3115_int__le__induct,axiom,
% 9.49/5.26      ! [I2: int,K: int,P: int > $o] :
% 9.49/5.26        ( ( ord_less_eq_int @ I2 @ K )
% 9.49/5.26       => ( ( P @ K )
% 9.49/5.26         => ( ! [I4: int] :
% 9.49/5.26                ( ( ord_less_eq_int @ I4 @ K )
% 9.49/5.26               => ( ( P @ I4 )
% 9.49/5.26                 => ( P @ ( minus_minus_int @ I4 @ one_one_int ) ) ) )
% 9.49/5.26           => ( P @ I2 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3116_int__less__induct,axiom,
% 9.49/5.26      ! [I2: int,K: int,P: int > $o] :
% 9.49/5.26        ( ( ord_less_int @ I2 @ K )
% 9.49/5.26       => ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
% 9.49/5.26         => ( ! [I4: int] :
% 9.49/5.26                ( ( ord_less_int @ I4 @ K )
% 9.49/5.26               => ( ( P @ I4 )
% 9.49/5.26                 => ( P @ ( minus_minus_int @ I4 @ one_one_int ) ) ) )
% 9.49/5.26           => ( P @ I2 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3117_int__induct,axiom,
% 9.49/5.26      ! [P: int > $o,K: int,I2: int] :
% 9.49/5.26        ( ( P @ K )
% 9.49/5.26       => ( ! [I4: int] :
% 9.49/5.26              ( ( ord_less_eq_int @ K @ I4 )
% 9.49/5.26             => ( ( P @ I4 )
% 9.49/5.26               => ( P @ ( plus_plus_int @ I4 @ one_one_int ) ) ) )
% 9.49/5.26         => ( ! [I4: int] :
% 9.49/5.26                ( ( ord_less_eq_int @ I4 @ K )
% 9.49/5.26               => ( ( P @ I4 )
% 9.49/5.26                 => ( P @ ( minus_minus_int @ I4 @ one_one_int ) ) ) )
% 9.49/5.26           => ( P @ I2 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3118_VEBT__internal_Omembermima_Opelims_I3_J,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat] :
% 9.49/5.26        ( ~ ( vEBT_VEBT_membermima @ X @ Xa2 )
% 9.49/5.26       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 9.49/5.26         => ( ! [Uu2: $o,Uv2: $o] :
% 9.49/5.26                ( ( X
% 9.49/5.26                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 9.49/5.26               => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) )
% 9.49/5.26           => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 9.49/5.26                  ( ( X
% 9.49/5.26                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 9.49/5.26                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) )
% 9.49/5.26             => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 9.49/5.26                    ( ( X
% 9.49/5.26                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 9.49/5.26                   => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) )
% 9.49/5.26                     => ( ( Xa2 = Mi2 )
% 9.49/5.26                        | ( Xa2 = Ma2 ) ) ) )
% 9.49/5.26               => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 9.49/5.26                      ( ( X
% 9.49/5.26                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 9.49/5.26                     => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) @ Xa2 ) )
% 9.49/5.26                       => ( ( Xa2 = Mi2 )
% 9.49/5.26                          | ( Xa2 = Ma2 )
% 9.49/5.26                          | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                             => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                            & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) )
% 9.49/5.26                 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 9.49/5.26                        ( ( X
% 9.49/5.26                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 9.49/5.26                       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) @ Xa2 ) )
% 9.49/5.26                         => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                             => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                            & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3119_VEBT__internal_Omembermima_Opelims_I1_J,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 9.49/5.26        ( ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 9.49/5.26          = Y2 )
% 9.49/5.26       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 9.49/5.26         => ( ! [Uu2: $o,Uv2: $o] :
% 9.49/5.26                ( ( X
% 9.49/5.26                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 9.49/5.26               => ( ~ Y2
% 9.49/5.26                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 9.49/5.26           => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 9.49/5.26                  ( ( X
% 9.49/5.26                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 9.49/5.26                 => ( ~ Y2
% 9.49/5.26                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) ) )
% 9.49/5.26             => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 9.49/5.26                    ( ( X
% 9.49/5.26                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 9.49/5.26                   => ( ( Y2
% 9.49/5.26                        = ( ( Xa2 = Mi2 )
% 9.49/5.26                          | ( Xa2 = Ma2 ) ) )
% 9.49/5.26                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) ) ) )
% 9.49/5.26               => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 9.49/5.26                      ( ( X
% 9.49/5.26                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 9.49/5.26                     => ( ( Y2
% 9.49/5.26                          = ( ( Xa2 = Mi2 )
% 9.49/5.26                            | ( Xa2 = Ma2 )
% 9.49/5.26                            | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 9.49/5.26                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) @ Xa2 ) ) ) )
% 9.49/5.26                 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 9.49/5.26                        ( ( X
% 9.49/5.26                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 9.49/5.26                       => ( ( Y2
% 9.49/5.26                            = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) )
% 9.49/5.26                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3120_VEBT__internal_Omembermima_Opelims_I2_J,axiom,
% 9.49/5.26      ! [X: vEBT_VEBT,Xa2: nat] :
% 9.49/5.26        ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 9.49/5.26       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 9.49/5.26         => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 9.49/5.26                ( ( X
% 9.49/5.26                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 9.49/5.26               => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) )
% 9.49/5.26                 => ~ ( ( Xa2 = Mi2 )
% 9.49/5.26                      | ( Xa2 = Ma2 ) ) ) )
% 9.49/5.26           => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 9.49/5.26                  ( ( X
% 9.49/5.26                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 9.49/5.26                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) @ Xa2 ) )
% 9.49/5.26                   => ~ ( ( Xa2 = Mi2 )
% 9.49/5.26                        | ( Xa2 = Ma2 )
% 9.49/5.26                        | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                           => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) )
% 9.49/5.26             => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 9.49/5.26                    ( ( X
% 9.49/5.26                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 9.49/5.26                   => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) @ Xa2 ) )
% 9.49/5.26                     => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 9.49/5.26                           => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.26                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3121_atLeastatMost__empty,axiom,
% 9.49/5.26      ! [B: rat,A: rat] :
% 9.49/5.26        ( ( ord_less_rat @ B @ A )
% 9.49/5.26       => ( ( set_or633870826150836451st_rat @ A @ B )
% 9.49/5.26          = bot_bot_set_rat ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3122_atLeastatMost__empty,axiom,
% 9.49/5.26      ! [B: num,A: num] :
% 9.49/5.26        ( ( ord_less_num @ B @ A )
% 9.49/5.26       => ( ( set_or7049704709247886629st_num @ A @ B )
% 9.49/5.26          = bot_bot_set_num ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3123_atLeastatMost__empty,axiom,
% 9.49/5.26      ! [B: nat,A: nat] :
% 9.49/5.26        ( ( ord_less_nat @ B @ A )
% 9.49/5.26       => ( ( set_or1269000886237332187st_nat @ A @ B )
% 9.49/5.26          = bot_bot_set_nat ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3124_atLeastatMost__empty,axiom,
% 9.49/5.26      ! [B: int,A: int] :
% 9.49/5.26        ( ( ord_less_int @ B @ A )
% 9.49/5.26       => ( ( set_or1266510415728281911st_int @ A @ B )
% 9.49/5.26          = bot_bot_set_int ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3125_atLeastatMost__empty,axiom,
% 9.49/5.26      ! [B: real,A: real] :
% 9.49/5.26        ( ( ord_less_real @ B @ A )
% 9.49/5.26       => ( ( set_or1222579329274155063t_real @ A @ B )
% 9.49/5.26          = bot_bot_set_real ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3126_atLeastatMost__subset__iff,axiom,
% 9.49/5.26      ! [A: set_real,B: set_real,C: set_real,D2: set_real] :
% 9.49/5.26        ( ( ord_le3558479182127378552t_real @ ( set_or7743017856606604397t_real @ A @ B ) @ ( set_or7743017856606604397t_real @ C @ D2 ) )
% 9.49/5.26        = ( ~ ( ord_less_eq_set_real @ A @ B )
% 9.49/5.26          | ( ( ord_less_eq_set_real @ C @ A )
% 9.49/5.26            & ( ord_less_eq_set_real @ B @ D2 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3127_atLeastatMost__subset__iff,axiom,
% 9.49/5.26      ! [A: set_nat,B: set_nat,C: set_nat,D2: set_nat] :
% 9.49/5.26        ( ( ord_le6893508408891458716et_nat @ ( set_or4548717258645045905et_nat @ A @ B ) @ ( set_or4548717258645045905et_nat @ C @ D2 ) )
% 9.49/5.26        = ( ~ ( ord_less_eq_set_nat @ A @ B )
% 9.49/5.26          | ( ( ord_less_eq_set_nat @ C @ A )
% 9.49/5.26            & ( ord_less_eq_set_nat @ B @ D2 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3128_atLeastatMost__subset__iff,axiom,
% 9.49/5.26      ! [A: num,B: num,C: num,D2: num] :
% 9.49/5.26        ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D2 ) )
% 9.49/5.26        = ( ~ ( ord_less_eq_num @ A @ B )
% 9.49/5.26          | ( ( ord_less_eq_num @ C @ A )
% 9.49/5.26            & ( ord_less_eq_num @ B @ D2 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3129_atLeastatMost__subset__iff,axiom,
% 9.49/5.26      ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.49/5.26        ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D2 ) )
% 9.49/5.26        = ( ~ ( ord_less_eq_nat @ A @ B )
% 9.49/5.26          | ( ( ord_less_eq_nat @ C @ A )
% 9.49/5.26            & ( ord_less_eq_nat @ B @ D2 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3130_atLeastatMost__subset__iff,axiom,
% 9.49/5.26      ! [A: int,B: int,C: int,D2: int] :
% 9.49/5.26        ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D2 ) )
% 9.49/5.26        = ( ~ ( ord_less_eq_int @ A @ B )
% 9.49/5.26          | ( ( ord_less_eq_int @ C @ A )
% 9.49/5.26            & ( ord_less_eq_int @ B @ D2 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3131_atLeastatMost__subset__iff,axiom,
% 9.49/5.26      ! [A: real,B: real,C: real,D2: real] :
% 9.49/5.26        ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D2 ) )
% 9.49/5.26        = ( ~ ( ord_less_eq_real @ A @ B )
% 9.49/5.26          | ( ( ord_less_eq_real @ C @ A )
% 9.49/5.26            & ( ord_less_eq_real @ B @ D2 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3132_atLeastatMost__empty__iff,axiom,
% 9.49/5.26      ! [A: set_real,B: set_real] :
% 9.49/5.26        ( ( ( set_or7743017856606604397t_real @ A @ B )
% 9.49/5.26          = bot_bot_set_set_real )
% 9.49/5.26        = ( ~ ( ord_less_eq_set_real @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3133_atLeastatMost__empty__iff,axiom,
% 9.49/5.26      ! [A: set_nat,B: set_nat] :
% 9.49/5.26        ( ( ( set_or4548717258645045905et_nat @ A @ B )
% 9.49/5.26          = bot_bot_set_set_nat )
% 9.49/5.26        = ( ~ ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3134_atLeastatMost__empty__iff,axiom,
% 9.49/5.26      ! [A: num,B: num] :
% 9.49/5.26        ( ( ( set_or7049704709247886629st_num @ A @ B )
% 9.49/5.26          = bot_bot_set_num )
% 9.49/5.26        = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3135_atLeastatMost__empty__iff,axiom,
% 9.49/5.26      ! [A: nat,B: nat] :
% 9.49/5.26        ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 9.49/5.26          = bot_bot_set_nat )
% 9.49/5.26        = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3136_atLeastatMost__empty__iff,axiom,
% 9.49/5.26      ! [A: int,B: int] :
% 9.49/5.26        ( ( ( set_or1266510415728281911st_int @ A @ B )
% 9.49/5.26          = bot_bot_set_int )
% 9.49/5.26        = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3137_atLeastatMost__empty__iff,axiom,
% 9.49/5.26      ! [A: real,B: real] :
% 9.49/5.26        ( ( ( set_or1222579329274155063t_real @ A @ B )
% 9.49/5.26          = bot_bot_set_real )
% 9.49/5.26        = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3138_atLeastatMost__empty__iff2,axiom,
% 9.49/5.26      ! [A: set_real,B: set_real] :
% 9.49/5.26        ( ( bot_bot_set_set_real
% 9.49/5.26          = ( set_or7743017856606604397t_real @ A @ B ) )
% 9.49/5.26        = ( ~ ( ord_less_eq_set_real @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3139_atLeastatMost__empty__iff2,axiom,
% 9.49/5.26      ! [A: set_nat,B: set_nat] :
% 9.49/5.26        ( ( bot_bot_set_set_nat
% 9.49/5.26          = ( set_or4548717258645045905et_nat @ A @ B ) )
% 9.49/5.26        = ( ~ ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3140_atLeastatMost__empty__iff2,axiom,
% 9.49/5.26      ! [A: num,B: num] :
% 9.49/5.26        ( ( bot_bot_set_num
% 9.49/5.26          = ( set_or7049704709247886629st_num @ A @ B ) )
% 9.49/5.26        = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3141_atLeastatMost__empty__iff2,axiom,
% 9.49/5.26      ! [A: nat,B: nat] :
% 9.49/5.26        ( ( bot_bot_set_nat
% 9.49/5.26          = ( set_or1269000886237332187st_nat @ A @ B ) )
% 9.49/5.26        = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3142_atLeastatMost__empty__iff2,axiom,
% 9.49/5.26      ! [A: int,B: int] :
% 9.49/5.26        ( ( bot_bot_set_int
% 9.49/5.26          = ( set_or1266510415728281911st_int @ A @ B ) )
% 9.49/5.26        = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3143_atLeastatMost__empty__iff2,axiom,
% 9.49/5.26      ! [A: real,B: real] :
% 9.49/5.26        ( ( bot_bot_set_real
% 9.49/5.26          = ( set_or1222579329274155063t_real @ A @ B ) )
% 9.49/5.26        = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3144_decr__mult__lemma,axiom,
% 9.49/5.26      ! [D2: int,P: int > $o,K: int] :
% 9.49/5.26        ( ( ord_less_int @ zero_zero_int @ D2 )
% 9.49/5.26       => ( ! [X3: int] :
% 9.49/5.26              ( ( P @ X3 )
% 9.49/5.26             => ( P @ ( minus_minus_int @ X3 @ D2 ) ) )
% 9.49/5.26         => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 9.49/5.26           => ! [X5: int] :
% 9.49/5.26                ( ( P @ X5 )
% 9.49/5.26               => ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K @ D2 ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3145_Icc__eq__Icc,axiom,
% 9.49/5.26      ! [L2: set_real,H2: set_real,L3: set_real,H3: set_real] :
% 9.49/5.26        ( ( ( set_or7743017856606604397t_real @ L2 @ H2 )
% 9.49/5.26          = ( set_or7743017856606604397t_real @ L3 @ H3 ) )
% 9.49/5.26        = ( ( ( L2 = L3 )
% 9.49/5.26            & ( H2 = H3 ) )
% 9.49/5.26          | ( ~ ( ord_less_eq_set_real @ L2 @ H2 )
% 9.49/5.26            & ~ ( ord_less_eq_set_real @ L3 @ H3 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3146_Icc__eq__Icc,axiom,
% 9.49/5.26      ! [L2: set_nat,H2: set_nat,L3: set_nat,H3: set_nat] :
% 9.49/5.26        ( ( ( set_or4548717258645045905et_nat @ L2 @ H2 )
% 9.49/5.26          = ( set_or4548717258645045905et_nat @ L3 @ H3 ) )
% 9.49/5.26        = ( ( ( L2 = L3 )
% 9.49/5.26            & ( H2 = H3 ) )
% 9.49/5.26          | ( ~ ( ord_less_eq_set_nat @ L2 @ H2 )
% 9.49/5.26            & ~ ( ord_less_eq_set_nat @ L3 @ H3 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3147_Icc__eq__Icc,axiom,
% 9.49/5.26      ! [L2: num,H2: num,L3: num,H3: num] :
% 9.49/5.26        ( ( ( set_or7049704709247886629st_num @ L2 @ H2 )
% 9.49/5.26          = ( set_or7049704709247886629st_num @ L3 @ H3 ) )
% 9.49/5.26        = ( ( ( L2 = L3 )
% 9.49/5.26            & ( H2 = H3 ) )
% 9.49/5.26          | ( ~ ( ord_less_eq_num @ L2 @ H2 )
% 9.49/5.26            & ~ ( ord_less_eq_num @ L3 @ H3 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3148_Icc__eq__Icc,axiom,
% 9.49/5.26      ! [L2: nat,H2: nat,L3: nat,H3: nat] :
% 9.49/5.26        ( ( ( set_or1269000886237332187st_nat @ L2 @ H2 )
% 9.49/5.26          = ( set_or1269000886237332187st_nat @ L3 @ H3 ) )
% 9.49/5.26        = ( ( ( L2 = L3 )
% 9.49/5.26            & ( H2 = H3 ) )
% 9.49/5.26          | ( ~ ( ord_less_eq_nat @ L2 @ H2 )
% 9.49/5.26            & ~ ( ord_less_eq_nat @ L3 @ H3 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3149_Icc__eq__Icc,axiom,
% 9.49/5.26      ! [L2: int,H2: int,L3: int,H3: int] :
% 9.49/5.26        ( ( ( set_or1266510415728281911st_int @ L2 @ H2 )
% 9.49/5.26          = ( set_or1266510415728281911st_int @ L3 @ H3 ) )
% 9.49/5.26        = ( ( ( L2 = L3 )
% 9.49/5.26            & ( H2 = H3 ) )
% 9.49/5.26          | ( ~ ( ord_less_eq_int @ L2 @ H2 )
% 9.49/5.26            & ~ ( ord_less_eq_int @ L3 @ H3 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3150_Icc__eq__Icc,axiom,
% 9.49/5.26      ! [L2: real,H2: real,L3: real,H3: real] :
% 9.49/5.26        ( ( ( set_or1222579329274155063t_real @ L2 @ H2 )
% 9.49/5.26          = ( set_or1222579329274155063t_real @ L3 @ H3 ) )
% 9.49/5.26        = ( ( ( L2 = L3 )
% 9.49/5.26            & ( H2 = H3 ) )
% 9.49/5.26          | ( ~ ( ord_less_eq_real @ L2 @ H2 )
% 9.49/5.26            & ~ ( ord_less_eq_real @ L3 @ H3 ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3151_atLeastAtMost__iff,axiom,
% 9.49/5.26      ! [I2: set_real,L2: set_real,U: set_real] :
% 9.49/5.26        ( ( member_set_real @ I2 @ ( set_or7743017856606604397t_real @ L2 @ U ) )
% 9.49/5.26        = ( ( ord_less_eq_set_real @ L2 @ I2 )
% 9.49/5.26          & ( ord_less_eq_set_real @ I2 @ U ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3152_atLeastAtMost__iff,axiom,
% 9.49/5.26      ! [I2: set_nat,L2: set_nat,U: set_nat] :
% 9.49/5.26        ( ( member_set_nat @ I2 @ ( set_or4548717258645045905et_nat @ L2 @ U ) )
% 9.49/5.26        = ( ( ord_less_eq_set_nat @ L2 @ I2 )
% 9.49/5.26          & ( ord_less_eq_set_nat @ I2 @ U ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3153_atLeastAtMost__iff,axiom,
% 9.49/5.26      ! [I2: num,L2: num,U: num] :
% 9.49/5.26        ( ( member_num @ I2 @ ( set_or7049704709247886629st_num @ L2 @ U ) )
% 9.49/5.26        = ( ( ord_less_eq_num @ L2 @ I2 )
% 9.49/5.26          & ( ord_less_eq_num @ I2 @ U ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3154_atLeastAtMost__iff,axiom,
% 9.49/5.26      ! [I2: nat,L2: nat,U: nat] :
% 9.49/5.26        ( ( member_nat @ I2 @ ( set_or1269000886237332187st_nat @ L2 @ U ) )
% 9.49/5.26        = ( ( ord_less_eq_nat @ L2 @ I2 )
% 9.49/5.26          & ( ord_less_eq_nat @ I2 @ U ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3155_atLeastAtMost__iff,axiom,
% 9.49/5.26      ! [I2: int,L2: int,U: int] :
% 9.49/5.26        ( ( member_int @ I2 @ ( set_or1266510415728281911st_int @ L2 @ U ) )
% 9.49/5.26        = ( ( ord_less_eq_int @ L2 @ I2 )
% 9.49/5.26          & ( ord_less_eq_int @ I2 @ U ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3156_atLeastAtMost__iff,axiom,
% 9.49/5.26      ! [I2: real,L2: real,U: real] :
% 9.49/5.26        ( ( member_real @ I2 @ ( set_or1222579329274155063t_real @ L2 @ U ) )
% 9.49/5.26        = ( ( ord_less_eq_real @ L2 @ I2 )
% 9.49/5.26          & ( ord_less_eq_real @ I2 @ U ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3157_aset_I2_J,axiom,
% 9.49/5.26      ! [D4: int,A2: set_int,P: int > $o,Q: int > $o] :
% 9.49/5.26        ( ! [X3: int] :
% 9.49/5.26            ( ! [Xa: int] :
% 9.49/5.26                ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 9.49/5.26               => ! [Xb2: int] :
% 9.49/5.26                    ( ( member_int @ Xb2 @ A2 )
% 9.49/5.26                   => ( X3
% 9.49/5.26                     != ( minus_minus_int @ Xb2 @ Xa ) ) ) )
% 9.49/5.26           => ( ( P @ X3 )
% 9.49/5.26             => ( P @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 9.49/5.26       => ( ! [X3: int] :
% 9.49/5.26              ( ! [Xa: int] :
% 9.49/5.26                  ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 9.49/5.26                 => ! [Xb2: int] :
% 9.49/5.26                      ( ( member_int @ Xb2 @ A2 )
% 9.49/5.26                     => ( X3
% 9.49/5.26                       != ( minus_minus_int @ Xb2 @ Xa ) ) ) )
% 9.49/5.26             => ( ( Q @ X3 )
% 9.49/5.26               => ( Q @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 9.49/5.26         => ! [X5: int] :
% 9.49/5.26              ( ! [Xa3: int] :
% 9.49/5.26                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 9.49/5.26                 => ! [Xb3: int] :
% 9.49/5.26                      ( ( member_int @ Xb3 @ A2 )
% 9.49/5.26                     => ( X5
% 9.49/5.26                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 9.49/5.26             => ( ( ( P @ X5 )
% 9.49/5.26                  | ( Q @ X5 ) )
% 9.49/5.26               => ( ( P @ ( plus_plus_int @ X5 @ D4 ) )
% 9.49/5.26                  | ( Q @ ( plus_plus_int @ X5 @ D4 ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3158_aset_I1_J,axiom,
% 9.49/5.26      ! [D4: int,A2: set_int,P: int > $o,Q: int > $o] :
% 9.49/5.26        ( ! [X3: int] :
% 9.49/5.26            ( ! [Xa: int] :
% 9.49/5.26                ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 9.49/5.26               => ! [Xb2: int] :
% 9.49/5.26                    ( ( member_int @ Xb2 @ A2 )
% 9.49/5.26                   => ( X3
% 9.49/5.26                     != ( minus_minus_int @ Xb2 @ Xa ) ) ) )
% 9.49/5.26           => ( ( P @ X3 )
% 9.49/5.26             => ( P @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 9.49/5.26       => ( ! [X3: int] :
% 9.49/5.26              ( ! [Xa: int] :
% 9.49/5.26                  ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 9.49/5.26                 => ! [Xb2: int] :
% 9.49/5.26                      ( ( member_int @ Xb2 @ A2 )
% 9.49/5.26                     => ( X3
% 9.49/5.26                       != ( minus_minus_int @ Xb2 @ Xa ) ) ) )
% 9.49/5.26             => ( ( Q @ X3 )
% 9.49/5.26               => ( Q @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 9.49/5.26         => ! [X5: int] :
% 9.49/5.26              ( ! [Xa3: int] :
% 9.49/5.26                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 9.49/5.26                 => ! [Xb3: int] :
% 9.49/5.26                      ( ( member_int @ Xb3 @ A2 )
% 9.49/5.26                     => ( X5
% 9.49/5.26                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 9.49/5.26             => ( ( ( P @ X5 )
% 9.49/5.26                  & ( Q @ X5 ) )
% 9.49/5.26               => ( ( P @ ( plus_plus_int @ X5 @ D4 ) )
% 9.49/5.26                  & ( Q @ ( plus_plus_int @ X5 @ D4 ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3159_bset_I2_J,axiom,
% 9.49/5.26      ! [D4: int,B2: set_int,P: int > $o,Q: int > $o] :
% 9.49/5.26        ( ! [X3: int] :
% 9.49/5.26            ( ! [Xa: int] :
% 9.49/5.26                ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 9.49/5.26               => ! [Xb2: int] :
% 9.49/5.26                    ( ( member_int @ Xb2 @ B2 )
% 9.49/5.26                   => ( X3
% 9.49/5.26                     != ( plus_plus_int @ Xb2 @ Xa ) ) ) )
% 9.49/5.26           => ( ( P @ X3 )
% 9.49/5.26             => ( P @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 9.49/5.26       => ( ! [X3: int] :
% 9.49/5.26              ( ! [Xa: int] :
% 9.49/5.26                  ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 9.49/5.26                 => ! [Xb2: int] :
% 9.49/5.26                      ( ( member_int @ Xb2 @ B2 )
% 9.49/5.26                     => ( X3
% 9.49/5.26                       != ( plus_plus_int @ Xb2 @ Xa ) ) ) )
% 9.49/5.26             => ( ( Q @ X3 )
% 9.49/5.26               => ( Q @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 9.49/5.26         => ! [X5: int] :
% 9.49/5.26              ( ! [Xa3: int] :
% 9.49/5.26                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 9.49/5.26                 => ! [Xb3: int] :
% 9.49/5.26                      ( ( member_int @ Xb3 @ B2 )
% 9.49/5.26                     => ( X5
% 9.49/5.26                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 9.49/5.26             => ( ( ( P @ X5 )
% 9.49/5.26                  | ( Q @ X5 ) )
% 9.49/5.26               => ( ( P @ ( minus_minus_int @ X5 @ D4 ) )
% 9.49/5.26                  | ( Q @ ( minus_minus_int @ X5 @ D4 ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3160_bset_I1_J,axiom,
% 9.49/5.26      ! [D4: int,B2: set_int,P: int > $o,Q: int > $o] :
% 9.49/5.26        ( ! [X3: int] :
% 9.49/5.26            ( ! [Xa: int] :
% 9.49/5.26                ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 9.49/5.26               => ! [Xb2: int] :
% 9.49/5.26                    ( ( member_int @ Xb2 @ B2 )
% 9.49/5.26                   => ( X3
% 9.49/5.26                     != ( plus_plus_int @ Xb2 @ Xa ) ) ) )
% 9.49/5.26           => ( ( P @ X3 )
% 9.49/5.26             => ( P @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 9.49/5.26       => ( ! [X3: int] :
% 9.49/5.26              ( ! [Xa: int] :
% 9.49/5.26                  ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 9.49/5.26                 => ! [Xb2: int] :
% 9.49/5.26                      ( ( member_int @ Xb2 @ B2 )
% 9.49/5.26                     => ( X3
% 9.49/5.26                       != ( plus_plus_int @ Xb2 @ Xa ) ) ) )
% 9.49/5.26             => ( ( Q @ X3 )
% 9.49/5.26               => ( Q @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 9.49/5.26         => ! [X5: int] :
% 9.49/5.26              ( ! [Xa3: int] :
% 9.49/5.26                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 9.49/5.26                 => ! [Xb3: int] :
% 9.49/5.26                      ( ( member_int @ Xb3 @ B2 )
% 9.49/5.26                     => ( X5
% 9.49/5.26                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 9.49/5.26             => ( ( ( P @ X5 )
% 9.49/5.26                  & ( Q @ X5 ) )
% 9.49/5.26               => ( ( P @ ( minus_minus_int @ X5 @ D4 ) )
% 9.49/5.26                  & ( Q @ ( minus_minus_int @ X5 @ D4 ) ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3161_minf_I7_J,axiom,
% 9.49/5.26      ! [T: real] :
% 9.49/5.26      ? [Z3: real] :
% 9.49/5.26      ! [X5: real] :
% 9.49/5.26        ( ( ord_less_real @ X5 @ Z3 )
% 9.49/5.26       => ~ ( ord_less_real @ T @ X5 ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3162_minf_I7_J,axiom,
% 9.49/5.26      ! [T: rat] :
% 9.49/5.26      ? [Z3: rat] :
% 9.49/5.26      ! [X5: rat] :
% 9.49/5.26        ( ( ord_less_rat @ X5 @ Z3 )
% 9.49/5.26       => ~ ( ord_less_rat @ T @ X5 ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3163_minf_I7_J,axiom,
% 9.49/5.26      ! [T: num] :
% 9.49/5.26      ? [Z3: num] :
% 9.49/5.26      ! [X5: num] :
% 9.49/5.26        ( ( ord_less_num @ X5 @ Z3 )
% 9.49/5.26       => ~ ( ord_less_num @ T @ X5 ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3164_minf_I7_J,axiom,
% 9.49/5.26      ! [T: nat] :
% 9.49/5.26      ? [Z3: nat] :
% 9.49/5.26      ! [X5: nat] :
% 9.49/5.26        ( ( ord_less_nat @ X5 @ Z3 )
% 9.49/5.26       => ~ ( ord_less_nat @ T @ X5 ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3165_minf_I7_J,axiom,
% 9.49/5.26      ! [T: int] :
% 9.49/5.26      ? [Z3: int] :
% 9.49/5.26      ! [X5: int] :
% 9.49/5.26        ( ( ord_less_int @ X5 @ Z3 )
% 9.49/5.26       => ~ ( ord_less_int @ T @ X5 ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3166_minf_I5_J,axiom,
% 9.49/5.26      ! [T: real] :
% 9.49/5.26      ? [Z3: real] :
% 9.49/5.26      ! [X5: real] :
% 9.49/5.26        ( ( ord_less_real @ X5 @ Z3 )
% 9.49/5.26       => ( ord_less_real @ X5 @ T ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3167_minf_I5_J,axiom,
% 9.49/5.26      ! [T: rat] :
% 9.49/5.26      ? [Z3: rat] :
% 9.49/5.26      ! [X5: rat] :
% 9.49/5.26        ( ( ord_less_rat @ X5 @ Z3 )
% 9.49/5.26       => ( ord_less_rat @ X5 @ T ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3168_minf_I5_J,axiom,
% 9.49/5.26      ! [T: num] :
% 9.49/5.26      ? [Z3: num] :
% 9.49/5.26      ! [X5: num] :
% 9.49/5.26        ( ( ord_less_num @ X5 @ Z3 )
% 9.49/5.26       => ( ord_less_num @ X5 @ T ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3169_minf_I5_J,axiom,
% 9.49/5.26      ! [T: nat] :
% 9.49/5.26      ? [Z3: nat] :
% 9.49/5.26      ! [X5: nat] :
% 9.49/5.26        ( ( ord_less_nat @ X5 @ Z3 )
% 9.49/5.26       => ( ord_less_nat @ X5 @ T ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3170_minf_I5_J,axiom,
% 9.49/5.26      ! [T: int] :
% 9.49/5.26      ? [Z3: int] :
% 9.49/5.26      ! [X5: int] :
% 9.49/5.26        ( ( ord_less_int @ X5 @ Z3 )
% 9.49/5.26       => ( ord_less_int @ X5 @ T ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3171_minf_I4_J,axiom,
% 9.49/5.26      ! [T: real] :
% 9.49/5.26      ? [Z3: real] :
% 9.49/5.26      ! [X5: real] :
% 9.49/5.26        ( ( ord_less_real @ X5 @ Z3 )
% 9.49/5.26       => ( X5 != T ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3172_minf_I4_J,axiom,
% 9.49/5.26      ! [T: rat] :
% 9.49/5.26      ? [Z3: rat] :
% 9.49/5.26      ! [X5: rat] :
% 9.49/5.26        ( ( ord_less_rat @ X5 @ Z3 )
% 9.49/5.26       => ( X5 != T ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3173_minf_I4_J,axiom,
% 9.49/5.26      ! [T: num] :
% 9.49/5.26      ? [Z3: num] :
% 9.49/5.26      ! [X5: num] :
% 9.49/5.26        ( ( ord_less_num @ X5 @ Z3 )
% 9.49/5.26       => ( X5 != T ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3174_minf_I4_J,axiom,
% 9.49/5.26      ! [T: nat] :
% 9.49/5.26      ? [Z3: nat] :
% 9.49/5.26      ! [X5: nat] :
% 9.49/5.26        ( ( ord_less_nat @ X5 @ Z3 )
% 9.49/5.26       => ( X5 != T ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3175_minf_I4_J,axiom,
% 9.49/5.26      ! [T: int] :
% 9.49/5.26      ? [Z3: int] :
% 9.49/5.26      ! [X5: int] :
% 9.49/5.26        ( ( ord_less_int @ X5 @ Z3 )
% 9.49/5.26       => ( X5 != T ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3176_minf_I3_J,axiom,
% 9.49/5.26      ! [T: real] :
% 9.49/5.26      ? [Z3: real] :
% 9.49/5.26      ! [X5: real] :
% 9.49/5.26        ( ( ord_less_real @ X5 @ Z3 )
% 9.49/5.26       => ( X5 != T ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3177_minf_I3_J,axiom,
% 9.49/5.26      ! [T: rat] :
% 9.49/5.26      ? [Z3: rat] :
% 9.49/5.26      ! [X5: rat] :
% 9.49/5.26        ( ( ord_less_rat @ X5 @ Z3 )
% 9.49/5.26       => ( X5 != T ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3178_minf_I3_J,axiom,
% 9.49/5.26      ! [T: num] :
% 9.49/5.26      ? [Z3: num] :
% 9.49/5.26      ! [X5: num] :
% 9.49/5.26        ( ( ord_less_num @ X5 @ Z3 )
% 9.49/5.26       => ( X5 != T ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3179_minf_I3_J,axiom,
% 9.49/5.26      ! [T: nat] :
% 9.49/5.26      ? [Z3: nat] :
% 9.49/5.26      ! [X5: nat] :
% 9.49/5.26        ( ( ord_less_nat @ X5 @ Z3 )
% 9.49/5.26       => ( X5 != T ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3180_minf_I3_J,axiom,
% 9.49/5.26      ! [T: int] :
% 9.49/5.26      ? [Z3: int] :
% 9.49/5.26      ! [X5: int] :
% 9.49/5.26        ( ( ord_less_int @ X5 @ Z3 )
% 9.49/5.26       => ( X5 != T ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3181_minf_I2_J,axiom,
% 9.49/5.26      ! [P: real > $o,P5: real > $o,Q: real > $o,Q6: real > $o] :
% 9.49/5.26        ( ? [Z2: real] :
% 9.49/5.26          ! [X3: real] :
% 9.49/5.26            ( ( ord_less_real @ X3 @ Z2 )
% 9.49/5.26           => ( ( P @ X3 )
% 9.49/5.26              = ( P5 @ X3 ) ) )
% 9.49/5.26       => ( ? [Z2: real] :
% 9.49/5.26            ! [X3: real] :
% 9.49/5.26              ( ( ord_less_real @ X3 @ Z2 )
% 9.49/5.26             => ( ( Q @ X3 )
% 9.49/5.26                = ( Q6 @ X3 ) ) )
% 9.49/5.26         => ? [Z3: real] :
% 9.49/5.26            ! [X5: real] :
% 9.49/5.26              ( ( ord_less_real @ X5 @ Z3 )
% 9.49/5.26             => ( ( ( P @ X5 )
% 9.49/5.26                  | ( Q @ X5 ) )
% 9.49/5.26                = ( ( P5 @ X5 )
% 9.49/5.26                  | ( Q6 @ X5 ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3182_minf_I2_J,axiom,
% 9.49/5.26      ! [P: rat > $o,P5: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 9.49/5.26        ( ? [Z2: rat] :
% 9.49/5.26          ! [X3: rat] :
% 9.49/5.26            ( ( ord_less_rat @ X3 @ Z2 )
% 9.49/5.26           => ( ( P @ X3 )
% 9.49/5.26              = ( P5 @ X3 ) ) )
% 9.49/5.26       => ( ? [Z2: rat] :
% 9.49/5.26            ! [X3: rat] :
% 9.49/5.26              ( ( ord_less_rat @ X3 @ Z2 )
% 9.49/5.26             => ( ( Q @ X3 )
% 9.49/5.26                = ( Q6 @ X3 ) ) )
% 9.49/5.26         => ? [Z3: rat] :
% 9.49/5.26            ! [X5: rat] :
% 9.49/5.26              ( ( ord_less_rat @ X5 @ Z3 )
% 9.49/5.26             => ( ( ( P @ X5 )
% 9.49/5.26                  | ( Q @ X5 ) )
% 9.49/5.26                = ( ( P5 @ X5 )
% 9.49/5.26                  | ( Q6 @ X5 ) ) ) ) ) ) ).
% 9.49/5.26  
% 9.49/5.26  thf(fact_3183_minf_I2_J,axiom,
% 9.49/5.26      ! [P: num > $o,P5: num > $o,Q: num > $o,Q6: num > $o] :
% 9.49/5.26        ( ? [Z2: num] :
% 9.49/5.26          ! [X3: num] :
% 9.49/5.27            ( ( ord_less_num @ X3 @ Z2 )
% 9.49/5.27           => ( ( P @ X3 )
% 9.49/5.27              = ( P5 @ X3 ) ) )
% 9.49/5.27       => ( ? [Z2: num] :
% 9.49/5.27            ! [X3: num] :
% 9.49/5.27              ( ( ord_less_num @ X3 @ Z2 )
% 9.49/5.27             => ( ( Q @ X3 )
% 9.49/5.27                = ( Q6 @ X3 ) ) )
% 9.49/5.27         => ? [Z3: num] :
% 9.49/5.27            ! [X5: num] :
% 9.49/5.27              ( ( ord_less_num @ X5 @ Z3 )
% 9.49/5.27             => ( ( ( P @ X5 )
% 9.49/5.27                  | ( Q @ X5 ) )
% 9.49/5.27                = ( ( P5 @ X5 )
% 9.49/5.27                  | ( Q6 @ X5 ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3184_minf_I2_J,axiom,
% 9.49/5.27      ! [P: nat > $o,P5: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 9.49/5.27        ( ? [Z2: nat] :
% 9.49/5.27          ! [X3: nat] :
% 9.49/5.27            ( ( ord_less_nat @ X3 @ Z2 )
% 9.49/5.27           => ( ( P @ X3 )
% 9.49/5.27              = ( P5 @ X3 ) ) )
% 9.49/5.27       => ( ? [Z2: nat] :
% 9.49/5.27            ! [X3: nat] :
% 9.49/5.27              ( ( ord_less_nat @ X3 @ Z2 )
% 9.49/5.27             => ( ( Q @ X3 )
% 9.49/5.27                = ( Q6 @ X3 ) ) )
% 9.49/5.27         => ? [Z3: nat] :
% 9.49/5.27            ! [X5: nat] :
% 9.49/5.27              ( ( ord_less_nat @ X5 @ Z3 )
% 9.49/5.27             => ( ( ( P @ X5 )
% 9.49/5.27                  | ( Q @ X5 ) )
% 9.49/5.27                = ( ( P5 @ X5 )
% 9.49/5.27                  | ( Q6 @ X5 ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3185_minf_I2_J,axiom,
% 9.49/5.27      ! [P: int > $o,P5: int > $o,Q: int > $o,Q6: int > $o] :
% 9.49/5.27        ( ? [Z2: int] :
% 9.49/5.27          ! [X3: int] :
% 9.49/5.27            ( ( ord_less_int @ X3 @ Z2 )
% 9.49/5.27           => ( ( P @ X3 )
% 9.49/5.27              = ( P5 @ X3 ) ) )
% 9.49/5.27       => ( ? [Z2: int] :
% 9.49/5.27            ! [X3: int] :
% 9.49/5.27              ( ( ord_less_int @ X3 @ Z2 )
% 9.49/5.27             => ( ( Q @ X3 )
% 9.49/5.27                = ( Q6 @ X3 ) ) )
% 9.49/5.27         => ? [Z3: int] :
% 9.49/5.27            ! [X5: int] :
% 9.49/5.27              ( ( ord_less_int @ X5 @ Z3 )
% 9.49/5.27             => ( ( ( P @ X5 )
% 9.49/5.27                  | ( Q @ X5 ) )
% 9.49/5.27                = ( ( P5 @ X5 )
% 9.49/5.27                  | ( Q6 @ X5 ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3186_minf_I1_J,axiom,
% 9.49/5.27      ! [P: real > $o,P5: real > $o,Q: real > $o,Q6: real > $o] :
% 9.49/5.27        ( ? [Z2: real] :
% 9.49/5.27          ! [X3: real] :
% 9.49/5.27            ( ( ord_less_real @ X3 @ Z2 )
% 9.49/5.27           => ( ( P @ X3 )
% 9.49/5.27              = ( P5 @ X3 ) ) )
% 9.49/5.27       => ( ? [Z2: real] :
% 9.49/5.27            ! [X3: real] :
% 9.49/5.27              ( ( ord_less_real @ X3 @ Z2 )
% 9.49/5.27             => ( ( Q @ X3 )
% 9.49/5.27                = ( Q6 @ X3 ) ) )
% 9.49/5.27         => ? [Z3: real] :
% 9.49/5.27            ! [X5: real] :
% 9.49/5.27              ( ( ord_less_real @ X5 @ Z3 )
% 9.49/5.27             => ( ( ( P @ X5 )
% 9.49/5.27                  & ( Q @ X5 ) )
% 9.49/5.27                = ( ( P5 @ X5 )
% 9.49/5.27                  & ( Q6 @ X5 ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3187_minf_I1_J,axiom,
% 9.49/5.27      ! [P: rat > $o,P5: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 9.49/5.27        ( ? [Z2: rat] :
% 9.49/5.27          ! [X3: rat] :
% 9.49/5.27            ( ( ord_less_rat @ X3 @ Z2 )
% 9.49/5.27           => ( ( P @ X3 )
% 9.49/5.27              = ( P5 @ X3 ) ) )
% 9.49/5.27       => ( ? [Z2: rat] :
% 9.49/5.27            ! [X3: rat] :
% 9.49/5.27              ( ( ord_less_rat @ X3 @ Z2 )
% 9.49/5.27             => ( ( Q @ X3 )
% 9.49/5.27                = ( Q6 @ X3 ) ) )
% 9.49/5.27         => ? [Z3: rat] :
% 9.49/5.27            ! [X5: rat] :
% 9.49/5.27              ( ( ord_less_rat @ X5 @ Z3 )
% 9.49/5.27             => ( ( ( P @ X5 )
% 9.49/5.27                  & ( Q @ X5 ) )
% 9.49/5.27                = ( ( P5 @ X5 )
% 9.49/5.27                  & ( Q6 @ X5 ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3188_minf_I1_J,axiom,
% 9.49/5.27      ! [P: num > $o,P5: num > $o,Q: num > $o,Q6: num > $o] :
% 9.49/5.27        ( ? [Z2: num] :
% 9.49/5.27          ! [X3: num] :
% 9.49/5.27            ( ( ord_less_num @ X3 @ Z2 )
% 9.49/5.27           => ( ( P @ X3 )
% 9.49/5.27              = ( P5 @ X3 ) ) )
% 9.49/5.27       => ( ? [Z2: num] :
% 9.49/5.27            ! [X3: num] :
% 9.49/5.27              ( ( ord_less_num @ X3 @ Z2 )
% 9.49/5.27             => ( ( Q @ X3 )
% 9.49/5.27                = ( Q6 @ X3 ) ) )
% 9.49/5.27         => ? [Z3: num] :
% 9.49/5.27            ! [X5: num] :
% 9.49/5.27              ( ( ord_less_num @ X5 @ Z3 )
% 9.49/5.27             => ( ( ( P @ X5 )
% 9.49/5.27                  & ( Q @ X5 ) )
% 9.49/5.27                = ( ( P5 @ X5 )
% 9.49/5.27                  & ( Q6 @ X5 ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3189_minf_I1_J,axiom,
% 9.49/5.27      ! [P: nat > $o,P5: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 9.49/5.27        ( ? [Z2: nat] :
% 9.49/5.27          ! [X3: nat] :
% 9.49/5.27            ( ( ord_less_nat @ X3 @ Z2 )
% 9.49/5.27           => ( ( P @ X3 )
% 9.49/5.27              = ( P5 @ X3 ) ) )
% 9.49/5.27       => ( ? [Z2: nat] :
% 9.49/5.27            ! [X3: nat] :
% 9.49/5.27              ( ( ord_less_nat @ X3 @ Z2 )
% 9.49/5.27             => ( ( Q @ X3 )
% 9.49/5.27                = ( Q6 @ X3 ) ) )
% 9.49/5.27         => ? [Z3: nat] :
% 9.49/5.27            ! [X5: nat] :
% 9.49/5.27              ( ( ord_less_nat @ X5 @ Z3 )
% 9.49/5.27             => ( ( ( P @ X5 )
% 9.49/5.27                  & ( Q @ X5 ) )
% 9.49/5.27                = ( ( P5 @ X5 )
% 9.49/5.27                  & ( Q6 @ X5 ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3190_minf_I1_J,axiom,
% 9.49/5.27      ! [P: int > $o,P5: int > $o,Q: int > $o,Q6: int > $o] :
% 9.49/5.27        ( ? [Z2: int] :
% 9.49/5.27          ! [X3: int] :
% 9.49/5.27            ( ( ord_less_int @ X3 @ Z2 )
% 9.49/5.27           => ( ( P @ X3 )
% 9.49/5.27              = ( P5 @ X3 ) ) )
% 9.49/5.27       => ( ? [Z2: int] :
% 9.49/5.27            ! [X3: int] :
% 9.49/5.27              ( ( ord_less_int @ X3 @ Z2 )
% 9.49/5.27             => ( ( Q @ X3 )
% 9.49/5.27                = ( Q6 @ X3 ) ) )
% 9.49/5.27         => ? [Z3: int] :
% 9.49/5.27            ! [X5: int] :
% 9.49/5.27              ( ( ord_less_int @ X5 @ Z3 )
% 9.49/5.27             => ( ( ( P @ X5 )
% 9.49/5.27                  & ( Q @ X5 ) )
% 9.49/5.27                = ( ( P5 @ X5 )
% 9.49/5.27                  & ( Q6 @ X5 ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3191_pinf_I7_J,axiom,
% 9.49/5.27      ! [T: real] :
% 9.49/5.27      ? [Z3: real] :
% 9.49/5.27      ! [X5: real] :
% 9.49/5.27        ( ( ord_less_real @ Z3 @ X5 )
% 9.49/5.27       => ( ord_less_real @ T @ X5 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3192_pinf_I7_J,axiom,
% 9.49/5.27      ! [T: rat] :
% 9.49/5.27      ? [Z3: rat] :
% 9.49/5.27      ! [X5: rat] :
% 9.49/5.27        ( ( ord_less_rat @ Z3 @ X5 )
% 9.49/5.27       => ( ord_less_rat @ T @ X5 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3193_pinf_I7_J,axiom,
% 9.49/5.27      ! [T: num] :
% 9.49/5.27      ? [Z3: num] :
% 9.49/5.27      ! [X5: num] :
% 9.49/5.27        ( ( ord_less_num @ Z3 @ X5 )
% 9.49/5.27       => ( ord_less_num @ T @ X5 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3194_pinf_I7_J,axiom,
% 9.49/5.27      ! [T: nat] :
% 9.49/5.27      ? [Z3: nat] :
% 9.49/5.27      ! [X5: nat] :
% 9.49/5.27        ( ( ord_less_nat @ Z3 @ X5 )
% 9.49/5.27       => ( ord_less_nat @ T @ X5 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3195_pinf_I7_J,axiom,
% 9.49/5.27      ! [T: int] :
% 9.49/5.27      ? [Z3: int] :
% 9.49/5.27      ! [X5: int] :
% 9.49/5.27        ( ( ord_less_int @ Z3 @ X5 )
% 9.49/5.27       => ( ord_less_int @ T @ X5 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3196_pinf_I5_J,axiom,
% 9.49/5.27      ! [T: real] :
% 9.49/5.27      ? [Z3: real] :
% 9.49/5.27      ! [X5: real] :
% 9.49/5.27        ( ( ord_less_real @ Z3 @ X5 )
% 9.49/5.27       => ~ ( ord_less_real @ X5 @ T ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3197_pinf_I5_J,axiom,
% 9.49/5.27      ! [T: rat] :
% 9.49/5.27      ? [Z3: rat] :
% 9.49/5.27      ! [X5: rat] :
% 9.49/5.27        ( ( ord_less_rat @ Z3 @ X5 )
% 9.49/5.27       => ~ ( ord_less_rat @ X5 @ T ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3198_pinf_I5_J,axiom,
% 9.49/5.27      ! [T: num] :
% 9.49/5.27      ? [Z3: num] :
% 9.49/5.27      ! [X5: num] :
% 9.49/5.27        ( ( ord_less_num @ Z3 @ X5 )
% 9.49/5.27       => ~ ( ord_less_num @ X5 @ T ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3199_pinf_I5_J,axiom,
% 9.49/5.27      ! [T: nat] :
% 9.49/5.27      ? [Z3: nat] :
% 9.49/5.27      ! [X5: nat] :
% 9.49/5.27        ( ( ord_less_nat @ Z3 @ X5 )
% 9.49/5.27       => ~ ( ord_less_nat @ X5 @ T ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3200_pinf_I5_J,axiom,
% 9.49/5.27      ! [T: int] :
% 9.49/5.27      ? [Z3: int] :
% 9.49/5.27      ! [X5: int] :
% 9.49/5.27        ( ( ord_less_int @ Z3 @ X5 )
% 9.49/5.27       => ~ ( ord_less_int @ X5 @ T ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3201_pinf_I4_J,axiom,
% 9.49/5.27      ! [T: real] :
% 9.49/5.27      ? [Z3: real] :
% 9.49/5.27      ! [X5: real] :
% 9.49/5.27        ( ( ord_less_real @ Z3 @ X5 )
% 9.49/5.27       => ( X5 != T ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3202_pinf_I4_J,axiom,
% 9.49/5.27      ! [T: rat] :
% 9.49/5.27      ? [Z3: rat] :
% 9.49/5.27      ! [X5: rat] :
% 9.49/5.27        ( ( ord_less_rat @ Z3 @ X5 )
% 9.49/5.27       => ( X5 != T ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3203_pinf_I4_J,axiom,
% 9.49/5.27      ! [T: num] :
% 9.49/5.27      ? [Z3: num] :
% 9.49/5.27      ! [X5: num] :
% 9.49/5.27        ( ( ord_less_num @ Z3 @ X5 )
% 9.49/5.27       => ( X5 != T ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3204_pinf_I4_J,axiom,
% 9.49/5.27      ! [T: nat] :
% 9.49/5.27      ? [Z3: nat] :
% 9.49/5.27      ! [X5: nat] :
% 9.49/5.27        ( ( ord_less_nat @ Z3 @ X5 )
% 9.49/5.27       => ( X5 != T ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3205_pinf_I4_J,axiom,
% 9.49/5.27      ! [T: int] :
% 9.49/5.27      ? [Z3: int] :
% 9.49/5.27      ! [X5: int] :
% 9.49/5.27        ( ( ord_less_int @ Z3 @ X5 )
% 9.49/5.27       => ( X5 != T ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3206_pinf_I3_J,axiom,
% 9.49/5.27      ! [T: real] :
% 9.49/5.27      ? [Z3: real] :
% 9.49/5.27      ! [X5: real] :
% 9.49/5.27        ( ( ord_less_real @ Z3 @ X5 )
% 9.49/5.27       => ( X5 != T ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3207_pinf_I3_J,axiom,
% 9.49/5.27      ! [T: rat] :
% 9.49/5.27      ? [Z3: rat] :
% 9.49/5.27      ! [X5: rat] :
% 9.49/5.27        ( ( ord_less_rat @ Z3 @ X5 )
% 9.49/5.27       => ( X5 != T ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3208_pinf_I3_J,axiom,
% 9.49/5.27      ! [T: num] :
% 9.49/5.27      ? [Z3: num] :
% 9.49/5.27      ! [X5: num] :
% 9.49/5.27        ( ( ord_less_num @ Z3 @ X5 )
% 9.49/5.27       => ( X5 != T ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3209_pinf_I3_J,axiom,
% 9.49/5.27      ! [T: nat] :
% 9.49/5.27      ? [Z3: nat] :
% 9.49/5.27      ! [X5: nat] :
% 9.49/5.27        ( ( ord_less_nat @ Z3 @ X5 )
% 9.49/5.27       => ( X5 != T ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3210_pinf_I3_J,axiom,
% 9.49/5.27      ! [T: int] :
% 9.49/5.27      ? [Z3: int] :
% 9.49/5.27      ! [X5: int] :
% 9.49/5.27        ( ( ord_less_int @ Z3 @ X5 )
% 9.49/5.27       => ( X5 != T ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3211_pinf_I2_J,axiom,
% 9.49/5.27      ! [P: real > $o,P5: real > $o,Q: real > $o,Q6: real > $o] :
% 9.49/5.27        ( ? [Z2: real] :
% 9.49/5.27          ! [X3: real] :
% 9.49/5.27            ( ( ord_less_real @ Z2 @ X3 )
% 9.49/5.27           => ( ( P @ X3 )
% 9.49/5.27              = ( P5 @ X3 ) ) )
% 9.49/5.27       => ( ? [Z2: real] :
% 9.49/5.27            ! [X3: real] :
% 9.49/5.27              ( ( ord_less_real @ Z2 @ X3 )
% 9.49/5.27             => ( ( Q @ X3 )
% 9.49/5.27                = ( Q6 @ X3 ) ) )
% 9.49/5.27         => ? [Z3: real] :
% 9.49/5.27            ! [X5: real] :
% 9.49/5.27              ( ( ord_less_real @ Z3 @ X5 )
% 9.49/5.27             => ( ( ( P @ X5 )
% 9.49/5.27                  | ( Q @ X5 ) )
% 9.49/5.27                = ( ( P5 @ X5 )
% 9.49/5.27                  | ( Q6 @ X5 ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3212_pinf_I2_J,axiom,
% 9.49/5.27      ! [P: rat > $o,P5: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 9.49/5.27        ( ? [Z2: rat] :
% 9.49/5.27          ! [X3: rat] :
% 9.49/5.27            ( ( ord_less_rat @ Z2 @ X3 )
% 9.49/5.27           => ( ( P @ X3 )
% 9.49/5.27              = ( P5 @ X3 ) ) )
% 9.49/5.27       => ( ? [Z2: rat] :
% 9.49/5.27            ! [X3: rat] :
% 9.49/5.27              ( ( ord_less_rat @ Z2 @ X3 )
% 9.49/5.27             => ( ( Q @ X3 )
% 9.49/5.27                = ( Q6 @ X3 ) ) )
% 9.49/5.27         => ? [Z3: rat] :
% 9.49/5.27            ! [X5: rat] :
% 9.49/5.27              ( ( ord_less_rat @ Z3 @ X5 )
% 9.49/5.27             => ( ( ( P @ X5 )
% 9.49/5.27                  | ( Q @ X5 ) )
% 9.49/5.27                = ( ( P5 @ X5 )
% 9.49/5.27                  | ( Q6 @ X5 ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3213_pinf_I2_J,axiom,
% 9.49/5.27      ! [P: num > $o,P5: num > $o,Q: num > $o,Q6: num > $o] :
% 9.49/5.27        ( ? [Z2: num] :
% 9.49/5.27          ! [X3: num] :
% 9.49/5.27            ( ( ord_less_num @ Z2 @ X3 )
% 9.49/5.27           => ( ( P @ X3 )
% 9.49/5.27              = ( P5 @ X3 ) ) )
% 9.49/5.27       => ( ? [Z2: num] :
% 9.49/5.27            ! [X3: num] :
% 9.49/5.27              ( ( ord_less_num @ Z2 @ X3 )
% 9.49/5.27             => ( ( Q @ X3 )
% 9.49/5.27                = ( Q6 @ X3 ) ) )
% 9.49/5.27         => ? [Z3: num] :
% 9.49/5.27            ! [X5: num] :
% 9.49/5.27              ( ( ord_less_num @ Z3 @ X5 )
% 9.49/5.27             => ( ( ( P @ X5 )
% 9.49/5.27                  | ( Q @ X5 ) )
% 9.49/5.27                = ( ( P5 @ X5 )
% 9.49/5.27                  | ( Q6 @ X5 ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3214_pinf_I2_J,axiom,
% 9.49/5.27      ! [P: nat > $o,P5: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 9.49/5.27        ( ? [Z2: nat] :
% 9.49/5.27          ! [X3: nat] :
% 9.49/5.27            ( ( ord_less_nat @ Z2 @ X3 )
% 9.49/5.27           => ( ( P @ X3 )
% 9.49/5.27              = ( P5 @ X3 ) ) )
% 9.49/5.27       => ( ? [Z2: nat] :
% 9.49/5.27            ! [X3: nat] :
% 9.49/5.27              ( ( ord_less_nat @ Z2 @ X3 )
% 9.49/5.27             => ( ( Q @ X3 )
% 9.49/5.27                = ( Q6 @ X3 ) ) )
% 9.49/5.27         => ? [Z3: nat] :
% 9.49/5.27            ! [X5: nat] :
% 9.49/5.27              ( ( ord_less_nat @ Z3 @ X5 )
% 9.49/5.27             => ( ( ( P @ X5 )
% 9.49/5.27                  | ( Q @ X5 ) )
% 9.49/5.27                = ( ( P5 @ X5 )
% 9.49/5.27                  | ( Q6 @ X5 ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3215_pinf_I2_J,axiom,
% 9.49/5.27      ! [P: int > $o,P5: int > $o,Q: int > $o,Q6: int > $o] :
% 9.49/5.27        ( ? [Z2: int] :
% 9.49/5.27          ! [X3: int] :
% 9.49/5.27            ( ( ord_less_int @ Z2 @ X3 )
% 9.49/5.27           => ( ( P @ X3 )
% 9.49/5.27              = ( P5 @ X3 ) ) )
% 9.49/5.27       => ( ? [Z2: int] :
% 9.49/5.27            ! [X3: int] :
% 9.49/5.27              ( ( ord_less_int @ Z2 @ X3 )
% 9.49/5.27             => ( ( Q @ X3 )
% 9.49/5.27                = ( Q6 @ X3 ) ) )
% 9.49/5.27         => ? [Z3: int] :
% 9.49/5.27            ! [X5: int] :
% 9.49/5.27              ( ( ord_less_int @ Z3 @ X5 )
% 9.49/5.27             => ( ( ( P @ X5 )
% 9.49/5.27                  | ( Q @ X5 ) )
% 9.49/5.27                = ( ( P5 @ X5 )
% 9.49/5.27                  | ( Q6 @ X5 ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3216_pinf_I1_J,axiom,
% 9.49/5.27      ! [P: real > $o,P5: real > $o,Q: real > $o,Q6: real > $o] :
% 9.49/5.27        ( ? [Z2: real] :
% 9.49/5.27          ! [X3: real] :
% 9.49/5.27            ( ( ord_less_real @ Z2 @ X3 )
% 9.49/5.27           => ( ( P @ X3 )
% 9.49/5.27              = ( P5 @ X3 ) ) )
% 9.49/5.27       => ( ? [Z2: real] :
% 9.49/5.27            ! [X3: real] :
% 9.49/5.27              ( ( ord_less_real @ Z2 @ X3 )
% 9.49/5.27             => ( ( Q @ X3 )
% 9.49/5.27                = ( Q6 @ X3 ) ) )
% 9.49/5.27         => ? [Z3: real] :
% 9.49/5.27            ! [X5: real] :
% 9.49/5.27              ( ( ord_less_real @ Z3 @ X5 )
% 9.49/5.27             => ( ( ( P @ X5 )
% 9.49/5.27                  & ( Q @ X5 ) )
% 9.49/5.27                = ( ( P5 @ X5 )
% 9.49/5.27                  & ( Q6 @ X5 ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3217_pinf_I1_J,axiom,
% 9.49/5.27      ! [P: rat > $o,P5: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 9.49/5.27        ( ? [Z2: rat] :
% 9.49/5.27          ! [X3: rat] :
% 9.49/5.27            ( ( ord_less_rat @ Z2 @ X3 )
% 9.49/5.27           => ( ( P @ X3 )
% 9.49/5.27              = ( P5 @ X3 ) ) )
% 9.49/5.27       => ( ? [Z2: rat] :
% 9.49/5.27            ! [X3: rat] :
% 9.49/5.27              ( ( ord_less_rat @ Z2 @ X3 )
% 9.49/5.27             => ( ( Q @ X3 )
% 9.49/5.27                = ( Q6 @ X3 ) ) )
% 9.49/5.27         => ? [Z3: rat] :
% 9.49/5.27            ! [X5: rat] :
% 9.49/5.27              ( ( ord_less_rat @ Z3 @ X5 )
% 9.49/5.27             => ( ( ( P @ X5 )
% 9.49/5.27                  & ( Q @ X5 ) )
% 9.49/5.27                = ( ( P5 @ X5 )
% 9.49/5.27                  & ( Q6 @ X5 ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3218_pinf_I1_J,axiom,
% 9.49/5.27      ! [P: num > $o,P5: num > $o,Q: num > $o,Q6: num > $o] :
% 9.49/5.27        ( ? [Z2: num] :
% 9.49/5.27          ! [X3: num] :
% 9.49/5.27            ( ( ord_less_num @ Z2 @ X3 )
% 9.49/5.27           => ( ( P @ X3 )
% 9.49/5.27              = ( P5 @ X3 ) ) )
% 9.49/5.27       => ( ? [Z2: num] :
% 9.49/5.27            ! [X3: num] :
% 9.49/5.27              ( ( ord_less_num @ Z2 @ X3 )
% 9.49/5.27             => ( ( Q @ X3 )
% 9.49/5.27                = ( Q6 @ X3 ) ) )
% 9.49/5.27         => ? [Z3: num] :
% 9.49/5.27            ! [X5: num] :
% 9.49/5.27              ( ( ord_less_num @ Z3 @ X5 )
% 9.49/5.27             => ( ( ( P @ X5 )
% 9.49/5.27                  & ( Q @ X5 ) )
% 9.49/5.27                = ( ( P5 @ X5 )
% 9.49/5.27                  & ( Q6 @ X5 ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3219_pinf_I1_J,axiom,
% 9.49/5.27      ! [P: nat > $o,P5: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 9.49/5.27        ( ? [Z2: nat] :
% 9.49/5.27          ! [X3: nat] :
% 9.49/5.27            ( ( ord_less_nat @ Z2 @ X3 )
% 9.49/5.27           => ( ( P @ X3 )
% 9.49/5.27              = ( P5 @ X3 ) ) )
% 9.49/5.27       => ( ? [Z2: nat] :
% 9.49/5.27            ! [X3: nat] :
% 9.49/5.27              ( ( ord_less_nat @ Z2 @ X3 )
% 9.49/5.27             => ( ( Q @ X3 )
% 9.49/5.27                = ( Q6 @ X3 ) ) )
% 9.49/5.27         => ? [Z3: nat] :
% 9.49/5.27            ! [X5: nat] :
% 9.49/5.27              ( ( ord_less_nat @ Z3 @ X5 )
% 9.49/5.27             => ( ( ( P @ X5 )
% 9.49/5.27                  & ( Q @ X5 ) )
% 9.49/5.27                = ( ( P5 @ X5 )
% 9.49/5.27                  & ( Q6 @ X5 ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3220_pinf_I1_J,axiom,
% 9.49/5.27      ! [P: int > $o,P5: int > $o,Q: int > $o,Q6: int > $o] :
% 9.49/5.27        ( ? [Z2: int] :
% 9.49/5.27          ! [X3: int] :
% 9.49/5.27            ( ( ord_less_int @ Z2 @ X3 )
% 9.49/5.27           => ( ( P @ X3 )
% 9.49/5.27              = ( P5 @ X3 ) ) )
% 9.49/5.27       => ( ? [Z2: int] :
% 9.49/5.27            ! [X3: int] :
% 9.49/5.27              ( ( ord_less_int @ Z2 @ X3 )
% 9.49/5.27             => ( ( Q @ X3 )
% 9.49/5.27                = ( Q6 @ X3 ) ) )
% 9.49/5.27         => ? [Z3: int] :
% 9.49/5.27            ! [X5: int] :
% 9.49/5.27              ( ( ord_less_int @ Z3 @ X5 )
% 9.49/5.27             => ( ( ( P @ X5 )
% 9.49/5.27                  & ( Q @ X5 ) )
% 9.49/5.27                = ( ( P5 @ X5 )
% 9.49/5.27                  & ( Q6 @ X5 ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3221_bounded__Max__nat,axiom,
% 9.49/5.27      ! [P: nat > $o,X: nat,M7: nat] :
% 9.49/5.27        ( ( P @ X )
% 9.49/5.27       => ( ! [X3: nat] :
% 9.49/5.27              ( ( P @ X3 )
% 9.49/5.27             => ( ord_less_eq_nat @ X3 @ M7 ) )
% 9.49/5.27         => ~ ! [M4: nat] :
% 9.49/5.27                ( ( P @ M4 )
% 9.49/5.27               => ~ ! [X5: nat] :
% 9.49/5.27                      ( ( P @ X5 )
% 9.49/5.27                     => ( ord_less_eq_nat @ X5 @ M4 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3222_fold__atLeastAtMost__nat_Ocases,axiom,
% 9.49/5.27      ! [X: produc3368934014287244435at_num] :
% 9.49/5.27        ~ ! [F2: nat > num > num,A4: nat,B3: nat,Acc: num] :
% 9.49/5.27            ( X
% 9.49/5.27           != ( produc851828971589881931at_num @ F2 @ ( produc1195630363706982562at_num @ A4 @ ( product_Pair_nat_num @ B3 @ Acc ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3223_fold__atLeastAtMost__nat_Ocases,axiom,
% 9.49/5.27      ! [X: produc4471711990508489141at_nat] :
% 9.49/5.27        ~ ! [F2: nat > nat > nat,A4: nat,B3: nat,Acc: nat] :
% 9.49/5.27            ( X
% 9.49/5.27           != ( produc3209952032786966637at_nat @ F2 @ ( produc487386426758144856at_nat @ A4 @ ( product_Pair_nat_nat @ B3 @ Acc ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3224_periodic__finite__ex,axiom,
% 9.49/5.27      ! [D2: int,P: int > $o] :
% 9.49/5.27        ( ( ord_less_int @ zero_zero_int @ D2 )
% 9.49/5.27       => ( ! [X3: int,K2: int] :
% 9.49/5.27              ( ( P @ X3 )
% 9.49/5.27              = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D2 ) ) ) )
% 9.49/5.27         => ( ( ? [X4: int] : ( P @ X4 ) )
% 9.49/5.27            = ( ? [X2: int] :
% 9.49/5.27                  ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D2 ) )
% 9.49/5.27                  & ( P @ X2 ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3225_aset_I7_J,axiom,
% 9.49/5.27      ! [D4: int,A2: set_int,T: int] :
% 9.49/5.27        ( ( ord_less_int @ zero_zero_int @ D4 )
% 9.49/5.27       => ! [X5: int] :
% 9.49/5.27            ( ! [Xa3: int] :
% 9.49/5.27                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 9.49/5.27               => ! [Xb3: int] :
% 9.49/5.27                    ( ( member_int @ Xb3 @ A2 )
% 9.49/5.27                   => ( X5
% 9.49/5.27                     != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 9.49/5.27           => ( ( ord_less_int @ T @ X5 )
% 9.49/5.27             => ( ord_less_int @ T @ ( plus_plus_int @ X5 @ D4 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3226_aset_I5_J,axiom,
% 9.49/5.27      ! [D4: int,T: int,A2: set_int] :
% 9.49/5.27        ( ( ord_less_int @ zero_zero_int @ D4 )
% 9.49/5.27       => ( ( member_int @ T @ A2 )
% 9.49/5.27         => ! [X5: int] :
% 9.49/5.27              ( ! [Xa3: int] :
% 9.49/5.27                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 9.49/5.27                 => ! [Xb3: int] :
% 9.49/5.27                      ( ( member_int @ Xb3 @ A2 )
% 9.49/5.27                     => ( X5
% 9.49/5.27                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 9.49/5.27             => ( ( ord_less_int @ X5 @ T )
% 9.49/5.27               => ( ord_less_int @ ( plus_plus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3227_aset_I4_J,axiom,
% 9.49/5.27      ! [D4: int,T: int,A2: set_int] :
% 9.49/5.27        ( ( ord_less_int @ zero_zero_int @ D4 )
% 9.49/5.27       => ( ( member_int @ T @ A2 )
% 9.49/5.27         => ! [X5: int] :
% 9.49/5.27              ( ! [Xa3: int] :
% 9.49/5.27                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 9.49/5.27                 => ! [Xb3: int] :
% 9.49/5.27                      ( ( member_int @ Xb3 @ A2 )
% 9.49/5.27                     => ( X5
% 9.49/5.27                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 9.49/5.27             => ( ( X5 != T )
% 9.49/5.27               => ( ( plus_plus_int @ X5 @ D4 )
% 9.49/5.27                 != T ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3228_aset_I3_J,axiom,
% 9.49/5.27      ! [D4: int,T: int,A2: set_int] :
% 9.49/5.27        ( ( ord_less_int @ zero_zero_int @ D4 )
% 9.49/5.27       => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 9.49/5.27         => ! [X5: int] :
% 9.49/5.27              ( ! [Xa3: int] :
% 9.49/5.27                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 9.49/5.27                 => ! [Xb3: int] :
% 9.49/5.27                      ( ( member_int @ Xb3 @ A2 )
% 9.49/5.27                     => ( X5
% 9.49/5.27                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 9.49/5.27             => ( ( X5 = T )
% 9.49/5.27               => ( ( plus_plus_int @ X5 @ D4 )
% 9.49/5.27                  = T ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3229_bset_I7_J,axiom,
% 9.49/5.27      ! [D4: int,T: int,B2: set_int] :
% 9.49/5.27        ( ( ord_less_int @ zero_zero_int @ D4 )
% 9.49/5.27       => ( ( member_int @ T @ B2 )
% 9.49/5.27         => ! [X5: int] :
% 9.49/5.27              ( ! [Xa3: int] :
% 9.49/5.27                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 9.49/5.27                 => ! [Xb3: int] :
% 9.49/5.27                      ( ( member_int @ Xb3 @ B2 )
% 9.49/5.27                     => ( X5
% 9.49/5.27                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 9.49/5.27             => ( ( ord_less_int @ T @ X5 )
% 9.49/5.27               => ( ord_less_int @ T @ ( minus_minus_int @ X5 @ D4 ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3230_bset_I5_J,axiom,
% 9.49/5.27      ! [D4: int,B2: set_int,T: int] :
% 9.49/5.27        ( ( ord_less_int @ zero_zero_int @ D4 )
% 9.49/5.27       => ! [X5: int] :
% 9.49/5.27            ( ! [Xa3: int] :
% 9.49/5.27                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 9.49/5.27               => ! [Xb3: int] :
% 9.49/5.27                    ( ( member_int @ Xb3 @ B2 )
% 9.49/5.27                   => ( X5
% 9.49/5.27                     != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 9.49/5.27           => ( ( ord_less_int @ X5 @ T )
% 9.49/5.27             => ( ord_less_int @ ( minus_minus_int @ X5 @ D4 ) @ T ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3231_bset_I4_J,axiom,
% 9.49/5.27      ! [D4: int,T: int,B2: set_int] :
% 9.49/5.27        ( ( ord_less_int @ zero_zero_int @ D4 )
% 9.49/5.27       => ( ( member_int @ T @ B2 )
% 9.49/5.27         => ! [X5: int] :
% 9.49/5.27              ( ! [Xa3: int] :
% 9.49/5.27                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 9.49/5.27                 => ! [Xb3: int] :
% 9.49/5.27                      ( ( member_int @ Xb3 @ B2 )
% 9.49/5.27                     => ( X5
% 9.49/5.27                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 9.49/5.27             => ( ( X5 != T )
% 9.49/5.27               => ( ( minus_minus_int @ X5 @ D4 )
% 9.49/5.27                 != T ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3232_bset_I3_J,axiom,
% 9.49/5.27      ! [D4: int,T: int,B2: set_int] :
% 9.49/5.27        ( ( ord_less_int @ zero_zero_int @ D4 )
% 9.49/5.27       => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B2 )
% 9.49/5.27         => ! [X5: int] :
% 9.49/5.27              ( ! [Xa3: int] :
% 9.49/5.27                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 9.49/5.27                 => ! [Xb3: int] :
% 9.49/5.27                      ( ( member_int @ Xb3 @ B2 )
% 9.49/5.27                     => ( X5
% 9.49/5.27                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 9.49/5.27             => ( ( X5 = T )
% 9.49/5.27               => ( ( minus_minus_int @ X5 @ D4 )
% 9.49/5.27                  = T ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3233_aset_I8_J,axiom,
% 9.49/5.27      ! [D4: int,A2: set_int,T: int] :
% 9.49/5.27        ( ( ord_less_int @ zero_zero_int @ D4 )
% 9.49/5.27       => ! [X5: int] :
% 9.49/5.27            ( ! [Xa3: int] :
% 9.49/5.27                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 9.49/5.27               => ! [Xb3: int] :
% 9.49/5.27                    ( ( member_int @ Xb3 @ A2 )
% 9.49/5.27                   => ( X5
% 9.49/5.27                     != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 9.49/5.27           => ( ( ord_less_eq_int @ T @ X5 )
% 9.49/5.27             => ( ord_less_eq_int @ T @ ( plus_plus_int @ X5 @ D4 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3234_aset_I6_J,axiom,
% 9.49/5.27      ! [D4: int,T: int,A2: set_int] :
% 9.49/5.27        ( ( ord_less_int @ zero_zero_int @ D4 )
% 9.49/5.27       => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 9.49/5.27         => ! [X5: int] :
% 9.49/5.27              ( ! [Xa3: int] :
% 9.49/5.27                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 9.49/5.27                 => ! [Xb3: int] :
% 9.49/5.27                      ( ( member_int @ Xb3 @ A2 )
% 9.49/5.27                     => ( X5
% 9.49/5.27                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 9.49/5.27             => ( ( ord_less_eq_int @ X5 @ T )
% 9.49/5.27               => ( ord_less_eq_int @ ( plus_plus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3235_bset_I8_J,axiom,
% 9.49/5.27      ! [D4: int,T: int,B2: set_int] :
% 9.49/5.27        ( ( ord_less_int @ zero_zero_int @ D4 )
% 9.49/5.27       => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B2 )
% 9.49/5.27         => ! [X5: int] :
% 9.49/5.27              ( ! [Xa3: int] :
% 9.49/5.27                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 9.49/5.27                 => ! [Xb3: int] :
% 9.49/5.27                      ( ( member_int @ Xb3 @ B2 )
% 9.49/5.27                     => ( X5
% 9.49/5.27                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 9.49/5.27             => ( ( ord_less_eq_int @ T @ X5 )
% 9.49/5.27               => ( ord_less_eq_int @ T @ ( minus_minus_int @ X5 @ D4 ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3236_bset_I6_J,axiom,
% 9.49/5.27      ! [D4: int,B2: set_int,T: int] :
% 9.49/5.27        ( ( ord_less_int @ zero_zero_int @ D4 )
% 9.49/5.27       => ! [X5: int] :
% 9.49/5.27            ( ! [Xa3: int] :
% 9.49/5.27                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 9.49/5.27               => ! [Xb3: int] :
% 9.49/5.27                    ( ( member_int @ Xb3 @ B2 )
% 9.49/5.27                   => ( X5
% 9.49/5.27                     != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 9.49/5.27           => ( ( ord_less_eq_int @ X5 @ T )
% 9.49/5.27             => ( ord_less_eq_int @ ( minus_minus_int @ X5 @ D4 ) @ T ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3237_cpmi,axiom,
% 9.49/5.27      ! [D4: int,P: int > $o,P5: int > $o,B2: set_int] :
% 9.49/5.27        ( ( ord_less_int @ zero_zero_int @ D4 )
% 9.49/5.27       => ( ? [Z2: int] :
% 9.49/5.27            ! [X3: int] :
% 9.49/5.27              ( ( ord_less_int @ X3 @ Z2 )
% 9.49/5.27             => ( ( P @ X3 )
% 9.49/5.27                = ( P5 @ X3 ) ) )
% 9.49/5.27         => ( ! [X3: int] :
% 9.49/5.27                ( ! [Xa: int] :
% 9.49/5.27                    ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 9.49/5.27                   => ! [Xb2: int] :
% 9.49/5.27                        ( ( member_int @ Xb2 @ B2 )
% 9.49/5.27                       => ( X3
% 9.49/5.27                         != ( plus_plus_int @ Xb2 @ Xa ) ) ) )
% 9.49/5.27               => ( ( P @ X3 )
% 9.49/5.27                 => ( P @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 9.49/5.27           => ( ! [X3: int,K2: int] :
% 9.49/5.27                  ( ( P5 @ X3 )
% 9.49/5.27                  = ( P5 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 9.49/5.27             => ( ( ? [X4: int] : ( P @ X4 ) )
% 9.49/5.27                = ( ? [X2: int] :
% 9.49/5.27                      ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 9.49/5.27                      & ( P5 @ X2 ) )
% 9.49/5.27                  | ? [X2: int] :
% 9.49/5.27                      ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 9.49/5.27                      & ? [Y: int] :
% 9.49/5.27                          ( ( member_int @ Y @ B2 )
% 9.49/5.27                          & ( P @ ( plus_plus_int @ Y @ X2 ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3238_cppi,axiom,
% 9.49/5.27      ! [D4: int,P: int > $o,P5: int > $o,A2: set_int] :
% 9.49/5.27        ( ( ord_less_int @ zero_zero_int @ D4 )
% 9.49/5.27       => ( ? [Z2: int] :
% 9.49/5.27            ! [X3: int] :
% 9.49/5.27              ( ( ord_less_int @ Z2 @ X3 )
% 9.49/5.27             => ( ( P @ X3 )
% 9.49/5.27                = ( P5 @ X3 ) ) )
% 9.49/5.27         => ( ! [X3: int] :
% 9.49/5.27                ( ! [Xa: int] :
% 9.49/5.27                    ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 9.49/5.27                   => ! [Xb2: int] :
% 9.49/5.27                        ( ( member_int @ Xb2 @ A2 )
% 9.49/5.27                       => ( X3
% 9.49/5.27                         != ( minus_minus_int @ Xb2 @ Xa ) ) ) )
% 9.49/5.27               => ( ( P @ X3 )
% 9.49/5.27                 => ( P @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 9.49/5.27           => ( ! [X3: int,K2: int] :
% 9.49/5.27                  ( ( P5 @ X3 )
% 9.49/5.27                  = ( P5 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 9.49/5.27             => ( ( ? [X4: int] : ( P @ X4 ) )
% 9.49/5.27                = ( ? [X2: int] :
% 9.49/5.27                      ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 9.49/5.27                      & ( P5 @ X2 ) )
% 9.49/5.27                  | ? [X2: int] :
% 9.49/5.27                      ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 9.49/5.27                      & ? [Y: int] :
% 9.49/5.27                          ( ( member_int @ Y @ A2 )
% 9.49/5.27                          & ( P @ ( minus_minus_int @ Y @ X2 ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3239_minf_I8_J,axiom,
% 9.49/5.27      ! [T: real] :
% 9.49/5.27      ? [Z3: real] :
% 9.49/5.27      ! [X5: real] :
% 9.49/5.27        ( ( ord_less_real @ X5 @ Z3 )
% 9.49/5.27       => ~ ( ord_less_eq_real @ T @ X5 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3240_minf_I8_J,axiom,
% 9.49/5.27      ! [T: rat] :
% 9.49/5.27      ? [Z3: rat] :
% 9.49/5.27      ! [X5: rat] :
% 9.49/5.27        ( ( ord_less_rat @ X5 @ Z3 )
% 9.49/5.27       => ~ ( ord_less_eq_rat @ T @ X5 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3241_minf_I8_J,axiom,
% 9.49/5.27      ! [T: num] :
% 9.49/5.27      ? [Z3: num] :
% 9.49/5.27      ! [X5: num] :
% 9.49/5.27        ( ( ord_less_num @ X5 @ Z3 )
% 9.49/5.27       => ~ ( ord_less_eq_num @ T @ X5 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3242_minf_I8_J,axiom,
% 9.49/5.27      ! [T: nat] :
% 9.49/5.27      ? [Z3: nat] :
% 9.49/5.27      ! [X5: nat] :
% 9.49/5.27        ( ( ord_less_nat @ X5 @ Z3 )
% 9.49/5.27       => ~ ( ord_less_eq_nat @ T @ X5 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3243_minf_I8_J,axiom,
% 9.49/5.27      ! [T: int] :
% 9.49/5.27      ? [Z3: int] :
% 9.49/5.27      ! [X5: int] :
% 9.49/5.27        ( ( ord_less_int @ X5 @ Z3 )
% 9.49/5.27       => ~ ( ord_less_eq_int @ T @ X5 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3244_minf_I6_J,axiom,
% 9.49/5.27      ! [T: real] :
% 9.49/5.27      ? [Z3: real] :
% 9.49/5.27      ! [X5: real] :
% 9.49/5.27        ( ( ord_less_real @ X5 @ Z3 )
% 9.49/5.27       => ( ord_less_eq_real @ X5 @ T ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3245_minf_I6_J,axiom,
% 9.49/5.27      ! [T: rat] :
% 9.49/5.27      ? [Z3: rat] :
% 9.49/5.27      ! [X5: rat] :
% 9.49/5.27        ( ( ord_less_rat @ X5 @ Z3 )
% 9.49/5.27       => ( ord_less_eq_rat @ X5 @ T ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3246_minf_I6_J,axiom,
% 9.49/5.27      ! [T: num] :
% 9.49/5.27      ? [Z3: num] :
% 9.49/5.27      ! [X5: num] :
% 9.49/5.27        ( ( ord_less_num @ X5 @ Z3 )
% 9.49/5.27       => ( ord_less_eq_num @ X5 @ T ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3247_minf_I6_J,axiom,
% 9.49/5.27      ! [T: nat] :
% 9.49/5.27      ? [Z3: nat] :
% 9.49/5.27      ! [X5: nat] :
% 9.49/5.27        ( ( ord_less_nat @ X5 @ Z3 )
% 9.49/5.27       => ( ord_less_eq_nat @ X5 @ T ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3248_minf_I6_J,axiom,
% 9.49/5.27      ! [T: int] :
% 9.49/5.27      ? [Z3: int] :
% 9.49/5.27      ! [X5: int] :
% 9.49/5.27        ( ( ord_less_int @ X5 @ Z3 )
% 9.49/5.27       => ( ord_less_eq_int @ X5 @ T ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3249_pinf_I8_J,axiom,
% 9.49/5.27      ! [T: real] :
% 9.49/5.27      ? [Z3: real] :
% 9.49/5.27      ! [X5: real] :
% 9.49/5.27        ( ( ord_less_real @ Z3 @ X5 )
% 9.49/5.27       => ( ord_less_eq_real @ T @ X5 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3250_pinf_I8_J,axiom,
% 9.49/5.27      ! [T: rat] :
% 9.49/5.27      ? [Z3: rat] :
% 9.49/5.27      ! [X5: rat] :
% 9.49/5.27        ( ( ord_less_rat @ Z3 @ X5 )
% 9.49/5.27       => ( ord_less_eq_rat @ T @ X5 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3251_pinf_I8_J,axiom,
% 9.49/5.27      ! [T: num] :
% 9.49/5.27      ? [Z3: num] :
% 9.49/5.27      ! [X5: num] :
% 9.49/5.27        ( ( ord_less_num @ Z3 @ X5 )
% 9.49/5.27       => ( ord_less_eq_num @ T @ X5 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3252_pinf_I8_J,axiom,
% 9.49/5.27      ! [T: nat] :
% 9.49/5.27      ? [Z3: nat] :
% 9.49/5.27      ! [X5: nat] :
% 9.49/5.27        ( ( ord_less_nat @ Z3 @ X5 )
% 9.49/5.27       => ( ord_less_eq_nat @ T @ X5 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3253_pinf_I8_J,axiom,
% 9.49/5.27      ! [T: int] :
% 9.49/5.27      ? [Z3: int] :
% 9.49/5.27      ! [X5: int] :
% 9.49/5.27        ( ( ord_less_int @ Z3 @ X5 )
% 9.49/5.27       => ( ord_less_eq_int @ T @ X5 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3254_pinf_I6_J,axiom,
% 9.49/5.27      ! [T: real] :
% 9.49/5.27      ? [Z3: real] :
% 9.49/5.27      ! [X5: real] :
% 9.49/5.27        ( ( ord_less_real @ Z3 @ X5 )
% 9.49/5.27       => ~ ( ord_less_eq_real @ X5 @ T ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3255_pinf_I6_J,axiom,
% 9.49/5.27      ! [T: rat] :
% 9.49/5.27      ? [Z3: rat] :
% 9.49/5.27      ! [X5: rat] :
% 9.49/5.27        ( ( ord_less_rat @ Z3 @ X5 )
% 9.49/5.27       => ~ ( ord_less_eq_rat @ X5 @ T ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3256_pinf_I6_J,axiom,
% 9.49/5.27      ! [T: num] :
% 9.49/5.27      ? [Z3: num] :
% 9.49/5.27      ! [X5: num] :
% 9.49/5.27        ( ( ord_less_num @ Z3 @ X5 )
% 9.49/5.27       => ~ ( ord_less_eq_num @ X5 @ T ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3257_pinf_I6_J,axiom,
% 9.49/5.27      ! [T: nat] :
% 9.49/5.27      ? [Z3: nat] :
% 9.49/5.27      ! [X5: nat] :
% 9.49/5.27        ( ( ord_less_nat @ Z3 @ X5 )
% 9.49/5.27       => ~ ( ord_less_eq_nat @ X5 @ T ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3258_pinf_I6_J,axiom,
% 9.49/5.27      ! [T: int] :
% 9.49/5.27      ? [Z3: int] :
% 9.49/5.27      ! [X5: int] :
% 9.49/5.27        ( ( ord_less_int @ Z3 @ X5 )
% 9.49/5.27       => ~ ( ord_less_eq_int @ X5 @ T ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3259_inf__period_I2_J,axiom,
% 9.49/5.27      ! [P: rat > $o,D4: rat,Q: rat > $o] :
% 9.49/5.27        ( ! [X3: rat,K2: rat] :
% 9.49/5.27            ( ( P @ X3 )
% 9.49/5.27            = ( P @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K2 @ D4 ) ) ) )
% 9.49/5.27       => ( ! [X3: rat,K2: rat] :
% 9.49/5.27              ( ( Q @ X3 )
% 9.49/5.27              = ( Q @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K2 @ D4 ) ) ) )
% 9.49/5.27         => ! [X5: rat,K4: rat] :
% 9.49/5.27              ( ( ( P @ X5 )
% 9.49/5.27                | ( Q @ X5 ) )
% 9.49/5.27              = ( ( P @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D4 ) ) )
% 9.49/5.27                | ( Q @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D4 ) ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3260_inf__period_I2_J,axiom,
% 9.49/5.27      ! [P: complex > $o,D4: complex,Q: complex > $o] :
% 9.49/5.27        ( ! [X3: complex,K2: complex] :
% 9.49/5.27            ( ( P @ X3 )
% 9.49/5.27            = ( P @ ( minus_minus_complex @ X3 @ ( times_times_complex @ K2 @ D4 ) ) ) )
% 9.49/5.27       => ( ! [X3: complex,K2: complex] :
% 9.49/5.27              ( ( Q @ X3 )
% 9.49/5.27              = ( Q @ ( minus_minus_complex @ X3 @ ( times_times_complex @ K2 @ D4 ) ) ) )
% 9.49/5.27         => ! [X5: complex,K4: complex] :
% 9.49/5.27              ( ( ( P @ X5 )
% 9.49/5.27                | ( Q @ X5 ) )
% 9.49/5.27              = ( ( P @ ( minus_minus_complex @ X5 @ ( times_times_complex @ K4 @ D4 ) ) )
% 9.49/5.27                | ( Q @ ( minus_minus_complex @ X5 @ ( times_times_complex @ K4 @ D4 ) ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3261_inf__period_I2_J,axiom,
% 9.49/5.27      ! [P: real > $o,D4: real,Q: real > $o] :
% 9.49/5.27        ( ! [X3: real,K2: real] :
% 9.49/5.27            ( ( P @ X3 )
% 9.49/5.27            = ( P @ ( minus_minus_real @ X3 @ ( times_times_real @ K2 @ D4 ) ) ) )
% 9.49/5.27       => ( ! [X3: real,K2: real] :
% 9.49/5.27              ( ( Q @ X3 )
% 9.49/5.27              = ( Q @ ( minus_minus_real @ X3 @ ( times_times_real @ K2 @ D4 ) ) ) )
% 9.49/5.27         => ! [X5: real,K4: real] :
% 9.49/5.27              ( ( ( P @ X5 )
% 9.49/5.27                | ( Q @ X5 ) )
% 9.49/5.27              = ( ( P @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D4 ) ) )
% 9.49/5.27                | ( Q @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D4 ) ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3262_inf__period_I2_J,axiom,
% 9.49/5.27      ! [P: int > $o,D4: int,Q: int > $o] :
% 9.49/5.27        ( ! [X3: int,K2: int] :
% 9.49/5.27            ( ( P @ X3 )
% 9.49/5.27            = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 9.49/5.27       => ( ! [X3: int,K2: int] :
% 9.49/5.27              ( ( Q @ X3 )
% 9.49/5.27              = ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 9.49/5.27         => ! [X5: int,K4: int] :
% 9.49/5.27              ( ( ( P @ X5 )
% 9.49/5.27                | ( Q @ X5 ) )
% 9.49/5.27              = ( ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D4 ) ) )
% 9.49/5.27                | ( Q @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D4 ) ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3263_inf__period_I1_J,axiom,
% 9.49/5.27      ! [P: rat > $o,D4: rat,Q: rat > $o] :
% 9.49/5.27        ( ! [X3: rat,K2: rat] :
% 9.49/5.27            ( ( P @ X3 )
% 9.49/5.27            = ( P @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K2 @ D4 ) ) ) )
% 9.49/5.27       => ( ! [X3: rat,K2: rat] :
% 9.49/5.27              ( ( Q @ X3 )
% 9.49/5.27              = ( Q @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K2 @ D4 ) ) ) )
% 9.49/5.27         => ! [X5: rat,K4: rat] :
% 9.49/5.27              ( ( ( P @ X5 )
% 9.49/5.27                & ( Q @ X5 ) )
% 9.49/5.27              = ( ( P @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D4 ) ) )
% 9.49/5.27                & ( Q @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D4 ) ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3264_inf__period_I1_J,axiom,
% 9.49/5.27      ! [P: complex > $o,D4: complex,Q: complex > $o] :
% 9.49/5.27        ( ! [X3: complex,K2: complex] :
% 9.49/5.27            ( ( P @ X3 )
% 9.49/5.27            = ( P @ ( minus_minus_complex @ X3 @ ( times_times_complex @ K2 @ D4 ) ) ) )
% 9.49/5.27       => ( ! [X3: complex,K2: complex] :
% 9.49/5.27              ( ( Q @ X3 )
% 9.49/5.27              = ( Q @ ( minus_minus_complex @ X3 @ ( times_times_complex @ K2 @ D4 ) ) ) )
% 9.49/5.27         => ! [X5: complex,K4: complex] :
% 9.49/5.27              ( ( ( P @ X5 )
% 9.49/5.27                & ( Q @ X5 ) )
% 9.49/5.27              = ( ( P @ ( minus_minus_complex @ X5 @ ( times_times_complex @ K4 @ D4 ) ) )
% 9.49/5.27                & ( Q @ ( minus_minus_complex @ X5 @ ( times_times_complex @ K4 @ D4 ) ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3265_inf__period_I1_J,axiom,
% 9.49/5.27      ! [P: real > $o,D4: real,Q: real > $o] :
% 9.49/5.27        ( ! [X3: real,K2: real] :
% 9.49/5.27            ( ( P @ X3 )
% 9.49/5.27            = ( P @ ( minus_minus_real @ X3 @ ( times_times_real @ K2 @ D4 ) ) ) )
% 9.49/5.27       => ( ! [X3: real,K2: real] :
% 9.49/5.27              ( ( Q @ X3 )
% 9.49/5.27              = ( Q @ ( minus_minus_real @ X3 @ ( times_times_real @ K2 @ D4 ) ) ) )
% 9.49/5.27         => ! [X5: real,K4: real] :
% 9.49/5.27              ( ( ( P @ X5 )
% 9.49/5.27                & ( Q @ X5 ) )
% 9.49/5.27              = ( ( P @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D4 ) ) )
% 9.49/5.27                & ( Q @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D4 ) ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3266_inf__period_I1_J,axiom,
% 9.49/5.27      ! [P: int > $o,D4: int,Q: int > $o] :
% 9.49/5.27        ( ! [X3: int,K2: int] :
% 9.49/5.27            ( ( P @ X3 )
% 9.49/5.27            = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 9.49/5.27       => ( ! [X3: int,K2: int] :
% 9.49/5.27              ( ( Q @ X3 )
% 9.49/5.27              = ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 9.49/5.27         => ! [X5: int,K4: int] :
% 9.49/5.27              ( ( ( P @ X5 )
% 9.49/5.27                & ( Q @ X5 ) )
% 9.49/5.27              = ( ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D4 ) ) )
% 9.49/5.27                & ( Q @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D4 ) ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3267_atLeastatMost__psubset__iff,axiom,
% 9.49/5.27      ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.49/5.27        ( ( ord_less_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D2 ) )
% 9.49/5.27        = ( ( ~ ( ord_less_eq_rat @ A @ B )
% 9.49/5.27            | ( ( ord_less_eq_rat @ C @ A )
% 9.49/5.27              & ( ord_less_eq_rat @ B @ D2 )
% 9.49/5.27              & ( ( ord_less_rat @ C @ A )
% 9.49/5.27                | ( ord_less_rat @ B @ D2 ) ) ) )
% 9.49/5.27          & ( ord_less_eq_rat @ C @ D2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3268_atLeastatMost__psubset__iff,axiom,
% 9.49/5.27      ! [A: set_real,B: set_real,C: set_real,D2: set_real] :
% 9.49/5.27        ( ( ord_le7926960851185191020t_real @ ( set_or7743017856606604397t_real @ A @ B ) @ ( set_or7743017856606604397t_real @ C @ D2 ) )
% 9.49/5.27        = ( ( ~ ( ord_less_eq_set_real @ A @ B )
% 9.49/5.27            | ( ( ord_less_eq_set_real @ C @ A )
% 9.49/5.27              & ( ord_less_eq_set_real @ B @ D2 )
% 9.49/5.27              & ( ( ord_less_set_real @ C @ A )
% 9.49/5.27                | ( ord_less_set_real @ B @ D2 ) ) ) )
% 9.49/5.27          & ( ord_less_eq_set_real @ C @ D2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3269_atLeastatMost__psubset__iff,axiom,
% 9.49/5.27      ! [A: set_nat,B: set_nat,C: set_nat,D2: set_nat] :
% 9.49/5.27        ( ( ord_less_set_set_nat @ ( set_or4548717258645045905et_nat @ A @ B ) @ ( set_or4548717258645045905et_nat @ C @ D2 ) )
% 9.49/5.27        = ( ( ~ ( ord_less_eq_set_nat @ A @ B )
% 9.49/5.27            | ( ( ord_less_eq_set_nat @ C @ A )
% 9.49/5.27              & ( ord_less_eq_set_nat @ B @ D2 )
% 9.49/5.27              & ( ( ord_less_set_nat @ C @ A )
% 9.49/5.27                | ( ord_less_set_nat @ B @ D2 ) ) ) )
% 9.49/5.27          & ( ord_less_eq_set_nat @ C @ D2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3270_atLeastatMost__psubset__iff,axiom,
% 9.49/5.27      ! [A: num,B: num,C: num,D2: num] :
% 9.49/5.27        ( ( ord_less_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D2 ) )
% 9.49/5.27        = ( ( ~ ( ord_less_eq_num @ A @ B )
% 9.49/5.27            | ( ( ord_less_eq_num @ C @ A )
% 9.49/5.27              & ( ord_less_eq_num @ B @ D2 )
% 9.49/5.27              & ( ( ord_less_num @ C @ A )
% 9.49/5.27                | ( ord_less_num @ B @ D2 ) ) ) )
% 9.49/5.27          & ( ord_less_eq_num @ C @ D2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3271_atLeastatMost__psubset__iff,axiom,
% 9.49/5.27      ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.49/5.27        ( ( ord_less_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D2 ) )
% 9.49/5.27        = ( ( ~ ( ord_less_eq_nat @ A @ B )
% 9.49/5.27            | ( ( ord_less_eq_nat @ C @ A )
% 9.49/5.27              & ( ord_less_eq_nat @ B @ D2 )
% 9.49/5.27              & ( ( ord_less_nat @ C @ A )
% 9.49/5.27                | ( ord_less_nat @ B @ D2 ) ) ) )
% 9.49/5.27          & ( ord_less_eq_nat @ C @ D2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3272_atLeastatMost__psubset__iff,axiom,
% 9.49/5.27      ! [A: int,B: int,C: int,D2: int] :
% 9.49/5.27        ( ( ord_less_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D2 ) )
% 9.49/5.27        = ( ( ~ ( ord_less_eq_int @ A @ B )
% 9.49/5.27            | ( ( ord_less_eq_int @ C @ A )
% 9.49/5.27              & ( ord_less_eq_int @ B @ D2 )
% 9.49/5.27              & ( ( ord_less_int @ C @ A )
% 9.49/5.27                | ( ord_less_int @ B @ D2 ) ) ) )
% 9.49/5.27          & ( ord_less_eq_int @ C @ D2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3273_atLeastatMost__psubset__iff,axiom,
% 9.49/5.27      ! [A: real,B: real,C: real,D2: real] :
% 9.49/5.27        ( ( ord_less_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D2 ) )
% 9.49/5.27        = ( ( ~ ( ord_less_eq_real @ A @ B )
% 9.49/5.27            | ( ( ord_less_eq_real @ C @ A )
% 9.49/5.27              & ( ord_less_eq_real @ B @ D2 )
% 9.49/5.27              & ( ( ord_less_real @ C @ A )
% 9.49/5.27                | ( ord_less_real @ B @ D2 ) ) ) )
% 9.49/5.27          & ( ord_less_eq_real @ C @ D2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3274_plusinfinity,axiom,
% 9.49/5.27      ! [D2: int,P5: int > $o,P: int > $o] :
% 9.49/5.27        ( ( ord_less_int @ zero_zero_int @ D2 )
% 9.49/5.27       => ( ! [X3: int,K2: int] :
% 9.49/5.27              ( ( P5 @ X3 )
% 9.49/5.27              = ( P5 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D2 ) ) ) )
% 9.49/5.27         => ( ? [Z2: int] :
% 9.49/5.27              ! [X3: int] :
% 9.49/5.27                ( ( ord_less_int @ Z2 @ X3 )
% 9.49/5.27               => ( ( P @ X3 )
% 9.49/5.27                  = ( P5 @ X3 ) ) )
% 9.49/5.27           => ( ? [X_1: int] : ( P5 @ X_1 )
% 9.49/5.27             => ? [X_12: int] : ( P @ X_12 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3275_minusinfinity,axiom,
% 9.49/5.27      ! [D2: int,P1: int > $o,P: int > $o] :
% 9.49/5.27        ( ( ord_less_int @ zero_zero_int @ D2 )
% 9.49/5.27       => ( ! [X3: int,K2: int] :
% 9.49/5.27              ( ( P1 @ X3 )
% 9.49/5.27              = ( P1 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D2 ) ) ) )
% 9.49/5.27         => ( ? [Z2: int] :
% 9.49/5.27              ! [X3: int] :
% 9.49/5.27                ( ( ord_less_int @ X3 @ Z2 )
% 9.49/5.27               => ( ( P @ X3 )
% 9.49/5.27                  = ( P1 @ X3 ) ) )
% 9.49/5.27           => ( ? [X_1: int] : ( P1 @ X_1 )
% 9.49/5.27             => ? [X_12: int] : ( P @ X_12 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3276_Diff__eq__empty__iff,axiom,
% 9.49/5.27      ! [A2: set_int,B2: set_int] :
% 9.49/5.27        ( ( ( minus_minus_set_int @ A2 @ B2 )
% 9.49/5.27          = bot_bot_set_int )
% 9.49/5.27        = ( ord_less_eq_set_int @ A2 @ B2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3277_Diff__eq__empty__iff,axiom,
% 9.49/5.27      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.49/5.27        ( ( ( minus_1356011639430497352at_nat @ A2 @ B2 )
% 9.49/5.27          = bot_bo2099793752762293965at_nat )
% 9.49/5.27        = ( ord_le3146513528884898305at_nat @ A2 @ B2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3278_Diff__eq__empty__iff,axiom,
% 9.49/5.27      ! [A2: set_real,B2: set_real] :
% 9.49/5.27        ( ( ( minus_minus_set_real @ A2 @ B2 )
% 9.49/5.27          = bot_bot_set_real )
% 9.49/5.27        = ( ord_less_eq_set_real @ A2 @ B2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3279_Diff__eq__empty__iff,axiom,
% 9.49/5.27      ! [A2: set_nat,B2: set_nat] :
% 9.49/5.27        ( ( ( minus_minus_set_nat @ A2 @ B2 )
% 9.49/5.27          = bot_bot_set_nat )
% 9.49/5.27        = ( ord_less_eq_set_nat @ A2 @ B2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3280_delete__correct,axiom,
% 9.49/5.27      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 9.49/5.27        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.27       => ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_delete @ T @ X ) )
% 9.49/5.27          = ( minus_minus_set_nat @ ( vEBT_set_vebt @ T ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3281_unset__bit__0,axiom,
% 9.49/5.27      ! [A: int] :
% 9.49/5.27        ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A )
% 9.49/5.27        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3282_unset__bit__0,axiom,
% 9.49/5.27      ! [A: nat] :
% 9.49/5.27        ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A )
% 9.49/5.27        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3283_Bolzano,axiom,
% 9.49/5.27      ! [A: real,B: real,P: real > real > $o] :
% 9.49/5.27        ( ( ord_less_eq_real @ A @ B )
% 9.49/5.27       => ( ! [A4: real,B3: real,C2: real] :
% 9.49/5.27              ( ( P @ A4 @ B3 )
% 9.49/5.27             => ( ( P @ B3 @ C2 )
% 9.49/5.27               => ( ( ord_less_eq_real @ A4 @ B3 )
% 9.49/5.27                 => ( ( ord_less_eq_real @ B3 @ C2 )
% 9.49/5.27                   => ( P @ A4 @ C2 ) ) ) ) )
% 9.49/5.27         => ( ! [X3: real] :
% 9.49/5.27                ( ( ord_less_eq_real @ A @ X3 )
% 9.49/5.27               => ( ( ord_less_eq_real @ X3 @ B )
% 9.49/5.27                 => ? [D5: real] :
% 9.49/5.27                      ( ( ord_less_real @ zero_zero_real @ D5 )
% 9.49/5.27                      & ! [A4: real,B3: real] :
% 9.49/5.27                          ( ( ( ord_less_eq_real @ A4 @ X3 )
% 9.49/5.27                            & ( ord_less_eq_real @ X3 @ B3 )
% 9.49/5.27                            & ( ord_less_real @ ( minus_minus_real @ B3 @ A4 ) @ D5 ) )
% 9.49/5.27                         => ( P @ A4 @ B3 ) ) ) ) )
% 9.49/5.27           => ( P @ A @ B ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3284_mult__le__cancel__iff1,axiom,
% 9.49/5.27      ! [Z: real,X: real,Y2: real] :
% 9.49/5.27        ( ( ord_less_real @ zero_zero_real @ Z )
% 9.49/5.27       => ( ( ord_less_eq_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y2 @ Z ) )
% 9.49/5.27          = ( ord_less_eq_real @ X @ Y2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3285_mult__le__cancel__iff1,axiom,
% 9.49/5.27      ! [Z: rat,X: rat,Y2: rat] :
% 9.49/5.27        ( ( ord_less_rat @ zero_zero_rat @ Z )
% 9.49/5.27       => ( ( ord_less_eq_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y2 @ Z ) )
% 9.49/5.27          = ( ord_less_eq_rat @ X @ Y2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3286_mult__le__cancel__iff1,axiom,
% 9.49/5.27      ! [Z: int,X: int,Y2: int] :
% 9.49/5.27        ( ( ord_less_int @ zero_zero_int @ Z )
% 9.49/5.27       => ( ( ord_less_eq_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y2 @ Z ) )
% 9.49/5.27          = ( ord_less_eq_int @ X @ Y2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3287_mult__le__cancel__iff2,axiom,
% 9.49/5.27      ! [Z: real,X: real,Y2: real] :
% 9.49/5.27        ( ( ord_less_real @ zero_zero_real @ Z )
% 9.49/5.27       => ( ( ord_less_eq_real @ ( times_times_real @ Z @ X ) @ ( times_times_real @ Z @ Y2 ) )
% 9.49/5.27          = ( ord_less_eq_real @ X @ Y2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3288_mult__le__cancel__iff2,axiom,
% 9.49/5.27      ! [Z: rat,X: rat,Y2: rat] :
% 9.49/5.27        ( ( ord_less_rat @ zero_zero_rat @ Z )
% 9.49/5.27       => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ X ) @ ( times_times_rat @ Z @ Y2 ) )
% 9.49/5.27          = ( ord_less_eq_rat @ X @ Y2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3289_mult__le__cancel__iff2,axiom,
% 9.49/5.27      ! [Z: int,X: int,Y2: int] :
% 9.49/5.27        ( ( ord_less_int @ zero_zero_int @ Z )
% 9.49/5.27       => ( ( ord_less_eq_int @ ( times_times_int @ Z @ X ) @ ( times_times_int @ Z @ Y2 ) )
% 9.49/5.27          = ( ord_less_eq_int @ X @ Y2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3290_DiffI,axiom,
% 9.49/5.27      ! [C: complex,A2: set_complex,B2: set_complex] :
% 9.49/5.27        ( ( member_complex @ C @ A2 )
% 9.49/5.27       => ( ~ ( member_complex @ C @ B2 )
% 9.49/5.27         => ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3291_DiffI,axiom,
% 9.49/5.27      ! [C: real,A2: set_real,B2: set_real] :
% 9.49/5.27        ( ( member_real @ C @ A2 )
% 9.49/5.27       => ( ~ ( member_real @ C @ B2 )
% 9.49/5.27         => ( member_real @ C @ ( minus_minus_set_real @ A2 @ B2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3292_DiffI,axiom,
% 9.49/5.27      ! [C: int,A2: set_int,B2: set_int] :
% 9.49/5.27        ( ( member_int @ C @ A2 )
% 9.49/5.27       => ( ~ ( member_int @ C @ B2 )
% 9.49/5.27         => ( member_int @ C @ ( minus_minus_set_int @ A2 @ B2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3293_DiffI,axiom,
% 9.49/5.27      ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.49/5.27        ( ( member8440522571783428010at_nat @ C @ A2 )
% 9.49/5.27       => ( ~ ( member8440522571783428010at_nat @ C @ B2 )
% 9.49/5.27         => ( member8440522571783428010at_nat @ C @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3294_DiffI,axiom,
% 9.49/5.27      ! [C: nat,A2: set_nat,B2: set_nat] :
% 9.49/5.27        ( ( member_nat @ C @ A2 )
% 9.49/5.27       => ( ~ ( member_nat @ C @ B2 )
% 9.49/5.27         => ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3295_Diff__iff,axiom,
% 9.49/5.27      ! [C: complex,A2: set_complex,B2: set_complex] :
% 9.49/5.27        ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B2 ) )
% 9.49/5.27        = ( ( member_complex @ C @ A2 )
% 9.49/5.27          & ~ ( member_complex @ C @ B2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3296_Diff__iff,axiom,
% 9.49/5.27      ! [C: real,A2: set_real,B2: set_real] :
% 9.49/5.27        ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B2 ) )
% 9.49/5.27        = ( ( member_real @ C @ A2 )
% 9.49/5.27          & ~ ( member_real @ C @ B2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3297_Diff__iff,axiom,
% 9.49/5.27      ! [C: int,A2: set_int,B2: set_int] :
% 9.49/5.27        ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B2 ) )
% 9.49/5.27        = ( ( member_int @ C @ A2 )
% 9.49/5.27          & ~ ( member_int @ C @ B2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3298_Diff__iff,axiom,
% 9.49/5.27      ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.49/5.27        ( ( member8440522571783428010at_nat @ C @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) )
% 9.49/5.27        = ( ( member8440522571783428010at_nat @ C @ A2 )
% 9.49/5.27          & ~ ( member8440522571783428010at_nat @ C @ B2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3299_Diff__iff,axiom,
% 9.49/5.27      ! [C: nat,A2: set_nat,B2: set_nat] :
% 9.49/5.27        ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 9.49/5.27        = ( ( member_nat @ C @ A2 )
% 9.49/5.27          & ~ ( member_nat @ C @ B2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3300_Diff__idemp,axiom,
% 9.49/5.27      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.49/5.27        ( ( minus_1356011639430497352at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) @ B2 )
% 9.49/5.27        = ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3301_Diff__idemp,axiom,
% 9.49/5.27      ! [A2: set_nat,B2: set_nat] :
% 9.49/5.27        ( ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ B2 )
% 9.49/5.27        = ( minus_minus_set_nat @ A2 @ B2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3302_delete__correct_H,axiom,
% 9.49/5.27      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 9.49/5.27        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.27       => ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_delete @ T @ X ) )
% 9.49/5.27          = ( minus_minus_set_nat @ ( vEBT_VEBT_set_vebt @ T ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3303_Diff__cancel,axiom,
% 9.49/5.27      ! [A2: set_int] :
% 9.49/5.27        ( ( minus_minus_set_int @ A2 @ A2 )
% 9.49/5.27        = bot_bot_set_int ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3304_Diff__cancel,axiom,
% 9.49/5.27      ! [A2: set_real] :
% 9.49/5.27        ( ( minus_minus_set_real @ A2 @ A2 )
% 9.49/5.27        = bot_bot_set_real ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3305_Diff__cancel,axiom,
% 9.49/5.27      ! [A2: set_Pr1261947904930325089at_nat] :
% 9.49/5.27        ( ( minus_1356011639430497352at_nat @ A2 @ A2 )
% 9.49/5.27        = bot_bo2099793752762293965at_nat ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3306_Diff__cancel,axiom,
% 9.49/5.27      ! [A2: set_nat] :
% 9.49/5.27        ( ( minus_minus_set_nat @ A2 @ A2 )
% 9.49/5.27        = bot_bot_set_nat ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3307_empty__Diff,axiom,
% 9.49/5.27      ! [A2: set_int] :
% 9.49/5.27        ( ( minus_minus_set_int @ bot_bot_set_int @ A2 )
% 9.49/5.27        = bot_bot_set_int ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3308_empty__Diff,axiom,
% 9.49/5.27      ! [A2: set_real] :
% 9.49/5.27        ( ( minus_minus_set_real @ bot_bot_set_real @ A2 )
% 9.49/5.27        = bot_bot_set_real ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3309_empty__Diff,axiom,
% 9.49/5.27      ! [A2: set_Pr1261947904930325089at_nat] :
% 9.49/5.27        ( ( minus_1356011639430497352at_nat @ bot_bo2099793752762293965at_nat @ A2 )
% 9.49/5.27        = bot_bo2099793752762293965at_nat ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3310_empty__Diff,axiom,
% 9.49/5.27      ! [A2: set_nat] :
% 9.49/5.27        ( ( minus_minus_set_nat @ bot_bot_set_nat @ A2 )
% 9.49/5.27        = bot_bot_set_nat ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3311_Diff__empty,axiom,
% 9.49/5.27      ! [A2: set_int] :
% 9.49/5.27        ( ( minus_minus_set_int @ A2 @ bot_bot_set_int )
% 9.49/5.27        = A2 ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3312_Diff__empty,axiom,
% 9.49/5.27      ! [A2: set_real] :
% 9.49/5.27        ( ( minus_minus_set_real @ A2 @ bot_bot_set_real )
% 9.49/5.27        = A2 ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3313_Diff__empty,axiom,
% 9.49/5.27      ! [A2: set_Pr1261947904930325089at_nat] :
% 9.49/5.27        ( ( minus_1356011639430497352at_nat @ A2 @ bot_bo2099793752762293965at_nat )
% 9.49/5.27        = A2 ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3314_Diff__empty,axiom,
% 9.49/5.27      ! [A2: set_nat] :
% 9.49/5.27        ( ( minus_minus_set_nat @ A2 @ bot_bot_set_nat )
% 9.49/5.27        = A2 ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3315_Diff__insert0,axiom,
% 9.49/5.27      ! [X: vEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT] :
% 9.49/5.27        ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 9.49/5.27       => ( ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ B2 ) )
% 9.49/5.27          = ( minus_5127226145743854075T_VEBT @ A2 @ B2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3316_Diff__insert0,axiom,
% 9.49/5.27      ! [X: complex,A2: set_complex,B2: set_complex] :
% 9.49/5.27        ( ~ ( member_complex @ X @ A2 )
% 9.49/5.27       => ( ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ B2 ) )
% 9.49/5.27          = ( minus_811609699411566653omplex @ A2 @ B2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3317_Diff__insert0,axiom,
% 9.49/5.27      ! [X: real,A2: set_real,B2: set_real] :
% 9.49/5.27        ( ~ ( member_real @ X @ A2 )
% 9.49/5.27       => ( ( minus_minus_set_real @ A2 @ ( insert_real @ X @ B2 ) )
% 9.49/5.27          = ( minus_minus_set_real @ A2 @ B2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3318_Diff__insert0,axiom,
% 9.49/5.27      ! [X: int,A2: set_int,B2: set_int] :
% 9.49/5.27        ( ~ ( member_int @ X @ A2 )
% 9.49/5.27       => ( ( minus_minus_set_int @ A2 @ ( insert_int @ X @ B2 ) )
% 9.49/5.27          = ( minus_minus_set_int @ A2 @ B2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3319_Diff__insert0,axiom,
% 9.49/5.27      ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.49/5.27        ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 9.49/5.27       => ( ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ B2 ) )
% 9.49/5.27          = ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3320_Diff__insert0,axiom,
% 9.49/5.27      ! [X: nat,A2: set_nat,B2: set_nat] :
% 9.49/5.27        ( ~ ( member_nat @ X @ A2 )
% 9.49/5.27       => ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ B2 ) )
% 9.49/5.27          = ( minus_minus_set_nat @ A2 @ B2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3321_insert__Diff1,axiom,
% 9.49/5.27      ! [X: vEBT_VEBT,B2: set_VEBT_VEBT,A2: set_VEBT_VEBT] :
% 9.49/5.27        ( ( member_VEBT_VEBT @ X @ B2 )
% 9.49/5.27       => ( ( minus_5127226145743854075T_VEBT @ ( insert_VEBT_VEBT @ X @ A2 ) @ B2 )
% 9.49/5.27          = ( minus_5127226145743854075T_VEBT @ A2 @ B2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3322_insert__Diff1,axiom,
% 9.49/5.27      ! [X: complex,B2: set_complex,A2: set_complex] :
% 9.49/5.27        ( ( member_complex @ X @ B2 )
% 9.49/5.27       => ( ( minus_811609699411566653omplex @ ( insert_complex @ X @ A2 ) @ B2 )
% 9.49/5.27          = ( minus_811609699411566653omplex @ A2 @ B2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3323_insert__Diff1,axiom,
% 9.49/5.27      ! [X: real,B2: set_real,A2: set_real] :
% 9.49/5.27        ( ( member_real @ X @ B2 )
% 9.49/5.27       => ( ( minus_minus_set_real @ ( insert_real @ X @ A2 ) @ B2 )
% 9.49/5.27          = ( minus_minus_set_real @ A2 @ B2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3324_insert__Diff1,axiom,
% 9.49/5.27      ! [X: int,B2: set_int,A2: set_int] :
% 9.49/5.27        ( ( member_int @ X @ B2 )
% 9.49/5.27       => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ B2 )
% 9.49/5.27          = ( minus_minus_set_int @ A2 @ B2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3325_insert__Diff1,axiom,
% 9.49/5.27      ! [X: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 9.49/5.27        ( ( member8440522571783428010at_nat @ X @ B2 )
% 9.49/5.27       => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X @ A2 ) @ B2 )
% 9.49/5.27          = ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3326_insert__Diff1,axiom,
% 9.49/5.27      ! [X: nat,B2: set_nat,A2: set_nat] :
% 9.49/5.27        ( ( member_nat @ X @ B2 )
% 9.49/5.27       => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ B2 )
% 9.49/5.27          = ( minus_minus_set_nat @ A2 @ B2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3327_unset__bit__nonnegative__int__iff,axiom,
% 9.49/5.27      ! [N: nat,K: int] :
% 9.49/5.27        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se4203085406695923979it_int @ N @ K ) )
% 9.49/5.27        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3328_unset__bit__negative__int__iff,axiom,
% 9.49/5.27      ! [N: nat,K: int] :
% 9.49/5.27        ( ( ord_less_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ zero_zero_int )
% 9.49/5.27        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3329_insert__Diff__single,axiom,
% 9.49/5.27      ! [A: vEBT_VEBT,A2: set_VEBT_VEBT] :
% 9.49/5.27        ( ( insert_VEBT_VEBT @ A @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 9.49/5.27        = ( insert_VEBT_VEBT @ A @ A2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3330_insert__Diff__single,axiom,
% 9.49/5.27      ! [A: int,A2: set_int] :
% 9.49/5.27        ( ( insert_int @ A @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 9.49/5.27        = ( insert_int @ A @ A2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3331_insert__Diff__single,axiom,
% 9.49/5.27      ! [A: real,A2: set_real] :
% 9.49/5.27        ( ( insert_real @ A @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 9.49/5.27        = ( insert_real @ A @ A2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3332_insert__Diff__single,axiom,
% 9.49/5.27      ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 9.49/5.27        ( ( insert8211810215607154385at_nat @ A @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 9.49/5.27        = ( insert8211810215607154385at_nat @ A @ A2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3333_insert__Diff__single,axiom,
% 9.49/5.27      ! [A: nat,A2: set_nat] :
% 9.49/5.27        ( ( insert_nat @ A @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 9.49/5.27        = ( insert_nat @ A @ A2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3334_Diff__insert,axiom,
% 9.49/5.27      ! [A2: set_VEBT_VEBT,A: vEBT_VEBT,B2: set_VEBT_VEBT] :
% 9.49/5.27        ( ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ B2 ) )
% 9.49/5.27        = ( minus_5127226145743854075T_VEBT @ ( minus_5127226145743854075T_VEBT @ A2 @ B2 ) @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3335_Diff__insert,axiom,
% 9.49/5.27      ! [A2: set_int,A: int,B2: set_int] :
% 9.49/5.27        ( ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B2 ) )
% 9.49/5.27        = ( minus_minus_set_int @ ( minus_minus_set_int @ A2 @ B2 ) @ ( insert_int @ A @ bot_bot_set_int ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3336_Diff__insert,axiom,
% 9.49/5.27      ! [A2: set_real,A: real,B2: set_real] :
% 9.49/5.27        ( ( minus_minus_set_real @ A2 @ ( insert_real @ A @ B2 ) )
% 9.49/5.27        = ( minus_minus_set_real @ ( minus_minus_set_real @ A2 @ B2 ) @ ( insert_real @ A @ bot_bot_set_real ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3337_Diff__insert,axiom,
% 9.49/5.27      ! [A2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.49/5.27        ( ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ B2 ) )
% 9.49/5.27        = ( minus_1356011639430497352at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3338_Diff__insert,axiom,
% 9.49/5.27      ! [A2: set_nat,A: nat,B2: set_nat] :
% 9.49/5.27        ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B2 ) )
% 9.49/5.27        = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3339_insert__Diff,axiom,
% 9.49/5.27      ! [A: vEBT_VEBT,A2: set_VEBT_VEBT] :
% 9.49/5.27        ( ( member_VEBT_VEBT @ A @ A2 )
% 9.49/5.27       => ( ( insert_VEBT_VEBT @ A @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 9.49/5.27          = A2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3340_insert__Diff,axiom,
% 9.49/5.27      ! [A: complex,A2: set_complex] :
% 9.49/5.27        ( ( member_complex @ A @ A2 )
% 9.49/5.27       => ( ( insert_complex @ A @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 9.49/5.27          = A2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3341_insert__Diff,axiom,
% 9.49/5.27      ! [A: int,A2: set_int] :
% 9.49/5.27        ( ( member_int @ A @ A2 )
% 9.49/5.27       => ( ( insert_int @ A @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 9.49/5.27          = A2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3342_insert__Diff,axiom,
% 9.49/5.27      ! [A: real,A2: set_real] :
% 9.49/5.27        ( ( member_real @ A @ A2 )
% 9.49/5.27       => ( ( insert_real @ A @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 9.49/5.27          = A2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3343_insert__Diff,axiom,
% 9.49/5.27      ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 9.49/5.27        ( ( member8440522571783428010at_nat @ A @ A2 )
% 9.49/5.27       => ( ( insert8211810215607154385at_nat @ A @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 9.49/5.27          = A2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3344_insert__Diff,axiom,
% 9.49/5.27      ! [A: nat,A2: set_nat] :
% 9.49/5.27        ( ( member_nat @ A @ A2 )
% 9.49/5.27       => ( ( insert_nat @ A @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 9.49/5.27          = A2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3345_Diff__insert2,axiom,
% 9.49/5.27      ! [A2: set_VEBT_VEBT,A: vEBT_VEBT,B2: set_VEBT_VEBT] :
% 9.49/5.27        ( ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ B2 ) )
% 9.49/5.27        = ( minus_5127226145743854075T_VEBT @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) @ B2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3346_Diff__insert2,axiom,
% 9.49/5.27      ! [A2: set_int,A: int,B2: set_int] :
% 9.49/5.27        ( ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B2 ) )
% 9.49/5.27        = ( minus_minus_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) @ B2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3347_Diff__insert2,axiom,
% 9.49/5.27      ! [A2: set_real,A: real,B2: set_real] :
% 9.49/5.27        ( ( minus_minus_set_real @ A2 @ ( insert_real @ A @ B2 ) )
% 9.49/5.27        = ( minus_minus_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) @ B2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3348_Diff__insert2,axiom,
% 9.49/5.27      ! [A2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.49/5.27        ( ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ B2 ) )
% 9.49/5.27        = ( minus_1356011639430497352at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) @ B2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3349_Diff__insert2,axiom,
% 9.49/5.27      ! [A2: set_nat,A: nat,B2: set_nat] :
% 9.49/5.27        ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B2 ) )
% 9.49/5.27        = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) @ B2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3350_Diff__insert__absorb,axiom,
% 9.49/5.27      ! [X: vEBT_VEBT,A2: set_VEBT_VEBT] :
% 9.49/5.27        ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 9.49/5.27       => ( ( minus_5127226145743854075T_VEBT @ ( insert_VEBT_VEBT @ X @ A2 ) @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) )
% 9.49/5.27          = A2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3351_Diff__insert__absorb,axiom,
% 9.49/5.27      ! [X: complex,A2: set_complex] :
% 9.49/5.27        ( ~ ( member_complex @ X @ A2 )
% 9.49/5.27       => ( ( minus_811609699411566653omplex @ ( insert_complex @ X @ A2 ) @ ( insert_complex @ X @ bot_bot_set_complex ) )
% 9.49/5.27          = A2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3352_Diff__insert__absorb,axiom,
% 9.49/5.27      ! [X: int,A2: set_int] :
% 9.49/5.27        ( ~ ( member_int @ X @ A2 )
% 9.49/5.27       => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ ( insert_int @ X @ bot_bot_set_int ) )
% 9.49/5.27          = A2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3353_Diff__insert__absorb,axiom,
% 9.49/5.27      ! [X: real,A2: set_real] :
% 9.49/5.27        ( ~ ( member_real @ X @ A2 )
% 9.49/5.27       => ( ( minus_minus_set_real @ ( insert_real @ X @ A2 ) @ ( insert_real @ X @ bot_bot_set_real ) )
% 9.49/5.27          = A2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3354_Diff__insert__absorb,axiom,
% 9.49/5.27      ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 9.49/5.27        ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 9.49/5.27       => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X @ A2 ) @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 9.49/5.27          = A2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3355_Diff__insert__absorb,axiom,
% 9.49/5.27      ! [X: nat,A2: set_nat] :
% 9.49/5.27        ( ~ ( member_nat @ X @ A2 )
% 9.49/5.27       => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 9.49/5.27          = A2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3356_subset__Diff__insert,axiom,
% 9.49/5.27      ! [A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,X: vEBT_VEBT,C4: set_VEBT_VEBT] :
% 9.49/5.27        ( ( ord_le4337996190870823476T_VEBT @ A2 @ ( minus_5127226145743854075T_VEBT @ B2 @ ( insert_VEBT_VEBT @ X @ C4 ) ) )
% 9.49/5.27        = ( ( ord_le4337996190870823476T_VEBT @ A2 @ ( minus_5127226145743854075T_VEBT @ B2 @ C4 ) )
% 9.49/5.27          & ~ ( member_VEBT_VEBT @ X @ A2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3357_subset__Diff__insert,axiom,
% 9.49/5.27      ! [A2: set_complex,B2: set_complex,X: complex,C4: set_complex] :
% 9.49/5.27        ( ( ord_le211207098394363844omplex @ A2 @ ( minus_811609699411566653omplex @ B2 @ ( insert_complex @ X @ C4 ) ) )
% 9.49/5.27        = ( ( ord_le211207098394363844omplex @ A2 @ ( minus_811609699411566653omplex @ B2 @ C4 ) )
% 9.49/5.27          & ~ ( member_complex @ X @ A2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3358_subset__Diff__insert,axiom,
% 9.49/5.27      ! [A2: set_int,B2: set_int,X: int,C4: set_int] :
% 9.49/5.27        ( ( ord_less_eq_set_int @ A2 @ ( minus_minus_set_int @ B2 @ ( insert_int @ X @ C4 ) ) )
% 9.49/5.27        = ( ( ord_less_eq_set_int @ A2 @ ( minus_minus_set_int @ B2 @ C4 ) )
% 9.49/5.27          & ~ ( member_int @ X @ A2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3359_subset__Diff__insert,axiom,
% 9.49/5.27      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,C4: set_Pr1261947904930325089at_nat] :
% 9.49/5.27        ( ( ord_le3146513528884898305at_nat @ A2 @ ( minus_1356011639430497352at_nat @ B2 @ ( insert8211810215607154385at_nat @ X @ C4 ) ) )
% 9.49/5.27        = ( ( ord_le3146513528884898305at_nat @ A2 @ ( minus_1356011639430497352at_nat @ B2 @ C4 ) )
% 9.49/5.27          & ~ ( member8440522571783428010at_nat @ X @ A2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3360_subset__Diff__insert,axiom,
% 9.49/5.27      ! [A2: set_real,B2: set_real,X: real,C4: set_real] :
% 9.49/5.27        ( ( ord_less_eq_set_real @ A2 @ ( minus_minus_set_real @ B2 @ ( insert_real @ X @ C4 ) ) )
% 9.49/5.27        = ( ( ord_less_eq_set_real @ A2 @ ( minus_minus_set_real @ B2 @ C4 ) )
% 9.49/5.27          & ~ ( member_real @ X @ A2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3361_subset__Diff__insert,axiom,
% 9.49/5.27      ! [A2: set_nat,B2: set_nat,X: nat,C4: set_nat] :
% 9.49/5.27        ( ( ord_less_eq_set_nat @ A2 @ ( minus_minus_set_nat @ B2 @ ( insert_nat @ X @ C4 ) ) )
% 9.49/5.27        = ( ( ord_less_eq_set_nat @ A2 @ ( minus_minus_set_nat @ B2 @ C4 ) )
% 9.49/5.27          & ~ ( member_nat @ X @ A2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3362_psubset__imp__ex__mem,axiom,
% 9.49/5.27      ! [A2: set_complex,B2: set_complex] :
% 9.49/5.27        ( ( ord_less_set_complex @ A2 @ B2 )
% 9.49/5.27       => ? [B3: complex] : ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B2 @ A2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3363_psubset__imp__ex__mem,axiom,
% 9.49/5.27      ! [A2: set_real,B2: set_real] :
% 9.49/5.27        ( ( ord_less_set_real @ A2 @ B2 )
% 9.49/5.27       => ? [B3: real] : ( member_real @ B3 @ ( minus_minus_set_real @ B2 @ A2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3364_psubset__imp__ex__mem,axiom,
% 9.49/5.27      ! [A2: set_int,B2: set_int] :
% 9.49/5.27        ( ( ord_less_set_int @ A2 @ B2 )
% 9.49/5.27       => ? [B3: int] : ( member_int @ B3 @ ( minus_minus_set_int @ B2 @ A2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3365_psubset__imp__ex__mem,axiom,
% 9.49/5.27      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.49/5.27        ( ( ord_le7866589430770878221at_nat @ A2 @ B2 )
% 9.49/5.27       => ? [B3: product_prod_nat_nat] : ( member8440522571783428010at_nat @ B3 @ ( minus_1356011639430497352at_nat @ B2 @ A2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3366_psubset__imp__ex__mem,axiom,
% 9.49/5.27      ! [A2: set_nat,B2: set_nat] :
% 9.49/5.27        ( ( ord_less_set_nat @ A2 @ B2 )
% 9.49/5.27       => ? [B3: nat] : ( member_nat @ B3 @ ( minus_minus_set_nat @ B2 @ A2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3367_DiffE,axiom,
% 9.49/5.27      ! [C: complex,A2: set_complex,B2: set_complex] :
% 9.49/5.27        ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B2 ) )
% 9.49/5.27       => ~ ( ( member_complex @ C @ A2 )
% 9.49/5.27           => ( member_complex @ C @ B2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3368_DiffE,axiom,
% 9.49/5.27      ! [C: real,A2: set_real,B2: set_real] :
% 9.49/5.27        ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B2 ) )
% 9.49/5.27       => ~ ( ( member_real @ C @ A2 )
% 9.49/5.27           => ( member_real @ C @ B2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3369_DiffE,axiom,
% 9.49/5.27      ! [C: int,A2: set_int,B2: set_int] :
% 9.49/5.27        ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B2 ) )
% 9.49/5.27       => ~ ( ( member_int @ C @ A2 )
% 9.49/5.27           => ( member_int @ C @ B2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3370_DiffE,axiom,
% 9.49/5.27      ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.49/5.27        ( ( member8440522571783428010at_nat @ C @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) )
% 9.49/5.27       => ~ ( ( member8440522571783428010at_nat @ C @ A2 )
% 9.49/5.27           => ( member8440522571783428010at_nat @ C @ B2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3371_DiffE,axiom,
% 9.49/5.27      ! [C: nat,A2: set_nat,B2: set_nat] :
% 9.49/5.27        ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 9.49/5.27       => ~ ( ( member_nat @ C @ A2 )
% 9.49/5.27           => ( member_nat @ C @ B2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3372_DiffD1,axiom,
% 9.49/5.27      ! [C: complex,A2: set_complex,B2: set_complex] :
% 9.49/5.27        ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B2 ) )
% 9.49/5.27       => ( member_complex @ C @ A2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3373_DiffD1,axiom,
% 9.49/5.27      ! [C: real,A2: set_real,B2: set_real] :
% 9.49/5.27        ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B2 ) )
% 9.49/5.27       => ( member_real @ C @ A2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3374_DiffD1,axiom,
% 9.49/5.27      ! [C: int,A2: set_int,B2: set_int] :
% 9.49/5.27        ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B2 ) )
% 9.49/5.27       => ( member_int @ C @ A2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3375_DiffD1,axiom,
% 9.49/5.27      ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.49/5.27        ( ( member8440522571783428010at_nat @ C @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) )
% 9.49/5.27       => ( member8440522571783428010at_nat @ C @ A2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3376_DiffD1,axiom,
% 9.49/5.27      ! [C: nat,A2: set_nat,B2: set_nat] :
% 9.49/5.27        ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 9.49/5.27       => ( member_nat @ C @ A2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3377_DiffD2,axiom,
% 9.49/5.27      ! [C: complex,A2: set_complex,B2: set_complex] :
% 9.49/5.27        ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B2 ) )
% 9.49/5.27       => ~ ( member_complex @ C @ B2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3378_DiffD2,axiom,
% 9.49/5.27      ! [C: real,A2: set_real,B2: set_real] :
% 9.49/5.27        ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B2 ) )
% 9.49/5.27       => ~ ( member_real @ C @ B2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3379_DiffD2,axiom,
% 9.49/5.27      ! [C: int,A2: set_int,B2: set_int] :
% 9.49/5.27        ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B2 ) )
% 9.49/5.27       => ~ ( member_int @ C @ B2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3380_DiffD2,axiom,
% 9.49/5.27      ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.49/5.27        ( ( member8440522571783428010at_nat @ C @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) )
% 9.49/5.27       => ~ ( member8440522571783428010at_nat @ C @ B2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3381_DiffD2,axiom,
% 9.49/5.27      ! [C: nat,A2: set_nat,B2: set_nat] :
% 9.49/5.27        ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 9.49/5.27       => ~ ( member_nat @ C @ B2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3382_insert__Diff__if,axiom,
% 9.49/5.27      ! [X: vEBT_VEBT,B2: set_VEBT_VEBT,A2: set_VEBT_VEBT] :
% 9.49/5.27        ( ( ( member_VEBT_VEBT @ X @ B2 )
% 9.49/5.27         => ( ( minus_5127226145743854075T_VEBT @ ( insert_VEBT_VEBT @ X @ A2 ) @ B2 )
% 9.49/5.27            = ( minus_5127226145743854075T_VEBT @ A2 @ B2 ) ) )
% 9.49/5.27        & ( ~ ( member_VEBT_VEBT @ X @ B2 )
% 9.49/5.27         => ( ( minus_5127226145743854075T_VEBT @ ( insert_VEBT_VEBT @ X @ A2 ) @ B2 )
% 9.49/5.27            = ( insert_VEBT_VEBT @ X @ ( minus_5127226145743854075T_VEBT @ A2 @ B2 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3383_insert__Diff__if,axiom,
% 9.49/5.27      ! [X: complex,B2: set_complex,A2: set_complex] :
% 9.49/5.27        ( ( ( member_complex @ X @ B2 )
% 9.49/5.27         => ( ( minus_811609699411566653omplex @ ( insert_complex @ X @ A2 ) @ B2 )
% 9.49/5.27            = ( minus_811609699411566653omplex @ A2 @ B2 ) ) )
% 9.49/5.27        & ( ~ ( member_complex @ X @ B2 )
% 9.49/5.27         => ( ( minus_811609699411566653omplex @ ( insert_complex @ X @ A2 ) @ B2 )
% 9.49/5.27            = ( insert_complex @ X @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3384_insert__Diff__if,axiom,
% 9.49/5.27      ! [X: real,B2: set_real,A2: set_real] :
% 9.49/5.27        ( ( ( member_real @ X @ B2 )
% 9.49/5.27         => ( ( minus_minus_set_real @ ( insert_real @ X @ A2 ) @ B2 )
% 9.49/5.27            = ( minus_minus_set_real @ A2 @ B2 ) ) )
% 9.49/5.27        & ( ~ ( member_real @ X @ B2 )
% 9.49/5.27         => ( ( minus_minus_set_real @ ( insert_real @ X @ A2 ) @ B2 )
% 9.49/5.27            = ( insert_real @ X @ ( minus_minus_set_real @ A2 @ B2 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3385_insert__Diff__if,axiom,
% 9.49/5.27      ! [X: int,B2: set_int,A2: set_int] :
% 9.49/5.27        ( ( ( member_int @ X @ B2 )
% 9.49/5.27         => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ B2 )
% 9.49/5.27            = ( minus_minus_set_int @ A2 @ B2 ) ) )
% 9.49/5.27        & ( ~ ( member_int @ X @ B2 )
% 9.49/5.27         => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ B2 )
% 9.49/5.27            = ( insert_int @ X @ ( minus_minus_set_int @ A2 @ B2 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3386_insert__Diff__if,axiom,
% 9.49/5.27      ! [X: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 9.49/5.27        ( ( ( member8440522571783428010at_nat @ X @ B2 )
% 9.49/5.27         => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X @ A2 ) @ B2 )
% 9.49/5.27            = ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) )
% 9.49/5.27        & ( ~ ( member8440522571783428010at_nat @ X @ B2 )
% 9.49/5.27         => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X @ A2 ) @ B2 )
% 9.49/5.27            = ( insert8211810215607154385at_nat @ X @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3387_insert__Diff__if,axiom,
% 9.49/5.27      ! [X: nat,B2: set_nat,A2: set_nat] :
% 9.49/5.27        ( ( ( member_nat @ X @ B2 )
% 9.49/5.27         => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ B2 )
% 9.49/5.27            = ( minus_minus_set_nat @ A2 @ B2 ) ) )
% 9.49/5.27        & ( ~ ( member_nat @ X @ B2 )
% 9.49/5.27         => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ B2 )
% 9.49/5.27            = ( insert_nat @ X @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3388_minus__set__def,axiom,
% 9.49/5.27      ( minus_minus_set_int
% 9.49/5.27      = ( ^ [A6: set_int,B6: set_int] :
% 9.49/5.27            ( collect_int
% 9.49/5.27            @ ( minus_minus_int_o
% 9.49/5.27              @ ^ [X2: int] : ( member_int @ X2 @ A6 )
% 9.49/5.27              @ ^ [X2: int] : ( member_int @ X2 @ B6 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3389_minus__set__def,axiom,
% 9.49/5.27      ( minus_811609699411566653omplex
% 9.49/5.27      = ( ^ [A6: set_complex,B6: set_complex] :
% 9.49/5.27            ( collect_complex
% 9.49/5.27            @ ( minus_8727706125548526216plex_o
% 9.49/5.27              @ ^ [X2: complex] : ( member_complex @ X2 @ A6 )
% 9.49/5.27              @ ^ [X2: complex] : ( member_complex @ X2 @ B6 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3390_minus__set__def,axiom,
% 9.49/5.27      ( minus_minus_set_real
% 9.49/5.27      = ( ^ [A6: set_real,B6: set_real] :
% 9.49/5.27            ( collect_real
% 9.49/5.27            @ ( minus_minus_real_o
% 9.49/5.27              @ ^ [X2: real] : ( member_real @ X2 @ A6 )
% 9.49/5.27              @ ^ [X2: real] : ( member_real @ X2 @ B6 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3391_minus__set__def,axiom,
% 9.49/5.27      ( minus_7954133019191499631st_nat
% 9.49/5.27      = ( ^ [A6: set_list_nat,B6: set_list_nat] :
% 9.49/5.27            ( collect_list_nat
% 9.49/5.27            @ ( minus_1139252259498527702_nat_o
% 9.49/5.27              @ ^ [X2: list_nat] : ( member_list_nat @ X2 @ A6 )
% 9.49/5.27              @ ^ [X2: list_nat] : ( member_list_nat @ X2 @ B6 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3392_minus__set__def,axiom,
% 9.49/5.27      ( minus_1356011639430497352at_nat
% 9.49/5.27      = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 9.49/5.27            ( collec3392354462482085612at_nat
% 9.49/5.27            @ ( minus_2270307095948843157_nat_o
% 9.49/5.27              @ ^ [X2: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X2 @ A6 )
% 9.49/5.27              @ ^ [X2: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X2 @ B6 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3393_minus__set__def,axiom,
% 9.49/5.27      ( minus_minus_set_nat
% 9.49/5.27      = ( ^ [A6: set_nat,B6: set_nat] :
% 9.49/5.27            ( collect_nat
% 9.49/5.27            @ ( minus_minus_nat_o
% 9.49/5.27              @ ^ [X2: nat] : ( member_nat @ X2 @ A6 )
% 9.49/5.27              @ ^ [X2: nat] : ( member_nat @ X2 @ B6 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3394_set__diff__eq,axiom,
% 9.49/5.27      ( minus_minus_set_int
% 9.49/5.27      = ( ^ [A6: set_int,B6: set_int] :
% 9.49/5.27            ( collect_int
% 9.49/5.27            @ ^ [X2: int] :
% 9.49/5.27                ( ( member_int @ X2 @ A6 )
% 9.49/5.27                & ~ ( member_int @ X2 @ B6 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3395_set__diff__eq,axiom,
% 9.49/5.27      ( minus_811609699411566653omplex
% 9.49/5.27      = ( ^ [A6: set_complex,B6: set_complex] :
% 9.49/5.27            ( collect_complex
% 9.49/5.27            @ ^ [X2: complex] :
% 9.49/5.27                ( ( member_complex @ X2 @ A6 )
% 9.49/5.27                & ~ ( member_complex @ X2 @ B6 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3396_set__diff__eq,axiom,
% 9.49/5.27      ( minus_minus_set_real
% 9.49/5.27      = ( ^ [A6: set_real,B6: set_real] :
% 9.49/5.27            ( collect_real
% 9.49/5.27            @ ^ [X2: real] :
% 9.49/5.27                ( ( member_real @ X2 @ A6 )
% 9.49/5.27                & ~ ( member_real @ X2 @ B6 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3397_set__diff__eq,axiom,
% 9.49/5.27      ( minus_7954133019191499631st_nat
% 9.49/5.27      = ( ^ [A6: set_list_nat,B6: set_list_nat] :
% 9.49/5.27            ( collect_list_nat
% 9.49/5.27            @ ^ [X2: list_nat] :
% 9.49/5.27                ( ( member_list_nat @ X2 @ A6 )
% 9.49/5.27                & ~ ( member_list_nat @ X2 @ B6 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3398_set__diff__eq,axiom,
% 9.49/5.27      ( minus_1356011639430497352at_nat
% 9.49/5.27      = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 9.49/5.27            ( collec3392354462482085612at_nat
% 9.49/5.27            @ ^ [X2: product_prod_nat_nat] :
% 9.49/5.27                ( ( member8440522571783428010at_nat @ X2 @ A6 )
% 9.49/5.27                & ~ ( member8440522571783428010at_nat @ X2 @ B6 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3399_set__diff__eq,axiom,
% 9.49/5.27      ( minus_minus_set_nat
% 9.49/5.27      = ( ^ [A6: set_nat,B6: set_nat] :
% 9.49/5.27            ( collect_nat
% 9.49/5.27            @ ^ [X2: nat] :
% 9.49/5.27                ( ( member_nat @ X2 @ A6 )
% 9.49/5.27                & ~ ( member_nat @ X2 @ B6 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3400_psubset__insert__iff,axiom,
% 9.49/5.27      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,B2: set_VEBT_VEBT] :
% 9.49/5.27        ( ( ord_le3480810397992357184T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ B2 ) )
% 9.49/5.27        = ( ( ( member_VEBT_VEBT @ X @ B2 )
% 9.49/5.27           => ( ord_le3480810397992357184T_VEBT @ A2 @ B2 ) )
% 9.49/5.27          & ( ~ ( member_VEBT_VEBT @ X @ B2 )
% 9.49/5.27           => ( ( ( member_VEBT_VEBT @ X @ A2 )
% 9.49/5.27               => ( ord_le3480810397992357184T_VEBT @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) @ B2 ) )
% 9.49/5.27              & ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 9.49/5.27               => ( ord_le4337996190870823476T_VEBT @ A2 @ B2 ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3401_psubset__insert__iff,axiom,
% 9.49/5.27      ! [A2: set_complex,X: complex,B2: set_complex] :
% 9.49/5.27        ( ( ord_less_set_complex @ A2 @ ( insert_complex @ X @ B2 ) )
% 9.49/5.27        = ( ( ( member_complex @ X @ B2 )
% 9.49/5.27           => ( ord_less_set_complex @ A2 @ B2 ) )
% 9.49/5.27          & ( ~ ( member_complex @ X @ B2 )
% 9.49/5.27           => ( ( ( member_complex @ X @ A2 )
% 9.49/5.27               => ( ord_less_set_complex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) @ B2 ) )
% 9.49/5.27              & ( ~ ( member_complex @ X @ A2 )
% 9.49/5.27               => ( ord_le211207098394363844omplex @ A2 @ B2 ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3402_psubset__insert__iff,axiom,
% 9.49/5.27      ! [A2: set_int,X: int,B2: set_int] :
% 9.49/5.27        ( ( ord_less_set_int @ A2 @ ( insert_int @ X @ B2 ) )
% 9.49/5.27        = ( ( ( member_int @ X @ B2 )
% 9.49/5.27           => ( ord_less_set_int @ A2 @ B2 ) )
% 9.49/5.27          & ( ~ ( member_int @ X @ B2 )
% 9.49/5.27           => ( ( ( member_int @ X @ A2 )
% 9.49/5.27               => ( ord_less_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B2 ) )
% 9.49/5.27              & ( ~ ( member_int @ X @ A2 )
% 9.49/5.27               => ( ord_less_eq_set_int @ A2 @ B2 ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3403_psubset__insert__iff,axiom,
% 9.49/5.27      ! [A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.49/5.27        ( ( ord_le7866589430770878221at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ B2 ) )
% 9.49/5.27        = ( ( ( member8440522571783428010at_nat @ X @ B2 )
% 9.49/5.27           => ( ord_le7866589430770878221at_nat @ A2 @ B2 ) )
% 9.49/5.27          & ( ~ ( member8440522571783428010at_nat @ X @ B2 )
% 9.49/5.27           => ( ( ( member8440522571783428010at_nat @ X @ A2 )
% 9.49/5.27               => ( ord_le7866589430770878221at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) @ B2 ) )
% 9.49/5.27              & ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 9.49/5.27               => ( ord_le3146513528884898305at_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3404_psubset__insert__iff,axiom,
% 9.49/5.27      ! [A2: set_real,X: real,B2: set_real] :
% 9.49/5.27        ( ( ord_less_set_real @ A2 @ ( insert_real @ X @ B2 ) )
% 9.49/5.27        = ( ( ( member_real @ X @ B2 )
% 9.49/5.27           => ( ord_less_set_real @ A2 @ B2 ) )
% 9.49/5.27          & ( ~ ( member_real @ X @ B2 )
% 9.49/5.27           => ( ( ( member_real @ X @ A2 )
% 9.49/5.27               => ( ord_less_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) @ B2 ) )
% 9.49/5.27              & ( ~ ( member_real @ X @ A2 )
% 9.49/5.27               => ( ord_less_eq_set_real @ A2 @ B2 ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3405_psubset__insert__iff,axiom,
% 9.49/5.27      ! [A2: set_nat,X: nat,B2: set_nat] :
% 9.49/5.27        ( ( ord_less_set_nat @ A2 @ ( insert_nat @ X @ B2 ) )
% 9.49/5.27        = ( ( ( member_nat @ X @ B2 )
% 9.49/5.27           => ( ord_less_set_nat @ A2 @ B2 ) )
% 9.49/5.27          & ( ~ ( member_nat @ X @ B2 )
% 9.49/5.27           => ( ( ( member_nat @ X @ A2 )
% 9.49/5.27               => ( ord_less_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B2 ) )
% 9.49/5.27              & ( ~ ( member_nat @ X @ A2 )
% 9.49/5.27               => ( ord_less_eq_set_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3406_Diff__single__insert,axiom,
% 9.49/5.27      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,B2: set_VEBT_VEBT] :
% 9.49/5.27        ( ( ord_le4337996190870823476T_VEBT @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) @ B2 )
% 9.49/5.27       => ( ord_le4337996190870823476T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ B2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3407_Diff__single__insert,axiom,
% 9.49/5.27      ! [A2: set_int,X: int,B2: set_int] :
% 9.49/5.27        ( ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B2 )
% 9.49/5.27       => ( ord_less_eq_set_int @ A2 @ ( insert_int @ X @ B2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3408_Diff__single__insert,axiom,
% 9.49/5.27      ! [A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.49/5.27        ( ( ord_le3146513528884898305at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) @ B2 )
% 9.49/5.27       => ( ord_le3146513528884898305at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ B2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3409_Diff__single__insert,axiom,
% 9.49/5.27      ! [A2: set_real,X: real,B2: set_real] :
% 9.49/5.27        ( ( ord_less_eq_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) @ B2 )
% 9.49/5.27       => ( ord_less_eq_set_real @ A2 @ ( insert_real @ X @ B2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3410_Diff__single__insert,axiom,
% 9.49/5.27      ! [A2: set_nat,X: nat,B2: set_nat] :
% 9.49/5.27        ( ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B2 )
% 9.49/5.27       => ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X @ B2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3411_subset__insert__iff,axiom,
% 9.49/5.27      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,B2: set_VEBT_VEBT] :
% 9.49/5.27        ( ( ord_le4337996190870823476T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ B2 ) )
% 9.49/5.27        = ( ( ( member_VEBT_VEBT @ X @ A2 )
% 9.49/5.27           => ( ord_le4337996190870823476T_VEBT @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) @ B2 ) )
% 9.49/5.27          & ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 9.49/5.27           => ( ord_le4337996190870823476T_VEBT @ A2 @ B2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3412_subset__insert__iff,axiom,
% 9.49/5.27      ! [A2: set_complex,X: complex,B2: set_complex] :
% 9.49/5.27        ( ( ord_le211207098394363844omplex @ A2 @ ( insert_complex @ X @ B2 ) )
% 9.49/5.27        = ( ( ( member_complex @ X @ A2 )
% 9.49/5.27           => ( ord_le211207098394363844omplex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) @ B2 ) )
% 9.49/5.27          & ( ~ ( member_complex @ X @ A2 )
% 9.49/5.27           => ( ord_le211207098394363844omplex @ A2 @ B2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3413_subset__insert__iff,axiom,
% 9.49/5.27      ! [A2: set_int,X: int,B2: set_int] :
% 9.49/5.27        ( ( ord_less_eq_set_int @ A2 @ ( insert_int @ X @ B2 ) )
% 9.49/5.27        = ( ( ( member_int @ X @ A2 )
% 9.49/5.27           => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B2 ) )
% 9.49/5.27          & ( ~ ( member_int @ X @ A2 )
% 9.49/5.27           => ( ord_less_eq_set_int @ A2 @ B2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3414_subset__insert__iff,axiom,
% 9.49/5.27      ! [A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.49/5.27        ( ( ord_le3146513528884898305at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ B2 ) )
% 9.49/5.27        = ( ( ( member8440522571783428010at_nat @ X @ A2 )
% 9.49/5.27           => ( ord_le3146513528884898305at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) @ B2 ) )
% 9.49/5.27          & ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 9.49/5.27           => ( ord_le3146513528884898305at_nat @ A2 @ B2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3415_subset__insert__iff,axiom,
% 9.49/5.27      ! [A2: set_real,X: real,B2: set_real] :
% 9.49/5.27        ( ( ord_less_eq_set_real @ A2 @ ( insert_real @ X @ B2 ) )
% 9.49/5.27        = ( ( ( member_real @ X @ A2 )
% 9.49/5.27           => ( ord_less_eq_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) @ B2 ) )
% 9.49/5.27          & ( ~ ( member_real @ X @ A2 )
% 9.49/5.27           => ( ord_less_eq_set_real @ A2 @ B2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3416_subset__insert__iff,axiom,
% 9.49/5.27      ! [A2: set_nat,X: nat,B2: set_nat] :
% 9.49/5.27        ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X @ B2 ) )
% 9.49/5.27        = ( ( ( member_nat @ X @ A2 )
% 9.49/5.27           => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B2 ) )
% 9.49/5.27          & ( ~ ( member_nat @ X @ A2 )
% 9.49/5.27           => ( ord_less_eq_set_nat @ A2 @ B2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3417_unset__bit__less__eq,axiom,
% 9.49/5.27      ! [N: nat,K: int] : ( ord_less_eq_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ K ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3418_atLeast0__atMost__Suc,axiom,
% 9.49/5.27      ! [N: nat] :
% 9.49/5.27        ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 9.49/5.27        = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3419_atLeastAtMost__insertL,axiom,
% 9.49/5.27      ! [M: nat,N: nat] :
% 9.49/5.27        ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.27       => ( ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 9.49/5.27          = ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3420_atLeastAtMostSuc__conv,axiom,
% 9.49/5.27      ! [M: nat,N: nat] :
% 9.49/5.27        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 9.49/5.27       => ( ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) )
% 9.49/5.27          = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3421_Icc__eq__insert__lb__nat,axiom,
% 9.49/5.27      ! [M: nat,N: nat] :
% 9.49/5.27        ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.27       => ( ( set_or1269000886237332187st_nat @ M @ N )
% 9.49/5.27          = ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3422_set__update__subset__insert,axiom,
% 9.49/5.27      ! [Xs2: list_int,I2: nat,X: int] : ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs2 @ I2 @ X ) ) @ ( insert_int @ X @ ( set_int2 @ Xs2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3423_set__update__subset__insert,axiom,
% 9.49/5.27      ! [Xs2: list_VEBT_VEBT,I2: nat,X: vEBT_VEBT] : ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) ) @ ( insert_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3424_set__update__subset__insert,axiom,
% 9.49/5.27      ! [Xs2: list_real,I2: nat,X: real] : ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs2 @ I2 @ X ) ) @ ( insert_real @ X @ ( set_real2 @ Xs2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3425_set__update__subset__insert,axiom,
% 9.49/5.27      ! [Xs2: list_nat,I2: nat,X: nat] : ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs2 @ I2 @ X ) ) @ ( insert_nat @ X @ ( set_nat2 @ Xs2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3426_double__diff,axiom,
% 9.49/5.27      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C4: set_Pr1261947904930325089at_nat] :
% 9.49/5.27        ( ( ord_le3146513528884898305at_nat @ A2 @ B2 )
% 9.49/5.27       => ( ( ord_le3146513528884898305at_nat @ B2 @ C4 )
% 9.49/5.27         => ( ( minus_1356011639430497352at_nat @ B2 @ ( minus_1356011639430497352at_nat @ C4 @ A2 ) )
% 9.49/5.27            = A2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3427_double__diff,axiom,
% 9.49/5.27      ! [A2: set_real,B2: set_real,C4: set_real] :
% 9.49/5.27        ( ( ord_less_eq_set_real @ A2 @ B2 )
% 9.49/5.27       => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 9.49/5.27         => ( ( minus_minus_set_real @ B2 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 9.49/5.27            = A2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3428_double__diff,axiom,
% 9.49/5.27      ! [A2: set_nat,B2: set_nat,C4: set_nat] :
% 9.49/5.27        ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 9.49/5.27       => ( ( ord_less_eq_set_nat @ B2 @ C4 )
% 9.49/5.27         => ( ( minus_minus_set_nat @ B2 @ ( minus_minus_set_nat @ C4 @ A2 ) )
% 9.49/5.27            = A2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3429_Diff__subset,axiom,
% 9.49/5.27      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) @ A2 ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3430_Diff__subset,axiom,
% 9.49/5.27      ! [A2: set_real,B2: set_real] : ( ord_less_eq_set_real @ ( minus_minus_set_real @ A2 @ B2 ) @ A2 ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3431_Diff__subset,axiom,
% 9.49/5.27      ! [A2: set_nat,B2: set_nat] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ A2 ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3432_Diff__mono,axiom,
% 9.49/5.27      ! [A2: set_Pr1261947904930325089at_nat,C4: set_Pr1261947904930325089at_nat,D4: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.49/5.27        ( ( ord_le3146513528884898305at_nat @ A2 @ C4 )
% 9.49/5.27       => ( ( ord_le3146513528884898305at_nat @ D4 @ B2 )
% 9.49/5.27         => ( ord_le3146513528884898305at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) @ ( minus_1356011639430497352at_nat @ C4 @ D4 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3433_Diff__mono,axiom,
% 9.49/5.27      ! [A2: set_real,C4: set_real,D4: set_real,B2: set_real] :
% 9.49/5.27        ( ( ord_less_eq_set_real @ A2 @ C4 )
% 9.49/5.27       => ( ( ord_less_eq_set_real @ D4 @ B2 )
% 9.49/5.27         => ( ord_less_eq_set_real @ ( minus_minus_set_real @ A2 @ B2 ) @ ( minus_minus_set_real @ C4 @ D4 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3434_Diff__mono,axiom,
% 9.49/5.27      ! [A2: set_nat,C4: set_nat,D4: set_nat,B2: set_nat] :
% 9.49/5.27        ( ( ord_less_eq_set_nat @ A2 @ C4 )
% 9.49/5.27       => ( ( ord_less_eq_set_nat @ D4 @ B2 )
% 9.49/5.27         => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ ( minus_minus_set_nat @ C4 @ D4 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3435_mult__less__iff1,axiom,
% 9.49/5.27      ! [Z: real,X: real,Y2: real] :
% 9.49/5.27        ( ( ord_less_real @ zero_zero_real @ Z )
% 9.49/5.27       => ( ( ord_less_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y2 @ Z ) )
% 9.49/5.27          = ( ord_less_real @ X @ Y2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3436_mult__less__iff1,axiom,
% 9.49/5.27      ! [Z: rat,X: rat,Y2: rat] :
% 9.49/5.27        ( ( ord_less_rat @ zero_zero_rat @ Z )
% 9.49/5.27       => ( ( ord_less_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y2 @ Z ) )
% 9.49/5.27          = ( ord_less_rat @ X @ Y2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3437_mult__less__iff1,axiom,
% 9.49/5.27      ! [Z: int,X: int,Y2: int] :
% 9.49/5.27        ( ( ord_less_int @ zero_zero_int @ Z )
% 9.49/5.27       => ( ( ord_less_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y2 @ Z ) )
% 9.49/5.27          = ( ord_less_int @ X @ Y2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3438_divmod__algorithm__code_I8_J,axiom,
% 9.49/5.27      ! [M: num,N: num] :
% 9.49/5.27        ( ( ( ord_less_num @ M @ N )
% 9.49/5.27         => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 9.49/5.27            = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) ) ) )
% 9.49/5.27        & ( ~ ( ord_less_num @ M @ N )
% 9.49/5.27         => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 9.49/5.27            = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3439_divmod__algorithm__code_I8_J,axiom,
% 9.49/5.27      ! [M: num,N: num] :
% 9.49/5.27        ( ( ( ord_less_num @ M @ N )
% 9.49/5.27         => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 9.49/5.27            = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) ) ) )
% 9.49/5.27        & ( ~ ( ord_less_num @ M @ N )
% 9.49/5.27         => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 9.49/5.27            = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3440_divmod__algorithm__code_I8_J,axiom,
% 9.49/5.27      ! [M: num,N: num] :
% 9.49/5.27        ( ( ( ord_less_num @ M @ N )
% 9.49/5.27         => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 9.49/5.27            = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) ) ) )
% 9.49/5.27        & ( ~ ( ord_less_num @ M @ N )
% 9.49/5.27         => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 9.49/5.27            = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3441_divmod__algorithm__code_I7_J,axiom,
% 9.49/5.27      ! [M: num,N: num] :
% 9.49/5.27        ( ( ( ord_less_eq_num @ M @ N )
% 9.49/5.27         => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 9.49/5.27            = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) ) ) )
% 9.49/5.27        & ( ~ ( ord_less_eq_num @ M @ N )
% 9.49/5.27         => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 9.49/5.27            = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3442_divmod__algorithm__code_I7_J,axiom,
% 9.49/5.27      ! [M: num,N: num] :
% 9.49/5.27        ( ( ( ord_less_eq_num @ M @ N )
% 9.49/5.27         => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 9.49/5.27            = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) ) ) )
% 9.49/5.27        & ( ~ ( ord_less_eq_num @ M @ N )
% 9.49/5.27         => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 9.49/5.27            = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3443_divmod__algorithm__code_I7_J,axiom,
% 9.49/5.27      ! [M: num,N: num] :
% 9.49/5.27        ( ( ( ord_less_eq_num @ M @ N )
% 9.49/5.27         => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 9.49/5.27            = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) ) ) )
% 9.49/5.27        & ( ~ ( ord_less_eq_num @ M @ N )
% 9.49/5.27         => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 9.49/5.27            = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3444_divides__aux__eq,axiom,
% 9.49/5.27      ! [Q2: nat,R: nat] :
% 9.49/5.27        ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q2 @ R ) )
% 9.49/5.27        = ( R = zero_zero_nat ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3445_divides__aux__eq,axiom,
% 9.49/5.27      ! [Q2: int,R: int] :
% 9.49/5.27        ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q2 @ R ) )
% 9.49/5.27        = ( R = zero_zero_int ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3446_neg__eucl__rel__int__mult__2,axiom,
% 9.49/5.27      ! [B: int,A: int,Q2: int,R: int] :
% 9.49/5.27        ( ( ord_less_eq_int @ B @ zero_zero_int )
% 9.49/5.27       => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 9.49/5.27         => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q2 @ ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R ) @ one_one_int ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3447_low__def,axiom,
% 9.49/5.27      ( vEBT_VEBT_low
% 9.49/5.27      = ( ^ [X2: nat,N2: nat] : ( modulo_modulo_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3448_obtain__set__succ,axiom,
% 9.49/5.27      ! [X: nat,Z: nat,A2: set_nat,B2: set_nat] :
% 9.49/5.27        ( ( ord_less_nat @ X @ Z )
% 9.49/5.27       => ( ( vEBT_VEBT_max_in_set @ A2 @ Z )
% 9.49/5.27         => ( ( finite_finite_nat @ B2 )
% 9.49/5.27           => ( ( A2 = B2 )
% 9.49/5.27             => ? [X_12: nat] : ( vEBT_is_succ_in_set @ A2 @ X @ X_12 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3449_obtain__set__pred,axiom,
% 9.49/5.27      ! [Z: nat,X: nat,A2: set_nat] :
% 9.49/5.27        ( ( ord_less_nat @ Z @ X )
% 9.49/5.27       => ( ( vEBT_VEBT_min_in_set @ A2 @ Z )
% 9.49/5.27         => ( ( finite_finite_nat @ A2 )
% 9.49/5.27           => ? [X_12: nat] : ( vEBT_is_pred_in_set @ A2 @ X @ X_12 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3450_set__vebt__finite,axiom,
% 9.49/5.27      ! [T: vEBT_VEBT,N: nat] :
% 9.49/5.27        ( ( vEBT_invar_vebt @ T @ N )
% 9.49/5.27       => ( finite_finite_nat @ ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3451_pred__none__empty,axiom,
% 9.49/5.27      ! [Xs2: set_nat,A: nat] :
% 9.49/5.27        ( ~ ? [X_12: nat] : ( vEBT_is_pred_in_set @ Xs2 @ A @ X_12 )
% 9.49/5.27       => ( ( finite_finite_nat @ Xs2 )
% 9.49/5.27         => ~ ? [X5: nat] :
% 9.49/5.27                ( ( member_nat @ X5 @ Xs2 )
% 9.49/5.27                & ( ord_less_nat @ X5 @ A ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3452_succ__none__empty,axiom,
% 9.49/5.27      ! [Xs2: set_nat,A: nat] :
% 9.49/5.27        ( ~ ? [X_12: nat] : ( vEBT_is_succ_in_set @ Xs2 @ A @ X_12 )
% 9.49/5.27       => ( ( finite_finite_nat @ Xs2 )
% 9.49/5.27         => ~ ? [X5: nat] :
% 9.49/5.27                ( ( member_nat @ X5 @ Xs2 )
% 9.49/5.27                & ( ord_less_nat @ A @ X5 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3453_old_Oprod_Oinject,axiom,
% 9.49/5.27      ! [A: product_prod_nat_nat,B: product_prod_nat_nat,A5: product_prod_nat_nat,B5: product_prod_nat_nat] :
% 9.49/5.27        ( ( ( produc6161850002892822231at_nat @ A @ B )
% 9.49/5.27          = ( produc6161850002892822231at_nat @ A5 @ B5 ) )
% 9.49/5.27        = ( ( A = A5 )
% 9.49/5.27          & ( B = B5 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3454_old_Oprod_Oinject,axiom,
% 9.49/5.27      ! [A: num,B: num,A5: num,B5: num] :
% 9.49/5.27        ( ( ( product_Pair_num_num @ A @ B )
% 9.49/5.27          = ( product_Pair_num_num @ A5 @ B5 ) )
% 9.49/5.27        = ( ( A = A5 )
% 9.49/5.27          & ( B = B5 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3455_old_Oprod_Oinject,axiom,
% 9.49/5.27      ! [A: nat,B: num,A5: nat,B5: num] :
% 9.49/5.27        ( ( ( product_Pair_nat_num @ A @ B )
% 9.49/5.27          = ( product_Pair_nat_num @ A5 @ B5 ) )
% 9.49/5.27        = ( ( A = A5 )
% 9.49/5.27          & ( B = B5 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3456_old_Oprod_Oinject,axiom,
% 9.49/5.27      ! [A: nat,B: nat,A5: nat,B5: nat] :
% 9.49/5.27        ( ( ( product_Pair_nat_nat @ A @ B )
% 9.49/5.27          = ( product_Pair_nat_nat @ A5 @ B5 ) )
% 9.49/5.27        = ( ( A = A5 )
% 9.49/5.27          & ( B = B5 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3457_old_Oprod_Oinject,axiom,
% 9.49/5.27      ! [A: int,B: int,A5: int,B5: int] :
% 9.49/5.27        ( ( ( product_Pair_int_int @ A @ B )
% 9.49/5.27          = ( product_Pair_int_int @ A5 @ B5 ) )
% 9.49/5.27        = ( ( A = A5 )
% 9.49/5.27          & ( B = B5 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3458_prod_Oinject,axiom,
% 9.49/5.27      ! [X1: product_prod_nat_nat,X23: product_prod_nat_nat,Y1: product_prod_nat_nat,Y22: product_prod_nat_nat] :
% 9.49/5.27        ( ( ( produc6161850002892822231at_nat @ X1 @ X23 )
% 9.49/5.27          = ( produc6161850002892822231at_nat @ Y1 @ Y22 ) )
% 9.49/5.27        = ( ( X1 = Y1 )
% 9.49/5.27          & ( X23 = Y22 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3459_prod_Oinject,axiom,
% 9.49/5.27      ! [X1: num,X23: num,Y1: num,Y22: num] :
% 9.49/5.27        ( ( ( product_Pair_num_num @ X1 @ X23 )
% 9.49/5.27          = ( product_Pair_num_num @ Y1 @ Y22 ) )
% 9.49/5.27        = ( ( X1 = Y1 )
% 9.49/5.27          & ( X23 = Y22 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3460_prod_Oinject,axiom,
% 9.49/5.27      ! [X1: nat,X23: num,Y1: nat,Y22: num] :
% 9.49/5.27        ( ( ( product_Pair_nat_num @ X1 @ X23 )
% 9.49/5.27          = ( product_Pair_nat_num @ Y1 @ Y22 ) )
% 9.49/5.27        = ( ( X1 = Y1 )
% 9.49/5.27          & ( X23 = Y22 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3461_prod_Oinject,axiom,
% 9.49/5.27      ! [X1: nat,X23: nat,Y1: nat,Y22: nat] :
% 9.49/5.27        ( ( ( product_Pair_nat_nat @ X1 @ X23 )
% 9.49/5.27          = ( product_Pair_nat_nat @ Y1 @ Y22 ) )
% 9.49/5.27        = ( ( X1 = Y1 )
% 9.49/5.27          & ( X23 = Y22 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3462_prod_Oinject,axiom,
% 9.49/5.27      ! [X1: int,X23: int,Y1: int,Y22: int] :
% 9.49/5.27        ( ( ( product_Pair_int_int @ X1 @ X23 )
% 9.49/5.27          = ( product_Pair_int_int @ Y1 @ Y22 ) )
% 9.49/5.27        = ( ( X1 = Y1 )
% 9.49/5.27          & ( X23 = Y22 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3463_mod__mod__trivial,axiom,
% 9.49/5.27      ! [A: nat,B: nat] :
% 9.49/5.27        ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 9.49/5.27        = ( modulo_modulo_nat @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3464_mod__mod__trivial,axiom,
% 9.49/5.27      ! [A: int,B: int] :
% 9.49/5.27        ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 9.49/5.27        = ( modulo_modulo_int @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3465_bits__mod__0,axiom,
% 9.49/5.27      ! [A: nat] :
% 9.49/5.27        ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 9.49/5.27        = zero_zero_nat ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3466_bits__mod__0,axiom,
% 9.49/5.27      ! [A: int] :
% 9.49/5.27        ( ( modulo_modulo_int @ zero_zero_int @ A )
% 9.49/5.27        = zero_zero_int ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3467_mod__add__self2,axiom,
% 9.49/5.27      ! [A: nat,B: nat] :
% 9.49/5.27        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 9.49/5.27        = ( modulo_modulo_nat @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3468_mod__add__self2,axiom,
% 9.49/5.27      ! [A: int,B: int] :
% 9.49/5.27        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ B )
% 9.49/5.27        = ( modulo_modulo_int @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3469_mod__add__self1,axiom,
% 9.49/5.27      ! [B: nat,A: nat] :
% 9.49/5.27        ( ( modulo_modulo_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 9.49/5.27        = ( modulo_modulo_nat @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3470_mod__add__self1,axiom,
% 9.49/5.27      ! [B: int,A: int] :
% 9.49/5.27        ( ( modulo_modulo_int @ ( plus_plus_int @ B @ A ) @ B )
% 9.49/5.27        = ( modulo_modulo_int @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3471_List_Ofinite__set,axiom,
% 9.49/5.27      ! [Xs2: list_VEBT_VEBT] : ( finite5795047828879050333T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3472_List_Ofinite__set,axiom,
% 9.49/5.27      ! [Xs2: list_int] : ( finite_finite_int @ ( set_int2 @ Xs2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3473_List_Ofinite__set,axiom,
% 9.49/5.27      ! [Xs2: list_nat] : ( finite_finite_nat @ ( set_nat2 @ Xs2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3474_List_Ofinite__set,axiom,
% 9.49/5.27      ! [Xs2: list_complex] : ( finite3207457112153483333omplex @ ( set_complex2 @ Xs2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3475_minus__mod__self2,axiom,
% 9.49/5.27      ! [A: int,B: int] :
% 9.49/5.27        ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ B )
% 9.49/5.27        = ( modulo_modulo_int @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3476_mod__less,axiom,
% 9.49/5.27      ! [M: nat,N: nat] :
% 9.49/5.27        ( ( ord_less_nat @ M @ N )
% 9.49/5.27       => ( ( modulo_modulo_nat @ M @ N )
% 9.49/5.27          = M ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3477_mod__mult__self2__is__0,axiom,
% 9.49/5.27      ! [A: nat,B: nat] :
% 9.49/5.27        ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ B )
% 9.49/5.27        = zero_zero_nat ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3478_mod__mult__self2__is__0,axiom,
% 9.49/5.27      ! [A: int,B: int] :
% 9.49/5.27        ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ B )
% 9.49/5.27        = zero_zero_int ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3479_mod__mult__self1__is__0,axiom,
% 9.49/5.27      ! [B: nat,A: nat] :
% 9.49/5.27        ( ( modulo_modulo_nat @ ( times_times_nat @ B @ A ) @ B )
% 9.49/5.27        = zero_zero_nat ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3480_mod__mult__self1__is__0,axiom,
% 9.49/5.27      ! [B: int,A: int] :
% 9.49/5.27        ( ( modulo_modulo_int @ ( times_times_int @ B @ A ) @ B )
% 9.49/5.27        = zero_zero_int ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3481_bits__mod__by__1,axiom,
% 9.49/5.27      ! [A: nat] :
% 9.49/5.27        ( ( modulo_modulo_nat @ A @ one_one_nat )
% 9.49/5.27        = zero_zero_nat ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3482_bits__mod__by__1,axiom,
% 9.49/5.27      ! [A: int] :
% 9.49/5.27        ( ( modulo_modulo_int @ A @ one_one_int )
% 9.49/5.27        = zero_zero_int ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3483_mod__by__1,axiom,
% 9.49/5.27      ! [A: nat] :
% 9.49/5.27        ( ( modulo_modulo_nat @ A @ one_one_nat )
% 9.49/5.27        = zero_zero_nat ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3484_mod__by__1,axiom,
% 9.49/5.27      ! [A: int] :
% 9.49/5.27        ( ( modulo_modulo_int @ A @ one_one_int )
% 9.49/5.27        = zero_zero_int ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3485_bits__mod__div__trivial,axiom,
% 9.49/5.27      ! [A: nat,B: nat] :
% 9.49/5.27        ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 9.49/5.27        = zero_zero_nat ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3486_bits__mod__div__trivial,axiom,
% 9.49/5.27      ! [A: int,B: int] :
% 9.49/5.27        ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 9.49/5.27        = zero_zero_int ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3487_mod__div__trivial,axiom,
% 9.49/5.27      ! [A: nat,B: nat] :
% 9.49/5.27        ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 9.49/5.27        = zero_zero_nat ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3488_mod__div__trivial,axiom,
% 9.49/5.27      ! [A: int,B: int] :
% 9.49/5.27        ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 9.49/5.27        = zero_zero_int ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3489_mod__mult__self4,axiom,
% 9.49/5.27      ! [B: nat,C: nat,A: nat] :
% 9.49/5.27        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 9.49/5.27        = ( modulo_modulo_nat @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3490_mod__mult__self4,axiom,
% 9.49/5.27      ! [B: int,C: int,A: int] :
% 9.49/5.27        ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 9.49/5.27        = ( modulo_modulo_int @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3491_mod__mult__self3,axiom,
% 9.49/5.27      ! [C: nat,B: nat,A: nat] :
% 9.49/5.27        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 9.49/5.27        = ( modulo_modulo_nat @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3492_mod__mult__self3,axiom,
% 9.49/5.27      ! [C: int,B: int,A: int] :
% 9.49/5.27        ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 9.49/5.27        = ( modulo_modulo_int @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3493_mod__mult__self2,axiom,
% 9.49/5.27      ! [A: nat,B: nat,C: nat] :
% 9.49/5.27        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 9.49/5.27        = ( modulo_modulo_nat @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3494_mod__mult__self2,axiom,
% 9.49/5.27      ! [A: int,B: int,C: int] :
% 9.49/5.27        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 9.49/5.27        = ( modulo_modulo_int @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3495_mod__mult__self1,axiom,
% 9.49/5.27      ! [A: nat,C: nat,B: nat] :
% 9.49/5.27        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 9.49/5.27        = ( modulo_modulo_nat @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3496_mod__mult__self1,axiom,
% 9.49/5.27      ! [A: int,C: int,B: int] :
% 9.49/5.27        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 9.49/5.27        = ( modulo_modulo_int @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3497_infinite__Icc__iff,axiom,
% 9.49/5.27      ! [A: rat,B: rat] :
% 9.49/5.27        ( ( ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) )
% 9.49/5.27        = ( ord_less_rat @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3498_infinite__Icc__iff,axiom,
% 9.49/5.27      ! [A: real,B: real] :
% 9.49/5.27        ( ( ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) )
% 9.49/5.27        = ( ord_less_real @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3499_mod__by__Suc__0,axiom,
% 9.49/5.27      ! [M: nat] :
% 9.49/5.27        ( ( modulo_modulo_nat @ M @ ( suc @ zero_zero_nat ) )
% 9.49/5.27        = zero_zero_nat ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3500_Suc__mod__mult__self1,axiom,
% 9.49/5.27      ! [M: nat,K: nat,N: nat] :
% 9.49/5.27        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ K @ N ) ) ) @ N )
% 9.49/5.27        = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3501_Suc__mod__mult__self2,axiom,
% 9.49/5.27      ! [M: nat,N: nat,K: nat] :
% 9.49/5.27        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ N @ K ) ) ) @ N )
% 9.49/5.27        = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3502_Suc__mod__mult__self3,axiom,
% 9.49/5.27      ! [K: nat,N: nat,M: nat] :
% 9.49/5.27        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K @ N ) @ M ) ) @ N )
% 9.49/5.27        = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3503_Suc__mod__mult__self4,axiom,
% 9.49/5.27      ! [N: nat,K: nat,M: nat] :
% 9.49/5.27        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N @ K ) @ M ) ) @ N )
% 9.49/5.27        = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3504_bits__one__mod__two__eq__one,axiom,
% 9.49/5.27      ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.27      = one_one_nat ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3505_bits__one__mod__two__eq__one,axiom,
% 9.49/5.27      ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.49/5.27      = one_one_int ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3506_one__mod__two__eq__one,axiom,
% 9.49/5.27      ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.27      = one_one_nat ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3507_one__mod__two__eq__one,axiom,
% 9.49/5.27      ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.49/5.27      = one_one_int ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3508_mod2__Suc__Suc,axiom,
% 9.49/5.27      ! [M: nat] :
% 9.49/5.27        ( ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.27        = ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3509_divmod__algorithm__code_I2_J,axiom,
% 9.49/5.27      ! [M: num] :
% 9.49/5.27        ( ( unique5055182867167087721od_nat @ M @ one )
% 9.49/5.27        = ( product_Pair_nat_nat @ ( numeral_numeral_nat @ M ) @ zero_zero_nat ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3510_divmod__algorithm__code_I2_J,axiom,
% 9.49/5.27      ! [M: num] :
% 9.49/5.27        ( ( unique5052692396658037445od_int @ M @ one )
% 9.49/5.27        = ( product_Pair_int_int @ ( numeral_numeral_int @ M ) @ zero_zero_int ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3511_Suc__times__numeral__mod__eq,axiom,
% 9.49/5.27      ! [K: num,N: nat] :
% 9.49/5.27        ( ( ( numeral_numeral_nat @ K )
% 9.49/5.27         != one_one_nat )
% 9.49/5.27       => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N ) ) @ ( numeral_numeral_nat @ K ) )
% 9.49/5.27          = one_one_nat ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3512_not__mod__2__eq__1__eq__0,axiom,
% 9.49/5.27      ! [A: nat] :
% 9.49/5.27        ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.27         != one_one_nat )
% 9.49/5.27        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.27          = zero_zero_nat ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3513_not__mod__2__eq__1__eq__0,axiom,
% 9.49/5.27      ! [A: int] :
% 9.49/5.27        ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.49/5.27         != one_one_int )
% 9.49/5.27        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.49/5.27          = zero_zero_int ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3514_not__mod__2__eq__0__eq__1,axiom,
% 9.49/5.27      ! [A: nat] :
% 9.49/5.27        ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.27         != zero_zero_nat )
% 9.49/5.27        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.27          = one_one_nat ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3515_not__mod__2__eq__0__eq__1,axiom,
% 9.49/5.27      ! [A: int] :
% 9.49/5.27        ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.49/5.27         != zero_zero_int )
% 9.49/5.27        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.49/5.27          = one_one_int ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3516_not__mod2__eq__Suc__0__eq__0,axiom,
% 9.49/5.27      ! [N: nat] :
% 9.49/5.27        ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.27         != ( suc @ zero_zero_nat ) )
% 9.49/5.27        = ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.27          = zero_zero_nat ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3517_add__self__mod__2,axiom,
% 9.49/5.27      ! [M: nat] :
% 9.49/5.27        ( ( modulo_modulo_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.27        = zero_zero_nat ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3518_divmod__algorithm__code_I3_J,axiom,
% 9.49/5.27      ! [N: num] :
% 9.49/5.27        ( ( unique5055182867167087721od_nat @ one @ ( bit0 @ N ) )
% 9.49/5.27        = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3519_divmod__algorithm__code_I3_J,axiom,
% 9.49/5.27      ! [N: num] :
% 9.49/5.27        ( ( unique5052692396658037445od_int @ one @ ( bit0 @ N ) )
% 9.49/5.27        = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3520_Suc__mod__eq__add3__mod__numeral,axiom,
% 9.49/5.27      ! [M: nat,V: num] :
% 9.49/5.27        ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 9.49/5.27        = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3521_mod__Suc__eq__mod__add3,axiom,
% 9.49/5.27      ! [M: nat,N: nat] :
% 9.49/5.27        ( ( modulo_modulo_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 9.49/5.27        = ( modulo_modulo_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3522_divmod__algorithm__code_I4_J,axiom,
% 9.49/5.27      ! [N: num] :
% 9.49/5.27        ( ( unique5055182867167087721od_nat @ one @ ( bit1 @ N ) )
% 9.49/5.27        = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3523_divmod__algorithm__code_I4_J,axiom,
% 9.49/5.27      ! [N: num] :
% 9.49/5.27        ( ( unique5052692396658037445od_int @ one @ ( bit1 @ N ) )
% 9.49/5.27        = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3524_mod2__gr__0,axiom,
% 9.49/5.27      ! [M: nat] :
% 9.49/5.27        ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.27        = ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.27          = one_one_nat ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3525_unique__quotient,axiom,
% 9.49/5.27      ! [A: int,B: int,Q2: int,R: int,Q5: int,R4: int] :
% 9.49/5.27        ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 9.49/5.27       => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q5 @ R4 ) )
% 9.49/5.27         => ( Q2 = Q5 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3526_unique__remainder,axiom,
% 9.49/5.27      ! [A: int,B: int,Q2: int,R: int,Q5: int,R4: int] :
% 9.49/5.27        ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 9.49/5.27       => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q5 @ R4 ) )
% 9.49/5.27         => ( R = R4 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3527_mod__mult__eq,axiom,
% 9.49/5.27      ! [A: nat,C: nat,B: nat] :
% 9.49/5.27        ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 9.49/5.27        = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3528_mod__mult__eq,axiom,
% 9.49/5.27      ! [A: int,C: int,B: int] :
% 9.49/5.27        ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 9.49/5.27        = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3529_mod__mult__cong,axiom,
% 9.49/5.27      ! [A: nat,C: nat,A5: nat,B: nat,B5: nat] :
% 9.49/5.27        ( ( ( modulo_modulo_nat @ A @ C )
% 9.49/5.27          = ( modulo_modulo_nat @ A5 @ C ) )
% 9.49/5.27       => ( ( ( modulo_modulo_nat @ B @ C )
% 9.49/5.27            = ( modulo_modulo_nat @ B5 @ C ) )
% 9.49/5.27         => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C )
% 9.49/5.27            = ( modulo_modulo_nat @ ( times_times_nat @ A5 @ B5 ) @ C ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3530_mod__mult__cong,axiom,
% 9.49/5.27      ! [A: int,C: int,A5: int,B: int,B5: int] :
% 9.49/5.27        ( ( ( modulo_modulo_int @ A @ C )
% 9.49/5.27          = ( modulo_modulo_int @ A5 @ C ) )
% 9.49/5.27       => ( ( ( modulo_modulo_int @ B @ C )
% 9.49/5.27            = ( modulo_modulo_int @ B5 @ C ) )
% 9.49/5.27         => ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C )
% 9.49/5.27            = ( modulo_modulo_int @ ( times_times_int @ A5 @ B5 ) @ C ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3531_mod__mult__mult2,axiom,
% 9.49/5.27      ! [A: nat,C: nat,B: nat] :
% 9.49/5.27        ( ( modulo_modulo_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 9.49/5.27        = ( times_times_nat @ ( modulo_modulo_nat @ A @ B ) @ C ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3532_mod__mult__mult2,axiom,
% 9.49/5.27      ! [A: int,C: int,B: int] :
% 9.49/5.27        ( ( modulo_modulo_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 9.49/5.27        = ( times_times_int @ ( modulo_modulo_int @ A @ B ) @ C ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3533_mult__mod__right,axiom,
% 9.49/5.27      ! [C: nat,A: nat,B: nat] :
% 9.49/5.27        ( ( times_times_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 9.49/5.27        = ( modulo_modulo_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3534_mult__mod__right,axiom,
% 9.49/5.27      ! [C: int,A: int,B: int] :
% 9.49/5.27        ( ( times_times_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 9.49/5.27        = ( modulo_modulo_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3535_mod__mult__left__eq,axiom,
% 9.49/5.27      ! [A: nat,C: nat,B: nat] :
% 9.49/5.27        ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 9.49/5.27        = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3536_mod__mult__left__eq,axiom,
% 9.49/5.27      ! [A: int,C: int,B: int] :
% 9.49/5.27        ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 9.49/5.27        = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3537_mod__mult__right__eq,axiom,
% 9.49/5.27      ! [A: nat,B: nat,C: nat] :
% 9.49/5.27        ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 9.49/5.27        = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3538_mod__mult__right__eq,axiom,
% 9.49/5.27      ! [A: int,B: int,C: int] :
% 9.49/5.27        ( ( modulo_modulo_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 9.49/5.27        = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3539_mod__add__right__eq,axiom,
% 9.49/5.27      ! [A: nat,B: nat,C: nat] :
% 9.49/5.27        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 9.49/5.27        = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3540_mod__add__right__eq,axiom,
% 9.49/5.27      ! [A: int,B: int,C: int] :
% 9.49/5.27        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 9.49/5.27        = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3541_mod__add__left__eq,axiom,
% 9.49/5.27      ! [A: nat,C: nat,B: nat] :
% 9.49/5.27        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 9.49/5.27        = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3542_mod__add__left__eq,axiom,
% 9.49/5.27      ! [A: int,C: int,B: int] :
% 9.49/5.27        ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 9.49/5.27        = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3543_mod__add__cong,axiom,
% 9.49/5.27      ! [A: nat,C: nat,A5: nat,B: nat,B5: nat] :
% 9.49/5.27        ( ( ( modulo_modulo_nat @ A @ C )
% 9.49/5.27          = ( modulo_modulo_nat @ A5 @ C ) )
% 9.49/5.27       => ( ( ( modulo_modulo_nat @ B @ C )
% 9.49/5.27            = ( modulo_modulo_nat @ B5 @ C ) )
% 9.49/5.27         => ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 9.49/5.27            = ( modulo_modulo_nat @ ( plus_plus_nat @ A5 @ B5 ) @ C ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3544_mod__add__cong,axiom,
% 9.49/5.27      ! [A: int,C: int,A5: int,B: int,B5: int] :
% 9.49/5.27        ( ( ( modulo_modulo_int @ A @ C )
% 9.49/5.27          = ( modulo_modulo_int @ A5 @ C ) )
% 9.49/5.27       => ( ( ( modulo_modulo_int @ B @ C )
% 9.49/5.27            = ( modulo_modulo_int @ B5 @ C ) )
% 9.49/5.27         => ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C )
% 9.49/5.27            = ( modulo_modulo_int @ ( plus_plus_int @ A5 @ B5 ) @ C ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3545_mod__add__eq,axiom,
% 9.49/5.27      ! [A: nat,C: nat,B: nat] :
% 9.49/5.27        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 9.49/5.27        = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3546_mod__add__eq,axiom,
% 9.49/5.27      ! [A: int,C: int,B: int] :
% 9.49/5.27        ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 9.49/5.27        = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3547_mod__diff__right__eq,axiom,
% 9.49/5.27      ! [A: int,B: int,C: int] :
% 9.49/5.27        ( ( modulo_modulo_int @ ( minus_minus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 9.49/5.27        = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3548_mod__diff__left__eq,axiom,
% 9.49/5.27      ! [A: int,C: int,B: int] :
% 9.49/5.27        ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 9.49/5.27        = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3549_mod__diff__cong,axiom,
% 9.49/5.27      ! [A: int,C: int,A5: int,B: int,B5: int] :
% 9.49/5.27        ( ( ( modulo_modulo_int @ A @ C )
% 9.49/5.27          = ( modulo_modulo_int @ A5 @ C ) )
% 9.49/5.27       => ( ( ( modulo_modulo_int @ B @ C )
% 9.49/5.27            = ( modulo_modulo_int @ B5 @ C ) )
% 9.49/5.27         => ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C )
% 9.49/5.27            = ( modulo_modulo_int @ ( minus_minus_int @ A5 @ B5 ) @ C ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3550_mod__diff__eq,axiom,
% 9.49/5.27      ! [A: int,C: int,B: int] :
% 9.49/5.27        ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 9.49/5.27        = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3551_power__mod,axiom,
% 9.49/5.27      ! [A: nat,B: nat,N: nat] :
% 9.49/5.27        ( ( modulo_modulo_nat @ ( power_power_nat @ ( modulo_modulo_nat @ A @ B ) @ N ) @ B )
% 9.49/5.27        = ( modulo_modulo_nat @ ( power_power_nat @ A @ N ) @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3552_power__mod,axiom,
% 9.49/5.27      ! [A: int,B: int,N: nat] :
% 9.49/5.27        ( ( modulo_modulo_int @ ( power_power_int @ ( modulo_modulo_int @ A @ B ) @ N ) @ B )
% 9.49/5.27        = ( modulo_modulo_int @ ( power_power_int @ A @ N ) @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3553_mod__Suc__Suc__eq,axiom,
% 9.49/5.27      ! [M: nat,N: nat] :
% 9.49/5.27        ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) @ N )
% 9.49/5.27        = ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ N ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3554_mod__Suc__eq,axiom,
% 9.49/5.27      ! [M: nat,N: nat] :
% 9.49/5.27        ( ( modulo_modulo_nat @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) @ N )
% 9.49/5.27        = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3555_mod__less__eq__dividend,axiom,
% 9.49/5.27      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ M ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3556_bounded__nat__set__is__finite,axiom,
% 9.49/5.27      ! [N4: set_nat,N: nat] :
% 9.49/5.27        ( ! [X3: nat] :
% 9.49/5.27            ( ( member_nat @ X3 @ N4 )
% 9.49/5.27           => ( ord_less_nat @ X3 @ N ) )
% 9.49/5.27       => ( finite_finite_nat @ N4 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3557_finite__nat__set__iff__bounded,axiom,
% 9.49/5.27      ( finite_finite_nat
% 9.49/5.27      = ( ^ [N6: set_nat] :
% 9.49/5.27          ? [M6: nat] :
% 9.49/5.27          ! [X2: nat] :
% 9.49/5.27            ( ( member_nat @ X2 @ N6 )
% 9.49/5.27           => ( ord_less_nat @ X2 @ M6 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3558_finite__nat__set__iff__bounded__le,axiom,
% 9.49/5.27      ( finite_finite_nat
% 9.49/5.27      = ( ^ [N6: set_nat] :
% 9.49/5.27          ? [M6: nat] :
% 9.49/5.27          ! [X2: nat] :
% 9.49/5.27            ( ( member_nat @ X2 @ N6 )
% 9.49/5.27           => ( ord_less_eq_nat @ X2 @ M6 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3559_finite__list,axiom,
% 9.49/5.27      ! [A2: set_VEBT_VEBT] :
% 9.49/5.27        ( ( finite5795047828879050333T_VEBT @ A2 )
% 9.49/5.27       => ? [Xs3: list_VEBT_VEBT] :
% 9.49/5.27            ( ( set_VEBT_VEBT2 @ Xs3 )
% 9.49/5.27            = A2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3560_finite__list,axiom,
% 9.49/5.27      ! [A2: set_int] :
% 9.49/5.27        ( ( finite_finite_int @ A2 )
% 9.49/5.27       => ? [Xs3: list_int] :
% 9.49/5.27            ( ( set_int2 @ Xs3 )
% 9.49/5.27            = A2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3561_finite__list,axiom,
% 9.49/5.27      ! [A2: set_nat] :
% 9.49/5.27        ( ( finite_finite_nat @ A2 )
% 9.49/5.27       => ? [Xs3: list_nat] :
% 9.49/5.27            ( ( set_nat2 @ Xs3 )
% 9.49/5.27            = A2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3562_finite__list,axiom,
% 9.49/5.27      ! [A2: set_complex] :
% 9.49/5.27        ( ( finite3207457112153483333omplex @ A2 )
% 9.49/5.27       => ? [Xs3: list_complex] :
% 9.49/5.27            ( ( set_complex2 @ Xs3 )
% 9.49/5.27            = A2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3563_finite__M__bounded__by__nat,axiom,
% 9.49/5.27      ! [P: nat > $o,I2: nat] :
% 9.49/5.27        ( finite_finite_nat
% 9.49/5.27        @ ( collect_nat
% 9.49/5.27          @ ^ [K3: nat] :
% 9.49/5.27              ( ( P @ K3 )
% 9.49/5.27              & ( ord_less_nat @ K3 @ I2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3564_finite__less__ub,axiom,
% 9.49/5.27      ! [F: nat > nat,U: nat] :
% 9.49/5.27        ( ! [N3: nat] : ( ord_less_eq_nat @ N3 @ ( F @ N3 ) )
% 9.49/5.27       => ( finite_finite_nat
% 9.49/5.27          @ ( collect_nat
% 9.49/5.27            @ ^ [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ U ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3565_divmod__def,axiom,
% 9.49/5.27      ( unique5055182867167087721od_nat
% 9.49/5.27      = ( ^ [M6: num,N2: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N2 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3566_divmod__def,axiom,
% 9.49/5.27      ( unique5052692396658037445od_int
% 9.49/5.27      = ( ^ [M6: num,N2: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N2 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3567_divmod_H__nat__def,axiom,
% 9.49/5.27      ( unique5055182867167087721od_nat
% 9.49/5.27      = ( ^ [M6: num,N2: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N2 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3568_finite__lists__length__eq,axiom,
% 9.49/5.27      ! [A2: set_complex,N: nat] :
% 9.49/5.27        ( ( finite3207457112153483333omplex @ A2 )
% 9.49/5.27       => ( finite8712137658972009173omplex
% 9.49/5.27          @ ( collect_list_complex
% 9.49/5.27            @ ^ [Xs: list_complex] :
% 9.49/5.27                ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A2 )
% 9.49/5.27                & ( ( size_s3451745648224563538omplex @ Xs )
% 9.49/5.27                  = N ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3569_finite__lists__length__eq,axiom,
% 9.49/5.27      ! [A2: set_VEBT_VEBT,N: nat] :
% 9.49/5.27        ( ( finite5795047828879050333T_VEBT @ A2 )
% 9.49/5.27       => ( finite3004134309566078307T_VEBT
% 9.49/5.27          @ ( collec5608196760682091941T_VEBT
% 9.49/5.27            @ ^ [Xs: list_VEBT_VEBT] :
% 9.49/5.27                ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A2 )
% 9.49/5.27                & ( ( size_s6755466524823107622T_VEBT @ Xs )
% 9.49/5.27                  = N ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3570_finite__lists__length__eq,axiom,
% 9.49/5.27      ! [A2: set_o,N: nat] :
% 9.49/5.27        ( ( finite_finite_o @ A2 )
% 9.49/5.27       => ( finite_finite_list_o
% 9.49/5.27          @ ( collect_list_o
% 9.49/5.27            @ ^ [Xs: list_o] :
% 9.49/5.27                ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A2 )
% 9.49/5.27                & ( ( size_size_list_o @ Xs )
% 9.49/5.27                  = N ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3571_finite__lists__length__eq,axiom,
% 9.49/5.27      ! [A2: set_int,N: nat] :
% 9.49/5.27        ( ( finite_finite_int @ A2 )
% 9.49/5.27       => ( finite3922522038869484883st_int
% 9.49/5.27          @ ( collect_list_int
% 9.49/5.27            @ ^ [Xs: list_int] :
% 9.49/5.27                ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A2 )
% 9.49/5.27                & ( ( size_size_list_int @ Xs )
% 9.49/5.27                  = N ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3572_finite__lists__length__eq,axiom,
% 9.49/5.27      ! [A2: set_real,N: nat] :
% 9.49/5.27        ( ( finite_finite_real @ A2 )
% 9.49/5.27       => ( finite306553202115118035t_real
% 9.49/5.27          @ ( collect_list_real
% 9.49/5.27            @ ^ [Xs: list_real] :
% 9.49/5.27                ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ A2 )
% 9.49/5.27                & ( ( size_size_list_real @ Xs )
% 9.49/5.27                  = N ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3573_finite__lists__length__eq,axiom,
% 9.49/5.27      ! [A2: set_nat,N: nat] :
% 9.49/5.27        ( ( finite_finite_nat @ A2 )
% 9.49/5.27       => ( finite8100373058378681591st_nat
% 9.49/5.27          @ ( collect_list_nat
% 9.49/5.27            @ ^ [Xs: list_nat] :
% 9.49/5.27                ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A2 )
% 9.49/5.27                & ( ( size_size_list_nat @ Xs )
% 9.49/5.27                  = N ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3574_eucl__rel__int__by0,axiom,
% 9.49/5.27      ! [K: int] : ( eucl_rel_int @ K @ zero_zero_int @ ( product_Pair_int_int @ zero_zero_int @ K ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3575_div__int__unique,axiom,
% 9.49/5.27      ! [K: int,L2: int,Q2: int,R: int] :
% 9.49/5.27        ( ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R ) )
% 9.49/5.27       => ( ( divide_divide_int @ K @ L2 )
% 9.49/5.27          = Q2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3576_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 9.49/5.27      ! [A: nat,B: nat] :
% 9.49/5.27        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.49/5.27       => ( ord_less_eq_nat @ ( modulo_modulo_nat @ A @ B ) @ A ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3577_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 9.49/5.27      ! [A: int,B: int] :
% 9.49/5.27        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.27       => ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ A ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3578_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 9.49/5.27      ! [B: nat,A: nat] :
% 9.49/5.27        ( ( ord_less_nat @ zero_zero_nat @ B )
% 9.49/5.27       => ( ord_less_nat @ ( modulo_modulo_nat @ A @ B ) @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3579_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 9.49/5.27      ! [B: int,A: int] :
% 9.49/5.27        ( ( ord_less_int @ zero_zero_int @ B )
% 9.49/5.27       => ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3580_cong__exp__iff__simps_I9_J,axiom,
% 9.49/5.27      ! [M: num,Q2: num,N: num] :
% 9.49/5.27        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 9.49/5.27          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 9.49/5.27        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 9.49/5.27          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3581_cong__exp__iff__simps_I9_J,axiom,
% 9.49/5.27      ! [M: num,Q2: num,N: num] :
% 9.49/5.27        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 9.49/5.27          = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 9.49/5.27        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 9.49/5.27          = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3582_cong__exp__iff__simps_I4_J,axiom,
% 9.49/5.27      ! [M: num,N: num] :
% 9.49/5.27        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ one ) )
% 9.49/5.27        = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3583_cong__exp__iff__simps_I4_J,axiom,
% 9.49/5.27      ! [M: num,N: num] :
% 9.49/5.27        ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ one ) )
% 9.49/5.27        = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3584_mod__eq__self__iff__div__eq__0,axiom,
% 9.49/5.27      ! [A: nat,B: nat] :
% 9.49/5.27        ( ( ( modulo_modulo_nat @ A @ B )
% 9.49/5.27          = A )
% 9.49/5.27        = ( ( divide_divide_nat @ A @ B )
% 9.49/5.27          = zero_zero_nat ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3585_mod__eq__self__iff__div__eq__0,axiom,
% 9.49/5.27      ! [A: int,B: int] :
% 9.49/5.27        ( ( ( modulo_modulo_int @ A @ B )
% 9.49/5.27          = A )
% 9.49/5.27        = ( ( divide_divide_int @ A @ B )
% 9.49/5.27          = zero_zero_int ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3586_mod__eqE,axiom,
% 9.49/5.27      ! [A: int,C: int,B: int] :
% 9.49/5.27        ( ( ( modulo_modulo_int @ A @ C )
% 9.49/5.27          = ( modulo_modulo_int @ B @ C ) )
% 9.49/5.27       => ~ ! [D3: int] :
% 9.49/5.27              ( B
% 9.49/5.27             != ( plus_plus_int @ A @ ( times_times_int @ C @ D3 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3587_div__add1__eq,axiom,
% 9.49/5.27      ! [A: nat,B: nat,C: nat] :
% 9.49/5.27        ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 9.49/5.27        = ( plus_plus_nat @ ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3588_div__add1__eq,axiom,
% 9.49/5.27      ! [A: int,B: int,C: int] :
% 9.49/5.27        ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 9.49/5.27        = ( plus_plus_int @ ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) @ ( divide_divide_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3589_mod__Suc,axiom,
% 9.49/5.27      ! [M: nat,N: nat] :
% 9.49/5.27        ( ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 9.49/5.27            = N )
% 9.49/5.27         => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 9.49/5.27            = zero_zero_nat ) )
% 9.49/5.27        & ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 9.49/5.27           != N )
% 9.49/5.27         => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 9.49/5.27            = ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3590_mod__induct,axiom,
% 9.49/5.27      ! [P: nat > $o,N: nat,P6: nat,M: nat] :
% 9.49/5.27        ( ( P @ N )
% 9.49/5.27       => ( ( ord_less_nat @ N @ P6 )
% 9.49/5.27         => ( ( ord_less_nat @ M @ P6 )
% 9.49/5.27           => ( ! [N3: nat] :
% 9.49/5.27                  ( ( ord_less_nat @ N3 @ P6 )
% 9.49/5.27                 => ( ( P @ N3 )
% 9.49/5.27                   => ( P @ ( modulo_modulo_nat @ ( suc @ N3 ) @ P6 ) ) ) )
% 9.49/5.27             => ( P @ M ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3591_mod__less__divisor,axiom,
% 9.49/5.27      ! [N: nat,M: nat] :
% 9.49/5.27        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.27       => ( ord_less_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3592_mod__Suc__le__divisor,axiom,
% 9.49/5.27      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ ( suc @ N ) ) @ N ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3593_mod__eq__0D,axiom,
% 9.49/5.27      ! [M: nat,D2: nat] :
% 9.49/5.27        ( ( ( modulo_modulo_nat @ M @ D2 )
% 9.49/5.27          = zero_zero_nat )
% 9.49/5.27       => ? [Q3: nat] :
% 9.49/5.27            ( M
% 9.49/5.27            = ( times_times_nat @ D2 @ Q3 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3594_mod__if,axiom,
% 9.49/5.27      ( modulo_modulo_nat
% 9.49/5.27      = ( ^ [M6: nat,N2: nat] : ( if_nat @ ( ord_less_nat @ M6 @ N2 ) @ M6 @ ( modulo_modulo_nat @ ( minus_minus_nat @ M6 @ N2 ) @ N2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3595_mod__geq,axiom,
% 9.49/5.27      ! [M: nat,N: nat] :
% 9.49/5.27        ( ~ ( ord_less_nat @ M @ N )
% 9.49/5.27       => ( ( modulo_modulo_nat @ M @ N )
% 9.49/5.27          = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3596_nat__mod__eq__iff,axiom,
% 9.49/5.27      ! [X: nat,N: nat,Y2: nat] :
% 9.49/5.27        ( ( ( modulo_modulo_nat @ X @ N )
% 9.49/5.27          = ( modulo_modulo_nat @ Y2 @ N ) )
% 9.49/5.27        = ( ? [Q1: nat,Q22: nat] :
% 9.49/5.27              ( ( plus_plus_nat @ X @ ( times_times_nat @ N @ Q1 ) )
% 9.49/5.27              = ( plus_plus_nat @ Y2 @ ( times_times_nat @ N @ Q22 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3597_le__mod__geq,axiom,
% 9.49/5.27      ! [N: nat,M: nat] :
% 9.49/5.27        ( ( ord_less_eq_nat @ N @ M )
% 9.49/5.27       => ( ( modulo_modulo_nat @ M @ N )
% 9.49/5.27          = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3598_infinite__Icc,axiom,
% 9.49/5.27      ! [A: rat,B: rat] :
% 9.49/5.27        ( ( ord_less_rat @ A @ B )
% 9.49/5.27       => ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3599_infinite__Icc,axiom,
% 9.49/5.27      ! [A: real,B: real] :
% 9.49/5.27        ( ( ord_less_real @ A @ B )
% 9.49/5.27       => ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3600_finite__lists__length__le,axiom,
% 9.49/5.27      ! [A2: set_complex,N: nat] :
% 9.49/5.27        ( ( finite3207457112153483333omplex @ A2 )
% 9.49/5.27       => ( finite8712137658972009173omplex
% 9.49/5.27          @ ( collect_list_complex
% 9.49/5.27            @ ^ [Xs: list_complex] :
% 9.49/5.27                ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A2 )
% 9.49/5.27                & ( ord_less_eq_nat @ ( size_s3451745648224563538omplex @ Xs ) @ N ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3601_finite__lists__length__le,axiom,
% 9.49/5.27      ! [A2: set_VEBT_VEBT,N: nat] :
% 9.49/5.27        ( ( finite5795047828879050333T_VEBT @ A2 )
% 9.49/5.27       => ( finite3004134309566078307T_VEBT
% 9.49/5.27          @ ( collec5608196760682091941T_VEBT
% 9.49/5.27            @ ^ [Xs: list_VEBT_VEBT] :
% 9.49/5.27                ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A2 )
% 9.49/5.27                & ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ N ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3602_finite__lists__length__le,axiom,
% 9.49/5.27      ! [A2: set_o,N: nat] :
% 9.49/5.27        ( ( finite_finite_o @ A2 )
% 9.49/5.27       => ( finite_finite_list_o
% 9.49/5.27          @ ( collect_list_o
% 9.49/5.27            @ ^ [Xs: list_o] :
% 9.49/5.27                ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A2 )
% 9.49/5.27                & ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ N ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3603_finite__lists__length__le,axiom,
% 9.49/5.27      ! [A2: set_int,N: nat] :
% 9.49/5.27        ( ( finite_finite_int @ A2 )
% 9.49/5.27       => ( finite3922522038869484883st_int
% 9.49/5.27          @ ( collect_list_int
% 9.49/5.27            @ ^ [Xs: list_int] :
% 9.49/5.27                ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A2 )
% 9.49/5.27                & ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ N ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3604_finite__lists__length__le,axiom,
% 9.49/5.27      ! [A2: set_real,N: nat] :
% 9.49/5.27        ( ( finite_finite_real @ A2 )
% 9.49/5.27       => ( finite306553202115118035t_real
% 9.49/5.27          @ ( collect_list_real
% 9.49/5.27            @ ^ [Xs: list_real] :
% 9.49/5.27                ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ A2 )
% 9.49/5.27                & ( ord_less_eq_nat @ ( size_size_list_real @ Xs ) @ N ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3605_finite__lists__length__le,axiom,
% 9.49/5.27      ! [A2: set_nat,N: nat] :
% 9.49/5.27        ( ( finite_finite_nat @ A2 )
% 9.49/5.27       => ( finite8100373058378681591st_nat
% 9.49/5.27          @ ( collect_list_nat
% 9.49/5.27            @ ^ [Xs: list_nat] :
% 9.49/5.27                ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A2 )
% 9.49/5.27                & ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ N ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3606_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 9.49/5.27      ! [A: nat,B: nat] :
% 9.49/5.27        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.49/5.27       => ( ( ord_less_nat @ A @ B )
% 9.49/5.27         => ( ( modulo_modulo_nat @ A @ B )
% 9.49/5.27            = A ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3607_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 9.49/5.27      ! [A: int,B: int] :
% 9.49/5.27        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.27       => ( ( ord_less_int @ A @ B )
% 9.49/5.27         => ( ( modulo_modulo_int @ A @ B )
% 9.49/5.27            = A ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3608_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 9.49/5.27      ! [B: nat,A: nat] :
% 9.49/5.27        ( ( ord_less_nat @ zero_zero_nat @ B )
% 9.49/5.27       => ( ord_less_eq_nat @ zero_zero_nat @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3609_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 9.49/5.27      ! [B: int,A: int] :
% 9.49/5.27        ( ( ord_less_int @ zero_zero_int @ B )
% 9.49/5.27       => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3610_cong__exp__iff__simps_I2_J,axiom,
% 9.49/5.27      ! [N: num,Q2: num] :
% 9.49/5.27        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 9.49/5.27          = zero_zero_nat )
% 9.49/5.27        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) )
% 9.49/5.27          = zero_zero_nat ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3611_cong__exp__iff__simps_I2_J,axiom,
% 9.49/5.27      ! [N: num,Q2: num] :
% 9.49/5.27        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 9.49/5.27          = zero_zero_int )
% 9.49/5.27        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) )
% 9.49/5.27          = zero_zero_int ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3612_cong__exp__iff__simps_I1_J,axiom,
% 9.49/5.27      ! [N: num] :
% 9.49/5.27        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) )
% 9.49/5.27        = zero_zero_nat ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3613_cong__exp__iff__simps_I1_J,axiom,
% 9.49/5.27      ! [N: num] :
% 9.49/5.27        ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) )
% 9.49/5.27        = zero_zero_int ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3614_cong__exp__iff__simps_I6_J,axiom,
% 9.49/5.27      ! [Q2: num,N: num] :
% 9.49/5.27        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 9.49/5.27       != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3615_cong__exp__iff__simps_I6_J,axiom,
% 9.49/5.27      ! [Q2: num,N: num] :
% 9.49/5.27        ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 9.49/5.27       != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3616_cong__exp__iff__simps_I8_J,axiom,
% 9.49/5.27      ! [M: num,Q2: num] :
% 9.49/5.27        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 9.49/5.27       != ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3617_cong__exp__iff__simps_I8_J,axiom,
% 9.49/5.27      ! [M: num,Q2: num] :
% 9.49/5.27        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 9.49/5.27       != ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3618_div__mult1__eq,axiom,
% 9.49/5.27      ! [A: nat,B: nat,C: nat] :
% 9.49/5.27        ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C )
% 9.49/5.27        = ( plus_plus_nat @ ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3619_div__mult1__eq,axiom,
% 9.49/5.27      ! [A: int,B: int,C: int] :
% 9.49/5.27        ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ C )
% 9.49/5.27        = ( plus_plus_int @ ( times_times_int @ A @ ( divide_divide_int @ B @ C ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3620_cancel__div__mod__rules_I2_J,axiom,
% 9.49/5.27      ! [B: nat,A: nat,C: nat] :
% 9.49/5.27        ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 9.49/5.27        = ( plus_plus_nat @ A @ C ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3621_cancel__div__mod__rules_I2_J,axiom,
% 9.49/5.27      ! [B: int,A: int,C: int] :
% 9.49/5.27        ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 9.49/5.27        = ( plus_plus_int @ A @ C ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3622_cancel__div__mod__rules_I1_J,axiom,
% 9.49/5.27      ! [A: nat,B: nat,C: nat] :
% 9.49/5.27        ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 9.49/5.27        = ( plus_plus_nat @ A @ C ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3623_cancel__div__mod__rules_I1_J,axiom,
% 9.49/5.27      ! [A: int,B: int,C: int] :
% 9.49/5.27        ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 9.49/5.27        = ( plus_plus_int @ A @ C ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3624_mod__div__decomp,axiom,
% 9.49/5.27      ! [A: nat,B: nat] :
% 9.49/5.27        ( A
% 9.49/5.27        = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3625_mod__div__decomp,axiom,
% 9.49/5.27      ! [A: int,B: int] :
% 9.49/5.27        ( A
% 9.49/5.27        = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3626_div__mult__mod__eq,axiom,
% 9.49/5.27      ! [A: nat,B: nat] :
% 9.49/5.27        ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
% 9.49/5.27        = A ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3627_div__mult__mod__eq,axiom,
% 9.49/5.27      ! [A: int,B: int] :
% 9.49/5.27        ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) )
% 9.49/5.27        = A ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3628_mod__div__mult__eq,axiom,
% 9.49/5.27      ! [A: nat,B: nat] :
% 9.49/5.27        ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 9.49/5.27        = A ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3629_mod__div__mult__eq,axiom,
% 9.49/5.27      ! [A: int,B: int] :
% 9.49/5.27        ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 9.49/5.27        = A ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3630_mod__mult__div__eq,axiom,
% 9.49/5.27      ! [A: nat,B: nat] :
% 9.49/5.27        ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 9.49/5.27        = A ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3631_mod__mult__div__eq,axiom,
% 9.49/5.27      ! [A: int,B: int] :
% 9.49/5.27        ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 9.49/5.27        = A ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3632_mult__div__mod__eq,axiom,
% 9.49/5.27      ! [B: nat,A: nat] :
% 9.49/5.27        ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
% 9.49/5.27        = A ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3633_mult__div__mod__eq,axiom,
% 9.49/5.27      ! [B: int,A: int] :
% 9.49/5.27        ( ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) )
% 9.49/5.27        = A ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3634_minus__div__mult__eq__mod,axiom,
% 9.49/5.27      ! [A: nat,B: nat] :
% 9.49/5.27        ( ( minus_minus_nat @ A @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 9.49/5.27        = ( modulo_modulo_nat @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3635_minus__div__mult__eq__mod,axiom,
% 9.49/5.27      ! [A: int,B: int] :
% 9.49/5.27        ( ( minus_minus_int @ A @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 9.49/5.27        = ( modulo_modulo_int @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3636_minus__mod__eq__div__mult,axiom,
% 9.49/5.27      ! [A: nat,B: nat] :
% 9.49/5.27        ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 9.49/5.27        = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3637_minus__mod__eq__div__mult,axiom,
% 9.49/5.27      ! [A: int,B: int] :
% 9.49/5.27        ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 9.49/5.27        = ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3638_minus__mod__eq__mult__div,axiom,
% 9.49/5.27      ! [A: nat,B: nat] :
% 9.49/5.27        ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 9.49/5.27        = ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3639_minus__mod__eq__mult__div,axiom,
% 9.49/5.27      ! [A: int,B: int] :
% 9.49/5.27        ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 9.49/5.27        = ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3640_minus__mult__div__eq__mod,axiom,
% 9.49/5.27      ! [A: nat,B: nat] :
% 9.49/5.27        ( ( minus_minus_nat @ A @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 9.49/5.27        = ( modulo_modulo_nat @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3641_minus__mult__div__eq__mod,axiom,
% 9.49/5.27      ! [A: int,B: int] :
% 9.49/5.27        ( ( minus_minus_int @ A @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 9.49/5.27        = ( modulo_modulo_int @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3642_cong__exp__iff__simps_I10_J,axiom,
% 9.49/5.27      ! [M: num,Q2: num,N: num] :
% 9.49/5.27        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 9.49/5.27       != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3643_cong__exp__iff__simps_I10_J,axiom,
% 9.49/5.27      ! [M: num,Q2: num,N: num] :
% 9.49/5.27        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 9.49/5.27       != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3644_cong__exp__iff__simps_I12_J,axiom,
% 9.49/5.27      ! [M: num,Q2: num,N: num] :
% 9.49/5.27        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 9.49/5.27       != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3645_cong__exp__iff__simps_I12_J,axiom,
% 9.49/5.27      ! [M: num,Q2: num,N: num] :
% 9.49/5.27        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 9.49/5.27       != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3646_cong__exp__iff__simps_I13_J,axiom,
% 9.49/5.27      ! [M: num,Q2: num,N: num] :
% 9.49/5.27        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 9.49/5.27          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 9.49/5.27        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 9.49/5.27          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3647_cong__exp__iff__simps_I13_J,axiom,
% 9.49/5.27      ! [M: num,Q2: num,N: num] :
% 9.49/5.27        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 9.49/5.27          = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 9.49/5.27        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 9.49/5.27          = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3648_mod__le__divisor,axiom,
% 9.49/5.27      ! [N: nat,M: nat] :
% 9.49/5.27        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.27       => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3649_mod__eq__nat1E,axiom,
% 9.49/5.27      ! [M: nat,Q2: nat,N: nat] :
% 9.49/5.27        ( ( ( modulo_modulo_nat @ M @ Q2 )
% 9.49/5.27          = ( modulo_modulo_nat @ N @ Q2 ) )
% 9.49/5.27       => ( ( ord_less_eq_nat @ N @ M )
% 9.49/5.27         => ~ ! [S: nat] :
% 9.49/5.27                ( M
% 9.49/5.27               != ( plus_plus_nat @ N @ ( times_times_nat @ Q2 @ S ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3650_mod__eq__nat2E,axiom,
% 9.49/5.27      ! [M: nat,Q2: nat,N: nat] :
% 9.49/5.27        ( ( ( modulo_modulo_nat @ M @ Q2 )
% 9.49/5.27          = ( modulo_modulo_nat @ N @ Q2 ) )
% 9.49/5.27       => ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.27         => ~ ! [S: nat] :
% 9.49/5.27                ( N
% 9.49/5.27               != ( plus_plus_nat @ M @ ( times_times_nat @ Q2 @ S ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3651_nat__mod__eq__lemma,axiom,
% 9.49/5.27      ! [X: nat,N: nat,Y2: nat] :
% 9.49/5.27        ( ( ( modulo_modulo_nat @ X @ N )
% 9.49/5.27          = ( modulo_modulo_nat @ Y2 @ N ) )
% 9.49/5.27       => ( ( ord_less_eq_nat @ Y2 @ X )
% 9.49/5.27         => ? [Q3: nat] :
% 9.49/5.27              ( X
% 9.49/5.27              = ( plus_plus_nat @ Y2 @ ( times_times_nat @ N @ Q3 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3652_mod__mult2__eq,axiom,
% 9.49/5.27      ! [M: nat,N: nat,Q2: nat] :
% 9.49/5.27        ( ( modulo_modulo_nat @ M @ ( times_times_nat @ N @ Q2 ) )
% 9.49/5.27        = ( plus_plus_nat @ ( times_times_nat @ N @ ( modulo_modulo_nat @ ( divide_divide_nat @ M @ N ) @ Q2 ) ) @ ( modulo_modulo_nat @ M @ N ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3653_eucl__rel__int__dividesI,axiom,
% 9.49/5.27      ! [L2: int,K: int,Q2: int] :
% 9.49/5.27        ( ( L2 != zero_zero_int )
% 9.49/5.27       => ( ( K
% 9.49/5.27            = ( times_times_int @ Q2 @ L2 ) )
% 9.49/5.27         => ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ zero_zero_int ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3654_modulo__nat__def,axiom,
% 9.49/5.27      ( modulo_modulo_nat
% 9.49/5.27      = ( ^ [M6: nat,N2: nat] : ( minus_minus_nat @ M6 @ ( times_times_nat @ ( divide_divide_nat @ M6 @ N2 ) @ N2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3655_Pair__inject,axiom,
% 9.49/5.27      ! [A: product_prod_nat_nat,B: product_prod_nat_nat,A5: product_prod_nat_nat,B5: product_prod_nat_nat] :
% 9.49/5.27        ( ( ( produc6161850002892822231at_nat @ A @ B )
% 9.49/5.27          = ( produc6161850002892822231at_nat @ A5 @ B5 ) )
% 9.49/5.27       => ~ ( ( A = A5 )
% 9.49/5.27           => ( B != B5 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3656_Pair__inject,axiom,
% 9.49/5.27      ! [A: num,B: num,A5: num,B5: num] :
% 9.49/5.27        ( ( ( product_Pair_num_num @ A @ B )
% 9.49/5.27          = ( product_Pair_num_num @ A5 @ B5 ) )
% 9.49/5.27       => ~ ( ( A = A5 )
% 9.49/5.27           => ( B != B5 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3657_Pair__inject,axiom,
% 9.49/5.27      ! [A: nat,B: num,A5: nat,B5: num] :
% 9.49/5.27        ( ( ( product_Pair_nat_num @ A @ B )
% 9.49/5.27          = ( product_Pair_nat_num @ A5 @ B5 ) )
% 9.49/5.27       => ~ ( ( A = A5 )
% 9.49/5.27           => ( B != B5 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3658_Pair__inject,axiom,
% 9.49/5.27      ! [A: nat,B: nat,A5: nat,B5: nat] :
% 9.49/5.27        ( ( ( product_Pair_nat_nat @ A @ B )
% 9.49/5.27          = ( product_Pair_nat_nat @ A5 @ B5 ) )
% 9.49/5.27       => ~ ( ( A = A5 )
% 9.49/5.27           => ( B != B5 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3659_Pair__inject,axiom,
% 9.49/5.27      ! [A: int,B: int,A5: int,B5: int] :
% 9.49/5.27        ( ( ( product_Pair_int_int @ A @ B )
% 9.49/5.27          = ( product_Pair_int_int @ A5 @ B5 ) )
% 9.49/5.27       => ~ ( ( A = A5 )
% 9.49/5.27           => ( B != B5 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3660_prod__cases,axiom,
% 9.49/5.27      ! [P: produc859450856879609959at_nat > $o,P6: produc859450856879609959at_nat] :
% 9.49/5.27        ( ! [A4: product_prod_nat_nat,B3: product_prod_nat_nat] : ( P @ ( produc6161850002892822231at_nat @ A4 @ B3 ) )
% 9.49/5.27       => ( P @ P6 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3661_prod__cases,axiom,
% 9.49/5.27      ! [P: product_prod_num_num > $o,P6: product_prod_num_num] :
% 9.49/5.27        ( ! [A4: num,B3: num] : ( P @ ( product_Pair_num_num @ A4 @ B3 ) )
% 9.49/5.27       => ( P @ P6 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3662_prod__cases,axiom,
% 9.49/5.27      ! [P: product_prod_nat_num > $o,P6: product_prod_nat_num] :
% 9.49/5.27        ( ! [A4: nat,B3: num] : ( P @ ( product_Pair_nat_num @ A4 @ B3 ) )
% 9.49/5.27       => ( P @ P6 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3663_prod__cases,axiom,
% 9.49/5.27      ! [P: product_prod_nat_nat > $o,P6: product_prod_nat_nat] :
% 9.49/5.27        ( ! [A4: nat,B3: nat] : ( P @ ( product_Pair_nat_nat @ A4 @ B3 ) )
% 9.49/5.27       => ( P @ P6 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3664_prod__cases,axiom,
% 9.49/5.27      ! [P: product_prod_int_int > $o,P6: product_prod_int_int] :
% 9.49/5.27        ( ! [A4: int,B3: int] : ( P @ ( product_Pair_int_int @ A4 @ B3 ) )
% 9.49/5.27       => ( P @ P6 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3665_surj__pair,axiom,
% 9.49/5.27      ! [P6: produc859450856879609959at_nat] :
% 9.49/5.27      ? [X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 9.49/5.27        ( P6
% 9.49/5.27        = ( produc6161850002892822231at_nat @ X3 @ Y3 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3666_surj__pair,axiom,
% 9.49/5.27      ! [P6: product_prod_num_num] :
% 9.49/5.27      ? [X3: num,Y3: num] :
% 9.49/5.27        ( P6
% 9.49/5.27        = ( product_Pair_num_num @ X3 @ Y3 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3667_surj__pair,axiom,
% 9.49/5.27      ! [P6: product_prod_nat_num] :
% 9.49/5.27      ? [X3: nat,Y3: num] :
% 9.49/5.27        ( P6
% 9.49/5.27        = ( product_Pair_nat_num @ X3 @ Y3 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3668_surj__pair,axiom,
% 9.49/5.27      ! [P6: product_prod_nat_nat] :
% 9.49/5.27      ? [X3: nat,Y3: nat] :
% 9.49/5.27        ( P6
% 9.49/5.27        = ( product_Pair_nat_nat @ X3 @ Y3 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3669_surj__pair,axiom,
% 9.49/5.27      ! [P6: product_prod_int_int] :
% 9.49/5.27      ? [X3: int,Y3: int] :
% 9.49/5.27        ( P6
% 9.49/5.27        = ( product_Pair_int_int @ X3 @ Y3 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3670_old_Oprod_Oexhaust,axiom,
% 9.49/5.27      ! [Y2: produc859450856879609959at_nat] :
% 9.49/5.27        ~ ! [A4: product_prod_nat_nat,B3: product_prod_nat_nat] :
% 9.49/5.27            ( Y2
% 9.49/5.27           != ( produc6161850002892822231at_nat @ A4 @ B3 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3671_old_Oprod_Oexhaust,axiom,
% 9.49/5.27      ! [Y2: product_prod_num_num] :
% 9.49/5.27        ~ ! [A4: num,B3: num] :
% 9.49/5.27            ( Y2
% 9.49/5.27           != ( product_Pair_num_num @ A4 @ B3 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3672_old_Oprod_Oexhaust,axiom,
% 9.49/5.27      ! [Y2: product_prod_nat_num] :
% 9.49/5.27        ~ ! [A4: nat,B3: num] :
% 9.49/5.27            ( Y2
% 9.49/5.27           != ( product_Pair_nat_num @ A4 @ B3 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3673_old_Oprod_Oexhaust,axiom,
% 9.49/5.27      ! [Y2: product_prod_nat_nat] :
% 9.49/5.27        ~ ! [A4: nat,B3: nat] :
% 9.49/5.27            ( Y2
% 9.49/5.27           != ( product_Pair_nat_nat @ A4 @ B3 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3674_old_Oprod_Oexhaust,axiom,
% 9.49/5.27      ! [Y2: product_prod_int_int] :
% 9.49/5.27        ~ ! [A4: int,B3: int] :
% 9.49/5.27            ( Y2
% 9.49/5.27           != ( product_Pair_int_int @ A4 @ B3 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3675_cong__exp__iff__simps_I3_J,axiom,
% 9.49/5.27      ! [N: num,Q2: num] :
% 9.49/5.27        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 9.49/5.27       != zero_zero_nat ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3676_cong__exp__iff__simps_I3_J,axiom,
% 9.49/5.27      ! [N: num,Q2: num] :
% 9.49/5.27        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 9.49/5.27       != zero_zero_int ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3677_split__mod,axiom,
% 9.49/5.27      ! [P: nat > $o,M: nat,N: nat] :
% 9.49/5.27        ( ( P @ ( modulo_modulo_nat @ M @ N ) )
% 9.49/5.27        = ( ( ( N = zero_zero_nat )
% 9.49/5.27           => ( P @ M ) )
% 9.49/5.27          & ( ( N != zero_zero_nat )
% 9.49/5.27           => ! [I3: nat,J3: nat] :
% 9.49/5.27                ( ( ord_less_nat @ J3 @ N )
% 9.49/5.27               => ( ( M
% 9.49/5.27                    = ( plus_plus_nat @ ( times_times_nat @ N @ I3 ) @ J3 ) )
% 9.49/5.27                 => ( P @ J3 ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3678_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 9.49/5.27      ! [C: nat,A: nat,B: nat] :
% 9.49/5.27        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 9.49/5.27       => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C ) )
% 9.49/5.27          = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3679_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 9.49/5.27      ! [C: int,A: int,B: int] :
% 9.49/5.27        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.49/5.27       => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 9.49/5.27          = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3680_cong__exp__iff__simps_I7_J,axiom,
% 9.49/5.27      ! [Q2: num,N: num] :
% 9.49/5.27        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 9.49/5.27          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 9.49/5.27        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) )
% 9.49/5.27          = zero_zero_nat ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3681_cong__exp__iff__simps_I7_J,axiom,
% 9.49/5.27      ! [Q2: num,N: num] :
% 9.49/5.27        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 9.49/5.27          = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 9.49/5.27        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) )
% 9.49/5.27          = zero_zero_int ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3682_cong__exp__iff__simps_I11_J,axiom,
% 9.49/5.27      ! [M: num,Q2: num] :
% 9.49/5.27        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 9.49/5.27          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 9.49/5.27        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 9.49/5.27          = zero_zero_nat ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3683_cong__exp__iff__simps_I11_J,axiom,
% 9.49/5.27      ! [M: num,Q2: num] :
% 9.49/5.27        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 9.49/5.27          = ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 9.49/5.27        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 9.49/5.27          = zero_zero_int ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3684_Suc__mod__eq__add3__mod,axiom,
% 9.49/5.27      ! [M: nat,N: nat] :
% 9.49/5.27        ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 9.49/5.27        = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3685_Suc__times__mod__eq,axiom,
% 9.49/5.27      ! [M: nat,N: nat] :
% 9.49/5.27        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 9.49/5.27       => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M @ N ) ) @ M )
% 9.49/5.27          = one_one_nat ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3686_divmod__digit__0_I2_J,axiom,
% 9.49/5.27      ! [B: nat,A: nat] :
% 9.49/5.27        ( ( ord_less_nat @ zero_zero_nat @ B )
% 9.49/5.27       => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 9.49/5.27         => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) )
% 9.49/5.27            = ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3687_divmod__digit__0_I2_J,axiom,
% 9.49/5.27      ! [B: int,A: int] :
% 9.49/5.27        ( ( ord_less_int @ zero_zero_int @ B )
% 9.49/5.27       => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 9.49/5.27         => ( ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) )
% 9.49/5.27            = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3688_bits__stable__imp__add__self,axiom,
% 9.49/5.27      ! [A: nat] :
% 9.49/5.27        ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.27          = A )
% 9.49/5.27       => ( ( plus_plus_nat @ A @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.27          = zero_zero_nat ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3689_bits__stable__imp__add__self,axiom,
% 9.49/5.27      ! [A: int] :
% 9.49/5.27        ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.49/5.27          = A )
% 9.49/5.27       => ( ( plus_plus_int @ A @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 9.49/5.27          = zero_zero_int ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3690_div__exp__mod__exp__eq,axiom,
% 9.49/5.27      ! [A: nat,N: nat,M: nat] :
% 9.49/5.27        ( ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 9.49/5.27        = ( divide_divide_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3691_div__exp__mod__exp__eq,axiom,
% 9.49/5.27      ! [A: int,N: nat,M: nat] :
% 9.49/5.27        ( ( modulo_modulo_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 9.49/5.27        = ( divide_divide_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3692_divmod__digit__0_I1_J,axiom,
% 9.49/5.27      ! [B: nat,A: nat] :
% 9.49/5.27        ( ( ord_less_nat @ zero_zero_nat @ B )
% 9.49/5.27       => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 9.49/5.27         => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 9.49/5.27            = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3693_divmod__digit__0_I1_J,axiom,
% 9.49/5.27      ! [B: int,A: int] :
% 9.49/5.27        ( ( ord_less_int @ zero_zero_int @ B )
% 9.49/5.27       => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 9.49/5.27         => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 9.49/5.27            = ( divide_divide_int @ A @ B ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3694_mult__exp__mod__exp__eq,axiom,
% 9.49/5.27      ! [M: nat,N: nat,A: nat] :
% 9.49/5.27        ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.27       => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.27          = ( times_times_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3695_mult__exp__mod__exp__eq,axiom,
% 9.49/5.27      ! [M: nat,N: nat,A: int] :
% 9.49/5.27        ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.27       => ( ( modulo_modulo_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.27          = ( times_times_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3696_prod__induct3,axiom,
% 9.49/5.27      ! [P: produc859450856879609959at_nat > $o,X: produc859450856879609959at_nat] :
% 9.49/5.27        ( ! [A4: product_prod_nat_nat,B3: nat,C2: nat] : ( P @ ( produc6161850002892822231at_nat @ A4 @ ( product_Pair_nat_nat @ B3 @ C2 ) ) )
% 9.49/5.27       => ( P @ X ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3697_prod__cases3,axiom,
% 9.49/5.27      ! [Y2: produc859450856879609959at_nat] :
% 9.49/5.27        ~ ! [A4: product_prod_nat_nat,B3: nat,C2: nat] :
% 9.49/5.27            ( Y2
% 9.49/5.27           != ( produc6161850002892822231at_nat @ A4 @ ( product_Pair_nat_nat @ B3 @ C2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3698_eucl__rel__int__iff,axiom,
% 9.49/5.27      ! [K: int,L2: int,Q2: int,R: int] :
% 9.49/5.27        ( ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R ) )
% 9.49/5.27        = ( ( K
% 9.49/5.27            = ( plus_plus_int @ ( times_times_int @ L2 @ Q2 ) @ R ) )
% 9.49/5.27          & ( ( ord_less_int @ zero_zero_int @ L2 )
% 9.49/5.27           => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 9.49/5.27              & ( ord_less_int @ R @ L2 ) ) )
% 9.49/5.27          & ( ~ ( ord_less_int @ zero_zero_int @ L2 )
% 9.49/5.27           => ( ( ( ord_less_int @ L2 @ zero_zero_int )
% 9.49/5.27               => ( ( ord_less_int @ L2 @ R )
% 9.49/5.27                  & ( ord_less_eq_int @ R @ zero_zero_int ) ) )
% 9.49/5.27              & ( ~ ( ord_less_int @ L2 @ zero_zero_int )
% 9.49/5.27               => ( Q2 = zero_zero_int ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3699_mod__double__modulus,axiom,
% 9.49/5.27      ! [M: nat,X: nat] :
% 9.49/5.27        ( ( ord_less_nat @ zero_zero_nat @ M )
% 9.49/5.27       => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 9.49/5.27         => ( ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 9.49/5.27              = ( modulo_modulo_nat @ X @ M ) )
% 9.49/5.27            | ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 9.49/5.27              = ( plus_plus_nat @ ( modulo_modulo_nat @ X @ M ) @ M ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3700_mod__double__modulus,axiom,
% 9.49/5.27      ! [M: int,X: int] :
% 9.49/5.27        ( ( ord_less_int @ zero_zero_int @ M )
% 9.49/5.27       => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 9.49/5.27         => ( ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 9.49/5.27              = ( modulo_modulo_int @ X @ M ) )
% 9.49/5.27            | ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 9.49/5.27              = ( plus_plus_int @ ( modulo_modulo_int @ X @ M ) @ M ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3701_divmod__digit__1_I2_J,axiom,
% 9.49/5.27      ! [A: nat,B: nat] :
% 9.49/5.27        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.49/5.27       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 9.49/5.27         => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 9.49/5.27           => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 9.49/5.27              = ( modulo_modulo_nat @ A @ B ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3702_divmod__digit__1_I2_J,axiom,
% 9.49/5.27      ! [A: int,B: int] :
% 9.49/5.27        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.27       => ( ( ord_less_int @ zero_zero_int @ B )
% 9.49/5.27         => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 9.49/5.27           => ( ( minus_minus_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 9.49/5.27              = ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3703_unset__bit__Suc,axiom,
% 9.49/5.27      ! [N: nat,A: int] :
% 9.49/5.27        ( ( bit_se4203085406695923979it_int @ ( suc @ N ) @ A )
% 9.49/5.27        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3704_unset__bit__Suc,axiom,
% 9.49/5.27      ! [N: nat,A: nat] :
% 9.49/5.27        ( ( bit_se4205575877204974255it_nat @ ( suc @ N ) @ A )
% 9.49/5.27        = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3705_set__bit__Suc,axiom,
% 9.49/5.27      ! [N: nat,A: int] :
% 9.49/5.27        ( ( bit_se7879613467334960850it_int @ ( suc @ N ) @ A )
% 9.49/5.27        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3706_set__bit__Suc,axiom,
% 9.49/5.27      ! [N: nat,A: nat] :
% 9.49/5.27        ( ( bit_se7882103937844011126it_nat @ ( suc @ N ) @ A )
% 9.49/5.27        = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3707_divmod__divmod__step,axiom,
% 9.49/5.27      ( unique5055182867167087721od_nat
% 9.49/5.27      = ( ^ [M6: num,N2: num] : ( if_Pro6206227464963214023at_nat @ ( ord_less_num @ M6 @ N2 ) @ ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ M6 ) ) @ ( unique5026877609467782581ep_nat @ N2 @ ( unique5055182867167087721od_nat @ M6 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3708_divmod__divmod__step,axiom,
% 9.49/5.27      ( unique5052692396658037445od_int
% 9.49/5.27      = ( ^ [M6: num,N2: num] : ( if_Pro3027730157355071871nt_int @ ( ord_less_num @ M6 @ N2 ) @ ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ M6 ) ) @ ( unique5024387138958732305ep_int @ N2 @ ( unique5052692396658037445od_int @ M6 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3709_divmod__divmod__step,axiom,
% 9.49/5.27      ( unique3479559517661332726nteger
% 9.49/5.27      = ( ^ [M6: num,N2: num] : ( if_Pro6119634080678213985nteger @ ( ord_less_num @ M6 @ N2 ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ M6 ) ) @ ( unique4921790084139445826nteger @ N2 @ ( unique3479559517661332726nteger @ M6 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3710_divmod__digit__1_I1_J,axiom,
% 9.49/5.27      ! [A: nat,B: nat] :
% 9.49/5.27        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.49/5.27       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 9.49/5.27         => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 9.49/5.27           => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_nat )
% 9.49/5.27              = ( divide_divide_nat @ A @ B ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3711_divmod__digit__1_I1_J,axiom,
% 9.49/5.27      ! [A: int,B: int] :
% 9.49/5.27        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.27       => ( ( ord_less_int @ zero_zero_int @ B )
% 9.49/5.27         => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 9.49/5.27           => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_int )
% 9.49/5.27              = ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3712_pos__eucl__rel__int__mult__2,axiom,
% 9.49/5.27      ! [B: int,A: int,Q2: int,R: int] :
% 9.49/5.27        ( ( ord_less_eq_int @ zero_zero_int @ B )
% 9.49/5.27       => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 9.49/5.27         => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q2 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3713_finite__Diff__insert,axiom,
% 9.49/5.27      ! [A2: set_int,A: int,B2: set_int] :
% 9.49/5.27        ( ( finite_finite_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B2 ) ) )
% 9.49/5.27        = ( finite_finite_int @ ( minus_minus_set_int @ A2 @ B2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3714_finite__Diff__insert,axiom,
% 9.49/5.27      ! [A2: set_VEBT_VEBT,A: vEBT_VEBT,B2: set_VEBT_VEBT] :
% 9.49/5.27        ( ( finite5795047828879050333T_VEBT @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ B2 ) ) )
% 9.49/5.27        = ( finite5795047828879050333T_VEBT @ ( minus_5127226145743854075T_VEBT @ A2 @ B2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3715_finite__Diff__insert,axiom,
% 9.49/5.27      ! [A2: set_real,A: real,B2: set_real] :
% 9.49/5.27        ( ( finite_finite_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ B2 ) ) )
% 9.49/5.27        = ( finite_finite_real @ ( minus_minus_set_real @ A2 @ B2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3716_finite__Diff__insert,axiom,
% 9.49/5.27      ! [A2: set_complex,A: complex,B2: set_complex] :
% 9.49/5.27        ( ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ B2 ) ) )
% 9.49/5.27        = ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3717_finite__Diff__insert,axiom,
% 9.49/5.27      ! [A2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.49/5.27        ( ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ B2 ) ) )
% 9.49/5.27        = ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3718_finite__Diff__insert,axiom,
% 9.49/5.27      ! [A2: set_nat,A: nat,B2: set_nat] :
% 9.49/5.27        ( ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B2 ) ) )
% 9.49/5.27        = ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3719_verit__le__mono__div,axiom,
% 9.49/5.27      ! [A2: nat,B2: nat,N: nat] :
% 9.49/5.27        ( ( ord_less_nat @ A2 @ B2 )
% 9.49/5.27       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.27         => ( ord_less_eq_nat
% 9.49/5.27            @ ( plus_plus_nat @ ( divide_divide_nat @ A2 @ N )
% 9.49/5.27              @ ( if_nat
% 9.49/5.27                @ ( ( modulo_modulo_nat @ B2 @ N )
% 9.49/5.27                  = zero_zero_nat )
% 9.49/5.27                @ one_one_nat
% 9.49/5.27                @ zero_zero_nat ) )
% 9.49/5.27            @ ( divide_divide_nat @ B2 @ N ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3720_mod__exhaust__less__4,axiom,
% 9.49/5.27      ! [M: nat] :
% 9.49/5.27        ( ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 9.49/5.27          = zero_zero_nat )
% 9.49/5.27        | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 9.49/5.27          = one_one_nat )
% 9.49/5.27        | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 9.49/5.27          = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.27        | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 9.49/5.27          = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3721_finite__Collect__le__nat,axiom,
% 9.49/5.27      ! [K: nat] :
% 9.49/5.27        ( finite_finite_nat
% 9.49/5.27        @ ( collect_nat
% 9.49/5.27          @ ^ [N2: nat] : ( ord_less_eq_nat @ N2 @ K ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3722_finite__Collect__less__nat,axiom,
% 9.49/5.27      ! [K: nat] :
% 9.49/5.27        ( finite_finite_nat
% 9.49/5.27        @ ( collect_nat
% 9.49/5.27          @ ^ [N2: nat] : ( ord_less_nat @ N2 @ K ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3723_finite__roots__unity,axiom,
% 9.49/5.27      ! [N: nat] :
% 9.49/5.27        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 9.49/5.27       => ( finite_finite_real
% 9.49/5.27          @ ( collect_real
% 9.49/5.27            @ ^ [Z4: real] :
% 9.49/5.27                ( ( power_power_real @ Z4 @ N )
% 9.49/5.27                = one_one_real ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3724_finite__roots__unity,axiom,
% 9.49/5.27      ! [N: nat] :
% 9.49/5.27        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 9.49/5.27       => ( finite3207457112153483333omplex
% 9.49/5.27          @ ( collect_complex
% 9.49/5.27            @ ^ [Z4: complex] :
% 9.49/5.27                ( ( power_power_complex @ Z4 @ N )
% 9.49/5.27                = one_one_complex ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3725_finite__induct__select,axiom,
% 9.49/5.27      ! [S2: set_VEBT_VEBT,P: set_VEBT_VEBT > $o] :
% 9.49/5.27        ( ( finite5795047828879050333T_VEBT @ S2 )
% 9.49/5.27       => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 9.49/5.27         => ( ! [T3: set_VEBT_VEBT] :
% 9.49/5.27                ( ( ord_le3480810397992357184T_VEBT @ T3 @ S2 )
% 9.49/5.27               => ( ( P @ T3 )
% 9.49/5.27                 => ? [X5: vEBT_VEBT] :
% 9.49/5.27                      ( ( member_VEBT_VEBT @ X5 @ ( minus_5127226145743854075T_VEBT @ S2 @ T3 ) )
% 9.49/5.27                      & ( P @ ( insert_VEBT_VEBT @ X5 @ T3 ) ) ) ) )
% 9.49/5.27           => ( P @ S2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3726_finite__induct__select,axiom,
% 9.49/5.27      ! [S2: set_complex,P: set_complex > $o] :
% 9.49/5.27        ( ( finite3207457112153483333omplex @ S2 )
% 9.49/5.27       => ( ( P @ bot_bot_set_complex )
% 9.49/5.27         => ( ! [T3: set_complex] :
% 9.49/5.27                ( ( ord_less_set_complex @ T3 @ S2 )
% 9.49/5.27               => ( ( P @ T3 )
% 9.49/5.27                 => ? [X5: complex] :
% 9.49/5.27                      ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ S2 @ T3 ) )
% 9.49/5.27                      & ( P @ ( insert_complex @ X5 @ T3 ) ) ) ) )
% 9.49/5.27           => ( P @ S2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3727_finite__induct__select,axiom,
% 9.49/5.27      ! [S2: set_int,P: set_int > $o] :
% 9.49/5.27        ( ( finite_finite_int @ S2 )
% 9.49/5.27       => ( ( P @ bot_bot_set_int )
% 9.49/5.27         => ( ! [T3: set_int] :
% 9.49/5.27                ( ( ord_less_set_int @ T3 @ S2 )
% 9.49/5.27               => ( ( P @ T3 )
% 9.49/5.27                 => ? [X5: int] :
% 9.49/5.27                      ( ( member_int @ X5 @ ( minus_minus_set_int @ S2 @ T3 ) )
% 9.49/5.27                      & ( P @ ( insert_int @ X5 @ T3 ) ) ) ) )
% 9.49/5.27           => ( P @ S2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3728_finite__induct__select,axiom,
% 9.49/5.27      ! [S2: set_real,P: set_real > $o] :
% 9.49/5.27        ( ( finite_finite_real @ S2 )
% 9.49/5.27       => ( ( P @ bot_bot_set_real )
% 9.49/5.27         => ( ! [T3: set_real] :
% 9.49/5.27                ( ( ord_less_set_real @ T3 @ S2 )
% 9.49/5.27               => ( ( P @ T3 )
% 9.49/5.27                 => ? [X5: real] :
% 9.49/5.27                      ( ( member_real @ X5 @ ( minus_minus_set_real @ S2 @ T3 ) )
% 9.49/5.27                      & ( P @ ( insert_real @ X5 @ T3 ) ) ) ) )
% 9.49/5.27           => ( P @ S2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3729_finite__induct__select,axiom,
% 9.49/5.27      ! [S2: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 9.49/5.27        ( ( finite6177210948735845034at_nat @ S2 )
% 9.49/5.27       => ( ( P @ bot_bo2099793752762293965at_nat )
% 9.49/5.27         => ( ! [T3: set_Pr1261947904930325089at_nat] :
% 9.49/5.27                ( ( ord_le7866589430770878221at_nat @ T3 @ S2 )
% 9.49/5.27               => ( ( P @ T3 )
% 9.49/5.27                 => ? [X5: product_prod_nat_nat] :
% 9.49/5.27                      ( ( member8440522571783428010at_nat @ X5 @ ( minus_1356011639430497352at_nat @ S2 @ T3 ) )
% 9.49/5.27                      & ( P @ ( insert8211810215607154385at_nat @ X5 @ T3 ) ) ) ) )
% 9.49/5.27           => ( P @ S2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3730_finite__induct__select,axiom,
% 9.49/5.27      ! [S2: set_nat,P: set_nat > $o] :
% 9.49/5.27        ( ( finite_finite_nat @ S2 )
% 9.49/5.27       => ( ( P @ bot_bot_set_nat )
% 9.49/5.27         => ( ! [T3: set_nat] :
% 9.49/5.27                ( ( ord_less_set_nat @ T3 @ S2 )
% 9.49/5.27               => ( ( P @ T3 )
% 9.49/5.27                 => ? [X5: nat] :
% 9.49/5.27                      ( ( member_nat @ X5 @ ( minus_minus_set_nat @ S2 @ T3 ) )
% 9.49/5.27                      & ( P @ ( insert_nat @ X5 @ T3 ) ) ) ) )
% 9.49/5.27           => ( P @ S2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3731_finite__Diff2,axiom,
% 9.49/5.27      ! [B2: set_complex,A2: set_complex] :
% 9.49/5.27        ( ( finite3207457112153483333omplex @ B2 )
% 9.49/5.27       => ( ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ B2 ) )
% 9.49/5.27          = ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3732_finite__Diff2,axiom,
% 9.49/5.27      ! [B2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 9.49/5.27        ( ( finite6177210948735845034at_nat @ B2 )
% 9.49/5.27       => ( ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) )
% 9.49/5.27          = ( finite6177210948735845034at_nat @ A2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3733_finite__Diff2,axiom,
% 9.49/5.27      ! [B2: set_nat,A2: set_nat] :
% 9.49/5.27        ( ( finite_finite_nat @ B2 )
% 9.49/5.27       => ( ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 9.49/5.27          = ( finite_finite_nat @ A2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3734_verit__eq__simplify_I8_J,axiom,
% 9.49/5.27      ! [X23: num,Y22: num] :
% 9.49/5.27        ( ( ( bit0 @ X23 )
% 9.49/5.27          = ( bit0 @ Y22 ) )
% 9.49/5.27        = ( X23 = Y22 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3735_verit__eq__simplify_I9_J,axiom,
% 9.49/5.27      ! [X33: num,Y32: num] :
% 9.49/5.27        ( ( ( bit1 @ X33 )
% 9.49/5.27          = ( bit1 @ Y32 ) )
% 9.49/5.27        = ( X33 = Y32 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3736_finite__Diff,axiom,
% 9.49/5.27      ! [A2: set_complex,B2: set_complex] :
% 9.49/5.27        ( ( finite3207457112153483333omplex @ A2 )
% 9.49/5.27       => ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3737_finite__Diff,axiom,
% 9.49/5.27      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.49/5.27        ( ( finite6177210948735845034at_nat @ A2 )
% 9.49/5.27       => ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3738_finite__Diff,axiom,
% 9.49/5.27      ! [A2: set_nat,B2: set_nat] :
% 9.49/5.27        ( ( finite_finite_nat @ A2 )
% 9.49/5.27       => ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3739_mod__neg__neg__trivial,axiom,
% 9.49/5.27      ! [K: int,L2: int] :
% 9.49/5.27        ( ( ord_less_eq_int @ K @ zero_zero_int )
% 9.49/5.27       => ( ( ord_less_int @ L2 @ K )
% 9.49/5.27         => ( ( modulo_modulo_int @ K @ L2 )
% 9.49/5.27            = K ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3740_mod__pos__pos__trivial,axiom,
% 9.49/5.27      ! [K: int,L2: int] :
% 9.49/5.27        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 9.49/5.27       => ( ( ord_less_int @ K @ L2 )
% 9.49/5.27         => ( ( modulo_modulo_int @ K @ L2 )
% 9.49/5.27            = K ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3741_zmod__numeral__Bit0,axiom,
% 9.49/5.27      ! [V: num,W: num] :
% 9.49/5.27        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 9.49/5.27        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3742_zmod__numeral__Bit1,axiom,
% 9.49/5.27      ! [V: num,W: num] :
% 9.49/5.27        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 9.49/5.27        = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) @ one_one_int ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3743_zmod__le__nonneg__dividend,axiom,
% 9.49/5.27      ! [M: int,K: int] :
% 9.49/5.27        ( ( ord_less_eq_int @ zero_zero_int @ M )
% 9.49/5.27       => ( ord_less_eq_int @ ( modulo_modulo_int @ M @ K ) @ M ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3744_neg__mod__bound,axiom,
% 9.49/5.27      ! [L2: int,K: int] :
% 9.49/5.27        ( ( ord_less_int @ L2 @ zero_zero_int )
% 9.49/5.27       => ( ord_less_int @ L2 @ ( modulo_modulo_int @ K @ L2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3745_Euclidean__Division_Opos__mod__bound,axiom,
% 9.49/5.27      ! [L2: int,K: int] :
% 9.49/5.27        ( ( ord_less_int @ zero_zero_int @ L2 )
% 9.49/5.27       => ( ord_less_int @ ( modulo_modulo_int @ K @ L2 ) @ L2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3746_zmod__eq__0__iff,axiom,
% 9.49/5.27      ! [M: int,D2: int] :
% 9.49/5.27        ( ( ( modulo_modulo_int @ M @ D2 )
% 9.49/5.27          = zero_zero_int )
% 9.49/5.27        = ( ? [Q4: int] :
% 9.49/5.27              ( M
% 9.49/5.27              = ( times_times_int @ D2 @ Q4 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3747_zmod__eq__0D,axiom,
% 9.49/5.27      ! [M: int,D2: int] :
% 9.49/5.27        ( ( ( modulo_modulo_int @ M @ D2 )
% 9.49/5.27          = zero_zero_int )
% 9.49/5.27       => ? [Q3: int] :
% 9.49/5.27            ( M
% 9.49/5.27            = ( times_times_int @ D2 @ Q3 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3748_zdiv__mono__strict,axiom,
% 9.49/5.27      ! [A2: int,B2: int,N: int] :
% 9.49/5.27        ( ( ord_less_int @ A2 @ B2 )
% 9.49/5.27       => ( ( ord_less_int @ zero_zero_int @ N )
% 9.49/5.27         => ( ( ( modulo_modulo_int @ A2 @ N )
% 9.49/5.27              = zero_zero_int )
% 9.49/5.27           => ( ( ( modulo_modulo_int @ B2 @ N )
% 9.49/5.27                = zero_zero_int )
% 9.49/5.27             => ( ord_less_int @ ( divide_divide_int @ A2 @ N ) @ ( divide_divide_int @ B2 @ N ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3749_finite__maxlen,axiom,
% 9.49/5.27      ! [M7: set_list_VEBT_VEBT] :
% 9.49/5.27        ( ( finite3004134309566078307T_VEBT @ M7 )
% 9.49/5.27       => ? [N3: nat] :
% 9.49/5.27          ! [X5: list_VEBT_VEBT] :
% 9.49/5.27            ( ( member2936631157270082147T_VEBT @ X5 @ M7 )
% 9.49/5.27           => ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ X5 ) @ N3 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3750_finite__maxlen,axiom,
% 9.49/5.27      ! [M7: set_list_o] :
% 9.49/5.27        ( ( finite_finite_list_o @ M7 )
% 9.49/5.27       => ? [N3: nat] :
% 9.49/5.27          ! [X5: list_o] :
% 9.49/5.27            ( ( member_list_o @ X5 @ M7 )
% 9.49/5.27           => ( ord_less_nat @ ( size_size_list_o @ X5 ) @ N3 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3751_finite__maxlen,axiom,
% 9.49/5.27      ! [M7: set_list_nat] :
% 9.49/5.27        ( ( finite8100373058378681591st_nat @ M7 )
% 9.49/5.27       => ? [N3: nat] :
% 9.49/5.27          ! [X5: list_nat] :
% 9.49/5.27            ( ( member_list_nat @ X5 @ M7 )
% 9.49/5.27           => ( ord_less_nat @ ( size_size_list_nat @ X5 ) @ N3 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3752_finite__maxlen,axiom,
% 9.49/5.27      ! [M7: set_list_int] :
% 9.49/5.27        ( ( finite3922522038869484883st_int @ M7 )
% 9.49/5.27       => ? [N3: nat] :
% 9.49/5.27          ! [X5: list_int] :
% 9.49/5.27            ( ( member_list_int @ X5 @ M7 )
% 9.49/5.27           => ( ord_less_nat @ ( size_size_list_int @ X5 ) @ N3 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3753_div__mod__decomp__int,axiom,
% 9.49/5.27      ! [A2: int,N: int] :
% 9.49/5.27        ( A2
% 9.49/5.27        = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A2 @ N ) @ N ) @ ( modulo_modulo_int @ A2 @ N ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3754_mod__int__unique,axiom,
% 9.49/5.27      ! [K: int,L2: int,Q2: int,R: int] :
% 9.49/5.27        ( ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R ) )
% 9.49/5.27       => ( ( modulo_modulo_int @ K @ L2 )
% 9.49/5.27          = R ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3755_neg__mod__conj,axiom,
% 9.49/5.27      ! [B: int,A: int] :
% 9.49/5.27        ( ( ord_less_int @ B @ zero_zero_int )
% 9.49/5.27       => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ zero_zero_int )
% 9.49/5.27          & ( ord_less_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3756_pos__mod__conj,axiom,
% 9.49/5.27      ! [B: int,A: int] :
% 9.49/5.27        ( ( ord_less_int @ zero_zero_int @ B )
% 9.49/5.27       => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 9.49/5.27          & ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3757_zmod__trivial__iff,axiom,
% 9.49/5.27      ! [I2: int,K: int] :
% 9.49/5.27        ( ( ( modulo_modulo_int @ I2 @ K )
% 9.49/5.27          = I2 )
% 9.49/5.27        = ( ( K = zero_zero_int )
% 9.49/5.27          | ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 9.49/5.27            & ( ord_less_int @ I2 @ K ) )
% 9.49/5.27          | ( ( ord_less_eq_int @ I2 @ zero_zero_int )
% 9.49/5.27            & ( ord_less_int @ K @ I2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3758_neg__mod__sign,axiom,
% 9.49/5.27      ! [L2: int,K: int] :
% 9.49/5.27        ( ( ord_less_int @ L2 @ zero_zero_int )
% 9.49/5.27       => ( ord_less_eq_int @ ( modulo_modulo_int @ K @ L2 ) @ zero_zero_int ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3759_Euclidean__Division_Opos__mod__sign,axiom,
% 9.49/5.27      ! [L2: int,K: int] :
% 9.49/5.27        ( ( ord_less_int @ zero_zero_int @ L2 )
% 9.49/5.27       => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3760_verit__la__disequality,axiom,
% 9.49/5.27      ! [A: num,B: num] :
% 9.49/5.27        ( ( A = B )
% 9.49/5.27        | ~ ( ord_less_eq_num @ A @ B )
% 9.49/5.27        | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3761_verit__la__disequality,axiom,
% 9.49/5.27      ! [A: nat,B: nat] :
% 9.49/5.27        ( ( A = B )
% 9.49/5.27        | ~ ( ord_less_eq_nat @ A @ B )
% 9.49/5.27        | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3762_verit__la__disequality,axiom,
% 9.49/5.27      ! [A: int,B: int] :
% 9.49/5.27        ( ( A = B )
% 9.49/5.27        | ~ ( ord_less_eq_int @ A @ B )
% 9.49/5.27        | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3763_verit__comp__simplify1_I2_J,axiom,
% 9.49/5.27      ! [A: set_real] : ( ord_less_eq_set_real @ A @ A ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3764_verit__comp__simplify1_I2_J,axiom,
% 9.49/5.27      ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3765_verit__comp__simplify1_I2_J,axiom,
% 9.49/5.27      ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3766_verit__comp__simplify1_I2_J,axiom,
% 9.49/5.27      ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3767_verit__comp__simplify1_I2_J,axiom,
% 9.49/5.27      ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3768_divmod__int__def,axiom,
% 9.49/5.27      ( unique5052692396658037445od_int
% 9.49/5.27      = ( ^ [M6: num,N2: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N2 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3769_verit__comp__simplify1_I1_J,axiom,
% 9.49/5.27      ! [A: real] :
% 9.49/5.27        ~ ( ord_less_real @ A @ A ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3770_verit__comp__simplify1_I1_J,axiom,
% 9.49/5.27      ! [A: rat] :
% 9.49/5.27        ~ ( ord_less_rat @ A @ A ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3771_verit__comp__simplify1_I1_J,axiom,
% 9.49/5.27      ! [A: num] :
% 9.49/5.27        ~ ( ord_less_num @ A @ A ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3772_verit__comp__simplify1_I1_J,axiom,
% 9.49/5.27      ! [A: nat] :
% 9.49/5.27        ~ ( ord_less_nat @ A @ A ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3773_verit__comp__simplify1_I1_J,axiom,
% 9.49/5.27      ! [A: int] :
% 9.49/5.27        ~ ( ord_less_int @ A @ A ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3774_eucl__rel__int,axiom,
% 9.49/5.27      ! [K: int,L2: int] : ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ ( divide_divide_int @ K @ L2 ) @ ( modulo_modulo_int @ K @ L2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3775_mod__pos__neg__trivial,axiom,
% 9.49/5.27      ! [K: int,L2: int] :
% 9.49/5.27        ( ( ord_less_int @ zero_zero_int @ K )
% 9.49/5.27       => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L2 ) @ zero_zero_int )
% 9.49/5.27         => ( ( modulo_modulo_int @ K @ L2 )
% 9.49/5.27            = ( plus_plus_int @ K @ L2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3776_mod__pos__geq,axiom,
% 9.49/5.27      ! [L2: int,K: int] :
% 9.49/5.27        ( ( ord_less_int @ zero_zero_int @ L2 )
% 9.49/5.27       => ( ( ord_less_eq_int @ L2 @ K )
% 9.49/5.27         => ( ( modulo_modulo_int @ K @ L2 )
% 9.49/5.27            = ( modulo_modulo_int @ ( minus_minus_int @ K @ L2 ) @ L2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3777_verit__le__mono__div__int,axiom,
% 9.49/5.27      ! [A2: int,B2: int,N: int] :
% 9.49/5.27        ( ( ord_less_int @ A2 @ B2 )
% 9.49/5.27       => ( ( ord_less_int @ zero_zero_int @ N )
% 9.49/5.27         => ( ord_less_eq_int
% 9.49/5.27            @ ( plus_plus_int @ ( divide_divide_int @ A2 @ N )
% 9.49/5.27              @ ( if_int
% 9.49/5.27                @ ( ( modulo_modulo_int @ B2 @ N )
% 9.49/5.27                  = zero_zero_int )
% 9.49/5.27                @ one_one_int
% 9.49/5.27                @ zero_zero_int ) )
% 9.49/5.27            @ ( divide_divide_int @ B2 @ N ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3778_split__zmod,axiom,
% 9.49/5.27      ! [P: int > $o,N: int,K: int] :
% 9.49/5.27        ( ( P @ ( modulo_modulo_int @ N @ K ) )
% 9.49/5.27        = ( ( ( K = zero_zero_int )
% 9.49/5.27           => ( P @ N ) )
% 9.49/5.27          & ( ( ord_less_int @ zero_zero_int @ K )
% 9.49/5.27           => ! [I3: int,J3: int] :
% 9.49/5.27                ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 9.49/5.27                  & ( ord_less_int @ J3 @ K )
% 9.49/5.27                  & ( N
% 9.49/5.27                    = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 9.49/5.27               => ( P @ J3 ) ) )
% 9.49/5.27          & ( ( ord_less_int @ K @ zero_zero_int )
% 9.49/5.27           => ! [I3: int,J3: int] :
% 9.49/5.27                ( ( ( ord_less_int @ K @ J3 )
% 9.49/5.27                  & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 9.49/5.27                  & ( N
% 9.49/5.27                    = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 9.49/5.27               => ( P @ J3 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3779_int__mod__neg__eq,axiom,
% 9.49/5.27      ! [A: int,B: int,Q2: int,R: int] :
% 9.49/5.27        ( ( A
% 9.49/5.27          = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 9.49/5.27       => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 9.49/5.27         => ( ( ord_less_int @ B @ R )
% 9.49/5.27           => ( ( modulo_modulo_int @ A @ B )
% 9.49/5.27              = R ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3780_int__mod__pos__eq,axiom,
% 9.49/5.27      ! [A: int,B: int,Q2: int,R: int] :
% 9.49/5.27        ( ( A
% 9.49/5.27          = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 9.49/5.27       => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 9.49/5.27         => ( ( ord_less_int @ R @ B )
% 9.49/5.27           => ( ( modulo_modulo_int @ A @ B )
% 9.49/5.27              = R ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3781_zmod__zmult2__eq,axiom,
% 9.49/5.27      ! [C: int,A: int,B: int] :
% 9.49/5.27        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.49/5.27       => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 9.49/5.27          = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3782_split__neg__lemma,axiom,
% 9.49/5.27      ! [K: int,P: int > int > $o,N: int] :
% 9.49/5.27        ( ( ord_less_int @ K @ zero_zero_int )
% 9.49/5.27       => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 9.49/5.27          = ( ! [I3: int,J3: int] :
% 9.49/5.27                ( ( ( ord_less_int @ K @ J3 )
% 9.49/5.27                  & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 9.49/5.27                  & ( N
% 9.49/5.27                    = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 9.49/5.27               => ( P @ I3 @ J3 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3783_split__pos__lemma,axiom,
% 9.49/5.27      ! [K: int,P: int > int > $o,N: int] :
% 9.49/5.27        ( ( ord_less_int @ zero_zero_int @ K )
% 9.49/5.27       => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 9.49/5.27          = ( ! [I3: int,J3: int] :
% 9.49/5.27                ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 9.49/5.27                  & ( ord_less_int @ J3 @ K )
% 9.49/5.27                  & ( N
% 9.49/5.27                    = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 9.49/5.27               => ( P @ I3 @ J3 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3784_verit__comp__simplify1_I3_J,axiom,
% 9.49/5.27      ! [B5: real,A5: real] :
% 9.49/5.27        ( ( ~ ( ord_less_eq_real @ B5 @ A5 ) )
% 9.49/5.27        = ( ord_less_real @ A5 @ B5 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3785_verit__comp__simplify1_I3_J,axiom,
% 9.49/5.27      ! [B5: rat,A5: rat] :
% 9.49/5.27        ( ( ~ ( ord_less_eq_rat @ B5 @ A5 ) )
% 9.49/5.27        = ( ord_less_rat @ A5 @ B5 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3786_verit__comp__simplify1_I3_J,axiom,
% 9.49/5.27      ! [B5: num,A5: num] :
% 9.49/5.27        ( ( ~ ( ord_less_eq_num @ B5 @ A5 ) )
% 9.49/5.27        = ( ord_less_num @ A5 @ B5 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3787_verit__comp__simplify1_I3_J,axiom,
% 9.49/5.27      ! [B5: nat,A5: nat] :
% 9.49/5.27        ( ( ~ ( ord_less_eq_nat @ B5 @ A5 ) )
% 9.49/5.27        = ( ord_less_nat @ A5 @ B5 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3788_verit__comp__simplify1_I3_J,axiom,
% 9.49/5.27      ! [B5: int,A5: int] :
% 9.49/5.27        ( ( ~ ( ord_less_eq_int @ B5 @ A5 ) )
% 9.49/5.27        = ( ord_less_int @ A5 @ B5 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3789_verit__sum__simplify,axiom,
% 9.49/5.27      ! [A: complex] :
% 9.49/5.27        ( ( plus_plus_complex @ A @ zero_zero_complex )
% 9.49/5.27        = A ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3790_verit__sum__simplify,axiom,
% 9.49/5.27      ! [A: real] :
% 9.49/5.27        ( ( plus_plus_real @ A @ zero_zero_real )
% 9.49/5.27        = A ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3791_verit__sum__simplify,axiom,
% 9.49/5.27      ! [A: rat] :
% 9.49/5.27        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 9.49/5.27        = A ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3792_verit__sum__simplify,axiom,
% 9.49/5.27      ! [A: nat] :
% 9.49/5.27        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 9.49/5.27        = A ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3793_verit__sum__simplify,axiom,
% 9.49/5.27      ! [A: int] :
% 9.49/5.27        ( ( plus_plus_int @ A @ zero_zero_int )
% 9.49/5.27        = A ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3794_verit__eq__simplify_I10_J,axiom,
% 9.49/5.27      ! [X23: num] :
% 9.49/5.27        ( one
% 9.49/5.27       != ( bit0 @ X23 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3795_finite__has__minimal2,axiom,
% 9.49/5.27      ! [A2: set_real,A: real] :
% 9.49/5.27        ( ( finite_finite_real @ A2 )
% 9.49/5.27       => ( ( member_real @ A @ A2 )
% 9.49/5.27         => ? [X3: real] :
% 9.49/5.27              ( ( member_real @ X3 @ A2 )
% 9.49/5.27              & ( ord_less_eq_real @ X3 @ A )
% 9.49/5.27              & ! [Xa: real] :
% 9.49/5.27                  ( ( member_real @ Xa @ A2 )
% 9.49/5.27                 => ( ( ord_less_eq_real @ Xa @ X3 )
% 9.49/5.27                   => ( X3 = Xa ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3796_finite__has__minimal2,axiom,
% 9.49/5.27      ! [A2: set_set_real,A: set_real] :
% 9.49/5.27        ( ( finite9007344921179782393t_real @ A2 )
% 9.49/5.27       => ( ( member_set_real @ A @ A2 )
% 9.49/5.27         => ? [X3: set_real] :
% 9.49/5.27              ( ( member_set_real @ X3 @ A2 )
% 9.49/5.27              & ( ord_less_eq_set_real @ X3 @ A )
% 9.49/5.27              & ! [Xa: set_real] :
% 9.49/5.27                  ( ( member_set_real @ Xa @ A2 )
% 9.49/5.27                 => ( ( ord_less_eq_set_real @ Xa @ X3 )
% 9.49/5.27                   => ( X3 = Xa ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3797_finite__has__minimal2,axiom,
% 9.49/5.27      ! [A2: set_set_nat,A: set_nat] :
% 9.49/5.27        ( ( finite1152437895449049373et_nat @ A2 )
% 9.49/5.27       => ( ( member_set_nat @ A @ A2 )
% 9.49/5.27         => ? [X3: set_nat] :
% 9.49/5.27              ( ( member_set_nat @ X3 @ A2 )
% 9.49/5.27              & ( ord_less_eq_set_nat @ X3 @ A )
% 9.49/5.27              & ! [Xa: set_nat] :
% 9.49/5.27                  ( ( member_set_nat @ Xa @ A2 )
% 9.49/5.27                 => ( ( ord_less_eq_set_nat @ Xa @ X3 )
% 9.49/5.27                   => ( X3 = Xa ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3798_finite__has__minimal2,axiom,
% 9.49/5.27      ! [A2: set_num,A: num] :
% 9.49/5.27        ( ( finite_finite_num @ A2 )
% 9.49/5.27       => ( ( member_num @ A @ A2 )
% 9.49/5.27         => ? [X3: num] :
% 9.49/5.27              ( ( member_num @ X3 @ A2 )
% 9.49/5.27              & ( ord_less_eq_num @ X3 @ A )
% 9.49/5.27              & ! [Xa: num] :
% 9.49/5.27                  ( ( member_num @ Xa @ A2 )
% 9.49/5.27                 => ( ( ord_less_eq_num @ Xa @ X3 )
% 9.49/5.27                   => ( X3 = Xa ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3799_finite__has__minimal2,axiom,
% 9.49/5.27      ! [A2: set_nat,A: nat] :
% 9.49/5.27        ( ( finite_finite_nat @ A2 )
% 9.49/5.27       => ( ( member_nat @ A @ A2 )
% 9.49/5.27         => ? [X3: nat] :
% 9.49/5.27              ( ( member_nat @ X3 @ A2 )
% 9.49/5.27              & ( ord_less_eq_nat @ X3 @ A )
% 9.49/5.27              & ! [Xa: nat] :
% 9.49/5.27                  ( ( member_nat @ Xa @ A2 )
% 9.49/5.27                 => ( ( ord_less_eq_nat @ Xa @ X3 )
% 9.49/5.27                   => ( X3 = Xa ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3800_finite__has__minimal2,axiom,
% 9.49/5.27      ! [A2: set_int,A: int] :
% 9.49/5.27        ( ( finite_finite_int @ A2 )
% 9.49/5.27       => ( ( member_int @ A @ A2 )
% 9.49/5.27         => ? [X3: int] :
% 9.49/5.27              ( ( member_int @ X3 @ A2 )
% 9.49/5.27              & ( ord_less_eq_int @ X3 @ A )
% 9.49/5.27              & ! [Xa: int] :
% 9.49/5.27                  ( ( member_int @ Xa @ A2 )
% 9.49/5.27                 => ( ( ord_less_eq_int @ Xa @ X3 )
% 9.49/5.27                   => ( X3 = Xa ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3801_finite__has__maximal2,axiom,
% 9.49/5.27      ! [A2: set_real,A: real] :
% 9.49/5.27        ( ( finite_finite_real @ A2 )
% 9.49/5.27       => ( ( member_real @ A @ A2 )
% 9.49/5.27         => ? [X3: real] :
% 9.49/5.27              ( ( member_real @ X3 @ A2 )
% 9.49/5.27              & ( ord_less_eq_real @ A @ X3 )
% 9.49/5.27              & ! [Xa: real] :
% 9.49/5.27                  ( ( member_real @ Xa @ A2 )
% 9.49/5.27                 => ( ( ord_less_eq_real @ X3 @ Xa )
% 9.49/5.27                   => ( X3 = Xa ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3802_finite__has__maximal2,axiom,
% 9.49/5.27      ! [A2: set_set_real,A: set_real] :
% 9.49/5.27        ( ( finite9007344921179782393t_real @ A2 )
% 9.49/5.27       => ( ( member_set_real @ A @ A2 )
% 9.49/5.27         => ? [X3: set_real] :
% 9.49/5.27              ( ( member_set_real @ X3 @ A2 )
% 9.49/5.27              & ( ord_less_eq_set_real @ A @ X3 )
% 9.49/5.27              & ! [Xa: set_real] :
% 9.49/5.27                  ( ( member_set_real @ Xa @ A2 )
% 9.49/5.27                 => ( ( ord_less_eq_set_real @ X3 @ Xa )
% 9.49/5.27                   => ( X3 = Xa ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3803_finite__has__maximal2,axiom,
% 9.49/5.27      ! [A2: set_set_nat,A: set_nat] :
% 9.49/5.27        ( ( finite1152437895449049373et_nat @ A2 )
% 9.49/5.27       => ( ( member_set_nat @ A @ A2 )
% 9.49/5.27         => ? [X3: set_nat] :
% 9.49/5.27              ( ( member_set_nat @ X3 @ A2 )
% 9.49/5.27              & ( ord_less_eq_set_nat @ A @ X3 )
% 9.49/5.27              & ! [Xa: set_nat] :
% 9.49/5.27                  ( ( member_set_nat @ Xa @ A2 )
% 9.49/5.27                 => ( ( ord_less_eq_set_nat @ X3 @ Xa )
% 9.49/5.27                   => ( X3 = Xa ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3804_finite__has__maximal2,axiom,
% 9.49/5.27      ! [A2: set_num,A: num] :
% 9.49/5.27        ( ( finite_finite_num @ A2 )
% 9.49/5.27       => ( ( member_num @ A @ A2 )
% 9.49/5.27         => ? [X3: num] :
% 9.49/5.27              ( ( member_num @ X3 @ A2 )
% 9.49/5.27              & ( ord_less_eq_num @ A @ X3 )
% 9.49/5.27              & ! [Xa: num] :
% 9.49/5.27                  ( ( member_num @ Xa @ A2 )
% 9.49/5.27                 => ( ( ord_less_eq_num @ X3 @ Xa )
% 9.49/5.27                   => ( X3 = Xa ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3805_finite__has__maximal2,axiom,
% 9.49/5.27      ! [A2: set_nat,A: nat] :
% 9.49/5.27        ( ( finite_finite_nat @ A2 )
% 9.49/5.27       => ( ( member_nat @ A @ A2 )
% 9.49/5.27         => ? [X3: nat] :
% 9.49/5.27              ( ( member_nat @ X3 @ A2 )
% 9.49/5.27              & ( ord_less_eq_nat @ A @ X3 )
% 9.49/5.27              & ! [Xa: nat] :
% 9.49/5.27                  ( ( member_nat @ Xa @ A2 )
% 9.49/5.27                 => ( ( ord_less_eq_nat @ X3 @ Xa )
% 9.49/5.27                   => ( X3 = Xa ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3806_finite__has__maximal2,axiom,
% 9.49/5.27      ! [A2: set_int,A: int] :
% 9.49/5.27        ( ( finite_finite_int @ A2 )
% 9.49/5.27       => ( ( member_int @ A @ A2 )
% 9.49/5.27         => ? [X3: int] :
% 9.49/5.27              ( ( member_int @ X3 @ A2 )
% 9.49/5.27              & ( ord_less_eq_int @ A @ X3 )
% 9.49/5.27              & ! [Xa: int] :
% 9.49/5.27                  ( ( member_int @ Xa @ A2 )
% 9.49/5.27                 => ( ( ord_less_eq_int @ X3 @ Xa )
% 9.49/5.27                   => ( X3 = Xa ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3807_verit__eq__simplify_I14_J,axiom,
% 9.49/5.27      ! [X23: num,X33: num] :
% 9.49/5.27        ( ( bit0 @ X23 )
% 9.49/5.27       != ( bit1 @ X33 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3808_verit__eq__simplify_I12_J,axiom,
% 9.49/5.27      ! [X33: num] :
% 9.49/5.27        ( one
% 9.49/5.27       != ( bit1 @ X33 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3809_Diff__infinite__finite,axiom,
% 9.49/5.27      ! [T4: set_complex,S2: set_complex] :
% 9.49/5.27        ( ( finite3207457112153483333omplex @ T4 )
% 9.49/5.27       => ( ~ ( finite3207457112153483333omplex @ S2 )
% 9.49/5.27         => ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ S2 @ T4 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3810_Diff__infinite__finite,axiom,
% 9.49/5.27      ! [T4: set_Pr1261947904930325089at_nat,S2: set_Pr1261947904930325089at_nat] :
% 9.49/5.27        ( ( finite6177210948735845034at_nat @ T4 )
% 9.49/5.27       => ( ~ ( finite6177210948735845034at_nat @ S2 )
% 9.49/5.27         => ~ ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ S2 @ T4 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3811_Diff__infinite__finite,axiom,
% 9.49/5.27      ! [T4: set_nat,S2: set_nat] :
% 9.49/5.27        ( ( finite_finite_nat @ T4 )
% 9.49/5.27       => ( ~ ( finite_finite_nat @ S2 )
% 9.49/5.27         => ~ ( finite_finite_nat @ ( minus_minus_set_nat @ S2 @ T4 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3812_eq__diff__eq_H,axiom,
% 9.49/5.27      ! [X: real,Y2: real,Z: real] :
% 9.49/5.27        ( ( X
% 9.49/5.27          = ( minus_minus_real @ Y2 @ Z ) )
% 9.49/5.27        = ( Y2
% 9.49/5.27          = ( plus_plus_real @ X @ Z ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3813_pos__zmod__mult__2,axiom,
% 9.49/5.27      ! [A: int,B: int] :
% 9.49/5.27        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.27       => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 9.49/5.27          = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3814_max__def__raw,axiom,
% 9.49/5.27      ( ord_ma741700101516333627d_enat
% 9.49/5.27      = ( ^ [A3: extended_enat,B4: extended_enat] : ( if_Extended_enat @ ( ord_le2932123472753598470d_enat @ A3 @ B4 ) @ B4 @ A3 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3815_max__def__raw,axiom,
% 9.49/5.27      ( ord_max_set_real
% 9.49/5.27      = ( ^ [A3: set_real,B4: set_real] : ( if_set_real @ ( ord_less_eq_set_real @ A3 @ B4 ) @ B4 @ A3 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3816_max__def__raw,axiom,
% 9.49/5.27      ( ord_max_set_nat
% 9.49/5.27      = ( ^ [A3: set_nat,B4: set_nat] : ( if_set_nat @ ( ord_less_eq_set_nat @ A3 @ B4 ) @ B4 @ A3 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3817_max__def__raw,axiom,
% 9.49/5.27      ( ord_max_num
% 9.49/5.27      = ( ^ [A3: num,B4: num] : ( if_num @ ( ord_less_eq_num @ A3 @ B4 ) @ B4 @ A3 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3818_max__def__raw,axiom,
% 9.49/5.27      ( ord_max_nat
% 9.49/5.27      = ( ^ [A3: nat,B4: nat] : ( if_nat @ ( ord_less_eq_nat @ A3 @ B4 ) @ B4 @ A3 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3819_max__def__raw,axiom,
% 9.49/5.27      ( ord_max_int
% 9.49/5.27      = ( ^ [A3: int,B4: int] : ( if_int @ ( ord_less_eq_int @ A3 @ B4 ) @ B4 @ A3 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3820_neg__zmod__mult__2,axiom,
% 9.49/5.27      ! [A: int,B: int] :
% 9.49/5.27        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 9.49/5.27       => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 9.49/5.27          = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) @ one_one_int ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3821_finite__has__maximal,axiom,
% 9.49/5.27      ! [A2: set_real] :
% 9.49/5.27        ( ( finite_finite_real @ A2 )
% 9.49/5.27       => ( ( A2 != bot_bot_set_real )
% 9.49/5.27         => ? [X3: real] :
% 9.49/5.27              ( ( member_real @ X3 @ A2 )
% 9.49/5.27              & ! [Xa: real] :
% 9.49/5.27                  ( ( member_real @ Xa @ A2 )
% 9.49/5.27                 => ( ( ord_less_eq_real @ X3 @ Xa )
% 9.49/5.27                   => ( X3 = Xa ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3822_finite__has__maximal,axiom,
% 9.49/5.27      ! [A2: set_set_real] :
% 9.49/5.27        ( ( finite9007344921179782393t_real @ A2 )
% 9.49/5.27       => ( ( A2 != bot_bot_set_set_real )
% 9.49/5.27         => ? [X3: set_real] :
% 9.49/5.27              ( ( member_set_real @ X3 @ A2 )
% 9.49/5.27              & ! [Xa: set_real] :
% 9.49/5.27                  ( ( member_set_real @ Xa @ A2 )
% 9.49/5.27                 => ( ( ord_less_eq_set_real @ X3 @ Xa )
% 9.49/5.27                   => ( X3 = Xa ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3823_finite__has__maximal,axiom,
% 9.49/5.27      ! [A2: set_set_nat] :
% 9.49/5.27        ( ( finite1152437895449049373et_nat @ A2 )
% 9.49/5.27       => ( ( A2 != bot_bot_set_set_nat )
% 9.49/5.27         => ? [X3: set_nat] :
% 9.49/5.27              ( ( member_set_nat @ X3 @ A2 )
% 9.49/5.27              & ! [Xa: set_nat] :
% 9.49/5.27                  ( ( member_set_nat @ Xa @ A2 )
% 9.49/5.27                 => ( ( ord_less_eq_set_nat @ X3 @ Xa )
% 9.49/5.27                   => ( X3 = Xa ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3824_finite__has__maximal,axiom,
% 9.49/5.27      ! [A2: set_num] :
% 9.49/5.27        ( ( finite_finite_num @ A2 )
% 9.49/5.27       => ( ( A2 != bot_bot_set_num )
% 9.49/5.27         => ? [X3: num] :
% 9.49/5.27              ( ( member_num @ X3 @ A2 )
% 9.49/5.27              & ! [Xa: num] :
% 9.49/5.27                  ( ( member_num @ Xa @ A2 )
% 9.49/5.27                 => ( ( ord_less_eq_num @ X3 @ Xa )
% 9.49/5.27                   => ( X3 = Xa ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3825_finite__has__maximal,axiom,
% 9.49/5.27      ! [A2: set_nat] :
% 9.49/5.27        ( ( finite_finite_nat @ A2 )
% 9.49/5.27       => ( ( A2 != bot_bot_set_nat )
% 9.49/5.27         => ? [X3: nat] :
% 9.49/5.27              ( ( member_nat @ X3 @ A2 )
% 9.49/5.27              & ! [Xa: nat] :
% 9.49/5.27                  ( ( member_nat @ Xa @ A2 )
% 9.49/5.27                 => ( ( ord_less_eq_nat @ X3 @ Xa )
% 9.49/5.27                   => ( X3 = Xa ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3826_finite__has__maximal,axiom,
% 9.49/5.27      ! [A2: set_int] :
% 9.49/5.27        ( ( finite_finite_int @ A2 )
% 9.49/5.27       => ( ( A2 != bot_bot_set_int )
% 9.49/5.27         => ? [X3: int] :
% 9.49/5.27              ( ( member_int @ X3 @ A2 )
% 9.49/5.27              & ! [Xa: int] :
% 9.49/5.27                  ( ( member_int @ Xa @ A2 )
% 9.49/5.27                 => ( ( ord_less_eq_int @ X3 @ Xa )
% 9.49/5.27                   => ( X3 = Xa ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3827_finite__has__minimal,axiom,
% 9.49/5.27      ! [A2: set_real] :
% 9.49/5.27        ( ( finite_finite_real @ A2 )
% 9.49/5.27       => ( ( A2 != bot_bot_set_real )
% 9.49/5.27         => ? [X3: real] :
% 9.49/5.27              ( ( member_real @ X3 @ A2 )
% 9.49/5.27              & ! [Xa: real] :
% 9.49/5.27                  ( ( member_real @ Xa @ A2 )
% 9.49/5.27                 => ( ( ord_less_eq_real @ Xa @ X3 )
% 9.49/5.27                   => ( X3 = Xa ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3828_finite__has__minimal,axiom,
% 9.49/5.27      ! [A2: set_set_real] :
% 9.49/5.27        ( ( finite9007344921179782393t_real @ A2 )
% 9.49/5.27       => ( ( A2 != bot_bot_set_set_real )
% 9.49/5.27         => ? [X3: set_real] :
% 9.49/5.27              ( ( member_set_real @ X3 @ A2 )
% 9.49/5.27              & ! [Xa: set_real] :
% 9.49/5.27                  ( ( member_set_real @ Xa @ A2 )
% 9.49/5.27                 => ( ( ord_less_eq_set_real @ Xa @ X3 )
% 9.49/5.27                   => ( X3 = Xa ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3829_finite__has__minimal,axiom,
% 9.49/5.27      ! [A2: set_set_nat] :
% 9.49/5.27        ( ( finite1152437895449049373et_nat @ A2 )
% 9.49/5.27       => ( ( A2 != bot_bot_set_set_nat )
% 9.49/5.27         => ? [X3: set_nat] :
% 9.49/5.27              ( ( member_set_nat @ X3 @ A2 )
% 9.49/5.27              & ! [Xa: set_nat] :
% 9.49/5.27                  ( ( member_set_nat @ Xa @ A2 )
% 9.49/5.27                 => ( ( ord_less_eq_set_nat @ Xa @ X3 )
% 9.49/5.27                   => ( X3 = Xa ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3830_finite__has__minimal,axiom,
% 9.49/5.27      ! [A2: set_num] :
% 9.49/5.27        ( ( finite_finite_num @ A2 )
% 9.49/5.27       => ( ( A2 != bot_bot_set_num )
% 9.49/5.27         => ? [X3: num] :
% 9.49/5.27              ( ( member_num @ X3 @ A2 )
% 9.49/5.27              & ! [Xa: num] :
% 9.49/5.27                  ( ( member_num @ Xa @ A2 )
% 9.49/5.27                 => ( ( ord_less_eq_num @ Xa @ X3 )
% 9.49/5.27                   => ( X3 = Xa ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3831_finite__has__minimal,axiom,
% 9.49/5.27      ! [A2: set_nat] :
% 9.49/5.27        ( ( finite_finite_nat @ A2 )
% 9.49/5.27       => ( ( A2 != bot_bot_set_nat )
% 9.49/5.27         => ? [X3: nat] :
% 9.49/5.27              ( ( member_nat @ X3 @ A2 )
% 9.49/5.27              & ! [Xa: nat] :
% 9.49/5.27                  ( ( member_nat @ Xa @ A2 )
% 9.49/5.27                 => ( ( ord_less_eq_nat @ Xa @ X3 )
% 9.49/5.27                   => ( X3 = Xa ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3832_finite__has__minimal,axiom,
% 9.49/5.27      ! [A2: set_int] :
% 9.49/5.27        ( ( finite_finite_int @ A2 )
% 9.49/5.27       => ( ( A2 != bot_bot_set_int )
% 9.49/5.27         => ? [X3: int] :
% 9.49/5.27              ( ( member_int @ X3 @ A2 )
% 9.49/5.27              & ! [Xa: int] :
% 9.49/5.27                  ( ( member_int @ Xa @ A2 )
% 9.49/5.27                 => ( ( ord_less_eq_int @ Xa @ X3 )
% 9.49/5.27                   => ( X3 = Xa ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3833_infinite__remove,axiom,
% 9.49/5.27      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT] :
% 9.49/5.27        ( ~ ( finite5795047828879050333T_VEBT @ S2 )
% 9.49/5.27       => ~ ( finite5795047828879050333T_VEBT @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3834_infinite__remove,axiom,
% 9.49/5.27      ! [S2: set_complex,A: complex] :
% 9.49/5.27        ( ~ ( finite3207457112153483333omplex @ S2 )
% 9.49/5.27       => ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3835_infinite__remove,axiom,
% 9.49/5.27      ! [S2: set_int,A: int] :
% 9.49/5.27        ( ~ ( finite_finite_int @ S2 )
% 9.49/5.27       => ~ ( finite_finite_int @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3836_infinite__remove,axiom,
% 9.49/5.27      ! [S2: set_real,A: real] :
% 9.49/5.27        ( ~ ( finite_finite_real @ S2 )
% 9.49/5.27       => ~ ( finite_finite_real @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3837_infinite__remove,axiom,
% 9.49/5.27      ! [S2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat] :
% 9.49/5.27        ( ~ ( finite6177210948735845034at_nat @ S2 )
% 9.49/5.27       => ~ ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ S2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3838_infinite__remove,axiom,
% 9.49/5.27      ! [S2: set_nat,A: nat] :
% 9.49/5.27        ( ~ ( finite_finite_nat @ S2 )
% 9.49/5.27       => ~ ( finite_finite_nat @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3839_infinite__coinduct,axiom,
% 9.49/5.27      ! [X8: set_VEBT_VEBT > $o,A2: set_VEBT_VEBT] :
% 9.49/5.27        ( ( X8 @ A2 )
% 9.49/5.27       => ( ! [A7: set_VEBT_VEBT] :
% 9.49/5.27              ( ( X8 @ A7 )
% 9.49/5.27             => ? [X5: vEBT_VEBT] :
% 9.49/5.27                  ( ( member_VEBT_VEBT @ X5 @ A7 )
% 9.49/5.27                  & ( ( X8 @ ( minus_5127226145743854075T_VEBT @ A7 @ ( insert_VEBT_VEBT @ X5 @ bot_bo8194388402131092736T_VEBT ) ) )
% 9.49/5.27                    | ~ ( finite5795047828879050333T_VEBT @ ( minus_5127226145743854075T_VEBT @ A7 @ ( insert_VEBT_VEBT @ X5 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 9.49/5.27         => ~ ( finite5795047828879050333T_VEBT @ A2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3840_infinite__coinduct,axiom,
% 9.49/5.27      ! [X8: set_complex > $o,A2: set_complex] :
% 9.49/5.27        ( ( X8 @ A2 )
% 9.49/5.27       => ( ! [A7: set_complex] :
% 9.49/5.27              ( ( X8 @ A7 )
% 9.49/5.27             => ? [X5: complex] :
% 9.49/5.27                  ( ( member_complex @ X5 @ A7 )
% 9.49/5.27                  & ( ( X8 @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ X5 @ bot_bot_set_complex ) ) )
% 9.49/5.27                    | ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ X5 @ bot_bot_set_complex ) ) ) ) ) )
% 9.49/5.27         => ~ ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3841_infinite__coinduct,axiom,
% 9.49/5.27      ! [X8: set_int > $o,A2: set_int] :
% 9.49/5.27        ( ( X8 @ A2 )
% 9.49/5.27       => ( ! [A7: set_int] :
% 9.49/5.27              ( ( X8 @ A7 )
% 9.49/5.27             => ? [X5: int] :
% 9.49/5.27                  ( ( member_int @ X5 @ A7 )
% 9.49/5.27                  & ( ( X8 @ ( minus_minus_set_int @ A7 @ ( insert_int @ X5 @ bot_bot_set_int ) ) )
% 9.49/5.27                    | ~ ( finite_finite_int @ ( minus_minus_set_int @ A7 @ ( insert_int @ X5 @ bot_bot_set_int ) ) ) ) ) )
% 9.49/5.27         => ~ ( finite_finite_int @ A2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3842_infinite__coinduct,axiom,
% 9.49/5.27      ! [X8: set_real > $o,A2: set_real] :
% 9.49/5.27        ( ( X8 @ A2 )
% 9.49/5.27       => ( ! [A7: set_real] :
% 9.49/5.27              ( ( X8 @ A7 )
% 9.49/5.27             => ? [X5: real] :
% 9.49/5.27                  ( ( member_real @ X5 @ A7 )
% 9.49/5.27                  & ( ( X8 @ ( minus_minus_set_real @ A7 @ ( insert_real @ X5 @ bot_bot_set_real ) ) )
% 9.49/5.27                    | ~ ( finite_finite_real @ ( minus_minus_set_real @ A7 @ ( insert_real @ X5 @ bot_bot_set_real ) ) ) ) ) )
% 9.49/5.27         => ~ ( finite_finite_real @ A2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3843_infinite__coinduct,axiom,
% 9.49/5.27      ! [X8: set_Pr1261947904930325089at_nat > $o,A2: set_Pr1261947904930325089at_nat] :
% 9.49/5.27        ( ( X8 @ A2 )
% 9.49/5.27       => ( ! [A7: set_Pr1261947904930325089at_nat] :
% 9.49/5.27              ( ( X8 @ A7 )
% 9.49/5.27             => ? [X5: product_prod_nat_nat] :
% 9.49/5.27                  ( ( member8440522571783428010at_nat @ X5 @ A7 )
% 9.49/5.27                  & ( ( X8 @ ( minus_1356011639430497352at_nat @ A7 @ ( insert8211810215607154385at_nat @ X5 @ bot_bo2099793752762293965at_nat ) ) )
% 9.49/5.27                    | ~ ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ A7 @ ( insert8211810215607154385at_nat @ X5 @ bot_bo2099793752762293965at_nat ) ) ) ) ) )
% 9.49/5.27         => ~ ( finite6177210948735845034at_nat @ A2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3844_infinite__coinduct,axiom,
% 9.49/5.27      ! [X8: set_nat > $o,A2: set_nat] :
% 9.49/5.27        ( ( X8 @ A2 )
% 9.49/5.27       => ( ! [A7: set_nat] :
% 9.49/5.27              ( ( X8 @ A7 )
% 9.49/5.27             => ? [X5: nat] :
% 9.49/5.27                  ( ( member_nat @ X5 @ A7 )
% 9.49/5.27                  & ( ( X8 @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ X5 @ bot_bot_set_nat ) ) )
% 9.49/5.27                    | ~ ( finite_finite_nat @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ X5 @ bot_bot_set_nat ) ) ) ) ) )
% 9.49/5.27         => ~ ( finite_finite_nat @ A2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3845_finite__empty__induct,axiom,
% 9.49/5.27      ! [A2: set_VEBT_VEBT,P: set_VEBT_VEBT > $o] :
% 9.49/5.27        ( ( finite5795047828879050333T_VEBT @ A2 )
% 9.49/5.27       => ( ( P @ A2 )
% 9.49/5.27         => ( ! [A4: vEBT_VEBT,A7: set_VEBT_VEBT] :
% 9.49/5.27                ( ( finite5795047828879050333T_VEBT @ A7 )
% 9.49/5.27               => ( ( member_VEBT_VEBT @ A4 @ A7 )
% 9.49/5.27                 => ( ( P @ A7 )
% 9.49/5.27                   => ( P @ ( minus_5127226145743854075T_VEBT @ A7 @ ( insert_VEBT_VEBT @ A4 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 9.49/5.27           => ( P @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3846_finite__empty__induct,axiom,
% 9.49/5.27      ! [A2: set_complex,P: set_complex > $o] :
% 9.49/5.27        ( ( finite3207457112153483333omplex @ A2 )
% 9.49/5.27       => ( ( P @ A2 )
% 9.49/5.27         => ( ! [A4: complex,A7: set_complex] :
% 9.49/5.27                ( ( finite3207457112153483333omplex @ A7 )
% 9.49/5.27               => ( ( member_complex @ A4 @ A7 )
% 9.49/5.27                 => ( ( P @ A7 )
% 9.49/5.27                   => ( P @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ A4 @ bot_bot_set_complex ) ) ) ) ) )
% 9.49/5.27           => ( P @ bot_bot_set_complex ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3847_finite__empty__induct,axiom,
% 9.49/5.27      ! [A2: set_int,P: set_int > $o] :
% 9.49/5.27        ( ( finite_finite_int @ A2 )
% 9.49/5.27       => ( ( P @ A2 )
% 9.49/5.27         => ( ! [A4: int,A7: set_int] :
% 9.49/5.27                ( ( finite_finite_int @ A7 )
% 9.49/5.27               => ( ( member_int @ A4 @ A7 )
% 9.49/5.27                 => ( ( P @ A7 )
% 9.49/5.27                   => ( P @ ( minus_minus_set_int @ A7 @ ( insert_int @ A4 @ bot_bot_set_int ) ) ) ) ) )
% 9.49/5.27           => ( P @ bot_bot_set_int ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3848_finite__empty__induct,axiom,
% 9.49/5.27      ! [A2: set_real,P: set_real > $o] :
% 9.49/5.27        ( ( finite_finite_real @ A2 )
% 9.49/5.27       => ( ( P @ A2 )
% 9.49/5.27         => ( ! [A4: real,A7: set_real] :
% 9.49/5.27                ( ( finite_finite_real @ A7 )
% 9.49/5.27               => ( ( member_real @ A4 @ A7 )
% 9.49/5.27                 => ( ( P @ A7 )
% 9.49/5.27                   => ( P @ ( minus_minus_set_real @ A7 @ ( insert_real @ A4 @ bot_bot_set_real ) ) ) ) ) )
% 9.49/5.27           => ( P @ bot_bot_set_real ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3849_finite__empty__induct,axiom,
% 9.49/5.27      ! [A2: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 9.49/5.27        ( ( finite6177210948735845034at_nat @ A2 )
% 9.49/5.27       => ( ( P @ A2 )
% 9.49/5.27         => ( ! [A4: product_prod_nat_nat,A7: set_Pr1261947904930325089at_nat] :
% 9.49/5.27                ( ( finite6177210948735845034at_nat @ A7 )
% 9.49/5.27               => ( ( member8440522571783428010at_nat @ A4 @ A7 )
% 9.49/5.27                 => ( ( P @ A7 )
% 9.49/5.27                   => ( P @ ( minus_1356011639430497352at_nat @ A7 @ ( insert8211810215607154385at_nat @ A4 @ bot_bo2099793752762293965at_nat ) ) ) ) ) )
% 9.49/5.27           => ( P @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3850_finite__empty__induct,axiom,
% 9.49/5.27      ! [A2: set_nat,P: set_nat > $o] :
% 9.49/5.27        ( ( finite_finite_nat @ A2 )
% 9.49/5.27       => ( ( P @ A2 )
% 9.49/5.27         => ( ! [A4: nat,A7: set_nat] :
% 9.49/5.27                ( ( finite_finite_nat @ A7 )
% 9.49/5.27               => ( ( member_nat @ A4 @ A7 )
% 9.49/5.27                 => ( ( P @ A7 )
% 9.49/5.27                   => ( P @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ A4 @ bot_bot_set_nat ) ) ) ) ) )
% 9.49/5.27           => ( P @ bot_bot_set_nat ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3851_div__less__mono,axiom,
% 9.49/5.27      ! [A2: nat,B2: nat,N: nat] :
% 9.49/5.27        ( ( ord_less_nat @ A2 @ B2 )
% 9.49/5.27       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.27         => ( ( ( modulo_modulo_nat @ A2 @ N )
% 9.49/5.27              = zero_zero_nat )
% 9.49/5.27           => ( ( ( modulo_modulo_nat @ B2 @ N )
% 9.49/5.27                = zero_zero_nat )
% 9.49/5.27             => ( ord_less_nat @ ( divide_divide_nat @ A2 @ N ) @ ( divide_divide_nat @ B2 @ N ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3852_div__mod__decomp,axiom,
% 9.49/5.27      ! [A2: nat,N: nat] :
% 9.49/5.27        ( A2
% 9.49/5.27        = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A2 @ N ) @ N ) @ ( modulo_modulo_nat @ A2 @ N ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3853_remove__induct,axiom,
% 9.49/5.27      ! [P: set_VEBT_VEBT > $o,B2: set_VEBT_VEBT] :
% 9.49/5.27        ( ( P @ bot_bo8194388402131092736T_VEBT )
% 9.49/5.27       => ( ( ~ ( finite5795047828879050333T_VEBT @ B2 )
% 9.49/5.27           => ( P @ B2 ) )
% 9.49/5.27         => ( ! [A7: set_VEBT_VEBT] :
% 9.49/5.27                ( ( finite5795047828879050333T_VEBT @ A7 )
% 9.49/5.27               => ( ( A7 != bot_bo8194388402131092736T_VEBT )
% 9.49/5.27                 => ( ( ord_le4337996190870823476T_VEBT @ A7 @ B2 )
% 9.49/5.27                   => ( ! [X5: vEBT_VEBT] :
% 9.49/5.27                          ( ( member_VEBT_VEBT @ X5 @ A7 )
% 9.49/5.27                         => ( P @ ( minus_5127226145743854075T_VEBT @ A7 @ ( insert_VEBT_VEBT @ X5 @ bot_bo8194388402131092736T_VEBT ) ) ) )
% 9.49/5.27                     => ( P @ A7 ) ) ) ) )
% 9.49/5.27           => ( P @ B2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3854_remove__induct,axiom,
% 9.49/5.27      ! [P: set_complex > $o,B2: set_complex] :
% 9.49/5.27        ( ( P @ bot_bot_set_complex )
% 9.49/5.27       => ( ( ~ ( finite3207457112153483333omplex @ B2 )
% 9.49/5.27           => ( P @ B2 ) )
% 9.49/5.27         => ( ! [A7: set_complex] :
% 9.49/5.27                ( ( finite3207457112153483333omplex @ A7 )
% 9.49/5.27               => ( ( A7 != bot_bot_set_complex )
% 9.49/5.27                 => ( ( ord_le211207098394363844omplex @ A7 @ B2 )
% 9.49/5.27                   => ( ! [X5: complex] :
% 9.49/5.27                          ( ( member_complex @ X5 @ A7 )
% 9.49/5.27                         => ( P @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ X5 @ bot_bot_set_complex ) ) ) )
% 9.49/5.27                     => ( P @ A7 ) ) ) ) )
% 9.49/5.27           => ( P @ B2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3855_remove__induct,axiom,
% 9.49/5.27      ! [P: set_int > $o,B2: set_int] :
% 9.49/5.27        ( ( P @ bot_bot_set_int )
% 9.49/5.27       => ( ( ~ ( finite_finite_int @ B2 )
% 9.49/5.27           => ( P @ B2 ) )
% 9.49/5.27         => ( ! [A7: set_int] :
% 9.49/5.27                ( ( finite_finite_int @ A7 )
% 9.49/5.27               => ( ( A7 != bot_bot_set_int )
% 9.49/5.27                 => ( ( ord_less_eq_set_int @ A7 @ B2 )
% 9.49/5.27                   => ( ! [X5: int] :
% 9.49/5.27                          ( ( member_int @ X5 @ A7 )
% 9.49/5.27                         => ( P @ ( minus_minus_set_int @ A7 @ ( insert_int @ X5 @ bot_bot_set_int ) ) ) )
% 9.49/5.27                     => ( P @ A7 ) ) ) ) )
% 9.49/5.27           => ( P @ B2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3856_remove__induct,axiom,
% 9.49/5.27      ! [P: set_Pr1261947904930325089at_nat > $o,B2: set_Pr1261947904930325089at_nat] :
% 9.49/5.27        ( ( P @ bot_bo2099793752762293965at_nat )
% 9.49/5.27       => ( ( ~ ( finite6177210948735845034at_nat @ B2 )
% 9.49/5.27           => ( P @ B2 ) )
% 9.49/5.27         => ( ! [A7: set_Pr1261947904930325089at_nat] :
% 9.49/5.27                ( ( finite6177210948735845034at_nat @ A7 )
% 9.49/5.27               => ( ( A7 != bot_bo2099793752762293965at_nat )
% 9.49/5.27                 => ( ( ord_le3146513528884898305at_nat @ A7 @ B2 )
% 9.49/5.27                   => ( ! [X5: product_prod_nat_nat] :
% 9.49/5.27                          ( ( member8440522571783428010at_nat @ X5 @ A7 )
% 9.49/5.27                         => ( P @ ( minus_1356011639430497352at_nat @ A7 @ ( insert8211810215607154385at_nat @ X5 @ bot_bo2099793752762293965at_nat ) ) ) )
% 9.49/5.27                     => ( P @ A7 ) ) ) ) )
% 9.49/5.27           => ( P @ B2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3857_remove__induct,axiom,
% 9.49/5.27      ! [P: set_real > $o,B2: set_real] :
% 9.49/5.27        ( ( P @ bot_bot_set_real )
% 9.49/5.27       => ( ( ~ ( finite_finite_real @ B2 )
% 9.49/5.27           => ( P @ B2 ) )
% 9.49/5.27         => ( ! [A7: set_real] :
% 9.49/5.27                ( ( finite_finite_real @ A7 )
% 9.49/5.27               => ( ( A7 != bot_bot_set_real )
% 9.49/5.27                 => ( ( ord_less_eq_set_real @ A7 @ B2 )
% 9.49/5.27                   => ( ! [X5: real] :
% 9.49/5.27                          ( ( member_real @ X5 @ A7 )
% 9.49/5.27                         => ( P @ ( minus_minus_set_real @ A7 @ ( insert_real @ X5 @ bot_bot_set_real ) ) ) )
% 9.49/5.27                     => ( P @ A7 ) ) ) ) )
% 9.49/5.27           => ( P @ B2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3858_remove__induct,axiom,
% 9.49/5.27      ! [P: set_nat > $o,B2: set_nat] :
% 9.49/5.27        ( ( P @ bot_bot_set_nat )
% 9.49/5.27       => ( ( ~ ( finite_finite_nat @ B2 )
% 9.49/5.27           => ( P @ B2 ) )
% 9.49/5.27         => ( ! [A7: set_nat] :
% 9.49/5.27                ( ( finite_finite_nat @ A7 )
% 9.49/5.27               => ( ( A7 != bot_bot_set_nat )
% 9.49/5.27                 => ( ( ord_less_eq_set_nat @ A7 @ B2 )
% 9.49/5.27                   => ( ! [X5: nat] :
% 9.49/5.27                          ( ( member_nat @ X5 @ A7 )
% 9.49/5.27                         => ( P @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ X5 @ bot_bot_set_nat ) ) ) )
% 9.49/5.27                     => ( P @ A7 ) ) ) ) )
% 9.49/5.27           => ( P @ B2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3859_finite__remove__induct,axiom,
% 9.49/5.27      ! [B2: set_VEBT_VEBT,P: set_VEBT_VEBT > $o] :
% 9.49/5.27        ( ( finite5795047828879050333T_VEBT @ B2 )
% 9.49/5.27       => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 9.49/5.27         => ( ! [A7: set_VEBT_VEBT] :
% 9.49/5.27                ( ( finite5795047828879050333T_VEBT @ A7 )
% 9.49/5.27               => ( ( A7 != bot_bo8194388402131092736T_VEBT )
% 9.49/5.27                 => ( ( ord_le4337996190870823476T_VEBT @ A7 @ B2 )
% 9.49/5.27                   => ( ! [X5: vEBT_VEBT] :
% 9.49/5.27                          ( ( member_VEBT_VEBT @ X5 @ A7 )
% 9.49/5.27                         => ( P @ ( minus_5127226145743854075T_VEBT @ A7 @ ( insert_VEBT_VEBT @ X5 @ bot_bo8194388402131092736T_VEBT ) ) ) )
% 9.49/5.27                     => ( P @ A7 ) ) ) ) )
% 9.49/5.27           => ( P @ B2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3860_finite__remove__induct,axiom,
% 9.49/5.27      ! [B2: set_complex,P: set_complex > $o] :
% 9.49/5.27        ( ( finite3207457112153483333omplex @ B2 )
% 9.49/5.27       => ( ( P @ bot_bot_set_complex )
% 9.49/5.27         => ( ! [A7: set_complex] :
% 9.49/5.27                ( ( finite3207457112153483333omplex @ A7 )
% 9.49/5.27               => ( ( A7 != bot_bot_set_complex )
% 9.49/5.27                 => ( ( ord_le211207098394363844omplex @ A7 @ B2 )
% 9.49/5.27                   => ( ! [X5: complex] :
% 9.49/5.27                          ( ( member_complex @ X5 @ A7 )
% 9.49/5.27                         => ( P @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ X5 @ bot_bot_set_complex ) ) ) )
% 9.49/5.27                     => ( P @ A7 ) ) ) ) )
% 9.49/5.27           => ( P @ B2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3861_finite__remove__induct,axiom,
% 9.49/5.27      ! [B2: set_int,P: set_int > $o] :
% 9.49/5.27        ( ( finite_finite_int @ B2 )
% 9.49/5.27       => ( ( P @ bot_bot_set_int )
% 9.49/5.27         => ( ! [A7: set_int] :
% 9.49/5.27                ( ( finite_finite_int @ A7 )
% 9.49/5.27               => ( ( A7 != bot_bot_set_int )
% 9.49/5.27                 => ( ( ord_less_eq_set_int @ A7 @ B2 )
% 9.49/5.27                   => ( ! [X5: int] :
% 9.49/5.27                          ( ( member_int @ X5 @ A7 )
% 9.49/5.27                         => ( P @ ( minus_minus_set_int @ A7 @ ( insert_int @ X5 @ bot_bot_set_int ) ) ) )
% 9.49/5.27                     => ( P @ A7 ) ) ) ) )
% 9.49/5.27           => ( P @ B2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3862_finite__remove__induct,axiom,
% 9.49/5.27      ! [B2: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 9.49/5.27        ( ( finite6177210948735845034at_nat @ B2 )
% 9.49/5.27       => ( ( P @ bot_bo2099793752762293965at_nat )
% 9.49/5.27         => ( ! [A7: set_Pr1261947904930325089at_nat] :
% 9.49/5.27                ( ( finite6177210948735845034at_nat @ A7 )
% 9.49/5.27               => ( ( A7 != bot_bo2099793752762293965at_nat )
% 9.49/5.27                 => ( ( ord_le3146513528884898305at_nat @ A7 @ B2 )
% 9.49/5.27                   => ( ! [X5: product_prod_nat_nat] :
% 9.49/5.27                          ( ( member8440522571783428010at_nat @ X5 @ A7 )
% 9.49/5.27                         => ( P @ ( minus_1356011639430497352at_nat @ A7 @ ( insert8211810215607154385at_nat @ X5 @ bot_bo2099793752762293965at_nat ) ) ) )
% 9.49/5.27                     => ( P @ A7 ) ) ) ) )
% 9.49/5.27           => ( P @ B2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3863_finite__remove__induct,axiom,
% 9.49/5.27      ! [B2: set_real,P: set_real > $o] :
% 9.49/5.27        ( ( finite_finite_real @ B2 )
% 9.49/5.27       => ( ( P @ bot_bot_set_real )
% 9.49/5.27         => ( ! [A7: set_real] :
% 9.49/5.27                ( ( finite_finite_real @ A7 )
% 9.49/5.27               => ( ( A7 != bot_bot_set_real )
% 9.49/5.27                 => ( ( ord_less_eq_set_real @ A7 @ B2 )
% 9.49/5.27                   => ( ! [X5: real] :
% 9.49/5.27                          ( ( member_real @ X5 @ A7 )
% 9.49/5.27                         => ( P @ ( minus_minus_set_real @ A7 @ ( insert_real @ X5 @ bot_bot_set_real ) ) ) )
% 9.49/5.27                     => ( P @ A7 ) ) ) ) )
% 9.49/5.27           => ( P @ B2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3864_finite__remove__induct,axiom,
% 9.49/5.27      ! [B2: set_nat,P: set_nat > $o] :
% 9.49/5.27        ( ( finite_finite_nat @ B2 )
% 9.49/5.27       => ( ( P @ bot_bot_set_nat )
% 9.49/5.27         => ( ! [A7: set_nat] :
% 9.49/5.27                ( ( finite_finite_nat @ A7 )
% 9.49/5.27               => ( ( A7 != bot_bot_set_nat )
% 9.49/5.27                 => ( ( ord_less_eq_set_nat @ A7 @ B2 )
% 9.49/5.27                   => ( ! [X5: nat] :
% 9.49/5.27                          ( ( member_nat @ X5 @ A7 )
% 9.49/5.27                         => ( P @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ X5 @ bot_bot_set_nat ) ) ) )
% 9.49/5.27                     => ( P @ A7 ) ) ) ) )
% 9.49/5.27           => ( P @ B2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3865_arcosh__1,axiom,
% 9.49/5.27      ( ( arcosh_real @ one_one_real )
% 9.49/5.27      = zero_zero_real ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3866_finite__nth__roots,axiom,
% 9.49/5.27      ! [N: nat,C: complex] :
% 9.49/5.27        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.27       => ( finite3207457112153483333omplex
% 9.49/5.27          @ ( collect_complex
% 9.49/5.27            @ ^ [Z4: complex] :
% 9.49/5.27                ( ( power_power_complex @ Z4 @ N )
% 9.49/5.27                = C ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3867_flip__bit__Suc,axiom,
% 9.49/5.27      ! [N: nat,A: int] :
% 9.49/5.27        ( ( bit_se2159334234014336723it_int @ ( suc @ N ) @ A )
% 9.49/5.27        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3868_flip__bit__Suc,axiom,
% 9.49/5.27      ! [N: nat,A: nat] :
% 9.49/5.27        ( ( bit_se2161824704523386999it_nat @ ( suc @ N ) @ A )
% 9.49/5.27        = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3869_finite__linorder__min__induct,axiom,
% 9.49/5.27      ! [A2: set_real,P: set_real > $o] :
% 9.49/5.27        ( ( finite_finite_real @ A2 )
% 9.49/5.27       => ( ( P @ bot_bot_set_real )
% 9.49/5.27         => ( ! [B3: real,A7: set_real] :
% 9.49/5.27                ( ( finite_finite_real @ A7 )
% 9.49/5.27               => ( ! [X5: real] :
% 9.49/5.27                      ( ( member_real @ X5 @ A7 )
% 9.49/5.27                     => ( ord_less_real @ B3 @ X5 ) )
% 9.49/5.27                 => ( ( P @ A7 )
% 9.49/5.27                   => ( P @ ( insert_real @ B3 @ A7 ) ) ) ) )
% 9.49/5.27           => ( P @ A2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3870_finite__linorder__min__induct,axiom,
% 9.49/5.27      ! [A2: set_rat,P: set_rat > $o] :
% 9.49/5.27        ( ( finite_finite_rat @ A2 )
% 9.49/5.27       => ( ( P @ bot_bot_set_rat )
% 9.49/5.27         => ( ! [B3: rat,A7: set_rat] :
% 9.49/5.27                ( ( finite_finite_rat @ A7 )
% 9.49/5.27               => ( ! [X5: rat] :
% 9.49/5.27                      ( ( member_rat @ X5 @ A7 )
% 9.49/5.27                     => ( ord_less_rat @ B3 @ X5 ) )
% 9.49/5.27                 => ( ( P @ A7 )
% 9.49/5.27                   => ( P @ ( insert_rat @ B3 @ A7 ) ) ) ) )
% 9.49/5.27           => ( P @ A2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3871_finite__linorder__min__induct,axiom,
% 9.49/5.27      ! [A2: set_num,P: set_num > $o] :
% 9.49/5.27        ( ( finite_finite_num @ A2 )
% 9.49/5.27       => ( ( P @ bot_bot_set_num )
% 9.49/5.27         => ( ! [B3: num,A7: set_num] :
% 9.49/5.27                ( ( finite_finite_num @ A7 )
% 9.49/5.27               => ( ! [X5: num] :
% 9.49/5.27                      ( ( member_num @ X5 @ A7 )
% 9.49/5.27                     => ( ord_less_num @ B3 @ X5 ) )
% 9.49/5.27                 => ( ( P @ A7 )
% 9.49/5.27                   => ( P @ ( insert_num @ B3 @ A7 ) ) ) ) )
% 9.49/5.27           => ( P @ A2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3872_finite__linorder__min__induct,axiom,
% 9.49/5.27      ! [A2: set_nat,P: set_nat > $o] :
% 9.49/5.27        ( ( finite_finite_nat @ A2 )
% 9.49/5.27       => ( ( P @ bot_bot_set_nat )
% 9.49/5.27         => ( ! [B3: nat,A7: set_nat] :
% 9.49/5.27                ( ( finite_finite_nat @ A7 )
% 9.49/5.27               => ( ! [X5: nat] :
% 9.49/5.27                      ( ( member_nat @ X5 @ A7 )
% 9.49/5.27                     => ( ord_less_nat @ B3 @ X5 ) )
% 9.49/5.27                 => ( ( P @ A7 )
% 9.49/5.27                   => ( P @ ( insert_nat @ B3 @ A7 ) ) ) ) )
% 9.49/5.27           => ( P @ A2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3873_finite__linorder__min__induct,axiom,
% 9.49/5.27      ! [A2: set_int,P: set_int > $o] :
% 9.49/5.27        ( ( finite_finite_int @ A2 )
% 9.49/5.27       => ( ( P @ bot_bot_set_int )
% 9.49/5.27         => ( ! [B3: int,A7: set_int] :
% 9.49/5.27                ( ( finite_finite_int @ A7 )
% 9.49/5.27               => ( ! [X5: int] :
% 9.49/5.27                      ( ( member_int @ X5 @ A7 )
% 9.49/5.27                     => ( ord_less_int @ B3 @ X5 ) )
% 9.49/5.27                 => ( ( P @ A7 )
% 9.49/5.27                   => ( P @ ( insert_int @ B3 @ A7 ) ) ) ) )
% 9.49/5.27           => ( P @ A2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3874_finite__linorder__max__induct,axiom,
% 9.49/5.27      ! [A2: set_real,P: set_real > $o] :
% 9.49/5.27        ( ( finite_finite_real @ A2 )
% 9.49/5.27       => ( ( P @ bot_bot_set_real )
% 9.49/5.27         => ( ! [B3: real,A7: set_real] :
% 9.49/5.27                ( ( finite_finite_real @ A7 )
% 9.49/5.27               => ( ! [X5: real] :
% 9.49/5.27                      ( ( member_real @ X5 @ A7 )
% 9.49/5.27                     => ( ord_less_real @ X5 @ B3 ) )
% 9.49/5.27                 => ( ( P @ A7 )
% 9.49/5.27                   => ( P @ ( insert_real @ B3 @ A7 ) ) ) ) )
% 9.49/5.27           => ( P @ A2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3875_finite__linorder__max__induct,axiom,
% 9.49/5.27      ! [A2: set_rat,P: set_rat > $o] :
% 9.49/5.27        ( ( finite_finite_rat @ A2 )
% 9.49/5.27       => ( ( P @ bot_bot_set_rat )
% 9.49/5.27         => ( ! [B3: rat,A7: set_rat] :
% 9.49/5.27                ( ( finite_finite_rat @ A7 )
% 9.49/5.27               => ( ! [X5: rat] :
% 9.49/5.27                      ( ( member_rat @ X5 @ A7 )
% 9.49/5.27                     => ( ord_less_rat @ X5 @ B3 ) )
% 9.49/5.27                 => ( ( P @ A7 )
% 9.49/5.27                   => ( P @ ( insert_rat @ B3 @ A7 ) ) ) ) )
% 9.49/5.27           => ( P @ A2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3876_finite__linorder__max__induct,axiom,
% 9.49/5.27      ! [A2: set_num,P: set_num > $o] :
% 9.49/5.27        ( ( finite_finite_num @ A2 )
% 9.49/5.27       => ( ( P @ bot_bot_set_num )
% 9.49/5.27         => ( ! [B3: num,A7: set_num] :
% 9.49/5.27                ( ( finite_finite_num @ A7 )
% 9.49/5.27               => ( ! [X5: num] :
% 9.49/5.27                      ( ( member_num @ X5 @ A7 )
% 9.49/5.27                     => ( ord_less_num @ X5 @ B3 ) )
% 9.49/5.27                 => ( ( P @ A7 )
% 9.49/5.27                   => ( P @ ( insert_num @ B3 @ A7 ) ) ) ) )
% 9.49/5.27           => ( P @ A2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3877_finite__linorder__max__induct,axiom,
% 9.49/5.27      ! [A2: set_nat,P: set_nat > $o] :
% 9.49/5.27        ( ( finite_finite_nat @ A2 )
% 9.49/5.27       => ( ( P @ bot_bot_set_nat )
% 9.49/5.27         => ( ! [B3: nat,A7: set_nat] :
% 9.49/5.27                ( ( finite_finite_nat @ A7 )
% 9.49/5.27               => ( ! [X5: nat] :
% 9.49/5.27                      ( ( member_nat @ X5 @ A7 )
% 9.49/5.27                     => ( ord_less_nat @ X5 @ B3 ) )
% 9.49/5.27                 => ( ( P @ A7 )
% 9.49/5.27                   => ( P @ ( insert_nat @ B3 @ A7 ) ) ) ) )
% 9.49/5.27           => ( P @ A2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3878_finite__linorder__max__induct,axiom,
% 9.49/5.27      ! [A2: set_int,P: set_int > $o] :
% 9.49/5.27        ( ( finite_finite_int @ A2 )
% 9.49/5.27       => ( ( P @ bot_bot_set_int )
% 9.49/5.27         => ( ! [B3: int,A7: set_int] :
% 9.49/5.27                ( ( finite_finite_int @ A7 )
% 9.49/5.27               => ( ! [X5: int] :
% 9.49/5.27                      ( ( member_int @ X5 @ A7 )
% 9.49/5.27                     => ( ord_less_int @ X5 @ B3 ) )
% 9.49/5.27                 => ( ( P @ A7 )
% 9.49/5.27                   => ( P @ ( insert_int @ B3 @ A7 ) ) ) ) )
% 9.49/5.27           => ( P @ A2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3879_finite__ranking__induct,axiom,
% 9.49/5.27      ! [S2: set_VEBT_VEBT,P: set_VEBT_VEBT > $o,F: vEBT_VEBT > num] :
% 9.49/5.27        ( ( finite5795047828879050333T_VEBT @ S2 )
% 9.49/5.27       => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 9.49/5.27         => ( ! [X3: vEBT_VEBT,S4: set_VEBT_VEBT] :
% 9.49/5.27                ( ( finite5795047828879050333T_VEBT @ S4 )
% 9.49/5.27               => ( ! [Y4: vEBT_VEBT] :
% 9.49/5.27                      ( ( member_VEBT_VEBT @ Y4 @ S4 )
% 9.49/5.27                     => ( ord_less_eq_num @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 9.49/5.27                 => ( ( P @ S4 )
% 9.49/5.27                   => ( P @ ( insert_VEBT_VEBT @ X3 @ S4 ) ) ) ) )
% 9.49/5.27           => ( P @ S2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3880_finite__ranking__induct,axiom,
% 9.49/5.27      ! [S2: set_complex,P: set_complex > $o,F: complex > num] :
% 9.49/5.27        ( ( finite3207457112153483333omplex @ S2 )
% 9.49/5.27       => ( ( P @ bot_bot_set_complex )
% 9.49/5.27         => ( ! [X3: complex,S4: set_complex] :
% 9.49/5.27                ( ( finite3207457112153483333omplex @ S4 )
% 9.49/5.27               => ( ! [Y4: complex] :
% 9.49/5.27                      ( ( member_complex @ Y4 @ S4 )
% 9.49/5.27                     => ( ord_less_eq_num @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 9.49/5.27                 => ( ( P @ S4 )
% 9.49/5.27                   => ( P @ ( insert_complex @ X3 @ S4 ) ) ) ) )
% 9.49/5.27           => ( P @ S2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3881_finite__ranking__induct,axiom,
% 9.49/5.27      ! [S2: set_nat,P: set_nat > $o,F: nat > num] :
% 9.49/5.27        ( ( finite_finite_nat @ S2 )
% 9.49/5.27       => ( ( P @ bot_bot_set_nat )
% 9.49/5.27         => ( ! [X3: nat,S4: set_nat] :
% 9.49/5.27                ( ( finite_finite_nat @ S4 )
% 9.49/5.27               => ( ! [Y4: nat] :
% 9.49/5.27                      ( ( member_nat @ Y4 @ S4 )
% 9.49/5.27                     => ( ord_less_eq_num @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 9.49/5.27                 => ( ( P @ S4 )
% 9.49/5.27                   => ( P @ ( insert_nat @ X3 @ S4 ) ) ) ) )
% 9.49/5.27           => ( P @ S2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3882_finite__ranking__induct,axiom,
% 9.49/5.27      ! [S2: set_int,P: set_int > $o,F: int > num] :
% 9.49/5.27        ( ( finite_finite_int @ S2 )
% 9.49/5.27       => ( ( P @ bot_bot_set_int )
% 9.49/5.27         => ( ! [X3: int,S4: set_int] :
% 9.49/5.27                ( ( finite_finite_int @ S4 )
% 9.49/5.27               => ( ! [Y4: int] :
% 9.49/5.27                      ( ( member_int @ Y4 @ S4 )
% 9.49/5.27                     => ( ord_less_eq_num @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 9.49/5.27                 => ( ( P @ S4 )
% 9.49/5.27                   => ( P @ ( insert_int @ X3 @ S4 ) ) ) ) )
% 9.49/5.27           => ( P @ S2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3883_finite__ranking__induct,axiom,
% 9.49/5.27      ! [S2: set_real,P: set_real > $o,F: real > num] :
% 9.49/5.27        ( ( finite_finite_real @ S2 )
% 9.49/5.27       => ( ( P @ bot_bot_set_real )
% 9.49/5.27         => ( ! [X3: real,S4: set_real] :
% 9.49/5.27                ( ( finite_finite_real @ S4 )
% 9.49/5.27               => ( ! [Y4: real] :
% 9.49/5.27                      ( ( member_real @ Y4 @ S4 )
% 9.49/5.27                     => ( ord_less_eq_num @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 9.49/5.27                 => ( ( P @ S4 )
% 9.49/5.27                   => ( P @ ( insert_real @ X3 @ S4 ) ) ) ) )
% 9.49/5.27           => ( P @ S2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3884_finite__ranking__induct,axiom,
% 9.49/5.27      ! [S2: set_VEBT_VEBT,P: set_VEBT_VEBT > $o,F: vEBT_VEBT > nat] :
% 9.49/5.27        ( ( finite5795047828879050333T_VEBT @ S2 )
% 9.49/5.27       => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 9.49/5.27         => ( ! [X3: vEBT_VEBT,S4: set_VEBT_VEBT] :
% 9.49/5.27                ( ( finite5795047828879050333T_VEBT @ S4 )
% 9.49/5.27               => ( ! [Y4: vEBT_VEBT] :
% 9.49/5.27                      ( ( member_VEBT_VEBT @ Y4 @ S4 )
% 9.49/5.27                     => ( ord_less_eq_nat @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 9.49/5.27                 => ( ( P @ S4 )
% 9.49/5.27                   => ( P @ ( insert_VEBT_VEBT @ X3 @ S4 ) ) ) ) )
% 9.49/5.27           => ( P @ S2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3885_finite__ranking__induct,axiom,
% 9.49/5.27      ! [S2: set_complex,P: set_complex > $o,F: complex > nat] :
% 9.49/5.27        ( ( finite3207457112153483333omplex @ S2 )
% 9.49/5.27       => ( ( P @ bot_bot_set_complex )
% 9.49/5.27         => ( ! [X3: complex,S4: set_complex] :
% 9.49/5.27                ( ( finite3207457112153483333omplex @ S4 )
% 9.49/5.27               => ( ! [Y4: complex] :
% 9.49/5.27                      ( ( member_complex @ Y4 @ S4 )
% 9.49/5.27                     => ( ord_less_eq_nat @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 9.49/5.27                 => ( ( P @ S4 )
% 9.49/5.27                   => ( P @ ( insert_complex @ X3 @ S4 ) ) ) ) )
% 9.49/5.27           => ( P @ S2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3886_finite__ranking__induct,axiom,
% 9.49/5.27      ! [S2: set_nat,P: set_nat > $o,F: nat > nat] :
% 9.49/5.27        ( ( finite_finite_nat @ S2 )
% 9.49/5.27       => ( ( P @ bot_bot_set_nat )
% 9.49/5.27         => ( ! [X3: nat,S4: set_nat] :
% 9.49/5.27                ( ( finite_finite_nat @ S4 )
% 9.49/5.27               => ( ! [Y4: nat] :
% 9.49/5.27                      ( ( member_nat @ Y4 @ S4 )
% 9.49/5.27                     => ( ord_less_eq_nat @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 9.49/5.27                 => ( ( P @ S4 )
% 9.49/5.27                   => ( P @ ( insert_nat @ X3 @ S4 ) ) ) ) )
% 9.49/5.27           => ( P @ S2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3887_finite__ranking__induct,axiom,
% 9.49/5.27      ! [S2: set_int,P: set_int > $o,F: int > nat] :
% 9.49/5.27        ( ( finite_finite_int @ S2 )
% 9.49/5.27       => ( ( P @ bot_bot_set_int )
% 9.49/5.27         => ( ! [X3: int,S4: set_int] :
% 9.49/5.27                ( ( finite_finite_int @ S4 )
% 9.49/5.27               => ( ! [Y4: int] :
% 9.49/5.27                      ( ( member_int @ Y4 @ S4 )
% 9.49/5.27                     => ( ord_less_eq_nat @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 9.49/5.27                 => ( ( P @ S4 )
% 9.49/5.27                   => ( P @ ( insert_int @ X3 @ S4 ) ) ) ) )
% 9.49/5.27           => ( P @ S2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3888_finite__ranking__induct,axiom,
% 9.49/5.27      ! [S2: set_real,P: set_real > $o,F: real > nat] :
% 9.49/5.27        ( ( finite_finite_real @ S2 )
% 9.49/5.27       => ( ( P @ bot_bot_set_real )
% 9.49/5.27         => ( ! [X3: real,S4: set_real] :
% 9.49/5.27                ( ( finite_finite_real @ S4 )
% 9.49/5.27               => ( ! [Y4: real] :
% 9.49/5.27                      ( ( member_real @ Y4 @ S4 )
% 9.49/5.27                     => ( ord_less_eq_nat @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 9.49/5.27                 => ( ( P @ S4 )
% 9.49/5.27                   => ( P @ ( insert_real @ X3 @ S4 ) ) ) ) )
% 9.49/5.27           => ( P @ S2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3889_product__nth,axiom,
% 9.49/5.27      ! [N: nat,Xs2: list_num,Ys: list_num] :
% 9.49/5.27        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_num @ Xs2 ) @ ( size_size_list_num @ Ys ) ) )
% 9.49/5.27       => ( ( nth_Pr6456567536196504476um_num @ ( product_num_num @ Xs2 @ Ys ) @ N )
% 9.49/5.27          = ( product_Pair_num_num @ ( nth_num @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_num @ Ys ) ) ) @ ( nth_num @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_num @ Ys ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3890_product__nth,axiom,
% 9.49/5.27      ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 9.49/5.27        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 9.49/5.27       => ( ( nth_Pr4953567300277697838T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs2 @ Ys ) @ N )
% 9.49/5.27          = ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3891_product__nth,axiom,
% 9.49/5.27      ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_o] :
% 9.49/5.27        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_o @ Ys ) ) )
% 9.49/5.27       => ( ( nth_Pr4606735188037164562VEBT_o @ ( product_VEBT_VEBT_o @ Xs2 @ Ys ) @ N )
% 9.49/5.27          = ( produc8721562602347293563VEBT_o @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3892_product__nth,axiom,
% 9.49/5.27      ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_nat] :
% 9.49/5.27        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) )
% 9.49/5.27       => ( ( nth_Pr1791586995822124652BT_nat @ ( produc7295137177222721919BT_nat @ Xs2 @ Ys ) @ N )
% 9.49/5.27          = ( produc738532404422230701BT_nat @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3893_product__nth,axiom,
% 9.49/5.27      ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_int] :
% 9.49/5.27        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_int @ Ys ) ) )
% 9.49/5.27       => ( ( nth_Pr6837108013167703752BT_int @ ( produc7292646706713671643BT_int @ Xs2 @ Ys ) @ N )
% 9.49/5.27          = ( produc736041933913180425BT_int @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3894_product__nth,axiom,
% 9.49/5.27      ! [N: nat,Xs2: list_o,Ys: list_VEBT_VEBT] :
% 9.49/5.27        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 9.49/5.27       => ( ( nth_Pr6777367263587873994T_VEBT @ ( product_o_VEBT_VEBT @ Xs2 @ Ys ) @ N )
% 9.49/5.27          = ( produc2982872950893828659T_VEBT @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3895_product__nth,axiom,
% 9.49/5.27      ! [N: nat,Xs2: list_o,Ys: list_o] :
% 9.49/5.27        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_o @ Ys ) ) )
% 9.49/5.27       => ( ( nth_Product_prod_o_o @ ( product_o_o @ Xs2 @ Ys ) @ N )
% 9.49/5.27          = ( product_Pair_o_o @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3896_product__nth,axiom,
% 9.49/5.27      ! [N: nat,Xs2: list_o,Ys: list_nat] :
% 9.49/5.27        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) )
% 9.49/5.27       => ( ( nth_Pr5826913651314560976_o_nat @ ( product_o_nat @ Xs2 @ Ys ) @ N )
% 9.49/5.27          = ( product_Pair_o_nat @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3897_product__nth,axiom,
% 9.49/5.27      ! [N: nat,Xs2: list_o,Ys: list_int] :
% 9.49/5.27        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_int @ Ys ) ) )
% 9.49/5.27       => ( ( nth_Pr1649062631805364268_o_int @ ( product_o_int @ Xs2 @ Ys ) @ N )
% 9.49/5.27          = ( product_Pair_o_int @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3898_product__nth,axiom,
% 9.49/5.27      ! [N: nat,Xs2: list_nat,Ys: list_num] :
% 9.49/5.27        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_size_list_num @ Ys ) ) )
% 9.49/5.27       => ( ( nth_Pr8326237132889035090at_num @ ( product_nat_num @ Xs2 @ Ys ) @ N )
% 9.49/5.27          = ( product_Pair_nat_num @ ( nth_nat @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_num @ Ys ) ) ) @ ( nth_num @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_num @ Ys ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3899_flip__bit__nonnegative__int__iff,axiom,
% 9.49/5.27      ! [N: nat,K: int] :
% 9.49/5.27        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se2159334234014336723it_int @ N @ K ) )
% 9.49/5.27        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3900_flip__bit__negative__int__iff,axiom,
% 9.49/5.27      ! [N: nat,K: int] :
% 9.49/5.27        ( ( ord_less_int @ ( bit_se2159334234014336723it_int @ N @ K ) @ zero_zero_int )
% 9.49/5.27        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3901_length__product,axiom,
% 9.49/5.27      ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 9.49/5.27        ( ( size_s7466405169056248089T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs2 @ Ys ) )
% 9.49/5.27        = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3902_length__product,axiom,
% 9.49/5.27      ! [Xs2: list_VEBT_VEBT,Ys: list_o] :
% 9.49/5.27        ( ( size_s9168528473962070013VEBT_o @ ( product_VEBT_VEBT_o @ Xs2 @ Ys ) )
% 9.49/5.27        = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3903_length__product,axiom,
% 9.49/5.27      ! [Xs2: list_VEBT_VEBT,Ys: list_nat] :
% 9.49/5.27        ( ( size_s6152045936467909847BT_nat @ ( produc7295137177222721919BT_nat @ Xs2 @ Ys ) )
% 9.49/5.27        = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3904_length__product,axiom,
% 9.49/5.27      ! [Xs2: list_VEBT_VEBT,Ys: list_int] :
% 9.49/5.27        ( ( size_s3661962791536183091BT_int @ ( produc7292646706713671643BT_int @ Xs2 @ Ys ) )
% 9.49/5.27        = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_int @ Ys ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3905_length__product,axiom,
% 9.49/5.27      ! [Xs2: list_o,Ys: list_VEBT_VEBT] :
% 9.49/5.27        ( ( size_s4313452262239582901T_VEBT @ ( product_o_VEBT_VEBT @ Xs2 @ Ys ) )
% 9.49/5.27        = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3906_length__product,axiom,
% 9.49/5.27      ! [Xs2: list_o,Ys: list_o] :
% 9.49/5.27        ( ( size_s1515746228057227161od_o_o @ ( product_o_o @ Xs2 @ Ys ) )
% 9.49/5.27        = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3907_length__product,axiom,
% 9.49/5.27      ! [Xs2: list_o,Ys: list_nat] :
% 9.49/5.27        ( ( size_s5443766701097040955_o_nat @ ( product_o_nat @ Xs2 @ Ys ) )
% 9.49/5.27        = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3908_length__product,axiom,
% 9.49/5.27      ! [Xs2: list_o,Ys: list_int] :
% 9.49/5.27        ( ( size_s2953683556165314199_o_int @ ( product_o_int @ Xs2 @ Ys ) )
% 9.49/5.27        = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_int @ Ys ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3909_length__product,axiom,
% 9.49/5.27      ! [Xs2: list_nat,Ys: list_VEBT_VEBT] :
% 9.49/5.27        ( ( size_s4762443039079500285T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs2 @ Ys ) )
% 9.49/5.27        = ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3910_length__product,axiom,
% 9.49/5.27      ! [Xs2: list_nat,Ys: list_o] :
% 9.49/5.27        ( ( size_s6491369823275344609_nat_o @ ( product_nat_o @ Xs2 @ Ys ) )
% 9.49/5.27        = ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3911_ex__min__if__finite,axiom,
% 9.49/5.27      ! [S2: set_real] :
% 9.49/5.27        ( ( finite_finite_real @ S2 )
% 9.49/5.27       => ( ( S2 != bot_bot_set_real )
% 9.49/5.27         => ? [X3: real] :
% 9.49/5.27              ( ( member_real @ X3 @ S2 )
% 9.49/5.27              & ~ ? [Xa: real] :
% 9.49/5.27                    ( ( member_real @ Xa @ S2 )
% 9.49/5.27                    & ( ord_less_real @ Xa @ X3 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3912_ex__min__if__finite,axiom,
% 9.49/5.27      ! [S2: set_rat] :
% 9.49/5.27        ( ( finite_finite_rat @ S2 )
% 9.49/5.27       => ( ( S2 != bot_bot_set_rat )
% 9.49/5.27         => ? [X3: rat] :
% 9.49/5.27              ( ( member_rat @ X3 @ S2 )
% 9.49/5.27              & ~ ? [Xa: rat] :
% 9.49/5.27                    ( ( member_rat @ Xa @ S2 )
% 9.49/5.27                    & ( ord_less_rat @ Xa @ X3 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3913_ex__min__if__finite,axiom,
% 9.49/5.27      ! [S2: set_num] :
% 9.49/5.27        ( ( finite_finite_num @ S2 )
% 9.49/5.27       => ( ( S2 != bot_bot_set_num )
% 9.49/5.27         => ? [X3: num] :
% 9.49/5.27              ( ( member_num @ X3 @ S2 )
% 9.49/5.27              & ~ ? [Xa: num] :
% 9.49/5.27                    ( ( member_num @ Xa @ S2 )
% 9.49/5.27                    & ( ord_less_num @ Xa @ X3 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3914_ex__min__if__finite,axiom,
% 9.49/5.27      ! [S2: set_nat] :
% 9.49/5.27        ( ( finite_finite_nat @ S2 )
% 9.49/5.27       => ( ( S2 != bot_bot_set_nat )
% 9.49/5.27         => ? [X3: nat] :
% 9.49/5.27              ( ( member_nat @ X3 @ S2 )
% 9.49/5.27              & ~ ? [Xa: nat] :
% 9.49/5.27                    ( ( member_nat @ Xa @ S2 )
% 9.49/5.27                    & ( ord_less_nat @ Xa @ X3 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3915_ex__min__if__finite,axiom,
% 9.49/5.27      ! [S2: set_int] :
% 9.49/5.27        ( ( finite_finite_int @ S2 )
% 9.49/5.27       => ( ( S2 != bot_bot_set_int )
% 9.49/5.27         => ? [X3: int] :
% 9.49/5.27              ( ( member_int @ X3 @ S2 )
% 9.49/5.27              & ~ ? [Xa: int] :
% 9.49/5.27                    ( ( member_int @ Xa @ S2 )
% 9.49/5.27                    & ( ord_less_int @ Xa @ X3 ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3916_infinite__growing,axiom,
% 9.49/5.27      ! [X8: set_real] :
% 9.49/5.27        ( ( X8 != bot_bot_set_real )
% 9.49/5.27       => ( ! [X3: real] :
% 9.49/5.27              ( ( member_real @ X3 @ X8 )
% 9.49/5.27             => ? [Xa: real] :
% 9.49/5.27                  ( ( member_real @ Xa @ X8 )
% 9.49/5.27                  & ( ord_less_real @ X3 @ Xa ) ) )
% 9.49/5.27         => ~ ( finite_finite_real @ X8 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3917_infinite__growing,axiom,
% 9.49/5.27      ! [X8: set_rat] :
% 9.49/5.27        ( ( X8 != bot_bot_set_rat )
% 9.49/5.27       => ( ! [X3: rat] :
% 9.49/5.27              ( ( member_rat @ X3 @ X8 )
% 9.49/5.27             => ? [Xa: rat] :
% 9.49/5.27                  ( ( member_rat @ Xa @ X8 )
% 9.49/5.27                  & ( ord_less_rat @ X3 @ Xa ) ) )
% 9.49/5.27         => ~ ( finite_finite_rat @ X8 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3918_infinite__growing,axiom,
% 9.49/5.27      ! [X8: set_num] :
% 9.49/5.27        ( ( X8 != bot_bot_set_num )
% 9.49/5.27       => ( ! [X3: num] :
% 9.49/5.27              ( ( member_num @ X3 @ X8 )
% 9.49/5.27             => ? [Xa: num] :
% 9.49/5.27                  ( ( member_num @ Xa @ X8 )
% 9.49/5.27                  & ( ord_less_num @ X3 @ Xa ) ) )
% 9.49/5.27         => ~ ( finite_finite_num @ X8 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3919_infinite__growing,axiom,
% 9.49/5.27      ! [X8: set_nat] :
% 9.49/5.27        ( ( X8 != bot_bot_set_nat )
% 9.49/5.27       => ( ! [X3: nat] :
% 9.49/5.27              ( ( member_nat @ X3 @ X8 )
% 9.49/5.27             => ? [Xa: nat] :
% 9.49/5.27                  ( ( member_nat @ Xa @ X8 )
% 9.49/5.27                  & ( ord_less_nat @ X3 @ Xa ) ) )
% 9.49/5.27         => ~ ( finite_finite_nat @ X8 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3920_infinite__growing,axiom,
% 9.49/5.27      ! [X8: set_int] :
% 9.49/5.27        ( ( X8 != bot_bot_set_int )
% 9.49/5.27       => ( ! [X3: int] :
% 9.49/5.27              ( ( member_int @ X3 @ X8 )
% 9.49/5.27             => ? [Xa: int] :
% 9.49/5.27                  ( ( member_int @ Xa @ X8 )
% 9.49/5.27                  & ( ord_less_int @ X3 @ Xa ) ) )
% 9.49/5.27         => ~ ( finite_finite_int @ X8 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3921_prod_Ofinite__Collect__op,axiom,
% 9.49/5.27      ! [I6: set_int,X: int > rat,Y2: int > rat] :
% 9.49/5.27        ( ( finite_finite_int
% 9.49/5.27          @ ( collect_int
% 9.49/5.27            @ ^ [I3: int] :
% 9.49/5.27                ( ( member_int @ I3 @ I6 )
% 9.49/5.27                & ( ( X @ I3 )
% 9.49/5.27                 != one_one_rat ) ) ) )
% 9.49/5.27       => ( ( finite_finite_int
% 9.49/5.27            @ ( collect_int
% 9.49/5.27              @ ^ [I3: int] :
% 9.49/5.27                  ( ( member_int @ I3 @ I6 )
% 9.49/5.27                  & ( ( Y2 @ I3 )
% 9.49/5.27                   != one_one_rat ) ) ) )
% 9.49/5.27         => ( finite_finite_int
% 9.49/5.27            @ ( collect_int
% 9.49/5.27              @ ^ [I3: int] :
% 9.49/5.27                  ( ( member_int @ I3 @ I6 )
% 9.49/5.27                  & ( ( times_times_rat @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 9.49/5.27                   != one_one_rat ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3922_prod_Ofinite__Collect__op,axiom,
% 9.49/5.27      ! [I6: set_real,X: real > rat,Y2: real > rat] :
% 9.49/5.27        ( ( finite_finite_real
% 9.49/5.27          @ ( collect_real
% 9.49/5.27            @ ^ [I3: real] :
% 9.49/5.27                ( ( member_real @ I3 @ I6 )
% 9.49/5.27                & ( ( X @ I3 )
% 9.49/5.27                 != one_one_rat ) ) ) )
% 9.49/5.27       => ( ( finite_finite_real
% 9.49/5.27            @ ( collect_real
% 9.49/5.27              @ ^ [I3: real] :
% 9.49/5.27                  ( ( member_real @ I3 @ I6 )
% 9.49/5.27                  & ( ( Y2 @ I3 )
% 9.49/5.27                   != one_one_rat ) ) ) )
% 9.49/5.27         => ( finite_finite_real
% 9.49/5.27            @ ( collect_real
% 9.49/5.27              @ ^ [I3: real] :
% 9.49/5.27                  ( ( member_real @ I3 @ I6 )
% 9.49/5.27                  & ( ( times_times_rat @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 9.49/5.27                   != one_one_rat ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3923_prod_Ofinite__Collect__op,axiom,
% 9.49/5.27      ! [I6: set_nat,X: nat > rat,Y2: nat > rat] :
% 9.49/5.27        ( ( finite_finite_nat
% 9.49/5.27          @ ( collect_nat
% 9.49/5.27            @ ^ [I3: nat] :
% 9.49/5.27                ( ( member_nat @ I3 @ I6 )
% 9.49/5.27                & ( ( X @ I3 )
% 9.49/5.27                 != one_one_rat ) ) ) )
% 9.49/5.27       => ( ( finite_finite_nat
% 9.49/5.27            @ ( collect_nat
% 9.49/5.27              @ ^ [I3: nat] :
% 9.49/5.27                  ( ( member_nat @ I3 @ I6 )
% 9.49/5.27                  & ( ( Y2 @ I3 )
% 9.49/5.27                   != one_one_rat ) ) ) )
% 9.49/5.27         => ( finite_finite_nat
% 9.49/5.27            @ ( collect_nat
% 9.49/5.27              @ ^ [I3: nat] :
% 9.49/5.27                  ( ( member_nat @ I3 @ I6 )
% 9.49/5.27                  & ( ( times_times_rat @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 9.49/5.27                   != one_one_rat ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3924_prod_Ofinite__Collect__op,axiom,
% 9.49/5.27      ! [I6: set_complex,X: complex > rat,Y2: complex > rat] :
% 9.49/5.27        ( ( finite3207457112153483333omplex
% 9.49/5.27          @ ( collect_complex
% 9.49/5.27            @ ^ [I3: complex] :
% 9.49/5.27                ( ( member_complex @ I3 @ I6 )
% 9.49/5.27                & ( ( X @ I3 )
% 9.49/5.27                 != one_one_rat ) ) ) )
% 9.49/5.27       => ( ( finite3207457112153483333omplex
% 9.49/5.27            @ ( collect_complex
% 9.49/5.27              @ ^ [I3: complex] :
% 9.49/5.27                  ( ( member_complex @ I3 @ I6 )
% 9.49/5.27                  & ( ( Y2 @ I3 )
% 9.49/5.27                   != one_one_rat ) ) ) )
% 9.49/5.27         => ( finite3207457112153483333omplex
% 9.49/5.27            @ ( collect_complex
% 9.49/5.27              @ ^ [I3: complex] :
% 9.49/5.27                  ( ( member_complex @ I3 @ I6 )
% 9.49/5.27                  & ( ( times_times_rat @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 9.49/5.27                   != one_one_rat ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3925_prod_Ofinite__Collect__op,axiom,
% 9.49/5.27      ! [I6: set_int,X: int > complex,Y2: int > complex] :
% 9.49/5.27        ( ( finite_finite_int
% 9.49/5.27          @ ( collect_int
% 9.49/5.27            @ ^ [I3: int] :
% 9.49/5.27                ( ( member_int @ I3 @ I6 )
% 9.49/5.27                & ( ( X @ I3 )
% 9.49/5.27                 != one_one_complex ) ) ) )
% 9.49/5.27       => ( ( finite_finite_int
% 9.49/5.27            @ ( collect_int
% 9.49/5.27              @ ^ [I3: int] :
% 9.49/5.27                  ( ( member_int @ I3 @ I6 )
% 9.49/5.27                  & ( ( Y2 @ I3 )
% 9.49/5.27                   != one_one_complex ) ) ) )
% 9.49/5.27         => ( finite_finite_int
% 9.49/5.27            @ ( collect_int
% 9.49/5.27              @ ^ [I3: int] :
% 9.49/5.27                  ( ( member_int @ I3 @ I6 )
% 9.49/5.27                  & ( ( times_times_complex @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 9.49/5.27                   != one_one_complex ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3926_prod_Ofinite__Collect__op,axiom,
% 9.49/5.27      ! [I6: set_real,X: real > complex,Y2: real > complex] :
% 9.49/5.27        ( ( finite_finite_real
% 9.49/5.27          @ ( collect_real
% 9.49/5.27            @ ^ [I3: real] :
% 9.49/5.27                ( ( member_real @ I3 @ I6 )
% 9.49/5.27                & ( ( X @ I3 )
% 9.49/5.27                 != one_one_complex ) ) ) )
% 9.49/5.27       => ( ( finite_finite_real
% 9.49/5.27            @ ( collect_real
% 9.49/5.27              @ ^ [I3: real] :
% 9.49/5.27                  ( ( member_real @ I3 @ I6 )
% 9.49/5.27                  & ( ( Y2 @ I3 )
% 9.49/5.27                   != one_one_complex ) ) ) )
% 9.49/5.27         => ( finite_finite_real
% 9.49/5.27            @ ( collect_real
% 9.49/5.27              @ ^ [I3: real] :
% 9.49/5.27                  ( ( member_real @ I3 @ I6 )
% 9.49/5.27                  & ( ( times_times_complex @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 9.49/5.27                   != one_one_complex ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3927_prod_Ofinite__Collect__op,axiom,
% 9.49/5.27      ! [I6: set_nat,X: nat > complex,Y2: nat > complex] :
% 9.49/5.27        ( ( finite_finite_nat
% 9.49/5.27          @ ( collect_nat
% 9.49/5.27            @ ^ [I3: nat] :
% 9.49/5.27                ( ( member_nat @ I3 @ I6 )
% 9.49/5.27                & ( ( X @ I3 )
% 9.49/5.27                 != one_one_complex ) ) ) )
% 9.49/5.27       => ( ( finite_finite_nat
% 9.49/5.27            @ ( collect_nat
% 9.49/5.27              @ ^ [I3: nat] :
% 9.49/5.27                  ( ( member_nat @ I3 @ I6 )
% 9.49/5.27                  & ( ( Y2 @ I3 )
% 9.49/5.27                   != one_one_complex ) ) ) )
% 9.49/5.27         => ( finite_finite_nat
% 9.49/5.27            @ ( collect_nat
% 9.49/5.27              @ ^ [I3: nat] :
% 9.49/5.27                  ( ( member_nat @ I3 @ I6 )
% 9.49/5.27                  & ( ( times_times_complex @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 9.49/5.27                   != one_one_complex ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3928_prod_Ofinite__Collect__op,axiom,
% 9.49/5.27      ! [I6: set_complex,X: complex > complex,Y2: complex > complex] :
% 9.49/5.27        ( ( finite3207457112153483333omplex
% 9.49/5.27          @ ( collect_complex
% 9.49/5.27            @ ^ [I3: complex] :
% 9.49/5.27                ( ( member_complex @ I3 @ I6 )
% 9.49/5.27                & ( ( X @ I3 )
% 9.49/5.27                 != one_one_complex ) ) ) )
% 9.49/5.27       => ( ( finite3207457112153483333omplex
% 9.49/5.27            @ ( collect_complex
% 9.49/5.27              @ ^ [I3: complex] :
% 9.49/5.27                  ( ( member_complex @ I3 @ I6 )
% 9.49/5.27                  & ( ( Y2 @ I3 )
% 9.49/5.27                   != one_one_complex ) ) ) )
% 9.49/5.27         => ( finite3207457112153483333omplex
% 9.49/5.27            @ ( collect_complex
% 9.49/5.27              @ ^ [I3: complex] :
% 9.49/5.27                  ( ( member_complex @ I3 @ I6 )
% 9.49/5.27                  & ( ( times_times_complex @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 9.49/5.27                   != one_one_complex ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3929_prod_Ofinite__Collect__op,axiom,
% 9.49/5.27      ! [I6: set_int,X: int > real,Y2: int > real] :
% 9.49/5.27        ( ( finite_finite_int
% 9.49/5.27          @ ( collect_int
% 9.49/5.27            @ ^ [I3: int] :
% 9.49/5.27                ( ( member_int @ I3 @ I6 )
% 9.49/5.27                & ( ( X @ I3 )
% 9.49/5.27                 != one_one_real ) ) ) )
% 9.49/5.27       => ( ( finite_finite_int
% 9.49/5.27            @ ( collect_int
% 9.49/5.27              @ ^ [I3: int] :
% 9.49/5.27                  ( ( member_int @ I3 @ I6 )
% 9.49/5.27                  & ( ( Y2 @ I3 )
% 9.49/5.27                   != one_one_real ) ) ) )
% 9.49/5.27         => ( finite_finite_int
% 9.49/5.27            @ ( collect_int
% 9.49/5.27              @ ^ [I3: int] :
% 9.49/5.27                  ( ( member_int @ I3 @ I6 )
% 9.49/5.27                  & ( ( times_times_real @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 9.49/5.27                   != one_one_real ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3930_prod_Ofinite__Collect__op,axiom,
% 9.49/5.27      ! [I6: set_real,X: real > real,Y2: real > real] :
% 9.49/5.27        ( ( finite_finite_real
% 9.49/5.27          @ ( collect_real
% 9.49/5.27            @ ^ [I3: real] :
% 9.49/5.27                ( ( member_real @ I3 @ I6 )
% 9.49/5.27                & ( ( X @ I3 )
% 9.49/5.27                 != one_one_real ) ) ) )
% 9.49/5.27       => ( ( finite_finite_real
% 9.49/5.27            @ ( collect_real
% 9.49/5.27              @ ^ [I3: real] :
% 9.49/5.27                  ( ( member_real @ I3 @ I6 )
% 9.49/5.27                  & ( ( Y2 @ I3 )
% 9.49/5.27                   != one_one_real ) ) ) )
% 9.49/5.27         => ( finite_finite_real
% 9.49/5.27            @ ( collect_real
% 9.49/5.27              @ ^ [I3: real] :
% 9.49/5.27                  ( ( member_real @ I3 @ I6 )
% 9.49/5.27                  & ( ( times_times_real @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 9.49/5.27                   != one_one_real ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3931_sum_Ofinite__Collect__op,axiom,
% 9.49/5.27      ! [I6: set_int,X: int > complex,Y2: int > complex] :
% 9.49/5.27        ( ( finite_finite_int
% 9.49/5.27          @ ( collect_int
% 9.49/5.27            @ ^ [I3: int] :
% 9.49/5.27                ( ( member_int @ I3 @ I6 )
% 9.49/5.27                & ( ( X @ I3 )
% 9.49/5.27                 != zero_zero_complex ) ) ) )
% 9.49/5.27       => ( ( finite_finite_int
% 9.49/5.27            @ ( collect_int
% 9.49/5.27              @ ^ [I3: int] :
% 9.49/5.27                  ( ( member_int @ I3 @ I6 )
% 9.49/5.27                  & ( ( Y2 @ I3 )
% 9.49/5.27                   != zero_zero_complex ) ) ) )
% 9.49/5.27         => ( finite_finite_int
% 9.49/5.27            @ ( collect_int
% 9.49/5.27              @ ^ [I3: int] :
% 9.49/5.27                  ( ( member_int @ I3 @ I6 )
% 9.49/5.27                  & ( ( plus_plus_complex @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 9.49/5.27                   != zero_zero_complex ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3932_sum_Ofinite__Collect__op,axiom,
% 9.49/5.27      ! [I6: set_real,X: real > complex,Y2: real > complex] :
% 9.49/5.27        ( ( finite_finite_real
% 9.49/5.27          @ ( collect_real
% 9.49/5.27            @ ^ [I3: real] :
% 9.49/5.27                ( ( member_real @ I3 @ I6 )
% 9.49/5.27                & ( ( X @ I3 )
% 9.49/5.27                 != zero_zero_complex ) ) ) )
% 9.49/5.27       => ( ( finite_finite_real
% 9.49/5.27            @ ( collect_real
% 9.49/5.27              @ ^ [I3: real] :
% 9.49/5.27                  ( ( member_real @ I3 @ I6 )
% 9.49/5.27                  & ( ( Y2 @ I3 )
% 9.49/5.27                   != zero_zero_complex ) ) ) )
% 9.49/5.27         => ( finite_finite_real
% 9.49/5.27            @ ( collect_real
% 9.49/5.27              @ ^ [I3: real] :
% 9.49/5.27                  ( ( member_real @ I3 @ I6 )
% 9.49/5.27                  & ( ( plus_plus_complex @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 9.49/5.27                   != zero_zero_complex ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3933_sum_Ofinite__Collect__op,axiom,
% 9.49/5.27      ! [I6: set_nat,X: nat > complex,Y2: nat > complex] :
% 9.49/5.27        ( ( finite_finite_nat
% 9.49/5.27          @ ( collect_nat
% 9.49/5.27            @ ^ [I3: nat] :
% 9.49/5.27                ( ( member_nat @ I3 @ I6 )
% 9.49/5.27                & ( ( X @ I3 )
% 9.49/5.27                 != zero_zero_complex ) ) ) )
% 9.49/5.27       => ( ( finite_finite_nat
% 9.49/5.27            @ ( collect_nat
% 9.49/5.27              @ ^ [I3: nat] :
% 9.49/5.27                  ( ( member_nat @ I3 @ I6 )
% 9.49/5.27                  & ( ( Y2 @ I3 )
% 9.49/5.27                   != zero_zero_complex ) ) ) )
% 9.49/5.27         => ( finite_finite_nat
% 9.49/5.27            @ ( collect_nat
% 9.49/5.27              @ ^ [I3: nat] :
% 9.49/5.27                  ( ( member_nat @ I3 @ I6 )
% 9.49/5.27                  & ( ( plus_plus_complex @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 9.49/5.27                   != zero_zero_complex ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3934_sum_Ofinite__Collect__op,axiom,
% 9.49/5.27      ! [I6: set_complex,X: complex > complex,Y2: complex > complex] :
% 9.49/5.27        ( ( finite3207457112153483333omplex
% 9.49/5.27          @ ( collect_complex
% 9.49/5.27            @ ^ [I3: complex] :
% 9.49/5.27                ( ( member_complex @ I3 @ I6 )
% 9.49/5.27                & ( ( X @ I3 )
% 9.49/5.27                 != zero_zero_complex ) ) ) )
% 9.49/5.27       => ( ( finite3207457112153483333omplex
% 9.49/5.27            @ ( collect_complex
% 9.49/5.27              @ ^ [I3: complex] :
% 9.49/5.27                  ( ( member_complex @ I3 @ I6 )
% 9.49/5.27                  & ( ( Y2 @ I3 )
% 9.49/5.27                   != zero_zero_complex ) ) ) )
% 9.49/5.27         => ( finite3207457112153483333omplex
% 9.49/5.27            @ ( collect_complex
% 9.49/5.27              @ ^ [I3: complex] :
% 9.49/5.27                  ( ( member_complex @ I3 @ I6 )
% 9.49/5.27                  & ( ( plus_plus_complex @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 9.49/5.27                   != zero_zero_complex ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3935_sum_Ofinite__Collect__op,axiom,
% 9.49/5.27      ! [I6: set_int,X: int > real,Y2: int > real] :
% 9.49/5.27        ( ( finite_finite_int
% 9.49/5.27          @ ( collect_int
% 9.49/5.27            @ ^ [I3: int] :
% 9.49/5.27                ( ( member_int @ I3 @ I6 )
% 9.49/5.27                & ( ( X @ I3 )
% 9.49/5.27                 != zero_zero_real ) ) ) )
% 9.49/5.27       => ( ( finite_finite_int
% 9.49/5.27            @ ( collect_int
% 9.49/5.27              @ ^ [I3: int] :
% 9.49/5.27                  ( ( member_int @ I3 @ I6 )
% 9.49/5.27                  & ( ( Y2 @ I3 )
% 9.49/5.27                   != zero_zero_real ) ) ) )
% 9.49/5.27         => ( finite_finite_int
% 9.49/5.27            @ ( collect_int
% 9.49/5.27              @ ^ [I3: int] :
% 9.49/5.27                  ( ( member_int @ I3 @ I6 )
% 9.49/5.27                  & ( ( plus_plus_real @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 9.49/5.27                   != zero_zero_real ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3936_sum_Ofinite__Collect__op,axiom,
% 9.49/5.27      ! [I6: set_real,X: real > real,Y2: real > real] :
% 9.49/5.27        ( ( finite_finite_real
% 9.49/5.27          @ ( collect_real
% 9.49/5.27            @ ^ [I3: real] :
% 9.49/5.27                ( ( member_real @ I3 @ I6 )
% 9.49/5.27                & ( ( X @ I3 )
% 9.49/5.27                 != zero_zero_real ) ) ) )
% 9.49/5.27       => ( ( finite_finite_real
% 9.49/5.27            @ ( collect_real
% 9.49/5.27              @ ^ [I3: real] :
% 9.49/5.27                  ( ( member_real @ I3 @ I6 )
% 9.49/5.27                  & ( ( Y2 @ I3 )
% 9.49/5.27                   != zero_zero_real ) ) ) )
% 9.49/5.27         => ( finite_finite_real
% 9.49/5.27            @ ( collect_real
% 9.49/5.27              @ ^ [I3: real] :
% 9.49/5.27                  ( ( member_real @ I3 @ I6 )
% 9.49/5.27                  & ( ( plus_plus_real @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 9.49/5.27                   != zero_zero_real ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3937_sum_Ofinite__Collect__op,axiom,
% 9.49/5.27      ! [I6: set_nat,X: nat > real,Y2: nat > real] :
% 9.49/5.27        ( ( finite_finite_nat
% 9.49/5.27          @ ( collect_nat
% 9.49/5.27            @ ^ [I3: nat] :
% 9.49/5.27                ( ( member_nat @ I3 @ I6 )
% 9.49/5.27                & ( ( X @ I3 )
% 9.49/5.27                 != zero_zero_real ) ) ) )
% 9.49/5.27       => ( ( finite_finite_nat
% 9.49/5.27            @ ( collect_nat
% 9.49/5.27              @ ^ [I3: nat] :
% 9.49/5.27                  ( ( member_nat @ I3 @ I6 )
% 9.49/5.27                  & ( ( Y2 @ I3 )
% 9.49/5.27                   != zero_zero_real ) ) ) )
% 9.49/5.27         => ( finite_finite_nat
% 9.49/5.27            @ ( collect_nat
% 9.49/5.27              @ ^ [I3: nat] :
% 9.49/5.27                  ( ( member_nat @ I3 @ I6 )
% 9.49/5.27                  & ( ( plus_plus_real @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 9.49/5.27                   != zero_zero_real ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3938_sum_Ofinite__Collect__op,axiom,
% 9.49/5.27      ! [I6: set_complex,X: complex > real,Y2: complex > real] :
% 9.49/5.27        ( ( finite3207457112153483333omplex
% 9.49/5.27          @ ( collect_complex
% 9.49/5.27            @ ^ [I3: complex] :
% 9.49/5.27                ( ( member_complex @ I3 @ I6 )
% 9.49/5.27                & ( ( X @ I3 )
% 9.49/5.27                 != zero_zero_real ) ) ) )
% 9.49/5.27       => ( ( finite3207457112153483333omplex
% 9.49/5.27            @ ( collect_complex
% 9.49/5.27              @ ^ [I3: complex] :
% 9.49/5.27                  ( ( member_complex @ I3 @ I6 )
% 9.49/5.27                  & ( ( Y2 @ I3 )
% 9.49/5.27                   != zero_zero_real ) ) ) )
% 9.49/5.27         => ( finite3207457112153483333omplex
% 9.49/5.27            @ ( collect_complex
% 9.49/5.27              @ ^ [I3: complex] :
% 9.49/5.27                  ( ( member_complex @ I3 @ I6 )
% 9.49/5.27                  & ( ( plus_plus_real @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 9.49/5.27                   != zero_zero_real ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3939_sum_Ofinite__Collect__op,axiom,
% 9.49/5.27      ! [I6: set_int,X: int > rat,Y2: int > rat] :
% 9.49/5.27        ( ( finite_finite_int
% 9.49/5.27          @ ( collect_int
% 9.49/5.27            @ ^ [I3: int] :
% 9.49/5.27                ( ( member_int @ I3 @ I6 )
% 9.49/5.27                & ( ( X @ I3 )
% 9.49/5.27                 != zero_zero_rat ) ) ) )
% 9.49/5.27       => ( ( finite_finite_int
% 9.49/5.27            @ ( collect_int
% 9.49/5.27              @ ^ [I3: int] :
% 9.49/5.27                  ( ( member_int @ I3 @ I6 )
% 9.49/5.27                  & ( ( Y2 @ I3 )
% 9.49/5.27                   != zero_zero_rat ) ) ) )
% 9.49/5.27         => ( finite_finite_int
% 9.49/5.27            @ ( collect_int
% 9.49/5.27              @ ^ [I3: int] :
% 9.49/5.27                  ( ( member_int @ I3 @ I6 )
% 9.49/5.27                  & ( ( plus_plus_rat @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 9.49/5.27                   != zero_zero_rat ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3940_sum_Ofinite__Collect__op,axiom,
% 9.49/5.27      ! [I6: set_real,X: real > rat,Y2: real > rat] :
% 9.49/5.27        ( ( finite_finite_real
% 9.49/5.27          @ ( collect_real
% 9.49/5.27            @ ^ [I3: real] :
% 9.49/5.27                ( ( member_real @ I3 @ I6 )
% 9.49/5.27                & ( ( X @ I3 )
% 9.49/5.27                 != zero_zero_rat ) ) ) )
% 9.49/5.27       => ( ( finite_finite_real
% 9.49/5.27            @ ( collect_real
% 9.49/5.27              @ ^ [I3: real] :
% 9.49/5.27                  ( ( member_real @ I3 @ I6 )
% 9.49/5.27                  & ( ( Y2 @ I3 )
% 9.49/5.27                   != zero_zero_rat ) ) ) )
% 9.49/5.27         => ( finite_finite_real
% 9.49/5.27            @ ( collect_real
% 9.49/5.27              @ ^ [I3: real] :
% 9.49/5.27                  ( ( member_real @ I3 @ I6 )
% 9.49/5.27                  & ( ( plus_plus_rat @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 9.49/5.27                   != zero_zero_rat ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3941_dbl__inc__simps_I3_J,axiom,
% 9.49/5.27      ( ( neg_nu8557863876264182079omplex @ one_one_complex )
% 9.49/5.27      = ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3942_dbl__inc__simps_I3_J,axiom,
% 9.49/5.27      ( ( neg_nu8295874005876285629c_real @ one_one_real )
% 9.49/5.27      = ( numeral_numeral_real @ ( bit1 @ one ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3943_dbl__inc__simps_I3_J,axiom,
% 9.49/5.27      ( ( neg_nu5219082963157363817nc_rat @ one_one_rat )
% 9.49/5.27      = ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3944_dbl__inc__simps_I3_J,axiom,
% 9.49/5.27      ( ( neg_nu5851722552734809277nc_int @ one_one_int )
% 9.49/5.27      = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3945_VEBT__internal_Oheight_Osimps_I1_J,axiom,
% 9.49/5.27      ! [A: $o,B: $o] :
% 9.49/5.27        ( ( vEBT_VEBT_height @ ( vEBT_Leaf @ A @ B ) )
% 9.49/5.27        = zero_zero_nat ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3946_divmod__BitM__2__eq,axiom,
% 9.49/5.27      ! [M: num] :
% 9.49/5.27        ( ( unique5052692396658037445od_int @ ( bitM @ M ) @ ( bit0 @ one ) )
% 9.49/5.27        = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ one_one_int ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3947_dbl__inc__simps_I2_J,axiom,
% 9.49/5.27      ( ( neg_nu8557863876264182079omplex @ zero_zero_complex )
% 9.49/5.27      = one_one_complex ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3948_dbl__inc__simps_I2_J,axiom,
% 9.49/5.27      ( ( neg_nu8295874005876285629c_real @ zero_zero_real )
% 9.49/5.27      = one_one_real ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3949_dbl__inc__simps_I2_J,axiom,
% 9.49/5.27      ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 9.49/5.27      = one_one_rat ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3950_dbl__inc__simps_I2_J,axiom,
% 9.49/5.27      ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 9.49/5.27      = one_one_int ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3951_dbl__inc__simps_I5_J,axiom,
% 9.49/5.27      ! [K: num] :
% 9.49/5.27        ( ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) )
% 9.49/5.27        = ( numera6690914467698888265omplex @ ( bit1 @ K ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3952_dbl__inc__simps_I5_J,axiom,
% 9.49/5.27      ! [K: num] :
% 9.49/5.27        ( ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) )
% 9.49/5.27        = ( numeral_numeral_real @ ( bit1 @ K ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3953_dbl__inc__simps_I5_J,axiom,
% 9.49/5.27      ! [K: num] :
% 9.49/5.27        ( ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) )
% 9.49/5.27        = ( numeral_numeral_rat @ ( bit1 @ K ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3954_dbl__inc__simps_I5_J,axiom,
% 9.49/5.27      ! [K: num] :
% 9.49/5.27        ( ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) )
% 9.49/5.27        = ( numeral_numeral_int @ ( bit1 @ K ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3955_semiring__norm_I26_J,axiom,
% 9.49/5.27      ( ( bitM @ one )
% 9.49/5.27      = one ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3956_semiring__norm_I28_J,axiom,
% 9.49/5.27      ! [N: num] :
% 9.49/5.27        ( ( bitM @ ( bit1 @ N ) )
% 9.49/5.27        = ( bit1 @ ( bit0 @ N ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3957_semiring__norm_I27_J,axiom,
% 9.49/5.27      ! [N: num] :
% 9.49/5.27        ( ( bitM @ ( bit0 @ N ) )
% 9.49/5.27        = ( bit1 @ ( bitM @ N ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3958_eval__nat__numeral_I2_J,axiom,
% 9.49/5.27      ! [N: num] :
% 9.49/5.27        ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 9.49/5.27        = ( suc @ ( numeral_numeral_nat @ ( bitM @ N ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3959_BitM__plus__one,axiom,
% 9.49/5.27      ! [N: num] :
% 9.49/5.27        ( ( plus_plus_num @ ( bitM @ N ) @ one )
% 9.49/5.27        = ( bit0 @ N ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3960_one__plus__BitM,axiom,
% 9.49/5.27      ! [N: num] :
% 9.49/5.27        ( ( plus_plus_num @ one @ ( bitM @ N ) )
% 9.49/5.27        = ( bit0 @ N ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3961_dbl__inc__def,axiom,
% 9.49/5.27      ( neg_nu8295874005876285629c_real
% 9.49/5.27      = ( ^ [X2: real] : ( plus_plus_real @ ( plus_plus_real @ X2 @ X2 ) @ one_one_real ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3962_dbl__inc__def,axiom,
% 9.49/5.27      ( neg_nu5219082963157363817nc_rat
% 9.49/5.27      = ( ^ [X2: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X2 @ X2 ) @ one_one_rat ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3963_dbl__inc__def,axiom,
% 9.49/5.27      ( neg_nu5851722552734809277nc_int
% 9.49/5.27      = ( ^ [X2: int] : ( plus_plus_int @ ( plus_plus_int @ X2 @ X2 ) @ one_one_int ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3964_dbl__inc__def,axiom,
% 9.49/5.27      ( neg_nu8557863876264182079omplex
% 9.49/5.27      = ( ^ [X2: complex] : ( plus_plus_complex @ ( plus_plus_complex @ X2 @ X2 ) @ one_one_complex ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3965_numeral__BitM,axiom,
% 9.49/5.27      ! [N: num] :
% 9.49/5.27        ( ( numera6690914467698888265omplex @ ( bitM @ N ) )
% 9.49/5.27        = ( minus_minus_complex @ ( numera6690914467698888265omplex @ ( bit0 @ N ) ) @ one_one_complex ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3966_numeral__BitM,axiom,
% 9.49/5.27      ! [N: num] :
% 9.49/5.27        ( ( numeral_numeral_real @ ( bitM @ N ) )
% 9.49/5.27        = ( minus_minus_real @ ( numeral_numeral_real @ ( bit0 @ N ) ) @ one_one_real ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3967_numeral__BitM,axiom,
% 9.49/5.27      ! [N: num] :
% 9.49/5.27        ( ( numeral_numeral_rat @ ( bitM @ N ) )
% 9.49/5.27        = ( minus_minus_rat @ ( numeral_numeral_rat @ ( bit0 @ N ) ) @ one_one_rat ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3968_numeral__BitM,axiom,
% 9.49/5.27      ! [N: num] :
% 9.49/5.27        ( ( numeral_numeral_int @ ( bitM @ N ) )
% 9.49/5.27        = ( minus_minus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ one_one_int ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3969_VEBT__internal_Oheight_Ocases,axiom,
% 9.49/5.27      ! [X: vEBT_VEBT] :
% 9.49/5.27        ( ! [A4: $o,B3: $o] :
% 9.49/5.27            ( X
% 9.49/5.27           != ( vEBT_Leaf @ A4 @ B3 ) )
% 9.49/5.27       => ~ ! [Uu2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.49/5.27              ( X
% 9.49/5.27             != ( vEBT_Node @ Uu2 @ Deg2 @ TreeList2 @ Summary2 ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3970_gcd__nat__induct,axiom,
% 9.49/5.27      ! [P: nat > nat > $o,M: nat,N: nat] :
% 9.49/5.27        ( ! [M4: nat] : ( P @ M4 @ zero_zero_nat )
% 9.49/5.27       => ( ! [M4: nat,N3: nat] :
% 9.49/5.27              ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 9.49/5.27             => ( ( P @ N3 @ ( modulo_modulo_nat @ M4 @ N3 ) )
% 9.49/5.27               => ( P @ M4 @ N3 ) ) )
% 9.49/5.27         => ( P @ M @ N ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3971_concat__bit__Suc,axiom,
% 9.49/5.27      ! [N: nat,K: int,L2: int] :
% 9.49/5.27        ( ( bit_concat_bit @ ( suc @ N ) @ K @ L2 )
% 9.49/5.27        = ( plus_plus_int @ ( modulo_modulo_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_concat_bit @ N @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ L2 ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3972_dbl__simps_I3_J,axiom,
% 9.49/5.27      ( ( neg_nu7009210354673126013omplex @ one_one_complex )
% 9.49/5.27      = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3973_dbl__simps_I3_J,axiom,
% 9.49/5.27      ( ( neg_numeral_dbl_real @ one_one_real )
% 9.49/5.27      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3974_dbl__simps_I3_J,axiom,
% 9.49/5.27      ( ( neg_numeral_dbl_rat @ one_one_rat )
% 9.49/5.27      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3975_dbl__simps_I3_J,axiom,
% 9.49/5.27      ( ( neg_numeral_dbl_int @ one_one_int )
% 9.49/5.27      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3976_even__succ__mod__exp,axiom,
% 9.49/5.27      ! [A: code_integer,N: nat] :
% 9.49/5.27        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.49/5.27       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.27         => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.27            = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3977_even__succ__mod__exp,axiom,
% 9.49/5.27      ! [A: nat,N: nat] :
% 9.49/5.27        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.49/5.27       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.27         => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.27            = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3978_even__succ__mod__exp,axiom,
% 9.49/5.27      ! [A: int,N: nat] :
% 9.49/5.27        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.49/5.27       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.27         => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.27            = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3979_divmod__algorithm__code_I6_J,axiom,
% 9.49/5.27      ! [M: num,N: num] :
% 9.49/5.27        ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 9.49/5.27        = ( produc2626176000494625587at_nat
% 9.49/5.27          @ ^ [Q4: nat,R5: nat] : ( product_Pair_nat_nat @ Q4 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) @ one_one_nat ) )
% 9.49/5.27          @ ( unique5055182867167087721od_nat @ M @ N ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3980_divmod__algorithm__code_I6_J,axiom,
% 9.49/5.27      ! [M: num,N: num] :
% 9.49/5.27        ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 9.49/5.27        = ( produc4245557441103728435nt_int
% 9.49/5.27          @ ^ [Q4: int,R5: int] : ( product_Pair_int_int @ Q4 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) @ one_one_int ) )
% 9.49/5.27          @ ( unique5052692396658037445od_int @ M @ N ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3981_even__succ__div__exp,axiom,
% 9.49/5.27      ! [A: code_integer,N: nat] :
% 9.49/5.27        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.49/5.27       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.27         => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.27            = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3982_even__succ__div__exp,axiom,
% 9.49/5.27      ! [A: nat,N: nat] :
% 9.49/5.27        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.49/5.27       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.27         => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.27            = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3983_even__succ__div__exp,axiom,
% 9.49/5.27      ! [A: int,N: nat] :
% 9.49/5.27        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.49/5.27       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.27         => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.27            = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3984_nat__dvd__1__iff__1,axiom,
% 9.49/5.27      ! [M: nat] :
% 9.49/5.27        ( ( dvd_dvd_nat @ M @ one_one_nat )
% 9.49/5.27        = ( M = one_one_nat ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3985_dvd__1__left,axiom,
% 9.49/5.27      ! [K: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3986_dvd__1__iff__1,axiom,
% 9.49/5.27      ! [M: nat] :
% 9.49/5.27        ( ( dvd_dvd_nat @ M @ ( suc @ zero_zero_nat ) )
% 9.49/5.27        = ( M
% 9.49/5.27          = ( suc @ zero_zero_nat ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3987_dvd__add__triv__right__iff,axiom,
% 9.49/5.27      ! [A: code_integer,B: code_integer] :
% 9.49/5.27        ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 9.49/5.27        = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3988_dvd__add__triv__right__iff,axiom,
% 9.49/5.27      ! [A: real,B: real] :
% 9.49/5.27        ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ A ) )
% 9.49/5.27        = ( dvd_dvd_real @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3989_dvd__add__triv__right__iff,axiom,
% 9.49/5.27      ! [A: rat,B: rat] :
% 9.49/5.27        ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 9.49/5.27        = ( dvd_dvd_rat @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3990_dvd__add__triv__right__iff,axiom,
% 9.49/5.27      ! [A: nat,B: nat] :
% 9.49/5.27        ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 9.49/5.27        = ( dvd_dvd_nat @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3991_dvd__add__triv__right__iff,axiom,
% 9.49/5.27      ! [A: int,B: int] :
% 9.49/5.27        ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ A ) )
% 9.49/5.27        = ( dvd_dvd_int @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3992_dvd__add__triv__right__iff,axiom,
% 9.49/5.27      ! [A: complex,B: complex] :
% 9.49/5.27        ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ B @ A ) )
% 9.49/5.27        = ( dvd_dvd_complex @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3993_dvd__add__triv__left__iff,axiom,
% 9.49/5.27      ! [A: code_integer,B: code_integer] :
% 9.49/5.27        ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 9.49/5.27        = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3994_dvd__add__triv__left__iff,axiom,
% 9.49/5.27      ! [A: real,B: real] :
% 9.49/5.27        ( ( dvd_dvd_real @ A @ ( plus_plus_real @ A @ B ) )
% 9.49/5.27        = ( dvd_dvd_real @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3995_dvd__add__triv__left__iff,axiom,
% 9.49/5.27      ! [A: rat,B: rat] :
% 9.49/5.27        ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 9.49/5.27        = ( dvd_dvd_rat @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3996_dvd__add__triv__left__iff,axiom,
% 9.49/5.27      ! [A: nat,B: nat] :
% 9.49/5.27        ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 9.49/5.27        = ( dvd_dvd_nat @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3997_dvd__add__triv__left__iff,axiom,
% 9.49/5.27      ! [A: int,B: int] :
% 9.49/5.27        ( ( dvd_dvd_int @ A @ ( plus_plus_int @ A @ B ) )
% 9.49/5.27        = ( dvd_dvd_int @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3998_dvd__add__triv__left__iff,axiom,
% 9.49/5.27      ! [A: complex,B: complex] :
% 9.49/5.27        ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ A @ B ) )
% 9.49/5.27        = ( dvd_dvd_complex @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_3999_div__dvd__div,axiom,
% 9.49/5.27      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.49/5.27        ( ( dvd_dvd_Code_integer @ A @ B )
% 9.49/5.27       => ( ( dvd_dvd_Code_integer @ A @ C )
% 9.49/5.27         => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ B @ A ) @ ( divide6298287555418463151nteger @ C @ A ) )
% 9.49/5.27            = ( dvd_dvd_Code_integer @ B @ C ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4000_div__dvd__div,axiom,
% 9.49/5.27      ! [A: nat,B: nat,C: nat] :
% 9.49/5.27        ( ( dvd_dvd_nat @ A @ B )
% 9.49/5.27       => ( ( dvd_dvd_nat @ A @ C )
% 9.49/5.27         => ( ( dvd_dvd_nat @ ( divide_divide_nat @ B @ A ) @ ( divide_divide_nat @ C @ A ) )
% 9.49/5.27            = ( dvd_dvd_nat @ B @ C ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4001_div__dvd__div,axiom,
% 9.49/5.27      ! [A: int,B: int,C: int] :
% 9.49/5.27        ( ( dvd_dvd_int @ A @ B )
% 9.49/5.27       => ( ( dvd_dvd_int @ A @ C )
% 9.49/5.27         => ( ( dvd_dvd_int @ ( divide_divide_int @ B @ A ) @ ( divide_divide_int @ C @ A ) )
% 9.49/5.27            = ( dvd_dvd_int @ B @ C ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4002_nat__mult__dvd__cancel__disj,axiom,
% 9.49/5.27      ! [K: nat,M: nat,N: nat] :
% 9.49/5.27        ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 9.49/5.27        = ( ( K = zero_zero_nat )
% 9.49/5.27          | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4003_concat__bit__0,axiom,
% 9.49/5.27      ! [K: int,L2: int] :
% 9.49/5.27        ( ( bit_concat_bit @ zero_zero_nat @ K @ L2 )
% 9.49/5.27        = L2 ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4004_case__prod__conv,axiom,
% 9.49/5.27      ! [F: nat > nat > nat,A: nat,B: nat] :
% 9.49/5.27        ( ( produc6842872674320459806at_nat @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 9.49/5.27        = ( F @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4005_case__prod__conv,axiom,
% 9.49/5.27      ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,A: nat,B: nat] :
% 9.49/5.27        ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 9.49/5.27        = ( F @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4006_case__prod__conv,axiom,
% 9.49/5.27      ! [F: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat] :
% 9.49/5.27        ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 9.49/5.27        = ( F @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4007_case__prod__conv,axiom,
% 9.49/5.27      ! [F: int > int > product_prod_int_int,A: int,B: int] :
% 9.49/5.27        ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 9.49/5.27        = ( F @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4008_case__prod__conv,axiom,
% 9.49/5.27      ! [F: int > int > int,A: int,B: int] :
% 9.49/5.27        ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 9.49/5.27        = ( F @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4009_dbl__simps_I2_J,axiom,
% 9.49/5.27      ( ( neg_nu7009210354673126013omplex @ zero_zero_complex )
% 9.49/5.27      = zero_zero_complex ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4010_dbl__simps_I2_J,axiom,
% 9.49/5.27      ( ( neg_numeral_dbl_real @ zero_zero_real )
% 9.49/5.27      = zero_zero_real ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4011_dbl__simps_I2_J,axiom,
% 9.49/5.27      ( ( neg_numeral_dbl_rat @ zero_zero_rat )
% 9.49/5.27      = zero_zero_rat ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4012_dbl__simps_I2_J,axiom,
% 9.49/5.27      ( ( neg_numeral_dbl_int @ zero_zero_int )
% 9.49/5.27      = zero_zero_int ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4013_dvd__times__right__cancel__iff,axiom,
% 9.49/5.27      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.49/5.27        ( ( A != zero_z3403309356797280102nteger )
% 9.49/5.27       => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ A ) @ ( times_3573771949741848930nteger @ C @ A ) )
% 9.49/5.27          = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4014_dvd__times__right__cancel__iff,axiom,
% 9.49/5.27      ! [A: nat,B: nat,C: nat] :
% 9.49/5.27        ( ( A != zero_zero_nat )
% 9.49/5.27       => ( ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) )
% 9.49/5.27          = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4015_dvd__times__right__cancel__iff,axiom,
% 9.49/5.27      ! [A: int,B: int,C: int] :
% 9.49/5.27        ( ( A != zero_zero_int )
% 9.49/5.27       => ( ( dvd_dvd_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) )
% 9.49/5.27          = ( dvd_dvd_int @ B @ C ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4016_dvd__times__left__cancel__iff,axiom,
% 9.49/5.27      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.49/5.27        ( ( A != zero_z3403309356797280102nteger )
% 9.49/5.27       => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) )
% 9.49/5.27          = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4017_dvd__times__left__cancel__iff,axiom,
% 9.49/5.27      ! [A: nat,B: nat,C: nat] :
% 9.49/5.27        ( ( A != zero_zero_nat )
% 9.49/5.27       => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
% 9.49/5.27          = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4018_dvd__times__left__cancel__iff,axiom,
% 9.49/5.27      ! [A: int,B: int,C: int] :
% 9.49/5.27        ( ( A != zero_zero_int )
% 9.49/5.27       => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
% 9.49/5.27          = ( dvd_dvd_int @ B @ C ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4019_dvd__mult__cancel__right,axiom,
% 9.49/5.27      ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.49/5.27        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 9.49/5.27        = ( ( C = zero_z3403309356797280102nteger )
% 9.49/5.27          | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4020_dvd__mult__cancel__right,axiom,
% 9.49/5.27      ! [A: rat,C: rat,B: rat] :
% 9.49/5.27        ( ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 9.49/5.27        = ( ( C = zero_zero_rat )
% 9.49/5.27          | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4021_dvd__mult__cancel__right,axiom,
% 9.49/5.27      ! [A: complex,C: complex,B: complex] :
% 9.49/5.27        ( ( dvd_dvd_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 9.49/5.27        = ( ( C = zero_zero_complex )
% 9.49/5.27          | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4022_dvd__mult__cancel__right,axiom,
% 9.49/5.27      ! [A: real,C: real,B: real] :
% 9.49/5.27        ( ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 9.49/5.27        = ( ( C = zero_zero_real )
% 9.49/5.27          | ( dvd_dvd_real @ A @ B ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4023_dvd__mult__cancel__right,axiom,
% 9.49/5.27      ! [A: int,C: int,B: int] :
% 9.49/5.27        ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 9.49/5.27        = ( ( C = zero_zero_int )
% 9.49/5.27          | ( dvd_dvd_int @ A @ B ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4024_dvd__mult__cancel__left,axiom,
% 9.49/5.27      ! [C: code_integer,A: code_integer,B: code_integer] :
% 9.49/5.27        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 9.49/5.27        = ( ( C = zero_z3403309356797280102nteger )
% 9.49/5.27          | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4025_dvd__mult__cancel__left,axiom,
% 9.49/5.27      ! [C: rat,A: rat,B: rat] :
% 9.49/5.27        ( ( dvd_dvd_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 9.49/5.27        = ( ( C = zero_zero_rat )
% 9.49/5.27          | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4026_dvd__mult__cancel__left,axiom,
% 9.49/5.27      ! [C: complex,A: complex,B: complex] :
% 9.49/5.27        ( ( dvd_dvd_complex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 9.49/5.27        = ( ( C = zero_zero_complex )
% 9.49/5.27          | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4027_dvd__mult__cancel__left,axiom,
% 9.49/5.27      ! [C: real,A: real,B: real] :
% 9.49/5.27        ( ( dvd_dvd_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 9.49/5.27        = ( ( C = zero_zero_real )
% 9.49/5.27          | ( dvd_dvd_real @ A @ B ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4028_dvd__mult__cancel__left,axiom,
% 9.49/5.27      ! [C: int,A: int,B: int] :
% 9.49/5.27        ( ( dvd_dvd_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 9.49/5.27        = ( ( C = zero_zero_int )
% 9.49/5.27          | ( dvd_dvd_int @ A @ B ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4029_unit__prod,axiom,
% 9.49/5.27      ! [A: code_integer,B: code_integer] :
% 9.49/5.27        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.49/5.27       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.49/5.27         => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4030_unit__prod,axiom,
% 9.49/5.27      ! [A: nat,B: nat] :
% 9.49/5.27        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.49/5.27       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.49/5.27         => ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4031_unit__prod,axiom,
% 9.49/5.27      ! [A: int,B: int] :
% 9.49/5.27        ( ( dvd_dvd_int @ A @ one_one_int )
% 9.49/5.27       => ( ( dvd_dvd_int @ B @ one_one_int )
% 9.49/5.27         => ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4032_dvd__add__times__triv__right__iff,axiom,
% 9.49/5.27      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.49/5.27        ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ C @ A ) ) )
% 9.49/5.27        = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4033_dvd__add__times__triv__right__iff,axiom,
% 9.49/5.27      ! [A: rat,B: rat,C: rat] :
% 9.49/5.27        ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ ( times_times_rat @ C @ A ) ) )
% 9.49/5.27        = ( dvd_dvd_rat @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4034_dvd__add__times__triv__right__iff,axiom,
% 9.49/5.27      ! [A: complex,B: complex,C: complex] :
% 9.49/5.27        ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ B @ ( times_times_complex @ C @ A ) ) )
% 9.49/5.27        = ( dvd_dvd_complex @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4035_dvd__add__times__triv__right__iff,axiom,
% 9.49/5.27      ! [A: real,B: real,C: real] :
% 9.49/5.27        ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ ( times_times_real @ C @ A ) ) )
% 9.49/5.27        = ( dvd_dvd_real @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4036_dvd__add__times__triv__right__iff,axiom,
% 9.49/5.27      ! [A: nat,B: nat,C: nat] :
% 9.49/5.27        ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ ( times_times_nat @ C @ A ) ) )
% 9.49/5.27        = ( dvd_dvd_nat @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4037_dvd__add__times__triv__right__iff,axiom,
% 9.49/5.27      ! [A: int,B: int,C: int] :
% 9.49/5.27        ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ C @ A ) ) )
% 9.49/5.27        = ( dvd_dvd_int @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4038_dvd__add__times__triv__left__iff,axiom,
% 9.49/5.27      ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.49/5.27        ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ A ) @ B ) )
% 9.49/5.27        = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4039_dvd__add__times__triv__left__iff,axiom,
% 9.49/5.27      ! [A: rat,C: rat,B: rat] :
% 9.49/5.27        ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ ( times_times_rat @ C @ A ) @ B ) )
% 9.49/5.27        = ( dvd_dvd_rat @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4040_dvd__add__times__triv__left__iff,axiom,
% 9.49/5.27      ! [A: complex,C: complex,B: complex] :
% 9.49/5.27        ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ ( times_times_complex @ C @ A ) @ B ) )
% 9.49/5.27        = ( dvd_dvd_complex @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4041_dvd__add__times__triv__left__iff,axiom,
% 9.49/5.27      ! [A: real,C: real,B: real] :
% 9.49/5.27        ( ( dvd_dvd_real @ A @ ( plus_plus_real @ ( times_times_real @ C @ A ) @ B ) )
% 9.49/5.27        = ( dvd_dvd_real @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4042_dvd__add__times__triv__left__iff,axiom,
% 9.49/5.27      ! [A: nat,C: nat,B: nat] :
% 9.49/5.27        ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ B ) )
% 9.49/5.27        = ( dvd_dvd_nat @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4043_dvd__add__times__triv__left__iff,axiom,
% 9.49/5.27      ! [A: int,C: int,B: int] :
% 9.49/5.27        ( ( dvd_dvd_int @ A @ ( plus_plus_int @ ( times_times_int @ C @ A ) @ B ) )
% 9.49/5.27        = ( dvd_dvd_int @ A @ B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4044_dvd__div__mult__self,axiom,
% 9.49/5.27      ! [A: code_integer,B: code_integer] :
% 9.49/5.27        ( ( dvd_dvd_Code_integer @ A @ B )
% 9.49/5.27       => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 9.49/5.27          = B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4045_dvd__div__mult__self,axiom,
% 9.49/5.27      ! [A: nat,B: nat] :
% 9.49/5.27        ( ( dvd_dvd_nat @ A @ B )
% 9.49/5.27       => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 9.49/5.27          = B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4046_dvd__div__mult__self,axiom,
% 9.49/5.27      ! [A: int,B: int] :
% 9.49/5.27        ( ( dvd_dvd_int @ A @ B )
% 9.49/5.27       => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 9.49/5.27          = B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4047_dvd__mult__div__cancel,axiom,
% 9.49/5.27      ! [A: code_integer,B: code_integer] :
% 9.49/5.27        ( ( dvd_dvd_Code_integer @ A @ B )
% 9.49/5.27       => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ A ) )
% 9.49/5.27          = B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4048_dvd__mult__div__cancel,axiom,
% 9.49/5.27      ! [A: nat,B: nat] :
% 9.49/5.27        ( ( dvd_dvd_nat @ A @ B )
% 9.49/5.27       => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ A ) )
% 9.49/5.27          = B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4049_dvd__mult__div__cancel,axiom,
% 9.49/5.27      ! [A: int,B: int] :
% 9.49/5.27        ( ( dvd_dvd_int @ A @ B )
% 9.49/5.27       => ( ( times_times_int @ A @ ( divide_divide_int @ B @ A ) )
% 9.49/5.27          = B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4050_unit__div__1__div__1,axiom,
% 9.49/5.27      ! [A: code_integer] :
% 9.49/5.27        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.49/5.27       => ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 9.49/5.27          = A ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4051_unit__div__1__div__1,axiom,
% 9.49/5.27      ! [A: nat] :
% 9.49/5.27        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.49/5.27       => ( ( divide_divide_nat @ one_one_nat @ ( divide_divide_nat @ one_one_nat @ A ) )
% 9.49/5.27          = A ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4052_unit__div__1__div__1,axiom,
% 9.49/5.27      ! [A: int] :
% 9.49/5.27        ( ( dvd_dvd_int @ A @ one_one_int )
% 9.49/5.27       => ( ( divide_divide_int @ one_one_int @ ( divide_divide_int @ one_one_int @ A ) )
% 9.49/5.27          = A ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4053_unit__div__1__unit,axiom,
% 9.49/5.27      ! [A: code_integer] :
% 9.49/5.27        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.49/5.27       => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) @ one_one_Code_integer ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4054_unit__div__1__unit,axiom,
% 9.49/5.27      ! [A: nat] :
% 9.49/5.27        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.49/5.27       => ( dvd_dvd_nat @ ( divide_divide_nat @ one_one_nat @ A ) @ one_one_nat ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4055_unit__div__1__unit,axiom,
% 9.49/5.27      ! [A: int] :
% 9.49/5.27        ( ( dvd_dvd_int @ A @ one_one_int )
% 9.49/5.27       => ( dvd_dvd_int @ ( divide_divide_int @ one_one_int @ A ) @ one_one_int ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4056_unit__div,axiom,
% 9.49/5.27      ! [A: code_integer,B: code_integer] :
% 9.49/5.27        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.49/5.27       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.49/5.27         => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4057_unit__div,axiom,
% 9.49/5.27      ! [A: nat,B: nat] :
% 9.49/5.27        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.49/5.27       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.49/5.27         => ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4058_unit__div,axiom,
% 9.49/5.27      ! [A: int,B: int] :
% 9.49/5.27        ( ( dvd_dvd_int @ A @ one_one_int )
% 9.49/5.27       => ( ( dvd_dvd_int @ B @ one_one_int )
% 9.49/5.27         => ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4059_div__add,axiom,
% 9.49/5.27      ! [C: code_integer,A: code_integer,B: code_integer] :
% 9.49/5.27        ( ( dvd_dvd_Code_integer @ C @ A )
% 9.49/5.27       => ( ( dvd_dvd_Code_integer @ C @ B )
% 9.49/5.27         => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 9.49/5.27            = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4060_div__add,axiom,
% 9.49/5.27      ! [C: nat,A: nat,B: nat] :
% 9.49/5.27        ( ( dvd_dvd_nat @ C @ A )
% 9.49/5.27       => ( ( dvd_dvd_nat @ C @ B )
% 9.49/5.27         => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 9.49/5.27            = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4061_div__add,axiom,
% 9.49/5.27      ! [C: int,A: int,B: int] :
% 9.49/5.27        ( ( dvd_dvd_int @ C @ A )
% 9.49/5.27       => ( ( dvd_dvd_int @ C @ B )
% 9.49/5.27         => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 9.49/5.27            = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4062_div__diff,axiom,
% 9.49/5.27      ! [C: code_integer,A: code_integer,B: code_integer] :
% 9.49/5.27        ( ( dvd_dvd_Code_integer @ C @ A )
% 9.49/5.27       => ( ( dvd_dvd_Code_integer @ C @ B )
% 9.49/5.27         => ( ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 9.49/5.27            = ( minus_8373710615458151222nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4063_div__diff,axiom,
% 9.49/5.27      ! [C: int,A: int,B: int] :
% 9.49/5.27        ( ( dvd_dvd_int @ C @ A )
% 9.49/5.27       => ( ( dvd_dvd_int @ C @ B )
% 9.49/5.27         => ( ( divide_divide_int @ ( minus_minus_int @ A @ B ) @ C )
% 9.49/5.27            = ( minus_minus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4064_concat__bit__nonnegative__iff,axiom,
% 9.49/5.27      ! [N: nat,K: int,L2: int] :
% 9.49/5.27        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_concat_bit @ N @ K @ L2 ) )
% 9.49/5.27        = ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4065_concat__bit__negative__iff,axiom,
% 9.49/5.27      ! [N: nat,K: int,L2: int] :
% 9.49/5.27        ( ( ord_less_int @ ( bit_concat_bit @ N @ K @ L2 ) @ zero_zero_int )
% 9.49/5.27        = ( ord_less_int @ L2 @ zero_zero_int ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4066_dbl__simps_I5_J,axiom,
% 9.49/5.27      ! [K: num] :
% 9.49/5.27        ( ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) )
% 9.49/5.27        = ( numera6690914467698888265omplex @ ( bit0 @ K ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4067_dbl__simps_I5_J,axiom,
% 9.49/5.27      ! [K: num] :
% 9.49/5.27        ( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) )
% 9.49/5.27        = ( numeral_numeral_real @ ( bit0 @ K ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4068_dbl__simps_I5_J,axiom,
% 9.49/5.27      ! [K: num] :
% 9.49/5.27        ( ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) )
% 9.49/5.27        = ( numeral_numeral_rat @ ( bit0 @ K ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4069_dbl__simps_I5_J,axiom,
% 9.49/5.27      ! [K: num] :
% 9.49/5.27        ( ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) )
% 9.49/5.27        = ( numeral_numeral_int @ ( bit0 @ K ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4070_even__Suc__Suc__iff,axiom,
% 9.49/5.27      ! [N: nat] :
% 9.49/5.27        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ N ) ) )
% 9.49/5.27        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4071_even__Suc,axiom,
% 9.49/5.27      ! [N: nat] :
% 9.49/5.27        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) )
% 9.49/5.27        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4072_unit__div__mult__self,axiom,
% 9.49/5.27      ! [A: code_integer,B: code_integer] :
% 9.49/5.27        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.49/5.27       => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 9.49/5.27          = B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4073_unit__div__mult__self,axiom,
% 9.49/5.27      ! [A: nat,B: nat] :
% 9.49/5.27        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.49/5.27       => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 9.49/5.27          = B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4074_unit__div__mult__self,axiom,
% 9.49/5.27      ! [A: int,B: int] :
% 9.49/5.27        ( ( dvd_dvd_int @ A @ one_one_int )
% 9.49/5.27       => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 9.49/5.27          = B ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4075_unit__mult__div__div,axiom,
% 9.49/5.27      ! [A: code_integer,B: code_integer] :
% 9.49/5.27        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.49/5.27       => ( ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 9.49/5.27          = ( divide6298287555418463151nteger @ B @ A ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4076_unit__mult__div__div,axiom,
% 9.49/5.27      ! [A: nat,B: nat] :
% 9.49/5.27        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.49/5.27       => ( ( times_times_nat @ B @ ( divide_divide_nat @ one_one_nat @ A ) )
% 9.49/5.27          = ( divide_divide_nat @ B @ A ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4077_unit__mult__div__div,axiom,
% 9.49/5.27      ! [A: int,B: int] :
% 9.49/5.27        ( ( dvd_dvd_int @ A @ one_one_int )
% 9.49/5.27       => ( ( times_times_int @ B @ ( divide_divide_int @ one_one_int @ A ) )
% 9.49/5.27          = ( divide_divide_int @ B @ A ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4078_pow__divides__pow__iff,axiom,
% 9.49/5.27      ! [N: nat,A: nat,B: nat] :
% 9.49/5.27        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.27       => ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 9.49/5.27          = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4079_pow__divides__pow__iff,axiom,
% 9.49/5.27      ! [N: nat,A: int,B: int] :
% 9.49/5.27        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.27       => ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 9.49/5.27          = ( dvd_dvd_int @ A @ B ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4080_even__mult__iff,axiom,
% 9.49/5.27      ! [A: code_integer,B: code_integer] :
% 9.49/5.27        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( times_3573771949741848930nteger @ A @ B ) )
% 9.49/5.27        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.49/5.27          | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4081_even__mult__iff,axiom,
% 9.49/5.27      ! [A: nat,B: nat] :
% 9.49/5.27        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ A @ B ) )
% 9.49/5.27        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.49/5.27          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4082_even__mult__iff,axiom,
% 9.49/5.27      ! [A: int,B: int] :
% 9.49/5.27        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ A @ B ) )
% 9.49/5.27        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.49/5.27          | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4083_even__add,axiom,
% 9.49/5.27      ! [A: code_integer,B: code_integer] :
% 9.49/5.27        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 9.49/5.27        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.49/5.27          = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4084_even__add,axiom,
% 9.49/5.27      ! [A: nat,B: nat] :
% 9.49/5.27        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) )
% 9.49/5.27        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.49/5.27          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4085_even__add,axiom,
% 9.49/5.27      ! [A: int,B: int] :
% 9.49/5.27        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) )
% 9.49/5.27        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.49/5.27          = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4086_odd__add,axiom,
% 9.49/5.27      ! [A: code_integer,B: code_integer] :
% 9.49/5.27        ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) )
% 9.49/5.27        = ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 9.49/5.27         != ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4087_odd__add,axiom,
% 9.49/5.27      ! [A: nat,B: nat] :
% 9.49/5.27        ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) )
% 9.49/5.27        = ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 9.49/5.27         != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4088_odd__add,axiom,
% 9.49/5.27      ! [A: int,B: int] :
% 9.49/5.27        ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) )
% 9.49/5.27        = ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 9.49/5.27         != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4089_even__Suc__div__two,axiom,
% 9.49/5.27      ! [N: nat] :
% 9.49/5.27        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.27       => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.27          = ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4090_odd__Suc__div__two,axiom,
% 9.49/5.27      ! [N: nat] :
% 9.49/5.27        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.27       => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.27          = ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4091_even__mod__2__iff,axiom,
% 9.49/5.27      ! [A: code_integer] :
% 9.49/5.27        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 9.49/5.27        = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4092_even__mod__2__iff,axiom,
% 9.49/5.27      ! [A: nat] :
% 9.49/5.27        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.27        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4093_even__mod__2__iff,axiom,
% 9.49/5.27      ! [A: int] :
% 9.49/5.27        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 9.49/5.27        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4094_dvd__numeral__simp,axiom,
% 9.49/5.27      ! [M: num,N: num] :
% 9.49/5.27        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) )
% 9.49/5.27        = ( unique5706413561485394159nteger @ ( unique3479559517661332726nteger @ N @ M ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4095_dvd__numeral__simp,axiom,
% 9.49/5.27      ! [M: num,N: num] :
% 9.49/5.27        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 9.49/5.27        = ( unique6322359934112328802ux_nat @ ( unique5055182867167087721od_nat @ N @ M ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4096_dvd__numeral__simp,axiom,
% 9.49/5.27      ! [M: num,N: num] :
% 9.49/5.27        ( ( dvd_dvd_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 9.49/5.27        = ( unique6319869463603278526ux_int @ ( unique5052692396658037445od_int @ N @ M ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4097_zero__le__power__eq__numeral,axiom,
% 9.49/5.27      ! [A: rat,W: num] :
% 9.49/5.27        ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 9.49/5.27        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 9.49/5.27          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 9.49/5.27            & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4098_zero__le__power__eq__numeral,axiom,
% 9.49/5.27      ! [A: real,W: num] :
% 9.49/5.27        ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 9.49/5.27        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 9.49/5.27          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 9.49/5.27            & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4099_zero__le__power__eq__numeral,axiom,
% 9.49/5.27      ! [A: int,W: num] :
% 9.49/5.27        ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 9.49/5.27        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 9.49/5.27          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 9.49/5.27            & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4100_power__less__zero__eq__numeral,axiom,
% 9.49/5.27      ! [A: real,W: num] :
% 9.49/5.27        ( ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 9.49/5.27        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 9.49/5.27          & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4101_power__less__zero__eq__numeral,axiom,
% 9.49/5.27      ! [A: rat,W: num] :
% 9.49/5.27        ( ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 9.49/5.27        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 9.49/5.27          & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4102_power__less__zero__eq__numeral,axiom,
% 9.49/5.27      ! [A: int,W: num] :
% 9.49/5.27        ( ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 9.49/5.27        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 9.49/5.27          & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4103_power__less__zero__eq,axiom,
% 9.49/5.27      ! [A: real,N: nat] :
% 9.49/5.27        ( ( ord_less_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 9.49/5.27        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.27          & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4104_power__less__zero__eq,axiom,
% 9.49/5.27      ! [A: rat,N: nat] :
% 9.49/5.27        ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 9.49/5.27        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.27          & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4105_power__less__zero__eq,axiom,
% 9.49/5.27      ! [A: int,N: nat] :
% 9.49/5.27        ( ( ord_less_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 9.49/5.27        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.27          & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4106_even__plus__one__iff,axiom,
% 9.49/5.27      ! [A: code_integer] :
% 9.49/5.27        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) )
% 9.49/5.27        = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4107_even__plus__one__iff,axiom,
% 9.49/5.27      ! [A: nat] :
% 9.49/5.27        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ one_one_nat ) )
% 9.49/5.27        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4108_even__plus__one__iff,axiom,
% 9.49/5.27      ! [A: int] :
% 9.49/5.27        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ one_one_int ) )
% 9.49/5.27        = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4109_even__diff,axiom,
% 9.49/5.27      ! [A: code_integer,B: code_integer] :
% 9.49/5.27        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ A @ B ) )
% 9.49/5.27        = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4110_even__diff,axiom,
% 9.49/5.27      ! [A: int,B: int] :
% 9.49/5.27        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ A @ B ) )
% 9.49/5.27        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4111_odd__Suc__minus__one,axiom,
% 9.49/5.27      ! [N: nat] :
% 9.49/5.27        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.27       => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 9.49/5.27          = N ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4112_even__diff__nat,axiom,
% 9.49/5.27      ! [M: nat,N: nat] :
% 9.49/5.27        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) )
% 9.49/5.27        = ( ( ord_less_nat @ M @ N )
% 9.49/5.27          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4113_zero__less__power__eq__numeral,axiom,
% 9.49/5.27      ! [A: real,W: num] :
% 9.49/5.27        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 9.49/5.27        = ( ( ( numeral_numeral_nat @ W )
% 9.49/5.27            = zero_zero_nat )
% 9.49/5.27          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 9.49/5.27            & ( A != zero_zero_real ) )
% 9.49/5.27          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 9.49/5.27            & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4114_zero__less__power__eq__numeral,axiom,
% 9.49/5.27      ! [A: rat,W: num] :
% 9.49/5.27        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 9.49/5.27        = ( ( ( numeral_numeral_nat @ W )
% 9.49/5.27            = zero_zero_nat )
% 9.49/5.27          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 9.49/5.27            & ( A != zero_zero_rat ) )
% 9.49/5.27          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 9.49/5.27            & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4115_zero__less__power__eq__numeral,axiom,
% 9.49/5.27      ! [A: int,W: num] :
% 9.49/5.27        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 9.49/5.27        = ( ( ( numeral_numeral_nat @ W )
% 9.49/5.27            = zero_zero_nat )
% 9.49/5.27          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 9.49/5.27            & ( A != zero_zero_int ) )
% 9.49/5.27          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 9.49/5.27            & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4116_even__succ__div__2,axiom,
% 9.49/5.27      ! [A: code_integer] :
% 9.49/5.27        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.49/5.27       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.49/5.27          = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4117_even__succ__div__2,axiom,
% 9.49/5.27      ! [A: nat] :
% 9.49/5.27        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.49/5.27       => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.27          = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4118_even__succ__div__2,axiom,
% 9.49/5.27      ! [A: int] :
% 9.49/5.27        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.49/5.27       => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.49/5.27          = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4119_even__succ__div__two,axiom,
% 9.49/5.27      ! [A: code_integer] :
% 9.49/5.27        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.49/5.27       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.49/5.27          = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4120_even__succ__div__two,axiom,
% 9.49/5.27      ! [A: nat] :
% 9.49/5.27        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.49/5.27       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.27          = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4121_even__succ__div__two,axiom,
% 9.49/5.27      ! [A: int] :
% 9.49/5.27        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.49/5.27       => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.49/5.27          = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4122_odd__succ__div__two,axiom,
% 9.49/5.27      ! [A: code_integer] :
% 9.49/5.27        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.49/5.27       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.49/5.27          = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4123_odd__succ__div__two,axiom,
% 9.49/5.27      ! [A: nat] :
% 9.49/5.27        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.49/5.27       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.27          = ( plus_plus_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4124_odd__succ__div__two,axiom,
% 9.49/5.27      ! [A: int] :
% 9.49/5.27        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.49/5.27       => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.49/5.27          = ( plus_plus_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 9.49/5.27  
% 9.49/5.27  thf(fact_4125_even__power,axiom,
% 9.49/5.27      ! [A: code_integer,N: nat] :
% 9.49/5.27        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 9.49/5.28        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.49/5.28          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4126_even__power,axiom,
% 9.49/5.28      ! [A: nat,N: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ A @ N ) )
% 9.49/5.28        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.49/5.28          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4127_even__power,axiom,
% 9.49/5.28      ! [A: int,N: nat] :
% 9.49/5.28        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ A @ N ) )
% 9.49/5.28        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.49/5.28          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4128_odd__two__times__div__two__nat,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28       => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.28          = ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4129_divmod__algorithm__code_I5_J,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 9.49/5.28        = ( produc2626176000494625587at_nat
% 9.49/5.28          @ ^ [Q4: nat,R5: nat] : ( product_Pair_nat_nat @ Q4 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) )
% 9.49/5.28          @ ( unique5055182867167087721od_nat @ M @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4130_divmod__algorithm__code_I5_J,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 9.49/5.28        = ( produc4245557441103728435nt_int
% 9.49/5.28          @ ^ [Q4: int,R5: int] : ( product_Pair_int_int @ Q4 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) )
% 9.49/5.28          @ ( unique5052692396658037445od_int @ M @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4131_odd__two__times__div__two__succ,axiom,
% 9.49/5.28      ! [A: code_integer] :
% 9.49/5.28        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.49/5.28       => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ one_one_Code_integer )
% 9.49/5.28          = A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4132_odd__two__times__div__two__succ,axiom,
% 9.49/5.28      ! [A: nat] :
% 9.49/5.28        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.49/5.28       => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 9.49/5.28          = A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4133_odd__two__times__div__two__succ,axiom,
% 9.49/5.28      ! [A: int] :
% 9.49/5.28        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.49/5.28       => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 9.49/5.28          = A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4134_power__le__zero__eq__numeral,axiom,
% 9.49/5.28      ! [A: rat,W: num] :
% 9.49/5.28        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 9.49/5.28        = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 9.49/5.28          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 9.49/5.28              & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 9.49/5.28            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 9.49/5.28              & ( A = zero_zero_rat ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4135_power__le__zero__eq__numeral,axiom,
% 9.49/5.28      ! [A: real,W: num] :
% 9.49/5.28        ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 9.49/5.28        = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 9.49/5.28          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 9.49/5.28              & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 9.49/5.28            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 9.49/5.28              & ( A = zero_zero_real ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4136_power__le__zero__eq__numeral,axiom,
% 9.49/5.28      ! [A: int,W: num] :
% 9.49/5.28        ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 9.49/5.28        = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 9.49/5.28          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 9.49/5.28              & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 9.49/5.28            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 9.49/5.28              & ( A = zero_zero_int ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4137_semiring__parity__class_Oeven__mask__iff,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) )
% 9.49/5.28        = ( N = zero_zero_nat ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4138_semiring__parity__class_Oeven__mask__iff,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) )
% 9.49/5.28        = ( N = zero_zero_nat ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4139_semiring__parity__class_Oeven__mask__iff,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 9.49/5.28        = ( N = zero_zero_nat ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4140_dvd__productE,axiom,
% 9.49/5.28      ! [P6: nat,A: nat,B: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ P6 @ ( times_times_nat @ A @ B ) )
% 9.49/5.28       => ~ ! [X3: nat,Y3: nat] :
% 9.49/5.28              ( ( P6
% 9.49/5.28                = ( times_times_nat @ X3 @ Y3 ) )
% 9.49/5.28             => ( ( dvd_dvd_nat @ X3 @ A )
% 9.49/5.28               => ~ ( dvd_dvd_nat @ Y3 @ B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4141_dvd__productE,axiom,
% 9.49/5.28      ! [P6: int,A: int,B: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ P6 @ ( times_times_int @ A @ B ) )
% 9.49/5.28       => ~ ! [X3: int,Y3: int] :
% 9.49/5.28              ( ( P6
% 9.49/5.28                = ( times_times_int @ X3 @ Y3 ) )
% 9.49/5.28             => ( ( dvd_dvd_int @ X3 @ A )
% 9.49/5.28               => ~ ( dvd_dvd_int @ Y3 @ B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4142_division__decomp,axiom,
% 9.49/5.28      ! [A: nat,B: nat,C: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 9.49/5.28       => ? [B7: nat,C5: nat] :
% 9.49/5.28            ( ( A
% 9.49/5.28              = ( times_times_nat @ B7 @ C5 ) )
% 9.49/5.28            & ( dvd_dvd_nat @ B7 @ B )
% 9.49/5.28            & ( dvd_dvd_nat @ C5 @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4143_division__decomp,axiom,
% 9.49/5.28      ! [A: int,B: int,C: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 9.49/5.28       => ? [B7: int,C5: int] :
% 9.49/5.28            ( ( A
% 9.49/5.28              = ( times_times_int @ B7 @ C5 ) )
% 9.49/5.28            & ( dvd_dvd_int @ B7 @ B )
% 9.49/5.28            & ( dvd_dvd_int @ C5 @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4144_dvdE,axiom,
% 9.49/5.28      ! [B: code_integer,A: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ B @ A )
% 9.49/5.28       => ~ ! [K2: code_integer] :
% 9.49/5.28              ( A
% 9.49/5.28             != ( times_3573771949741848930nteger @ B @ K2 ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4145_dvdE,axiom,
% 9.49/5.28      ! [B: complex,A: complex] :
% 9.49/5.28        ( ( dvd_dvd_complex @ B @ A )
% 9.49/5.28       => ~ ! [K2: complex] :
% 9.49/5.28              ( A
% 9.49/5.28             != ( times_times_complex @ B @ K2 ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4146_dvdE,axiom,
% 9.49/5.28      ! [B: real,A: real] :
% 9.49/5.28        ( ( dvd_dvd_real @ B @ A )
% 9.49/5.28       => ~ ! [K2: real] :
% 9.49/5.28              ( A
% 9.49/5.28             != ( times_times_real @ B @ K2 ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4147_dvdE,axiom,
% 9.49/5.28      ! [B: nat,A: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ B @ A )
% 9.49/5.28       => ~ ! [K2: nat] :
% 9.49/5.28              ( A
% 9.49/5.28             != ( times_times_nat @ B @ K2 ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4148_dvdE,axiom,
% 9.49/5.28      ! [B: int,A: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ B @ A )
% 9.49/5.28       => ~ ! [K2: int] :
% 9.49/5.28              ( A
% 9.49/5.28             != ( times_times_int @ B @ K2 ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4149_dvdI,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer,K: code_integer] :
% 9.49/5.28        ( ( A
% 9.49/5.28          = ( times_3573771949741848930nteger @ B @ K ) )
% 9.49/5.28       => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4150_dvdI,axiom,
% 9.49/5.28      ! [A: complex,B: complex,K: complex] :
% 9.49/5.28        ( ( A
% 9.49/5.28          = ( times_times_complex @ B @ K ) )
% 9.49/5.28       => ( dvd_dvd_complex @ B @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4151_dvdI,axiom,
% 9.49/5.28      ! [A: real,B: real,K: real] :
% 9.49/5.28        ( ( A
% 9.49/5.28          = ( times_times_real @ B @ K ) )
% 9.49/5.28       => ( dvd_dvd_real @ B @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4152_dvdI,axiom,
% 9.49/5.28      ! [A: nat,B: nat,K: nat] :
% 9.49/5.28        ( ( A
% 9.49/5.28          = ( times_times_nat @ B @ K ) )
% 9.49/5.28       => ( dvd_dvd_nat @ B @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4153_dvdI,axiom,
% 9.49/5.28      ! [A: int,B: int,K: int] :
% 9.49/5.28        ( ( A
% 9.49/5.28          = ( times_times_int @ B @ K ) )
% 9.49/5.28       => ( dvd_dvd_int @ B @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4154_dvd__def,axiom,
% 9.49/5.28      ( dvd_dvd_Code_integer
% 9.49/5.28      = ( ^ [B4: code_integer,A3: code_integer] :
% 9.49/5.28          ? [K3: code_integer] :
% 9.49/5.28            ( A3
% 9.49/5.28            = ( times_3573771949741848930nteger @ B4 @ K3 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4155_dvd__def,axiom,
% 9.49/5.28      ( dvd_dvd_complex
% 9.49/5.28      = ( ^ [B4: complex,A3: complex] :
% 9.49/5.28          ? [K3: complex] :
% 9.49/5.28            ( A3
% 9.49/5.28            = ( times_times_complex @ B4 @ K3 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4156_dvd__def,axiom,
% 9.49/5.28      ( dvd_dvd_real
% 9.49/5.28      = ( ^ [B4: real,A3: real] :
% 9.49/5.28          ? [K3: real] :
% 9.49/5.28            ( A3
% 9.49/5.28            = ( times_times_real @ B4 @ K3 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4157_dvd__def,axiom,
% 9.49/5.28      ( dvd_dvd_nat
% 9.49/5.28      = ( ^ [B4: nat,A3: nat] :
% 9.49/5.28          ? [K3: nat] :
% 9.49/5.28            ( A3
% 9.49/5.28            = ( times_times_nat @ B4 @ K3 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4158_dvd__def,axiom,
% 9.49/5.28      ( dvd_dvd_int
% 9.49/5.28      = ( ^ [B4: int,A3: int] :
% 9.49/5.28          ? [K3: int] :
% 9.49/5.28            ( A3
% 9.49/5.28            = ( times_times_int @ B4 @ K3 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4159_dvd__mult,axiom,
% 9.49/5.28      ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ A @ C )
% 9.49/5.28       => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4160_dvd__mult,axiom,
% 9.49/5.28      ! [A: complex,C: complex,B: complex] :
% 9.49/5.28        ( ( dvd_dvd_complex @ A @ C )
% 9.49/5.28       => ( dvd_dvd_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4161_dvd__mult,axiom,
% 9.49/5.28      ! [A: real,C: real,B: real] :
% 9.49/5.28        ( ( dvd_dvd_real @ A @ C )
% 9.49/5.28       => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4162_dvd__mult,axiom,
% 9.49/5.28      ! [A: nat,C: nat,B: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ A @ C )
% 9.49/5.28       => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4163_dvd__mult,axiom,
% 9.49/5.28      ! [A: int,C: int,B: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ A @ C )
% 9.49/5.28       => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4164_dvd__mult2,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ A @ B )
% 9.49/5.28       => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4165_dvd__mult2,axiom,
% 9.49/5.28      ! [A: complex,B: complex,C: complex] :
% 9.49/5.28        ( ( dvd_dvd_complex @ A @ B )
% 9.49/5.28       => ( dvd_dvd_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4166_dvd__mult2,axiom,
% 9.49/5.28      ! [A: real,B: real,C: real] :
% 9.49/5.28        ( ( dvd_dvd_real @ A @ B )
% 9.49/5.28       => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4167_dvd__mult2,axiom,
% 9.49/5.28      ! [A: nat,B: nat,C: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ A @ B )
% 9.49/5.28       => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4168_dvd__mult2,axiom,
% 9.49/5.28      ! [A: int,B: int,C: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ A @ B )
% 9.49/5.28       => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4169_dvd__mult__left,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 9.49/5.28       => ( dvd_dvd_Code_integer @ A @ C ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4170_dvd__mult__left,axiom,
% 9.49/5.28      ! [A: complex,B: complex,C: complex] :
% 9.49/5.28        ( ( dvd_dvd_complex @ ( times_times_complex @ A @ B ) @ C )
% 9.49/5.28       => ( dvd_dvd_complex @ A @ C ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4171_dvd__mult__left,axiom,
% 9.49/5.28      ! [A: real,B: real,C: real] :
% 9.49/5.28        ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 9.49/5.28       => ( dvd_dvd_real @ A @ C ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4172_dvd__mult__left,axiom,
% 9.49/5.28      ! [A: nat,B: nat,C: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 9.49/5.28       => ( dvd_dvd_nat @ A @ C ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4173_dvd__mult__left,axiom,
% 9.49/5.28      ! [A: int,B: int,C: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 9.49/5.28       => ( dvd_dvd_int @ A @ C ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4174_dvd__triv__left,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ A @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4175_dvd__triv__left,axiom,
% 9.49/5.28      ! [A: complex,B: complex] : ( dvd_dvd_complex @ A @ ( times_times_complex @ A @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4176_dvd__triv__left,axiom,
% 9.49/5.28      ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ A @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4177_dvd__triv__left,axiom,
% 9.49/5.28      ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4178_dvd__triv__left,axiom,
% 9.49/5.28      ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ A @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4179_mult__dvd__mono,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ A @ B )
% 9.49/5.28       => ( ( dvd_dvd_Code_integer @ C @ D2 )
% 9.49/5.28         => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4180_mult__dvd__mono,axiom,
% 9.49/5.28      ! [A: complex,B: complex,C: complex,D2: complex] :
% 9.49/5.28        ( ( dvd_dvd_complex @ A @ B )
% 9.49/5.28       => ( ( dvd_dvd_complex @ C @ D2 )
% 9.49/5.28         => ( dvd_dvd_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ D2 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4181_mult__dvd__mono,axiom,
% 9.49/5.28      ! [A: real,B: real,C: real,D2: real] :
% 9.49/5.28        ( ( dvd_dvd_real @ A @ B )
% 9.49/5.28       => ( ( dvd_dvd_real @ C @ D2 )
% 9.49/5.28         => ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4182_mult__dvd__mono,axiom,
% 9.49/5.28      ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ A @ B )
% 9.49/5.28       => ( ( dvd_dvd_nat @ C @ D2 )
% 9.49/5.28         => ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4183_mult__dvd__mono,axiom,
% 9.49/5.28      ! [A: int,B: int,C: int,D2: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ A @ B )
% 9.49/5.28       => ( ( dvd_dvd_int @ C @ D2 )
% 9.49/5.28         => ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4184_dvd__mult__right,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 9.49/5.28       => ( dvd_dvd_Code_integer @ B @ C ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4185_dvd__mult__right,axiom,
% 9.49/5.28      ! [A: complex,B: complex,C: complex] :
% 9.49/5.28        ( ( dvd_dvd_complex @ ( times_times_complex @ A @ B ) @ C )
% 9.49/5.28       => ( dvd_dvd_complex @ B @ C ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4186_dvd__mult__right,axiom,
% 9.49/5.28      ! [A: real,B: real,C: real] :
% 9.49/5.28        ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 9.49/5.28       => ( dvd_dvd_real @ B @ C ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4187_dvd__mult__right,axiom,
% 9.49/5.28      ! [A: nat,B: nat,C: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 9.49/5.28       => ( dvd_dvd_nat @ B @ C ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4188_dvd__mult__right,axiom,
% 9.49/5.28      ! [A: int,B: int,C: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 9.49/5.28       => ( dvd_dvd_int @ B @ C ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4189_dvd__triv__right,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4190_dvd__triv__right,axiom,
% 9.49/5.28      ! [A: complex,B: complex] : ( dvd_dvd_complex @ A @ ( times_times_complex @ B @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4191_dvd__triv__right,axiom,
% 9.49/5.28      ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ B @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4192_dvd__triv__right,axiom,
% 9.49/5.28      ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4193_dvd__triv__right,axiom,
% 9.49/5.28      ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ B @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4194_dvd__unit__imp__unit,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ A @ B )
% 9.49/5.28       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.49/5.28         => ( dvd_dvd_Code_integer @ A @ one_one_Code_integer ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4195_dvd__unit__imp__unit,axiom,
% 9.49/5.28      ! [A: nat,B: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ A @ B )
% 9.49/5.28       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.49/5.28         => ( dvd_dvd_nat @ A @ one_one_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4196_dvd__unit__imp__unit,axiom,
% 9.49/5.28      ! [A: int,B: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ A @ B )
% 9.49/5.28       => ( ( dvd_dvd_int @ B @ one_one_int )
% 9.49/5.28         => ( dvd_dvd_int @ A @ one_one_int ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4197_unit__imp__dvd,axiom,
% 9.49/5.28      ! [B: code_integer,A: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.49/5.28       => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4198_unit__imp__dvd,axiom,
% 9.49/5.28      ! [B: nat,A: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.49/5.28       => ( dvd_dvd_nat @ B @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4199_unit__imp__dvd,axiom,
% 9.49/5.28      ! [B: int,A: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ B @ one_one_int )
% 9.49/5.28       => ( dvd_dvd_int @ B @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4200_one__dvd,axiom,
% 9.49/5.28      ! [A: code_integer] : ( dvd_dvd_Code_integer @ one_one_Code_integer @ A ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4201_one__dvd,axiom,
% 9.49/5.28      ! [A: complex] : ( dvd_dvd_complex @ one_one_complex @ A ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4202_one__dvd,axiom,
% 9.49/5.28      ! [A: real] : ( dvd_dvd_real @ one_one_real @ A ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4203_one__dvd,axiom,
% 9.49/5.28      ! [A: rat] : ( dvd_dvd_rat @ one_one_rat @ A ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4204_one__dvd,axiom,
% 9.49/5.28      ! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4205_one__dvd,axiom,
% 9.49/5.28      ! [A: int] : ( dvd_dvd_int @ one_one_int @ A ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4206_dvd__add__right__iff,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ A @ B )
% 9.49/5.28       => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 9.49/5.28          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4207_dvd__add__right__iff,axiom,
% 9.49/5.28      ! [A: real,B: real,C: real] :
% 9.49/5.28        ( ( dvd_dvd_real @ A @ B )
% 9.49/5.28       => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 9.49/5.28          = ( dvd_dvd_real @ A @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4208_dvd__add__right__iff,axiom,
% 9.49/5.28      ! [A: rat,B: rat,C: rat] :
% 9.49/5.28        ( ( dvd_dvd_rat @ A @ B )
% 9.49/5.28       => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 9.49/5.28          = ( dvd_dvd_rat @ A @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4209_dvd__add__right__iff,axiom,
% 9.49/5.28      ! [A: nat,B: nat,C: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ A @ B )
% 9.49/5.28       => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 9.49/5.28          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4210_dvd__add__right__iff,axiom,
% 9.49/5.28      ! [A: int,B: int,C: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ A @ B )
% 9.49/5.28       => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 9.49/5.28          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4211_dvd__add__right__iff,axiom,
% 9.49/5.28      ! [A: complex,B: complex,C: complex] :
% 9.49/5.28        ( ( dvd_dvd_complex @ A @ B )
% 9.49/5.28       => ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ B @ C ) )
% 9.49/5.28          = ( dvd_dvd_complex @ A @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4212_dvd__add__left__iff,axiom,
% 9.49/5.28      ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ A @ C )
% 9.49/5.28       => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 9.49/5.28          = ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4213_dvd__add__left__iff,axiom,
% 9.49/5.28      ! [A: real,C: real,B: real] :
% 9.49/5.28        ( ( dvd_dvd_real @ A @ C )
% 9.49/5.28       => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 9.49/5.28          = ( dvd_dvd_real @ A @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4214_dvd__add__left__iff,axiom,
% 9.49/5.28      ! [A: rat,C: rat,B: rat] :
% 9.49/5.28        ( ( dvd_dvd_rat @ A @ C )
% 9.49/5.28       => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 9.49/5.28          = ( dvd_dvd_rat @ A @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4215_dvd__add__left__iff,axiom,
% 9.49/5.28      ! [A: nat,C: nat,B: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ A @ C )
% 9.49/5.28       => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 9.49/5.28          = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4216_dvd__add__left__iff,axiom,
% 9.49/5.28      ! [A: int,C: int,B: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ A @ C )
% 9.49/5.28       => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 9.49/5.28          = ( dvd_dvd_int @ A @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4217_dvd__add__left__iff,axiom,
% 9.49/5.28      ! [A: complex,C: complex,B: complex] :
% 9.49/5.28        ( ( dvd_dvd_complex @ A @ C )
% 9.49/5.28       => ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ B @ C ) )
% 9.49/5.28          = ( dvd_dvd_complex @ A @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4218_dvd__add,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ A @ B )
% 9.49/5.28       => ( ( dvd_dvd_Code_integer @ A @ C )
% 9.49/5.28         => ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4219_dvd__add,axiom,
% 9.49/5.28      ! [A: real,B: real,C: real] :
% 9.49/5.28        ( ( dvd_dvd_real @ A @ B )
% 9.49/5.28       => ( ( dvd_dvd_real @ A @ C )
% 9.49/5.28         => ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4220_dvd__add,axiom,
% 9.49/5.28      ! [A: rat,B: rat,C: rat] :
% 9.49/5.28        ( ( dvd_dvd_rat @ A @ B )
% 9.49/5.28       => ( ( dvd_dvd_rat @ A @ C )
% 9.49/5.28         => ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4221_dvd__add,axiom,
% 9.49/5.28      ! [A: nat,B: nat,C: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ A @ B )
% 9.49/5.28       => ( ( dvd_dvd_nat @ A @ C )
% 9.49/5.28         => ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4222_dvd__add,axiom,
% 9.49/5.28      ! [A: int,B: int,C: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ A @ B )
% 9.49/5.28       => ( ( dvd_dvd_int @ A @ C )
% 9.49/5.28         => ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4223_dvd__add,axiom,
% 9.49/5.28      ! [A: complex,B: complex,C: complex] :
% 9.49/5.28        ( ( dvd_dvd_complex @ A @ B )
% 9.49/5.28       => ( ( dvd_dvd_complex @ A @ C )
% 9.49/5.28         => ( dvd_dvd_complex @ A @ ( plus_plus_complex @ B @ C ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4224_dvd__diff__commute,axiom,
% 9.49/5.28      ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ C @ B ) )
% 9.49/5.28        = ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ B @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4225_dvd__diff__commute,axiom,
% 9.49/5.28      ! [A: int,C: int,B: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ A @ ( minus_minus_int @ C @ B ) )
% 9.49/5.28        = ( dvd_dvd_int @ A @ ( minus_minus_int @ B @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4226_dvd__diff,axiom,
% 9.49/5.28      ! [X: code_integer,Y2: code_integer,Z: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ X @ Y2 )
% 9.49/5.28       => ( ( dvd_dvd_Code_integer @ X @ Z )
% 9.49/5.28         => ( dvd_dvd_Code_integer @ X @ ( minus_8373710615458151222nteger @ Y2 @ Z ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4227_dvd__diff,axiom,
% 9.49/5.28      ! [X: rat,Y2: rat,Z: rat] :
% 9.49/5.28        ( ( dvd_dvd_rat @ X @ Y2 )
% 9.49/5.28       => ( ( dvd_dvd_rat @ X @ Z )
% 9.49/5.28         => ( dvd_dvd_rat @ X @ ( minus_minus_rat @ Y2 @ Z ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4228_dvd__diff,axiom,
% 9.49/5.28      ! [X: int,Y2: int,Z: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ X @ Y2 )
% 9.49/5.28       => ( ( dvd_dvd_int @ X @ Z )
% 9.49/5.28         => ( dvd_dvd_int @ X @ ( minus_minus_int @ Y2 @ Z ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4229_dvd__div__eq__iff,axiom,
% 9.49/5.28      ! [C: code_integer,A: code_integer,B: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ C @ A )
% 9.49/5.28       => ( ( dvd_dvd_Code_integer @ C @ B )
% 9.49/5.28         => ( ( ( divide6298287555418463151nteger @ A @ C )
% 9.49/5.28              = ( divide6298287555418463151nteger @ B @ C ) )
% 9.49/5.28            = ( A = B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4230_dvd__div__eq__iff,axiom,
% 9.49/5.28      ! [C: complex,A: complex,B: complex] :
% 9.49/5.28        ( ( dvd_dvd_complex @ C @ A )
% 9.49/5.28       => ( ( dvd_dvd_complex @ C @ B )
% 9.49/5.28         => ( ( ( divide1717551699836669952omplex @ A @ C )
% 9.49/5.28              = ( divide1717551699836669952omplex @ B @ C ) )
% 9.49/5.28            = ( A = B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4231_dvd__div__eq__iff,axiom,
% 9.49/5.28      ! [C: real,A: real,B: real] :
% 9.49/5.28        ( ( dvd_dvd_real @ C @ A )
% 9.49/5.28       => ( ( dvd_dvd_real @ C @ B )
% 9.49/5.28         => ( ( ( divide_divide_real @ A @ C )
% 9.49/5.28              = ( divide_divide_real @ B @ C ) )
% 9.49/5.28            = ( A = B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4232_dvd__div__eq__iff,axiom,
% 9.49/5.28      ! [C: rat,A: rat,B: rat] :
% 9.49/5.28        ( ( dvd_dvd_rat @ C @ A )
% 9.49/5.28       => ( ( dvd_dvd_rat @ C @ B )
% 9.49/5.28         => ( ( ( divide_divide_rat @ A @ C )
% 9.49/5.28              = ( divide_divide_rat @ B @ C ) )
% 9.49/5.28            = ( A = B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4233_dvd__div__eq__iff,axiom,
% 9.49/5.28      ! [C: nat,A: nat,B: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ C @ A )
% 9.49/5.28       => ( ( dvd_dvd_nat @ C @ B )
% 9.49/5.28         => ( ( ( divide_divide_nat @ A @ C )
% 9.49/5.28              = ( divide_divide_nat @ B @ C ) )
% 9.49/5.28            = ( A = B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4234_dvd__div__eq__iff,axiom,
% 9.49/5.28      ! [C: int,A: int,B: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ C @ A )
% 9.49/5.28       => ( ( dvd_dvd_int @ C @ B )
% 9.49/5.28         => ( ( ( divide_divide_int @ A @ C )
% 9.49/5.28              = ( divide_divide_int @ B @ C ) )
% 9.49/5.28            = ( A = B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4235_dvd__div__eq__cancel,axiom,
% 9.49/5.28      ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.49/5.28        ( ( ( divide6298287555418463151nteger @ A @ C )
% 9.49/5.28          = ( divide6298287555418463151nteger @ B @ C ) )
% 9.49/5.28       => ( ( dvd_dvd_Code_integer @ C @ A )
% 9.49/5.28         => ( ( dvd_dvd_Code_integer @ C @ B )
% 9.49/5.28           => ( A = B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4236_dvd__div__eq__cancel,axiom,
% 9.49/5.28      ! [A: complex,C: complex,B: complex] :
% 9.49/5.28        ( ( ( divide1717551699836669952omplex @ A @ C )
% 9.49/5.28          = ( divide1717551699836669952omplex @ B @ C ) )
% 9.49/5.28       => ( ( dvd_dvd_complex @ C @ A )
% 9.49/5.28         => ( ( dvd_dvd_complex @ C @ B )
% 9.49/5.28           => ( A = B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4237_dvd__div__eq__cancel,axiom,
% 9.49/5.28      ! [A: real,C: real,B: real] :
% 9.49/5.28        ( ( ( divide_divide_real @ A @ C )
% 9.49/5.28          = ( divide_divide_real @ B @ C ) )
% 9.49/5.28       => ( ( dvd_dvd_real @ C @ A )
% 9.49/5.28         => ( ( dvd_dvd_real @ C @ B )
% 9.49/5.28           => ( A = B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4238_dvd__div__eq__cancel,axiom,
% 9.49/5.28      ! [A: rat,C: rat,B: rat] :
% 9.49/5.28        ( ( ( divide_divide_rat @ A @ C )
% 9.49/5.28          = ( divide_divide_rat @ B @ C ) )
% 9.49/5.28       => ( ( dvd_dvd_rat @ C @ A )
% 9.49/5.28         => ( ( dvd_dvd_rat @ C @ B )
% 9.49/5.28           => ( A = B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4239_dvd__div__eq__cancel,axiom,
% 9.49/5.28      ! [A: nat,C: nat,B: nat] :
% 9.49/5.28        ( ( ( divide_divide_nat @ A @ C )
% 9.49/5.28          = ( divide_divide_nat @ B @ C ) )
% 9.49/5.28       => ( ( dvd_dvd_nat @ C @ A )
% 9.49/5.28         => ( ( dvd_dvd_nat @ C @ B )
% 9.49/5.28           => ( A = B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4240_dvd__div__eq__cancel,axiom,
% 9.49/5.28      ! [A: int,C: int,B: int] :
% 9.49/5.28        ( ( ( divide_divide_int @ A @ C )
% 9.49/5.28          = ( divide_divide_int @ B @ C ) )
% 9.49/5.28       => ( ( dvd_dvd_int @ C @ A )
% 9.49/5.28         => ( ( dvd_dvd_int @ C @ B )
% 9.49/5.28           => ( A = B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4241_div__div__div__same,axiom,
% 9.49/5.28      ! [D2: code_integer,B: code_integer,A: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ D2 @ B )
% 9.49/5.28       => ( ( dvd_dvd_Code_integer @ B @ A )
% 9.49/5.28         => ( ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ D2 ) @ ( divide6298287555418463151nteger @ B @ D2 ) )
% 9.49/5.28            = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4242_div__div__div__same,axiom,
% 9.49/5.28      ! [D2: nat,B: nat,A: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ D2 @ B )
% 9.49/5.28       => ( ( dvd_dvd_nat @ B @ A )
% 9.49/5.28         => ( ( divide_divide_nat @ ( divide_divide_nat @ A @ D2 ) @ ( divide_divide_nat @ B @ D2 ) )
% 9.49/5.28            = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4243_div__div__div__same,axiom,
% 9.49/5.28      ! [D2: int,B: int,A: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ D2 @ B )
% 9.49/5.28       => ( ( dvd_dvd_int @ B @ A )
% 9.49/5.28         => ( ( divide_divide_int @ ( divide_divide_int @ A @ D2 ) @ ( divide_divide_int @ B @ D2 ) )
% 9.49/5.28            = ( divide_divide_int @ A @ B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4244_dvd__power__same,axiom,
% 9.49/5.28      ! [X: code_integer,Y2: code_integer,N: nat] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ X @ Y2 )
% 9.49/5.28       => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ N ) @ ( power_8256067586552552935nteger @ Y2 @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4245_dvd__power__same,axiom,
% 9.49/5.28      ! [X: nat,Y2: nat,N: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ X @ Y2 )
% 9.49/5.28       => ( dvd_dvd_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y2 @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4246_dvd__power__same,axiom,
% 9.49/5.28      ! [X: real,Y2: real,N: nat] :
% 9.49/5.28        ( ( dvd_dvd_real @ X @ Y2 )
% 9.49/5.28       => ( dvd_dvd_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y2 @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4247_dvd__power__same,axiom,
% 9.49/5.28      ! [X: int,Y2: int,N: nat] :
% 9.49/5.28        ( ( dvd_dvd_int @ X @ Y2 )
% 9.49/5.28       => ( dvd_dvd_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y2 @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4248_dvd__power__same,axiom,
% 9.49/5.28      ! [X: complex,Y2: complex,N: nat] :
% 9.49/5.28        ( ( dvd_dvd_complex @ X @ Y2 )
% 9.49/5.28       => ( dvd_dvd_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y2 @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4249_old_Oprod_Ocase,axiom,
% 9.49/5.28      ! [F: nat > nat > nat,X1: nat,X23: nat] :
% 9.49/5.28        ( ( produc6842872674320459806at_nat @ F @ ( product_Pair_nat_nat @ X1 @ X23 ) )
% 9.49/5.28        = ( F @ X1 @ X23 ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4250_old_Oprod_Ocase,axiom,
% 9.49/5.28      ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X1: nat,X23: nat] :
% 9.49/5.28        ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ X1 @ X23 ) )
% 9.49/5.28        = ( F @ X1 @ X23 ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4251_old_Oprod_Ocase,axiom,
% 9.49/5.28      ! [F: nat > nat > product_prod_nat_nat > $o,X1: nat,X23: nat] :
% 9.49/5.28        ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ X1 @ X23 ) )
% 9.49/5.28        = ( F @ X1 @ X23 ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4252_old_Oprod_Ocase,axiom,
% 9.49/5.28      ! [F: int > int > product_prod_int_int,X1: int,X23: int] :
% 9.49/5.28        ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ X1 @ X23 ) )
% 9.49/5.28        = ( F @ X1 @ X23 ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4253_old_Oprod_Ocase,axiom,
% 9.49/5.28      ! [F: int > int > int,X1: int,X23: int] :
% 9.49/5.28        ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ X1 @ X23 ) )
% 9.49/5.28        = ( F @ X1 @ X23 ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4254_mod__mod__cancel,axiom,
% 9.49/5.28      ! [C: code_integer,B: code_integer,A: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ C @ B )
% 9.49/5.28       => ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C )
% 9.49/5.28          = ( modulo364778990260209775nteger @ A @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4255_mod__mod__cancel,axiom,
% 9.49/5.28      ! [C: nat,B: nat,A: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ C @ B )
% 9.49/5.28       => ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ C )
% 9.49/5.28          = ( modulo_modulo_nat @ A @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4256_mod__mod__cancel,axiom,
% 9.49/5.28      ! [C: int,B: int,A: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ C @ B )
% 9.49/5.28       => ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ C )
% 9.49/5.28          = ( modulo_modulo_int @ A @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4257_dvd__mod,axiom,
% 9.49/5.28      ! [K: code_integer,M: code_integer,N: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ K @ M )
% 9.49/5.28       => ( ( dvd_dvd_Code_integer @ K @ N )
% 9.49/5.28         => ( dvd_dvd_Code_integer @ K @ ( modulo364778990260209775nteger @ M @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4258_dvd__mod,axiom,
% 9.49/5.28      ! [K: nat,M: nat,N: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ K @ M )
% 9.49/5.28       => ( ( dvd_dvd_nat @ K @ N )
% 9.49/5.28         => ( dvd_dvd_nat @ K @ ( modulo_modulo_nat @ M @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4259_dvd__mod,axiom,
% 9.49/5.28      ! [K: int,M: int,N: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ K @ M )
% 9.49/5.28       => ( ( dvd_dvd_int @ K @ N )
% 9.49/5.28         => ( dvd_dvd_int @ K @ ( modulo_modulo_int @ M @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4260_dvd__diff__nat,axiom,
% 9.49/5.28      ! [K: nat,M: nat,N: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ K @ M )
% 9.49/5.28       => ( ( dvd_dvd_nat @ K @ N )
% 9.49/5.28         => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4261_zdvd__zdiffD,axiom,
% 9.49/5.28      ! [K: int,M: int,N: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ K @ ( minus_minus_int @ M @ N ) )
% 9.49/5.28       => ( ( dvd_dvd_int @ K @ N )
% 9.49/5.28         => ( dvd_dvd_int @ K @ M ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4262_dvd__pos__nat,axiom,
% 9.49/5.28      ! [N: nat,M: nat] :
% 9.49/5.28        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.28       => ( ( dvd_dvd_nat @ M @ N )
% 9.49/5.28         => ( ord_less_nat @ zero_zero_nat @ M ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4263_bezout__lemma__nat,axiom,
% 9.49/5.28      ! [D2: nat,A: nat,B: nat,X: nat,Y2: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ D2 @ A )
% 9.49/5.28       => ( ( dvd_dvd_nat @ D2 @ B )
% 9.49/5.28         => ( ( ( ( times_times_nat @ A @ X )
% 9.49/5.28                = ( plus_plus_nat @ ( times_times_nat @ B @ Y2 ) @ D2 ) )
% 9.49/5.28              | ( ( times_times_nat @ B @ X )
% 9.49/5.28                = ( plus_plus_nat @ ( times_times_nat @ A @ Y2 ) @ D2 ) ) )
% 9.49/5.28           => ? [X3: nat,Y3: nat] :
% 9.49/5.28                ( ( dvd_dvd_nat @ D2 @ A )
% 9.49/5.28                & ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ A @ B ) )
% 9.49/5.28                & ( ( ( times_times_nat @ A @ X3 )
% 9.49/5.28                    = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ Y3 ) @ D2 ) )
% 9.49/5.28                  | ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ X3 )
% 9.49/5.28                    = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D2 ) ) ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4264_bezout__add__nat,axiom,
% 9.49/5.28      ! [A: nat,B: nat] :
% 9.49/5.28      ? [D3: nat,X3: nat,Y3: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ D3 @ A )
% 9.49/5.28        & ( dvd_dvd_nat @ D3 @ B )
% 9.49/5.28        & ( ( ( times_times_nat @ A @ X3 )
% 9.49/5.28            = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D3 ) )
% 9.49/5.28          | ( ( times_times_nat @ B @ X3 )
% 9.49/5.28            = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D3 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4265_bezout1__nat,axiom,
% 9.49/5.28      ! [A: nat,B: nat] :
% 9.49/5.28      ? [D3: nat,X3: nat,Y3: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ D3 @ A )
% 9.49/5.28        & ( dvd_dvd_nat @ D3 @ B )
% 9.49/5.28        & ( ( ( minus_minus_nat @ ( times_times_nat @ A @ X3 ) @ ( times_times_nat @ B @ Y3 ) )
% 9.49/5.28            = D3 )
% 9.49/5.28          | ( ( minus_minus_nat @ ( times_times_nat @ B @ X3 ) @ ( times_times_nat @ A @ Y3 ) )
% 9.49/5.28            = D3 ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4266_cond__case__prod__eta,axiom,
% 9.49/5.28      ! [F: nat > nat > nat,G: product_prod_nat_nat > nat] :
% 9.49/5.28        ( ! [X3: nat,Y3: nat] :
% 9.49/5.28            ( ( F @ X3 @ Y3 )
% 9.49/5.28            = ( G @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) )
% 9.49/5.28       => ( ( produc6842872674320459806at_nat @ F )
% 9.49/5.28          = G ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4267_cond__case__prod__eta,axiom,
% 9.49/5.28      ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,G: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 9.49/5.28        ( ! [X3: nat,Y3: nat] :
% 9.49/5.28            ( ( F @ X3 @ Y3 )
% 9.49/5.28            = ( G @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) )
% 9.49/5.28       => ( ( produc27273713700761075at_nat @ F )
% 9.49/5.28          = G ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4268_cond__case__prod__eta,axiom,
% 9.49/5.28      ! [F: nat > nat > product_prod_nat_nat > $o,G: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 9.49/5.28        ( ! [X3: nat,Y3: nat] :
% 9.49/5.28            ( ( F @ X3 @ Y3 )
% 9.49/5.28            = ( G @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) )
% 9.49/5.28       => ( ( produc8739625826339149834_nat_o @ F )
% 9.49/5.28          = G ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4269_cond__case__prod__eta,axiom,
% 9.49/5.28      ! [F: int > int > product_prod_int_int,G: product_prod_int_int > product_prod_int_int] :
% 9.49/5.28        ( ! [X3: int,Y3: int] :
% 9.49/5.28            ( ( F @ X3 @ Y3 )
% 9.49/5.28            = ( G @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 9.49/5.28       => ( ( produc4245557441103728435nt_int @ F )
% 9.49/5.28          = G ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4270_cond__case__prod__eta,axiom,
% 9.49/5.28      ! [F: int > int > int,G: product_prod_int_int > int] :
% 9.49/5.28        ( ! [X3: int,Y3: int] :
% 9.49/5.28            ( ( F @ X3 @ Y3 )
% 9.49/5.28            = ( G @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 9.49/5.28       => ( ( produc8211389475949308722nt_int @ F )
% 9.49/5.28          = G ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4271_case__prod__eta,axiom,
% 9.49/5.28      ! [F: product_prod_nat_nat > nat] :
% 9.49/5.28        ( ( produc6842872674320459806at_nat
% 9.49/5.28          @ ^ [X2: nat,Y: nat] : ( F @ ( product_Pair_nat_nat @ X2 @ Y ) ) )
% 9.49/5.28        = F ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4272_case__prod__eta,axiom,
% 9.49/5.28      ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 9.49/5.28        ( ( produc27273713700761075at_nat
% 9.49/5.28          @ ^ [X2: nat,Y: nat] : ( F @ ( product_Pair_nat_nat @ X2 @ Y ) ) )
% 9.49/5.28        = F ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4273_case__prod__eta,axiom,
% 9.49/5.28      ! [F: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 9.49/5.28        ( ( produc8739625826339149834_nat_o
% 9.49/5.28          @ ^ [X2: nat,Y: nat] : ( F @ ( product_Pair_nat_nat @ X2 @ Y ) ) )
% 9.49/5.28        = F ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4274_case__prod__eta,axiom,
% 9.49/5.28      ! [F: product_prod_int_int > product_prod_int_int] :
% 9.49/5.28        ( ( produc4245557441103728435nt_int
% 9.49/5.28          @ ^ [X2: int,Y: int] : ( F @ ( product_Pair_int_int @ X2 @ Y ) ) )
% 9.49/5.28        = F ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4275_case__prod__eta,axiom,
% 9.49/5.28      ! [F: product_prod_int_int > int] :
% 9.49/5.28        ( ( produc8211389475949308722nt_int
% 9.49/5.28          @ ^ [X2: int,Y: int] : ( F @ ( product_Pair_int_int @ X2 @ Y ) ) )
% 9.49/5.28        = F ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4276_case__prodE2,axiom,
% 9.49/5.28      ! [Q: nat > $o,P: nat > nat > nat,Z: product_prod_nat_nat] :
% 9.49/5.28        ( ( Q @ ( produc6842872674320459806at_nat @ P @ Z ) )
% 9.49/5.28       => ~ ! [X3: nat,Y3: nat] :
% 9.49/5.28              ( ( Z
% 9.49/5.28                = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 9.49/5.28             => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4277_case__prodE2,axiom,
% 9.49/5.28      ! [Q: ( product_prod_nat_nat > product_prod_nat_nat ) > $o,P: nat > nat > product_prod_nat_nat > product_prod_nat_nat,Z: product_prod_nat_nat] :
% 9.49/5.28        ( ( Q @ ( produc27273713700761075at_nat @ P @ Z ) )
% 9.49/5.28       => ~ ! [X3: nat,Y3: nat] :
% 9.49/5.28              ( ( Z
% 9.49/5.28                = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 9.49/5.28             => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4278_case__prodE2,axiom,
% 9.49/5.28      ! [Q: ( product_prod_nat_nat > $o ) > $o,P: nat > nat > product_prod_nat_nat > $o,Z: product_prod_nat_nat] :
% 9.49/5.28        ( ( Q @ ( produc8739625826339149834_nat_o @ P @ Z ) )
% 9.49/5.28       => ~ ! [X3: nat,Y3: nat] :
% 9.49/5.28              ( ( Z
% 9.49/5.28                = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 9.49/5.28             => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4279_case__prodE2,axiom,
% 9.49/5.28      ! [Q: product_prod_int_int > $o,P: int > int > product_prod_int_int,Z: product_prod_int_int] :
% 9.49/5.28        ( ( Q @ ( produc4245557441103728435nt_int @ P @ Z ) )
% 9.49/5.28       => ~ ! [X3: int,Y3: int] :
% 9.49/5.28              ( ( Z
% 9.49/5.28                = ( product_Pair_int_int @ X3 @ Y3 ) )
% 9.49/5.28             => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4280_case__prodE2,axiom,
% 9.49/5.28      ! [Q: int > $o,P: int > int > int,Z: product_prod_int_int] :
% 9.49/5.28        ( ( Q @ ( produc8211389475949308722nt_int @ P @ Z ) )
% 9.49/5.28       => ~ ! [X3: int,Y3: int] :
% 9.49/5.28              ( ( Z
% 9.49/5.28                = ( product_Pair_int_int @ X3 @ Y3 ) )
% 9.49/5.28             => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4281_concat__bit__assoc,axiom,
% 9.49/5.28      ! [N: nat,K: int,M: nat,L2: int,R: int] :
% 9.49/5.28        ( ( bit_concat_bit @ N @ K @ ( bit_concat_bit @ M @ L2 @ R ) )
% 9.49/5.28        = ( bit_concat_bit @ ( plus_plus_nat @ M @ N ) @ ( bit_concat_bit @ N @ K @ L2 ) @ R ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4282_not__is__unit__0,axiom,
% 9.49/5.28      ~ ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4283_not__is__unit__0,axiom,
% 9.49/5.28      ~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4284_not__is__unit__0,axiom,
% 9.49/5.28      ~ ( dvd_dvd_int @ zero_zero_int @ one_one_int ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4285_pinf_I9_J,axiom,
% 9.49/5.28      ! [D2: code_integer,S3: code_integer] :
% 9.49/5.28      ? [Z3: code_integer] :
% 9.49/5.28      ! [X5: code_integer] :
% 9.49/5.28        ( ( ord_le6747313008572928689nteger @ Z3 @ X5 )
% 9.49/5.28       => ( ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X5 @ S3 ) )
% 9.49/5.28          = ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X5 @ S3 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4286_pinf_I9_J,axiom,
% 9.49/5.28      ! [D2: real,S3: real] :
% 9.49/5.28      ? [Z3: real] :
% 9.49/5.28      ! [X5: real] :
% 9.49/5.28        ( ( ord_less_real @ Z3 @ X5 )
% 9.49/5.28       => ( ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X5 @ S3 ) )
% 9.49/5.28          = ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X5 @ S3 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4287_pinf_I9_J,axiom,
% 9.49/5.28      ! [D2: rat,S3: rat] :
% 9.49/5.28      ? [Z3: rat] :
% 9.49/5.28      ! [X5: rat] :
% 9.49/5.28        ( ( ord_less_rat @ Z3 @ X5 )
% 9.49/5.28       => ( ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X5 @ S3 ) )
% 9.49/5.28          = ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X5 @ S3 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4288_pinf_I9_J,axiom,
% 9.49/5.28      ! [D2: nat,S3: nat] :
% 9.49/5.28      ? [Z3: nat] :
% 9.49/5.28      ! [X5: nat] :
% 9.49/5.28        ( ( ord_less_nat @ Z3 @ X5 )
% 9.49/5.28       => ( ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X5 @ S3 ) )
% 9.49/5.28          = ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X5 @ S3 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4289_pinf_I9_J,axiom,
% 9.49/5.28      ! [D2: int,S3: int] :
% 9.49/5.28      ? [Z3: int] :
% 9.49/5.28      ! [X5: int] :
% 9.49/5.28        ( ( ord_less_int @ Z3 @ X5 )
% 9.49/5.28       => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ S3 ) )
% 9.49/5.28          = ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ S3 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4290_pinf_I10_J,axiom,
% 9.49/5.28      ! [D2: code_integer,S3: code_integer] :
% 9.49/5.28      ? [Z3: code_integer] :
% 9.49/5.28      ! [X5: code_integer] :
% 9.49/5.28        ( ( ord_le6747313008572928689nteger @ Z3 @ X5 )
% 9.49/5.28       => ( ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X5 @ S3 ) ) )
% 9.49/5.28          = ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X5 @ S3 ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4291_pinf_I10_J,axiom,
% 9.49/5.28      ! [D2: real,S3: real] :
% 9.49/5.28      ? [Z3: real] :
% 9.49/5.28      ! [X5: real] :
% 9.49/5.28        ( ( ord_less_real @ Z3 @ X5 )
% 9.49/5.28       => ( ( ~ ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X5 @ S3 ) ) )
% 9.49/5.28          = ( ~ ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X5 @ S3 ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4292_pinf_I10_J,axiom,
% 9.49/5.28      ! [D2: rat,S3: rat] :
% 9.49/5.28      ? [Z3: rat] :
% 9.49/5.28      ! [X5: rat] :
% 9.49/5.28        ( ( ord_less_rat @ Z3 @ X5 )
% 9.49/5.28       => ( ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X5 @ S3 ) ) )
% 9.49/5.28          = ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X5 @ S3 ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4293_pinf_I10_J,axiom,
% 9.49/5.28      ! [D2: nat,S3: nat] :
% 9.49/5.28      ? [Z3: nat] :
% 9.49/5.28      ! [X5: nat] :
% 9.49/5.28        ( ( ord_less_nat @ Z3 @ X5 )
% 9.49/5.28       => ( ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X5 @ S3 ) ) )
% 9.49/5.28          = ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X5 @ S3 ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4294_pinf_I10_J,axiom,
% 9.49/5.28      ! [D2: int,S3: int] :
% 9.49/5.28      ? [Z3: int] :
% 9.49/5.28      ! [X5: int] :
% 9.49/5.28        ( ( ord_less_int @ Z3 @ X5 )
% 9.49/5.28       => ( ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ S3 ) ) )
% 9.49/5.28          = ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ S3 ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4295_minf_I9_J,axiom,
% 9.49/5.28      ! [D2: code_integer,S3: code_integer] :
% 9.49/5.28      ? [Z3: code_integer] :
% 9.49/5.28      ! [X5: code_integer] :
% 9.49/5.28        ( ( ord_le6747313008572928689nteger @ X5 @ Z3 )
% 9.49/5.28       => ( ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X5 @ S3 ) )
% 9.49/5.28          = ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X5 @ S3 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4296_minf_I9_J,axiom,
% 9.49/5.28      ! [D2: real,S3: real] :
% 9.49/5.28      ? [Z3: real] :
% 9.49/5.28      ! [X5: real] :
% 9.49/5.28        ( ( ord_less_real @ X5 @ Z3 )
% 9.49/5.28       => ( ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X5 @ S3 ) )
% 9.49/5.28          = ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X5 @ S3 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4297_minf_I9_J,axiom,
% 9.49/5.28      ! [D2: rat,S3: rat] :
% 9.49/5.28      ? [Z3: rat] :
% 9.49/5.28      ! [X5: rat] :
% 9.49/5.28        ( ( ord_less_rat @ X5 @ Z3 )
% 9.49/5.28       => ( ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X5 @ S3 ) )
% 9.49/5.28          = ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X5 @ S3 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4298_minf_I9_J,axiom,
% 9.49/5.28      ! [D2: nat,S3: nat] :
% 9.49/5.28      ? [Z3: nat] :
% 9.49/5.28      ! [X5: nat] :
% 9.49/5.28        ( ( ord_less_nat @ X5 @ Z3 )
% 9.49/5.28       => ( ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X5 @ S3 ) )
% 9.49/5.28          = ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X5 @ S3 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4299_minf_I9_J,axiom,
% 9.49/5.28      ! [D2: int,S3: int] :
% 9.49/5.28      ? [Z3: int] :
% 9.49/5.28      ! [X5: int] :
% 9.49/5.28        ( ( ord_less_int @ X5 @ Z3 )
% 9.49/5.28       => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ S3 ) )
% 9.49/5.28          = ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ S3 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4300_minf_I10_J,axiom,
% 9.49/5.28      ! [D2: code_integer,S3: code_integer] :
% 9.49/5.28      ? [Z3: code_integer] :
% 9.49/5.28      ! [X5: code_integer] :
% 9.49/5.28        ( ( ord_le6747313008572928689nteger @ X5 @ Z3 )
% 9.49/5.28       => ( ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X5 @ S3 ) ) )
% 9.49/5.28          = ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X5 @ S3 ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4301_minf_I10_J,axiom,
% 9.49/5.28      ! [D2: real,S3: real] :
% 9.49/5.28      ? [Z3: real] :
% 9.49/5.28      ! [X5: real] :
% 9.49/5.28        ( ( ord_less_real @ X5 @ Z3 )
% 9.49/5.28       => ( ( ~ ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X5 @ S3 ) ) )
% 9.49/5.28          = ( ~ ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X5 @ S3 ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4302_minf_I10_J,axiom,
% 9.49/5.28      ! [D2: rat,S3: rat] :
% 9.49/5.28      ? [Z3: rat] :
% 9.49/5.28      ! [X5: rat] :
% 9.49/5.28        ( ( ord_less_rat @ X5 @ Z3 )
% 9.49/5.28       => ( ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X5 @ S3 ) ) )
% 9.49/5.28          = ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X5 @ S3 ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4303_minf_I10_J,axiom,
% 9.49/5.28      ! [D2: nat,S3: nat] :
% 9.49/5.28      ? [Z3: nat] :
% 9.49/5.28      ! [X5: nat] :
% 9.49/5.28        ( ( ord_less_nat @ X5 @ Z3 )
% 9.49/5.28       => ( ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X5 @ S3 ) ) )
% 9.49/5.28          = ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X5 @ S3 ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4304_minf_I10_J,axiom,
% 9.49/5.28      ! [D2: int,S3: int] :
% 9.49/5.28      ? [Z3: int] :
% 9.49/5.28      ! [X5: int] :
% 9.49/5.28        ( ( ord_less_int @ X5 @ Z3 )
% 9.49/5.28       => ( ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ S3 ) ) )
% 9.49/5.28          = ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ S3 ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4305_dvd__div__eq__0__iff,axiom,
% 9.49/5.28      ! [B: code_integer,A: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ B @ A )
% 9.49/5.28       => ( ( ( divide6298287555418463151nteger @ A @ B )
% 9.49/5.28            = zero_z3403309356797280102nteger )
% 9.49/5.28          = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4306_dvd__div__eq__0__iff,axiom,
% 9.49/5.28      ! [B: complex,A: complex] :
% 9.49/5.28        ( ( dvd_dvd_complex @ B @ A )
% 9.49/5.28       => ( ( ( divide1717551699836669952omplex @ A @ B )
% 9.49/5.28            = zero_zero_complex )
% 9.49/5.28          = ( A = zero_zero_complex ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4307_dvd__div__eq__0__iff,axiom,
% 9.49/5.28      ! [B: real,A: real] :
% 9.49/5.28        ( ( dvd_dvd_real @ B @ A )
% 9.49/5.28       => ( ( ( divide_divide_real @ A @ B )
% 9.49/5.28            = zero_zero_real )
% 9.49/5.28          = ( A = zero_zero_real ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4308_dvd__div__eq__0__iff,axiom,
% 9.49/5.28      ! [B: rat,A: rat] :
% 9.49/5.28        ( ( dvd_dvd_rat @ B @ A )
% 9.49/5.28       => ( ( ( divide_divide_rat @ A @ B )
% 9.49/5.28            = zero_zero_rat )
% 9.49/5.28          = ( A = zero_zero_rat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4309_dvd__div__eq__0__iff,axiom,
% 9.49/5.28      ! [B: nat,A: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ B @ A )
% 9.49/5.28       => ( ( ( divide_divide_nat @ A @ B )
% 9.49/5.28            = zero_zero_nat )
% 9.49/5.28          = ( A = zero_zero_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4310_dvd__div__eq__0__iff,axiom,
% 9.49/5.28      ! [B: int,A: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ B @ A )
% 9.49/5.28       => ( ( ( divide_divide_int @ A @ B )
% 9.49/5.28            = zero_zero_int )
% 9.49/5.28          = ( A = zero_zero_int ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4311_unit__mult__right__cancel,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.49/5.28       => ( ( ( times_3573771949741848930nteger @ B @ A )
% 9.49/5.28            = ( times_3573771949741848930nteger @ C @ A ) )
% 9.49/5.28          = ( B = C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4312_unit__mult__right__cancel,axiom,
% 9.49/5.28      ! [A: nat,B: nat,C: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.49/5.28       => ( ( ( times_times_nat @ B @ A )
% 9.49/5.28            = ( times_times_nat @ C @ A ) )
% 9.49/5.28          = ( B = C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4313_unit__mult__right__cancel,axiom,
% 9.49/5.28      ! [A: int,B: int,C: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ A @ one_one_int )
% 9.49/5.28       => ( ( ( times_times_int @ B @ A )
% 9.49/5.28            = ( times_times_int @ C @ A ) )
% 9.49/5.28          = ( B = C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4314_unit__mult__left__cancel,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.49/5.28       => ( ( ( times_3573771949741848930nteger @ A @ B )
% 9.49/5.28            = ( times_3573771949741848930nteger @ A @ C ) )
% 9.49/5.28          = ( B = C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4315_unit__mult__left__cancel,axiom,
% 9.49/5.28      ! [A: nat,B: nat,C: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.49/5.28       => ( ( ( times_times_nat @ A @ B )
% 9.49/5.28            = ( times_times_nat @ A @ C ) )
% 9.49/5.28          = ( B = C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4316_unit__mult__left__cancel,axiom,
% 9.49/5.28      ! [A: int,B: int,C: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ A @ one_one_int )
% 9.49/5.28       => ( ( ( times_times_int @ A @ B )
% 9.49/5.28            = ( times_times_int @ A @ C ) )
% 9.49/5.28          = ( B = C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4317_mult__unit__dvd__iff_H,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.49/5.28       => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 9.49/5.28          = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4318_mult__unit__dvd__iff_H,axiom,
% 9.49/5.28      ! [A: nat,B: nat,C: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.49/5.28       => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 9.49/5.28          = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4319_mult__unit__dvd__iff_H,axiom,
% 9.49/5.28      ! [A: int,B: int,C: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ A @ one_one_int )
% 9.49/5.28       => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 9.49/5.28          = ( dvd_dvd_int @ B @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4320_dvd__mult__unit__iff_H,axiom,
% 9.49/5.28      ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.49/5.28       => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 9.49/5.28          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4321_dvd__mult__unit__iff_H,axiom,
% 9.49/5.28      ! [B: nat,A: nat,C: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.49/5.28       => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 9.49/5.28          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4322_dvd__mult__unit__iff_H,axiom,
% 9.49/5.28      ! [B: int,A: int,C: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ B @ one_one_int )
% 9.49/5.28       => ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 9.49/5.28          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4323_mult__unit__dvd__iff,axiom,
% 9.49/5.28      ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.49/5.28       => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 9.49/5.28          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4324_mult__unit__dvd__iff,axiom,
% 9.49/5.28      ! [B: nat,A: nat,C: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.49/5.28       => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 9.49/5.28          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4325_mult__unit__dvd__iff,axiom,
% 9.49/5.28      ! [B: int,A: int,C: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ B @ one_one_int )
% 9.49/5.28       => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 9.49/5.28          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4326_dvd__mult__unit__iff,axiom,
% 9.49/5.28      ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.49/5.28       => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) )
% 9.49/5.28          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4327_dvd__mult__unit__iff,axiom,
% 9.49/5.28      ! [B: nat,A: nat,C: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.49/5.28       => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) )
% 9.49/5.28          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4328_dvd__mult__unit__iff,axiom,
% 9.49/5.28      ! [B: int,A: int,C: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ B @ one_one_int )
% 9.49/5.28       => ( ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) )
% 9.49/5.28          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4329_is__unit__mult__iff,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer )
% 9.49/5.28        = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.49/5.28          & ( dvd_dvd_Code_integer @ B @ one_one_Code_integer ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4330_is__unit__mult__iff,axiom,
% 9.49/5.28      ! [A: nat,B: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat )
% 9.49/5.28        = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.49/5.28          & ( dvd_dvd_nat @ B @ one_one_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4331_is__unit__mult__iff,axiom,
% 9.49/5.28      ! [A: int,B: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int )
% 9.49/5.28        = ( ( dvd_dvd_int @ A @ one_one_int )
% 9.49/5.28          & ( dvd_dvd_int @ B @ one_one_int ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4332_dvd__div__mult,axiom,
% 9.49/5.28      ! [C: code_integer,B: code_integer,A: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ C @ B )
% 9.49/5.28       => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ C ) @ A )
% 9.49/5.28          = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ B @ A ) @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4333_dvd__div__mult,axiom,
% 9.49/5.28      ! [C: nat,B: nat,A: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ C @ B )
% 9.49/5.28       => ( ( times_times_nat @ ( divide_divide_nat @ B @ C ) @ A )
% 9.49/5.28          = ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4334_dvd__div__mult,axiom,
% 9.49/5.28      ! [C: int,B: int,A: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ C @ B )
% 9.49/5.28       => ( ( times_times_int @ ( divide_divide_int @ B @ C ) @ A )
% 9.49/5.28          = ( divide_divide_int @ ( times_times_int @ B @ A ) @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4335_div__mult__swap,axiom,
% 9.49/5.28      ! [C: code_integer,B: code_integer,A: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ C @ B )
% 9.49/5.28       => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 9.49/5.28          = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4336_div__mult__swap,axiom,
% 9.49/5.28      ! [C: nat,B: nat,A: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ C @ B )
% 9.49/5.28       => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 9.49/5.28          = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4337_div__mult__swap,axiom,
% 9.49/5.28      ! [C: int,B: int,A: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ C @ B )
% 9.49/5.28       => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 9.49/5.28          = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4338_div__div__eq__right,axiom,
% 9.49/5.28      ! [C: code_integer,B: code_integer,A: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ C @ B )
% 9.49/5.28       => ( ( dvd_dvd_Code_integer @ B @ A )
% 9.49/5.28         => ( ( divide6298287555418463151nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 9.49/5.28            = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4339_div__div__eq__right,axiom,
% 9.49/5.28      ! [C: nat,B: nat,A: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ C @ B )
% 9.49/5.28       => ( ( dvd_dvd_nat @ B @ A )
% 9.49/5.28         => ( ( divide_divide_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 9.49/5.28            = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4340_div__div__eq__right,axiom,
% 9.49/5.28      ! [C: int,B: int,A: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ C @ B )
% 9.49/5.28       => ( ( dvd_dvd_int @ B @ A )
% 9.49/5.28         => ( ( divide_divide_int @ A @ ( divide_divide_int @ B @ C ) )
% 9.49/5.28            = ( times_times_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4341_dvd__div__mult2__eq,axiom,
% 9.49/5.28      ! [B: code_integer,C: code_integer,A: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ C ) @ A )
% 9.49/5.28       => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 9.49/5.28          = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4342_dvd__div__mult2__eq,axiom,
% 9.49/5.28      ! [B: nat,C: nat,A: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ ( times_times_nat @ B @ C ) @ A )
% 9.49/5.28       => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 9.49/5.28          = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4343_dvd__div__mult2__eq,axiom,
% 9.49/5.28      ! [B: int,C: int,A: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ ( times_times_int @ B @ C ) @ A )
% 9.49/5.28       => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 9.49/5.28          = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4344_dvd__mult__imp__div,axiom,
% 9.49/5.28      ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B )
% 9.49/5.28       => ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4345_dvd__mult__imp__div,axiom,
% 9.49/5.28      ! [A: nat,C: nat,B: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B )
% 9.49/5.28       => ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4346_dvd__mult__imp__div,axiom,
% 9.49/5.28      ! [A: int,C: int,B: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B )
% 9.49/5.28       => ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4347_div__mult__div__if__dvd,axiom,
% 9.49/5.28      ! [B: code_integer,A: code_integer,D2: code_integer,C: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ B @ A )
% 9.49/5.28       => ( ( dvd_dvd_Code_integer @ D2 @ C )
% 9.49/5.28         => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ ( divide6298287555418463151nteger @ C @ D2 ) )
% 9.49/5.28            = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4348_div__mult__div__if__dvd,axiom,
% 9.49/5.28      ! [B: nat,A: nat,D2: nat,C: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ B @ A )
% 9.49/5.28       => ( ( dvd_dvd_nat @ D2 @ C )
% 9.49/5.28         => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ ( divide_divide_nat @ C @ D2 ) )
% 9.49/5.28            = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4349_div__mult__div__if__dvd,axiom,
% 9.49/5.28      ! [B: int,A: int,D2: int,C: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ B @ A )
% 9.49/5.28       => ( ( dvd_dvd_int @ D2 @ C )
% 9.49/5.28         => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ C @ D2 ) )
% 9.49/5.28            = ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4350_dvd__div__unit__iff,axiom,
% 9.49/5.28      ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.49/5.28       => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ C @ B ) )
% 9.49/5.28          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4351_dvd__div__unit__iff,axiom,
% 9.49/5.28      ! [B: nat,A: nat,C: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.49/5.28       => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ C @ B ) )
% 9.49/5.28          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4352_dvd__div__unit__iff,axiom,
% 9.49/5.28      ! [B: int,A: int,C: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ B @ one_one_int )
% 9.49/5.28       => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ C @ B ) )
% 9.49/5.28          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4353_div__unit__dvd__iff,axiom,
% 9.49/5.28      ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.49/5.28       => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 9.49/5.28          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4354_div__unit__dvd__iff,axiom,
% 9.49/5.28      ! [B: nat,A: nat,C: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.49/5.28       => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 9.49/5.28          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4355_div__unit__dvd__iff,axiom,
% 9.49/5.28      ! [B: int,A: int,C: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ B @ one_one_int )
% 9.49/5.28       => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 9.49/5.28          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4356_unit__div__cancel,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.49/5.28       => ( ( ( divide6298287555418463151nteger @ B @ A )
% 9.49/5.28            = ( divide6298287555418463151nteger @ C @ A ) )
% 9.49/5.28          = ( B = C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4357_unit__div__cancel,axiom,
% 9.49/5.28      ! [A: nat,B: nat,C: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.49/5.28       => ( ( ( divide_divide_nat @ B @ A )
% 9.49/5.28            = ( divide_divide_nat @ C @ A ) )
% 9.49/5.28          = ( B = C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4358_unit__div__cancel,axiom,
% 9.49/5.28      ! [A: int,B: int,C: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ A @ one_one_int )
% 9.49/5.28       => ( ( ( divide_divide_int @ B @ A )
% 9.49/5.28            = ( divide_divide_int @ C @ A ) )
% 9.49/5.28          = ( B = C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4359_div__plus__div__distrib__dvd__right,axiom,
% 9.49/5.28      ! [C: code_integer,B: code_integer,A: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ C @ B )
% 9.49/5.28       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 9.49/5.28          = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4360_div__plus__div__distrib__dvd__right,axiom,
% 9.49/5.28      ! [C: nat,B: nat,A: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ C @ B )
% 9.49/5.28       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 9.49/5.28          = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4361_div__plus__div__distrib__dvd__right,axiom,
% 9.49/5.28      ! [C: int,B: int,A: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ C @ B )
% 9.49/5.28       => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 9.49/5.28          = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4362_div__plus__div__distrib__dvd__left,axiom,
% 9.49/5.28      ! [C: code_integer,A: code_integer,B: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ C @ A )
% 9.49/5.28       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 9.49/5.28          = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4363_div__plus__div__distrib__dvd__left,axiom,
% 9.49/5.28      ! [C: nat,A: nat,B: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ C @ A )
% 9.49/5.28       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 9.49/5.28          = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4364_div__plus__div__distrib__dvd__left,axiom,
% 9.49/5.28      ! [C: int,A: int,B: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ C @ A )
% 9.49/5.28       => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 9.49/5.28          = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4365_div__power,axiom,
% 9.49/5.28      ! [B: code_integer,A: code_integer,N: nat] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ B @ A )
% 9.49/5.28       => ( ( power_8256067586552552935nteger @ ( divide6298287555418463151nteger @ A @ B ) @ N )
% 9.49/5.28          = ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4366_div__power,axiom,
% 9.49/5.28      ! [B: nat,A: nat,N: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ B @ A )
% 9.49/5.28       => ( ( power_power_nat @ ( divide_divide_nat @ A @ B ) @ N )
% 9.49/5.28          = ( divide_divide_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4367_div__power,axiom,
% 9.49/5.28      ! [B: int,A: int,N: nat] :
% 9.49/5.28        ( ( dvd_dvd_int @ B @ A )
% 9.49/5.28       => ( ( power_power_int @ ( divide_divide_int @ A @ B ) @ N )
% 9.49/5.28          = ( divide_divide_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4368_dvd__power__le,axiom,
% 9.49/5.28      ! [X: code_integer,Y2: code_integer,N: nat,M: nat] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ X @ Y2 )
% 9.49/5.28       => ( ( ord_less_eq_nat @ N @ M )
% 9.49/5.28         => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ N ) @ ( power_8256067586552552935nteger @ Y2 @ M ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4369_dvd__power__le,axiom,
% 9.49/5.28      ! [X: nat,Y2: nat,N: nat,M: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ X @ Y2 )
% 9.49/5.28       => ( ( ord_less_eq_nat @ N @ M )
% 9.49/5.28         => ( dvd_dvd_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y2 @ M ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4370_dvd__power__le,axiom,
% 9.49/5.28      ! [X: real,Y2: real,N: nat,M: nat] :
% 9.49/5.28        ( ( dvd_dvd_real @ X @ Y2 )
% 9.49/5.28       => ( ( ord_less_eq_nat @ N @ M )
% 9.49/5.28         => ( dvd_dvd_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y2 @ M ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4371_dvd__power__le,axiom,
% 9.49/5.28      ! [X: int,Y2: int,N: nat,M: nat] :
% 9.49/5.28        ( ( dvd_dvd_int @ X @ Y2 )
% 9.49/5.28       => ( ( ord_less_eq_nat @ N @ M )
% 9.49/5.28         => ( dvd_dvd_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y2 @ M ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4372_dvd__power__le,axiom,
% 9.49/5.28      ! [X: complex,Y2: complex,N: nat,M: nat] :
% 9.49/5.28        ( ( dvd_dvd_complex @ X @ Y2 )
% 9.49/5.28       => ( ( ord_less_eq_nat @ N @ M )
% 9.49/5.28         => ( dvd_dvd_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y2 @ M ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4373_power__le__dvd,axiom,
% 9.49/5.28      ! [A: code_integer,N: nat,B: code_integer,M: nat] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ B )
% 9.49/5.28       => ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.28         => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4374_power__le__dvd,axiom,
% 9.49/5.28      ! [A: nat,N: nat,B: nat,M: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ B )
% 9.49/5.28       => ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.28         => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4375_power__le__dvd,axiom,
% 9.49/5.28      ! [A: real,N: nat,B: real,M: nat] :
% 9.49/5.28        ( ( dvd_dvd_real @ ( power_power_real @ A @ N ) @ B )
% 9.49/5.28       => ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.28         => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4376_power__le__dvd,axiom,
% 9.49/5.28      ! [A: int,N: nat,B: int,M: nat] :
% 9.49/5.28        ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ B )
% 9.49/5.28       => ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.28         => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4377_power__le__dvd,axiom,
% 9.49/5.28      ! [A: complex,N: nat,B: complex,M: nat] :
% 9.49/5.28        ( ( dvd_dvd_complex @ ( power_power_complex @ A @ N ) @ B )
% 9.49/5.28       => ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.28         => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4378_le__imp__power__dvd,axiom,
% 9.49/5.28      ! [M: nat,N: nat,A: code_integer] :
% 9.49/5.28        ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.28       => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4379_le__imp__power__dvd,axiom,
% 9.49/5.28      ! [M: nat,N: nat,A: nat] :
% 9.49/5.28        ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.28       => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4380_le__imp__power__dvd,axiom,
% 9.49/5.28      ! [M: nat,N: nat,A: real] :
% 9.49/5.28        ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.28       => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4381_le__imp__power__dvd,axiom,
% 9.49/5.28      ! [M: nat,N: nat,A: int] :
% 9.49/5.28        ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.28       => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4382_le__imp__power__dvd,axiom,
% 9.49/5.28      ! [M: nat,N: nat,A: complex] :
% 9.49/5.28        ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.28       => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4383_dvd__minus__mod,axiom,
% 9.49/5.28      ! [B: code_integer,A: code_integer] : ( dvd_dvd_Code_integer @ B @ ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4384_dvd__minus__mod,axiom,
% 9.49/5.28      ! [B: nat,A: nat] : ( dvd_dvd_nat @ B @ ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4385_dvd__minus__mod,axiom,
% 9.49/5.28      ! [B: int,A: int] : ( dvd_dvd_int @ B @ ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4386_mod__eq__dvd__iff,axiom,
% 9.49/5.28      ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.49/5.28        ( ( ( modulo364778990260209775nteger @ A @ C )
% 9.49/5.28          = ( modulo364778990260209775nteger @ B @ C ) )
% 9.49/5.28        = ( dvd_dvd_Code_integer @ C @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4387_mod__eq__dvd__iff,axiom,
% 9.49/5.28      ! [A: int,C: int,B: int] :
% 9.49/5.28        ( ( ( modulo_modulo_int @ A @ C )
% 9.49/5.28          = ( modulo_modulo_int @ B @ C ) )
% 9.49/5.28        = ( dvd_dvd_int @ C @ ( minus_minus_int @ A @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4388_bezout__add__strong__nat,axiom,
% 9.49/5.28      ! [A: nat,B: nat] :
% 9.49/5.28        ( ( A != zero_zero_nat )
% 9.49/5.28       => ? [D3: nat,X3: nat,Y3: nat] :
% 9.49/5.28            ( ( dvd_dvd_nat @ D3 @ A )
% 9.49/5.28            & ( dvd_dvd_nat @ D3 @ B )
% 9.49/5.28            & ( ( times_times_nat @ A @ X3 )
% 9.49/5.28              = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D3 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4389_nat__dvd__not__less,axiom,
% 9.49/5.28      ! [M: nat,N: nat] :
% 9.49/5.28        ( ( ord_less_nat @ zero_zero_nat @ M )
% 9.49/5.28       => ( ( ord_less_nat @ M @ N )
% 9.49/5.28         => ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4390_dvd__minus__self,axiom,
% 9.49/5.28      ! [M: nat,N: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) )
% 9.49/5.28        = ( ( ord_less_nat @ N @ M )
% 9.49/5.28          | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4391_dvd__diffD,axiom,
% 9.49/5.28      ! [K: nat,M: nat,N: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 9.49/5.28       => ( ( dvd_dvd_nat @ K @ N )
% 9.49/5.28         => ( ( ord_less_eq_nat @ N @ M )
% 9.49/5.28           => ( dvd_dvd_nat @ K @ M ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4392_dvd__diffD1,axiom,
% 9.49/5.28      ! [K: nat,M: nat,N: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 9.49/5.28       => ( ( dvd_dvd_nat @ K @ M )
% 9.49/5.28         => ( ( ord_less_eq_nat @ N @ M )
% 9.49/5.28           => ( dvd_dvd_nat @ K @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4393_less__eq__dvd__minus,axiom,
% 9.49/5.28      ! [M: nat,N: nat] :
% 9.49/5.28        ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.28       => ( ( dvd_dvd_nat @ M @ N )
% 9.49/5.28          = ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4394_dbl__def,axiom,
% 9.49/5.28      ( neg_numeral_dbl_real
% 9.49/5.28      = ( ^ [X2: real] : ( plus_plus_real @ X2 @ X2 ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4395_dbl__def,axiom,
% 9.49/5.28      ( neg_numeral_dbl_rat
% 9.49/5.28      = ( ^ [X2: rat] : ( plus_plus_rat @ X2 @ X2 ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4396_dbl__def,axiom,
% 9.49/5.28      ( neg_numeral_dbl_int
% 9.49/5.28      = ( ^ [X2: int] : ( plus_plus_int @ X2 @ X2 ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4397_dbl__def,axiom,
% 9.49/5.28      ( neg_nu7009210354673126013omplex
% 9.49/5.28      = ( ^ [X2: complex] : ( plus_plus_complex @ X2 @ X2 ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4398_finite__divisors__nat,axiom,
% 9.49/5.28      ! [M: nat] :
% 9.49/5.28        ( ( ord_less_nat @ zero_zero_nat @ M )
% 9.49/5.28       => ( finite_finite_nat
% 9.49/5.28          @ ( collect_nat
% 9.49/5.28            @ ^ [D: nat] : ( dvd_dvd_nat @ D @ M ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4399_div2__even__ext__nat,axiom,
% 9.49/5.28      ! [X: nat,Y2: nat] :
% 9.49/5.28        ( ( ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.28          = ( divide_divide_nat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.28       => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X )
% 9.49/5.28            = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y2 ) )
% 9.49/5.28         => ( X = Y2 ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4400_unit__dvdE,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.49/5.28       => ~ ( ( A != zero_z3403309356797280102nteger )
% 9.49/5.28           => ! [C2: code_integer] :
% 9.49/5.28                ( B
% 9.49/5.28               != ( times_3573771949741848930nteger @ A @ C2 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4401_unit__dvdE,axiom,
% 9.49/5.28      ! [A: nat,B: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.49/5.28       => ~ ( ( A != zero_zero_nat )
% 9.49/5.28           => ! [C2: nat] :
% 9.49/5.28                ( B
% 9.49/5.28               != ( times_times_nat @ A @ C2 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4402_unit__dvdE,axiom,
% 9.49/5.28      ! [A: int,B: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ A @ one_one_int )
% 9.49/5.28       => ~ ( ( A != zero_zero_int )
% 9.49/5.28           => ! [C2: int] :
% 9.49/5.28                ( B
% 9.49/5.28               != ( times_times_int @ A @ C2 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4403_unity__coeff__ex,axiom,
% 9.49/5.28      ! [P: code_integer > $o,L2: code_integer] :
% 9.49/5.28        ( ( ? [X2: code_integer] : ( P @ ( times_3573771949741848930nteger @ L2 @ X2 ) ) )
% 9.49/5.28        = ( ? [X2: code_integer] :
% 9.49/5.28              ( ( dvd_dvd_Code_integer @ L2 @ ( plus_p5714425477246183910nteger @ X2 @ zero_z3403309356797280102nteger ) )
% 9.49/5.28              & ( P @ X2 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4404_unity__coeff__ex,axiom,
% 9.49/5.28      ! [P: rat > $o,L2: rat] :
% 9.49/5.28        ( ( ? [X2: rat] : ( P @ ( times_times_rat @ L2 @ X2 ) ) )
% 9.49/5.28        = ( ? [X2: rat] :
% 9.49/5.28              ( ( dvd_dvd_rat @ L2 @ ( plus_plus_rat @ X2 @ zero_zero_rat ) )
% 9.49/5.28              & ( P @ X2 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4405_unity__coeff__ex,axiom,
% 9.49/5.28      ! [P: complex > $o,L2: complex] :
% 9.49/5.28        ( ( ? [X2: complex] : ( P @ ( times_times_complex @ L2 @ X2 ) ) )
% 9.49/5.28        = ( ? [X2: complex] :
% 9.49/5.28              ( ( dvd_dvd_complex @ L2 @ ( plus_plus_complex @ X2 @ zero_zero_complex ) )
% 9.49/5.28              & ( P @ X2 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4406_unity__coeff__ex,axiom,
% 9.49/5.28      ! [P: real > $o,L2: real] :
% 9.49/5.28        ( ( ? [X2: real] : ( P @ ( times_times_real @ L2 @ X2 ) ) )
% 9.49/5.28        = ( ? [X2: real] :
% 9.49/5.28              ( ( dvd_dvd_real @ L2 @ ( plus_plus_real @ X2 @ zero_zero_real ) )
% 9.49/5.28              & ( P @ X2 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4407_unity__coeff__ex,axiom,
% 9.49/5.28      ! [P: nat > $o,L2: nat] :
% 9.49/5.28        ( ( ? [X2: nat] : ( P @ ( times_times_nat @ L2 @ X2 ) ) )
% 9.49/5.28        = ( ? [X2: nat] :
% 9.49/5.28              ( ( dvd_dvd_nat @ L2 @ ( plus_plus_nat @ X2 @ zero_zero_nat ) )
% 9.49/5.28              & ( P @ X2 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4408_unity__coeff__ex,axiom,
% 9.49/5.28      ! [P: int > $o,L2: int] :
% 9.49/5.28        ( ( ? [X2: int] : ( P @ ( times_times_int @ L2 @ X2 ) ) )
% 9.49/5.28        = ( ? [X2: int] :
% 9.49/5.28              ( ( dvd_dvd_int @ L2 @ ( plus_plus_int @ X2 @ zero_zero_int ) )
% 9.49/5.28              & ( P @ X2 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4409_even__numeral,axiom,
% 9.49/5.28      ! [N: num] : ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4410_even__numeral,axiom,
% 9.49/5.28      ! [N: num] : ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4411_even__numeral,axiom,
% 9.49/5.28      ! [N: num] : ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4412_dvd__div__eq__mult,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.49/5.28        ( ( A != zero_z3403309356797280102nteger )
% 9.49/5.28       => ( ( dvd_dvd_Code_integer @ A @ B )
% 9.49/5.28         => ( ( ( divide6298287555418463151nteger @ B @ A )
% 9.49/5.28              = C )
% 9.49/5.28            = ( B
% 9.49/5.28              = ( times_3573771949741848930nteger @ C @ A ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4413_dvd__div__eq__mult,axiom,
% 9.49/5.28      ! [A: nat,B: nat,C: nat] :
% 9.49/5.28        ( ( A != zero_zero_nat )
% 9.49/5.28       => ( ( dvd_dvd_nat @ A @ B )
% 9.49/5.28         => ( ( ( divide_divide_nat @ B @ A )
% 9.49/5.28              = C )
% 9.49/5.28            = ( B
% 9.49/5.28              = ( times_times_nat @ C @ A ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4414_dvd__div__eq__mult,axiom,
% 9.49/5.28      ! [A: int,B: int,C: int] :
% 9.49/5.28        ( ( A != zero_zero_int )
% 9.49/5.28       => ( ( dvd_dvd_int @ A @ B )
% 9.49/5.28         => ( ( ( divide_divide_int @ B @ A )
% 9.49/5.28              = C )
% 9.49/5.28            = ( B
% 9.49/5.28              = ( times_times_int @ C @ A ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4415_div__dvd__iff__mult,axiom,
% 9.49/5.28      ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.49/5.28        ( ( B != zero_z3403309356797280102nteger )
% 9.49/5.28       => ( ( dvd_dvd_Code_integer @ B @ A )
% 9.49/5.28         => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 9.49/5.28            = ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4416_div__dvd__iff__mult,axiom,
% 9.49/5.28      ! [B: nat,A: nat,C: nat] :
% 9.49/5.28        ( ( B != zero_zero_nat )
% 9.49/5.28       => ( ( dvd_dvd_nat @ B @ A )
% 9.49/5.28         => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 9.49/5.28            = ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4417_div__dvd__iff__mult,axiom,
% 9.49/5.28      ! [B: int,A: int,C: int] :
% 9.49/5.28        ( ( B != zero_zero_int )
% 9.49/5.28       => ( ( dvd_dvd_int @ B @ A )
% 9.49/5.28         => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 9.49/5.28            = ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4418_dvd__div__iff__mult,axiom,
% 9.49/5.28      ! [C: code_integer,B: code_integer,A: code_integer] :
% 9.49/5.28        ( ( C != zero_z3403309356797280102nteger )
% 9.49/5.28       => ( ( dvd_dvd_Code_integer @ C @ B )
% 9.49/5.28         => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 9.49/5.28            = ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4419_dvd__div__iff__mult,axiom,
% 9.49/5.28      ! [C: nat,B: nat,A: nat] :
% 9.49/5.28        ( ( C != zero_zero_nat )
% 9.49/5.28       => ( ( dvd_dvd_nat @ C @ B )
% 9.49/5.28         => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 9.49/5.28            = ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4420_dvd__div__iff__mult,axiom,
% 9.49/5.28      ! [C: int,B: int,A: int] :
% 9.49/5.28        ( ( C != zero_zero_int )
% 9.49/5.28       => ( ( dvd_dvd_int @ C @ B )
% 9.49/5.28         => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) )
% 9.49/5.28            = ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4421_dvd__div__div__eq__mult,axiom,
% 9.49/5.28      ! [A: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 9.49/5.28        ( ( A != zero_z3403309356797280102nteger )
% 9.49/5.28       => ( ( C != zero_z3403309356797280102nteger )
% 9.49/5.28         => ( ( dvd_dvd_Code_integer @ A @ B )
% 9.49/5.28           => ( ( dvd_dvd_Code_integer @ C @ D2 )
% 9.49/5.28             => ( ( ( divide6298287555418463151nteger @ B @ A )
% 9.49/5.28                  = ( divide6298287555418463151nteger @ D2 @ C ) )
% 9.49/5.28                = ( ( times_3573771949741848930nteger @ B @ C )
% 9.49/5.28                  = ( times_3573771949741848930nteger @ A @ D2 ) ) ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4422_dvd__div__div__eq__mult,axiom,
% 9.49/5.28      ! [A: nat,C: nat,B: nat,D2: nat] :
% 9.49/5.28        ( ( A != zero_zero_nat )
% 9.49/5.28       => ( ( C != zero_zero_nat )
% 9.49/5.28         => ( ( dvd_dvd_nat @ A @ B )
% 9.49/5.28           => ( ( dvd_dvd_nat @ C @ D2 )
% 9.49/5.28             => ( ( ( divide_divide_nat @ B @ A )
% 9.49/5.28                  = ( divide_divide_nat @ D2 @ C ) )
% 9.49/5.28                = ( ( times_times_nat @ B @ C )
% 9.49/5.28                  = ( times_times_nat @ A @ D2 ) ) ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4423_dvd__div__div__eq__mult,axiom,
% 9.49/5.28      ! [A: int,C: int,B: int,D2: int] :
% 9.49/5.28        ( ( A != zero_zero_int )
% 9.49/5.28       => ( ( C != zero_zero_int )
% 9.49/5.28         => ( ( dvd_dvd_int @ A @ B )
% 9.49/5.28           => ( ( dvd_dvd_int @ C @ D2 )
% 9.49/5.28             => ( ( ( divide_divide_int @ B @ A )
% 9.49/5.28                  = ( divide_divide_int @ D2 @ C ) )
% 9.49/5.28                = ( ( times_times_int @ B @ C )
% 9.49/5.28                  = ( times_times_int @ A @ D2 ) ) ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4424_unit__div__eq__0__iff,axiom,
% 9.49/5.28      ! [B: code_integer,A: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.49/5.28       => ( ( ( divide6298287555418463151nteger @ A @ B )
% 9.49/5.28            = zero_z3403309356797280102nteger )
% 9.49/5.28          = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4425_unit__div__eq__0__iff,axiom,
% 9.49/5.28      ! [B: nat,A: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.49/5.28       => ( ( ( divide_divide_nat @ A @ B )
% 9.49/5.28            = zero_zero_nat )
% 9.49/5.28          = ( A = zero_zero_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4426_unit__div__eq__0__iff,axiom,
% 9.49/5.28      ! [B: int,A: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ B @ one_one_int )
% 9.49/5.28       => ( ( ( divide_divide_int @ A @ B )
% 9.49/5.28            = zero_zero_int )
% 9.49/5.28          = ( A = zero_zero_int ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4427_inf__period_I4_J,axiom,
% 9.49/5.28      ! [D2: code_integer,D4: code_integer,T: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ D2 @ D4 )
% 9.49/5.28       => ! [X5: code_integer,K4: code_integer] :
% 9.49/5.28            ( ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X5 @ T ) ) )
% 9.49/5.28            = ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X5 @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4428_inf__period_I4_J,axiom,
% 9.49/5.28      ! [D2: rat,D4: rat,T: rat] :
% 9.49/5.28        ( ( dvd_dvd_rat @ D2 @ D4 )
% 9.49/5.28       => ! [X5: rat,K4: rat] :
% 9.49/5.28            ( ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X5 @ T ) ) )
% 9.49/5.28            = ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4429_inf__period_I4_J,axiom,
% 9.49/5.28      ! [D2: complex,D4: complex,T: complex] :
% 9.49/5.28        ( ( dvd_dvd_complex @ D2 @ D4 )
% 9.49/5.28       => ! [X5: complex,K4: complex] :
% 9.49/5.28            ( ( ~ ( dvd_dvd_complex @ D2 @ ( plus_plus_complex @ X5 @ T ) ) )
% 9.49/5.28            = ( ~ ( dvd_dvd_complex @ D2 @ ( plus_plus_complex @ ( minus_minus_complex @ X5 @ ( times_times_complex @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4430_inf__period_I4_J,axiom,
% 9.49/5.28      ! [D2: real,D4: real,T: real] :
% 9.49/5.28        ( ( dvd_dvd_real @ D2 @ D4 )
% 9.49/5.28       => ! [X5: real,K4: real] :
% 9.49/5.28            ( ( ~ ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X5 @ T ) ) )
% 9.49/5.28            = ( ~ ( dvd_dvd_real @ D2 @ ( plus_plus_real @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4431_inf__period_I4_J,axiom,
% 9.49/5.28      ! [D2: int,D4: int,T: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ D2 @ D4 )
% 9.49/5.28       => ! [X5: int,K4: int] :
% 9.49/5.28            ( ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ T ) ) )
% 9.49/5.28            = ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4432_inf__period_I3_J,axiom,
% 9.49/5.28      ! [D2: code_integer,D4: code_integer,T: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ D2 @ D4 )
% 9.49/5.28       => ! [X5: code_integer,K4: code_integer] :
% 9.49/5.28            ( ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X5 @ T ) )
% 9.49/5.28            = ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X5 @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4433_inf__period_I3_J,axiom,
% 9.49/5.28      ! [D2: rat,D4: rat,T: rat] :
% 9.49/5.28        ( ( dvd_dvd_rat @ D2 @ D4 )
% 9.49/5.28       => ! [X5: rat,K4: rat] :
% 9.49/5.28            ( ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X5 @ T ) )
% 9.49/5.28            = ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4434_inf__period_I3_J,axiom,
% 9.49/5.28      ! [D2: complex,D4: complex,T: complex] :
% 9.49/5.28        ( ( dvd_dvd_complex @ D2 @ D4 )
% 9.49/5.28       => ! [X5: complex,K4: complex] :
% 9.49/5.28            ( ( dvd_dvd_complex @ D2 @ ( plus_plus_complex @ X5 @ T ) )
% 9.49/5.28            = ( dvd_dvd_complex @ D2 @ ( plus_plus_complex @ ( minus_minus_complex @ X5 @ ( times_times_complex @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4435_inf__period_I3_J,axiom,
% 9.49/5.28      ! [D2: real,D4: real,T: real] :
% 9.49/5.28        ( ( dvd_dvd_real @ D2 @ D4 )
% 9.49/5.28       => ! [X5: real,K4: real] :
% 9.49/5.28            ( ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X5 @ T ) )
% 9.49/5.28            = ( dvd_dvd_real @ D2 @ ( plus_plus_real @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4436_inf__period_I3_J,axiom,
% 9.49/5.28      ! [D2: int,D4: int,T: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ D2 @ D4 )
% 9.49/5.28       => ! [X5: int,K4: int] :
% 9.49/5.28            ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ T ) )
% 9.49/5.28            = ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4437_unit__eq__div1,axiom,
% 9.49/5.28      ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.49/5.28       => ( ( ( divide6298287555418463151nteger @ A @ B )
% 9.49/5.28            = C )
% 9.49/5.28          = ( A
% 9.49/5.28            = ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4438_unit__eq__div1,axiom,
% 9.49/5.28      ! [B: nat,A: nat,C: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.49/5.28       => ( ( ( divide_divide_nat @ A @ B )
% 9.49/5.28            = C )
% 9.49/5.28          = ( A
% 9.49/5.28            = ( times_times_nat @ C @ B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4439_unit__eq__div1,axiom,
% 9.49/5.28      ! [B: int,A: int,C: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ B @ one_one_int )
% 9.49/5.28       => ( ( ( divide_divide_int @ A @ B )
% 9.49/5.28            = C )
% 9.49/5.28          = ( A
% 9.49/5.28            = ( times_times_int @ C @ B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4440_unit__eq__div2,axiom,
% 9.49/5.28      ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.49/5.28       => ( ( A
% 9.49/5.28            = ( divide6298287555418463151nteger @ C @ B ) )
% 9.49/5.28          = ( ( times_3573771949741848930nteger @ A @ B )
% 9.49/5.28            = C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4441_unit__eq__div2,axiom,
% 9.49/5.28      ! [B: nat,A: nat,C: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.49/5.28       => ( ( A
% 9.49/5.28            = ( divide_divide_nat @ C @ B ) )
% 9.49/5.28          = ( ( times_times_nat @ A @ B )
% 9.49/5.28            = C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4442_unit__eq__div2,axiom,
% 9.49/5.28      ! [B: int,A: int,C: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ B @ one_one_int )
% 9.49/5.28       => ( ( A
% 9.49/5.28            = ( divide_divide_int @ C @ B ) )
% 9.49/5.28          = ( ( times_times_int @ A @ B )
% 9.49/5.28            = C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4443_div__mult__unit2,axiom,
% 9.49/5.28      ! [C: code_integer,B: code_integer,A: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 9.49/5.28       => ( ( dvd_dvd_Code_integer @ B @ A )
% 9.49/5.28         => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 9.49/5.28            = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4444_div__mult__unit2,axiom,
% 9.49/5.28      ! [C: nat,B: nat,A: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ C @ one_one_nat )
% 9.49/5.28       => ( ( dvd_dvd_nat @ B @ A )
% 9.49/5.28         => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 9.49/5.28            = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4445_div__mult__unit2,axiom,
% 9.49/5.28      ! [C: int,B: int,A: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ C @ one_one_int )
% 9.49/5.28       => ( ( dvd_dvd_int @ B @ A )
% 9.49/5.28         => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 9.49/5.28            = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4446_unit__div__commute,axiom,
% 9.49/5.28      ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.49/5.28       => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 9.49/5.28          = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4447_unit__div__commute,axiom,
% 9.49/5.28      ! [B: nat,A: nat,C: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.49/5.28       => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 9.49/5.28          = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4448_unit__div__commute,axiom,
% 9.49/5.28      ! [B: int,A: int,C: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ B @ one_one_int )
% 9.49/5.28       => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ C )
% 9.49/5.28          = ( divide_divide_int @ ( times_times_int @ A @ C ) @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4449_unit__div__mult__swap,axiom,
% 9.49/5.28      ! [C: code_integer,A: code_integer,B: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 9.49/5.28       => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 9.49/5.28          = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4450_unit__div__mult__swap,axiom,
% 9.49/5.28      ! [C: nat,A: nat,B: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ C @ one_one_nat )
% 9.49/5.28       => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 9.49/5.28          = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4451_unit__div__mult__swap,axiom,
% 9.49/5.28      ! [C: int,A: int,B: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ C @ one_one_int )
% 9.49/5.28       => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 9.49/5.28          = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4452_is__unit__div__mult2__eq,axiom,
% 9.49/5.28      ! [B: code_integer,C: code_integer,A: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.49/5.28       => ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 9.49/5.28         => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 9.49/5.28            = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4453_is__unit__div__mult2__eq,axiom,
% 9.49/5.28      ! [B: nat,C: nat,A: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.49/5.28       => ( ( dvd_dvd_nat @ C @ one_one_nat )
% 9.49/5.28         => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 9.49/5.28            = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4454_is__unit__div__mult2__eq,axiom,
% 9.49/5.28      ! [B: int,C: int,A: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ B @ one_one_int )
% 9.49/5.28       => ( ( dvd_dvd_int @ C @ one_one_int )
% 9.49/5.28         => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 9.49/5.28            = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4455_is__unit__power__iff,axiom,
% 9.49/5.28      ! [A: code_integer,N: nat] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ one_one_Code_integer )
% 9.49/5.28        = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.49/5.28          | ( N = zero_zero_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4456_is__unit__power__iff,axiom,
% 9.49/5.28      ! [A: nat,N: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ one_one_nat )
% 9.49/5.28        = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.49/5.28          | ( N = zero_zero_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4457_is__unit__power__iff,axiom,
% 9.49/5.28      ! [A: int,N: nat] :
% 9.49/5.28        ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ one_one_int )
% 9.49/5.28        = ( ( dvd_dvd_int @ A @ one_one_int )
% 9.49/5.28          | ( N = zero_zero_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4458_unit__imp__mod__eq__0,axiom,
% 9.49/5.28      ! [B: code_integer,A: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.49/5.28       => ( ( modulo364778990260209775nteger @ A @ B )
% 9.49/5.28          = zero_z3403309356797280102nteger ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4459_unit__imp__mod__eq__0,axiom,
% 9.49/5.28      ! [B: nat,A: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.49/5.28       => ( ( modulo_modulo_nat @ A @ B )
% 9.49/5.28          = zero_zero_nat ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4460_unit__imp__mod__eq__0,axiom,
% 9.49/5.28      ! [B: int,A: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ B @ one_one_int )
% 9.49/5.28       => ( ( modulo_modulo_int @ A @ B )
% 9.49/5.28          = zero_zero_int ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4461_dvd__imp__le,axiom,
% 9.49/5.28      ! [K: nat,N: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ K @ N )
% 9.49/5.28       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.28         => ( ord_less_eq_nat @ K @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4462_dvd__mult__cancel,axiom,
% 9.49/5.28      ! [K: nat,M: nat,N: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 9.49/5.28       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 9.49/5.28         => ( dvd_dvd_nat @ M @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4463_nat__mult__dvd__cancel1,axiom,
% 9.49/5.28      ! [K: nat,M: nat,N: nat] :
% 9.49/5.28        ( ( ord_less_nat @ zero_zero_nat @ K )
% 9.49/5.28       => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 9.49/5.28          = ( dvd_dvd_nat @ M @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4464_mod__greater__zero__iff__not__dvd,axiom,
% 9.49/5.28      ! [M: nat,N: nat] :
% 9.49/5.28        ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ N ) )
% 9.49/5.28        = ( ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4465_mod__eq__dvd__iff__nat,axiom,
% 9.49/5.28      ! [N: nat,M: nat,Q2: nat] :
% 9.49/5.28        ( ( ord_less_eq_nat @ N @ M )
% 9.49/5.28       => ( ( ( modulo_modulo_nat @ M @ Q2 )
% 9.49/5.28            = ( modulo_modulo_nat @ N @ Q2 ) )
% 9.49/5.28          = ( dvd_dvd_nat @ Q2 @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4466_prod__decode__aux_Ocases,axiom,
% 9.49/5.28      ! [X: product_prod_nat_nat] :
% 9.49/5.28        ~ ! [K2: nat,M4: nat] :
% 9.49/5.28            ( X
% 9.49/5.28           != ( product_Pair_nat_nat @ K2 @ M4 ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4467_even__zero,axiom,
% 9.49/5.28      dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ zero_z3403309356797280102nteger ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4468_even__zero,axiom,
% 9.49/5.28      dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ zero_zero_nat ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4469_even__zero,axiom,
% 9.49/5.28      dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ zero_zero_int ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4470_evenE,axiom,
% 9.49/5.28      ! [A: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.49/5.28       => ~ ! [B3: code_integer] :
% 9.49/5.28              ( A
% 9.49/5.28             != ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B3 ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4471_evenE,axiom,
% 9.49/5.28      ! [A: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.49/5.28       => ~ ! [B3: nat] :
% 9.49/5.28              ( A
% 9.49/5.28             != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4472_evenE,axiom,
% 9.49/5.28      ! [A: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.49/5.28       => ~ ! [B3: int] :
% 9.49/5.28              ( A
% 9.49/5.28             != ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4473_odd__one,axiom,
% 9.49/5.28      ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ one_one_Code_integer ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4474_odd__one,axiom,
% 9.49/5.28      ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ one_one_nat ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4475_odd__one,axiom,
% 9.49/5.28      ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ one_one_int ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4476_is__unitE,axiom,
% 9.49/5.28      ! [A: code_integer,C: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.49/5.28       => ~ ( ( A != zero_z3403309356797280102nteger )
% 9.49/5.28           => ! [B3: code_integer] :
% 9.49/5.28                ( ( B3 != zero_z3403309356797280102nteger )
% 9.49/5.28               => ( ( dvd_dvd_Code_integer @ B3 @ one_one_Code_integer )
% 9.49/5.28                 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ A )
% 9.49/5.28                      = B3 )
% 9.49/5.28                   => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ B3 )
% 9.49/5.28                        = A )
% 9.49/5.28                     => ( ( ( times_3573771949741848930nteger @ A @ B3 )
% 9.49/5.28                          = one_one_Code_integer )
% 9.49/5.28                       => ( ( divide6298287555418463151nteger @ C @ A )
% 9.49/5.28                         != ( times_3573771949741848930nteger @ C @ B3 ) ) ) ) ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4477_is__unitE,axiom,
% 9.49/5.28      ! [A: nat,C: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.49/5.28       => ~ ( ( A != zero_zero_nat )
% 9.49/5.28           => ! [B3: nat] :
% 9.49/5.28                ( ( B3 != zero_zero_nat )
% 9.49/5.28               => ( ( dvd_dvd_nat @ B3 @ one_one_nat )
% 9.49/5.28                 => ( ( ( divide_divide_nat @ one_one_nat @ A )
% 9.49/5.28                      = B3 )
% 9.49/5.28                   => ( ( ( divide_divide_nat @ one_one_nat @ B3 )
% 9.49/5.28                        = A )
% 9.49/5.28                     => ( ( ( times_times_nat @ A @ B3 )
% 9.49/5.28                          = one_one_nat )
% 9.49/5.28                       => ( ( divide_divide_nat @ C @ A )
% 9.49/5.28                         != ( times_times_nat @ C @ B3 ) ) ) ) ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4478_is__unitE,axiom,
% 9.49/5.28      ! [A: int,C: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ A @ one_one_int )
% 9.49/5.28       => ~ ( ( A != zero_zero_int )
% 9.49/5.28           => ! [B3: int] :
% 9.49/5.28                ( ( B3 != zero_zero_int )
% 9.49/5.28               => ( ( dvd_dvd_int @ B3 @ one_one_int )
% 9.49/5.28                 => ( ( ( divide_divide_int @ one_one_int @ A )
% 9.49/5.28                      = B3 )
% 9.49/5.28                   => ( ( ( divide_divide_int @ one_one_int @ B3 )
% 9.49/5.28                        = A )
% 9.49/5.28                     => ( ( ( times_times_int @ A @ B3 )
% 9.49/5.28                          = one_one_int )
% 9.49/5.28                       => ( ( divide_divide_int @ C @ A )
% 9.49/5.28                         != ( times_times_int @ C @ B3 ) ) ) ) ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4479_is__unit__div__mult__cancel__left,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer] :
% 9.49/5.28        ( ( A != zero_z3403309356797280102nteger )
% 9.49/5.28       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.49/5.28         => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ A @ B ) )
% 9.49/5.28            = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4480_is__unit__div__mult__cancel__left,axiom,
% 9.49/5.28      ! [A: nat,B: nat] :
% 9.49/5.28        ( ( A != zero_zero_nat )
% 9.49/5.28       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.49/5.28         => ( ( divide_divide_nat @ A @ ( times_times_nat @ A @ B ) )
% 9.49/5.28            = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4481_is__unit__div__mult__cancel__left,axiom,
% 9.49/5.28      ! [A: int,B: int] :
% 9.49/5.28        ( ( A != zero_zero_int )
% 9.49/5.28       => ( ( dvd_dvd_int @ B @ one_one_int )
% 9.49/5.28         => ( ( divide_divide_int @ A @ ( times_times_int @ A @ B ) )
% 9.49/5.28            = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4482_is__unit__div__mult__cancel__right,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer] :
% 9.49/5.28        ( ( A != zero_z3403309356797280102nteger )
% 9.49/5.28       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.49/5.28         => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ A ) )
% 9.49/5.28            = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4483_is__unit__div__mult__cancel__right,axiom,
% 9.49/5.28      ! [A: nat,B: nat] :
% 9.49/5.28        ( ( A != zero_zero_nat )
% 9.49/5.28       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.49/5.28         => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ A ) )
% 9.49/5.28            = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4484_is__unit__div__mult__cancel__right,axiom,
% 9.49/5.28      ! [A: int,B: int] :
% 9.49/5.28        ( ( A != zero_zero_int )
% 9.49/5.28       => ( ( dvd_dvd_int @ B @ one_one_int )
% 9.49/5.28         => ( ( divide_divide_int @ A @ ( times_times_int @ B @ A ) )
% 9.49/5.28            = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4485_odd__even__add,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer] :
% 9.49/5.28        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.49/5.28       => ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B )
% 9.49/5.28         => ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4486_odd__even__add,axiom,
% 9.49/5.28      ! [A: nat,B: nat] :
% 9.49/5.28        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.49/5.28       => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 9.49/5.28         => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4487_odd__even__add,axiom,
% 9.49/5.28      ! [A: int,B: int] :
% 9.49/5.28        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.49/5.28       => ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B )
% 9.49/5.28         => ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4488_bit__eq__rec,axiom,
% 9.49/5.28      ( ( ^ [Y5: code_integer,Z5: code_integer] : ( Y5 = Z5 ) )
% 9.49/5.28      = ( ^ [A3: code_integer,B4: code_integer] :
% 9.49/5.28            ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 )
% 9.49/5.28              = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B4 ) )
% 9.49/5.28            & ( ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.49/5.28              = ( divide6298287555418463151nteger @ B4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4489_bit__eq__rec,axiom,
% 9.49/5.28      ( ( ^ [Y5: nat,Z5: nat] : ( Y5 = Z5 ) )
% 9.49/5.28      = ( ^ [A3: nat,B4: nat] :
% 9.49/5.28            ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 )
% 9.49/5.28              = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B4 ) )
% 9.49/5.28            & ( ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.28              = ( divide_divide_nat @ B4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4490_bit__eq__rec,axiom,
% 9.49/5.28      ( ( ^ [Y5: int,Z5: int] : ( Y5 = Z5 ) )
% 9.49/5.28      = ( ^ [A3: int,B4: int] :
% 9.49/5.28            ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 )
% 9.49/5.28              = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B4 ) )
% 9.49/5.28            & ( ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.49/5.28              = ( divide_divide_int @ B4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4491_odd__numeral,axiom,
% 9.49/5.28      ! [N: num] :
% 9.49/5.28        ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4492_odd__numeral,axiom,
% 9.49/5.28      ! [N: num] :
% 9.49/5.28        ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4493_odd__numeral,axiom,
% 9.49/5.28      ! [N: num] :
% 9.49/5.28        ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4494_dvd__power__iff,axiom,
% 9.49/5.28      ! [X: code_integer,M: nat,N: nat] :
% 9.49/5.28        ( ( X != zero_z3403309356797280102nteger )
% 9.49/5.28       => ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ M ) @ ( power_8256067586552552935nteger @ X @ N ) )
% 9.49/5.28          = ( ( dvd_dvd_Code_integer @ X @ one_one_Code_integer )
% 9.49/5.28            | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4495_dvd__power__iff,axiom,
% 9.49/5.28      ! [X: nat,M: nat,N: nat] :
% 9.49/5.28        ( ( X != zero_zero_nat )
% 9.49/5.28       => ( ( dvd_dvd_nat @ ( power_power_nat @ X @ M ) @ ( power_power_nat @ X @ N ) )
% 9.49/5.28          = ( ( dvd_dvd_nat @ X @ one_one_nat )
% 9.49/5.28            | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4496_dvd__power__iff,axiom,
% 9.49/5.28      ! [X: int,M: nat,N: nat] :
% 9.49/5.28        ( ( X != zero_zero_int )
% 9.49/5.28       => ( ( dvd_dvd_int @ ( power_power_int @ X @ M ) @ ( power_power_int @ X @ N ) )
% 9.49/5.28          = ( ( dvd_dvd_int @ X @ one_one_int )
% 9.49/5.28            | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4497_dvd__power,axiom,
% 9.49/5.28      ! [N: nat,X: code_integer] :
% 9.49/5.28        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.28          | ( X = one_one_Code_integer ) )
% 9.49/5.28       => ( dvd_dvd_Code_integer @ X @ ( power_8256067586552552935nteger @ X @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4498_dvd__power,axiom,
% 9.49/5.28      ! [N: nat,X: rat] :
% 9.49/5.28        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.28          | ( X = one_one_rat ) )
% 9.49/5.28       => ( dvd_dvd_rat @ X @ ( power_power_rat @ X @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4499_dvd__power,axiom,
% 9.49/5.28      ! [N: nat,X: nat] :
% 9.49/5.28        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.28          | ( X = one_one_nat ) )
% 9.49/5.28       => ( dvd_dvd_nat @ X @ ( power_power_nat @ X @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4500_dvd__power,axiom,
% 9.49/5.28      ! [N: nat,X: real] :
% 9.49/5.28        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.28          | ( X = one_one_real ) )
% 9.49/5.28       => ( dvd_dvd_real @ X @ ( power_power_real @ X @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4501_dvd__power,axiom,
% 9.49/5.28      ! [N: nat,X: int] :
% 9.49/5.28        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.28          | ( X = one_one_int ) )
% 9.49/5.28       => ( dvd_dvd_int @ X @ ( power_power_int @ X @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4502_dvd__power,axiom,
% 9.49/5.28      ! [N: nat,X: complex] :
% 9.49/5.28        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.28          | ( X = one_one_complex ) )
% 9.49/5.28       => ( dvd_dvd_complex @ X @ ( power_power_complex @ X @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4503_dvd__mult__cancel1,axiom,
% 9.49/5.28      ! [M: nat,N: nat] :
% 9.49/5.28        ( ( ord_less_nat @ zero_zero_nat @ M )
% 9.49/5.28       => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N ) @ M )
% 9.49/5.28          = ( N = one_one_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4504_dvd__mult__cancel2,axiom,
% 9.49/5.28      ! [M: nat,N: nat] :
% 9.49/5.28        ( ( ord_less_nat @ zero_zero_nat @ M )
% 9.49/5.28       => ( ( dvd_dvd_nat @ ( times_times_nat @ N @ M ) @ M )
% 9.49/5.28          = ( N = one_one_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4505_even__even__mod__4__iff,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4506_odd__numeral__BitM,axiom,
% 9.49/5.28      ! [W: num] :
% 9.49/5.28        ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bitM @ W ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4507_odd__numeral__BitM,axiom,
% 9.49/5.28      ! [W: num] :
% 9.49/5.28        ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bitM @ W ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4508_odd__numeral__BitM,axiom,
% 9.49/5.28      ! [W: num] :
% 9.49/5.28        ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bitM @ W ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4509_power__dvd__imp__le,axiom,
% 9.49/5.28      ! [I2: nat,M: nat,N: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ ( power_power_nat @ I2 @ M ) @ ( power_power_nat @ I2 @ N ) )
% 9.49/5.28       => ( ( ord_less_nat @ one_one_nat @ I2 )
% 9.49/5.28         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4510_dvd__minus__add,axiom,
% 9.49/5.28      ! [Q2: nat,N: nat,R: nat,M: nat] :
% 9.49/5.28        ( ( ord_less_eq_nat @ Q2 @ N )
% 9.49/5.28       => ( ( ord_less_eq_nat @ Q2 @ ( times_times_nat @ R @ M ) )
% 9.49/5.28         => ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ Q2 ) )
% 9.49/5.28            = ( dvd_dvd_nat @ M @ ( plus_plus_nat @ N @ ( minus_minus_nat @ ( times_times_nat @ R @ M ) @ Q2 ) ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4511_mod__nat__eqI,axiom,
% 9.49/5.28      ! [R: nat,N: nat,M: nat] :
% 9.49/5.28        ( ( ord_less_nat @ R @ N )
% 9.49/5.28       => ( ( ord_less_eq_nat @ R @ M )
% 9.49/5.28         => ( ( dvd_dvd_nat @ N @ ( minus_minus_nat @ M @ R ) )
% 9.49/5.28           => ( ( modulo_modulo_nat @ M @ N )
% 9.49/5.28              = R ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4512_mod__int__pos__iff,axiom,
% 9.49/5.28      ! [K: int,L2: int] :
% 9.49/5.28        ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L2 ) )
% 9.49/5.28        = ( ( dvd_dvd_int @ L2 @ K )
% 9.49/5.28          | ( ( L2 = zero_zero_int )
% 9.49/5.28            & ( ord_less_eq_int @ zero_zero_int @ K ) )
% 9.49/5.28          | ( ord_less_int @ zero_zero_int @ L2 ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4513_aset_I10_J,axiom,
% 9.49/5.28      ! [D2: int,D4: int,A2: set_int,T: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ D2 @ D4 )
% 9.49/5.28       => ! [X5: int] :
% 9.49/5.28            ( ! [Xa3: int] :
% 9.49/5.28                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 9.49/5.28               => ! [Xb3: int] :
% 9.49/5.28                    ( ( member_int @ Xb3 @ A2 )
% 9.49/5.28                   => ( X5
% 9.49/5.28                     != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 9.49/5.28           => ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ T ) )
% 9.49/5.28             => ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( plus_plus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4514_aset_I9_J,axiom,
% 9.49/5.28      ! [D2: int,D4: int,A2: set_int,T: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ D2 @ D4 )
% 9.49/5.28       => ! [X5: int] :
% 9.49/5.28            ( ! [Xa3: int] :
% 9.49/5.28                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 9.49/5.28               => ! [Xb3: int] :
% 9.49/5.28                    ( ( member_int @ Xb3 @ A2 )
% 9.49/5.28                   => ( X5
% 9.49/5.28                     != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 9.49/5.28           => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ T ) )
% 9.49/5.28             => ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( plus_plus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4515_bset_I10_J,axiom,
% 9.49/5.28      ! [D2: int,D4: int,B2: set_int,T: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ D2 @ D4 )
% 9.49/5.28       => ! [X5: int] :
% 9.49/5.28            ( ! [Xa3: int] :
% 9.49/5.28                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 9.49/5.28               => ! [Xb3: int] :
% 9.49/5.28                    ( ( member_int @ Xb3 @ B2 )
% 9.49/5.28                   => ( X5
% 9.49/5.28                     != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 9.49/5.28           => ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ T ) )
% 9.49/5.28             => ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4516_bset_I9_J,axiom,
% 9.49/5.28      ! [D2: int,D4: int,B2: set_int,T: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ D2 @ D4 )
% 9.49/5.28       => ! [X5: int] :
% 9.49/5.28            ( ! [Xa3: int] :
% 9.49/5.28                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 9.49/5.28               => ! [Xb3: int] :
% 9.49/5.28                    ( ( member_int @ Xb3 @ B2 )
% 9.49/5.28                   => ( X5
% 9.49/5.28                     != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 9.49/5.28           => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ T ) )
% 9.49/5.28             => ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4517_even__two__times__div__two,axiom,
% 9.49/5.28      ! [A: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.49/5.28       => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 9.49/5.28          = A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4518_even__two__times__div__two,axiom,
% 9.49/5.28      ! [A: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.49/5.28       => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.28          = A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4519_even__two__times__div__two,axiom,
% 9.49/5.28      ! [A: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.49/5.28       => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 9.49/5.28          = A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4520_even__iff__mod__2__eq__zero,axiom,
% 9.49/5.28      ! [A: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.49/5.28        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.49/5.28          = zero_z3403309356797280102nteger ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4521_even__iff__mod__2__eq__zero,axiom,
% 9.49/5.28      ! [A: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.49/5.28        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.28          = zero_zero_nat ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4522_even__iff__mod__2__eq__zero,axiom,
% 9.49/5.28      ! [A: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.49/5.28        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.49/5.28          = zero_zero_int ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4523_odd__iff__mod__2__eq__one,axiom,
% 9.49/5.28      ! [A: code_integer] :
% 9.49/5.28        ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 9.49/5.28        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.49/5.28          = one_one_Code_integer ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4524_odd__iff__mod__2__eq__one,axiom,
% 9.49/5.28      ! [A: nat] :
% 9.49/5.28        ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 9.49/5.28        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.28          = one_one_nat ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4525_odd__iff__mod__2__eq__one,axiom,
% 9.49/5.28      ! [A: int] :
% 9.49/5.28        ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 9.49/5.28        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.49/5.28          = one_one_int ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4526_power__mono__odd,axiom,
% 9.49/5.28      ! [N: nat,A: real,B: real] :
% 9.49/5.28        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28       => ( ( ord_less_eq_real @ A @ B )
% 9.49/5.28         => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4527_power__mono__odd,axiom,
% 9.49/5.28      ! [N: nat,A: int,B: int] :
% 9.49/5.28        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28       => ( ( ord_less_eq_int @ A @ B )
% 9.49/5.28         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4528_odd__pos,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28       => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4529_dvd__power__iff__le,axiom,
% 9.49/5.28      ! [K: nat,M: nat,N: nat] :
% 9.49/5.28        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 9.49/5.28       => ( ( dvd_dvd_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) )
% 9.49/5.28          = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4530_even__unset__bit__iff,axiom,
% 9.49/5.28      ! [M: nat,A: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ M @ A ) )
% 9.49/5.28        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.49/5.28          | ( M = zero_zero_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4531_even__unset__bit__iff,axiom,
% 9.49/5.28      ! [M: nat,A: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 9.49/5.28        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.49/5.28          | ( M = zero_zero_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4532_even__unset__bit__iff,axiom,
% 9.49/5.28      ! [M: nat,A: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 9.49/5.28        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.49/5.28          | ( M = zero_zero_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4533_even__set__bit__iff,axiom,
% 9.49/5.28      ! [M: nat,A: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ M @ A ) )
% 9.49/5.28        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.49/5.28          & ( M != zero_zero_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4534_even__set__bit__iff,axiom,
% 9.49/5.28      ! [M: nat,A: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 9.49/5.28        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.49/5.28          & ( M != zero_zero_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4535_even__set__bit__iff,axiom,
% 9.49/5.28      ! [M: nat,A: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 9.49/5.28        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.49/5.28          & ( M != zero_zero_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4536_even__flip__bit__iff,axiom,
% 9.49/5.28      ! [M: nat,A: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ M @ A ) )
% 9.49/5.28        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.49/5.28         != ( M = zero_zero_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4537_even__flip__bit__iff,axiom,
% 9.49/5.28      ! [M: nat,A: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 9.49/5.28        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.49/5.28         != ( M = zero_zero_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4538_even__flip__bit__iff,axiom,
% 9.49/5.28      ! [M: nat,A: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 9.49/5.28        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.49/5.28         != ( M = zero_zero_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4539_even__diff__iff,axiom,
% 9.49/5.28      ! [K: int,L2: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ K @ L2 ) )
% 9.49/5.28        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4540_oddE,axiom,
% 9.49/5.28      ! [A: code_integer] :
% 9.49/5.28        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.49/5.28       => ~ ! [B3: code_integer] :
% 9.49/5.28              ( A
% 9.49/5.28             != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B3 ) @ one_one_Code_integer ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4541_oddE,axiom,
% 9.49/5.28      ! [A: nat] :
% 9.49/5.28        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.49/5.28       => ~ ! [B3: nat] :
% 9.49/5.28              ( A
% 9.49/5.28             != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) @ one_one_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4542_oddE,axiom,
% 9.49/5.28      ! [A: int] :
% 9.49/5.28        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.49/5.28       => ~ ! [B3: int] :
% 9.49/5.28              ( A
% 9.49/5.28             != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) @ one_one_int ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4543_parity__cases,axiom,
% 9.49/5.28      ! [A: code_integer] :
% 9.49/5.28        ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.49/5.28         => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.49/5.28           != zero_z3403309356797280102nteger ) )
% 9.49/5.28       => ~ ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.49/5.28           => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.49/5.28             != one_one_Code_integer ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4544_parity__cases,axiom,
% 9.49/5.28      ! [A: nat] :
% 9.49/5.28        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.49/5.28         => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.28           != zero_zero_nat ) )
% 9.49/5.28       => ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.49/5.28           => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.28             != one_one_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4545_parity__cases,axiom,
% 9.49/5.28      ! [A: int] :
% 9.49/5.28        ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.49/5.28         => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.49/5.28           != zero_zero_int ) )
% 9.49/5.28       => ~ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.49/5.28           => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.49/5.28             != one_one_int ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4546_mod2__eq__if,axiom,
% 9.49/5.28      ! [A: code_integer] :
% 9.49/5.28        ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.49/5.28         => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.49/5.28            = zero_z3403309356797280102nteger ) )
% 9.49/5.28        & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.49/5.28         => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.49/5.28            = one_one_Code_integer ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4547_mod2__eq__if,axiom,
% 9.49/5.28      ! [A: nat] :
% 9.49/5.28        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.49/5.28         => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.28            = zero_zero_nat ) )
% 9.49/5.28        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.49/5.28         => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.28            = one_one_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4548_mod2__eq__if,axiom,
% 9.49/5.28      ! [A: int] :
% 9.49/5.28        ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.49/5.28         => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.49/5.28            = zero_zero_int ) )
% 9.49/5.28        & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.49/5.28         => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.49/5.28            = one_one_int ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4549_zero__le__even__power,axiom,
% 9.49/5.28      ! [N: nat,A: rat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28       => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4550_zero__le__even__power,axiom,
% 9.49/5.28      ! [N: nat,A: real] :
% 9.49/5.28        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28       => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4551_zero__le__even__power,axiom,
% 9.49/5.28      ! [N: nat,A: int] :
% 9.49/5.28        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28       => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4552_zero__le__odd__power,axiom,
% 9.49/5.28      ! [N: nat,A: rat] :
% 9.49/5.28        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28       => ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 9.49/5.28          = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4553_zero__le__odd__power,axiom,
% 9.49/5.28      ! [N: nat,A: real] :
% 9.49/5.28        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28       => ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 9.49/5.28          = ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4554_zero__le__odd__power,axiom,
% 9.49/5.28      ! [N: nat,A: int] :
% 9.49/5.28        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28       => ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 9.49/5.28          = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4555_zero__le__power__eq,axiom,
% 9.49/5.28      ! [A: rat,N: nat] :
% 9.49/5.28        ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 9.49/5.28        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28            & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4556_zero__le__power__eq,axiom,
% 9.49/5.28      ! [A: real,N: nat] :
% 9.49/5.28        ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 9.49/5.28        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28            & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4557_zero__le__power__eq,axiom,
% 9.49/5.28      ! [A: int,N: nat] :
% 9.49/5.28        ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 9.49/5.28        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28            & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4558_list__decode_Ocases,axiom,
% 9.49/5.28      ! [X: nat] :
% 9.49/5.28        ( ( X != zero_zero_nat )
% 9.49/5.28       => ~ ! [N3: nat] :
% 9.49/5.28              ( X
% 9.49/5.28             != ( suc @ N3 ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4559_Euclid__induct,axiom,
% 9.49/5.28      ! [P: nat > nat > $o,A: nat,B: nat] :
% 9.49/5.28        ( ! [A4: nat,B3: nat] :
% 9.49/5.28            ( ( P @ A4 @ B3 )
% 9.49/5.28            = ( P @ B3 @ A4 ) )
% 9.49/5.28       => ( ! [A4: nat] : ( P @ A4 @ zero_zero_nat )
% 9.49/5.28         => ( ! [A4: nat,B3: nat] :
% 9.49/5.28                ( ( P @ A4 @ B3 )
% 9.49/5.28               => ( P @ A4 @ ( plus_plus_nat @ A4 @ B3 ) ) )
% 9.49/5.28           => ( P @ A @ B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4560_zero__less__power__eq,axiom,
% 9.49/5.28      ! [A: real,N: nat] :
% 9.49/5.28        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 9.49/5.28        = ( ( N = zero_zero_nat )
% 9.49/5.28          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28            & ( A != zero_zero_real ) )
% 9.49/5.28          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28            & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4561_zero__less__power__eq,axiom,
% 9.49/5.28      ! [A: rat,N: nat] :
% 9.49/5.28        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 9.49/5.28        = ( ( N = zero_zero_nat )
% 9.49/5.28          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28            & ( A != zero_zero_rat ) )
% 9.49/5.28          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28            & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4562_zero__less__power__eq,axiom,
% 9.49/5.28      ! [A: int,N: nat] :
% 9.49/5.28        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 9.49/5.28        = ( ( N = zero_zero_nat )
% 9.49/5.28          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28            & ( A != zero_zero_int ) )
% 9.49/5.28          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28            & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4563_even__mask__div__iff_H,axiom,
% 9.49/5.28      ! [M: nat,N: nat] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 9.49/5.28        = ( ord_less_eq_nat @ M @ N ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4564_even__mask__div__iff_H,axiom,
% 9.49/5.28      ! [M: nat,N: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 9.49/5.28        = ( ord_less_eq_nat @ M @ N ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4565_even__mask__div__iff_H,axiom,
% 9.49/5.28      ! [M: nat,N: nat] :
% 9.49/5.28        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 9.49/5.28        = ( ord_less_eq_nat @ M @ N ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4566_power__le__zero__eq,axiom,
% 9.49/5.28      ! [A: rat,N: nat] :
% 9.49/5.28        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 9.49/5.28        = ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.28          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28              & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 9.49/5.28            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28              & ( A = zero_zero_rat ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4567_power__le__zero__eq,axiom,
% 9.49/5.28      ! [A: real,N: nat] :
% 9.49/5.28        ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 9.49/5.28        = ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.28          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28              & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 9.49/5.28            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28              & ( A = zero_zero_real ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4568_power__le__zero__eq,axiom,
% 9.49/5.28      ! [A: int,N: nat] :
% 9.49/5.28        ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 9.49/5.28        = ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.49/5.28          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28              & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 9.49/5.28            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28              & ( A = zero_zero_int ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4569_even__mod__4__div__2,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 9.49/5.28          = ( suc @ zero_zero_nat ) )
% 9.49/5.28       => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4570_divmod__step__nat__def,axiom,
% 9.49/5.28      ( unique5026877609467782581ep_nat
% 9.49/5.28      = ( ^ [L: num] :
% 9.49/5.28            ( produc2626176000494625587at_nat
% 9.49/5.28            @ ^ [Q4: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R5 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ one_one_nat ) @ ( minus_minus_nat @ R5 @ ( numeral_numeral_nat @ L ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4571_even__mask__div__iff,axiom,
% 9.49/5.28      ! [M: nat,N: nat] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 9.49/5.28        = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 9.49/5.28            = zero_z3403309356797280102nteger )
% 9.49/5.28          | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4572_even__mask__div__iff,axiom,
% 9.49/5.28      ! [M: nat,N: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 9.49/5.28        = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28            = zero_zero_nat )
% 9.49/5.28          | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4573_even__mask__div__iff,axiom,
% 9.49/5.28      ! [M: nat,N: nat] :
% 9.49/5.28        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 9.49/5.28        = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 9.49/5.28            = zero_zero_int )
% 9.49/5.28          | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4574_divmod__step__int__def,axiom,
% 9.49/5.28      ( unique5024387138958732305ep_int
% 9.49/5.28      = ( ^ [L: num] :
% 9.49/5.28            ( produc4245557441103728435nt_int
% 9.49/5.28            @ ^ [Q4: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R5 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ one_one_int ) @ ( minus_minus_int @ R5 @ ( numeral_numeral_int @ L ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4575_odd__mod__4__div__2,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 9.49/5.28          = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 9.49/5.28       => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4576_even__mult__exp__div__exp__iff,axiom,
% 9.49/5.28      ! [A: code_integer,M: nat,N: nat] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 9.49/5.28        = ( ( ord_less_nat @ N @ M )
% 9.49/5.28          | ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 9.49/5.28            = zero_z3403309356797280102nteger )
% 9.49/5.28          | ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.28            & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4577_even__mult__exp__div__exp__iff,axiom,
% 9.49/5.28      ! [A: nat,M: nat,N: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 9.49/5.28        = ( ( ord_less_nat @ N @ M )
% 9.49/5.28          | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28            = zero_zero_nat )
% 9.49/5.28          | ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.28            & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4578_even__mult__exp__div__exp__iff,axiom,
% 9.49/5.28      ! [A: int,M: nat,N: nat] :
% 9.49/5.28        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 9.49/5.28        = ( ( ord_less_nat @ N @ M )
% 9.49/5.28          | ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 9.49/5.28            = zero_zero_int )
% 9.49/5.28          | ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.28            & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4579_divmod__step__def,axiom,
% 9.49/5.28      ( unique5026877609467782581ep_nat
% 9.49/5.28      = ( ^ [L: num] :
% 9.49/5.28            ( produc2626176000494625587at_nat
% 9.49/5.28            @ ^ [Q4: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R5 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ one_one_nat ) @ ( minus_minus_nat @ R5 @ ( numeral_numeral_nat @ L ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4580_divmod__step__def,axiom,
% 9.49/5.28      ( unique5024387138958732305ep_int
% 9.49/5.28      = ( ^ [L: num] :
% 9.49/5.28            ( produc4245557441103728435nt_int
% 9.49/5.28            @ ^ [Q4: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R5 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ one_one_int ) @ ( minus_minus_int @ R5 @ ( numeral_numeral_int @ L ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4581_divmod__step__def,axiom,
% 9.49/5.28      ( unique4921790084139445826nteger
% 9.49/5.28      = ( ^ [L: num] :
% 9.49/5.28            ( produc6916734918728496179nteger
% 9.49/5.28            @ ^ [Q4: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4582_set__encode__insert,axiom,
% 9.49/5.28      ! [A2: set_nat,N: nat] :
% 9.49/5.28        ( ( finite_finite_nat @ A2 )
% 9.49/5.28       => ( ~ ( member_nat @ N @ A2 )
% 9.49/5.28         => ( ( nat_set_encode @ ( insert_nat @ N @ A2 ) )
% 9.49/5.28            = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( nat_set_encode @ A2 ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4583_triangle__def,axiom,
% 9.49/5.28      ( nat_triangle
% 9.49/5.28      = ( ^ [N2: nat] : ( divide_divide_nat @ ( times_times_nat @ N2 @ ( suc @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4584_vebt__buildup_Oelims,axiom,
% 9.49/5.28      ! [X: nat,Y2: vEBT_VEBT] :
% 9.49/5.28        ( ( ( vEBT_vebt_buildup @ X )
% 9.49/5.28          = Y2 )
% 9.49/5.28       => ( ( ( X = zero_zero_nat )
% 9.49/5.28           => ( Y2
% 9.49/5.28             != ( vEBT_Leaf @ $false @ $false ) ) )
% 9.49/5.28         => ( ( ( X
% 9.49/5.28                = ( suc @ zero_zero_nat ) )
% 9.49/5.28             => ( Y2
% 9.49/5.28               != ( vEBT_Leaf @ $false @ $false ) ) )
% 9.49/5.28           => ~ ! [Va2: nat] :
% 9.49/5.28                  ( ( X
% 9.49/5.28                    = ( suc @ ( suc @ Va2 ) ) )
% 9.49/5.28                 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 9.49/5.28                       => ( Y2
% 9.49/5.28                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 9.49/5.28                      & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 9.49/5.28                       => ( Y2
% 9.49/5.28                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4585_divmod__nat__if,axiom,
% 9.49/5.28      ( divmod_nat
% 9.49/5.28      = ( ^ [M6: nat,N2: nat] :
% 9.49/5.28            ( if_Pro6206227464963214023at_nat
% 9.49/5.28            @ ( ( N2 = zero_zero_nat )
% 9.49/5.28              | ( ord_less_nat @ M6 @ N2 ) )
% 9.49/5.28            @ ( product_Pair_nat_nat @ zero_zero_nat @ M6 )
% 9.49/5.28            @ ( produc2626176000494625587at_nat
% 9.49/5.28              @ ^ [Q4: nat] : ( product_Pair_nat_nat @ ( suc @ Q4 ) )
% 9.49/5.28              @ ( divmod_nat @ ( minus_minus_nat @ M6 @ N2 ) @ N2 ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4586_flip__bit__0,axiom,
% 9.49/5.28      ! [A: code_integer] :
% 9.49/5.28        ( ( bit_se1345352211410354436nteger @ zero_zero_nat @ A )
% 9.49/5.28        = ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4587_flip__bit__0,axiom,
% 9.49/5.28      ! [A: int] :
% 9.49/5.28        ( ( bit_se2159334234014336723it_int @ zero_zero_nat @ A )
% 9.49/5.28        = ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4588_flip__bit__0,axiom,
% 9.49/5.28      ! [A: nat] :
% 9.49/5.28        ( ( bit_se2161824704523386999it_nat @ zero_zero_nat @ A )
% 9.49/5.28        = ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4589_signed__take__bit__Suc,axiom,
% 9.49/5.28      ! [N: nat,A: int] :
% 9.49/5.28        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ A )
% 9.49/5.28        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4590_option_Osize__gen_I2_J,axiom,
% 9.49/5.28      ! [X: product_prod_nat_nat > nat,X23: product_prod_nat_nat] :
% 9.49/5.28        ( ( size_o8335143837870341156at_nat @ X @ ( some_P7363390416028606310at_nat @ X23 ) )
% 9.49/5.28        = ( plus_plus_nat @ ( X @ X23 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4591_option_Osize__gen_I2_J,axiom,
% 9.49/5.28      ! [X: nat > nat,X23: nat] :
% 9.49/5.28        ( ( size_option_nat @ X @ ( some_nat @ X23 ) )
% 9.49/5.28        = ( plus_plus_nat @ ( X @ X23 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4592_option_Osize__gen_I2_J,axiom,
% 9.49/5.28      ! [X: num > nat,X23: num] :
% 9.49/5.28        ( ( size_option_num @ X @ ( some_num @ X23 ) )
% 9.49/5.28        = ( plus_plus_nat @ ( X @ X23 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4593_intind,axiom,
% 9.49/5.28      ! [I2: nat,N: nat,P: nat > $o,X: nat] :
% 9.49/5.28        ( ( ord_less_nat @ I2 @ N )
% 9.49/5.28       => ( ( P @ X )
% 9.49/5.28         => ( P @ ( nth_nat @ ( replicate_nat @ N @ X ) @ I2 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4594_intind,axiom,
% 9.49/5.28      ! [I2: nat,N: nat,P: vEBT_VEBT > $o,X: vEBT_VEBT] :
% 9.49/5.28        ( ( ord_less_nat @ I2 @ N )
% 9.49/5.28       => ( ( P @ X )
% 9.49/5.28         => ( P @ ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X ) @ I2 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4595_case__prodI,axiom,
% 9.49/5.28      ! [F: product_prod_nat_nat > product_prod_nat_nat > $o,A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 9.49/5.28        ( ( F @ A @ B )
% 9.49/5.28       => ( produc6590410687421337004_nat_o @ F @ ( produc6161850002892822231at_nat @ A @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4596_case__prodI,axiom,
% 9.49/5.28      ! [F: num > num > $o,A: num,B: num] :
% 9.49/5.28        ( ( F @ A @ B )
% 9.49/5.28       => ( produc5703948589228662326_num_o @ F @ ( product_Pair_num_num @ A @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4597_case__prodI,axiom,
% 9.49/5.28      ! [F: nat > num > $o,A: nat,B: num] :
% 9.49/5.28        ( ( F @ A @ B )
% 9.49/5.28       => ( produc4927758841916487424_num_o @ F @ ( product_Pair_nat_num @ A @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4598_case__prodI,axiom,
% 9.49/5.28      ! [F: nat > nat > $o,A: nat,B: nat] :
% 9.49/5.28        ( ( F @ A @ B )
% 9.49/5.28       => ( produc6081775807080527818_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4599_case__prodI,axiom,
% 9.49/5.28      ! [F: int > int > $o,A: int,B: int] :
% 9.49/5.28        ( ( F @ A @ B )
% 9.49/5.28       => ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4600_case__prodI2,axiom,
% 9.49/5.28      ! [P6: produc859450856879609959at_nat,C: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 9.49/5.28        ( ! [A4: product_prod_nat_nat,B3: product_prod_nat_nat] :
% 9.49/5.28            ( ( P6
% 9.49/5.28              = ( produc6161850002892822231at_nat @ A4 @ B3 ) )
% 9.49/5.28           => ( C @ A4 @ B3 ) )
% 9.49/5.28       => ( produc6590410687421337004_nat_o @ C @ P6 ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4601_case__prodI2,axiom,
% 9.49/5.28      ! [P6: product_prod_num_num,C: num > num > $o] :
% 9.49/5.28        ( ! [A4: num,B3: num] :
% 9.49/5.28            ( ( P6
% 9.49/5.28              = ( product_Pair_num_num @ A4 @ B3 ) )
% 9.49/5.28           => ( C @ A4 @ B3 ) )
% 9.49/5.28       => ( produc5703948589228662326_num_o @ C @ P6 ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4602_case__prodI2,axiom,
% 9.49/5.28      ! [P6: product_prod_nat_num,C: nat > num > $o] :
% 9.49/5.28        ( ! [A4: nat,B3: num] :
% 9.49/5.28            ( ( P6
% 9.49/5.28              = ( product_Pair_nat_num @ A4 @ B3 ) )
% 9.49/5.28           => ( C @ A4 @ B3 ) )
% 9.49/5.28       => ( produc4927758841916487424_num_o @ C @ P6 ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4603_case__prodI2,axiom,
% 9.49/5.28      ! [P6: product_prod_nat_nat,C: nat > nat > $o] :
% 9.49/5.28        ( ! [A4: nat,B3: nat] :
% 9.49/5.28            ( ( P6
% 9.49/5.28              = ( product_Pair_nat_nat @ A4 @ B3 ) )
% 9.49/5.28           => ( C @ A4 @ B3 ) )
% 9.49/5.28       => ( produc6081775807080527818_nat_o @ C @ P6 ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4604_case__prodI2,axiom,
% 9.49/5.28      ! [P6: product_prod_int_int,C: int > int > $o] :
% 9.49/5.28        ( ! [A4: int,B3: int] :
% 9.49/5.28            ( ( P6
% 9.49/5.28              = ( product_Pair_int_int @ A4 @ B3 ) )
% 9.49/5.28           => ( C @ A4 @ B3 ) )
% 9.49/5.28       => ( produc4947309494688390418_int_o @ C @ P6 ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4605_mem__case__prodI,axiom,
% 9.49/5.28      ! [Z: complex,C: num > num > set_complex,A: num,B: num] :
% 9.49/5.28        ( ( member_complex @ Z @ ( C @ A @ B ) )
% 9.49/5.28       => ( member_complex @ Z @ ( produc2866383454006189126omplex @ C @ ( product_Pair_num_num @ A @ B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4606_mem__case__prodI,axiom,
% 9.49/5.28      ! [Z: real,C: num > num > set_real,A: num,B: num] :
% 9.49/5.28        ( ( member_real @ Z @ ( C @ A @ B ) )
% 9.49/5.28       => ( member_real @ Z @ ( produc8296048397933160132t_real @ C @ ( product_Pair_num_num @ A @ B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4607_mem__case__prodI,axiom,
% 9.49/5.28      ! [Z: nat,C: num > num > set_nat,A: num,B: num] :
% 9.49/5.28        ( ( member_nat @ Z @ ( C @ A @ B ) )
% 9.49/5.28       => ( member_nat @ Z @ ( produc1361121860356118632et_nat @ C @ ( product_Pair_num_num @ A @ B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4608_mem__case__prodI,axiom,
% 9.49/5.28      ! [Z: int,C: num > num > set_int,A: num,B: num] :
% 9.49/5.28        ( ( member_int @ Z @ ( C @ A @ B ) )
% 9.49/5.28       => ( member_int @ Z @ ( produc6406642877701697732et_int @ C @ ( product_Pair_num_num @ A @ B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4609_mem__case__prodI,axiom,
% 9.49/5.28      ! [Z: complex,C: nat > num > set_complex,A: nat,B: num] :
% 9.49/5.28        ( ( member_complex @ Z @ ( C @ A @ B ) )
% 9.49/5.28       => ( member_complex @ Z @ ( produc6231982587499038204omplex @ C @ ( product_Pair_nat_num @ A @ B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4610_mem__case__prodI,axiom,
% 9.49/5.28      ! [Z: real,C: nat > num > set_real,A: nat,B: num] :
% 9.49/5.28        ( ( member_real @ Z @ ( C @ A @ B ) )
% 9.49/5.28       => ( member_real @ Z @ ( produc1435849484188172666t_real @ C @ ( product_Pair_nat_num @ A @ B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4611_mem__case__prodI,axiom,
% 9.49/5.28      ! [Z: nat,C: nat > num > set_nat,A: nat,B: num] :
% 9.49/5.28        ( ( member_nat @ Z @ ( C @ A @ B ) )
% 9.49/5.28       => ( member_nat @ Z @ ( produc4130284055270567454et_nat @ C @ ( product_Pair_nat_num @ A @ B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4612_mem__case__prodI,axiom,
% 9.49/5.28      ! [Z: int,C: nat > num > set_int,A: nat,B: num] :
% 9.49/5.28        ( ( member_int @ Z @ ( C @ A @ B ) )
% 9.49/5.28       => ( member_int @ Z @ ( produc9175805072616146554et_int @ C @ ( product_Pair_nat_num @ A @ B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4613_mem__case__prodI,axiom,
% 9.49/5.28      ! [Z: complex,C: nat > nat > set_complex,A: nat,B: nat] :
% 9.49/5.28        ( ( member_complex @ Z @ ( C @ A @ B ) )
% 9.49/5.28       => ( member_complex @ Z @ ( produc3453488052772718514omplex @ C @ ( product_Pair_nat_nat @ A @ B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4614_mem__case__prodI,axiom,
% 9.49/5.28      ! [Z: real,C: nat > nat > set_real,A: nat,B: nat] :
% 9.49/5.28        ( ( member_real @ Z @ ( C @ A @ B ) )
% 9.49/5.28       => ( member_real @ Z @ ( produc3668448655016342576t_real @ C @ ( product_Pair_nat_nat @ A @ B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4615_mem__case__prodI2,axiom,
% 9.49/5.28      ! [P6: product_prod_num_num,Z: complex,C: num > num > set_complex] :
% 9.49/5.28        ( ! [A4: num,B3: num] :
% 9.49/5.28            ( ( P6
% 9.49/5.28              = ( product_Pair_num_num @ A4 @ B3 ) )
% 9.49/5.28           => ( member_complex @ Z @ ( C @ A4 @ B3 ) ) )
% 9.49/5.28       => ( member_complex @ Z @ ( produc2866383454006189126omplex @ C @ P6 ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4616_mem__case__prodI2,axiom,
% 9.49/5.28      ! [P6: product_prod_num_num,Z: real,C: num > num > set_real] :
% 9.49/5.28        ( ! [A4: num,B3: num] :
% 9.49/5.28            ( ( P6
% 9.49/5.28              = ( product_Pair_num_num @ A4 @ B3 ) )
% 9.49/5.28           => ( member_real @ Z @ ( C @ A4 @ B3 ) ) )
% 9.49/5.28       => ( member_real @ Z @ ( produc8296048397933160132t_real @ C @ P6 ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4617_mem__case__prodI2,axiom,
% 9.49/5.28      ! [P6: product_prod_num_num,Z: nat,C: num > num > set_nat] :
% 9.49/5.28        ( ! [A4: num,B3: num] :
% 9.49/5.28            ( ( P6
% 9.49/5.28              = ( product_Pair_num_num @ A4 @ B3 ) )
% 9.49/5.28           => ( member_nat @ Z @ ( C @ A4 @ B3 ) ) )
% 9.49/5.28       => ( member_nat @ Z @ ( produc1361121860356118632et_nat @ C @ P6 ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4618_mem__case__prodI2,axiom,
% 9.49/5.28      ! [P6: product_prod_num_num,Z: int,C: num > num > set_int] :
% 9.49/5.28        ( ! [A4: num,B3: num] :
% 9.49/5.28            ( ( P6
% 9.49/5.28              = ( product_Pair_num_num @ A4 @ B3 ) )
% 9.49/5.28           => ( member_int @ Z @ ( C @ A4 @ B3 ) ) )
% 9.49/5.28       => ( member_int @ Z @ ( produc6406642877701697732et_int @ C @ P6 ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4619_mem__case__prodI2,axiom,
% 9.49/5.28      ! [P6: product_prod_nat_num,Z: complex,C: nat > num > set_complex] :
% 9.49/5.28        ( ! [A4: nat,B3: num] :
% 9.49/5.28            ( ( P6
% 9.49/5.28              = ( product_Pair_nat_num @ A4 @ B3 ) )
% 9.49/5.28           => ( member_complex @ Z @ ( C @ A4 @ B3 ) ) )
% 9.49/5.28       => ( member_complex @ Z @ ( produc6231982587499038204omplex @ C @ P6 ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4620_mem__case__prodI2,axiom,
% 9.49/5.28      ! [P6: product_prod_nat_num,Z: real,C: nat > num > set_real] :
% 9.49/5.28        ( ! [A4: nat,B3: num] :
% 9.49/5.28            ( ( P6
% 9.49/5.28              = ( product_Pair_nat_num @ A4 @ B3 ) )
% 9.49/5.28           => ( member_real @ Z @ ( C @ A4 @ B3 ) ) )
% 9.49/5.28       => ( member_real @ Z @ ( produc1435849484188172666t_real @ C @ P6 ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4621_mem__case__prodI2,axiom,
% 9.49/5.28      ! [P6: product_prod_nat_num,Z: nat,C: nat > num > set_nat] :
% 9.49/5.28        ( ! [A4: nat,B3: num] :
% 9.49/5.28            ( ( P6
% 9.49/5.28              = ( product_Pair_nat_num @ A4 @ B3 ) )
% 9.49/5.28           => ( member_nat @ Z @ ( C @ A4 @ B3 ) ) )
% 9.49/5.28       => ( member_nat @ Z @ ( produc4130284055270567454et_nat @ C @ P6 ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4622_mem__case__prodI2,axiom,
% 9.49/5.28      ! [P6: product_prod_nat_num,Z: int,C: nat > num > set_int] :
% 9.49/5.28        ( ! [A4: nat,B3: num] :
% 9.49/5.28            ( ( P6
% 9.49/5.28              = ( product_Pair_nat_num @ A4 @ B3 ) )
% 9.49/5.28           => ( member_int @ Z @ ( C @ A4 @ B3 ) ) )
% 9.49/5.28       => ( member_int @ Z @ ( produc9175805072616146554et_int @ C @ P6 ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4623_mem__case__prodI2,axiom,
% 9.49/5.28      ! [P6: product_prod_nat_nat,Z: complex,C: nat > nat > set_complex] :
% 9.49/5.28        ( ! [A4: nat,B3: nat] :
% 9.49/5.28            ( ( P6
% 9.49/5.28              = ( product_Pair_nat_nat @ A4 @ B3 ) )
% 9.49/5.28           => ( member_complex @ Z @ ( C @ A4 @ B3 ) ) )
% 9.49/5.28       => ( member_complex @ Z @ ( produc3453488052772718514omplex @ C @ P6 ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4624_mem__case__prodI2,axiom,
% 9.49/5.28      ! [P6: product_prod_nat_nat,Z: real,C: nat > nat > set_real] :
% 9.49/5.28        ( ! [A4: nat,B3: nat] :
% 9.49/5.28            ( ( P6
% 9.49/5.28              = ( product_Pair_nat_nat @ A4 @ B3 ) )
% 9.49/5.28           => ( member_real @ Z @ ( C @ A4 @ B3 ) ) )
% 9.49/5.28       => ( member_real @ Z @ ( produc3668448655016342576t_real @ C @ P6 ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4625_case__prodI2_H,axiom,
% 9.49/5.28      ! [P6: product_prod_nat_nat,C: nat > nat > product_prod_nat_nat > $o,X: product_prod_nat_nat] :
% 9.49/5.28        ( ! [A4: nat,B3: nat] :
% 9.49/5.28            ( ( ( product_Pair_nat_nat @ A4 @ B3 )
% 9.49/5.28              = P6 )
% 9.49/5.28           => ( C @ A4 @ B3 @ X ) )
% 9.49/5.28       => ( produc8739625826339149834_nat_o @ C @ P6 @ X ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4626_of__bool__less__eq__iff,axiom,
% 9.49/5.28      ! [P: $o,Q: $o] :
% 9.49/5.28        ( ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 9.49/5.28        = ( P
% 9.49/5.28         => Q ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4627_of__bool__less__eq__iff,axiom,
% 9.49/5.28      ! [P: $o,Q: $o] :
% 9.49/5.28        ( ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 9.49/5.28        = ( P
% 9.49/5.28         => Q ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4628_of__bool__less__eq__iff,axiom,
% 9.49/5.28      ! [P: $o,Q: $o] :
% 9.49/5.28        ( ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 9.49/5.28        = ( P
% 9.49/5.28         => Q ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4629_of__bool__less__iff,axiom,
% 9.49/5.28      ! [P: $o,Q: $o] :
% 9.49/5.28        ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) )
% 9.49/5.28        = ( ~ P
% 9.49/5.28          & Q ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4630_of__bool__less__iff,axiom,
% 9.49/5.28      ! [P: $o,Q: $o] :
% 9.49/5.28        ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 9.49/5.28        = ( ~ P
% 9.49/5.28          & Q ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4631_of__bool__less__iff,axiom,
% 9.49/5.28      ! [P: $o,Q: $o] :
% 9.49/5.28        ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 9.49/5.28        = ( ~ P
% 9.49/5.28          & Q ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4632_of__bool__less__iff,axiom,
% 9.49/5.28      ! [P: $o,Q: $o] :
% 9.49/5.28        ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 9.49/5.28        = ( ~ P
% 9.49/5.28          & Q ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4633_of__bool__less__iff,axiom,
% 9.49/5.28      ! [P: $o,Q: $o] :
% 9.49/5.28        ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 9.49/5.28        = ( ~ P
% 9.49/5.28          & Q ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4634_of__bool__eq_I2_J,axiom,
% 9.49/5.28      ( ( zero_n1201886186963655149omplex @ $true )
% 9.49/5.28      = one_one_complex ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4635_of__bool__eq_I2_J,axiom,
% 9.49/5.28      ( ( zero_n3304061248610475627l_real @ $true )
% 9.49/5.28      = one_one_real ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4636_of__bool__eq_I2_J,axiom,
% 9.49/5.28      ( ( zero_n2052037380579107095ol_rat @ $true )
% 9.49/5.28      = one_one_rat ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4637_of__bool__eq_I2_J,axiom,
% 9.49/5.28      ( ( zero_n2687167440665602831ol_nat @ $true )
% 9.49/5.28      = one_one_nat ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4638_of__bool__eq_I2_J,axiom,
% 9.49/5.28      ( ( zero_n2684676970156552555ol_int @ $true )
% 9.49/5.28      = one_one_int ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4639_of__bool__eq_I2_J,axiom,
% 9.49/5.28      ( ( zero_n356916108424825756nteger @ $true )
% 9.49/5.28      = one_one_Code_integer ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4640_of__bool__eq__1__iff,axiom,
% 9.49/5.28      ! [P: $o] :
% 9.49/5.28        ( ( ( zero_n1201886186963655149omplex @ P )
% 9.49/5.28          = one_one_complex )
% 9.49/5.28        = P ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4641_of__bool__eq__1__iff,axiom,
% 9.49/5.28      ! [P: $o] :
% 9.49/5.28        ( ( ( zero_n3304061248610475627l_real @ P )
% 9.49/5.28          = one_one_real )
% 9.49/5.28        = P ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4642_of__bool__eq__1__iff,axiom,
% 9.49/5.28      ! [P: $o] :
% 9.49/5.28        ( ( ( zero_n2052037380579107095ol_rat @ P )
% 9.49/5.28          = one_one_rat )
% 9.49/5.28        = P ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4643_of__bool__eq__1__iff,axiom,
% 9.49/5.28      ! [P: $o] :
% 9.49/5.28        ( ( ( zero_n2687167440665602831ol_nat @ P )
% 9.49/5.28          = one_one_nat )
% 9.49/5.28        = P ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4644_of__bool__eq__1__iff,axiom,
% 9.49/5.28      ! [P: $o] :
% 9.49/5.28        ( ( ( zero_n2684676970156552555ol_int @ P )
% 9.49/5.28          = one_one_int )
% 9.49/5.28        = P ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4645_of__bool__eq__1__iff,axiom,
% 9.49/5.28      ! [P: $o] :
% 9.49/5.28        ( ( ( zero_n356916108424825756nteger @ P )
% 9.49/5.28          = one_one_Code_integer )
% 9.49/5.28        = P ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4646_signed__take__bit__of__0,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ( bit_ri631733984087533419it_int @ N @ zero_zero_int )
% 9.49/5.28        = zero_zero_int ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4647_length__replicate,axiom,
% 9.49/5.28      ! [N: nat,X: vEBT_VEBT] :
% 9.49/5.28        ( ( size_s6755466524823107622T_VEBT @ ( replicate_VEBT_VEBT @ N @ X ) )
% 9.49/5.28        = N ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4648_length__replicate,axiom,
% 9.49/5.28      ! [N: nat,X: $o] :
% 9.49/5.28        ( ( size_size_list_o @ ( replicate_o @ N @ X ) )
% 9.49/5.28        = N ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4649_length__replicate,axiom,
% 9.49/5.28      ! [N: nat,X: nat] :
% 9.49/5.28        ( ( size_size_list_nat @ ( replicate_nat @ N @ X ) )
% 9.49/5.28        = N ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4650_length__replicate,axiom,
% 9.49/5.28      ! [N: nat,X: int] :
% 9.49/5.28        ( ( size_size_list_int @ ( replicate_int @ N @ X ) )
% 9.49/5.28        = N ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4651_zero__less__of__bool__iff,axiom,
% 9.49/5.28      ! [P: $o] :
% 9.49/5.28        ( ( ord_less_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) )
% 9.49/5.28        = P ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4652_zero__less__of__bool__iff,axiom,
% 9.49/5.28      ! [P: $o] :
% 9.49/5.28        ( ( ord_less_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 9.49/5.28        = P ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4653_zero__less__of__bool__iff,axiom,
% 9.49/5.28      ! [P: $o] :
% 9.49/5.28        ( ( ord_less_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 9.49/5.28        = P ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4654_zero__less__of__bool__iff,axiom,
% 9.49/5.28      ! [P: $o] :
% 9.49/5.28        ( ( ord_less_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 9.49/5.28        = P ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4655_zero__less__of__bool__iff,axiom,
% 9.49/5.28      ! [P: $o] :
% 9.49/5.28        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) )
% 9.49/5.28        = P ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4656_of__bool__less__one__iff,axiom,
% 9.49/5.28      ! [P: $o] :
% 9.49/5.28        ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real )
% 9.49/5.28        = ~ P ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4657_of__bool__less__one__iff,axiom,
% 9.49/5.28      ! [P: $o] :
% 9.49/5.28        ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat )
% 9.49/5.28        = ~ P ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4658_of__bool__less__one__iff,axiom,
% 9.49/5.28      ! [P: $o] :
% 9.49/5.28        ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat )
% 9.49/5.28        = ~ P ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4659_of__bool__less__one__iff,axiom,
% 9.49/5.28      ! [P: $o] :
% 9.49/5.28        ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int )
% 9.49/5.28        = ~ P ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4660_of__bool__less__one__iff,axiom,
% 9.49/5.28      ! [P: $o] :
% 9.49/5.28        ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer )
% 9.49/5.28        = ~ P ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4661_of__bool__not__iff,axiom,
% 9.49/5.28      ! [P: $o] :
% 9.49/5.28        ( ( zero_n1201886186963655149omplex @ ~ P )
% 9.49/5.28        = ( minus_minus_complex @ one_one_complex @ ( zero_n1201886186963655149omplex @ P ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4662_of__bool__not__iff,axiom,
% 9.49/5.28      ! [P: $o] :
% 9.49/5.28        ( ( zero_n3304061248610475627l_real @ ~ P )
% 9.49/5.28        = ( minus_minus_real @ one_one_real @ ( zero_n3304061248610475627l_real @ P ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4663_of__bool__not__iff,axiom,
% 9.49/5.28      ! [P: $o] :
% 9.49/5.28        ( ( zero_n2052037380579107095ol_rat @ ~ P )
% 9.49/5.28        = ( minus_minus_rat @ one_one_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4664_of__bool__not__iff,axiom,
% 9.49/5.28      ! [P: $o] :
% 9.49/5.28        ( ( zero_n2684676970156552555ol_int @ ~ P )
% 9.49/5.28        = ( minus_minus_int @ one_one_int @ ( zero_n2684676970156552555ol_int @ P ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4665_of__bool__not__iff,axiom,
% 9.49/5.28      ! [P: $o] :
% 9.49/5.28        ( ( zero_n356916108424825756nteger @ ~ P )
% 9.49/5.28        = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( zero_n356916108424825756nteger @ P ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4666_Suc__0__mod__eq,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N )
% 9.49/5.28        = ( zero_n2687167440665602831ol_nat
% 9.49/5.28          @ ( N
% 9.49/5.28           != ( suc @ zero_zero_nat ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4667_signed__take__bit__Suc__1,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ one_one_int )
% 9.49/5.28        = one_one_int ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4668_signed__take__bit__numeral__of__1,axiom,
% 9.49/5.28      ! [K: num] :
% 9.49/5.28        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ K ) @ one_one_int )
% 9.49/5.28        = one_one_int ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4669_Ball__set__replicate,axiom,
% 9.49/5.28      ! [N: nat,A: int,P: int > $o] :
% 9.49/5.28        ( ( ! [X2: int] :
% 9.49/5.28              ( ( member_int @ X2 @ ( set_int2 @ ( replicate_int @ N @ A ) ) )
% 9.49/5.28             => ( P @ X2 ) ) )
% 9.49/5.28        = ( ( P @ A )
% 9.49/5.28          | ( N = zero_zero_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4670_Ball__set__replicate,axiom,
% 9.49/5.28      ! [N: nat,A: nat,P: nat > $o] :
% 9.49/5.28        ( ( ! [X2: nat] :
% 9.49/5.28              ( ( member_nat @ X2 @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 9.49/5.28             => ( P @ X2 ) ) )
% 9.49/5.28        = ( ( P @ A )
% 9.49/5.28          | ( N = zero_zero_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4671_Ball__set__replicate,axiom,
% 9.49/5.28      ! [N: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 9.49/5.28        ( ( ! [X2: vEBT_VEBT] :
% 9.49/5.28              ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 9.49/5.28             => ( P @ X2 ) ) )
% 9.49/5.28        = ( ( P @ A )
% 9.49/5.28          | ( N = zero_zero_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4672_Bex__set__replicate,axiom,
% 9.49/5.28      ! [N: nat,A: int,P: int > $o] :
% 9.49/5.28        ( ( ? [X2: int] :
% 9.49/5.28              ( ( member_int @ X2 @ ( set_int2 @ ( replicate_int @ N @ A ) ) )
% 9.49/5.28              & ( P @ X2 ) ) )
% 9.49/5.28        = ( ( P @ A )
% 9.49/5.28          & ( N != zero_zero_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4673_Bex__set__replicate,axiom,
% 9.49/5.28      ! [N: nat,A: nat,P: nat > $o] :
% 9.49/5.28        ( ( ? [X2: nat] :
% 9.49/5.28              ( ( member_nat @ X2 @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 9.49/5.28              & ( P @ X2 ) ) )
% 9.49/5.28        = ( ( P @ A )
% 9.49/5.28          & ( N != zero_zero_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4674_Bex__set__replicate,axiom,
% 9.49/5.28      ! [N: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 9.49/5.28        ( ( ? [X2: vEBT_VEBT] :
% 9.49/5.28              ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 9.49/5.28              & ( P @ X2 ) ) )
% 9.49/5.28        = ( ( P @ A )
% 9.49/5.28          & ( N != zero_zero_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4675_in__set__replicate,axiom,
% 9.49/5.28      ! [X: product_prod_nat_nat,N: nat,Y2: product_prod_nat_nat] :
% 9.49/5.28        ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ ( replic4235873036481779905at_nat @ N @ Y2 ) ) )
% 9.49/5.28        = ( ( X = Y2 )
% 9.49/5.28          & ( N != zero_zero_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4676_in__set__replicate,axiom,
% 9.49/5.28      ! [X: complex,N: nat,Y2: complex] :
% 9.49/5.28        ( ( member_complex @ X @ ( set_complex2 @ ( replicate_complex @ N @ Y2 ) ) )
% 9.49/5.28        = ( ( X = Y2 )
% 9.49/5.28          & ( N != zero_zero_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4677_in__set__replicate,axiom,
% 9.49/5.28      ! [X: real,N: nat,Y2: real] :
% 9.49/5.28        ( ( member_real @ X @ ( set_real2 @ ( replicate_real @ N @ Y2 ) ) )
% 9.49/5.28        = ( ( X = Y2 )
% 9.49/5.28          & ( N != zero_zero_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4678_in__set__replicate,axiom,
% 9.49/5.28      ! [X: int,N: nat,Y2: int] :
% 9.49/5.28        ( ( member_int @ X @ ( set_int2 @ ( replicate_int @ N @ Y2 ) ) )
% 9.49/5.28        = ( ( X = Y2 )
% 9.49/5.28          & ( N != zero_zero_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4679_in__set__replicate,axiom,
% 9.49/5.28      ! [X: nat,N: nat,Y2: nat] :
% 9.49/5.28        ( ( member_nat @ X @ ( set_nat2 @ ( replicate_nat @ N @ Y2 ) ) )
% 9.49/5.28        = ( ( X = Y2 )
% 9.49/5.28          & ( N != zero_zero_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4680_in__set__replicate,axiom,
% 9.49/5.28      ! [X: vEBT_VEBT,N: nat,Y2: vEBT_VEBT] :
% 9.49/5.28        ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ Y2 ) ) )
% 9.49/5.28        = ( ( X = Y2 )
% 9.49/5.28          & ( N != zero_zero_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4681_nth__replicate,axiom,
% 9.49/5.28      ! [I2: nat,N: nat,X: nat] :
% 9.49/5.28        ( ( ord_less_nat @ I2 @ N )
% 9.49/5.28       => ( ( nth_nat @ ( replicate_nat @ N @ X ) @ I2 )
% 9.49/5.28          = X ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4682_nth__replicate,axiom,
% 9.49/5.28      ! [I2: nat,N: nat,X: vEBT_VEBT] :
% 9.49/5.28        ( ( ord_less_nat @ I2 @ N )
% 9.49/5.28       => ( ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X ) @ I2 )
% 9.49/5.28          = X ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4683_triangle__Suc,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ( nat_triangle @ ( suc @ N ) )
% 9.49/5.28        = ( plus_plus_nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4684_signed__take__bit__Suc__bit0,axiom,
% 9.49/5.28      ! [N: nat,K: num] :
% 9.49/5.28        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 9.49/5.28        = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4685_odd__of__bool__self,axiom,
% 9.49/5.28      ! [P6: $o] :
% 9.49/5.28        ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( zero_n2687167440665602831ol_nat @ P6 ) ) )
% 9.49/5.28        = P6 ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4686_odd__of__bool__self,axiom,
% 9.49/5.28      ! [P6: $o] :
% 9.49/5.28        ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( zero_n2684676970156552555ol_int @ P6 ) ) )
% 9.49/5.28        = P6 ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4687_odd__of__bool__self,axiom,
% 9.49/5.28      ! [P6: $o] :
% 9.49/5.28        ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( zero_n356916108424825756nteger @ P6 ) ) )
% 9.49/5.28        = P6 ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4688_set__replicate,axiom,
% 9.49/5.28      ! [N: nat,X: vEBT_VEBT] :
% 9.49/5.28        ( ( N != zero_zero_nat )
% 9.49/5.28       => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X ) )
% 9.49/5.28          = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4689_set__replicate,axiom,
% 9.49/5.28      ! [N: nat,X: nat] :
% 9.49/5.28        ( ( N != zero_zero_nat )
% 9.49/5.28       => ( ( set_nat2 @ ( replicate_nat @ N @ X ) )
% 9.49/5.28          = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4690_set__replicate,axiom,
% 9.49/5.28      ! [N: nat,X: int] :
% 9.49/5.28        ( ( N != zero_zero_nat )
% 9.49/5.28       => ( ( set_int2 @ ( replicate_int @ N @ X ) )
% 9.49/5.28          = ( insert_int @ X @ bot_bot_set_int ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4691_set__replicate,axiom,
% 9.49/5.28      ! [N: nat,X: real] :
% 9.49/5.28        ( ( N != zero_zero_nat )
% 9.49/5.28       => ( ( set_real2 @ ( replicate_real @ N @ X ) )
% 9.49/5.28          = ( insert_real @ X @ bot_bot_set_real ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4692_of__bool__half__eq__0,axiom,
% 9.49/5.28      ! [B: $o] :
% 9.49/5.28        ( ( divide_divide_nat @ ( zero_n2687167440665602831ol_nat @ B ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.28        = zero_zero_nat ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4693_of__bool__half__eq__0,axiom,
% 9.49/5.28      ! [B: $o] :
% 9.49/5.28        ( ( divide_divide_int @ ( zero_n2684676970156552555ol_int @ B ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.49/5.28        = zero_zero_int ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4694_of__bool__half__eq__0,axiom,
% 9.49/5.28      ! [B: $o] :
% 9.49/5.28        ( ( divide6298287555418463151nteger @ ( zero_n356916108424825756nteger @ B ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.49/5.28        = zero_z3403309356797280102nteger ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4695_one__div__2__pow__eq,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.28        = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4696_one__div__2__pow__eq,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.28        = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4697_one__div__2__pow__eq,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.28        = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4698_bits__1__div__exp,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.28        = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4699_bits__1__div__exp,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.28        = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4700_bits__1__div__exp,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.28        = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4701_signed__take__bit__Suc__bit1,axiom,
% 9.49/5.28      ! [N: nat,K: num] :
% 9.49/5.28        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 9.49/5.28        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4702_one__mod__2__pow__eq,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ( modulo_modulo_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.28        = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4703_one__mod__2__pow__eq,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ( modulo_modulo_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.28        = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4704_one__mod__2__pow__eq,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.28        = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4705_dvd__antisym,axiom,
% 9.49/5.28      ! [M: nat,N: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ M @ N )
% 9.49/5.28       => ( ( dvd_dvd_nat @ N @ M )
% 9.49/5.28         => ( M = N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4706_of__bool__conj,axiom,
% 9.49/5.28      ! [P: $o,Q: $o] :
% 9.49/5.28        ( ( zero_n1201886186963655149omplex
% 9.49/5.28          @ ( P
% 9.49/5.28            & Q ) )
% 9.49/5.28        = ( times_times_complex @ ( zero_n1201886186963655149omplex @ P ) @ ( zero_n1201886186963655149omplex @ Q ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4707_of__bool__conj,axiom,
% 9.49/5.28      ! [P: $o,Q: $o] :
% 9.49/5.28        ( ( zero_n3304061248610475627l_real
% 9.49/5.28          @ ( P
% 9.49/5.28            & Q ) )
% 9.49/5.28        = ( times_times_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4708_of__bool__conj,axiom,
% 9.49/5.28      ! [P: $o,Q: $o] :
% 9.49/5.28        ( ( zero_n2687167440665602831ol_nat
% 9.49/5.28          @ ( P
% 9.49/5.28            & Q ) )
% 9.49/5.28        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4709_of__bool__conj,axiom,
% 9.49/5.28      ! [P: $o,Q: $o] :
% 9.49/5.28        ( ( zero_n2684676970156552555ol_int
% 9.49/5.28          @ ( P
% 9.49/5.28            & Q ) )
% 9.49/5.28        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4710_of__bool__conj,axiom,
% 9.49/5.28      ! [P: $o,Q: $o] :
% 9.49/5.28        ( ( zero_n356916108424825756nteger
% 9.49/5.28          @ ( P
% 9.49/5.28            & Q ) )
% 9.49/5.28        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4711_mem__case__prodE,axiom,
% 9.49/5.28      ! [Z: complex,C: num > num > set_complex,P6: product_prod_num_num] :
% 9.49/5.28        ( ( member_complex @ Z @ ( produc2866383454006189126omplex @ C @ P6 ) )
% 9.49/5.28       => ~ ! [X3: num,Y3: num] :
% 9.49/5.28              ( ( P6
% 9.49/5.28                = ( product_Pair_num_num @ X3 @ Y3 ) )
% 9.49/5.28             => ~ ( member_complex @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4712_mem__case__prodE,axiom,
% 9.49/5.28      ! [Z: real,C: num > num > set_real,P6: product_prod_num_num] :
% 9.49/5.28        ( ( member_real @ Z @ ( produc8296048397933160132t_real @ C @ P6 ) )
% 9.49/5.28       => ~ ! [X3: num,Y3: num] :
% 9.49/5.28              ( ( P6
% 9.49/5.28                = ( product_Pair_num_num @ X3 @ Y3 ) )
% 9.49/5.28             => ~ ( member_real @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4713_mem__case__prodE,axiom,
% 9.49/5.28      ! [Z: nat,C: num > num > set_nat,P6: product_prod_num_num] :
% 9.49/5.28        ( ( member_nat @ Z @ ( produc1361121860356118632et_nat @ C @ P6 ) )
% 9.49/5.28       => ~ ! [X3: num,Y3: num] :
% 9.49/5.28              ( ( P6
% 9.49/5.28                = ( product_Pair_num_num @ X3 @ Y3 ) )
% 9.49/5.28             => ~ ( member_nat @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4714_mem__case__prodE,axiom,
% 9.49/5.28      ! [Z: int,C: num > num > set_int,P6: product_prod_num_num] :
% 9.49/5.28        ( ( member_int @ Z @ ( produc6406642877701697732et_int @ C @ P6 ) )
% 9.49/5.28       => ~ ! [X3: num,Y3: num] :
% 9.49/5.28              ( ( P6
% 9.49/5.28                = ( product_Pair_num_num @ X3 @ Y3 ) )
% 9.49/5.28             => ~ ( member_int @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4715_mem__case__prodE,axiom,
% 9.49/5.28      ! [Z: complex,C: nat > num > set_complex,P6: product_prod_nat_num] :
% 9.49/5.28        ( ( member_complex @ Z @ ( produc6231982587499038204omplex @ C @ P6 ) )
% 9.49/5.28       => ~ ! [X3: nat,Y3: num] :
% 9.49/5.28              ( ( P6
% 9.49/5.28                = ( product_Pair_nat_num @ X3 @ Y3 ) )
% 9.49/5.28             => ~ ( member_complex @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4716_mem__case__prodE,axiom,
% 9.49/5.28      ! [Z: real,C: nat > num > set_real,P6: product_prod_nat_num] :
% 9.49/5.28        ( ( member_real @ Z @ ( produc1435849484188172666t_real @ C @ P6 ) )
% 9.49/5.28       => ~ ! [X3: nat,Y3: num] :
% 9.49/5.28              ( ( P6
% 9.49/5.28                = ( product_Pair_nat_num @ X3 @ Y3 ) )
% 9.49/5.28             => ~ ( member_real @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4717_mem__case__prodE,axiom,
% 9.49/5.28      ! [Z: nat,C: nat > num > set_nat,P6: product_prod_nat_num] :
% 9.49/5.28        ( ( member_nat @ Z @ ( produc4130284055270567454et_nat @ C @ P6 ) )
% 9.49/5.28       => ~ ! [X3: nat,Y3: num] :
% 9.49/5.28              ( ( P6
% 9.49/5.28                = ( product_Pair_nat_num @ X3 @ Y3 ) )
% 9.49/5.28             => ~ ( member_nat @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4718_mem__case__prodE,axiom,
% 9.49/5.28      ! [Z: int,C: nat > num > set_int,P6: product_prod_nat_num] :
% 9.49/5.28        ( ( member_int @ Z @ ( produc9175805072616146554et_int @ C @ P6 ) )
% 9.49/5.28       => ~ ! [X3: nat,Y3: num] :
% 9.49/5.28              ( ( P6
% 9.49/5.28                = ( product_Pair_nat_num @ X3 @ Y3 ) )
% 9.49/5.28             => ~ ( member_int @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4719_mem__case__prodE,axiom,
% 9.49/5.28      ! [Z: complex,C: nat > nat > set_complex,P6: product_prod_nat_nat] :
% 9.49/5.28        ( ( member_complex @ Z @ ( produc3453488052772718514omplex @ C @ P6 ) )
% 9.49/5.28       => ~ ! [X3: nat,Y3: nat] :
% 9.49/5.28              ( ( P6
% 9.49/5.28                = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 9.49/5.28             => ~ ( member_complex @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4720_mem__case__prodE,axiom,
% 9.49/5.28      ! [Z: real,C: nat > nat > set_real,P6: product_prod_nat_nat] :
% 9.49/5.28        ( ( member_real @ Z @ ( produc3668448655016342576t_real @ C @ P6 ) )
% 9.49/5.28       => ~ ! [X3: nat,Y3: nat] :
% 9.49/5.28              ( ( P6
% 9.49/5.28                = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 9.49/5.28             => ~ ( member_real @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4721_signed__take__bit__mult,axiom,
% 9.49/5.28      ! [N: nat,K: int,L2: int] :
% 9.49/5.28        ( ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L2 ) ) )
% 9.49/5.28        = ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ K @ L2 ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4722_signed__take__bit__add,axiom,
% 9.49/5.28      ! [N: nat,K: int,L2: int] :
% 9.49/5.28        ( ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L2 ) ) )
% 9.49/5.28        = ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4723_signed__take__bit__diff,axiom,
% 9.49/5.28      ! [N: nat,K: int,L2: int] :
% 9.49/5.28        ( ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L2 ) ) )
% 9.49/5.28        = ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ K @ L2 ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4724_case__prodD,axiom,
% 9.49/5.28      ! [F: product_prod_nat_nat > product_prod_nat_nat > $o,A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 9.49/5.28        ( ( produc6590410687421337004_nat_o @ F @ ( produc6161850002892822231at_nat @ A @ B ) )
% 9.49/5.28       => ( F @ A @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4725_case__prodD,axiom,
% 9.49/5.28      ! [F: num > num > $o,A: num,B: num] :
% 9.49/5.28        ( ( produc5703948589228662326_num_o @ F @ ( product_Pair_num_num @ A @ B ) )
% 9.49/5.28       => ( F @ A @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4726_case__prodD,axiom,
% 9.49/5.28      ! [F: nat > num > $o,A: nat,B: num] :
% 9.49/5.28        ( ( produc4927758841916487424_num_o @ F @ ( product_Pair_nat_num @ A @ B ) )
% 9.49/5.28       => ( F @ A @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4727_case__prodD,axiom,
% 9.49/5.28      ! [F: nat > nat > $o,A: nat,B: nat] :
% 9.49/5.28        ( ( produc6081775807080527818_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 9.49/5.28       => ( F @ A @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4728_case__prodD,axiom,
% 9.49/5.28      ! [F: int > int > $o,A: int,B: int] :
% 9.49/5.28        ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) )
% 9.49/5.28       => ( F @ A @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4729_case__prodE,axiom,
% 9.49/5.28      ! [C: product_prod_nat_nat > product_prod_nat_nat > $o,P6: produc859450856879609959at_nat] :
% 9.49/5.28        ( ( produc6590410687421337004_nat_o @ C @ P6 )
% 9.49/5.28       => ~ ! [X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 9.49/5.28              ( ( P6
% 9.49/5.28                = ( produc6161850002892822231at_nat @ X3 @ Y3 ) )
% 9.49/5.28             => ~ ( C @ X3 @ Y3 ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4730_case__prodE,axiom,
% 9.49/5.28      ! [C: num > num > $o,P6: product_prod_num_num] :
% 9.49/5.28        ( ( produc5703948589228662326_num_o @ C @ P6 )
% 9.49/5.28       => ~ ! [X3: num,Y3: num] :
% 9.49/5.28              ( ( P6
% 9.49/5.28                = ( product_Pair_num_num @ X3 @ Y3 ) )
% 9.49/5.28             => ~ ( C @ X3 @ Y3 ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4731_case__prodE,axiom,
% 9.49/5.28      ! [C: nat > num > $o,P6: product_prod_nat_num] :
% 9.49/5.28        ( ( produc4927758841916487424_num_o @ C @ P6 )
% 9.49/5.28       => ~ ! [X3: nat,Y3: num] :
% 9.49/5.28              ( ( P6
% 9.49/5.28                = ( product_Pair_nat_num @ X3 @ Y3 ) )
% 9.49/5.28             => ~ ( C @ X3 @ Y3 ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4732_case__prodE,axiom,
% 9.49/5.28      ! [C: nat > nat > $o,P6: product_prod_nat_nat] :
% 9.49/5.28        ( ( produc6081775807080527818_nat_o @ C @ P6 )
% 9.49/5.28       => ~ ! [X3: nat,Y3: nat] :
% 9.49/5.28              ( ( P6
% 9.49/5.28                = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 9.49/5.28             => ~ ( C @ X3 @ Y3 ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4733_case__prodE,axiom,
% 9.49/5.28      ! [C: int > int > $o,P6: product_prod_int_int] :
% 9.49/5.28        ( ( produc4947309494688390418_int_o @ C @ P6 )
% 9.49/5.28       => ~ ! [X3: int,Y3: int] :
% 9.49/5.28              ( ( P6
% 9.49/5.28                = ( product_Pair_int_int @ X3 @ Y3 ) )
% 9.49/5.28             => ~ ( C @ X3 @ Y3 ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4734_case__prodD_H,axiom,
% 9.49/5.28      ! [R2: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat,C: product_prod_nat_nat] :
% 9.49/5.28        ( ( produc8739625826339149834_nat_o @ R2 @ ( product_Pair_nat_nat @ A @ B ) @ C )
% 9.49/5.28       => ( R2 @ A @ B @ C ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4735_case__prodE_H,axiom,
% 9.49/5.28      ! [C: nat > nat > product_prod_nat_nat > $o,P6: product_prod_nat_nat,Z: product_prod_nat_nat] :
% 9.49/5.28        ( ( produc8739625826339149834_nat_o @ C @ P6 @ Z )
% 9.49/5.28       => ~ ! [X3: nat,Y3: nat] :
% 9.49/5.28              ( ( P6
% 9.49/5.28                = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 9.49/5.28             => ~ ( C @ X3 @ Y3 @ Z ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4736_zero__less__eq__of__bool,axiom,
% 9.49/5.28      ! [P: $o] : ( ord_less_eq_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4737_zero__less__eq__of__bool,axiom,
% 9.49/5.28      ! [P: $o] : ( ord_less_eq_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4738_zero__less__eq__of__bool,axiom,
% 9.49/5.28      ! [P: $o] : ( ord_less_eq_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4739_zero__less__eq__of__bool,axiom,
% 9.49/5.28      ! [P: $o] : ( ord_less_eq_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4740_zero__less__eq__of__bool,axiom,
% 9.49/5.28      ! [P: $o] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4741_of__bool__less__eq__one,axiom,
% 9.49/5.28      ! [P: $o] : ( ord_less_eq_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4742_of__bool__less__eq__one,axiom,
% 9.49/5.28      ! [P: $o] : ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4743_of__bool__less__eq__one,axiom,
% 9.49/5.28      ! [P: $o] : ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4744_of__bool__less__eq__one,axiom,
% 9.49/5.28      ! [P: $o] : ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4745_of__bool__less__eq__one,axiom,
% 9.49/5.28      ! [P: $o] : ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4746_of__bool__def,axiom,
% 9.49/5.28      ( zero_n1201886186963655149omplex
% 9.49/5.28      = ( ^ [P4: $o] : ( if_complex @ P4 @ one_one_complex @ zero_zero_complex ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4747_of__bool__def,axiom,
% 9.49/5.28      ( zero_n3304061248610475627l_real
% 9.49/5.28      = ( ^ [P4: $o] : ( if_real @ P4 @ one_one_real @ zero_zero_real ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4748_of__bool__def,axiom,
% 9.49/5.28      ( zero_n2052037380579107095ol_rat
% 9.49/5.28      = ( ^ [P4: $o] : ( if_rat @ P4 @ one_one_rat @ zero_zero_rat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4749_of__bool__def,axiom,
% 9.49/5.28      ( zero_n2687167440665602831ol_nat
% 9.49/5.28      = ( ^ [P4: $o] : ( if_nat @ P4 @ one_one_nat @ zero_zero_nat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4750_of__bool__def,axiom,
% 9.49/5.28      ( zero_n2684676970156552555ol_int
% 9.49/5.28      = ( ^ [P4: $o] : ( if_int @ P4 @ one_one_int @ zero_zero_int ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4751_of__bool__def,axiom,
% 9.49/5.28      ( zero_n356916108424825756nteger
% 9.49/5.28      = ( ^ [P4: $o] : ( if_Code_integer @ P4 @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4752_split__of__bool,axiom,
% 9.49/5.28      ! [P: complex > $o,P6: $o] :
% 9.49/5.28        ( ( P @ ( zero_n1201886186963655149omplex @ P6 ) )
% 9.49/5.28        = ( ( P6
% 9.49/5.28           => ( P @ one_one_complex ) )
% 9.49/5.28          & ( ~ P6
% 9.49/5.28           => ( P @ zero_zero_complex ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4753_split__of__bool,axiom,
% 9.49/5.28      ! [P: real > $o,P6: $o] :
% 9.49/5.28        ( ( P @ ( zero_n3304061248610475627l_real @ P6 ) )
% 9.49/5.28        = ( ( P6
% 9.49/5.28           => ( P @ one_one_real ) )
% 9.49/5.28          & ( ~ P6
% 9.49/5.28           => ( P @ zero_zero_real ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4754_split__of__bool,axiom,
% 9.49/5.28      ! [P: rat > $o,P6: $o] :
% 9.49/5.28        ( ( P @ ( zero_n2052037380579107095ol_rat @ P6 ) )
% 9.49/5.28        = ( ( P6
% 9.49/5.28           => ( P @ one_one_rat ) )
% 9.49/5.28          & ( ~ P6
% 9.49/5.28           => ( P @ zero_zero_rat ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4755_split__of__bool,axiom,
% 9.49/5.28      ! [P: nat > $o,P6: $o] :
% 9.49/5.28        ( ( P @ ( zero_n2687167440665602831ol_nat @ P6 ) )
% 9.49/5.28        = ( ( P6
% 9.49/5.28           => ( P @ one_one_nat ) )
% 9.49/5.28          & ( ~ P6
% 9.49/5.28           => ( P @ zero_zero_nat ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4756_split__of__bool,axiom,
% 9.49/5.28      ! [P: int > $o,P6: $o] :
% 9.49/5.28        ( ( P @ ( zero_n2684676970156552555ol_int @ P6 ) )
% 9.49/5.28        = ( ( P6
% 9.49/5.28           => ( P @ one_one_int ) )
% 9.49/5.28          & ( ~ P6
% 9.49/5.28           => ( P @ zero_zero_int ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4757_split__of__bool,axiom,
% 9.49/5.28      ! [P: code_integer > $o,P6: $o] :
% 9.49/5.28        ( ( P @ ( zero_n356916108424825756nteger @ P6 ) )
% 9.49/5.28        = ( ( P6
% 9.49/5.28           => ( P @ one_one_Code_integer ) )
% 9.49/5.28          & ( ~ P6
% 9.49/5.28           => ( P @ zero_z3403309356797280102nteger ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4758_split__of__bool__asm,axiom,
% 9.49/5.28      ! [P: complex > $o,P6: $o] :
% 9.49/5.28        ( ( P @ ( zero_n1201886186963655149omplex @ P6 ) )
% 9.49/5.28        = ( ~ ( ( P6
% 9.49/5.28                & ~ ( P @ one_one_complex ) )
% 9.49/5.28              | ( ~ P6
% 9.49/5.28                & ~ ( P @ zero_zero_complex ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4759_split__of__bool__asm,axiom,
% 9.49/5.28      ! [P: real > $o,P6: $o] :
% 9.49/5.28        ( ( P @ ( zero_n3304061248610475627l_real @ P6 ) )
% 9.49/5.28        = ( ~ ( ( P6
% 9.49/5.28                & ~ ( P @ one_one_real ) )
% 9.49/5.28              | ( ~ P6
% 9.49/5.28                & ~ ( P @ zero_zero_real ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4760_split__of__bool__asm,axiom,
% 9.49/5.28      ! [P: rat > $o,P6: $o] :
% 9.49/5.28        ( ( P @ ( zero_n2052037380579107095ol_rat @ P6 ) )
% 9.49/5.28        = ( ~ ( ( P6
% 9.49/5.28                & ~ ( P @ one_one_rat ) )
% 9.49/5.28              | ( ~ P6
% 9.49/5.28                & ~ ( P @ zero_zero_rat ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4761_split__of__bool__asm,axiom,
% 9.49/5.28      ! [P: nat > $o,P6: $o] :
% 9.49/5.28        ( ( P @ ( zero_n2687167440665602831ol_nat @ P6 ) )
% 9.49/5.28        = ( ~ ( ( P6
% 9.49/5.28                & ~ ( P @ one_one_nat ) )
% 9.49/5.28              | ( ~ P6
% 9.49/5.28                & ~ ( P @ zero_zero_nat ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4762_split__of__bool__asm,axiom,
% 9.49/5.28      ! [P: int > $o,P6: $o] :
% 9.49/5.28        ( ( P @ ( zero_n2684676970156552555ol_int @ P6 ) )
% 9.49/5.28        = ( ~ ( ( P6
% 9.49/5.28                & ~ ( P @ one_one_int ) )
% 9.49/5.28              | ( ~ P6
% 9.49/5.28                & ~ ( P @ zero_zero_int ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4763_split__of__bool__asm,axiom,
% 9.49/5.28      ! [P: code_integer > $o,P6: $o] :
% 9.49/5.28        ( ( P @ ( zero_n356916108424825756nteger @ P6 ) )
% 9.49/5.28        = ( ~ ( ( P6
% 9.49/5.28                & ~ ( P @ one_one_Code_integer ) )
% 9.49/5.28              | ( ~ P6
% 9.49/5.28                & ~ ( P @ zero_z3403309356797280102nteger ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4764_replicate__eqI,axiom,
% 9.49/5.28      ! [Xs2: list_P6011104703257516679at_nat,N: nat,X: product_prod_nat_nat] :
% 9.49/5.28        ( ( ( size_s5460976970255530739at_nat @ Xs2 )
% 9.49/5.28          = N )
% 9.49/5.28       => ( ! [Y3: product_prod_nat_nat] :
% 9.49/5.28              ( ( member8440522571783428010at_nat @ Y3 @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 9.49/5.28             => ( Y3 = X ) )
% 9.49/5.28         => ( Xs2
% 9.49/5.28            = ( replic4235873036481779905at_nat @ N @ X ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4765_replicate__eqI,axiom,
% 9.49/5.28      ! [Xs2: list_complex,N: nat,X: complex] :
% 9.49/5.28        ( ( ( size_s3451745648224563538omplex @ Xs2 )
% 9.49/5.28          = N )
% 9.49/5.28       => ( ! [Y3: complex] :
% 9.49/5.28              ( ( member_complex @ Y3 @ ( set_complex2 @ Xs2 ) )
% 9.49/5.28             => ( Y3 = X ) )
% 9.49/5.28         => ( Xs2
% 9.49/5.28            = ( replicate_complex @ N @ X ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4766_replicate__eqI,axiom,
% 9.49/5.28      ! [Xs2: list_real,N: nat,X: real] :
% 9.49/5.28        ( ( ( size_size_list_real @ Xs2 )
% 9.49/5.28          = N )
% 9.49/5.28       => ( ! [Y3: real] :
% 9.49/5.28              ( ( member_real @ Y3 @ ( set_real2 @ Xs2 ) )
% 9.49/5.28             => ( Y3 = X ) )
% 9.49/5.28         => ( Xs2
% 9.49/5.28            = ( replicate_real @ N @ X ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4767_replicate__eqI,axiom,
% 9.49/5.28      ! [Xs2: list_VEBT_VEBT,N: nat,X: vEBT_VEBT] :
% 9.49/5.28        ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 9.49/5.28          = N )
% 9.49/5.28       => ( ! [Y3: vEBT_VEBT] :
% 9.49/5.28              ( ( member_VEBT_VEBT @ Y3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 9.49/5.28             => ( Y3 = X ) )
% 9.49/5.28         => ( Xs2
% 9.49/5.28            = ( replicate_VEBT_VEBT @ N @ X ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4768_replicate__eqI,axiom,
% 9.49/5.28      ! [Xs2: list_o,N: nat,X: $o] :
% 9.49/5.28        ( ( ( size_size_list_o @ Xs2 )
% 9.49/5.28          = N )
% 9.49/5.28       => ( ! [Y3: $o] :
% 9.49/5.28              ( ( member_o @ Y3 @ ( set_o2 @ Xs2 ) )
% 9.49/5.28             => ( Y3 = X ) )
% 9.49/5.28         => ( Xs2
% 9.49/5.28            = ( replicate_o @ N @ X ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4769_replicate__eqI,axiom,
% 9.49/5.28      ! [Xs2: list_nat,N: nat,X: nat] :
% 9.49/5.28        ( ( ( size_size_list_nat @ Xs2 )
% 9.49/5.28          = N )
% 9.49/5.28       => ( ! [Y3: nat] :
% 9.49/5.28              ( ( member_nat @ Y3 @ ( set_nat2 @ Xs2 ) )
% 9.49/5.28             => ( Y3 = X ) )
% 9.49/5.28         => ( Xs2
% 9.49/5.28            = ( replicate_nat @ N @ X ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4770_replicate__eqI,axiom,
% 9.49/5.28      ! [Xs2: list_int,N: nat,X: int] :
% 9.49/5.28        ( ( ( size_size_list_int @ Xs2 )
% 9.49/5.28          = N )
% 9.49/5.28       => ( ! [Y3: int] :
% 9.49/5.28              ( ( member_int @ Y3 @ ( set_int2 @ Xs2 ) )
% 9.49/5.28             => ( Y3 = X ) )
% 9.49/5.28         => ( Xs2
% 9.49/5.28            = ( replicate_int @ N @ X ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4771_replicate__length__same,axiom,
% 9.49/5.28      ! [Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 9.49/5.28        ( ! [X3: vEBT_VEBT] :
% 9.49/5.28            ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 9.49/5.28           => ( X3 = X ) )
% 9.49/5.28       => ( ( replicate_VEBT_VEBT @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ X )
% 9.49/5.28          = Xs2 ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4772_replicate__length__same,axiom,
% 9.49/5.28      ! [Xs2: list_o,X: $o] :
% 9.49/5.28        ( ! [X3: $o] :
% 9.49/5.28            ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 9.49/5.28           => ( X3 = X ) )
% 9.49/5.28       => ( ( replicate_o @ ( size_size_list_o @ Xs2 ) @ X )
% 9.49/5.28          = Xs2 ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4773_replicate__length__same,axiom,
% 9.49/5.28      ! [Xs2: list_nat,X: nat] :
% 9.49/5.28        ( ! [X3: nat] :
% 9.49/5.28            ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 9.49/5.28           => ( X3 = X ) )
% 9.49/5.28       => ( ( replicate_nat @ ( size_size_list_nat @ Xs2 ) @ X )
% 9.49/5.28          = Xs2 ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4774_replicate__length__same,axiom,
% 9.49/5.28      ! [Xs2: list_int,X: int] :
% 9.49/5.28        ( ! [X3: int] :
% 9.49/5.28            ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 9.49/5.28           => ( X3 = X ) )
% 9.49/5.28       => ( ( replicate_int @ ( size_size_list_int @ Xs2 ) @ X )
% 9.49/5.28          = Xs2 ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4775_set__replicate__Suc,axiom,
% 9.49/5.28      ! [N: nat,X: vEBT_VEBT] :
% 9.49/5.28        ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ ( suc @ N ) @ X ) )
% 9.49/5.28        = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4776_set__replicate__Suc,axiom,
% 9.49/5.28      ! [N: nat,X: nat] :
% 9.49/5.28        ( ( set_nat2 @ ( replicate_nat @ ( suc @ N ) @ X ) )
% 9.49/5.28        = ( insert_nat @ X @ bot_bot_set_nat ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4777_set__replicate__Suc,axiom,
% 9.49/5.28      ! [N: nat,X: int] :
% 9.49/5.28        ( ( set_int2 @ ( replicate_int @ ( suc @ N ) @ X ) )
% 9.49/5.28        = ( insert_int @ X @ bot_bot_set_int ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4778_set__replicate__Suc,axiom,
% 9.49/5.28      ! [N: nat,X: real] :
% 9.49/5.28        ( ( set_real2 @ ( replicate_real @ ( suc @ N ) @ X ) )
% 9.49/5.28        = ( insert_real @ X @ bot_bot_set_real ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4779_set__replicate__conv__if,axiom,
% 9.49/5.28      ! [N: nat,X: vEBT_VEBT] :
% 9.49/5.28        ( ( ( N = zero_zero_nat )
% 9.49/5.28         => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X ) )
% 9.49/5.28            = bot_bo8194388402131092736T_VEBT ) )
% 9.49/5.28        & ( ( N != zero_zero_nat )
% 9.49/5.28         => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X ) )
% 9.49/5.28            = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4780_set__replicate__conv__if,axiom,
% 9.49/5.28      ! [N: nat,X: nat] :
% 9.49/5.28        ( ( ( N = zero_zero_nat )
% 9.49/5.28         => ( ( set_nat2 @ ( replicate_nat @ N @ X ) )
% 9.49/5.28            = bot_bot_set_nat ) )
% 9.49/5.28        & ( ( N != zero_zero_nat )
% 9.49/5.28         => ( ( set_nat2 @ ( replicate_nat @ N @ X ) )
% 9.49/5.28            = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4781_set__replicate__conv__if,axiom,
% 9.49/5.28      ! [N: nat,X: int] :
% 9.49/5.28        ( ( ( N = zero_zero_nat )
% 9.49/5.28         => ( ( set_int2 @ ( replicate_int @ N @ X ) )
% 9.49/5.28            = bot_bot_set_int ) )
% 9.49/5.28        & ( ( N != zero_zero_nat )
% 9.49/5.28         => ( ( set_int2 @ ( replicate_int @ N @ X ) )
% 9.49/5.28            = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4782_set__replicate__conv__if,axiom,
% 9.49/5.28      ! [N: nat,X: real] :
% 9.49/5.28        ( ( ( N = zero_zero_nat )
% 9.49/5.28         => ( ( set_real2 @ ( replicate_real @ N @ X ) )
% 9.49/5.28            = bot_bot_set_real ) )
% 9.49/5.28        & ( ( N != zero_zero_nat )
% 9.49/5.28         => ( ( set_real2 @ ( replicate_real @ N @ X ) )
% 9.49/5.28            = ( insert_real @ X @ bot_bot_set_real ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4783_of__bool__odd__eq__mod__2,axiom,
% 9.49/5.28      ! [A: nat] :
% 9.49/5.28        ( ( zero_n2687167440665602831ol_nat
% 9.49/5.28          @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 9.49/5.28        = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4784_of__bool__odd__eq__mod__2,axiom,
% 9.49/5.28      ! [A: int] :
% 9.49/5.28        ( ( zero_n2684676970156552555ol_int
% 9.49/5.28          @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 9.49/5.28        = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4785_of__bool__odd__eq__mod__2,axiom,
% 9.49/5.28      ! [A: code_integer] :
% 9.49/5.28        ( ( zero_n356916108424825756nteger
% 9.49/5.28          @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 9.49/5.28        = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4786_signed__take__bit__int__less__exp,axiom,
% 9.49/5.28      ! [N: nat,K: int] : ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4787_even__signed__take__bit__iff,axiom,
% 9.49/5.28      ! [M: nat,A: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ M @ A ) )
% 9.49/5.28        = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4788_even__signed__take__bit__iff,axiom,
% 9.49/5.28      ! [M: nat,A: int] :
% 9.49/5.28        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ M @ A ) )
% 9.49/5.28        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4789_bits__induct,axiom,
% 9.49/5.28      ! [P: nat > $o,A: nat] :
% 9.49/5.28        ( ! [A4: nat] :
% 9.49/5.28            ( ( ( divide_divide_nat @ A4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.28              = A4 )
% 9.49/5.28           => ( P @ A4 ) )
% 9.49/5.28       => ( ! [A4: nat,B3: $o] :
% 9.49/5.28              ( ( P @ A4 )
% 9.49/5.28             => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B3 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.28                  = A4 )
% 9.49/5.28               => ( P @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B3 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A4 ) ) ) ) )
% 9.49/5.28         => ( P @ A ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4790_bits__induct,axiom,
% 9.49/5.28      ! [P: int > $o,A: int] :
% 9.49/5.28        ( ! [A4: int] :
% 9.49/5.28            ( ( ( divide_divide_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.49/5.28              = A4 )
% 9.49/5.28           => ( P @ A4 ) )
% 9.49/5.28       => ( ! [A4: int,B3: $o] :
% 9.49/5.28              ( ( P @ A4 )
% 9.49/5.28             => ( ( ( divide_divide_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B3 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A4 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.49/5.28                  = A4 )
% 9.49/5.28               => ( P @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B3 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A4 ) ) ) ) )
% 9.49/5.28         => ( P @ A ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4791_bits__induct,axiom,
% 9.49/5.28      ! [P: code_integer > $o,A: code_integer] :
% 9.49/5.28        ( ! [A4: code_integer] :
% 9.49/5.28            ( ( ( divide6298287555418463151nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.49/5.28              = A4 )
% 9.49/5.28           => ( P @ A4 ) )
% 9.49/5.28       => ( ! [A4: code_integer,B3: $o] :
% 9.49/5.28              ( ( P @ A4 )
% 9.49/5.28             => ( ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B3 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A4 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.49/5.28                  = A4 )
% 9.49/5.28               => ( P @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B3 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A4 ) ) ) ) )
% 9.49/5.28         => ( P @ A ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4792_signed__take__bit__int__less__self__iff,axiom,
% 9.49/5.28      ! [N: nat,K: int] :
% 9.49/5.28        ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 9.49/5.28        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4793_signed__take__bit__int__greater__eq__self__iff,axiom,
% 9.49/5.28      ! [K: int,N: nat] :
% 9.49/5.28        ( ( ord_less_eq_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 9.49/5.28        = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4794_exp__mod__exp,axiom,
% 9.49/5.28      ! [M: nat,N: nat] :
% 9.49/5.28        ( ( modulo_modulo_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.28        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ M @ N ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4795_exp__mod__exp,axiom,
% 9.49/5.28      ! [M: nat,N: nat] :
% 9.49/5.28        ( ( modulo_modulo_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.28        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ M @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4796_exp__mod__exp,axiom,
% 9.49/5.28      ! [M: nat,N: nat] :
% 9.49/5.28        ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.28        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ M @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4797_divmod__nat__def,axiom,
% 9.49/5.28      ( divmod_nat
% 9.49/5.28      = ( ^ [M6: nat,N2: nat] : ( product_Pair_nat_nat @ ( divide_divide_nat @ M6 @ N2 ) @ ( modulo_modulo_nat @ M6 @ N2 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4798_signed__take__bit__int__less__eq,axiom,
% 9.49/5.28      ! [N: nat,K: int] :
% 9.49/5.28        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 9.49/5.28       => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4799_option_Osize__gen_I1_J,axiom,
% 9.49/5.28      ! [X: product_prod_nat_nat > nat] :
% 9.49/5.28        ( ( size_o8335143837870341156at_nat @ X @ none_P5556105721700978146at_nat )
% 9.49/5.28        = ( suc @ zero_zero_nat ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4800_option_Osize__gen_I1_J,axiom,
% 9.49/5.28      ! [X: nat > nat] :
% 9.49/5.28        ( ( size_option_nat @ X @ none_nat )
% 9.49/5.28        = ( suc @ zero_zero_nat ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4801_option_Osize__gen_I1_J,axiom,
% 9.49/5.28      ! [X: num > nat] :
% 9.49/5.28        ( ( size_option_num @ X @ none_num )
% 9.49/5.28        = ( suc @ zero_zero_nat ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4802_even__set__encode__iff,axiom,
% 9.49/5.28      ! [A2: set_nat] :
% 9.49/5.28        ( ( finite_finite_nat @ A2 )
% 9.49/5.28       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A2 ) )
% 9.49/5.28          = ( ~ ( member_nat @ zero_zero_nat @ A2 ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4803_exp__div__exp__eq,axiom,
% 9.49/5.28      ! [M: nat,N: nat] :
% 9.49/5.28        ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.28        = ( times_times_nat
% 9.49/5.28          @ ( zero_n2687167440665602831ol_nat
% 9.49/5.28            @ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 9.49/5.28               != zero_zero_nat )
% 9.49/5.28              & ( ord_less_eq_nat @ N @ M ) ) )
% 9.49/5.28          @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4804_exp__div__exp__eq,axiom,
% 9.49/5.28      ! [M: nat,N: nat] :
% 9.49/5.28        ( ( divide_divide_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.28        = ( times_times_int
% 9.49/5.28          @ ( zero_n2684676970156552555ol_int
% 9.49/5.28            @ ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 9.49/5.28               != zero_zero_int )
% 9.49/5.28              & ( ord_less_eq_nat @ N @ M ) ) )
% 9.49/5.28          @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4805_exp__div__exp__eq,axiom,
% 9.49/5.28      ! [M: nat,N: nat] :
% 9.49/5.28        ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.28        = ( times_3573771949741848930nteger
% 9.49/5.28          @ ( zero_n356916108424825756nteger
% 9.49/5.28            @ ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M )
% 9.49/5.28               != zero_z3403309356797280102nteger )
% 9.49/5.28              & ( ord_less_eq_nat @ N @ M ) ) )
% 9.49/5.28          @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4806_vebt__buildup_Osimps_I3_J,axiom,
% 9.49/5.28      ! [Va: nat] :
% 9.49/5.28        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 9.49/5.28         => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 9.49/5.28            = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 9.49/5.28        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 9.49/5.28         => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 9.49/5.28            = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4807_Divides_Oadjust__div__eq,axiom,
% 9.49/5.28      ! [Q2: int,R: int] :
% 9.49/5.28        ( ( adjust_div @ ( product_Pair_int_int @ Q2 @ R ) )
% 9.49/5.28        = ( plus_plus_int @ Q2 @ ( zero_n2684676970156552555ol_int @ ( R != zero_zero_int ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4808_signed__take__bit__Suc__minus__bit1,axiom,
% 9.49/5.28      ! [N: nat,K: num] :
% 9.49/5.28        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 9.49/5.28        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4809_signed__take__bit__rec,axiom,
% 9.49/5.28      ( bit_ri6519982836138164636nteger
% 9.49/5.28      = ( ^ [N2: nat,A3: code_integer] : ( if_Code_integer @ ( N2 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4810_signed__take__bit__rec,axiom,
% 9.49/5.28      ( bit_ri631733984087533419it_int
% 9.49/5.28      = ( ^ [N2: nat,A3: int] : ( if_int @ ( N2 = zero_zero_nat ) @ ( uminus_uminus_int @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( plus_plus_int @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4811_signed__take__bit__numeral__bit1,axiom,
% 9.49/5.28      ! [L2: num,K: num] :
% 9.49/5.28        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 9.49/5.28        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4812_vebt__buildup_Opelims,axiom,
% 9.49/5.28      ! [X: nat,Y2: vEBT_VEBT] :
% 9.49/5.28        ( ( ( vEBT_vebt_buildup @ X )
% 9.49/5.28          = Y2 )
% 9.49/5.28       => ( ( accp_nat @ vEBT_v4011308405150292612up_rel @ X )
% 9.49/5.28         => ( ( ( X = zero_zero_nat )
% 9.49/5.28             => ( ( Y2
% 9.49/5.28                  = ( vEBT_Leaf @ $false @ $false ) )
% 9.49/5.28               => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat ) ) )
% 9.49/5.28           => ( ( ( X
% 9.49/5.28                  = ( suc @ zero_zero_nat ) )
% 9.49/5.28               => ( ( Y2
% 9.49/5.28                    = ( vEBT_Leaf @ $false @ $false ) )
% 9.49/5.28                 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ zero_zero_nat ) ) ) )
% 9.49/5.28             => ~ ! [Va2: nat] :
% 9.49/5.28                    ( ( X
% 9.49/5.28                      = ( suc @ ( suc @ Va2 ) ) )
% 9.49/5.28                   => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 9.49/5.28                         => ( Y2
% 9.49/5.28                            = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 9.49/5.28                        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 9.49/5.28                         => ( Y2
% 9.49/5.28                            = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 9.49/5.28                     => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ ( suc @ Va2 ) ) ) ) ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4813_set__decode__0,axiom,
% 9.49/5.28      ! [X: nat] :
% 9.49/5.28        ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X ) )
% 9.49/5.28        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4814_set__decode__Suc,axiom,
% 9.49/5.28      ! [N: nat,X: nat] :
% 9.49/5.28        ( ( member_nat @ ( suc @ N ) @ ( nat_set_decode @ X ) )
% 9.49/5.28        = ( member_nat @ N @ ( nat_set_decode @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4815_neg__le__iff__le,axiom,
% 9.49/5.28      ! [B: real,A: real] :
% 9.49/5.28        ( ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 9.49/5.28        = ( ord_less_eq_real @ A @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4816_neg__le__iff__le,axiom,
% 9.49/5.28      ! [B: code_integer,A: code_integer] :
% 9.49/5.28        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 9.49/5.28        = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4817_neg__le__iff__le,axiom,
% 9.49/5.28      ! [B: rat,A: rat] :
% 9.49/5.28        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 9.49/5.28        = ( ord_less_eq_rat @ A @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4818_neg__le__iff__le,axiom,
% 9.49/5.28      ! [B: int,A: int] :
% 9.49/5.28        ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 9.49/5.28        = ( ord_less_eq_int @ A @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4819_neg__less__iff__less,axiom,
% 9.49/5.28      ! [B: int,A: int] :
% 9.49/5.28        ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 9.49/5.28        = ( ord_less_int @ A @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4820_neg__less__iff__less,axiom,
% 9.49/5.28      ! [B: real,A: real] :
% 9.49/5.28        ( ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 9.49/5.28        = ( ord_less_real @ A @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4821_neg__less__iff__less,axiom,
% 9.49/5.28      ! [B: code_integer,A: code_integer] :
% 9.49/5.28        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 9.49/5.28        = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4822_neg__less__iff__less,axiom,
% 9.49/5.28      ! [B: rat,A: rat] :
% 9.49/5.28        ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 9.49/5.28        = ( ord_less_rat @ A @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4823_neg__numeral__eq__iff,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 9.49/5.28          = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.49/5.28        = ( M = N ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4824_neg__numeral__eq__iff,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 9.49/5.28          = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 9.49/5.28        = ( M = N ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4825_neg__numeral__eq__iff,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 9.49/5.28          = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 9.49/5.28        = ( M = N ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4826_neg__numeral__eq__iff,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 9.49/5.28          = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 9.49/5.28        = ( M = N ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4827_neg__numeral__eq__iff,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 9.49/5.28          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 9.49/5.28        = ( M = N ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4828_mult__minus__left,axiom,
% 9.49/5.28      ! [A: int,B: int] :
% 9.49/5.28        ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 9.49/5.28        = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4829_mult__minus__left,axiom,
% 9.49/5.28      ! [A: real,B: real] :
% 9.49/5.28        ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 9.49/5.28        = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4830_mult__minus__left,axiom,
% 9.49/5.28      ! [A: complex,B: complex] :
% 9.49/5.28        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 9.49/5.28        = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4831_mult__minus__left,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer] :
% 9.49/5.28        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 9.49/5.28        = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4832_mult__minus__left,axiom,
% 9.49/5.28      ! [A: rat,B: rat] :
% 9.49/5.28        ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 9.49/5.28        = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4833_minus__mult__minus,axiom,
% 9.49/5.28      ! [A: int,B: int] :
% 9.49/5.28        ( ( times_times_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 9.49/5.28        = ( times_times_int @ A @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4834_minus__mult__minus,axiom,
% 9.49/5.28      ! [A: real,B: real] :
% 9.49/5.28        ( ( times_times_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 9.49/5.28        = ( times_times_real @ A @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4835_minus__mult__minus,axiom,
% 9.49/5.28      ! [A: complex,B: complex] :
% 9.49/5.28        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 9.49/5.28        = ( times_times_complex @ A @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4836_minus__mult__minus,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer] :
% 9.49/5.28        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 9.49/5.28        = ( times_3573771949741848930nteger @ A @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4837_minus__mult__minus,axiom,
% 9.49/5.28      ! [A: rat,B: rat] :
% 9.49/5.28        ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 9.49/5.28        = ( times_times_rat @ A @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4838_mult__minus__right,axiom,
% 9.49/5.28      ! [A: int,B: int] :
% 9.49/5.28        ( ( times_times_int @ A @ ( uminus_uminus_int @ B ) )
% 9.49/5.28        = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4839_mult__minus__right,axiom,
% 9.49/5.28      ! [A: real,B: real] :
% 9.49/5.28        ( ( times_times_real @ A @ ( uminus_uminus_real @ B ) )
% 9.49/5.28        = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4840_mult__minus__right,axiom,
% 9.49/5.28      ! [A: complex,B: complex] :
% 9.49/5.28        ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 9.49/5.28        = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4841_mult__minus__right,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer] :
% 9.49/5.28        ( ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 9.49/5.28        = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4842_mult__minus__right,axiom,
% 9.49/5.28      ! [A: rat,B: rat] :
% 9.49/5.28        ( ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) )
% 9.49/5.28        = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4843_minus__add__distrib,axiom,
% 9.49/5.28      ! [A: int,B: int] :
% 9.49/5.28        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 9.49/5.28        = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4844_minus__add__distrib,axiom,
% 9.49/5.28      ! [A: real,B: real] :
% 9.49/5.28        ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 9.49/5.28        = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4845_minus__add__distrib,axiom,
% 9.49/5.28      ! [A: complex,B: complex] :
% 9.49/5.28        ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 9.49/5.28        = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4846_minus__add__distrib,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer] :
% 9.49/5.28        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 9.49/5.28        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4847_minus__add__distrib,axiom,
% 9.49/5.28      ! [A: rat,B: rat] :
% 9.49/5.28        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 9.49/5.28        = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4848_minus__add__cancel,axiom,
% 9.49/5.28      ! [A: int,B: int] :
% 9.49/5.28        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 9.49/5.28        = B ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4849_minus__add__cancel,axiom,
% 9.49/5.28      ! [A: real,B: real] :
% 9.49/5.28        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
% 9.49/5.28        = B ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4850_minus__add__cancel,axiom,
% 9.49/5.28      ! [A: complex,B: complex] :
% 9.49/5.28        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( plus_plus_complex @ A @ B ) )
% 9.49/5.28        = B ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4851_minus__add__cancel,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer] :
% 9.49/5.28        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 9.49/5.28        = B ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4852_minus__add__cancel,axiom,
% 9.49/5.28      ! [A: rat,B: rat] :
% 9.49/5.28        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 9.49/5.28        = B ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4853_add__minus__cancel,axiom,
% 9.49/5.28      ! [A: int,B: int] :
% 9.49/5.28        ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 9.49/5.28        = B ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4854_add__minus__cancel,axiom,
% 9.49/5.28      ! [A: real,B: real] :
% 9.49/5.28        ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
% 9.49/5.28        = B ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4855_add__minus__cancel,axiom,
% 9.49/5.28      ! [A: complex,B: complex] :
% 9.49/5.28        ( ( plus_plus_complex @ A @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) )
% 9.49/5.28        = B ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4856_add__minus__cancel,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer] :
% 9.49/5.28        ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) )
% 9.49/5.28        = B ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4857_add__minus__cancel,axiom,
% 9.49/5.28      ! [A: rat,B: rat] :
% 9.49/5.28        ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 9.49/5.28        = B ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4858_minus__diff__eq,axiom,
% 9.49/5.28      ! [A: int,B: int] :
% 9.49/5.28        ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
% 9.49/5.28        = ( minus_minus_int @ B @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4859_minus__diff__eq,axiom,
% 9.49/5.28      ! [A: real,B: real] :
% 9.49/5.28        ( ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) )
% 9.49/5.28        = ( minus_minus_real @ B @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4860_minus__diff__eq,axiom,
% 9.49/5.28      ! [A: complex,B: complex] :
% 9.49/5.28        ( ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) )
% 9.49/5.28        = ( minus_minus_complex @ B @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4861_minus__diff__eq,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer] :
% 9.49/5.28        ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 9.49/5.28        = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4862_minus__diff__eq,axiom,
% 9.49/5.28      ! [A: rat,B: rat] :
% 9.49/5.28        ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) )
% 9.49/5.28        = ( minus_minus_rat @ B @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4863_div__minus__minus,axiom,
% 9.49/5.28      ! [A: int,B: int] :
% 9.49/5.28        ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 9.49/5.28        = ( divide_divide_int @ A @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4864_div__minus__minus,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer] :
% 9.49/5.28        ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 9.49/5.28        = ( divide6298287555418463151nteger @ A @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4865_mod__minus__minus,axiom,
% 9.49/5.28      ! [A: int,B: int] :
% 9.49/5.28        ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 9.49/5.28        = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4866_mod__minus__minus,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer] :
% 9.49/5.28        ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 9.49/5.28        = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4867_real__add__minus__iff,axiom,
% 9.49/5.28      ! [X: real,A: real] :
% 9.49/5.28        ( ( ( plus_plus_real @ X @ ( uminus_uminus_real @ A ) )
% 9.49/5.28          = zero_zero_real )
% 9.49/5.28        = ( X = A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4868_neg__less__eq__nonneg,axiom,
% 9.49/5.28      ! [A: real] :
% 9.49/5.28        ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
% 9.49/5.28        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4869_neg__less__eq__nonneg,axiom,
% 9.49/5.28      ! [A: code_integer] :
% 9.49/5.28        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 9.49/5.28        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4870_neg__less__eq__nonneg,axiom,
% 9.49/5.28      ! [A: rat] :
% 9.49/5.28        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 9.49/5.28        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4871_neg__less__eq__nonneg,axiom,
% 9.49/5.28      ! [A: int] :
% 9.49/5.28        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 9.49/5.28        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4872_less__eq__neg__nonpos,axiom,
% 9.49/5.28      ! [A: real] :
% 9.49/5.28        ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
% 9.49/5.28        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4873_less__eq__neg__nonpos,axiom,
% 9.49/5.28      ! [A: code_integer] :
% 9.49/5.28        ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 9.49/5.28        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4874_less__eq__neg__nonpos,axiom,
% 9.49/5.28      ! [A: rat] :
% 9.49/5.28        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 9.49/5.28        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4875_less__eq__neg__nonpos,axiom,
% 9.49/5.28      ! [A: int] :
% 9.49/5.28        ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 9.49/5.28        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4876_neg__le__0__iff__le,axiom,
% 9.49/5.28      ! [A: real] :
% 9.49/5.28        ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 9.49/5.28        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4877_neg__le__0__iff__le,axiom,
% 9.49/5.28      ! [A: code_integer] :
% 9.49/5.28        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 9.49/5.28        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4878_neg__le__0__iff__le,axiom,
% 9.49/5.28      ! [A: rat] :
% 9.49/5.28        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 9.49/5.28        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4879_neg__le__0__iff__le,axiom,
% 9.49/5.28      ! [A: int] :
% 9.49/5.28        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 9.49/5.28        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4880_neg__0__le__iff__le,axiom,
% 9.49/5.28      ! [A: real] :
% 9.49/5.28        ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 9.49/5.28        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4881_neg__0__le__iff__le,axiom,
% 9.49/5.28      ! [A: code_integer] :
% 9.49/5.28        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 9.49/5.28        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4882_neg__0__le__iff__le,axiom,
% 9.49/5.28      ! [A: rat] :
% 9.49/5.28        ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 9.49/5.28        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4883_neg__0__le__iff__le,axiom,
% 9.49/5.28      ! [A: int] :
% 9.49/5.28        ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 9.49/5.28        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4884_neg__less__0__iff__less,axiom,
% 9.49/5.28      ! [A: int] :
% 9.49/5.28        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 9.49/5.28        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4885_neg__less__0__iff__less,axiom,
% 9.49/5.28      ! [A: real] :
% 9.49/5.28        ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 9.49/5.28        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4886_neg__less__0__iff__less,axiom,
% 9.49/5.28      ! [A: code_integer] :
% 9.49/5.28        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 9.49/5.28        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4887_neg__less__0__iff__less,axiom,
% 9.49/5.28      ! [A: rat] :
% 9.49/5.28        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 9.49/5.28        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4888_neg__0__less__iff__less,axiom,
% 9.49/5.28      ! [A: int] :
% 9.49/5.28        ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 9.49/5.28        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4889_neg__0__less__iff__less,axiom,
% 9.49/5.28      ! [A: real] :
% 9.49/5.28        ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 9.49/5.28        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4890_neg__0__less__iff__less,axiom,
% 9.49/5.28      ! [A: code_integer] :
% 9.49/5.28        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 9.49/5.28        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4891_neg__0__less__iff__less,axiom,
% 9.49/5.28      ! [A: rat] :
% 9.49/5.28        ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 9.49/5.28        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4892_neg__less__pos,axiom,
% 9.49/5.28      ! [A: int] :
% 9.49/5.28        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 9.49/5.28        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4893_neg__less__pos,axiom,
% 9.49/5.28      ! [A: real] :
% 9.49/5.28        ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
% 9.49/5.28        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4894_neg__less__pos,axiom,
% 9.49/5.28      ! [A: code_integer] :
% 9.49/5.28        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 9.49/5.28        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4895_neg__less__pos,axiom,
% 9.49/5.28      ! [A: rat] :
% 9.49/5.28        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 9.49/5.28        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4896_less__neg__neg,axiom,
% 9.49/5.28      ! [A: int] :
% 9.49/5.28        ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 9.49/5.28        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4897_less__neg__neg,axiom,
% 9.49/5.28      ! [A: real] :
% 9.49/5.28        ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
% 9.49/5.28        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4898_less__neg__neg,axiom,
% 9.49/5.28      ! [A: code_integer] :
% 9.49/5.28        ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 9.49/5.28        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4899_less__neg__neg,axiom,
% 9.49/5.28      ! [A: rat] :
% 9.49/5.28        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 9.49/5.28        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4900_ab__left__minus,axiom,
% 9.49/5.28      ! [A: int] :
% 9.49/5.28        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 9.49/5.28        = zero_zero_int ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4901_ab__left__minus,axiom,
% 9.49/5.28      ! [A: real] :
% 9.49/5.28        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 9.49/5.28        = zero_zero_real ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4902_ab__left__minus,axiom,
% 9.49/5.28      ! [A: complex] :
% 9.49/5.28        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 9.49/5.28        = zero_zero_complex ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4903_ab__left__minus,axiom,
% 9.49/5.28      ! [A: code_integer] :
% 9.49/5.28        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 9.49/5.28        = zero_z3403309356797280102nteger ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4904_ab__left__minus,axiom,
% 9.49/5.28      ! [A: rat] :
% 9.49/5.28        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 9.49/5.28        = zero_zero_rat ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4905_add_Oright__inverse,axiom,
% 9.49/5.28      ! [A: int] :
% 9.49/5.28        ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 9.49/5.28        = zero_zero_int ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4906_add_Oright__inverse,axiom,
% 9.49/5.28      ! [A: real] :
% 9.49/5.28        ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
% 9.49/5.28        = zero_zero_real ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4907_add_Oright__inverse,axiom,
% 9.49/5.28      ! [A: complex] :
% 9.49/5.28        ( ( plus_plus_complex @ A @ ( uminus1482373934393186551omplex @ A ) )
% 9.49/5.28        = zero_zero_complex ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4908_add_Oright__inverse,axiom,
% 9.49/5.28      ! [A: code_integer] :
% 9.49/5.28        ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 9.49/5.28        = zero_z3403309356797280102nteger ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4909_add_Oright__inverse,axiom,
% 9.49/5.28      ! [A: rat] :
% 9.49/5.28        ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 9.49/5.28        = zero_zero_rat ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4910_diff__0,axiom,
% 9.49/5.28      ! [A: int] :
% 9.49/5.28        ( ( minus_minus_int @ zero_zero_int @ A )
% 9.49/5.28        = ( uminus_uminus_int @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4911_diff__0,axiom,
% 9.49/5.28      ! [A: real] :
% 9.49/5.28        ( ( minus_minus_real @ zero_zero_real @ A )
% 9.49/5.28        = ( uminus_uminus_real @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4912_diff__0,axiom,
% 9.49/5.28      ! [A: complex] :
% 9.49/5.28        ( ( minus_minus_complex @ zero_zero_complex @ A )
% 9.49/5.28        = ( uminus1482373934393186551omplex @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4913_diff__0,axiom,
% 9.49/5.28      ! [A: code_integer] :
% 9.49/5.28        ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ A )
% 9.49/5.28        = ( uminus1351360451143612070nteger @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4914_diff__0,axiom,
% 9.49/5.28      ! [A: rat] :
% 9.49/5.28        ( ( minus_minus_rat @ zero_zero_rat @ A )
% 9.49/5.28        = ( uminus_uminus_rat @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4915_verit__minus__simplify_I3_J,axiom,
% 9.49/5.28      ! [B: int] :
% 9.49/5.28        ( ( minus_minus_int @ zero_zero_int @ B )
% 9.49/5.28        = ( uminus_uminus_int @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4916_verit__minus__simplify_I3_J,axiom,
% 9.49/5.28      ! [B: real] :
% 9.49/5.28        ( ( minus_minus_real @ zero_zero_real @ B )
% 9.49/5.28        = ( uminus_uminus_real @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4917_verit__minus__simplify_I3_J,axiom,
% 9.49/5.28      ! [B: complex] :
% 9.49/5.28        ( ( minus_minus_complex @ zero_zero_complex @ B )
% 9.49/5.28        = ( uminus1482373934393186551omplex @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4918_verit__minus__simplify_I3_J,axiom,
% 9.49/5.28      ! [B: code_integer] :
% 9.49/5.28        ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ B )
% 9.49/5.28        = ( uminus1351360451143612070nteger @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4919_verit__minus__simplify_I3_J,axiom,
% 9.49/5.28      ! [B: rat] :
% 9.49/5.28        ( ( minus_minus_rat @ zero_zero_rat @ B )
% 9.49/5.28        = ( uminus_uminus_rat @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4920_add__neg__numeral__simps_I3_J,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.49/5.28        = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4921_add__neg__numeral__simps_I3_J,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 9.49/5.28        = ( uminus_uminus_real @ ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4922_add__neg__numeral__simps_I3_J,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 9.49/5.28        = ( uminus1482373934393186551omplex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4923_add__neg__numeral__simps_I3_J,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 9.49/5.28        = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4924_add__neg__numeral__simps_I3_J,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 9.49/5.28        = ( uminus_uminus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4925_mult__minus1__right,axiom,
% 9.49/5.28      ! [Z: int] :
% 9.49/5.28        ( ( times_times_int @ Z @ ( uminus_uminus_int @ one_one_int ) )
% 9.49/5.28        = ( uminus_uminus_int @ Z ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4926_mult__minus1__right,axiom,
% 9.49/5.28      ! [Z: real] :
% 9.49/5.28        ( ( times_times_real @ Z @ ( uminus_uminus_real @ one_one_real ) )
% 9.49/5.28        = ( uminus_uminus_real @ Z ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4927_mult__minus1__right,axiom,
% 9.49/5.28      ! [Z: complex] :
% 9.49/5.28        ( ( times_times_complex @ Z @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 9.49/5.28        = ( uminus1482373934393186551omplex @ Z ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4928_mult__minus1__right,axiom,
% 9.49/5.28      ! [Z: code_integer] :
% 9.49/5.28        ( ( times_3573771949741848930nteger @ Z @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.49/5.28        = ( uminus1351360451143612070nteger @ Z ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4929_mult__minus1__right,axiom,
% 9.49/5.28      ! [Z: rat] :
% 9.49/5.28        ( ( times_times_rat @ Z @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.49/5.28        = ( uminus_uminus_rat @ Z ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4930_mult__minus1,axiom,
% 9.49/5.28      ! [Z: int] :
% 9.49/5.28        ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z )
% 9.49/5.28        = ( uminus_uminus_int @ Z ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4931_mult__minus1,axiom,
% 9.49/5.28      ! [Z: real] :
% 9.49/5.28        ( ( times_times_real @ ( uminus_uminus_real @ one_one_real ) @ Z )
% 9.49/5.28        = ( uminus_uminus_real @ Z ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4932_mult__minus1,axiom,
% 9.49/5.28      ! [Z: complex] :
% 9.49/5.28        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ Z )
% 9.49/5.28        = ( uminus1482373934393186551omplex @ Z ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4933_mult__minus1,axiom,
% 9.49/5.28      ! [Z: code_integer] :
% 9.49/5.28        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z )
% 9.49/5.28        = ( uminus1351360451143612070nteger @ Z ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4934_mult__minus1,axiom,
% 9.49/5.28      ! [Z: rat] :
% 9.49/5.28        ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z )
% 9.49/5.28        = ( uminus_uminus_rat @ Z ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4935_diff__minus__eq__add,axiom,
% 9.49/5.28      ! [A: int,B: int] :
% 9.49/5.28        ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 9.49/5.28        = ( plus_plus_int @ A @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4936_diff__minus__eq__add,axiom,
% 9.49/5.28      ! [A: real,B: real] :
% 9.49/5.28        ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
% 9.49/5.28        = ( plus_plus_real @ A @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4937_diff__minus__eq__add,axiom,
% 9.49/5.28      ! [A: complex,B: complex] :
% 9.49/5.28        ( ( minus_minus_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 9.49/5.28        = ( plus_plus_complex @ A @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4938_diff__minus__eq__add,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer] :
% 9.49/5.28        ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 9.49/5.28        = ( plus_p5714425477246183910nteger @ A @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4939_diff__minus__eq__add,axiom,
% 9.49/5.28      ! [A: rat,B: rat] :
% 9.49/5.28        ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 9.49/5.28        = ( plus_plus_rat @ A @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4940_uminus__add__conv__diff,axiom,
% 9.49/5.28      ! [A: int,B: int] :
% 9.49/5.28        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 9.49/5.28        = ( minus_minus_int @ B @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4941_uminus__add__conv__diff,axiom,
% 9.49/5.28      ! [A: real,B: real] :
% 9.49/5.28        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
% 9.49/5.28        = ( minus_minus_real @ B @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4942_uminus__add__conv__diff,axiom,
% 9.49/5.28      ! [A: complex,B: complex] :
% 9.49/5.28        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 9.49/5.28        = ( minus_minus_complex @ B @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4943_uminus__add__conv__diff,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer] :
% 9.49/5.28        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 9.49/5.28        = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4944_uminus__add__conv__diff,axiom,
% 9.49/5.28      ! [A: rat,B: rat] :
% 9.49/5.28        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 9.49/5.28        = ( minus_minus_rat @ B @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4945_div__minus1__right,axiom,
% 9.49/5.28      ! [A: int] :
% 9.49/5.28        ( ( divide_divide_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 9.49/5.28        = ( uminus_uminus_int @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4946_div__minus1__right,axiom,
% 9.49/5.28      ! [A: code_integer] :
% 9.49/5.28        ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.49/5.28        = ( uminus1351360451143612070nteger @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4947_divide__minus1,axiom,
% 9.49/5.28      ! [X: real] :
% 9.49/5.28        ( ( divide_divide_real @ X @ ( uminus_uminus_real @ one_one_real ) )
% 9.49/5.28        = ( uminus_uminus_real @ X ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4948_divide__minus1,axiom,
% 9.49/5.28      ! [X: complex] :
% 9.49/5.28        ( ( divide1717551699836669952omplex @ X @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 9.49/5.28        = ( uminus1482373934393186551omplex @ X ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4949_divide__minus1,axiom,
% 9.49/5.28      ! [X: rat] :
% 9.49/5.28        ( ( divide_divide_rat @ X @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.49/5.28        = ( uminus_uminus_rat @ X ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4950_minus__mod__self1,axiom,
% 9.49/5.28      ! [B: int,A: int] :
% 9.49/5.28        ( ( modulo_modulo_int @ ( minus_minus_int @ B @ A ) @ B )
% 9.49/5.28        = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4951_minus__mod__self1,axiom,
% 9.49/5.28      ! [B: code_integer,A: code_integer] :
% 9.49/5.28        ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ B )
% 9.49/5.28        = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4952_signed__take__bit__of__minus__1,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ( bit_ri6519982836138164636nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.49/5.28        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4953_signed__take__bit__of__minus__1,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 9.49/5.28        = ( uminus_uminus_int @ one_one_int ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4954_pred__numeral__simps_I1_J,axiom,
% 9.49/5.28      ( ( pred_numeral @ one )
% 9.49/5.28      = zero_zero_nat ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4955_Suc__eq__numeral,axiom,
% 9.49/5.28      ! [N: nat,K: num] :
% 9.49/5.28        ( ( ( suc @ N )
% 9.49/5.28          = ( numeral_numeral_nat @ K ) )
% 9.49/5.28        = ( N
% 9.49/5.28          = ( pred_numeral @ K ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4956_eq__numeral__Suc,axiom,
% 9.49/5.28      ! [K: num,N: nat] :
% 9.49/5.28        ( ( ( numeral_numeral_nat @ K )
% 9.49/5.28          = ( suc @ N ) )
% 9.49/5.28        = ( ( pred_numeral @ K )
% 9.49/5.28          = N ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4957_dbl__simps_I1_J,axiom,
% 9.49/5.28      ! [K: num] :
% 9.49/5.28        ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 9.49/5.28        = ( uminus_uminus_int @ ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4958_dbl__simps_I1_J,axiom,
% 9.49/5.28      ! [K: num] :
% 9.49/5.28        ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 9.49/5.28        = ( uminus_uminus_real @ ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4959_dbl__simps_I1_J,axiom,
% 9.49/5.28      ! [K: num] :
% 9.49/5.28        ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 9.49/5.28        = ( uminus1482373934393186551omplex @ ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4960_dbl__simps_I1_J,axiom,
% 9.49/5.28      ! [K: num] :
% 9.49/5.28        ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 9.49/5.28        = ( uminus1351360451143612070nteger @ ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4961_dbl__simps_I1_J,axiom,
% 9.49/5.28      ! [K: num] :
% 9.49/5.28        ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 9.49/5.28        = ( uminus_uminus_rat @ ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4962_dbl__inc__simps_I4_J,axiom,
% 9.49/5.28      ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 9.49/5.28      = ( uminus_uminus_int @ one_one_int ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4963_dbl__inc__simps_I4_J,axiom,
% 9.49/5.28      ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ one_one_real ) )
% 9.49/5.28      = ( uminus_uminus_real @ one_one_real ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4964_dbl__inc__simps_I4_J,axiom,
% 9.49/5.28      ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 9.49/5.28      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4965_dbl__inc__simps_I4_J,axiom,
% 9.49/5.28      ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.49/5.28      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4966_dbl__inc__simps_I4_J,axiom,
% 9.49/5.28      ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.49/5.28      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4967_add__neg__numeral__special_I7_J,axiom,
% 9.49/5.28      ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 9.49/5.28      = zero_zero_int ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4968_add__neg__numeral__special_I7_J,axiom,
% 9.49/5.28      ( ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 9.49/5.28      = zero_zero_real ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4969_add__neg__numeral__special_I7_J,axiom,
% 9.49/5.28      ( ( plus_plus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 9.49/5.28      = zero_zero_complex ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4970_add__neg__numeral__special_I7_J,axiom,
% 9.49/5.28      ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.49/5.28      = zero_z3403309356797280102nteger ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4971_add__neg__numeral__special_I7_J,axiom,
% 9.49/5.28      ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.49/5.28      = zero_zero_rat ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4972_add__neg__numeral__special_I8_J,axiom,
% 9.49/5.28      ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 9.49/5.28      = zero_zero_int ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4973_add__neg__numeral__special_I8_J,axiom,
% 9.49/5.28      ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 9.49/5.28      = zero_zero_real ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4974_add__neg__numeral__special_I8_J,axiom,
% 9.49/5.28      ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 9.49/5.28      = zero_zero_complex ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4975_add__neg__numeral__special_I8_J,axiom,
% 9.49/5.28      ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 9.49/5.28      = zero_z3403309356797280102nteger ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4976_add__neg__numeral__special_I8_J,axiom,
% 9.49/5.28      ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 9.49/5.28      = zero_zero_rat ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4977_diff__numeral__special_I12_J,axiom,
% 9.49/5.28      ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 9.49/5.28      = zero_zero_int ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4978_diff__numeral__special_I12_J,axiom,
% 9.49/5.28      ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 9.49/5.28      = zero_zero_real ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4979_diff__numeral__special_I12_J,axiom,
% 9.49/5.28      ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 9.49/5.28      = zero_zero_complex ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4980_diff__numeral__special_I12_J,axiom,
% 9.49/5.28      ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.49/5.28      = zero_z3403309356797280102nteger ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4981_diff__numeral__special_I12_J,axiom,
% 9.49/5.28      ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.49/5.28      = zero_zero_rat ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4982_numeral__eq__neg__one__iff,axiom,
% 9.49/5.28      ! [N: num] :
% 9.49/5.28        ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ N ) )
% 9.49/5.28          = ( uminus_uminus_int @ one_one_int ) )
% 9.49/5.28        = ( N = one ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4983_numeral__eq__neg__one__iff,axiom,
% 9.49/5.28      ! [N: num] :
% 9.49/5.28        ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ N ) )
% 9.49/5.28          = ( uminus_uminus_real @ one_one_real ) )
% 9.49/5.28        = ( N = one ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4984_numeral__eq__neg__one__iff,axiom,
% 9.49/5.28      ! [N: num] :
% 9.49/5.28        ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) )
% 9.49/5.28          = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 9.49/5.28        = ( N = one ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4985_numeral__eq__neg__one__iff,axiom,
% 9.49/5.28      ! [N: num] :
% 9.49/5.28        ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) )
% 9.49/5.28          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.49/5.28        = ( N = one ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4986_numeral__eq__neg__one__iff,axiom,
% 9.49/5.28      ! [N: num] :
% 9.49/5.28        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) )
% 9.49/5.28          = ( uminus_uminus_rat @ one_one_rat ) )
% 9.49/5.28        = ( N = one ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4987_neg__one__eq__numeral__iff,axiom,
% 9.49/5.28      ! [N: num] :
% 9.49/5.28        ( ( ( uminus_uminus_int @ one_one_int )
% 9.49/5.28          = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.49/5.28        = ( N = one ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4988_neg__one__eq__numeral__iff,axiom,
% 9.49/5.28      ! [N: num] :
% 9.49/5.28        ( ( ( uminus_uminus_real @ one_one_real )
% 9.49/5.28          = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 9.49/5.28        = ( N = one ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4989_neg__one__eq__numeral__iff,axiom,
% 9.49/5.28      ! [N: num] :
% 9.49/5.28        ( ( ( uminus1482373934393186551omplex @ one_one_complex )
% 9.49/5.28          = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 9.49/5.28        = ( N = one ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4990_neg__one__eq__numeral__iff,axiom,
% 9.49/5.28      ! [N: num] :
% 9.49/5.28        ( ( ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 9.49/5.28          = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 9.49/5.28        = ( N = one ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4991_neg__one__eq__numeral__iff,axiom,
% 9.49/5.28      ! [N: num] :
% 9.49/5.28        ( ( ( uminus_uminus_rat @ one_one_rat )
% 9.49/5.28          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 9.49/5.28        = ( N = one ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4992_left__minus__one__mult__self,axiom,
% 9.49/5.28      ! [N: nat,A: int] :
% 9.49/5.28        ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ A ) )
% 9.49/5.28        = A ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4993_left__minus__one__mult__self,axiom,
% 9.49/5.28      ! [N: nat,A: real] :
% 9.49/5.28        ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ A ) )
% 9.49/5.28        = A ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4994_left__minus__one__mult__self,axiom,
% 9.49/5.28      ! [N: nat,A: complex] :
% 9.49/5.28        ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ A ) )
% 9.49/5.28        = A ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4995_left__minus__one__mult__self,axiom,
% 9.49/5.28      ! [N: nat,A: code_integer] :
% 9.49/5.28        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ A ) )
% 9.49/5.28        = A ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4996_left__minus__one__mult__self,axiom,
% 9.49/5.28      ! [N: nat,A: rat] :
% 9.49/5.28        ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ A ) )
% 9.49/5.28        = A ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4997_minus__one__mult__self,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) )
% 9.49/5.28        = one_one_int ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4998_minus__one__mult__self,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) )
% 9.49/5.28        = one_one_real ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_4999_minus__one__mult__self,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) )
% 9.49/5.28        = one_one_complex ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5000_minus__one__mult__self,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) )
% 9.49/5.28        = one_one_Code_integer ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5001_minus__one__mult__self,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) )
% 9.49/5.28        = one_one_rat ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5002_mod__minus1__right,axiom,
% 9.49/5.28      ! [A: int] :
% 9.49/5.28        ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 9.49/5.28        = zero_zero_int ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5003_mod__minus1__right,axiom,
% 9.49/5.28      ! [A: code_integer] :
% 9.49/5.28        ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.49/5.28        = zero_z3403309356797280102nteger ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5004_max__number__of_I4_J,axiom,
% 9.49/5.28      ! [U: num,V: num] :
% 9.49/5.28        ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 9.49/5.28         => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 9.49/5.28            = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 9.49/5.28        & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 9.49/5.28         => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 9.49/5.28            = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5005_max__number__of_I4_J,axiom,
% 9.49/5.28      ! [U: num,V: num] :
% 9.49/5.28        ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 9.49/5.28         => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 9.49/5.28            = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 9.49/5.28        & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 9.49/5.28         => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 9.49/5.28            = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5006_max__number__of_I4_J,axiom,
% 9.49/5.28      ! [U: num,V: num] :
% 9.49/5.28        ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 9.49/5.28         => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 9.49/5.28            = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 9.49/5.28        & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 9.49/5.28         => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 9.49/5.28            = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5007_max__number__of_I4_J,axiom,
% 9.49/5.28      ! [U: num,V: num] :
% 9.49/5.28        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 9.49/5.28         => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 9.49/5.28            = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 9.49/5.28        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 9.49/5.28         => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 9.49/5.28            = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5008_max__number__of_I3_J,axiom,
% 9.49/5.28      ! [U: num,V: num] :
% 9.49/5.28        ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 9.49/5.28         => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 9.49/5.28            = ( numeral_numeral_real @ V ) ) )
% 9.49/5.28        & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 9.49/5.28         => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 9.49/5.28            = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5009_max__number__of_I3_J,axiom,
% 9.49/5.28      ! [U: num,V: num] :
% 9.49/5.28        ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 9.49/5.28         => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 9.49/5.28            = ( numera6620942414471956472nteger @ V ) ) )
% 9.49/5.28        & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 9.49/5.28         => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 9.49/5.28            = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5010_max__number__of_I3_J,axiom,
% 9.49/5.28      ! [U: num,V: num] :
% 9.49/5.28        ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 9.49/5.28         => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 9.49/5.28            = ( numeral_numeral_rat @ V ) ) )
% 9.49/5.28        & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 9.49/5.28         => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 9.49/5.28            = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5011_max__number__of_I3_J,axiom,
% 9.49/5.28      ! [U: num,V: num] :
% 9.49/5.28        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 9.49/5.28         => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 9.49/5.28            = ( numeral_numeral_int @ V ) ) )
% 9.49/5.28        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 9.49/5.28         => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 9.49/5.28            = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5012_max__number__of_I2_J,axiom,
% 9.49/5.28      ! [U: num,V: num] :
% 9.49/5.28        ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 9.49/5.28         => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 9.49/5.28            = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 9.49/5.28        & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 9.49/5.28         => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 9.49/5.28            = ( numeral_numeral_real @ U ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5013_max__number__of_I2_J,axiom,
% 9.49/5.28      ! [U: num,V: num] :
% 9.49/5.28        ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 9.49/5.28         => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 9.49/5.28            = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 9.49/5.28        & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 9.49/5.28         => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 9.49/5.28            = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5014_max__number__of_I2_J,axiom,
% 9.49/5.28      ! [U: num,V: num] :
% 9.49/5.28        ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 9.49/5.28         => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 9.49/5.28            = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 9.49/5.28        & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 9.49/5.28         => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 9.49/5.28            = ( numeral_numeral_rat @ U ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5015_max__number__of_I2_J,axiom,
% 9.49/5.28      ! [U: num,V: num] :
% 9.49/5.28        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 9.49/5.28         => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 9.49/5.28            = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 9.49/5.28        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 9.49/5.28         => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 9.49/5.28            = ( numeral_numeral_int @ U ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5016_semiring__norm_I168_J,axiom,
% 9.49/5.28      ! [V: num,W: num,Y2: int] :
% 9.49/5.28        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y2 ) )
% 9.49/5.28        = ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) ) @ Y2 ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5017_semiring__norm_I168_J,axiom,
% 9.49/5.28      ! [V: num,W: num,Y2: real] :
% 9.49/5.28        ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y2 ) )
% 9.49/5.28        = ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) ) @ Y2 ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5018_semiring__norm_I168_J,axiom,
% 9.49/5.28      ! [V: num,W: num,Y2: complex] :
% 9.49/5.28        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y2 ) )
% 9.49/5.28        = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) ) @ Y2 ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5019_semiring__norm_I168_J,axiom,
% 9.49/5.28      ! [V: num,W: num,Y2: code_integer] :
% 9.49/5.28        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y2 ) )
% 9.49/5.28        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W ) ) ) @ Y2 ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5020_semiring__norm_I168_J,axiom,
% 9.49/5.28      ! [V: num,W: num,Y2: rat] :
% 9.49/5.28        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y2 ) )
% 9.49/5.28        = ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) ) @ Y2 ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5021_diff__numeral__simps_I3_J,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 9.49/5.28        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5022_diff__numeral__simps_I3_J,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) )
% 9.49/5.28        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5023_diff__numeral__simps_I3_J,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N ) )
% 9.49/5.28        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5024_diff__numeral__simps_I3_J,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 9.49/5.28        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5025_diff__numeral__simps_I3_J,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 9.49/5.28        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5026_diff__numeral__simps_I2_J,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.49/5.28        = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5027_diff__numeral__simps_I2_J,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 9.49/5.28        = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5028_diff__numeral__simps_I2_J,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 9.49/5.28        = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5029_diff__numeral__simps_I2_J,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 9.49/5.28        = ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5030_diff__numeral__simps_I2_J,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 9.49/5.28        = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5031_semiring__norm_I172_J,axiom,
% 9.49/5.28      ! [V: num,W: num,Y2: int] :
% 9.49/5.28        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y2 ) )
% 9.49/5.28        = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Y2 ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5032_semiring__norm_I172_J,axiom,
% 9.49/5.28      ! [V: num,W: num,Y2: real] :
% 9.49/5.28        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y2 ) )
% 9.49/5.28        = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Y2 ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5033_semiring__norm_I172_J,axiom,
% 9.49/5.28      ! [V: num,W: num,Y2: complex] :
% 9.49/5.28        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y2 ) )
% 9.49/5.28        = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Y2 ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5034_semiring__norm_I172_J,axiom,
% 9.49/5.28      ! [V: num,W: num,Y2: code_integer] :
% 9.49/5.28        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y2 ) )
% 9.49/5.28        = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) @ Y2 ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5035_semiring__norm_I172_J,axiom,
% 9.49/5.28      ! [V: num,W: num,Y2: rat] :
% 9.49/5.28        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y2 ) )
% 9.49/5.28        = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Y2 ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5036_semiring__norm_I171_J,axiom,
% 9.49/5.28      ! [V: num,W: num,Y2: int] :
% 9.49/5.28        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y2 ) )
% 9.49/5.28        = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5037_semiring__norm_I171_J,axiom,
% 9.49/5.28      ! [V: num,W: num,Y2: real] :
% 9.49/5.28        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y2 ) )
% 9.49/5.28        = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5038_semiring__norm_I171_J,axiom,
% 9.49/5.28      ! [V: num,W: num,Y2: complex] :
% 9.49/5.28        ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y2 ) )
% 9.49/5.28        = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5039_semiring__norm_I171_J,axiom,
% 9.49/5.28      ! [V: num,W: num,Y2: code_integer] :
% 9.49/5.28        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y2 ) )
% 9.49/5.28        = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5040_semiring__norm_I171_J,axiom,
% 9.49/5.28      ! [V: num,W: num,Y2: rat] :
% 9.49/5.28        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y2 ) )
% 9.49/5.28        = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5041_semiring__norm_I170_J,axiom,
% 9.49/5.28      ! [V: num,W: num,Y2: int] :
% 9.49/5.28        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Y2 ) )
% 9.49/5.28        = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5042_semiring__norm_I170_J,axiom,
% 9.49/5.28      ! [V: num,W: num,Y2: real] :
% 9.49/5.28        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Y2 ) )
% 9.49/5.28        = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5043_semiring__norm_I170_J,axiom,
% 9.49/5.28      ! [V: num,W: num,Y2: complex] :
% 9.49/5.28        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Y2 ) )
% 9.49/5.28        = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5044_semiring__norm_I170_J,axiom,
% 9.49/5.28      ! [V: num,W: num,Y2: code_integer] :
% 9.49/5.28        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ Y2 ) )
% 9.49/5.28        = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5045_semiring__norm_I170_J,axiom,
% 9.49/5.28      ! [V: num,W: num,Y2: rat] :
% 9.49/5.28        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Y2 ) )
% 9.49/5.28        = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5046_mult__neg__numeral__simps_I3_J,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.49/5.28        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5047_mult__neg__numeral__simps_I3_J,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 9.49/5.28        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5048_mult__neg__numeral__simps_I3_J,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 9.49/5.28        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5049_mult__neg__numeral__simps_I3_J,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 9.49/5.28        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5050_mult__neg__numeral__simps_I3_J,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 9.49/5.28        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5051_mult__neg__numeral__simps_I2_J,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 9.49/5.28        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5052_mult__neg__numeral__simps_I2_J,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) )
% 9.49/5.28        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5053_mult__neg__numeral__simps_I2_J,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N ) )
% 9.49/5.28        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5054_mult__neg__numeral__simps_I2_J,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 9.49/5.28        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5055_mult__neg__numeral__simps_I2_J,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 9.49/5.28        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5056_mult__neg__numeral__simps_I1_J,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.49/5.28        = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5057_mult__neg__numeral__simps_I1_J,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 9.49/5.28        = ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5058_mult__neg__numeral__simps_I1_J,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 9.49/5.28        = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5059_mult__neg__numeral__simps_I1_J,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 9.49/5.28        = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5060_mult__neg__numeral__simps_I1_J,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 9.49/5.28        = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5061_less__Suc__numeral,axiom,
% 9.49/5.28      ! [N: nat,K: num] :
% 9.49/5.28        ( ( ord_less_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 9.49/5.28        = ( ord_less_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5062_less__numeral__Suc,axiom,
% 9.49/5.28      ! [K: num,N: nat] :
% 9.49/5.28        ( ( ord_less_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 9.49/5.28        = ( ord_less_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5063_pred__numeral__simps_I3_J,axiom,
% 9.49/5.28      ! [K: num] :
% 9.49/5.28        ( ( pred_numeral @ ( bit1 @ K ) )
% 9.49/5.28        = ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5064_le__Suc__numeral,axiom,
% 9.49/5.28      ! [N: nat,K: num] :
% 9.49/5.28        ( ( ord_less_eq_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 9.49/5.28        = ( ord_less_eq_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5065_le__numeral__Suc,axiom,
% 9.49/5.28      ! [K: num,N: nat] :
% 9.49/5.28        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 9.49/5.28        = ( ord_less_eq_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5066_diff__numeral__Suc,axiom,
% 9.49/5.28      ! [K: num,N: nat] :
% 9.49/5.28        ( ( minus_minus_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 9.49/5.28        = ( minus_minus_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5067_diff__Suc__numeral,axiom,
% 9.49/5.28      ! [N: nat,K: num] :
% 9.49/5.28        ( ( minus_minus_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 9.49/5.28        = ( minus_minus_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5068_neg__numeral__le__iff,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 9.49/5.28        = ( ord_less_eq_num @ N @ M ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5069_neg__numeral__le__iff,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 9.49/5.28        = ( ord_less_eq_num @ N @ M ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5070_neg__numeral__le__iff,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 9.49/5.28        = ( ord_less_eq_num @ N @ M ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5071_neg__numeral__le__iff,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.49/5.28        = ( ord_less_eq_num @ N @ M ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5072_neg__numeral__less__iff,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.49/5.28        = ( ord_less_num @ N @ M ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5073_neg__numeral__less__iff,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 9.49/5.28        = ( ord_less_num @ N @ M ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5074_neg__numeral__less__iff,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 9.49/5.28        = ( ord_less_num @ N @ M ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5075_neg__numeral__less__iff,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 9.49/5.28        = ( ord_less_num @ N @ M ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5076_max__numeral__Suc,axiom,
% 9.49/5.28      ! [K: num,N: nat] :
% 9.49/5.28        ( ( ord_max_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 9.49/5.28        = ( suc @ ( ord_max_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5077_max__Suc__numeral,axiom,
% 9.49/5.28      ! [N: nat,K: num] :
% 9.49/5.28        ( ( ord_max_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 9.49/5.28        = ( suc @ ( ord_max_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5078_pred__numeral__simps_I2_J,axiom,
% 9.49/5.28      ! [K: num] :
% 9.49/5.28        ( ( pred_numeral @ ( bit0 @ K ) )
% 9.49/5.28        = ( numeral_numeral_nat @ ( bitM @ K ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5079_not__neg__one__le__neg__numeral__iff,axiom,
% 9.49/5.28      ! [M: num] :
% 9.49/5.28        ( ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) )
% 9.49/5.28        = ( M != one ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5080_not__neg__one__le__neg__numeral__iff,axiom,
% 9.49/5.28      ! [M: num] :
% 9.49/5.28        ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) )
% 9.49/5.28        = ( M != one ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5081_not__neg__one__le__neg__numeral__iff,axiom,
% 9.49/5.28      ! [M: num] :
% 9.49/5.28        ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) )
% 9.49/5.28        = ( M != one ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5082_not__neg__one__le__neg__numeral__iff,axiom,
% 9.49/5.28      ! [M: num] :
% 9.49/5.28        ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) )
% 9.49/5.28        = ( M != one ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5083_neg__numeral__less__neg__one__iff,axiom,
% 9.49/5.28      ! [M: num] :
% 9.49/5.28        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 9.49/5.28        = ( M != one ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5084_neg__numeral__less__neg__one__iff,axiom,
% 9.49/5.28      ! [M: num] :
% 9.49/5.28        ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 9.49/5.28        = ( M != one ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5085_neg__numeral__less__neg__one__iff,axiom,
% 9.49/5.28      ! [M: num] :
% 9.49/5.28        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.49/5.28        = ( M != one ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5086_neg__numeral__less__neg__one__iff,axiom,
% 9.49/5.28      ! [M: num] :
% 9.49/5.28        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.49/5.28        = ( M != one ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5087_divide__le__eq__numeral1_I2_J,axiom,
% 9.49/5.28      ! [B: real,W: num,A: real] :
% 9.49/5.28        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 9.49/5.28        = ( ord_less_eq_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5088_divide__le__eq__numeral1_I2_J,axiom,
% 9.49/5.28      ! [B: rat,W: num,A: rat] :
% 9.49/5.28        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 9.49/5.28        = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5089_le__divide__eq__numeral1_I2_J,axiom,
% 9.49/5.28      ! [A: real,B: real,W: num] :
% 9.49/5.28        ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 9.49/5.28        = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5090_le__divide__eq__numeral1_I2_J,axiom,
% 9.49/5.28      ! [A: rat,B: rat,W: num] :
% 9.49/5.28        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 9.49/5.28        = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5091_divide__eq__eq__numeral1_I2_J,axiom,
% 9.49/5.28      ! [B: real,W: num,A: real] :
% 9.49/5.28        ( ( ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 9.49/5.28          = A )
% 9.49/5.28        = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 9.49/5.28             != zero_zero_real )
% 9.49/5.28           => ( B
% 9.49/5.28              = ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) )
% 9.49/5.28          & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 9.49/5.28              = zero_zero_real )
% 9.49/5.28           => ( A = zero_zero_real ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5092_divide__eq__eq__numeral1_I2_J,axiom,
% 9.49/5.28      ! [B: complex,W: num,A: complex] :
% 9.49/5.28        ( ( ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 9.49/5.28          = A )
% 9.49/5.28        = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 9.49/5.28             != zero_zero_complex )
% 9.49/5.28           => ( B
% 9.49/5.28              = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) )
% 9.49/5.28          & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 9.49/5.28              = zero_zero_complex )
% 9.49/5.28           => ( A = zero_zero_complex ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5093_divide__eq__eq__numeral1_I2_J,axiom,
% 9.49/5.28      ! [B: rat,W: num,A: rat] :
% 9.49/5.28        ( ( ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 9.49/5.28          = A )
% 9.49/5.28        = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 9.49/5.28             != zero_zero_rat )
% 9.49/5.28           => ( B
% 9.49/5.28              = ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) )
% 9.49/5.28          & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 9.49/5.28              = zero_zero_rat )
% 9.49/5.28           => ( A = zero_zero_rat ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5094_eq__divide__eq__numeral1_I2_J,axiom,
% 9.49/5.28      ! [A: real,B: real,W: num] :
% 9.49/5.28        ( ( A
% 9.49/5.28          = ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 9.49/5.28        = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 9.49/5.28             != zero_zero_real )
% 9.49/5.28           => ( ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 9.49/5.28              = B ) )
% 9.49/5.28          & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 9.49/5.28              = zero_zero_real )
% 9.49/5.28           => ( A = zero_zero_real ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5095_eq__divide__eq__numeral1_I2_J,axiom,
% 9.49/5.28      ! [A: complex,B: complex,W: num] :
% 9.49/5.28        ( ( A
% 9.49/5.28          = ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) )
% 9.49/5.28        = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 9.49/5.28             != zero_zero_complex )
% 9.49/5.28           => ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 9.49/5.28              = B ) )
% 9.49/5.28          & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 9.49/5.28              = zero_zero_complex )
% 9.49/5.28           => ( A = zero_zero_complex ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5096_eq__divide__eq__numeral1_I2_J,axiom,
% 9.49/5.28      ! [A: rat,B: rat,W: num] :
% 9.49/5.28        ( ( A
% 9.49/5.28          = ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 9.49/5.28        = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 9.49/5.28             != zero_zero_rat )
% 9.49/5.28           => ( ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 9.49/5.28              = B ) )
% 9.49/5.28          & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 9.49/5.28              = zero_zero_rat )
% 9.49/5.28           => ( A = zero_zero_rat ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5097_divide__less__eq__numeral1_I2_J,axiom,
% 9.49/5.28      ! [B: real,W: num,A: real] :
% 9.49/5.28        ( ( ord_less_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 9.49/5.28        = ( ord_less_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5098_divide__less__eq__numeral1_I2_J,axiom,
% 9.49/5.28      ! [B: rat,W: num,A: rat] :
% 9.49/5.28        ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 9.49/5.28        = ( ord_less_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5099_less__divide__eq__numeral1_I2_J,axiom,
% 9.49/5.28      ! [A: real,B: real,W: num] :
% 9.49/5.28        ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 9.49/5.28        = ( ord_less_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5100_less__divide__eq__numeral1_I2_J,axiom,
% 9.49/5.28      ! [A: rat,B: rat,W: num] :
% 9.49/5.28        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 9.49/5.28        = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5101_power2__minus,axiom,
% 9.49/5.28      ! [A: int] :
% 9.49/5.28        ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.28        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5102_power2__minus,axiom,
% 9.49/5.28      ! [A: real] :
% 9.49/5.28        ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.28        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5103_power2__minus,axiom,
% 9.49/5.28      ! [A: complex] :
% 9.49/5.28        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.28        = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5104_power2__minus,axiom,
% 9.49/5.28      ! [A: code_integer] :
% 9.49/5.28        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.28        = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5105_power2__minus,axiom,
% 9.49/5.28      ! [A: rat] :
% 9.49/5.28        ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.28        = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5106_add__neg__numeral__special_I9_J,axiom,
% 9.49/5.28      ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 9.49/5.28      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5107_add__neg__numeral__special_I9_J,axiom,
% 9.49/5.28      ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 9.49/5.28      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5108_add__neg__numeral__special_I9_J,axiom,
% 9.49/5.28      ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 9.49/5.28      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5109_add__neg__numeral__special_I9_J,axiom,
% 9.49/5.28      ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.49/5.28      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5110_add__neg__numeral__special_I9_J,axiom,
% 9.49/5.28      ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.49/5.28      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5111_diff__numeral__special_I10_J,axiom,
% 9.49/5.28      ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 9.49/5.28      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5112_diff__numeral__special_I10_J,axiom,
% 9.49/5.28      ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 9.49/5.28      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5113_diff__numeral__special_I10_J,axiom,
% 9.49/5.28      ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 9.49/5.28      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5114_diff__numeral__special_I10_J,axiom,
% 9.49/5.28      ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 9.49/5.28      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5115_diff__numeral__special_I10_J,axiom,
% 9.49/5.28      ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 9.49/5.28      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5116_diff__numeral__special_I11_J,axiom,
% 9.49/5.28      ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 9.49/5.28      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5117_diff__numeral__special_I11_J,axiom,
% 9.49/5.28      ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 9.49/5.28      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5118_diff__numeral__special_I11_J,axiom,
% 9.49/5.28      ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 9.49/5.28      = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5119_diff__numeral__special_I11_J,axiom,
% 9.49/5.28      ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.49/5.28      = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5120_diff__numeral__special_I11_J,axiom,
% 9.49/5.28      ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.49/5.28      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5121_minus__1__div__2__eq,axiom,
% 9.49/5.28      ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.49/5.28      = ( uminus_uminus_int @ one_one_int ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5122_minus__1__div__2__eq,axiom,
% 9.49/5.28      ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.49/5.28      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5123_bits__minus__1__mod__2__eq,axiom,
% 9.49/5.28      ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.49/5.28      = one_one_int ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5124_bits__minus__1__mod__2__eq,axiom,
% 9.49/5.28      ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.49/5.28      = one_one_Code_integer ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5125_minus__1__mod__2__eq,axiom,
% 9.49/5.28      ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.49/5.28      = one_one_int ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5126_minus__1__mod__2__eq,axiom,
% 9.49/5.28      ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.49/5.28      = one_one_Code_integer ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5127_Power_Oring__1__class_Opower__minus__even,axiom,
% 9.49/5.28      ! [A: int,N: nat] :
% 9.49/5.28        ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.28        = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5128_Power_Oring__1__class_Opower__minus__even,axiom,
% 9.49/5.28      ! [A: real,N: nat] :
% 9.49/5.28        ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.28        = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5129_Power_Oring__1__class_Opower__minus__even,axiom,
% 9.49/5.28      ! [A: complex,N: nat] :
% 9.49/5.28        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.28        = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5130_Power_Oring__1__class_Opower__minus__even,axiom,
% 9.49/5.28      ! [A: code_integer,N: nat] :
% 9.49/5.28        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.28        = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5131_Power_Oring__1__class_Opower__minus__even,axiom,
% 9.49/5.28      ! [A: rat,N: nat] :
% 9.49/5.28        ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.28        = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5132_Parity_Oring__1__class_Opower__minus__even,axiom,
% 9.49/5.28      ! [N: nat,A: int] :
% 9.49/5.28        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28       => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 9.49/5.28          = ( power_power_int @ A @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5133_Parity_Oring__1__class_Opower__minus__even,axiom,
% 9.49/5.28      ! [N: nat,A: real] :
% 9.49/5.28        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28       => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 9.49/5.28          = ( power_power_real @ A @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5134_Parity_Oring__1__class_Opower__minus__even,axiom,
% 9.49/5.28      ! [N: nat,A: complex] :
% 9.49/5.28        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 9.49/5.28          = ( power_power_complex @ A @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5135_Parity_Oring__1__class_Opower__minus__even,axiom,
% 9.49/5.28      ! [N: nat,A: code_integer] :
% 9.49/5.28        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 9.49/5.28          = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5136_Parity_Oring__1__class_Opower__minus__even,axiom,
% 9.49/5.28      ! [N: nat,A: rat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28       => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 9.49/5.28          = ( power_power_rat @ A @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5137_power__minus__odd,axiom,
% 9.49/5.28      ! [N: nat,A: int] :
% 9.49/5.28        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28       => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 9.49/5.28          = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5138_power__minus__odd,axiom,
% 9.49/5.28      ! [N: nat,A: real] :
% 9.49/5.28        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28       => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 9.49/5.28          = ( uminus_uminus_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5139_power__minus__odd,axiom,
% 9.49/5.28      ! [N: nat,A: complex] :
% 9.49/5.28        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 9.49/5.28          = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5140_power__minus__odd,axiom,
% 9.49/5.28      ! [N: nat,A: code_integer] :
% 9.49/5.28        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 9.49/5.28          = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5141_power__minus__odd,axiom,
% 9.49/5.28      ! [N: nat,A: rat] :
% 9.49/5.28        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28       => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 9.49/5.28          = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5142_diff__numeral__special_I3_J,axiom,
% 9.49/5.28      ! [N: num] :
% 9.49/5.28        ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.49/5.28        = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5143_diff__numeral__special_I3_J,axiom,
% 9.49/5.28      ! [N: num] :
% 9.49/5.28        ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 9.49/5.28        = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5144_diff__numeral__special_I3_J,axiom,
% 9.49/5.28      ! [N: num] :
% 9.49/5.28        ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 9.49/5.28        = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5145_diff__numeral__special_I3_J,axiom,
% 9.49/5.28      ! [N: num] :
% 9.49/5.28        ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 9.49/5.28        = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5146_diff__numeral__special_I3_J,axiom,
% 9.49/5.28      ! [N: num] :
% 9.49/5.28        ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 9.49/5.28        = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5147_diff__numeral__special_I4_J,axiom,
% 9.49/5.28      ! [M: num] :
% 9.49/5.28        ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int )
% 9.49/5.28        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5148_diff__numeral__special_I4_J,axiom,
% 9.49/5.28      ! [M: num] :
% 9.49/5.28        ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real )
% 9.49/5.28        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5149_diff__numeral__special_I4_J,axiom,
% 9.49/5.28      ! [M: num] :
% 9.49/5.28        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ one_one_complex )
% 9.49/5.28        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5150_diff__numeral__special_I4_J,axiom,
% 9.49/5.28      ! [M: num] :
% 9.49/5.28        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer )
% 9.49/5.28        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5151_diff__numeral__special_I4_J,axiom,
% 9.49/5.28      ! [M: num] :
% 9.49/5.28        ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat )
% 9.49/5.28        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5152_numeral__div__minus__numeral,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( divide_divide_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.49/5.28        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5153_minus__numeral__div__numeral,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 9.49/5.28        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5154_dbl__simps_I4_J,axiom,
% 9.49/5.28      ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ one_one_int ) )
% 9.49/5.28      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5155_dbl__simps_I4_J,axiom,
% 9.49/5.28      ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ one_one_real ) )
% 9.49/5.28      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5156_dbl__simps_I4_J,axiom,
% 9.49/5.28      ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 9.49/5.28      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5157_dbl__simps_I4_J,axiom,
% 9.49/5.28      ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.49/5.28      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5158_dbl__simps_I4_J,axiom,
% 9.49/5.28      ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.49/5.28      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5159_power__minus1__even,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.28        = one_one_int ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5160_power__minus1__even,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.28        = one_one_real ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5161_power__minus1__even,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.28        = one_one_complex ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5162_power__minus1__even,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.28        = one_one_Code_integer ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5163_power__minus1__even,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.28        = one_one_rat ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5164_neg__one__even__power,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28       => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 9.49/5.28          = one_one_int ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5165_neg__one__even__power,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28       => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 9.49/5.28          = one_one_real ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5166_neg__one__even__power,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 9.49/5.28          = one_one_complex ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5167_neg__one__even__power,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 9.49/5.28          = one_one_Code_integer ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5168_neg__one__even__power,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28       => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 9.49/5.28          = one_one_rat ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5169_neg__one__odd__power,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28       => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 9.49/5.28          = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5170_neg__one__odd__power,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28       => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 9.49/5.28          = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5171_neg__one__odd__power,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 9.49/5.28          = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5172_neg__one__odd__power,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 9.49/5.28          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5173_neg__one__odd__power,axiom,
% 9.49/5.28      ! [N: nat] :
% 9.49/5.28        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.28       => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 9.49/5.28          = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5174_signed__take__bit__0,axiom,
% 9.49/5.28      ! [A: code_integer] :
% 9.49/5.28        ( ( bit_ri6519982836138164636nteger @ zero_zero_nat @ A )
% 9.49/5.28        = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5175_signed__take__bit__0,axiom,
% 9.49/5.28      ! [A: int] :
% 9.49/5.28        ( ( bit_ri631733984087533419it_int @ zero_zero_nat @ A )
% 9.49/5.28        = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5176_signed__take__bit__Suc__minus__bit0,axiom,
% 9.49/5.28      ! [N: nat,K: num] :
% 9.49/5.28        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 9.49/5.28        = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5177_signed__take__bit__numeral__bit0,axiom,
% 9.49/5.28      ! [L2: num,K: num] :
% 9.49/5.28        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 9.49/5.28        = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5178_one__div__minus__numeral,axiom,
% 9.49/5.28      ! [N: num] :
% 9.49/5.28        ( ( divide_divide_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.49/5.28        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5179_minus__one__div__numeral,axiom,
% 9.49/5.28      ! [N: num] :
% 9.49/5.28        ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 9.49/5.28        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5180_signed__take__bit__numeral__minus__bit0,axiom,
% 9.49/5.28      ! [L2: num,K: num] :
% 9.49/5.28        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 9.49/5.28        = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5181_signed__take__bit__numeral__minus__bit1,axiom,
% 9.49/5.28      ! [L2: num,K: num] :
% 9.49/5.28        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 9.49/5.28        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5182_signed__take__bit__minus,axiom,
% 9.49/5.28      ! [N: nat,K: int] :
% 9.49/5.28        ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( bit_ri631733984087533419it_int @ N @ K ) ) )
% 9.49/5.28        = ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5183_le__minus__iff,axiom,
% 9.49/5.28      ! [A: real,B: real] :
% 9.49/5.28        ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B ) )
% 9.49/5.28        = ( ord_less_eq_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5184_le__minus__iff,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer] :
% 9.49/5.28        ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 9.49/5.28        = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5185_le__minus__iff,axiom,
% 9.49/5.28      ! [A: rat,B: rat] :
% 9.49/5.28        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 9.49/5.28        = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5186_le__minus__iff,axiom,
% 9.49/5.28      ! [A: int,B: int] :
% 9.49/5.28        ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 9.49/5.28        = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5187_minus__le__iff,axiom,
% 9.49/5.28      ! [A: real,B: real] :
% 9.49/5.28        ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 9.49/5.28        = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5188_minus__le__iff,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer] :
% 9.49/5.28        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 9.49/5.28        = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5189_minus__le__iff,axiom,
% 9.49/5.28      ! [A: rat,B: rat] :
% 9.49/5.28        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 9.49/5.28        = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5190_minus__le__iff,axiom,
% 9.49/5.28      ! [A: int,B: int] :
% 9.49/5.28        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 9.49/5.28        = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5191_le__imp__neg__le,axiom,
% 9.49/5.28      ! [A: real,B: real] :
% 9.49/5.28        ( ( ord_less_eq_real @ A @ B )
% 9.49/5.28       => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5192_le__imp__neg__le,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer] :
% 9.49/5.28        ( ( ord_le3102999989581377725nteger @ A @ B )
% 9.49/5.28       => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5193_le__imp__neg__le,axiom,
% 9.49/5.28      ! [A: rat,B: rat] :
% 9.49/5.28        ( ( ord_less_eq_rat @ A @ B )
% 9.49/5.28       => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5194_le__imp__neg__le,axiom,
% 9.49/5.28      ! [A: int,B: int] :
% 9.49/5.28        ( ( ord_less_eq_int @ A @ B )
% 9.49/5.28       => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5195_less__minus__iff,axiom,
% 9.49/5.28      ! [A: int,B: int] :
% 9.49/5.28        ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 9.49/5.28        = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5196_less__minus__iff,axiom,
% 9.49/5.28      ! [A: real,B: real] :
% 9.49/5.28        ( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
% 9.49/5.28        = ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5197_less__minus__iff,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer] :
% 9.49/5.28        ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 9.49/5.28        = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5198_less__minus__iff,axiom,
% 9.49/5.28      ! [A: rat,B: rat] :
% 9.49/5.28        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 9.49/5.28        = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5199_minus__less__iff,axiom,
% 9.49/5.28      ! [A: int,B: int] :
% 9.49/5.28        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 9.49/5.28        = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5200_minus__less__iff,axiom,
% 9.49/5.28      ! [A: real,B: real] :
% 9.49/5.28        ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
% 9.49/5.28        = ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5201_minus__less__iff,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer] :
% 9.49/5.28        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 9.49/5.28        = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5202_minus__less__iff,axiom,
% 9.49/5.28      ! [A: rat,B: rat] :
% 9.49/5.28        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 9.49/5.28        = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5203_verit__negate__coefficient_I2_J,axiom,
% 9.49/5.28      ! [A: int,B: int] :
% 9.49/5.28        ( ( ord_less_int @ A @ B )
% 9.49/5.28       => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5204_verit__negate__coefficient_I2_J,axiom,
% 9.49/5.28      ! [A: real,B: real] :
% 9.49/5.28        ( ( ord_less_real @ A @ B )
% 9.49/5.28       => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5205_verit__negate__coefficient_I2_J,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer] :
% 9.49/5.28        ( ( ord_le6747313008572928689nteger @ A @ B )
% 9.49/5.28       => ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5206_verit__negate__coefficient_I2_J,axiom,
% 9.49/5.28      ! [A: rat,B: rat] :
% 9.49/5.28        ( ( ord_less_rat @ A @ B )
% 9.49/5.28       => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5207_numeral__neq__neg__numeral,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( numeral_numeral_int @ M )
% 9.49/5.28       != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5208_numeral__neq__neg__numeral,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( numeral_numeral_real @ M )
% 9.49/5.28       != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5209_numeral__neq__neg__numeral,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( numera6690914467698888265omplex @ M )
% 9.49/5.28       != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5210_numeral__neq__neg__numeral,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( numera6620942414471956472nteger @ M )
% 9.49/5.28       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5211_numeral__neq__neg__numeral,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( numeral_numeral_rat @ M )
% 9.49/5.28       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5212_neg__numeral__neq__numeral,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 9.49/5.28       != ( numeral_numeral_int @ N ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5213_neg__numeral__neq__numeral,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 9.49/5.28       != ( numeral_numeral_real @ N ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5214_neg__numeral__neq__numeral,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 9.49/5.28       != ( numera6690914467698888265omplex @ N ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5215_neg__numeral__neq__numeral,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 9.49/5.28       != ( numera6620942414471956472nteger @ N ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5216_neg__numeral__neq__numeral,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 9.49/5.28       != ( numeral_numeral_rat @ N ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5217_square__eq__iff,axiom,
% 9.49/5.28      ! [A: int,B: int] :
% 9.49/5.28        ( ( ( times_times_int @ A @ A )
% 9.49/5.28          = ( times_times_int @ B @ B ) )
% 9.49/5.28        = ( ( A = B )
% 9.49/5.28          | ( A
% 9.49/5.28            = ( uminus_uminus_int @ B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5218_square__eq__iff,axiom,
% 9.49/5.28      ! [A: real,B: real] :
% 9.49/5.28        ( ( ( times_times_real @ A @ A )
% 9.49/5.28          = ( times_times_real @ B @ B ) )
% 9.49/5.28        = ( ( A = B )
% 9.49/5.28          | ( A
% 9.49/5.28            = ( uminus_uminus_real @ B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5219_square__eq__iff,axiom,
% 9.49/5.28      ! [A: complex,B: complex] :
% 9.49/5.28        ( ( ( times_times_complex @ A @ A )
% 9.49/5.28          = ( times_times_complex @ B @ B ) )
% 9.49/5.28        = ( ( A = B )
% 9.49/5.28          | ( A
% 9.49/5.28            = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5220_square__eq__iff,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer] :
% 9.49/5.28        ( ( ( times_3573771949741848930nteger @ A @ A )
% 9.49/5.28          = ( times_3573771949741848930nteger @ B @ B ) )
% 9.49/5.28        = ( ( A = B )
% 9.49/5.28          | ( A
% 9.49/5.28            = ( uminus1351360451143612070nteger @ B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5221_square__eq__iff,axiom,
% 9.49/5.28      ! [A: rat,B: rat] :
% 9.49/5.28        ( ( ( times_times_rat @ A @ A )
% 9.49/5.28          = ( times_times_rat @ B @ B ) )
% 9.49/5.28        = ( ( A = B )
% 9.49/5.28          | ( A
% 9.49/5.28            = ( uminus_uminus_rat @ B ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5222_minus__mult__commute,axiom,
% 9.49/5.28      ! [A: int,B: int] :
% 9.49/5.28        ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 9.49/5.28        = ( times_times_int @ A @ ( uminus_uminus_int @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5223_minus__mult__commute,axiom,
% 9.49/5.28      ! [A: real,B: real] :
% 9.49/5.28        ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 9.49/5.28        = ( times_times_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5224_minus__mult__commute,axiom,
% 9.49/5.28      ! [A: complex,B: complex] :
% 9.49/5.28        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 9.49/5.28        = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5225_minus__mult__commute,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer] :
% 9.49/5.28        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 9.49/5.28        = ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5226_minus__mult__commute,axiom,
% 9.49/5.28      ! [A: rat,B: rat] :
% 9.49/5.28        ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 9.49/5.28        = ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5227_one__neq__neg__one,axiom,
% 9.49/5.28      ( one_one_int
% 9.49/5.28     != ( uminus_uminus_int @ one_one_int ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5228_one__neq__neg__one,axiom,
% 9.49/5.28      ( one_one_real
% 9.49/5.28     != ( uminus_uminus_real @ one_one_real ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5229_one__neq__neg__one,axiom,
% 9.49/5.28      ( one_one_complex
% 9.49/5.28     != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5230_one__neq__neg__one,axiom,
% 9.49/5.28      ( one_one_Code_integer
% 9.49/5.28     != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5231_one__neq__neg__one,axiom,
% 9.49/5.28      ( one_one_rat
% 9.49/5.28     != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5232_is__num__normalize_I8_J,axiom,
% 9.49/5.28      ! [A: int,B: int] :
% 9.49/5.28        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 9.49/5.28        = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5233_is__num__normalize_I8_J,axiom,
% 9.49/5.28      ! [A: real,B: real] :
% 9.49/5.28        ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 9.49/5.28        = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5234_is__num__normalize_I8_J,axiom,
% 9.49/5.28      ! [A: complex,B: complex] :
% 9.49/5.28        ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 9.49/5.28        = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5235_is__num__normalize_I8_J,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer] :
% 9.49/5.28        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 9.49/5.28        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5236_is__num__normalize_I8_J,axiom,
% 9.49/5.28      ! [A: rat,B: rat] :
% 9.49/5.28        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 9.49/5.28        = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5237_add_Oinverse__distrib__swap,axiom,
% 9.49/5.28      ! [A: int,B: int] :
% 9.49/5.28        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 9.49/5.28        = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5238_add_Oinverse__distrib__swap,axiom,
% 9.49/5.28      ! [A: real,B: real] :
% 9.49/5.28        ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 9.49/5.28        = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5239_add_Oinverse__distrib__swap,axiom,
% 9.49/5.28      ! [A: complex,B: complex] :
% 9.49/5.28        ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 9.49/5.28        = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5240_add_Oinverse__distrib__swap,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer] :
% 9.49/5.28        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 9.49/5.28        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5241_add_Oinverse__distrib__swap,axiom,
% 9.49/5.28      ! [A: rat,B: rat] :
% 9.49/5.28        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 9.49/5.28        = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5242_group__cancel_Oneg1,axiom,
% 9.49/5.28      ! [A2: int,K: int,A: int] :
% 9.49/5.28        ( ( A2
% 9.49/5.28          = ( plus_plus_int @ K @ A ) )
% 9.49/5.28       => ( ( uminus_uminus_int @ A2 )
% 9.49/5.28          = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5243_group__cancel_Oneg1,axiom,
% 9.49/5.28      ! [A2: real,K: real,A: real] :
% 9.49/5.28        ( ( A2
% 9.49/5.28          = ( plus_plus_real @ K @ A ) )
% 9.49/5.28       => ( ( uminus_uminus_real @ A2 )
% 9.49/5.28          = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( uminus_uminus_real @ A ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5244_group__cancel_Oneg1,axiom,
% 9.49/5.28      ! [A2: complex,K: complex,A: complex] :
% 9.49/5.28        ( ( A2
% 9.49/5.28          = ( plus_plus_complex @ K @ A ) )
% 9.49/5.28       => ( ( uminus1482373934393186551omplex @ A2 )
% 9.49/5.28          = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5245_group__cancel_Oneg1,axiom,
% 9.49/5.28      ! [A2: code_integer,K: code_integer,A: code_integer] :
% 9.49/5.28        ( ( A2
% 9.49/5.28          = ( plus_p5714425477246183910nteger @ K @ A ) )
% 9.49/5.28       => ( ( uminus1351360451143612070nteger @ A2 )
% 9.49/5.28          = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5246_group__cancel_Oneg1,axiom,
% 9.49/5.28      ! [A2: rat,K: rat,A: rat] :
% 9.49/5.28        ( ( A2
% 9.49/5.28          = ( plus_plus_rat @ K @ A ) )
% 9.49/5.28       => ( ( uminus_uminus_rat @ A2 )
% 9.49/5.28          = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5247_minus__diff__minus,axiom,
% 9.49/5.28      ! [A: int,B: int] :
% 9.49/5.28        ( ( minus_minus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 9.49/5.28        = ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5248_minus__diff__minus,axiom,
% 9.49/5.28      ! [A: real,B: real] :
% 9.49/5.28        ( ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 9.49/5.28        = ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5249_minus__diff__minus,axiom,
% 9.49/5.28      ! [A: complex,B: complex] :
% 9.49/5.28        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 9.49/5.28        = ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5250_minus__diff__minus,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer] :
% 9.49/5.28        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 9.49/5.28        = ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5251_minus__diff__minus,axiom,
% 9.49/5.28      ! [A: rat,B: rat] :
% 9.49/5.28        ( ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 9.49/5.28        = ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5252_minus__diff__commute,axiom,
% 9.49/5.28      ! [B: int,A: int] :
% 9.49/5.28        ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
% 9.49/5.28        = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5253_minus__diff__commute,axiom,
% 9.49/5.28      ! [B: real,A: real] :
% 9.49/5.28        ( ( minus_minus_real @ ( uminus_uminus_real @ B ) @ A )
% 9.49/5.28        = ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5254_minus__diff__commute,axiom,
% 9.49/5.28      ! [B: complex,A: complex] :
% 9.49/5.28        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ B ) @ A )
% 9.49/5.28        = ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5255_minus__diff__commute,axiom,
% 9.49/5.28      ! [B: code_integer,A: code_integer] :
% 9.49/5.28        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ B ) @ A )
% 9.49/5.28        = ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5256_minus__diff__commute,axiom,
% 9.49/5.28      ! [B: rat,A: rat] :
% 9.49/5.28        ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A )
% 9.49/5.28        = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5257_div__minus__right,axiom,
% 9.49/5.28      ! [A: int,B: int] :
% 9.49/5.28        ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 9.49/5.28        = ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5258_div__minus__right,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer] :
% 9.49/5.28        ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 9.49/5.28        = ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5259_minus__divide__right,axiom,
% 9.49/5.28      ! [A: real,B: real] :
% 9.49/5.28        ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 9.49/5.28        = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5260_minus__divide__right,axiom,
% 9.49/5.28      ! [A: complex,B: complex] :
% 9.49/5.28        ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 9.49/5.28        = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5261_minus__divide__right,axiom,
% 9.49/5.28      ! [A: rat,B: rat] :
% 9.49/5.28        ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 9.49/5.28        = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5262_minus__divide__divide,axiom,
% 9.49/5.28      ! [A: real,B: real] :
% 9.49/5.28        ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 9.49/5.28        = ( divide_divide_real @ A @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5263_minus__divide__divide,axiom,
% 9.49/5.28      ! [A: complex,B: complex] :
% 9.49/5.28        ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 9.49/5.28        = ( divide1717551699836669952omplex @ A @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5264_minus__divide__divide,axiom,
% 9.49/5.28      ! [A: rat,B: rat] :
% 9.49/5.28        ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 9.49/5.28        = ( divide_divide_rat @ A @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5265_minus__divide__left,axiom,
% 9.49/5.28      ! [A: real,B: real] :
% 9.49/5.28        ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 9.49/5.28        = ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5266_minus__divide__left,axiom,
% 9.49/5.28      ! [A: complex,B: complex] :
% 9.49/5.28        ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 9.49/5.28        = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5267_minus__divide__left,axiom,
% 9.49/5.28      ! [A: rat,B: rat] :
% 9.49/5.28        ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 9.49/5.28        = ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5268_mod__minus__right,axiom,
% 9.49/5.28      ! [A: int,B: int] :
% 9.49/5.28        ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 9.49/5.28        = ( uminus_uminus_int @ ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5269_mod__minus__right,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer] :
% 9.49/5.28        ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 9.49/5.28        = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5270_mod__minus__cong,axiom,
% 9.49/5.28      ! [A: int,B: int,A5: int] :
% 9.49/5.28        ( ( ( modulo_modulo_int @ A @ B )
% 9.49/5.28          = ( modulo_modulo_int @ A5 @ B ) )
% 9.49/5.28       => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 9.49/5.28          = ( modulo_modulo_int @ ( uminus_uminus_int @ A5 ) @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5271_mod__minus__cong,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer,A5: code_integer] :
% 9.49/5.28        ( ( ( modulo364778990260209775nteger @ A @ B )
% 9.49/5.28          = ( modulo364778990260209775nteger @ A5 @ B ) )
% 9.49/5.28       => ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 9.49/5.28          = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A5 ) @ B ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5272_mod__minus__eq,axiom,
% 9.49/5.28      ! [A: int,B: int] :
% 9.49/5.28        ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) @ B )
% 9.49/5.28        = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5273_mod__minus__eq,axiom,
% 9.49/5.28      ! [A: code_integer,B: code_integer] :
% 9.49/5.28        ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) @ B )
% 9.49/5.28        = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5274_neg__numeral__le__numeral,axiom,
% 9.49/5.28      ! [M: num,N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5275_neg__numeral__le__numeral,axiom,
% 9.49/5.28      ! [M: num,N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5276_neg__numeral__le__numeral,axiom,
% 9.49/5.28      ! [M: num,N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5277_neg__numeral__le__numeral,axiom,
% 9.49/5.28      ! [M: num,N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5278_not__numeral__le__neg__numeral,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5279_not__numeral__le__neg__numeral,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5280_not__numeral__le__neg__numeral,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5281_not__numeral__le__neg__numeral,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5282_zero__neq__neg__numeral,axiom,
% 9.49/5.28      ! [N: num] :
% 9.49/5.28        ( zero_zero_int
% 9.49/5.28       != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5283_zero__neq__neg__numeral,axiom,
% 9.49/5.28      ! [N: num] :
% 9.49/5.28        ( zero_zero_real
% 9.49/5.28       != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5284_zero__neq__neg__numeral,axiom,
% 9.49/5.28      ! [N: num] :
% 9.49/5.28        ( zero_zero_complex
% 9.49/5.28       != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5285_zero__neq__neg__numeral,axiom,
% 9.49/5.28      ! [N: num] :
% 9.49/5.28        ( zero_z3403309356797280102nteger
% 9.49/5.28       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5286_zero__neq__neg__numeral,axiom,
% 9.49/5.28      ! [N: num] :
% 9.49/5.28        ( zero_zero_rat
% 9.49/5.28       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5287_not__numeral__less__neg__numeral,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5288_not__numeral__less__neg__numeral,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5289_not__numeral__less__neg__numeral,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5290_not__numeral__less__neg__numeral,axiom,
% 9.49/5.28      ! [M: num,N: num] :
% 9.49/5.28        ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5291_neg__numeral__less__numeral,axiom,
% 9.49/5.28      ! [M: num,N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5292_neg__numeral__less__numeral,axiom,
% 9.49/5.28      ! [M: num,N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5293_neg__numeral__less__numeral,axiom,
% 9.49/5.28      ! [M: num,N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5294_neg__numeral__less__numeral,axiom,
% 9.49/5.28      ! [M: num,N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5295_le__minus__one__simps_I4_J,axiom,
% 9.49/5.28      ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5296_le__minus__one__simps_I4_J,axiom,
% 9.49/5.28      ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5297_le__minus__one__simps_I4_J,axiom,
% 9.49/5.28      ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5298_le__minus__one__simps_I4_J,axiom,
% 9.49/5.28      ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5299_le__minus__one__simps_I2_J,axiom,
% 9.49/5.28      ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5300_le__minus__one__simps_I2_J,axiom,
% 9.49/5.28      ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 9.49/5.28  
% 9.49/5.28  thf(fact_5301_le__minus__one__simps_I2_J,axiom,
% 9.49/5.29      ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5302_le__minus__one__simps_I2_J,axiom,
% 9.49/5.29      ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5303_zero__neq__neg__one,axiom,
% 9.49/5.29      ( zero_zero_int
% 9.49/5.29     != ( uminus_uminus_int @ one_one_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5304_zero__neq__neg__one,axiom,
% 9.49/5.29      ( zero_zero_real
% 9.49/5.29     != ( uminus_uminus_real @ one_one_real ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5305_zero__neq__neg__one,axiom,
% 9.49/5.29      ( zero_zero_complex
% 9.49/5.29     != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5306_zero__neq__neg__one,axiom,
% 9.49/5.29      ( zero_z3403309356797280102nteger
% 9.49/5.29     != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5307_zero__neq__neg__one,axiom,
% 9.49/5.29      ( zero_zero_rat
% 9.49/5.29     != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5308_add__eq__0__iff,axiom,
% 9.49/5.29      ! [A: int,B: int] :
% 9.49/5.29        ( ( ( plus_plus_int @ A @ B )
% 9.49/5.29          = zero_zero_int )
% 9.49/5.29        = ( B
% 9.49/5.29          = ( uminus_uminus_int @ A ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5309_add__eq__0__iff,axiom,
% 9.49/5.29      ! [A: real,B: real] :
% 9.49/5.29        ( ( ( plus_plus_real @ A @ B )
% 9.49/5.29          = zero_zero_real )
% 9.49/5.29        = ( B
% 9.49/5.29          = ( uminus_uminus_real @ A ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5310_add__eq__0__iff,axiom,
% 9.49/5.29      ! [A: complex,B: complex] :
% 9.49/5.29        ( ( ( plus_plus_complex @ A @ B )
% 9.49/5.29          = zero_zero_complex )
% 9.49/5.29        = ( B
% 9.49/5.29          = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5311_add__eq__0__iff,axiom,
% 9.49/5.29      ! [A: code_integer,B: code_integer] :
% 9.49/5.29        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 9.49/5.29          = zero_z3403309356797280102nteger )
% 9.49/5.29        = ( B
% 9.49/5.29          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5312_add__eq__0__iff,axiom,
% 9.49/5.29      ! [A: rat,B: rat] :
% 9.49/5.29        ( ( ( plus_plus_rat @ A @ B )
% 9.49/5.29          = zero_zero_rat )
% 9.49/5.29        = ( B
% 9.49/5.29          = ( uminus_uminus_rat @ A ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5313_ab__group__add__class_Oab__left__minus,axiom,
% 9.49/5.29      ! [A: int] :
% 9.49/5.29        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 9.49/5.29        = zero_zero_int ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5314_ab__group__add__class_Oab__left__minus,axiom,
% 9.49/5.29      ! [A: real] :
% 9.49/5.29        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 9.49/5.29        = zero_zero_real ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5315_ab__group__add__class_Oab__left__minus,axiom,
% 9.49/5.29      ! [A: complex] :
% 9.49/5.29        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 9.49/5.29        = zero_zero_complex ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5316_ab__group__add__class_Oab__left__minus,axiom,
% 9.49/5.29      ! [A: code_integer] :
% 9.49/5.29        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 9.49/5.29        = zero_z3403309356797280102nteger ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5317_ab__group__add__class_Oab__left__minus,axiom,
% 9.49/5.29      ! [A: rat] :
% 9.49/5.29        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 9.49/5.29        = zero_zero_rat ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5318_add_Oinverse__unique,axiom,
% 9.49/5.29      ! [A: int,B: int] :
% 9.49/5.29        ( ( ( plus_plus_int @ A @ B )
% 9.49/5.29          = zero_zero_int )
% 9.49/5.29       => ( ( uminus_uminus_int @ A )
% 9.49/5.29          = B ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5319_add_Oinverse__unique,axiom,
% 9.49/5.29      ! [A: real,B: real] :
% 9.49/5.29        ( ( ( plus_plus_real @ A @ B )
% 9.49/5.29          = zero_zero_real )
% 9.49/5.29       => ( ( uminus_uminus_real @ A )
% 9.49/5.29          = B ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5320_add_Oinverse__unique,axiom,
% 9.49/5.29      ! [A: complex,B: complex] :
% 9.49/5.29        ( ( ( plus_plus_complex @ A @ B )
% 9.49/5.29          = zero_zero_complex )
% 9.49/5.29       => ( ( uminus1482373934393186551omplex @ A )
% 9.49/5.29          = B ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5321_add_Oinverse__unique,axiom,
% 9.49/5.29      ! [A: code_integer,B: code_integer] :
% 9.49/5.29        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 9.49/5.29          = zero_z3403309356797280102nteger )
% 9.49/5.29       => ( ( uminus1351360451143612070nteger @ A )
% 9.49/5.29          = B ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5322_add_Oinverse__unique,axiom,
% 9.49/5.29      ! [A: rat,B: rat] :
% 9.49/5.29        ( ( ( plus_plus_rat @ A @ B )
% 9.49/5.29          = zero_zero_rat )
% 9.49/5.29       => ( ( uminus_uminus_rat @ A )
% 9.49/5.29          = B ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5323_eq__neg__iff__add__eq__0,axiom,
% 9.49/5.29      ! [A: int,B: int] :
% 9.49/5.29        ( ( A
% 9.49/5.29          = ( uminus_uminus_int @ B ) )
% 9.49/5.29        = ( ( plus_plus_int @ A @ B )
% 9.49/5.29          = zero_zero_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5324_eq__neg__iff__add__eq__0,axiom,
% 9.49/5.29      ! [A: real,B: real] :
% 9.49/5.29        ( ( A
% 9.49/5.29          = ( uminus_uminus_real @ B ) )
% 9.49/5.29        = ( ( plus_plus_real @ A @ B )
% 9.49/5.29          = zero_zero_real ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5325_eq__neg__iff__add__eq__0,axiom,
% 9.49/5.29      ! [A: complex,B: complex] :
% 9.49/5.29        ( ( A
% 9.49/5.29          = ( uminus1482373934393186551omplex @ B ) )
% 9.49/5.29        = ( ( plus_plus_complex @ A @ B )
% 9.49/5.29          = zero_zero_complex ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5326_eq__neg__iff__add__eq__0,axiom,
% 9.49/5.29      ! [A: code_integer,B: code_integer] :
% 9.49/5.29        ( ( A
% 9.49/5.29          = ( uminus1351360451143612070nteger @ B ) )
% 9.49/5.29        = ( ( plus_p5714425477246183910nteger @ A @ B )
% 9.49/5.29          = zero_z3403309356797280102nteger ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5327_eq__neg__iff__add__eq__0,axiom,
% 9.49/5.29      ! [A: rat,B: rat] :
% 9.49/5.29        ( ( A
% 9.49/5.29          = ( uminus_uminus_rat @ B ) )
% 9.49/5.29        = ( ( plus_plus_rat @ A @ B )
% 9.49/5.29          = zero_zero_rat ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5328_neg__eq__iff__add__eq__0,axiom,
% 9.49/5.29      ! [A: int,B: int] :
% 9.49/5.29        ( ( ( uminus_uminus_int @ A )
% 9.49/5.29          = B )
% 9.49/5.29        = ( ( plus_plus_int @ A @ B )
% 9.49/5.29          = zero_zero_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5329_neg__eq__iff__add__eq__0,axiom,
% 9.49/5.29      ! [A: real,B: real] :
% 9.49/5.29        ( ( ( uminus_uminus_real @ A )
% 9.49/5.29          = B )
% 9.49/5.29        = ( ( plus_plus_real @ A @ B )
% 9.49/5.29          = zero_zero_real ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5330_neg__eq__iff__add__eq__0,axiom,
% 9.49/5.29      ! [A: complex,B: complex] :
% 9.49/5.29        ( ( ( uminus1482373934393186551omplex @ A )
% 9.49/5.29          = B )
% 9.49/5.29        = ( ( plus_plus_complex @ A @ B )
% 9.49/5.29          = zero_zero_complex ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5331_neg__eq__iff__add__eq__0,axiom,
% 9.49/5.29      ! [A: code_integer,B: code_integer] :
% 9.49/5.29        ( ( ( uminus1351360451143612070nteger @ A )
% 9.49/5.29          = B )
% 9.49/5.29        = ( ( plus_p5714425477246183910nteger @ A @ B )
% 9.49/5.29          = zero_z3403309356797280102nteger ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5332_neg__eq__iff__add__eq__0,axiom,
% 9.49/5.29      ! [A: rat,B: rat] :
% 9.49/5.29        ( ( ( uminus_uminus_rat @ A )
% 9.49/5.29          = B )
% 9.49/5.29        = ( ( plus_plus_rat @ A @ B )
% 9.49/5.29          = zero_zero_rat ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5333_less__minus__one__simps_I2_J,axiom,
% 9.49/5.29      ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5334_less__minus__one__simps_I2_J,axiom,
% 9.49/5.29      ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5335_less__minus__one__simps_I2_J,axiom,
% 9.49/5.29      ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5336_less__minus__one__simps_I2_J,axiom,
% 9.49/5.29      ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5337_less__minus__one__simps_I4_J,axiom,
% 9.49/5.29      ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5338_less__minus__one__simps_I4_J,axiom,
% 9.49/5.29      ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5339_less__minus__one__simps_I4_J,axiom,
% 9.49/5.29      ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5340_less__minus__one__simps_I4_J,axiom,
% 9.49/5.29      ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5341_numeral__times__minus__swap,axiom,
% 9.49/5.29      ! [W: num,X: int] :
% 9.49/5.29        ( ( times_times_int @ ( numeral_numeral_int @ W ) @ ( uminus_uminus_int @ X ) )
% 9.49/5.29        = ( times_times_int @ X @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5342_numeral__times__minus__swap,axiom,
% 9.49/5.29      ! [W: num,X: real] :
% 9.49/5.29        ( ( times_times_real @ ( numeral_numeral_real @ W ) @ ( uminus_uminus_real @ X ) )
% 9.49/5.29        = ( times_times_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5343_numeral__times__minus__swap,axiom,
% 9.49/5.29      ! [W: num,X: complex] :
% 9.49/5.29        ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ ( uminus1482373934393186551omplex @ X ) )
% 9.49/5.29        = ( times_times_complex @ X @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5344_numeral__times__minus__swap,axiom,
% 9.49/5.29      ! [W: num,X: code_integer] :
% 9.49/5.29        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ ( uminus1351360451143612070nteger @ X ) )
% 9.49/5.29        = ( times_3573771949741848930nteger @ X @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5345_numeral__times__minus__swap,axiom,
% 9.49/5.29      ! [W: num,X: rat] :
% 9.49/5.29        ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ ( uminus_uminus_rat @ X ) )
% 9.49/5.29        = ( times_times_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5346_one__neq__neg__numeral,axiom,
% 9.49/5.29      ! [N: num] :
% 9.49/5.29        ( one_one_int
% 9.49/5.29       != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5347_one__neq__neg__numeral,axiom,
% 9.49/5.29      ! [N: num] :
% 9.49/5.29        ( one_one_real
% 9.49/5.29       != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5348_one__neq__neg__numeral,axiom,
% 9.49/5.29      ! [N: num] :
% 9.49/5.29        ( one_one_complex
% 9.49/5.29       != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5349_one__neq__neg__numeral,axiom,
% 9.49/5.29      ! [N: num] :
% 9.49/5.29        ( one_one_Code_integer
% 9.49/5.29       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5350_one__neq__neg__numeral,axiom,
% 9.49/5.29      ! [N: num] :
% 9.49/5.29        ( one_one_rat
% 9.49/5.29       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5351_numeral__neq__neg__one,axiom,
% 9.49/5.29      ! [N: num] :
% 9.49/5.29        ( ( numeral_numeral_int @ N )
% 9.49/5.29       != ( uminus_uminus_int @ one_one_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5352_numeral__neq__neg__one,axiom,
% 9.49/5.29      ! [N: num] :
% 9.49/5.29        ( ( numeral_numeral_real @ N )
% 9.49/5.29       != ( uminus_uminus_real @ one_one_real ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5353_numeral__neq__neg__one,axiom,
% 9.49/5.29      ! [N: num] :
% 9.49/5.29        ( ( numera6690914467698888265omplex @ N )
% 9.49/5.29       != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5354_numeral__neq__neg__one,axiom,
% 9.49/5.29      ! [N: num] :
% 9.49/5.29        ( ( numera6620942414471956472nteger @ N )
% 9.49/5.29       != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5355_numeral__neq__neg__one,axiom,
% 9.49/5.29      ! [N: num] :
% 9.49/5.29        ( ( numeral_numeral_rat @ N )
% 9.49/5.29       != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5356_nonzero__minus__divide__right,axiom,
% 9.49/5.29      ! [B: real,A: real] :
% 9.49/5.29        ( ( B != zero_zero_real )
% 9.49/5.29       => ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 9.49/5.29          = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5357_nonzero__minus__divide__right,axiom,
% 9.49/5.29      ! [B: complex,A: complex] :
% 9.49/5.29        ( ( B != zero_zero_complex )
% 9.49/5.29       => ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 9.49/5.29          = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5358_nonzero__minus__divide__right,axiom,
% 9.49/5.29      ! [B: rat,A: rat] :
% 9.49/5.29        ( ( B != zero_zero_rat )
% 9.49/5.29       => ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 9.49/5.29          = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5359_nonzero__minus__divide__divide,axiom,
% 9.49/5.29      ! [B: real,A: real] :
% 9.49/5.29        ( ( B != zero_zero_real )
% 9.49/5.29       => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 9.49/5.29          = ( divide_divide_real @ A @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5360_nonzero__minus__divide__divide,axiom,
% 9.49/5.29      ! [B: complex,A: complex] :
% 9.49/5.29        ( ( B != zero_zero_complex )
% 9.49/5.29       => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 9.49/5.29          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5361_nonzero__minus__divide__divide,axiom,
% 9.49/5.29      ! [B: rat,A: rat] :
% 9.49/5.29        ( ( B != zero_zero_rat )
% 9.49/5.29       => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 9.49/5.29          = ( divide_divide_rat @ A @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5362_square__eq__1__iff,axiom,
% 9.49/5.29      ! [X: int] :
% 9.49/5.29        ( ( ( times_times_int @ X @ X )
% 9.49/5.29          = one_one_int )
% 9.49/5.29        = ( ( X = one_one_int )
% 9.49/5.29          | ( X
% 9.49/5.29            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5363_square__eq__1__iff,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ( times_times_real @ X @ X )
% 9.49/5.29          = one_one_real )
% 9.49/5.29        = ( ( X = one_one_real )
% 9.49/5.29          | ( X
% 9.49/5.29            = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5364_square__eq__1__iff,axiom,
% 9.49/5.29      ! [X: complex] :
% 9.49/5.29        ( ( ( times_times_complex @ X @ X )
% 9.49/5.29          = one_one_complex )
% 9.49/5.29        = ( ( X = one_one_complex )
% 9.49/5.29          | ( X
% 9.49/5.29            = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5365_square__eq__1__iff,axiom,
% 9.49/5.29      ! [X: code_integer] :
% 9.49/5.29        ( ( ( times_3573771949741848930nteger @ X @ X )
% 9.49/5.29          = one_one_Code_integer )
% 9.49/5.29        = ( ( X = one_one_Code_integer )
% 9.49/5.29          | ( X
% 9.49/5.29            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5366_square__eq__1__iff,axiom,
% 9.49/5.29      ! [X: rat] :
% 9.49/5.29        ( ( ( times_times_rat @ X @ X )
% 9.49/5.29          = one_one_rat )
% 9.49/5.29        = ( ( X = one_one_rat )
% 9.49/5.29          | ( X
% 9.49/5.29            = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5367_group__cancel_Osub2,axiom,
% 9.49/5.29      ! [B2: int,K: int,B: int,A: int] :
% 9.49/5.29        ( ( B2
% 9.49/5.29          = ( plus_plus_int @ K @ B ) )
% 9.49/5.29       => ( ( minus_minus_int @ A @ B2 )
% 9.49/5.29          = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5368_group__cancel_Osub2,axiom,
% 9.49/5.29      ! [B2: real,K: real,B: real,A: real] :
% 9.49/5.29        ( ( B2
% 9.49/5.29          = ( plus_plus_real @ K @ B ) )
% 9.49/5.29       => ( ( minus_minus_real @ A @ B2 )
% 9.49/5.29          = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5369_group__cancel_Osub2,axiom,
% 9.49/5.29      ! [B2: complex,K: complex,B: complex,A: complex] :
% 9.49/5.29        ( ( B2
% 9.49/5.29          = ( plus_plus_complex @ K @ B ) )
% 9.49/5.29       => ( ( minus_minus_complex @ A @ B2 )
% 9.49/5.29          = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( minus_minus_complex @ A @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5370_group__cancel_Osub2,axiom,
% 9.49/5.29      ! [B2: code_integer,K: code_integer,B: code_integer,A: code_integer] :
% 9.49/5.29        ( ( B2
% 9.49/5.29          = ( plus_p5714425477246183910nteger @ K @ B ) )
% 9.49/5.29       => ( ( minus_8373710615458151222nteger @ A @ B2 )
% 9.49/5.29          = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5371_group__cancel_Osub2,axiom,
% 9.49/5.29      ! [B2: rat,K: rat,B: rat,A: rat] :
% 9.49/5.29        ( ( B2
% 9.49/5.29          = ( plus_plus_rat @ K @ B ) )
% 9.49/5.29       => ( ( minus_minus_rat @ A @ B2 )
% 9.49/5.29          = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5372_diff__conv__add__uminus,axiom,
% 9.49/5.29      ( minus_minus_int
% 9.49/5.29      = ( ^ [A3: int,B4: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B4 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5373_diff__conv__add__uminus,axiom,
% 9.49/5.29      ( minus_minus_real
% 9.49/5.29      = ( ^ [A3: real,B4: real] : ( plus_plus_real @ A3 @ ( uminus_uminus_real @ B4 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5374_diff__conv__add__uminus,axiom,
% 9.49/5.29      ( minus_minus_complex
% 9.49/5.29      = ( ^ [A3: complex,B4: complex] : ( plus_plus_complex @ A3 @ ( uminus1482373934393186551omplex @ B4 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5375_diff__conv__add__uminus,axiom,
% 9.49/5.29      ( minus_8373710615458151222nteger
% 9.49/5.29      = ( ^ [A3: code_integer,B4: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B4 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5376_diff__conv__add__uminus,axiom,
% 9.49/5.29      ( minus_minus_rat
% 9.49/5.29      = ( ^ [A3: rat,B4: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B4 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5377_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 9.49/5.29      ( minus_minus_int
% 9.49/5.29      = ( ^ [A3: int,B4: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B4 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5378_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 9.49/5.29      ( minus_minus_real
% 9.49/5.29      = ( ^ [A3: real,B4: real] : ( plus_plus_real @ A3 @ ( uminus_uminus_real @ B4 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5379_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 9.49/5.29      ( minus_minus_complex
% 9.49/5.29      = ( ^ [A3: complex,B4: complex] : ( plus_plus_complex @ A3 @ ( uminus1482373934393186551omplex @ B4 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5380_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 9.49/5.29      ( minus_8373710615458151222nteger
% 9.49/5.29      = ( ^ [A3: code_integer,B4: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B4 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5381_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 9.49/5.29      ( minus_minus_rat
% 9.49/5.29      = ( ^ [A3: rat,B4: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B4 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5382_dvd__div__neg,axiom,
% 9.49/5.29      ! [B: int,A: int] :
% 9.49/5.29        ( ( dvd_dvd_int @ B @ A )
% 9.49/5.29       => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 9.49/5.29          = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5383_dvd__div__neg,axiom,
% 9.49/5.29      ! [B: real,A: real] :
% 9.49/5.29        ( ( dvd_dvd_real @ B @ A )
% 9.49/5.29       => ( ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) )
% 9.49/5.29          = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5384_dvd__div__neg,axiom,
% 9.49/5.29      ! [B: complex,A: complex] :
% 9.49/5.29        ( ( dvd_dvd_complex @ B @ A )
% 9.49/5.29       => ( ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 9.49/5.29          = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5385_dvd__div__neg,axiom,
% 9.49/5.29      ! [B: code_integer,A: code_integer] :
% 9.49/5.29        ( ( dvd_dvd_Code_integer @ B @ A )
% 9.49/5.29       => ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 9.49/5.29          = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5386_dvd__div__neg,axiom,
% 9.49/5.29      ! [B: rat,A: rat] :
% 9.49/5.29        ( ( dvd_dvd_rat @ B @ A )
% 9.49/5.29       => ( ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) )
% 9.49/5.29          = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5387_dvd__neg__div,axiom,
% 9.49/5.29      ! [B: int,A: int] :
% 9.49/5.29        ( ( dvd_dvd_int @ B @ A )
% 9.49/5.29       => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 9.49/5.29          = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5388_dvd__neg__div,axiom,
% 9.49/5.29      ! [B: real,A: real] :
% 9.49/5.29        ( ( dvd_dvd_real @ B @ A )
% 9.49/5.29       => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B )
% 9.49/5.29          = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5389_dvd__neg__div,axiom,
% 9.49/5.29      ! [B: complex,A: complex] :
% 9.49/5.29        ( ( dvd_dvd_complex @ B @ A )
% 9.49/5.29       => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 9.49/5.29          = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5390_dvd__neg__div,axiom,
% 9.49/5.29      ! [B: code_integer,A: code_integer] :
% 9.49/5.29        ( ( dvd_dvd_Code_integer @ B @ A )
% 9.49/5.29       => ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 9.49/5.29          = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5391_dvd__neg__div,axiom,
% 9.49/5.29      ! [B: rat,A: rat] :
% 9.49/5.29        ( ( dvd_dvd_rat @ B @ A )
% 9.49/5.29       => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B )
% 9.49/5.29          = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5392_real__minus__mult__self__le,axiom,
% 9.49/5.29      ! [U: real,X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( times_times_real @ U @ U ) ) @ ( times_times_real @ X @ X ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5393_numeral__eq__Suc,axiom,
% 9.49/5.29      ( numeral_numeral_nat
% 9.49/5.29      = ( ^ [K3: num] : ( suc @ ( pred_numeral @ K3 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5394_minus__int__code_I2_J,axiom,
% 9.49/5.29      ! [L2: int] :
% 9.49/5.29        ( ( minus_minus_int @ zero_zero_int @ L2 )
% 9.49/5.29        = ( uminus_uminus_int @ L2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5395_zmod__zminus2__not__zero,axiom,
% 9.49/5.29      ! [K: int,L2: int] :
% 9.49/5.29        ( ( ( modulo_modulo_int @ K @ ( uminus_uminus_int @ L2 ) )
% 9.49/5.29         != zero_zero_int )
% 9.49/5.29       => ( ( modulo_modulo_int @ K @ L2 )
% 9.49/5.29         != zero_zero_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5396_zmod__zminus1__not__zero,axiom,
% 9.49/5.29      ! [K: int,L2: int] :
% 9.49/5.29        ( ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L2 )
% 9.49/5.29         != zero_zero_int )
% 9.49/5.29       => ( ( modulo_modulo_int @ K @ L2 )
% 9.49/5.29         != zero_zero_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5397_minus__real__def,axiom,
% 9.49/5.29      ( minus_minus_real
% 9.49/5.29      = ( ^ [X2: real,Y: real] : ( plus_plus_real @ X2 @ ( uminus_uminus_real @ Y ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5398_neg__numeral__le__zero,axiom,
% 9.49/5.29      ! [N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5399_neg__numeral__le__zero,axiom,
% 9.49/5.29      ! [N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5400_neg__numeral__le__zero,axiom,
% 9.49/5.29      ! [N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5401_neg__numeral__le__zero,axiom,
% 9.49/5.29      ! [N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5402_not__zero__le__neg__numeral,axiom,
% 9.49/5.29      ! [N: num] :
% 9.49/5.29        ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5403_not__zero__le__neg__numeral,axiom,
% 9.49/5.29      ! [N: num] :
% 9.49/5.29        ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5404_not__zero__le__neg__numeral,axiom,
% 9.49/5.29      ! [N: num] :
% 9.49/5.29        ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5405_not__zero__le__neg__numeral,axiom,
% 9.49/5.29      ! [N: num] :
% 9.49/5.29        ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5406_neg__numeral__less__zero,axiom,
% 9.49/5.29      ! [N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5407_neg__numeral__less__zero,axiom,
% 9.49/5.29      ! [N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5408_neg__numeral__less__zero,axiom,
% 9.49/5.29      ! [N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5409_neg__numeral__less__zero,axiom,
% 9.49/5.29      ! [N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5410_not__zero__less__neg__numeral,axiom,
% 9.49/5.29      ! [N: num] :
% 9.49/5.29        ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5411_not__zero__less__neg__numeral,axiom,
% 9.49/5.29      ! [N: num] :
% 9.49/5.29        ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5412_not__zero__less__neg__numeral,axiom,
% 9.49/5.29      ! [N: num] :
% 9.49/5.29        ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5413_not__zero__less__neg__numeral,axiom,
% 9.49/5.29      ! [N: num] :
% 9.49/5.29        ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5414_le__minus__one__simps_I3_J,axiom,
% 9.49/5.29      ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5415_le__minus__one__simps_I3_J,axiom,
% 9.49/5.29      ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5416_le__minus__one__simps_I3_J,axiom,
% 9.49/5.29      ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5417_le__minus__one__simps_I3_J,axiom,
% 9.49/5.29      ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5418_le__minus__one__simps_I1_J,axiom,
% 9.49/5.29      ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5419_le__minus__one__simps_I1_J,axiom,
% 9.49/5.29      ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5420_le__minus__one__simps_I1_J,axiom,
% 9.49/5.29      ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5421_le__minus__one__simps_I1_J,axiom,
% 9.49/5.29      ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5422_less__minus__one__simps_I3_J,axiom,
% 9.49/5.29      ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5423_less__minus__one__simps_I3_J,axiom,
% 9.49/5.29      ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5424_less__minus__one__simps_I3_J,axiom,
% 9.49/5.29      ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5425_less__minus__one__simps_I3_J,axiom,
% 9.49/5.29      ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5426_less__minus__one__simps_I1_J,axiom,
% 9.49/5.29      ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5427_less__minus__one__simps_I1_J,axiom,
% 9.49/5.29      ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5428_less__minus__one__simps_I1_J,axiom,
% 9.49/5.29      ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5429_less__minus__one__simps_I1_J,axiom,
% 9.49/5.29      ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5430_not__one__le__neg__numeral,axiom,
% 9.49/5.29      ! [M: num] :
% 9.49/5.29        ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5431_not__one__le__neg__numeral,axiom,
% 9.49/5.29      ! [M: num] :
% 9.49/5.29        ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5432_not__one__le__neg__numeral,axiom,
% 9.49/5.29      ! [M: num] :
% 9.49/5.29        ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5433_not__one__le__neg__numeral,axiom,
% 9.49/5.29      ! [M: num] :
% 9.49/5.29        ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5434_not__numeral__le__neg__one,axiom,
% 9.49/5.29      ! [M: num] :
% 9.49/5.29        ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5435_not__numeral__le__neg__one,axiom,
% 9.49/5.29      ! [M: num] :
% 9.49/5.29        ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5436_not__numeral__le__neg__one,axiom,
% 9.49/5.29      ! [M: num] :
% 9.49/5.29        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5437_not__numeral__le__neg__one,axiom,
% 9.49/5.29      ! [M: num] :
% 9.49/5.29        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5438_neg__numeral__le__neg__one,axiom,
% 9.49/5.29      ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5439_neg__numeral__le__neg__one,axiom,
% 9.49/5.29      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5440_neg__numeral__le__neg__one,axiom,
% 9.49/5.29      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5441_neg__numeral__le__neg__one,axiom,
% 9.49/5.29      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5442_neg__one__le__numeral,axiom,
% 9.49/5.29      ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5443_neg__one__le__numeral,axiom,
% 9.49/5.29      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5444_neg__one__le__numeral,axiom,
% 9.49/5.29      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5445_neg__one__le__numeral,axiom,
% 9.49/5.29      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5446_neg__numeral__le__one,axiom,
% 9.49/5.29      ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5447_neg__numeral__le__one,axiom,
% 9.49/5.29      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5448_neg__numeral__le__one,axiom,
% 9.49/5.29      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5449_neg__numeral__le__one,axiom,
% 9.49/5.29      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5450_not__neg__one__less__neg__numeral,axiom,
% 9.49/5.29      ! [M: num] :
% 9.49/5.29        ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5451_not__neg__one__less__neg__numeral,axiom,
% 9.49/5.29      ! [M: num] :
% 9.49/5.29        ~ ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5452_not__neg__one__less__neg__numeral,axiom,
% 9.49/5.29      ! [M: num] :
% 9.49/5.29        ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5453_not__neg__one__less__neg__numeral,axiom,
% 9.49/5.29      ! [M: num] :
% 9.49/5.29        ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5454_not__one__less__neg__numeral,axiom,
% 9.49/5.29      ! [M: num] :
% 9.49/5.29        ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5455_not__one__less__neg__numeral,axiom,
% 9.49/5.29      ! [M: num] :
% 9.49/5.29        ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5456_not__one__less__neg__numeral,axiom,
% 9.49/5.29      ! [M: num] :
% 9.49/5.29        ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5457_not__one__less__neg__numeral,axiom,
% 9.49/5.29      ! [M: num] :
% 9.49/5.29        ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5458_not__numeral__less__neg__one,axiom,
% 9.49/5.29      ! [M: num] :
% 9.49/5.29        ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5459_not__numeral__less__neg__one,axiom,
% 9.49/5.29      ! [M: num] :
% 9.49/5.29        ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5460_not__numeral__less__neg__one,axiom,
% 9.49/5.29      ! [M: num] :
% 9.49/5.29        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5461_not__numeral__less__neg__one,axiom,
% 9.49/5.29      ! [M: num] :
% 9.49/5.29        ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5462_neg__one__less__numeral,axiom,
% 9.49/5.29      ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5463_neg__one__less__numeral,axiom,
% 9.49/5.29      ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5464_neg__one__less__numeral,axiom,
% 9.49/5.29      ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5465_neg__one__less__numeral,axiom,
% 9.49/5.29      ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5466_neg__numeral__less__one,axiom,
% 9.49/5.29      ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5467_neg__numeral__less__one,axiom,
% 9.49/5.29      ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5468_neg__numeral__less__one,axiom,
% 9.49/5.29      ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5469_neg__numeral__less__one,axiom,
% 9.49/5.29      ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5470_mult__1s__ring__1_I1_J,axiom,
% 9.49/5.29      ! [B: int] :
% 9.49/5.29        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) @ B )
% 9.49/5.29        = ( uminus_uminus_int @ B ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5471_mult__1s__ring__1_I1_J,axiom,
% 9.49/5.29      ! [B: real] :
% 9.49/5.29        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) @ B )
% 9.49/5.29        = ( uminus_uminus_real @ B ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5472_mult__1s__ring__1_I1_J,axiom,
% 9.49/5.29      ! [B: complex] :
% 9.49/5.29        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) @ B )
% 9.49/5.29        = ( uminus1482373934393186551omplex @ B ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5473_mult__1s__ring__1_I1_J,axiom,
% 9.49/5.29      ! [B: code_integer] :
% 9.49/5.29        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) @ B )
% 9.49/5.29        = ( uminus1351360451143612070nteger @ B ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5474_mult__1s__ring__1_I1_J,axiom,
% 9.49/5.29      ! [B: rat] :
% 9.49/5.29        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) @ B )
% 9.49/5.29        = ( uminus_uminus_rat @ B ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5475_mult__1s__ring__1_I2_J,axiom,
% 9.49/5.29      ! [B: int] :
% 9.49/5.29        ( ( times_times_int @ B @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) )
% 9.49/5.29        = ( uminus_uminus_int @ B ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5476_mult__1s__ring__1_I2_J,axiom,
% 9.49/5.29      ! [B: real] :
% 9.49/5.29        ( ( times_times_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) )
% 9.49/5.29        = ( uminus_uminus_real @ B ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5477_mult__1s__ring__1_I2_J,axiom,
% 9.49/5.29      ! [B: complex] :
% 9.49/5.29        ( ( times_times_complex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) )
% 9.49/5.29        = ( uminus1482373934393186551omplex @ B ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5478_mult__1s__ring__1_I2_J,axiom,
% 9.49/5.29      ! [B: code_integer] :
% 9.49/5.29        ( ( times_3573771949741848930nteger @ B @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) )
% 9.49/5.29        = ( uminus1351360451143612070nteger @ B ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5479_mult__1s__ring__1_I2_J,axiom,
% 9.49/5.29      ! [B: rat] :
% 9.49/5.29        ( ( times_times_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) )
% 9.49/5.29        = ( uminus_uminus_rat @ B ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5480_uminus__numeral__One,axiom,
% 9.49/5.29      ( ( uminus_uminus_int @ ( numeral_numeral_int @ one ) )
% 9.49/5.29      = ( uminus_uminus_int @ one_one_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5481_uminus__numeral__One,axiom,
% 9.49/5.29      ( ( uminus_uminus_real @ ( numeral_numeral_real @ one ) )
% 9.49/5.29      = ( uminus_uminus_real @ one_one_real ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5482_uminus__numeral__One,axiom,
% 9.49/5.29      ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) )
% 9.49/5.29      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5483_uminus__numeral__One,axiom,
% 9.49/5.29      ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) )
% 9.49/5.29      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5484_uminus__numeral__One,axiom,
% 9.49/5.29      ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) )
% 9.49/5.29      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5485_eq__minus__divide__eq,axiom,
% 9.49/5.29      ! [A: real,B: real,C: real] :
% 9.49/5.29        ( ( A
% 9.49/5.29          = ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 9.49/5.29        = ( ( ( C != zero_zero_real )
% 9.49/5.29           => ( ( times_times_real @ A @ C )
% 9.49/5.29              = ( uminus_uminus_real @ B ) ) )
% 9.49/5.29          & ( ( C = zero_zero_real )
% 9.49/5.29           => ( A = zero_zero_real ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5486_eq__minus__divide__eq,axiom,
% 9.49/5.29      ! [A: complex,B: complex,C: complex] :
% 9.49/5.29        ( ( A
% 9.49/5.29          = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) ) )
% 9.49/5.29        = ( ( ( C != zero_zero_complex )
% 9.49/5.29           => ( ( times_times_complex @ A @ C )
% 9.49/5.29              = ( uminus1482373934393186551omplex @ B ) ) )
% 9.49/5.29          & ( ( C = zero_zero_complex )
% 9.49/5.29           => ( A = zero_zero_complex ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5487_eq__minus__divide__eq,axiom,
% 9.49/5.29      ! [A: rat,B: rat,C: rat] :
% 9.49/5.29        ( ( A
% 9.49/5.29          = ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 9.49/5.29        = ( ( ( C != zero_zero_rat )
% 9.49/5.29           => ( ( times_times_rat @ A @ C )
% 9.49/5.29              = ( uminus_uminus_rat @ B ) ) )
% 9.49/5.29          & ( ( C = zero_zero_rat )
% 9.49/5.29           => ( A = zero_zero_rat ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5488_minus__divide__eq__eq,axiom,
% 9.49/5.29      ! [B: real,C: real,A: real] :
% 9.49/5.29        ( ( ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) )
% 9.49/5.29          = A )
% 9.49/5.29        = ( ( ( C != zero_zero_real )
% 9.49/5.29           => ( ( uminus_uminus_real @ B )
% 9.49/5.29              = ( times_times_real @ A @ C ) ) )
% 9.49/5.29          & ( ( C = zero_zero_real )
% 9.49/5.29           => ( A = zero_zero_real ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5489_minus__divide__eq__eq,axiom,
% 9.49/5.29      ! [B: complex,C: complex,A: complex] :
% 9.49/5.29        ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) )
% 9.49/5.29          = A )
% 9.49/5.29        = ( ( ( C != zero_zero_complex )
% 9.49/5.29           => ( ( uminus1482373934393186551omplex @ B )
% 9.49/5.29              = ( times_times_complex @ A @ C ) ) )
% 9.49/5.29          & ( ( C = zero_zero_complex )
% 9.49/5.29           => ( A = zero_zero_complex ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5490_minus__divide__eq__eq,axiom,
% 9.49/5.29      ! [B: rat,C: rat,A: rat] :
% 9.49/5.29        ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) )
% 9.49/5.29          = A )
% 9.49/5.29        = ( ( ( C != zero_zero_rat )
% 9.49/5.29           => ( ( uminus_uminus_rat @ B )
% 9.49/5.29              = ( times_times_rat @ A @ C ) ) )
% 9.49/5.29          & ( ( C = zero_zero_rat )
% 9.49/5.29           => ( A = zero_zero_rat ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5491_nonzero__neg__divide__eq__eq,axiom,
% 9.49/5.29      ! [B: real,A: real,C: real] :
% 9.49/5.29        ( ( B != zero_zero_real )
% 9.49/5.29       => ( ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 9.49/5.29            = C )
% 9.49/5.29          = ( ( uminus_uminus_real @ A )
% 9.49/5.29            = ( times_times_real @ C @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5492_nonzero__neg__divide__eq__eq,axiom,
% 9.49/5.29      ! [B: complex,A: complex,C: complex] :
% 9.49/5.29        ( ( B != zero_zero_complex )
% 9.49/5.29       => ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 9.49/5.29            = C )
% 9.49/5.29          = ( ( uminus1482373934393186551omplex @ A )
% 9.49/5.29            = ( times_times_complex @ C @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5493_nonzero__neg__divide__eq__eq,axiom,
% 9.49/5.29      ! [B: rat,A: rat,C: rat] :
% 9.49/5.29        ( ( B != zero_zero_rat )
% 9.49/5.29       => ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 9.49/5.29            = C )
% 9.49/5.29          = ( ( uminus_uminus_rat @ A )
% 9.49/5.29            = ( times_times_rat @ C @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5494_nonzero__neg__divide__eq__eq2,axiom,
% 9.49/5.29      ! [B: real,C: real,A: real] :
% 9.49/5.29        ( ( B != zero_zero_real )
% 9.49/5.29       => ( ( C
% 9.49/5.29            = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) )
% 9.49/5.29          = ( ( times_times_real @ C @ B )
% 9.49/5.29            = ( uminus_uminus_real @ A ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5495_nonzero__neg__divide__eq__eq2,axiom,
% 9.49/5.29      ! [B: complex,C: complex,A: complex] :
% 9.49/5.29        ( ( B != zero_zero_complex )
% 9.49/5.29       => ( ( C
% 9.49/5.29            = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 9.49/5.29          = ( ( times_times_complex @ C @ B )
% 9.49/5.29            = ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5496_nonzero__neg__divide__eq__eq2,axiom,
% 9.49/5.29      ! [B: rat,C: rat,A: rat] :
% 9.49/5.29        ( ( B != zero_zero_rat )
% 9.49/5.29       => ( ( C
% 9.49/5.29            = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) )
% 9.49/5.29          = ( ( times_times_rat @ C @ B )
% 9.49/5.29            = ( uminus_uminus_rat @ A ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5497_divide__eq__minus__1__iff,axiom,
% 9.49/5.29      ! [A: real,B: real] :
% 9.49/5.29        ( ( ( divide_divide_real @ A @ B )
% 9.49/5.29          = ( uminus_uminus_real @ one_one_real ) )
% 9.49/5.29        = ( ( B != zero_zero_real )
% 9.49/5.29          & ( A
% 9.49/5.29            = ( uminus_uminus_real @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5498_divide__eq__minus__1__iff,axiom,
% 9.49/5.29      ! [A: complex,B: complex] :
% 9.49/5.29        ( ( ( divide1717551699836669952omplex @ A @ B )
% 9.49/5.29          = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 9.49/5.29        = ( ( B != zero_zero_complex )
% 9.49/5.29          & ( A
% 9.49/5.29            = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5499_divide__eq__minus__1__iff,axiom,
% 9.49/5.29      ! [A: rat,B: rat] :
% 9.49/5.29        ( ( ( divide_divide_rat @ A @ B )
% 9.49/5.29          = ( uminus_uminus_rat @ one_one_rat ) )
% 9.49/5.29        = ( ( B != zero_zero_rat )
% 9.49/5.29          & ( A
% 9.49/5.29            = ( uminus_uminus_rat @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5500_power__minus,axiom,
% 9.49/5.29      ! [A: int,N: nat] :
% 9.49/5.29        ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 9.49/5.29        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ A @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5501_power__minus,axiom,
% 9.49/5.29      ! [A: real,N: nat] :
% 9.49/5.29        ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 9.49/5.29        = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ A @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5502_power__minus,axiom,
% 9.49/5.29      ! [A: complex,N: nat] :
% 9.49/5.29        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 9.49/5.29        = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ A @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5503_power__minus,axiom,
% 9.49/5.29      ! [A: code_integer,N: nat] :
% 9.49/5.29        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 9.49/5.29        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5504_power__minus,axiom,
% 9.49/5.29      ! [A: rat,N: nat] :
% 9.49/5.29        ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 9.49/5.29        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ A @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5505_power__minus__Bit0,axiom,
% 9.49/5.29      ! [X: int,K: num] :
% 9.49/5.29        ( ( power_power_int @ ( uminus_uminus_int @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 9.49/5.29        = ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5506_power__minus__Bit0,axiom,
% 9.49/5.29      ! [X: real,K: num] :
% 9.49/5.29        ( ( power_power_real @ ( uminus_uminus_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 9.49/5.29        = ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5507_power__minus__Bit0,axiom,
% 9.49/5.29      ! [X: complex,K: num] :
% 9.49/5.29        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 9.49/5.29        = ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5508_power__minus__Bit0,axiom,
% 9.49/5.29      ! [X: code_integer,K: num] :
% 9.49/5.29        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 9.49/5.29        = ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5509_power__minus__Bit0,axiom,
% 9.49/5.29      ! [X: rat,K: num] :
% 9.49/5.29        ( ( power_power_rat @ ( uminus_uminus_rat @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 9.49/5.29        = ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5510_power__minus__Bit1,axiom,
% 9.49/5.29      ! [X: int,K: num] :
% 9.49/5.29        ( ( power_power_int @ ( uminus_uminus_int @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 9.49/5.29        = ( uminus_uminus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5511_power__minus__Bit1,axiom,
% 9.49/5.29      ! [X: real,K: num] :
% 9.49/5.29        ( ( power_power_real @ ( uminus_uminus_real @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 9.49/5.29        = ( uminus_uminus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5512_power__minus__Bit1,axiom,
% 9.49/5.29      ! [X: complex,K: num] :
% 9.49/5.29        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 9.49/5.29        = ( uminus1482373934393186551omplex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5513_power__minus__Bit1,axiom,
% 9.49/5.29      ! [X: code_integer,K: num] :
% 9.49/5.29        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 9.49/5.29        = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5514_power__minus__Bit1,axiom,
% 9.49/5.29      ! [X: rat,K: num] :
% 9.49/5.29        ( ( power_power_rat @ ( uminus_uminus_rat @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 9.49/5.29        = ( uminus_uminus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5515_Compl__insert,axiom,
% 9.49/5.29      ! [X: vEBT_VEBT,A2: set_VEBT_VEBT] :
% 9.49/5.29        ( ( uminus8041839845116263051T_VEBT @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 9.49/5.29        = ( minus_5127226145743854075T_VEBT @ ( uminus8041839845116263051T_VEBT @ A2 ) @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5516_Compl__insert,axiom,
% 9.49/5.29      ! [X: int,A2: set_int] :
% 9.49/5.29        ( ( uminus1532241313380277803et_int @ ( insert_int @ X @ A2 ) )
% 9.49/5.29        = ( minus_minus_set_int @ ( uminus1532241313380277803et_int @ A2 ) @ ( insert_int @ X @ bot_bot_set_int ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5517_Compl__insert,axiom,
% 9.49/5.29      ! [X: real,A2: set_real] :
% 9.49/5.29        ( ( uminus612125837232591019t_real @ ( insert_real @ X @ A2 ) )
% 9.49/5.29        = ( minus_minus_set_real @ ( uminus612125837232591019t_real @ A2 ) @ ( insert_real @ X @ bot_bot_set_real ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5518_Compl__insert,axiom,
% 9.49/5.29      ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 9.49/5.29        ( ( uminus6524753893492686040at_nat @ ( insert8211810215607154385at_nat @ X @ A2 ) )
% 9.49/5.29        = ( minus_1356011639430497352at_nat @ ( uminus6524753893492686040at_nat @ A2 ) @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5519_Compl__insert,axiom,
% 9.49/5.29      ! [X: nat,A2: set_nat] :
% 9.49/5.29        ( ( uminus5710092332889474511et_nat @ ( insert_nat @ X @ A2 ) )
% 9.49/5.29        = ( minus_minus_set_nat @ ( uminus5710092332889474511et_nat @ A2 ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5520_real__0__less__add__iff,axiom,
% 9.49/5.29      ! [X: real,Y2: real] :
% 9.49/5.29        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X @ Y2 ) )
% 9.49/5.29        = ( ord_less_real @ ( uminus_uminus_real @ X ) @ Y2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5521_real__add__less__0__iff,axiom,
% 9.49/5.29      ! [X: real,Y2: real] :
% 9.49/5.29        ( ( ord_less_real @ ( plus_plus_real @ X @ Y2 ) @ zero_zero_real )
% 9.49/5.29        = ( ord_less_real @ Y2 @ ( uminus_uminus_real @ X ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5522_real__0__le__add__iff,axiom,
% 9.49/5.29      ! [X: real,Y2: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ X @ Y2 ) )
% 9.49/5.29        = ( ord_less_eq_real @ ( uminus_uminus_real @ X ) @ Y2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5523_real__add__le__0__iff,axiom,
% 9.49/5.29      ! [X: real,Y2: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ ( plus_plus_real @ X @ Y2 ) @ zero_zero_real )
% 9.49/5.29        = ( ord_less_eq_real @ Y2 @ ( uminus_uminus_real @ X ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5524_pred__numeral__def,axiom,
% 9.49/5.29      ( pred_numeral
% 9.49/5.29      = ( ^ [K3: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K3 ) @ one_one_nat ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5525_zmod__zminus2__eq__if,axiom,
% 9.49/5.29      ! [A: int,B: int] :
% 9.49/5.29        ( ( ( ( modulo_modulo_int @ A @ B )
% 9.49/5.29            = zero_zero_int )
% 9.49/5.29         => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 9.49/5.29            = zero_zero_int ) )
% 9.49/5.29        & ( ( ( modulo_modulo_int @ A @ B )
% 9.49/5.29           != zero_zero_int )
% 9.49/5.29         => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 9.49/5.29            = ( minus_minus_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5526_zmod__zminus1__eq__if,axiom,
% 9.49/5.29      ! [A: int,B: int] :
% 9.49/5.29        ( ( ( ( modulo_modulo_int @ A @ B )
% 9.49/5.29            = zero_zero_int )
% 9.49/5.29         => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 9.49/5.29            = zero_zero_int ) )
% 9.49/5.29        & ( ( ( modulo_modulo_int @ A @ B )
% 9.49/5.29           != zero_zero_int )
% 9.49/5.29         => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 9.49/5.29            = ( minus_minus_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5527_less__minus__divide__eq,axiom,
% 9.49/5.29      ! [A: real,B: real,C: real] :
% 9.49/5.29        ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 9.49/5.29        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.29           => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 9.49/5.29          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.29           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.29               => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 9.49/5.29              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.29               => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5528_less__minus__divide__eq,axiom,
% 9.49/5.29      ! [A: rat,B: rat,C: rat] :
% 9.49/5.29        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 9.49/5.29        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.29           => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 9.49/5.29          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.29           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.29               => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 9.49/5.29              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.29               => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5529_minus__divide__less__eq,axiom,
% 9.49/5.29      ! [B: real,C: real,A: real] :
% 9.49/5.29        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 9.49/5.29        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.29           => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 9.49/5.29          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.29           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.29               => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 9.49/5.29              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.29               => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5530_minus__divide__less__eq,axiom,
% 9.49/5.29      ! [B: rat,C: rat,A: rat] :
% 9.49/5.29        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 9.49/5.29        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.29           => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 9.49/5.29          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.29           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.29               => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 9.49/5.29              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.29               => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5531_neg__less__minus__divide__eq,axiom,
% 9.49/5.29      ! [C: real,A: real,B: real] :
% 9.49/5.29        ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.29       => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 9.49/5.29          = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5532_neg__less__minus__divide__eq,axiom,
% 9.49/5.29      ! [C: rat,A: rat,B: rat] :
% 9.49/5.29        ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.29       => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 9.49/5.29          = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5533_neg__minus__divide__less__eq,axiom,
% 9.49/5.29      ! [C: real,B: real,A: real] :
% 9.49/5.29        ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.29       => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 9.49/5.29          = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5534_neg__minus__divide__less__eq,axiom,
% 9.49/5.29      ! [C: rat,B: rat,A: rat] :
% 9.49/5.29        ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.29       => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 9.49/5.29          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5535_pos__less__minus__divide__eq,axiom,
% 9.49/5.29      ! [C: real,A: real,B: real] :
% 9.49/5.29        ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.29       => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 9.49/5.29          = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5536_pos__less__minus__divide__eq,axiom,
% 9.49/5.29      ! [C: rat,A: rat,B: rat] :
% 9.49/5.29        ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.29       => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 9.49/5.29          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5537_pos__minus__divide__less__eq,axiom,
% 9.49/5.29      ! [C: real,B: real,A: real] :
% 9.49/5.29        ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.29       => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 9.49/5.29          = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5538_pos__minus__divide__less__eq,axiom,
% 9.49/5.29      ! [C: rat,B: rat,A: rat] :
% 9.49/5.29        ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.29       => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 9.49/5.29          = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5539_divide__eq__eq__numeral_I2_J,axiom,
% 9.49/5.29      ! [B: real,C: real,W: num] :
% 9.49/5.29        ( ( ( divide_divide_real @ B @ C )
% 9.49/5.29          = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 9.49/5.29        = ( ( ( C != zero_zero_real )
% 9.49/5.29           => ( B
% 9.49/5.29              = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 9.49/5.29          & ( ( C = zero_zero_real )
% 9.49/5.29           => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 9.49/5.29              = zero_zero_real ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5540_divide__eq__eq__numeral_I2_J,axiom,
% 9.49/5.29      ! [B: complex,C: complex,W: num] :
% 9.49/5.29        ( ( ( divide1717551699836669952omplex @ B @ C )
% 9.49/5.29          = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 9.49/5.29        = ( ( ( C != zero_zero_complex )
% 9.49/5.29           => ( B
% 9.49/5.29              = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C ) ) )
% 9.49/5.29          & ( ( C = zero_zero_complex )
% 9.49/5.29           => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 9.49/5.29              = zero_zero_complex ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5541_divide__eq__eq__numeral_I2_J,axiom,
% 9.49/5.29      ! [B: rat,C: rat,W: num] :
% 9.49/5.29        ( ( ( divide_divide_rat @ B @ C )
% 9.49/5.29          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 9.49/5.29        = ( ( ( C != zero_zero_rat )
% 9.49/5.29           => ( B
% 9.49/5.29              = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 9.49/5.29          & ( ( C = zero_zero_rat )
% 9.49/5.29           => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 9.49/5.29              = zero_zero_rat ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5542_eq__divide__eq__numeral_I2_J,axiom,
% 9.49/5.29      ! [W: num,B: real,C: real] :
% 9.49/5.29        ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 9.49/5.29          = ( divide_divide_real @ B @ C ) )
% 9.49/5.29        = ( ( ( C != zero_zero_real )
% 9.49/5.29           => ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C )
% 9.49/5.29              = B ) )
% 9.49/5.29          & ( ( C = zero_zero_real )
% 9.49/5.29           => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 9.49/5.29              = zero_zero_real ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5543_eq__divide__eq__numeral_I2_J,axiom,
% 9.49/5.29      ! [W: num,B: complex,C: complex] :
% 9.49/5.29        ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 9.49/5.29          = ( divide1717551699836669952omplex @ B @ C ) )
% 9.49/5.29        = ( ( ( C != zero_zero_complex )
% 9.49/5.29           => ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C )
% 9.49/5.29              = B ) )
% 9.49/5.29          & ( ( C = zero_zero_complex )
% 9.49/5.29           => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 9.49/5.29              = zero_zero_complex ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5544_eq__divide__eq__numeral_I2_J,axiom,
% 9.49/5.29      ! [W: num,B: rat,C: rat] :
% 9.49/5.29        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 9.49/5.29          = ( divide_divide_rat @ B @ C ) )
% 9.49/5.29        = ( ( ( C != zero_zero_rat )
% 9.49/5.29           => ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C )
% 9.49/5.29              = B ) )
% 9.49/5.29          & ( ( C = zero_zero_rat )
% 9.49/5.29           => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 9.49/5.29              = zero_zero_rat ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5545_add__divide__eq__if__simps_I3_J,axiom,
% 9.49/5.29      ! [Z: real,A: real,B: real] :
% 9.49/5.29        ( ( ( Z = zero_zero_real )
% 9.49/5.29         => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 9.49/5.29            = B ) )
% 9.49/5.29        & ( ( Z != zero_zero_real )
% 9.49/5.29         => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 9.49/5.29            = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5546_add__divide__eq__if__simps_I3_J,axiom,
% 9.49/5.29      ! [Z: complex,A: complex,B: complex] :
% 9.49/5.29        ( ( ( Z = zero_zero_complex )
% 9.49/5.29         => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 9.49/5.29            = B ) )
% 9.49/5.29        & ( ( Z != zero_zero_complex )
% 9.49/5.29         => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 9.49/5.29            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5547_add__divide__eq__if__simps_I3_J,axiom,
% 9.49/5.29      ! [Z: rat,A: rat,B: rat] :
% 9.49/5.29        ( ( ( Z = zero_zero_rat )
% 9.49/5.29         => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 9.49/5.29            = B ) )
% 9.49/5.29        & ( ( Z != zero_zero_rat )
% 9.49/5.29         => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 9.49/5.29            = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5548_minus__divide__add__eq__iff,axiom,
% 9.49/5.29      ! [Z: real,X: real,Y2: real] :
% 9.49/5.29        ( ( Z != zero_zero_real )
% 9.49/5.29       => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X @ Z ) ) @ Y2 )
% 9.49/5.29          = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ Y2 @ Z ) ) @ Z ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5549_minus__divide__add__eq__iff,axiom,
% 9.49/5.29      ! [Z: complex,X: complex,Y2: complex] :
% 9.49/5.29        ( ( Z != zero_zero_complex )
% 9.49/5.29       => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X @ Z ) ) @ Y2 )
% 9.49/5.29          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ X ) @ ( times_times_complex @ Y2 @ Z ) ) @ Z ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5550_minus__divide__add__eq__iff,axiom,
% 9.49/5.29      ! [Z: rat,X: rat,Y2: rat] :
% 9.49/5.29        ( ( Z != zero_zero_rat )
% 9.49/5.29       => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z ) ) @ Y2 )
% 9.49/5.29          = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y2 @ Z ) ) @ Z ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5551_subset__decode__imp__le,axiom,
% 9.49/5.29      ! [M: nat,N: nat] :
% 9.49/5.29        ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M ) @ ( nat_set_decode @ N ) )
% 9.49/5.29       => ( ord_less_eq_nat @ M @ N ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5552_add__divide__eq__if__simps_I6_J,axiom,
% 9.49/5.29      ! [Z: real,A: real,B: real] :
% 9.49/5.29        ( ( ( Z = zero_zero_real )
% 9.49/5.29         => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 9.49/5.29            = ( uminus_uminus_real @ B ) ) )
% 9.49/5.29        & ( ( Z != zero_zero_real )
% 9.49/5.29         => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 9.49/5.29            = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5553_add__divide__eq__if__simps_I6_J,axiom,
% 9.49/5.29      ! [Z: complex,A: complex,B: complex] :
% 9.49/5.29        ( ( ( Z = zero_zero_complex )
% 9.49/5.29         => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 9.49/5.29            = ( uminus1482373934393186551omplex @ B ) ) )
% 9.49/5.29        & ( ( Z != zero_zero_complex )
% 9.49/5.29         => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 9.49/5.29            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5554_add__divide__eq__if__simps_I6_J,axiom,
% 9.49/5.29      ! [Z: rat,A: rat,B: rat] :
% 9.49/5.29        ( ( ( Z = zero_zero_rat )
% 9.49/5.29         => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 9.49/5.29            = ( uminus_uminus_rat @ B ) ) )
% 9.49/5.29        & ( ( Z != zero_zero_rat )
% 9.49/5.29         => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 9.49/5.29            = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5555_add__divide__eq__if__simps_I5_J,axiom,
% 9.49/5.29      ! [Z: real,A: real,B: real] :
% 9.49/5.29        ( ( ( Z = zero_zero_real )
% 9.49/5.29         => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 9.49/5.29            = ( uminus_uminus_real @ B ) ) )
% 9.49/5.29        & ( ( Z != zero_zero_real )
% 9.49/5.29         => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 9.49/5.29            = ( divide_divide_real @ ( minus_minus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5556_add__divide__eq__if__simps_I5_J,axiom,
% 9.49/5.29      ! [Z: complex,A: complex,B: complex] :
% 9.49/5.29        ( ( ( Z = zero_zero_complex )
% 9.49/5.29         => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 9.49/5.29            = ( uminus1482373934393186551omplex @ B ) ) )
% 9.49/5.29        & ( ( Z != zero_zero_complex )
% 9.49/5.29         => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 9.49/5.29            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5557_add__divide__eq__if__simps_I5_J,axiom,
% 9.49/5.29      ! [Z: rat,A: rat,B: rat] :
% 9.49/5.29        ( ( ( Z = zero_zero_rat )
% 9.49/5.29         => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 9.49/5.29            = ( uminus_uminus_rat @ B ) ) )
% 9.49/5.29        & ( ( Z != zero_zero_rat )
% 9.49/5.29         => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 9.49/5.29            = ( divide_divide_rat @ ( minus_minus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5558_minus__divide__diff__eq__iff,axiom,
% 9.49/5.29      ! [Z: real,X: real,Y2: real] :
% 9.49/5.29        ( ( Z != zero_zero_real )
% 9.49/5.29       => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X @ Z ) ) @ Y2 )
% 9.49/5.29          = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ Y2 @ Z ) ) @ Z ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5559_minus__divide__diff__eq__iff,axiom,
% 9.49/5.29      ! [Z: complex,X: complex,Y2: complex] :
% 9.49/5.29        ( ( Z != zero_zero_complex )
% 9.49/5.29       => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X @ Z ) ) @ Y2 )
% 9.49/5.29          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X ) @ ( times_times_complex @ Y2 @ Z ) ) @ Z ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5560_minus__divide__diff__eq__iff,axiom,
% 9.49/5.29      ! [Z: rat,X: rat,Y2: rat] :
% 9.49/5.29        ( ( Z != zero_zero_rat )
% 9.49/5.29       => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z ) ) @ Y2 )
% 9.49/5.29          = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y2 @ Z ) ) @ Z ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5561_even__minus,axiom,
% 9.49/5.29      ! [A: int] :
% 9.49/5.29        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( uminus_uminus_int @ A ) )
% 9.49/5.29        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5562_even__minus,axiom,
% 9.49/5.29      ! [A: code_integer] :
% 9.49/5.29        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( uminus1351360451143612070nteger @ A ) )
% 9.49/5.29        = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5563_power2__eq__iff,axiom,
% 9.49/5.29      ! [X: int,Y2: int] :
% 9.49/5.29        ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.29          = ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.29        = ( ( X = Y2 )
% 9.49/5.29          | ( X
% 9.49/5.29            = ( uminus_uminus_int @ Y2 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5564_power2__eq__iff,axiom,
% 9.49/5.29      ! [X: real,Y2: real] :
% 9.49/5.29        ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.29          = ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.29        = ( ( X = Y2 )
% 9.49/5.29          | ( X
% 9.49/5.29            = ( uminus_uminus_real @ Y2 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5565_power2__eq__iff,axiom,
% 9.49/5.29      ! [X: complex,Y2: complex] :
% 9.49/5.29        ( ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.29          = ( power_power_complex @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.29        = ( ( X = Y2 )
% 9.49/5.29          | ( X
% 9.49/5.29            = ( uminus1482373934393186551omplex @ Y2 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5566_power2__eq__iff,axiom,
% 9.49/5.29      ! [X: code_integer,Y2: code_integer] :
% 9.49/5.29        ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.29          = ( power_8256067586552552935nteger @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.29        = ( ( X = Y2 )
% 9.49/5.29          | ( X
% 9.49/5.29            = ( uminus1351360451143612070nteger @ Y2 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5567_power2__eq__iff,axiom,
% 9.49/5.29      ! [X: rat,Y2: rat] :
% 9.49/5.29        ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.29          = ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.29        = ( ( X = Y2 )
% 9.49/5.29          | ( X
% 9.49/5.29            = ( uminus_uminus_rat @ Y2 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5568_verit__less__mono__div__int2,axiom,
% 9.49/5.29      ! [A2: int,B2: int,N: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ A2 @ B2 )
% 9.49/5.29       => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N ) )
% 9.49/5.29         => ( ord_less_eq_int @ ( divide_divide_int @ B2 @ N ) @ ( divide_divide_int @ A2 @ N ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5569_div__eq__minus1,axiom,
% 9.49/5.29      ! [B: int] :
% 9.49/5.29        ( ( ord_less_int @ zero_zero_int @ B )
% 9.49/5.29       => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 9.49/5.29          = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5570_le__minus__divide__eq,axiom,
% 9.49/5.29      ! [A: real,B: real,C: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 9.49/5.29        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.29           => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 9.49/5.29          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.29           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.29               => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 9.49/5.29              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.29               => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5571_le__minus__divide__eq,axiom,
% 9.49/5.29      ! [A: rat,B: rat,C: rat] :
% 9.49/5.29        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 9.49/5.29        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.29           => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 9.49/5.29          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.29           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.29               => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 9.49/5.29              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.29               => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5572_minus__divide__le__eq,axiom,
% 9.49/5.29      ! [B: real,C: real,A: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 9.49/5.29        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.29           => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 9.49/5.29          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.29           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.29               => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 9.49/5.29              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.29               => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5573_minus__divide__le__eq,axiom,
% 9.49/5.29      ! [B: rat,C: rat,A: rat] :
% 9.49/5.29        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 9.49/5.29        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.29           => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 9.49/5.29          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.29           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.29               => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 9.49/5.29              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.29               => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5574_neg__le__minus__divide__eq,axiom,
% 9.49/5.29      ! [C: real,A: real,B: real] :
% 9.49/5.29        ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.29       => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 9.49/5.29          = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5575_neg__le__minus__divide__eq,axiom,
% 9.49/5.29      ! [C: rat,A: rat,B: rat] :
% 9.49/5.29        ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.29       => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 9.49/5.29          = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5576_neg__minus__divide__le__eq,axiom,
% 9.49/5.29      ! [C: real,B: real,A: real] :
% 9.49/5.29        ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.29       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 9.49/5.29          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5577_neg__minus__divide__le__eq,axiom,
% 9.49/5.29      ! [C: rat,B: rat,A: rat] :
% 9.49/5.29        ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.29       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 9.49/5.29          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5578_pos__le__minus__divide__eq,axiom,
% 9.49/5.29      ! [C: real,A: real,B: real] :
% 9.49/5.29        ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.29       => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 9.49/5.29          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5579_pos__le__minus__divide__eq,axiom,
% 9.49/5.29      ! [C: rat,A: rat,B: rat] :
% 9.49/5.29        ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.29       => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 9.49/5.29          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5580_pos__minus__divide__le__eq,axiom,
% 9.49/5.29      ! [C: real,B: real,A: real] :
% 9.49/5.29        ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.29       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 9.49/5.29          = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5581_pos__minus__divide__le__eq,axiom,
% 9.49/5.29      ! [C: rat,B: rat,A: rat] :
% 9.49/5.29        ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.29       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 9.49/5.29          = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5582_divide__less__eq__numeral_I2_J,axiom,
% 9.49/5.29      ! [B: real,C: real,W: num] :
% 9.49/5.29        ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 9.49/5.29        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.29           => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 9.49/5.29          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.29           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.29               => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 9.49/5.29              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.29               => ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5583_divide__less__eq__numeral_I2_J,axiom,
% 9.49/5.29      ! [B: rat,C: rat,W: num] :
% 9.49/5.29        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 9.49/5.29        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.29           => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 9.49/5.29          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.29           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.29               => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 9.49/5.29              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.29               => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5584_less__divide__eq__numeral_I2_J,axiom,
% 9.49/5.29      ! [W: num,B: real,C: real] :
% 9.49/5.29        ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 9.49/5.29        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.29           => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 9.49/5.29          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.29           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.29               => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 9.49/5.29              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.29               => ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5585_less__divide__eq__numeral_I2_J,axiom,
% 9.49/5.29      ! [W: num,B: rat,C: rat] :
% 9.49/5.29        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 9.49/5.29        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.29           => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 9.49/5.29          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.29           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.29               => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 9.49/5.29              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.29               => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5586_power2__eq__1__iff,axiom,
% 9.49/5.29      ! [A: int] :
% 9.49/5.29        ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.29          = one_one_int )
% 9.49/5.29        = ( ( A = one_one_int )
% 9.49/5.29          | ( A
% 9.49/5.29            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5587_power2__eq__1__iff,axiom,
% 9.49/5.29      ! [A: real] :
% 9.49/5.29        ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.29          = one_one_real )
% 9.49/5.29        = ( ( A = one_one_real )
% 9.49/5.29          | ( A
% 9.49/5.29            = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5588_power2__eq__1__iff,axiom,
% 9.49/5.29      ! [A: complex] :
% 9.49/5.29        ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.29          = one_one_complex )
% 9.49/5.29        = ( ( A = one_one_complex )
% 9.49/5.29          | ( A
% 9.49/5.29            = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5589_power2__eq__1__iff,axiom,
% 9.49/5.29      ! [A: code_integer] :
% 9.49/5.29        ( ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.29          = one_one_Code_integer )
% 9.49/5.29        = ( ( A = one_one_Code_integer )
% 9.49/5.29          | ( A
% 9.49/5.29            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5590_power2__eq__1__iff,axiom,
% 9.49/5.29      ! [A: rat] :
% 9.49/5.29        ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.29          = one_one_rat )
% 9.49/5.29        = ( ( A = one_one_rat )
% 9.49/5.29          | ( A
% 9.49/5.29            = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5591_uminus__power__if,axiom,
% 9.49/5.29      ! [N: nat,A: int] :
% 9.49/5.29        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.29         => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 9.49/5.29            = ( power_power_int @ A @ N ) ) )
% 9.49/5.29        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.29         => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 9.49/5.29            = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5592_uminus__power__if,axiom,
% 9.49/5.29      ! [N: nat,A: real] :
% 9.49/5.29        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.29         => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 9.49/5.29            = ( power_power_real @ A @ N ) ) )
% 9.49/5.29        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.29         => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 9.49/5.29            = ( uminus_uminus_real @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5593_uminus__power__if,axiom,
% 9.49/5.29      ! [N: nat,A: complex] :
% 9.49/5.29        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.29         => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 9.49/5.29            = ( power_power_complex @ A @ N ) ) )
% 9.49/5.29        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.29         => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 9.49/5.29            = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5594_uminus__power__if,axiom,
% 9.49/5.29      ! [N: nat,A: code_integer] :
% 9.49/5.29        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.29         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 9.49/5.29            = ( power_8256067586552552935nteger @ A @ N ) ) )
% 9.49/5.29        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.29         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 9.49/5.29            = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5595_uminus__power__if,axiom,
% 9.49/5.29      ! [N: nat,A: rat] :
% 9.49/5.29        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.29         => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 9.49/5.29            = ( power_power_rat @ A @ N ) ) )
% 9.49/5.29        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.29         => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 9.49/5.29            = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5596_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 9.49/5.29      ! [K: nat,N: nat] :
% 9.49/5.29        ( ( ord_less_eq_nat @ K @ N )
% 9.49/5.29       => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N @ K ) )
% 9.49/5.29          = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5597_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 9.49/5.29      ! [K: nat,N: nat] :
% 9.49/5.29        ( ( ord_less_eq_nat @ K @ N )
% 9.49/5.29       => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( plus_plus_nat @ N @ K ) )
% 9.49/5.29          = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5598_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 9.49/5.29      ! [K: nat,N: nat] :
% 9.49/5.29        ( ( ord_less_eq_nat @ K @ N )
% 9.49/5.29       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( plus_plus_nat @ N @ K ) )
% 9.49/5.29          = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5599_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 9.49/5.29      ! [K: nat,N: nat] :
% 9.49/5.29        ( ( ord_less_eq_nat @ K @ N )
% 9.49/5.29       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N @ K ) )
% 9.49/5.29          = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5600_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 9.49/5.29      ! [K: nat,N: nat] :
% 9.49/5.29        ( ( ord_less_eq_nat @ K @ N )
% 9.49/5.29       => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N @ K ) )
% 9.49/5.29          = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5601_realpow__square__minus__le,axiom,
% 9.49/5.29      ! [U: real,X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5602_signed__take__bit__int__greater__eq__minus__exp,axiom,
% 9.49/5.29      ! [N: nat,K: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5603_signed__take__bit__int__less__eq__self__iff,axiom,
% 9.49/5.29      ! [N: nat,K: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 9.49/5.29        = ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5604_signed__take__bit__int__greater__self__iff,axiom,
% 9.49/5.29      ! [K: int,N: nat] :
% 9.49/5.29        ( ( ord_less_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 9.49/5.29        = ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5605_minus__mod__int__eq,axiom,
% 9.49/5.29      ! [L2: int,K: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ zero_zero_int @ L2 )
% 9.49/5.29       => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L2 )
% 9.49/5.29          = ( minus_minus_int @ ( minus_minus_int @ L2 @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K @ one_one_int ) @ L2 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5606_zmod__minus1,axiom,
% 9.49/5.29      ! [B: int] :
% 9.49/5.29        ( ( ord_less_int @ zero_zero_int @ B )
% 9.49/5.29       => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 9.49/5.29          = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5607_zdiv__zminus2__eq__if,axiom,
% 9.49/5.29      ! [B: int,A: int] :
% 9.49/5.29        ( ( B != zero_zero_int )
% 9.49/5.29       => ( ( ( ( modulo_modulo_int @ A @ B )
% 9.49/5.29              = zero_zero_int )
% 9.49/5.29           => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 9.49/5.29              = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 9.49/5.29          & ( ( ( modulo_modulo_int @ A @ B )
% 9.49/5.29             != zero_zero_int )
% 9.49/5.29           => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 9.49/5.29              = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5608_zdiv__zminus1__eq__if,axiom,
% 9.49/5.29      ! [B: int,A: int] :
% 9.49/5.29        ( ( B != zero_zero_int )
% 9.49/5.29       => ( ( ( ( modulo_modulo_int @ A @ B )
% 9.49/5.29              = zero_zero_int )
% 9.49/5.29           => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 9.49/5.29              = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 9.49/5.29          & ( ( ( modulo_modulo_int @ A @ B )
% 9.49/5.29             != zero_zero_int )
% 9.49/5.29           => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 9.49/5.29              = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5609_zminus1__lemma,axiom,
% 9.49/5.29      ! [A: int,B: int,Q2: int,R: int] :
% 9.49/5.29        ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 9.49/5.29       => ( ( B != zero_zero_int )
% 9.49/5.29         => ( eucl_rel_int @ ( uminus_uminus_int @ A ) @ B @ ( product_Pair_int_int @ ( if_int @ ( R = zero_zero_int ) @ ( uminus_uminus_int @ Q2 ) @ ( minus_minus_int @ ( uminus_uminus_int @ Q2 ) @ one_one_int ) ) @ ( if_int @ ( R = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ B @ R ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5610_Divides_Oadjust__div__def,axiom,
% 9.49/5.29      ( adjust_div
% 9.49/5.29      = ( produc8211389475949308722nt_int
% 9.49/5.29        @ ^ [Q4: int,R5: int] : ( plus_plus_int @ Q4 @ ( zero_n2684676970156552555ol_int @ ( R5 != zero_zero_int ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5611_divide__le__eq__numeral_I2_J,axiom,
% 9.49/5.29      ! [B: real,C: real,W: num] :
% 9.49/5.29        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 9.49/5.29        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.29           => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 9.49/5.29          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.29           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.29               => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 9.49/5.29              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.29               => ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5612_divide__le__eq__numeral_I2_J,axiom,
% 9.49/5.29      ! [B: rat,C: rat,W: num] :
% 9.49/5.29        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 9.49/5.29        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.29           => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 9.49/5.29          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.29           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.29               => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 9.49/5.29              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.29               => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5613_le__divide__eq__numeral_I2_J,axiom,
% 9.49/5.29      ! [W: num,B: real,C: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 9.49/5.29        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.29           => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 9.49/5.29          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 9.49/5.29           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.29               => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 9.49/5.29              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 9.49/5.29               => ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5614_le__divide__eq__numeral_I2_J,axiom,
% 9.49/5.29      ! [W: num,B: rat,C: rat] :
% 9.49/5.29        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 9.49/5.29        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.29           => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 9.49/5.29          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 9.49/5.29           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.29               => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 9.49/5.29              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 9.49/5.29               => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5615_square__le__1,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 9.49/5.29       => ( ( ord_less_eq_real @ X @ one_one_real )
% 9.49/5.29         => ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5616_square__le__1,axiom,
% 9.49/5.29      ! [X: code_integer] :
% 9.49/5.29        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 9.49/5.29       => ( ( ord_le3102999989581377725nteger @ X @ one_one_Code_integer )
% 9.49/5.29         => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5617_square__le__1,axiom,
% 9.49/5.29      ! [X: rat] :
% 9.49/5.29        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X )
% 9.49/5.29       => ( ( ord_less_eq_rat @ X @ one_one_rat )
% 9.49/5.29         => ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5618_square__le__1,axiom,
% 9.49/5.29      ! [X: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 9.49/5.29       => ( ( ord_less_eq_int @ X @ one_one_int )
% 9.49/5.29         => ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5619_minus__power__mult__self,axiom,
% 9.49/5.29      ! [A: int,N: nat] :
% 9.49/5.29        ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 9.49/5.29        = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5620_minus__power__mult__self,axiom,
% 9.49/5.29      ! [A: real,N: nat] :
% 9.49/5.29        ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 9.49/5.29        = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5621_minus__power__mult__self,axiom,
% 9.49/5.29      ! [A: complex,N: nat] :
% 9.49/5.29        ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) )
% 9.49/5.29        = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5622_minus__power__mult__self,axiom,
% 9.49/5.29      ! [A: code_integer,N: nat] :
% 9.49/5.29        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 9.49/5.29        = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5623_minus__power__mult__self,axiom,
% 9.49/5.29      ! [A: rat,N: nat] :
% 9.49/5.29        ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 9.49/5.29        = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5624_minus__one__power__iff,axiom,
% 9.49/5.29      ! [N: nat] :
% 9.49/5.29        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.29         => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 9.49/5.29            = one_one_int ) )
% 9.49/5.29        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.29         => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 9.49/5.29            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5625_minus__one__power__iff,axiom,
% 9.49/5.29      ! [N: nat] :
% 9.49/5.29        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.29         => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 9.49/5.29            = one_one_real ) )
% 9.49/5.29        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.29         => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 9.49/5.29            = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5626_minus__one__power__iff,axiom,
% 9.49/5.29      ! [N: nat] :
% 9.49/5.29        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.29         => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 9.49/5.29            = one_one_complex ) )
% 9.49/5.29        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.29         => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 9.49/5.29            = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5627_minus__one__power__iff,axiom,
% 9.49/5.29      ! [N: nat] :
% 9.49/5.29        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.29         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 9.49/5.29            = one_one_Code_integer ) )
% 9.49/5.29        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.29         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 9.49/5.29            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5628_minus__one__power__iff,axiom,
% 9.49/5.29      ! [N: nat] :
% 9.49/5.29        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.29         => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 9.49/5.29            = one_one_rat ) )
% 9.49/5.29        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.29         => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 9.49/5.29            = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5629_signed__take__bit__int__eq__self__iff,axiom,
% 9.49/5.29      ! [N: nat,K: int] :
% 9.49/5.29        ( ( ( bit_ri631733984087533419it_int @ N @ K )
% 9.49/5.29          = K )
% 9.49/5.29        = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 9.49/5.29          & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5630_signed__take__bit__int__eq__self,axiom,
% 9.49/5.29      ! [N: nat,K: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 9.49/5.29       => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.29         => ( ( bit_ri631733984087533419it_int @ N @ K )
% 9.49/5.29            = K ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5631_minus__1__div__exp__eq__int,axiom,
% 9.49/5.29      ! [N: nat] :
% 9.49/5.29        ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.29        = ( uminus_uminus_int @ one_one_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5632_div__pos__neg__trivial,axiom,
% 9.49/5.29      ! [K: int,L2: int] :
% 9.49/5.29        ( ( ord_less_int @ zero_zero_int @ K )
% 9.49/5.29       => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L2 ) @ zero_zero_int )
% 9.49/5.29         => ( ( divide_divide_int @ K @ L2 )
% 9.49/5.29            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5633_power__minus1__odd,axiom,
% 9.49/5.29      ! [N: nat] :
% 9.49/5.29        ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 9.49/5.29        = ( uminus_uminus_int @ one_one_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5634_power__minus1__odd,axiom,
% 9.49/5.29      ! [N: nat] :
% 9.49/5.29        ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 9.49/5.29        = ( uminus_uminus_real @ one_one_real ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5635_power__minus1__odd,axiom,
% 9.49/5.29      ! [N: nat] :
% 9.49/5.29        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 9.49/5.29        = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5636_power__minus1__odd,axiom,
% 9.49/5.29      ! [N: nat] :
% 9.49/5.29        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 9.49/5.29        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5637_power__minus1__odd,axiom,
% 9.49/5.29      ! [N: nat] :
% 9.49/5.29        ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 9.49/5.29        = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5638_int__bit__induct,axiom,
% 9.49/5.29      ! [P: int > $o,K: int] :
% 9.49/5.29        ( ( P @ zero_zero_int )
% 9.49/5.29       => ( ( P @ ( uminus_uminus_int @ one_one_int ) )
% 9.49/5.29         => ( ! [K2: int] :
% 9.49/5.29                ( ( P @ K2 )
% 9.49/5.29               => ( ( K2 != zero_zero_int )
% 9.49/5.29                 => ( P @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 9.49/5.29           => ( ! [K2: int] :
% 9.49/5.29                  ( ( P @ K2 )
% 9.49/5.29                 => ( ( K2
% 9.49/5.29                     != ( uminus_uminus_int @ one_one_int ) )
% 9.49/5.29                   => ( P @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 9.49/5.29             => ( P @ K ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5639_signed__take__bit__int__greater__eq,axiom,
% 9.49/5.29      ! [K: int,N: nat] :
% 9.49/5.29        ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 9.49/5.29       => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5640_set__decode__plus__power__2,axiom,
% 9.49/5.29      ! [N: nat,Z: nat] :
% 9.49/5.29        ( ~ ( member_nat @ N @ ( nat_set_decode @ Z ) )
% 9.49/5.29       => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ Z ) )
% 9.49/5.29          = ( insert_nat @ N @ ( nat_set_decode @ Z ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5641_set__decode__def,axiom,
% 9.49/5.29      ( nat_set_decode
% 9.49/5.29      = ( ^ [X2: nat] :
% 9.49/5.29            ( collect_nat
% 9.49/5.29            @ ^ [N2: nat] :
% 9.49/5.29                ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5642_compl__le__compl__iff,axiom,
% 9.49/5.29      ! [X: set_real,Y2: set_real] :
% 9.49/5.29        ( ( ord_less_eq_set_real @ ( uminus612125837232591019t_real @ X ) @ ( uminus612125837232591019t_real @ Y2 ) )
% 9.49/5.29        = ( ord_less_eq_set_real @ Y2 @ X ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5643_compl__le__compl__iff,axiom,
% 9.49/5.29      ! [X: set_nat,Y2: set_nat] :
% 9.49/5.29        ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ ( uminus5710092332889474511et_nat @ Y2 ) )
% 9.49/5.29        = ( ord_less_eq_set_nat @ Y2 @ X ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5644_dbl__dec__simps_I4_J,axiom,
% 9.49/5.29      ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ one_one_int ) )
% 9.49/5.29      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5645_dbl__dec__simps_I4_J,axiom,
% 9.49/5.29      ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ one_one_real ) )
% 9.49/5.29      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5646_dbl__dec__simps_I4_J,axiom,
% 9.49/5.29      ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 9.49/5.29      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5647_dbl__dec__simps_I4_J,axiom,
% 9.49/5.29      ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.49/5.29      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5648_dbl__dec__simps_I4_J,axiom,
% 9.49/5.29      ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.49/5.29      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5649_and__int_Osimps,axiom,
% 9.49/5.29      ( bit_se725231765392027082nd_int
% 9.49/5.29      = ( ^ [K3: int,L: int] :
% 9.49/5.29            ( if_int
% 9.49/5.29            @ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 9.49/5.29              & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 9.49/5.29            @ ( uminus_uminus_int
% 9.49/5.29              @ ( zero_n2684676970156552555ol_int
% 9.49/5.29                @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 9.49/5.29                  & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) )
% 9.49/5.29            @ ( plus_plus_int
% 9.49/5.29              @ ( zero_n2684676970156552555ol_int
% 9.49/5.29                @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 9.49/5.29                  & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 9.49/5.29              @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5650_and__int_Oelims,axiom,
% 9.49/5.29      ! [X: int,Xa2: int,Y2: int] :
% 9.49/5.29        ( ( ( bit_se725231765392027082nd_int @ X @ Xa2 )
% 9.49/5.29          = Y2 )
% 9.49/5.29       => ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 9.49/5.29              & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 9.49/5.29           => ( Y2
% 9.49/5.29              = ( uminus_uminus_int
% 9.49/5.29                @ ( zero_n2684676970156552555ol_int
% 9.49/5.29                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 9.49/5.29                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 9.49/5.29          & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 9.49/5.29                & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 9.49/5.29           => ( Y2
% 9.49/5.29              = ( plus_plus_int
% 9.49/5.29                @ ( zero_n2684676970156552555ol_int
% 9.49/5.29                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 9.49/5.29                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 9.49/5.29                @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5651_of__int__code__if,axiom,
% 9.49/5.29      ( ring_1_of_int_int
% 9.49/5.29      = ( ^ [K3: int] :
% 9.49/5.29            ( if_int @ ( K3 = zero_zero_int ) @ zero_zero_int
% 9.49/5.29            @ ( if_int @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_int @ ( ring_1_of_int_int @ ( uminus_uminus_int @ K3 ) ) )
% 9.49/5.29              @ ( if_int
% 9.49/5.29                @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.49/5.29                  = zero_zero_int )
% 9.49/5.29                @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 9.49/5.29                @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_int ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5652_of__int__code__if,axiom,
% 9.49/5.29      ( ring_1_of_int_real
% 9.49/5.29      = ( ^ [K3: int] :
% 9.49/5.29            ( if_real @ ( K3 = zero_zero_int ) @ zero_zero_real
% 9.49/5.29            @ ( if_real @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_real @ ( ring_1_of_int_real @ ( uminus_uminus_int @ K3 ) ) )
% 9.49/5.29              @ ( if_real
% 9.49/5.29                @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.49/5.29                  = zero_zero_int )
% 9.49/5.29                @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 9.49/5.29                @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5653_of__int__code__if,axiom,
% 9.49/5.29      ( ring_17405671764205052669omplex
% 9.49/5.29      = ( ^ [K3: int] :
% 9.49/5.29            ( if_complex @ ( K3 = zero_zero_int ) @ zero_zero_complex
% 9.49/5.29            @ ( if_complex @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ K3 ) ) )
% 9.49/5.29              @ ( if_complex
% 9.49/5.29                @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.49/5.29                  = zero_zero_int )
% 9.49/5.29                @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 9.49/5.29                @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_complex ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5654_of__int__code__if,axiom,
% 9.49/5.29      ( ring_18347121197199848620nteger
% 9.49/5.29      = ( ^ [K3: int] :
% 9.49/5.29            ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 9.49/5.29            @ ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ K3 ) ) )
% 9.49/5.29              @ ( if_Code_integer
% 9.49/5.29                @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.49/5.29                  = zero_zero_int )
% 9.49/5.29                @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 9.49/5.29                @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5655_of__int__code__if,axiom,
% 9.49/5.29      ( ring_1_of_int_rat
% 9.49/5.29      = ( ^ [K3: int] :
% 9.49/5.29            ( if_rat @ ( K3 = zero_zero_int ) @ zero_zero_rat
% 9.49/5.29            @ ( if_rat @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( ring_1_of_int_rat @ ( uminus_uminus_int @ K3 ) ) )
% 9.49/5.29              @ ( if_rat
% 9.49/5.29                @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.49/5.29                  = zero_zero_int )
% 9.49/5.29                @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 9.49/5.29                @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_rat ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5656_diff__shunt__var,axiom,
% 9.49/5.29      ! [X: set_int,Y2: set_int] :
% 9.49/5.29        ( ( ( minus_minus_set_int @ X @ Y2 )
% 9.49/5.29          = bot_bot_set_int )
% 9.49/5.29        = ( ord_less_eq_set_int @ X @ Y2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5657_diff__shunt__var,axiom,
% 9.49/5.29      ! [X: set_Pr1261947904930325089at_nat,Y2: set_Pr1261947904930325089at_nat] :
% 9.49/5.29        ( ( ( minus_1356011639430497352at_nat @ X @ Y2 )
% 9.49/5.29          = bot_bo2099793752762293965at_nat )
% 9.49/5.29        = ( ord_le3146513528884898305at_nat @ X @ Y2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5658_diff__shunt__var,axiom,
% 9.49/5.29      ! [X: set_real,Y2: set_real] :
% 9.49/5.29        ( ( ( minus_minus_set_real @ X @ Y2 )
% 9.49/5.29          = bot_bot_set_real )
% 9.49/5.29        = ( ord_less_eq_set_real @ X @ Y2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5659_diff__shunt__var,axiom,
% 9.49/5.29      ! [X: set_nat,Y2: set_nat] :
% 9.49/5.29        ( ( ( minus_minus_set_nat @ X @ Y2 )
% 9.49/5.29          = bot_bot_set_nat )
% 9.49/5.29        = ( ord_less_eq_set_nat @ X @ Y2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5660_and_Oidem,axiom,
% 9.49/5.29      ! [A: int] :
% 9.49/5.29        ( ( bit_se725231765392027082nd_int @ A @ A )
% 9.49/5.29        = A ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5661_and_Oidem,axiom,
% 9.49/5.29      ! [A: nat] :
% 9.49/5.29        ( ( bit_se727722235901077358nd_nat @ A @ A )
% 9.49/5.29        = A ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5662_and_Oleft__idem,axiom,
% 9.49/5.29      ! [A: int,B: int] :
% 9.49/5.29        ( ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 9.49/5.29        = ( bit_se725231765392027082nd_int @ A @ B ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5663_and_Oleft__idem,axiom,
% 9.49/5.29      ! [A: nat,B: nat] :
% 9.49/5.29        ( ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 9.49/5.29        = ( bit_se727722235901077358nd_nat @ A @ B ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5664_and_Oright__idem,axiom,
% 9.49/5.29      ! [A: int,B: int] :
% 9.49/5.29        ( ( bit_se725231765392027082nd_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ B )
% 9.49/5.29        = ( bit_se725231765392027082nd_int @ A @ B ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5665_and_Oright__idem,axiom,
% 9.49/5.29      ! [A: nat,B: nat] :
% 9.49/5.29        ( ( bit_se727722235901077358nd_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ B )
% 9.49/5.29        = ( bit_se727722235901077358nd_nat @ A @ B ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5666_and__zero__eq,axiom,
% 9.49/5.29      ! [A: int] :
% 9.49/5.29        ( ( bit_se725231765392027082nd_int @ A @ zero_zero_int )
% 9.49/5.29        = zero_zero_int ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5667_and__zero__eq,axiom,
% 9.49/5.29      ! [A: nat] :
% 9.49/5.29        ( ( bit_se727722235901077358nd_nat @ A @ zero_zero_nat )
% 9.49/5.29        = zero_zero_nat ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5668_zero__and__eq,axiom,
% 9.49/5.29      ! [A: int] :
% 9.49/5.29        ( ( bit_se725231765392027082nd_int @ zero_zero_int @ A )
% 9.49/5.29        = zero_zero_int ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5669_zero__and__eq,axiom,
% 9.49/5.29      ! [A: nat] :
% 9.49/5.29        ( ( bit_se727722235901077358nd_nat @ zero_zero_nat @ A )
% 9.49/5.29        = zero_zero_nat ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5670_bit_Oconj__zero__left,axiom,
% 9.49/5.29      ! [X: int] :
% 9.49/5.29        ( ( bit_se725231765392027082nd_int @ zero_zero_int @ X )
% 9.49/5.29        = zero_zero_int ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5671_bit_Oconj__zero__right,axiom,
% 9.49/5.29      ! [X: int] :
% 9.49/5.29        ( ( bit_se725231765392027082nd_int @ X @ zero_zero_int )
% 9.49/5.29        = zero_zero_int ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5672_dbl__dec__simps_I3_J,axiom,
% 9.49/5.29      ( ( neg_nu6511756317524482435omplex @ one_one_complex )
% 9.49/5.29      = one_one_complex ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5673_dbl__dec__simps_I3_J,axiom,
% 9.49/5.29      ( ( neg_nu6075765906172075777c_real @ one_one_real )
% 9.49/5.29      = one_one_real ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5674_dbl__dec__simps_I3_J,axiom,
% 9.49/5.29      ( ( neg_nu3179335615603231917ec_rat @ one_one_rat )
% 9.49/5.29      = one_one_rat ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5675_dbl__dec__simps_I3_J,axiom,
% 9.49/5.29      ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 9.49/5.29      = one_one_int ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5676_bit_Oconj__one__right,axiom,
% 9.49/5.29      ! [X: code_integer] :
% 9.49/5.29        ( ( bit_se3949692690581998587nteger @ X @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.49/5.29        = X ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5677_bit_Oconj__one__right,axiom,
% 9.49/5.29      ! [X: int] :
% 9.49/5.29        ( ( bit_se725231765392027082nd_int @ X @ ( uminus_uminus_int @ one_one_int ) )
% 9.49/5.29        = X ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5678_and_Oright__neutral,axiom,
% 9.49/5.29      ! [A: code_integer] :
% 9.49/5.29        ( ( bit_se3949692690581998587nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.49/5.29        = A ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5679_and_Oright__neutral,axiom,
% 9.49/5.29      ! [A: int] :
% 9.49/5.29        ( ( bit_se725231765392027082nd_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 9.49/5.29        = A ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5680_and_Oleft__neutral,axiom,
% 9.49/5.29      ! [A: code_integer] :
% 9.49/5.29        ( ( bit_se3949692690581998587nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ A )
% 9.49/5.29        = A ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5681_and_Oleft__neutral,axiom,
% 9.49/5.29      ! [A: int] :
% 9.49/5.29        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ one_one_int ) @ A )
% 9.49/5.29        = A ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5682_of__int__numeral,axiom,
% 9.49/5.29      ! [K: num] :
% 9.49/5.29        ( ( ring_17405671764205052669omplex @ ( numeral_numeral_int @ K ) )
% 9.49/5.29        = ( numera6690914467698888265omplex @ K ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5683_of__int__numeral,axiom,
% 9.49/5.29      ! [K: num] :
% 9.49/5.29        ( ( ring_1_of_int_real @ ( numeral_numeral_int @ K ) )
% 9.49/5.29        = ( numeral_numeral_real @ K ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5684_of__int__numeral,axiom,
% 9.49/5.29      ! [K: num] :
% 9.49/5.29        ( ( ring_1_of_int_rat @ ( numeral_numeral_int @ K ) )
% 9.49/5.29        = ( numeral_numeral_rat @ K ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5685_of__int__numeral,axiom,
% 9.49/5.29      ! [K: num] :
% 9.49/5.29        ( ( ring_1_of_int_int @ ( numeral_numeral_int @ K ) )
% 9.49/5.29        = ( numeral_numeral_int @ K ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5686_of__int__eq__numeral__iff,axiom,
% 9.49/5.29      ! [Z: int,N: num] :
% 9.49/5.29        ( ( ( ring_17405671764205052669omplex @ Z )
% 9.49/5.29          = ( numera6690914467698888265omplex @ N ) )
% 9.49/5.29        = ( Z
% 9.49/5.29          = ( numeral_numeral_int @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5687_of__int__eq__numeral__iff,axiom,
% 9.49/5.29      ! [Z: int,N: num] :
% 9.49/5.29        ( ( ( ring_1_of_int_real @ Z )
% 9.49/5.29          = ( numeral_numeral_real @ N ) )
% 9.49/5.29        = ( Z
% 9.49/5.29          = ( numeral_numeral_int @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5688_of__int__eq__numeral__iff,axiom,
% 9.49/5.29      ! [Z: int,N: num] :
% 9.49/5.29        ( ( ( ring_1_of_int_rat @ Z )
% 9.49/5.29          = ( numeral_numeral_rat @ N ) )
% 9.49/5.29        = ( Z
% 9.49/5.29          = ( numeral_numeral_int @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5689_of__int__eq__numeral__iff,axiom,
% 9.49/5.29      ! [Z: int,N: num] :
% 9.49/5.29        ( ( ( ring_1_of_int_int @ Z )
% 9.49/5.29          = ( numeral_numeral_int @ N ) )
% 9.49/5.29        = ( Z
% 9.49/5.29          = ( numeral_numeral_int @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5690_of__int__le__iff,axiom,
% 9.49/5.29      ! [W: int,Z: int] :
% 9.49/5.29        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 9.49/5.29        = ( ord_less_eq_int @ W @ Z ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5691_of__int__le__iff,axiom,
% 9.49/5.29      ! [W: int,Z: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 9.49/5.29        = ( ord_less_eq_int @ W @ Z ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5692_of__int__less__iff,axiom,
% 9.49/5.29      ! [W: int,Z: int] :
% 9.49/5.29        ( ( ord_less_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 9.49/5.29        = ( ord_less_int @ W @ Z ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5693_of__int__less__iff,axiom,
% 9.49/5.29      ! [W: int,Z: int] :
% 9.49/5.29        ( ( ord_less_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 9.49/5.29        = ( ord_less_int @ W @ Z ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5694_of__int__less__iff,axiom,
% 9.49/5.29      ! [W: int,Z: int] :
% 9.49/5.29        ( ( ord_less_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 9.49/5.29        = ( ord_less_int @ W @ Z ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5695_of__int__eq__1__iff,axiom,
% 9.49/5.29      ! [Z: int] :
% 9.49/5.29        ( ( ( ring_17405671764205052669omplex @ Z )
% 9.49/5.29          = one_one_complex )
% 9.49/5.29        = ( Z = one_one_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5696_of__int__eq__1__iff,axiom,
% 9.49/5.29      ! [Z: int] :
% 9.49/5.29        ( ( ( ring_1_of_int_rat @ Z )
% 9.49/5.29          = one_one_rat )
% 9.49/5.29        = ( Z = one_one_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5697_of__int__eq__1__iff,axiom,
% 9.49/5.29      ! [Z: int] :
% 9.49/5.29        ( ( ( ring_1_of_int_int @ Z )
% 9.49/5.29          = one_one_int )
% 9.49/5.29        = ( Z = one_one_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5698_of__int__eq__1__iff,axiom,
% 9.49/5.29      ! [Z: int] :
% 9.49/5.29        ( ( ( ring_1_of_int_real @ Z )
% 9.49/5.29          = one_one_real )
% 9.49/5.29        = ( Z = one_one_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5699_of__int__1,axiom,
% 9.49/5.29      ( ( ring_17405671764205052669omplex @ one_one_int )
% 9.49/5.29      = one_one_complex ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5700_of__int__1,axiom,
% 9.49/5.29      ( ( ring_1_of_int_rat @ one_one_int )
% 9.49/5.29      = one_one_rat ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5701_of__int__1,axiom,
% 9.49/5.29      ( ( ring_1_of_int_int @ one_one_int )
% 9.49/5.29      = one_one_int ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5702_of__int__1,axiom,
% 9.49/5.29      ( ( ring_1_of_int_real @ one_one_int )
% 9.49/5.29      = one_one_real ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5703_of__int__mult,axiom,
% 9.49/5.29      ! [W: int,Z: int] :
% 9.49/5.29        ( ( ring_17405671764205052669omplex @ ( times_times_int @ W @ Z ) )
% 9.49/5.29        = ( times_times_complex @ ( ring_17405671764205052669omplex @ W ) @ ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5704_of__int__mult,axiom,
% 9.49/5.29      ! [W: int,Z: int] :
% 9.49/5.29        ( ( ring_1_of_int_real @ ( times_times_int @ W @ Z ) )
% 9.49/5.29        = ( times_times_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5705_of__int__mult,axiom,
% 9.49/5.29      ! [W: int,Z: int] :
% 9.49/5.29        ( ( ring_1_of_int_int @ ( times_times_int @ W @ Z ) )
% 9.49/5.29        = ( times_times_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5706_of__int__add,axiom,
% 9.49/5.29      ! [W: int,Z: int] :
% 9.49/5.29        ( ( ring_1_of_int_rat @ ( plus_plus_int @ W @ Z ) )
% 9.49/5.29        = ( plus_plus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5707_of__int__add,axiom,
% 9.49/5.29      ! [W: int,Z: int] :
% 9.49/5.29        ( ( ring_1_of_int_int @ ( plus_plus_int @ W @ Z ) )
% 9.49/5.29        = ( plus_plus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5708_of__int__add,axiom,
% 9.49/5.29      ! [W: int,Z: int] :
% 9.49/5.29        ( ( ring_17405671764205052669omplex @ ( plus_plus_int @ W @ Z ) )
% 9.49/5.29        = ( plus_plus_complex @ ( ring_17405671764205052669omplex @ W ) @ ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5709_of__int__add,axiom,
% 9.49/5.29      ! [W: int,Z: int] :
% 9.49/5.29        ( ( ring_1_of_int_real @ ( plus_plus_int @ W @ Z ) )
% 9.49/5.29        = ( plus_plus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5710_of__int__diff,axiom,
% 9.49/5.29      ! [W: int,Z: int] :
% 9.49/5.29        ( ( ring_1_of_int_real @ ( minus_minus_int @ W @ Z ) )
% 9.49/5.29        = ( minus_minus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5711_of__int__diff,axiom,
% 9.49/5.29      ! [W: int,Z: int] :
% 9.49/5.29        ( ( ring_1_of_int_rat @ ( minus_minus_int @ W @ Z ) )
% 9.49/5.29        = ( minus_minus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5712_of__int__diff,axiom,
% 9.49/5.29      ! [W: int,Z: int] :
% 9.49/5.29        ( ( ring_1_of_int_int @ ( minus_minus_int @ W @ Z ) )
% 9.49/5.29        = ( minus_minus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5713_of__int__power,axiom,
% 9.49/5.29      ! [Z: int,N: nat] :
% 9.49/5.29        ( ( ring_1_of_int_real @ ( power_power_int @ Z @ N ) )
% 9.49/5.29        = ( power_power_real @ ( ring_1_of_int_real @ Z ) @ N ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5714_of__int__power,axiom,
% 9.49/5.29      ! [Z: int,N: nat] :
% 9.49/5.29        ( ( ring_1_of_int_int @ ( power_power_int @ Z @ N ) )
% 9.49/5.29        = ( power_power_int @ ( ring_1_of_int_int @ Z ) @ N ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5715_of__int__power,axiom,
% 9.49/5.29      ! [Z: int,N: nat] :
% 9.49/5.29        ( ( ring_17405671764205052669omplex @ ( power_power_int @ Z @ N ) )
% 9.49/5.29        = ( power_power_complex @ ( ring_17405671764205052669omplex @ Z ) @ N ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5716_of__int__eq__of__int__power__cancel__iff,axiom,
% 9.49/5.29      ! [B: int,W: nat,X: int] :
% 9.49/5.29        ( ( ( power_power_real @ ( ring_1_of_int_real @ B ) @ W )
% 9.49/5.29          = ( ring_1_of_int_real @ X ) )
% 9.49/5.29        = ( ( power_power_int @ B @ W )
% 9.49/5.29          = X ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5717_of__int__eq__of__int__power__cancel__iff,axiom,
% 9.49/5.29      ! [B: int,W: nat,X: int] :
% 9.49/5.29        ( ( ( power_power_int @ ( ring_1_of_int_int @ B ) @ W )
% 9.49/5.29          = ( ring_1_of_int_int @ X ) )
% 9.49/5.29        = ( ( power_power_int @ B @ W )
% 9.49/5.29          = X ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5718_of__int__eq__of__int__power__cancel__iff,axiom,
% 9.49/5.29      ! [B: int,W: nat,X: int] :
% 9.49/5.29        ( ( ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W )
% 9.49/5.29          = ( ring_17405671764205052669omplex @ X ) )
% 9.49/5.29        = ( ( power_power_int @ B @ W )
% 9.49/5.29          = X ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5719_of__int__power__eq__of__int__cancel__iff,axiom,
% 9.49/5.29      ! [X: int,B: int,W: nat] :
% 9.49/5.29        ( ( ( ring_1_of_int_real @ X )
% 9.49/5.29          = ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 9.49/5.29        = ( X
% 9.49/5.29          = ( power_power_int @ B @ W ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5720_of__int__power__eq__of__int__cancel__iff,axiom,
% 9.49/5.29      ! [X: int,B: int,W: nat] :
% 9.49/5.29        ( ( ( ring_1_of_int_int @ X )
% 9.49/5.29          = ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 9.49/5.29        = ( X
% 9.49/5.29          = ( power_power_int @ B @ W ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5721_of__int__power__eq__of__int__cancel__iff,axiom,
% 9.49/5.29      ! [X: int,B: int,W: nat] :
% 9.49/5.29        ( ( ( ring_17405671764205052669omplex @ X )
% 9.49/5.29          = ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W ) )
% 9.49/5.29        = ( X
% 9.49/5.29          = ( power_power_int @ B @ W ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5722_and__nonnegative__int__iff,axiom,
% 9.49/5.29      ! [K: int,L2: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) )
% 9.49/5.29        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 9.49/5.29          | ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5723_and__negative__int__iff,axiom,
% 9.49/5.29      ! [K: int,L2: int] :
% 9.49/5.29        ( ( ord_less_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) @ zero_zero_int )
% 9.49/5.29        = ( ( ord_less_int @ K @ zero_zero_int )
% 9.49/5.29          & ( ord_less_int @ L2 @ zero_zero_int ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5724_dbl__dec__simps_I5_J,axiom,
% 9.49/5.29      ! [K: num] :
% 9.49/5.29        ( ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) )
% 9.49/5.29        = ( numera6690914467698888265omplex @ ( bitM @ K ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5725_dbl__dec__simps_I5_J,axiom,
% 9.49/5.29      ! [K: num] :
% 9.49/5.29        ( ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) )
% 9.49/5.29        = ( numeral_numeral_real @ ( bitM @ K ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5726_dbl__dec__simps_I5_J,axiom,
% 9.49/5.29      ! [K: num] :
% 9.49/5.29        ( ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) )
% 9.49/5.29        = ( numeral_numeral_rat @ ( bitM @ K ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5727_dbl__dec__simps_I5_J,axiom,
% 9.49/5.29      ! [K: num] :
% 9.49/5.29        ( ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) )
% 9.49/5.29        = ( numeral_numeral_int @ ( bitM @ K ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5728_and__numerals_I8_J,axiom,
% 9.49/5.29      ! [X: num] :
% 9.49/5.29        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ one_one_int )
% 9.49/5.29        = one_one_int ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5729_and__numerals_I8_J,axiom,
% 9.49/5.29      ! [X: num] :
% 9.49/5.29        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ one_one_nat )
% 9.49/5.29        = one_one_nat ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5730_and__numerals_I2_J,axiom,
% 9.49/5.29      ! [Y2: num] :
% 9.49/5.29        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y2 ) ) )
% 9.49/5.29        = one_one_int ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5731_and__numerals_I2_J,axiom,
% 9.49/5.29      ! [Y2: num] :
% 9.49/5.29        ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) )
% 9.49/5.29        = one_one_nat ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5732_dbl__dec__simps_I2_J,axiom,
% 9.49/5.29      ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 9.49/5.29      = ( uminus_uminus_int @ one_one_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5733_dbl__dec__simps_I2_J,axiom,
% 9.49/5.29      ( ( neg_nu6075765906172075777c_real @ zero_zero_real )
% 9.49/5.29      = ( uminus_uminus_real @ one_one_real ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5734_dbl__dec__simps_I2_J,axiom,
% 9.49/5.29      ( ( neg_nu6511756317524482435omplex @ zero_zero_complex )
% 9.49/5.29      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5735_dbl__dec__simps_I2_J,axiom,
% 9.49/5.29      ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 9.49/5.29      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5736_dbl__dec__simps_I2_J,axiom,
% 9.49/5.29      ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 9.49/5.29      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5737_dbl__dec__simps_I1_J,axiom,
% 9.49/5.29      ! [K: num] :
% 9.49/5.29        ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 9.49/5.29        = ( uminus_uminus_int @ ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5738_dbl__dec__simps_I1_J,axiom,
% 9.49/5.29      ! [K: num] :
% 9.49/5.29        ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 9.49/5.29        = ( uminus_uminus_real @ ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5739_dbl__dec__simps_I1_J,axiom,
% 9.49/5.29      ! [K: num] :
% 9.49/5.29        ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 9.49/5.29        = ( uminus1482373934393186551omplex @ ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5740_dbl__dec__simps_I1_J,axiom,
% 9.49/5.29      ! [K: num] :
% 9.49/5.29        ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 9.49/5.29        = ( uminus1351360451143612070nteger @ ( neg_nu5831290666863070958nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5741_dbl__dec__simps_I1_J,axiom,
% 9.49/5.29      ! [K: num] :
% 9.49/5.29        ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 9.49/5.29        = ( uminus_uminus_rat @ ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5742_dbl__inc__simps_I1_J,axiom,
% 9.49/5.29      ! [K: num] :
% 9.49/5.29        ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 9.49/5.29        = ( uminus_uminus_int @ ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5743_dbl__inc__simps_I1_J,axiom,
% 9.49/5.29      ! [K: num] :
% 9.49/5.29        ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 9.49/5.29        = ( uminus_uminus_real @ ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5744_dbl__inc__simps_I1_J,axiom,
% 9.49/5.29      ! [K: num] :
% 9.49/5.29        ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 9.49/5.29        = ( uminus1482373934393186551omplex @ ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5745_dbl__inc__simps_I1_J,axiom,
% 9.49/5.29      ! [K: num] :
% 9.49/5.29        ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 9.49/5.29        = ( uminus1351360451143612070nteger @ ( neg_nu7757733837767384882nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5746_dbl__inc__simps_I1_J,axiom,
% 9.49/5.29      ! [K: num] :
% 9.49/5.29        ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 9.49/5.29        = ( uminus_uminus_rat @ ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5747_and__numerals_I5_J,axiom,
% 9.49/5.29      ! [X: num] :
% 9.49/5.29        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ one_one_int )
% 9.49/5.29        = zero_zero_int ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5748_and__numerals_I5_J,axiom,
% 9.49/5.29      ! [X: num] :
% 9.49/5.29        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ one_one_nat )
% 9.49/5.29        = zero_zero_nat ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5749_and__numerals_I1_J,axiom,
% 9.49/5.29      ! [Y2: num] :
% 9.49/5.29        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y2 ) ) )
% 9.49/5.29        = zero_zero_int ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5750_and__numerals_I1_J,axiom,
% 9.49/5.29      ! [Y2: num] :
% 9.49/5.29        ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) )
% 9.49/5.29        = zero_zero_nat ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5751_and__numerals_I3_J,axiom,
% 9.49/5.29      ! [X: num,Y2: num] :
% 9.49/5.29        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y2 ) ) )
% 9.49/5.29        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y2 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5752_and__numerals_I3_J,axiom,
% 9.49/5.29      ! [X: num,Y2: num] :
% 9.49/5.29        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) )
% 9.49/5.29        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y2 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5753_of__int__0__le__iff,axiom,
% 9.49/5.29      ! [Z: int] :
% 9.49/5.29        ( ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 9.49/5.29        = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5754_of__int__0__le__iff,axiom,
% 9.49/5.29      ! [Z: int] :
% 9.49/5.29        ( ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 9.49/5.29        = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5755_of__int__0__le__iff,axiom,
% 9.49/5.29      ! [Z: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 9.49/5.29        = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5756_of__int__le__0__iff,axiom,
% 9.49/5.29      ! [Z: int] :
% 9.49/5.29        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 9.49/5.29        = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5757_of__int__le__0__iff,axiom,
% 9.49/5.29      ! [Z: int] :
% 9.49/5.29        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 9.49/5.29        = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5758_of__int__le__0__iff,axiom,
% 9.49/5.29      ! [Z: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 9.49/5.29        = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5759_of__int__0__less__iff,axiom,
% 9.49/5.29      ! [Z: int] :
% 9.49/5.29        ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 9.49/5.29        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5760_of__int__0__less__iff,axiom,
% 9.49/5.29      ! [Z: int] :
% 9.49/5.29        ( ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 9.49/5.29        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5761_of__int__0__less__iff,axiom,
% 9.49/5.29      ! [Z: int] :
% 9.49/5.29        ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 9.49/5.29        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5762_of__int__less__0__iff,axiom,
% 9.49/5.29      ! [Z: int] :
% 9.49/5.29        ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 9.49/5.29        = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5763_of__int__less__0__iff,axiom,
% 9.49/5.29      ! [Z: int] :
% 9.49/5.29        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 9.49/5.29        = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5764_of__int__less__0__iff,axiom,
% 9.49/5.29      ! [Z: int] :
% 9.49/5.29        ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 9.49/5.29        = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5765_of__int__numeral__le__iff,axiom,
% 9.49/5.29      ! [N: num,Z: int] :
% 9.49/5.29        ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 9.49/5.29        = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5766_of__int__numeral__le__iff,axiom,
% 9.49/5.29      ! [N: num,Z: int] :
% 9.49/5.29        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 9.49/5.29        = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5767_of__int__numeral__le__iff,axiom,
% 9.49/5.29      ! [N: num,Z: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 9.49/5.29        = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5768_of__int__le__numeral__iff,axiom,
% 9.49/5.29      ! [Z: int,N: num] :
% 9.49/5.29        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 9.49/5.29        = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5769_of__int__le__numeral__iff,axiom,
% 9.49/5.29      ! [Z: int,N: num] :
% 9.49/5.29        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 9.49/5.29        = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5770_of__int__le__numeral__iff,axiom,
% 9.49/5.29      ! [Z: int,N: num] :
% 9.49/5.29        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 9.49/5.29        = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5771_of__int__numeral__less__iff,axiom,
% 9.49/5.29      ! [N: num,Z: int] :
% 9.49/5.29        ( ( ord_less_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 9.49/5.29        = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5772_of__int__numeral__less__iff,axiom,
% 9.49/5.29      ! [N: num,Z: int] :
% 9.49/5.29        ( ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 9.49/5.29        = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5773_of__int__numeral__less__iff,axiom,
% 9.49/5.29      ! [N: num,Z: int] :
% 9.49/5.29        ( ( ord_less_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 9.49/5.29        = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5774_of__int__less__numeral__iff,axiom,
% 9.49/5.29      ! [Z: int,N: num] :
% 9.49/5.29        ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 9.49/5.29        = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5775_of__int__less__numeral__iff,axiom,
% 9.49/5.29      ! [Z: int,N: num] :
% 9.49/5.29        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 9.49/5.29        = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5776_of__int__less__numeral__iff,axiom,
% 9.49/5.29      ! [Z: int,N: num] :
% 9.49/5.29        ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 9.49/5.29        = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5777_of__int__le__1__iff,axiom,
% 9.49/5.29      ! [Z: int] :
% 9.49/5.29        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 9.49/5.29        = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5778_of__int__le__1__iff,axiom,
% 9.49/5.29      ! [Z: int] :
% 9.49/5.29        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 9.49/5.29        = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5779_of__int__le__1__iff,axiom,
% 9.49/5.29      ! [Z: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 9.49/5.29        = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5780_of__int__1__le__iff,axiom,
% 9.49/5.29      ! [Z: int] :
% 9.49/5.29        ( ( ord_less_eq_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 9.49/5.29        = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5781_of__int__1__le__iff,axiom,
% 9.49/5.29      ! [Z: int] :
% 9.49/5.29        ( ( ord_less_eq_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 9.49/5.29        = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5782_of__int__1__le__iff,axiom,
% 9.49/5.29      ! [Z: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 9.49/5.29        = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5783_of__int__less__1__iff,axiom,
% 9.49/5.29      ! [Z: int] :
% 9.49/5.29        ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 9.49/5.29        = ( ord_less_int @ Z @ one_one_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5784_of__int__less__1__iff,axiom,
% 9.49/5.29      ! [Z: int] :
% 9.49/5.29        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 9.49/5.29        = ( ord_less_int @ Z @ one_one_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5785_of__int__less__1__iff,axiom,
% 9.49/5.29      ! [Z: int] :
% 9.49/5.29        ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 9.49/5.29        = ( ord_less_int @ Z @ one_one_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5786_of__int__1__less__iff,axiom,
% 9.49/5.29      ! [Z: int] :
% 9.49/5.29        ( ( ord_less_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 9.49/5.29        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5787_of__int__1__less__iff,axiom,
% 9.49/5.29      ! [Z: int] :
% 9.49/5.29        ( ( ord_less_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 9.49/5.29        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5788_of__int__1__less__iff,axiom,
% 9.49/5.29      ! [Z: int] :
% 9.49/5.29        ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 9.49/5.29        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5789_of__int__eq__numeral__power__cancel__iff,axiom,
% 9.49/5.29      ! [Y2: int,X: num,N: nat] :
% 9.49/5.29        ( ( ( ring_17405671764205052669omplex @ Y2 )
% 9.49/5.29          = ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N ) )
% 9.49/5.29        = ( Y2
% 9.49/5.29          = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5790_of__int__eq__numeral__power__cancel__iff,axiom,
% 9.49/5.29      ! [Y2: int,X: num,N: nat] :
% 9.49/5.29        ( ( ( ring_1_of_int_real @ Y2 )
% 9.49/5.29          = ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 9.49/5.29        = ( Y2
% 9.49/5.29          = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5791_of__int__eq__numeral__power__cancel__iff,axiom,
% 9.49/5.29      ! [Y2: int,X: num,N: nat] :
% 9.49/5.29        ( ( ( ring_1_of_int_rat @ Y2 )
% 9.49/5.29          = ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 9.49/5.29        = ( Y2
% 9.49/5.29          = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5792_of__int__eq__numeral__power__cancel__iff,axiom,
% 9.49/5.29      ! [Y2: int,X: num,N: nat] :
% 9.49/5.29        ( ( ( ring_1_of_int_int @ Y2 )
% 9.49/5.29          = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 9.49/5.29        = ( Y2
% 9.49/5.29          = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5793_numeral__power__eq__of__int__cancel__iff,axiom,
% 9.49/5.29      ! [X: num,N: nat,Y2: int] :
% 9.49/5.29        ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N )
% 9.49/5.29          = ( ring_17405671764205052669omplex @ Y2 ) )
% 9.49/5.29        = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 9.49/5.29          = Y2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5794_numeral__power__eq__of__int__cancel__iff,axiom,
% 9.49/5.29      ! [X: num,N: nat,Y2: int] :
% 9.49/5.29        ( ( ( power_power_real @ ( numeral_numeral_real @ X ) @ N )
% 9.49/5.29          = ( ring_1_of_int_real @ Y2 ) )
% 9.49/5.29        = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 9.49/5.29          = Y2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5795_numeral__power__eq__of__int__cancel__iff,axiom,
% 9.49/5.29      ! [X: num,N: nat,Y2: int] :
% 9.49/5.29        ( ( ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N )
% 9.49/5.29          = ( ring_1_of_int_rat @ Y2 ) )
% 9.49/5.29        = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 9.49/5.29          = Y2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5796_numeral__power__eq__of__int__cancel__iff,axiom,
% 9.49/5.29      ! [X: num,N: nat,Y2: int] :
% 9.49/5.29        ( ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 9.49/5.29          = ( ring_1_of_int_int @ Y2 ) )
% 9.49/5.29        = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 9.49/5.29          = Y2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5797_of__int__power__le__of__int__cancel__iff,axiom,
% 9.49/5.29      ! [X: int,B: int,W: nat] :
% 9.49/5.29        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 9.49/5.29        = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5798_of__int__power__le__of__int__cancel__iff,axiom,
% 9.49/5.29      ! [X: int,B: int,W: nat] :
% 9.49/5.29        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ X ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 9.49/5.29        = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5799_of__int__le__of__int__power__cancel__iff,axiom,
% 9.49/5.29      ! [B: int,W: nat,X: int] :
% 9.49/5.29        ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X ) )
% 9.49/5.29        = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5800_of__int__le__of__int__power__cancel__iff,axiom,
% 9.49/5.29      ! [B: int,W: nat,X: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X ) )
% 9.49/5.29        = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5801_of__int__power__less__of__int__cancel__iff,axiom,
% 9.49/5.29      ! [X: int,B: int,W: nat] :
% 9.49/5.29        ( ( ord_less_real @ ( ring_1_of_int_real @ X ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 9.49/5.29        = ( ord_less_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5802_of__int__power__less__of__int__cancel__iff,axiom,
% 9.49/5.29      ! [X: int,B: int,W: nat] :
% 9.49/5.29        ( ( ord_less_rat @ ( ring_1_of_int_rat @ X ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 9.49/5.29        = ( ord_less_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5803_of__int__power__less__of__int__cancel__iff,axiom,
% 9.49/5.29      ! [X: int,B: int,W: nat] :
% 9.49/5.29        ( ( ord_less_int @ ( ring_1_of_int_int @ X ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 9.49/5.29        = ( ord_less_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5804_of__int__less__of__int__power__cancel__iff,axiom,
% 9.49/5.29      ! [B: int,W: nat,X: int] :
% 9.49/5.29        ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X ) )
% 9.49/5.29        = ( ord_less_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5805_of__int__less__of__int__power__cancel__iff,axiom,
% 9.49/5.29      ! [B: int,W: nat,X: int] :
% 9.49/5.29        ( ( ord_less_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X ) )
% 9.49/5.29        = ( ord_less_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5806_of__int__less__of__int__power__cancel__iff,axiom,
% 9.49/5.29      ! [B: int,W: nat,X: int] :
% 9.49/5.29        ( ( ord_less_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X ) )
% 9.49/5.29        = ( ord_less_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5807_and__minus__numerals_I6_J,axiom,
% 9.49/5.29      ! [N: num] :
% 9.49/5.29        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 9.49/5.29        = one_one_int ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5808_and__minus__numerals_I2_J,axiom,
% 9.49/5.29      ! [N: num] :
% 9.49/5.29        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 9.49/5.29        = one_one_int ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5809_and__numerals_I6_J,axiom,
% 9.49/5.29      ! [X: num,Y2: num] :
% 9.49/5.29        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y2 ) ) )
% 9.49/5.29        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y2 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5810_and__numerals_I6_J,axiom,
% 9.49/5.29      ! [X: num,Y2: num] :
% 9.49/5.29        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) )
% 9.49/5.29        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y2 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5811_and__numerals_I4_J,axiom,
% 9.49/5.29      ! [X: num,Y2: num] :
% 9.49/5.29        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y2 ) ) )
% 9.49/5.29        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y2 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5812_and__numerals_I4_J,axiom,
% 9.49/5.29      ! [X: num,Y2: num] :
% 9.49/5.29        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) )
% 9.49/5.29        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y2 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5813_and__minus__numerals_I1_J,axiom,
% 9.49/5.29      ! [N: num] :
% 9.49/5.29        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 9.49/5.29        = zero_zero_int ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5814_and__minus__numerals_I5_J,axiom,
% 9.49/5.29      ! [N: num] :
% 9.49/5.29        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 9.49/5.29        = zero_zero_int ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5815_of__int__le__numeral__power__cancel__iff,axiom,
% 9.49/5.29      ! [A: int,X: num,N: nat] :
% 9.49/5.29        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 9.49/5.29        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5816_of__int__le__numeral__power__cancel__iff,axiom,
% 9.49/5.29      ! [A: int,X: num,N: nat] :
% 9.49/5.29        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 9.49/5.29        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5817_of__int__le__numeral__power__cancel__iff,axiom,
% 9.49/5.29      ! [A: int,X: num,N: nat] :
% 9.49/5.29        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 9.49/5.29        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5818_numeral__power__le__of__int__cancel__iff,axiom,
% 9.49/5.29      ! [X: num,N: nat,A: int] :
% 9.49/5.29        ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 9.49/5.29        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5819_numeral__power__le__of__int__cancel__iff,axiom,
% 9.49/5.29      ! [X: num,N: nat,A: int] :
% 9.49/5.29        ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 9.49/5.29        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5820_numeral__power__le__of__int__cancel__iff,axiom,
% 9.49/5.29      ! [X: num,N: nat,A: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 9.49/5.29        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5821_of__int__less__numeral__power__cancel__iff,axiom,
% 9.49/5.29      ! [A: int,X: num,N: nat] :
% 9.49/5.29        ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 9.49/5.29        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5822_of__int__less__numeral__power__cancel__iff,axiom,
% 9.49/5.29      ! [A: int,X: num,N: nat] :
% 9.49/5.29        ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 9.49/5.29        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5823_of__int__less__numeral__power__cancel__iff,axiom,
% 9.49/5.29      ! [A: int,X: num,N: nat] :
% 9.49/5.29        ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 9.49/5.29        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5824_numeral__power__less__of__int__cancel__iff,axiom,
% 9.49/5.29      ! [X: num,N: nat,A: int] :
% 9.49/5.29        ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 9.49/5.29        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5825_numeral__power__less__of__int__cancel__iff,axiom,
% 9.49/5.29      ! [X: num,N: nat,A: int] :
% 9.49/5.29        ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 9.49/5.29        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5826_numeral__power__less__of__int__cancel__iff,axiom,
% 9.49/5.29      ! [X: num,N: nat,A: int] :
% 9.49/5.29        ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 9.49/5.29        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5827_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 9.49/5.29      ! [Y2: int,X: num,N: nat] :
% 9.49/5.29        ( ( ( ring_1_of_int_int @ Y2 )
% 9.49/5.29          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 9.49/5.29        = ( Y2
% 9.49/5.29          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5828_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 9.49/5.29      ! [Y2: int,X: num,N: nat] :
% 9.49/5.29        ( ( ( ring_1_of_int_real @ Y2 )
% 9.49/5.29          = ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) )
% 9.49/5.29        = ( Y2
% 9.49/5.29          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5829_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 9.49/5.29      ! [Y2: int,X: num,N: nat] :
% 9.49/5.29        ( ( ( ring_17405671764205052669omplex @ Y2 )
% 9.49/5.29          = ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X ) ) @ N ) )
% 9.49/5.29        = ( Y2
% 9.49/5.29          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5830_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 9.49/5.29      ! [Y2: int,X: num,N: nat] :
% 9.49/5.29        ( ( ( ring_18347121197199848620nteger @ Y2 )
% 9.49/5.29          = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 9.49/5.29        = ( Y2
% 9.49/5.29          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5831_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 9.49/5.29      ! [Y2: int,X: num,N: nat] :
% 9.49/5.29        ( ( ( ring_1_of_int_rat @ Y2 )
% 9.49/5.29          = ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 9.49/5.29        = ( Y2
% 9.49/5.29          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5832_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 9.49/5.29      ! [X: num,N: nat,Y2: int] :
% 9.49/5.29        ( ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 9.49/5.29          = ( ring_1_of_int_int @ Y2 ) )
% 9.49/5.29        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 9.49/5.29          = Y2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5833_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 9.49/5.29      ! [X: num,N: nat,Y2: int] :
% 9.49/5.29        ( ( ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N )
% 9.49/5.29          = ( ring_1_of_int_real @ Y2 ) )
% 9.49/5.29        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 9.49/5.29          = Y2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5834_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 9.49/5.29      ! [X: num,N: nat,Y2: int] :
% 9.49/5.29        ( ( ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X ) ) @ N )
% 9.49/5.29          = ( ring_17405671764205052669omplex @ Y2 ) )
% 9.49/5.29        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 9.49/5.29          = Y2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5835_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 9.49/5.29      ! [X: num,N: nat,Y2: int] :
% 9.49/5.29        ( ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N )
% 9.49/5.29          = ( ring_18347121197199848620nteger @ Y2 ) )
% 9.49/5.29        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 9.49/5.29          = Y2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5836_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 9.49/5.29      ! [X: num,N: nat,Y2: int] :
% 9.49/5.29        ( ( ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N )
% 9.49/5.29          = ( ring_1_of_int_rat @ Y2 ) )
% 9.49/5.29        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 9.49/5.29          = Y2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5837_and__numerals_I7_J,axiom,
% 9.49/5.29      ! [X: num,Y2: num] :
% 9.49/5.29        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y2 ) ) )
% 9.49/5.29        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y2 ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5838_and__numerals_I7_J,axiom,
% 9.49/5.29      ! [X: num,Y2: num] :
% 9.49/5.29        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) )
% 9.49/5.29        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y2 ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5839_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 9.49/5.29      ! [A: int,X: num,N: nat] :
% 9.49/5.29        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) )
% 9.49/5.29        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5840_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 9.49/5.29      ! [A: int,X: num,N: nat] :
% 9.49/5.29        ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 9.49/5.29        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5841_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 9.49/5.29      ! [A: int,X: num,N: nat] :
% 9.49/5.29        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 9.49/5.29        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5842_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 9.49/5.29      ! [A: int,X: num,N: nat] :
% 9.49/5.29        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 9.49/5.29        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5843_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 9.49/5.29      ! [X: num,N: nat,A: int] :
% 9.49/5.29        ( ( ord_less_eq_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 9.49/5.29        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5844_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 9.49/5.29      ! [X: num,N: nat,A: int] :
% 9.49/5.29        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 9.49/5.29        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5845_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 9.49/5.29      ! [X: num,N: nat,A: int] :
% 9.49/5.29        ( ( ord_less_eq_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 9.49/5.29        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5846_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 9.49/5.29      ! [X: num,N: nat,A: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 9.49/5.29        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5847_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 9.49/5.29      ! [A: int,X: num,N: nat] :
% 9.49/5.29        ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 9.49/5.29        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5848_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 9.49/5.29      ! [A: int,X: num,N: nat] :
% 9.49/5.29        ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) )
% 9.49/5.29        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5849_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 9.49/5.29      ! [A: int,X: num,N: nat] :
% 9.49/5.29        ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 9.49/5.29        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5850_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 9.49/5.29      ! [A: int,X: num,N: nat] :
% 9.49/5.29        ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 9.49/5.29        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5851_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 9.49/5.29      ! [X: num,N: nat,A: int] :
% 9.49/5.29        ( ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 9.49/5.29        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5852_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 9.49/5.29      ! [X: num,N: nat,A: int] :
% 9.49/5.29        ( ( ord_less_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 9.49/5.29        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5853_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 9.49/5.29      ! [X: num,N: nat,A: int] :
% 9.49/5.29        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 9.49/5.29        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5854_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 9.49/5.29      ! [X: num,N: nat,A: int] :
% 9.49/5.29        ( ( ord_less_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 9.49/5.29        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5855_of__int__and__eq,axiom,
% 9.49/5.29      ! [K: int,L2: int] :
% 9.49/5.29        ( ( ring_1_of_int_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) )
% 9.49/5.29        = ( bit_se725231765392027082nd_int @ ( ring_1_of_int_int @ K ) @ ( ring_1_of_int_int @ L2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5856_and_Oassoc,axiom,
% 9.49/5.29      ! [A: int,B: int,C: int] :
% 9.49/5.29        ( ( bit_se725231765392027082nd_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ C )
% 9.49/5.29        = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ B @ C ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5857_and_Oassoc,axiom,
% 9.49/5.29      ! [A: nat,B: nat,C: nat] :
% 9.49/5.29        ( ( bit_se727722235901077358nd_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ C )
% 9.49/5.29        = ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ B @ C ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5858_and_Ocommute,axiom,
% 9.49/5.29      ( bit_se725231765392027082nd_int
% 9.49/5.29      = ( ^ [A3: int,B4: int] : ( bit_se725231765392027082nd_int @ B4 @ A3 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5859_and_Ocommute,axiom,
% 9.49/5.29      ( bit_se727722235901077358nd_nat
% 9.49/5.29      = ( ^ [A3: nat,B4: nat] : ( bit_se727722235901077358nd_nat @ B4 @ A3 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5860_and_Oleft__commute,axiom,
% 9.49/5.29      ! [B: int,A: int,C: int] :
% 9.49/5.29        ( ( bit_se725231765392027082nd_int @ B @ ( bit_se725231765392027082nd_int @ A @ C ) )
% 9.49/5.29        = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ B @ C ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5861_and_Oleft__commute,axiom,
% 9.49/5.29      ! [B: nat,A: nat,C: nat] :
% 9.49/5.29        ( ( bit_se727722235901077358nd_nat @ B @ ( bit_se727722235901077358nd_nat @ A @ C ) )
% 9.49/5.29        = ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ B @ C ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5862_mult__of__int__commute,axiom,
% 9.49/5.29      ! [X: int,Y2: complex] :
% 9.49/5.29        ( ( times_times_complex @ ( ring_17405671764205052669omplex @ X ) @ Y2 )
% 9.49/5.29        = ( times_times_complex @ Y2 @ ( ring_17405671764205052669omplex @ X ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5863_mult__of__int__commute,axiom,
% 9.49/5.29      ! [X: int,Y2: real] :
% 9.49/5.29        ( ( times_times_real @ ( ring_1_of_int_real @ X ) @ Y2 )
% 9.49/5.29        = ( times_times_real @ Y2 @ ( ring_1_of_int_real @ X ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5864_mult__of__int__commute,axiom,
% 9.49/5.29      ! [X: int,Y2: int] :
% 9.49/5.29        ( ( times_times_int @ ( ring_1_of_int_int @ X ) @ Y2 )
% 9.49/5.29        = ( times_times_int @ Y2 @ ( ring_1_of_int_int @ X ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5865_bot__nat__def,axiom,
% 9.49/5.29      bot_bot_nat = zero_zero_nat ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5866_bot__enat__def,axiom,
% 9.49/5.29      bot_bo4199563552545308370d_enat = zero_z5237406670263579293d_enat ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5867_and__eq__minus__1__iff,axiom,
% 9.49/5.29      ! [A: code_integer,B: code_integer] :
% 9.49/5.29        ( ( ( bit_se3949692690581998587nteger @ A @ B )
% 9.49/5.29          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.49/5.29        = ( ( A
% 9.49/5.29            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.49/5.29          & ( B
% 9.49/5.29            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5868_and__eq__minus__1__iff,axiom,
% 9.49/5.29      ! [A: int,B: int] :
% 9.49/5.29        ( ( ( bit_se725231765392027082nd_int @ A @ B )
% 9.49/5.29          = ( uminus_uminus_int @ one_one_int ) )
% 9.49/5.29        = ( ( A
% 9.49/5.29            = ( uminus_uminus_int @ one_one_int ) )
% 9.49/5.29          & ( B
% 9.49/5.29            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5869_AND__lower,axiom,
% 9.49/5.29      ! [X: int,Y2: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 9.49/5.29       => ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ X @ Y2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5870_AND__upper1,axiom,
% 9.49/5.29      ! [X: int,Y2: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 9.49/5.29       => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y2 ) @ X ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5871_AND__upper2,axiom,
% 9.49/5.29      ! [Y2: int,X: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 9.49/5.29       => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y2 ) @ Y2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5872_AND__upper1_H,axiom,
% 9.49/5.29      ! [Y2: int,Z: int,Ya: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 9.49/5.29       => ( ( ord_less_eq_int @ Y2 @ Z )
% 9.49/5.29         => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ Y2 @ Ya ) @ Z ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5873_AND__upper2_H,axiom,
% 9.49/5.29      ! [Y2: int,Z: int,X: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 9.49/5.29       => ( ( ord_less_eq_int @ Y2 @ Z )
% 9.49/5.29         => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y2 ) @ Z ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5874_and__less__eq,axiom,
% 9.49/5.29      ! [L2: int,K: int] :
% 9.49/5.29        ( ( ord_less_int @ L2 @ zero_zero_int )
% 9.49/5.29       => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) @ K ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5875_AND__upper1_H_H,axiom,
% 9.49/5.29      ! [Y2: int,Z: int,Ya: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 9.49/5.29       => ( ( ord_less_int @ Y2 @ Z )
% 9.49/5.29         => ( ord_less_int @ ( bit_se725231765392027082nd_int @ Y2 @ Ya ) @ Z ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5876_AND__upper2_H_H,axiom,
% 9.49/5.29      ! [Y2: int,Z: int,X: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 9.49/5.29       => ( ( ord_less_int @ Y2 @ Z )
% 9.49/5.29         => ( ord_less_int @ ( bit_se725231765392027082nd_int @ X @ Y2 ) @ Z ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5877_real__of__int__div4,axiom,
% 9.49/5.29      ! [N: int,X: int] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5878_real__of__int__div,axiom,
% 9.49/5.29      ! [D2: int,N: int] :
% 9.49/5.29        ( ( dvd_dvd_int @ D2 @ N )
% 9.49/5.29       => ( ( ring_1_of_int_real @ ( divide_divide_int @ N @ D2 ) )
% 9.49/5.29          = ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ D2 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5879_even__and__iff,axiom,
% 9.49/5.29      ! [A: code_integer,B: code_integer] :
% 9.49/5.29        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ A @ B ) )
% 9.49/5.29        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.49/5.29          | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5880_even__and__iff,axiom,
% 9.49/5.29      ! [A: int,B: int] :
% 9.49/5.29        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 9.49/5.29        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.49/5.29          | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5881_even__and__iff,axiom,
% 9.49/5.29      ! [A: nat,B: nat] :
% 9.49/5.29        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 9.49/5.29        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.49/5.29          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5882_of__int__nonneg,axiom,
% 9.49/5.29      ! [Z: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 9.49/5.29       => ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5883_of__int__nonneg,axiom,
% 9.49/5.29      ! [Z: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 9.49/5.29       => ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5884_of__int__nonneg,axiom,
% 9.49/5.29      ! [Z: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 9.49/5.29       => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5885_even__and__iff__int,axiom,
% 9.49/5.29      ! [K: int,L2: int] :
% 9.49/5.29        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ K @ L2 ) )
% 9.49/5.29        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 9.49/5.29          | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5886_of__int__pos,axiom,
% 9.49/5.29      ! [Z: int] :
% 9.49/5.29        ( ( ord_less_int @ zero_zero_int @ Z )
% 9.49/5.29       => ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5887_of__int__pos,axiom,
% 9.49/5.29      ! [Z: int] :
% 9.49/5.29        ( ( ord_less_int @ zero_zero_int @ Z )
% 9.49/5.29       => ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5888_of__int__pos,axiom,
% 9.49/5.29      ! [Z: int] :
% 9.49/5.29        ( ( ord_less_int @ zero_zero_int @ Z )
% 9.49/5.29       => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5889_of__int__neg__numeral,axiom,
% 9.49/5.29      ! [K: num] :
% 9.49/5.29        ( ( ring_1_of_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 9.49/5.29        = ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5890_of__int__neg__numeral,axiom,
% 9.49/5.29      ! [K: num] :
% 9.49/5.29        ( ( ring_1_of_int_real @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 9.49/5.29        = ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5891_of__int__neg__numeral,axiom,
% 9.49/5.29      ! [K: num] :
% 9.49/5.29        ( ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 9.49/5.29        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5892_of__int__neg__numeral,axiom,
% 9.49/5.29      ! [K: num] :
% 9.49/5.29        ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 9.49/5.29        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5893_of__int__neg__numeral,axiom,
% 9.49/5.29      ! [K: num] :
% 9.49/5.29        ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 9.49/5.29        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5894_int__le__real__less,axiom,
% 9.49/5.29      ( ord_less_eq_int
% 9.49/5.29      = ( ^ [N2: int,M6: int] : ( ord_less_real @ ( ring_1_of_int_real @ N2 ) @ ( plus_plus_real @ ( ring_1_of_int_real @ M6 ) @ one_one_real ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5895_int__less__real__le,axiom,
% 9.49/5.29      ( ord_less_int
% 9.49/5.29      = ( ^ [N2: int,M6: int] : ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) @ ( ring_1_of_int_real @ M6 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5896_real__of__int__div__aux,axiom,
% 9.49/5.29      ! [X: int,D2: int] :
% 9.49/5.29        ( ( divide_divide_real @ ( ring_1_of_int_real @ X ) @ ( ring_1_of_int_real @ D2 ) )
% 9.49/5.29        = ( plus_plus_real @ ( ring_1_of_int_real @ ( divide_divide_int @ X @ D2 ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ ( modulo_modulo_int @ X @ D2 ) ) @ ( ring_1_of_int_real @ D2 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5897_and__one__eq,axiom,
% 9.49/5.29      ! [A: int] :
% 9.49/5.29        ( ( bit_se725231765392027082nd_int @ A @ one_one_int )
% 9.49/5.29        = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5898_and__one__eq,axiom,
% 9.49/5.29      ! [A: nat] :
% 9.49/5.29        ( ( bit_se727722235901077358nd_nat @ A @ one_one_nat )
% 9.49/5.29        = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5899_one__and__eq,axiom,
% 9.49/5.29      ! [A: int] :
% 9.49/5.29        ( ( bit_se725231765392027082nd_int @ one_one_int @ A )
% 9.49/5.29        = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5900_one__and__eq,axiom,
% 9.49/5.29      ! [A: nat] :
% 9.49/5.29        ( ( bit_se727722235901077358nd_nat @ one_one_nat @ A )
% 9.49/5.29        = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5901_real__of__int__div2,axiom,
% 9.49/5.29      ! [N: int,X: int] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5902_real__of__int__div3,axiom,
% 9.49/5.29      ! [N: int,X: int] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X ) ) ) @ one_one_real ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5903_even__of__int__iff,axiom,
% 9.49/5.29      ! [K: int] :
% 9.49/5.29        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ K ) )
% 9.49/5.29        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5904_even__of__int__iff,axiom,
% 9.49/5.29      ! [K: int] :
% 9.49/5.29        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ K ) )
% 9.49/5.29        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5905_dbl__dec__def,axiom,
% 9.49/5.29      ( neg_nu6075765906172075777c_real
% 9.49/5.29      = ( ^ [X2: real] : ( minus_minus_real @ ( plus_plus_real @ X2 @ X2 ) @ one_one_real ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5906_dbl__dec__def,axiom,
% 9.49/5.29      ( neg_nu6511756317524482435omplex
% 9.49/5.29      = ( ^ [X2: complex] : ( minus_minus_complex @ ( plus_plus_complex @ X2 @ X2 ) @ one_one_complex ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5907_dbl__dec__def,axiom,
% 9.49/5.29      ( neg_nu3179335615603231917ec_rat
% 9.49/5.29      = ( ^ [X2: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X2 @ X2 ) @ one_one_rat ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5908_dbl__dec__def,axiom,
% 9.49/5.29      ( neg_nu3811975205180677377ec_int
% 9.49/5.29      = ( ^ [X2: int] : ( minus_minus_int @ ( plus_plus_int @ X2 @ X2 ) @ one_one_int ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5909_compl__le__swap2,axiom,
% 9.49/5.29      ! [Y2: set_real,X: set_real] :
% 9.49/5.29        ( ( ord_less_eq_set_real @ ( uminus612125837232591019t_real @ Y2 ) @ X )
% 9.49/5.29       => ( ord_less_eq_set_real @ ( uminus612125837232591019t_real @ X ) @ Y2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5910_compl__le__swap2,axiom,
% 9.49/5.29      ! [Y2: set_nat,X: set_nat] :
% 9.49/5.29        ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y2 ) @ X )
% 9.49/5.29       => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ Y2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5911_compl__le__swap1,axiom,
% 9.49/5.29      ! [Y2: set_real,X: set_real] :
% 9.49/5.29        ( ( ord_less_eq_set_real @ Y2 @ ( uminus612125837232591019t_real @ X ) )
% 9.49/5.29       => ( ord_less_eq_set_real @ X @ ( uminus612125837232591019t_real @ Y2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5912_compl__le__swap1,axiom,
% 9.49/5.29      ! [Y2: set_nat,X: set_nat] :
% 9.49/5.29        ( ( ord_less_eq_set_nat @ Y2 @ ( uminus5710092332889474511et_nat @ X ) )
% 9.49/5.29       => ( ord_less_eq_set_nat @ X @ ( uminus5710092332889474511et_nat @ Y2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5913_compl__mono,axiom,
% 9.49/5.29      ! [X: set_real,Y2: set_real] :
% 9.49/5.29        ( ( ord_less_eq_set_real @ X @ Y2 )
% 9.49/5.29       => ( ord_less_eq_set_real @ ( uminus612125837232591019t_real @ Y2 ) @ ( uminus612125837232591019t_real @ X ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5914_compl__mono,axiom,
% 9.49/5.29      ! [X: set_nat,Y2: set_nat] :
% 9.49/5.29        ( ( ord_less_eq_set_nat @ X @ Y2 )
% 9.49/5.29       => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y2 ) @ ( uminus5710092332889474511et_nat @ X ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5915_and__int__rec,axiom,
% 9.49/5.29      ( bit_se725231765392027082nd_int
% 9.49/5.29      = ( ^ [K3: int,L: int] :
% 9.49/5.29            ( plus_plus_int
% 9.49/5.29            @ ( zero_n2684676970156552555ol_int
% 9.49/5.29              @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 9.49/5.29                & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 9.49/5.29            @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5916_and__int__unfold,axiom,
% 9.49/5.29      ( bit_se725231765392027082nd_int
% 9.49/5.29      = ( ^ [K3: int,L: int] :
% 9.49/5.29            ( if_int
% 9.49/5.29            @ ( ( K3 = zero_zero_int )
% 9.49/5.29              | ( L = zero_zero_int ) )
% 9.49/5.29            @ zero_zero_int
% 9.49/5.29            @ ( if_int
% 9.49/5.29              @ ( K3
% 9.49/5.29                = ( uminus_uminus_int @ one_one_int ) )
% 9.49/5.29              @ L
% 9.49/5.29              @ ( if_int
% 9.49/5.29                @ ( L
% 9.49/5.29                  = ( uminus_uminus_int @ one_one_int ) )
% 9.49/5.29                @ K3
% 9.49/5.29                @ ( plus_plus_int @ ( times_times_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5917_floor__exists1,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29      ? [X3: int] :
% 9.49/5.29        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X3 ) @ X )
% 9.49/5.29        & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ X3 @ one_one_int ) ) )
% 9.49/5.29        & ! [Y4: int] :
% 9.49/5.29            ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y4 ) @ X )
% 9.49/5.29              & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Y4 @ one_one_int ) ) ) )
% 9.49/5.29           => ( Y4 = X3 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5918_floor__exists1,axiom,
% 9.49/5.29      ! [X: rat] :
% 9.49/5.29      ? [X3: int] :
% 9.49/5.29        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X3 ) @ X )
% 9.49/5.29        & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ X3 @ one_one_int ) ) )
% 9.49/5.29        & ! [Y4: int] :
% 9.49/5.29            ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y4 ) @ X )
% 9.49/5.29              & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Y4 @ one_one_int ) ) ) )
% 9.49/5.29           => ( Y4 = X3 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5919_floor__exists,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29      ? [Z3: int] :
% 9.49/5.29        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z3 ) @ X )
% 9.49/5.29        & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5920_floor__exists,axiom,
% 9.49/5.29      ! [X: rat] :
% 9.49/5.29      ? [Z3: int] :
% 9.49/5.29        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z3 ) @ X )
% 9.49/5.29        & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5921_and__int_Opelims,axiom,
% 9.49/5.29      ! [X: int,Xa2: int,Y2: int] :
% 9.49/5.29        ( ( ( bit_se725231765392027082nd_int @ X @ Xa2 )
% 9.49/5.29          = Y2 )
% 9.49/5.29       => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa2 ) )
% 9.49/5.29         => ~ ( ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 9.49/5.29                    & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 9.49/5.29                 => ( Y2
% 9.49/5.29                    = ( uminus_uminus_int
% 9.49/5.29                      @ ( zero_n2684676970156552555ol_int
% 9.49/5.29                        @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 9.49/5.29                          & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 9.49/5.29                & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 9.49/5.29                      & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 9.49/5.29                 => ( Y2
% 9.49/5.29                    = ( plus_plus_int
% 9.49/5.29                      @ ( zero_n2684676970156552555ol_int
% 9.49/5.29                        @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 9.49/5.29                          & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 9.49/5.29                      @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 9.49/5.29             => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa2 ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5922_and__int_Opsimps,axiom,
% 9.49/5.29      ! [K: int,L2: int] :
% 9.49/5.29        ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L2 ) )
% 9.49/5.29       => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 9.49/5.29              & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 9.49/5.29           => ( ( bit_se725231765392027082nd_int @ K @ L2 )
% 9.49/5.29              = ( uminus_uminus_int
% 9.49/5.29                @ ( zero_n2684676970156552555ol_int
% 9.49/5.29                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 9.49/5.29                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) ) ) )
% 9.49/5.29          & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 9.49/5.29                & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 9.49/5.29           => ( ( bit_se725231765392027082nd_int @ K @ L2 )
% 9.49/5.29              = ( plus_plus_int
% 9.49/5.29                @ ( zero_n2684676970156552555ol_int
% 9.49/5.29                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 9.49/5.29                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 9.49/5.29                @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5923_ln__one__minus__pos__lower__bound,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.49/5.29       => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.49/5.29         => ( ord_less_eq_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5924_add__scale__eq__noteq,axiom,
% 9.49/5.29      ! [R: rat,A: rat,B: rat,C: rat,D2: rat] :
% 9.49/5.29        ( ( R != zero_zero_rat )
% 9.49/5.29       => ( ( ( A = B )
% 9.49/5.29            & ( C != D2 ) )
% 9.49/5.29         => ( ( plus_plus_rat @ A @ ( times_times_rat @ R @ C ) )
% 9.49/5.29           != ( plus_plus_rat @ B @ ( times_times_rat @ R @ D2 ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5925_add__scale__eq__noteq,axiom,
% 9.49/5.29      ! [R: complex,A: complex,B: complex,C: complex,D2: complex] :
% 9.49/5.29        ( ( R != zero_zero_complex )
% 9.49/5.29       => ( ( ( A = B )
% 9.49/5.29            & ( C != D2 ) )
% 9.49/5.29         => ( ( plus_plus_complex @ A @ ( times_times_complex @ R @ C ) )
% 9.49/5.29           != ( plus_plus_complex @ B @ ( times_times_complex @ R @ D2 ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5926_add__scale__eq__noteq,axiom,
% 9.49/5.29      ! [R: real,A: real,B: real,C: real,D2: real] :
% 9.49/5.29        ( ( R != zero_zero_real )
% 9.49/5.29       => ( ( ( A = B )
% 9.49/5.29            & ( C != D2 ) )
% 9.49/5.29         => ( ( plus_plus_real @ A @ ( times_times_real @ R @ C ) )
% 9.49/5.29           != ( plus_plus_real @ B @ ( times_times_real @ R @ D2 ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5927_add__scale__eq__noteq,axiom,
% 9.49/5.29      ! [R: nat,A: nat,B: nat,C: nat,D2: nat] :
% 9.49/5.29        ( ( R != zero_zero_nat )
% 9.49/5.29       => ( ( ( A = B )
% 9.49/5.29            & ( C != D2 ) )
% 9.49/5.29         => ( ( plus_plus_nat @ A @ ( times_times_nat @ R @ C ) )
% 9.49/5.29           != ( plus_plus_nat @ B @ ( times_times_nat @ R @ D2 ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5928_add__scale__eq__noteq,axiom,
% 9.49/5.29      ! [R: int,A: int,B: int,C: int,D2: int] :
% 9.49/5.29        ( ( R != zero_zero_int )
% 9.49/5.29       => ( ( ( A = B )
% 9.49/5.29            & ( C != D2 ) )
% 9.49/5.29         => ( ( plus_plus_int @ A @ ( times_times_int @ R @ C ) )
% 9.49/5.29           != ( plus_plus_int @ B @ ( times_times_int @ R @ D2 ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5929_ln__one,axiom,
% 9.49/5.29      ( ( ln_ln_real @ one_one_real )
% 9.49/5.29      = zero_zero_real ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5930_ln__less__cancel__iff,axiom,
% 9.49/5.29      ! [X: real,Y2: real] :
% 9.49/5.29        ( ( ord_less_real @ zero_zero_real @ X )
% 9.49/5.29       => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 9.49/5.29         => ( ( ord_less_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y2 ) )
% 9.49/5.29            = ( ord_less_real @ X @ Y2 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5931_ln__inj__iff,axiom,
% 9.49/5.29      ! [X: real,Y2: real] :
% 9.49/5.29        ( ( ord_less_real @ zero_zero_real @ X )
% 9.49/5.29       => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 9.49/5.29         => ( ( ( ln_ln_real @ X )
% 9.49/5.29              = ( ln_ln_real @ Y2 ) )
% 9.49/5.29            = ( X = Y2 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5932_and__nat__numerals_I1_J,axiom,
% 9.49/5.29      ! [Y2: num] :
% 9.49/5.29        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) )
% 9.49/5.29        = zero_zero_nat ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5933_and__nat__numerals_I3_J,axiom,
% 9.49/5.29      ! [X: num] :
% 9.49/5.29        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 9.49/5.29        = zero_zero_nat ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5934_ln__le__cancel__iff,axiom,
% 9.49/5.29      ! [X: real,Y2: real] :
% 9.49/5.29        ( ( ord_less_real @ zero_zero_real @ X )
% 9.49/5.29       => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 9.49/5.29         => ( ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y2 ) )
% 9.49/5.29            = ( ord_less_eq_real @ X @ Y2 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5935_ln__eq__zero__iff,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_real @ zero_zero_real @ X )
% 9.49/5.29       => ( ( ( ln_ln_real @ X )
% 9.49/5.29            = zero_zero_real )
% 9.49/5.29          = ( X = one_one_real ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5936_ln__gt__zero__iff,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_real @ zero_zero_real @ X )
% 9.49/5.29       => ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 9.49/5.29          = ( ord_less_real @ one_one_real @ X ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5937_ln__less__zero__iff,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_real @ zero_zero_real @ X )
% 9.49/5.29       => ( ( ord_less_real @ ( ln_ln_real @ X ) @ zero_zero_real )
% 9.49/5.29          = ( ord_less_real @ X @ one_one_real ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5938_and__nat__numerals_I2_J,axiom,
% 9.49/5.29      ! [Y2: num] :
% 9.49/5.29        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) )
% 9.49/5.29        = one_one_nat ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5939_and__nat__numerals_I4_J,axiom,
% 9.49/5.29      ! [X: num] :
% 9.49/5.29        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 9.49/5.29        = one_one_nat ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5940_ln__le__zero__iff,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_real @ zero_zero_real @ X )
% 9.49/5.29       => ( ( ord_less_eq_real @ ( ln_ln_real @ X ) @ zero_zero_real )
% 9.49/5.29          = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5941_ln__ge__zero__iff,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_real @ zero_zero_real @ X )
% 9.49/5.29       => ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 9.49/5.29          = ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5942_and__Suc__0__eq,axiom,
% 9.49/5.29      ! [N: nat] :
% 9.49/5.29        ( ( bit_se727722235901077358nd_nat @ N @ ( suc @ zero_zero_nat ) )
% 9.49/5.29        = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5943_Suc__0__and__eq,axiom,
% 9.49/5.29      ! [N: nat] :
% 9.49/5.29        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N )
% 9.49/5.29        = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5944_ln__less__self,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_real @ zero_zero_real @ X )
% 9.49/5.29       => ( ord_less_real @ ( ln_ln_real @ X ) @ X ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5945_ln__bound,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_real @ zero_zero_real @ X )
% 9.49/5.29       => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ X ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5946_ln__gt__zero,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_real @ one_one_real @ X )
% 9.49/5.29       => ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5947_ln__less__zero,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_real @ zero_zero_real @ X )
% 9.49/5.29       => ( ( ord_less_real @ X @ one_one_real )
% 9.49/5.29         => ( ord_less_real @ ( ln_ln_real @ X ) @ zero_zero_real ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5948_ln__gt__zero__imp__gt__one,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 9.49/5.29       => ( ( ord_less_real @ zero_zero_real @ X )
% 9.49/5.29         => ( ord_less_real @ one_one_real @ X ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5949_ln__ge__zero,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ one_one_real @ X )
% 9.49/5.29       => ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5950_ln__ge__zero__imp__ge__one,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 9.49/5.29       => ( ( ord_less_real @ zero_zero_real @ X )
% 9.49/5.29         => ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5951_ln__add__one__self__le__self,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.49/5.29       => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5952_ln__mult,axiom,
% 9.49/5.29      ! [X: real,Y2: real] :
% 9.49/5.29        ( ( ord_less_real @ zero_zero_real @ X )
% 9.49/5.29       => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 9.49/5.29         => ( ( ln_ln_real @ ( times_times_real @ X @ Y2 ) )
% 9.49/5.29            = ( plus_plus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y2 ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5953_ln__eq__minus__one,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_real @ zero_zero_real @ X )
% 9.49/5.29       => ( ( ( ln_ln_real @ X )
% 9.49/5.29            = ( minus_minus_real @ X @ one_one_real ) )
% 9.49/5.29         => ( X = one_one_real ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5954_ln__div,axiom,
% 9.49/5.29      ! [X: real,Y2: real] :
% 9.49/5.29        ( ( ord_less_real @ zero_zero_real @ X )
% 9.49/5.29       => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 9.49/5.29         => ( ( ln_ln_real @ ( divide_divide_real @ X @ Y2 ) )
% 9.49/5.29            = ( minus_minus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y2 ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5955_ln__2__less__1,axiom,
% 9.49/5.29      ord_less_real @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ one_one_real ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5956_ln__le__minus__one,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_real @ zero_zero_real @ X )
% 9.49/5.29       => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5957_ln__diff__le,axiom,
% 9.49/5.29      ! [X: real,Y2: real] :
% 9.49/5.29        ( ( ord_less_real @ zero_zero_real @ X )
% 9.49/5.29       => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 9.49/5.29         => ( ord_less_eq_real @ ( minus_minus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y2 ) ) @ ( divide_divide_real @ ( minus_minus_real @ X @ Y2 ) @ Y2 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5958_ln__add__one__self__le__self2,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 9.49/5.29       => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5959_ln__one__minus__pos__upper__bound,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.49/5.29       => ( ( ord_less_real @ X @ one_one_real )
% 9.49/5.29         => ( ord_less_eq_real @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X ) ) @ ( uminus_uminus_real @ X ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5960_add__0__iff,axiom,
% 9.49/5.29      ! [B: complex,A: complex] :
% 9.49/5.29        ( ( B
% 9.49/5.29          = ( plus_plus_complex @ B @ A ) )
% 9.49/5.29        = ( A = zero_zero_complex ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5961_add__0__iff,axiom,
% 9.49/5.29      ! [B: real,A: real] :
% 9.49/5.29        ( ( B
% 9.49/5.29          = ( plus_plus_real @ B @ A ) )
% 9.49/5.29        = ( A = zero_zero_real ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5962_add__0__iff,axiom,
% 9.49/5.29      ! [B: rat,A: rat] :
% 9.49/5.29        ( ( B
% 9.49/5.29          = ( plus_plus_rat @ B @ A ) )
% 9.49/5.29        = ( A = zero_zero_rat ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5963_add__0__iff,axiom,
% 9.49/5.29      ! [B: nat,A: nat] :
% 9.49/5.29        ( ( B
% 9.49/5.29          = ( plus_plus_nat @ B @ A ) )
% 9.49/5.29        = ( A = zero_zero_nat ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5964_add__0__iff,axiom,
% 9.49/5.29      ! [B: int,A: int] :
% 9.49/5.29        ( ( B
% 9.49/5.29          = ( plus_plus_int @ B @ A ) )
% 9.49/5.29        = ( A = zero_zero_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5965_crossproduct__noteq,axiom,
% 9.49/5.29      ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.49/5.29        ( ( ( A != B )
% 9.49/5.29          & ( C != D2 ) )
% 9.49/5.29        = ( ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) )
% 9.49/5.29         != ( plus_plus_rat @ ( times_times_rat @ A @ D2 ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5966_crossproduct__noteq,axiom,
% 9.49/5.29      ! [A: complex,B: complex,C: complex,D2: complex] :
% 9.49/5.29        ( ( ( A != B )
% 9.49/5.29          & ( C != D2 ) )
% 9.49/5.29        = ( ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ D2 ) )
% 9.49/5.29         != ( plus_plus_complex @ ( times_times_complex @ A @ D2 ) @ ( times_times_complex @ B @ C ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5967_crossproduct__noteq,axiom,
% 9.49/5.29      ! [A: real,B: real,C: real,D2: real] :
% 9.49/5.29        ( ( ( A != B )
% 9.49/5.29          & ( C != D2 ) )
% 9.49/5.29        = ( ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) )
% 9.49/5.29         != ( plus_plus_real @ ( times_times_real @ A @ D2 ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5968_crossproduct__noteq,axiom,
% 9.49/5.29      ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.49/5.29        ( ( ( A != B )
% 9.49/5.29          & ( C != D2 ) )
% 9.49/5.29        = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) )
% 9.49/5.29         != ( plus_plus_nat @ ( times_times_nat @ A @ D2 ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5969_crossproduct__noteq,axiom,
% 9.49/5.29      ! [A: int,B: int,C: int,D2: int] :
% 9.49/5.29        ( ( ( A != B )
% 9.49/5.29          & ( C != D2 ) )
% 9.49/5.29        = ( ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) )
% 9.49/5.29         != ( plus_plus_int @ ( times_times_int @ A @ D2 ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5970_crossproduct__eq,axiom,
% 9.49/5.29      ! [W: rat,Y2: rat,X: rat,Z: rat] :
% 9.49/5.29        ( ( ( plus_plus_rat @ ( times_times_rat @ W @ Y2 ) @ ( times_times_rat @ X @ Z ) )
% 9.49/5.29          = ( plus_plus_rat @ ( times_times_rat @ W @ Z ) @ ( times_times_rat @ X @ Y2 ) ) )
% 9.49/5.29        = ( ( W = X )
% 9.49/5.29          | ( Y2 = Z ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5971_crossproduct__eq,axiom,
% 9.49/5.29      ! [W: complex,Y2: complex,X: complex,Z: complex] :
% 9.49/5.29        ( ( ( plus_plus_complex @ ( times_times_complex @ W @ Y2 ) @ ( times_times_complex @ X @ Z ) )
% 9.49/5.29          = ( plus_plus_complex @ ( times_times_complex @ W @ Z ) @ ( times_times_complex @ X @ Y2 ) ) )
% 9.49/5.29        = ( ( W = X )
% 9.49/5.29          | ( Y2 = Z ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5972_crossproduct__eq,axiom,
% 9.49/5.29      ! [W: real,Y2: real,X: real,Z: real] :
% 9.49/5.29        ( ( ( plus_plus_real @ ( times_times_real @ W @ Y2 ) @ ( times_times_real @ X @ Z ) )
% 9.49/5.29          = ( plus_plus_real @ ( times_times_real @ W @ Z ) @ ( times_times_real @ X @ Y2 ) ) )
% 9.49/5.29        = ( ( W = X )
% 9.49/5.29          | ( Y2 = Z ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5973_crossproduct__eq,axiom,
% 9.49/5.29      ! [W: nat,Y2: nat,X: nat,Z: nat] :
% 9.49/5.29        ( ( ( plus_plus_nat @ ( times_times_nat @ W @ Y2 ) @ ( times_times_nat @ X @ Z ) )
% 9.49/5.29          = ( plus_plus_nat @ ( times_times_nat @ W @ Z ) @ ( times_times_nat @ X @ Y2 ) ) )
% 9.49/5.29        = ( ( W = X )
% 9.49/5.29          | ( Y2 = Z ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5974_crossproduct__eq,axiom,
% 9.49/5.29      ! [W: int,Y2: int,X: int,Z: int] :
% 9.49/5.29        ( ( ( plus_plus_int @ ( times_times_int @ W @ Y2 ) @ ( times_times_int @ X @ Z ) )
% 9.49/5.29          = ( plus_plus_int @ ( times_times_int @ W @ Z ) @ ( times_times_int @ X @ Y2 ) ) )
% 9.49/5.29        = ( ( W = X )
% 9.49/5.29          | ( Y2 = Z ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5975_exists__least__lemma,axiom,
% 9.49/5.29      ! [P: nat > $o] :
% 9.49/5.29        ( ~ ( P @ zero_zero_nat )
% 9.49/5.29       => ( ? [X_1: nat] : ( P @ X_1 )
% 9.49/5.29         => ? [N3: nat] :
% 9.49/5.29              ( ~ ( P @ N3 )
% 9.49/5.29              & ( P @ ( suc @ N3 ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5976_ex__le__of__int,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29      ? [Z3: int] : ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ Z3 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5977_ex__of__int__less,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29      ? [Z3: int] : ( ord_less_real @ ( ring_1_of_int_real @ Z3 ) @ X ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5978_ex__of__int__less,axiom,
% 9.49/5.29      ! [X: rat] :
% 9.49/5.29      ? [Z3: int] : ( ord_less_rat @ ( ring_1_of_int_rat @ Z3 ) @ X ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5979_ex__less__of__int,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29      ? [Z3: int] : ( ord_less_real @ X @ ( ring_1_of_int_real @ Z3 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5980_ex__less__of__int,axiom,
% 9.49/5.29      ! [X: rat] :
% 9.49/5.29      ? [Z3: int] : ( ord_less_rat @ X @ ( ring_1_of_int_rat @ Z3 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5981_and__nat__unfold,axiom,
% 9.49/5.29      ( bit_se727722235901077358nd_nat
% 9.49/5.29      = ( ^ [M6: nat,N2: nat] :
% 9.49/5.29            ( if_nat
% 9.49/5.29            @ ( ( M6 = zero_zero_nat )
% 9.49/5.29              | ( N2 = zero_zero_nat ) )
% 9.49/5.29            @ zero_zero_nat
% 9.49/5.29            @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5982_and__nat__rec,axiom,
% 9.49/5.29      ( bit_se727722235901077358nd_nat
% 9.49/5.29      = ( ^ [M6: nat,N2: nat] :
% 9.49/5.29            ( plus_plus_nat
% 9.49/5.29            @ ( zero_n2687167440665602831ol_nat
% 9.49/5.29              @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 )
% 9.49/5.29                & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 9.49/5.29            @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5983_and__int_Opinduct,axiom,
% 9.49/5.29      ! [A0: int,A12: int,P: int > int > $o] :
% 9.49/5.29        ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 9.49/5.29       => ( ! [K2: int,L4: int] :
% 9.49/5.29              ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K2 @ L4 ) )
% 9.49/5.29             => ( ( ~ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 9.49/5.29                      & ( member_int @ L4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 9.49/5.29                 => ( P @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 9.49/5.29               => ( P @ K2 @ L4 ) ) )
% 9.49/5.29         => ( P @ A0 @ A12 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5984_ln__one__plus__pos__lower__bound,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.49/5.29       => ( ( ord_less_eq_real @ X @ one_one_real )
% 9.49/5.29         => ( ord_less_eq_real @ ( minus_minus_real @ X @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5985_artanh__def,axiom,
% 9.49/5.29      ( artanh_real
% 9.49/5.29      = ( ^ [X2: real] : ( divide_divide_real @ ( ln_ln_real @ ( divide_divide_real @ ( plus_plus_real @ one_one_real @ X2 ) @ ( minus_minus_real @ one_one_real @ X2 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5986_abs__ln__one__plus__x__minus__x__bound__nonpos,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 9.49/5.29       => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 9.49/5.29         => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5987_round__unique,axiom,
% 9.49/5.29      ! [X: real,Y2: int] :
% 9.49/5.29        ( ( ord_less_real @ ( minus_minus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ Y2 ) )
% 9.49/5.29       => ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y2 ) @ ( plus_plus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 9.49/5.29         => ( ( archim8280529875227126926d_real @ X )
% 9.49/5.29            = Y2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5988_round__unique,axiom,
% 9.49/5.29      ! [X: rat,Y2: int] :
% 9.49/5.29        ( ( ord_less_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ Y2 ) )
% 9.49/5.29       => ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y2 ) @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) )
% 9.49/5.29         => ( ( archim7778729529865785530nd_rat @ X )
% 9.49/5.29            = Y2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5989_tanh__ln__real,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_real @ zero_zero_real @ X )
% 9.49/5.29       => ( ( tanh_real @ ( ln_ln_real @ X ) )
% 9.49/5.29          = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5990_abs__ln__one__plus__x__minus__x__bound,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.49/5.29       => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5991_of__int__round__gt,axiom,
% 9.49/5.29      ! [X: real] : ( ord_less_real @ ( minus_minus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5992_of__int__round__gt,axiom,
% 9.49/5.29      ! [X: rat] : ( ord_less_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5993_abs__numeral,axiom,
% 9.49/5.29      ! [N: num] :
% 9.49/5.29        ( ( abs_abs_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 9.49/5.29        = ( numera6620942414471956472nteger @ N ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5994_abs__numeral,axiom,
% 9.49/5.29      ! [N: num] :
% 9.49/5.29        ( ( abs_abs_real @ ( numeral_numeral_real @ N ) )
% 9.49/5.29        = ( numeral_numeral_real @ N ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5995_abs__numeral,axiom,
% 9.49/5.29      ! [N: num] :
% 9.49/5.29        ( ( abs_abs_rat @ ( numeral_numeral_rat @ N ) )
% 9.49/5.29        = ( numeral_numeral_rat @ N ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5996_abs__numeral,axiom,
% 9.49/5.29      ! [N: num] :
% 9.49/5.29        ( ( abs_abs_int @ ( numeral_numeral_int @ N ) )
% 9.49/5.29        = ( numeral_numeral_int @ N ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5997_abs__mult__self__eq,axiom,
% 9.49/5.29      ! [A: code_integer] :
% 9.49/5.29        ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 9.49/5.29        = ( times_3573771949741848930nteger @ A @ A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5998_abs__mult__self__eq,axiom,
% 9.49/5.29      ! [A: real] :
% 9.49/5.29        ( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
% 9.49/5.29        = ( times_times_real @ A @ A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_5999_abs__mult__self__eq,axiom,
% 9.49/5.29      ! [A: int] :
% 9.49/5.29        ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ A ) )
% 9.49/5.29        = ( times_times_int @ A @ A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6000_abs__1,axiom,
% 9.49/5.29      ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 9.49/5.29      = one_one_Code_integer ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6001_abs__1,axiom,
% 9.49/5.29      ( ( abs_abs_complex @ one_one_complex )
% 9.49/5.29      = one_one_complex ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6002_abs__1,axiom,
% 9.49/5.29      ( ( abs_abs_real @ one_one_real )
% 9.49/5.29      = one_one_real ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6003_abs__1,axiom,
% 9.49/5.29      ( ( abs_abs_rat @ one_one_rat )
% 9.49/5.29      = one_one_rat ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6004_abs__1,axiom,
% 9.49/5.29      ( ( abs_abs_int @ one_one_int )
% 9.49/5.29      = one_one_int ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6005_abs__add__abs,axiom,
% 9.49/5.29      ! [A: code_integer,B: code_integer] :
% 9.49/5.29        ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) )
% 9.49/5.29        = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6006_abs__add__abs,axiom,
% 9.49/5.29      ! [A: real,B: real] :
% 9.49/5.29        ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) )
% 9.49/5.29        = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6007_abs__add__abs,axiom,
% 9.49/5.29      ! [A: rat,B: rat] :
% 9.49/5.29        ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) )
% 9.49/5.29        = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6008_abs__add__abs,axiom,
% 9.49/5.29      ! [A: int,B: int] :
% 9.49/5.29        ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 9.49/5.29        = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6009_abs__divide,axiom,
% 9.49/5.29      ! [A: complex,B: complex] :
% 9.49/5.29        ( ( abs_abs_complex @ ( divide1717551699836669952omplex @ A @ B ) )
% 9.49/5.29        = ( divide1717551699836669952omplex @ ( abs_abs_complex @ A ) @ ( abs_abs_complex @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6010_abs__divide,axiom,
% 9.49/5.29      ! [A: real,B: real] :
% 9.49/5.29        ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 9.49/5.29        = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6011_abs__divide,axiom,
% 9.49/5.29      ! [A: rat,B: rat] :
% 9.49/5.29        ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 9.49/5.29        = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6012_tanh__real__less__iff,axiom,
% 9.49/5.29      ! [X: real,Y2: real] :
% 9.49/5.29        ( ( ord_less_real @ ( tanh_real @ X ) @ ( tanh_real @ Y2 ) )
% 9.49/5.29        = ( ord_less_real @ X @ Y2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6013_tanh__real__le__iff,axiom,
% 9.49/5.29      ! [X: real,Y2: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ ( tanh_real @ X ) @ ( tanh_real @ Y2 ) )
% 9.49/5.29        = ( ord_less_eq_real @ X @ Y2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6014_abs__of__nonneg,axiom,
% 9.49/5.29      ! [A: code_integer] :
% 9.49/5.29        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 9.49/5.29       => ( ( abs_abs_Code_integer @ A )
% 9.49/5.29          = A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6015_abs__of__nonneg,axiom,
% 9.49/5.29      ! [A: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 9.49/5.29       => ( ( abs_abs_real @ A )
% 9.49/5.29          = A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6016_abs__of__nonneg,axiom,
% 9.49/5.29      ! [A: rat] :
% 9.49/5.29        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.49/5.29       => ( ( abs_abs_rat @ A )
% 9.49/5.29          = A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6017_abs__of__nonneg,axiom,
% 9.49/5.29      ! [A: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.29       => ( ( abs_abs_int @ A )
% 9.49/5.29          = A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6018_abs__le__self__iff,axiom,
% 9.49/5.29      ! [A: code_integer] :
% 9.49/5.29        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 9.49/5.29        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6019_abs__le__self__iff,axiom,
% 9.49/5.29      ! [A: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ A )
% 9.49/5.29        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6020_abs__le__self__iff,axiom,
% 9.49/5.29      ! [A: rat] :
% 9.49/5.29        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 9.49/5.29        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6021_abs__le__self__iff,axiom,
% 9.49/5.29      ! [A: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 9.49/5.29        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6022_abs__le__zero__iff,axiom,
% 9.49/5.29      ! [A: code_integer] :
% 9.49/5.29        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 9.49/5.29        = ( A = zero_z3403309356797280102nteger ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6023_abs__le__zero__iff,axiom,
% 9.49/5.29      ! [A: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ zero_zero_real )
% 9.49/5.29        = ( A = zero_zero_real ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6024_abs__le__zero__iff,axiom,
% 9.49/5.29      ! [A: rat] :
% 9.49/5.29        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 9.49/5.29        = ( A = zero_zero_rat ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6025_abs__le__zero__iff,axiom,
% 9.49/5.29      ! [A: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 9.49/5.29        = ( A = zero_zero_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6026_zero__less__abs__iff,axiom,
% 9.49/5.29      ! [A: code_integer] :
% 9.49/5.29        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 9.49/5.29        = ( A != zero_z3403309356797280102nteger ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6027_zero__less__abs__iff,axiom,
% 9.49/5.29      ! [A: real] :
% 9.49/5.29        ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ A ) )
% 9.49/5.29        = ( A != zero_zero_real ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6028_zero__less__abs__iff,axiom,
% 9.49/5.29      ! [A: rat] :
% 9.49/5.29        ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 9.49/5.29        = ( A != zero_zero_rat ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6029_zero__less__abs__iff,axiom,
% 9.49/5.29      ! [A: int] :
% 9.49/5.29        ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 9.49/5.29        = ( A != zero_zero_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6030_abs__neg__numeral,axiom,
% 9.49/5.29      ! [N: num] :
% 9.49/5.29        ( ( abs_abs_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.49/5.29        = ( numeral_numeral_int @ N ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6031_abs__neg__numeral,axiom,
% 9.49/5.29      ! [N: num] :
% 9.49/5.29        ( ( abs_abs_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 9.49/5.29        = ( numeral_numeral_real @ N ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6032_abs__neg__numeral,axiom,
% 9.49/5.29      ! [N: num] :
% 9.49/5.29        ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 9.49/5.29        = ( numera6620942414471956472nteger @ N ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6033_abs__neg__numeral,axiom,
% 9.49/5.29      ! [N: num] :
% 9.49/5.29        ( ( abs_abs_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 9.49/5.29        = ( numeral_numeral_rat @ N ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6034_abs__neg__one,axiom,
% 9.49/5.29      ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 9.49/5.29      = one_one_int ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6035_abs__neg__one,axiom,
% 9.49/5.29      ( ( abs_abs_real @ ( uminus_uminus_real @ one_one_real ) )
% 9.49/5.29      = one_one_real ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6036_abs__neg__one,axiom,
% 9.49/5.29      ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.49/5.29      = one_one_Code_integer ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6037_abs__neg__one,axiom,
% 9.49/5.29      ( ( abs_abs_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.49/5.29      = one_one_rat ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6038_abs__power__minus,axiom,
% 9.49/5.29      ! [A: int,N: nat] :
% 9.49/5.29        ( ( abs_abs_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 9.49/5.29        = ( abs_abs_int @ ( power_power_int @ A @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6039_abs__power__minus,axiom,
% 9.49/5.29      ! [A: real,N: nat] :
% 9.49/5.29        ( ( abs_abs_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 9.49/5.29        = ( abs_abs_real @ ( power_power_real @ A @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6040_abs__power__minus,axiom,
% 9.49/5.29      ! [A: code_integer,N: nat] :
% 9.49/5.29        ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 9.49/5.29        = ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6041_abs__power__minus,axiom,
% 9.49/5.29      ! [A: rat,N: nat] :
% 9.49/5.29        ( ( abs_abs_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 9.49/5.29        = ( abs_abs_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6042_tanh__real__pos__iff,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_real @ zero_zero_real @ ( tanh_real @ X ) )
% 9.49/5.29        = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6043_tanh__real__neg__iff,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_real @ ( tanh_real @ X ) @ zero_zero_real )
% 9.49/5.29        = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6044_tanh__real__nonpos__iff,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ ( tanh_real @ X ) @ zero_zero_real )
% 9.49/5.29        = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6045_tanh__real__nonneg__iff,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ zero_zero_real @ ( tanh_real @ X ) )
% 9.49/5.29        = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6046_round__numeral,axiom,
% 9.49/5.29      ! [N: num] :
% 9.49/5.29        ( ( archim8280529875227126926d_real @ ( numeral_numeral_real @ N ) )
% 9.49/5.29        = ( numeral_numeral_int @ N ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6047_round__numeral,axiom,
% 9.49/5.29      ! [N: num] :
% 9.49/5.29        ( ( archim7778729529865785530nd_rat @ ( numeral_numeral_rat @ N ) )
% 9.49/5.29        = ( numeral_numeral_int @ N ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6048_round__1,axiom,
% 9.49/5.29      ( ( archim8280529875227126926d_real @ one_one_real )
% 9.49/5.29      = one_one_int ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6049_round__1,axiom,
% 9.49/5.29      ( ( archim7778729529865785530nd_rat @ one_one_rat )
% 9.49/5.29      = one_one_int ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6050_zero__le__divide__abs__iff,axiom,
% 9.49/5.29      ! [A: real,B: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) )
% 9.49/5.29        = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 9.49/5.29          | ( B = zero_zero_real ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6051_zero__le__divide__abs__iff,axiom,
% 9.49/5.29      ! [A: rat,B: rat] :
% 9.49/5.29        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) )
% 9.49/5.29        = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.49/5.29          | ( B = zero_zero_rat ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6052_divide__le__0__abs__iff,axiom,
% 9.49/5.29      ! [A: real,B: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) @ zero_zero_real )
% 9.49/5.29        = ( ( ord_less_eq_real @ A @ zero_zero_real )
% 9.49/5.29          | ( B = zero_zero_real ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6053_divide__le__0__abs__iff,axiom,
% 9.49/5.29      ! [A: rat,B: rat] :
% 9.49/5.29        ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) @ zero_zero_rat )
% 9.49/5.29        = ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 9.49/5.29          | ( B = zero_zero_rat ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6054_abs__of__nonpos,axiom,
% 9.49/5.29      ! [A: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 9.49/5.29       => ( ( abs_abs_real @ A )
% 9.49/5.29          = ( uminus_uminus_real @ A ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6055_abs__of__nonpos,axiom,
% 9.49/5.29      ! [A: code_integer] :
% 9.49/5.29        ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 9.49/5.29       => ( ( abs_abs_Code_integer @ A )
% 9.49/5.29          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6056_abs__of__nonpos,axiom,
% 9.49/5.29      ! [A: rat] :
% 9.49/5.29        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 9.49/5.29       => ( ( abs_abs_rat @ A )
% 9.49/5.29          = ( uminus_uminus_rat @ A ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6057_abs__of__nonpos,axiom,
% 9.49/5.29      ! [A: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 9.49/5.29       => ( ( abs_abs_int @ A )
% 9.49/5.29          = ( uminus_uminus_int @ A ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6058_artanh__minus__real,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 9.49/5.29       => ( ( artanh_real @ ( uminus_uminus_real @ X ) )
% 9.49/5.29          = ( uminus_uminus_real @ ( artanh_real @ X ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6059_zero__less__power__abs__iff,axiom,
% 9.49/5.29      ! [A: code_integer,N: nat] :
% 9.49/5.29        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) )
% 9.49/5.29        = ( ( A != zero_z3403309356797280102nteger )
% 9.49/5.29          | ( N = zero_zero_nat ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6060_zero__less__power__abs__iff,axiom,
% 9.49/5.29      ! [A: real,N: nat] :
% 9.49/5.29        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 9.49/5.29        = ( ( A != zero_zero_real )
% 9.49/5.29          | ( N = zero_zero_nat ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6061_zero__less__power__abs__iff,axiom,
% 9.49/5.29      ! [A: rat,N: nat] :
% 9.49/5.29        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) )
% 9.49/5.29        = ( ( A != zero_zero_rat )
% 9.49/5.29          | ( N = zero_zero_nat ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6062_zero__less__power__abs__iff,axiom,
% 9.49/5.29      ! [A: int,N: nat] :
% 9.49/5.29        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) )
% 9.49/5.29        = ( ( A != zero_zero_int )
% 9.49/5.29          | ( N = zero_zero_nat ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6063_abs__power2,axiom,
% 9.49/5.29      ! [A: code_integer] :
% 9.49/5.29        ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.29        = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6064_abs__power2,axiom,
% 9.49/5.29      ! [A: real] :
% 9.49/5.29        ( ( abs_abs_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.29        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6065_abs__power2,axiom,
% 9.49/5.29      ! [A: int] :
% 9.49/5.29        ( ( abs_abs_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.29        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6066_power2__abs,axiom,
% 9.49/5.29      ! [A: code_integer] :
% 9.49/5.29        ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.29        = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6067_power2__abs,axiom,
% 9.49/5.29      ! [A: real] :
% 9.49/5.29        ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.29        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6068_power2__abs,axiom,
% 9.49/5.29      ! [A: int] :
% 9.49/5.29        ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.29        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6069_round__neg__numeral,axiom,
% 9.49/5.29      ! [N: num] :
% 9.49/5.29        ( ( archim8280529875227126926d_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 9.49/5.29        = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6070_round__neg__numeral,axiom,
% 9.49/5.29      ! [N: num] :
% 9.49/5.29        ( ( archim7778729529865785530nd_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 9.49/5.29        = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6071_power__even__abs__numeral,axiom,
% 9.49/5.29      ! [W: num,A: code_integer] :
% 9.49/5.29        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 9.49/5.29       => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ W ) )
% 9.49/5.29          = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6072_power__even__abs__numeral,axiom,
% 9.49/5.29      ! [W: num,A: real] :
% 9.49/5.29        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 9.49/5.29       => ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ W ) )
% 9.49/5.29          = ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6073_power__even__abs__numeral,axiom,
% 9.49/5.29      ! [W: num,A: int] :
% 9.49/5.29        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 9.49/5.29       => ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ W ) )
% 9.49/5.29          = ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6074_abs__ge__self,axiom,
% 9.49/5.29      ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6075_abs__ge__self,axiom,
% 9.49/5.29      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6076_abs__ge__self,axiom,
% 9.49/5.29      ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6077_abs__le__D1,axiom,
% 9.49/5.29      ! [A: real,B: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 9.49/5.29       => ( ord_less_eq_real @ A @ B ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6078_abs__le__D1,axiom,
% 9.49/5.29      ! [A: code_integer,B: code_integer] :
% 9.49/5.29        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 9.49/5.29       => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6079_abs__le__D1,axiom,
% 9.49/5.29      ! [A: int,B: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 9.49/5.29       => ( ord_less_eq_int @ A @ B ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6080_abs__mult,axiom,
% 9.49/5.29      ! [A: code_integer,B: code_integer] :
% 9.49/5.29        ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 9.49/5.29        = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6081_abs__mult,axiom,
% 9.49/5.29      ! [A: complex,B: complex] :
% 9.49/5.29        ( ( abs_abs_complex @ ( times_times_complex @ A @ B ) )
% 9.49/5.29        = ( times_times_complex @ ( abs_abs_complex @ A ) @ ( abs_abs_complex @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6082_abs__mult,axiom,
% 9.49/5.29      ! [A: real,B: real] :
% 9.49/5.29        ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 9.49/5.29        = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6083_abs__mult,axiom,
% 9.49/5.29      ! [A: int,B: int] :
% 9.49/5.29        ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 9.49/5.29        = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6084_abs__one,axiom,
% 9.49/5.29      ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 9.49/5.29      = one_one_Code_integer ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6085_abs__one,axiom,
% 9.49/5.29      ( ( abs_abs_real @ one_one_real )
% 9.49/5.29      = one_one_real ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6086_abs__one,axiom,
% 9.49/5.29      ( ( abs_abs_rat @ one_one_rat )
% 9.49/5.29      = one_one_rat ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6087_abs__one,axiom,
% 9.49/5.29      ( ( abs_abs_int @ one_one_int )
% 9.49/5.29      = one_one_int ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6088_abs__minus__commute,axiom,
% 9.49/5.29      ! [A: real,B: real] :
% 9.49/5.29        ( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
% 9.49/5.29        = ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6089_abs__minus__commute,axiom,
% 9.49/5.29      ! [A: code_integer,B: code_integer] :
% 9.49/5.29        ( ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) )
% 9.49/5.29        = ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6090_abs__minus__commute,axiom,
% 9.49/5.29      ! [A: rat,B: rat] :
% 9.49/5.29        ( ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) )
% 9.49/5.29        = ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6091_abs__minus__commute,axiom,
% 9.49/5.29      ! [A: int,B: int] :
% 9.49/5.29        ( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
% 9.49/5.29        = ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6092_power__abs,axiom,
% 9.49/5.29      ! [A: code_integer,N: nat] :
% 9.49/5.29        ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) )
% 9.49/5.29        = ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6093_power__abs,axiom,
% 9.49/5.29      ! [A: real,N: nat] :
% 9.49/5.29        ( ( abs_abs_real @ ( power_power_real @ A @ N ) )
% 9.49/5.29        = ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6094_power__abs,axiom,
% 9.49/5.29      ! [A: int,N: nat] :
% 9.49/5.29        ( ( abs_abs_int @ ( power_power_int @ A @ N ) )
% 9.49/5.29        = ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6095_round__diff__minimal,axiom,
% 9.49/5.29      ! [Z: real,M: int] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ Z ) ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ Z @ ( ring_1_of_int_real @ M ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6096_round__diff__minimal,axiom,
% 9.49/5.29      ! [Z: rat,M: int] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ Z @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ Z ) ) ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ Z @ ( ring_1_of_int_rat @ M ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6097_abs__ge__zero,axiom,
% 9.49/5.29      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6098_abs__ge__zero,axiom,
% 9.49/5.29      ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6099_abs__ge__zero,axiom,
% 9.49/5.29      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6100_abs__ge__zero,axiom,
% 9.49/5.29      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6101_abs__not__less__zero,axiom,
% 9.49/5.29      ! [A: code_integer] :
% 9.49/5.29        ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6102_abs__not__less__zero,axiom,
% 9.49/5.29      ! [A: real] :
% 9.49/5.29        ~ ( ord_less_real @ ( abs_abs_real @ A ) @ zero_zero_real ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6103_abs__not__less__zero,axiom,
% 9.49/5.29      ! [A: rat] :
% 9.49/5.29        ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6104_abs__not__less__zero,axiom,
% 9.49/5.29      ! [A: int] :
% 9.49/5.29        ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6105_abs__of__pos,axiom,
% 9.49/5.29      ! [A: code_integer] :
% 9.49/5.29        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 9.49/5.29       => ( ( abs_abs_Code_integer @ A )
% 9.49/5.29          = A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6106_abs__of__pos,axiom,
% 9.49/5.29      ! [A: real] :
% 9.49/5.29        ( ( ord_less_real @ zero_zero_real @ A )
% 9.49/5.29       => ( ( abs_abs_real @ A )
% 9.49/5.29          = A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6107_abs__of__pos,axiom,
% 9.49/5.29      ! [A: rat] :
% 9.49/5.29        ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.49/5.29       => ( ( abs_abs_rat @ A )
% 9.49/5.29          = A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6108_abs__of__pos,axiom,
% 9.49/5.29      ! [A: int] :
% 9.49/5.29        ( ( ord_less_int @ zero_zero_int @ A )
% 9.49/5.29       => ( ( abs_abs_int @ A )
% 9.49/5.29          = A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6109_abs__triangle__ineq,axiom,
% 9.49/5.29      ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6110_abs__triangle__ineq,axiom,
% 9.49/5.29      ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6111_abs__triangle__ineq,axiom,
% 9.49/5.29      ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( plus_plus_rat @ A @ B ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6112_abs__triangle__ineq,axiom,
% 9.49/5.29      ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6113_abs__mult__less,axiom,
% 9.49/5.29      ! [A: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 9.49/5.29        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ C )
% 9.49/5.29       => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ B ) @ D2 )
% 9.49/5.29         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( times_3573771949741848930nteger @ C @ D2 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6114_abs__mult__less,axiom,
% 9.49/5.29      ! [A: real,C: real,B: real,D2: real] :
% 9.49/5.29        ( ( ord_less_real @ ( abs_abs_real @ A ) @ C )
% 9.49/5.29       => ( ( ord_less_real @ ( abs_abs_real @ B ) @ D2 )
% 9.49/5.29         => ( ord_less_real @ ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( times_times_real @ C @ D2 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6115_abs__mult__less,axiom,
% 9.49/5.29      ! [A: rat,C: rat,B: rat,D2: rat] :
% 9.49/5.29        ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ C )
% 9.49/5.29       => ( ( ord_less_rat @ ( abs_abs_rat @ B ) @ D2 )
% 9.49/5.29         => ( ord_less_rat @ ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( times_times_rat @ C @ D2 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6116_abs__mult__less,axiom,
% 9.49/5.29      ! [A: int,C: int,B: int,D2: int] :
% 9.49/5.29        ( ( ord_less_int @ ( abs_abs_int @ A ) @ C )
% 9.49/5.29       => ( ( ord_less_int @ ( abs_abs_int @ B ) @ D2 )
% 9.49/5.29         => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( times_times_int @ C @ D2 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6117_abs__triangle__ineq2__sym,axiom,
% 9.49/5.29      ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6118_abs__triangle__ineq2__sym,axiom,
% 9.49/5.29      ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6119_abs__triangle__ineq2__sym,axiom,
% 9.49/5.29      ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6120_abs__triangle__ineq2__sym,axiom,
% 9.49/5.29      ! [A: int,B: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6121_abs__triangle__ineq3,axiom,
% 9.49/5.29      ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6122_abs__triangle__ineq3,axiom,
% 9.49/5.29      ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6123_abs__triangle__ineq3,axiom,
% 9.49/5.29      ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6124_abs__triangle__ineq3,axiom,
% 9.49/5.29      ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6125_abs__triangle__ineq2,axiom,
% 9.49/5.29      ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6126_abs__triangle__ineq2,axiom,
% 9.49/5.29      ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6127_abs__triangle__ineq2,axiom,
% 9.49/5.29      ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6128_abs__triangle__ineq2,axiom,
% 9.49/5.29      ! [A: int,B: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6129_nonzero__abs__divide,axiom,
% 9.49/5.29      ! [B: real,A: real] :
% 9.49/5.29        ( ( B != zero_zero_real )
% 9.49/5.29       => ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 9.49/5.29          = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6130_nonzero__abs__divide,axiom,
% 9.49/5.29      ! [B: rat,A: rat] :
% 9.49/5.29        ( ( B != zero_zero_rat )
% 9.49/5.29       => ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 9.49/5.29          = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6131_abs__ge__minus__self,axiom,
% 9.49/5.29      ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ ( abs_abs_real @ A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6132_abs__ge__minus__self,axiom,
% 9.49/5.29      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6133_abs__ge__minus__self,axiom,
% 9.49/5.29      ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6134_abs__ge__minus__self,axiom,
% 9.49/5.29      ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6135_abs__le__iff,axiom,
% 9.49/5.29      ! [A: real,B: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 9.49/5.29        = ( ( ord_less_eq_real @ A @ B )
% 9.49/5.29          & ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6136_abs__le__iff,axiom,
% 9.49/5.29      ! [A: code_integer,B: code_integer] :
% 9.49/5.29        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 9.49/5.29        = ( ( ord_le3102999989581377725nteger @ A @ B )
% 9.49/5.29          & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6137_abs__le__iff,axiom,
% 9.49/5.29      ! [A: rat,B: rat] :
% 9.49/5.29        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 9.49/5.29        = ( ( ord_less_eq_rat @ A @ B )
% 9.49/5.29          & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6138_abs__le__iff,axiom,
% 9.49/5.29      ! [A: int,B: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 9.49/5.29        = ( ( ord_less_eq_int @ A @ B )
% 9.49/5.29          & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6139_abs__le__D2,axiom,
% 9.49/5.29      ! [A: real,B: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 9.49/5.29       => ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6140_abs__le__D2,axiom,
% 9.49/5.29      ! [A: code_integer,B: code_integer] :
% 9.49/5.29        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 9.49/5.29       => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6141_abs__le__D2,axiom,
% 9.49/5.29      ! [A: rat,B: rat] :
% 9.49/5.29        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 9.49/5.29       => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6142_abs__le__D2,axiom,
% 9.49/5.29      ! [A: int,B: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 9.49/5.29       => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6143_abs__leI,axiom,
% 9.49/5.29      ! [A: real,B: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ A @ B )
% 9.49/5.29       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 9.49/5.29         => ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6144_abs__leI,axiom,
% 9.49/5.29      ! [A: code_integer,B: code_integer] :
% 9.49/5.29        ( ( ord_le3102999989581377725nteger @ A @ B )
% 9.49/5.29       => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 9.49/5.29         => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6145_abs__leI,axiom,
% 9.49/5.29      ! [A: rat,B: rat] :
% 9.49/5.29        ( ( ord_less_eq_rat @ A @ B )
% 9.49/5.29       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 9.49/5.29         => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6146_abs__leI,axiom,
% 9.49/5.29      ! [A: int,B: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ A @ B )
% 9.49/5.29       => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 9.49/5.29         => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6147_abs__less__iff,axiom,
% 9.49/5.29      ! [A: int,B: int] :
% 9.49/5.29        ( ( ord_less_int @ ( abs_abs_int @ A ) @ B )
% 9.49/5.29        = ( ( ord_less_int @ A @ B )
% 9.49/5.29          & ( ord_less_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6148_abs__less__iff,axiom,
% 9.49/5.29      ! [A: real,B: real] :
% 9.49/5.29        ( ( ord_less_real @ ( abs_abs_real @ A ) @ B )
% 9.49/5.29        = ( ( ord_less_real @ A @ B )
% 9.49/5.29          & ( ord_less_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6149_abs__less__iff,axiom,
% 9.49/5.29      ! [A: code_integer,B: code_integer] :
% 9.49/5.29        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 9.49/5.29        = ( ( ord_le6747313008572928689nteger @ A @ B )
% 9.49/5.29          & ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6150_abs__less__iff,axiom,
% 9.49/5.29      ! [A: rat,B: rat] :
% 9.49/5.29        ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ B )
% 9.49/5.29        = ( ( ord_less_rat @ A @ B )
% 9.49/5.29          & ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6151_tanh__real__lt__1,axiom,
% 9.49/5.29      ! [X: real] : ( ord_less_real @ ( tanh_real @ X ) @ one_one_real ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6152_dense__eq0__I,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ! [E2: real] :
% 9.49/5.29            ( ( ord_less_real @ zero_zero_real @ E2 )
% 9.49/5.29           => ( ord_less_eq_real @ ( abs_abs_real @ X ) @ E2 ) )
% 9.49/5.29       => ( X = zero_zero_real ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6153_dense__eq0__I,axiom,
% 9.49/5.29      ! [X: rat] :
% 9.49/5.29        ( ! [E2: rat] :
% 9.49/5.29            ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 9.49/5.29           => ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ E2 ) )
% 9.49/5.29       => ( X = zero_zero_rat ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6154_abs__eq__mult,axiom,
% 9.49/5.29      ! [A: code_integer,B: code_integer] :
% 9.49/5.29        ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 9.49/5.29            | ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 9.49/5.29          & ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 9.49/5.29            | ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 9.49/5.29       => ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 9.49/5.29          = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6155_abs__eq__mult,axiom,
% 9.49/5.29      ! [A: rat,B: rat] :
% 9.49/5.29        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.49/5.29            | ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 9.49/5.29          & ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 9.49/5.29            | ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 9.49/5.29       => ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 9.49/5.29          = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6156_abs__eq__mult,axiom,
% 9.49/5.29      ! [A: real,B: real] :
% 9.49/5.29        ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 9.49/5.29            | ( ord_less_eq_real @ A @ zero_zero_real ) )
% 9.49/5.29          & ( ( ord_less_eq_real @ zero_zero_real @ B )
% 9.49/5.29            | ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 9.49/5.29       => ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 9.49/5.29          = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6157_abs__eq__mult,axiom,
% 9.49/5.29      ! [A: int,B: int] :
% 9.49/5.29        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.29            | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 9.49/5.29          & ( ( ord_less_eq_int @ zero_zero_int @ B )
% 9.49/5.29            | ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 9.49/5.29       => ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 9.49/5.29          = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6158_abs__mult__pos,axiom,
% 9.49/5.29      ! [X: code_integer,Y2: code_integer] :
% 9.49/5.29        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 9.49/5.29       => ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ Y2 ) @ X )
% 9.49/5.29          = ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ Y2 @ X ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6159_abs__mult__pos,axiom,
% 9.49/5.29      ! [X: rat,Y2: rat] :
% 9.49/5.29        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 9.49/5.29       => ( ( times_times_rat @ ( abs_abs_rat @ Y2 ) @ X )
% 9.49/5.29          = ( abs_abs_rat @ ( times_times_rat @ Y2 @ X ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6160_abs__mult__pos,axiom,
% 9.49/5.29      ! [X: real,Y2: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.49/5.29       => ( ( times_times_real @ ( abs_abs_real @ Y2 ) @ X )
% 9.49/5.29          = ( abs_abs_real @ ( times_times_real @ Y2 @ X ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6161_abs__mult__pos,axiom,
% 9.49/5.29      ! [X: int,Y2: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 9.49/5.29       => ( ( times_times_int @ ( abs_abs_int @ Y2 ) @ X )
% 9.49/5.29          = ( abs_abs_int @ ( times_times_int @ Y2 @ X ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6162_eq__abs__iff_H,axiom,
% 9.49/5.29      ! [A: real,B: real] :
% 9.49/5.29        ( ( A
% 9.49/5.29          = ( abs_abs_real @ B ) )
% 9.49/5.29        = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 9.49/5.29          & ( ( B = A )
% 9.49/5.29            | ( B
% 9.49/5.29              = ( uminus_uminus_real @ A ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6163_eq__abs__iff_H,axiom,
% 9.49/5.29      ! [A: code_integer,B: code_integer] :
% 9.49/5.29        ( ( A
% 9.49/5.29          = ( abs_abs_Code_integer @ B ) )
% 9.49/5.29        = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 9.49/5.29          & ( ( B = A )
% 9.49/5.29            | ( B
% 9.49/5.29              = ( uminus1351360451143612070nteger @ A ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6164_eq__abs__iff_H,axiom,
% 9.49/5.29      ! [A: rat,B: rat] :
% 9.49/5.29        ( ( A
% 9.49/5.29          = ( abs_abs_rat @ B ) )
% 9.49/5.29        = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.49/5.29          & ( ( B = A )
% 9.49/5.29            | ( B
% 9.49/5.29              = ( uminus_uminus_rat @ A ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6165_eq__abs__iff_H,axiom,
% 9.49/5.29      ! [A: int,B: int] :
% 9.49/5.29        ( ( A
% 9.49/5.29          = ( abs_abs_int @ B ) )
% 9.49/5.29        = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.49/5.29          & ( ( B = A )
% 9.49/5.29            | ( B
% 9.49/5.29              = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6166_abs__eq__iff_H,axiom,
% 9.49/5.29      ! [A: real,B: real] :
% 9.49/5.29        ( ( ( abs_abs_real @ A )
% 9.49/5.29          = B )
% 9.49/5.29        = ( ( ord_less_eq_real @ zero_zero_real @ B )
% 9.49/5.29          & ( ( A = B )
% 9.49/5.29            | ( A
% 9.49/5.29              = ( uminus_uminus_real @ B ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6167_abs__eq__iff_H,axiom,
% 9.49/5.29      ! [A: code_integer,B: code_integer] :
% 9.49/5.29        ( ( ( abs_abs_Code_integer @ A )
% 9.49/5.29          = B )
% 9.49/5.29        = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 9.49/5.29          & ( ( A = B )
% 9.49/5.29            | ( A
% 9.49/5.29              = ( uminus1351360451143612070nteger @ B ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6168_abs__eq__iff_H,axiom,
% 9.49/5.29      ! [A: rat,B: rat] :
% 9.49/5.29        ( ( ( abs_abs_rat @ A )
% 9.49/5.29          = B )
% 9.49/5.29        = ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 9.49/5.29          & ( ( A = B )
% 9.49/5.29            | ( A
% 9.49/5.29              = ( uminus_uminus_rat @ B ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6169_abs__eq__iff_H,axiom,
% 9.49/5.29      ! [A: int,B: int] :
% 9.49/5.29        ( ( ( abs_abs_int @ A )
% 9.49/5.29          = B )
% 9.49/5.29        = ( ( ord_less_eq_int @ zero_zero_int @ B )
% 9.49/5.29          & ( ( A = B )
% 9.49/5.29            | ( A
% 9.49/5.29              = ( uminus_uminus_int @ B ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6170_abs__minus__le__zero,axiom,
% 9.49/5.29      ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( abs_abs_real @ A ) ) @ zero_zero_real ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6171_abs__minus__le__zero,axiom,
% 9.49/5.29      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6172_abs__minus__le__zero,axiom,
% 9.49/5.29      ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6173_abs__minus__le__zero,axiom,
% 9.49/5.29      ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6174_abs__div__pos,axiom,
% 9.49/5.29      ! [Y2: real,X: real] :
% 9.49/5.29        ( ( ord_less_real @ zero_zero_real @ Y2 )
% 9.49/5.29       => ( ( divide_divide_real @ ( abs_abs_real @ X ) @ Y2 )
% 9.49/5.29          = ( abs_abs_real @ ( divide_divide_real @ X @ Y2 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6175_abs__div__pos,axiom,
% 9.49/5.29      ! [Y2: rat,X: rat] :
% 9.49/5.29        ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 9.49/5.29       => ( ( divide_divide_rat @ ( abs_abs_rat @ X ) @ Y2 )
% 9.49/5.29          = ( abs_abs_rat @ ( divide_divide_rat @ X @ Y2 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6176_zero__le__power__abs,axiom,
% 9.49/5.29      ! [A: code_integer,N: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6177_zero__le__power__abs,axiom,
% 9.49/5.29      ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6178_zero__le__power__abs,axiom,
% 9.49/5.29      ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6179_zero__le__power__abs,axiom,
% 9.49/5.29      ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6180_abs__if__raw,axiom,
% 9.49/5.29      ( abs_abs_int
% 9.49/5.29      = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6181_abs__if__raw,axiom,
% 9.49/5.29      ( abs_abs_real
% 9.49/5.29      = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6182_abs__if__raw,axiom,
% 9.49/5.29      ( abs_abs_Code_integer
% 9.49/5.29      = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6183_abs__if__raw,axiom,
% 9.49/5.29      ( abs_abs_rat
% 9.49/5.29      = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6184_abs__if,axiom,
% 9.49/5.29      ( abs_abs_int
% 9.49/5.29      = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6185_abs__if,axiom,
% 9.49/5.29      ( abs_abs_real
% 9.49/5.29      = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6186_abs__if,axiom,
% 9.49/5.29      ( abs_abs_Code_integer
% 9.49/5.29      = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6187_abs__if,axiom,
% 9.49/5.29      ( abs_abs_rat
% 9.49/5.29      = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6188_abs__of__neg,axiom,
% 9.49/5.29      ! [A: int] :
% 9.49/5.29        ( ( ord_less_int @ A @ zero_zero_int )
% 9.49/5.29       => ( ( abs_abs_int @ A )
% 9.49/5.29          = ( uminus_uminus_int @ A ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6189_abs__of__neg,axiom,
% 9.49/5.29      ! [A: real] :
% 9.49/5.29        ( ( ord_less_real @ A @ zero_zero_real )
% 9.49/5.29       => ( ( abs_abs_real @ A )
% 9.49/5.29          = ( uminus_uminus_real @ A ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6190_abs__of__neg,axiom,
% 9.49/5.29      ! [A: code_integer] :
% 9.49/5.29        ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 9.49/5.29       => ( ( abs_abs_Code_integer @ A )
% 9.49/5.29          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6191_abs__of__neg,axiom,
% 9.49/5.29      ! [A: rat] :
% 9.49/5.29        ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.49/5.29       => ( ( abs_abs_rat @ A )
% 9.49/5.29          = ( uminus_uminus_rat @ A ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6192_abs__diff__triangle__ineq,axiom,
% 9.49/5.29      ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( plus_p5714425477246183910nteger @ C @ D2 ) ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ C ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ D2 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6193_abs__diff__triangle__ineq,axiom,
% 9.49/5.29      ! [A: real,B: real,C: real,D2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D2 ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ ( minus_minus_real @ A @ C ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ D2 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6194_abs__diff__triangle__ineq,axiom,
% 9.49/5.29      ! [A: rat,B: rat,C: rat,D2: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ C @ D2 ) ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ C ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ D2 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6195_abs__diff__triangle__ineq,axiom,
% 9.49/5.29      ! [A: int,B: int,C: int,D2: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D2 ) ) ) @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ A @ C ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ D2 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6196_abs__triangle__ineq4,axiom,
% 9.49/5.29      ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6197_abs__triangle__ineq4,axiom,
% 9.49/5.29      ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6198_abs__triangle__ineq4,axiom,
% 9.49/5.29      ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6199_abs__triangle__ineq4,axiom,
% 9.49/5.29      ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6200_abs__diff__le__iff,axiom,
% 9.49/5.29      ! [X: code_integer,A: code_integer,R: code_integer] :
% 9.49/5.29        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R )
% 9.49/5.29        = ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ R ) @ X )
% 9.49/5.29          & ( ord_le3102999989581377725nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6201_abs__diff__le__iff,axiom,
% 9.49/5.29      ! [X: real,A: real,R: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ X @ A ) ) @ R )
% 9.49/5.29        = ( ( ord_less_eq_real @ ( minus_minus_real @ A @ R ) @ X )
% 9.49/5.29          & ( ord_less_eq_real @ X @ ( plus_plus_real @ A @ R ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6202_abs__diff__le__iff,axiom,
% 9.49/5.29      ! [X: rat,A: rat,R: rat] :
% 9.49/5.29        ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R )
% 9.49/5.29        = ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ R ) @ X )
% 9.49/5.29          & ( ord_less_eq_rat @ X @ ( plus_plus_rat @ A @ R ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6203_abs__diff__le__iff,axiom,
% 9.49/5.29      ! [X: int,A: int,R: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R )
% 9.49/5.29        = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R ) @ X )
% 9.49/5.29          & ( ord_less_eq_int @ X @ ( plus_plus_int @ A @ R ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6204_abs__diff__less__iff,axiom,
% 9.49/5.29      ! [X: code_integer,A: code_integer,R: code_integer] :
% 9.49/5.29        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R )
% 9.49/5.29        = ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ R ) @ X )
% 9.49/5.29          & ( ord_le6747313008572928689nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6205_abs__diff__less__iff,axiom,
% 9.49/5.29      ! [X: real,A: real,R: real] :
% 9.49/5.29        ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ A ) ) @ R )
% 9.49/5.29        = ( ( ord_less_real @ ( minus_minus_real @ A @ R ) @ X )
% 9.49/5.29          & ( ord_less_real @ X @ ( plus_plus_real @ A @ R ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6206_abs__diff__less__iff,axiom,
% 9.49/5.29      ! [X: rat,A: rat,R: rat] :
% 9.49/5.29        ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R )
% 9.49/5.29        = ( ( ord_less_rat @ ( minus_minus_rat @ A @ R ) @ X )
% 9.49/5.29          & ( ord_less_rat @ X @ ( plus_plus_rat @ A @ R ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6207_abs__diff__less__iff,axiom,
% 9.49/5.29      ! [X: int,A: int,R: int] :
% 9.49/5.29        ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R )
% 9.49/5.29        = ( ( ord_less_int @ ( minus_minus_int @ A @ R ) @ X )
% 9.49/5.29          & ( ord_less_int @ X @ ( plus_plus_int @ A @ R ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6208_abs__real__def,axiom,
% 9.49/5.29      ( abs_abs_real
% 9.49/5.29      = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6209_lemma__interval__lt,axiom,
% 9.49/5.29      ! [A: real,X: real,B: real] :
% 9.49/5.29        ( ( ord_less_real @ A @ X )
% 9.49/5.29       => ( ( ord_less_real @ X @ B )
% 9.49/5.29         => ? [D3: real] :
% 9.49/5.29              ( ( ord_less_real @ zero_zero_real @ D3 )
% 9.49/5.29              & ! [Y4: real] :
% 9.49/5.29                  ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y4 ) ) @ D3 )
% 9.49/5.29                 => ( ( ord_less_real @ A @ Y4 )
% 9.49/5.29                    & ( ord_less_real @ Y4 @ B ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6210_sin__bound__lemma,axiom,
% 9.49/5.29      ! [X: real,Y2: real,U: real,V: real] :
% 9.49/5.29        ( ( X = Y2 )
% 9.49/5.29       => ( ( ord_less_eq_real @ ( abs_abs_real @ U ) @ V )
% 9.49/5.29         => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ X @ U ) @ Y2 ) ) @ V ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6211_tanh__real__gt__neg1,axiom,
% 9.49/5.29      ! [X: real] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( tanh_real @ X ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6212_abs__add__one__gt__zero,axiom,
% 9.49/5.29      ! [X: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6213_abs__add__one__gt__zero,axiom,
% 9.49/5.29      ! [X: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ ( abs_abs_real @ X ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6214_abs__add__one__gt__zero,axiom,
% 9.49/5.29      ! [X: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6215_abs__add__one__gt__zero,axiom,
% 9.49/5.29      ! [X: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6216_of__int__leD,axiom,
% 9.49/5.29      ! [N: int,X: code_integer] :
% 9.49/5.29        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X )
% 9.49/5.29       => ( ( N = zero_zero_int )
% 9.49/5.29          | ( ord_le3102999989581377725nteger @ one_one_Code_integer @ X ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6217_of__int__leD,axiom,
% 9.49/5.29      ! [N: int,X: rat] :
% 9.49/5.29        ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X )
% 9.49/5.29       => ( ( N = zero_zero_int )
% 9.49/5.29          | ( ord_less_eq_rat @ one_one_rat @ X ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6218_of__int__leD,axiom,
% 9.49/5.29      ! [N: int,X: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X )
% 9.49/5.29       => ( ( N = zero_zero_int )
% 9.49/5.29          | ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6219_of__int__leD,axiom,
% 9.49/5.29      ! [N: int,X: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X )
% 9.49/5.29       => ( ( N = zero_zero_int )
% 9.49/5.29          | ( ord_less_eq_int @ one_one_int @ X ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6220_of__int__lessD,axiom,
% 9.49/5.29      ! [N: int,X: code_integer] :
% 9.49/5.29        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X )
% 9.49/5.29       => ( ( N = zero_zero_int )
% 9.49/5.29          | ( ord_le6747313008572928689nteger @ one_one_Code_integer @ X ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6221_of__int__lessD,axiom,
% 9.49/5.29      ! [N: int,X: real] :
% 9.49/5.29        ( ( ord_less_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X )
% 9.49/5.29       => ( ( N = zero_zero_int )
% 9.49/5.29          | ( ord_less_real @ one_one_real @ X ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6222_of__int__lessD,axiom,
% 9.49/5.29      ! [N: int,X: rat] :
% 9.49/5.29        ( ( ord_less_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X )
% 9.49/5.29       => ( ( N = zero_zero_int )
% 9.49/5.29          | ( ord_less_rat @ one_one_rat @ X ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6223_of__int__lessD,axiom,
% 9.49/5.29      ! [N: int,X: int] :
% 9.49/5.29        ( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X )
% 9.49/5.29       => ( ( N = zero_zero_int )
% 9.49/5.29          | ( ord_less_int @ one_one_int @ X ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6224_lemma__interval,axiom,
% 9.49/5.29      ! [A: real,X: real,B: real] :
% 9.49/5.29        ( ( ord_less_real @ A @ X )
% 9.49/5.29       => ( ( ord_less_real @ X @ B )
% 9.49/5.29         => ? [D3: real] :
% 9.49/5.29              ( ( ord_less_real @ zero_zero_real @ D3 )
% 9.49/5.29              & ! [Y4: real] :
% 9.49/5.29                  ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y4 ) ) @ D3 )
% 9.49/5.29                 => ( ( ord_less_eq_real @ A @ Y4 )
% 9.49/5.29                    & ( ord_less_eq_real @ Y4 @ B ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6225_of__int__round__abs__le,axiom,
% 9.49/5.29      ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) @ X ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6226_of__int__round__abs__le,axiom,
% 9.49/5.29      ! [X: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) @ X ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6227_round__unique_H,axiom,
% 9.49/5.29      ! [X: real,N: int] :
% 9.49/5.29        ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ ( ring_1_of_int_real @ N ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.49/5.29       => ( ( archim8280529875227126926d_real @ X )
% 9.49/5.29          = N ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6228_round__unique_H,axiom,
% 9.49/5.29      ! [X: rat,N: int] :
% 9.49/5.29        ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ ( ring_1_of_int_rat @ N ) ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 9.49/5.29       => ( ( archim7778729529865785530nd_rat @ X )
% 9.49/5.29          = N ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6229_abs__le__square__iff,axiom,
% 9.49/5.29      ! [X: code_integer,Y2: code_integer] :
% 9.49/5.29        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ ( abs_abs_Code_integer @ Y2 ) )
% 9.49/5.29        = ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6230_abs__le__square__iff,axiom,
% 9.49/5.29      ! [X: real,Y2: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ Y2 ) )
% 9.49/5.29        = ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6231_abs__le__square__iff,axiom,
% 9.49/5.29      ! [X: int,Y2: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ ( abs_abs_int @ X ) @ ( abs_abs_int @ Y2 ) )
% 9.49/5.29        = ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6232_abs__square__eq__1,axiom,
% 9.49/5.29      ! [X: code_integer] :
% 9.49/5.29        ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.29          = one_one_Code_integer )
% 9.49/5.29        = ( ( abs_abs_Code_integer @ X )
% 9.49/5.29          = one_one_Code_integer ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6233_abs__square__eq__1,axiom,
% 9.49/5.29      ! [X: rat] :
% 9.49/5.29        ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.29          = one_one_rat )
% 9.49/5.29        = ( ( abs_abs_rat @ X )
% 9.49/5.29          = one_one_rat ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6234_abs__square__eq__1,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.29          = one_one_real )
% 9.49/5.29        = ( ( abs_abs_real @ X )
% 9.49/5.29          = one_one_real ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6235_abs__square__eq__1,axiom,
% 9.49/5.29      ! [X: int] :
% 9.49/5.29        ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.29          = one_one_int )
% 9.49/5.29        = ( ( abs_abs_int @ X )
% 9.49/5.29          = one_one_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6236_power__even__abs,axiom,
% 9.49/5.29      ! [N: nat,A: code_integer] :
% 9.49/5.29        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.29       => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N )
% 9.49/5.29          = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6237_power__even__abs,axiom,
% 9.49/5.29      ! [N: nat,A: real] :
% 9.49/5.29        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.29       => ( ( power_power_real @ ( abs_abs_real @ A ) @ N )
% 9.49/5.29          = ( power_power_real @ A @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6238_power__even__abs,axiom,
% 9.49/5.29      ! [N: nat,A: int] :
% 9.49/5.29        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.29       => ( ( power_power_int @ ( abs_abs_int @ A ) @ N )
% 9.49/5.29          = ( power_power_int @ A @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6239_power2__le__iff__abs__le,axiom,
% 9.49/5.29      ! [Y2: code_integer,X: code_integer] :
% 9.49/5.29        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y2 )
% 9.49/5.29       => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.29          = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ Y2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6240_power2__le__iff__abs__le,axiom,
% 9.49/5.29      ! [Y2: rat,X: rat] :
% 9.49/5.29        ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 9.49/5.29       => ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.29          = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ Y2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6241_power2__le__iff__abs__le,axiom,
% 9.49/5.29      ! [Y2: real,X: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 9.49/5.29       => ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.29          = ( ord_less_eq_real @ ( abs_abs_real @ X ) @ Y2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6242_power2__le__iff__abs__le,axiom,
% 9.49/5.29      ! [Y2: int,X: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 9.49/5.29       => ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.49/5.29          = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ Y2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6243_abs__sqrt__wlog,axiom,
% 9.49/5.29      ! [P: code_integer > code_integer > $o,X: code_integer] :
% 9.49/5.29        ( ! [X3: code_integer] :
% 9.49/5.29            ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X3 )
% 9.49/5.29           => ( P @ X3 @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.49/5.29       => ( P @ ( abs_abs_Code_integer @ X ) @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6244_abs__sqrt__wlog,axiom,
% 9.49/5.29      ! [P: rat > rat > $o,X: rat] :
% 9.49/5.29        ( ! [X3: rat] :
% 9.49/5.29            ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 9.49/5.29           => ( P @ X3 @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.49/5.29       => ( P @ ( abs_abs_rat @ X ) @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6245_abs__sqrt__wlog,axiom,
% 9.49/5.29      ! [P: real > real > $o,X: real] :
% 9.49/5.29        ( ! [X3: real] :
% 9.49/5.29            ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 9.49/5.29           => ( P @ X3 @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.49/5.29       => ( P @ ( abs_abs_real @ X ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6246_abs__sqrt__wlog,axiom,
% 9.49/5.29      ! [P: int > int > $o,X: int] :
% 9.49/5.29        ( ! [X3: int] :
% 9.49/5.29            ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 9.49/5.29           => ( P @ X3 @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.49/5.29       => ( P @ ( abs_abs_int @ X ) @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6247_abs__square__le__1,axiom,
% 9.49/5.29      ! [X: code_integer] :
% 9.49/5.29        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 9.49/5.29        = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6248_abs__square__le__1,axiom,
% 9.49/5.29      ! [X: rat] :
% 9.49/5.29        ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 9.49/5.29        = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6249_abs__square__le__1,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 9.49/5.29        = ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6250_abs__square__le__1,axiom,
% 9.49/5.29      ! [X: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 9.49/5.29        = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6251_abs__square__less__1,axiom,
% 9.49/5.29      ! [X: code_integer] :
% 9.49/5.29        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 9.49/5.29        = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6252_abs__square__less__1,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 9.49/5.29        = ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6253_abs__square__less__1,axiom,
% 9.49/5.29      ! [X: rat] :
% 9.49/5.29        ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 9.49/5.29        = ( ord_less_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6254_abs__square__less__1,axiom,
% 9.49/5.29      ! [X: int] :
% 9.49/5.29        ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 9.49/5.29        = ( ord_less_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6255_power__mono__even,axiom,
% 9.49/5.29      ! [N: nat,A: code_integer,B: code_integer] :
% 9.49/5.29        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.29       => ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) )
% 9.49/5.29         => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6256_power__mono__even,axiom,
% 9.49/5.29      ! [N: nat,A: real,B: real] :
% 9.49/5.29        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.29       => ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) )
% 9.49/5.29         => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6257_power__mono__even,axiom,
% 9.49/5.29      ! [N: nat,A: int,B: int] :
% 9.49/5.29        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.49/5.29       => ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) )
% 9.49/5.29         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6258_abs__ln__one__plus__x__minus__x__bound__nonneg,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.49/5.29       => ( ( ord_less_eq_real @ X @ one_one_real )
% 9.49/5.29         => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6259_of__int__round__le,axiom,
% 9.49/5.29      ! [X: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) @ ( plus_plus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6260_of__int__round__le,axiom,
% 9.49/5.29      ! [X: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6261_of__int__round__ge,axiom,
% 9.49/5.29      ! [X: real] : ( ord_less_eq_real @ ( minus_minus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6262_of__int__round__ge,axiom,
% 9.49/5.29      ! [X: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6263_arctan__double,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 9.49/5.29       => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ X ) )
% 9.49/5.29          = ( arctan @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6264_Sum__Icc__int,axiom,
% 9.49/5.29      ! [M: int,N: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ M @ N )
% 9.49/5.29       => ( ( groups4538972089207619220nt_int
% 9.49/5.29            @ ^ [X2: int] : X2
% 9.49/5.29            @ ( set_or1266510415728281911st_int @ M @ N ) )
% 9.49/5.29          = ( divide_divide_int @ ( minus_minus_int @ ( times_times_int @ N @ ( plus_plus_int @ N @ one_one_int ) ) @ ( times_times_int @ M @ ( minus_minus_int @ M @ one_one_int ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6265_mask__numeral,axiom,
% 9.49/5.29      ! [N: num] :
% 9.49/5.29        ( ( bit_se2002935070580805687sk_nat @ ( numeral_numeral_nat @ N ) )
% 9.49/5.29        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ ( pred_numeral @ N ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6266_mask__numeral,axiom,
% 9.49/5.29      ! [N: num] :
% 9.49/5.29        ( ( bit_se2000444600071755411sk_int @ ( numeral_numeral_nat @ N ) )
% 9.49/5.29        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ ( pred_numeral @ N ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6267_take__bit__rec,axiom,
% 9.49/5.29      ( bit_se2923211474154528505it_int
% 9.49/5.29      = ( ^ [N2: nat,A3: int] : ( if_int @ ( N2 = zero_zero_nat ) @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6268_take__bit__rec,axiom,
% 9.49/5.29      ( bit_se2925701944663578781it_nat
% 9.49/5.29      = ( ^ [N2: nat,A3: nat] : ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6269_num_Osize__gen_I3_J,axiom,
% 9.49/5.29      ! [X33: num] :
% 9.49/5.29        ( ( size_num @ ( bit1 @ X33 ) )
% 9.49/5.29        = ( plus_plus_nat @ ( size_num @ X33 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6270_tanh__real__altdef,axiom,
% 9.49/5.29      ( tanh_real
% 9.49/5.29      = ( ^ [X2: real] : ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 ) ) ) @ ( plus_plus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6271_mask__nat__positive__iff,axiom,
% 9.49/5.29      ! [N: nat] :
% 9.49/5.29        ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 9.49/5.29        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6272_take__bit__of__0,axiom,
% 9.49/5.29      ! [N: nat] :
% 9.49/5.29        ( ( bit_se2923211474154528505it_int @ N @ zero_zero_int )
% 9.49/5.29        = zero_zero_int ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6273_take__bit__of__0,axiom,
% 9.49/5.29      ! [N: nat] :
% 9.49/5.29        ( ( bit_se2925701944663578781it_nat @ N @ zero_zero_nat )
% 9.49/5.29        = zero_zero_nat ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6274_exp__less__cancel__iff,axiom,
% 9.49/5.29      ! [X: real,Y2: real] :
% 9.49/5.29        ( ( ord_less_real @ ( exp_real @ X ) @ ( exp_real @ Y2 ) )
% 9.49/5.29        = ( ord_less_real @ X @ Y2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6275_exp__less__mono,axiom,
% 9.49/5.29      ! [X: real,Y2: real] :
% 9.49/5.29        ( ( ord_less_real @ X @ Y2 )
% 9.49/5.29       => ( ord_less_real @ ( exp_real @ X ) @ ( exp_real @ Y2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6276_take__bit__and,axiom,
% 9.49/5.29      ! [N: nat,A: int,B: int] :
% 9.49/5.29        ( ( bit_se2923211474154528505it_int @ N @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 9.49/5.29        = ( bit_se725231765392027082nd_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_se2923211474154528505it_int @ N @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6277_take__bit__and,axiom,
% 9.49/5.29      ! [N: nat,A: nat,B: nat] :
% 9.49/5.29        ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 9.49/5.29        = ( bit_se727722235901077358nd_nat @ ( bit_se2925701944663578781it_nat @ N @ A ) @ ( bit_se2925701944663578781it_nat @ N @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6278_exp__le__cancel__iff,axiom,
% 9.49/5.29      ! [X: real,Y2: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ ( exp_real @ X ) @ ( exp_real @ Y2 ) )
% 9.49/5.29        = ( ord_less_eq_real @ X @ Y2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6279_concat__bit__of__zero__2,axiom,
% 9.49/5.29      ! [N: nat,K: int] :
% 9.49/5.29        ( ( bit_concat_bit @ N @ K @ zero_zero_int )
% 9.49/5.29        = ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6280_exp__zero,axiom,
% 9.49/5.29      ( ( exp_complex @ zero_zero_complex )
% 9.49/5.29      = one_one_complex ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6281_exp__zero,axiom,
% 9.49/5.29      ( ( exp_real @ zero_zero_real )
% 9.49/5.29      = one_one_real ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6282_take__bit__0,axiom,
% 9.49/5.29      ! [A: int] :
% 9.49/5.29        ( ( bit_se2923211474154528505it_int @ zero_zero_nat @ A )
% 9.49/5.29        = zero_zero_int ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6283_take__bit__0,axiom,
% 9.49/5.29      ! [A: nat] :
% 9.49/5.29        ( ( bit_se2925701944663578781it_nat @ zero_zero_nat @ A )
% 9.49/5.29        = zero_zero_nat ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6284_take__bit__Suc__1,axiom,
% 9.49/5.29      ! [N: nat] :
% 9.49/5.29        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ one_one_int )
% 9.49/5.29        = one_one_int ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6285_take__bit__Suc__1,axiom,
% 9.49/5.29      ! [N: nat] :
% 9.49/5.29        ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ one_one_nat )
% 9.49/5.29        = one_one_nat ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6286_take__bit__numeral__1,axiom,
% 9.49/5.29      ! [L2: num] :
% 9.49/5.29        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ one_one_int )
% 9.49/5.29        = one_one_int ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6287_take__bit__numeral__1,axiom,
% 9.49/5.29      ! [L2: num] :
% 9.49/5.29        ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L2 ) @ one_one_nat )
% 9.49/5.29        = one_one_nat ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6288_mask__eq__0__iff,axiom,
% 9.49/5.29      ! [N: nat] :
% 9.49/5.29        ( ( ( bit_se2002935070580805687sk_nat @ N )
% 9.49/5.29          = zero_zero_nat )
% 9.49/5.29        = ( N = zero_zero_nat ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6289_mask__eq__0__iff,axiom,
% 9.49/5.29      ! [N: nat] :
% 9.49/5.29        ( ( ( bit_se2000444600071755411sk_int @ N )
% 9.49/5.29          = zero_zero_int )
% 9.49/5.29        = ( N = zero_zero_nat ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6290_mask__0,axiom,
% 9.49/5.29      ( ( bit_se2002935070580805687sk_nat @ zero_zero_nat )
% 9.49/5.29      = zero_zero_nat ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6291_mask__0,axiom,
% 9.49/5.29      ( ( bit_se2000444600071755411sk_int @ zero_zero_nat )
% 9.49/5.29      = zero_zero_int ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6292_arctan__less__zero__iff,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_real @ ( arctan @ X ) @ zero_zero_real )
% 9.49/5.29        = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6293_zero__less__arctan__iff,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_real @ zero_zero_real @ ( arctan @ X ) )
% 9.49/5.29        = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6294_exp__eq__one__iff,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ( exp_real @ X )
% 9.49/5.29          = one_one_real )
% 9.49/5.29        = ( X = zero_zero_real ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6295_arctan__le__zero__iff,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ ( arctan @ X ) @ zero_zero_real )
% 9.49/5.29        = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6296_zero__le__arctan__iff,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ zero_zero_real @ ( arctan @ X ) )
% 9.49/5.29        = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6297_sum__abs,axiom,
% 9.49/5.29      ! [F: int > int,A2: set_int] :
% 9.49/5.29        ( ord_less_eq_int @ ( abs_abs_int @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 9.49/5.29        @ ( groups4538972089207619220nt_int
% 9.49/5.29          @ ^ [I3: int] : ( abs_abs_int @ ( F @ I3 ) )
% 9.49/5.29          @ A2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6298_sum__abs,axiom,
% 9.49/5.29      ! [F: nat > real,A2: set_nat] :
% 9.49/5.29        ( ord_less_eq_real @ ( abs_abs_real @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 9.49/5.29        @ ( groups6591440286371151544t_real
% 9.49/5.29          @ ^ [I3: nat] : ( abs_abs_real @ ( F @ I3 ) )
% 9.49/5.29          @ A2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6299_sum_Oinsert,axiom,
% 9.49/5.29      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > real] :
% 9.49/5.29        ( ( finite5795047828879050333T_VEBT @ A2 )
% 9.49/5.29       => ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 9.49/5.29         => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 9.49/5.29            = ( plus_plus_real @ ( G @ X ) @ ( groups2240296850493347238T_real @ G @ A2 ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6300_sum_Oinsert,axiom,
% 9.49/5.29      ! [A2: set_real,X: real,G: real > real] :
% 9.49/5.29        ( ( finite_finite_real @ A2 )
% 9.49/5.29       => ( ~ ( member_real @ X @ A2 )
% 9.49/5.29         => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X @ A2 ) )
% 9.49/5.29            = ( plus_plus_real @ ( G @ X ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6301_sum_Oinsert,axiom,
% 9.49/5.29      ! [A2: set_int,X: int,G: int > real] :
% 9.49/5.29        ( ( finite_finite_int @ A2 )
% 9.49/5.29       => ( ~ ( member_int @ X @ A2 )
% 9.49/5.29         => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X @ A2 ) )
% 9.49/5.29            = ( plus_plus_real @ ( G @ X ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6302_sum_Oinsert,axiom,
% 9.49/5.29      ! [A2: set_complex,X: complex,G: complex > real] :
% 9.49/5.29        ( ( finite3207457112153483333omplex @ A2 )
% 9.49/5.29       => ( ~ ( member_complex @ X @ A2 )
% 9.49/5.29         => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A2 ) )
% 9.49/5.29            = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6303_sum_Oinsert,axiom,
% 9.49/5.29      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 9.49/5.29        ( ( finite5795047828879050333T_VEBT @ A2 )
% 9.49/5.29       => ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 9.49/5.29         => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 9.49/5.29            = ( plus_plus_rat @ ( G @ X ) @ ( groups136491112297645522BT_rat @ G @ A2 ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6304_sum_Oinsert,axiom,
% 9.49/5.29      ! [A2: set_real,X: real,G: real > rat] :
% 9.49/5.29        ( ( finite_finite_real @ A2 )
% 9.49/5.29       => ( ~ ( member_real @ X @ A2 )
% 9.49/5.29         => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X @ A2 ) )
% 9.49/5.29            = ( plus_plus_rat @ ( G @ X ) @ ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6305_sum_Oinsert,axiom,
% 9.49/5.29      ! [A2: set_int,X: int,G: int > rat] :
% 9.49/5.29        ( ( finite_finite_int @ A2 )
% 9.49/5.29       => ( ~ ( member_int @ X @ A2 )
% 9.49/5.29         => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X @ A2 ) )
% 9.49/5.29            = ( plus_plus_rat @ ( G @ X ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6306_sum_Oinsert,axiom,
% 9.49/5.29      ! [A2: set_nat,X: nat,G: nat > rat] :
% 9.49/5.29        ( ( finite_finite_nat @ A2 )
% 9.49/5.29       => ( ~ ( member_nat @ X @ A2 )
% 9.49/5.29         => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A2 ) )
% 9.49/5.29            = ( plus_plus_rat @ ( G @ X ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6307_sum_Oinsert,axiom,
% 9.49/5.29      ! [A2: set_complex,X: complex,G: complex > rat] :
% 9.49/5.29        ( ( finite3207457112153483333omplex @ A2 )
% 9.49/5.29       => ( ~ ( member_complex @ X @ A2 )
% 9.49/5.29         => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X @ A2 ) )
% 9.49/5.29            = ( plus_plus_rat @ ( G @ X ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6308_sum_Oinsert,axiom,
% 9.49/5.29      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > nat] :
% 9.49/5.29        ( ( finite5795047828879050333T_VEBT @ A2 )
% 9.49/5.29       => ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 9.49/5.29         => ( ( groups771621172384141258BT_nat @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 9.49/5.29            = ( plus_plus_nat @ ( G @ X ) @ ( groups771621172384141258BT_nat @ G @ A2 ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6309_take__bit__of__1__eq__0__iff,axiom,
% 9.49/5.29      ! [N: nat] :
% 9.49/5.29        ( ( ( bit_se2923211474154528505it_int @ N @ one_one_int )
% 9.49/5.29          = zero_zero_int )
% 9.49/5.29        = ( N = zero_zero_nat ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6310_take__bit__of__1__eq__0__iff,axiom,
% 9.49/5.29      ! [N: nat] :
% 9.49/5.29        ( ( ( bit_se2925701944663578781it_nat @ N @ one_one_nat )
% 9.49/5.29          = zero_zero_nat )
% 9.49/5.29        = ( N = zero_zero_nat ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6311_mask__Suc__0,axiom,
% 9.49/5.29      ( ( bit_se2002935070580805687sk_nat @ ( suc @ zero_zero_nat ) )
% 9.49/5.29      = one_one_nat ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6312_mask__Suc__0,axiom,
% 9.49/5.29      ( ( bit_se2000444600071755411sk_int @ ( suc @ zero_zero_nat ) )
% 9.49/5.29      = one_one_int ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6313_exp__less__one__iff,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_real @ ( exp_real @ X ) @ one_one_real )
% 9.49/5.29        = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6314_one__less__exp__iff,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_real @ one_one_real @ ( exp_real @ X ) )
% 9.49/5.29        = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6315_one__le__exp__iff,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ one_one_real @ ( exp_real @ X ) )
% 9.49/5.29        = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6316_exp__le__one__iff,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ ( exp_real @ X ) @ one_one_real )
% 9.49/5.29        = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6317_take__bit__minus__one__eq__mask,axiom,
% 9.49/5.29      ! [N: nat] :
% 9.49/5.29        ( ( bit_se1745604003318907178nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.49/5.29        = ( bit_se2119862282449309892nteger @ N ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6318_take__bit__minus__one__eq__mask,axiom,
% 9.49/5.29      ! [N: nat] :
% 9.49/5.29        ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 9.49/5.29        = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6319_exp__ln__iff,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ( exp_real @ ( ln_ln_real @ X ) )
% 9.49/5.29          = X )
% 9.49/5.29        = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6320_exp__ln,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ( ( ord_less_real @ zero_zero_real @ X )
% 9.49/5.29       => ( ( exp_real @ ( ln_ln_real @ X ) )
% 9.49/5.29          = X ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6321_take__bit__of__Suc__0,axiom,
% 9.49/5.29      ! [N: nat] :
% 9.49/5.29        ( ( bit_se2925701944663578781it_nat @ N @ ( suc @ zero_zero_nat ) )
% 9.49/5.29        = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6322_sum__abs__ge__zero,axiom,
% 9.49/5.29      ! [F: int > int,A2: set_int] :
% 9.49/5.29        ( ord_less_eq_int @ zero_zero_int
% 9.49/5.29        @ ( groups4538972089207619220nt_int
% 9.49/5.29          @ ^ [I3: int] : ( abs_abs_int @ ( F @ I3 ) )
% 9.49/5.29          @ A2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6323_sum__abs__ge__zero,axiom,
% 9.49/5.29      ! [F: nat > real,A2: set_nat] :
% 9.49/5.29        ( ord_less_eq_real @ zero_zero_real
% 9.49/5.29        @ ( groups6591440286371151544t_real
% 9.49/5.29          @ ^ [I3: nat] : ( abs_abs_real @ ( F @ I3 ) )
% 9.49/5.29          @ A2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6324_take__bit__of__1,axiom,
% 9.49/5.29      ! [N: nat] :
% 9.49/5.29        ( ( bit_se1745604003318907178nteger @ N @ one_one_Code_integer )
% 9.49/5.29        = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6325_take__bit__of__1,axiom,
% 9.49/5.29      ! [N: nat] :
% 9.49/5.29        ( ( bit_se2923211474154528505it_int @ N @ one_one_int )
% 9.49/5.29        = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6326_take__bit__of__1,axiom,
% 9.49/5.29      ! [N: nat] :
% 9.49/5.29        ( ( bit_se2925701944663578781it_nat @ N @ one_one_nat )
% 9.49/5.29        = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6327_even__take__bit__eq,axiom,
% 9.49/5.29      ! [N: nat,A: code_integer] :
% 9.49/5.29        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1745604003318907178nteger @ N @ A ) )
% 9.49/5.29        = ( ( N = zero_zero_nat )
% 9.49/5.29          | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6328_even__take__bit__eq,axiom,
% 9.49/5.29      ! [N: nat,A: int] :
% 9.49/5.29        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2923211474154528505it_int @ N @ A ) )
% 9.49/5.29        = ( ( N = zero_zero_nat )
% 9.49/5.29          | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6329_even__take__bit__eq,axiom,
% 9.49/5.29      ! [N: nat,A: nat] :
% 9.49/5.29        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2925701944663578781it_nat @ N @ A ) )
% 9.49/5.29        = ( ( N = zero_zero_nat )
% 9.49/5.29          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6330_take__bit__Suc__0,axiom,
% 9.49/5.29      ! [A: int] :
% 9.49/5.29        ( ( bit_se2923211474154528505it_int @ ( suc @ zero_zero_nat ) @ A )
% 9.49/5.29        = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6331_take__bit__Suc__0,axiom,
% 9.49/5.29      ! [A: nat] :
% 9.49/5.29        ( ( bit_se2925701944663578781it_nat @ ( suc @ zero_zero_nat ) @ A )
% 9.49/5.29        = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6332_take__bit__of__exp,axiom,
% 9.49/5.29      ! [M: nat,N: nat] :
% 9.49/5.29        ( ( bit_se1745604003318907178nteger @ M @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.29        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ N @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6333_take__bit__of__exp,axiom,
% 9.49/5.29      ! [M: nat,N: nat] :
% 9.49/5.29        ( ( bit_se2923211474154528505it_int @ M @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.29        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ N @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6334_take__bit__of__exp,axiom,
% 9.49/5.29      ! [M: nat,N: nat] :
% 9.49/5.29        ( ( bit_se2925701944663578781it_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.49/5.29        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ N @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6335_take__bit__of__2,axiom,
% 9.49/5.29      ! [N: nat] :
% 9.49/5.29        ( ( bit_se1745604003318907178nteger @ N @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.49/5.29        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6336_take__bit__of__2,axiom,
% 9.49/5.29      ! [N: nat] :
% 9.49/5.29        ( ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.49/5.29        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6337_take__bit__of__2,axiom,
% 9.49/5.29      ! [N: nat] :
% 9.49/5.29        ( ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.49/5.29        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6338_take__bit__eq__mask,axiom,
% 9.49/5.29      ( bit_se2923211474154528505it_int
% 9.49/5.29      = ( ^ [N2: nat,A3: int] : ( bit_se725231765392027082nd_int @ A3 @ ( bit_se2000444600071755411sk_int @ N2 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6339_take__bit__eq__mask,axiom,
% 9.49/5.29      ( bit_se2925701944663578781it_nat
% 9.49/5.29      = ( ^ [N2: nat,A3: nat] : ( bit_se727722235901077358nd_nat @ A3 @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6340_take__bit__of__int,axiom,
% 9.49/5.29      ! [N: nat,K: int] :
% 9.49/5.29        ( ( bit_se2923211474154528505it_int @ N @ ( ring_1_of_int_int @ K ) )
% 9.49/5.29        = ( ring_1_of_int_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6341_of__int__mask__eq,axiom,
% 9.49/5.29      ! [N: nat] :
% 9.49/5.29        ( ( ring_1_of_int_int @ ( bit_se2000444600071755411sk_int @ N ) )
% 9.49/5.29        = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6342_take__bit__add,axiom,
% 9.49/5.29      ! [N: nat,A: int,B: int] :
% 9.49/5.29        ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_se2923211474154528505it_int @ N @ B ) ) )
% 9.49/5.29        = ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ A @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6343_take__bit__add,axiom,
% 9.49/5.29      ! [N: nat,A: nat,B: nat] :
% 9.49/5.29        ( ( bit_se2925701944663578781it_nat @ N @ ( plus_plus_nat @ ( bit_se2925701944663578781it_nat @ N @ A ) @ ( bit_se2925701944663578781it_nat @ N @ B ) ) )
% 9.49/5.29        = ( bit_se2925701944663578781it_nat @ N @ ( plus_plus_nat @ A @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6344_take__bit__tightened,axiom,
% 9.49/5.29      ! [N: nat,A: int,B: int,M: nat] :
% 9.49/5.29        ( ( ( bit_se2923211474154528505it_int @ N @ A )
% 9.49/5.29          = ( bit_se2923211474154528505it_int @ N @ B ) )
% 9.49/5.29       => ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.29         => ( ( bit_se2923211474154528505it_int @ M @ A )
% 9.49/5.29            = ( bit_se2923211474154528505it_int @ M @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6345_take__bit__tightened,axiom,
% 9.49/5.29      ! [N: nat,A: nat,B: nat,M: nat] :
% 9.49/5.29        ( ( ( bit_se2925701944663578781it_nat @ N @ A )
% 9.49/5.29          = ( bit_se2925701944663578781it_nat @ N @ B ) )
% 9.49/5.29       => ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.29         => ( ( bit_se2925701944663578781it_nat @ M @ A )
% 9.49/5.29            = ( bit_se2925701944663578781it_nat @ M @ B ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6346_take__bit__nat__less__eq__self,axiom,
% 9.49/5.29      ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6347_take__bit__tightened__less__eq__nat,axiom,
% 9.49/5.29      ! [M: nat,N: nat,Q2: nat] :
% 9.49/5.29        ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.29       => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M @ Q2 ) @ ( bit_se2925701944663578781it_nat @ N @ Q2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6348_exp__less__cancel,axiom,
% 9.49/5.29      ! [X: real,Y2: real] :
% 9.49/5.29        ( ( ord_less_real @ ( exp_real @ X ) @ ( exp_real @ Y2 ) )
% 9.49/5.29       => ( ord_less_real @ X @ Y2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6349_exp__times__arg__commute,axiom,
% 9.49/5.29      ! [A2: complex] :
% 9.49/5.29        ( ( times_times_complex @ ( exp_complex @ A2 ) @ A2 )
% 9.49/5.29        = ( times_times_complex @ A2 @ ( exp_complex @ A2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6350_exp__times__arg__commute,axiom,
% 9.49/5.29      ! [A2: real] :
% 9.49/5.29        ( ( times_times_real @ ( exp_real @ A2 ) @ A2 )
% 9.49/5.29        = ( times_times_real @ A2 @ ( exp_real @ A2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6351_take__bit__minus,axiom,
% 9.49/5.29      ! [N: nat,K: int] :
% 9.49/5.29        ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 9.49/5.29        = ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6352_take__bit__mult,axiom,
% 9.49/5.29      ! [N: nat,K: int,L2: int] :
% 9.49/5.29        ( ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( bit_se2923211474154528505it_int @ N @ L2 ) ) )
% 9.49/5.29        = ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ K @ L2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6353_take__bit__diff,axiom,
% 9.49/5.29      ! [N: nat,K: int,L2: int] :
% 9.49/5.29        ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( bit_se2923211474154528505it_int @ N @ L2 ) ) )
% 9.49/5.29        = ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ L2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6354_arctan__monotone,axiom,
% 9.49/5.29      ! [X: real,Y2: real] :
% 9.49/5.29        ( ( ord_less_real @ X @ Y2 )
% 9.49/5.29       => ( ord_less_real @ ( arctan @ X ) @ ( arctan @ Y2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6355_arctan__less__iff,axiom,
% 9.49/5.29      ! [X: real,Y2: real] :
% 9.49/5.29        ( ( ord_less_real @ ( arctan @ X ) @ ( arctan @ Y2 ) )
% 9.49/5.29        = ( ord_less_real @ X @ Y2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6356_arctan__le__iff,axiom,
% 9.49/5.29      ! [X: real,Y2: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ ( arctan @ X ) @ ( arctan @ Y2 ) )
% 9.49/5.29        = ( ord_less_eq_real @ X @ Y2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6357_arctan__monotone_H,axiom,
% 9.49/5.29      ! [X: real,Y2: real] :
% 9.49/5.29        ( ( ord_less_eq_real @ X @ Y2 )
% 9.49/5.29       => ( ord_less_eq_real @ ( arctan @ X ) @ ( arctan @ Y2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6358_concat__bit__take__bit__eq,axiom,
% 9.49/5.29      ! [N: nat,B: int] :
% 9.49/5.29        ( ( bit_concat_bit @ N @ ( bit_se2923211474154528505it_int @ N @ B ) )
% 9.49/5.29        = ( bit_concat_bit @ N @ B ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6359_concat__bit__eq__iff,axiom,
% 9.49/5.29      ! [N: nat,K: int,L2: int,R: int,S3: int] :
% 9.49/5.29        ( ( ( bit_concat_bit @ N @ K @ L2 )
% 9.49/5.29          = ( bit_concat_bit @ N @ R @ S3 ) )
% 9.49/5.29        = ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 9.49/5.29            = ( bit_se2923211474154528505it_int @ N @ R ) )
% 9.49/5.29          & ( L2 = S3 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6360_less__eq__mask,axiom,
% 9.49/5.29      ! [N: nat] : ( ord_less_eq_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6361_sum__mono,axiom,
% 9.49/5.29      ! [K5: set_complex,F: complex > nat,G: complex > nat] :
% 9.49/5.29        ( ! [I4: complex] :
% 9.49/5.29            ( ( member_complex @ I4 @ K5 )
% 9.49/5.29           => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 9.49/5.29       => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ K5 ) @ ( groups5693394587270226106ex_nat @ G @ K5 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6362_sum__mono,axiom,
% 9.49/5.29      ! [K5: set_real,F: real > nat,G: real > nat] :
% 9.49/5.29        ( ! [I4: real] :
% 9.49/5.29            ( ( member_real @ I4 @ K5 )
% 9.49/5.29           => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 9.49/5.29       => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ K5 ) @ ( groups1935376822645274424al_nat @ G @ K5 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6363_sum__mono,axiom,
% 9.49/5.29      ! [K5: set_int,F: int > nat,G: int > nat] :
% 9.49/5.29        ( ! [I4: int] :
% 9.49/5.29            ( ( member_int @ I4 @ K5 )
% 9.49/5.29           => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 9.49/5.29       => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ K5 ) @ ( groups4541462559716669496nt_nat @ G @ K5 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6364_sum__mono,axiom,
% 9.49/5.29      ! [K5: set_complex,F: complex > int,G: complex > int] :
% 9.49/5.29        ( ! [I4: complex] :
% 9.49/5.29            ( ( member_complex @ I4 @ K5 )
% 9.49/5.29           => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 9.49/5.29       => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F @ K5 ) @ ( groups5690904116761175830ex_int @ G @ K5 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6365_sum__mono,axiom,
% 9.49/5.29      ! [K5: set_real,F: real > int,G: real > int] :
% 9.49/5.29        ( ! [I4: real] :
% 9.49/5.29            ( ( member_real @ I4 @ K5 )
% 9.49/5.29           => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 9.49/5.29       => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ K5 ) @ ( groups1932886352136224148al_int @ G @ K5 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6366_sum__mono,axiom,
% 9.49/5.29      ! [K5: set_nat,F: nat > int,G: nat > int] :
% 9.49/5.29        ( ! [I4: nat] :
% 9.49/5.29            ( ( member_nat @ I4 @ K5 )
% 9.49/5.29           => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 9.49/5.29       => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ K5 ) @ ( groups3539618377306564664at_int @ G @ K5 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6367_sum__mono,axiom,
% 9.49/5.29      ! [K5: set_int,F: int > int,G: int > int] :
% 9.49/5.29        ( ! [I4: int] :
% 9.49/5.29            ( ( member_int @ I4 @ K5 )
% 9.49/5.29           => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 9.49/5.29       => ( ord_less_eq_int @ ( groups4538972089207619220nt_int @ F @ K5 ) @ ( groups4538972089207619220nt_int @ G @ K5 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6368_sum__mono,axiom,
% 9.49/5.29      ! [K5: set_nat,F: nat > nat,G: nat > nat] :
% 9.49/5.29        ( ! [I4: nat] :
% 9.49/5.29            ( ( member_nat @ I4 @ K5 )
% 9.49/5.29           => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 9.49/5.29       => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ K5 ) @ ( groups3542108847815614940at_nat @ G @ K5 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6369_sum__mono,axiom,
% 9.49/5.29      ! [K5: set_nat,F: nat > real,G: nat > real] :
% 9.49/5.29        ( ! [I4: nat] :
% 9.49/5.29            ( ( member_nat @ I4 @ K5 )
% 9.49/5.29           => ( ord_less_eq_real @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 9.49/5.29       => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ K5 ) @ ( groups6591440286371151544t_real @ G @ K5 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6370_sum__mono,axiom,
% 9.49/5.29      ! [K5: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat,G: product_prod_nat_nat > nat] :
% 9.49/5.29        ( ! [I4: product_prod_nat_nat] :
% 9.49/5.29            ( ( member8440522571783428010at_nat @ I4 @ K5 )
% 9.49/5.29           => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 9.49/5.29       => ( ord_less_eq_nat @ ( groups977919841031483927at_nat @ F @ K5 ) @ ( groups977919841031483927at_nat @ G @ K5 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6371_sum__product,axiom,
% 9.49/5.29      ! [F: int > int,A2: set_int,G: int > int,B2: set_int] :
% 9.49/5.29        ( ( times_times_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ G @ B2 ) )
% 9.49/5.29        = ( groups4538972089207619220nt_int
% 9.49/5.29          @ ^ [I3: int] :
% 9.49/5.29              ( groups4538972089207619220nt_int
% 9.49/5.29              @ ^ [J3: int] : ( times_times_int @ ( F @ I3 ) @ ( G @ J3 ) )
% 9.49/5.29              @ B2 )
% 9.49/5.29          @ A2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6372_sum__product,axiom,
% 9.49/5.29      ! [F: complex > complex,A2: set_complex,G: complex > complex,B2: set_complex] :
% 9.49/5.29        ( ( times_times_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ ( groups7754918857620584856omplex @ G @ B2 ) )
% 9.49/5.29        = ( groups7754918857620584856omplex
% 9.49/5.29          @ ^ [I3: complex] :
% 9.49/5.29              ( groups7754918857620584856omplex
% 9.49/5.29              @ ^ [J3: complex] : ( times_times_complex @ ( F @ I3 ) @ ( G @ J3 ) )
% 9.49/5.29              @ B2 )
% 9.49/5.29          @ A2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6373_sum__product,axiom,
% 9.49/5.29      ! [F: nat > nat,A2: set_nat,G: nat > nat,B2: set_nat] :
% 9.49/5.29        ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ B2 ) )
% 9.49/5.29        = ( groups3542108847815614940at_nat
% 9.49/5.29          @ ^ [I3: nat] :
% 9.49/5.29              ( groups3542108847815614940at_nat
% 9.49/5.29              @ ^ [J3: nat] : ( times_times_nat @ ( F @ I3 ) @ ( G @ J3 ) )
% 9.49/5.29              @ B2 )
% 9.49/5.29          @ A2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6374_sum__product,axiom,
% 9.49/5.29      ! [F: nat > real,A2: set_nat,G: nat > real,B2: set_nat] :
% 9.49/5.29        ( ( times_times_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ G @ B2 ) )
% 9.49/5.29        = ( groups6591440286371151544t_real
% 9.49/5.29          @ ^ [I3: nat] :
% 9.49/5.29              ( groups6591440286371151544t_real
% 9.49/5.29              @ ^ [J3: nat] : ( times_times_real @ ( F @ I3 ) @ ( G @ J3 ) )
% 9.49/5.29              @ B2 )
% 9.49/5.29          @ A2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6375_sum__distrib__right,axiom,
% 9.49/5.29      ! [F: int > int,A2: set_int,R: int] :
% 9.49/5.29        ( ( times_times_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ R )
% 9.49/5.29        = ( groups4538972089207619220nt_int
% 9.49/5.29          @ ^ [N2: int] : ( times_times_int @ ( F @ N2 ) @ R )
% 9.49/5.29          @ A2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6376_sum__distrib__right,axiom,
% 9.49/5.29      ! [F: complex > complex,A2: set_complex,R: complex] :
% 9.49/5.29        ( ( times_times_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ R )
% 9.49/5.29        = ( groups7754918857620584856omplex
% 9.49/5.29          @ ^ [N2: complex] : ( times_times_complex @ ( F @ N2 ) @ R )
% 9.49/5.29          @ A2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6377_sum__distrib__right,axiom,
% 9.49/5.29      ! [F: nat > nat,A2: set_nat,R: nat] :
% 9.49/5.29        ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ R )
% 9.49/5.29        = ( groups3542108847815614940at_nat
% 9.49/5.29          @ ^ [N2: nat] : ( times_times_nat @ ( F @ N2 ) @ R )
% 9.49/5.29          @ A2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6378_sum__distrib__right,axiom,
% 9.49/5.29      ! [F: nat > real,A2: set_nat,R: real] :
% 9.49/5.29        ( ( times_times_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ R )
% 9.49/5.29        = ( groups6591440286371151544t_real
% 9.49/5.29          @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ R )
% 9.49/5.29          @ A2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6379_sum__distrib__left,axiom,
% 9.49/5.29      ! [R: int,F: int > int,A2: set_int] :
% 9.49/5.29        ( ( times_times_int @ R @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 9.49/5.29        = ( groups4538972089207619220nt_int
% 9.49/5.29          @ ^ [N2: int] : ( times_times_int @ R @ ( F @ N2 ) )
% 9.49/5.29          @ A2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6380_sum__distrib__left,axiom,
% 9.49/5.29      ! [R: complex,F: complex > complex,A2: set_complex] :
% 9.49/5.29        ( ( times_times_complex @ R @ ( groups7754918857620584856omplex @ F @ A2 ) )
% 9.49/5.29        = ( groups7754918857620584856omplex
% 9.49/5.29          @ ^ [N2: complex] : ( times_times_complex @ R @ ( F @ N2 ) )
% 9.49/5.29          @ A2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6381_sum__distrib__left,axiom,
% 9.49/5.29      ! [R: nat,F: nat > nat,A2: set_nat] :
% 9.49/5.29        ( ( times_times_nat @ R @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 9.49/5.29        = ( groups3542108847815614940at_nat
% 9.49/5.29          @ ^ [N2: nat] : ( times_times_nat @ R @ ( F @ N2 ) )
% 9.49/5.29          @ A2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6382_sum__distrib__left,axiom,
% 9.49/5.29      ! [R: real,F: nat > real,A2: set_nat] :
% 9.49/5.29        ( ( times_times_real @ R @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 9.49/5.29        = ( groups6591440286371151544t_real
% 9.49/5.29          @ ^ [N2: nat] : ( times_times_real @ R @ ( F @ N2 ) )
% 9.49/5.29          @ A2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6383_sum_Odistrib,axiom,
% 9.49/5.29      ! [G: int > int,H2: int > int,A2: set_int] :
% 9.49/5.29        ( ( groups4538972089207619220nt_int
% 9.49/5.29          @ ^ [X2: int] : ( plus_plus_int @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 9.49/5.29          @ A2 )
% 9.49/5.29        = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ A2 ) @ ( groups4538972089207619220nt_int @ H2 @ A2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6384_sum_Odistrib,axiom,
% 9.49/5.29      ! [G: complex > complex,H2: complex > complex,A2: set_complex] :
% 9.49/5.29        ( ( groups7754918857620584856omplex
% 9.49/5.29          @ ^ [X2: complex] : ( plus_plus_complex @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 9.49/5.29          @ A2 )
% 9.49/5.29        = ( plus_plus_complex @ ( groups7754918857620584856omplex @ G @ A2 ) @ ( groups7754918857620584856omplex @ H2 @ A2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6385_sum_Odistrib,axiom,
% 9.49/5.29      ! [G: nat > nat,H2: nat > nat,A2: set_nat] :
% 9.49/5.29        ( ( groups3542108847815614940at_nat
% 9.49/5.29          @ ^ [X2: nat] : ( plus_plus_nat @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 9.49/5.29          @ A2 )
% 9.49/5.29        = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ A2 ) @ ( groups3542108847815614940at_nat @ H2 @ A2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6386_sum_Odistrib,axiom,
% 9.49/5.29      ! [G: nat > real,H2: nat > real,A2: set_nat] :
% 9.49/5.29        ( ( groups6591440286371151544t_real
% 9.49/5.29          @ ^ [X2: nat] : ( plus_plus_real @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 9.49/5.29          @ A2 )
% 9.49/5.29        = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ A2 ) @ ( groups6591440286371151544t_real @ H2 @ A2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6387_sum__subtractf,axiom,
% 9.49/5.29      ! [F: int > int,G: int > int,A2: set_int] :
% 9.49/5.29        ( ( groups4538972089207619220nt_int
% 9.49/5.29          @ ^ [X2: int] : ( minus_minus_int @ ( F @ X2 ) @ ( G @ X2 ) )
% 9.49/5.29          @ A2 )
% 9.49/5.29        = ( minus_minus_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ G @ A2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6388_sum__subtractf,axiom,
% 9.49/5.29      ! [F: complex > complex,G: complex > complex,A2: set_complex] :
% 9.49/5.29        ( ( groups7754918857620584856omplex
% 9.49/5.29          @ ^ [X2: complex] : ( minus_minus_complex @ ( F @ X2 ) @ ( G @ X2 ) )
% 9.49/5.29          @ A2 )
% 9.49/5.29        = ( minus_minus_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ ( groups7754918857620584856omplex @ G @ A2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6389_sum__subtractf,axiom,
% 9.49/5.29      ! [F: nat > real,G: nat > real,A2: set_nat] :
% 9.49/5.29        ( ( groups6591440286371151544t_real
% 9.49/5.29          @ ^ [X2: nat] : ( minus_minus_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 9.49/5.29          @ A2 )
% 9.49/5.29        = ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ G @ A2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6390_sum__divide__distrib,axiom,
% 9.49/5.29      ! [F: complex > complex,A2: set_complex,R: complex] :
% 9.49/5.29        ( ( divide1717551699836669952omplex @ ( groups7754918857620584856omplex @ F @ A2 ) @ R )
% 9.49/5.29        = ( groups7754918857620584856omplex
% 9.49/5.29          @ ^ [N2: complex] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ R )
% 9.49/5.29          @ A2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6391_sum__divide__distrib,axiom,
% 9.49/5.29      ! [F: nat > real,A2: set_nat,R: real] :
% 9.49/5.29        ( ( divide_divide_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ R )
% 9.49/5.29        = ( groups6591440286371151544t_real
% 9.49/5.29          @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ R )
% 9.49/5.29          @ A2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6392_mod__sum__eq,axiom,
% 9.49/5.29      ! [F: int > int,A: int,A2: set_int] :
% 9.49/5.29        ( ( modulo_modulo_int
% 9.49/5.29          @ ( groups4538972089207619220nt_int
% 9.49/5.29            @ ^ [I3: int] : ( modulo_modulo_int @ ( F @ I3 ) @ A )
% 9.49/5.29            @ A2 )
% 9.49/5.29          @ A )
% 9.49/5.29        = ( modulo_modulo_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6393_mod__sum__eq,axiom,
% 9.49/5.29      ! [F: nat > nat,A: nat,A2: set_nat] :
% 9.49/5.29        ( ( modulo_modulo_nat
% 9.49/5.29          @ ( groups3542108847815614940at_nat
% 9.49/5.29            @ ^ [I3: nat] : ( modulo_modulo_nat @ ( F @ I3 ) @ A )
% 9.49/5.29            @ A2 )
% 9.49/5.29          @ A )
% 9.49/5.29        = ( modulo_modulo_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6394_take__bit__eq__mask__iff,axiom,
% 9.49/5.29      ! [N: nat,K: int] :
% 9.49/5.29        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 9.49/5.29          = ( bit_se2000444600071755411sk_int @ N ) )
% 9.49/5.29        = ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 9.49/5.29          = zero_zero_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6395_sum__nonpos,axiom,
% 9.49/5.29      ! [A2: set_complex,F: complex > real] :
% 9.49/5.29        ( ! [X3: complex] :
% 9.49/5.29            ( ( member_complex @ X3 @ A2 )
% 9.49/5.29           => ( ord_less_eq_real @ ( F @ X3 ) @ zero_zero_real ) )
% 9.49/5.29       => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6396_sum__nonpos,axiom,
% 9.49/5.29      ! [A2: set_real,F: real > real] :
% 9.49/5.29        ( ! [X3: real] :
% 9.49/5.29            ( ( member_real @ X3 @ A2 )
% 9.49/5.29           => ( ord_less_eq_real @ ( F @ X3 ) @ zero_zero_real ) )
% 9.49/5.29       => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6397_sum__nonpos,axiom,
% 9.49/5.29      ! [A2: set_int,F: int > real] :
% 9.49/5.29        ( ! [X3: int] :
% 9.49/5.29            ( ( member_int @ X3 @ A2 )
% 9.49/5.29           => ( ord_less_eq_real @ ( F @ X3 ) @ zero_zero_real ) )
% 9.49/5.29       => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6398_sum__nonpos,axiom,
% 9.49/5.29      ! [A2: set_complex,F: complex > rat] :
% 9.49/5.29        ( ! [X3: complex] :
% 9.49/5.29            ( ( member_complex @ X3 @ A2 )
% 9.49/5.29           => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 9.49/5.29       => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6399_sum__nonpos,axiom,
% 9.49/5.29      ! [A2: set_real,F: real > rat] :
% 9.49/5.29        ( ! [X3: real] :
% 9.49/5.29            ( ( member_real @ X3 @ A2 )
% 9.49/5.29           => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 9.49/5.29       => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6400_sum__nonpos,axiom,
% 9.49/5.29      ! [A2: set_nat,F: nat > rat] :
% 9.49/5.29        ( ! [X3: nat] :
% 9.49/5.29            ( ( member_nat @ X3 @ A2 )
% 9.49/5.29           => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 9.49/5.29       => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6401_sum__nonpos,axiom,
% 9.49/5.29      ! [A2: set_int,F: int > rat] :
% 9.49/5.29        ( ! [X3: int] :
% 9.49/5.29            ( ( member_int @ X3 @ A2 )
% 9.49/5.29           => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 9.49/5.29       => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6402_sum__nonpos,axiom,
% 9.49/5.29      ! [A2: set_complex,F: complex > nat] :
% 9.49/5.29        ( ! [X3: complex] :
% 9.49/5.29            ( ( member_complex @ X3 @ A2 )
% 9.49/5.29           => ( ord_less_eq_nat @ ( F @ X3 ) @ zero_zero_nat ) )
% 9.49/5.29       => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6403_sum__nonpos,axiom,
% 9.49/5.29      ! [A2: set_real,F: real > nat] :
% 9.49/5.29        ( ! [X3: real] :
% 9.49/5.29            ( ( member_real @ X3 @ A2 )
% 9.49/5.29           => ( ord_less_eq_nat @ ( F @ X3 ) @ zero_zero_nat ) )
% 9.49/5.29       => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6404_sum__nonpos,axiom,
% 9.49/5.29      ! [A2: set_int,F: int > nat] :
% 9.49/5.29        ( ! [X3: int] :
% 9.49/5.29            ( ( member_int @ X3 @ A2 )
% 9.49/5.29           => ( ord_less_eq_nat @ ( F @ X3 ) @ zero_zero_nat ) )
% 9.49/5.29       => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6405_sum__nonneg,axiom,
% 9.49/5.29      ! [A2: set_complex,F: complex > real] :
% 9.49/5.29        ( ! [X3: complex] :
% 9.49/5.29            ( ( member_complex @ X3 @ A2 )
% 9.49/5.29           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 9.49/5.29       => ( ord_less_eq_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ A2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6406_sum__nonneg,axiom,
% 9.49/5.29      ! [A2: set_real,F: real > real] :
% 9.49/5.29        ( ! [X3: real] :
% 9.49/5.29            ( ( member_real @ X3 @ A2 )
% 9.49/5.29           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 9.49/5.29       => ( ord_less_eq_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ A2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6407_sum__nonneg,axiom,
% 9.49/5.29      ! [A2: set_int,F: int > real] :
% 9.49/5.29        ( ! [X3: int] :
% 9.49/5.29            ( ( member_int @ X3 @ A2 )
% 9.49/5.29           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 9.49/5.29       => ( ord_less_eq_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ A2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6408_sum__nonneg,axiom,
% 9.49/5.29      ! [A2: set_complex,F: complex > rat] :
% 9.49/5.29        ( ! [X3: complex] :
% 9.49/5.29            ( ( member_complex @ X3 @ A2 )
% 9.49/5.29           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 9.49/5.29       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6409_sum__nonneg,axiom,
% 9.49/5.29      ! [A2: set_real,F: real > rat] :
% 9.49/5.29        ( ! [X3: real] :
% 9.49/5.29            ( ( member_real @ X3 @ A2 )
% 9.49/5.29           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 9.49/5.29       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6410_sum__nonneg,axiom,
% 9.49/5.29      ! [A2: set_nat,F: nat > rat] :
% 9.49/5.29        ( ! [X3: nat] :
% 9.49/5.29            ( ( member_nat @ X3 @ A2 )
% 9.49/5.29           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 9.49/5.29       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6411_sum__nonneg,axiom,
% 9.49/5.29      ! [A2: set_int,F: int > rat] :
% 9.49/5.29        ( ! [X3: int] :
% 9.49/5.29            ( ( member_int @ X3 @ A2 )
% 9.49/5.29           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 9.49/5.29       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6412_sum__nonneg,axiom,
% 9.49/5.29      ! [A2: set_complex,F: complex > nat] :
% 9.49/5.29        ( ! [X3: complex] :
% 9.49/5.29            ( ( member_complex @ X3 @ A2 )
% 9.49/5.29           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 9.49/5.29       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6413_sum__nonneg,axiom,
% 9.49/5.29      ! [A2: set_real,F: real > nat] :
% 9.49/5.29        ( ! [X3: real] :
% 9.49/5.29            ( ( member_real @ X3 @ A2 )
% 9.49/5.29           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 9.49/5.29       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6414_sum__nonneg,axiom,
% 9.49/5.29      ! [A2: set_int,F: int > nat] :
% 9.49/5.29        ( ! [X3: int] :
% 9.49/5.29            ( ( member_int @ X3 @ A2 )
% 9.49/5.29           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 9.49/5.29       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6415_sum__mono__inv,axiom,
% 9.49/5.29      ! [F: real > nat,I6: set_real,G: real > nat,I2: real] :
% 9.49/5.29        ( ( ( groups1935376822645274424al_nat @ F @ I6 )
% 9.49/5.29          = ( groups1935376822645274424al_nat @ G @ I6 ) )
% 9.49/5.29       => ( ! [I4: real] :
% 9.49/5.29              ( ( member_real @ I4 @ I6 )
% 9.49/5.29             => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 9.49/5.29         => ( ( member_real @ I2 @ I6 )
% 9.49/5.29           => ( ( finite_finite_real @ I6 )
% 9.49/5.29             => ( ( F @ I2 )
% 9.49/5.29                = ( G @ I2 ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6416_sum__mono__inv,axiom,
% 9.49/5.29      ! [F: int > nat,I6: set_int,G: int > nat,I2: int] :
% 9.49/5.29        ( ( ( groups4541462559716669496nt_nat @ F @ I6 )
% 9.49/5.29          = ( groups4541462559716669496nt_nat @ G @ I6 ) )
% 9.49/5.29       => ( ! [I4: int] :
% 9.49/5.29              ( ( member_int @ I4 @ I6 )
% 9.49/5.29             => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 9.49/5.29         => ( ( member_int @ I2 @ I6 )
% 9.49/5.29           => ( ( finite_finite_int @ I6 )
% 9.49/5.29             => ( ( F @ I2 )
% 9.49/5.29                = ( G @ I2 ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6417_sum__mono__inv,axiom,
% 9.49/5.29      ! [F: complex > nat,I6: set_complex,G: complex > nat,I2: complex] :
% 9.49/5.29        ( ( ( groups5693394587270226106ex_nat @ F @ I6 )
% 9.49/5.29          = ( groups5693394587270226106ex_nat @ G @ I6 ) )
% 9.49/5.29       => ( ! [I4: complex] :
% 9.49/5.29              ( ( member_complex @ I4 @ I6 )
% 9.49/5.29             => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 9.49/5.29         => ( ( member_complex @ I2 @ I6 )
% 9.49/5.29           => ( ( finite3207457112153483333omplex @ I6 )
% 9.49/5.29             => ( ( F @ I2 )
% 9.49/5.29                = ( G @ I2 ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6418_sum__mono__inv,axiom,
% 9.49/5.29      ! [F: real > int,I6: set_real,G: real > int,I2: real] :
% 9.49/5.29        ( ( ( groups1932886352136224148al_int @ F @ I6 )
% 9.49/5.29          = ( groups1932886352136224148al_int @ G @ I6 ) )
% 9.49/5.29       => ( ! [I4: real] :
% 9.49/5.29              ( ( member_real @ I4 @ I6 )
% 9.49/5.29             => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 9.49/5.29         => ( ( member_real @ I2 @ I6 )
% 9.49/5.29           => ( ( finite_finite_real @ I6 )
% 9.49/5.29             => ( ( F @ I2 )
% 9.49/5.29                = ( G @ I2 ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6419_sum__mono__inv,axiom,
% 9.49/5.29      ! [F: nat > int,I6: set_nat,G: nat > int,I2: nat] :
% 9.49/5.29        ( ( ( groups3539618377306564664at_int @ F @ I6 )
% 9.49/5.29          = ( groups3539618377306564664at_int @ G @ I6 ) )
% 9.49/5.29       => ( ! [I4: nat] :
% 9.49/5.29              ( ( member_nat @ I4 @ I6 )
% 9.49/5.29             => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 9.49/5.29         => ( ( member_nat @ I2 @ I6 )
% 9.49/5.29           => ( ( finite_finite_nat @ I6 )
% 9.49/5.29             => ( ( F @ I2 )
% 9.49/5.29                = ( G @ I2 ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6420_sum__mono__inv,axiom,
% 9.49/5.29      ! [F: complex > int,I6: set_complex,G: complex > int,I2: complex] :
% 9.49/5.29        ( ( ( groups5690904116761175830ex_int @ F @ I6 )
% 9.49/5.29          = ( groups5690904116761175830ex_int @ G @ I6 ) )
% 9.49/5.29       => ( ! [I4: complex] :
% 9.49/5.29              ( ( member_complex @ I4 @ I6 )
% 9.49/5.29             => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 9.49/5.29         => ( ( member_complex @ I2 @ I6 )
% 9.49/5.29           => ( ( finite3207457112153483333omplex @ I6 )
% 9.49/5.29             => ( ( F @ I2 )
% 9.49/5.29                = ( G @ I2 ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6421_sum__mono__inv,axiom,
% 9.49/5.29      ! [F: int > int,I6: set_int,G: int > int,I2: int] :
% 9.49/5.29        ( ( ( groups4538972089207619220nt_int @ F @ I6 )
% 9.49/5.29          = ( groups4538972089207619220nt_int @ G @ I6 ) )
% 9.49/5.29       => ( ! [I4: int] :
% 9.49/5.29              ( ( member_int @ I4 @ I6 )
% 9.49/5.29             => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 9.49/5.29         => ( ( member_int @ I2 @ I6 )
% 9.49/5.29           => ( ( finite_finite_int @ I6 )
% 9.49/5.29             => ( ( F @ I2 )
% 9.49/5.29                = ( G @ I2 ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6422_sum__mono__inv,axiom,
% 9.49/5.29      ! [F: nat > nat,I6: set_nat,G: nat > nat,I2: nat] :
% 9.49/5.29        ( ( ( groups3542108847815614940at_nat @ F @ I6 )
% 9.49/5.29          = ( groups3542108847815614940at_nat @ G @ I6 ) )
% 9.49/5.29       => ( ! [I4: nat] :
% 9.49/5.29              ( ( member_nat @ I4 @ I6 )
% 9.49/5.29             => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 9.49/5.29         => ( ( member_nat @ I2 @ I6 )
% 9.49/5.29           => ( ( finite_finite_nat @ I6 )
% 9.49/5.29             => ( ( F @ I2 )
% 9.49/5.29                = ( G @ I2 ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6423_sum__mono__inv,axiom,
% 9.49/5.29      ! [F: nat > real,I6: set_nat,G: nat > real,I2: nat] :
% 9.49/5.29        ( ( ( groups6591440286371151544t_real @ F @ I6 )
% 9.49/5.29          = ( groups6591440286371151544t_real @ G @ I6 ) )
% 9.49/5.29       => ( ! [I4: nat] :
% 9.49/5.29              ( ( member_nat @ I4 @ I6 )
% 9.49/5.29             => ( ord_less_eq_real @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 9.49/5.29         => ( ( member_nat @ I2 @ I6 )
% 9.49/5.29           => ( ( finite_finite_nat @ I6 )
% 9.49/5.29             => ( ( F @ I2 )
% 9.49/5.29                = ( G @ I2 ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6424_sum__mono__inv,axiom,
% 9.49/5.29      ! [F: product_prod_nat_nat > nat,I6: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > nat,I2: product_prod_nat_nat] :
% 9.49/5.29        ( ( ( groups977919841031483927at_nat @ F @ I6 )
% 9.49/5.29          = ( groups977919841031483927at_nat @ G @ I6 ) )
% 9.49/5.29       => ( ! [I4: product_prod_nat_nat] :
% 9.49/5.29              ( ( member8440522571783428010at_nat @ I4 @ I6 )
% 9.49/5.29             => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 9.49/5.29         => ( ( member8440522571783428010at_nat @ I2 @ I6 )
% 9.49/5.29           => ( ( finite6177210948735845034at_nat @ I6 )
% 9.49/5.29             => ( ( F @ I2 )
% 9.49/5.29                = ( G @ I2 ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6425_not__exp__less__zero,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ~ ( ord_less_real @ ( exp_real @ X ) @ zero_zero_real ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6426_exp__gt__zero,axiom,
% 9.49/5.29      ! [X: real] : ( ord_less_real @ zero_zero_real @ ( exp_real @ X ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6427_exp__total,axiom,
% 9.49/5.29      ! [Y2: real] :
% 9.49/5.29        ( ( ord_less_real @ zero_zero_real @ Y2 )
% 9.49/5.29       => ? [X3: real] :
% 9.49/5.29            ( ( exp_real @ X3 )
% 9.49/5.29            = Y2 ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6428_not__exp__le__zero,axiom,
% 9.49/5.29      ! [X: real] :
% 9.49/5.29        ~ ( ord_less_eq_real @ ( exp_real @ X ) @ zero_zero_real ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6429_exp__ge__zero,axiom,
% 9.49/5.29      ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( exp_real @ X ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6430_take__bit__tightened__less__eq__int,axiom,
% 9.49/5.29      ! [M: nat,N: nat,K: int] :
% 9.49/5.29        ( ( ord_less_eq_nat @ M @ N )
% 9.49/5.29       => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M @ K ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6431_signed__take__bit__eq__iff__take__bit__eq,axiom,
% 9.49/5.29      ! [N: nat,A: int,B: int] :
% 9.49/5.29        ( ( ( bit_ri631733984087533419it_int @ N @ A )
% 9.49/5.29          = ( bit_ri631733984087533419it_int @ N @ B ) )
% 9.49/5.29        = ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A )
% 9.49/5.29          = ( bit_se2923211474154528505it_int @ ( suc @ N ) @ B ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6432_take__bit__int__less__eq__self__iff,axiom,
% 9.49/5.29      ! [N: nat,K: int] :
% 9.49/5.29        ( ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 9.49/5.29        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6433_take__bit__nonnegative,axiom,
% 9.49/5.29      ! [N: nat,K: int] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6434_not__take__bit__negative,axiom,
% 9.49/5.29      ! [N: nat,K: int] :
% 9.49/5.29        ~ ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ zero_zero_int ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6435_take__bit__int__greater__self__iff,axiom,
% 9.49/5.29      ! [K: int,N: nat] :
% 9.49/5.29        ( ( ord_less_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 9.49/5.29        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6436_signed__take__bit__take__bit,axiom,
% 9.49/5.29      ! [M: nat,N: nat,A: int] :
% 9.49/5.29        ( ( bit_ri631733984087533419it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) )
% 9.49/5.29        = ( if_int_int @ ( ord_less_eq_nat @ N @ M ) @ ( bit_se2923211474154528505it_int @ N ) @ ( bit_ri631733984087533419it_int @ M ) @ A ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6437_exp__add__commuting,axiom,
% 9.49/5.29      ! [X: complex,Y2: complex] :
% 9.49/5.29        ( ( ( times_times_complex @ X @ Y2 )
% 9.49/5.29          = ( times_times_complex @ Y2 @ X ) )
% 9.49/5.29       => ( ( exp_complex @ ( plus_plus_complex @ X @ Y2 ) )
% 9.49/5.29          = ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ Y2 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6438_exp__add__commuting,axiom,
% 9.49/5.29      ! [X: real,Y2: real] :
% 9.49/5.29        ( ( ( times_times_real @ X @ Y2 )
% 9.49/5.29          = ( times_times_real @ Y2 @ X ) )
% 9.49/5.29       => ( ( exp_real @ ( plus_plus_real @ X @ Y2 ) )
% 9.49/5.29          = ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ Y2 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6439_mult__exp__exp,axiom,
% 9.49/5.29      ! [X: complex,Y2: complex] :
% 9.49/5.29        ( ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ Y2 ) )
% 9.49/5.29        = ( exp_complex @ ( plus_plus_complex @ X @ Y2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6440_mult__exp__exp,axiom,
% 9.49/5.29      ! [X: real,Y2: real] :
% 9.49/5.29        ( ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ Y2 ) )
% 9.49/5.29        = ( exp_real @ ( plus_plus_real @ X @ Y2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6441_exp__diff,axiom,
% 9.49/5.29      ! [X: complex,Y2: complex] :
% 9.49/5.29        ( ( exp_complex @ ( minus_minus_complex @ X @ Y2 ) )
% 9.49/5.29        = ( divide1717551699836669952omplex @ ( exp_complex @ X ) @ ( exp_complex @ Y2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6442_exp__diff,axiom,
% 9.49/5.29      ! [X: real,Y2: real] :
% 9.49/5.29        ( ( exp_real @ ( minus_minus_real @ X @ Y2 ) )
% 9.49/5.29        = ( divide_divide_real @ ( exp_real @ X ) @ ( exp_real @ Y2 ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6443_take__bit__unset__bit__eq,axiom,
% 9.49/5.29      ! [N: nat,M: nat,A: int] :
% 9.49/5.29        ( ( ( ord_less_eq_nat @ N @ M )
% 9.49/5.29         => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 9.49/5.29            = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 9.49/5.29        & ( ~ ( ord_less_eq_nat @ N @ M )
% 9.49/5.29         => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 9.49/5.29            = ( bit_se4203085406695923979it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6444_take__bit__unset__bit__eq,axiom,
% 9.49/5.29      ! [N: nat,M: nat,A: nat] :
% 9.49/5.29        ( ( ( ord_less_eq_nat @ N @ M )
% 9.49/5.29         => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 9.49/5.29            = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 9.49/5.29        & ( ~ ( ord_less_eq_nat @ N @ M )
% 9.49/5.29         => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 9.49/5.29            = ( bit_se4205575877204974255it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6445_take__bit__set__bit__eq,axiom,
% 9.49/5.29      ! [N: nat,M: nat,A: int] :
% 9.49/5.29        ( ( ( ord_less_eq_nat @ N @ M )
% 9.49/5.29         => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 9.49/5.29            = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 9.49/5.29        & ( ~ ( ord_less_eq_nat @ N @ M )
% 9.49/5.29         => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 9.49/5.29            = ( bit_se7879613467334960850it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6446_take__bit__set__bit__eq,axiom,
% 9.49/5.29      ! [N: nat,M: nat,A: nat] :
% 9.49/5.29        ( ( ( ord_less_eq_nat @ N @ M )
% 9.49/5.29         => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 9.49/5.29            = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 9.49/5.29        & ( ~ ( ord_less_eq_nat @ N @ M )
% 9.49/5.29         => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 9.49/5.29            = ( bit_se7882103937844011126it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6447_take__bit__flip__bit__eq,axiom,
% 9.49/5.29      ! [N: nat,M: nat,A: int] :
% 9.49/5.29        ( ( ( ord_less_eq_nat @ N @ M )
% 9.49/5.29         => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 9.49/5.29            = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 9.49/5.29        & ( ~ ( ord_less_eq_nat @ N @ M )
% 9.49/5.29         => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 9.49/5.29            = ( bit_se2159334234014336723it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6448_take__bit__flip__bit__eq,axiom,
% 9.49/5.29      ! [N: nat,M: nat,A: nat] :
% 9.49/5.29        ( ( ( ord_less_eq_nat @ N @ M )
% 9.49/5.29         => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 9.49/5.29            = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 9.49/5.29        & ( ~ ( ord_less_eq_nat @ N @ M )
% 9.49/5.29         => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 9.49/5.29            = ( bit_se2161824704523386999it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6449_abs__div,axiom,
% 9.49/5.29      ! [Y2: int,X: int] :
% 9.49/5.29        ( ( dvd_dvd_int @ Y2 @ X )
% 9.49/5.29       => ( ( abs_abs_int @ ( divide_divide_int @ X @ Y2 ) )
% 9.49/5.29          = ( divide_divide_int @ ( abs_abs_int @ X ) @ ( abs_abs_int @ Y2 ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6450_mask__nonnegative__int,axiom,
% 9.49/5.29      ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2000444600071755411sk_int @ N ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6451_not__mask__negative__int,axiom,
% 9.49/5.29      ! [N: nat] :
% 9.49/5.29        ~ ( ord_less_int @ ( bit_se2000444600071755411sk_int @ N ) @ zero_zero_int ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6452_sum__nonneg__eq__0__iff,axiom,
% 9.49/5.29      ! [A2: set_real,F: real > real] :
% 9.49/5.29        ( ( finite_finite_real @ A2 )
% 9.49/5.29       => ( ! [X3: real] :
% 9.49/5.29              ( ( member_real @ X3 @ A2 )
% 9.49/5.29             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 9.49/5.29         => ( ( ( groups8097168146408367636l_real @ F @ A2 )
% 9.49/5.29              = zero_zero_real )
% 9.49/5.29            = ( ! [X2: real] :
% 9.49/5.29                  ( ( member_real @ X2 @ A2 )
% 9.49/5.29                 => ( ( F @ X2 )
% 9.49/5.29                    = zero_zero_real ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6453_sum__nonneg__eq__0__iff,axiom,
% 9.49/5.29      ! [A2: set_int,F: int > real] :
% 9.49/5.29        ( ( finite_finite_int @ A2 )
% 9.49/5.29       => ( ! [X3: int] :
% 9.49/5.29              ( ( member_int @ X3 @ A2 )
% 9.49/5.29             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 9.49/5.29         => ( ( ( groups8778361861064173332t_real @ F @ A2 )
% 9.49/5.29              = zero_zero_real )
% 9.49/5.29            = ( ! [X2: int] :
% 9.49/5.29                  ( ( member_int @ X2 @ A2 )
% 9.49/5.29                 => ( ( F @ X2 )
% 9.49/5.29                    = zero_zero_real ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6454_sum__nonneg__eq__0__iff,axiom,
% 9.49/5.29      ! [A2: set_complex,F: complex > real] :
% 9.49/5.29        ( ( finite3207457112153483333omplex @ A2 )
% 9.49/5.29       => ( ! [X3: complex] :
% 9.49/5.29              ( ( member_complex @ X3 @ A2 )
% 9.49/5.29             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 9.49/5.29         => ( ( ( groups5808333547571424918x_real @ F @ A2 )
% 9.49/5.29              = zero_zero_real )
% 9.49/5.29            = ( ! [X2: complex] :
% 9.49/5.29                  ( ( member_complex @ X2 @ A2 )
% 9.49/5.29                 => ( ( F @ X2 )
% 9.49/5.29                    = zero_zero_real ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6455_sum__nonneg__eq__0__iff,axiom,
% 9.49/5.29      ! [A2: set_real,F: real > rat] :
% 9.49/5.29        ( ( finite_finite_real @ A2 )
% 9.49/5.29       => ( ! [X3: real] :
% 9.49/5.29              ( ( member_real @ X3 @ A2 )
% 9.49/5.29             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 9.49/5.29         => ( ( ( groups1300246762558778688al_rat @ F @ A2 )
% 9.49/5.29              = zero_zero_rat )
% 9.49/5.29            = ( ! [X2: real] :
% 9.49/5.29                  ( ( member_real @ X2 @ A2 )
% 9.49/5.29                 => ( ( F @ X2 )
% 9.49/5.29                    = zero_zero_rat ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6456_sum__nonneg__eq__0__iff,axiom,
% 9.49/5.29      ! [A2: set_int,F: int > rat] :
% 9.49/5.29        ( ( finite_finite_int @ A2 )
% 9.49/5.29       => ( ! [X3: int] :
% 9.49/5.29              ( ( member_int @ X3 @ A2 )
% 9.49/5.29             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 9.49/5.29         => ( ( ( groups3906332499630173760nt_rat @ F @ A2 )
% 9.49/5.29              = zero_zero_rat )
% 9.49/5.29            = ( ! [X2: int] :
% 9.49/5.29                  ( ( member_int @ X2 @ A2 )
% 9.49/5.29                 => ( ( F @ X2 )
% 9.49/5.29                    = zero_zero_rat ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6457_sum__nonneg__eq__0__iff,axiom,
% 9.49/5.29      ! [A2: set_nat,F: nat > rat] :
% 9.49/5.29        ( ( finite_finite_nat @ A2 )
% 9.49/5.29       => ( ! [X3: nat] :
% 9.49/5.29              ( ( member_nat @ X3 @ A2 )
% 9.49/5.29             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 9.49/5.29         => ( ( ( groups2906978787729119204at_rat @ F @ A2 )
% 9.49/5.29              = zero_zero_rat )
% 9.49/5.29            = ( ! [X2: nat] :
% 9.49/5.29                  ( ( member_nat @ X2 @ A2 )
% 9.49/5.29                 => ( ( F @ X2 )
% 9.49/5.29                    = zero_zero_rat ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6458_sum__nonneg__eq__0__iff,axiom,
% 9.49/5.29      ! [A2: set_complex,F: complex > rat] :
% 9.49/5.29        ( ( finite3207457112153483333omplex @ A2 )
% 9.49/5.29       => ( ! [X3: complex] :
% 9.49/5.29              ( ( member_complex @ X3 @ A2 )
% 9.49/5.29             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 9.49/5.29         => ( ( ( groups5058264527183730370ex_rat @ F @ A2 )
% 9.49/5.29              = zero_zero_rat )
% 9.49/5.29            = ( ! [X2: complex] :
% 9.49/5.29                  ( ( member_complex @ X2 @ A2 )
% 9.49/5.29                 => ( ( F @ X2 )
% 9.49/5.29                    = zero_zero_rat ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6459_sum__nonneg__eq__0__iff,axiom,
% 9.49/5.29      ! [A2: set_real,F: real > nat] :
% 9.49/5.29        ( ( finite_finite_real @ A2 )
% 9.49/5.29       => ( ! [X3: real] :
% 9.49/5.29              ( ( member_real @ X3 @ A2 )
% 9.49/5.29             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 9.49/5.29         => ( ( ( groups1935376822645274424al_nat @ F @ A2 )
% 9.49/5.29              = zero_zero_nat )
% 9.49/5.29            = ( ! [X2: real] :
% 9.49/5.29                  ( ( member_real @ X2 @ A2 )
% 9.49/5.29                 => ( ( F @ X2 )
% 9.49/5.29                    = zero_zero_nat ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6460_sum__nonneg__eq__0__iff,axiom,
% 9.49/5.29      ! [A2: set_int,F: int > nat] :
% 9.49/5.29        ( ( finite_finite_int @ A2 )
% 9.49/5.29       => ( ! [X3: int] :
% 9.49/5.29              ( ( member_int @ X3 @ A2 )
% 9.49/5.29             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 9.49/5.29         => ( ( ( groups4541462559716669496nt_nat @ F @ A2 )
% 9.49/5.29              = zero_zero_nat )
% 9.49/5.29            = ( ! [X2: int] :
% 9.49/5.29                  ( ( member_int @ X2 @ A2 )
% 9.49/5.29                 => ( ( F @ X2 )
% 9.49/5.29                    = zero_zero_nat ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6461_sum__nonneg__eq__0__iff,axiom,
% 9.49/5.29      ! [A2: set_complex,F: complex > nat] :
% 9.49/5.29        ( ( finite3207457112153483333omplex @ A2 )
% 9.49/5.29       => ( ! [X3: complex] :
% 9.49/5.29              ( ( member_complex @ X3 @ A2 )
% 9.49/5.29             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 9.49/5.29         => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 9.49/5.29              = zero_zero_nat )
% 9.49/5.29            = ( ! [X2: complex] :
% 9.49/5.29                  ( ( member_complex @ X2 @ A2 )
% 9.49/5.29                 => ( ( F @ X2 )
% 9.49/5.29                    = zero_zero_nat ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6462_sum__le__included,axiom,
% 9.49/5.29      ! [S3: set_complex,T: set_complex,G: complex > real,I2: complex > complex,F: complex > real] :
% 9.49/5.29        ( ( finite3207457112153483333omplex @ S3 )
% 9.49/5.29       => ( ( finite3207457112153483333omplex @ T )
% 9.49/5.29         => ( ! [X3: complex] :
% 9.49/5.29                ( ( member_complex @ X3 @ T )
% 9.49/5.29               => ( ord_less_eq_real @ zero_zero_real @ ( G @ X3 ) ) )
% 9.49/5.29           => ( ! [X3: complex] :
% 9.49/5.29                  ( ( member_complex @ X3 @ S3 )
% 9.49/5.29                 => ? [Xa: complex] :
% 9.49/5.29                      ( ( member_complex @ Xa @ T )
% 9.49/5.29                      & ( ( I2 @ Xa )
% 9.49/5.29                        = X3 )
% 9.49/5.29                      & ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 9.49/5.29             => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S3 ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6463_sum__le__included,axiom,
% 9.49/5.29      ! [S3: set_nat,T: set_nat,G: nat > rat,I2: nat > nat,F: nat > rat] :
% 9.49/5.29        ( ( finite_finite_nat @ S3 )
% 9.49/5.29       => ( ( finite_finite_nat @ T )
% 9.49/5.29         => ( ! [X3: nat] :
% 9.49/5.29                ( ( member_nat @ X3 @ T )
% 9.49/5.29               => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 9.49/5.29           => ( ! [X3: nat] :
% 9.49/5.29                  ( ( member_nat @ X3 @ S3 )
% 9.49/5.29                 => ? [Xa: nat] :
% 9.49/5.29                      ( ( member_nat @ Xa @ T )
% 9.49/5.29                      & ( ( I2 @ Xa )
% 9.49/5.29                        = X3 )
% 9.49/5.29                      & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 9.49/5.29             => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S3 ) @ ( groups2906978787729119204at_rat @ G @ T ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6464_sum__le__included,axiom,
% 9.49/5.29      ! [S3: set_nat,T: set_complex,G: complex > rat,I2: complex > nat,F: nat > rat] :
% 9.49/5.29        ( ( finite_finite_nat @ S3 )
% 9.49/5.29       => ( ( finite3207457112153483333omplex @ T )
% 9.49/5.29         => ( ! [X3: complex] :
% 9.49/5.29                ( ( member_complex @ X3 @ T )
% 9.49/5.29               => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 9.49/5.29           => ( ! [X3: nat] :
% 9.49/5.29                  ( ( member_nat @ X3 @ S3 )
% 9.49/5.29                 => ? [Xa: complex] :
% 9.49/5.29                      ( ( member_complex @ Xa @ T )
% 9.49/5.29                      & ( ( I2 @ Xa )
% 9.49/5.29                        = X3 )
% 9.49/5.29                      & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 9.49/5.29             => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S3 ) @ ( groups5058264527183730370ex_rat @ G @ T ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6465_sum__le__included,axiom,
% 9.49/5.29      ! [S3: set_complex,T: set_nat,G: nat > rat,I2: nat > complex,F: complex > rat] :
% 9.49/5.29        ( ( finite3207457112153483333omplex @ S3 )
% 9.49/5.29       => ( ( finite_finite_nat @ T )
% 9.49/5.29         => ( ! [X3: nat] :
% 9.49/5.29                ( ( member_nat @ X3 @ T )
% 9.49/5.29               => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 9.49/5.29           => ( ! [X3: complex] :
% 9.49/5.29                  ( ( member_complex @ X3 @ S3 )
% 9.49/5.29                 => ? [Xa: nat] :
% 9.49/5.29                      ( ( member_nat @ Xa @ T )
% 9.49/5.29                      & ( ( I2 @ Xa )
% 9.49/5.29                        = X3 )
% 9.49/5.29                      & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 9.49/5.29             => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ S3 ) @ ( groups2906978787729119204at_rat @ G @ T ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6466_sum__le__included,axiom,
% 9.49/5.29      ! [S3: set_complex,T: set_complex,G: complex > rat,I2: complex > complex,F: complex > rat] :
% 9.49/5.29        ( ( finite3207457112153483333omplex @ S3 )
% 9.49/5.29       => ( ( finite3207457112153483333omplex @ T )
% 9.49/5.29         => ( ! [X3: complex] :
% 9.49/5.29                ( ( member_complex @ X3 @ T )
% 9.49/5.29               => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 9.49/5.29           => ( ! [X3: complex] :
% 9.49/5.29                  ( ( member_complex @ X3 @ S3 )
% 9.49/5.29                 => ? [Xa: complex] :
% 9.49/5.29                      ( ( member_complex @ Xa @ T )
% 9.49/5.29                      & ( ( I2 @ Xa )
% 9.49/5.29                        = X3 )
% 9.49/5.29                      & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 9.49/5.29             => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ S3 ) @ ( groups5058264527183730370ex_rat @ G @ T ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6467_sum__le__included,axiom,
% 9.49/5.29      ! [S3: set_complex,T: set_complex,G: complex > nat,I2: complex > complex,F: complex > nat] :
% 9.49/5.29        ( ( finite3207457112153483333omplex @ S3 )
% 9.49/5.29       => ( ( finite3207457112153483333omplex @ T )
% 9.49/5.29         => ( ! [X3: complex] :
% 9.49/5.29                ( ( member_complex @ X3 @ T )
% 9.49/5.29               => ( ord_less_eq_nat @ zero_zero_nat @ ( G @ X3 ) ) )
% 9.49/5.29           => ( ! [X3: complex] :
% 9.49/5.29                  ( ( member_complex @ X3 @ S3 )
% 9.49/5.29                 => ? [Xa: complex] :
% 9.49/5.29                      ( ( member_complex @ Xa @ T )
% 9.49/5.29                      & ( ( I2 @ Xa )
% 9.49/5.29                        = X3 )
% 9.49/5.29                      & ( ord_less_eq_nat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 9.49/5.29             => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ S3 ) @ ( groups5693394587270226106ex_nat @ G @ T ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6468_sum__le__included,axiom,
% 9.49/5.29      ! [S3: set_nat,T: set_nat,G: nat > int,I2: nat > nat,F: nat > int] :
% 9.49/5.29        ( ( finite_finite_nat @ S3 )
% 9.49/5.29       => ( ( finite_finite_nat @ T )
% 9.49/5.29         => ( ! [X3: nat] :
% 9.49/5.29                ( ( member_nat @ X3 @ T )
% 9.49/5.29               => ( ord_less_eq_int @ zero_zero_int @ ( G @ X3 ) ) )
% 9.49/5.29           => ( ! [X3: nat] :
% 9.49/5.29                  ( ( member_nat @ X3 @ S3 )
% 9.49/5.29                 => ? [Xa: nat] :
% 9.49/5.29                      ( ( member_nat @ Xa @ T )
% 9.49/5.29                      & ( ( I2 @ Xa )
% 9.49/5.29                        = X3 )
% 9.49/5.29                      & ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 9.49/5.29             => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ S3 ) @ ( groups3539618377306564664at_int @ G @ T ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6469_sum__le__included,axiom,
% 9.49/5.29      ! [S3: set_nat,T: set_complex,G: complex > int,I2: complex > nat,F: nat > int] :
% 9.49/5.29        ( ( finite_finite_nat @ S3 )
% 9.49/5.29       => ( ( finite3207457112153483333omplex @ T )
% 9.49/5.29         => ( ! [X3: complex] :
% 9.49/5.29                ( ( member_complex @ X3 @ T )
% 9.49/5.29               => ( ord_less_eq_int @ zero_zero_int @ ( G @ X3 ) ) )
% 9.49/5.29           => ( ! [X3: nat] :
% 9.49/5.29                  ( ( member_nat @ X3 @ S3 )
% 9.49/5.29                 => ? [Xa: complex] :
% 9.49/5.29                      ( ( member_complex @ Xa @ T )
% 9.49/5.29                      & ( ( I2 @ Xa )
% 9.49/5.29                        = X3 )
% 9.49/5.29                      & ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 9.49/5.29             => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ S3 ) @ ( groups5690904116761175830ex_int @ G @ T ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6470_sum__le__included,axiom,
% 9.49/5.29      ! [S3: set_complex,T: set_nat,G: nat > int,I2: nat > complex,F: complex > int] :
% 9.49/5.29        ( ( finite3207457112153483333omplex @ S3 )
% 9.49/5.29       => ( ( finite_finite_nat @ T )
% 9.49/5.29         => ( ! [X3: nat] :
% 9.49/5.29                ( ( member_nat @ X3 @ T )
% 9.49/5.29               => ( ord_less_eq_int @ zero_zero_int @ ( G @ X3 ) ) )
% 9.49/5.29           => ( ! [X3: complex] :
% 9.49/5.29                  ( ( member_complex @ X3 @ S3 )
% 9.49/5.29                 => ? [Xa: nat] :
% 9.49/5.29                      ( ( member_nat @ Xa @ T )
% 9.49/5.29                      & ( ( I2 @ Xa )
% 9.49/5.29                        = X3 )
% 9.49/5.29                      & ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 9.49/5.29             => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F @ S3 ) @ ( groups3539618377306564664at_int @ G @ T ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6471_sum__le__included,axiom,
% 9.49/5.29      ! [S3: set_complex,T: set_complex,G: complex > int,I2: complex > complex,F: complex > int] :
% 9.49/5.29        ( ( finite3207457112153483333omplex @ S3 )
% 9.49/5.29       => ( ( finite3207457112153483333omplex @ T )
% 9.49/5.29         => ( ! [X3: complex] :
% 9.49/5.29                ( ( member_complex @ X3 @ T )
% 9.49/5.29               => ( ord_less_eq_int @ zero_zero_int @ ( G @ X3 ) ) )
% 9.49/5.29           => ( ! [X3: complex] :
% 9.49/5.29                  ( ( member_complex @ X3 @ S3 )
% 9.49/5.29                 => ? [Xa: complex] :
% 9.49/5.29                      ( ( member_complex @ Xa @ T )
% 9.49/5.29                      & ( ( I2 @ Xa )
% 9.49/5.29                        = X3 )
% 9.49/5.29                      & ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 9.49/5.29             => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F @ S3 ) @ ( groups5690904116761175830ex_int @ G @ T ) ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6472_sum__strict__mono__ex1,axiom,
% 9.49/5.29      ! [A2: set_complex,F: complex > real,G: complex > real] :
% 9.49/5.29        ( ( finite3207457112153483333omplex @ A2 )
% 9.49/5.29       => ( ! [X3: complex] :
% 9.49/5.29              ( ( member_complex @ X3 @ A2 )
% 9.49/5.29             => ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 9.49/5.29         => ( ? [X5: complex] :
% 9.49/5.29                ( ( member_complex @ X5 @ A2 )
% 9.49/5.29                & ( ord_less_real @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 9.49/5.29           => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6473_sum__strict__mono__ex1,axiom,
% 9.49/5.29      ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 9.49/5.29        ( ( finite_finite_nat @ A2 )
% 9.49/5.29       => ( ! [X3: nat] :
% 9.49/5.29              ( ( member_nat @ X3 @ A2 )
% 9.49/5.29             => ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 9.49/5.29         => ( ? [X5: nat] :
% 9.49/5.29                ( ( member_nat @ X5 @ A2 )
% 9.49/5.29                & ( ord_less_rat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 9.49/5.29           => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6474_sum__strict__mono__ex1,axiom,
% 9.49/5.29      ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 9.49/5.29        ( ( finite3207457112153483333omplex @ A2 )
% 9.49/5.29       => ( ! [X3: complex] :
% 9.49/5.29              ( ( member_complex @ X3 @ A2 )
% 9.49/5.29             => ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 9.49/5.29         => ( ? [X5: complex] :
% 9.49/5.29                ( ( member_complex @ X5 @ A2 )
% 9.49/5.29                & ( ord_less_rat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 9.49/5.29           => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6475_sum__strict__mono__ex1,axiom,
% 9.49/5.29      ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 9.49/5.29        ( ( finite3207457112153483333omplex @ A2 )
% 9.49/5.29       => ( ! [X3: complex] :
% 9.49/5.29              ( ( member_complex @ X3 @ A2 )
% 9.49/5.29             => ( ord_less_eq_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 9.49/5.29         => ( ? [X5: complex] :
% 9.49/5.29                ( ( member_complex @ X5 @ A2 )
% 9.49/5.29                & ( ord_less_nat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 9.49/5.29           => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6476_sum__strict__mono__ex1,axiom,
% 9.49/5.29      ! [A2: set_nat,F: nat > int,G: nat > int] :
% 9.49/5.29        ( ( finite_finite_nat @ A2 )
% 9.49/5.29       => ( ! [X3: nat] :
% 9.49/5.29              ( ( member_nat @ X3 @ A2 )
% 9.49/5.29             => ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 9.49/5.29         => ( ? [X5: nat] :
% 9.49/5.29                ( ( member_nat @ X5 @ A2 )
% 9.49/5.29                & ( ord_less_int @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 9.49/5.29           => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ G @ A2 ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6477_sum__strict__mono__ex1,axiom,
% 9.49/5.29      ! [A2: set_complex,F: complex > int,G: complex > int] :
% 9.49/5.29        ( ( finite3207457112153483333omplex @ A2 )
% 9.49/5.29       => ( ! [X3: complex] :
% 9.49/5.29              ( ( member_complex @ X3 @ A2 )
% 9.49/5.29             => ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 9.49/5.29         => ( ? [X5: complex] :
% 9.49/5.29                ( ( member_complex @ X5 @ A2 )
% 9.49/5.29                & ( ord_less_int @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 9.49/5.29           => ( ord_less_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ G @ A2 ) ) ) ) ) ).
% 9.49/5.29  
% 9.49/5.29  thf(fact_6478_sum__strict__mono__ex1,axiom,
% 9.49/5.29      ! [A2: set_int,F: int > int,G: int > int] :
% 9.49/5.30        ( ( finite_finite_int @ A2 )
% 9.49/5.30       => ( ! [X3: int] :
% 9.49/5.30              ( ( member_int @ X3 @ A2 )
% 9.49/5.30             => ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 9.49/5.30         => ( ? [X5: int] :
% 9.49/5.30                ( ( member_int @ X5 @ A2 )
% 9.49/5.30                & ( ord_less_int @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 9.49/5.30           => ( ord_less_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ G @ A2 ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6479_sum__strict__mono__ex1,axiom,
% 9.49/5.30      ! [A2: set_nat,F: nat > nat,G: nat > nat] :
% 9.49/5.30        ( ( finite_finite_nat @ A2 )
% 9.49/5.30       => ( ! [X3: nat] :
% 9.49/5.30              ( ( member_nat @ X3 @ A2 )
% 9.49/5.30             => ( ord_less_eq_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 9.49/5.30         => ( ? [X5: nat] :
% 9.49/5.30                ( ( member_nat @ X5 @ A2 )
% 9.49/5.30                & ( ord_less_nat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 9.49/5.30           => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6480_sum__strict__mono__ex1,axiom,
% 9.49/5.30      ! [A2: set_nat,F: nat > real,G: nat > real] :
% 9.49/5.30        ( ( finite_finite_nat @ A2 )
% 9.49/5.30       => ( ! [X3: nat] :
% 9.49/5.30              ( ( member_nat @ X3 @ A2 )
% 9.49/5.30             => ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 9.49/5.30         => ( ? [X5: nat] :
% 9.49/5.30                ( ( member_nat @ X5 @ A2 )
% 9.49/5.30                & ( ord_less_real @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 9.49/5.30           => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ G @ A2 ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6481_sum_Orelated,axiom,
% 9.49/5.30      ! [R2: complex > complex > $o,S2: set_nat,H2: nat > complex,G: nat > complex] :
% 9.49/5.30        ( ( R2 @ zero_zero_complex @ zero_zero_complex )
% 9.49/5.30       => ( ! [X15: complex,Y15: complex,X22: complex,Y23: complex] :
% 9.49/5.30              ( ( ( R2 @ X15 @ X22 )
% 9.49/5.30                & ( R2 @ Y15 @ Y23 ) )
% 9.49/5.30             => ( R2 @ ( plus_plus_complex @ X15 @ Y15 ) @ ( plus_plus_complex @ X22 @ Y23 ) ) )
% 9.49/5.30         => ( ( finite_finite_nat @ S2 )
% 9.49/5.30           => ( ! [X3: nat] :
% 9.49/5.30                  ( ( member_nat @ X3 @ S2 )
% 9.49/5.30                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 9.49/5.30             => ( R2 @ ( groups2073611262835488442omplex @ H2 @ S2 ) @ ( groups2073611262835488442omplex @ G @ S2 ) ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6482_sum_Orelated,axiom,
% 9.49/5.30      ! [R2: real > real > $o,S2: set_complex,H2: complex > real,G: complex > real] :
% 9.49/5.30        ( ( R2 @ zero_zero_real @ zero_zero_real )
% 9.49/5.30       => ( ! [X15: real,Y15: real,X22: real,Y23: real] :
% 9.49/5.30              ( ( ( R2 @ X15 @ X22 )
% 9.49/5.30                & ( R2 @ Y15 @ Y23 ) )
% 9.49/5.30             => ( R2 @ ( plus_plus_real @ X15 @ Y15 ) @ ( plus_plus_real @ X22 @ Y23 ) ) )
% 9.49/5.30         => ( ( finite3207457112153483333omplex @ S2 )
% 9.49/5.30           => ( ! [X3: complex] :
% 9.49/5.30                  ( ( member_complex @ X3 @ S2 )
% 9.49/5.30                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 9.49/5.30             => ( R2 @ ( groups5808333547571424918x_real @ H2 @ S2 ) @ ( groups5808333547571424918x_real @ G @ S2 ) ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6483_sum_Orelated,axiom,
% 9.49/5.30      ! [R2: rat > rat > $o,S2: set_nat,H2: nat > rat,G: nat > rat] :
% 9.49/5.30        ( ( R2 @ zero_zero_rat @ zero_zero_rat )
% 9.49/5.30       => ( ! [X15: rat,Y15: rat,X22: rat,Y23: rat] :
% 9.49/5.30              ( ( ( R2 @ X15 @ X22 )
% 9.49/5.30                & ( R2 @ Y15 @ Y23 ) )
% 9.49/5.30             => ( R2 @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X22 @ Y23 ) ) )
% 9.49/5.30         => ( ( finite_finite_nat @ S2 )
% 9.49/5.30           => ( ! [X3: nat] :
% 9.49/5.30                  ( ( member_nat @ X3 @ S2 )
% 9.49/5.30                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 9.49/5.30             => ( R2 @ ( groups2906978787729119204at_rat @ H2 @ S2 ) @ ( groups2906978787729119204at_rat @ G @ S2 ) ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6484_sum_Orelated,axiom,
% 9.49/5.30      ! [R2: rat > rat > $o,S2: set_complex,H2: complex > rat,G: complex > rat] :
% 9.49/5.30        ( ( R2 @ zero_zero_rat @ zero_zero_rat )
% 9.49/5.30       => ( ! [X15: rat,Y15: rat,X22: rat,Y23: rat] :
% 9.49/5.30              ( ( ( R2 @ X15 @ X22 )
% 9.49/5.30                & ( R2 @ Y15 @ Y23 ) )
% 9.49/5.30             => ( R2 @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X22 @ Y23 ) ) )
% 9.49/5.30         => ( ( finite3207457112153483333omplex @ S2 )
% 9.49/5.30           => ( ! [X3: complex] :
% 9.49/5.30                  ( ( member_complex @ X3 @ S2 )
% 9.49/5.30                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 9.49/5.30             => ( R2 @ ( groups5058264527183730370ex_rat @ H2 @ S2 ) @ ( groups5058264527183730370ex_rat @ G @ S2 ) ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6485_sum_Orelated,axiom,
% 9.49/5.30      ! [R2: nat > nat > $o,S2: set_complex,H2: complex > nat,G: complex > nat] :
% 9.49/5.30        ( ( R2 @ zero_zero_nat @ zero_zero_nat )
% 9.49/5.30       => ( ! [X15: nat,Y15: nat,X22: nat,Y23: nat] :
% 9.49/5.30              ( ( ( R2 @ X15 @ X22 )
% 9.49/5.30                & ( R2 @ Y15 @ Y23 ) )
% 9.49/5.30             => ( R2 @ ( plus_plus_nat @ X15 @ Y15 ) @ ( plus_plus_nat @ X22 @ Y23 ) ) )
% 9.49/5.30         => ( ( finite3207457112153483333omplex @ S2 )
% 9.49/5.30           => ( ! [X3: complex] :
% 9.49/5.30                  ( ( member_complex @ X3 @ S2 )
% 9.49/5.30                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 9.49/5.30             => ( R2 @ ( groups5693394587270226106ex_nat @ H2 @ S2 ) @ ( groups5693394587270226106ex_nat @ G @ S2 ) ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6486_sum_Orelated,axiom,
% 9.49/5.30      ! [R2: int > int > $o,S2: set_nat,H2: nat > int,G: nat > int] :
% 9.49/5.30        ( ( R2 @ zero_zero_int @ zero_zero_int )
% 9.49/5.30       => ( ! [X15: int,Y15: int,X22: int,Y23: int] :
% 9.49/5.30              ( ( ( R2 @ X15 @ X22 )
% 9.49/5.30                & ( R2 @ Y15 @ Y23 ) )
% 9.49/5.30             => ( R2 @ ( plus_plus_int @ X15 @ Y15 ) @ ( plus_plus_int @ X22 @ Y23 ) ) )
% 9.49/5.30         => ( ( finite_finite_nat @ S2 )
% 9.49/5.30           => ( ! [X3: nat] :
% 9.49/5.30                  ( ( member_nat @ X3 @ S2 )
% 9.49/5.30                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 9.49/5.30             => ( R2 @ ( groups3539618377306564664at_int @ H2 @ S2 ) @ ( groups3539618377306564664at_int @ G @ S2 ) ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6487_sum_Orelated,axiom,
% 9.49/5.30      ! [R2: int > int > $o,S2: set_complex,H2: complex > int,G: complex > int] :
% 9.49/5.30        ( ( R2 @ zero_zero_int @ zero_zero_int )
% 9.49/5.30       => ( ! [X15: int,Y15: int,X22: int,Y23: int] :
% 9.49/5.30              ( ( ( R2 @ X15 @ X22 )
% 9.49/5.30                & ( R2 @ Y15 @ Y23 ) )
% 9.49/5.30             => ( R2 @ ( plus_plus_int @ X15 @ Y15 ) @ ( plus_plus_int @ X22 @ Y23 ) ) )
% 9.49/5.30         => ( ( finite3207457112153483333omplex @ S2 )
% 9.49/5.30           => ( ! [X3: complex] :
% 9.49/5.30                  ( ( member_complex @ X3 @ S2 )
% 9.49/5.30                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 9.49/5.30             => ( R2 @ ( groups5690904116761175830ex_int @ H2 @ S2 ) @ ( groups5690904116761175830ex_int @ G @ S2 ) ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6488_sum_Orelated,axiom,
% 9.49/5.30      ! [R2: int > int > $o,S2: set_int,H2: int > int,G: int > int] :
% 9.49/5.30        ( ( R2 @ zero_zero_int @ zero_zero_int )
% 9.49/5.30       => ( ! [X15: int,Y15: int,X22: int,Y23: int] :
% 9.49/5.30              ( ( ( R2 @ X15 @ X22 )
% 9.49/5.30                & ( R2 @ Y15 @ Y23 ) )
% 9.49/5.30             => ( R2 @ ( plus_plus_int @ X15 @ Y15 ) @ ( plus_plus_int @ X22 @ Y23 ) ) )
% 9.49/5.30         => ( ( finite_finite_int @ S2 )
% 9.49/5.30           => ( ! [X3: int] :
% 9.49/5.30                  ( ( member_int @ X3 @ S2 )
% 9.49/5.30                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 9.49/5.30             => ( R2 @ ( groups4538972089207619220nt_int @ H2 @ S2 ) @ ( groups4538972089207619220nt_int @ G @ S2 ) ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6489_sum_Orelated,axiom,
% 9.49/5.30      ! [R2: complex > complex > $o,S2: set_complex,H2: complex > complex,G: complex > complex] :
% 9.49/5.30        ( ( R2 @ zero_zero_complex @ zero_zero_complex )
% 9.49/5.30       => ( ! [X15: complex,Y15: complex,X22: complex,Y23: complex] :
% 9.49/5.30              ( ( ( R2 @ X15 @ X22 )
% 9.49/5.30                & ( R2 @ Y15 @ Y23 ) )
% 9.49/5.30             => ( R2 @ ( plus_plus_complex @ X15 @ Y15 ) @ ( plus_plus_complex @ X22 @ Y23 ) ) )
% 9.49/5.30         => ( ( finite3207457112153483333omplex @ S2 )
% 9.49/5.30           => ( ! [X3: complex] :
% 9.49/5.30                  ( ( member_complex @ X3 @ S2 )
% 9.49/5.30                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 9.49/5.30             => ( R2 @ ( groups7754918857620584856omplex @ H2 @ S2 ) @ ( groups7754918857620584856omplex @ G @ S2 ) ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6490_sum_Orelated,axiom,
% 9.49/5.30      ! [R2: nat > nat > $o,S2: set_nat,H2: nat > nat,G: nat > nat] :
% 9.49/5.30        ( ( R2 @ zero_zero_nat @ zero_zero_nat )
% 9.49/5.30       => ( ! [X15: nat,Y15: nat,X22: nat,Y23: nat] :
% 9.49/5.30              ( ( ( R2 @ X15 @ X22 )
% 9.49/5.30                & ( R2 @ Y15 @ Y23 ) )
% 9.49/5.30             => ( R2 @ ( plus_plus_nat @ X15 @ Y15 ) @ ( plus_plus_nat @ X22 @ Y23 ) ) )
% 9.49/5.30         => ( ( finite_finite_nat @ S2 )
% 9.49/5.30           => ( ! [X3: nat] :
% 9.49/5.30                  ( ( member_nat @ X3 @ S2 )
% 9.49/5.30                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 9.49/5.30             => ( R2 @ ( groups3542108847815614940at_nat @ H2 @ S2 ) @ ( groups3542108847815614940at_nat @ G @ S2 ) ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6491_sum__strict__mono,axiom,
% 9.49/5.30      ! [A2: set_complex,F: complex > real,G: complex > real] :
% 9.49/5.30        ( ( finite3207457112153483333omplex @ A2 )
% 9.49/5.30       => ( ( A2 != bot_bot_set_complex )
% 9.49/5.30         => ( ! [X3: complex] :
% 9.49/5.30                ( ( member_complex @ X3 @ A2 )
% 9.49/5.30               => ( ord_less_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 9.49/5.30           => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6492_sum__strict__mono,axiom,
% 9.49/5.30      ! [A2: set_int,F: int > real,G: int > real] :
% 9.49/5.30        ( ( finite_finite_int @ A2 )
% 9.49/5.30       => ( ( A2 != bot_bot_set_int )
% 9.49/5.30         => ( ! [X3: int] :
% 9.49/5.30                ( ( member_int @ X3 @ A2 )
% 9.49/5.30               => ( ord_less_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 9.49/5.30           => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6493_sum__strict__mono,axiom,
% 9.49/5.30      ! [A2: set_real,F: real > real,G: real > real] :
% 9.49/5.30        ( ( finite_finite_real @ A2 )
% 9.49/5.30       => ( ( A2 != bot_bot_set_real )
% 9.49/5.30         => ( ! [X3: real] :
% 9.49/5.30                ( ( member_real @ X3 @ A2 )
% 9.49/5.30               => ( ord_less_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 9.49/5.30           => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6494_sum__strict__mono,axiom,
% 9.49/5.30      ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 9.49/5.30        ( ( finite3207457112153483333omplex @ A2 )
% 9.49/5.30       => ( ( A2 != bot_bot_set_complex )
% 9.49/5.30         => ( ! [X3: complex] :
% 9.49/5.30                ( ( member_complex @ X3 @ A2 )
% 9.49/5.30               => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 9.49/5.30           => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6495_sum__strict__mono,axiom,
% 9.49/5.30      ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 9.49/5.30        ( ( finite_finite_nat @ A2 )
% 9.49/5.30       => ( ( A2 != bot_bot_set_nat )
% 9.49/5.30         => ( ! [X3: nat] :
% 9.49/5.30                ( ( member_nat @ X3 @ A2 )
% 9.49/5.30               => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 9.49/5.30           => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6496_sum__strict__mono,axiom,
% 9.49/5.30      ! [A2: set_int,F: int > rat,G: int > rat] :
% 9.49/5.30        ( ( finite_finite_int @ A2 )
% 9.49/5.30       => ( ( A2 != bot_bot_set_int )
% 9.49/5.30         => ( ! [X3: int] :
% 9.49/5.30                ( ( member_int @ X3 @ A2 )
% 9.49/5.30               => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 9.49/5.30           => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6497_sum__strict__mono,axiom,
% 9.49/5.30      ! [A2: set_real,F: real > rat,G: real > rat] :
% 9.49/5.30        ( ( finite_finite_real @ A2 )
% 9.49/5.30       => ( ( A2 != bot_bot_set_real )
% 9.49/5.30         => ( ! [X3: real] :
% 9.49/5.30                ( ( member_real @ X3 @ A2 )
% 9.49/5.30               => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 9.49/5.30           => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6498_sum__strict__mono,axiom,
% 9.49/5.30      ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 9.49/5.30        ( ( finite3207457112153483333omplex @ A2 )
% 9.49/5.30       => ( ( A2 != bot_bot_set_complex )
% 9.49/5.30         => ( ! [X3: complex] :
% 9.49/5.30                ( ( member_complex @ X3 @ A2 )
% 9.49/5.30               => ( ord_less_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 9.49/5.30           => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6499_sum__strict__mono,axiom,
% 9.49/5.30      ! [A2: set_int,F: int > nat,G: int > nat] :
% 9.49/5.30        ( ( finite_finite_int @ A2 )
% 9.49/5.30       => ( ( A2 != bot_bot_set_int )
% 9.49/5.30         => ( ! [X3: int] :
% 9.49/5.30                ( ( member_int @ X3 @ A2 )
% 9.49/5.30               => ( ord_less_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 9.49/5.30           => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6500_sum__strict__mono,axiom,
% 9.49/5.30      ! [A2: set_real,F: real > nat,G: real > nat] :
% 9.49/5.30        ( ( finite_finite_real @ A2 )
% 9.49/5.30       => ( ( A2 != bot_bot_set_real )
% 9.49/5.30         => ( ! [X3: real] :
% 9.49/5.30                ( ( member_real @ X3 @ A2 )
% 9.49/5.30               => ( ord_less_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 9.49/5.30           => ( ord_less_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6501_sum_Oinsert__if,axiom,
% 9.49/5.30      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > real] :
% 9.49/5.30        ( ( finite5795047828879050333T_VEBT @ A2 )
% 9.49/5.30       => ( ( ( member_VEBT_VEBT @ X @ A2 )
% 9.49/5.30           => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 9.49/5.30              = ( groups2240296850493347238T_real @ G @ A2 ) ) )
% 9.49/5.30          & ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 9.49/5.30           => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 9.49/5.30              = ( plus_plus_real @ ( G @ X ) @ ( groups2240296850493347238T_real @ G @ A2 ) ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6502_sum_Oinsert__if,axiom,
% 9.49/5.30      ! [A2: set_real,X: real,G: real > real] :
% 9.49/5.30        ( ( finite_finite_real @ A2 )
% 9.49/5.30       => ( ( ( member_real @ X @ A2 )
% 9.49/5.30           => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X @ A2 ) )
% 9.49/5.30              = ( groups8097168146408367636l_real @ G @ A2 ) ) )
% 9.49/5.30          & ( ~ ( member_real @ X @ A2 )
% 9.49/5.30           => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X @ A2 ) )
% 9.49/5.30              = ( plus_plus_real @ ( G @ X ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6503_sum_Oinsert__if,axiom,
% 9.49/5.30      ! [A2: set_int,X: int,G: int > real] :
% 9.49/5.30        ( ( finite_finite_int @ A2 )
% 9.49/5.30       => ( ( ( member_int @ X @ A2 )
% 9.49/5.30           => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X @ A2 ) )
% 9.49/5.30              = ( groups8778361861064173332t_real @ G @ A2 ) ) )
% 9.49/5.30          & ( ~ ( member_int @ X @ A2 )
% 9.49/5.30           => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X @ A2 ) )
% 9.49/5.30              = ( plus_plus_real @ ( G @ X ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6504_sum_Oinsert__if,axiom,
% 9.49/5.30      ! [A2: set_complex,X: complex,G: complex > real] :
% 9.49/5.30        ( ( finite3207457112153483333omplex @ A2 )
% 9.49/5.30       => ( ( ( member_complex @ X @ A2 )
% 9.49/5.30           => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A2 ) )
% 9.49/5.30              = ( groups5808333547571424918x_real @ G @ A2 ) ) )
% 9.49/5.30          & ( ~ ( member_complex @ X @ A2 )
% 9.49/5.30           => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A2 ) )
% 9.49/5.30              = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6505_sum_Oinsert__if,axiom,
% 9.49/5.30      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 9.49/5.30        ( ( finite5795047828879050333T_VEBT @ A2 )
% 9.49/5.30       => ( ( ( member_VEBT_VEBT @ X @ A2 )
% 9.49/5.30           => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 9.49/5.30              = ( groups136491112297645522BT_rat @ G @ A2 ) ) )
% 9.49/5.30          & ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 9.49/5.30           => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 9.49/5.30              = ( plus_plus_rat @ ( G @ X ) @ ( groups136491112297645522BT_rat @ G @ A2 ) ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6506_sum_Oinsert__if,axiom,
% 9.49/5.30      ! [A2: set_real,X: real,G: real > rat] :
% 9.49/5.30        ( ( finite_finite_real @ A2 )
% 9.49/5.30       => ( ( ( member_real @ X @ A2 )
% 9.49/5.30           => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X @ A2 ) )
% 9.49/5.30              = ( groups1300246762558778688al_rat @ G @ A2 ) ) )
% 9.49/5.30          & ( ~ ( member_real @ X @ A2 )
% 9.49/5.30           => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X @ A2 ) )
% 9.49/5.30              = ( plus_plus_rat @ ( G @ X ) @ ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6507_sum_Oinsert__if,axiom,
% 9.49/5.30      ! [A2: set_int,X: int,G: int > rat] :
% 9.49/5.30        ( ( finite_finite_int @ A2 )
% 9.49/5.30       => ( ( ( member_int @ X @ A2 )
% 9.49/5.30           => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X @ A2 ) )
% 9.49/5.30              = ( groups3906332499630173760nt_rat @ G @ A2 ) ) )
% 9.49/5.30          & ( ~ ( member_int @ X @ A2 )
% 9.49/5.30           => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X @ A2 ) )
% 9.49/5.30              = ( plus_plus_rat @ ( G @ X ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6508_sum_Oinsert__if,axiom,
% 9.49/5.30      ! [A2: set_nat,X: nat,G: nat > rat] :
% 9.49/5.30        ( ( finite_finite_nat @ A2 )
% 9.49/5.30       => ( ( ( member_nat @ X @ A2 )
% 9.49/5.30           => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A2 ) )
% 9.49/5.30              = ( groups2906978787729119204at_rat @ G @ A2 ) ) )
% 9.49/5.30          & ( ~ ( member_nat @ X @ A2 )
% 9.49/5.30           => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A2 ) )
% 9.49/5.30              = ( plus_plus_rat @ ( G @ X ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6509_sum_Oinsert__if,axiom,
% 9.49/5.30      ! [A2: set_complex,X: complex,G: complex > rat] :
% 9.49/5.30        ( ( finite3207457112153483333omplex @ A2 )
% 9.49/5.30       => ( ( ( member_complex @ X @ A2 )
% 9.49/5.30           => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X @ A2 ) )
% 9.49/5.30              = ( groups5058264527183730370ex_rat @ G @ A2 ) ) )
% 9.49/5.30          & ( ~ ( member_complex @ X @ A2 )
% 9.49/5.30           => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X @ A2 ) )
% 9.49/5.30              = ( plus_plus_rat @ ( G @ X ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6510_sum_Oinsert__if,axiom,
% 9.49/5.30      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > nat] :
% 9.49/5.30        ( ( finite5795047828879050333T_VEBT @ A2 )
% 9.49/5.30       => ( ( ( member_VEBT_VEBT @ X @ A2 )
% 9.49/5.30           => ( ( groups771621172384141258BT_nat @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 9.49/5.30              = ( groups771621172384141258BT_nat @ G @ A2 ) ) )
% 9.49/5.30          & ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 9.49/5.30           => ( ( groups771621172384141258BT_nat @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 9.49/5.30              = ( plus_plus_nat @ ( G @ X ) @ ( groups771621172384141258BT_nat @ G @ A2 ) ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6511_sum_Oreindex__bij__witness__not__neutral,axiom,
% 9.49/5.30      ! [S5: set_real,T5: set_real,S2: set_real,I2: real > real,J: real > real,T4: set_real,G: real > complex,H2: real > complex] :
% 9.49/5.30        ( ( finite_finite_real @ S5 )
% 9.49/5.30       => ( ( finite_finite_real @ T5 )
% 9.49/5.30         => ( ! [A4: real] :
% 9.49/5.30                ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 9.49/5.30               => ( ( I2 @ ( J @ A4 ) )
% 9.49/5.30                  = A4 ) )
% 9.49/5.30           => ( ! [A4: real] :
% 9.49/5.30                  ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 9.49/5.30                 => ( member_real @ ( J @ A4 ) @ ( minus_minus_set_real @ T4 @ T5 ) ) )
% 9.49/5.30             => ( ! [B3: real] :
% 9.49/5.30                    ( ( member_real @ B3 @ ( minus_minus_set_real @ T4 @ T5 ) )
% 9.49/5.30                   => ( ( J @ ( I2 @ B3 ) )
% 9.49/5.30                      = B3 ) )
% 9.49/5.30               => ( ! [B3: real] :
% 9.49/5.30                      ( ( member_real @ B3 @ ( minus_minus_set_real @ T4 @ T5 ) )
% 9.49/5.30                     => ( member_real @ ( I2 @ B3 ) @ ( minus_minus_set_real @ S2 @ S5 ) ) )
% 9.49/5.30                 => ( ! [A4: real] :
% 9.49/5.30                        ( ( member_real @ A4 @ S5 )
% 9.49/5.30                       => ( ( G @ A4 )
% 9.49/5.30                          = zero_zero_complex ) )
% 9.49/5.30                   => ( ! [B3: real] :
% 9.49/5.30                          ( ( member_real @ B3 @ T5 )
% 9.49/5.30                         => ( ( H2 @ B3 )
% 9.49/5.30                            = zero_zero_complex ) )
% 9.49/5.30                     => ( ! [A4: real] :
% 9.49/5.30                            ( ( member_real @ A4 @ S2 )
% 9.49/5.30                           => ( ( H2 @ ( J @ A4 ) )
% 9.49/5.30                              = ( G @ A4 ) ) )
% 9.49/5.30                       => ( ( groups5754745047067104278omplex @ G @ S2 )
% 9.49/5.30                          = ( groups5754745047067104278omplex @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6512_sum_Oreindex__bij__witness__not__neutral,axiom,
% 9.49/5.30      ! [S5: set_real,T5: set_int,S2: set_real,I2: int > real,J: real > int,T4: set_int,G: real > complex,H2: int > complex] :
% 9.49/5.30        ( ( finite_finite_real @ S5 )
% 9.49/5.30       => ( ( finite_finite_int @ T5 )
% 9.49/5.30         => ( ! [A4: real] :
% 9.49/5.30                ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 9.49/5.30               => ( ( I2 @ ( J @ A4 ) )
% 9.49/5.30                  = A4 ) )
% 9.49/5.30           => ( ! [A4: real] :
% 9.49/5.30                  ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 9.49/5.30                 => ( member_int @ ( J @ A4 ) @ ( minus_minus_set_int @ T4 @ T5 ) ) )
% 9.49/5.30             => ( ! [B3: int] :
% 9.49/5.30                    ( ( member_int @ B3 @ ( minus_minus_set_int @ T4 @ T5 ) )
% 9.49/5.30                   => ( ( J @ ( I2 @ B3 ) )
% 9.49/5.30                      = B3 ) )
% 9.49/5.30               => ( ! [B3: int] :
% 9.49/5.30                      ( ( member_int @ B3 @ ( minus_minus_set_int @ T4 @ T5 ) )
% 9.49/5.30                     => ( member_real @ ( I2 @ B3 ) @ ( minus_minus_set_real @ S2 @ S5 ) ) )
% 9.49/5.30                 => ( ! [A4: real] :
% 9.49/5.30                        ( ( member_real @ A4 @ S5 )
% 9.49/5.30                       => ( ( G @ A4 )
% 9.49/5.30                          = zero_zero_complex ) )
% 9.49/5.30                   => ( ! [B3: int] :
% 9.49/5.30                          ( ( member_int @ B3 @ T5 )
% 9.49/5.30                         => ( ( H2 @ B3 )
% 9.49/5.30                            = zero_zero_complex ) )
% 9.49/5.30                     => ( ! [A4: real] :
% 9.49/5.30                            ( ( member_real @ A4 @ S2 )
% 9.49/5.30                           => ( ( H2 @ ( J @ A4 ) )
% 9.49/5.30                              = ( G @ A4 ) ) )
% 9.49/5.30                       => ( ( groups5754745047067104278omplex @ G @ S2 )
% 9.49/5.30                          = ( groups3049146728041665814omplex @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6513_sum_Oreindex__bij__witness__not__neutral,axiom,
% 9.49/5.30      ! [S5: set_int,T5: set_real,S2: set_int,I2: real > int,J: int > real,T4: set_real,G: int > complex,H2: real > complex] :
% 9.49/5.30        ( ( finite_finite_int @ S5 )
% 9.49/5.30       => ( ( finite_finite_real @ T5 )
% 9.49/5.30         => ( ! [A4: int] :
% 9.49/5.30                ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 9.49/5.30               => ( ( I2 @ ( J @ A4 ) )
% 9.49/5.30                  = A4 ) )
% 9.49/5.30           => ( ! [A4: int] :
% 9.49/5.30                  ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 9.49/5.30                 => ( member_real @ ( J @ A4 ) @ ( minus_minus_set_real @ T4 @ T5 ) ) )
% 9.49/5.30             => ( ! [B3: real] :
% 9.49/5.30                    ( ( member_real @ B3 @ ( minus_minus_set_real @ T4 @ T5 ) )
% 9.49/5.30                   => ( ( J @ ( I2 @ B3 ) )
% 9.49/5.30                      = B3 ) )
% 9.49/5.30               => ( ! [B3: real] :
% 9.49/5.30                      ( ( member_real @ B3 @ ( minus_minus_set_real @ T4 @ T5 ) )
% 9.49/5.30                     => ( member_int @ ( I2 @ B3 ) @ ( minus_minus_set_int @ S2 @ S5 ) ) )
% 9.49/5.30                 => ( ! [A4: int] :
% 9.49/5.30                        ( ( member_int @ A4 @ S5 )
% 9.49/5.30                       => ( ( G @ A4 )
% 9.49/5.30                          = zero_zero_complex ) )
% 9.49/5.30                   => ( ! [B3: real] :
% 9.49/5.30                          ( ( member_real @ B3 @ T5 )
% 9.49/5.30                         => ( ( H2 @ B3 )
% 9.49/5.30                            = zero_zero_complex ) )
% 9.49/5.30                     => ( ! [A4: int] :
% 9.49/5.30                            ( ( member_int @ A4 @ S2 )
% 9.49/5.30                           => ( ( H2 @ ( J @ A4 ) )
% 9.49/5.30                              = ( G @ A4 ) ) )
% 9.49/5.30                       => ( ( groups3049146728041665814omplex @ G @ S2 )
% 9.49/5.30                          = ( groups5754745047067104278omplex @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6514_sum_Oreindex__bij__witness__not__neutral,axiom,
% 9.49/5.30      ! [S5: set_int,T5: set_int,S2: set_int,I2: int > int,J: int > int,T4: set_int,G: int > complex,H2: int > complex] :
% 9.49/5.30        ( ( finite_finite_int @ S5 )
% 9.49/5.30       => ( ( finite_finite_int @ T5 )
% 9.49/5.30         => ( ! [A4: int] :
% 9.49/5.30                ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 9.49/5.30               => ( ( I2 @ ( J @ A4 ) )
% 9.49/5.30                  = A4 ) )
% 9.49/5.30           => ( ! [A4: int] :
% 9.49/5.30                  ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 9.49/5.30                 => ( member_int @ ( J @ A4 ) @ ( minus_minus_set_int @ T4 @ T5 ) ) )
% 9.49/5.30             => ( ! [B3: int] :
% 9.49/5.30                    ( ( member_int @ B3 @ ( minus_minus_set_int @ T4 @ T5 ) )
% 9.49/5.30                   => ( ( J @ ( I2 @ B3 ) )
% 9.49/5.30                      = B3 ) )
% 9.49/5.30               => ( ! [B3: int] :
% 9.49/5.30                      ( ( member_int @ B3 @ ( minus_minus_set_int @ T4 @ T5 ) )
% 9.49/5.30                     => ( member_int @ ( I2 @ B3 ) @ ( minus_minus_set_int @ S2 @ S5 ) ) )
% 9.49/5.30                 => ( ! [A4: int] :
% 9.49/5.30                        ( ( member_int @ A4 @ S5 )
% 9.49/5.30                       => ( ( G @ A4 )
% 9.49/5.30                          = zero_zero_complex ) )
% 9.49/5.30                   => ( ! [B3: int] :
% 9.49/5.30                          ( ( member_int @ B3 @ T5 )
% 9.49/5.30                         => ( ( H2 @ B3 )
% 9.49/5.30                            = zero_zero_complex ) )
% 9.49/5.30                     => ( ! [A4: int] :
% 9.49/5.30                            ( ( member_int @ A4 @ S2 )
% 9.49/5.30                           => ( ( H2 @ ( J @ A4 ) )
% 9.49/5.30                              = ( G @ A4 ) ) )
% 9.49/5.30                       => ( ( groups3049146728041665814omplex @ G @ S2 )
% 9.49/5.30                          = ( groups3049146728041665814omplex @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6515_sum_Oreindex__bij__witness__not__neutral,axiom,
% 9.49/5.30      ! [S5: set_real,T5: set_real,S2: set_real,I2: real > real,J: real > real,T4: set_real,G: real > real,H2: real > real] :
% 9.49/5.30        ( ( finite_finite_real @ S5 )
% 9.49/5.30       => ( ( finite_finite_real @ T5 )
% 9.49/5.30         => ( ! [A4: real] :
% 9.49/5.30                ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 9.49/5.30               => ( ( I2 @ ( J @ A4 ) )
% 9.49/5.30                  = A4 ) )
% 9.49/5.30           => ( ! [A4: real] :
% 9.49/5.30                  ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 9.49/5.30                 => ( member_real @ ( J @ A4 ) @ ( minus_minus_set_real @ T4 @ T5 ) ) )
% 9.49/5.30             => ( ! [B3: real] :
% 9.49/5.30                    ( ( member_real @ B3 @ ( minus_minus_set_real @ T4 @ T5 ) )
% 9.49/5.30                   => ( ( J @ ( I2 @ B3 ) )
% 9.49/5.30                      = B3 ) )
% 9.49/5.30               => ( ! [B3: real] :
% 9.49/5.30                      ( ( member_real @ B3 @ ( minus_minus_set_real @ T4 @ T5 ) )
% 9.49/5.30                     => ( member_real @ ( I2 @ B3 ) @ ( minus_minus_set_real @ S2 @ S5 ) ) )
% 9.49/5.30                 => ( ! [A4: real] :
% 9.49/5.30                        ( ( member_real @ A4 @ S5 )
% 9.49/5.30                       => ( ( G @ A4 )
% 9.49/5.30                          = zero_zero_real ) )
% 9.49/5.30                   => ( ! [B3: real] :
% 9.49/5.30                          ( ( member_real @ B3 @ T5 )
% 9.49/5.30                         => ( ( H2 @ B3 )
% 9.49/5.30                            = zero_zero_real ) )
% 9.49/5.30                     => ( ! [A4: real] :
% 9.49/5.30                            ( ( member_real @ A4 @ S2 )
% 9.49/5.30                           => ( ( H2 @ ( J @ A4 ) )
% 9.49/5.30                              = ( G @ A4 ) ) )
% 9.49/5.30                       => ( ( groups8097168146408367636l_real @ G @ S2 )
% 9.49/5.30                          = ( groups8097168146408367636l_real @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6516_sum_Oreindex__bij__witness__not__neutral,axiom,
% 9.49/5.30      ! [S5: set_real,T5: set_int,S2: set_real,I2: int > real,J: real > int,T4: set_int,G: real > real,H2: int > real] :
% 9.49/5.30        ( ( finite_finite_real @ S5 )
% 9.49/5.30       => ( ( finite_finite_int @ T5 )
% 9.49/5.30         => ( ! [A4: real] :
% 9.49/5.30                ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 9.49/5.30               => ( ( I2 @ ( J @ A4 ) )
% 9.49/5.30                  = A4 ) )
% 9.49/5.30           => ( ! [A4: real] :
% 9.49/5.30                  ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 9.49/5.30                 => ( member_int @ ( J @ A4 ) @ ( minus_minus_set_int @ T4 @ T5 ) ) )
% 9.49/5.30             => ( ! [B3: int] :
% 9.49/5.30                    ( ( member_int @ B3 @ ( minus_minus_set_int @ T4 @ T5 ) )
% 9.49/5.30                   => ( ( J @ ( I2 @ B3 ) )
% 9.49/5.30                      = B3 ) )
% 9.49/5.30               => ( ! [B3: int] :
% 9.49/5.30                      ( ( member_int @ B3 @ ( minus_minus_set_int @ T4 @ T5 ) )
% 9.49/5.30                     => ( member_real @ ( I2 @ B3 ) @ ( minus_minus_set_real @ S2 @ S5 ) ) )
% 9.49/5.30                 => ( ! [A4: real] :
% 9.49/5.30                        ( ( member_real @ A4 @ S5 )
% 9.49/5.30                       => ( ( G @ A4 )
% 9.49/5.30                          = zero_zero_real ) )
% 9.49/5.30                   => ( ! [B3: int] :
% 9.49/5.30                          ( ( member_int @ B3 @ T5 )
% 9.49/5.30                         => ( ( H2 @ B3 )
% 9.49/5.30                            = zero_zero_real ) )
% 9.49/5.30                     => ( ! [A4: real] :
% 9.49/5.30                            ( ( member_real @ A4 @ S2 )
% 9.49/5.30                           => ( ( H2 @ ( J @ A4 ) )
% 9.49/5.30                              = ( G @ A4 ) ) )
% 9.49/5.30                       => ( ( groups8097168146408367636l_real @ G @ S2 )
% 9.49/5.30                          = ( groups8778361861064173332t_real @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6517_sum_Oreindex__bij__witness__not__neutral,axiom,
% 9.49/5.30      ! [S5: set_int,T5: set_real,S2: set_int,I2: real > int,J: int > real,T4: set_real,G: int > real,H2: real > real] :
% 9.49/5.30        ( ( finite_finite_int @ S5 )
% 9.49/5.30       => ( ( finite_finite_real @ T5 )
% 9.49/5.30         => ( ! [A4: int] :
% 9.49/5.30                ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 9.49/5.30               => ( ( I2 @ ( J @ A4 ) )
% 9.49/5.30                  = A4 ) )
% 9.49/5.30           => ( ! [A4: int] :
% 9.49/5.30                  ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 9.49/5.30                 => ( member_real @ ( J @ A4 ) @ ( minus_minus_set_real @ T4 @ T5 ) ) )
% 9.49/5.30             => ( ! [B3: real] :
% 9.49/5.30                    ( ( member_real @ B3 @ ( minus_minus_set_real @ T4 @ T5 ) )
% 9.49/5.30                   => ( ( J @ ( I2 @ B3 ) )
% 9.49/5.30                      = B3 ) )
% 9.49/5.30               => ( ! [B3: real] :
% 9.49/5.30                      ( ( member_real @ B3 @ ( minus_minus_set_real @ T4 @ T5 ) )
% 9.49/5.30                     => ( member_int @ ( I2 @ B3 ) @ ( minus_minus_set_int @ S2 @ S5 ) ) )
% 9.49/5.30                 => ( ! [A4: int] :
% 9.49/5.30                        ( ( member_int @ A4 @ S5 )
% 9.49/5.30                       => ( ( G @ A4 )
% 9.49/5.30                          = zero_zero_real ) )
% 9.49/5.30                   => ( ! [B3: real] :
% 9.49/5.30                          ( ( member_real @ B3 @ T5 )
% 9.49/5.30                         => ( ( H2 @ B3 )
% 9.49/5.30                            = zero_zero_real ) )
% 9.49/5.30                     => ( ! [A4: int] :
% 9.49/5.30                            ( ( member_int @ A4 @ S2 )
% 9.49/5.30                           => ( ( H2 @ ( J @ A4 ) )
% 9.49/5.30                              = ( G @ A4 ) ) )
% 9.49/5.30                       => ( ( groups8778361861064173332t_real @ G @ S2 )
% 9.49/5.30                          = ( groups8097168146408367636l_real @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6518_sum_Oreindex__bij__witness__not__neutral,axiom,
% 9.49/5.30      ! [S5: set_int,T5: set_int,S2: set_int,I2: int > int,J: int > int,T4: set_int,G: int > real,H2: int > real] :
% 9.49/5.30        ( ( finite_finite_int @ S5 )
% 9.49/5.30       => ( ( finite_finite_int @ T5 )
% 9.49/5.30         => ( ! [A4: int] :
% 9.49/5.30                ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 9.49/5.30               => ( ( I2 @ ( J @ A4 ) )
% 9.49/5.30                  = A4 ) )
% 9.49/5.30           => ( ! [A4: int] :
% 9.49/5.30                  ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 9.49/5.30                 => ( member_int @ ( J @ A4 ) @ ( minus_minus_set_int @ T4 @ T5 ) ) )
% 9.49/5.30             => ( ! [B3: int] :
% 9.49/5.30                    ( ( member_int @ B3 @ ( minus_minus_set_int @ T4 @ T5 ) )
% 9.49/5.30                   => ( ( J @ ( I2 @ B3 ) )
% 9.49/5.30                      = B3 ) )
% 9.49/5.30               => ( ! [B3: int] :
% 9.49/5.30                      ( ( member_int @ B3 @ ( minus_minus_set_int @ T4 @ T5 ) )
% 9.49/5.30                     => ( member_int @ ( I2 @ B3 ) @ ( minus_minus_set_int @ S2 @ S5 ) ) )
% 9.49/5.30                 => ( ! [A4: int] :
% 9.49/5.30                        ( ( member_int @ A4 @ S5 )
% 9.49/5.30                       => ( ( G @ A4 )
% 9.49/5.30                          = zero_zero_real ) )
% 9.49/5.30                   => ( ! [B3: int] :
% 9.49/5.30                          ( ( member_int @ B3 @ T5 )
% 9.49/5.30                         => ( ( H2 @ B3 )
% 9.49/5.30                            = zero_zero_real ) )
% 9.49/5.30                     => ( ! [A4: int] :
% 9.49/5.30                            ( ( member_int @ A4 @ S2 )
% 9.49/5.30                           => ( ( H2 @ ( J @ A4 ) )
% 9.49/5.30                              = ( G @ A4 ) ) )
% 9.49/5.30                       => ( ( groups8778361861064173332t_real @ G @ S2 )
% 9.49/5.30                          = ( groups8778361861064173332t_real @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6519_sum_Oreindex__bij__witness__not__neutral,axiom,
% 9.49/5.30      ! [S5: set_real,T5: set_complex,S2: set_real,I2: complex > real,J: real > complex,T4: set_complex,G: real > real,H2: complex > real] :
% 9.49/5.30        ( ( finite_finite_real @ S5 )
% 9.49/5.30       => ( ( finite3207457112153483333omplex @ T5 )
% 9.49/5.30         => ( ! [A4: real] :
% 9.49/5.30                ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 9.49/5.30               => ( ( I2 @ ( J @ A4 ) )
% 9.49/5.30                  = A4 ) )
% 9.49/5.30           => ( ! [A4: real] :
% 9.49/5.30                  ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 9.49/5.30                 => ( member_complex @ ( J @ A4 ) @ ( minus_811609699411566653omplex @ T4 @ T5 ) ) )
% 9.49/5.30             => ( ! [B3: complex] :
% 9.49/5.30                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T4 @ T5 ) )
% 9.49/5.30                   => ( ( J @ ( I2 @ B3 ) )
% 9.49/5.30                      = B3 ) )
% 9.49/5.30               => ( ! [B3: complex] :
% 9.49/5.30                      ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T4 @ T5 ) )
% 9.49/5.30                     => ( member_real @ ( I2 @ B3 ) @ ( minus_minus_set_real @ S2 @ S5 ) ) )
% 9.49/5.30                 => ( ! [A4: real] :
% 9.49/5.30                        ( ( member_real @ A4 @ S5 )
% 9.49/5.30                       => ( ( G @ A4 )
% 9.49/5.30                          = zero_zero_real ) )
% 9.49/5.30                   => ( ! [B3: complex] :
% 9.49/5.30                          ( ( member_complex @ B3 @ T5 )
% 9.49/5.30                         => ( ( H2 @ B3 )
% 9.49/5.30                            = zero_zero_real ) )
% 9.49/5.30                     => ( ! [A4: real] :
% 9.49/5.30                            ( ( member_real @ A4 @ S2 )
% 9.49/5.30                           => ( ( H2 @ ( J @ A4 ) )
% 9.49/5.30                              = ( G @ A4 ) ) )
% 9.49/5.30                       => ( ( groups8097168146408367636l_real @ G @ S2 )
% 9.49/5.30                          = ( groups5808333547571424918x_real @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6520_sum_Oreindex__bij__witness__not__neutral,axiom,
% 9.49/5.30      ! [S5: set_int,T5: set_complex,S2: set_int,I2: complex > int,J: int > complex,T4: set_complex,G: int > real,H2: complex > real] :
% 9.49/5.30        ( ( finite_finite_int @ S5 )
% 9.49/5.30       => ( ( finite3207457112153483333omplex @ T5 )
% 9.49/5.30         => ( ! [A4: int] :
% 9.49/5.30                ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 9.49/5.30               => ( ( I2 @ ( J @ A4 ) )
% 9.49/5.30                  = A4 ) )
% 9.49/5.30           => ( ! [A4: int] :
% 9.49/5.30                  ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 9.49/5.30                 => ( member_complex @ ( J @ A4 ) @ ( minus_811609699411566653omplex @ T4 @ T5 ) ) )
% 9.49/5.30             => ( ! [B3: complex] :
% 9.49/5.30                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T4 @ T5 ) )
% 9.49/5.30                   => ( ( J @ ( I2 @ B3 ) )
% 9.49/5.30                      = B3 ) )
% 9.49/5.30               => ( ! [B3: complex] :
% 9.49/5.30                      ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T4 @ T5 ) )
% 9.49/5.30                     => ( member_int @ ( I2 @ B3 ) @ ( minus_minus_set_int @ S2 @ S5 ) ) )
% 9.49/5.30                 => ( ! [A4: int] :
% 9.49/5.30                        ( ( member_int @ A4 @ S5 )
% 9.49/5.30                       => ( ( G @ A4 )
% 9.49/5.30                          = zero_zero_real ) )
% 9.49/5.30                   => ( ! [B3: complex] :
% 9.49/5.30                          ( ( member_complex @ B3 @ T5 )
% 9.49/5.30                         => ( ( H2 @ B3 )
% 9.49/5.30                            = zero_zero_real ) )
% 9.49/5.30                     => ( ! [A4: int] :
% 9.49/5.30                            ( ( member_int @ A4 @ S2 )
% 9.49/5.30                           => ( ( H2 @ ( J @ A4 ) )
% 9.49/5.30                              = ( G @ A4 ) ) )
% 9.49/5.30                       => ( ( groups8778361861064173332t_real @ G @ S2 )
% 9.49/5.30                          = ( groups5808333547571424918x_real @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6521_exp__gt__one,axiom,
% 9.49/5.30      ! [X: real] :
% 9.49/5.30        ( ( ord_less_real @ zero_zero_real @ X )
% 9.49/5.30       => ( ord_less_real @ one_one_real @ ( exp_real @ X ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6522_take__bit__signed__take__bit,axiom,
% 9.49/5.30      ! [M: nat,N: nat,A: int] :
% 9.49/5.30        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 9.49/5.30       => ( ( bit_se2923211474154528505it_int @ M @ ( bit_ri631733984087533419it_int @ N @ A ) )
% 9.49/5.30          = ( bit_se2923211474154528505it_int @ M @ A ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6523_exp__ge__add__one__self,axiom,
% 9.49/5.30      ! [X: real] : ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X ) @ ( exp_real @ X ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6524_exp__minus__inverse,axiom,
% 9.49/5.30      ! [X: real] :
% 9.49/5.30        ( ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) )
% 9.49/5.30        = one_one_real ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6525_exp__minus__inverse,axiom,
% 9.49/5.30      ! [X: complex] :
% 9.49/5.30        ( ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) )
% 9.49/5.30        = one_one_complex ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6526_take__bit__decr__eq,axiom,
% 9.49/5.30      ! [N: nat,K: int] :
% 9.49/5.30        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 9.49/5.30         != zero_zero_int )
% 9.49/5.30       => ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ one_one_int ) )
% 9.49/5.30          = ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ one_one_int ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6527_sum__nonneg__0,axiom,
% 9.49/5.30      ! [S3: set_real,F: real > real,I2: real] :
% 9.49/5.30        ( ( finite_finite_real @ S3 )
% 9.49/5.30       => ( ! [I4: real] :
% 9.49/5.30              ( ( member_real @ I4 @ S3 )
% 9.49/5.30             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 9.49/5.30         => ( ( ( groups8097168146408367636l_real @ F @ S3 )
% 9.49/5.30              = zero_zero_real )
% 9.49/5.30           => ( ( member_real @ I2 @ S3 )
% 9.49/5.30             => ( ( F @ I2 )
% 9.49/5.30                = zero_zero_real ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6528_sum__nonneg__0,axiom,
% 9.49/5.30      ! [S3: set_int,F: int > real,I2: int] :
% 9.49/5.30        ( ( finite_finite_int @ S3 )
% 9.49/5.30       => ( ! [I4: int] :
% 9.49/5.30              ( ( member_int @ I4 @ S3 )
% 9.49/5.30             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 9.49/5.30         => ( ( ( groups8778361861064173332t_real @ F @ S3 )
% 9.49/5.30              = zero_zero_real )
% 9.49/5.30           => ( ( member_int @ I2 @ S3 )
% 9.49/5.30             => ( ( F @ I2 )
% 9.49/5.30                = zero_zero_real ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6529_sum__nonneg__0,axiom,
% 9.49/5.30      ! [S3: set_complex,F: complex > real,I2: complex] :
% 9.49/5.30        ( ( finite3207457112153483333omplex @ S3 )
% 9.49/5.30       => ( ! [I4: complex] :
% 9.49/5.30              ( ( member_complex @ I4 @ S3 )
% 9.49/5.30             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 9.49/5.30         => ( ( ( groups5808333547571424918x_real @ F @ S3 )
% 9.49/5.30              = zero_zero_real )
% 9.49/5.30           => ( ( member_complex @ I2 @ S3 )
% 9.49/5.30             => ( ( F @ I2 )
% 9.49/5.30                = zero_zero_real ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6530_sum__nonneg__0,axiom,
% 9.49/5.30      ! [S3: set_real,F: real > rat,I2: real] :
% 9.49/5.30        ( ( finite_finite_real @ S3 )
% 9.49/5.30       => ( ! [I4: real] :
% 9.49/5.30              ( ( member_real @ I4 @ S3 )
% 9.49/5.30             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 9.49/5.30         => ( ( ( groups1300246762558778688al_rat @ F @ S3 )
% 9.49/5.30              = zero_zero_rat )
% 9.49/5.30           => ( ( member_real @ I2 @ S3 )
% 9.49/5.30             => ( ( F @ I2 )
% 9.49/5.30                = zero_zero_rat ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6531_sum__nonneg__0,axiom,
% 9.49/5.30      ! [S3: set_int,F: int > rat,I2: int] :
% 9.49/5.30        ( ( finite_finite_int @ S3 )
% 9.49/5.30       => ( ! [I4: int] :
% 9.49/5.30              ( ( member_int @ I4 @ S3 )
% 9.49/5.30             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 9.49/5.30         => ( ( ( groups3906332499630173760nt_rat @ F @ S3 )
% 9.49/5.30              = zero_zero_rat )
% 9.49/5.30           => ( ( member_int @ I2 @ S3 )
% 9.49/5.30             => ( ( F @ I2 )
% 9.49/5.30                = zero_zero_rat ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6532_sum__nonneg__0,axiom,
% 9.49/5.30      ! [S3: set_nat,F: nat > rat,I2: nat] :
% 9.49/5.30        ( ( finite_finite_nat @ S3 )
% 9.49/5.30       => ( ! [I4: nat] :
% 9.49/5.30              ( ( member_nat @ I4 @ S3 )
% 9.49/5.30             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 9.49/5.30         => ( ( ( groups2906978787729119204at_rat @ F @ S3 )
% 9.49/5.30              = zero_zero_rat )
% 9.49/5.30           => ( ( member_nat @ I2 @ S3 )
% 9.49/5.30             => ( ( F @ I2 )
% 9.49/5.30                = zero_zero_rat ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6533_sum__nonneg__0,axiom,
% 9.49/5.30      ! [S3: set_complex,F: complex > rat,I2: complex] :
% 9.49/5.30        ( ( finite3207457112153483333omplex @ S3 )
% 9.49/5.30       => ( ! [I4: complex] :
% 9.49/5.30              ( ( member_complex @ I4 @ S3 )
% 9.49/5.30             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 9.49/5.30         => ( ( ( groups5058264527183730370ex_rat @ F @ S3 )
% 9.49/5.30              = zero_zero_rat )
% 9.49/5.30           => ( ( member_complex @ I2 @ S3 )
% 9.49/5.30             => ( ( F @ I2 )
% 9.49/5.30                = zero_zero_rat ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6534_sum__nonneg__0,axiom,
% 9.49/5.30      ! [S3: set_real,F: real > nat,I2: real] :
% 9.49/5.30        ( ( finite_finite_real @ S3 )
% 9.49/5.30       => ( ! [I4: real] :
% 9.49/5.30              ( ( member_real @ I4 @ S3 )
% 9.49/5.30             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 9.49/5.30         => ( ( ( groups1935376822645274424al_nat @ F @ S3 )
% 9.49/5.30              = zero_zero_nat )
% 9.49/5.30           => ( ( member_real @ I2 @ S3 )
% 9.49/5.30             => ( ( F @ I2 )
% 9.49/5.30                = zero_zero_nat ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6535_sum__nonneg__0,axiom,
% 9.49/5.30      ! [S3: set_int,F: int > nat,I2: int] :
% 9.49/5.30        ( ( finite_finite_int @ S3 )
% 9.49/5.30       => ( ! [I4: int] :
% 9.49/5.30              ( ( member_int @ I4 @ S3 )
% 9.49/5.30             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 9.49/5.30         => ( ( ( groups4541462559716669496nt_nat @ F @ S3 )
% 9.49/5.30              = zero_zero_nat )
% 9.49/5.30           => ( ( member_int @ I2 @ S3 )
% 9.49/5.30             => ( ( F @ I2 )
% 9.49/5.30                = zero_zero_nat ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6536_sum__nonneg__0,axiom,
% 9.49/5.30      ! [S3: set_complex,F: complex > nat,I2: complex] :
% 9.49/5.30        ( ( finite3207457112153483333omplex @ S3 )
% 9.49/5.30       => ( ! [I4: complex] :
% 9.49/5.30              ( ( member_complex @ I4 @ S3 )
% 9.49/5.30             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 9.49/5.30         => ( ( ( groups5693394587270226106ex_nat @ F @ S3 )
% 9.49/5.30              = zero_zero_nat )
% 9.49/5.30           => ( ( member_complex @ I2 @ S3 )
% 9.49/5.30             => ( ( F @ I2 )
% 9.49/5.30                = zero_zero_nat ) ) ) ) ) ).
% 9.49/5.30  
% 9.49/5.30  thf(fact_6537_sum__nonneg__leq__bound,axiom,
% 9.53/5.30      ! [S3: set_real,F: real > real,B2: real,I2: real] :
% 9.53/5.30        ( ( finite_finite_real @ S3 )
% 9.53/5.30       => ( ! [I4: real] :
% 9.53/5.30              ( ( member_real @ I4 @ S3 )
% 9.53/5.30             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 9.53/5.30         => ( ( ( groups8097168146408367636l_real @ F @ S3 )
% 9.53/5.30              = B2 )
% 9.53/5.30           => ( ( member_real @ I2 @ S3 )
% 9.53/5.30             => ( ord_less_eq_real @ ( F @ I2 ) @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6538_sum__nonneg__leq__bound,axiom,
% 9.53/5.30      ! [S3: set_int,F: int > real,B2: real,I2: int] :
% 9.53/5.30        ( ( finite_finite_int @ S3 )
% 9.53/5.30       => ( ! [I4: int] :
% 9.53/5.30              ( ( member_int @ I4 @ S3 )
% 9.53/5.30             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 9.53/5.30         => ( ( ( groups8778361861064173332t_real @ F @ S3 )
% 9.53/5.30              = B2 )
% 9.53/5.30           => ( ( member_int @ I2 @ S3 )
% 9.53/5.30             => ( ord_less_eq_real @ ( F @ I2 ) @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6539_sum__nonneg__leq__bound,axiom,
% 9.53/5.30      ! [S3: set_complex,F: complex > real,B2: real,I2: complex] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ S3 )
% 9.53/5.30       => ( ! [I4: complex] :
% 9.53/5.30              ( ( member_complex @ I4 @ S3 )
% 9.53/5.30             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 9.53/5.30         => ( ( ( groups5808333547571424918x_real @ F @ S3 )
% 9.53/5.30              = B2 )
% 9.53/5.30           => ( ( member_complex @ I2 @ S3 )
% 9.53/5.30             => ( ord_less_eq_real @ ( F @ I2 ) @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6540_sum__nonneg__leq__bound,axiom,
% 9.53/5.30      ! [S3: set_real,F: real > rat,B2: rat,I2: real] :
% 9.53/5.30        ( ( finite_finite_real @ S3 )
% 9.53/5.30       => ( ! [I4: real] :
% 9.53/5.30              ( ( member_real @ I4 @ S3 )
% 9.53/5.30             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 9.53/5.30         => ( ( ( groups1300246762558778688al_rat @ F @ S3 )
% 9.53/5.30              = B2 )
% 9.53/5.30           => ( ( member_real @ I2 @ S3 )
% 9.53/5.30             => ( ord_less_eq_rat @ ( F @ I2 ) @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6541_sum__nonneg__leq__bound,axiom,
% 9.53/5.30      ! [S3: set_int,F: int > rat,B2: rat,I2: int] :
% 9.53/5.30        ( ( finite_finite_int @ S3 )
% 9.53/5.30       => ( ! [I4: int] :
% 9.53/5.30              ( ( member_int @ I4 @ S3 )
% 9.53/5.30             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 9.53/5.30         => ( ( ( groups3906332499630173760nt_rat @ F @ S3 )
% 9.53/5.30              = B2 )
% 9.53/5.30           => ( ( member_int @ I2 @ S3 )
% 9.53/5.30             => ( ord_less_eq_rat @ ( F @ I2 ) @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6542_sum__nonneg__leq__bound,axiom,
% 9.53/5.30      ! [S3: set_nat,F: nat > rat,B2: rat,I2: nat] :
% 9.53/5.30        ( ( finite_finite_nat @ S3 )
% 9.53/5.30       => ( ! [I4: nat] :
% 9.53/5.30              ( ( member_nat @ I4 @ S3 )
% 9.53/5.30             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 9.53/5.30         => ( ( ( groups2906978787729119204at_rat @ F @ S3 )
% 9.53/5.30              = B2 )
% 9.53/5.30           => ( ( member_nat @ I2 @ S3 )
% 9.53/5.30             => ( ord_less_eq_rat @ ( F @ I2 ) @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6543_sum__nonneg__leq__bound,axiom,
% 9.53/5.30      ! [S3: set_complex,F: complex > rat,B2: rat,I2: complex] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ S3 )
% 9.53/5.30       => ( ! [I4: complex] :
% 9.53/5.30              ( ( member_complex @ I4 @ S3 )
% 9.53/5.30             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 9.53/5.30         => ( ( ( groups5058264527183730370ex_rat @ F @ S3 )
% 9.53/5.30              = B2 )
% 9.53/5.30           => ( ( member_complex @ I2 @ S3 )
% 9.53/5.30             => ( ord_less_eq_rat @ ( F @ I2 ) @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6544_sum__nonneg__leq__bound,axiom,
% 9.53/5.30      ! [S3: set_real,F: real > nat,B2: nat,I2: real] :
% 9.53/5.30        ( ( finite_finite_real @ S3 )
% 9.53/5.30       => ( ! [I4: real] :
% 9.53/5.30              ( ( member_real @ I4 @ S3 )
% 9.53/5.30             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 9.53/5.30         => ( ( ( groups1935376822645274424al_nat @ F @ S3 )
% 9.53/5.30              = B2 )
% 9.53/5.30           => ( ( member_real @ I2 @ S3 )
% 9.53/5.30             => ( ord_less_eq_nat @ ( F @ I2 ) @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6545_sum__nonneg__leq__bound,axiom,
% 9.53/5.30      ! [S3: set_int,F: int > nat,B2: nat,I2: int] :
% 9.53/5.30        ( ( finite_finite_int @ S3 )
% 9.53/5.30       => ( ! [I4: int] :
% 9.53/5.30              ( ( member_int @ I4 @ S3 )
% 9.53/5.30             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 9.53/5.30         => ( ( ( groups4541462559716669496nt_nat @ F @ S3 )
% 9.53/5.30              = B2 )
% 9.53/5.30           => ( ( member_int @ I2 @ S3 )
% 9.53/5.30             => ( ord_less_eq_nat @ ( F @ I2 ) @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6546_sum__nonneg__leq__bound,axiom,
% 9.53/5.30      ! [S3: set_complex,F: complex > nat,B2: nat,I2: complex] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ S3 )
% 9.53/5.30       => ( ! [I4: complex] :
% 9.53/5.30              ( ( member_complex @ I4 @ S3 )
% 9.53/5.30             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 9.53/5.30         => ( ( ( groups5693394587270226106ex_nat @ F @ S3 )
% 9.53/5.30              = B2 )
% 9.53/5.30           => ( ( member_complex @ I2 @ S3 )
% 9.53/5.30             => ( ord_less_eq_nat @ ( F @ I2 ) @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6547_abs__mod__less,axiom,
% 9.53/5.30      ! [L2: int,K: int] :
% 9.53/5.30        ( ( L2 != zero_zero_int )
% 9.53/5.30       => ( ord_less_int @ ( abs_abs_int @ ( modulo_modulo_int @ K @ L2 ) ) @ ( abs_abs_int @ L2 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6548_sum_Osetdiff__irrelevant,axiom,
% 9.53/5.30      ! [A2: set_real,G: real > complex] :
% 9.53/5.30        ( ( finite_finite_real @ A2 )
% 9.53/5.30       => ( ( groups5754745047067104278omplex @ G
% 9.53/5.30            @ ( minus_minus_set_real @ A2
% 9.53/5.30              @ ( collect_real
% 9.53/5.30                @ ^ [X2: real] :
% 9.53/5.30                    ( ( G @ X2 )
% 9.53/5.30                    = zero_zero_complex ) ) ) )
% 9.53/5.30          = ( groups5754745047067104278omplex @ G @ A2 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6549_sum_Osetdiff__irrelevant,axiom,
% 9.53/5.30      ! [A2: set_real,G: real > real] :
% 9.53/5.30        ( ( finite_finite_real @ A2 )
% 9.53/5.30       => ( ( groups8097168146408367636l_real @ G
% 9.53/5.30            @ ( minus_minus_set_real @ A2
% 9.53/5.30              @ ( collect_real
% 9.53/5.30                @ ^ [X2: real] :
% 9.53/5.30                    ( ( G @ X2 )
% 9.53/5.30                    = zero_zero_real ) ) ) )
% 9.53/5.30          = ( groups8097168146408367636l_real @ G @ A2 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6550_sum_Osetdiff__irrelevant,axiom,
% 9.53/5.30      ! [A2: set_complex,G: complex > real] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.30       => ( ( groups5808333547571424918x_real @ G
% 9.53/5.30            @ ( minus_811609699411566653omplex @ A2
% 9.53/5.30              @ ( collect_complex
% 9.53/5.30                @ ^ [X2: complex] :
% 9.53/5.30                    ( ( G @ X2 )
% 9.53/5.30                    = zero_zero_real ) ) ) )
% 9.53/5.30          = ( groups5808333547571424918x_real @ G @ A2 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6551_sum_Osetdiff__irrelevant,axiom,
% 9.53/5.30      ! [A2: set_real,G: real > rat] :
% 9.53/5.30        ( ( finite_finite_real @ A2 )
% 9.53/5.30       => ( ( groups1300246762558778688al_rat @ G
% 9.53/5.30            @ ( minus_minus_set_real @ A2
% 9.53/5.30              @ ( collect_real
% 9.53/5.30                @ ^ [X2: real] :
% 9.53/5.30                    ( ( G @ X2 )
% 9.53/5.30                    = zero_zero_rat ) ) ) )
% 9.53/5.30          = ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6552_sum_Osetdiff__irrelevant,axiom,
% 9.53/5.30      ! [A2: set_complex,G: complex > rat] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.30       => ( ( groups5058264527183730370ex_rat @ G
% 9.53/5.30            @ ( minus_811609699411566653omplex @ A2
% 9.53/5.30              @ ( collect_complex
% 9.53/5.30                @ ^ [X2: complex] :
% 9.53/5.30                    ( ( G @ X2 )
% 9.53/5.30                    = zero_zero_rat ) ) ) )
% 9.53/5.30          = ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6553_sum_Osetdiff__irrelevant,axiom,
% 9.53/5.30      ! [A2: set_real,G: real > nat] :
% 9.53/5.30        ( ( finite_finite_real @ A2 )
% 9.53/5.30       => ( ( groups1935376822645274424al_nat @ G
% 9.53/5.30            @ ( minus_minus_set_real @ A2
% 9.53/5.30              @ ( collect_real
% 9.53/5.30                @ ^ [X2: real] :
% 9.53/5.30                    ( ( G @ X2 )
% 9.53/5.30                    = zero_zero_nat ) ) ) )
% 9.53/5.30          = ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6554_sum_Osetdiff__irrelevant,axiom,
% 9.53/5.30      ! [A2: set_complex,G: complex > nat] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.30       => ( ( groups5693394587270226106ex_nat @ G
% 9.53/5.30            @ ( minus_811609699411566653omplex @ A2
% 9.53/5.30              @ ( collect_complex
% 9.53/5.30                @ ^ [X2: complex] :
% 9.53/5.30                    ( ( G @ X2 )
% 9.53/5.30                    = zero_zero_nat ) ) ) )
% 9.53/5.30          = ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6555_sum_Osetdiff__irrelevant,axiom,
% 9.53/5.30      ! [A2: set_real,G: real > int] :
% 9.53/5.30        ( ( finite_finite_real @ A2 )
% 9.53/5.30       => ( ( groups1932886352136224148al_int @ G
% 9.53/5.30            @ ( minus_minus_set_real @ A2
% 9.53/5.30              @ ( collect_real
% 9.53/5.30                @ ^ [X2: real] :
% 9.53/5.30                    ( ( G @ X2 )
% 9.53/5.30                    = zero_zero_int ) ) ) )
% 9.53/5.30          = ( groups1932886352136224148al_int @ G @ A2 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6556_sum_Osetdiff__irrelevant,axiom,
% 9.53/5.30      ! [A2: set_complex,G: complex > int] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.30       => ( ( groups5690904116761175830ex_int @ G
% 9.53/5.30            @ ( minus_811609699411566653omplex @ A2
% 9.53/5.30              @ ( collect_complex
% 9.53/5.30                @ ^ [X2: complex] :
% 9.53/5.30                    ( ( G @ X2 )
% 9.53/5.30                    = zero_zero_int ) ) ) )
% 9.53/5.30          = ( groups5690904116761175830ex_int @ G @ A2 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6557_sum_Osetdiff__irrelevant,axiom,
% 9.53/5.30      ! [A2: set_nat,G: nat > complex] :
% 9.53/5.30        ( ( finite_finite_nat @ A2 )
% 9.53/5.30       => ( ( groups2073611262835488442omplex @ G
% 9.53/5.30            @ ( minus_minus_set_nat @ A2
% 9.53/5.30              @ ( collect_nat
% 9.53/5.30                @ ^ [X2: nat] :
% 9.53/5.30                    ( ( G @ X2 )
% 9.53/5.30                    = zero_zero_complex ) ) ) )
% 9.53/5.30          = ( groups2073611262835488442omplex @ G @ A2 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6558_less__mask,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 9.53/5.30       => ( ord_less_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6559_take__bit__eq__mask__iff__exp__dvd,axiom,
% 9.53/5.30      ! [N: nat,K: int] :
% 9.53/5.30        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 9.53/5.30          = ( bit_se2000444600071755411sk_int @ N ) )
% 9.53/5.30        = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( plus_plus_int @ K @ one_one_int ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6560_sum__pos2,axiom,
% 9.53/5.30      ! [I6: set_real,I2: real,F: real > real] :
% 9.53/5.30        ( ( finite_finite_real @ I6 )
% 9.53/5.30       => ( ( member_real @ I2 @ I6 )
% 9.53/5.30         => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 9.53/5.30           => ( ! [I4: real] :
% 9.53/5.30                  ( ( member_real @ I4 @ I6 )
% 9.53/5.30                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 9.53/5.30             => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I6 ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6561_sum__pos2,axiom,
% 9.53/5.30      ! [I6: set_int,I2: int,F: int > real] :
% 9.53/5.30        ( ( finite_finite_int @ I6 )
% 9.53/5.30       => ( ( member_int @ I2 @ I6 )
% 9.53/5.30         => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 9.53/5.30           => ( ! [I4: int] :
% 9.53/5.30                  ( ( member_int @ I4 @ I6 )
% 9.53/5.30                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 9.53/5.30             => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I6 ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6562_sum__pos2,axiom,
% 9.53/5.30      ! [I6: set_complex,I2: complex,F: complex > real] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ I6 )
% 9.53/5.30       => ( ( member_complex @ I2 @ I6 )
% 9.53/5.30         => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 9.53/5.30           => ( ! [I4: complex] :
% 9.53/5.30                  ( ( member_complex @ I4 @ I6 )
% 9.53/5.30                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 9.53/5.30             => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I6 ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6563_sum__pos2,axiom,
% 9.53/5.30      ! [I6: set_real,I2: real,F: real > rat] :
% 9.53/5.30        ( ( finite_finite_real @ I6 )
% 9.53/5.30       => ( ( member_real @ I2 @ I6 )
% 9.53/5.30         => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) )
% 9.53/5.30           => ( ! [I4: real] :
% 9.53/5.30                  ( ( member_real @ I4 @ I6 )
% 9.53/5.30                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 9.53/5.30             => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I6 ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6564_sum__pos2,axiom,
% 9.53/5.30      ! [I6: set_int,I2: int,F: int > rat] :
% 9.53/5.30        ( ( finite_finite_int @ I6 )
% 9.53/5.30       => ( ( member_int @ I2 @ I6 )
% 9.53/5.30         => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) )
% 9.53/5.30           => ( ! [I4: int] :
% 9.53/5.30                  ( ( member_int @ I4 @ I6 )
% 9.53/5.30                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 9.53/5.30             => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I6 ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6565_sum__pos2,axiom,
% 9.53/5.30      ! [I6: set_nat,I2: nat,F: nat > rat] :
% 9.53/5.30        ( ( finite_finite_nat @ I6 )
% 9.53/5.30       => ( ( member_nat @ I2 @ I6 )
% 9.53/5.30         => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) )
% 9.53/5.30           => ( ! [I4: nat] :
% 9.53/5.30                  ( ( member_nat @ I4 @ I6 )
% 9.53/5.30                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 9.53/5.30             => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I6 ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6566_sum__pos2,axiom,
% 9.53/5.30      ! [I6: set_complex,I2: complex,F: complex > rat] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ I6 )
% 9.53/5.30       => ( ( member_complex @ I2 @ I6 )
% 9.53/5.30         => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) )
% 9.53/5.30           => ( ! [I4: complex] :
% 9.53/5.30                  ( ( member_complex @ I4 @ I6 )
% 9.53/5.30                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 9.53/5.30             => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I6 ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6567_sum__pos2,axiom,
% 9.53/5.30      ! [I6: set_real,I2: real,F: real > nat] :
% 9.53/5.30        ( ( finite_finite_real @ I6 )
% 9.53/5.30       => ( ( member_real @ I2 @ I6 )
% 9.53/5.30         => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 9.53/5.30           => ( ! [I4: real] :
% 9.53/5.30                  ( ( member_real @ I4 @ I6 )
% 9.53/5.30                 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 9.53/5.30             => ( ord_less_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ I6 ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6568_sum__pos2,axiom,
% 9.53/5.30      ! [I6: set_int,I2: int,F: int > nat] :
% 9.53/5.30        ( ( finite_finite_int @ I6 )
% 9.53/5.30       => ( ( member_int @ I2 @ I6 )
% 9.53/5.30         => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 9.53/5.30           => ( ! [I4: int] :
% 9.53/5.30                  ( ( member_int @ I4 @ I6 )
% 9.53/5.30                 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 9.53/5.30             => ( ord_less_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ I6 ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6569_sum__pos2,axiom,
% 9.53/5.30      ! [I6: set_complex,I2: complex,F: complex > nat] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ I6 )
% 9.53/5.30       => ( ( member_complex @ I2 @ I6 )
% 9.53/5.30         => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 9.53/5.30           => ( ! [I4: complex] :
% 9.53/5.30                  ( ( member_complex @ I4 @ I6 )
% 9.53/5.30                 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 9.53/5.30             => ( ord_less_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ I6 ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6570_sum__pos,axiom,
% 9.53/5.30      ! [I6: set_complex,F: complex > real] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ I6 )
% 9.53/5.30       => ( ( I6 != bot_bot_set_complex )
% 9.53/5.30         => ( ! [I4: complex] :
% 9.53/5.30                ( ( member_complex @ I4 @ I6 )
% 9.53/5.30               => ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) )
% 9.53/5.30           => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I6 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6571_sum__pos,axiom,
% 9.53/5.30      ! [I6: set_int,F: int > real] :
% 9.53/5.30        ( ( finite_finite_int @ I6 )
% 9.53/5.30       => ( ( I6 != bot_bot_set_int )
% 9.53/5.30         => ( ! [I4: int] :
% 9.53/5.30                ( ( member_int @ I4 @ I6 )
% 9.53/5.30               => ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) )
% 9.53/5.30           => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I6 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6572_sum__pos,axiom,
% 9.53/5.30      ! [I6: set_real,F: real > real] :
% 9.53/5.30        ( ( finite_finite_real @ I6 )
% 9.53/5.30       => ( ( I6 != bot_bot_set_real )
% 9.53/5.30         => ( ! [I4: real] :
% 9.53/5.30                ( ( member_real @ I4 @ I6 )
% 9.53/5.30               => ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) )
% 9.53/5.30           => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I6 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6573_sum__pos,axiom,
% 9.53/5.30      ! [I6: set_complex,F: complex > rat] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ I6 )
% 9.53/5.30       => ( ( I6 != bot_bot_set_complex )
% 9.53/5.30         => ( ! [I4: complex] :
% 9.53/5.30                ( ( member_complex @ I4 @ I6 )
% 9.53/5.30               => ( ord_less_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 9.53/5.30           => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I6 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6574_sum__pos,axiom,
% 9.53/5.30      ! [I6: set_nat,F: nat > rat] :
% 9.53/5.30        ( ( finite_finite_nat @ I6 )
% 9.53/5.30       => ( ( I6 != bot_bot_set_nat )
% 9.53/5.30         => ( ! [I4: nat] :
% 9.53/5.30                ( ( member_nat @ I4 @ I6 )
% 9.53/5.30               => ( ord_less_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 9.53/5.30           => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I6 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6575_sum__pos,axiom,
% 9.53/5.30      ! [I6: set_int,F: int > rat] :
% 9.53/5.30        ( ( finite_finite_int @ I6 )
% 9.53/5.30       => ( ( I6 != bot_bot_set_int )
% 9.53/5.30         => ( ! [I4: int] :
% 9.53/5.30                ( ( member_int @ I4 @ I6 )
% 9.53/5.30               => ( ord_less_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 9.53/5.30           => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I6 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6576_sum__pos,axiom,
% 9.53/5.30      ! [I6: set_real,F: real > rat] :
% 9.53/5.30        ( ( finite_finite_real @ I6 )
% 9.53/5.30       => ( ( I6 != bot_bot_set_real )
% 9.53/5.30         => ( ! [I4: real] :
% 9.53/5.30                ( ( member_real @ I4 @ I6 )
% 9.53/5.30               => ( ord_less_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 9.53/5.30           => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I6 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6577_sum__pos,axiom,
% 9.53/5.30      ! [I6: set_complex,F: complex > nat] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ I6 )
% 9.53/5.30       => ( ( I6 != bot_bot_set_complex )
% 9.53/5.30         => ( ! [I4: complex] :
% 9.53/5.30                ( ( member_complex @ I4 @ I6 )
% 9.53/5.30               => ( ord_less_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 9.53/5.30           => ( ord_less_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ I6 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6578_sum__pos,axiom,
% 9.53/5.30      ! [I6: set_int,F: int > nat] :
% 9.53/5.30        ( ( finite_finite_int @ I6 )
% 9.53/5.30       => ( ( I6 != bot_bot_set_int )
% 9.53/5.30         => ( ! [I4: int] :
% 9.53/5.30                ( ( member_int @ I4 @ I6 )
% 9.53/5.30               => ( ord_less_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 9.53/5.30           => ( ord_less_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ I6 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6579_sum__pos,axiom,
% 9.53/5.30      ! [I6: set_real,F: real > nat] :
% 9.53/5.30        ( ( finite_finite_real @ I6 )
% 9.53/5.30       => ( ( I6 != bot_bot_set_real )
% 9.53/5.30         => ( ! [I4: real] :
% 9.53/5.30                ( ( member_real @ I4 @ I6 )
% 9.53/5.30               => ( ord_less_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 9.53/5.30           => ( ord_less_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ I6 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6580_sum_Osame__carrier,axiom,
% 9.53/5.30      ! [C4: set_int,A2: set_int,B2: set_int,G: int > complex,H2: int > complex] :
% 9.53/5.30        ( ( finite_finite_int @ C4 )
% 9.53/5.30       => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 9.53/5.30         => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 9.53/5.30           => ( ! [A4: int] :
% 9.53/5.30                  ( ( member_int @ A4 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 9.53/5.30                 => ( ( G @ A4 )
% 9.53/5.30                    = zero_zero_complex ) )
% 9.53/5.30             => ( ! [B3: int] :
% 9.53/5.30                    ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 9.53/5.30                   => ( ( H2 @ B3 )
% 9.53/5.30                      = zero_zero_complex ) )
% 9.53/5.30               => ( ( ( groups3049146728041665814omplex @ G @ A2 )
% 9.53/5.30                    = ( groups3049146728041665814omplex @ H2 @ B2 ) )
% 9.53/5.30                  = ( ( groups3049146728041665814omplex @ G @ C4 )
% 9.53/5.30                    = ( groups3049146728041665814omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6581_sum_Osame__carrier,axiom,
% 9.53/5.30      ! [C4: set_int,A2: set_int,B2: set_int,G: int > real,H2: int > real] :
% 9.53/5.30        ( ( finite_finite_int @ C4 )
% 9.53/5.30       => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 9.53/5.30         => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 9.53/5.30           => ( ! [A4: int] :
% 9.53/5.30                  ( ( member_int @ A4 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 9.53/5.30                 => ( ( G @ A4 )
% 9.53/5.30                    = zero_zero_real ) )
% 9.53/5.30             => ( ! [B3: int] :
% 9.53/5.30                    ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 9.53/5.30                   => ( ( H2 @ B3 )
% 9.53/5.30                      = zero_zero_real ) )
% 9.53/5.30               => ( ( ( groups8778361861064173332t_real @ G @ A2 )
% 9.53/5.30                    = ( groups8778361861064173332t_real @ H2 @ B2 ) )
% 9.53/5.30                  = ( ( groups8778361861064173332t_real @ G @ C4 )
% 9.53/5.30                    = ( groups8778361861064173332t_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6582_sum_Osame__carrier,axiom,
% 9.53/5.30      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > real,H2: complex > real] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ C4 )
% 9.53/5.30       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 9.53/5.30         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 9.53/5.30           => ( ! [A4: complex] :
% 9.53/5.30                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 9.53/5.30                 => ( ( G @ A4 )
% 9.53/5.30                    = zero_zero_real ) )
% 9.53/5.30             => ( ! [B3: complex] :
% 9.53/5.30                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 9.53/5.30                   => ( ( H2 @ B3 )
% 9.53/5.30                      = zero_zero_real ) )
% 9.53/5.30               => ( ( ( groups5808333547571424918x_real @ G @ A2 )
% 9.53/5.30                    = ( groups5808333547571424918x_real @ H2 @ B2 ) )
% 9.53/5.30                  = ( ( groups5808333547571424918x_real @ G @ C4 )
% 9.53/5.30                    = ( groups5808333547571424918x_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6583_sum_Osame__carrier,axiom,
% 9.53/5.30      ! [C4: set_int,A2: set_int,B2: set_int,G: int > rat,H2: int > rat] :
% 9.53/5.30        ( ( finite_finite_int @ C4 )
% 9.53/5.30       => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 9.53/5.30         => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 9.53/5.30           => ( ! [A4: int] :
% 9.53/5.30                  ( ( member_int @ A4 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 9.53/5.30                 => ( ( G @ A4 )
% 9.53/5.30                    = zero_zero_rat ) )
% 9.53/5.30             => ( ! [B3: int] :
% 9.53/5.30                    ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 9.53/5.30                   => ( ( H2 @ B3 )
% 9.53/5.30                      = zero_zero_rat ) )
% 9.53/5.30               => ( ( ( groups3906332499630173760nt_rat @ G @ A2 )
% 9.53/5.30                    = ( groups3906332499630173760nt_rat @ H2 @ B2 ) )
% 9.53/5.30                  = ( ( groups3906332499630173760nt_rat @ G @ C4 )
% 9.53/5.30                    = ( groups3906332499630173760nt_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6584_sum_Osame__carrier,axiom,
% 9.53/5.30      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > rat,H2: complex > rat] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ C4 )
% 9.53/5.30       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 9.53/5.30         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 9.53/5.30           => ( ! [A4: complex] :
% 9.53/5.30                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 9.53/5.30                 => ( ( G @ A4 )
% 9.53/5.30                    = zero_zero_rat ) )
% 9.53/5.30             => ( ! [B3: complex] :
% 9.53/5.30                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 9.53/5.30                   => ( ( H2 @ B3 )
% 9.53/5.30                      = zero_zero_rat ) )
% 9.53/5.30               => ( ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 9.53/5.30                    = ( groups5058264527183730370ex_rat @ H2 @ B2 ) )
% 9.53/5.30                  = ( ( groups5058264527183730370ex_rat @ G @ C4 )
% 9.53/5.30                    = ( groups5058264527183730370ex_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6585_sum_Osame__carrier,axiom,
% 9.53/5.30      ! [C4: set_int,A2: set_int,B2: set_int,G: int > nat,H2: int > nat] :
% 9.53/5.30        ( ( finite_finite_int @ C4 )
% 9.53/5.30       => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 9.53/5.30         => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 9.53/5.30           => ( ! [A4: int] :
% 9.53/5.30                  ( ( member_int @ A4 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 9.53/5.30                 => ( ( G @ A4 )
% 9.53/5.30                    = zero_zero_nat ) )
% 9.53/5.30             => ( ! [B3: int] :
% 9.53/5.30                    ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 9.53/5.30                   => ( ( H2 @ B3 )
% 9.53/5.30                      = zero_zero_nat ) )
% 9.53/5.30               => ( ( ( groups4541462559716669496nt_nat @ G @ A2 )
% 9.53/5.30                    = ( groups4541462559716669496nt_nat @ H2 @ B2 ) )
% 9.53/5.30                  = ( ( groups4541462559716669496nt_nat @ G @ C4 )
% 9.53/5.30                    = ( groups4541462559716669496nt_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6586_sum_Osame__carrier,axiom,
% 9.53/5.30      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > nat,H2: complex > nat] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ C4 )
% 9.53/5.30       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 9.53/5.30         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 9.53/5.30           => ( ! [A4: complex] :
% 9.53/5.30                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 9.53/5.30                 => ( ( G @ A4 )
% 9.53/5.30                    = zero_zero_nat ) )
% 9.53/5.30             => ( ! [B3: complex] :
% 9.53/5.30                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 9.53/5.30                   => ( ( H2 @ B3 )
% 9.53/5.30                      = zero_zero_nat ) )
% 9.53/5.30               => ( ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 9.53/5.30                    = ( groups5693394587270226106ex_nat @ H2 @ B2 ) )
% 9.53/5.30                  = ( ( groups5693394587270226106ex_nat @ G @ C4 )
% 9.53/5.30                    = ( groups5693394587270226106ex_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6587_sum_Osame__carrier,axiom,
% 9.53/5.30      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > int,H2: complex > int] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ C4 )
% 9.53/5.30       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 9.53/5.30         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 9.53/5.30           => ( ! [A4: complex] :
% 9.53/5.30                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 9.53/5.30                 => ( ( G @ A4 )
% 9.53/5.30                    = zero_zero_int ) )
% 9.53/5.30             => ( ! [B3: complex] :
% 9.53/5.30                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 9.53/5.30                   => ( ( H2 @ B3 )
% 9.53/5.30                      = zero_zero_int ) )
% 9.53/5.30               => ( ( ( groups5690904116761175830ex_int @ G @ A2 )
% 9.53/5.30                    = ( groups5690904116761175830ex_int @ H2 @ B2 ) )
% 9.53/5.30                  = ( ( groups5690904116761175830ex_int @ G @ C4 )
% 9.53/5.30                    = ( groups5690904116761175830ex_int @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6588_sum_Osame__carrier,axiom,
% 9.53/5.30      ! [C4: set_real,A2: set_real,B2: set_real,G: real > complex,H2: real > complex] :
% 9.53/5.30        ( ( finite_finite_real @ C4 )
% 9.53/5.30       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 9.53/5.30         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 9.53/5.30           => ( ! [A4: real] :
% 9.53/5.30                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 9.53/5.30                 => ( ( G @ A4 )
% 9.53/5.30                    = zero_zero_complex ) )
% 9.53/5.30             => ( ! [B3: real] :
% 9.53/5.30                    ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 9.53/5.30                   => ( ( H2 @ B3 )
% 9.53/5.30                      = zero_zero_complex ) )
% 9.53/5.30               => ( ( ( groups5754745047067104278omplex @ G @ A2 )
% 9.53/5.30                    = ( groups5754745047067104278omplex @ H2 @ B2 ) )
% 9.53/5.30                  = ( ( groups5754745047067104278omplex @ G @ C4 )
% 9.53/5.30                    = ( groups5754745047067104278omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6589_sum_Osame__carrier,axiom,
% 9.53/5.30      ! [C4: set_real,A2: set_real,B2: set_real,G: real > real,H2: real > real] :
% 9.53/5.30        ( ( finite_finite_real @ C4 )
% 9.53/5.30       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 9.53/5.30         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 9.53/5.30           => ( ! [A4: real] :
% 9.53/5.30                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 9.53/5.30                 => ( ( G @ A4 )
% 9.53/5.30                    = zero_zero_real ) )
% 9.53/5.30             => ( ! [B3: real] :
% 9.53/5.30                    ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 9.53/5.30                   => ( ( H2 @ B3 )
% 9.53/5.30                      = zero_zero_real ) )
% 9.53/5.30               => ( ( ( groups8097168146408367636l_real @ G @ A2 )
% 9.53/5.30                    = ( groups8097168146408367636l_real @ H2 @ B2 ) )
% 9.53/5.30                  = ( ( groups8097168146408367636l_real @ G @ C4 )
% 9.53/5.30                    = ( groups8097168146408367636l_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6590_sum_Osame__carrierI,axiom,
% 9.53/5.30      ! [C4: set_int,A2: set_int,B2: set_int,G: int > complex,H2: int > complex] :
% 9.53/5.30        ( ( finite_finite_int @ C4 )
% 9.53/5.30       => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 9.53/5.30         => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 9.53/5.30           => ( ! [A4: int] :
% 9.53/5.30                  ( ( member_int @ A4 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 9.53/5.30                 => ( ( G @ A4 )
% 9.53/5.30                    = zero_zero_complex ) )
% 9.53/5.30             => ( ! [B3: int] :
% 9.53/5.30                    ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 9.53/5.30                   => ( ( H2 @ B3 )
% 9.53/5.30                      = zero_zero_complex ) )
% 9.53/5.30               => ( ( ( groups3049146728041665814omplex @ G @ C4 )
% 9.53/5.30                    = ( groups3049146728041665814omplex @ H2 @ C4 ) )
% 9.53/5.30                 => ( ( groups3049146728041665814omplex @ G @ A2 )
% 9.53/5.30                    = ( groups3049146728041665814omplex @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6591_sum_Osame__carrierI,axiom,
% 9.53/5.30      ! [C4: set_int,A2: set_int,B2: set_int,G: int > real,H2: int > real] :
% 9.53/5.30        ( ( finite_finite_int @ C4 )
% 9.53/5.30       => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 9.53/5.30         => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 9.53/5.30           => ( ! [A4: int] :
% 9.53/5.30                  ( ( member_int @ A4 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 9.53/5.30                 => ( ( G @ A4 )
% 9.53/5.30                    = zero_zero_real ) )
% 9.53/5.30             => ( ! [B3: int] :
% 9.53/5.30                    ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 9.53/5.30                   => ( ( H2 @ B3 )
% 9.53/5.30                      = zero_zero_real ) )
% 9.53/5.30               => ( ( ( groups8778361861064173332t_real @ G @ C4 )
% 9.53/5.30                    = ( groups8778361861064173332t_real @ H2 @ C4 ) )
% 9.53/5.30                 => ( ( groups8778361861064173332t_real @ G @ A2 )
% 9.53/5.30                    = ( groups8778361861064173332t_real @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6592_sum_Osame__carrierI,axiom,
% 9.53/5.30      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > real,H2: complex > real] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ C4 )
% 9.53/5.30       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 9.53/5.30         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 9.53/5.30           => ( ! [A4: complex] :
% 9.53/5.30                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 9.53/5.30                 => ( ( G @ A4 )
% 9.53/5.30                    = zero_zero_real ) )
% 9.53/5.30             => ( ! [B3: complex] :
% 9.53/5.30                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 9.53/5.30                   => ( ( H2 @ B3 )
% 9.53/5.30                      = zero_zero_real ) )
% 9.53/5.30               => ( ( ( groups5808333547571424918x_real @ G @ C4 )
% 9.53/5.30                    = ( groups5808333547571424918x_real @ H2 @ C4 ) )
% 9.53/5.30                 => ( ( groups5808333547571424918x_real @ G @ A2 )
% 9.53/5.30                    = ( groups5808333547571424918x_real @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6593_sum_Osame__carrierI,axiom,
% 9.53/5.30      ! [C4: set_int,A2: set_int,B2: set_int,G: int > rat,H2: int > rat] :
% 9.53/5.30        ( ( finite_finite_int @ C4 )
% 9.53/5.30       => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 9.53/5.30         => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 9.53/5.30           => ( ! [A4: int] :
% 9.53/5.30                  ( ( member_int @ A4 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 9.53/5.30                 => ( ( G @ A4 )
% 9.53/5.30                    = zero_zero_rat ) )
% 9.53/5.30             => ( ! [B3: int] :
% 9.53/5.30                    ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 9.53/5.30                   => ( ( H2 @ B3 )
% 9.53/5.30                      = zero_zero_rat ) )
% 9.53/5.30               => ( ( ( groups3906332499630173760nt_rat @ G @ C4 )
% 9.53/5.30                    = ( groups3906332499630173760nt_rat @ H2 @ C4 ) )
% 9.53/5.30                 => ( ( groups3906332499630173760nt_rat @ G @ A2 )
% 9.53/5.30                    = ( groups3906332499630173760nt_rat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6594_sum_Osame__carrierI,axiom,
% 9.53/5.30      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > rat,H2: complex > rat] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ C4 )
% 9.53/5.30       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 9.53/5.30         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 9.53/5.30           => ( ! [A4: complex] :
% 9.53/5.30                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 9.53/5.30                 => ( ( G @ A4 )
% 9.53/5.30                    = zero_zero_rat ) )
% 9.53/5.30             => ( ! [B3: complex] :
% 9.53/5.30                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 9.53/5.30                   => ( ( H2 @ B3 )
% 9.53/5.30                      = zero_zero_rat ) )
% 9.53/5.30               => ( ( ( groups5058264527183730370ex_rat @ G @ C4 )
% 9.53/5.30                    = ( groups5058264527183730370ex_rat @ H2 @ C4 ) )
% 9.53/5.30                 => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 9.53/5.30                    = ( groups5058264527183730370ex_rat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6595_sum_Osame__carrierI,axiom,
% 9.53/5.30      ! [C4: set_int,A2: set_int,B2: set_int,G: int > nat,H2: int > nat] :
% 9.53/5.30        ( ( finite_finite_int @ C4 )
% 9.53/5.30       => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 9.53/5.30         => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 9.53/5.30           => ( ! [A4: int] :
% 9.53/5.30                  ( ( member_int @ A4 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 9.53/5.30                 => ( ( G @ A4 )
% 9.53/5.30                    = zero_zero_nat ) )
% 9.53/5.30             => ( ! [B3: int] :
% 9.53/5.30                    ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 9.53/5.30                   => ( ( H2 @ B3 )
% 9.53/5.30                      = zero_zero_nat ) )
% 9.53/5.30               => ( ( ( groups4541462559716669496nt_nat @ G @ C4 )
% 9.53/5.30                    = ( groups4541462559716669496nt_nat @ H2 @ C4 ) )
% 9.53/5.30                 => ( ( groups4541462559716669496nt_nat @ G @ A2 )
% 9.53/5.30                    = ( groups4541462559716669496nt_nat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6596_sum_Osame__carrierI,axiom,
% 9.53/5.30      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > nat,H2: complex > nat] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ C4 )
% 9.53/5.30       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 9.53/5.30         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 9.53/5.30           => ( ! [A4: complex] :
% 9.53/5.30                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 9.53/5.30                 => ( ( G @ A4 )
% 9.53/5.30                    = zero_zero_nat ) )
% 9.53/5.30             => ( ! [B3: complex] :
% 9.53/5.30                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 9.53/5.30                   => ( ( H2 @ B3 )
% 9.53/5.30                      = zero_zero_nat ) )
% 9.53/5.30               => ( ( ( groups5693394587270226106ex_nat @ G @ C4 )
% 9.53/5.30                    = ( groups5693394587270226106ex_nat @ H2 @ C4 ) )
% 9.53/5.30                 => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 9.53/5.30                    = ( groups5693394587270226106ex_nat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6597_sum_Osame__carrierI,axiom,
% 9.53/5.30      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > int,H2: complex > int] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ C4 )
% 9.53/5.30       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 9.53/5.30         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 9.53/5.30           => ( ! [A4: complex] :
% 9.53/5.30                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 9.53/5.30                 => ( ( G @ A4 )
% 9.53/5.30                    = zero_zero_int ) )
% 9.53/5.30             => ( ! [B3: complex] :
% 9.53/5.30                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 9.53/5.30                   => ( ( H2 @ B3 )
% 9.53/5.30                      = zero_zero_int ) )
% 9.53/5.30               => ( ( ( groups5690904116761175830ex_int @ G @ C4 )
% 9.53/5.30                    = ( groups5690904116761175830ex_int @ H2 @ C4 ) )
% 9.53/5.30                 => ( ( groups5690904116761175830ex_int @ G @ A2 )
% 9.53/5.30                    = ( groups5690904116761175830ex_int @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6598_sum_Osame__carrierI,axiom,
% 9.53/5.30      ! [C4: set_real,A2: set_real,B2: set_real,G: real > complex,H2: real > complex] :
% 9.53/5.30        ( ( finite_finite_real @ C4 )
% 9.53/5.30       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 9.53/5.30         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 9.53/5.30           => ( ! [A4: real] :
% 9.53/5.30                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 9.53/5.30                 => ( ( G @ A4 )
% 9.53/5.30                    = zero_zero_complex ) )
% 9.53/5.30             => ( ! [B3: real] :
% 9.53/5.30                    ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 9.53/5.30                   => ( ( H2 @ B3 )
% 9.53/5.30                      = zero_zero_complex ) )
% 9.53/5.30               => ( ( ( groups5754745047067104278omplex @ G @ C4 )
% 9.53/5.30                    = ( groups5754745047067104278omplex @ H2 @ C4 ) )
% 9.53/5.30                 => ( ( groups5754745047067104278omplex @ G @ A2 )
% 9.53/5.30                    = ( groups5754745047067104278omplex @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6599_sum_Osame__carrierI,axiom,
% 9.53/5.30      ! [C4: set_real,A2: set_real,B2: set_real,G: real > real,H2: real > real] :
% 9.53/5.30        ( ( finite_finite_real @ C4 )
% 9.53/5.30       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 9.53/5.30         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 9.53/5.30           => ( ! [A4: real] :
% 9.53/5.30                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 9.53/5.30                 => ( ( G @ A4 )
% 9.53/5.30                    = zero_zero_real ) )
% 9.53/5.30             => ( ! [B3: real] :
% 9.53/5.30                    ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 9.53/5.30                   => ( ( H2 @ B3 )
% 9.53/5.30                      = zero_zero_real ) )
% 9.53/5.30               => ( ( ( groups8097168146408367636l_real @ G @ C4 )
% 9.53/5.30                    = ( groups8097168146408367636l_real @ H2 @ C4 ) )
% 9.53/5.30                 => ( ( groups8097168146408367636l_real @ G @ A2 )
% 9.53/5.30                    = ( groups8097168146408367636l_real @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6600_sum_Omono__neutral__left,axiom,
% 9.53/5.30      ! [T4: set_complex,S2: set_complex,G: complex > real] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ T4 )
% 9.53/5.30       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: complex] :
% 9.53/5.30                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 9.53/5.30               => ( ( G @ X3 )
% 9.53/5.30                  = zero_zero_real ) )
% 9.53/5.30           => ( ( groups5808333547571424918x_real @ G @ S2 )
% 9.53/5.30              = ( groups5808333547571424918x_real @ G @ T4 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6601_sum_Omono__neutral__left,axiom,
% 9.53/5.30      ! [T4: set_complex,S2: set_complex,G: complex > rat] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ T4 )
% 9.53/5.30       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: complex] :
% 9.53/5.30                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 9.53/5.30               => ( ( G @ X3 )
% 9.53/5.30                  = zero_zero_rat ) )
% 9.53/5.30           => ( ( groups5058264527183730370ex_rat @ G @ S2 )
% 9.53/5.30              = ( groups5058264527183730370ex_rat @ G @ T4 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6602_sum_Omono__neutral__left,axiom,
% 9.53/5.30      ! [T4: set_complex,S2: set_complex,G: complex > nat] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ T4 )
% 9.53/5.30       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: complex] :
% 9.53/5.30                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 9.53/5.30               => ( ( G @ X3 )
% 9.53/5.30                  = zero_zero_nat ) )
% 9.53/5.30           => ( ( groups5693394587270226106ex_nat @ G @ S2 )
% 9.53/5.30              = ( groups5693394587270226106ex_nat @ G @ T4 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6603_sum_Omono__neutral__left,axiom,
% 9.53/5.30      ! [T4: set_complex,S2: set_complex,G: complex > int] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ T4 )
% 9.53/5.30       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: complex] :
% 9.53/5.30                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 9.53/5.30               => ( ( G @ X3 )
% 9.53/5.30                  = zero_zero_int ) )
% 9.53/5.30           => ( ( groups5690904116761175830ex_int @ G @ S2 )
% 9.53/5.30              = ( groups5690904116761175830ex_int @ G @ T4 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6604_sum_Omono__neutral__left,axiom,
% 9.53/5.30      ! [T4: set_real,S2: set_real,G: real > complex] :
% 9.53/5.30        ( ( finite_finite_real @ T4 )
% 9.53/5.30       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: real] :
% 9.53/5.30                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 9.53/5.30               => ( ( G @ X3 )
% 9.53/5.30                  = zero_zero_complex ) )
% 9.53/5.30           => ( ( groups5754745047067104278omplex @ G @ S2 )
% 9.53/5.30              = ( groups5754745047067104278omplex @ G @ T4 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6605_sum_Omono__neutral__left,axiom,
% 9.53/5.30      ! [T4: set_real,S2: set_real,G: real > real] :
% 9.53/5.30        ( ( finite_finite_real @ T4 )
% 9.53/5.30       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: real] :
% 9.53/5.30                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 9.53/5.30               => ( ( G @ X3 )
% 9.53/5.30                  = zero_zero_real ) )
% 9.53/5.30           => ( ( groups8097168146408367636l_real @ G @ S2 )
% 9.53/5.30              = ( groups8097168146408367636l_real @ G @ T4 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6606_sum_Omono__neutral__left,axiom,
% 9.53/5.30      ! [T4: set_real,S2: set_real,G: real > rat] :
% 9.53/5.30        ( ( finite_finite_real @ T4 )
% 9.53/5.30       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: real] :
% 9.53/5.30                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 9.53/5.30               => ( ( G @ X3 )
% 9.53/5.30                  = zero_zero_rat ) )
% 9.53/5.30           => ( ( groups1300246762558778688al_rat @ G @ S2 )
% 9.53/5.30              = ( groups1300246762558778688al_rat @ G @ T4 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6607_sum_Omono__neutral__left,axiom,
% 9.53/5.30      ! [T4: set_real,S2: set_real,G: real > nat] :
% 9.53/5.30        ( ( finite_finite_real @ T4 )
% 9.53/5.30       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: real] :
% 9.53/5.30                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 9.53/5.30               => ( ( G @ X3 )
% 9.53/5.30                  = zero_zero_nat ) )
% 9.53/5.30           => ( ( groups1935376822645274424al_nat @ G @ S2 )
% 9.53/5.30              = ( groups1935376822645274424al_nat @ G @ T4 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6608_sum_Omono__neutral__left,axiom,
% 9.53/5.30      ! [T4: set_real,S2: set_real,G: real > int] :
% 9.53/5.30        ( ( finite_finite_real @ T4 )
% 9.53/5.30       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: real] :
% 9.53/5.30                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 9.53/5.30               => ( ( G @ X3 )
% 9.53/5.30                  = zero_zero_int ) )
% 9.53/5.30           => ( ( groups1932886352136224148al_int @ G @ S2 )
% 9.53/5.30              = ( groups1932886352136224148al_int @ G @ T4 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6609_sum_Omono__neutral__left,axiom,
% 9.53/5.30      ! [T4: set_nat,S2: set_nat,G: nat > complex] :
% 9.53/5.30        ( ( finite_finite_nat @ T4 )
% 9.53/5.30       => ( ( ord_less_eq_set_nat @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: nat] :
% 9.53/5.30                ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T4 @ S2 ) )
% 9.53/5.30               => ( ( G @ X3 )
% 9.53/5.30                  = zero_zero_complex ) )
% 9.53/5.30           => ( ( groups2073611262835488442omplex @ G @ S2 )
% 9.53/5.30              = ( groups2073611262835488442omplex @ G @ T4 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6610_sum_Omono__neutral__right,axiom,
% 9.53/5.30      ! [T4: set_complex,S2: set_complex,G: complex > real] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ T4 )
% 9.53/5.30       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: complex] :
% 9.53/5.30                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 9.53/5.30               => ( ( G @ X3 )
% 9.53/5.30                  = zero_zero_real ) )
% 9.53/5.30           => ( ( groups5808333547571424918x_real @ G @ T4 )
% 9.53/5.30              = ( groups5808333547571424918x_real @ G @ S2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6611_sum_Omono__neutral__right,axiom,
% 9.53/5.30      ! [T4: set_complex,S2: set_complex,G: complex > rat] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ T4 )
% 9.53/5.30       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: complex] :
% 9.53/5.30                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 9.53/5.30               => ( ( G @ X3 )
% 9.53/5.30                  = zero_zero_rat ) )
% 9.53/5.30           => ( ( groups5058264527183730370ex_rat @ G @ T4 )
% 9.53/5.30              = ( groups5058264527183730370ex_rat @ G @ S2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6612_sum_Omono__neutral__right,axiom,
% 9.53/5.30      ! [T4: set_complex,S2: set_complex,G: complex > nat] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ T4 )
% 9.53/5.30       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: complex] :
% 9.53/5.30                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 9.53/5.30               => ( ( G @ X3 )
% 9.53/5.30                  = zero_zero_nat ) )
% 9.53/5.30           => ( ( groups5693394587270226106ex_nat @ G @ T4 )
% 9.53/5.30              = ( groups5693394587270226106ex_nat @ G @ S2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6613_sum_Omono__neutral__right,axiom,
% 9.53/5.30      ! [T4: set_complex,S2: set_complex,G: complex > int] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ T4 )
% 9.53/5.30       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: complex] :
% 9.53/5.30                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 9.53/5.30               => ( ( G @ X3 )
% 9.53/5.30                  = zero_zero_int ) )
% 9.53/5.30           => ( ( groups5690904116761175830ex_int @ G @ T4 )
% 9.53/5.30              = ( groups5690904116761175830ex_int @ G @ S2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6614_sum_Omono__neutral__right,axiom,
% 9.53/5.30      ! [T4: set_real,S2: set_real,G: real > complex] :
% 9.53/5.30        ( ( finite_finite_real @ T4 )
% 9.53/5.30       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: real] :
% 9.53/5.30                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 9.53/5.30               => ( ( G @ X3 )
% 9.53/5.30                  = zero_zero_complex ) )
% 9.53/5.30           => ( ( groups5754745047067104278omplex @ G @ T4 )
% 9.53/5.30              = ( groups5754745047067104278omplex @ G @ S2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6615_sum_Omono__neutral__right,axiom,
% 9.53/5.30      ! [T4: set_real,S2: set_real,G: real > real] :
% 9.53/5.30        ( ( finite_finite_real @ T4 )
% 9.53/5.30       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: real] :
% 9.53/5.30                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 9.53/5.30               => ( ( G @ X3 )
% 9.53/5.30                  = zero_zero_real ) )
% 9.53/5.30           => ( ( groups8097168146408367636l_real @ G @ T4 )
% 9.53/5.30              = ( groups8097168146408367636l_real @ G @ S2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6616_sum_Omono__neutral__right,axiom,
% 9.53/5.30      ! [T4: set_real,S2: set_real,G: real > rat] :
% 9.53/5.30        ( ( finite_finite_real @ T4 )
% 9.53/5.30       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: real] :
% 9.53/5.30                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 9.53/5.30               => ( ( G @ X3 )
% 9.53/5.30                  = zero_zero_rat ) )
% 9.53/5.30           => ( ( groups1300246762558778688al_rat @ G @ T4 )
% 9.53/5.30              = ( groups1300246762558778688al_rat @ G @ S2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6617_sum_Omono__neutral__right,axiom,
% 9.53/5.30      ! [T4: set_real,S2: set_real,G: real > nat] :
% 9.53/5.30        ( ( finite_finite_real @ T4 )
% 9.53/5.30       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: real] :
% 9.53/5.30                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 9.53/5.30               => ( ( G @ X3 )
% 9.53/5.30                  = zero_zero_nat ) )
% 9.53/5.30           => ( ( groups1935376822645274424al_nat @ G @ T4 )
% 9.53/5.30              = ( groups1935376822645274424al_nat @ G @ S2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6618_sum_Omono__neutral__right,axiom,
% 9.53/5.30      ! [T4: set_real,S2: set_real,G: real > int] :
% 9.53/5.30        ( ( finite_finite_real @ T4 )
% 9.53/5.30       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: real] :
% 9.53/5.30                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 9.53/5.30               => ( ( G @ X3 )
% 9.53/5.30                  = zero_zero_int ) )
% 9.53/5.30           => ( ( groups1932886352136224148al_int @ G @ T4 )
% 9.53/5.30              = ( groups1932886352136224148al_int @ G @ S2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6619_sum_Omono__neutral__right,axiom,
% 9.53/5.30      ! [T4: set_nat,S2: set_nat,G: nat > complex] :
% 9.53/5.30        ( ( finite_finite_nat @ T4 )
% 9.53/5.30       => ( ( ord_less_eq_set_nat @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: nat] :
% 9.53/5.30                ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T4 @ S2 ) )
% 9.53/5.30               => ( ( G @ X3 )
% 9.53/5.30                  = zero_zero_complex ) )
% 9.53/5.30           => ( ( groups2073611262835488442omplex @ G @ T4 )
% 9.53/5.30              = ( groups2073611262835488442omplex @ G @ S2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6620_sum_Omono__neutral__cong__left,axiom,
% 9.53/5.30      ! [T4: set_int,S2: set_int,H2: int > complex,G: int > complex] :
% 9.53/5.30        ( ( finite_finite_int @ T4 )
% 9.53/5.30       => ( ( ord_less_eq_set_int @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: int] :
% 9.53/5.30                ( ( member_int @ X3 @ ( minus_minus_set_int @ T4 @ S2 ) )
% 9.53/5.30               => ( ( H2 @ X3 )
% 9.53/5.30                  = zero_zero_complex ) )
% 9.53/5.30           => ( ! [X3: int] :
% 9.53/5.30                  ( ( member_int @ X3 @ S2 )
% 9.53/5.30                 => ( ( G @ X3 )
% 9.53/5.30                    = ( H2 @ X3 ) ) )
% 9.53/5.30             => ( ( groups3049146728041665814omplex @ G @ S2 )
% 9.53/5.30                = ( groups3049146728041665814omplex @ H2 @ T4 ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6621_sum_Omono__neutral__cong__left,axiom,
% 9.53/5.30      ! [T4: set_int,S2: set_int,H2: int > real,G: int > real] :
% 9.53/5.30        ( ( finite_finite_int @ T4 )
% 9.53/5.30       => ( ( ord_less_eq_set_int @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: int] :
% 9.53/5.30                ( ( member_int @ X3 @ ( minus_minus_set_int @ T4 @ S2 ) )
% 9.53/5.30               => ( ( H2 @ X3 )
% 9.53/5.30                  = zero_zero_real ) )
% 9.53/5.30           => ( ! [X3: int] :
% 9.53/5.30                  ( ( member_int @ X3 @ S2 )
% 9.53/5.30                 => ( ( G @ X3 )
% 9.53/5.30                    = ( H2 @ X3 ) ) )
% 9.53/5.30             => ( ( groups8778361861064173332t_real @ G @ S2 )
% 9.53/5.30                = ( groups8778361861064173332t_real @ H2 @ T4 ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6622_sum_Omono__neutral__cong__left,axiom,
% 9.53/5.30      ! [T4: set_complex,S2: set_complex,H2: complex > real,G: complex > real] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ T4 )
% 9.53/5.30       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: complex] :
% 9.53/5.30                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 9.53/5.30               => ( ( H2 @ X3 )
% 9.53/5.30                  = zero_zero_real ) )
% 9.53/5.30           => ( ! [X3: complex] :
% 9.53/5.30                  ( ( member_complex @ X3 @ S2 )
% 9.53/5.30                 => ( ( G @ X3 )
% 9.53/5.30                    = ( H2 @ X3 ) ) )
% 9.53/5.30             => ( ( groups5808333547571424918x_real @ G @ S2 )
% 9.53/5.30                = ( groups5808333547571424918x_real @ H2 @ T4 ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6623_sum_Omono__neutral__cong__left,axiom,
% 9.53/5.30      ! [T4: set_int,S2: set_int,H2: int > rat,G: int > rat] :
% 9.53/5.30        ( ( finite_finite_int @ T4 )
% 9.53/5.30       => ( ( ord_less_eq_set_int @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: int] :
% 9.53/5.30                ( ( member_int @ X3 @ ( minus_minus_set_int @ T4 @ S2 ) )
% 9.53/5.30               => ( ( H2 @ X3 )
% 9.53/5.30                  = zero_zero_rat ) )
% 9.53/5.30           => ( ! [X3: int] :
% 9.53/5.30                  ( ( member_int @ X3 @ S2 )
% 9.53/5.30                 => ( ( G @ X3 )
% 9.53/5.30                    = ( H2 @ X3 ) ) )
% 9.53/5.30             => ( ( groups3906332499630173760nt_rat @ G @ S2 )
% 9.53/5.30                = ( groups3906332499630173760nt_rat @ H2 @ T4 ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6624_sum_Omono__neutral__cong__left,axiom,
% 9.53/5.30      ! [T4: set_complex,S2: set_complex,H2: complex > rat,G: complex > rat] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ T4 )
% 9.53/5.30       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: complex] :
% 9.53/5.30                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 9.53/5.30               => ( ( H2 @ X3 )
% 9.53/5.30                  = zero_zero_rat ) )
% 9.53/5.30           => ( ! [X3: complex] :
% 9.53/5.30                  ( ( member_complex @ X3 @ S2 )
% 9.53/5.30                 => ( ( G @ X3 )
% 9.53/5.30                    = ( H2 @ X3 ) ) )
% 9.53/5.30             => ( ( groups5058264527183730370ex_rat @ G @ S2 )
% 9.53/5.30                = ( groups5058264527183730370ex_rat @ H2 @ T4 ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6625_sum_Omono__neutral__cong__left,axiom,
% 9.53/5.30      ! [T4: set_int,S2: set_int,H2: int > nat,G: int > nat] :
% 9.53/5.30        ( ( finite_finite_int @ T4 )
% 9.53/5.30       => ( ( ord_less_eq_set_int @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: int] :
% 9.53/5.30                ( ( member_int @ X3 @ ( minus_minus_set_int @ T4 @ S2 ) )
% 9.53/5.30               => ( ( H2 @ X3 )
% 9.53/5.30                  = zero_zero_nat ) )
% 9.53/5.30           => ( ! [X3: int] :
% 9.53/5.30                  ( ( member_int @ X3 @ S2 )
% 9.53/5.30                 => ( ( G @ X3 )
% 9.53/5.30                    = ( H2 @ X3 ) ) )
% 9.53/5.30             => ( ( groups4541462559716669496nt_nat @ G @ S2 )
% 9.53/5.30                = ( groups4541462559716669496nt_nat @ H2 @ T4 ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6626_sum_Omono__neutral__cong__left,axiom,
% 9.53/5.30      ! [T4: set_complex,S2: set_complex,H2: complex > nat,G: complex > nat] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ T4 )
% 9.53/5.30       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: complex] :
% 9.53/5.30                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 9.53/5.30               => ( ( H2 @ X3 )
% 9.53/5.30                  = zero_zero_nat ) )
% 9.53/5.30           => ( ! [X3: complex] :
% 9.53/5.30                  ( ( member_complex @ X3 @ S2 )
% 9.53/5.30                 => ( ( G @ X3 )
% 9.53/5.30                    = ( H2 @ X3 ) ) )
% 9.53/5.30             => ( ( groups5693394587270226106ex_nat @ G @ S2 )
% 9.53/5.30                = ( groups5693394587270226106ex_nat @ H2 @ T4 ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6627_sum_Omono__neutral__cong__left,axiom,
% 9.53/5.30      ! [T4: set_complex,S2: set_complex,H2: complex > int,G: complex > int] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ T4 )
% 9.53/5.30       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: complex] :
% 9.53/5.30                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 9.53/5.30               => ( ( H2 @ X3 )
% 9.53/5.30                  = zero_zero_int ) )
% 9.53/5.30           => ( ! [X3: complex] :
% 9.53/5.30                  ( ( member_complex @ X3 @ S2 )
% 9.53/5.30                 => ( ( G @ X3 )
% 9.53/5.30                    = ( H2 @ X3 ) ) )
% 9.53/5.30             => ( ( groups5690904116761175830ex_int @ G @ S2 )
% 9.53/5.30                = ( groups5690904116761175830ex_int @ H2 @ T4 ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6628_sum_Omono__neutral__cong__left,axiom,
% 9.53/5.30      ! [T4: set_real,S2: set_real,H2: real > complex,G: real > complex] :
% 9.53/5.30        ( ( finite_finite_real @ T4 )
% 9.53/5.30       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: real] :
% 9.53/5.30                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 9.53/5.30               => ( ( H2 @ X3 )
% 9.53/5.30                  = zero_zero_complex ) )
% 9.53/5.30           => ( ! [X3: real] :
% 9.53/5.30                  ( ( member_real @ X3 @ S2 )
% 9.53/5.30                 => ( ( G @ X3 )
% 9.53/5.30                    = ( H2 @ X3 ) ) )
% 9.53/5.30             => ( ( groups5754745047067104278omplex @ G @ S2 )
% 9.53/5.30                = ( groups5754745047067104278omplex @ H2 @ T4 ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6629_sum_Omono__neutral__cong__left,axiom,
% 9.53/5.30      ! [T4: set_real,S2: set_real,H2: real > real,G: real > real] :
% 9.53/5.30        ( ( finite_finite_real @ T4 )
% 9.53/5.30       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: real] :
% 9.53/5.30                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 9.53/5.30               => ( ( H2 @ X3 )
% 9.53/5.30                  = zero_zero_real ) )
% 9.53/5.30           => ( ! [X3: real] :
% 9.53/5.30                  ( ( member_real @ X3 @ S2 )
% 9.53/5.30                 => ( ( G @ X3 )
% 9.53/5.30                    = ( H2 @ X3 ) ) )
% 9.53/5.30             => ( ( groups8097168146408367636l_real @ G @ S2 )
% 9.53/5.30                = ( groups8097168146408367636l_real @ H2 @ T4 ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6630_sum_Omono__neutral__cong__right,axiom,
% 9.53/5.30      ! [T4: set_int,S2: set_int,G: int > complex,H2: int > complex] :
% 9.53/5.30        ( ( finite_finite_int @ T4 )
% 9.53/5.30       => ( ( ord_less_eq_set_int @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: int] :
% 9.53/5.30                ( ( member_int @ X3 @ ( minus_minus_set_int @ T4 @ S2 ) )
% 9.53/5.30               => ( ( G @ X3 )
% 9.53/5.30                  = zero_zero_complex ) )
% 9.53/5.30           => ( ! [X3: int] :
% 9.53/5.30                  ( ( member_int @ X3 @ S2 )
% 9.53/5.30                 => ( ( G @ X3 )
% 9.53/5.30                    = ( H2 @ X3 ) ) )
% 9.53/5.30             => ( ( groups3049146728041665814omplex @ G @ T4 )
% 9.53/5.30                = ( groups3049146728041665814omplex @ H2 @ S2 ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6631_sum_Omono__neutral__cong__right,axiom,
% 9.53/5.30      ! [T4: set_int,S2: set_int,G: int > real,H2: int > real] :
% 9.53/5.30        ( ( finite_finite_int @ T4 )
% 9.53/5.30       => ( ( ord_less_eq_set_int @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: int] :
% 9.53/5.30                ( ( member_int @ X3 @ ( minus_minus_set_int @ T4 @ S2 ) )
% 9.53/5.30               => ( ( G @ X3 )
% 9.53/5.30                  = zero_zero_real ) )
% 9.53/5.30           => ( ! [X3: int] :
% 9.53/5.30                  ( ( member_int @ X3 @ S2 )
% 9.53/5.30                 => ( ( G @ X3 )
% 9.53/5.30                    = ( H2 @ X3 ) ) )
% 9.53/5.30             => ( ( groups8778361861064173332t_real @ G @ T4 )
% 9.53/5.30                = ( groups8778361861064173332t_real @ H2 @ S2 ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6632_sum_Omono__neutral__cong__right,axiom,
% 9.53/5.30      ! [T4: set_complex,S2: set_complex,G: complex > real,H2: complex > real] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ T4 )
% 9.53/5.30       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: complex] :
% 9.53/5.30                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 9.53/5.30               => ( ( G @ X3 )
% 9.53/5.30                  = zero_zero_real ) )
% 9.53/5.30           => ( ! [X3: complex] :
% 9.53/5.30                  ( ( member_complex @ X3 @ S2 )
% 9.53/5.30                 => ( ( G @ X3 )
% 9.53/5.30                    = ( H2 @ X3 ) ) )
% 9.53/5.30             => ( ( groups5808333547571424918x_real @ G @ T4 )
% 9.53/5.30                = ( groups5808333547571424918x_real @ H2 @ S2 ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6633_sum_Omono__neutral__cong__right,axiom,
% 9.53/5.30      ! [T4: set_int,S2: set_int,G: int > rat,H2: int > rat] :
% 9.53/5.30        ( ( finite_finite_int @ T4 )
% 9.53/5.30       => ( ( ord_less_eq_set_int @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: int] :
% 9.53/5.30                ( ( member_int @ X3 @ ( minus_minus_set_int @ T4 @ S2 ) )
% 9.53/5.30               => ( ( G @ X3 )
% 9.53/5.30                  = zero_zero_rat ) )
% 9.53/5.30           => ( ! [X3: int] :
% 9.53/5.30                  ( ( member_int @ X3 @ S2 )
% 9.53/5.30                 => ( ( G @ X3 )
% 9.53/5.30                    = ( H2 @ X3 ) ) )
% 9.53/5.30             => ( ( groups3906332499630173760nt_rat @ G @ T4 )
% 9.53/5.30                = ( groups3906332499630173760nt_rat @ H2 @ S2 ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6634_sum_Omono__neutral__cong__right,axiom,
% 9.53/5.30      ! [T4: set_complex,S2: set_complex,G: complex > rat,H2: complex > rat] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ T4 )
% 9.53/5.30       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: complex] :
% 9.53/5.30                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 9.53/5.30               => ( ( G @ X3 )
% 9.53/5.30                  = zero_zero_rat ) )
% 9.53/5.30           => ( ! [X3: complex] :
% 9.53/5.30                  ( ( member_complex @ X3 @ S2 )
% 9.53/5.30                 => ( ( G @ X3 )
% 9.53/5.30                    = ( H2 @ X3 ) ) )
% 9.53/5.30             => ( ( groups5058264527183730370ex_rat @ G @ T4 )
% 9.53/5.30                = ( groups5058264527183730370ex_rat @ H2 @ S2 ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6635_sum_Omono__neutral__cong__right,axiom,
% 9.53/5.30      ! [T4: set_int,S2: set_int,G: int > nat,H2: int > nat] :
% 9.53/5.30        ( ( finite_finite_int @ T4 )
% 9.53/5.30       => ( ( ord_less_eq_set_int @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: int] :
% 9.53/5.30                ( ( member_int @ X3 @ ( minus_minus_set_int @ T4 @ S2 ) )
% 9.53/5.30               => ( ( G @ X3 )
% 9.53/5.30                  = zero_zero_nat ) )
% 9.53/5.30           => ( ! [X3: int] :
% 9.53/5.30                  ( ( member_int @ X3 @ S2 )
% 9.53/5.30                 => ( ( G @ X3 )
% 9.53/5.30                    = ( H2 @ X3 ) ) )
% 9.53/5.30             => ( ( groups4541462559716669496nt_nat @ G @ T4 )
% 9.53/5.30                = ( groups4541462559716669496nt_nat @ H2 @ S2 ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6636_sum_Omono__neutral__cong__right,axiom,
% 9.53/5.30      ! [T4: set_complex,S2: set_complex,G: complex > nat,H2: complex > nat] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ T4 )
% 9.53/5.30       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: complex] :
% 9.53/5.30                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 9.53/5.30               => ( ( G @ X3 )
% 9.53/5.30                  = zero_zero_nat ) )
% 9.53/5.30           => ( ! [X3: complex] :
% 9.53/5.30                  ( ( member_complex @ X3 @ S2 )
% 9.53/5.30                 => ( ( G @ X3 )
% 9.53/5.30                    = ( H2 @ X3 ) ) )
% 9.53/5.30             => ( ( groups5693394587270226106ex_nat @ G @ T4 )
% 9.53/5.30                = ( groups5693394587270226106ex_nat @ H2 @ S2 ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6637_sum_Omono__neutral__cong__right,axiom,
% 9.53/5.30      ! [T4: set_complex,S2: set_complex,G: complex > int,H2: complex > int] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ T4 )
% 9.53/5.30       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: complex] :
% 9.53/5.30                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 9.53/5.30               => ( ( G @ X3 )
% 9.53/5.30                  = zero_zero_int ) )
% 9.53/5.30           => ( ! [X3: complex] :
% 9.53/5.30                  ( ( member_complex @ X3 @ S2 )
% 9.53/5.30                 => ( ( G @ X3 )
% 9.53/5.30                    = ( H2 @ X3 ) ) )
% 9.53/5.30             => ( ( groups5690904116761175830ex_int @ G @ T4 )
% 9.53/5.30                = ( groups5690904116761175830ex_int @ H2 @ S2 ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6638_sum_Omono__neutral__cong__right,axiom,
% 9.53/5.30      ! [T4: set_real,S2: set_real,G: real > complex,H2: real > complex] :
% 9.53/5.30        ( ( finite_finite_real @ T4 )
% 9.53/5.30       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: real] :
% 9.53/5.30                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 9.53/5.30               => ( ( G @ X3 )
% 9.53/5.30                  = zero_zero_complex ) )
% 9.53/5.30           => ( ! [X3: real] :
% 9.53/5.30                  ( ( member_real @ X3 @ S2 )
% 9.53/5.30                 => ( ( G @ X3 )
% 9.53/5.30                    = ( H2 @ X3 ) ) )
% 9.53/5.30             => ( ( groups5754745047067104278omplex @ G @ T4 )
% 9.53/5.30                = ( groups5754745047067104278omplex @ H2 @ S2 ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6639_sum_Omono__neutral__cong__right,axiom,
% 9.53/5.30      ! [T4: set_real,S2: set_real,G: real > real,H2: real > real] :
% 9.53/5.30        ( ( finite_finite_real @ T4 )
% 9.53/5.30       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 9.53/5.30         => ( ! [X3: real] :
% 9.53/5.30                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 9.53/5.30               => ( ( G @ X3 )
% 9.53/5.30                  = zero_zero_real ) )
% 9.53/5.30           => ( ! [X3: real] :
% 9.53/5.30                  ( ( member_real @ X3 @ S2 )
% 9.53/5.30                 => ( ( G @ X3 )
% 9.53/5.30                    = ( H2 @ X3 ) ) )
% 9.53/5.30             => ( ( groups8097168146408367636l_real @ G @ T4 )
% 9.53/5.30                = ( groups8097168146408367636l_real @ H2 @ S2 ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6640_sum_Osubset__diff,axiom,
% 9.53/5.30      ! [B2: set_complex,A2: set_complex,G: complex > real] :
% 9.53/5.30        ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 9.53/5.30       => ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.30         => ( ( groups5808333547571424918x_real @ G @ A2 )
% 9.53/5.30            = ( plus_plus_real @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups5808333547571424918x_real @ G @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6641_sum_Osubset__diff,axiom,
% 9.53/5.30      ! [B2: set_complex,A2: set_complex,G: complex > rat] :
% 9.53/5.30        ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 9.53/5.30       => ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.30         => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 9.53/5.30            = ( plus_plus_rat @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups5058264527183730370ex_rat @ G @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6642_sum_Osubset__diff,axiom,
% 9.53/5.30      ! [B2: set_complex,A2: set_complex,G: complex > nat] :
% 9.53/5.30        ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 9.53/5.30       => ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.30         => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 9.53/5.30            = ( plus_plus_nat @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups5693394587270226106ex_nat @ G @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6643_sum_Osubset__diff,axiom,
% 9.53/5.30      ! [B2: set_complex,A2: set_complex,G: complex > int] :
% 9.53/5.30        ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 9.53/5.30       => ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.30         => ( ( groups5690904116761175830ex_int @ G @ A2 )
% 9.53/5.30            = ( plus_plus_int @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups5690904116761175830ex_int @ G @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6644_sum_Osubset__diff,axiom,
% 9.53/5.30      ! [B2: set_real,A2: set_real,G: real > real] :
% 9.53/5.30        ( ( ord_less_eq_set_real @ B2 @ A2 )
% 9.53/5.30       => ( ( finite_finite_real @ A2 )
% 9.53/5.30         => ( ( groups8097168146408367636l_real @ G @ A2 )
% 9.53/5.30            = ( plus_plus_real @ ( groups8097168146408367636l_real @ G @ ( minus_minus_set_real @ A2 @ B2 ) ) @ ( groups8097168146408367636l_real @ G @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6645_sum_Osubset__diff,axiom,
% 9.53/5.30      ! [B2: set_real,A2: set_real,G: real > rat] :
% 9.53/5.30        ( ( ord_less_eq_set_real @ B2 @ A2 )
% 9.53/5.30       => ( ( finite_finite_real @ A2 )
% 9.53/5.30         => ( ( groups1300246762558778688al_rat @ G @ A2 )
% 9.53/5.30            = ( plus_plus_rat @ ( groups1300246762558778688al_rat @ G @ ( minus_minus_set_real @ A2 @ B2 ) ) @ ( groups1300246762558778688al_rat @ G @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6646_sum_Osubset__diff,axiom,
% 9.53/5.30      ! [B2: set_real,A2: set_real,G: real > nat] :
% 9.53/5.30        ( ( ord_less_eq_set_real @ B2 @ A2 )
% 9.53/5.30       => ( ( finite_finite_real @ A2 )
% 9.53/5.30         => ( ( groups1935376822645274424al_nat @ G @ A2 )
% 9.53/5.30            = ( plus_plus_nat @ ( groups1935376822645274424al_nat @ G @ ( minus_minus_set_real @ A2 @ B2 ) ) @ ( groups1935376822645274424al_nat @ G @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6647_sum_Osubset__diff,axiom,
% 9.53/5.30      ! [B2: set_real,A2: set_real,G: real > int] :
% 9.53/5.30        ( ( ord_less_eq_set_real @ B2 @ A2 )
% 9.53/5.30       => ( ( finite_finite_real @ A2 )
% 9.53/5.30         => ( ( groups1932886352136224148al_int @ G @ A2 )
% 9.53/5.30            = ( plus_plus_int @ ( groups1932886352136224148al_int @ G @ ( minus_minus_set_real @ A2 @ B2 ) ) @ ( groups1932886352136224148al_int @ G @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6648_sum_Osubset__diff,axiom,
% 9.53/5.30      ! [B2: set_real,A2: set_real,G: real > complex] :
% 9.53/5.30        ( ( ord_less_eq_set_real @ B2 @ A2 )
% 9.53/5.30       => ( ( finite_finite_real @ A2 )
% 9.53/5.30         => ( ( groups5754745047067104278omplex @ G @ A2 )
% 9.53/5.30            = ( plus_plus_complex @ ( groups5754745047067104278omplex @ G @ ( minus_minus_set_real @ A2 @ B2 ) ) @ ( groups5754745047067104278omplex @ G @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6649_sum_Osubset__diff,axiom,
% 9.53/5.30      ! [B2: set_nat,A2: set_nat,G: nat > rat] :
% 9.53/5.30        ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 9.53/5.30       => ( ( finite_finite_nat @ A2 )
% 9.53/5.30         => ( ( groups2906978787729119204at_rat @ G @ A2 )
% 9.53/5.30            = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups2906978787729119204at_rat @ G @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6650_sum__diff,axiom,
% 9.53/5.30      ! [A2: set_complex,B2: set_complex,F: complex > rat] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.30       => ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 9.53/5.30         => ( ( groups5058264527183730370ex_rat @ F @ ( minus_811609699411566653omplex @ A2 @ B2 ) )
% 9.53/5.30            = ( minus_minus_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ F @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6651_sum__diff,axiom,
% 9.53/5.30      ! [A2: set_complex,B2: set_complex,F: complex > int] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.30       => ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 9.53/5.30         => ( ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ B2 ) )
% 9.53/5.30            = ( minus_minus_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ F @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6652_sum__diff,axiom,
% 9.53/5.30      ! [A2: set_real,B2: set_real,F: real > rat] :
% 9.53/5.30        ( ( finite_finite_real @ A2 )
% 9.53/5.30       => ( ( ord_less_eq_set_real @ B2 @ A2 )
% 9.53/5.30         => ( ( groups1300246762558778688al_rat @ F @ ( minus_minus_set_real @ A2 @ B2 ) )
% 9.53/5.30            = ( minus_minus_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ F @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6653_sum__diff,axiom,
% 9.53/5.30      ! [A2: set_real,B2: set_real,F: real > int] :
% 9.53/5.30        ( ( finite_finite_real @ A2 )
% 9.53/5.30       => ( ( ord_less_eq_set_real @ B2 @ A2 )
% 9.53/5.30         => ( ( groups1932886352136224148al_int @ F @ ( minus_minus_set_real @ A2 @ B2 ) )
% 9.53/5.30            = ( minus_minus_int @ ( groups1932886352136224148al_int @ F @ A2 ) @ ( groups1932886352136224148al_int @ F @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6654_sum__diff,axiom,
% 9.53/5.30      ! [A2: set_nat,B2: set_nat,F: nat > rat] :
% 9.53/5.30        ( ( finite_finite_nat @ A2 )
% 9.53/5.30       => ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 9.53/5.30         => ( ( groups2906978787729119204at_rat @ F @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 9.53/5.30            = ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ F @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6655_sum__diff,axiom,
% 9.53/5.30      ! [A2: set_nat,B2: set_nat,F: nat > int] :
% 9.53/5.30        ( ( finite_finite_nat @ A2 )
% 9.53/5.30       => ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 9.53/5.30         => ( ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 9.53/5.30            = ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ F @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6656_sum__diff,axiom,
% 9.53/5.30      ! [A2: set_int,B2: set_int,F: int > int] :
% 9.53/5.30        ( ( finite_finite_int @ A2 )
% 9.53/5.30       => ( ( ord_less_eq_set_int @ B2 @ A2 )
% 9.53/5.30         => ( ( groups4538972089207619220nt_int @ F @ ( minus_minus_set_int @ A2 @ B2 ) )
% 9.53/5.30            = ( minus_minus_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ F @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6657_sum__diff,axiom,
% 9.53/5.30      ! [A2: set_complex,B2: set_complex,F: complex > complex] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.30       => ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 9.53/5.30         => ( ( groups7754918857620584856omplex @ F @ ( minus_811609699411566653omplex @ A2 @ B2 ) )
% 9.53/5.30            = ( minus_minus_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ ( groups7754918857620584856omplex @ F @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6658_sum__diff,axiom,
% 9.53/5.30      ! [A2: set_nat,B2: set_nat,F: nat > real] :
% 9.53/5.30        ( ( finite_finite_nat @ A2 )
% 9.53/5.30       => ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 9.53/5.30         => ( ( groups6591440286371151544t_real @ F @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 9.53/5.30            = ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ F @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6659_sum__diff,axiom,
% 9.53/5.30      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > rat] :
% 9.53/5.30        ( ( finite6177210948735845034at_nat @ A2 )
% 9.53/5.30       => ( ( ord_le3146513528884898305at_nat @ B2 @ A2 )
% 9.53/5.30         => ( ( groups342789780944988191at_rat @ F @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) )
% 9.53/5.30            = ( minus_minus_rat @ ( groups342789780944988191at_rat @ F @ A2 ) @ ( groups342789780944988191at_rat @ F @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6660_exp__ge__add__one__self__aux,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.30       => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X ) @ ( exp_real @ X ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6661_lemma__exp__total,axiom,
% 9.53/5.30      ! [Y2: real] :
% 9.53/5.30        ( ( ord_less_eq_real @ one_one_real @ Y2 )
% 9.53/5.30       => ? [X3: real] :
% 9.53/5.30            ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 9.53/5.30            & ( ord_less_eq_real @ X3 @ ( minus_minus_real @ Y2 @ one_one_real ) )
% 9.53/5.30            & ( ( exp_real @ X3 )
% 9.53/5.30              = Y2 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6662_ln__ge__iff,axiom,
% 9.53/5.30      ! [X: real,Y2: real] :
% 9.53/5.30        ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.30       => ( ( ord_less_eq_real @ Y2 @ ( ln_ln_real @ X ) )
% 9.53/5.30          = ( ord_less_eq_real @ ( exp_real @ Y2 ) @ X ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6663_ln__x__over__x__mono,axiom,
% 9.53/5.30      ! [X: real,Y2: real] :
% 9.53/5.30        ( ( ord_less_eq_real @ ( exp_real @ one_one_real ) @ X )
% 9.53/5.30       => ( ( ord_less_eq_real @ X @ Y2 )
% 9.53/5.30         => ( ord_less_eq_real @ ( divide_divide_real @ ( ln_ln_real @ Y2 ) @ Y2 ) @ ( divide_divide_real @ ( ln_ln_real @ X ) @ X ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6664_take__bit__Suc__bit0,axiom,
% 9.53/5.30      ! [N: nat,K: num] :
% 9.53/5.30        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 9.53/5.30        = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6665_take__bit__Suc__bit0,axiom,
% 9.53/5.30      ! [N: nat,K: num] :
% 9.53/5.30        ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 9.53/5.30        = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6666_take__bit__eq__mod,axiom,
% 9.53/5.30      ( bit_se2923211474154528505it_int
% 9.53/5.30      = ( ^ [N2: nat,A3: int] : ( modulo_modulo_int @ A3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6667_take__bit__eq__mod,axiom,
% 9.53/5.30      ( bit_se2925701944663578781it_nat
% 9.53/5.30      = ( ^ [N2: nat,A3: nat] : ( modulo_modulo_nat @ A3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6668_sum__mono2,axiom,
% 9.53/5.30      ! [B2: set_int,A2: set_int,F: int > real] :
% 9.53/5.30        ( ( finite_finite_int @ B2 )
% 9.53/5.30       => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 9.53/5.30         => ( ! [B3: int] :
% 9.53/5.30                ( ( member_int @ B3 @ ( minus_minus_set_int @ B2 @ A2 ) )
% 9.53/5.30               => ( ord_less_eq_real @ zero_zero_real @ ( F @ B3 ) ) )
% 9.53/5.30           => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ F @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6669_sum__mono2,axiom,
% 9.53/5.30      ! [B2: set_complex,A2: set_complex,F: complex > real] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ B2 )
% 9.53/5.30       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 9.53/5.30         => ( ! [B3: complex] :
% 9.53/5.30                ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 9.53/5.30               => ( ord_less_eq_real @ zero_zero_real @ ( F @ B3 ) ) )
% 9.53/5.30           => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6670_sum__mono2,axiom,
% 9.53/5.30      ! [B2: set_int,A2: set_int,F: int > rat] :
% 9.53/5.30        ( ( finite_finite_int @ B2 )
% 9.53/5.30       => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 9.53/5.30         => ( ! [B3: int] :
% 9.53/5.30                ( ( member_int @ B3 @ ( minus_minus_set_int @ B2 @ A2 ) )
% 9.53/5.30               => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B3 ) ) )
% 9.53/5.30           => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ F @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6671_sum__mono2,axiom,
% 9.53/5.30      ! [B2: set_complex,A2: set_complex,F: complex > rat] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ B2 )
% 9.53/5.30       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 9.53/5.30         => ( ! [B3: complex] :
% 9.53/5.30                ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 9.53/5.30               => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B3 ) ) )
% 9.53/5.30           => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ F @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6672_sum__mono2,axiom,
% 9.53/5.30      ! [B2: set_int,A2: set_int,F: int > nat] :
% 9.53/5.30        ( ( finite_finite_int @ B2 )
% 9.53/5.30       => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 9.53/5.30         => ( ! [B3: int] :
% 9.53/5.30                ( ( member_int @ B3 @ ( minus_minus_set_int @ B2 @ A2 ) )
% 9.53/5.30               => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B3 ) ) )
% 9.53/5.30           => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ F @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6673_sum__mono2,axiom,
% 9.53/5.30      ! [B2: set_complex,A2: set_complex,F: complex > nat] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ B2 )
% 9.53/5.30       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 9.53/5.30         => ( ! [B3: complex] :
% 9.53/5.30                ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 9.53/5.30               => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B3 ) ) )
% 9.53/5.30           => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6674_sum__mono2,axiom,
% 9.53/5.30      ! [B2: set_complex,A2: set_complex,F: complex > int] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ B2 )
% 9.53/5.30       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 9.53/5.30         => ( ! [B3: complex] :
% 9.53/5.30                ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 9.53/5.30               => ( ord_less_eq_int @ zero_zero_int @ ( F @ B3 ) ) )
% 9.53/5.30           => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ F @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6675_sum__mono2,axiom,
% 9.53/5.30      ! [B2: set_real,A2: set_real,F: real > real] :
% 9.53/5.30        ( ( finite_finite_real @ B2 )
% 9.53/5.30       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 9.53/5.30         => ( ! [B3: real] :
% 9.53/5.30                ( ( member_real @ B3 @ ( minus_minus_set_real @ B2 @ A2 ) )
% 9.53/5.30               => ( ord_less_eq_real @ zero_zero_real @ ( F @ B3 ) ) )
% 9.53/5.30           => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ F @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6676_sum__mono2,axiom,
% 9.53/5.30      ! [B2: set_real,A2: set_real,F: real > rat] :
% 9.53/5.30        ( ( finite_finite_real @ B2 )
% 9.53/5.30       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 9.53/5.30         => ( ! [B3: real] :
% 9.53/5.30                ( ( member_real @ B3 @ ( minus_minus_set_real @ B2 @ A2 ) )
% 9.53/5.30               => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B3 ) ) )
% 9.53/5.30           => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ F @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6677_sum__mono2,axiom,
% 9.53/5.30      ! [B2: set_real,A2: set_real,F: real > nat] :
% 9.53/5.30        ( ( finite_finite_real @ B2 )
% 9.53/5.30       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 9.53/5.30         => ( ! [B3: real] :
% 9.53/5.30                ( ( member_real @ B3 @ ( minus_minus_set_real @ B2 @ A2 ) )
% 9.53/5.30               => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B3 ) ) )
% 9.53/5.30           => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ F @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6678_take__bit__nat__eq__self__iff,axiom,
% 9.53/5.30      ! [N: nat,M: nat] :
% 9.53/5.30        ( ( ( bit_se2925701944663578781it_nat @ N @ M )
% 9.53/5.30          = M )
% 9.53/5.30        = ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6679_take__bit__nat__less__exp,axiom,
% 9.53/5.30      ! [N: nat,M: nat] : ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6680_take__bit__nat__eq__self,axiom,
% 9.53/5.30      ! [M: nat,N: nat] :
% 9.53/5.30        ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.53/5.30       => ( ( bit_se2925701944663578781it_nat @ N @ M )
% 9.53/5.30          = M ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6681_sum_Oinsert__remove,axiom,
% 9.53/5.30      ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > real,X: vEBT_VEBT] :
% 9.53/5.30        ( ( finite5795047828879050333T_VEBT @ A2 )
% 9.53/5.30       => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 9.53/5.30          = ( plus_plus_real @ ( G @ X ) @ ( groups2240296850493347238T_real @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6682_sum_Oinsert__remove,axiom,
% 9.53/5.30      ! [A2: set_complex,G: complex > real,X: complex] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.30       => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A2 ) )
% 9.53/5.30          = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6683_sum_Oinsert__remove,axiom,
% 9.53/5.30      ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > rat,X: vEBT_VEBT] :
% 9.53/5.30        ( ( finite5795047828879050333T_VEBT @ A2 )
% 9.53/5.30       => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 9.53/5.30          = ( plus_plus_rat @ ( G @ X ) @ ( groups136491112297645522BT_rat @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6684_sum_Oinsert__remove,axiom,
% 9.53/5.30      ! [A2: set_complex,G: complex > rat,X: complex] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.30       => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X @ A2 ) )
% 9.53/5.30          = ( plus_plus_rat @ ( G @ X ) @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6685_sum_Oinsert__remove,axiom,
% 9.53/5.30      ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > nat,X: vEBT_VEBT] :
% 9.53/5.30        ( ( finite5795047828879050333T_VEBT @ A2 )
% 9.53/5.30       => ( ( groups771621172384141258BT_nat @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 9.53/5.30          = ( plus_plus_nat @ ( G @ X ) @ ( groups771621172384141258BT_nat @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6686_sum_Oinsert__remove,axiom,
% 9.53/5.30      ! [A2: set_complex,G: complex > nat,X: complex] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.30       => ( ( groups5693394587270226106ex_nat @ G @ ( insert_complex @ X @ A2 ) )
% 9.53/5.30          = ( plus_plus_nat @ ( G @ X ) @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6687_sum_Oinsert__remove,axiom,
% 9.53/5.30      ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > int,X: vEBT_VEBT] :
% 9.53/5.30        ( ( finite5795047828879050333T_VEBT @ A2 )
% 9.53/5.30       => ( ( groups769130701875090982BT_int @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 9.53/5.30          = ( plus_plus_int @ ( G @ X ) @ ( groups769130701875090982BT_int @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6688_sum_Oinsert__remove,axiom,
% 9.53/5.30      ! [A2: set_complex,G: complex > int,X: complex] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.30       => ( ( groups5690904116761175830ex_int @ G @ ( insert_complex @ X @ A2 ) )
% 9.53/5.30          = ( plus_plus_int @ ( G @ X ) @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6689_sum_Oinsert__remove,axiom,
% 9.53/5.30      ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > complex,X: vEBT_VEBT] :
% 9.53/5.30        ( ( finite5795047828879050333T_VEBT @ A2 )
% 9.53/5.30       => ( ( groups1794756597179926696omplex @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 9.53/5.30          = ( plus_plus_complex @ ( G @ X ) @ ( groups1794756597179926696omplex @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6690_sum_Oinsert__remove,axiom,
% 9.53/5.30      ! [A2: set_int,G: int > real,X: int] :
% 9.53/5.30        ( ( finite_finite_int @ A2 )
% 9.53/5.30       => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X @ A2 ) )
% 9.53/5.30          = ( plus_plus_real @ ( G @ X ) @ ( groups8778361861064173332t_real @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6691_sum_Oremove,axiom,
% 9.53/5.30      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > real] :
% 9.53/5.30        ( ( finite5795047828879050333T_VEBT @ A2 )
% 9.53/5.30       => ( ( member_VEBT_VEBT @ X @ A2 )
% 9.53/5.30         => ( ( groups2240296850493347238T_real @ G @ A2 )
% 9.53/5.30            = ( plus_plus_real @ ( G @ X ) @ ( groups2240296850493347238T_real @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6692_sum_Oremove,axiom,
% 9.53/5.30      ! [A2: set_complex,X: complex,G: complex > real] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.30       => ( ( member_complex @ X @ A2 )
% 9.53/5.30         => ( ( groups5808333547571424918x_real @ G @ A2 )
% 9.53/5.30            = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6693_sum_Oremove,axiom,
% 9.53/5.30      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 9.53/5.30        ( ( finite5795047828879050333T_VEBT @ A2 )
% 9.53/5.30       => ( ( member_VEBT_VEBT @ X @ A2 )
% 9.53/5.30         => ( ( groups136491112297645522BT_rat @ G @ A2 )
% 9.53/5.30            = ( plus_plus_rat @ ( G @ X ) @ ( groups136491112297645522BT_rat @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6694_sum_Oremove,axiom,
% 9.53/5.30      ! [A2: set_complex,X: complex,G: complex > rat] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.30       => ( ( member_complex @ X @ A2 )
% 9.53/5.30         => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 9.53/5.30            = ( plus_plus_rat @ ( G @ X ) @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6695_sum_Oremove,axiom,
% 9.53/5.30      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > nat] :
% 9.53/5.30        ( ( finite5795047828879050333T_VEBT @ A2 )
% 9.53/5.30       => ( ( member_VEBT_VEBT @ X @ A2 )
% 9.53/5.30         => ( ( groups771621172384141258BT_nat @ G @ A2 )
% 9.53/5.30            = ( plus_plus_nat @ ( G @ X ) @ ( groups771621172384141258BT_nat @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6696_sum_Oremove,axiom,
% 9.53/5.30      ! [A2: set_complex,X: complex,G: complex > nat] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.30       => ( ( member_complex @ X @ A2 )
% 9.53/5.30         => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 9.53/5.30            = ( plus_plus_nat @ ( G @ X ) @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6697_sum_Oremove,axiom,
% 9.53/5.30      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > int] :
% 9.53/5.30        ( ( finite5795047828879050333T_VEBT @ A2 )
% 9.53/5.30       => ( ( member_VEBT_VEBT @ X @ A2 )
% 9.53/5.30         => ( ( groups769130701875090982BT_int @ G @ A2 )
% 9.53/5.30            = ( plus_plus_int @ ( G @ X ) @ ( groups769130701875090982BT_int @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6698_sum_Oremove,axiom,
% 9.53/5.30      ! [A2: set_complex,X: complex,G: complex > int] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.30       => ( ( member_complex @ X @ A2 )
% 9.53/5.30         => ( ( groups5690904116761175830ex_int @ G @ A2 )
% 9.53/5.30            = ( plus_plus_int @ ( G @ X ) @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6699_sum_Oremove,axiom,
% 9.53/5.30      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > complex] :
% 9.53/5.30        ( ( finite5795047828879050333T_VEBT @ A2 )
% 9.53/5.30       => ( ( member_VEBT_VEBT @ X @ A2 )
% 9.53/5.30         => ( ( groups1794756597179926696omplex @ G @ A2 )
% 9.53/5.30            = ( plus_plus_complex @ ( G @ X ) @ ( groups1794756597179926696omplex @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6700_sum_Oremove,axiom,
% 9.53/5.30      ! [A2: set_int,X: int,G: int > real] :
% 9.53/5.30        ( ( finite_finite_int @ A2 )
% 9.53/5.30       => ( ( member_int @ X @ A2 )
% 9.53/5.30         => ( ( groups8778361861064173332t_real @ G @ A2 )
% 9.53/5.30            = ( plus_plus_real @ ( G @ X ) @ ( groups8778361861064173332t_real @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6701_sum__diff1,axiom,
% 9.53/5.30      ! [A2: set_VEBT_VEBT,A: vEBT_VEBT,F: vEBT_VEBT > rat] :
% 9.53/5.30        ( ( finite5795047828879050333T_VEBT @ A2 )
% 9.53/5.30       => ( ( ( member_VEBT_VEBT @ A @ A2 )
% 9.53/5.30           => ( ( groups136491112297645522BT_rat @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 9.53/5.30              = ( minus_minus_rat @ ( groups136491112297645522BT_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 9.53/5.30          & ( ~ ( member_VEBT_VEBT @ A @ A2 )
% 9.53/5.30           => ( ( groups136491112297645522BT_rat @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 9.53/5.30              = ( groups136491112297645522BT_rat @ F @ A2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6702_sum__diff1,axiom,
% 9.53/5.30      ! [A2: set_complex,A: complex,F: complex > rat] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.30       => ( ( ( member_complex @ A @ A2 )
% 9.53/5.30           => ( ( groups5058264527183730370ex_rat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 9.53/5.30              = ( minus_minus_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 9.53/5.30          & ( ~ ( member_complex @ A @ A2 )
% 9.53/5.30           => ( ( groups5058264527183730370ex_rat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 9.53/5.30              = ( groups5058264527183730370ex_rat @ F @ A2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6703_sum__diff1,axiom,
% 9.53/5.30      ! [A2: set_int,A: int,F: int > rat] :
% 9.53/5.30        ( ( finite_finite_int @ A2 )
% 9.53/5.30       => ( ( ( member_int @ A @ A2 )
% 9.53/5.30           => ( ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 9.53/5.30              = ( minus_minus_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 9.53/5.30          & ( ~ ( member_int @ A @ A2 )
% 9.53/5.30           => ( ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 9.53/5.30              = ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6704_sum__diff1,axiom,
% 9.53/5.30      ! [A2: set_real,A: real,F: real > rat] :
% 9.53/5.30        ( ( finite_finite_real @ A2 )
% 9.53/5.30       => ( ( ( member_real @ A @ A2 )
% 9.53/5.30           => ( ( groups1300246762558778688al_rat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 9.53/5.30              = ( minus_minus_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 9.53/5.30          & ( ~ ( member_real @ A @ A2 )
% 9.53/5.30           => ( ( groups1300246762558778688al_rat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 9.53/5.30              = ( groups1300246762558778688al_rat @ F @ A2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6705_sum__diff1,axiom,
% 9.53/5.30      ! [A2: set_VEBT_VEBT,A: vEBT_VEBT,F: vEBT_VEBT > int] :
% 9.53/5.30        ( ( finite5795047828879050333T_VEBT @ A2 )
% 9.53/5.30       => ( ( ( member_VEBT_VEBT @ A @ A2 )
% 9.53/5.30           => ( ( groups769130701875090982BT_int @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 9.53/5.30              = ( minus_minus_int @ ( groups769130701875090982BT_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 9.53/5.30          & ( ~ ( member_VEBT_VEBT @ A @ A2 )
% 9.53/5.30           => ( ( groups769130701875090982BT_int @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 9.53/5.30              = ( groups769130701875090982BT_int @ F @ A2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6706_sum__diff1,axiom,
% 9.53/5.30      ! [A2: set_complex,A: complex,F: complex > int] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.30       => ( ( ( member_complex @ A @ A2 )
% 9.53/5.30           => ( ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 9.53/5.30              = ( minus_minus_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 9.53/5.30          & ( ~ ( member_complex @ A @ A2 )
% 9.53/5.30           => ( ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 9.53/5.30              = ( groups5690904116761175830ex_int @ F @ A2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6707_sum__diff1,axiom,
% 9.53/5.30      ! [A2: set_real,A: real,F: real > int] :
% 9.53/5.30        ( ( finite_finite_real @ A2 )
% 9.53/5.30       => ( ( ( member_real @ A @ A2 )
% 9.53/5.30           => ( ( groups1932886352136224148al_int @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 9.53/5.30              = ( minus_minus_int @ ( groups1932886352136224148al_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 9.53/5.30          & ( ~ ( member_real @ A @ A2 )
% 9.53/5.30           => ( ( groups1932886352136224148al_int @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 9.53/5.30              = ( groups1932886352136224148al_int @ F @ A2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6708_sum__diff1,axiom,
% 9.53/5.30      ! [A2: set_nat,A: nat,F: nat > rat] :
% 9.53/5.30        ( ( finite_finite_nat @ A2 )
% 9.53/5.30       => ( ( ( member_nat @ A @ A2 )
% 9.53/5.30           => ( ( groups2906978787729119204at_rat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 9.53/5.30              = ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 9.53/5.30          & ( ~ ( member_nat @ A @ A2 )
% 9.53/5.30           => ( ( groups2906978787729119204at_rat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 9.53/5.30              = ( groups2906978787729119204at_rat @ F @ A2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6709_sum__diff1,axiom,
% 9.53/5.30      ! [A2: set_nat,A: nat,F: nat > int] :
% 9.53/5.30        ( ( finite_finite_nat @ A2 )
% 9.53/5.30       => ( ( ( member_nat @ A @ A2 )
% 9.53/5.30           => ( ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 9.53/5.30              = ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 9.53/5.30          & ( ~ ( member_nat @ A @ A2 )
% 9.53/5.30           => ( ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 9.53/5.30              = ( groups3539618377306564664at_int @ F @ A2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6710_sum__diff1,axiom,
% 9.53/5.30      ! [A2: set_int,A: int,F: int > int] :
% 9.53/5.30        ( ( finite_finite_int @ A2 )
% 9.53/5.30       => ( ( ( member_int @ A @ A2 )
% 9.53/5.30           => ( ( groups4538972089207619220nt_int @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 9.53/5.30              = ( minus_minus_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 9.53/5.30          & ( ~ ( member_int @ A @ A2 )
% 9.53/5.30           => ( ( groups4538972089207619220nt_int @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 9.53/5.30              = ( groups4538972089207619220nt_int @ F @ A2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6711_take__bit__nat__def,axiom,
% 9.53/5.30      ( bit_se2925701944663578781it_nat
% 9.53/5.30      = ( ^ [N2: nat,M6: nat] : ( modulo_modulo_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6712_exp__le,axiom,
% 9.53/5.30      ord_less_eq_real @ ( exp_real @ one_one_real ) @ ( numeral_numeral_real @ ( bit1 @ one ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6713_take__bit__int__less__exp,axiom,
% 9.53/5.30      ! [N: nat,K: int] : ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6714_take__bit__int__def,axiom,
% 9.53/5.30      ( bit_se2923211474154528505it_int
% 9.53/5.30      = ( ^ [N2: nat,K3: int] : ( modulo_modulo_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6715_even__abs__add__iff,axiom,
% 9.53/5.30      ! [K: int,L2: int] :
% 9.53/5.30        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ ( abs_abs_int @ K ) @ L2 ) )
% 9.53/5.30        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6716_even__add__abs__iff,axiom,
% 9.53/5.30      ! [K: int,L2: int] :
% 9.53/5.30        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ ( abs_abs_int @ L2 ) ) )
% 9.53/5.30        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6717_sum_Odelta__remove,axiom,
% 9.53/5.30      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > real,C: vEBT_VEBT > real] :
% 9.53/5.30        ( ( finite5795047828879050333T_VEBT @ S2 )
% 9.53/5.30       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 9.53/5.30           => ( ( groups2240296850493347238T_real
% 9.53/5.30                @ ^ [K3: vEBT_VEBT] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.30                @ S2 )
% 9.53/5.30              = ( plus_plus_real @ ( B @ A ) @ ( groups2240296850493347238T_real @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 9.53/5.30          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 9.53/5.30           => ( ( groups2240296850493347238T_real
% 9.53/5.30                @ ^ [K3: vEBT_VEBT] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.30                @ S2 )
% 9.53/5.30              = ( groups2240296850493347238T_real @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6718_sum_Odelta__remove,axiom,
% 9.53/5.30      ! [S2: set_complex,A: complex,B: complex > real,C: complex > real] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ S2 )
% 9.53/5.30       => ( ( ( member_complex @ A @ S2 )
% 9.53/5.30           => ( ( groups5808333547571424918x_real
% 9.53/5.30                @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.30                @ S2 )
% 9.53/5.30              = ( plus_plus_real @ ( B @ A ) @ ( groups5808333547571424918x_real @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 9.53/5.30          & ( ~ ( member_complex @ A @ S2 )
% 9.53/5.30           => ( ( groups5808333547571424918x_real
% 9.53/5.30                @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.30                @ S2 )
% 9.53/5.30              = ( groups5808333547571424918x_real @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6719_sum_Odelta__remove,axiom,
% 9.53/5.30      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > rat,C: vEBT_VEBT > rat] :
% 9.53/5.30        ( ( finite5795047828879050333T_VEBT @ S2 )
% 9.53/5.30       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 9.53/5.30           => ( ( groups136491112297645522BT_rat
% 9.53/5.30                @ ^ [K3: vEBT_VEBT] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.30                @ S2 )
% 9.53/5.30              = ( plus_plus_rat @ ( B @ A ) @ ( groups136491112297645522BT_rat @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 9.53/5.30          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 9.53/5.30           => ( ( groups136491112297645522BT_rat
% 9.53/5.30                @ ^ [K3: vEBT_VEBT] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.30                @ S2 )
% 9.53/5.30              = ( groups136491112297645522BT_rat @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6720_sum_Odelta__remove,axiom,
% 9.53/5.30      ! [S2: set_complex,A: complex,B: complex > rat,C: complex > rat] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ S2 )
% 9.53/5.30       => ( ( ( member_complex @ A @ S2 )
% 9.53/5.30           => ( ( groups5058264527183730370ex_rat
% 9.53/5.30                @ ^ [K3: complex] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.30                @ S2 )
% 9.53/5.30              = ( plus_plus_rat @ ( B @ A ) @ ( groups5058264527183730370ex_rat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 9.53/5.30          & ( ~ ( member_complex @ A @ S2 )
% 9.53/5.30           => ( ( groups5058264527183730370ex_rat
% 9.53/5.30                @ ^ [K3: complex] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.30                @ S2 )
% 9.53/5.30              = ( groups5058264527183730370ex_rat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6721_sum_Odelta__remove,axiom,
% 9.53/5.30      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > nat,C: vEBT_VEBT > nat] :
% 9.53/5.30        ( ( finite5795047828879050333T_VEBT @ S2 )
% 9.53/5.30       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 9.53/5.30           => ( ( groups771621172384141258BT_nat
% 9.53/5.30                @ ^ [K3: vEBT_VEBT] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.30                @ S2 )
% 9.53/5.30              = ( plus_plus_nat @ ( B @ A ) @ ( groups771621172384141258BT_nat @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 9.53/5.30          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 9.53/5.30           => ( ( groups771621172384141258BT_nat
% 9.53/5.30                @ ^ [K3: vEBT_VEBT] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.30                @ S2 )
% 9.53/5.30              = ( groups771621172384141258BT_nat @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6722_sum_Odelta__remove,axiom,
% 9.53/5.30      ! [S2: set_complex,A: complex,B: complex > nat,C: complex > nat] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ S2 )
% 9.53/5.30       => ( ( ( member_complex @ A @ S2 )
% 9.53/5.30           => ( ( groups5693394587270226106ex_nat
% 9.53/5.30                @ ^ [K3: complex] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.30                @ S2 )
% 9.53/5.30              = ( plus_plus_nat @ ( B @ A ) @ ( groups5693394587270226106ex_nat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 9.53/5.30          & ( ~ ( member_complex @ A @ S2 )
% 9.53/5.30           => ( ( groups5693394587270226106ex_nat
% 9.53/5.30                @ ^ [K3: complex] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.30                @ S2 )
% 9.53/5.30              = ( groups5693394587270226106ex_nat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6723_sum_Odelta__remove,axiom,
% 9.53/5.30      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > int,C: vEBT_VEBT > int] :
% 9.53/5.30        ( ( finite5795047828879050333T_VEBT @ S2 )
% 9.53/5.30       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 9.53/5.30           => ( ( groups769130701875090982BT_int
% 9.53/5.30                @ ^ [K3: vEBT_VEBT] : ( if_int @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.30                @ S2 )
% 9.53/5.30              = ( plus_plus_int @ ( B @ A ) @ ( groups769130701875090982BT_int @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 9.53/5.30          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 9.53/5.30           => ( ( groups769130701875090982BT_int
% 9.53/5.30                @ ^ [K3: vEBT_VEBT] : ( if_int @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.30                @ S2 )
% 9.53/5.30              = ( groups769130701875090982BT_int @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6724_sum_Odelta__remove,axiom,
% 9.53/5.30      ! [S2: set_complex,A: complex,B: complex > int,C: complex > int] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ S2 )
% 9.53/5.30       => ( ( ( member_complex @ A @ S2 )
% 9.53/5.30           => ( ( groups5690904116761175830ex_int
% 9.53/5.30                @ ^ [K3: complex] : ( if_int @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.30                @ S2 )
% 9.53/5.30              = ( plus_plus_int @ ( B @ A ) @ ( groups5690904116761175830ex_int @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 9.53/5.30          & ( ~ ( member_complex @ A @ S2 )
% 9.53/5.30           => ( ( groups5690904116761175830ex_int
% 9.53/5.30                @ ^ [K3: complex] : ( if_int @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.30                @ S2 )
% 9.53/5.30              = ( groups5690904116761175830ex_int @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6725_sum_Odelta__remove,axiom,
% 9.53/5.30      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > complex,C: vEBT_VEBT > complex] :
% 9.53/5.30        ( ( finite5795047828879050333T_VEBT @ S2 )
% 9.53/5.30       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 9.53/5.30           => ( ( groups1794756597179926696omplex
% 9.53/5.30                @ ^ [K3: vEBT_VEBT] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.30                @ S2 )
% 9.53/5.30              = ( plus_plus_complex @ ( B @ A ) @ ( groups1794756597179926696omplex @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 9.53/5.30          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 9.53/5.30           => ( ( groups1794756597179926696omplex
% 9.53/5.30                @ ^ [K3: vEBT_VEBT] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.30                @ S2 )
% 9.53/5.30              = ( groups1794756597179926696omplex @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6726_sum_Odelta__remove,axiom,
% 9.53/5.30      ! [S2: set_int,A: int,B: int > real,C: int > real] :
% 9.53/5.30        ( ( finite_finite_int @ S2 )
% 9.53/5.30       => ( ( ( member_int @ A @ S2 )
% 9.53/5.30           => ( ( groups8778361861064173332t_real
% 9.53/5.30                @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.30                @ S2 )
% 9.53/5.30              = ( plus_plus_real @ ( B @ A ) @ ( groups8778361861064173332t_real @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 9.53/5.30          & ( ~ ( member_int @ A @ S2 )
% 9.53/5.30           => ( ( groups8778361861064173332t_real
% 9.53/5.30                @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.30                @ S2 )
% 9.53/5.30              = ( groups8778361861064173332t_real @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6727_tanh__altdef,axiom,
% 9.53/5.30      ( tanh_real
% 9.53/5.30      = ( ^ [X2: real] : ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X2 ) @ ( exp_real @ ( uminus_uminus_real @ X2 ) ) ) @ ( plus_plus_real @ ( exp_real @ X2 ) @ ( exp_real @ ( uminus_uminus_real @ X2 ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6728_tanh__altdef,axiom,
% 9.53/5.30      ( tanh_complex
% 9.53/5.30      = ( ^ [X2: complex] : ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( exp_complex @ X2 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X2 ) ) ) @ ( plus_plus_complex @ ( exp_complex @ X2 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X2 ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6729_num_Osize__gen_I1_J,axiom,
% 9.53/5.30      ( ( size_num @ one )
% 9.53/5.30      = zero_zero_nat ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6730_take__bit__eq__0__iff,axiom,
% 9.53/5.30      ! [N: nat,A: code_integer] :
% 9.53/5.30        ( ( ( bit_se1745604003318907178nteger @ N @ A )
% 9.53/5.30          = zero_z3403309356797280102nteger )
% 9.53/5.30        = ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6731_take__bit__eq__0__iff,axiom,
% 9.53/5.30      ! [N: nat,A: int] :
% 9.53/5.30        ( ( ( bit_se2923211474154528505it_int @ N @ A )
% 9.53/5.30          = zero_zero_int )
% 9.53/5.30        = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6732_take__bit__eq__0__iff,axiom,
% 9.53/5.30      ! [N: nat,A: nat] :
% 9.53/5.30        ( ( ( bit_se2925701944663578781it_nat @ N @ A )
% 9.53/5.30          = zero_zero_nat )
% 9.53/5.30        = ( dvd_dvd_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6733_sum__strict__mono2,axiom,
% 9.53/5.30      ! [B2: set_int,A2: set_int,B: int,F: int > real] :
% 9.53/5.30        ( ( finite_finite_int @ B2 )
% 9.53/5.30       => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 9.53/5.30         => ( ( member_int @ B @ ( minus_minus_set_int @ B2 @ A2 ) )
% 9.53/5.30           => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 9.53/5.30             => ( ! [X3: int] :
% 9.53/5.30                    ( ( member_int @ X3 @ B2 )
% 9.53/5.30                   => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 9.53/5.30               => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ F @ B2 ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6734_sum__strict__mono2,axiom,
% 9.53/5.30      ! [B2: set_complex,A2: set_complex,B: complex,F: complex > real] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ B2 )
% 9.53/5.30       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 9.53/5.30         => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 9.53/5.30           => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 9.53/5.30             => ( ! [X3: complex] :
% 9.53/5.30                    ( ( member_complex @ X3 @ B2 )
% 9.53/5.30                   => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 9.53/5.30               => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B2 ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6735_sum__strict__mono2,axiom,
% 9.53/5.30      ! [B2: set_int,A2: set_int,B: int,F: int > rat] :
% 9.53/5.30        ( ( finite_finite_int @ B2 )
% 9.53/5.30       => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 9.53/5.30         => ( ( member_int @ B @ ( minus_minus_set_int @ B2 @ A2 ) )
% 9.53/5.30           => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 9.53/5.30             => ( ! [X3: int] :
% 9.53/5.30                    ( ( member_int @ X3 @ B2 )
% 9.53/5.30                   => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 9.53/5.30               => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ F @ B2 ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6736_sum__strict__mono2,axiom,
% 9.53/5.30      ! [B2: set_complex,A2: set_complex,B: complex,F: complex > rat] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ B2 )
% 9.53/5.30       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 9.53/5.30         => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 9.53/5.30           => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 9.53/5.30             => ( ! [X3: complex] :
% 9.53/5.30                    ( ( member_complex @ X3 @ B2 )
% 9.53/5.30                   => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 9.53/5.30               => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ F @ B2 ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6737_sum__strict__mono2,axiom,
% 9.53/5.30      ! [B2: set_int,A2: set_int,B: int,F: int > nat] :
% 9.53/5.30        ( ( finite_finite_int @ B2 )
% 9.53/5.30       => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 9.53/5.30         => ( ( member_int @ B @ ( minus_minus_set_int @ B2 @ A2 ) )
% 9.53/5.30           => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 9.53/5.30             => ( ! [X3: int] :
% 9.53/5.30                    ( ( member_int @ X3 @ B2 )
% 9.53/5.30                   => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 9.53/5.30               => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ F @ B2 ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6738_sum__strict__mono2,axiom,
% 9.53/5.30      ! [B2: set_complex,A2: set_complex,B: complex,F: complex > nat] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ B2 )
% 9.53/5.30       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 9.53/5.30         => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 9.53/5.30           => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 9.53/5.30             => ( ! [X3: complex] :
% 9.53/5.30                    ( ( member_complex @ X3 @ B2 )
% 9.53/5.30                   => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 9.53/5.30               => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B2 ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6739_sum__strict__mono2,axiom,
% 9.53/5.30      ! [B2: set_complex,A2: set_complex,B: complex,F: complex > int] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ B2 )
% 9.53/5.30       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 9.53/5.30         => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 9.53/5.30           => ( ( ord_less_int @ zero_zero_int @ ( F @ B ) )
% 9.53/5.30             => ( ! [X3: complex] :
% 9.53/5.30                    ( ( member_complex @ X3 @ B2 )
% 9.53/5.30                   => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 9.53/5.30               => ( ord_less_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ F @ B2 ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6740_sum__strict__mono2,axiom,
% 9.53/5.30      ! [B2: set_real,A2: set_real,B: real,F: real > real] :
% 9.53/5.30        ( ( finite_finite_real @ B2 )
% 9.53/5.30       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 9.53/5.30         => ( ( member_real @ B @ ( minus_minus_set_real @ B2 @ A2 ) )
% 9.53/5.30           => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 9.53/5.30             => ( ! [X3: real] :
% 9.53/5.30                    ( ( member_real @ X3 @ B2 )
% 9.53/5.30                   => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 9.53/5.30               => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ F @ B2 ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6741_sum__strict__mono2,axiom,
% 9.53/5.30      ! [B2: set_real,A2: set_real,B: real,F: real > rat] :
% 9.53/5.30        ( ( finite_finite_real @ B2 )
% 9.53/5.30       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 9.53/5.30         => ( ( member_real @ B @ ( minus_minus_set_real @ B2 @ A2 ) )
% 9.53/5.30           => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 9.53/5.30             => ( ! [X3: real] :
% 9.53/5.30                    ( ( member_real @ X3 @ B2 )
% 9.53/5.30                   => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 9.53/5.30               => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ F @ B2 ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6742_sum__strict__mono2,axiom,
% 9.53/5.30      ! [B2: set_real,A2: set_real,B: real,F: real > nat] :
% 9.53/5.30        ( ( finite_finite_real @ B2 )
% 9.53/5.30       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 9.53/5.30         => ( ( member_real @ B @ ( minus_minus_set_real @ B2 @ A2 ) )
% 9.53/5.30           => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 9.53/5.30             => ( ! [X3: real] :
% 9.53/5.30                    ( ( member_real @ X3 @ B2 )
% 9.53/5.30                   => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 9.53/5.30               => ( ord_less_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ F @ B2 ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6743_member__le__sum,axiom,
% 9.53/5.30      ! [I2: vEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 9.53/5.30        ( ( member_VEBT_VEBT @ I2 @ A2 )
% 9.53/5.30       => ( ! [X3: vEBT_VEBT] :
% 9.53/5.30              ( ( member_VEBT_VEBT @ X3 @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ I2 @ bot_bo8194388402131092736T_VEBT ) ) )
% 9.53/5.30             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 9.53/5.30         => ( ( finite5795047828879050333T_VEBT @ A2 )
% 9.53/5.30           => ( ord_less_eq_real @ ( F @ I2 ) @ ( groups2240296850493347238T_real @ F @ A2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6744_member__le__sum,axiom,
% 9.53/5.30      ! [I2: complex,A2: set_complex,F: complex > real] :
% 9.53/5.30        ( ( member_complex @ I2 @ A2 )
% 9.53/5.30       => ( ! [X3: complex] :
% 9.53/5.30              ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ I2 @ bot_bot_set_complex ) ) )
% 9.53/5.30             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 9.53/5.30         => ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.30           => ( ord_less_eq_real @ ( F @ I2 ) @ ( groups5808333547571424918x_real @ F @ A2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6745_member__le__sum,axiom,
% 9.53/5.30      ! [I2: vEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 9.53/5.30        ( ( member_VEBT_VEBT @ I2 @ A2 )
% 9.53/5.30       => ( ! [X3: vEBT_VEBT] :
% 9.53/5.30              ( ( member_VEBT_VEBT @ X3 @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ I2 @ bot_bo8194388402131092736T_VEBT ) ) )
% 9.53/5.30             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 9.53/5.30         => ( ( finite5795047828879050333T_VEBT @ A2 )
% 9.53/5.30           => ( ord_less_eq_rat @ ( F @ I2 ) @ ( groups136491112297645522BT_rat @ F @ A2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6746_member__le__sum,axiom,
% 9.53/5.30      ! [I2: complex,A2: set_complex,F: complex > rat] :
% 9.53/5.30        ( ( member_complex @ I2 @ A2 )
% 9.53/5.30       => ( ! [X3: complex] :
% 9.53/5.30              ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ I2 @ bot_bot_set_complex ) ) )
% 9.53/5.30             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 9.53/5.30         => ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.30           => ( ord_less_eq_rat @ ( F @ I2 ) @ ( groups5058264527183730370ex_rat @ F @ A2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6747_member__le__sum,axiom,
% 9.53/5.30      ! [I2: int,A2: set_int,F: int > real] :
% 9.53/5.30        ( ( member_int @ I2 @ A2 )
% 9.53/5.30       => ( ! [X3: int] :
% 9.53/5.30              ( ( member_int @ X3 @ ( minus_minus_set_int @ A2 @ ( insert_int @ I2 @ bot_bot_set_int ) ) )
% 9.53/5.30             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 9.53/5.30         => ( ( finite_finite_int @ A2 )
% 9.53/5.30           => ( ord_less_eq_real @ ( F @ I2 ) @ ( groups8778361861064173332t_real @ F @ A2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6748_member__le__sum,axiom,
% 9.53/5.30      ! [I2: int,A2: set_int,F: int > rat] :
% 9.53/5.30        ( ( member_int @ I2 @ A2 )
% 9.53/5.30       => ( ! [X3: int] :
% 9.53/5.30              ( ( member_int @ X3 @ ( minus_minus_set_int @ A2 @ ( insert_int @ I2 @ bot_bot_set_int ) ) )
% 9.53/5.30             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 9.53/5.30         => ( ( finite_finite_int @ A2 )
% 9.53/5.30           => ( ord_less_eq_rat @ ( F @ I2 ) @ ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6749_member__le__sum,axiom,
% 9.53/5.30      ! [I2: real,A2: set_real,F: real > real] :
% 9.53/5.30        ( ( member_real @ I2 @ A2 )
% 9.53/5.30       => ( ! [X3: real] :
% 9.53/5.30              ( ( member_real @ X3 @ ( minus_minus_set_real @ A2 @ ( insert_real @ I2 @ bot_bot_set_real ) ) )
% 9.53/5.30             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 9.53/5.30         => ( ( finite_finite_real @ A2 )
% 9.53/5.30           => ( ord_less_eq_real @ ( F @ I2 ) @ ( groups8097168146408367636l_real @ F @ A2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6750_member__le__sum,axiom,
% 9.53/5.30      ! [I2: real,A2: set_real,F: real > rat] :
% 9.53/5.30        ( ( member_real @ I2 @ A2 )
% 9.53/5.30       => ( ! [X3: real] :
% 9.53/5.30              ( ( member_real @ X3 @ ( minus_minus_set_real @ A2 @ ( insert_real @ I2 @ bot_bot_set_real ) ) )
% 9.53/5.30             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 9.53/5.30         => ( ( finite_finite_real @ A2 )
% 9.53/5.30           => ( ord_less_eq_rat @ ( F @ I2 ) @ ( groups1300246762558778688al_rat @ F @ A2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6751_member__le__sum,axiom,
% 9.53/5.30      ! [I2: nat,A2: set_nat,F: nat > rat] :
% 9.53/5.30        ( ( member_nat @ I2 @ A2 )
% 9.53/5.30       => ( ! [X3: nat] :
% 9.53/5.30              ( ( member_nat @ X3 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ I2 @ bot_bot_set_nat ) ) )
% 9.53/5.30             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 9.53/5.30         => ( ( finite_finite_nat @ A2 )
% 9.53/5.30           => ( ord_less_eq_rat @ ( F @ I2 ) @ ( groups2906978787729119204at_rat @ F @ A2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6752_member__le__sum,axiom,
% 9.53/5.30      ! [I2: vEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 9.53/5.30        ( ( member_VEBT_VEBT @ I2 @ A2 )
% 9.53/5.30       => ( ! [X3: vEBT_VEBT] :
% 9.53/5.30              ( ( member_VEBT_VEBT @ X3 @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ I2 @ bot_bo8194388402131092736T_VEBT ) ) )
% 9.53/5.30             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 9.53/5.30         => ( ( finite5795047828879050333T_VEBT @ A2 )
% 9.53/5.30           => ( ord_less_eq_nat @ ( F @ I2 ) @ ( groups771621172384141258BT_nat @ F @ A2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6753_take__bit__numeral__bit0,axiom,
% 9.53/5.30      ! [L2: num,K: num] :
% 9.53/5.30        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 9.53/5.30        = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6754_take__bit__numeral__bit0,axiom,
% 9.53/5.30      ! [L2: num,K: num] :
% 9.53/5.30        ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 9.53/5.30        = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L2 ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6755_take__bit__nat__less__self__iff,axiom,
% 9.53/5.30      ! [N: nat,M: nat] :
% 9.53/5.30        ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M )
% 9.53/5.30        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6756_Suc__mask__eq__exp,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( suc @ ( bit_se2002935070580805687sk_nat @ N ) )
% 9.53/5.30        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6757_mask__nat__less__exp,axiom,
% 9.53/5.30      ! [N: nat] : ( ord_less_nat @ ( bit_se2002935070580805687sk_nat @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6758_exp__half__le2,axiom,
% 9.53/5.30      ord_less_eq_real @ ( exp_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6759_take__bit__Suc__minus__bit0,axiom,
% 9.53/5.30      ! [N: nat,K: num] :
% 9.53/5.30        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 9.53/5.30        = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6760_convex__sum__bound__le,axiom,
% 9.53/5.30      ! [I6: set_complex,X: complex > code_integer,A: complex > code_integer,B: code_integer,Delta: code_integer] :
% 9.53/5.30        ( ! [I4: complex] :
% 9.53/5.30            ( ( member_complex @ I4 @ I6 )
% 9.53/5.30           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I4 ) ) )
% 9.53/5.30       => ( ( ( groups6621422865394947399nteger @ X @ I6 )
% 9.53/5.30            = one_one_Code_integer )
% 9.53/5.30         => ( ! [I4: complex] :
% 9.53/5.30                ( ( member_complex @ I4 @ I6 )
% 9.53/5.30               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 9.53/5.30           => ( ord_le3102999989581377725nteger
% 9.53/5.30              @ ( abs_abs_Code_integer
% 9.53/5.30                @ ( minus_8373710615458151222nteger
% 9.53/5.30                  @ ( groups6621422865394947399nteger
% 9.53/5.30                    @ ^ [I3: complex] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X @ I3 ) )
% 9.53/5.30                    @ I6 )
% 9.53/5.30                  @ B ) )
% 9.53/5.30              @ Delta ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6761_convex__sum__bound__le,axiom,
% 9.53/5.30      ! [I6: set_real,X: real > code_integer,A: real > code_integer,B: code_integer,Delta: code_integer] :
% 9.53/5.30        ( ! [I4: real] :
% 9.53/5.30            ( ( member_real @ I4 @ I6 )
% 9.53/5.30           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I4 ) ) )
% 9.53/5.30       => ( ( ( groups7713935264441627589nteger @ X @ I6 )
% 9.53/5.30            = one_one_Code_integer )
% 9.53/5.30         => ( ! [I4: real] :
% 9.53/5.30                ( ( member_real @ I4 @ I6 )
% 9.53/5.30               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 9.53/5.30           => ( ord_le3102999989581377725nteger
% 9.53/5.30              @ ( abs_abs_Code_integer
% 9.53/5.30                @ ( minus_8373710615458151222nteger
% 9.53/5.30                  @ ( groups7713935264441627589nteger
% 9.53/5.30                    @ ^ [I3: real] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X @ I3 ) )
% 9.53/5.30                    @ I6 )
% 9.53/5.30                  @ B ) )
% 9.53/5.30              @ Delta ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6762_convex__sum__bound__le,axiom,
% 9.53/5.30      ! [I6: set_nat,X: nat > code_integer,A: nat > code_integer,B: code_integer,Delta: code_integer] :
% 9.53/5.30        ( ! [I4: nat] :
% 9.53/5.30            ( ( member_nat @ I4 @ I6 )
% 9.53/5.30           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I4 ) ) )
% 9.53/5.30       => ( ( ( groups7501900531339628137nteger @ X @ I6 )
% 9.53/5.30            = one_one_Code_integer )
% 9.53/5.30         => ( ! [I4: nat] :
% 9.53/5.30                ( ( member_nat @ I4 @ I6 )
% 9.53/5.30               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 9.53/5.30           => ( ord_le3102999989581377725nteger
% 9.53/5.30              @ ( abs_abs_Code_integer
% 9.53/5.30                @ ( minus_8373710615458151222nteger
% 9.53/5.30                  @ ( groups7501900531339628137nteger
% 9.53/5.30                    @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X @ I3 ) )
% 9.53/5.30                    @ I6 )
% 9.53/5.30                  @ B ) )
% 9.53/5.30              @ Delta ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6763_convex__sum__bound__le,axiom,
% 9.53/5.30      ! [I6: set_int,X: int > code_integer,A: int > code_integer,B: code_integer,Delta: code_integer] :
% 9.53/5.30        ( ! [I4: int] :
% 9.53/5.30            ( ( member_int @ I4 @ I6 )
% 9.53/5.30           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I4 ) ) )
% 9.53/5.30       => ( ( ( groups7873554091576472773nteger @ X @ I6 )
% 9.53/5.30            = one_one_Code_integer )
% 9.53/5.30         => ( ! [I4: int] :
% 9.53/5.30                ( ( member_int @ I4 @ I6 )
% 9.53/5.30               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 9.53/5.30           => ( ord_le3102999989581377725nteger
% 9.53/5.30              @ ( abs_abs_Code_integer
% 9.53/5.30                @ ( minus_8373710615458151222nteger
% 9.53/5.30                  @ ( groups7873554091576472773nteger
% 9.53/5.30                    @ ^ [I3: int] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X @ I3 ) )
% 9.53/5.30                    @ I6 )
% 9.53/5.30                  @ B ) )
% 9.53/5.30              @ Delta ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6764_convex__sum__bound__le,axiom,
% 9.53/5.30      ! [I6: set_complex,X: complex > rat,A: complex > rat,B: rat,Delta: rat] :
% 9.53/5.30        ( ! [I4: complex] :
% 9.53/5.30            ( ( member_complex @ I4 @ I6 )
% 9.53/5.30           => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I4 ) ) )
% 9.53/5.30       => ( ( ( groups5058264527183730370ex_rat @ X @ I6 )
% 9.53/5.30            = one_one_rat )
% 9.53/5.30         => ( ! [I4: complex] :
% 9.53/5.30                ( ( member_complex @ I4 @ I6 )
% 9.53/5.30               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 9.53/5.30           => ( ord_less_eq_rat
% 9.53/5.30              @ ( abs_abs_rat
% 9.53/5.30                @ ( minus_minus_rat
% 9.53/5.30                  @ ( groups5058264527183730370ex_rat
% 9.53/5.30                    @ ^ [I3: complex] : ( times_times_rat @ ( A @ I3 ) @ ( X @ I3 ) )
% 9.53/5.30                    @ I6 )
% 9.53/5.30                  @ B ) )
% 9.53/5.30              @ Delta ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6765_convex__sum__bound__le,axiom,
% 9.53/5.30      ! [I6: set_real,X: real > rat,A: real > rat,B: rat,Delta: rat] :
% 9.53/5.30        ( ! [I4: real] :
% 9.53/5.30            ( ( member_real @ I4 @ I6 )
% 9.53/5.30           => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I4 ) ) )
% 9.53/5.30       => ( ( ( groups1300246762558778688al_rat @ X @ I6 )
% 9.53/5.30            = one_one_rat )
% 9.53/5.30         => ( ! [I4: real] :
% 9.53/5.30                ( ( member_real @ I4 @ I6 )
% 9.53/5.30               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 9.53/5.30           => ( ord_less_eq_rat
% 9.53/5.30              @ ( abs_abs_rat
% 9.53/5.30                @ ( minus_minus_rat
% 9.53/5.30                  @ ( groups1300246762558778688al_rat
% 9.53/5.30                    @ ^ [I3: real] : ( times_times_rat @ ( A @ I3 ) @ ( X @ I3 ) )
% 9.53/5.30                    @ I6 )
% 9.53/5.30                  @ B ) )
% 9.53/5.30              @ Delta ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6766_convex__sum__bound__le,axiom,
% 9.53/5.30      ! [I6: set_nat,X: nat > rat,A: nat > rat,B: rat,Delta: rat] :
% 9.53/5.30        ( ! [I4: nat] :
% 9.53/5.30            ( ( member_nat @ I4 @ I6 )
% 9.53/5.30           => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I4 ) ) )
% 9.53/5.30       => ( ( ( groups2906978787729119204at_rat @ X @ I6 )
% 9.53/5.30            = one_one_rat )
% 9.53/5.30         => ( ! [I4: nat] :
% 9.53/5.30                ( ( member_nat @ I4 @ I6 )
% 9.53/5.30               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 9.53/5.30           => ( ord_less_eq_rat
% 9.53/5.30              @ ( abs_abs_rat
% 9.53/5.30                @ ( minus_minus_rat
% 9.53/5.30                  @ ( groups2906978787729119204at_rat
% 9.53/5.30                    @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( X @ I3 ) )
% 9.53/5.30                    @ I6 )
% 9.53/5.30                  @ B ) )
% 9.53/5.30              @ Delta ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6767_convex__sum__bound__le,axiom,
% 9.53/5.30      ! [I6: set_int,X: int > rat,A: int > rat,B: rat,Delta: rat] :
% 9.53/5.30        ( ! [I4: int] :
% 9.53/5.30            ( ( member_int @ I4 @ I6 )
% 9.53/5.30           => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I4 ) ) )
% 9.53/5.30       => ( ( ( groups3906332499630173760nt_rat @ X @ I6 )
% 9.53/5.30            = one_one_rat )
% 9.53/5.30         => ( ! [I4: int] :
% 9.53/5.30                ( ( member_int @ I4 @ I6 )
% 9.53/5.30               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 9.53/5.30           => ( ord_less_eq_rat
% 9.53/5.30              @ ( abs_abs_rat
% 9.53/5.30                @ ( minus_minus_rat
% 9.53/5.30                  @ ( groups3906332499630173760nt_rat
% 9.53/5.30                    @ ^ [I3: int] : ( times_times_rat @ ( A @ I3 ) @ ( X @ I3 ) )
% 9.53/5.30                    @ I6 )
% 9.53/5.30                  @ B ) )
% 9.53/5.30              @ Delta ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6768_convex__sum__bound__le,axiom,
% 9.53/5.30      ! [I6: set_complex,X: complex > real,A: complex > real,B: real,Delta: real] :
% 9.53/5.30        ( ! [I4: complex] :
% 9.53/5.30            ( ( member_complex @ I4 @ I6 )
% 9.53/5.30           => ( ord_less_eq_real @ zero_zero_real @ ( X @ I4 ) ) )
% 9.53/5.30       => ( ( ( groups5808333547571424918x_real @ X @ I6 )
% 9.53/5.30            = one_one_real )
% 9.53/5.30         => ( ! [I4: complex] :
% 9.53/5.30                ( ( member_complex @ I4 @ I6 )
% 9.53/5.30               => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 9.53/5.30           => ( ord_less_eq_real
% 9.53/5.30              @ ( abs_abs_real
% 9.53/5.30                @ ( minus_minus_real
% 9.53/5.30                  @ ( groups5808333547571424918x_real
% 9.53/5.30                    @ ^ [I3: complex] : ( times_times_real @ ( A @ I3 ) @ ( X @ I3 ) )
% 9.53/5.30                    @ I6 )
% 9.53/5.30                  @ B ) )
% 9.53/5.30              @ Delta ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6769_convex__sum__bound__le,axiom,
% 9.53/5.30      ! [I6: set_real,X: real > real,A: real > real,B: real,Delta: real] :
% 9.53/5.30        ( ! [I4: real] :
% 9.53/5.30            ( ( member_real @ I4 @ I6 )
% 9.53/5.30           => ( ord_less_eq_real @ zero_zero_real @ ( X @ I4 ) ) )
% 9.53/5.30       => ( ( ( groups8097168146408367636l_real @ X @ I6 )
% 9.53/5.30            = one_one_real )
% 9.53/5.30         => ( ! [I4: real] :
% 9.53/5.30                ( ( member_real @ I4 @ I6 )
% 9.53/5.30               => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 9.53/5.30           => ( ord_less_eq_real
% 9.53/5.30              @ ( abs_abs_real
% 9.53/5.30                @ ( minus_minus_real
% 9.53/5.30                  @ ( groups8097168146408367636l_real
% 9.53/5.30                    @ ^ [I3: real] : ( times_times_real @ ( A @ I3 ) @ ( X @ I3 ) )
% 9.53/5.30                    @ I6 )
% 9.53/5.30                  @ B ) )
% 9.53/5.30              @ Delta ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6770_take__bit__int__greater__eq__self__iff,axiom,
% 9.53/5.30      ! [K: int,N: nat] :
% 9.53/5.30        ( ( ord_less_eq_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 9.53/5.30        = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6771_take__bit__int__less__self__iff,axiom,
% 9.53/5.30      ! [N: nat,K: int] :
% 9.53/5.30        ( ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 9.53/5.30        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6772_exp__double,axiom,
% 9.53/5.30      ! [Z: complex] :
% 9.53/5.30        ( ( exp_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) )
% 9.53/5.30        = ( power_power_complex @ ( exp_complex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6773_exp__double,axiom,
% 9.53/5.30      ! [Z: real] :
% 9.53/5.30        ( ( exp_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) )
% 9.53/5.30        = ( power_power_real @ ( exp_real @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6774_nat__intermed__int__val,axiom,
% 9.53/5.30      ! [M: nat,N: nat,F: nat > int,K: int] :
% 9.53/5.30        ( ! [I4: nat] :
% 9.53/5.30            ( ( ( ord_less_eq_nat @ M @ I4 )
% 9.53/5.30              & ( ord_less_nat @ I4 @ N ) )
% 9.53/5.30           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
% 9.53/5.30       => ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.30         => ( ( ord_less_eq_int @ ( F @ M ) @ K )
% 9.53/5.30           => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 9.53/5.30             => ? [I4: nat] :
% 9.53/5.30                  ( ( ord_less_eq_nat @ M @ I4 )
% 9.53/5.30                  & ( ord_less_eq_nat @ I4 @ N )
% 9.53/5.30                  & ( ( F @ I4 )
% 9.53/5.30                    = K ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6775_decr__lemma,axiom,
% 9.53/5.30      ! [D2: int,X: int,Z: int] :
% 9.53/5.30        ( ( ord_less_int @ zero_zero_int @ D2 )
% 9.53/5.30       => ( ord_less_int @ ( minus_minus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D2 ) ) @ Z ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6776_incr__lemma,axiom,
% 9.53/5.30      ! [D2: int,Z: int,X: int] :
% 9.53/5.30        ( ( ord_less_int @ zero_zero_int @ D2 )
% 9.53/5.30       => ( ord_less_int @ Z @ ( plus_plus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D2 ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6777_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2119862282449309892nteger @ N ) )
% 9.53/5.30        = ( N = zero_zero_nat ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6778_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ N ) )
% 9.53/5.30        = ( N = zero_zero_nat ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6779_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ N ) )
% 9.53/5.30        = ( N = zero_zero_nat ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6780_mask__nat__def,axiom,
% 9.53/5.30      ( bit_se2002935070580805687sk_nat
% 9.53/5.30      = ( ^ [N2: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6781_take__bit__int__eq__self__iff,axiom,
% 9.53/5.30      ! [N: nat,K: int] :
% 9.53/5.30        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 9.53/5.30          = K )
% 9.53/5.30        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 9.53/5.30          & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6782_take__bit__int__eq__self,axiom,
% 9.53/5.30      ! [K: int,N: nat] :
% 9.53/5.30        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 9.53/5.30       => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 9.53/5.30         => ( ( bit_se2923211474154528505it_int @ N @ K )
% 9.53/5.30            = K ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6783_mask__half__int,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( divide_divide_int @ ( bit_se2000444600071755411sk_int @ N ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.53/5.30        = ( bit_se2000444600071755411sk_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6784_take__bit__numeral__minus__bit0,axiom,
% 9.53/5.30      ! [L2: num,K: num] :
% 9.53/5.30        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 9.53/5.30        = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6785_take__bit__incr__eq,axiom,
% 9.53/5.30      ! [N: nat,K: int] :
% 9.53/5.30        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 9.53/5.30         != ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 9.53/5.30       => ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 9.53/5.30          = ( plus_plus_int @ one_one_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6786_mask__int__def,axiom,
% 9.53/5.30      ( bit_se2000444600071755411sk_int
% 9.53/5.30      = ( ^ [N2: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6787_nat__ivt__aux,axiom,
% 9.53/5.30      ! [N: nat,F: nat > int,K: int] :
% 9.53/5.30        ( ! [I4: nat] :
% 9.53/5.30            ( ( ord_less_nat @ I4 @ N )
% 9.53/5.30           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
% 9.53/5.30       => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 9.53/5.30         => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 9.53/5.30           => ? [I4: nat] :
% 9.53/5.30                ( ( ord_less_eq_nat @ I4 @ N )
% 9.53/5.30                & ( ( F @ I4 )
% 9.53/5.30                  = K ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6788_take__bit__Suc__bit1,axiom,
% 9.53/5.30      ! [N: nat,K: num] :
% 9.53/5.30        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 9.53/5.30        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6789_take__bit__Suc__bit1,axiom,
% 9.53/5.30      ! [N: nat,K: num] :
% 9.53/5.30        ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 9.53/5.30        = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6790_take__bit__Suc__minus__1__eq,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.53/5.30        = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_Code_integer ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6791_take__bit__Suc__minus__1__eq,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ one_one_int ) )
% 9.53/5.30        = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_int ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6792_take__bit__numeral__minus__1__eq,axiom,
% 9.53/5.30      ! [K: num] :
% 9.53/5.30        ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ K ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.53/5.30        = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_Code_integer ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6793_take__bit__numeral__minus__1__eq,axiom,
% 9.53/5.30      ! [K: num] :
% 9.53/5.30        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ K ) @ ( uminus_uminus_int @ one_one_int ) )
% 9.53/5.30        = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_int ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6794_take__bit__Suc,axiom,
% 9.53/5.30      ! [N: nat,A: int] :
% 9.53/5.30        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A )
% 9.53/5.30        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6795_take__bit__Suc,axiom,
% 9.53/5.30      ! [N: nat,A: nat] :
% 9.53/5.30        ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ A )
% 9.53/5.30        = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6796_mask__eq__exp__minus__1,axiom,
% 9.53/5.30      ( bit_se2002935070580805687sk_nat
% 9.53/5.30      = ( ^ [N2: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6797_mask__eq__exp__minus__1,axiom,
% 9.53/5.30      ( bit_se2000444600071755411sk_int
% 9.53/5.30      = ( ^ [N2: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6798_exp__bound,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.30       => ( ( ord_less_eq_real @ X @ one_one_real )
% 9.53/5.30         => ( ord_less_eq_real @ ( exp_real @ X ) @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6799_take__bit__int__less__eq,axiom,
% 9.53/5.30      ! [N: nat,K: int] :
% 9.53/5.30        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 9.53/5.30       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.30         => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6800_take__bit__int__greater__eq,axiom,
% 9.53/5.30      ! [K: int,N: nat] :
% 9.53/5.30        ( ( ord_less_int @ K @ zero_zero_int )
% 9.53/5.30       => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6801_signed__take__bit__eq__take__bit__shift,axiom,
% 9.53/5.30      ( bit_ri631733984087533419it_int
% 9.53/5.30      = ( ^ [N2: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( plus_plus_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6802_nat0__intermed__int__val,axiom,
% 9.53/5.30      ! [N: nat,F: nat > int,K: int] :
% 9.53/5.30        ( ! [I4: nat] :
% 9.53/5.30            ( ( ord_less_nat @ I4 @ N )
% 9.53/5.30           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I4 @ one_one_nat ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
% 9.53/5.30       => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 9.53/5.30         => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 9.53/5.30           => ? [I4: nat] :
% 9.53/5.30                ( ( ord_less_eq_nat @ I4 @ N )
% 9.53/5.30                & ( ( F @ I4 )
% 9.53/5.30                  = K ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6803_stable__imp__take__bit__eq,axiom,
% 9.53/5.30      ! [A: code_integer,N: nat] :
% 9.53/5.30        ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.53/5.30          = A )
% 9.53/5.30       => ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.53/5.30           => ( ( bit_se1745604003318907178nteger @ N @ A )
% 9.53/5.30              = zero_z3403309356797280102nteger ) )
% 9.53/5.30          & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.53/5.30           => ( ( bit_se1745604003318907178nteger @ N @ A )
% 9.53/5.30              = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6804_stable__imp__take__bit__eq,axiom,
% 9.53/5.30      ! [A: int,N: nat] :
% 9.53/5.30        ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.53/5.30          = A )
% 9.53/5.30       => ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.53/5.30           => ( ( bit_se2923211474154528505it_int @ N @ A )
% 9.53/5.30              = zero_zero_int ) )
% 9.53/5.30          & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.53/5.30           => ( ( bit_se2923211474154528505it_int @ N @ A )
% 9.53/5.30              = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6805_stable__imp__take__bit__eq,axiom,
% 9.53/5.30      ! [A: nat,N: nat] :
% 9.53/5.30        ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.53/5.30          = A )
% 9.53/5.30       => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.53/5.30           => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 9.53/5.30              = zero_zero_nat ) )
% 9.53/5.30          & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.53/5.30           => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 9.53/5.30              = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6806_take__bit__numeral__bit1,axiom,
% 9.53/5.30      ! [L2: num,K: num] :
% 9.53/5.30        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 9.53/5.30        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6807_take__bit__numeral__bit1,axiom,
% 9.53/5.30      ! [L2: num,K: num] :
% 9.53/5.30        ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 9.53/5.30        = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L2 ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6808_real__exp__bound__lemma,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.30       => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.30         => ( ord_less_eq_real @ ( exp_real @ X ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6809_arctan__add,axiom,
% 9.53/5.30      ! [X: real,Y2: real] :
% 9.53/5.30        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 9.53/5.30       => ( ( ord_less_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 9.53/5.30         => ( ( plus_plus_real @ ( arctan @ X ) @ ( arctan @ Y2 ) )
% 9.53/5.30            = ( arctan @ ( divide_divide_real @ ( plus_plus_real @ X @ Y2 ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ X @ Y2 ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6810_take__bit__minus__small__eq,axiom,
% 9.53/5.30      ! [K: int,N: nat] :
% 9.53/5.30        ( ( ord_less_int @ zero_zero_int @ K )
% 9.53/5.30       => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 9.53/5.30         => ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) )
% 9.53/5.30            = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6811_exp__lower__Taylor__quadratic,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.30       => ( ord_less_eq_real @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X ) @ ( divide_divide_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( exp_real @ X ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6812_num_Osize__gen_I2_J,axiom,
% 9.53/5.30      ! [X23: num] :
% 9.53/5.30        ( ( size_num @ ( bit0 @ X23 ) )
% 9.53/5.30        = ( plus_plus_nat @ ( size_num @ X23 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6813_take__bit__numeral__minus__bit1,axiom,
% 9.53/5.30      ! [L2: num,K: num] :
% 9.53/5.30        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 9.53/5.30        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6814_take__bit__Suc__minus__bit1,axiom,
% 9.53/5.30      ! [N: nat,K: num] :
% 9.53/5.30        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 9.53/5.30        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6815_log__base__10__eq1,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30        ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.30       => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 9.53/5.30          = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( ln_ln_real @ X ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6816_power__numeral,axiom,
% 9.53/5.30      ! [K: num,L2: num] :
% 9.53/5.30        ( ( power_power_complex @ ( numera6690914467698888265omplex @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 9.53/5.30        = ( numera6690914467698888265omplex @ ( pow @ K @ L2 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6817_power__numeral,axiom,
% 9.53/5.30      ! [K: num,L2: num] :
% 9.53/5.30        ( ( power_power_real @ ( numeral_numeral_real @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 9.53/5.30        = ( numeral_numeral_real @ ( pow @ K @ L2 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6818_power__numeral,axiom,
% 9.53/5.30      ! [K: num,L2: num] :
% 9.53/5.30        ( ( power_power_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 9.53/5.30        = ( numeral_numeral_rat @ ( pow @ K @ L2 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6819_power__numeral,axiom,
% 9.53/5.30      ! [K: num,L2: num] :
% 9.53/5.30        ( ( power_power_nat @ ( numeral_numeral_nat @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 9.53/5.30        = ( numeral_numeral_nat @ ( pow @ K @ L2 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6820_power__numeral,axiom,
% 9.53/5.30      ! [K: num,L2: num] :
% 9.53/5.30        ( ( power_power_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 9.53/5.30        = ( numeral_numeral_int @ ( pow @ K @ L2 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6821_or__int__unfold,axiom,
% 9.53/5.30      ( bit_se1409905431419307370or_int
% 9.53/5.30      = ( ^ [K3: int,L: int] :
% 9.53/5.30            ( if_int
% 9.53/5.30            @ ( ( K3
% 9.53/5.30                = ( uminus_uminus_int @ one_one_int ) )
% 9.53/5.30              | ( L
% 9.53/5.30                = ( uminus_uminus_int @ one_one_int ) ) )
% 9.53/5.30            @ ( uminus_uminus_int @ one_one_int )
% 9.53/5.30            @ ( if_int @ ( K3 = zero_zero_int ) @ L @ ( if_int @ ( L = zero_zero_int ) @ K3 @ ( plus_plus_int @ ( ord_max_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6822_arctan__half,axiom,
% 9.53/5.30      ( arctan
% 9.53/5.30      = ( ^ [X2: real] : ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ ( divide_divide_real @ X2 @ ( plus_plus_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6823_or_Oidem,axiom,
% 9.53/5.30      ! [A: int] :
% 9.53/5.30        ( ( bit_se1409905431419307370or_int @ A @ A )
% 9.53/5.30        = A ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6824_or_Oidem,axiom,
% 9.53/5.30      ! [A: nat] :
% 9.53/5.30        ( ( bit_se1412395901928357646or_nat @ A @ A )
% 9.53/5.30        = A ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6825_or_Oleft__idem,axiom,
% 9.53/5.30      ! [A: int,B: int] :
% 9.53/5.30        ( ( bit_se1409905431419307370or_int @ A @ ( bit_se1409905431419307370or_int @ A @ B ) )
% 9.53/5.30        = ( bit_se1409905431419307370or_int @ A @ B ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6826_or_Oleft__idem,axiom,
% 9.53/5.30      ! [A: nat,B: nat] :
% 9.53/5.30        ( ( bit_se1412395901928357646or_nat @ A @ ( bit_se1412395901928357646or_nat @ A @ B ) )
% 9.53/5.30        = ( bit_se1412395901928357646or_nat @ A @ B ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6827_or_Oright__idem,axiom,
% 9.53/5.30      ! [A: int,B: int] :
% 9.53/5.30        ( ( bit_se1409905431419307370or_int @ ( bit_se1409905431419307370or_int @ A @ B ) @ B )
% 9.53/5.30        = ( bit_se1409905431419307370or_int @ A @ B ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6828_or_Oright__idem,axiom,
% 9.53/5.30      ! [A: nat,B: nat] :
% 9.53/5.30        ( ( bit_se1412395901928357646or_nat @ ( bit_se1412395901928357646or_nat @ A @ B ) @ B )
% 9.53/5.30        = ( bit_se1412395901928357646or_nat @ A @ B ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6829_real__sqrt__eq__iff,axiom,
% 9.53/5.30      ! [X: real,Y2: real] :
% 9.53/5.30        ( ( ( sqrt @ X )
% 9.53/5.30          = ( sqrt @ Y2 ) )
% 9.53/5.30        = ( X = Y2 ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6830_or_Oleft__neutral,axiom,
% 9.53/5.30      ! [A: int] :
% 9.53/5.30        ( ( bit_se1409905431419307370or_int @ zero_zero_int @ A )
% 9.53/5.30        = A ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6831_or_Oleft__neutral,axiom,
% 9.53/5.30      ! [A: nat] :
% 9.53/5.30        ( ( bit_se1412395901928357646or_nat @ zero_zero_nat @ A )
% 9.53/5.30        = A ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6832_or_Oright__neutral,axiom,
% 9.53/5.30      ! [A: int] :
% 9.53/5.30        ( ( bit_se1409905431419307370or_int @ A @ zero_zero_int )
% 9.53/5.30        = A ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6833_or_Oright__neutral,axiom,
% 9.53/5.30      ! [A: nat] :
% 9.53/5.30        ( ( bit_se1412395901928357646or_nat @ A @ zero_zero_nat )
% 9.53/5.30        = A ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6834_real__sqrt__zero,axiom,
% 9.53/5.30      ( ( sqrt @ zero_zero_real )
% 9.53/5.30      = zero_zero_real ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6835_real__sqrt__eq__zero__cancel__iff,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30        ( ( ( sqrt @ X )
% 9.53/5.30          = zero_zero_real )
% 9.53/5.30        = ( X = zero_zero_real ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6836_real__sqrt__less__iff,axiom,
% 9.53/5.30      ! [X: real,Y2: real] :
% 9.53/5.30        ( ( ord_less_real @ ( sqrt @ X ) @ ( sqrt @ Y2 ) )
% 9.53/5.30        = ( ord_less_real @ X @ Y2 ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6837_real__sqrt__le__iff,axiom,
% 9.53/5.30      ! [X: real,Y2: real] :
% 9.53/5.30        ( ( ord_less_eq_real @ ( sqrt @ X ) @ ( sqrt @ Y2 ) )
% 9.53/5.30        = ( ord_less_eq_real @ X @ Y2 ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6838_real__sqrt__eq__1__iff,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30        ( ( ( sqrt @ X )
% 9.53/5.30          = one_one_real )
% 9.53/5.30        = ( X = one_one_real ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6839_real__sqrt__one,axiom,
% 9.53/5.30      ( ( sqrt @ one_one_real )
% 9.53/5.30      = one_one_real ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6840_take__bit__or,axiom,
% 9.53/5.30      ! [N: nat,A: int,B: int] :
% 9.53/5.30        ( ( bit_se2923211474154528505it_int @ N @ ( bit_se1409905431419307370or_int @ A @ B ) )
% 9.53/5.30        = ( bit_se1409905431419307370or_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_se2923211474154528505it_int @ N @ B ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6841_take__bit__or,axiom,
% 9.53/5.30      ! [N: nat,A: nat,B: nat] :
% 9.53/5.30        ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se1412395901928357646or_nat @ A @ B ) )
% 9.53/5.30        = ( bit_se1412395901928357646or_nat @ ( bit_se2925701944663578781it_nat @ N @ A ) @ ( bit_se2925701944663578781it_nat @ N @ B ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6842_bit_Odisj__one__right,axiom,
% 9.53/5.30      ! [X: code_integer] :
% 9.53/5.30        ( ( bit_se1080825931792720795nteger @ X @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.53/5.30        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6843_bit_Odisj__one__right,axiom,
% 9.53/5.30      ! [X: int] :
% 9.53/5.30        ( ( bit_se1409905431419307370or_int @ X @ ( uminus_uminus_int @ one_one_int ) )
% 9.53/5.30        = ( uminus_uminus_int @ one_one_int ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6844_bit_Odisj__one__left,axiom,
% 9.53/5.30      ! [X: code_integer] :
% 9.53/5.30        ( ( bit_se1080825931792720795nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 9.53/5.30        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6845_bit_Odisj__one__left,axiom,
% 9.53/5.30      ! [X: int] :
% 9.53/5.30        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 9.53/5.30        = ( uminus_uminus_int @ one_one_int ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6846_real__sqrt__lt__0__iff,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30        ( ( ord_less_real @ ( sqrt @ X ) @ zero_zero_real )
% 9.53/5.30        = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6847_real__sqrt__gt__0__iff,axiom,
% 9.53/5.30      ! [Y2: real] :
% 9.53/5.30        ( ( ord_less_real @ zero_zero_real @ ( sqrt @ Y2 ) )
% 9.53/5.30        = ( ord_less_real @ zero_zero_real @ Y2 ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6848_real__sqrt__le__0__iff,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30        ( ( ord_less_eq_real @ ( sqrt @ X ) @ zero_zero_real )
% 9.53/5.30        = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6849_real__sqrt__ge__0__iff,axiom,
% 9.53/5.30      ! [Y2: real] :
% 9.53/5.30        ( ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ Y2 ) )
% 9.53/5.30        = ( ord_less_eq_real @ zero_zero_real @ Y2 ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6850_real__sqrt__lt__1__iff,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30        ( ( ord_less_real @ ( sqrt @ X ) @ one_one_real )
% 9.53/5.30        = ( ord_less_real @ X @ one_one_real ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6851_real__sqrt__gt__1__iff,axiom,
% 9.53/5.30      ! [Y2: real] :
% 9.53/5.30        ( ( ord_less_real @ one_one_real @ ( sqrt @ Y2 ) )
% 9.53/5.30        = ( ord_less_real @ one_one_real @ Y2 ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6852_real__sqrt__le__1__iff,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30        ( ( ord_less_eq_real @ ( sqrt @ X ) @ one_one_real )
% 9.53/5.30        = ( ord_less_eq_real @ X @ one_one_real ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6853_real__sqrt__ge__1__iff,axiom,
% 9.53/5.30      ! [Y2: real] :
% 9.53/5.30        ( ( ord_less_eq_real @ one_one_real @ ( sqrt @ Y2 ) )
% 9.53/5.30        = ( ord_less_eq_real @ one_one_real @ Y2 ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6854_log__one,axiom,
% 9.53/5.30      ! [A: real] :
% 9.53/5.30        ( ( log @ A @ one_one_real )
% 9.53/5.30        = zero_zero_real ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6855_real__sqrt__mult__self,axiom,
% 9.53/5.30      ! [A: real] :
% 9.53/5.30        ( ( times_times_real @ ( sqrt @ A ) @ ( sqrt @ A ) )
% 9.53/5.30        = ( abs_abs_real @ A ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6856_real__sqrt__abs2,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30        ( ( sqrt @ ( times_times_real @ X @ X ) )
% 9.53/5.30        = ( abs_abs_real @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6857_or__nonnegative__int__iff,axiom,
% 9.53/5.30      ! [K: int,L2: int] :
% 9.53/5.30        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) )
% 9.53/5.30        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 9.53/5.30          & ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6858_or__negative__int__iff,axiom,
% 9.53/5.30      ! [K: int,L2: int] :
% 9.53/5.30        ( ( ord_less_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) @ zero_zero_int )
% 9.53/5.30        = ( ( ord_less_int @ K @ zero_zero_int )
% 9.53/5.30          | ( ord_less_int @ L2 @ zero_zero_int ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6859_pred__numeral__inc,axiom,
% 9.53/5.30      ! [K: num] :
% 9.53/5.30        ( ( pred_numeral @ ( inc @ K ) )
% 9.53/5.30        = ( numeral_numeral_nat @ K ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6860_or__numerals_I8_J,axiom,
% 9.53/5.30      ! [X: num] :
% 9.53/5.30        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ one_one_int )
% 9.53/5.30        = ( numeral_numeral_int @ ( bit1 @ X ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6861_or__numerals_I8_J,axiom,
% 9.53/5.30      ! [X: num] :
% 9.53/5.30        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ one_one_nat )
% 9.53/5.30        = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6862_or__numerals_I2_J,axiom,
% 9.53/5.30      ! [Y2: num] :
% 9.53/5.30        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y2 ) ) )
% 9.53/5.30        = ( numeral_numeral_int @ ( bit1 @ Y2 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6863_or__numerals_I2_J,axiom,
% 9.53/5.30      ! [Y2: num] :
% 9.53/5.30        ( ( bit_se1412395901928357646or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) )
% 9.53/5.30        = ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6864_real__sqrt__four,axiom,
% 9.53/5.30      ( ( sqrt @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 9.53/5.30      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6865_zero__less__log__cancel__iff,axiom,
% 9.53/5.30      ! [A: real,X: real] :
% 9.53/5.30        ( ( ord_less_real @ one_one_real @ A )
% 9.53/5.30       => ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.30         => ( ( ord_less_real @ zero_zero_real @ ( log @ A @ X ) )
% 9.53/5.30            = ( ord_less_real @ one_one_real @ X ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6866_log__less__zero__cancel__iff,axiom,
% 9.53/5.30      ! [A: real,X: real] :
% 9.53/5.30        ( ( ord_less_real @ one_one_real @ A )
% 9.53/5.30       => ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.30         => ( ( ord_less_real @ ( log @ A @ X ) @ zero_zero_real )
% 9.53/5.30            = ( ord_less_real @ X @ one_one_real ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6867_one__less__log__cancel__iff,axiom,
% 9.53/5.30      ! [A: real,X: real] :
% 9.53/5.30        ( ( ord_less_real @ one_one_real @ A )
% 9.53/5.30       => ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.30         => ( ( ord_less_real @ one_one_real @ ( log @ A @ X ) )
% 9.53/5.30            = ( ord_less_real @ A @ X ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6868_log__less__one__cancel__iff,axiom,
% 9.53/5.30      ! [A: real,X: real] :
% 9.53/5.30        ( ( ord_less_real @ one_one_real @ A )
% 9.53/5.30       => ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.30         => ( ( ord_less_real @ ( log @ A @ X ) @ one_one_real )
% 9.53/5.30            = ( ord_less_real @ X @ A ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6869_log__less__cancel__iff,axiom,
% 9.53/5.30      ! [A: real,X: real,Y2: real] :
% 9.53/5.30        ( ( ord_less_real @ one_one_real @ A )
% 9.53/5.30       => ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.30         => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 9.53/5.30           => ( ( ord_less_real @ ( log @ A @ X ) @ ( log @ A @ Y2 ) )
% 9.53/5.30              = ( ord_less_real @ X @ Y2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6870_log__eq__one,axiom,
% 9.53/5.30      ! [A: real] :
% 9.53/5.30        ( ( ord_less_real @ zero_zero_real @ A )
% 9.53/5.30       => ( ( A != one_one_real )
% 9.53/5.30         => ( ( log @ A @ A )
% 9.53/5.30            = one_one_real ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6871_or__numerals_I3_J,axiom,
% 9.53/5.30      ! [X: num,Y2: num] :
% 9.53/5.30        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y2 ) ) )
% 9.53/5.30        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y2 ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6872_or__numerals_I3_J,axiom,
% 9.53/5.30      ! [X: num,Y2: num] :
% 9.53/5.30        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) )
% 9.53/5.30        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y2 ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6873_sum_Ocl__ivl__Suc,axiom,
% 9.53/5.30      ! [N: nat,M: nat,G: nat > complex] :
% 9.53/5.30        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 9.53/5.30         => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.53/5.30            = zero_zero_complex ) )
% 9.53/5.30        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 9.53/5.30         => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.53/5.30            = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6874_sum_Ocl__ivl__Suc,axiom,
% 9.53/5.30      ! [N: nat,M: nat,G: nat > rat] :
% 9.53/5.30        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 9.53/5.30         => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.53/5.30            = zero_zero_rat ) )
% 9.53/5.30        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 9.53/5.30         => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.53/5.30            = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6875_sum_Ocl__ivl__Suc,axiom,
% 9.53/5.30      ! [N: nat,M: nat,G: nat > int] :
% 9.53/5.30        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 9.53/5.30         => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.53/5.30            = zero_zero_int ) )
% 9.53/5.30        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 9.53/5.30         => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.53/5.30            = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6876_sum_Ocl__ivl__Suc,axiom,
% 9.53/5.30      ! [N: nat,M: nat,G: nat > nat] :
% 9.53/5.30        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 9.53/5.30         => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.53/5.30            = zero_zero_nat ) )
% 9.53/5.30        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 9.53/5.30         => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.53/5.30            = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6877_sum_Ocl__ivl__Suc,axiom,
% 9.53/5.30      ! [N: nat,M: nat,G: nat > real] :
% 9.53/5.30        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 9.53/5.30         => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.53/5.30            = zero_zero_real ) )
% 9.53/5.30        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 9.53/5.30         => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.53/5.30            = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6878_or__numerals_I5_J,axiom,
% 9.53/5.30      ! [X: num] :
% 9.53/5.30        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ one_one_int )
% 9.53/5.30        = ( numeral_numeral_int @ ( bit1 @ X ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6879_or__numerals_I5_J,axiom,
% 9.53/5.30      ! [X: num] :
% 9.53/5.30        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ one_one_nat )
% 9.53/5.30        = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6880_or__numerals_I1_J,axiom,
% 9.53/5.30      ! [Y2: num] :
% 9.53/5.30        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y2 ) ) )
% 9.53/5.30        = ( numeral_numeral_int @ ( bit1 @ Y2 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6881_or__numerals_I1_J,axiom,
% 9.53/5.30      ! [Y2: num] :
% 9.53/5.30        ( ( bit_se1412395901928357646or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) )
% 9.53/5.30        = ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6882_log__le__cancel__iff,axiom,
% 9.53/5.30      ! [A: real,X: real,Y2: real] :
% 9.53/5.30        ( ( ord_less_real @ one_one_real @ A )
% 9.53/5.30       => ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.30         => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 9.53/5.30           => ( ( ord_less_eq_real @ ( log @ A @ X ) @ ( log @ A @ Y2 ) )
% 9.53/5.30              = ( ord_less_eq_real @ X @ Y2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6883_log__le__one__cancel__iff,axiom,
% 9.53/5.30      ! [A: real,X: real] :
% 9.53/5.30        ( ( ord_less_real @ one_one_real @ A )
% 9.53/5.30       => ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.30         => ( ( ord_less_eq_real @ ( log @ A @ X ) @ one_one_real )
% 9.53/5.30            = ( ord_less_eq_real @ X @ A ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6884_one__le__log__cancel__iff,axiom,
% 9.53/5.30      ! [A: real,X: real] :
% 9.53/5.30        ( ( ord_less_real @ one_one_real @ A )
% 9.53/5.30       => ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.30         => ( ( ord_less_eq_real @ one_one_real @ ( log @ A @ X ) )
% 9.53/5.30            = ( ord_less_eq_real @ A @ X ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6885_log__le__zero__cancel__iff,axiom,
% 9.53/5.30      ! [A: real,X: real] :
% 9.53/5.30        ( ( ord_less_real @ one_one_real @ A )
% 9.53/5.30       => ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.30         => ( ( ord_less_eq_real @ ( log @ A @ X ) @ zero_zero_real )
% 9.53/5.30            = ( ord_less_eq_real @ X @ one_one_real ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6886_zero__le__log__cancel__iff,axiom,
% 9.53/5.30      ! [A: real,X: real] :
% 9.53/5.30        ( ( ord_less_real @ one_one_real @ A )
% 9.53/5.30       => ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.30         => ( ( ord_less_eq_real @ zero_zero_real @ ( log @ A @ X ) )
% 9.53/5.30            = ( ord_less_eq_real @ one_one_real @ X ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6887_add__neg__numeral__special_I6_J,axiom,
% 9.53/5.30      ! [M: num] :
% 9.53/5.30        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 9.53/5.30        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ M ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6888_add__neg__numeral__special_I6_J,axiom,
% 9.53/5.30      ! [M: num] :
% 9.53/5.30        ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 9.53/5.30        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ M ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6889_add__neg__numeral__special_I6_J,axiom,
% 9.53/5.30      ! [M: num] :
% 9.53/5.30        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 9.53/5.30        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6890_add__neg__numeral__special_I6_J,axiom,
% 9.53/5.30      ! [M: num] :
% 9.53/5.30        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.53/5.30        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6891_add__neg__numeral__special_I6_J,axiom,
% 9.53/5.30      ! [M: num] :
% 9.53/5.30        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.53/5.30        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ M ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6892_add__neg__numeral__special_I5_J,axiom,
% 9.53/5.30      ! [N: num] :
% 9.53/5.30        ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.53/5.30        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6893_add__neg__numeral__special_I5_J,axiom,
% 9.53/5.30      ! [N: num] :
% 9.53/5.30        ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 9.53/5.30        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6894_add__neg__numeral__special_I5_J,axiom,
% 9.53/5.30      ! [N: num] :
% 9.53/5.30        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 9.53/5.30        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6895_add__neg__numeral__special_I5_J,axiom,
% 9.53/5.30      ! [N: num] :
% 9.53/5.30        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 9.53/5.30        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6896_add__neg__numeral__special_I5_J,axiom,
% 9.53/5.30      ! [N: num] :
% 9.53/5.30        ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 9.53/5.30        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6897_diff__numeral__special_I6_J,axiom,
% 9.53/5.30      ! [M: num] :
% 9.53/5.30        ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) )
% 9.53/5.30        = ( numeral_numeral_int @ ( inc @ M ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6898_diff__numeral__special_I6_J,axiom,
% 9.53/5.30      ! [M: num] :
% 9.53/5.30        ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) )
% 9.53/5.30        = ( numeral_numeral_real @ ( inc @ M ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6899_diff__numeral__special_I6_J,axiom,
% 9.53/5.30      ! [M: num] :
% 9.53/5.30        ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 9.53/5.30        = ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6900_diff__numeral__special_I6_J,axiom,
% 9.53/5.30      ! [M: num] :
% 9.53/5.30        ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.53/5.30        = ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6901_diff__numeral__special_I6_J,axiom,
% 9.53/5.30      ! [M: num] :
% 9.53/5.30        ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.53/5.30        = ( numeral_numeral_rat @ ( inc @ M ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6902_diff__numeral__special_I5_J,axiom,
% 9.53/5.30      ! [N: num] :
% 9.53/5.30        ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 9.53/5.30        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6903_diff__numeral__special_I5_J,axiom,
% 9.53/5.30      ! [N: num] :
% 9.53/5.30        ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ N ) )
% 9.53/5.30        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6904_diff__numeral__special_I5_J,axiom,
% 9.53/5.30      ! [N: num] :
% 9.53/5.30        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( numera6690914467698888265omplex @ N ) )
% 9.53/5.30        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6905_diff__numeral__special_I5_J,axiom,
% 9.53/5.30      ! [N: num] :
% 9.53/5.30        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ N ) )
% 9.53/5.30        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6906_diff__numeral__special_I5_J,axiom,
% 9.53/5.30      ! [N: num] :
% 9.53/5.30        ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ N ) )
% 9.53/5.30        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6907_or__minus__numerals_I6_J,axiom,
% 9.53/5.30      ! [N: num] :
% 9.53/5.30        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 9.53/5.30        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6908_or__minus__numerals_I2_J,axiom,
% 9.53/5.30      ! [N: num] :
% 9.53/5.30        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 9.53/5.30        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6909_sum__zero__power,axiom,
% 9.53/5.30      ! [A2: set_nat,C: nat > rat] :
% 9.53/5.30        ( ( ( ( finite_finite_nat @ A2 )
% 9.53/5.30            & ( member_nat @ zero_zero_nat @ A2 ) )
% 9.53/5.30         => ( ( groups2906978787729119204at_rat
% 9.53/5.30              @ ^ [I3: nat] : ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ zero_zero_rat @ I3 ) )
% 9.53/5.30              @ A2 )
% 9.53/5.30            = ( C @ zero_zero_nat ) ) )
% 9.53/5.30        & ( ~ ( ( finite_finite_nat @ A2 )
% 9.53/5.30              & ( member_nat @ zero_zero_nat @ A2 ) )
% 9.53/5.30         => ( ( groups2906978787729119204at_rat
% 9.53/5.30              @ ^ [I3: nat] : ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ zero_zero_rat @ I3 ) )
% 9.53/5.30              @ A2 )
% 9.53/5.30            = zero_zero_rat ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6910_sum__zero__power,axiom,
% 9.53/5.30      ! [A2: set_nat,C: nat > complex] :
% 9.53/5.30        ( ( ( ( finite_finite_nat @ A2 )
% 9.53/5.30            & ( member_nat @ zero_zero_nat @ A2 ) )
% 9.53/5.30         => ( ( groups2073611262835488442omplex
% 9.53/5.30              @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ zero_zero_complex @ I3 ) )
% 9.53/5.30              @ A2 )
% 9.53/5.30            = ( C @ zero_zero_nat ) ) )
% 9.53/5.30        & ( ~ ( ( finite_finite_nat @ A2 )
% 9.53/5.30              & ( member_nat @ zero_zero_nat @ A2 ) )
% 9.53/5.30         => ( ( groups2073611262835488442omplex
% 9.53/5.30              @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ zero_zero_complex @ I3 ) )
% 9.53/5.30              @ A2 )
% 9.53/5.30            = zero_zero_complex ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6911_sum__zero__power,axiom,
% 9.53/5.30      ! [A2: set_nat,C: nat > real] :
% 9.53/5.30        ( ( ( ( finite_finite_nat @ A2 )
% 9.53/5.30            & ( member_nat @ zero_zero_nat @ A2 ) )
% 9.53/5.30         => ( ( groups6591440286371151544t_real
% 9.53/5.30              @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ zero_zero_real @ I3 ) )
% 9.53/5.30              @ A2 )
% 9.53/5.30            = ( C @ zero_zero_nat ) ) )
% 9.53/5.30        & ( ~ ( ( finite_finite_nat @ A2 )
% 9.53/5.30              & ( member_nat @ zero_zero_nat @ A2 ) )
% 9.53/5.30         => ( ( groups6591440286371151544t_real
% 9.53/5.30              @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ zero_zero_real @ I3 ) )
% 9.53/5.30              @ A2 )
% 9.53/5.30            = zero_zero_real ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6912_real__sqrt__abs,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30        ( ( sqrt @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.53/5.30        = ( abs_abs_real @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6913_sum__zero__power_H,axiom,
% 9.53/5.30      ! [A2: set_nat,C: nat > complex,D2: nat > complex] :
% 9.53/5.30        ( ( ( ( finite_finite_nat @ A2 )
% 9.53/5.30            & ( member_nat @ zero_zero_nat @ A2 ) )
% 9.53/5.30         => ( ( groups2073611262835488442omplex
% 9.53/5.30              @ ^ [I3: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ zero_zero_complex @ I3 ) ) @ ( D2 @ I3 ) )
% 9.53/5.30              @ A2 )
% 9.53/5.30            = ( divide1717551699836669952omplex @ ( C @ zero_zero_nat ) @ ( D2 @ zero_zero_nat ) ) ) )
% 9.53/5.30        & ( ~ ( ( finite_finite_nat @ A2 )
% 9.53/5.30              & ( member_nat @ zero_zero_nat @ A2 ) )
% 9.53/5.30         => ( ( groups2073611262835488442omplex
% 9.53/5.30              @ ^ [I3: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ zero_zero_complex @ I3 ) ) @ ( D2 @ I3 ) )
% 9.53/5.30              @ A2 )
% 9.53/5.30            = zero_zero_complex ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6914_sum__zero__power_H,axiom,
% 9.53/5.30      ! [A2: set_nat,C: nat > rat,D2: nat > rat] :
% 9.53/5.30        ( ( ( ( finite_finite_nat @ A2 )
% 9.53/5.30            & ( member_nat @ zero_zero_nat @ A2 ) )
% 9.53/5.30         => ( ( groups2906978787729119204at_rat
% 9.53/5.30              @ ^ [I3: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ zero_zero_rat @ I3 ) ) @ ( D2 @ I3 ) )
% 9.53/5.30              @ A2 )
% 9.53/5.30            = ( divide_divide_rat @ ( C @ zero_zero_nat ) @ ( D2 @ zero_zero_nat ) ) ) )
% 9.53/5.30        & ( ~ ( ( finite_finite_nat @ A2 )
% 9.53/5.30              & ( member_nat @ zero_zero_nat @ A2 ) )
% 9.53/5.30         => ( ( groups2906978787729119204at_rat
% 9.53/5.30              @ ^ [I3: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ zero_zero_rat @ I3 ) ) @ ( D2 @ I3 ) )
% 9.53/5.30              @ A2 )
% 9.53/5.30            = zero_zero_rat ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6915_sum__zero__power_H,axiom,
% 9.53/5.30      ! [A2: set_nat,C: nat > real,D2: nat > real] :
% 9.53/5.30        ( ( ( ( finite_finite_nat @ A2 )
% 9.53/5.30            & ( member_nat @ zero_zero_nat @ A2 ) )
% 9.53/5.30         => ( ( groups6591440286371151544t_real
% 9.53/5.30              @ ^ [I3: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ zero_zero_real @ I3 ) ) @ ( D2 @ I3 ) )
% 9.53/5.30              @ A2 )
% 9.53/5.30            = ( divide_divide_real @ ( C @ zero_zero_nat ) @ ( D2 @ zero_zero_nat ) ) ) )
% 9.53/5.30        & ( ~ ( ( finite_finite_nat @ A2 )
% 9.53/5.30              & ( member_nat @ zero_zero_nat @ A2 ) )
% 9.53/5.30         => ( ( groups6591440286371151544t_real
% 9.53/5.30              @ ^ [I3: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ zero_zero_real @ I3 ) ) @ ( D2 @ I3 ) )
% 9.53/5.30              @ A2 )
% 9.53/5.30            = zero_zero_real ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6916_real__sqrt__pow2,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.30       => ( ( power_power_real @ ( sqrt @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.53/5.30          = X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6917_real__sqrt__pow2__iff,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30        ( ( ( power_power_real @ ( sqrt @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.53/5.30          = X )
% 9.53/5.30        = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6918_real__sqrt__sum__squares__mult__squared__eq,axiom,
% 9.53/5.30      ! [X: real,Y2: real,Xa2: real,Ya: real] :
% 9.53/5.30        ( ( power_power_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.53/5.30        = ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6919_or__numerals_I7_J,axiom,
% 9.53/5.30      ! [X: num,Y2: num] :
% 9.53/5.30        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y2 ) ) )
% 9.53/5.30        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6920_or__numerals_I7_J,axiom,
% 9.53/5.30      ! [X: num,Y2: num] :
% 9.53/5.30        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) )
% 9.53/5.30        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6921_or__numerals_I6_J,axiom,
% 9.53/5.30      ! [X: num,Y2: num] :
% 9.53/5.30        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y2 ) ) )
% 9.53/5.30        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6922_or__numerals_I6_J,axiom,
% 9.53/5.30      ! [X: num,Y2: num] :
% 9.53/5.30        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) )
% 9.53/5.30        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6923_or__numerals_I4_J,axiom,
% 9.53/5.30      ! [X: num,Y2: num] :
% 9.53/5.30        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y2 ) ) )
% 9.53/5.30        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6924_or__numerals_I4_J,axiom,
% 9.53/5.30      ! [X: num,Y2: num] :
% 9.53/5.30        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) )
% 9.53/5.30        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6925_of__int__or__eq,axiom,
% 9.53/5.30      ! [K: int,L2: int] :
% 9.53/5.30        ( ( ring_1_of_int_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) )
% 9.53/5.30        = ( bit_se1409905431419307370or_int @ ( ring_1_of_int_int @ K ) @ ( ring_1_of_int_int @ L2 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6926_or_Oassoc,axiom,
% 9.53/5.30      ! [A: int,B: int,C: int] :
% 9.53/5.30        ( ( bit_se1409905431419307370or_int @ ( bit_se1409905431419307370or_int @ A @ B ) @ C )
% 9.53/5.30        = ( bit_se1409905431419307370or_int @ A @ ( bit_se1409905431419307370or_int @ B @ C ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6927_or_Oassoc,axiom,
% 9.53/5.30      ! [A: nat,B: nat,C: nat] :
% 9.53/5.30        ( ( bit_se1412395901928357646or_nat @ ( bit_se1412395901928357646or_nat @ A @ B ) @ C )
% 9.53/5.30        = ( bit_se1412395901928357646or_nat @ A @ ( bit_se1412395901928357646or_nat @ B @ C ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6928_or_Ocommute,axiom,
% 9.53/5.30      ( bit_se1409905431419307370or_int
% 9.53/5.30      = ( ^ [A3: int,B4: int] : ( bit_se1409905431419307370or_int @ B4 @ A3 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6929_or_Ocommute,axiom,
% 9.53/5.30      ( bit_se1412395901928357646or_nat
% 9.53/5.30      = ( ^ [A3: nat,B4: nat] : ( bit_se1412395901928357646or_nat @ B4 @ A3 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6930_or_Oleft__commute,axiom,
% 9.53/5.30      ! [B: int,A: int,C: int] :
% 9.53/5.30        ( ( bit_se1409905431419307370or_int @ B @ ( bit_se1409905431419307370or_int @ A @ C ) )
% 9.53/5.30        = ( bit_se1409905431419307370or_int @ A @ ( bit_se1409905431419307370or_int @ B @ C ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6931_or_Oleft__commute,axiom,
% 9.53/5.30      ! [B: nat,A: nat,C: nat] :
% 9.53/5.30        ( ( bit_se1412395901928357646or_nat @ B @ ( bit_se1412395901928357646or_nat @ A @ C ) )
% 9.53/5.30        = ( bit_se1412395901928357646or_nat @ A @ ( bit_se1412395901928357646or_nat @ B @ C ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6932_or__eq__0__iff,axiom,
% 9.53/5.30      ! [A: int,B: int] :
% 9.53/5.30        ( ( ( bit_se1409905431419307370or_int @ A @ B )
% 9.53/5.30          = zero_zero_int )
% 9.53/5.30        = ( ( A = zero_zero_int )
% 9.53/5.30          & ( B = zero_zero_int ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6933_or__eq__0__iff,axiom,
% 9.53/5.30      ! [A: nat,B: nat] :
% 9.53/5.30        ( ( ( bit_se1412395901928357646or_nat @ A @ B )
% 9.53/5.30          = zero_zero_nat )
% 9.53/5.30        = ( ( A = zero_zero_nat )
% 9.53/5.30          & ( B = zero_zero_nat ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6934_bit_Odisj__zero__right,axiom,
% 9.53/5.30      ! [X: int] :
% 9.53/5.30        ( ( bit_se1409905431419307370or_int @ X @ zero_zero_int )
% 9.53/5.30        = X ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6935_real__sqrt__less__mono,axiom,
% 9.53/5.30      ! [X: real,Y2: real] :
% 9.53/5.30        ( ( ord_less_real @ X @ Y2 )
% 9.53/5.30       => ( ord_less_real @ ( sqrt @ X ) @ ( sqrt @ Y2 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6936_real__sqrt__le__mono,axiom,
% 9.53/5.30      ! [X: real,Y2: real] :
% 9.53/5.30        ( ( ord_less_eq_real @ X @ Y2 )
% 9.53/5.30       => ( ord_less_eq_real @ ( sqrt @ X ) @ ( sqrt @ Y2 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6937_real__sqrt__divide,axiom,
% 9.53/5.30      ! [X: real,Y2: real] :
% 9.53/5.30        ( ( sqrt @ ( divide_divide_real @ X @ Y2 ) )
% 9.53/5.30        = ( divide_divide_real @ ( sqrt @ X ) @ ( sqrt @ Y2 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6938_real__sqrt__mult,axiom,
% 9.53/5.30      ! [X: real,Y2: real] :
% 9.53/5.30        ( ( sqrt @ ( times_times_real @ X @ Y2 ) )
% 9.53/5.30        = ( times_times_real @ ( sqrt @ X ) @ ( sqrt @ Y2 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6939_real__sqrt__power,axiom,
% 9.53/5.30      ! [X: real,K: nat] :
% 9.53/5.30        ( ( sqrt @ ( power_power_real @ X @ K ) )
% 9.53/5.30        = ( power_power_real @ ( sqrt @ X ) @ K ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6940_real__sqrt__minus,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30        ( ( sqrt @ ( uminus_uminus_real @ X ) )
% 9.53/5.30        = ( uminus_uminus_real @ ( sqrt @ X ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6941_bit_Oconj__disj__distrib,axiom,
% 9.53/5.30      ! [X: int,Y2: int,Z: int] :
% 9.53/5.30        ( ( bit_se725231765392027082nd_int @ X @ ( bit_se1409905431419307370or_int @ Y2 @ Z ) )
% 9.53/5.30        = ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ X @ Y2 ) @ ( bit_se725231765392027082nd_int @ X @ Z ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6942_bit_Odisj__conj__distrib,axiom,
% 9.53/5.30      ! [X: int,Y2: int,Z: int] :
% 9.53/5.30        ( ( bit_se1409905431419307370or_int @ X @ ( bit_se725231765392027082nd_int @ Y2 @ Z ) )
% 9.53/5.30        = ( bit_se725231765392027082nd_int @ ( bit_se1409905431419307370or_int @ X @ Y2 ) @ ( bit_se1409905431419307370or_int @ X @ Z ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6943_bit_Oconj__disj__distrib2,axiom,
% 9.53/5.30      ! [Y2: int,Z: int,X: int] :
% 9.53/5.30        ( ( bit_se725231765392027082nd_int @ ( bit_se1409905431419307370or_int @ Y2 @ Z ) @ X )
% 9.53/5.30        = ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ Y2 @ X ) @ ( bit_se725231765392027082nd_int @ Z @ X ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6944_bit_Odisj__conj__distrib2,axiom,
% 9.53/5.30      ! [Y2: int,Z: int,X: int] :
% 9.53/5.30        ( ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ Y2 @ Z ) @ X )
% 9.53/5.30        = ( bit_se725231765392027082nd_int @ ( bit_se1409905431419307370or_int @ Y2 @ X ) @ ( bit_se1409905431419307370or_int @ Z @ X ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6945_num__induct,axiom,
% 9.53/5.30      ! [P: num > $o,X: num] :
% 9.53/5.30        ( ( P @ one )
% 9.53/5.30       => ( ! [X3: num] :
% 9.53/5.30              ( ( P @ X3 )
% 9.53/5.30             => ( P @ ( inc @ X3 ) ) )
% 9.53/5.30         => ( P @ X ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6946_add__inc,axiom,
% 9.53/5.30      ! [X: num,Y2: num] :
% 9.53/5.30        ( ( plus_plus_num @ X @ ( inc @ Y2 ) )
% 9.53/5.30        = ( inc @ ( plus_plus_num @ X @ Y2 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6947_real__sqrt__gt__zero,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30        ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.30       => ( ord_less_real @ zero_zero_real @ ( sqrt @ X ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6948_real__sqrt__eq__zero__cancel,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.30       => ( ( ( sqrt @ X )
% 9.53/5.30            = zero_zero_real )
% 9.53/5.30         => ( X = zero_zero_real ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6949_real__sqrt__ge__zero,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.30       => ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ X ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6950_sum__cong__Suc,axiom,
% 9.53/5.30      ! [A2: set_nat,F: nat > nat,G: nat > nat] :
% 9.53/5.30        ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 9.53/5.30       => ( ! [X3: nat] :
% 9.53/5.30              ( ( member_nat @ ( suc @ X3 ) @ A2 )
% 9.53/5.30             => ( ( F @ ( suc @ X3 ) )
% 9.53/5.30                = ( G @ ( suc @ X3 ) ) ) )
% 9.53/5.30         => ( ( groups3542108847815614940at_nat @ F @ A2 )
% 9.53/5.30            = ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6951_sum__cong__Suc,axiom,
% 9.53/5.30      ! [A2: set_nat,F: nat > real,G: nat > real] :
% 9.53/5.30        ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 9.53/5.30       => ( ! [X3: nat] :
% 9.53/5.30              ( ( member_nat @ ( suc @ X3 ) @ A2 )
% 9.53/5.30             => ( ( F @ ( suc @ X3 ) )
% 9.53/5.30                = ( G @ ( suc @ X3 ) ) ) )
% 9.53/5.30         => ( ( groups6591440286371151544t_real @ F @ A2 )
% 9.53/5.30            = ( groups6591440286371151544t_real @ G @ A2 ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6952_real__sqrt__ge__one,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30        ( ( ord_less_eq_real @ one_one_real @ X )
% 9.53/5.30       => ( ord_less_eq_real @ one_one_real @ ( sqrt @ X ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6953_OR__lower,axiom,
% 9.53/5.30      ! [X: int,Y2: int] :
% 9.53/5.30        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 9.53/5.30       => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 9.53/5.30         => ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ X @ Y2 ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6954_or__greater__eq,axiom,
% 9.53/5.30      ! [L2: int,K: int] :
% 9.53/5.30        ( ( ord_less_eq_int @ zero_zero_int @ L2 )
% 9.53/5.30       => ( ord_less_eq_int @ K @ ( bit_se1409905431419307370or_int @ K @ L2 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6955_log__def,axiom,
% 9.53/5.30      ( log
% 9.53/5.30      = ( ^ [A3: real,X2: real] : ( divide_divide_real @ ( ln_ln_real @ X2 ) @ ( ln_ln_real @ A3 ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6956_plus__and__or,axiom,
% 9.53/5.30      ! [X: int,Y2: int] :
% 9.53/5.30        ( ( plus_plus_int @ ( bit_se725231765392027082nd_int @ X @ Y2 ) @ ( bit_se1409905431419307370or_int @ X @ Y2 ) )
% 9.53/5.30        = ( plus_plus_int @ X @ Y2 ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6957_sum__subtractf__nat,axiom,
% 9.53/5.30      ! [A2: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > nat,F: product_prod_nat_nat > nat] :
% 9.53/5.30        ( ! [X3: product_prod_nat_nat] :
% 9.53/5.30            ( ( member8440522571783428010at_nat @ X3 @ A2 )
% 9.53/5.30           => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 9.53/5.30       => ( ( groups977919841031483927at_nat
% 9.53/5.30            @ ^ [X2: product_prod_nat_nat] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 9.53/5.30            @ A2 )
% 9.53/5.30          = ( minus_minus_nat @ ( groups977919841031483927at_nat @ F @ A2 ) @ ( groups977919841031483927at_nat @ G @ A2 ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6958_sum__subtractf__nat,axiom,
% 9.53/5.30      ! [A2: set_complex,G: complex > nat,F: complex > nat] :
% 9.53/5.30        ( ! [X3: complex] :
% 9.53/5.30            ( ( member_complex @ X3 @ A2 )
% 9.53/5.30           => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 9.53/5.30       => ( ( groups5693394587270226106ex_nat
% 9.53/5.30            @ ^ [X2: complex] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 9.53/5.30            @ A2 )
% 9.53/5.30          = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6959_sum__subtractf__nat,axiom,
% 9.53/5.30      ! [A2: set_real,G: real > nat,F: real > nat] :
% 9.53/5.30        ( ! [X3: real] :
% 9.53/5.30            ( ( member_real @ X3 @ A2 )
% 9.53/5.30           => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 9.53/5.30       => ( ( groups1935376822645274424al_nat
% 9.53/5.30            @ ^ [X2: real] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 9.53/5.30            @ A2 )
% 9.53/5.30          = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6960_sum__subtractf__nat,axiom,
% 9.53/5.30      ! [A2: set_int,G: int > nat,F: int > nat] :
% 9.53/5.30        ( ! [X3: int] :
% 9.53/5.30            ( ( member_int @ X3 @ A2 )
% 9.53/5.30           => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 9.53/5.30       => ( ( groups4541462559716669496nt_nat
% 9.53/5.30            @ ^ [X2: int] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 9.53/5.30            @ A2 )
% 9.53/5.30          = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6961_sum__subtractf__nat,axiom,
% 9.53/5.30      ! [A2: set_nat,G: nat > nat,F: nat > nat] :
% 9.53/5.30        ( ! [X3: nat] :
% 9.53/5.30            ( ( member_nat @ X3 @ A2 )
% 9.53/5.30           => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 9.53/5.30       => ( ( groups3542108847815614940at_nat
% 9.53/5.30            @ ^ [X2: nat] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 9.53/5.30            @ A2 )
% 9.53/5.30          = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6962_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 9.53/5.30      ! [G: nat > nat,M: nat,N: nat] :
% 9.53/5.30        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 9.53/5.30        = ( groups3542108847815614940at_nat
% 9.53/5.30          @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.53/5.30          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6963_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 9.53/5.30      ! [G: nat > real,M: nat,N: nat] :
% 9.53/5.30        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 9.53/5.30        = ( groups6591440286371151544t_real
% 9.53/5.30          @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.53/5.30          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6964_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 9.53/5.30      ! [G: nat > nat,M: nat,K: nat,N: nat] :
% 9.53/5.30        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 9.53/5.30        = ( groups3542108847815614940at_nat
% 9.53/5.30          @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 9.53/5.30          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6965_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 9.53/5.30      ! [G: nat > real,M: nat,K: nat,N: nat] :
% 9.53/5.30        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 9.53/5.30        = ( groups6591440286371151544t_real
% 9.53/5.30          @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 9.53/5.30          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6966_pow_Osimps_I1_J,axiom,
% 9.53/5.30      ! [X: num] :
% 9.53/5.30        ( ( pow @ X @ one )
% 9.53/5.30        = X ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6967_inc_Osimps_I1_J,axiom,
% 9.53/5.30      ( ( inc @ one )
% 9.53/5.30      = ( bit0 @ one ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6968_inc_Osimps_I3_J,axiom,
% 9.53/5.30      ! [X: num] :
% 9.53/5.30        ( ( inc @ ( bit1 @ X ) )
% 9.53/5.30        = ( bit0 @ ( inc @ X ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6969_inc_Osimps_I2_J,axiom,
% 9.53/5.30      ! [X: num] :
% 9.53/5.30        ( ( inc @ ( bit0 @ X ) )
% 9.53/5.30        = ( bit1 @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6970_sum__eq__Suc0__iff,axiom,
% 9.53/5.30      ! [A2: set_complex,F: complex > nat] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.30       => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 9.53/5.30            = ( suc @ zero_zero_nat ) )
% 9.53/5.30          = ( ? [X2: complex] :
% 9.53/5.30                ( ( member_complex @ X2 @ A2 )
% 9.53/5.30                & ( ( F @ X2 )
% 9.53/5.30                  = ( suc @ zero_zero_nat ) )
% 9.53/5.30                & ! [Y: complex] :
% 9.53/5.30                    ( ( member_complex @ Y @ A2 )
% 9.53/5.30                   => ( ( X2 != Y )
% 9.53/5.30                     => ( ( F @ Y )
% 9.53/5.30                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6971_sum__eq__Suc0__iff,axiom,
% 9.53/5.30      ! [A2: set_nat,F: nat > nat] :
% 9.53/5.30        ( ( finite_finite_nat @ A2 )
% 9.53/5.30       => ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 9.53/5.30            = ( suc @ zero_zero_nat ) )
% 9.53/5.30          = ( ? [X2: nat] :
% 9.53/5.30                ( ( member_nat @ X2 @ A2 )
% 9.53/5.30                & ( ( F @ X2 )
% 9.53/5.30                  = ( suc @ zero_zero_nat ) )
% 9.53/5.30                & ! [Y: nat] :
% 9.53/5.30                    ( ( member_nat @ Y @ A2 )
% 9.53/5.30                   => ( ( X2 != Y )
% 9.53/5.30                     => ( ( F @ Y )
% 9.53/5.30                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6972_sum__SucD,axiom,
% 9.53/5.30      ! [F: nat > nat,A2: set_nat,N: nat] :
% 9.53/5.30        ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 9.53/5.30          = ( suc @ N ) )
% 9.53/5.30       => ? [X3: nat] :
% 9.53/5.30            ( ( member_nat @ X3 @ A2 )
% 9.53/5.30            & ( ord_less_nat @ zero_zero_nat @ ( F @ X3 ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6973_sum__eq__1__iff,axiom,
% 9.53/5.30      ! [A2: set_complex,F: complex > nat] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.30       => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 9.53/5.30            = one_one_nat )
% 9.53/5.30          = ( ? [X2: complex] :
% 9.53/5.30                ( ( member_complex @ X2 @ A2 )
% 9.53/5.30                & ( ( F @ X2 )
% 9.53/5.30                  = one_one_nat )
% 9.53/5.30                & ! [Y: complex] :
% 9.53/5.30                    ( ( member_complex @ Y @ A2 )
% 9.53/5.30                   => ( ( X2 != Y )
% 9.53/5.30                     => ( ( F @ Y )
% 9.53/5.30                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6974_sum__eq__1__iff,axiom,
% 9.53/5.30      ! [A2: set_nat,F: nat > nat] :
% 9.53/5.30        ( ( finite_finite_nat @ A2 )
% 9.53/5.30       => ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 9.53/5.30            = one_one_nat )
% 9.53/5.30          = ( ? [X2: nat] :
% 9.53/5.30                ( ( member_nat @ X2 @ A2 )
% 9.53/5.30                & ( ( F @ X2 )
% 9.53/5.30                  = one_one_nat )
% 9.53/5.30                & ! [Y: nat] :
% 9.53/5.30                    ( ( member_nat @ Y @ A2 )
% 9.53/5.30                   => ( ( X2 != Y )
% 9.53/5.30                     => ( ( F @ Y )
% 9.53/5.30                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6975_real__div__sqrt,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.30       => ( ( divide_divide_real @ X @ ( sqrt @ X ) )
% 9.53/5.30          = ( sqrt @ X ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6976_add__One,axiom,
% 9.53/5.30      ! [X: num] :
% 9.53/5.30        ( ( plus_plus_num @ X @ one )
% 9.53/5.30        = ( inc @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6977_sqrt__add__le__add__sqrt,axiom,
% 9.53/5.30      ! [X: real,Y2: real] :
% 9.53/5.30        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.30       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 9.53/5.30         => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ X @ Y2 ) ) @ ( plus_plus_real @ ( sqrt @ X ) @ ( sqrt @ Y2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6978_le__real__sqrt__sumsq,axiom,
% 9.53/5.30      ! [X: real,Y2: real] : ( ord_less_eq_real @ X @ ( sqrt @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y2 @ Y2 ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6979_inc__BitM__eq,axiom,
% 9.53/5.30      ! [N: num] :
% 9.53/5.30        ( ( inc @ ( bitM @ N ) )
% 9.53/5.30        = ( bit0 @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6980_BitM__inc__eq,axiom,
% 9.53/5.30      ! [N: num] :
% 9.53/5.30        ( ( bitM @ ( inc @ N ) )
% 9.53/5.30        = ( bit1 @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6981_log__ln,axiom,
% 9.53/5.30      ( ln_ln_real
% 9.53/5.30      = ( log @ ( exp_real @ one_one_real ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6982_mult__inc,axiom,
% 9.53/5.30      ! [X: num,Y2: num] :
% 9.53/5.30        ( ( times_times_num @ X @ ( inc @ Y2 ) )
% 9.53/5.30        = ( plus_plus_num @ ( times_times_num @ X @ Y2 ) @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6983_sum__power__add,axiom,
% 9.53/5.30      ! [X: complex,M: nat,I6: set_nat] :
% 9.53/5.30        ( ( groups2073611262835488442omplex
% 9.53/5.30          @ ^ [I3: nat] : ( power_power_complex @ X @ ( plus_plus_nat @ M @ I3 ) )
% 9.53/5.30          @ I6 )
% 9.53/5.30        = ( times_times_complex @ ( power_power_complex @ X @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ I6 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6984_sum__power__add,axiom,
% 9.53/5.30      ! [X: int,M: nat,I6: set_nat] :
% 9.53/5.30        ( ( groups3539618377306564664at_int
% 9.53/5.30          @ ^ [I3: nat] : ( power_power_int @ X @ ( plus_plus_nat @ M @ I3 ) )
% 9.53/5.30          @ I6 )
% 9.53/5.30        = ( times_times_int @ ( power_power_int @ X @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ I6 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6985_sum__power__add,axiom,
% 9.53/5.30      ! [X: real,M: nat,I6: set_nat] :
% 9.53/5.30        ( ( groups6591440286371151544t_real
% 9.53/5.30          @ ^ [I3: nat] : ( power_power_real @ X @ ( plus_plus_nat @ M @ I3 ) )
% 9.53/5.30          @ I6 )
% 9.53/5.30        = ( times_times_real @ ( power_power_real @ X @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ I6 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6986_sum_OatLeastAtMost__rev,axiom,
% 9.53/5.30      ! [G: nat > nat,N: nat,M: nat] :
% 9.53/5.30        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 9.53/5.30        = ( groups3542108847815614940at_nat
% 9.53/5.30          @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I3 ) )
% 9.53/5.30          @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6987_sum_OatLeastAtMost__rev,axiom,
% 9.53/5.30      ! [G: nat > real,N: nat,M: nat] :
% 9.53/5.30        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 9.53/5.30        = ( groups6591440286371151544t_real
% 9.53/5.30          @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I3 ) )
% 9.53/5.30          @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6988_sum__roots__unity,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( ord_less_nat @ one_one_nat @ N )
% 9.53/5.30       => ( ( groups7754918857620584856omplex
% 9.53/5.30            @ ^ [X2: complex] : X2
% 9.53/5.30            @ ( collect_complex
% 9.53/5.30              @ ^ [Z4: complex] :
% 9.53/5.30                  ( ( power_power_complex @ Z4 @ N )
% 9.53/5.30                  = one_one_complex ) ) )
% 9.53/5.30          = zero_zero_complex ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6989_sum__nth__roots,axiom,
% 9.53/5.30      ! [N: nat,C: complex] :
% 9.53/5.30        ( ( ord_less_nat @ one_one_nat @ N )
% 9.53/5.30       => ( ( groups7754918857620584856omplex
% 9.53/5.30            @ ^ [X2: complex] : X2
% 9.53/5.30            @ ( collect_complex
% 9.53/5.30              @ ^ [Z4: complex] :
% 9.53/5.30                  ( ( power_power_complex @ Z4 @ N )
% 9.53/5.30                  = C ) ) )
% 9.53/5.30          = zero_zero_complex ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6990_sqrt2__less__2,axiom,
% 9.53/5.30      ord_less_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6991_even__or__iff,axiom,
% 9.53/5.30      ! [A: code_integer,B: code_integer] :
% 9.53/5.30        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1080825931792720795nteger @ A @ B ) )
% 9.53/5.30        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.53/5.30          & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6992_even__or__iff,axiom,
% 9.53/5.30      ! [A: int,B: int] :
% 9.53/5.30        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ A @ B ) )
% 9.53/5.30        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.53/5.30          & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6993_even__or__iff,axiom,
% 9.53/5.30      ! [A: nat,B: nat] :
% 9.53/5.30        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ A @ B ) )
% 9.53/5.30        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.53/5.30          & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6994_log__base__change,axiom,
% 9.53/5.30      ! [A: real,B: real,X: real] :
% 9.53/5.30        ( ( ord_less_real @ zero_zero_real @ A )
% 9.53/5.30       => ( ( A != one_one_real )
% 9.53/5.30         => ( ( log @ B @ X )
% 9.53/5.30            = ( divide_divide_real @ ( log @ A @ X ) @ ( log @ A @ B ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6995_sum__diff__nat,axiom,
% 9.53/5.30      ! [B2: set_complex,A2: set_complex,F: complex > nat] :
% 9.53/5.30        ( ( finite3207457112153483333omplex @ B2 )
% 9.53/5.30       => ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 9.53/5.30         => ( ( groups5693394587270226106ex_nat @ F @ ( minus_811609699411566653omplex @ A2 @ B2 ) )
% 9.53/5.30            = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6996_sum__diff__nat,axiom,
% 9.53/5.30      ! [B2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 9.53/5.30        ( ( finite6177210948735845034at_nat @ B2 )
% 9.53/5.30       => ( ( ord_le3146513528884898305at_nat @ B2 @ A2 )
% 9.53/5.30         => ( ( groups977919841031483927at_nat @ F @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) )
% 9.53/5.30            = ( minus_minus_nat @ ( groups977919841031483927at_nat @ F @ A2 ) @ ( groups977919841031483927at_nat @ F @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6997_sum__diff__nat,axiom,
% 9.53/5.30      ! [B2: set_real,A2: set_real,F: real > nat] :
% 9.53/5.30        ( ( finite_finite_real @ B2 )
% 9.53/5.30       => ( ( ord_less_eq_set_real @ B2 @ A2 )
% 9.53/5.30         => ( ( groups1935376822645274424al_nat @ F @ ( minus_minus_set_real @ A2 @ B2 ) )
% 9.53/5.30            = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ F @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6998_sum__diff__nat,axiom,
% 9.53/5.30      ! [B2: set_nat,A2: set_nat,F: nat > nat] :
% 9.53/5.30        ( ( finite_finite_nat @ B2 )
% 9.53/5.30       => ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 9.53/5.30         => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 9.53/5.30            = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ F @ B2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_6999_bit_Ocomplement__unique,axiom,
% 9.53/5.30      ! [A: code_integer,X: code_integer,Y2: code_integer] :
% 9.53/5.30        ( ( ( bit_se3949692690581998587nteger @ A @ X )
% 9.53/5.30          = zero_z3403309356797280102nteger )
% 9.53/5.30       => ( ( ( bit_se1080825931792720795nteger @ A @ X )
% 9.53/5.30            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.53/5.30         => ( ( ( bit_se3949692690581998587nteger @ A @ Y2 )
% 9.53/5.30              = zero_z3403309356797280102nteger )
% 9.53/5.30           => ( ( ( bit_se1080825931792720795nteger @ A @ Y2 )
% 9.53/5.30                = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.53/5.30             => ( X = Y2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7000_bit_Ocomplement__unique,axiom,
% 9.53/5.30      ! [A: int,X: int,Y2: int] :
% 9.53/5.30        ( ( ( bit_se725231765392027082nd_int @ A @ X )
% 9.53/5.30          = zero_zero_int )
% 9.53/5.30       => ( ( ( bit_se1409905431419307370or_int @ A @ X )
% 9.53/5.30            = ( uminus_uminus_int @ one_one_int ) )
% 9.53/5.30         => ( ( ( bit_se725231765392027082nd_int @ A @ Y2 )
% 9.53/5.30              = zero_zero_int )
% 9.53/5.30           => ( ( ( bit_se1409905431419307370or_int @ A @ Y2 )
% 9.53/5.30                = ( uminus_uminus_int @ one_one_int ) )
% 9.53/5.30             => ( X = Y2 ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7001_sum__diff1__nat,axiom,
% 9.53/5.30      ! [A: vEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 9.53/5.30        ( ( ( member_VEBT_VEBT @ A @ A2 )
% 9.53/5.30         => ( ( groups771621172384141258BT_nat @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 9.53/5.30            = ( minus_minus_nat @ ( groups771621172384141258BT_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 9.53/5.30        & ( ~ ( member_VEBT_VEBT @ A @ A2 )
% 9.53/5.30         => ( ( groups771621172384141258BT_nat @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 9.53/5.30            = ( groups771621172384141258BT_nat @ F @ A2 ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7002_sum__diff1__nat,axiom,
% 9.53/5.30      ! [A: complex,A2: set_complex,F: complex > nat] :
% 9.53/5.30        ( ( ( member_complex @ A @ A2 )
% 9.53/5.30         => ( ( groups5693394587270226106ex_nat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 9.53/5.30            = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 9.53/5.30        & ( ~ ( member_complex @ A @ A2 )
% 9.53/5.30         => ( ( groups5693394587270226106ex_nat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 9.53/5.30            = ( groups5693394587270226106ex_nat @ F @ A2 ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7003_sum__diff1__nat,axiom,
% 9.53/5.30      ! [A: int,A2: set_int,F: int > nat] :
% 9.53/5.30        ( ( ( member_int @ A @ A2 )
% 9.53/5.30         => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 9.53/5.30            = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 9.53/5.30        & ( ~ ( member_int @ A @ A2 )
% 9.53/5.30         => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 9.53/5.30            = ( groups4541462559716669496nt_nat @ F @ A2 ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7004_sum__diff1__nat,axiom,
% 9.53/5.30      ! [A: real,A2: set_real,F: real > nat] :
% 9.53/5.30        ( ( ( member_real @ A @ A2 )
% 9.53/5.30         => ( ( groups1935376822645274424al_nat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 9.53/5.30            = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 9.53/5.30        & ( ~ ( member_real @ A @ A2 )
% 9.53/5.30         => ( ( groups1935376822645274424al_nat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 9.53/5.30            = ( groups1935376822645274424al_nat @ F @ A2 ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7005_sum__diff1__nat,axiom,
% 9.53/5.30      ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 9.53/5.30        ( ( ( member8440522571783428010at_nat @ A @ A2 )
% 9.53/5.30         => ( ( groups977919841031483927at_nat @ F @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 9.53/5.30            = ( minus_minus_nat @ ( groups977919841031483927at_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 9.53/5.30        & ( ~ ( member8440522571783428010at_nat @ A @ A2 )
% 9.53/5.30         => ( ( groups977919841031483927at_nat @ F @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 9.53/5.30            = ( groups977919841031483927at_nat @ F @ A2 ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7006_sum__diff1__nat,axiom,
% 9.53/5.30      ! [A: nat,A2: set_nat,F: nat > nat] :
% 9.53/5.30        ( ( ( member_nat @ A @ A2 )
% 9.53/5.30         => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 9.53/5.30            = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 9.53/5.30        & ( ~ ( member_nat @ A @ A2 )
% 9.53/5.30         => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 9.53/5.30            = ( groups3542108847815614940at_nat @ F @ A2 ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7007_sum__shift__lb__Suc0__0,axiom,
% 9.53/5.30      ! [F: nat > complex,K: nat] :
% 9.53/5.30        ( ( ( F @ zero_zero_nat )
% 9.53/5.30          = zero_zero_complex )
% 9.53/5.30       => ( ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 9.53/5.30          = ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7008_sum__shift__lb__Suc0__0,axiom,
% 9.53/5.30      ! [F: nat > rat,K: nat] :
% 9.53/5.30        ( ( ( F @ zero_zero_nat )
% 9.53/5.30          = zero_zero_rat )
% 9.53/5.30       => ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 9.53/5.30          = ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7009_sum__shift__lb__Suc0__0,axiom,
% 9.53/5.30      ! [F: nat > int,K: nat] :
% 9.53/5.30        ( ( ( F @ zero_zero_nat )
% 9.53/5.30          = zero_zero_int )
% 9.53/5.30       => ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 9.53/5.30          = ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7010_sum__shift__lb__Suc0__0,axiom,
% 9.53/5.30      ! [F: nat > nat,K: nat] :
% 9.53/5.30        ( ( ( F @ zero_zero_nat )
% 9.53/5.30          = zero_zero_nat )
% 9.53/5.30       => ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 9.53/5.30          = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7011_sum__shift__lb__Suc0__0,axiom,
% 9.53/5.30      ! [F: nat > real,K: nat] :
% 9.53/5.30        ( ( ( F @ zero_zero_nat )
% 9.53/5.30          = zero_zero_real )
% 9.53/5.30       => ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 9.53/5.30          = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7012_sum_OatLeast0__atMost__Suc,axiom,
% 9.53/5.30      ! [G: nat > rat,N: nat] :
% 9.53/5.30        ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 9.53/5.30        = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7013_sum_OatLeast0__atMost__Suc,axiom,
% 9.53/5.30      ! [G: nat > int,N: nat] :
% 9.53/5.30        ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 9.53/5.30        = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7014_sum_OatLeast0__atMost__Suc,axiom,
% 9.53/5.30      ! [G: nat > complex,N: nat] :
% 9.53/5.30        ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 9.53/5.30        = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7015_sum_OatLeast0__atMost__Suc,axiom,
% 9.53/5.30      ! [G: nat > nat,N: nat] :
% 9.53/5.30        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 9.53/5.30        = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7016_sum_OatLeast0__atMost__Suc,axiom,
% 9.53/5.30      ! [G: nat > real,N: nat] :
% 9.53/5.30        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 9.53/5.30        = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7017_sum_Onat__ivl__Suc_H,axiom,
% 9.53/5.30      ! [M: nat,N: nat,G: nat > rat] :
% 9.53/5.30        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 9.53/5.30       => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.53/5.30          = ( plus_plus_rat @ ( G @ ( suc @ N ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7018_sum_Onat__ivl__Suc_H,axiom,
% 9.53/5.30      ! [M: nat,N: nat,G: nat > int] :
% 9.53/5.30        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 9.53/5.30       => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.53/5.30          = ( plus_plus_int @ ( G @ ( suc @ N ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7019_sum_Onat__ivl__Suc_H,axiom,
% 9.53/5.30      ! [M: nat,N: nat,G: nat > complex] :
% 9.53/5.30        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 9.53/5.30       => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.53/5.30          = ( plus_plus_complex @ ( G @ ( suc @ N ) ) @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7020_sum_Onat__ivl__Suc_H,axiom,
% 9.53/5.30      ! [M: nat,N: nat,G: nat > nat] :
% 9.53/5.30        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 9.53/5.30       => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.53/5.30          = ( plus_plus_nat @ ( G @ ( suc @ N ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7021_sum_Onat__ivl__Suc_H,axiom,
% 9.53/5.30      ! [M: nat,N: nat,G: nat > real] :
% 9.53/5.30        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 9.53/5.30       => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.53/5.30          = ( plus_plus_real @ ( G @ ( suc @ N ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7022_sum_OatLeast__Suc__atMost,axiom,
% 9.53/5.30      ! [M: nat,N: nat,G: nat > rat] :
% 9.53/5.30        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.30       => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.53/5.30          = ( plus_plus_rat @ ( G @ M ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7023_sum_OatLeast__Suc__atMost,axiom,
% 9.53/5.30      ! [M: nat,N: nat,G: nat > int] :
% 9.53/5.30        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.30       => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.53/5.30          = ( plus_plus_int @ ( G @ M ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7024_sum_OatLeast__Suc__atMost,axiom,
% 9.53/5.30      ! [M: nat,N: nat,G: nat > complex] :
% 9.53/5.30        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.30       => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.53/5.30          = ( plus_plus_complex @ ( G @ M ) @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7025_sum_OatLeast__Suc__atMost,axiom,
% 9.53/5.30      ! [M: nat,N: nat,G: nat > nat] :
% 9.53/5.30        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.30       => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.53/5.30          = ( plus_plus_nat @ ( G @ M ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7026_sum_OatLeast__Suc__atMost,axiom,
% 9.53/5.30      ! [M: nat,N: nat,G: nat > real] :
% 9.53/5.30        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.30       => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.53/5.30          = ( plus_plus_real @ ( G @ M ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7027_numeral__inc,axiom,
% 9.53/5.30      ! [X: num] :
% 9.53/5.30        ( ( numera6690914467698888265omplex @ ( inc @ X ) )
% 9.53/5.30        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X ) @ one_one_complex ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7028_numeral__inc,axiom,
% 9.53/5.30      ! [X: num] :
% 9.53/5.30        ( ( numeral_numeral_real @ ( inc @ X ) )
% 9.53/5.30        = ( plus_plus_real @ ( numeral_numeral_real @ X ) @ one_one_real ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7029_numeral__inc,axiom,
% 9.53/5.30      ! [X: num] :
% 9.53/5.30        ( ( numeral_numeral_rat @ ( inc @ X ) )
% 9.53/5.30        = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7030_numeral__inc,axiom,
% 9.53/5.30      ! [X: num] :
% 9.53/5.30        ( ( numeral_numeral_nat @ ( inc @ X ) )
% 9.53/5.30        = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7031_numeral__inc,axiom,
% 9.53/5.30      ! [X: num] :
% 9.53/5.30        ( ( numeral_numeral_int @ ( inc @ X ) )
% 9.53/5.30        = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7032_sum_OSuc__reindex__ivl,axiom,
% 9.53/5.30      ! [M: nat,N: nat,G: nat > rat] :
% 9.53/5.30        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.30       => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 9.53/5.30          = ( plus_plus_rat @ ( G @ M )
% 9.53/5.30            @ ( groups2906978787729119204at_rat
% 9.53/5.30              @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.53/5.30              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7033_sum_OSuc__reindex__ivl,axiom,
% 9.53/5.30      ! [M: nat,N: nat,G: nat > int] :
% 9.53/5.30        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.30       => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 9.53/5.30          = ( plus_plus_int @ ( G @ M )
% 9.53/5.30            @ ( groups3539618377306564664at_int
% 9.53/5.30              @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.53/5.30              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7034_sum_OSuc__reindex__ivl,axiom,
% 9.53/5.30      ! [M: nat,N: nat,G: nat > complex] :
% 9.53/5.30        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.30       => ( ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 9.53/5.30          = ( plus_plus_complex @ ( G @ M )
% 9.53/5.30            @ ( groups2073611262835488442omplex
% 9.53/5.30              @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.53/5.30              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7035_sum_OSuc__reindex__ivl,axiom,
% 9.53/5.30      ! [M: nat,N: nat,G: nat > nat] :
% 9.53/5.30        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.30       => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 9.53/5.30          = ( plus_plus_nat @ ( G @ M )
% 9.53/5.30            @ ( groups3542108847815614940at_nat
% 9.53/5.30              @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.53/5.30              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7036_sum_OSuc__reindex__ivl,axiom,
% 9.53/5.30      ! [M: nat,N: nat,G: nat > real] :
% 9.53/5.30        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.30       => ( ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 9.53/5.30          = ( plus_plus_real @ ( G @ M )
% 9.53/5.30            @ ( groups6591440286371151544t_real
% 9.53/5.30              @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.53/5.30              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7037_sum__Suc__diff,axiom,
% 9.53/5.30      ! [M: nat,N: nat,F: nat > rat] :
% 9.53/5.30        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 9.53/5.30       => ( ( groups2906978787729119204at_rat
% 9.53/5.30            @ ^ [I3: nat] : ( minus_minus_rat @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 9.53/5.30            @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.53/5.30          = ( minus_minus_rat @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7038_sum__Suc__diff,axiom,
% 9.53/5.30      ! [M: nat,N: nat,F: nat > int] :
% 9.53/5.30        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 9.53/5.30       => ( ( groups3539618377306564664at_int
% 9.53/5.30            @ ^ [I3: nat] : ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 9.53/5.30            @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.53/5.30          = ( minus_minus_int @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7039_sum__Suc__diff,axiom,
% 9.53/5.30      ! [M: nat,N: nat,F: nat > real] :
% 9.53/5.30        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 9.53/5.30       => ( ( groups6591440286371151544t_real
% 9.53/5.30            @ ^ [I3: nat] : ( minus_minus_real @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 9.53/5.30            @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.53/5.30          = ( minus_minus_real @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7040_real__less__rsqrt,axiom,
% 9.53/5.30      ! [X: real,Y2: real] :
% 9.53/5.30        ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y2 )
% 9.53/5.30       => ( ord_less_real @ X @ ( sqrt @ Y2 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7041_sqrt__le__D,axiom,
% 9.53/5.30      ! [X: real,Y2: real] :
% 9.53/5.30        ( ( ord_less_eq_real @ ( sqrt @ X ) @ Y2 )
% 9.53/5.30       => ( ord_less_eq_real @ X @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7042_real__le__rsqrt,axiom,
% 9.53/5.30      ! [X: real,Y2: real] :
% 9.53/5.30        ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y2 )
% 9.53/5.30       => ( ord_less_eq_real @ X @ ( sqrt @ Y2 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7043_log__mult,axiom,
% 9.53/5.30      ! [A: real,X: real,Y2: real] :
% 9.53/5.30        ( ( ord_less_real @ zero_zero_real @ A )
% 9.53/5.30       => ( ( A != one_one_real )
% 9.53/5.30         => ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.30           => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 9.53/5.30             => ( ( log @ A @ ( times_times_real @ X @ Y2 ) )
% 9.53/5.30                = ( plus_plus_real @ ( log @ A @ X ) @ ( log @ A @ Y2 ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7044_log__divide,axiom,
% 9.53/5.30      ! [A: real,X: real,Y2: real] :
% 9.53/5.30        ( ( ord_less_real @ zero_zero_real @ A )
% 9.53/5.30       => ( ( A != one_one_real )
% 9.53/5.30         => ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.30           => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 9.53/5.30             => ( ( log @ A @ ( divide_divide_real @ X @ Y2 ) )
% 9.53/5.30                = ( minus_minus_real @ ( log @ A @ X ) @ ( log @ A @ Y2 ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7045_sum_Oub__add__nat,axiom,
% 9.53/5.30      ! [M: nat,N: nat,G: nat > rat,P6: nat] :
% 9.53/5.30        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 9.53/5.30       => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 9.53/5.30          = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7046_sum_Oub__add__nat,axiom,
% 9.53/5.30      ! [M: nat,N: nat,G: nat > int,P6: nat] :
% 9.53/5.30        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 9.53/5.30       => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 9.53/5.30          = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7047_sum_Oub__add__nat,axiom,
% 9.53/5.30      ! [M: nat,N: nat,G: nat > complex,P6: nat] :
% 9.53/5.30        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 9.53/5.30       => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 9.53/5.30          = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7048_sum_Oub__add__nat,axiom,
% 9.53/5.30      ! [M: nat,N: nat,G: nat > nat,P6: nat] :
% 9.53/5.30        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 9.53/5.30       => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 9.53/5.30          = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7049_sum_Oub__add__nat,axiom,
% 9.53/5.30      ! [M: nat,N: nat,G: nat > real,P6: nat] :
% 9.53/5.30        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 9.53/5.30       => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 9.53/5.30          = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7050_set__encode__def,axiom,
% 9.53/5.30      ( nat_set_encode
% 9.53/5.30      = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7051_real__le__lsqrt,axiom,
% 9.53/5.30      ! [X: real,Y2: real] :
% 9.53/5.30        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.30       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 9.53/5.30         => ( ( ord_less_eq_real @ X @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.53/5.30           => ( ord_less_eq_real @ ( sqrt @ X ) @ Y2 ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7052_real__sqrt__unique,axiom,
% 9.53/5.30      ! [Y2: real,X: real] :
% 9.53/5.30        ( ( ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.53/5.30          = X )
% 9.53/5.30       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 9.53/5.30         => ( ( sqrt @ X )
% 9.53/5.30            = Y2 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7053_lemma__real__divide__sqrt__less,axiom,
% 9.53/5.30      ! [U: real] :
% 9.53/5.30        ( ( ord_less_real @ zero_zero_real @ U )
% 9.53/5.30       => ( ord_less_real @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ U ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7054_real__sqrt__sum__squares__eq__cancel,axiom,
% 9.53/5.30      ! [X: real,Y2: real] :
% 9.53/5.30        ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.53/5.30          = X )
% 9.53/5.30       => ( Y2 = zero_zero_real ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7055_real__sqrt__sum__squares__eq__cancel2,axiom,
% 9.53/5.30      ! [X: real,Y2: real] :
% 9.53/5.30        ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.53/5.30          = Y2 )
% 9.53/5.30       => ( X = zero_zero_real ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7056_real__sqrt__sum__squares__ge1,axiom,
% 9.53/5.30      ! [X: real,Y2: real] : ( ord_less_eq_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7057_real__sqrt__sum__squares__ge2,axiom,
% 9.53/5.30      ! [Y2: real,X: real] : ( ord_less_eq_real @ Y2 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7058_real__sqrt__sum__squares__triangle__ineq,axiom,
% 9.53/5.30      ! [A: real,C: real,B: real,D2: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ ( plus_plus_real @ A @ C ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( plus_plus_real @ B @ D2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ C @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ D2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7059_sqrt__ge__absD,axiom,
% 9.53/5.30      ! [X: real,Y2: real] :
% 9.53/5.30        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( sqrt @ Y2 ) )
% 9.53/5.30       => ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y2 ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7060_log__eq__div__ln__mult__log,axiom,
% 9.53/5.30      ! [A: real,B: real,X: real] :
% 9.53/5.30        ( ( ord_less_real @ zero_zero_real @ A )
% 9.53/5.30       => ( ( A != one_one_real )
% 9.53/5.30         => ( ( ord_less_real @ zero_zero_real @ B )
% 9.53/5.30           => ( ( B != one_one_real )
% 9.53/5.30             => ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.30               => ( ( log @ A @ X )
% 9.53/5.30                  = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ B ) @ ( ln_ln_real @ A ) ) @ ( log @ B @ X ) ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7061_mask__Suc__exp,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( bit_se2002935070580805687sk_nat @ ( suc @ N ) )
% 9.53/5.30        = ( bit_se1412395901928357646or_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7062_mask__Suc__exp,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( bit_se2000444600071755411sk_int @ ( suc @ N ) )
% 9.53/5.30        = ( bit_se1409905431419307370or_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( bit_se2000444600071755411sk_int @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7063_sum__natinterval__diff,axiom,
% 9.53/5.30      ! [M: nat,N: nat,F: nat > complex] :
% 9.53/5.30        ( ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.30         => ( ( groups2073611262835488442omplex
% 9.53/5.30              @ ^ [K3: nat] : ( minus_minus_complex @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 9.53/5.30              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.53/5.30            = ( minus_minus_complex @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 9.53/5.30        & ( ~ ( ord_less_eq_nat @ M @ N )
% 9.53/5.30         => ( ( groups2073611262835488442omplex
% 9.53/5.30              @ ^ [K3: nat] : ( minus_minus_complex @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 9.53/5.30              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.53/5.30            = zero_zero_complex ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7064_sum__natinterval__diff,axiom,
% 9.53/5.30      ! [M: nat,N: nat,F: nat > rat] :
% 9.53/5.30        ( ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.30         => ( ( groups2906978787729119204at_rat
% 9.53/5.30              @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 9.53/5.30              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.53/5.30            = ( minus_minus_rat @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 9.53/5.30        & ( ~ ( ord_less_eq_nat @ M @ N )
% 9.53/5.30         => ( ( groups2906978787729119204at_rat
% 9.53/5.30              @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 9.53/5.30              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.53/5.30            = zero_zero_rat ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7065_sum__natinterval__diff,axiom,
% 9.53/5.30      ! [M: nat,N: nat,F: nat > int] :
% 9.53/5.30        ( ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.30         => ( ( groups3539618377306564664at_int
% 9.53/5.30              @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 9.53/5.30              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.53/5.30            = ( minus_minus_int @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 9.53/5.30        & ( ~ ( ord_less_eq_nat @ M @ N )
% 9.53/5.30         => ( ( groups3539618377306564664at_int
% 9.53/5.30              @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 9.53/5.30              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.53/5.30            = zero_zero_int ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7066_sum__natinterval__diff,axiom,
% 9.53/5.30      ! [M: nat,N: nat,F: nat > real] :
% 9.53/5.30        ( ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.30         => ( ( groups6591440286371151544t_real
% 9.53/5.30              @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 9.53/5.30              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.53/5.30            = ( minus_minus_real @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 9.53/5.30        & ( ~ ( ord_less_eq_nat @ M @ N )
% 9.53/5.30         => ( ( groups6591440286371151544t_real
% 9.53/5.30              @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 9.53/5.30              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.53/5.30            = zero_zero_real ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7067_sum__telescope_H_H,axiom,
% 9.53/5.30      ! [M: nat,N: nat,F: nat > rat] :
% 9.53/5.30        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.30       => ( ( groups2906978787729119204at_rat
% 9.53/5.30            @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 9.53/5.30            @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 9.53/5.30          = ( minus_minus_rat @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7068_sum__telescope_H_H,axiom,
% 9.53/5.30      ! [M: nat,N: nat,F: nat > int] :
% 9.53/5.30        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.30       => ( ( groups3539618377306564664at_int
% 9.53/5.30            @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 9.53/5.30            @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 9.53/5.30          = ( minus_minus_int @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7069_sum__telescope_H_H,axiom,
% 9.53/5.30      ! [M: nat,N: nat,F: nat > real] :
% 9.53/5.30        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.30       => ( ( groups6591440286371151544t_real
% 9.53/5.30            @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 9.53/5.30            @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 9.53/5.30          = ( minus_minus_real @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7070_real__less__lsqrt,axiom,
% 9.53/5.30      ! [X: real,Y2: real] :
% 9.53/5.30        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.30       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 9.53/5.30         => ( ( ord_less_real @ X @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.53/5.30           => ( ord_less_real @ ( sqrt @ X ) @ Y2 ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7071_sqrt__sum__squares__le__sum,axiom,
% 9.53/5.30      ! [X: real,Y2: real] :
% 9.53/5.30        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.30       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 9.53/5.30         => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ X @ Y2 ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7072_one__or__eq,axiom,
% 9.53/5.30      ! [A: code_integer] :
% 9.53/5.30        ( ( bit_se1080825931792720795nteger @ one_one_Code_integer @ A )
% 9.53/5.30        = ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7073_one__or__eq,axiom,
% 9.53/5.30      ! [A: int] :
% 9.53/5.30        ( ( bit_se1409905431419307370or_int @ one_one_int @ A )
% 9.53/5.30        = ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7074_one__or__eq,axiom,
% 9.53/5.30      ! [A: nat] :
% 9.53/5.30        ( ( bit_se1412395901928357646or_nat @ one_one_nat @ A )
% 9.53/5.30        = ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7075_or__one__eq,axiom,
% 9.53/5.30      ! [A: code_integer] :
% 9.53/5.30        ( ( bit_se1080825931792720795nteger @ A @ one_one_Code_integer )
% 9.53/5.30        = ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7076_or__one__eq,axiom,
% 9.53/5.30      ! [A: int] :
% 9.53/5.30        ( ( bit_se1409905431419307370or_int @ A @ one_one_int )
% 9.53/5.30        = ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7077_or__one__eq,axiom,
% 9.53/5.30      ! [A: nat] :
% 9.53/5.30        ( ( bit_se1412395901928357646or_nat @ A @ one_one_nat )
% 9.53/5.30        = ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7078_sqrt__even__pow2,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.53/5.30       => ( ( sqrt @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 9.53/5.30          = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7079_mask__Suc__double,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( bit_se2002935070580805687sk_nat @ ( suc @ N ) )
% 9.53/5.30        = ( bit_se1412395901928357646or_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7080_mask__Suc__double,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( bit_se2000444600071755411sk_int @ ( suc @ N ) )
% 9.53/5.30        = ( bit_se1409905431419307370or_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ N ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7081_sqrt__sum__squares__le__sum__abs,axiom,
% 9.53/5.30      ! [X: real,Y2: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ Y2 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7082_real__sqrt__ge__abs2,axiom,
% 9.53/5.30      ! [Y2: real,X: real] : ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7083_real__sqrt__ge__abs1,axiom,
% 9.53/5.30      ! [X: real,Y2: real] : ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7084_ln__sqrt,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30        ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.30       => ( ( ln_ln_real @ ( sqrt @ X ) )
% 9.53/5.30          = ( divide_divide_real @ ( ln_ln_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7085_OR__upper,axiom,
% 9.53/5.30      ! [X: int,N: nat,Y2: int] :
% 9.53/5.30        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 9.53/5.30       => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 9.53/5.30         => ( ( ord_less_int @ Y2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 9.53/5.30           => ( ord_less_int @ ( bit_se1409905431419307370or_int @ X @ Y2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7086_mask__eq__sum__exp,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int )
% 9.53/5.30        = ( groups3539618377306564664at_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.53/5.30          @ ( collect_nat
% 9.53/5.30            @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7087_mask__eq__sum__exp,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat )
% 9.53/5.30        = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.53/5.30          @ ( collect_nat
% 9.53/5.30            @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7088_sum__gp__multiplied,axiom,
% 9.53/5.30      ! [M: nat,N: nat,X: rat] :
% 9.53/5.30        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.30       => ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 9.53/5.30          = ( minus_minus_rat @ ( power_power_rat @ X @ M ) @ ( power_power_rat @ X @ ( suc @ N ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7089_sum__gp__multiplied,axiom,
% 9.53/5.30      ! [M: nat,N: nat,X: complex] :
% 9.53/5.30        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.30       => ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 9.53/5.30          = ( minus_minus_complex @ ( power_power_complex @ X @ M ) @ ( power_power_complex @ X @ ( suc @ N ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7090_sum__gp__multiplied,axiom,
% 9.53/5.30      ! [M: nat,N: nat,X: int] :
% 9.53/5.30        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.30       => ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 9.53/5.30          = ( minus_minus_int @ ( power_power_int @ X @ M ) @ ( power_power_int @ X @ ( suc @ N ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7091_sum__gp__multiplied,axiom,
% 9.53/5.30      ! [M: nat,N: nat,X: real] :
% 9.53/5.30        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.30       => ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 9.53/5.30          = ( minus_minus_real @ ( power_power_real @ X @ M ) @ ( power_power_real @ X @ ( suc @ N ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7092_sum_Oin__pairs,axiom,
% 9.53/5.30      ! [G: nat > rat,M: nat,N: nat] :
% 9.53/5.30        ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 9.53/5.30        = ( groups2906978787729119204at_rat
% 9.53/5.30          @ ^ [I3: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.53/5.30          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7093_sum_Oin__pairs,axiom,
% 9.53/5.30      ! [G: nat > int,M: nat,N: nat] :
% 9.53/5.30        ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 9.53/5.30        = ( groups3539618377306564664at_int
% 9.53/5.30          @ ^ [I3: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.53/5.30          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7094_sum_Oin__pairs,axiom,
% 9.53/5.30      ! [G: nat > complex,M: nat,N: nat] :
% 9.53/5.30        ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 9.53/5.30        = ( groups2073611262835488442omplex
% 9.53/5.30          @ ^ [I3: nat] : ( plus_plus_complex @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.53/5.30          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7095_sum_Oin__pairs,axiom,
% 9.53/5.30      ! [G: nat > nat,M: nat,N: nat] :
% 9.53/5.30        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 9.53/5.30        = ( groups3542108847815614940at_nat
% 9.53/5.30          @ ^ [I3: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.53/5.30          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7096_sum_Oin__pairs,axiom,
% 9.53/5.30      ! [G: nat > real,M: nat,N: nat] :
% 9.53/5.30        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 9.53/5.30        = ( groups6591440286371151544t_real
% 9.53/5.30          @ ^ [I3: nat] : ( plus_plus_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.53/5.30          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7097_real__sqrt__power__even,axiom,
% 9.53/5.30      ! [N: nat,X: real] :
% 9.53/5.30        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.53/5.30       => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.30         => ( ( power_power_real @ ( sqrt @ X ) @ N )
% 9.53/5.30            = ( power_power_real @ X @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7098_arsinh__real__aux,axiom,
% 9.53/5.30      ! [X: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7099_real__sqrt__sum__squares__mult__ge__zero,axiom,
% 9.53/5.30      ! [X: real,Y2: real,Xa2: real,Ya: real] : ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7100_arith__geo__mean__sqrt,axiom,
% 9.53/5.30      ! [X: real,Y2: real] :
% 9.53/5.30        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.30       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 9.53/5.30         => ( ord_less_eq_real @ ( sqrt @ ( times_times_real @ X @ Y2 ) ) @ ( divide_divide_real @ ( plus_plus_real @ X @ Y2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7101_or__int__rec,axiom,
% 9.53/5.30      ( bit_se1409905431419307370or_int
% 9.53/5.30      = ( ^ [K3: int,L: int] :
% 9.53/5.30            ( plus_plus_int
% 9.53/5.30            @ ( zero_n2684676970156552555ol_int
% 9.53/5.30              @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 9.53/5.30                | ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 9.53/5.30            @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7102_mask__eq__sum__exp__nat,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( suc @ zero_zero_nat ) )
% 9.53/5.30        = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.53/5.30          @ ( collect_nat
% 9.53/5.30            @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7103_gauss__sum__nat,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( groups3542108847815614940at_nat
% 9.53/5.30          @ ^ [X2: nat] : X2
% 9.53/5.30          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 9.53/5.30        = ( divide_divide_nat @ ( times_times_nat @ N @ ( suc @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7104_cos__x__y__le__one,axiom,
% 9.53/5.30      ! [X: real,Y2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( divide_divide_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ one_one_real ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7105_real__sqrt__sum__squares__less,axiom,
% 9.53/5.30      ! [X: real,U: real,Y2: real] :
% 9.53/5.30        ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 9.53/5.30       => ( ( ord_less_real @ ( abs_abs_real @ Y2 ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 9.53/5.30         => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7106_arcosh__real__def,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30        ( ( ord_less_eq_real @ one_one_real @ X )
% 9.53/5.30       => ( ( arcosh_real @ X )
% 9.53/5.30          = ( ln_ln_real @ ( plus_plus_real @ X @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7107_arith__series__nat,axiom,
% 9.53/5.30      ! [A: nat,D2: nat,N: nat] :
% 9.53/5.30        ( ( groups3542108847815614940at_nat
% 9.53/5.30          @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I3 @ D2 ) )
% 9.53/5.30          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 9.53/5.30        = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ N @ D2 ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7108_Sum__Icc__nat,axiom,
% 9.53/5.30      ! [M: nat,N: nat] :
% 9.53/5.30        ( ( groups3542108847815614940at_nat
% 9.53/5.30          @ ^ [X2: nat] : X2
% 9.53/5.30          @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.53/5.30        = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( plus_plus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7109_sqrt__sum__squares__half__less,axiom,
% 9.53/5.30      ! [X: real,U: real,Y2: real] :
% 9.53/5.30        ( ( ord_less_real @ X @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.30       => ( ( ord_less_real @ Y2 @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.30         => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.30           => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 9.53/5.30             => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7110_log__base__10__eq2,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30        ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.30       => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 9.53/5.30          = ( times_times_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ X ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7111_height__double__log__univ__size,axiom,
% 9.53/5.30      ! [U: real,Deg: nat,T: vEBT_VEBT] :
% 9.53/5.30        ( ( U
% 9.53/5.30          = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Deg ) )
% 9.53/5.30       => ( ( vEBT_invar_vebt @ T @ Deg )
% 9.53/5.30         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_VEBT_height @ T ) ) @ ( plus_plus_real @ one_one_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7112_log__ceil__idem,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30        ( ( ord_less_eq_real @ one_one_real @ X )
% 9.53/5.30       => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 9.53/5.30          = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7113_arsinh__real__def,axiom,
% 9.53/5.30      ( arsinh_real
% 9.53/5.30      = ( ^ [X2: real] : ( ln_ln_real @ ( plus_plus_real @ X2 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7114_member__bound__size__univ,axiom,
% 9.53/5.30      ! [T: vEBT_VEBT,N: nat,U: real,X: nat] :
% 9.53/5.30        ( ( vEBT_invar_vebt @ T @ N )
% 9.53/5.30       => ( ( U
% 9.53/5.30            = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 9.53/5.30         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_m_e_m_b_e_r @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7115_succ__bound__size__univ,axiom,
% 9.53/5.30      ! [T: vEBT_VEBT,N: nat,U: real,X: nat] :
% 9.53/5.30        ( ( vEBT_invar_vebt @ T @ N )
% 9.53/5.30       => ( ( U
% 9.53/5.30            = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 9.53/5.30         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_s_u_c_c @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7116_pred__bound__size__univ,axiom,
% 9.53/5.30      ! [T: vEBT_VEBT,N: nat,U: real,X: nat] :
% 9.53/5.30        ( ( vEBT_invar_vebt @ T @ N )
% 9.53/5.30       => ( ( U
% 9.53/5.30            = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 9.53/5.30         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_p_r_e_d @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7117_of__nat__eq__iff,axiom,
% 9.53/5.30      ! [M: nat,N: nat] :
% 9.53/5.30        ( ( ( semiri5074537144036343181t_real @ M )
% 9.53/5.30          = ( semiri5074537144036343181t_real @ N ) )
% 9.53/5.30        = ( M = N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7118_of__nat__eq__iff,axiom,
% 9.53/5.30      ! [M: nat,N: nat] :
% 9.53/5.30        ( ( ( semiri1314217659103216013at_int @ M )
% 9.53/5.30          = ( semiri1314217659103216013at_int @ N ) )
% 9.53/5.30        = ( M = N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7119_of__nat__eq__iff,axiom,
% 9.53/5.30      ! [M: nat,N: nat] :
% 9.53/5.30        ( ( ( semiri1316708129612266289at_nat @ M )
% 9.53/5.30          = ( semiri1316708129612266289at_nat @ N ) )
% 9.53/5.30        = ( M = N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7120_of__nat__eq__iff,axiom,
% 9.53/5.30      ! [M: nat,N: nat] :
% 9.53/5.30        ( ( ( semiri8010041392384452111omplex @ M )
% 9.53/5.30          = ( semiri8010041392384452111omplex @ N ) )
% 9.53/5.30        = ( M = N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7121_abs__of__nat,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( abs_abs_Code_integer @ ( semiri4939895301339042750nteger @ N ) )
% 9.53/5.30        = ( semiri4939895301339042750nteger @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7122_abs__of__nat,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( abs_abs_real @ ( semiri5074537144036343181t_real @ N ) )
% 9.53/5.30        = ( semiri5074537144036343181t_real @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7123_abs__of__nat,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( abs_abs_int @ ( semiri1314217659103216013at_int @ N ) )
% 9.53/5.30        = ( semiri1314217659103216013at_int @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7124_of__int__ceiling__cancel,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30        ( ( ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) )
% 9.53/5.30          = X )
% 9.53/5.30        = ( ? [N2: int] :
% 9.53/5.30              ( X
% 9.53/5.30              = ( ring_1_of_int_real @ N2 ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7125_of__nat__eq__0__iff,axiom,
% 9.53/5.30      ! [M: nat] :
% 9.53/5.30        ( ( ( semiri681578069525770553at_rat @ M )
% 9.53/5.30          = zero_zero_rat )
% 9.53/5.30        = ( M = zero_zero_nat ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7126_of__nat__eq__0__iff,axiom,
% 9.53/5.30      ! [M: nat] :
% 9.53/5.30        ( ( ( semiri5074537144036343181t_real @ M )
% 9.53/5.30          = zero_zero_real )
% 9.53/5.30        = ( M = zero_zero_nat ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7127_of__nat__eq__0__iff,axiom,
% 9.53/5.30      ! [M: nat] :
% 9.53/5.30        ( ( ( semiri1314217659103216013at_int @ M )
% 9.53/5.30          = zero_zero_int )
% 9.53/5.30        = ( M = zero_zero_nat ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7128_of__nat__eq__0__iff,axiom,
% 9.53/5.30      ! [M: nat] :
% 9.53/5.30        ( ( ( semiri1316708129612266289at_nat @ M )
% 9.53/5.30          = zero_zero_nat )
% 9.53/5.30        = ( M = zero_zero_nat ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7129_of__nat__eq__0__iff,axiom,
% 9.53/5.30      ! [M: nat] :
% 9.53/5.30        ( ( ( semiri8010041392384452111omplex @ M )
% 9.53/5.30          = zero_zero_complex )
% 9.53/5.30        = ( M = zero_zero_nat ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7130_of__nat__0__eq__iff,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( zero_zero_rat
% 9.53/5.30          = ( semiri681578069525770553at_rat @ N ) )
% 9.53/5.30        = ( zero_zero_nat = N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7131_of__nat__0__eq__iff,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( zero_zero_real
% 9.53/5.30          = ( semiri5074537144036343181t_real @ N ) )
% 9.53/5.30        = ( zero_zero_nat = N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7132_of__nat__0__eq__iff,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( zero_zero_int
% 9.53/5.30          = ( semiri1314217659103216013at_int @ N ) )
% 9.53/5.30        = ( zero_zero_nat = N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7133_of__nat__0__eq__iff,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( zero_zero_nat
% 9.53/5.30          = ( semiri1316708129612266289at_nat @ N ) )
% 9.53/5.30        = ( zero_zero_nat = N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7134_of__nat__0__eq__iff,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( zero_zero_complex
% 9.53/5.30          = ( semiri8010041392384452111omplex @ N ) )
% 9.53/5.30        = ( zero_zero_nat = N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7135_of__nat__0,axiom,
% 9.53/5.30      ( ( semiri681578069525770553at_rat @ zero_zero_nat )
% 9.53/5.30      = zero_zero_rat ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7136_of__nat__0,axiom,
% 9.53/5.30      ( ( semiri5074537144036343181t_real @ zero_zero_nat )
% 9.53/5.30      = zero_zero_real ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7137_of__nat__0,axiom,
% 9.53/5.30      ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 9.53/5.30      = zero_zero_int ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7138_of__nat__0,axiom,
% 9.53/5.30      ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 9.53/5.30      = zero_zero_nat ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7139_of__nat__0,axiom,
% 9.53/5.30      ( ( semiri8010041392384452111omplex @ zero_zero_nat )
% 9.53/5.30      = zero_zero_complex ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7140_of__nat__numeral,axiom,
% 9.53/5.30      ! [N: num] :
% 9.53/5.30        ( ( semiri681578069525770553at_rat @ ( numeral_numeral_nat @ N ) )
% 9.53/5.30        = ( numeral_numeral_rat @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7141_of__nat__numeral,axiom,
% 9.53/5.30      ! [N: num] :
% 9.53/5.30        ( ( semiri5074537144036343181t_real @ ( numeral_numeral_nat @ N ) )
% 9.53/5.30        = ( numeral_numeral_real @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7142_of__nat__numeral,axiom,
% 9.53/5.30      ! [N: num] :
% 9.53/5.30        ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 9.53/5.30        = ( numeral_numeral_int @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7143_of__nat__numeral,axiom,
% 9.53/5.30      ! [N: num] :
% 9.53/5.30        ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N ) )
% 9.53/5.30        = ( numeral_numeral_nat @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7144_of__nat__numeral,axiom,
% 9.53/5.30      ! [N: num] :
% 9.53/5.30        ( ( semiri8010041392384452111omplex @ ( numeral_numeral_nat @ N ) )
% 9.53/5.30        = ( numera6690914467698888265omplex @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7145_of__nat__less__iff,axiom,
% 9.53/5.30      ! [M: nat,N: nat] :
% 9.53/5.30        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 9.53/5.30        = ( ord_less_nat @ M @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7146_of__nat__less__iff,axiom,
% 9.53/5.30      ! [M: nat,N: nat] :
% 9.53/5.30        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 9.53/5.30        = ( ord_less_nat @ M @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7147_of__nat__less__iff,axiom,
% 9.53/5.30      ! [M: nat,N: nat] :
% 9.53/5.30        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 9.53/5.30        = ( ord_less_nat @ M @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7148_of__nat__less__iff,axiom,
% 9.53/5.30      ! [M: nat,N: nat] :
% 9.53/5.30        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 9.53/5.30        = ( ord_less_nat @ M @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7149_of__nat__le__iff,axiom,
% 9.53/5.30      ! [M: nat,N: nat] :
% 9.53/5.30        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 9.53/5.30        = ( ord_less_eq_nat @ M @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7150_of__nat__le__iff,axiom,
% 9.53/5.30      ! [M: nat,N: nat] :
% 9.53/5.30        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 9.53/5.30        = ( ord_less_eq_nat @ M @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7151_of__nat__le__iff,axiom,
% 9.53/5.30      ! [M: nat,N: nat] :
% 9.53/5.30        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 9.53/5.30        = ( ord_less_eq_nat @ M @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7152_of__nat__add,axiom,
% 9.53/5.30      ! [M: nat,N: nat] :
% 9.53/5.30        ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ N ) )
% 9.53/5.30        = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7153_of__nat__add,axiom,
% 9.53/5.30      ! [M: nat,N: nat] :
% 9.53/5.30        ( ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ N ) )
% 9.53/5.30        = ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7154_of__nat__add,axiom,
% 9.53/5.30      ! [M: nat,N: nat] :
% 9.53/5.30        ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) )
% 9.53/5.30        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7155_of__nat__add,axiom,
% 9.53/5.30      ! [M: nat,N: nat] :
% 9.53/5.30        ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N ) )
% 9.53/5.30        = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7156_of__nat__add,axiom,
% 9.53/5.30      ! [M: nat,N: nat] :
% 9.53/5.30        ( ( semiri8010041392384452111omplex @ ( plus_plus_nat @ M @ N ) )
% 9.53/5.30        = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7157_of__nat__eq__1__iff,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( ( semiri681578069525770553at_rat @ N )
% 9.53/5.30          = one_one_rat )
% 9.53/5.30        = ( N = one_one_nat ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7158_of__nat__eq__1__iff,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( ( semiri5074537144036343181t_real @ N )
% 9.53/5.30          = one_one_real )
% 9.53/5.30        = ( N = one_one_nat ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7159_of__nat__eq__1__iff,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( ( semiri1314217659103216013at_int @ N )
% 9.53/5.30          = one_one_int )
% 9.53/5.30        = ( N = one_one_nat ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7160_of__nat__eq__1__iff,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( ( semiri1316708129612266289at_nat @ N )
% 9.53/5.30          = one_one_nat )
% 9.53/5.30        = ( N = one_one_nat ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7161_of__nat__eq__1__iff,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( ( semiri8010041392384452111omplex @ N )
% 9.53/5.30          = one_one_complex )
% 9.53/5.30        = ( N = one_one_nat ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7162_of__nat__1__eq__iff,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( one_one_rat
% 9.53/5.30          = ( semiri681578069525770553at_rat @ N ) )
% 9.53/5.30        = ( N = one_one_nat ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7163_of__nat__1__eq__iff,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( one_one_real
% 9.53/5.30          = ( semiri5074537144036343181t_real @ N ) )
% 9.53/5.30        = ( N = one_one_nat ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7164_of__nat__1__eq__iff,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( one_one_int
% 9.53/5.30          = ( semiri1314217659103216013at_int @ N ) )
% 9.53/5.30        = ( N = one_one_nat ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7165_of__nat__1__eq__iff,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( one_one_nat
% 9.53/5.30          = ( semiri1316708129612266289at_nat @ N ) )
% 9.53/5.30        = ( N = one_one_nat ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7166_of__nat__1__eq__iff,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( one_one_complex
% 9.53/5.30          = ( semiri8010041392384452111omplex @ N ) )
% 9.53/5.30        = ( N = one_one_nat ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7167_of__nat__1,axiom,
% 9.53/5.30      ( ( semiri681578069525770553at_rat @ one_one_nat )
% 9.53/5.30      = one_one_rat ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7168_of__nat__1,axiom,
% 9.53/5.30      ( ( semiri5074537144036343181t_real @ one_one_nat )
% 9.53/5.30      = one_one_real ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7169_of__nat__1,axiom,
% 9.53/5.30      ( ( semiri1314217659103216013at_int @ one_one_nat )
% 9.53/5.30      = one_one_int ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7170_of__nat__1,axiom,
% 9.53/5.30      ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 9.53/5.30      = one_one_nat ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7171_of__nat__1,axiom,
% 9.53/5.30      ( ( semiri8010041392384452111omplex @ one_one_nat )
% 9.53/5.30      = one_one_complex ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7172_of__nat__mult,axiom,
% 9.53/5.30      ! [M: nat,N: nat] :
% 9.53/5.30        ( ( semiri5074537144036343181t_real @ ( times_times_nat @ M @ N ) )
% 9.53/5.30        = ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7173_of__nat__mult,axiom,
% 9.53/5.30      ! [M: nat,N: nat] :
% 9.53/5.30        ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M @ N ) )
% 9.53/5.30        = ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7174_of__nat__mult,axiom,
% 9.53/5.30      ! [M: nat,N: nat] :
% 9.53/5.30        ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N ) )
% 9.53/5.30        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7175_of__nat__mult,axiom,
% 9.53/5.30      ! [M: nat,N: nat] :
% 9.53/5.30        ( ( semiri8010041392384452111omplex @ ( times_times_nat @ M @ N ) )
% 9.53/5.30        = ( times_times_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7176_of__nat__power,axiom,
% 9.53/5.30      ! [M: nat,N: nat] :
% 9.53/5.30        ( ( semiri5074537144036343181t_real @ ( power_power_nat @ M @ N ) )
% 9.53/5.30        = ( power_power_real @ ( semiri5074537144036343181t_real @ M ) @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7177_of__nat__power,axiom,
% 9.53/5.30      ! [M: nat,N: nat] :
% 9.53/5.30        ( ( semiri1314217659103216013at_int @ ( power_power_nat @ M @ N ) )
% 9.53/5.30        = ( power_power_int @ ( semiri1314217659103216013at_int @ M ) @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7178_of__nat__power,axiom,
% 9.53/5.30      ! [M: nat,N: nat] :
% 9.53/5.30        ( ( semiri1316708129612266289at_nat @ ( power_power_nat @ M @ N ) )
% 9.53/5.30        = ( power_power_nat @ ( semiri1316708129612266289at_nat @ M ) @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7179_of__nat__power,axiom,
% 9.53/5.30      ! [M: nat,N: nat] :
% 9.53/5.30        ( ( semiri8010041392384452111omplex @ ( power_power_nat @ M @ N ) )
% 9.53/5.30        = ( power_power_complex @ ( semiri8010041392384452111omplex @ M ) @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7180_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 9.53/5.30      ! [B: nat,W: nat,X: nat] :
% 9.53/5.30        ( ( ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W )
% 9.53/5.30          = ( semiri5074537144036343181t_real @ X ) )
% 9.53/5.30        = ( ( power_power_nat @ B @ W )
% 9.53/5.30          = X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7181_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 9.53/5.30      ! [B: nat,W: nat,X: nat] :
% 9.53/5.30        ( ( ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W )
% 9.53/5.30          = ( semiri1314217659103216013at_int @ X ) )
% 9.53/5.30        = ( ( power_power_nat @ B @ W )
% 9.53/5.30          = X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7182_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 9.53/5.30      ! [B: nat,W: nat,X: nat] :
% 9.53/5.30        ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W )
% 9.53/5.30          = ( semiri1316708129612266289at_nat @ X ) )
% 9.53/5.30        = ( ( power_power_nat @ B @ W )
% 9.53/5.30          = X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7183_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 9.53/5.30      ! [B: nat,W: nat,X: nat] :
% 9.53/5.30        ( ( ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W )
% 9.53/5.30          = ( semiri8010041392384452111omplex @ X ) )
% 9.53/5.30        = ( ( power_power_nat @ B @ W )
% 9.53/5.30          = X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7184_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 9.53/5.30      ! [X: nat,B: nat,W: nat] :
% 9.53/5.30        ( ( ( semiri5074537144036343181t_real @ X )
% 9.53/5.30          = ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 9.53/5.30        = ( X
% 9.53/5.30          = ( power_power_nat @ B @ W ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7185_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 9.53/5.30      ! [X: nat,B: nat,W: nat] :
% 9.53/5.30        ( ( ( semiri1314217659103216013at_int @ X )
% 9.53/5.30          = ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 9.53/5.30        = ( X
% 9.53/5.30          = ( power_power_nat @ B @ W ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7186_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 9.53/5.30      ! [X: nat,B: nat,W: nat] :
% 9.53/5.30        ( ( ( semiri1316708129612266289at_nat @ X )
% 9.53/5.30          = ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 9.53/5.30        = ( X
% 9.53/5.30          = ( power_power_nat @ B @ W ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7187_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 9.53/5.30      ! [X: nat,B: nat,W: nat] :
% 9.53/5.30        ( ( ( semiri8010041392384452111omplex @ X )
% 9.53/5.30          = ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W ) )
% 9.53/5.30        = ( X
% 9.53/5.30          = ( power_power_nat @ B @ W ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7188_ceiling__numeral,axiom,
% 9.53/5.30      ! [V: num] :
% 9.53/5.30        ( ( archim7802044766580827645g_real @ ( numeral_numeral_real @ V ) )
% 9.53/5.30        = ( numeral_numeral_int @ V ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7189_ceiling__numeral,axiom,
% 9.53/5.30      ! [V: num] :
% 9.53/5.30        ( ( archim2889992004027027881ng_rat @ ( numeral_numeral_rat @ V ) )
% 9.53/5.30        = ( numeral_numeral_int @ V ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7190_ceiling__one,axiom,
% 9.53/5.30      ( ( archim2889992004027027881ng_rat @ one_one_rat )
% 9.53/5.30      = one_one_int ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7191_ceiling__one,axiom,
% 9.53/5.30      ( ( archim7802044766580827645g_real @ one_one_real )
% 9.53/5.30      = one_one_int ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7192_of__nat__of__bool,axiom,
% 9.53/5.30      ! [P: $o] :
% 9.53/5.30        ( ( semiri5074537144036343181t_real @ ( zero_n2687167440665602831ol_nat @ P ) )
% 9.53/5.30        = ( zero_n3304061248610475627l_real @ P ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7193_of__nat__of__bool,axiom,
% 9.53/5.30      ! [P: $o] :
% 9.53/5.30        ( ( semiri8010041392384452111omplex @ ( zero_n2687167440665602831ol_nat @ P ) )
% 9.53/5.30        = ( zero_n1201886186963655149omplex @ P ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7194_of__nat__of__bool,axiom,
% 9.53/5.30      ! [P: $o] :
% 9.53/5.30        ( ( semiri1316708129612266289at_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 9.53/5.30        = ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7195_of__nat__of__bool,axiom,
% 9.53/5.30      ! [P: $o] :
% 9.53/5.30        ( ( semiri1314217659103216013at_int @ ( zero_n2687167440665602831ol_nat @ P ) )
% 9.53/5.30        = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7196_of__nat__of__bool,axiom,
% 9.53/5.30      ! [P: $o] :
% 9.53/5.30        ( ( semiri4939895301339042750nteger @ ( zero_n2687167440665602831ol_nat @ P ) )
% 9.53/5.30        = ( zero_n356916108424825756nteger @ P ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7197_of__nat__le__0__iff,axiom,
% 9.53/5.30      ! [M: nat] :
% 9.53/5.30        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat )
% 9.53/5.30        = ( M = zero_zero_nat ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7198_of__nat__le__0__iff,axiom,
% 9.53/5.30      ! [M: nat] :
% 9.53/5.30        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real )
% 9.53/5.30        = ( M = zero_zero_nat ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7199_of__nat__le__0__iff,axiom,
% 9.53/5.30      ! [M: nat] :
% 9.53/5.30        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat )
% 9.53/5.30        = ( M = zero_zero_nat ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7200_of__nat__le__0__iff,axiom,
% 9.53/5.30      ! [M: nat] :
% 9.53/5.30        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int )
% 9.53/5.30        = ( M = zero_zero_nat ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7201_of__nat__Suc,axiom,
% 9.53/5.30      ! [M: nat] :
% 9.53/5.30        ( ( semiri681578069525770553at_rat @ ( suc @ M ) )
% 9.53/5.30        = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7202_of__nat__Suc,axiom,
% 9.53/5.30      ! [M: nat] :
% 9.53/5.30        ( ( semiri5074537144036343181t_real @ ( suc @ M ) )
% 9.53/5.30        = ( plus_plus_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7203_of__nat__Suc,axiom,
% 9.53/5.30      ! [M: nat] :
% 9.53/5.30        ( ( semiri1314217659103216013at_int @ ( suc @ M ) )
% 9.53/5.30        = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7204_of__nat__Suc,axiom,
% 9.53/5.30      ! [M: nat] :
% 9.53/5.30        ( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
% 9.53/5.30        = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7205_of__nat__Suc,axiom,
% 9.53/5.30      ! [M: nat] :
% 9.53/5.30        ( ( semiri8010041392384452111omplex @ ( suc @ M ) )
% 9.53/5.30        = ( plus_plus_complex @ one_one_complex @ ( semiri8010041392384452111omplex @ M ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7206_or__nat__numerals_I2_J,axiom,
% 9.53/5.30      ! [Y2: num] :
% 9.53/5.30        ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) )
% 9.53/5.30        = ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7207_or__nat__numerals_I4_J,axiom,
% 9.53/5.30      ! [X: num] :
% 9.53/5.30        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 9.53/5.30        = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7208_ceiling__add__of__int,axiom,
% 9.53/5.30      ! [X: rat,Z: int] :
% 9.53/5.30        ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ ( ring_1_of_int_rat @ Z ) ) )
% 9.53/5.30        = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ Z ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7209_ceiling__add__of__int,axiom,
% 9.53/5.30      ! [X: real,Z: int] :
% 9.53/5.30        ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X @ ( ring_1_of_int_real @ Z ) ) )
% 9.53/5.30        = ( plus_plus_int @ ( archim7802044766580827645g_real @ X ) @ Z ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7210_ceiling__diff__of__int,axiom,
% 9.53/5.30      ! [X: rat,Z: int] :
% 9.53/5.30        ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X @ ( ring_1_of_int_rat @ Z ) ) )
% 9.53/5.30        = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X ) @ Z ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7211_ceiling__diff__of__int,axiom,
% 9.53/5.30      ! [X: real,Z: int] :
% 9.53/5.30        ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X @ ( ring_1_of_int_real @ Z ) ) )
% 9.53/5.30        = ( minus_minus_int @ ( archim7802044766580827645g_real @ X ) @ Z ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7212_of__nat__0__less__iff,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) )
% 9.53/5.30        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7213_of__nat__0__less__iff,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( ord_less_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) )
% 9.53/5.30        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7214_of__nat__0__less__iff,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) )
% 9.53/5.30        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7215_of__nat__0__less__iff,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) )
% 9.53/5.30        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7216_or__nat__numerals_I1_J,axiom,
% 9.53/5.30      ! [Y2: num] :
% 9.53/5.30        ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) )
% 9.53/5.30        = ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7217_or__nat__numerals_I3_J,axiom,
% 9.53/5.30      ! [X: num] :
% 9.53/5.30        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 9.53/5.30        = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7218_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 9.53/5.30      ! [Y2: nat,X: num,N: nat] :
% 9.53/5.30        ( ( ( semiri681578069525770553at_rat @ Y2 )
% 9.53/5.30          = ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 9.53/5.30        = ( Y2
% 9.53/5.30          = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7219_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 9.53/5.30      ! [Y2: nat,X: num,N: nat] :
% 9.53/5.30        ( ( ( semiri5074537144036343181t_real @ Y2 )
% 9.53/5.30          = ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 9.53/5.30        = ( Y2
% 9.53/5.30          = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7220_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 9.53/5.30      ! [Y2: nat,X: num,N: nat] :
% 9.53/5.30        ( ( ( semiri1314217659103216013at_int @ Y2 )
% 9.53/5.30          = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 9.53/5.30        = ( Y2
% 9.53/5.30          = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7221_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 9.53/5.30      ! [Y2: nat,X: num,N: nat] :
% 9.53/5.30        ( ( ( semiri1316708129612266289at_nat @ Y2 )
% 9.53/5.30          = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 9.53/5.30        = ( Y2
% 9.53/5.30          = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7222_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 9.53/5.30      ! [Y2: nat,X: num,N: nat] :
% 9.53/5.30        ( ( ( semiri8010041392384452111omplex @ Y2 )
% 9.53/5.30          = ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N ) )
% 9.53/5.30        = ( Y2
% 9.53/5.30          = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7223_numeral__power__eq__of__nat__cancel__iff,axiom,
% 9.53/5.30      ! [X: num,N: nat,Y2: nat] :
% 9.53/5.30        ( ( ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N )
% 9.53/5.30          = ( semiri681578069525770553at_rat @ Y2 ) )
% 9.53/5.30        = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 9.53/5.30          = Y2 ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7224_numeral__power__eq__of__nat__cancel__iff,axiom,
% 9.53/5.30      ! [X: num,N: nat,Y2: nat] :
% 9.53/5.30        ( ( ( power_power_real @ ( numeral_numeral_real @ X ) @ N )
% 9.53/5.30          = ( semiri5074537144036343181t_real @ Y2 ) )
% 9.53/5.30        = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 9.53/5.30          = Y2 ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7225_numeral__power__eq__of__nat__cancel__iff,axiom,
% 9.53/5.30      ! [X: num,N: nat,Y2: nat] :
% 9.53/5.30        ( ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 9.53/5.30          = ( semiri1314217659103216013at_int @ Y2 ) )
% 9.53/5.30        = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 9.53/5.30          = Y2 ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7226_numeral__power__eq__of__nat__cancel__iff,axiom,
% 9.53/5.30      ! [X: num,N: nat,Y2: nat] :
% 9.53/5.30        ( ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 9.53/5.30          = ( semiri1316708129612266289at_nat @ Y2 ) )
% 9.53/5.30        = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 9.53/5.30          = Y2 ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7227_numeral__power__eq__of__nat__cancel__iff,axiom,
% 9.53/5.30      ! [X: num,N: nat,Y2: nat] :
% 9.53/5.30        ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N )
% 9.53/5.30          = ( semiri8010041392384452111omplex @ Y2 ) )
% 9.53/5.30        = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 9.53/5.30          = Y2 ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7228_of__nat__less__of__nat__power__cancel__iff,axiom,
% 9.53/5.30      ! [B: nat,W: nat,X: nat] :
% 9.53/5.30        ( ( ord_less_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X ) )
% 9.53/5.30        = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7229_of__nat__less__of__nat__power__cancel__iff,axiom,
% 9.53/5.30      ! [B: nat,W: nat,X: nat] :
% 9.53/5.30        ( ( ord_less_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X ) )
% 9.53/5.30        = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7230_of__nat__less__of__nat__power__cancel__iff,axiom,
% 9.53/5.30      ! [B: nat,W: nat,X: nat] :
% 9.53/5.30        ( ( ord_less_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X ) )
% 9.53/5.30        = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7231_of__nat__less__of__nat__power__cancel__iff,axiom,
% 9.53/5.30      ! [B: nat,W: nat,X: nat] :
% 9.53/5.30        ( ( ord_less_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X ) )
% 9.53/5.30        = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7232_of__nat__power__less__of__nat__cancel__iff,axiom,
% 9.53/5.30      ! [X: nat,B: nat,W: nat] :
% 9.53/5.30        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 9.53/5.30        = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7233_of__nat__power__less__of__nat__cancel__iff,axiom,
% 9.53/5.30      ! [X: nat,B: nat,W: nat] :
% 9.53/5.30        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 9.53/5.30        = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7234_of__nat__power__less__of__nat__cancel__iff,axiom,
% 9.53/5.30      ! [X: nat,B: nat,W: nat] :
% 9.53/5.30        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 9.53/5.30        = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7235_of__nat__power__less__of__nat__cancel__iff,axiom,
% 9.53/5.30      ! [X: nat,B: nat,W: nat] :
% 9.53/5.30        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 9.53/5.30        = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7236_of__nat__le__of__nat__power__cancel__iff,axiom,
% 9.53/5.30      ! [B: nat,W: nat,X: nat] :
% 9.53/5.30        ( ( ord_less_eq_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X ) )
% 9.53/5.30        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7237_of__nat__le__of__nat__power__cancel__iff,axiom,
% 9.53/5.30      ! [B: nat,W: nat,X: nat] :
% 9.53/5.30        ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X ) )
% 9.53/5.30        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7238_of__nat__le__of__nat__power__cancel__iff,axiom,
% 9.53/5.30      ! [B: nat,W: nat,X: nat] :
% 9.53/5.30        ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X ) )
% 9.53/5.30        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7239_of__nat__power__le__of__nat__cancel__iff,axiom,
% 9.53/5.30      ! [X: nat,B: nat,W: nat] :
% 9.53/5.30        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 9.53/5.30        = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7240_of__nat__power__le__of__nat__cancel__iff,axiom,
% 9.53/5.30      ! [X: nat,B: nat,W: nat] :
% 9.53/5.30        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 9.53/5.30        = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7241_of__nat__power__le__of__nat__cancel__iff,axiom,
% 9.53/5.30      ! [X: nat,B: nat,W: nat] :
% 9.53/5.30        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 9.53/5.30        = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7242_ceiling__le__zero,axiom,
% 9.53/5.30      ! [X: rat] :
% 9.53/5.30        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ zero_zero_int )
% 9.53/5.30        = ( ord_less_eq_rat @ X @ zero_zero_rat ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7243_ceiling__le__zero,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30        ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ zero_zero_int )
% 9.53/5.30        = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7244_zero__less__ceiling,axiom,
% 9.53/5.30      ! [X: rat] :
% 9.53/5.30        ( ( ord_less_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X ) )
% 9.53/5.30        = ( ord_less_rat @ zero_zero_rat @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7245_zero__less__ceiling,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30        ( ( ord_less_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X ) )
% 9.53/5.30        = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7246_numeral__less__real__of__nat__iff,axiom,
% 9.53/5.30      ! [W: num,N: nat] :
% 9.53/5.30        ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( semiri5074537144036343181t_real @ N ) )
% 9.53/5.30        = ( ord_less_nat @ ( numeral_numeral_nat @ W ) @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7247_real__of__nat__less__numeral__iff,axiom,
% 9.53/5.30      ! [N: nat,W: num] :
% 9.53/5.30        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( numeral_numeral_real @ W ) )
% 9.53/5.30        = ( ord_less_nat @ N @ ( numeral_numeral_nat @ W ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7248_ceiling__le__numeral,axiom,
% 9.53/5.30      ! [X: real,V: num] :
% 9.53/5.30        ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ ( numeral_numeral_int @ V ) )
% 9.53/5.30        = ( ord_less_eq_real @ X @ ( numeral_numeral_real @ V ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7249_ceiling__le__numeral,axiom,
% 9.53/5.30      ! [X: rat,V: num] :
% 9.53/5.30        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 9.53/5.30        = ( ord_less_eq_rat @ X @ ( numeral_numeral_rat @ V ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7250_numeral__less__ceiling,axiom,
% 9.53/5.30      ! [V: num,X: real] :
% 9.53/5.30        ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X ) )
% 9.53/5.30        = ( ord_less_real @ ( numeral_numeral_real @ V ) @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7251_numeral__less__ceiling,axiom,
% 9.53/5.30      ! [V: num,X: rat] :
% 9.53/5.30        ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X ) )
% 9.53/5.30        = ( ord_less_rat @ ( numeral_numeral_rat @ V ) @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7252_ceiling__less__one,axiom,
% 9.53/5.30      ! [X: rat] :
% 9.53/5.30        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int )
% 9.53/5.30        = ( ord_less_eq_rat @ X @ zero_zero_rat ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7253_ceiling__less__one,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30        ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int )
% 9.53/5.30        = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7254_numeral__le__real__of__nat__iff,axiom,
% 9.53/5.30      ! [N: num,M: nat] :
% 9.53/5.30        ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( semiri5074537144036343181t_real @ M ) )
% 9.53/5.30        = ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ M ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7255_one__le__ceiling,axiom,
% 9.53/5.30      ! [X: rat] :
% 9.53/5.30        ( ( ord_less_eq_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X ) )
% 9.53/5.30        = ( ord_less_rat @ zero_zero_rat @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7256_one__le__ceiling,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30        ( ( ord_less_eq_int @ one_one_int @ ( archim7802044766580827645g_real @ X ) )
% 9.53/5.30        = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7257_ceiling__le__one,axiom,
% 9.53/5.30      ! [X: rat] :
% 9.53/5.30        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int )
% 9.53/5.30        = ( ord_less_eq_rat @ X @ one_one_rat ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7258_ceiling__le__one,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30        ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int )
% 9.53/5.30        = ( ord_less_eq_real @ X @ one_one_real ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7259_one__less__ceiling,axiom,
% 9.53/5.30      ! [X: rat] :
% 9.53/5.30        ( ( ord_less_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X ) )
% 9.53/5.30        = ( ord_less_rat @ one_one_rat @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7260_one__less__ceiling,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30        ( ( ord_less_int @ one_one_int @ ( archim7802044766580827645g_real @ X ) )
% 9.53/5.30        = ( ord_less_real @ one_one_real @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7261_ceiling__add__numeral,axiom,
% 9.53/5.30      ! [X: real,V: num] :
% 9.53/5.30        ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X @ ( numeral_numeral_real @ V ) ) )
% 9.53/5.30        = ( plus_plus_int @ ( archim7802044766580827645g_real @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7262_ceiling__add__numeral,axiom,
% 9.53/5.30      ! [X: rat,V: num] :
% 9.53/5.30        ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ ( numeral_numeral_rat @ V ) ) )
% 9.53/5.30        = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7263_ceiling__neg__numeral,axiom,
% 9.53/5.30      ! [V: num] :
% 9.53/5.30        ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 9.53/5.30        = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7264_ceiling__neg__numeral,axiom,
% 9.53/5.30      ! [V: num] :
% 9.53/5.30        ( ( archim2889992004027027881ng_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 9.53/5.30        = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7265_ceiling__add__one,axiom,
% 9.53/5.30      ! [X: rat] :
% 9.53/5.30        ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ one_one_rat ) )
% 9.53/5.30        = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7266_ceiling__add__one,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30        ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X @ one_one_real ) )
% 9.53/5.30        = ( plus_plus_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7267_ceiling__diff__numeral,axiom,
% 9.53/5.30      ! [X: real,V: num] :
% 9.53/5.30        ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X @ ( numeral_numeral_real @ V ) ) )
% 9.53/5.30        = ( minus_minus_int @ ( archim7802044766580827645g_real @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7268_ceiling__diff__numeral,axiom,
% 9.53/5.30      ! [X: rat,V: num] :
% 9.53/5.30        ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X @ ( numeral_numeral_rat @ V ) ) )
% 9.53/5.30        = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7269_ceiling__diff__one,axiom,
% 9.53/5.30      ! [X: rat] :
% 9.53/5.30        ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X @ one_one_rat ) )
% 9.53/5.30        = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7270_ceiling__diff__one,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30        ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X @ one_one_real ) )
% 9.53/5.30        = ( minus_minus_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7271_ceiling__numeral__power,axiom,
% 9.53/5.30      ! [X: num,N: nat] :
% 9.53/5.30        ( ( archim7802044766580827645g_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 9.53/5.30        = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7272_ceiling__numeral__power,axiom,
% 9.53/5.30      ! [X: num,N: nat] :
% 9.53/5.30        ( ( archim2889992004027027881ng_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 9.53/5.30        = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7273_of__nat__zero__less__power__iff,axiom,
% 9.53/5.30      ! [X: nat,N: nat] :
% 9.53/5.30        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X ) @ N ) )
% 9.53/5.30        = ( ( ord_less_nat @ zero_zero_nat @ X )
% 9.53/5.30          | ( N = zero_zero_nat ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7274_of__nat__zero__less__power__iff,axiom,
% 9.53/5.30      ! [X: nat,N: nat] :
% 9.53/5.30        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ X ) @ N ) )
% 9.53/5.30        = ( ( ord_less_nat @ zero_zero_nat @ X )
% 9.53/5.30          | ( N = zero_zero_nat ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7275_of__nat__zero__less__power__iff,axiom,
% 9.53/5.30      ! [X: nat,N: nat] :
% 9.53/5.30        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X ) @ N ) )
% 9.53/5.30        = ( ( ord_less_nat @ zero_zero_nat @ X )
% 9.53/5.30          | ( N = zero_zero_nat ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7276_of__nat__zero__less__power__iff,axiom,
% 9.53/5.30      ! [X: nat,N: nat] :
% 9.53/5.30        ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X ) @ N ) )
% 9.53/5.30        = ( ( ord_less_nat @ zero_zero_nat @ X )
% 9.53/5.30          | ( N = zero_zero_nat ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7277_ceiling__less__zero,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30        ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ zero_zero_int )
% 9.53/5.30        = ( ord_less_eq_real @ X @ ( uminus_uminus_real @ one_one_real ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7278_ceiling__less__zero,axiom,
% 9.53/5.30      ! [X: rat] :
% 9.53/5.30        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ zero_zero_int )
% 9.53/5.30        = ( ord_less_eq_rat @ X @ ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7279_zero__le__ceiling,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30        ( ( ord_less_eq_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X ) )
% 9.53/5.30        = ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7280_zero__le__ceiling,axiom,
% 9.53/5.30      ! [X: rat] :
% 9.53/5.30        ( ( ord_less_eq_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X ) )
% 9.53/5.30        = ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7281_log__pow__cancel,axiom,
% 9.53/5.30      ! [A: real,B: nat] :
% 9.53/5.30        ( ( ord_less_real @ zero_zero_real @ A )
% 9.53/5.30       => ( ( A != one_one_real )
% 9.53/5.30         => ( ( log @ A @ ( power_power_real @ A @ B ) )
% 9.53/5.30            = ( semiri5074537144036343181t_real @ B ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7282_ceiling__divide__eq__div__numeral,axiom,
% 9.53/5.30      ! [A: num,B: num] :
% 9.53/5.30        ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 9.53/5.30        = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7283_of__nat__less__numeral__power__cancel__iff,axiom,
% 9.53/5.30      ! [X: nat,I2: num,N: nat] :
% 9.53/5.30        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N ) )
% 9.53/5.30        = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7284_of__nat__less__numeral__power__cancel__iff,axiom,
% 9.53/5.30      ! [X: nat,I2: num,N: nat] :
% 9.53/5.30        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N ) )
% 9.53/5.30        = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7285_of__nat__less__numeral__power__cancel__iff,axiom,
% 9.53/5.30      ! [X: nat,I2: num,N: nat] :
% 9.53/5.30        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N ) )
% 9.53/5.30        = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7286_of__nat__less__numeral__power__cancel__iff,axiom,
% 9.53/5.30      ! [X: nat,I2: num,N: nat] :
% 9.53/5.30        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) )
% 9.53/5.30        = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7287_numeral__power__less__of__nat__cancel__iff,axiom,
% 9.53/5.30      ! [I2: num,N: nat,X: nat] :
% 9.53/5.30        ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N ) @ ( semiri681578069525770553at_rat @ X ) )
% 9.53/5.30        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7288_numeral__power__less__of__nat__cancel__iff,axiom,
% 9.53/5.30      ! [I2: num,N: nat,X: nat] :
% 9.53/5.30        ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N ) @ ( semiri5074537144036343181t_real @ X ) )
% 9.53/5.30        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7289_numeral__power__less__of__nat__cancel__iff,axiom,
% 9.53/5.30      ! [I2: num,N: nat,X: nat] :
% 9.53/5.30        ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N ) @ ( semiri1314217659103216013at_int @ X ) )
% 9.53/5.30        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7290_numeral__power__less__of__nat__cancel__iff,axiom,
% 9.53/5.30      ! [I2: num,N: nat,X: nat] :
% 9.53/5.30        ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ ( semiri1316708129612266289at_nat @ X ) )
% 9.53/5.30        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7291_even__of__nat,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( semiri4939895301339042750nteger @ N ) )
% 9.53/5.30        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7292_even__of__nat,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ N ) )
% 9.53/5.30        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7293_even__of__nat,axiom,
% 9.53/5.30      ! [N: nat] :
% 9.53/5.30        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ N ) )
% 9.53/5.30        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7294_numeral__power__le__of__nat__cancel__iff,axiom,
% 9.53/5.30      ! [I2: num,N: nat,X: nat] :
% 9.53/5.30        ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N ) @ ( semiri681578069525770553at_rat @ X ) )
% 9.53/5.30        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7295_numeral__power__le__of__nat__cancel__iff,axiom,
% 9.53/5.30      ! [I2: num,N: nat,X: nat] :
% 9.53/5.30        ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N ) @ ( semiri5074537144036343181t_real @ X ) )
% 9.53/5.30        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7296_numeral__power__le__of__nat__cancel__iff,axiom,
% 9.53/5.30      ! [I2: num,N: nat,X: nat] :
% 9.53/5.30        ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ ( semiri1316708129612266289at_nat @ X ) )
% 9.53/5.30        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7297_numeral__power__le__of__nat__cancel__iff,axiom,
% 9.53/5.30      ! [I2: num,N: nat,X: nat] :
% 9.53/5.30        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N ) @ ( semiri1314217659103216013at_int @ X ) )
% 9.53/5.30        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7298_of__nat__le__numeral__power__cancel__iff,axiom,
% 9.53/5.30      ! [X: nat,I2: num,N: nat] :
% 9.53/5.30        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N ) )
% 9.53/5.30        = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7299_of__nat__le__numeral__power__cancel__iff,axiom,
% 9.53/5.30      ! [X: nat,I2: num,N: nat] :
% 9.53/5.30        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N ) )
% 9.53/5.30        = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7300_of__nat__le__numeral__power__cancel__iff,axiom,
% 9.53/5.30      ! [X: nat,I2: num,N: nat] :
% 9.53/5.30        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) )
% 9.53/5.30        = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7301_of__nat__le__numeral__power__cancel__iff,axiom,
% 9.53/5.30      ! [X: nat,I2: num,N: nat] :
% 9.53/5.30        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N ) )
% 9.53/5.30        = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7302_ceiling__less__numeral,axiom,
% 9.53/5.30      ! [X: real,V: num] :
% 9.53/5.30        ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ ( numeral_numeral_int @ V ) )
% 9.53/5.30        = ( ord_less_eq_real @ X @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7303_ceiling__less__numeral,axiom,
% 9.53/5.30      ! [X: rat,V: num] :
% 9.53/5.30        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 9.53/5.30        = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7304_numeral__le__ceiling,axiom,
% 9.53/5.30      ! [V: num,X: real] :
% 9.53/5.30        ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X ) )
% 9.53/5.30        = ( ord_less_real @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7305_numeral__le__ceiling,axiom,
% 9.53/5.30      ! [V: num,X: rat] :
% 9.53/5.30        ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X ) )
% 9.53/5.30        = ( ord_less_rat @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7306_ceiling__le__neg__numeral,axiom,
% 9.53/5.30      ! [X: real,V: num] :
% 9.53/5.30        ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 9.53/5.30        = ( ord_less_eq_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7307_ceiling__le__neg__numeral,axiom,
% 9.53/5.30      ! [X: rat,V: num] :
% 9.53/5.30        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 9.53/5.30        = ( ord_less_eq_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7308_neg__numeral__less__ceiling,axiom,
% 9.53/5.30      ! [V: num,X: real] :
% 9.53/5.30        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X ) )
% 9.53/5.30        = ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7309_neg__numeral__less__ceiling,axiom,
% 9.53/5.30      ! [V: num,X: rat] :
% 9.53/5.30        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X ) )
% 9.53/5.30        = ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7310_ceiling__minus__divide__eq__div__numeral,axiom,
% 9.53/5.30      ! [A: num,B: num] :
% 9.53/5.30        ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 9.53/5.30        = ( uminus_uminus_int @ ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7311_ceiling__less__neg__numeral,axiom,
% 9.53/5.30      ! [X: real,V: num] :
% 9.53/5.30        ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 9.53/5.30        = ( ord_less_eq_real @ X @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7312_ceiling__less__neg__numeral,axiom,
% 9.53/5.30      ! [X: rat,V: num] :
% 9.53/5.30        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 9.53/5.30        = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7313_neg__numeral__le__ceiling,axiom,
% 9.53/5.30      ! [V: num,X: real] :
% 9.53/5.30        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X ) )
% 9.53/5.30        = ( ord_less_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7314_neg__numeral__le__ceiling,axiom,
% 9.53/5.30      ! [V: num,X: rat] :
% 9.53/5.30        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X ) )
% 9.53/5.30        = ( ord_less_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7315_real__arch__simple,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30      ? [N3: nat] : ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7316_reals__Archimedean2,axiom,
% 9.53/5.30      ! [X: rat] :
% 9.53/5.30      ? [N3: nat] : ( ord_less_rat @ X @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7317_reals__Archimedean2,axiom,
% 9.53/5.30      ! [X: real] :
% 9.53/5.30      ? [N3: nat] : ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7318_mult__of__nat__commute,axiom,
% 9.53/5.30      ! [X: nat,Y2: real] :
% 9.53/5.30        ( ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ Y2 )
% 9.53/5.30        = ( times_times_real @ Y2 @ ( semiri5074537144036343181t_real @ X ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7319_mult__of__nat__commute,axiom,
% 9.53/5.30      ! [X: nat,Y2: int] :
% 9.53/5.30        ( ( times_times_int @ ( semiri1314217659103216013at_int @ X ) @ Y2 )
% 9.53/5.30        = ( times_times_int @ Y2 @ ( semiri1314217659103216013at_int @ X ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7320_mult__of__nat__commute,axiom,
% 9.53/5.30      ! [X: nat,Y2: nat] :
% 9.53/5.30        ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X ) @ Y2 )
% 9.53/5.30        = ( times_times_nat @ Y2 @ ( semiri1316708129612266289at_nat @ X ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7321_mult__of__nat__commute,axiom,
% 9.53/5.30      ! [X: nat,Y2: complex] :
% 9.53/5.30        ( ( times_times_complex @ ( semiri8010041392384452111omplex @ X ) @ Y2 )
% 9.53/5.30        = ( times_times_complex @ Y2 @ ( semiri8010041392384452111omplex @ X ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7322_of__nat__or__eq,axiom,
% 9.53/5.30      ! [M: nat,N: nat] :
% 9.53/5.30        ( ( semiri1314217659103216013at_int @ ( bit_se1412395901928357646or_nat @ M @ N ) )
% 9.53/5.30        = ( bit_se1409905431419307370or_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7323_of__nat__or__eq,axiom,
% 9.53/5.30      ! [M: nat,N: nat] :
% 9.53/5.30        ( ( semiri1316708129612266289at_nat @ ( bit_se1412395901928357646or_nat @ M @ N ) )
% 9.53/5.30        = ( bit_se1412395901928357646or_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7324_of__nat__less__of__int__iff,axiom,
% 9.53/5.30      ! [N: nat,X: int] :
% 9.53/5.30        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( ring_1_of_int_rat @ X ) )
% 9.53/5.30        = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7325_of__nat__less__of__int__iff,axiom,
% 9.53/5.30      ! [N: nat,X: int] :
% 9.53/5.30        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( ring_1_of_int_real @ X ) )
% 9.53/5.30        = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7326_of__nat__less__of__int__iff,axiom,
% 9.53/5.30      ! [N: nat,X: int] :
% 9.53/5.30        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( ring_1_of_int_int @ X ) )
% 9.53/5.30        = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7327_of__nat__0__le__iff,axiom,
% 9.53/5.30      ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7328_of__nat__0__le__iff,axiom,
% 9.53/5.30      ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7329_of__nat__0__le__iff,axiom,
% 9.53/5.30      ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7330_of__nat__0__le__iff,axiom,
% 9.53/5.30      ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7331_of__nat__less__0__iff,axiom,
% 9.53/5.30      ! [M: nat] :
% 9.53/5.30        ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7332_of__nat__less__0__iff,axiom,
% 9.53/5.30      ! [M: nat] :
% 9.53/5.30        ~ ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real ) ).
% 9.53/5.30  
% 9.53/5.30  thf(fact_7333_of__nat__less__0__iff,axiom,
% 9.53/5.30      ! [M: nat] :
% 9.53/5.31        ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7334_of__nat__less__0__iff,axiom,
% 9.53/5.31      ! [M: nat] :
% 9.53/5.31        ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7335_ceiling__mono,axiom,
% 9.53/5.31      ! [Y2: real,X: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ Y2 @ X )
% 9.53/5.31       => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ Y2 ) @ ( archim7802044766580827645g_real @ X ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7336_of__nat__neq__0,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( semiri681578069525770553at_rat @ ( suc @ N ) )
% 9.53/5.31       != zero_zero_rat ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7337_of__nat__neq__0,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( semiri5074537144036343181t_real @ ( suc @ N ) )
% 9.53/5.31       != zero_zero_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7338_of__nat__neq__0,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 9.53/5.31       != zero_zero_int ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7339_of__nat__neq__0,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( semiri1316708129612266289at_nat @ ( suc @ N ) )
% 9.53/5.31       != zero_zero_nat ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7340_of__nat__neq__0,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( semiri8010041392384452111omplex @ ( suc @ N ) )
% 9.53/5.31       != zero_zero_complex ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7341_le__of__int__ceiling,axiom,
% 9.53/5.31      ! [X: real] : ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7342_ceiling__less__cancel,axiom,
% 9.53/5.31      ! [X: rat,Y2: rat] :
% 9.53/5.31        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ ( archim2889992004027027881ng_rat @ Y2 ) )
% 9.53/5.31       => ( ord_less_rat @ X @ Y2 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7343_ceiling__less__cancel,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ ( archim7802044766580827645g_real @ Y2 ) )
% 9.53/5.31       => ( ord_less_real @ X @ Y2 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7344_div__mult2__eq_H,axiom,
% 9.53/5.31      ! [A: int,M: nat,N: nat] :
% 9.53/5.31        ( ( divide_divide_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 9.53/5.31        = ( divide_divide_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7345_div__mult2__eq_H,axiom,
% 9.53/5.31      ! [A: nat,M: nat,N: nat] :
% 9.53/5.31        ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 9.53/5.31        = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7346_less__imp__of__nat__less,axiom,
% 9.53/5.31      ! [M: nat,N: nat] :
% 9.53/5.31        ( ( ord_less_nat @ M @ N )
% 9.53/5.31       => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7347_less__imp__of__nat__less,axiom,
% 9.53/5.31      ! [M: nat,N: nat] :
% 9.53/5.31        ( ( ord_less_nat @ M @ N )
% 9.53/5.31       => ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7348_less__imp__of__nat__less,axiom,
% 9.53/5.31      ! [M: nat,N: nat] :
% 9.53/5.31        ( ( ord_less_nat @ M @ N )
% 9.53/5.31       => ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7349_less__imp__of__nat__less,axiom,
% 9.53/5.31      ! [M: nat,N: nat] :
% 9.53/5.31        ( ( ord_less_nat @ M @ N )
% 9.53/5.31       => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7350_of__nat__less__imp__less,axiom,
% 9.53/5.31      ! [M: nat,N: nat] :
% 9.53/5.31        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 9.53/5.31       => ( ord_less_nat @ M @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7351_of__nat__less__imp__less,axiom,
% 9.53/5.31      ! [M: nat,N: nat] :
% 9.53/5.31        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 9.53/5.31       => ( ord_less_nat @ M @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7352_of__nat__less__imp__less,axiom,
% 9.53/5.31      ! [M: nat,N: nat] :
% 9.53/5.31        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 9.53/5.31       => ( ord_less_nat @ M @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7353_of__nat__less__imp__less,axiom,
% 9.53/5.31      ! [M: nat,N: nat] :
% 9.53/5.31        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 9.53/5.31       => ( ord_less_nat @ M @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7354_of__nat__mono,axiom,
% 9.53/5.31      ! [I2: nat,J: nat] :
% 9.53/5.31        ( ( ord_less_eq_nat @ I2 @ J )
% 9.53/5.31       => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ I2 ) @ ( semiri5074537144036343181t_real @ J ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7355_of__nat__mono,axiom,
% 9.53/5.31      ! [I2: nat,J: nat] :
% 9.53/5.31        ( ( ord_less_eq_nat @ I2 @ J )
% 9.53/5.31       => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I2 ) @ ( semiri1316708129612266289at_nat @ J ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7356_of__nat__mono,axiom,
% 9.53/5.31      ! [I2: nat,J: nat] :
% 9.53/5.31        ( ( ord_less_eq_nat @ I2 @ J )
% 9.53/5.31       => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ J ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7357_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 9.53/5.31      ! [M: nat,N: nat] :
% 9.53/5.31        ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) )
% 9.53/5.31        = ( divide_divide_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7358_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 9.53/5.31      ! [M: nat,N: nat] :
% 9.53/5.31        ( ( semiri1316708129612266289at_nat @ ( divide_divide_nat @ M @ N ) )
% 9.53/5.31        = ( divide_divide_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7359_of__nat__dvd__iff,axiom,
% 9.53/5.31      ! [M: nat,N: nat] :
% 9.53/5.31        ( ( dvd_dvd_Code_integer @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) )
% 9.53/5.31        = ( dvd_dvd_nat @ M @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7360_of__nat__dvd__iff,axiom,
% 9.53/5.31      ! [M: nat,N: nat] :
% 9.53/5.31        ( ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 9.53/5.31        = ( dvd_dvd_nat @ M @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7361_of__nat__dvd__iff,axiom,
% 9.53/5.31      ! [M: nat,N: nat] :
% 9.53/5.31        ( ( dvd_dvd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 9.53/5.31        = ( dvd_dvd_nat @ M @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7362_of__nat__mod,axiom,
% 9.53/5.31      ! [M: nat,N: nat] :
% 9.53/5.31        ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) )
% 9.53/5.31        = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7363_of__nat__mod,axiom,
% 9.53/5.31      ! [M: nat,N: nat] :
% 9.53/5.31        ( ( semiri1316708129612266289at_nat @ ( modulo_modulo_nat @ M @ N ) )
% 9.53/5.31        = ( modulo_modulo_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7364_of__nat__max,axiom,
% 9.53/5.31      ! [X: nat,Y2: nat] :
% 9.53/5.31        ( ( semiri4216267220026989637d_enat @ ( ord_max_nat @ X @ Y2 ) )
% 9.53/5.31        = ( ord_ma741700101516333627d_enat @ ( semiri4216267220026989637d_enat @ X ) @ ( semiri4216267220026989637d_enat @ Y2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7365_of__nat__max,axiom,
% 9.53/5.31      ! [X: nat,Y2: nat] :
% 9.53/5.31        ( ( semiri5074537144036343181t_real @ ( ord_max_nat @ X @ Y2 ) )
% 9.53/5.31        = ( ord_max_real @ ( semiri5074537144036343181t_real @ X ) @ ( semiri5074537144036343181t_real @ Y2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7366_of__nat__max,axiom,
% 9.53/5.31      ! [X: nat,Y2: nat] :
% 9.53/5.31        ( ( semiri1314217659103216013at_int @ ( ord_max_nat @ X @ Y2 ) )
% 9.53/5.31        = ( ord_max_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7367_of__nat__max,axiom,
% 9.53/5.31      ! [X: nat,Y2: nat] :
% 9.53/5.31        ( ( semiri1316708129612266289at_nat @ ( ord_max_nat @ X @ Y2 ) )
% 9.53/5.31        = ( ord_max_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( semiri1316708129612266289at_nat @ Y2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7368_take__bit__of__nat,axiom,
% 9.53/5.31      ! [N: nat,M: nat] :
% 9.53/5.31        ( ( bit_se2923211474154528505it_int @ N @ ( semiri1314217659103216013at_int @ M ) )
% 9.53/5.31        = ( semiri1314217659103216013at_int @ ( bit_se2925701944663578781it_nat @ N @ M ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7369_take__bit__of__nat,axiom,
% 9.53/5.31      ! [N: nat,M: nat] :
% 9.53/5.31        ( ( bit_se2925701944663578781it_nat @ N @ ( semiri1316708129612266289at_nat @ M ) )
% 9.53/5.31        = ( semiri1316708129612266289at_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7370_of__nat__and__eq,axiom,
% 9.53/5.31      ! [M: nat,N: nat] :
% 9.53/5.31        ( ( semiri1314217659103216013at_int @ ( bit_se727722235901077358nd_nat @ M @ N ) )
% 9.53/5.31        = ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7371_of__nat__and__eq,axiom,
% 9.53/5.31      ! [M: nat,N: nat] :
% 9.53/5.31        ( ( semiri1316708129612266289at_nat @ ( bit_se727722235901077358nd_nat @ M @ N ) )
% 9.53/5.31        = ( bit_se727722235901077358nd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7372_of__nat__mask__eq,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( semiri1316708129612266289at_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 9.53/5.31        = ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7373_of__nat__mask__eq,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( semiri1314217659103216013at_int @ ( bit_se2002935070580805687sk_nat @ N ) )
% 9.53/5.31        = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7374_ex__less__of__nat__mult,axiom,
% 9.53/5.31      ! [X: rat,Y2: rat] :
% 9.53/5.31        ( ( ord_less_rat @ zero_zero_rat @ X )
% 9.53/5.31       => ? [N3: nat] : ( ord_less_rat @ Y2 @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N3 ) @ X ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7375_ex__less__of__nat__mult,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.31       => ? [N3: nat] : ( ord_less_real @ Y2 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7376_ceiling__le__iff,axiom,
% 9.53/5.31      ! [X: real,Z: int] :
% 9.53/5.31        ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ Z )
% 9.53/5.31        = ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ Z ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7377_ceiling__le,axiom,
% 9.53/5.31      ! [X: real,A: int] :
% 9.53/5.31        ( ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ A ) )
% 9.53/5.31       => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ A ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7378_less__ceiling__iff,axiom,
% 9.53/5.31      ! [Z: int,X: rat] :
% 9.53/5.31        ( ( ord_less_int @ Z @ ( archim2889992004027027881ng_rat @ X ) )
% 9.53/5.31        = ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ X ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7379_less__ceiling__iff,axiom,
% 9.53/5.31      ! [Z: int,X: real] :
% 9.53/5.31        ( ( ord_less_int @ Z @ ( archim7802044766580827645g_real @ X ) )
% 9.53/5.31        = ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ X ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7380_ceiling__add__le,axiom,
% 9.53/5.31      ! [X: rat,Y2: rat] : ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ Y2 ) ) @ ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ ( archim2889992004027027881ng_rat @ Y2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7381_ceiling__add__le,axiom,
% 9.53/5.31      ! [X: real,Y2: real] : ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( plus_plus_real @ X @ Y2 ) ) @ ( plus_plus_int @ ( archim7802044766580827645g_real @ X ) @ ( archim7802044766580827645g_real @ Y2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7382_of__nat__diff,axiom,
% 9.53/5.31      ! [N: nat,M: nat] :
% 9.53/5.31        ( ( ord_less_eq_nat @ N @ M )
% 9.53/5.31       => ( ( semiri681578069525770553at_rat @ ( minus_minus_nat @ M @ N ) )
% 9.53/5.31          = ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7383_of__nat__diff,axiom,
% 9.53/5.31      ! [N: nat,M: nat] :
% 9.53/5.31        ( ( ord_less_eq_nat @ N @ M )
% 9.53/5.31       => ( ( semiri5074537144036343181t_real @ ( minus_minus_nat @ M @ N ) )
% 9.53/5.31          = ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7384_of__nat__diff,axiom,
% 9.53/5.31      ! [N: nat,M: nat] :
% 9.53/5.31        ( ( ord_less_eq_nat @ N @ M )
% 9.53/5.31       => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M @ N ) )
% 9.53/5.31          = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7385_of__nat__diff,axiom,
% 9.53/5.31      ! [N: nat,M: nat] :
% 9.53/5.31        ( ( ord_less_eq_nat @ N @ M )
% 9.53/5.31       => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M @ N ) )
% 9.53/5.31          = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7386_of__nat__diff,axiom,
% 9.53/5.31      ! [N: nat,M: nat] :
% 9.53/5.31        ( ( ord_less_eq_nat @ N @ M )
% 9.53/5.31       => ( ( semiri8010041392384452111omplex @ ( minus_minus_nat @ M @ N ) )
% 9.53/5.31          = ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7387_exp__of__nat2__mult,axiom,
% 9.53/5.31      ! [X: real,N: nat] :
% 9.53/5.31        ( ( exp_real @ ( times_times_real @ X @ ( semiri5074537144036343181t_real @ N ) ) )
% 9.53/5.31        = ( power_power_real @ ( exp_real @ X ) @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7388_exp__of__nat2__mult,axiom,
% 9.53/5.31      ! [X: complex,N: nat] :
% 9.53/5.31        ( ( exp_complex @ ( times_times_complex @ X @ ( semiri8010041392384452111omplex @ N ) ) )
% 9.53/5.31        = ( power_power_complex @ ( exp_complex @ X ) @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7389_exp__of__nat__mult,axiom,
% 9.53/5.31      ! [N: nat,X: real] :
% 9.53/5.31        ( ( exp_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) )
% 9.53/5.31        = ( power_power_real @ ( exp_real @ X ) @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7390_exp__of__nat__mult,axiom,
% 9.53/5.31      ! [N: nat,X: complex] :
% 9.53/5.31        ( ( exp_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ X ) )
% 9.53/5.31        = ( power_power_complex @ ( exp_complex @ X ) @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7391_reals__Archimedean3,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.31       => ! [Y4: real] :
% 9.53/5.31          ? [N3: nat] : ( ord_less_real @ Y4 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7392_real__of__nat__div4,axiom,
% 9.53/5.31      ! [N: nat,X: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7393_real__of__nat__div,axiom,
% 9.53/5.31      ! [D2: nat,N: nat] :
% 9.53/5.31        ( ( dvd_dvd_nat @ D2 @ N )
% 9.53/5.31       => ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ D2 ) )
% 9.53/5.31          = ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ D2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7394_of__int__ceiling__le__add__one,axiom,
% 9.53/5.31      ! [R: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R ) ) @ ( plus_plus_rat @ R @ one_one_rat ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7395_of__int__ceiling__le__add__one,axiom,
% 9.53/5.31      ! [R: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R ) ) @ ( plus_plus_real @ R @ one_one_real ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7396_of__int__ceiling__diff__one__le,axiom,
% 9.53/5.31      ! [R: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R ) ) @ one_one_rat ) @ R ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7397_of__int__ceiling__diff__one__le,axiom,
% 9.53/5.31      ! [R: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R ) ) @ one_one_real ) @ R ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7398_mod__mult2__eq_H,axiom,
% 9.53/5.31      ! [A: int,M: nat,N: nat] :
% 9.53/5.31        ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 9.53/5.31        = ( plus_plus_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( modulo_modulo_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) @ ( modulo_modulo_int @ A @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7399_mod__mult2__eq_H,axiom,
% 9.53/5.31      ! [A: nat,M: nat,N: nat] :
% 9.53/5.31        ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 9.53/5.31        = ( plus_plus_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) @ ( modulo_modulo_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7400_ceiling__divide__eq__div,axiom,
% 9.53/5.31      ! [A: int,B: int] :
% 9.53/5.31        ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B ) ) )
% 9.53/5.31        = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7401_ceiling__divide__eq__div,axiom,
% 9.53/5.31      ! [A: int,B: int] :
% 9.53/5.31        ( ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ A ) @ ( ring_1_of_int_rat @ B ) ) )
% 9.53/5.31        = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7402_field__char__0__class_Oof__nat__div,axiom,
% 9.53/5.31      ! [M: nat,N: nat] :
% 9.53/5.31        ( ( semiri681578069525770553at_rat @ ( divide_divide_nat @ M @ N ) )
% 9.53/5.31        = ( divide_divide_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7403_field__char__0__class_Oof__nat__div,axiom,
% 9.53/5.31      ! [M: nat,N: nat] :
% 9.53/5.31        ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ M @ N ) )
% 9.53/5.31        = ( divide_divide_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7404_field__char__0__class_Oof__nat__div,axiom,
% 9.53/5.31      ! [M: nat,N: nat] :
% 9.53/5.31        ( ( semiri8010041392384452111omplex @ ( divide_divide_nat @ M @ N ) )
% 9.53/5.31        = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7405_nat__less__real__le,axiom,
% 9.53/5.31      ( ord_less_nat
% 9.53/5.31      = ( ^ [N2: nat,M6: nat] : ( ord_less_eq_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ M6 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7406_nat__le__real__less,axiom,
% 9.53/5.31      ( ord_less_eq_nat
% 9.53/5.31      = ( ^ [N2: nat,M6: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M6 ) @ one_one_real ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7407_less__log__of__power,axiom,
% 9.53/5.31      ! [B: real,N: nat,M: real] :
% 9.53/5.31        ( ( ord_less_real @ ( power_power_real @ B @ N ) @ M )
% 9.53/5.31       => ( ( ord_less_real @ one_one_real @ B )
% 9.53/5.31         => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7408_log__of__power__eq,axiom,
% 9.53/5.31      ! [M: nat,B: real,N: nat] :
% 9.53/5.31        ( ( ( semiri5074537144036343181t_real @ M )
% 9.53/5.31          = ( power_power_real @ B @ N ) )
% 9.53/5.31       => ( ( ord_less_real @ one_one_real @ B )
% 9.53/5.31         => ( ( semiri5074537144036343181t_real @ N )
% 9.53/5.31            = ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7409_real__of__nat__div__aux,axiom,
% 9.53/5.31      ! [X: nat,D2: nat] :
% 9.53/5.31        ( ( divide_divide_real @ ( semiri5074537144036343181t_real @ X ) @ ( semiri5074537144036343181t_real @ D2 ) )
% 9.53/5.31        = ( plus_plus_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ X @ D2 ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ X @ D2 ) ) @ ( semiri5074537144036343181t_real @ D2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7410_ceiling__split,axiom,
% 9.53/5.31      ! [P: int > $o,T: rat] :
% 9.53/5.31        ( ( P @ ( archim2889992004027027881ng_rat @ T ) )
% 9.53/5.31        = ( ! [I3: int] :
% 9.53/5.31              ( ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ I3 ) @ one_one_rat ) @ T )
% 9.53/5.31                & ( ord_less_eq_rat @ T @ ( ring_1_of_int_rat @ I3 ) ) )
% 9.53/5.31             => ( P @ I3 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7411_ceiling__split,axiom,
% 9.53/5.31      ! [P: int > $o,T: real] :
% 9.53/5.31        ( ( P @ ( archim7802044766580827645g_real @ T ) )
% 9.53/5.31        = ( ! [I3: int] :
% 9.53/5.31              ( ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ I3 ) @ one_one_real ) @ T )
% 9.53/5.31                & ( ord_less_eq_real @ T @ ( ring_1_of_int_real @ I3 ) ) )
% 9.53/5.31             => ( P @ I3 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7412_ceiling__eq__iff,axiom,
% 9.53/5.31      ! [X: rat,A: int] :
% 9.53/5.31        ( ( ( archim2889992004027027881ng_rat @ X )
% 9.53/5.31          = A )
% 9.53/5.31        = ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) @ X )
% 9.53/5.31          & ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ A ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7413_ceiling__eq__iff,axiom,
% 9.53/5.31      ! [X: real,A: int] :
% 9.53/5.31        ( ( ( archim7802044766580827645g_real @ X )
% 9.53/5.31          = A )
% 9.53/5.31        = ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) @ X )
% 9.53/5.31          & ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ A ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7414_ceiling__unique,axiom,
% 9.53/5.31      ! [Z: int,X: rat] :
% 9.53/5.31        ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X )
% 9.53/5.31       => ( ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ Z ) )
% 9.53/5.31         => ( ( archim2889992004027027881ng_rat @ X )
% 9.53/5.31            = Z ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7415_ceiling__unique,axiom,
% 9.53/5.31      ! [Z: int,X: real] :
% 9.53/5.31        ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X )
% 9.53/5.31       => ( ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ Z ) )
% 9.53/5.31         => ( ( archim7802044766580827645g_real @ X )
% 9.53/5.31            = Z ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7416_ceiling__correct,axiom,
% 9.53/5.31      ! [X: rat] :
% 9.53/5.31        ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X ) ) @ one_one_rat ) @ X )
% 9.53/5.31        & ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7417_ceiling__correct,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) ) @ one_one_real ) @ X )
% 9.53/5.31        & ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7418_mult__ceiling__le,axiom,
% 9.53/5.31      ! [A: rat,B: rat] :
% 9.53/5.31        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.53/5.31       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 9.53/5.31         => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7419_mult__ceiling__le,axiom,
% 9.53/5.31      ! [A: real,B: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 9.53/5.31       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 9.53/5.31         => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B ) ) @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7420_nat__approx__posE,axiom,
% 9.53/5.31      ! [E: rat] :
% 9.53/5.31        ( ( ord_less_rat @ zero_zero_rat @ E )
% 9.53/5.31       => ~ ! [N3: nat] :
% 9.53/5.31              ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N3 ) ) ) @ E ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7421_nat__approx__posE,axiom,
% 9.53/5.31      ! [E: real] :
% 9.53/5.31        ( ( ord_less_real @ zero_zero_real @ E )
% 9.53/5.31       => ~ ! [N3: nat] :
% 9.53/5.31              ~ ( ord_less_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ E ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7422_of__nat__less__two__power,axiom,
% 9.53/5.31      ! [N: nat] : ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7423_of__nat__less__two__power,axiom,
% 9.53/5.31      ! [N: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7424_of__nat__less__two__power,axiom,
% 9.53/5.31      ! [N: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7425_ceiling__less__iff,axiom,
% 9.53/5.31      ! [X: rat,Z: int] :
% 9.53/5.31        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ Z )
% 9.53/5.31        = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7426_ceiling__less__iff,axiom,
% 9.53/5.31      ! [X: real,Z: int] :
% 9.53/5.31        ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ Z )
% 9.53/5.31        = ( ord_less_eq_real @ X @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7427_le__ceiling__iff,axiom,
% 9.53/5.31      ! [Z: int,X: rat] :
% 9.53/5.31        ( ( ord_less_eq_int @ Z @ ( archim2889992004027027881ng_rat @ X ) )
% 9.53/5.31        = ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7428_le__ceiling__iff,axiom,
% 9.53/5.31      ! [Z: int,X: real] :
% 9.53/5.31        ( ( ord_less_eq_int @ Z @ ( archim7802044766580827645g_real @ X ) )
% 9.53/5.31        = ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7429_inverse__of__nat__le,axiom,
% 9.53/5.31      ! [N: nat,M: nat] :
% 9.53/5.31        ( ( ord_less_eq_nat @ N @ M )
% 9.53/5.31       => ( ( N != zero_zero_nat )
% 9.53/5.31         => ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ N ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7430_inverse__of__nat__le,axiom,
% 9.53/5.31      ! [N: nat,M: nat] :
% 9.53/5.31        ( ( ord_less_eq_nat @ N @ M )
% 9.53/5.31       => ( ( N != zero_zero_nat )
% 9.53/5.31         => ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7431_exp__divide__power__eq,axiom,
% 9.53/5.31      ! [N: nat,X: real] :
% 9.53/5.31        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.31       => ( ( power_power_real @ ( exp_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N )
% 9.53/5.31          = ( exp_real @ X ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7432_exp__divide__power__eq,axiom,
% 9.53/5.31      ! [N: nat,X: complex] :
% 9.53/5.31        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.31       => ( ( power_power_complex @ ( exp_complex @ ( divide1717551699836669952omplex @ X @ ( semiri8010041392384452111omplex @ N ) ) ) @ N )
% 9.53/5.31          = ( exp_complex @ X ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7433_real__archimedian__rdiv__eq__0,axiom,
% 9.53/5.31      ! [X: real,C: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.31       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 9.53/5.31         => ( ! [M4: nat] :
% 9.53/5.31                ( ( ord_less_nat @ zero_zero_nat @ M4 )
% 9.53/5.31               => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M4 ) @ X ) @ C ) )
% 9.53/5.31           => ( X = zero_zero_real ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7434_real__of__nat__div2,axiom,
% 9.53/5.31      ! [N: nat,X: nat] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7435_real__of__nat__div3,axiom,
% 9.53/5.31      ! [N: nat,X: nat] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) ) @ one_one_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7436_le__log__of__power,axiom,
% 9.53/5.31      ! [B: real,N: nat,M: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( power_power_real @ B @ N ) @ M )
% 9.53/5.31       => ( ( ord_less_real @ one_one_real @ B )
% 9.53/5.31         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7437_log__base__pow,axiom,
% 9.53/5.31      ! [A: real,N: nat,X: real] :
% 9.53/5.31        ( ( ord_less_real @ zero_zero_real @ A )
% 9.53/5.31       => ( ( log @ ( power_power_real @ A @ N ) @ X )
% 9.53/5.31          = ( divide_divide_real @ ( log @ A @ X ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7438_log__nat__power,axiom,
% 9.53/5.31      ! [X: real,B: real,N: nat] :
% 9.53/5.31        ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.31       => ( ( log @ B @ ( power_power_real @ X @ N ) )
% 9.53/5.31          = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7439_ln__realpow,axiom,
% 9.53/5.31      ! [X: real,N: nat] :
% 9.53/5.31        ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.31       => ( ( ln_ln_real @ ( power_power_real @ X @ N ) )
% 9.53/5.31          = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( ln_ln_real @ X ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7440_ceiling__divide__upper,axiom,
% 9.53/5.31      ! [Q2: real,P6: real] :
% 9.53/5.31        ( ( ord_less_real @ zero_zero_real @ Q2 )
% 9.53/5.31       => ( ord_less_eq_real @ P6 @ ( times_times_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P6 @ Q2 ) ) ) @ Q2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7441_ceiling__divide__upper,axiom,
% 9.53/5.31      ! [Q2: rat,P6: rat] :
% 9.53/5.31        ( ( ord_less_rat @ zero_zero_rat @ Q2 )
% 9.53/5.31       => ( ord_less_eq_rat @ P6 @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P6 @ Q2 ) ) ) @ Q2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7442_ceiling__log2__div2,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.53/5.31       => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 9.53/5.31          = ( plus_plus_int @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( divide_divide_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) @ one_one_int ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7443_log2__of__power__eq,axiom,
% 9.53/5.31      ! [M: nat,N: nat] :
% 9.53/5.31        ( ( M
% 9.53/5.31          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.53/5.31       => ( ( semiri5074537144036343181t_real @ N )
% 9.53/5.31          = ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7444_log__of__power__less,axiom,
% 9.53/5.31      ! [M: nat,B: real,N: nat] :
% 9.53/5.31        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 9.53/5.31       => ( ( ord_less_real @ one_one_real @ B )
% 9.53/5.31         => ( ( ord_less_nat @ zero_zero_nat @ M )
% 9.53/5.31           => ( ord_less_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7445_linear__plus__1__le__power,axiom,
% 9.53/5.31      ! [X: real,N: nat] :
% 9.53/5.31        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.31       => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) @ one_one_real ) @ ( power_power_real @ ( plus_plus_real @ X @ one_one_real ) @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7446_Bernoulli__inequality,axiom,
% 9.53/5.31      ! [X: real,N: nat] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 9.53/5.31       => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X ) @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7447_ceiling__divide__lower,axiom,
% 9.53/5.31      ! [Q2: real,P6: real] :
% 9.53/5.31        ( ( ord_less_real @ zero_zero_real @ Q2 )
% 9.53/5.31       => ( ord_less_real @ ( times_times_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P6 @ Q2 ) ) ) @ one_one_real ) @ Q2 ) @ P6 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7448_ceiling__divide__lower,axiom,
% 9.53/5.31      ! [Q2: rat,P6: rat] :
% 9.53/5.31        ( ( ord_less_rat @ zero_zero_rat @ Q2 )
% 9.53/5.31       => ( ord_less_rat @ ( times_times_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P6 @ Q2 ) ) ) @ one_one_rat ) @ Q2 ) @ P6 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7449_ceiling__eq,axiom,
% 9.53/5.31      ! [N: int,X: rat] :
% 9.53/5.31        ( ( ord_less_rat @ ( ring_1_of_int_rat @ N ) @ X )
% 9.53/5.31       => ( ( ord_less_eq_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ N ) @ one_one_rat ) )
% 9.53/5.31         => ( ( archim2889992004027027881ng_rat @ X )
% 9.53/5.31            = ( plus_plus_int @ N @ one_one_int ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7450_ceiling__eq,axiom,
% 9.53/5.31      ! [N: int,X: real] :
% 9.53/5.31        ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X )
% 9.53/5.31       => ( ( ord_less_eq_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 9.53/5.31         => ( ( archim7802044766580827645g_real @ X )
% 9.53/5.31            = ( plus_plus_int @ N @ one_one_int ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7451_log__of__power__le,axiom,
% 9.53/5.31      ! [M: nat,B: real,N: nat] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 9.53/5.31       => ( ( ord_less_real @ one_one_real @ B )
% 9.53/5.31         => ( ( ord_less_nat @ zero_zero_nat @ M )
% 9.53/5.31           => ( ord_less_eq_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7452_or__Suc__0__eq,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( bit_se1412395901928357646or_nat @ N @ ( suc @ zero_zero_nat ) )
% 9.53/5.31        = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7453_Suc__0__or__eq,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N )
% 9.53/5.31        = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7454_or__nat__rec,axiom,
% 9.53/5.31      ( bit_se1412395901928357646or_nat
% 9.53/5.31      = ( ^ [M6: nat,N2: nat] :
% 9.53/5.31            ( plus_plus_nat
% 9.53/5.31            @ ( zero_n2687167440665602831ol_nat
% 9.53/5.31              @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 )
% 9.53/5.31                | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 9.53/5.31            @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7455_double__arith__series,axiom,
% 9.53/5.31      ! [A: rat,D2: rat,N: nat] :
% 9.53/5.31        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 9.53/5.31          @ ( groups2906978787729119204at_rat
% 9.53/5.31            @ ^ [I3: nat] : ( plus_plus_rat @ A @ ( times_times_rat @ ( semiri681578069525770553at_rat @ I3 ) @ D2 ) )
% 9.53/5.31            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 9.53/5.31        = ( times_times_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ D2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7456_double__arith__series,axiom,
% 9.53/5.31      ! [A: int,D2: int,N: nat] :
% 9.53/5.31        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 9.53/5.31          @ ( groups3539618377306564664at_int
% 9.53/5.31            @ ^ [I3: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I3 ) @ D2 ) )
% 9.53/5.31            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 9.53/5.31        = ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ D2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7457_double__arith__series,axiom,
% 9.53/5.31      ! [A: complex,D2: complex,N: nat] :
% 9.53/5.31        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 9.53/5.31          @ ( groups2073611262835488442omplex
% 9.53/5.31            @ ^ [I3: nat] : ( plus_plus_complex @ A @ ( times_times_complex @ ( semiri8010041392384452111omplex @ I3 ) @ D2 ) )
% 9.53/5.31            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 9.53/5.31        = ( times_times_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ D2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7458_double__arith__series,axiom,
% 9.53/5.31      ! [A: nat,D2: nat,N: nat] :
% 9.53/5.31        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 9.53/5.31          @ ( groups3542108847815614940at_nat
% 9.53/5.31            @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I3 ) @ D2 ) )
% 9.53/5.31            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 9.53/5.31        = ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ D2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7459_double__arith__series,axiom,
% 9.53/5.31      ! [A: real,D2: real,N: nat] :
% 9.53/5.31        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 9.53/5.31          @ ( groups6591440286371151544t_real
% 9.53/5.31            @ ^ [I3: nat] : ( plus_plus_real @ A @ ( times_times_real @ ( semiri5074537144036343181t_real @ I3 ) @ D2 ) )
% 9.53/5.31            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 9.53/5.31        = ( times_times_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ D2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7460_double__gauss__sum,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 9.53/5.31        = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7461_double__gauss__sum,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 9.53/5.31        = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7462_double__gauss__sum,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 9.53/5.31        = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7463_double__gauss__sum,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 9.53/5.31        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7464_double__gauss__sum,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 9.53/5.31        = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7465_less__log2__of__power,axiom,
% 9.53/5.31      ! [N: nat,M: nat] :
% 9.53/5.31        ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 9.53/5.31       => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7466_le__log2__of__power,axiom,
% 9.53/5.31      ! [N: nat,M: nat] :
% 9.53/5.31        ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 9.53/5.31       => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7467_or__nat__unfold,axiom,
% 9.53/5.31      ( bit_se1412395901928357646or_nat
% 9.53/5.31      = ( ^ [M6: nat,N2: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N2 @ ( if_nat @ ( N2 = zero_zero_nat ) @ M6 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7468_double__gauss__sum__from__Suc__0,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 9.53/5.31        = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7469_double__gauss__sum__from__Suc__0,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 9.53/5.31        = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7470_double__gauss__sum__from__Suc__0,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 9.53/5.31        = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7471_double__gauss__sum__from__Suc__0,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 9.53/5.31        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7472_double__gauss__sum__from__Suc__0,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 9.53/5.31        = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7473_arith__series,axiom,
% 9.53/5.31      ! [A: int,D2: int,N: nat] :
% 9.53/5.31        ( ( groups3539618377306564664at_int
% 9.53/5.31          @ ^ [I3: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I3 ) @ D2 ) )
% 9.53/5.31          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 9.53/5.31        = ( divide_divide_int @ ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ D2 ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7474_arith__series,axiom,
% 9.53/5.31      ! [A: nat,D2: nat,N: nat] :
% 9.53/5.31        ( ( groups3542108847815614940at_nat
% 9.53/5.31          @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I3 ) @ D2 ) )
% 9.53/5.31          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 9.53/5.31        = ( divide_divide_nat @ ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ D2 ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7475_gauss__sum,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 9.53/5.31        = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7476_gauss__sum,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 9.53/5.31        = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7477_log2__of__power__less,axiom,
% 9.53/5.31      ! [M: nat,N: nat] :
% 9.53/5.31        ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.53/5.31       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 9.53/5.31         => ( ord_less_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7478_sum__gp__offset,axiom,
% 9.53/5.31      ! [X: rat,M: nat,N: nat] :
% 9.53/5.31        ( ( ( X = one_one_rat )
% 9.53/5.31         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 9.53/5.31            = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) )
% 9.53/5.31        & ( ( X != one_one_rat )
% 9.53/5.31         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 9.53/5.31            = ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ X @ M ) @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N ) ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7479_sum__gp__offset,axiom,
% 9.53/5.31      ! [X: complex,M: nat,N: nat] :
% 9.53/5.31        ( ( ( X = one_one_complex )
% 9.53/5.31         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 9.53/5.31            = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) )
% 9.53/5.31        & ( ( X != one_one_complex )
% 9.53/5.31         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 9.53/5.31            = ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ X @ M ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ ( suc @ N ) ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7480_sum__gp__offset,axiom,
% 9.53/5.31      ! [X: real,M: nat,N: nat] :
% 9.53/5.31        ( ( ( X = one_one_real )
% 9.53/5.31         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 9.53/5.31            = ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) )
% 9.53/5.31        & ( ( X != one_one_real )
% 9.53/5.31         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 9.53/5.31            = ( divide_divide_real @ ( times_times_real @ ( power_power_real @ X @ M ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( suc @ N ) ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7481_Bernoulli__inequality__even,axiom,
% 9.53/5.31      ! [N: nat,X: real] :
% 9.53/5.31        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.53/5.31       => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X ) @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7482_exp__ge__one__plus__x__over__n__power__n,axiom,
% 9.53/5.31      ! [N: nat,X: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ X )
% 9.53/5.31       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.31         => ( ord_less_eq_real @ ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ X ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7483_exp__ge__one__minus__x__over__n__power__n,axiom,
% 9.53/5.31      ! [X: real,N: nat] :
% 9.53/5.31        ( ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N ) )
% 9.53/5.31       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.31         => ( ord_less_eq_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7484_pred__bound__size__univ_H,axiom,
% 9.53/5.31      ! [T: vEBT_VEBT,N: nat,U: real,X: nat] :
% 9.53/5.31        ( ( vEBT_invar_vebt @ T @ N )
% 9.53/5.31       => ( ( U
% 9.53/5.31            = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 9.53/5.31         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_p_r_e_d2 @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7485_succ__bound__size__univ_H,axiom,
% 9.53/5.31      ! [T: vEBT_VEBT,N: nat,U: real,X: nat] :
% 9.53/5.31        ( ( vEBT_invar_vebt @ T @ N )
% 9.53/5.31       => ( ( U
% 9.53/5.31            = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 9.53/5.31         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_s_u_c_c2 @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7486_gauss__sum__from__Suc__0,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 9.53/5.31        = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7487_gauss__sum__from__Suc__0,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 9.53/5.31        = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7488_log2__of__power__le,axiom,
% 9.53/5.31      ! [M: nat,N: nat] :
% 9.53/5.31        ( ( ord_less_eq_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.53/5.31       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 9.53/5.31         => ( ord_less_eq_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7489_sum__gp,axiom,
% 9.53/5.31      ! [N: nat,M: nat,X: rat] :
% 9.53/5.31        ( ( ( ord_less_nat @ N @ M )
% 9.53/5.31         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.53/5.31            = zero_zero_rat ) )
% 9.53/5.31        & ( ~ ( ord_less_nat @ N @ M )
% 9.53/5.31         => ( ( ( X = one_one_rat )
% 9.53/5.31             => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.53/5.31                = ( semiri681578069525770553at_rat @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 9.53/5.31            & ( ( X != one_one_rat )
% 9.53/5.31             => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.53/5.31                = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ M ) @ ( power_power_rat @ X @ ( suc @ N ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7490_sum__gp,axiom,
% 9.53/5.31      ! [N: nat,M: nat,X: complex] :
% 9.53/5.31        ( ( ( ord_less_nat @ N @ M )
% 9.53/5.31         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.53/5.31            = zero_zero_complex ) )
% 9.53/5.31        & ( ~ ( ord_less_nat @ N @ M )
% 9.53/5.31         => ( ( ( X = one_one_complex )
% 9.53/5.31             => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.53/5.31                = ( semiri8010041392384452111omplex @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 9.53/5.31            & ( ( X != one_one_complex )
% 9.53/5.31             => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.53/5.31                = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X @ M ) @ ( power_power_complex @ X @ ( suc @ N ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7491_sum__gp,axiom,
% 9.53/5.31      ! [N: nat,M: nat,X: real] :
% 9.53/5.31        ( ( ( ord_less_nat @ N @ M )
% 9.53/5.31         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.53/5.31            = zero_zero_real ) )
% 9.53/5.31        & ( ~ ( ord_less_nat @ N @ M )
% 9.53/5.31         => ( ( ( X = one_one_real )
% 9.53/5.31             => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.53/5.31                = ( semiri5074537144036343181t_real @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 9.53/5.31            & ( ( X != one_one_real )
% 9.53/5.31             => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.53/5.31                = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ M ) @ ( power_power_real @ X @ ( suc @ N ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7492_insert__bound__size__univ,axiom,
% 9.53/5.31      ! [T: vEBT_VEBT,N: nat,U: real,X: nat] :
% 9.53/5.31        ( ( vEBT_invar_vebt @ T @ N )
% 9.53/5.31       => ( ( U
% 9.53/5.31            = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 9.53/5.31         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_i_n_s_e_r_t @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7493_of__nat__code__if,axiom,
% 9.53/5.31      ( semiri681578069525770553at_rat
% 9.53/5.31      = ( ^ [N2: nat] :
% 9.53/5.31            ( if_rat @ ( N2 = zero_zero_nat ) @ zero_zero_rat
% 9.53/5.31            @ ( produc6207742614233964070at_rat
% 9.53/5.31              @ ^ [M6: nat,Q4: nat] : ( if_rat @ ( Q4 = zero_zero_nat ) @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M6 ) ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M6 ) ) @ one_one_rat ) )
% 9.53/5.31              @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7494_of__nat__code__if,axiom,
% 9.53/5.31      ( semiri5074537144036343181t_real
% 9.53/5.31      = ( ^ [N2: nat] :
% 9.53/5.31            ( if_real @ ( N2 = zero_zero_nat ) @ zero_zero_real
% 9.53/5.31            @ ( produc1703576794950452218t_real
% 9.53/5.31              @ ^ [M6: nat,Q4: nat] : ( if_real @ ( Q4 = zero_zero_nat ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M6 ) ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M6 ) ) @ one_one_real ) )
% 9.53/5.31              @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7495_of__nat__code__if,axiom,
% 9.53/5.31      ( semiri1314217659103216013at_int
% 9.53/5.31      = ( ^ [N2: nat] :
% 9.53/5.31            ( if_int @ ( N2 = zero_zero_nat ) @ zero_zero_int
% 9.53/5.31            @ ( produc6840382203811409530at_int
% 9.53/5.31              @ ^ [M6: nat,Q4: nat] : ( if_int @ ( Q4 = zero_zero_nat ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ M6 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ M6 ) ) @ one_one_int ) )
% 9.53/5.31              @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7496_of__nat__code__if,axiom,
% 9.53/5.31      ( semiri8010041392384452111omplex
% 9.53/5.31      = ( ^ [N2: nat] :
% 9.53/5.31            ( if_complex @ ( N2 = zero_zero_nat ) @ zero_zero_complex
% 9.53/5.31            @ ( produc1917071388513777916omplex
% 9.53/5.31              @ ^ [M6: nat,Q4: nat] : ( if_complex @ ( Q4 = zero_zero_nat ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M6 ) ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M6 ) ) @ one_one_complex ) )
% 9.53/5.31              @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7497_of__nat__code__if,axiom,
% 9.53/5.31      ( semiri1316708129612266289at_nat
% 9.53/5.31      = ( ^ [N2: nat] :
% 9.53/5.31            ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat
% 9.53/5.31            @ ( produc6842872674320459806at_nat
% 9.53/5.31              @ ^ [M6: nat,Q4: nat] : ( if_nat @ ( Q4 = zero_zero_nat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ M6 ) ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ M6 ) ) @ one_one_nat ) )
% 9.53/5.31              @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7498_heigt__uplog__rel,axiom,
% 9.53/5.31      ! [T: vEBT_VEBT,N: nat] :
% 9.53/5.31        ( ( vEBT_invar_vebt @ T @ N )
% 9.53/5.31       => ( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ T ) )
% 9.53/5.31          = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7499_monoseq__arctan__series,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 9.53/5.31       => ( topolo6980174941875973593q_real
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7500_lemma__termdiff3,axiom,
% 9.53/5.31      ! [H2: real,Z: real,K5: real,N: nat] :
% 9.53/5.31        ( ( H2 != zero_zero_real )
% 9.53/5.31       => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ K5 )
% 9.53/5.31         => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ Z @ H2 ) ) @ K5 )
% 9.53/5.31           => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ N ) @ ( power_power_real @ Z @ N ) ) @ H2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V7735802525324610683m_real @ H2 ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7501_lemma__termdiff3,axiom,
% 9.53/5.31      ! [H2: complex,Z: complex,K5: real,N: nat] :
% 9.53/5.31        ( ( H2 != zero_zero_complex )
% 9.53/5.31       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ K5 )
% 9.53/5.31         => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ Z @ H2 ) ) @ K5 )
% 9.53/5.31           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ N ) @ ( power_power_complex @ Z @ N ) ) @ H2 ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V1022390504157884413omplex @ H2 ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7502_ln__series,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.31       => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 9.53/5.31         => ( ( ln_ln_real @ X )
% 9.53/5.31            = ( suminf_real
% 9.53/5.31              @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) @ ( power_power_real @ ( minus_minus_real @ X @ one_one_real ) @ ( suc @ N2 ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7503_int__eq__iff__numeral,axiom,
% 9.53/5.31      ! [M: nat,V: num] :
% 9.53/5.31        ( ( ( semiri1314217659103216013at_int @ M )
% 9.53/5.31          = ( numeral_numeral_int @ V ) )
% 9.53/5.31        = ( M
% 9.53/5.31          = ( numeral_numeral_nat @ V ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7504_negative__zless,axiom,
% 9.53/5.31      ! [N: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7505_powser__zero,axiom,
% 9.53/5.31      ! [F: nat > complex] :
% 9.53/5.31        ( ( suminf_complex
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) ) )
% 9.53/5.31        = ( F @ zero_zero_nat ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7506_powser__zero,axiom,
% 9.53/5.31      ! [F: nat > real] :
% 9.53/5.31        ( ( suminf_real
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) ) )
% 9.53/5.31        = ( F @ zero_zero_nat ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7507_int__diff__cases,axiom,
% 9.53/5.31      ! [Z: int] :
% 9.53/5.31        ~ ! [M4: nat,N3: nat] :
% 9.53/5.31            ( Z
% 9.53/5.31           != ( minus_minus_int @ ( semiri1314217659103216013at_int @ M4 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7508_int__ops_I3_J,axiom,
% 9.53/5.31      ! [N: num] :
% 9.53/5.31        ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 9.53/5.31        = ( numeral_numeral_int @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7509_complex__mod__minus__le__complex__mod,axiom,
% 9.53/5.31      ! [X: complex] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7510_int__of__nat__induct,axiom,
% 9.53/5.31      ! [P: int > $o,Z: int] :
% 9.53/5.31        ( ! [N3: nat] : ( P @ ( semiri1314217659103216013at_int @ N3 ) )
% 9.53/5.31       => ( ! [N3: nat] : ( P @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) )
% 9.53/5.31         => ( P @ Z ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7511_int__cases,axiom,
% 9.53/5.31      ! [Z: int] :
% 9.53/5.31        ( ! [N3: nat] :
% 9.53/5.31            ( Z
% 9.53/5.31           != ( semiri1314217659103216013at_int @ N3 ) )
% 9.53/5.31       => ~ ! [N3: nat] :
% 9.53/5.31              ( Z
% 9.53/5.31             != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7512_nat__int__comparison_I2_J,axiom,
% 9.53/5.31      ( ord_less_nat
% 9.53/5.31      = ( ^ [A3: nat,B4: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7513_nat__int__comparison_I3_J,axiom,
% 9.53/5.31      ( ord_less_eq_nat
% 9.53/5.31      = ( ^ [A3: nat,B4: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7514_zle__int,axiom,
% 9.53/5.31      ! [M: nat,N: nat] :
% 9.53/5.31        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 9.53/5.31        = ( ord_less_eq_nat @ M @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7515_int__ops_I2_J,axiom,
% 9.53/5.31      ( ( semiri1314217659103216013at_int @ one_one_nat )
% 9.53/5.31      = one_one_int ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7516_complex__mod__triangle__ineq2,axiom,
% 9.53/5.31      ! [B: complex,A: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ B @ A ) ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ A ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7517_int__ops_I5_J,axiom,
% 9.53/5.31      ! [A: nat,B: nat] :
% 9.53/5.31        ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B ) )
% 9.53/5.31        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7518_int__plus,axiom,
% 9.53/5.31      ! [N: nat,M: nat] :
% 9.53/5.31        ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N @ M ) )
% 9.53/5.31        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7519_zadd__int__left,axiom,
% 9.53/5.31      ! [M: nat,N: nat,Z: int] :
% 9.53/5.31        ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ Z ) )
% 9.53/5.31        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) ) @ Z ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7520_int__ops_I7_J,axiom,
% 9.53/5.31      ! [A: nat,B: nat] :
% 9.53/5.31        ( ( semiri1314217659103216013at_int @ ( times_times_nat @ A @ B ) )
% 9.53/5.31        = ( times_times_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7521_zdiv__int,axiom,
% 9.53/5.31      ! [A: nat,B: nat] :
% 9.53/5.31        ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ A @ B ) )
% 9.53/5.31        = ( divide_divide_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7522_zmod__int,axiom,
% 9.53/5.31      ! [A: nat,B: nat] :
% 9.53/5.31        ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ A @ B ) )
% 9.53/5.31        = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7523_nat__less__as__int,axiom,
% 9.53/5.31      ( ord_less_nat
% 9.53/5.31      = ( ^ [A3: nat,B4: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7524_nat__leq__as__int,axiom,
% 9.53/5.31      ( ord_less_eq_nat
% 9.53/5.31      = ( ^ [A3: nat,B4: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7525_int__cases4,axiom,
% 9.53/5.31      ! [M: int] :
% 9.53/5.31        ( ! [N3: nat] :
% 9.53/5.31            ( M
% 9.53/5.31           != ( semiri1314217659103216013at_int @ N3 ) )
% 9.53/5.31       => ~ ! [N3: nat] :
% 9.53/5.31              ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 9.53/5.31             => ( M
% 9.53/5.31               != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7526_int__Suc,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 9.53/5.31        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7527_int__ops_I4_J,axiom,
% 9.53/5.31      ! [A: nat] :
% 9.53/5.31        ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 9.53/5.31        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7528_zless__iff__Suc__zadd,axiom,
% 9.53/5.31      ( ord_less_int
% 9.53/5.31      = ( ^ [W2: int,Z4: int] :
% 9.53/5.31          ? [N2: nat] :
% 9.53/5.31            ( Z4
% 9.53/5.31            = ( plus_plus_int @ W2 @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7529_norm__exp,axiom,
% 9.53/5.31      ! [X: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ X ) ) @ ( exp_real @ ( real_V7735802525324610683m_real @ X ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7530_norm__exp,axiom,
% 9.53/5.31      ! [X: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ X ) ) @ ( exp_real @ ( real_V1022390504157884413omplex @ X ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7531_pos__int__cases,axiom,
% 9.53/5.31      ! [K: int] :
% 9.53/5.31        ( ( ord_less_int @ zero_zero_int @ K )
% 9.53/5.31       => ~ ! [N3: nat] :
% 9.53/5.31              ( ( K
% 9.53/5.31                = ( semiri1314217659103216013at_int @ N3 ) )
% 9.53/5.31             => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7532_zero__less__imp__eq__int,axiom,
% 9.53/5.31      ! [K: int] :
% 9.53/5.31        ( ( ord_less_int @ zero_zero_int @ K )
% 9.53/5.31       => ? [N3: nat] :
% 9.53/5.31            ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 9.53/5.31            & ( K
% 9.53/5.31              = ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7533_int__cases3,axiom,
% 9.53/5.31      ! [K: int] :
% 9.53/5.31        ( ( K != zero_zero_int )
% 9.53/5.31       => ( ! [N3: nat] :
% 9.53/5.31              ( ( K
% 9.53/5.31                = ( semiri1314217659103216013at_int @ N3 ) )
% 9.53/5.31             => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) )
% 9.53/5.31         => ~ ! [N3: nat] :
% 9.53/5.31                ( ( K
% 9.53/5.31                  = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 9.53/5.31               => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7534_zmult__zless__mono2__lemma,axiom,
% 9.53/5.31      ! [I2: int,J: int,K: nat] :
% 9.53/5.31        ( ( ord_less_int @ I2 @ J )
% 9.53/5.31       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 9.53/5.31         => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I2 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7535_not__zle__0__negative,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7536_negative__zless__0,axiom,
% 9.53/5.31      ! [N: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ zero_zero_int ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7537_negD,axiom,
% 9.53/5.31      ! [X: int] :
% 9.53/5.31        ( ( ord_less_int @ X @ zero_zero_int )
% 9.53/5.31       => ? [N3: nat] :
% 9.53/5.31            ( X
% 9.53/5.31            = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7538_int__ops_I6_J,axiom,
% 9.53/5.31      ! [A: nat,B: nat] :
% 9.53/5.31        ( ( ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 9.53/5.31         => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 9.53/5.31            = zero_zero_int ) )
% 9.53/5.31        & ( ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 9.53/5.31         => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 9.53/5.31            = ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7539_neg__int__cases,axiom,
% 9.53/5.31      ! [K: int] :
% 9.53/5.31        ( ( ord_less_int @ K @ zero_zero_int )
% 9.53/5.31       => ~ ! [N3: nat] :
% 9.53/5.31              ( ( K
% 9.53/5.31                = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 9.53/5.31             => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7540_zdiff__int__split,axiom,
% 9.53/5.31      ! [P: int > $o,X: nat,Y2: nat] :
% 9.53/5.31        ( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X @ Y2 ) ) )
% 9.53/5.31        = ( ( ( ord_less_eq_nat @ Y2 @ X )
% 9.53/5.31           => ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y2 ) ) ) )
% 9.53/5.31          & ( ( ord_less_nat @ X @ Y2 )
% 9.53/5.31           => ( P @ zero_zero_int ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7541_monoseq__realpow,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.31       => ( ( ord_less_eq_real @ X @ one_one_real )
% 9.53/5.31         => ( topolo6980174941875973593q_real @ ( power_power_real @ X ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7542_exp__bound__half,axiom,
% 9.53/5.31      ! [Z: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7543_exp__bound__half,axiom,
% 9.53/5.31      ! [Z: complex] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7544_exp__bound__lemma,axiom,
% 9.53/5.31      ! [Z: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ Z ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( real_V7735802525324610683m_real @ Z ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7545_exp__bound__lemma,axiom,
% 9.53/5.31      ! [Z: complex] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ Z ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7546_ceiling__log__nat__eq__if,axiom,
% 9.53/5.31      ! [B: nat,N: nat,K: nat] :
% 9.53/5.31        ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 9.53/5.31       => ( ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 9.53/5.31         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 9.53/5.31           => ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 9.53/5.31              = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7547_arctan__series,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 9.53/5.31       => ( ( arctan @ X )
% 9.53/5.31          = ( suminf_real
% 9.53/5.31            @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7548_ceiling__log__nat__eq__powr__iff,axiom,
% 9.53/5.31      ! [B: nat,K: nat,N: nat] :
% 9.53/5.31        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 9.53/5.31       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 9.53/5.31         => ( ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 9.53/5.31              = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) )
% 9.53/5.31            = ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 9.53/5.31              & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7549_norm__divide__numeral,axiom,
% 9.53/5.31      ! [A: real,W: num] :
% 9.53/5.31        ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ W ) ) )
% 9.53/5.31        = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7550_norm__divide__numeral,axiom,
% 9.53/5.31      ! [A: complex,W: num] :
% 9.53/5.31        ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 9.53/5.31        = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7551_norm__mult__numeral2,axiom,
% 9.53/5.31      ! [A: real,W: num] :
% 9.53/5.31        ( ( real_V7735802525324610683m_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) )
% 9.53/5.31        = ( times_times_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7552_norm__mult__numeral2,axiom,
% 9.53/5.31      ! [A: complex,W: num] :
% 9.53/5.31        ( ( real_V1022390504157884413omplex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 9.53/5.31        = ( times_times_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7553_norm__mult__numeral1,axiom,
% 9.53/5.31      ! [W: num,A: real] :
% 9.53/5.31        ( ( real_V7735802525324610683m_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 9.53/5.31        = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V7735802525324610683m_real @ A ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7554_norm__mult__numeral1,axiom,
% 9.53/5.31      ! [W: num,A: complex] :
% 9.53/5.31        ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 9.53/5.31        = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V1022390504157884413omplex @ A ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7555_norm__neg__numeral,axiom,
% 9.53/5.31      ! [W: num] :
% 9.53/5.31        ( ( real_V7735802525324610683m_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 9.53/5.31        = ( numeral_numeral_real @ W ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7556_norm__neg__numeral,axiom,
% 9.53/5.31      ! [W: num] :
% 9.53/5.31        ( ( real_V1022390504157884413omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 9.53/5.31        = ( numeral_numeral_real @ W ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7557_norm__le__zero__iff,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X ) @ zero_zero_real )
% 9.53/5.31        = ( X = zero_zero_real ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7558_norm__le__zero__iff,axiom,
% 9.53/5.31      ! [X: complex] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ zero_zero_real )
% 9.53/5.31        = ( X = zero_zero_complex ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7559_norm__one,axiom,
% 9.53/5.31      ( ( real_V7735802525324610683m_real @ one_one_real )
% 9.53/5.31      = one_one_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7560_norm__one,axiom,
% 9.53/5.31      ( ( real_V1022390504157884413omplex @ one_one_complex )
% 9.53/5.31      = one_one_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7561_norm__numeral,axiom,
% 9.53/5.31      ! [W: num] :
% 9.53/5.31        ( ( real_V7735802525324610683m_real @ ( numeral_numeral_real @ W ) )
% 9.53/5.31        = ( numeral_numeral_real @ W ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7562_norm__numeral,axiom,
% 9.53/5.31      ! [W: num] :
% 9.53/5.31        ( ( real_V1022390504157884413omplex @ ( numera6690914467698888265omplex @ W ) )
% 9.53/5.31        = ( numeral_numeral_real @ W ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7563_zero__less__norm__iff,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_real @ zero_zero_real @ ( real_V7735802525324610683m_real @ X ) )
% 9.53/5.31        = ( X != zero_zero_real ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7564_zero__less__norm__iff,axiom,
% 9.53/5.31      ! [X: complex] :
% 9.53/5.31        ( ( ord_less_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X ) )
% 9.53/5.31        = ( X != zero_zero_complex ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7565_norm__minus__commute,axiom,
% 9.53/5.31      ! [A: complex,B: complex] :
% 9.53/5.31        ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) )
% 9.53/5.31        = ( real_V1022390504157884413omplex @ ( minus_minus_complex @ B @ A ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7566_norm__not__less__zero,axiom,
% 9.53/5.31      ! [X: complex] :
% 9.53/5.31        ~ ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ zero_zero_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7567_norm__ge__zero,axiom,
% 9.53/5.31      ! [X: complex] : ( ord_less_eq_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7568_norm__mult,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y2 ) )
% 9.53/5.31        = ( times_times_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7569_norm__mult,axiom,
% 9.53/5.31      ! [X: complex,Y2: complex] :
% 9.53/5.31        ( ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y2 ) )
% 9.53/5.31        = ( times_times_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7570_norm__divide,axiom,
% 9.53/5.31      ! [A: real,B: real] :
% 9.53/5.31        ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 9.53/5.31        = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7571_norm__divide,axiom,
% 9.53/5.31      ! [A: complex,B: complex] :
% 9.53/5.31        ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 9.53/5.31        = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7572_sum__norm__le,axiom,
% 9.53/5.31      ! [S2: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > complex,G: product_prod_nat_nat > real] :
% 9.53/5.31        ( ! [X3: product_prod_nat_nat] :
% 9.53/5.31            ( ( member8440522571783428010at_nat @ X3 @ S2 )
% 9.53/5.31           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X3 ) ) @ ( G @ X3 ) ) )
% 9.53/5.31       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups6381953495645901045omplex @ F @ S2 ) ) @ ( groups4567486121110086003t_real @ G @ S2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7573_sum__norm__le,axiom,
% 9.53/5.31      ! [S2: set_real,F: real > complex,G: real > real] :
% 9.53/5.31        ( ! [X3: real] :
% 9.53/5.31            ( ( member_real @ X3 @ S2 )
% 9.53/5.31           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X3 ) ) @ ( G @ X3 ) ) )
% 9.53/5.31       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups5754745047067104278omplex @ F @ S2 ) ) @ ( groups8097168146408367636l_real @ G @ S2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7574_sum__norm__le,axiom,
% 9.53/5.31      ! [S2: set_int,F: int > complex,G: int > real] :
% 9.53/5.31        ( ! [X3: int] :
% 9.53/5.31            ( ( member_int @ X3 @ S2 )
% 9.53/5.31           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X3 ) ) @ ( G @ X3 ) ) )
% 9.53/5.31       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups3049146728041665814omplex @ F @ S2 ) ) @ ( groups8778361861064173332t_real @ G @ S2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7575_sum__norm__le,axiom,
% 9.53/5.31      ! [S2: set_nat,F: nat > complex,G: nat > real] :
% 9.53/5.31        ( ! [X3: nat] :
% 9.53/5.31            ( ( member_nat @ X3 @ S2 )
% 9.53/5.31           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X3 ) ) @ ( G @ X3 ) ) )
% 9.53/5.31       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ S2 ) ) @ ( groups6591440286371151544t_real @ G @ S2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7576_sum__norm__le,axiom,
% 9.53/5.31      ! [S2: set_complex,F: complex > complex,G: complex > real] :
% 9.53/5.31        ( ! [X3: complex] :
% 9.53/5.31            ( ( member_complex @ X3 @ S2 )
% 9.53/5.31           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X3 ) ) @ ( G @ X3 ) ) )
% 9.53/5.31       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ S2 ) ) @ ( groups5808333547571424918x_real @ G @ S2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7577_sum__norm__le,axiom,
% 9.53/5.31      ! [S2: set_nat,F: nat > real,G: nat > real] :
% 9.53/5.31        ( ! [X3: nat] :
% 9.53/5.31            ( ( member_nat @ X3 @ S2 )
% 9.53/5.31           => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ X3 ) ) @ ( G @ X3 ) ) )
% 9.53/5.31       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ S2 ) ) @ ( groups6591440286371151544t_real @ G @ S2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7578_norm__power,axiom,
% 9.53/5.31      ! [X: real,N: nat] :
% 9.53/5.31        ( ( real_V7735802525324610683m_real @ ( power_power_real @ X @ N ) )
% 9.53/5.31        = ( power_power_real @ ( real_V7735802525324610683m_real @ X ) @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7579_norm__power,axiom,
% 9.53/5.31      ! [X: complex,N: nat] :
% 9.53/5.31        ( ( real_V1022390504157884413omplex @ ( power_power_complex @ X @ N ) )
% 9.53/5.31        = ( power_power_real @ ( real_V1022390504157884413omplex @ X ) @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7580_norm__sum,axiom,
% 9.53/5.31      ! [F: nat > complex,A2: set_nat] :
% 9.53/5.31        ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ A2 ) )
% 9.53/5.31        @ ( groups6591440286371151544t_real
% 9.53/5.31          @ ^ [I3: nat] : ( real_V1022390504157884413omplex @ ( F @ I3 ) )
% 9.53/5.31          @ A2 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7581_norm__sum,axiom,
% 9.53/5.31      ! [F: complex > complex,A2: set_complex] :
% 9.53/5.31        ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ A2 ) )
% 9.53/5.31        @ ( groups5808333547571424918x_real
% 9.53/5.31          @ ^ [I3: complex] : ( real_V1022390504157884413omplex @ ( F @ I3 ) )
% 9.53/5.31          @ A2 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7582_norm__sum,axiom,
% 9.53/5.31      ! [F: nat > real,A2: set_nat] :
% 9.53/5.31        ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 9.53/5.31        @ ( groups6591440286371151544t_real
% 9.53/5.31          @ ^ [I3: nat] : ( real_V7735802525324610683m_real @ ( F @ I3 ) )
% 9.53/5.31          @ A2 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7583_norm__uminus__minus,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ Y2 ) )
% 9.53/5.31        = ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7584_norm__uminus__minus,axiom,
% 9.53/5.31      ! [X: complex,Y2: complex] :
% 9.53/5.31        ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X ) @ Y2 ) )
% 9.53/5.31        = ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7585_nonzero__norm__divide,axiom,
% 9.53/5.31      ! [B: real,A: real] :
% 9.53/5.31        ( ( B != zero_zero_real )
% 9.53/5.31       => ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 9.53/5.31          = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7586_nonzero__norm__divide,axiom,
% 9.53/5.31      ! [B: complex,A: complex] :
% 9.53/5.31        ( ( B != zero_zero_complex )
% 9.53/5.31       => ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 9.53/5.31          = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7587_power__eq__imp__eq__norm,axiom,
% 9.53/5.31      ! [W: real,N: nat,Z: real] :
% 9.53/5.31        ( ( ( power_power_real @ W @ N )
% 9.53/5.31          = ( power_power_real @ Z @ N ) )
% 9.53/5.31       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.31         => ( ( real_V7735802525324610683m_real @ W )
% 9.53/5.31            = ( real_V7735802525324610683m_real @ Z ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7588_power__eq__imp__eq__norm,axiom,
% 9.53/5.31      ! [W: complex,N: nat,Z: complex] :
% 9.53/5.31        ( ( ( power_power_complex @ W @ N )
% 9.53/5.31          = ( power_power_complex @ Z @ N ) )
% 9.53/5.31       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.31         => ( ( real_V1022390504157884413omplex @ W )
% 9.53/5.31            = ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7589_norm__mult__less,axiom,
% 9.53/5.31      ! [X: real,R: real,Y2: real,S3: real] :
% 9.53/5.31        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ R )
% 9.53/5.31       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y2 ) @ S3 )
% 9.53/5.31         => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y2 ) ) @ ( times_times_real @ R @ S3 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7590_norm__mult__less,axiom,
% 9.53/5.31      ! [X: complex,R: real,Y2: complex,S3: real] :
% 9.53/5.31        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ R )
% 9.53/5.31       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y2 ) @ S3 )
% 9.53/5.31         => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y2 ) ) @ ( times_times_real @ R @ S3 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7591_norm__mult__ineq,axiom,
% 9.53/5.31      ! [X: real,Y2: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y2 ) ) @ ( times_times_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7592_norm__mult__ineq,axiom,
% 9.53/5.31      ! [X: complex,Y2: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y2 ) ) @ ( times_times_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7593_norm__triangle__lt,axiom,
% 9.53/5.31      ! [X: real,Y2: real,E: real] :
% 9.53/5.31        ( ( ord_less_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y2 ) ) @ E )
% 9.53/5.31       => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y2 ) ) @ E ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7594_norm__triangle__lt,axiom,
% 9.53/5.31      ! [X: complex,Y2: complex,E: real] :
% 9.53/5.31        ( ( ord_less_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y2 ) ) @ E )
% 9.53/5.31       => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y2 ) ) @ E ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7595_norm__add__less,axiom,
% 9.53/5.31      ! [X: real,R: real,Y2: real,S3: real] :
% 9.53/5.31        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ R )
% 9.53/5.31       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y2 ) @ S3 )
% 9.53/5.31         => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y2 ) ) @ ( plus_plus_real @ R @ S3 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7596_norm__add__less,axiom,
% 9.53/5.31      ! [X: complex,R: real,Y2: complex,S3: real] :
% 9.53/5.31        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ R )
% 9.53/5.31       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y2 ) @ S3 )
% 9.53/5.31         => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y2 ) ) @ ( plus_plus_real @ R @ S3 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7597_norm__triangle__mono,axiom,
% 9.53/5.31      ! [A: real,R: real,B: real,S3: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ A ) @ R )
% 9.53/5.31       => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ S3 )
% 9.53/5.31         => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ R @ S3 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7598_norm__triangle__mono,axiom,
% 9.53/5.31      ! [A: complex,R: real,B: complex,S3: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ A ) @ R )
% 9.53/5.31       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ S3 )
% 9.53/5.31         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ ( plus_plus_real @ R @ S3 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7599_norm__triangle__ineq,axiom,
% 9.53/5.31      ! [X: real,Y2: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y2 ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7600_norm__triangle__ineq,axiom,
% 9.53/5.31      ! [X: complex,Y2: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y2 ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7601_norm__triangle__le,axiom,
% 9.53/5.31      ! [X: real,Y2: real,E: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y2 ) ) @ E )
% 9.53/5.31       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y2 ) ) @ E ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7602_norm__triangle__le,axiom,
% 9.53/5.31      ! [X: complex,Y2: complex,E: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y2 ) ) @ E )
% 9.53/5.31       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y2 ) ) @ E ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7603_norm__add__leD,axiom,
% 9.53/5.31      ! [A: real,B: real,C: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ C )
% 9.53/5.31       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ C ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7604_norm__add__leD,axiom,
% 9.53/5.31      ! [A: complex,B: complex,C: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ C )
% 9.53/5.31       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ C ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7605_norm__power__ineq,axiom,
% 9.53/5.31      ! [X: real,N: nat] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( power_power_real @ X @ N ) ) @ ( power_power_real @ ( real_V7735802525324610683m_real @ X ) @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7606_norm__power__ineq,axiom,
% 9.53/5.31      ! [X: complex,N: nat] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( power_power_complex @ X @ N ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ X ) @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7607_norm__diff__triangle__less,axiom,
% 9.53/5.31      ! [X: complex,Y2: complex,E1: real,Z: complex,E22: real] :
% 9.53/5.31        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y2 ) ) @ E1 )
% 9.53/5.31       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y2 @ Z ) ) @ E22 )
% 9.53/5.31         => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7608_norm__triangle__sub,axiom,
% 9.53/5.31      ! [X: complex,Y2: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Y2 ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7609_norm__triangle__ineq4,axiom,
% 9.53/5.31      ! [A: complex,B: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7610_norm__diff__triangle__le,axiom,
% 9.53/5.31      ! [X: complex,Y2: complex,E1: real,Z: complex,E22: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y2 ) ) @ E1 )
% 9.53/5.31       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y2 @ Z ) ) @ E22 )
% 9.53/5.31         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7611_norm__triangle__le__diff,axiom,
% 9.53/5.31      ! [X: complex,Y2: complex,E: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y2 ) ) @ E )
% 9.53/5.31       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y2 ) ) @ E ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7612_norm__diff__ineq,axiom,
% 9.53/5.31      ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7613_norm__diff__ineq,axiom,
% 9.53/5.31      ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7614_norm__triangle__ineq2,axiom,
% 9.53/5.31      ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7615_power__eq__1__iff,axiom,
% 9.53/5.31      ! [W: real,N: nat] :
% 9.53/5.31        ( ( ( power_power_real @ W @ N )
% 9.53/5.31          = one_one_real )
% 9.53/5.31       => ( ( ( real_V7735802525324610683m_real @ W )
% 9.53/5.31            = one_one_real )
% 9.53/5.31          | ( N = zero_zero_nat ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7616_power__eq__1__iff,axiom,
% 9.53/5.31      ! [W: complex,N: nat] :
% 9.53/5.31        ( ( ( power_power_complex @ W @ N )
% 9.53/5.31          = one_one_complex )
% 9.53/5.31       => ( ( ( real_V1022390504157884413omplex @ W )
% 9.53/5.31            = one_one_real )
% 9.53/5.31          | ( N = zero_zero_nat ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7617_norm__diff__triangle__ineq,axiom,
% 9.53/5.31      ! [A: real,B: real,C: real,D2: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D2 ) ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ C ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ B @ D2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7618_norm__diff__triangle__ineq,axiom,
% 9.53/5.31      ! [A: complex,B: complex,C: complex,D2: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ ( plus_plus_complex @ C @ D2 ) ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ C ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ B @ D2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7619_norm__triangle__ineq3,axiom,
% 9.53/5.31      ! [A: complex,B: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7620_square__norm__one,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.53/5.31          = one_one_real )
% 9.53/5.31       => ( ( real_V7735802525324610683m_real @ X )
% 9.53/5.31          = one_one_real ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7621_square__norm__one,axiom,
% 9.53/5.31      ! [X: complex] :
% 9.53/5.31        ( ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.53/5.31          = one_one_complex )
% 9.53/5.31       => ( ( real_V1022390504157884413omplex @ X )
% 9.53/5.31          = one_one_real ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7622_norm__power__diff,axiom,
% 9.53/5.31      ! [Z: real,W: real,M: nat] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 9.53/5.31       => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ W ) @ one_one_real )
% 9.53/5.31         => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( power_power_real @ Z @ M ) @ ( power_power_real @ W @ M ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Z @ W ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7623_norm__power__diff,axiom,
% 9.53/5.31      ! [Z: complex,W: complex,M: nat] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 9.53/5.31       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ W ) @ one_one_real )
% 9.53/5.31         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( power_power_complex @ Z @ M ) @ ( power_power_complex @ W @ M ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Z @ W ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7624_suminf__geometric,axiom,
% 9.53/5.31      ! [C: real] :
% 9.53/5.31        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 9.53/5.31       => ( ( suminf_real @ ( power_power_real @ C ) )
% 9.53/5.31          = ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7625_suminf__geometric,axiom,
% 9.53/5.31      ! [C: complex] :
% 9.53/5.31        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 9.53/5.31       => ( ( suminf_complex @ ( power_power_complex @ C ) )
% 9.53/5.31          = ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7626_pi__series,axiom,
% 9.53/5.31      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 9.53/5.31      = ( suminf_real
% 9.53/5.31        @ ^ [K3: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7627_lemma__termdiff2,axiom,
% 9.53/5.31      ! [H2: rat,Z: rat,N: nat] :
% 9.53/5.31        ( ( H2 != zero_zero_rat )
% 9.53/5.31       => ( ( minus_minus_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ N ) @ ( power_power_rat @ Z @ N ) ) @ H2 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 9.53/5.31          = ( times_times_rat @ H2
% 9.53/5.31            @ ( groups2906978787729119204at_rat
% 9.53/5.31              @ ^ [P4: nat] :
% 9.53/5.31                  ( groups2906978787729119204at_rat
% 9.53/5.31                  @ ^ [Q4: nat] : ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ Q4 ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q4 ) ) )
% 9.53/5.31                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P4 ) ) )
% 9.53/5.31              @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7628_lemma__termdiff2,axiom,
% 9.53/5.31      ! [H2: complex,Z: complex,N: nat] :
% 9.53/5.31        ( ( H2 != zero_zero_complex )
% 9.53/5.31       => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ N ) @ ( power_power_complex @ Z @ N ) ) @ H2 ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 9.53/5.31          = ( times_times_complex @ H2
% 9.53/5.31            @ ( groups2073611262835488442omplex
% 9.53/5.31              @ ^ [P4: nat] :
% 9.53/5.31                  ( groups2073611262835488442omplex
% 9.53/5.31                  @ ^ [Q4: nat] : ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ Q4 ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q4 ) ) )
% 9.53/5.31                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P4 ) ) )
% 9.53/5.31              @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7629_lemma__termdiff2,axiom,
% 9.53/5.31      ! [H2: real,Z: real,N: nat] :
% 9.53/5.31        ( ( H2 != zero_zero_real )
% 9.53/5.31       => ( ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ N ) @ ( power_power_real @ Z @ N ) ) @ H2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 9.53/5.31          = ( times_times_real @ H2
% 9.53/5.31            @ ( groups6591440286371151544t_real
% 9.53/5.31              @ ^ [P4: nat] :
% 9.53/5.31                  ( groups6591440286371151544t_real
% 9.53/5.31                  @ ^ [Q4: nat] : ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ Q4 ) @ ( power_power_real @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q4 ) ) )
% 9.53/5.31                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P4 ) ) )
% 9.53/5.31              @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7630_summable__arctan__series,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 9.53/5.31       => ( summable_real
% 9.53/5.31          @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7631_ceiling__log__eq__powr__iff,axiom,
% 9.53/5.31      ! [X: real,B: real,K: nat] :
% 9.53/5.31        ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.31       => ( ( ord_less_real @ one_one_real @ B )
% 9.53/5.31         => ( ( ( archim7802044766580827645g_real @ ( log @ B @ X ) )
% 9.53/5.31              = ( plus_plus_int @ ( semiri1314217659103216013at_int @ K ) @ one_one_int ) )
% 9.53/5.31            = ( ( ord_less_real @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ X )
% 9.53/5.31              & ( ord_less_eq_real @ X @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7632_lessThan__iff,axiom,
% 9.53/5.31      ! [I2: rat,K: rat] :
% 9.53/5.31        ( ( member_rat @ I2 @ ( set_ord_lessThan_rat @ K ) )
% 9.53/5.31        = ( ord_less_rat @ I2 @ K ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7633_lessThan__iff,axiom,
% 9.53/5.31      ! [I2: num,K: num] :
% 9.53/5.31        ( ( member_num @ I2 @ ( set_ord_lessThan_num @ K ) )
% 9.53/5.31        = ( ord_less_num @ I2 @ K ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7634_lessThan__iff,axiom,
% 9.53/5.31      ! [I2: int,K: int] :
% 9.53/5.31        ( ( member_int @ I2 @ ( set_ord_lessThan_int @ K ) )
% 9.53/5.31        = ( ord_less_int @ I2 @ K ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7635_lessThan__iff,axiom,
% 9.53/5.31      ! [I2: nat,K: nat] :
% 9.53/5.31        ( ( member_nat @ I2 @ ( set_ord_lessThan_nat @ K ) )
% 9.53/5.31        = ( ord_less_nat @ I2 @ K ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7636_lessThan__iff,axiom,
% 9.53/5.31      ! [I2: real,K: real] :
% 9.53/5.31        ( ( member_real @ I2 @ ( set_or5984915006950818249n_real @ K ) )
% 9.53/5.31        = ( ord_less_real @ I2 @ K ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7637_powr__one__eq__one,axiom,
% 9.53/5.31      ! [A: real] :
% 9.53/5.31        ( ( powr_real @ one_one_real @ A )
% 9.53/5.31        = one_one_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7638_summable__iff__shift,axiom,
% 9.53/5.31      ! [F: nat > real,K: nat] :
% 9.53/5.31        ( ( summable_real
% 9.53/5.31          @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ K ) ) )
% 9.53/5.31        = ( summable_real @ F ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7639_lessThan__subset__iff,axiom,
% 9.53/5.31      ! [X: num,Y2: num] :
% 9.53/5.31        ( ( ord_less_eq_set_num @ ( set_ord_lessThan_num @ X ) @ ( set_ord_lessThan_num @ Y2 ) )
% 9.53/5.31        = ( ord_less_eq_num @ X @ Y2 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7640_lessThan__subset__iff,axiom,
% 9.53/5.31      ! [X: int,Y2: int] :
% 9.53/5.31        ( ( ord_less_eq_set_int @ ( set_ord_lessThan_int @ X ) @ ( set_ord_lessThan_int @ Y2 ) )
% 9.53/5.31        = ( ord_less_eq_int @ X @ Y2 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7641_lessThan__subset__iff,axiom,
% 9.53/5.31      ! [X: nat,Y2: nat] :
% 9.53/5.31        ( ( ord_less_eq_set_nat @ ( set_ord_lessThan_nat @ X ) @ ( set_ord_lessThan_nat @ Y2 ) )
% 9.53/5.31        = ( ord_less_eq_nat @ X @ Y2 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7642_lessThan__subset__iff,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_set_real @ ( set_or5984915006950818249n_real @ X ) @ ( set_or5984915006950818249n_real @ Y2 ) )
% 9.53/5.31        = ( ord_less_eq_real @ X @ Y2 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7643_powr__zero__eq__one,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ( X = zero_zero_real )
% 9.53/5.31         => ( ( powr_real @ X @ zero_zero_real )
% 9.53/5.31            = zero_zero_real ) )
% 9.53/5.31        & ( ( X != zero_zero_real )
% 9.53/5.31         => ( ( powr_real @ X @ zero_zero_real )
% 9.53/5.31            = one_one_real ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7644_powr__gt__zero,axiom,
% 9.53/5.31      ! [X: real,A: real] :
% 9.53/5.31        ( ( ord_less_real @ zero_zero_real @ ( powr_real @ X @ A ) )
% 9.53/5.31        = ( X != zero_zero_real ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7645_powr__nonneg__iff,axiom,
% 9.53/5.31      ! [A: real,X: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( powr_real @ A @ X ) @ zero_zero_real )
% 9.53/5.31        = ( A = zero_zero_real ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7646_powr__less__cancel__iff,axiom,
% 9.53/5.31      ! [X: real,A: real,B: real] :
% 9.53/5.31        ( ( ord_less_real @ one_one_real @ X )
% 9.53/5.31       => ( ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 9.53/5.31          = ( ord_less_real @ A @ B ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7647_summable__cmult__iff,axiom,
% 9.53/5.31      ! [C: complex,F: nat > complex] :
% 9.53/5.31        ( ( summable_complex
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) ) )
% 9.53/5.31        = ( ( C = zero_zero_complex )
% 9.53/5.31          | ( summable_complex @ F ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7648_summable__cmult__iff,axiom,
% 9.53/5.31      ! [C: real,F: nat > real] :
% 9.53/5.31        ( ( summable_real
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) ) )
% 9.53/5.31        = ( ( C = zero_zero_real )
% 9.53/5.31          | ( summable_real @ F ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7649_summable__divide__iff,axiom,
% 9.53/5.31      ! [F: nat > complex,C: complex] :
% 9.53/5.31        ( ( summable_complex
% 9.53/5.31          @ ^ [N2: nat] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ C ) )
% 9.53/5.31        = ( ( C = zero_zero_complex )
% 9.53/5.31          | ( summable_complex @ F ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7650_summable__divide__iff,axiom,
% 9.53/5.31      ! [F: nat > real,C: real] :
% 9.53/5.31        ( ( summable_real
% 9.53/5.31          @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ C ) )
% 9.53/5.31        = ( ( C = zero_zero_real )
% 9.53/5.31          | ( summable_real @ F ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7651_sum_OlessThan__Suc,axiom,
% 9.53/5.31      ! [G: nat > rat,N: nat] :
% 9.53/5.31        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 9.53/5.31        = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7652_sum_OlessThan__Suc,axiom,
% 9.53/5.31      ! [G: nat > int,N: nat] :
% 9.53/5.31        ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 9.53/5.31        = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7653_sum_OlessThan__Suc,axiom,
% 9.53/5.31      ! [G: nat > complex,N: nat] :
% 9.53/5.31        ( ( groups2073611262835488442omplex @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 9.53/5.31        = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7654_sum_OlessThan__Suc,axiom,
% 9.53/5.31      ! [G: nat > nat,N: nat] :
% 9.53/5.31        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 9.53/5.31        = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7655_sum_OlessThan__Suc,axiom,
% 9.53/5.31      ! [G: nat > real,N: nat] :
% 9.53/5.31        ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 9.53/5.31        = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7656_single__Diff__lessThan,axiom,
% 9.53/5.31      ! [K: int] :
% 9.53/5.31        ( ( minus_minus_set_int @ ( insert_int @ K @ bot_bot_set_int ) @ ( set_ord_lessThan_int @ K ) )
% 9.53/5.31        = ( insert_int @ K @ bot_bot_set_int ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7657_single__Diff__lessThan,axiom,
% 9.53/5.31      ! [K: nat] :
% 9.53/5.31        ( ( minus_minus_set_nat @ ( insert_nat @ K @ bot_bot_set_nat ) @ ( set_ord_lessThan_nat @ K ) )
% 9.53/5.31        = ( insert_nat @ K @ bot_bot_set_nat ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7658_single__Diff__lessThan,axiom,
% 9.53/5.31      ! [K: real] :
% 9.53/5.31        ( ( minus_minus_set_real @ ( insert_real @ K @ bot_bot_set_real ) @ ( set_or5984915006950818249n_real @ K ) )
% 9.53/5.31        = ( insert_real @ K @ bot_bot_set_real ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7659_powr__eq__one__iff,axiom,
% 9.53/5.31      ! [A: real,X: real] :
% 9.53/5.31        ( ( ord_less_real @ one_one_real @ A )
% 9.53/5.31       => ( ( ( powr_real @ A @ X )
% 9.53/5.31            = one_one_real )
% 9.53/5.31          = ( X = zero_zero_real ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7660_powr__one,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.31       => ( ( powr_real @ X @ one_one_real )
% 9.53/5.31          = X ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7661_powr__one__gt__zero__iff,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ( powr_real @ X @ one_one_real )
% 9.53/5.31          = X )
% 9.53/5.31        = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7662_powr__le__cancel__iff,axiom,
% 9.53/5.31      ! [X: real,A: real,B: real] :
% 9.53/5.31        ( ( ord_less_real @ one_one_real @ X )
% 9.53/5.31       => ( ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 9.53/5.31          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7663_numeral__powr__numeral__real,axiom,
% 9.53/5.31      ! [M: num,N: num] :
% 9.53/5.31        ( ( powr_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 9.53/5.31        = ( power_power_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7664_log__powr__cancel,axiom,
% 9.53/5.31      ! [A: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_real @ zero_zero_real @ A )
% 9.53/5.31       => ( ( A != one_one_real )
% 9.53/5.31         => ( ( log @ A @ ( powr_real @ A @ Y2 ) )
% 9.53/5.31            = Y2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7665_powr__log__cancel,axiom,
% 9.53/5.31      ! [A: real,X: real] :
% 9.53/5.31        ( ( ord_less_real @ zero_zero_real @ A )
% 9.53/5.31       => ( ( A != one_one_real )
% 9.53/5.31         => ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.31           => ( ( powr_real @ A @ ( log @ A @ X ) )
% 9.53/5.31              = X ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7666_summable__geometric__iff,axiom,
% 9.53/5.31      ! [C: real] :
% 9.53/5.31        ( ( summable_real @ ( power_power_real @ C ) )
% 9.53/5.31        = ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7667_summable__geometric__iff,axiom,
% 9.53/5.31      ! [C: complex] :
% 9.53/5.31        ( ( summable_complex @ ( power_power_complex @ C ) )
% 9.53/5.31        = ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7668_powr__numeral,axiom,
% 9.53/5.31      ! [X: real,N: num] :
% 9.53/5.31        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.31       => ( ( powr_real @ X @ ( numeral_numeral_real @ N ) )
% 9.53/5.31          = ( power_power_real @ X @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7669_square__powr__half,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( powr_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31        = ( abs_abs_real @ X ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7670_suminf__le__const,axiom,
% 9.53/5.31      ! [F: nat > int,X: int] :
% 9.53/5.31        ( ( summable_int @ F )
% 9.53/5.31       => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X )
% 9.53/5.31         => ( ord_less_eq_int @ ( suminf_int @ F ) @ X ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7671_suminf__le__const,axiom,
% 9.53/5.31      ! [F: nat > nat,X: nat] :
% 9.53/5.31        ( ( summable_nat @ F )
% 9.53/5.31       => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X )
% 9.53/5.31         => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ X ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7672_suminf__le__const,axiom,
% 9.53/5.31      ! [F: nat > real,X: real] :
% 9.53/5.31        ( ( summable_real @ F )
% 9.53/5.31       => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X )
% 9.53/5.31         => ( ord_less_eq_real @ ( suminf_real @ F ) @ X ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7673_summable__comparison__test,axiom,
% 9.53/5.31      ! [F: nat > real,G: nat > real] :
% 9.53/5.31        ( ? [N7: nat] :
% 9.53/5.31          ! [N3: nat] :
% 9.53/5.31            ( ( ord_less_eq_nat @ N7 @ N3 )
% 9.53/5.31           => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 9.53/5.31       => ( ( summable_real @ G )
% 9.53/5.31         => ( summable_real @ F ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7674_summable__comparison__test,axiom,
% 9.53/5.31      ! [F: nat > complex,G: nat > real] :
% 9.53/5.31        ( ? [N7: nat] :
% 9.53/5.31          ! [N3: nat] :
% 9.53/5.31            ( ( ord_less_eq_nat @ N7 @ N3 )
% 9.53/5.31           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 9.53/5.31       => ( ( summable_real @ G )
% 9.53/5.31         => ( summable_complex @ F ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7675_summable__comparison__test_H,axiom,
% 9.53/5.31      ! [G: nat > real,N4: nat,F: nat > real] :
% 9.53/5.31        ( ( summable_real @ G )
% 9.53/5.31       => ( ! [N3: nat] :
% 9.53/5.31              ( ( ord_less_eq_nat @ N4 @ N3 )
% 9.53/5.31             => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 9.53/5.31         => ( summable_real @ F ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7676_summable__comparison__test_H,axiom,
% 9.53/5.31      ! [G: nat > real,N4: nat,F: nat > complex] :
% 9.53/5.31        ( ( summable_real @ G )
% 9.53/5.31       => ( ! [N3: nat] :
% 9.53/5.31              ( ( ord_less_eq_nat @ N4 @ N3 )
% 9.53/5.31             => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 9.53/5.31         => ( summable_complex @ F ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7677_summable__add,axiom,
% 9.53/5.31      ! [F: nat > real,G: nat > real] :
% 9.53/5.31        ( ( summable_real @ F )
% 9.53/5.31       => ( ( summable_real @ G )
% 9.53/5.31         => ( summable_real
% 9.53/5.31            @ ^ [N2: nat] : ( plus_plus_real @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7678_summable__add,axiom,
% 9.53/5.31      ! [F: nat > nat,G: nat > nat] :
% 9.53/5.31        ( ( summable_nat @ F )
% 9.53/5.31       => ( ( summable_nat @ G )
% 9.53/5.31         => ( summable_nat
% 9.53/5.31            @ ^ [N2: nat] : ( plus_plus_nat @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7679_summable__add,axiom,
% 9.53/5.31      ! [F: nat > int,G: nat > int] :
% 9.53/5.31        ( ( summable_int @ F )
% 9.53/5.31       => ( ( summable_int @ G )
% 9.53/5.31         => ( summable_int
% 9.53/5.31            @ ^ [N2: nat] : ( plus_plus_int @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7680_summable__add,axiom,
% 9.53/5.31      ! [F: nat > complex,G: nat > complex] :
% 9.53/5.31        ( ( summable_complex @ F )
% 9.53/5.31       => ( ( summable_complex @ G )
% 9.53/5.31         => ( summable_complex
% 9.53/5.31            @ ^ [N2: nat] : ( plus_plus_complex @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7681_summable__ignore__initial__segment,axiom,
% 9.53/5.31      ! [F: nat > real,K: nat] :
% 9.53/5.31        ( ( summable_real @ F )
% 9.53/5.31       => ( summable_real
% 9.53/5.31          @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ K ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7682_powr__powr,axiom,
% 9.53/5.31      ! [X: real,A: real,B: real] :
% 9.53/5.31        ( ( powr_real @ ( powr_real @ X @ A ) @ B )
% 9.53/5.31        = ( powr_real @ X @ ( times_times_real @ A @ B ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7683_summable__divide,axiom,
% 9.53/5.31      ! [F: nat > complex,C: complex] :
% 9.53/5.31        ( ( summable_complex @ F )
% 9.53/5.31       => ( summable_complex
% 9.53/5.31          @ ^ [N2: nat] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ C ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7684_summable__divide,axiom,
% 9.53/5.31      ! [F: nat > real,C: real] :
% 9.53/5.31        ( ( summable_real @ F )
% 9.53/5.31       => ( summable_real
% 9.53/5.31          @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ C ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7685_summable__diff,axiom,
% 9.53/5.31      ! [F: nat > real,G: nat > real] :
% 9.53/5.31        ( ( summable_real @ F )
% 9.53/5.31       => ( ( summable_real @ G )
% 9.53/5.31         => ( summable_real
% 9.53/5.31            @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7686_summable__Suc__iff,axiom,
% 9.53/5.31      ! [F: nat > real] :
% 9.53/5.31        ( ( summable_real
% 9.53/5.31          @ ^ [N2: nat] : ( F @ ( suc @ N2 ) ) )
% 9.53/5.31        = ( summable_real @ F ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7687_summable__mult2,axiom,
% 9.53/5.31      ! [F: nat > complex,C: complex] :
% 9.53/5.31        ( ( summable_complex @ F )
% 9.53/5.31       => ( summable_complex
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ C ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7688_summable__mult2,axiom,
% 9.53/5.31      ! [F: nat > real,C: real] :
% 9.53/5.31        ( ( summable_real @ F )
% 9.53/5.31       => ( summable_real
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ C ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7689_summable__mult,axiom,
% 9.53/5.31      ! [F: nat > complex,C: complex] :
% 9.53/5.31        ( ( summable_complex @ F )
% 9.53/5.31       => ( summable_complex
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7690_summable__mult,axiom,
% 9.53/5.31      ! [F: nat > real,C: real] :
% 9.53/5.31        ( ( summable_real @ F )
% 9.53/5.31       => ( summable_real
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7691_summableI__nonneg__bounded,axiom,
% 9.53/5.31      ! [F: nat > int,X: int] :
% 9.53/5.31        ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 9.53/5.31       => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X )
% 9.53/5.31         => ( summable_int @ F ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7692_summableI__nonneg__bounded,axiom,
% 9.53/5.31      ! [F: nat > nat,X: nat] :
% 9.53/5.31        ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 9.53/5.31       => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X )
% 9.53/5.31         => ( summable_nat @ F ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7693_summableI__nonneg__bounded,axiom,
% 9.53/5.31      ! [F: nat > real,X: real] :
% 9.53/5.31        ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 9.53/5.31       => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X )
% 9.53/5.31         => ( summable_real @ F ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7694_suminf__le,axiom,
% 9.53/5.31      ! [F: nat > real,G: nat > real] :
% 9.53/5.31        ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 9.53/5.31       => ( ( summable_real @ F )
% 9.53/5.31         => ( ( summable_real @ G )
% 9.53/5.31           => ( ord_less_eq_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7695_suminf__le,axiom,
% 9.53/5.31      ! [F: nat > nat,G: nat > nat] :
% 9.53/5.31        ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( G @ N3 ) )
% 9.53/5.31       => ( ( summable_nat @ F )
% 9.53/5.31         => ( ( summable_nat @ G )
% 9.53/5.31           => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7696_suminf__le,axiom,
% 9.53/5.31      ! [F: nat > int,G: nat > int] :
% 9.53/5.31        ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( G @ N3 ) )
% 9.53/5.31       => ( ( summable_int @ F )
% 9.53/5.31         => ( ( summable_int @ G )
% 9.53/5.31           => ( ord_less_eq_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7697_summable__mult__D,axiom,
% 9.53/5.31      ! [C: complex,F: nat > complex] :
% 9.53/5.31        ( ( summable_complex
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) ) )
% 9.53/5.31       => ( ( C != zero_zero_complex )
% 9.53/5.31         => ( summable_complex @ F ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7698_summable__mult__D,axiom,
% 9.53/5.31      ! [C: real,F: nat > real] :
% 9.53/5.31        ( ( summable_real
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) ) )
% 9.53/5.31       => ( ( C != zero_zero_real )
% 9.53/5.31         => ( summable_real @ F ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7699_summable__zero__power,axiom,
% 9.53/5.31      summable_real @ ( power_power_real @ zero_zero_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7700_summable__zero__power,axiom,
% 9.53/5.31      summable_int @ ( power_power_int @ zero_zero_int ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7701_summable__zero__power,axiom,
% 9.53/5.31      summable_complex @ ( power_power_complex @ zero_zero_complex ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7702_lessThan__def,axiom,
% 9.53/5.31      ( set_ord_lessThan_rat
% 9.53/5.31      = ( ^ [U2: rat] :
% 9.53/5.31            ( collect_rat
% 9.53/5.31            @ ^ [X2: rat] : ( ord_less_rat @ X2 @ U2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7703_lessThan__def,axiom,
% 9.53/5.31      ( set_ord_lessThan_num
% 9.53/5.31      = ( ^ [U2: num] :
% 9.53/5.31            ( collect_num
% 9.53/5.31            @ ^ [X2: num] : ( ord_less_num @ X2 @ U2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7704_lessThan__def,axiom,
% 9.53/5.31      ( set_ord_lessThan_int
% 9.53/5.31      = ( ^ [U2: int] :
% 9.53/5.31            ( collect_int
% 9.53/5.31            @ ^ [X2: int] : ( ord_less_int @ X2 @ U2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7705_lessThan__def,axiom,
% 9.53/5.31      ( set_ord_lessThan_nat
% 9.53/5.31      = ( ^ [U2: nat] :
% 9.53/5.31            ( collect_nat
% 9.53/5.31            @ ^ [X2: nat] : ( ord_less_nat @ X2 @ U2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7706_lessThan__def,axiom,
% 9.53/5.31      ( set_or5984915006950818249n_real
% 9.53/5.31      = ( ^ [U2: real] :
% 9.53/5.31            ( collect_real
% 9.53/5.31            @ ^ [X2: real] : ( ord_less_real @ X2 @ U2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7707_suminf__mult,axiom,
% 9.53/5.31      ! [F: nat > complex,C: complex] :
% 9.53/5.31        ( ( summable_complex @ F )
% 9.53/5.31       => ( ( suminf_complex
% 9.53/5.31            @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) ) )
% 9.53/5.31          = ( times_times_complex @ C @ ( suminf_complex @ F ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7708_suminf__mult,axiom,
% 9.53/5.31      ! [F: nat > real,C: real] :
% 9.53/5.31        ( ( summable_real @ F )
% 9.53/5.31       => ( ( suminf_real
% 9.53/5.31            @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) ) )
% 9.53/5.31          = ( times_times_real @ C @ ( suminf_real @ F ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7709_suminf__mult2,axiom,
% 9.53/5.31      ! [F: nat > complex,C: complex] :
% 9.53/5.31        ( ( summable_complex @ F )
% 9.53/5.31       => ( ( times_times_complex @ ( suminf_complex @ F ) @ C )
% 9.53/5.31          = ( suminf_complex
% 9.53/5.31            @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ C ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7710_suminf__mult2,axiom,
% 9.53/5.31      ! [F: nat > real,C: real] :
% 9.53/5.31        ( ( summable_real @ F )
% 9.53/5.31       => ( ( times_times_real @ ( suminf_real @ F ) @ C )
% 9.53/5.31          = ( suminf_real
% 9.53/5.31            @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ C ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7711_suminf__add,axiom,
% 9.53/5.31      ! [F: nat > real,G: nat > real] :
% 9.53/5.31        ( ( summable_real @ F )
% 9.53/5.31       => ( ( summable_real @ G )
% 9.53/5.31         => ( ( plus_plus_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) )
% 9.53/5.31            = ( suminf_real
% 9.53/5.31              @ ^ [N2: nat] : ( plus_plus_real @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7712_suminf__add,axiom,
% 9.53/5.31      ! [F: nat > nat,G: nat > nat] :
% 9.53/5.31        ( ( summable_nat @ F )
% 9.53/5.31       => ( ( summable_nat @ G )
% 9.53/5.31         => ( ( plus_plus_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) )
% 9.53/5.31            = ( suminf_nat
% 9.53/5.31              @ ^ [N2: nat] : ( plus_plus_nat @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7713_suminf__add,axiom,
% 9.53/5.31      ! [F: nat > int,G: nat > int] :
% 9.53/5.31        ( ( summable_int @ F )
% 9.53/5.31       => ( ( summable_int @ G )
% 9.53/5.31         => ( ( plus_plus_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) )
% 9.53/5.31            = ( suminf_int
% 9.53/5.31              @ ^ [N2: nat] : ( plus_plus_int @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7714_suminf__add,axiom,
% 9.53/5.31      ! [F: nat > complex,G: nat > complex] :
% 9.53/5.31        ( ( summable_complex @ F )
% 9.53/5.31       => ( ( summable_complex @ G )
% 9.53/5.31         => ( ( plus_plus_complex @ ( suminf_complex @ F ) @ ( suminf_complex @ G ) )
% 9.53/5.31            = ( suminf_complex
% 9.53/5.31              @ ^ [N2: nat] : ( plus_plus_complex @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7715_suminf__diff,axiom,
% 9.53/5.31      ! [F: nat > real,G: nat > real] :
% 9.53/5.31        ( ( summable_real @ F )
% 9.53/5.31       => ( ( summable_real @ G )
% 9.53/5.31         => ( ( minus_minus_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) )
% 9.53/5.31            = ( suminf_real
% 9.53/5.31              @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7716_suminf__divide,axiom,
% 9.53/5.31      ! [F: nat > complex,C: complex] :
% 9.53/5.31        ( ( summable_complex @ F )
% 9.53/5.31       => ( ( suminf_complex
% 9.53/5.31            @ ^ [N2: nat] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ C ) )
% 9.53/5.31          = ( divide1717551699836669952omplex @ ( suminf_complex @ F ) @ C ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7717_suminf__divide,axiom,
% 9.53/5.31      ! [F: nat > real,C: real] :
% 9.53/5.31        ( ( summable_real @ F )
% 9.53/5.31       => ( ( suminf_real
% 9.53/5.31            @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ C ) )
% 9.53/5.31          = ( divide_divide_real @ ( suminf_real @ F ) @ C ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7718_suminf__split__initial__segment,axiom,
% 9.53/5.31      ! [F: nat > complex,K: nat] :
% 9.53/5.31        ( ( summable_complex @ F )
% 9.53/5.31       => ( ( suminf_complex @ F )
% 9.53/5.31          = ( plus_plus_complex
% 9.53/5.31            @ ( suminf_complex
% 9.53/5.31              @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ K ) ) )
% 9.53/5.31            @ ( groups2073611262835488442omplex @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7719_suminf__split__initial__segment,axiom,
% 9.53/5.31      ! [F: nat > real,K: nat] :
% 9.53/5.31        ( ( summable_real @ F )
% 9.53/5.31       => ( ( suminf_real @ F )
% 9.53/5.31          = ( plus_plus_real
% 9.53/5.31            @ ( suminf_real
% 9.53/5.31              @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ K ) ) )
% 9.53/5.31            @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7720_suminf__minus__initial__segment,axiom,
% 9.53/5.31      ! [F: nat > real,K: nat] :
% 9.53/5.31        ( ( summable_real @ F )
% 9.53/5.31       => ( ( suminf_real
% 9.53/5.31            @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ K ) ) )
% 9.53/5.31          = ( minus_minus_real @ ( suminf_real @ F ) @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7721_sum__less__suminf,axiom,
% 9.53/5.31      ! [F: nat > int,N: nat] :
% 9.53/5.31        ( ( summable_int @ F )
% 9.53/5.31       => ( ! [M4: nat] :
% 9.53/5.31              ( ( ord_less_eq_nat @ N @ M4 )
% 9.53/5.31             => ( ord_less_int @ zero_zero_int @ ( F @ M4 ) ) )
% 9.53/5.31         => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_int @ F ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7722_sum__less__suminf,axiom,
% 9.53/5.31      ! [F: nat > nat,N: nat] :
% 9.53/5.31        ( ( summable_nat @ F )
% 9.53/5.31       => ( ! [M4: nat] :
% 9.53/5.31              ( ( ord_less_eq_nat @ N @ M4 )
% 9.53/5.31             => ( ord_less_nat @ zero_zero_nat @ ( F @ M4 ) ) )
% 9.53/5.31         => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_nat @ F ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7723_sum__less__suminf,axiom,
% 9.53/5.31      ! [F: nat > real,N: nat] :
% 9.53/5.31        ( ( summable_real @ F )
% 9.53/5.31       => ( ! [M4: nat] :
% 9.53/5.31              ( ( ord_less_eq_nat @ N @ M4 )
% 9.53/5.31             => ( ord_less_real @ zero_zero_real @ ( F @ M4 ) ) )
% 9.53/5.31         => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_real @ F ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7724_powser__insidea,axiom,
% 9.53/5.31      ! [F: nat > real,X: real,Z: real] :
% 9.53/5.31        ( ( summable_real
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ X @ N2 ) ) )
% 9.53/5.31       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ ( real_V7735802525324610683m_real @ X ) )
% 9.53/5.31         => ( summable_real
% 9.53/5.31            @ ^ [N2: nat] : ( real_V7735802525324610683m_real @ ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7725_powser__insidea,axiom,
% 9.53/5.31      ! [F: nat > complex,X: complex,Z: complex] :
% 9.53/5.31        ( ( summable_complex
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ X @ N2 ) ) )
% 9.53/5.31       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ ( real_V1022390504157884413omplex @ X ) )
% 9.53/5.31         => ( summable_real
% 9.53/5.31            @ ^ [N2: nat] : ( real_V1022390504157884413omplex @ ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7726_suminf__eq__zero__iff,axiom,
% 9.53/5.31      ! [F: nat > real] :
% 9.53/5.31        ( ( summable_real @ F )
% 9.53/5.31       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 9.53/5.31         => ( ( ( suminf_real @ F )
% 9.53/5.31              = zero_zero_real )
% 9.53/5.31            = ( ! [N2: nat] :
% 9.53/5.31                  ( ( F @ N2 )
% 9.53/5.31                  = zero_zero_real ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7727_suminf__eq__zero__iff,axiom,
% 9.53/5.31      ! [F: nat > nat] :
% 9.53/5.31        ( ( summable_nat @ F )
% 9.53/5.31       => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 9.53/5.31         => ( ( ( suminf_nat @ F )
% 9.53/5.31              = zero_zero_nat )
% 9.53/5.31            = ( ! [N2: nat] :
% 9.53/5.31                  ( ( F @ N2 )
% 9.53/5.31                  = zero_zero_nat ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7728_suminf__eq__zero__iff,axiom,
% 9.53/5.31      ! [F: nat > int] :
% 9.53/5.31        ( ( summable_int @ F )
% 9.53/5.31       => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 9.53/5.31         => ( ( ( suminf_int @ F )
% 9.53/5.31              = zero_zero_int )
% 9.53/5.31            = ( ! [N2: nat] :
% 9.53/5.31                  ( ( F @ N2 )
% 9.53/5.31                  = zero_zero_int ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7729_suminf__nonneg,axiom,
% 9.53/5.31      ! [F: nat > real] :
% 9.53/5.31        ( ( summable_real @ F )
% 9.53/5.31       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 9.53/5.31         => ( ord_less_eq_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7730_suminf__nonneg,axiom,
% 9.53/5.31      ! [F: nat > nat] :
% 9.53/5.31        ( ( summable_nat @ F )
% 9.53/5.31       => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 9.53/5.31         => ( ord_less_eq_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7731_suminf__nonneg,axiom,
% 9.53/5.31      ! [F: nat > int] :
% 9.53/5.31        ( ( summable_int @ F )
% 9.53/5.31       => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 9.53/5.31         => ( ord_less_eq_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7732_suminf__pos,axiom,
% 9.53/5.31      ! [F: nat > real] :
% 9.53/5.31        ( ( summable_real @ F )
% 9.53/5.31       => ( ! [N3: nat] : ( ord_less_real @ zero_zero_real @ ( F @ N3 ) )
% 9.53/5.31         => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7733_suminf__pos,axiom,
% 9.53/5.31      ! [F: nat > nat] :
% 9.53/5.31        ( ( summable_nat @ F )
% 9.53/5.31       => ( ! [N3: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ N3 ) )
% 9.53/5.31         => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7734_suminf__pos,axiom,
% 9.53/5.31      ! [F: nat > int] :
% 9.53/5.31        ( ( summable_int @ F )
% 9.53/5.31       => ( ! [N3: nat] : ( ord_less_int @ zero_zero_int @ ( F @ N3 ) )
% 9.53/5.31         => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7735_powr__non__neg,axiom,
% 9.53/5.31      ! [A: real,X: real] :
% 9.53/5.31        ~ ( ord_less_real @ ( powr_real @ A @ X ) @ zero_zero_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7736_powr__less__mono2__neg,axiom,
% 9.53/5.31      ! [A: real,X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_real @ A @ zero_zero_real )
% 9.53/5.31       => ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.31         => ( ( ord_less_real @ X @ Y2 )
% 9.53/5.31           => ( ord_less_real @ ( powr_real @ Y2 @ A ) @ ( powr_real @ X @ A ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7737_powr__mono2,axiom,
% 9.53/5.31      ! [A: real,X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 9.53/5.31       => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.31         => ( ( ord_less_eq_real @ X @ Y2 )
% 9.53/5.31           => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y2 @ A ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7738_powr__ge__pzero,axiom,
% 9.53/5.31      ! [X: real,Y2: real] : ( ord_less_eq_real @ zero_zero_real @ ( powr_real @ X @ Y2 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7739_powr__less__cancel,axiom,
% 9.53/5.31      ! [X: real,A: real,B: real] :
% 9.53/5.31        ( ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 9.53/5.31       => ( ( ord_less_real @ one_one_real @ X )
% 9.53/5.31         => ( ord_less_real @ A @ B ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7740_powr__less__mono,axiom,
% 9.53/5.31      ! [A: real,B: real,X: real] :
% 9.53/5.31        ( ( ord_less_real @ A @ B )
% 9.53/5.31       => ( ( ord_less_real @ one_one_real @ X )
% 9.53/5.31         => ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7741_powr__mono,axiom,
% 9.53/5.31      ! [A: real,B: real,X: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ A @ B )
% 9.53/5.31       => ( ( ord_less_eq_real @ one_one_real @ X )
% 9.53/5.31         => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7742_lessThan__strict__subset__iff,axiom,
% 9.53/5.31      ! [M: rat,N: rat] :
% 9.53/5.31        ( ( ord_less_set_rat @ ( set_ord_lessThan_rat @ M ) @ ( set_ord_lessThan_rat @ N ) )
% 9.53/5.31        = ( ord_less_rat @ M @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7743_lessThan__strict__subset__iff,axiom,
% 9.53/5.31      ! [M: num,N: num] :
% 9.53/5.31        ( ( ord_less_set_num @ ( set_ord_lessThan_num @ M ) @ ( set_ord_lessThan_num @ N ) )
% 9.53/5.31        = ( ord_less_num @ M @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7744_lessThan__strict__subset__iff,axiom,
% 9.53/5.31      ! [M: int,N: int] :
% 9.53/5.31        ( ( ord_less_set_int @ ( set_ord_lessThan_int @ M ) @ ( set_ord_lessThan_int @ N ) )
% 9.53/5.31        = ( ord_less_int @ M @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7745_lessThan__strict__subset__iff,axiom,
% 9.53/5.31      ! [M: nat,N: nat] :
% 9.53/5.31        ( ( ord_less_set_nat @ ( set_ord_lessThan_nat @ M ) @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.31        = ( ord_less_nat @ M @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7746_lessThan__strict__subset__iff,axiom,
% 9.53/5.31      ! [M: real,N: real] :
% 9.53/5.31        ( ( ord_less_set_real @ ( set_or5984915006950818249n_real @ M ) @ ( set_or5984915006950818249n_real @ N ) )
% 9.53/5.31        = ( ord_less_real @ M @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7747_summable__0__powser,axiom,
% 9.53/5.31      ! [F: nat > complex] :
% 9.53/5.31        ( summable_complex
% 9.53/5.31        @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7748_summable__0__powser,axiom,
% 9.53/5.31      ! [F: nat > real] :
% 9.53/5.31        ( summable_real
% 9.53/5.31        @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7749_summable__zero__power_H,axiom,
% 9.53/5.31      ! [F: nat > complex] :
% 9.53/5.31        ( summable_complex
% 9.53/5.31        @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7750_summable__zero__power_H,axiom,
% 9.53/5.31      ! [F: nat > real] :
% 9.53/5.31        ( summable_real
% 9.53/5.31        @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7751_summable__zero__power_H,axiom,
% 9.53/5.31      ! [F: nat > int] :
% 9.53/5.31        ( summable_int
% 9.53/5.31        @ ^ [N2: nat] : ( times_times_int @ ( F @ N2 ) @ ( power_power_int @ zero_zero_int @ N2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7752_summable__powser__split__head,axiom,
% 9.53/5.31      ! [F: nat > complex,Z: complex] :
% 9.53/5.31        ( ( summable_complex
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_complex @ ( F @ ( suc @ N2 ) ) @ ( power_power_complex @ Z @ N2 ) ) )
% 9.53/5.31        = ( summable_complex
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7753_summable__powser__split__head,axiom,
% 9.53/5.31      ! [F: nat > real,Z: real] :
% 9.53/5.31        ( ( summable_real
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_real @ ( F @ ( suc @ N2 ) ) @ ( power_power_real @ Z @ N2 ) ) )
% 9.53/5.31        = ( summable_real
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7754_powser__split__head_I3_J,axiom,
% 9.53/5.31      ! [F: nat > complex,Z: complex] :
% 9.53/5.31        ( ( summable_complex
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) )
% 9.53/5.31       => ( summable_complex
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_complex @ ( F @ ( suc @ N2 ) ) @ ( power_power_complex @ Z @ N2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7755_powser__split__head_I3_J,axiom,
% 9.53/5.31      ! [F: nat > real,Z: real] :
% 9.53/5.31        ( ( summable_real
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) )
% 9.53/5.31       => ( summable_real
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_real @ ( F @ ( suc @ N2 ) ) @ ( power_power_real @ Z @ N2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7756_summable__powser__ignore__initial__segment,axiom,
% 9.53/5.31      ! [F: nat > complex,M: nat,Z: complex] :
% 9.53/5.31        ( ( summable_complex
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_complex @ ( F @ ( plus_plus_nat @ N2 @ M ) ) @ ( power_power_complex @ Z @ N2 ) ) )
% 9.53/5.31        = ( summable_complex
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7757_summable__powser__ignore__initial__segment,axiom,
% 9.53/5.31      ! [F: nat > real,M: nat,Z: real] :
% 9.53/5.31        ( ( summable_real
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_real @ ( F @ ( plus_plus_nat @ N2 @ M ) ) @ ( power_power_real @ Z @ N2 ) ) )
% 9.53/5.31        = ( summable_real
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7758_pi__gt__zero,axiom,
% 9.53/5.31      ord_less_real @ zero_zero_real @ pi ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7759_pi__not__less__zero,axiom,
% 9.53/5.31      ~ ( ord_less_real @ pi @ zero_zero_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7760_pi__ge__zero,axiom,
% 9.53/5.31      ord_less_eq_real @ zero_zero_real @ pi ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7761_sum__less__suminf2,axiom,
% 9.53/5.31      ! [F: nat > int,N: nat,I2: nat] :
% 9.53/5.31        ( ( summable_int @ F )
% 9.53/5.31       => ( ! [M4: nat] :
% 9.53/5.31              ( ( ord_less_eq_nat @ N @ M4 )
% 9.53/5.31             => ( ord_less_eq_int @ zero_zero_int @ ( F @ M4 ) ) )
% 9.53/5.31         => ( ( ord_less_eq_nat @ N @ I2 )
% 9.53/5.31           => ( ( ord_less_int @ zero_zero_int @ ( F @ I2 ) )
% 9.53/5.31             => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_int @ F ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7762_sum__less__suminf2,axiom,
% 9.53/5.31      ! [F: nat > nat,N: nat,I2: nat] :
% 9.53/5.31        ( ( summable_nat @ F )
% 9.53/5.31       => ( ! [M4: nat] :
% 9.53/5.31              ( ( ord_less_eq_nat @ N @ M4 )
% 9.53/5.31             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ M4 ) ) )
% 9.53/5.31         => ( ( ord_less_eq_nat @ N @ I2 )
% 9.53/5.31           => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 9.53/5.31             => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_nat @ F ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7763_sum__less__suminf2,axiom,
% 9.53/5.31      ! [F: nat > real,N: nat,I2: nat] :
% 9.53/5.31        ( ( summable_real @ F )
% 9.53/5.31       => ( ! [M4: nat] :
% 9.53/5.31              ( ( ord_less_eq_nat @ N @ M4 )
% 9.53/5.31             => ( ord_less_eq_real @ zero_zero_real @ ( F @ M4 ) ) )
% 9.53/5.31         => ( ( ord_less_eq_nat @ N @ I2 )
% 9.53/5.31           => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 9.53/5.31             => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_real @ F ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7764_lessThan__Suc,axiom,
% 9.53/5.31      ! [K: nat] :
% 9.53/5.31        ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 9.53/5.31        = ( insert_nat @ K @ ( set_ord_lessThan_nat @ K ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7765_summable__norm__comparison__test,axiom,
% 9.53/5.31      ! [F: nat > complex,G: nat > real] :
% 9.53/5.31        ( ? [N7: nat] :
% 9.53/5.31          ! [N3: nat] :
% 9.53/5.31            ( ( ord_less_eq_nat @ N7 @ N3 )
% 9.53/5.31           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 9.53/5.31       => ( ( summable_real @ G )
% 9.53/5.31         => ( summable_real
% 9.53/5.31            @ ^ [N2: nat] : ( real_V1022390504157884413omplex @ ( F @ N2 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7766_summable__rabs__comparison__test,axiom,
% 9.53/5.31      ! [F: nat > real,G: nat > real] :
% 9.53/5.31        ( ? [N7: nat] :
% 9.53/5.31          ! [N3: nat] :
% 9.53/5.31            ( ( ord_less_eq_nat @ N7 @ N3 )
% 9.53/5.31           => ( ord_less_eq_real @ ( abs_abs_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 9.53/5.31       => ( ( summable_real @ G )
% 9.53/5.31         => ( summable_real
% 9.53/5.31            @ ^ [N2: nat] : ( abs_abs_real @ ( F @ N2 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7767_summable__rabs,axiom,
% 9.53/5.31      ! [F: nat > real] :
% 9.53/5.31        ( ( summable_real
% 9.53/5.31          @ ^ [N2: nat] : ( abs_abs_real @ ( F @ N2 ) ) )
% 9.53/5.31       => ( ord_less_eq_real @ ( abs_abs_real @ ( suminf_real @ F ) )
% 9.53/5.31          @ ( suminf_real
% 9.53/5.31            @ ^ [N2: nat] : ( abs_abs_real @ ( F @ N2 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7768_suminf__pos2,axiom,
% 9.53/5.31      ! [F: nat > real,I2: nat] :
% 9.53/5.31        ( ( summable_real @ F )
% 9.53/5.31       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 9.53/5.31         => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 9.53/5.31           => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7769_suminf__pos2,axiom,
% 9.53/5.31      ! [F: nat > nat,I2: nat] :
% 9.53/5.31        ( ( summable_nat @ F )
% 9.53/5.31       => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 9.53/5.31         => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 9.53/5.31           => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7770_suminf__pos2,axiom,
% 9.53/5.31      ! [F: nat > int,I2: nat] :
% 9.53/5.31        ( ( summable_int @ F )
% 9.53/5.31       => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 9.53/5.31         => ( ( ord_less_int @ zero_zero_int @ ( F @ I2 ) )
% 9.53/5.31           => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7771_suminf__pos__iff,axiom,
% 9.53/5.31      ! [F: nat > real] :
% 9.53/5.31        ( ( summable_real @ F )
% 9.53/5.31       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 9.53/5.31         => ( ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) )
% 9.53/5.31            = ( ? [I3: nat] : ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7772_suminf__pos__iff,axiom,
% 9.53/5.31      ! [F: nat > nat] :
% 9.53/5.31        ( ( summable_nat @ F )
% 9.53/5.31       => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 9.53/5.31         => ( ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) )
% 9.53/5.31            = ( ? [I3: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ I3 ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7773_suminf__pos__iff,axiom,
% 9.53/5.31      ! [F: nat > int] :
% 9.53/5.31        ( ( summable_int @ F )
% 9.53/5.31       => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 9.53/5.31         => ( ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) )
% 9.53/5.31            = ( ? [I3: nat] : ( ord_less_int @ zero_zero_int @ ( F @ I3 ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7774_powr__mono2_H,axiom,
% 9.53/5.31      ! [A: real,X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 9.53/5.31       => ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.31         => ( ( ord_less_eq_real @ X @ Y2 )
% 9.53/5.31           => ( ord_less_eq_real @ ( powr_real @ Y2 @ A ) @ ( powr_real @ X @ A ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7775_powr__less__mono2,axiom,
% 9.53/5.31      ! [A: real,X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_real @ zero_zero_real @ A )
% 9.53/5.31       => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.31         => ( ( ord_less_real @ X @ Y2 )
% 9.53/5.31           => ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y2 @ A ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7776_gr__one__powr,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_real @ one_one_real @ X )
% 9.53/5.31       => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 9.53/5.31         => ( ord_less_real @ one_one_real @ ( powr_real @ X @ Y2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7777_powr__inj,axiom,
% 9.53/5.31      ! [A: real,X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_real @ zero_zero_real @ A )
% 9.53/5.31       => ( ( A != one_one_real )
% 9.53/5.31         => ( ( ( powr_real @ A @ X )
% 9.53/5.31              = ( powr_real @ A @ Y2 ) )
% 9.53/5.31            = ( X = Y2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7778_powr__le1,axiom,
% 9.53/5.31      ! [A: real,X: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 9.53/5.31       => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.31         => ( ( ord_less_eq_real @ X @ one_one_real )
% 9.53/5.31           => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ one_one_real ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7779_powr__mono__both,axiom,
% 9.53/5.31      ! [A: real,B: real,X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 9.53/5.31       => ( ( ord_less_eq_real @ A @ B )
% 9.53/5.31         => ( ( ord_less_eq_real @ one_one_real @ X )
% 9.53/5.31           => ( ( ord_less_eq_real @ X @ Y2 )
% 9.53/5.31             => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y2 @ B ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7780_ge__one__powr__ge__zero,axiom,
% 9.53/5.31      ! [X: real,A: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ one_one_real @ X )
% 9.53/5.31       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 9.53/5.31         => ( ord_less_eq_real @ one_one_real @ ( powr_real @ X @ A ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7781_complete__algebra__summable__geometric,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ one_one_real )
% 9.53/5.31       => ( summable_real @ ( power_power_real @ X ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7782_complete__algebra__summable__geometric,axiom,
% 9.53/5.31      ! [X: complex] :
% 9.53/5.31        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ one_one_real )
% 9.53/5.31       => ( summable_complex @ ( power_power_complex @ X ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7783_summable__geometric,axiom,
% 9.53/5.31      ! [C: real] :
% 9.53/5.31        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 9.53/5.31       => ( summable_real @ ( power_power_real @ C ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7784_summable__geometric,axiom,
% 9.53/5.31      ! [C: complex] :
% 9.53/5.31        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 9.53/5.31       => ( summable_complex @ ( power_power_complex @ C ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7785_suminf__split__head,axiom,
% 9.53/5.31      ! [F: nat > real] :
% 9.53/5.31        ( ( summable_real @ F )
% 9.53/5.31       => ( ( suminf_real
% 9.53/5.31            @ ^ [N2: nat] : ( F @ ( suc @ N2 ) ) )
% 9.53/5.31          = ( minus_minus_real @ ( suminf_real @ F ) @ ( F @ zero_zero_nat ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7786_powr__divide,axiom,
% 9.53/5.31      ! [X: real,Y2: real,A: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.31       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 9.53/5.31         => ( ( powr_real @ ( divide_divide_real @ X @ Y2 ) @ A )
% 9.53/5.31            = ( divide_divide_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y2 @ A ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7787_powr__mult,axiom,
% 9.53/5.31      ! [X: real,Y2: real,A: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.31       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 9.53/5.31         => ( ( powr_real @ ( times_times_real @ X @ Y2 ) @ A )
% 9.53/5.31            = ( times_times_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y2 @ A ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7788_divide__powr__uminus,axiom,
% 9.53/5.31      ! [A: real,B: real,C: real] :
% 9.53/5.31        ( ( divide_divide_real @ A @ ( powr_real @ B @ C ) )
% 9.53/5.31        = ( times_times_real @ A @ ( powr_real @ B @ ( uminus_uminus_real @ C ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7789_log__base__powr,axiom,
% 9.53/5.31      ! [A: real,B: real,X: real] :
% 9.53/5.31        ( ( A != zero_zero_real )
% 9.53/5.31       => ( ( log @ ( powr_real @ A @ B ) @ X )
% 9.53/5.31          = ( divide_divide_real @ ( log @ A @ X ) @ B ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7790_log__powr,axiom,
% 9.53/5.31      ! [X: real,B: real,Y2: real] :
% 9.53/5.31        ( ( X != zero_zero_real )
% 9.53/5.31       => ( ( log @ B @ ( powr_real @ X @ Y2 ) )
% 9.53/5.31          = ( times_times_real @ Y2 @ ( log @ B @ X ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7791_ln__powr,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( X != zero_zero_real )
% 9.53/5.31       => ( ( ln_ln_real @ ( powr_real @ X @ Y2 ) )
% 9.53/5.31          = ( times_times_real @ Y2 @ ( ln_ln_real @ X ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7792_powr__add,axiom,
% 9.53/5.31      ! [X: real,A: real,B: real] :
% 9.53/5.31        ( ( powr_real @ X @ ( plus_plus_real @ A @ B ) )
% 9.53/5.31        = ( times_times_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7793_powr__diff,axiom,
% 9.53/5.31      ! [W: real,Z1: real,Z22: real] :
% 9.53/5.31        ( ( powr_real @ W @ ( minus_minus_real @ Z1 @ Z22 ) )
% 9.53/5.31        = ( divide_divide_real @ ( powr_real @ W @ Z1 ) @ ( powr_real @ W @ Z22 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7794_summable__norm,axiom,
% 9.53/5.31      ! [F: nat > real] :
% 9.53/5.31        ( ( summable_real
% 9.53/5.31          @ ^ [N2: nat] : ( real_V7735802525324610683m_real @ ( F @ N2 ) ) )
% 9.53/5.31       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( suminf_real @ F ) )
% 9.53/5.31          @ ( suminf_real
% 9.53/5.31            @ ^ [N2: nat] : ( real_V7735802525324610683m_real @ ( F @ N2 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7795_summable__norm,axiom,
% 9.53/5.31      ! [F: nat > complex] :
% 9.53/5.31        ( ( summable_real
% 9.53/5.31          @ ^ [N2: nat] : ( real_V1022390504157884413omplex @ ( F @ N2 ) ) )
% 9.53/5.31       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( suminf_complex @ F ) )
% 9.53/5.31          @ ( suminf_real
% 9.53/5.31            @ ^ [N2: nat] : ( real_V1022390504157884413omplex @ ( F @ N2 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7796_lessThan__nat__numeral,axiom,
% 9.53/5.31      ! [K: num] :
% 9.53/5.31        ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K ) )
% 9.53/5.31        = ( insert_nat @ ( pred_numeral @ K ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7797_sum_Onat__diff__reindex,axiom,
% 9.53/5.31      ! [G: nat > nat,N: nat] :
% 9.53/5.31        ( ( groups3542108847815614940at_nat
% 9.53/5.31          @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 9.53/5.31          @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.31        = ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7798_sum_Onat__diff__reindex,axiom,
% 9.53/5.31      ! [G: nat > real,N: nat] :
% 9.53/5.31        ( ( groups6591440286371151544t_real
% 9.53/5.31          @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 9.53/5.31          @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.31        = ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7799_sum__le__suminf,axiom,
% 9.53/5.31      ! [F: nat > int,I6: set_nat] :
% 9.53/5.31        ( ( summable_int @ F )
% 9.53/5.31       => ( ( finite_finite_nat @ I6 )
% 9.53/5.31         => ( ! [N3: nat] :
% 9.53/5.31                ( ( member_nat @ N3 @ ( uminus5710092332889474511et_nat @ I6 ) )
% 9.53/5.31               => ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) ) )
% 9.53/5.31           => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ I6 ) @ ( suminf_int @ F ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7800_sum__le__suminf,axiom,
% 9.53/5.31      ! [F: nat > nat,I6: set_nat] :
% 9.53/5.31        ( ( summable_nat @ F )
% 9.53/5.31       => ( ( finite_finite_nat @ I6 )
% 9.53/5.31         => ( ! [N3: nat] :
% 9.53/5.31                ( ( member_nat @ N3 @ ( uminus5710092332889474511et_nat @ I6 ) )
% 9.53/5.31               => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) ) )
% 9.53/5.31           => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ I6 ) @ ( suminf_nat @ F ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7801_sum__le__suminf,axiom,
% 9.53/5.31      ! [F: nat > real,I6: set_nat] :
% 9.53/5.31        ( ( summable_real @ F )
% 9.53/5.31       => ( ( finite_finite_nat @ I6 )
% 9.53/5.31         => ( ! [N3: nat] :
% 9.53/5.31                ( ( member_nat @ N3 @ ( uminus5710092332889474511et_nat @ I6 ) )
% 9.53/5.31               => ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) ) )
% 9.53/5.31           => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ I6 ) @ ( suminf_real @ F ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7802_sum__diff__distrib,axiom,
% 9.53/5.31      ! [Q: real > nat,P: real > nat,N: real] :
% 9.53/5.31        ( ! [X3: real] : ( ord_less_eq_nat @ ( Q @ X3 ) @ ( P @ X3 ) )
% 9.53/5.31       => ( ( minus_minus_nat @ ( groups1935376822645274424al_nat @ P @ ( set_or5984915006950818249n_real @ N ) ) @ ( groups1935376822645274424al_nat @ Q @ ( set_or5984915006950818249n_real @ N ) ) )
% 9.53/5.31          = ( groups1935376822645274424al_nat
% 9.53/5.31            @ ^ [X2: real] : ( minus_minus_nat @ ( P @ X2 ) @ ( Q @ X2 ) )
% 9.53/5.31            @ ( set_or5984915006950818249n_real @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7803_sum__diff__distrib,axiom,
% 9.53/5.31      ! [Q: nat > nat,P: nat > nat,N: nat] :
% 9.53/5.31        ( ! [X3: nat] : ( ord_less_eq_nat @ ( Q @ X3 ) @ ( P @ X3 ) )
% 9.53/5.31       => ( ( minus_minus_nat @ ( groups3542108847815614940at_nat @ P @ ( set_ord_lessThan_nat @ N ) ) @ ( groups3542108847815614940at_nat @ Q @ ( set_ord_lessThan_nat @ N ) ) )
% 9.53/5.31          = ( groups3542108847815614940at_nat
% 9.53/5.31            @ ^ [X2: nat] : ( minus_minus_nat @ ( P @ X2 ) @ ( Q @ X2 ) )
% 9.53/5.31            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7804_powr__realpow,axiom,
% 9.53/5.31      ! [X: real,N: nat] :
% 9.53/5.31        ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.31       => ( ( powr_real @ X @ ( semiri5074537144036343181t_real @ N ) )
% 9.53/5.31          = ( power_power_real @ X @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7805_less__log__iff,axiom,
% 9.53/5.31      ! [B: real,X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_real @ one_one_real @ B )
% 9.53/5.31       => ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.31         => ( ( ord_less_real @ Y2 @ ( log @ B @ X ) )
% 9.53/5.31            = ( ord_less_real @ ( powr_real @ B @ Y2 ) @ X ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7806_log__less__iff,axiom,
% 9.53/5.31      ! [B: real,X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_real @ one_one_real @ B )
% 9.53/5.31       => ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.31         => ( ( ord_less_real @ ( log @ B @ X ) @ Y2 )
% 9.53/5.31            = ( ord_less_real @ X @ ( powr_real @ B @ Y2 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7807_less__powr__iff,axiom,
% 9.53/5.31      ! [B: real,X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_real @ one_one_real @ B )
% 9.53/5.31       => ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.31         => ( ( ord_less_real @ X @ ( powr_real @ B @ Y2 ) )
% 9.53/5.31            = ( ord_less_real @ ( log @ B @ X ) @ Y2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7808_powr__less__iff,axiom,
% 9.53/5.31      ! [B: real,X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_real @ one_one_real @ B )
% 9.53/5.31       => ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.31         => ( ( ord_less_real @ ( powr_real @ B @ Y2 ) @ X )
% 9.53/5.31            = ( ord_less_real @ Y2 @ ( log @ B @ X ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7809_powser__inside,axiom,
% 9.53/5.31      ! [F: nat > real,X: real,Z: real] :
% 9.53/5.31        ( ( summable_real
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ X @ N2 ) ) )
% 9.53/5.31       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ ( real_V7735802525324610683m_real @ X ) )
% 9.53/5.31         => ( summable_real
% 9.53/5.31            @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7810_powser__inside,axiom,
% 9.53/5.31      ! [F: nat > complex,X: complex,Z: complex] :
% 9.53/5.31        ( ( summable_complex
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ X @ N2 ) ) )
% 9.53/5.31       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ ( real_V1022390504157884413omplex @ X ) )
% 9.53/5.31         => ( summable_complex
% 9.53/5.31            @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7811_pi__less__4,axiom,
% 9.53/5.31      ord_less_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7812_pi__ge__two,axiom,
% 9.53/5.31      ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7813_pi__half__neq__two,axiom,
% 9.53/5.31      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 9.53/5.31     != ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7814_sum__pos__lt__pair,axiom,
% 9.53/5.31      ! [F: nat > real,K: nat] :
% 9.53/5.31        ( ( summable_real @ F )
% 9.53/5.31       => ( ! [D3: nat] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( F @ ( plus_plus_nat @ K @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D3 ) ) ) @ ( F @ ( plus_plus_nat @ K @ ( plus_plus_nat @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D3 ) @ one_one_nat ) ) ) ) )
% 9.53/5.31         => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) @ ( suminf_real @ F ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7815_powser__split__head_I1_J,axiom,
% 9.53/5.31      ! [F: nat > complex,Z: complex] :
% 9.53/5.31        ( ( summable_complex
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) )
% 9.53/5.31       => ( ( suminf_complex
% 9.53/5.31            @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) )
% 9.53/5.31          = ( plus_plus_complex @ ( F @ zero_zero_nat )
% 9.53/5.31            @ ( times_times_complex
% 9.53/5.31              @ ( suminf_complex
% 9.53/5.31                @ ^ [N2: nat] : ( times_times_complex @ ( F @ ( suc @ N2 ) ) @ ( power_power_complex @ Z @ N2 ) ) )
% 9.53/5.31              @ Z ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7816_powser__split__head_I1_J,axiom,
% 9.53/5.31      ! [F: nat > real,Z: real] :
% 9.53/5.31        ( ( summable_real
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) )
% 9.53/5.31       => ( ( suminf_real
% 9.53/5.31            @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) )
% 9.53/5.31          = ( plus_plus_real @ ( F @ zero_zero_nat )
% 9.53/5.31            @ ( times_times_real
% 9.53/5.31              @ ( suminf_real
% 9.53/5.31                @ ^ [N2: nat] : ( times_times_real @ ( F @ ( suc @ N2 ) ) @ ( power_power_real @ Z @ N2 ) ) )
% 9.53/5.31              @ Z ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7817_sum_OlessThan__Suc__shift,axiom,
% 9.53/5.31      ! [G: nat > rat,N: nat] :
% 9.53/5.31        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 9.53/5.31        = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 9.53/5.31          @ ( groups2906978787729119204at_rat
% 9.53/5.31            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.53/5.31            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7818_sum_OlessThan__Suc__shift,axiom,
% 9.53/5.31      ! [G: nat > int,N: nat] :
% 9.53/5.31        ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 9.53/5.31        = ( plus_plus_int @ ( G @ zero_zero_nat )
% 9.53/5.31          @ ( groups3539618377306564664at_int
% 9.53/5.31            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.53/5.31            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7819_sum_OlessThan__Suc__shift,axiom,
% 9.53/5.31      ! [G: nat > complex,N: nat] :
% 9.53/5.31        ( ( groups2073611262835488442omplex @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 9.53/5.31        = ( plus_plus_complex @ ( G @ zero_zero_nat )
% 9.53/5.31          @ ( groups2073611262835488442omplex
% 9.53/5.31            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.53/5.31            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7820_sum_OlessThan__Suc__shift,axiom,
% 9.53/5.31      ! [G: nat > nat,N: nat] :
% 9.53/5.31        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 9.53/5.31        = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 9.53/5.31          @ ( groups3542108847815614940at_nat
% 9.53/5.31            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.53/5.31            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7821_sum_OlessThan__Suc__shift,axiom,
% 9.53/5.31      ! [G: nat > real,N: nat] :
% 9.53/5.31        ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 9.53/5.31        = ( plus_plus_real @ ( G @ zero_zero_nat )
% 9.53/5.31          @ ( groups6591440286371151544t_real
% 9.53/5.31            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.53/5.31            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7822_powser__split__head_I2_J,axiom,
% 9.53/5.31      ! [F: nat > complex,Z: complex] :
% 9.53/5.31        ( ( summable_complex
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) )
% 9.53/5.31       => ( ( times_times_complex
% 9.53/5.31            @ ( suminf_complex
% 9.53/5.31              @ ^ [N2: nat] : ( times_times_complex @ ( F @ ( suc @ N2 ) ) @ ( power_power_complex @ Z @ N2 ) ) )
% 9.53/5.31            @ Z )
% 9.53/5.31          = ( minus_minus_complex
% 9.53/5.31            @ ( suminf_complex
% 9.53/5.31              @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) )
% 9.53/5.31            @ ( F @ zero_zero_nat ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7823_powser__split__head_I2_J,axiom,
% 9.53/5.31      ! [F: nat > real,Z: real] :
% 9.53/5.31        ( ( summable_real
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) )
% 9.53/5.31       => ( ( times_times_real
% 9.53/5.31            @ ( suminf_real
% 9.53/5.31              @ ^ [N2: nat] : ( times_times_real @ ( F @ ( suc @ N2 ) ) @ ( power_power_real @ Z @ N2 ) ) )
% 9.53/5.31            @ Z )
% 9.53/5.31          = ( minus_minus_real
% 9.53/5.31            @ ( suminf_real
% 9.53/5.31              @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) )
% 9.53/5.31            @ ( F @ zero_zero_nat ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7824_sum__lessThan__telescope_H,axiom,
% 9.53/5.31      ! [F: nat > rat,M: nat] :
% 9.53/5.31        ( ( groups2906978787729119204at_rat
% 9.53/5.31          @ ^ [N2: nat] : ( minus_minus_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 9.53/5.31          @ ( set_ord_lessThan_nat @ M ) )
% 9.53/5.31        = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7825_sum__lessThan__telescope_H,axiom,
% 9.53/5.31      ! [F: nat > int,M: nat] :
% 9.53/5.31        ( ( groups3539618377306564664at_int
% 9.53/5.31          @ ^ [N2: nat] : ( minus_minus_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 9.53/5.31          @ ( set_ord_lessThan_nat @ M ) )
% 9.53/5.31        = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7826_sum__lessThan__telescope_H,axiom,
% 9.53/5.31      ! [F: nat > real,M: nat] :
% 9.53/5.31        ( ( groups6591440286371151544t_real
% 9.53/5.31          @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 9.53/5.31          @ ( set_ord_lessThan_nat @ M ) )
% 9.53/5.31        = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7827_sum__lessThan__telescope,axiom,
% 9.53/5.31      ! [F: nat > rat,M: nat] :
% 9.53/5.31        ( ( groups2906978787729119204at_rat
% 9.53/5.31          @ ^ [N2: nat] : ( minus_minus_rat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 9.53/5.31          @ ( set_ord_lessThan_nat @ M ) )
% 9.53/5.31        = ( minus_minus_rat @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7828_sum__lessThan__telescope,axiom,
% 9.53/5.31      ! [F: nat > int,M: nat] :
% 9.53/5.31        ( ( groups3539618377306564664at_int
% 9.53/5.31          @ ^ [N2: nat] : ( minus_minus_int @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 9.53/5.31          @ ( set_ord_lessThan_nat @ M ) )
% 9.53/5.31        = ( minus_minus_int @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7829_sum__lessThan__telescope,axiom,
% 9.53/5.31      ! [F: nat > real,M: nat] :
% 9.53/5.31        ( ( groups6591440286371151544t_real
% 9.53/5.31          @ ^ [N2: nat] : ( minus_minus_real @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 9.53/5.31          @ ( set_ord_lessThan_nat @ M ) )
% 9.53/5.31        = ( minus_minus_real @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7830_sumr__diff__mult__const2,axiom,
% 9.53/5.31      ! [F: nat > rat,N: nat,R: rat] :
% 9.53/5.31        ( ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ R ) )
% 9.53/5.31        = ( groups2906978787729119204at_rat
% 9.53/5.31          @ ^ [I3: nat] : ( minus_minus_rat @ ( F @ I3 ) @ R )
% 9.53/5.31          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7831_sumr__diff__mult__const2,axiom,
% 9.53/5.31      ! [F: nat > int,N: nat,R: int] :
% 9.53/5.31        ( ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ R ) )
% 9.53/5.31        = ( groups3539618377306564664at_int
% 9.53/5.31          @ ^ [I3: nat] : ( minus_minus_int @ ( F @ I3 ) @ R )
% 9.53/5.31          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7832_sumr__diff__mult__const2,axiom,
% 9.53/5.31      ! [F: nat > complex,N: nat,R: complex] :
% 9.53/5.31        ( ( minus_minus_complex @ ( groups2073611262835488442omplex @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ R ) )
% 9.53/5.31        = ( groups2073611262835488442omplex
% 9.53/5.31          @ ^ [I3: nat] : ( minus_minus_complex @ ( F @ I3 ) @ R )
% 9.53/5.31          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7833_sumr__diff__mult__const2,axiom,
% 9.53/5.31      ! [F: nat > real,N: nat,R: real] :
% 9.53/5.31        ( ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ R ) )
% 9.53/5.31        = ( groups6591440286371151544t_real
% 9.53/5.31          @ ^ [I3: nat] : ( minus_minus_real @ ( F @ I3 ) @ R )
% 9.53/5.31          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7834_sum_OatLeast1__atMost__eq,axiom,
% 9.53/5.31      ! [G: nat > nat,N: nat] :
% 9.53/5.31        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 9.53/5.31        = ( groups3542108847815614940at_nat
% 9.53/5.31          @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 9.53/5.31          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7835_sum_OatLeast1__atMost__eq,axiom,
% 9.53/5.31      ! [G: nat > real,N: nat] :
% 9.53/5.31        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 9.53/5.31        = ( groups6591440286371151544t_real
% 9.53/5.31          @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 9.53/5.31          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7836_suminf__exist__split,axiom,
% 9.53/5.31      ! [R: real,F: nat > real] :
% 9.53/5.31        ( ( ord_less_real @ zero_zero_real @ R )
% 9.53/5.31       => ( ( summable_real @ F )
% 9.53/5.31         => ? [N8: nat] :
% 9.53/5.31            ! [N9: nat] :
% 9.53/5.31              ( ( ord_less_eq_nat @ N8 @ N9 )
% 9.53/5.31             => ( ord_less_real
% 9.53/5.31                @ ( real_V7735802525324610683m_real
% 9.53/5.31                  @ ( suminf_real
% 9.53/5.31                    @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N9 ) ) ) )
% 9.53/5.31                @ R ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7837_suminf__exist__split,axiom,
% 9.53/5.31      ! [R: real,F: nat > complex] :
% 9.53/5.31        ( ( ord_less_real @ zero_zero_real @ R )
% 9.53/5.31       => ( ( summable_complex @ F )
% 9.53/5.31         => ? [N8: nat] :
% 9.53/5.31            ! [N9: nat] :
% 9.53/5.31              ( ( ord_less_eq_nat @ N8 @ N9 )
% 9.53/5.31             => ( ord_less_real
% 9.53/5.31                @ ( real_V1022390504157884413omplex
% 9.53/5.31                  @ ( suminf_complex
% 9.53/5.31                    @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N9 ) ) ) )
% 9.53/5.31                @ R ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7838_summable__partial__sum__bound,axiom,
% 9.53/5.31      ! [F: nat > complex,E: real] :
% 9.53/5.31        ( ( summable_complex @ F )
% 9.53/5.31       => ( ( ord_less_real @ zero_zero_real @ E )
% 9.53/5.31         => ~ ! [N8: nat] :
% 9.53/5.31                ~ ! [M5: nat] :
% 9.53/5.31                    ( ( ord_less_eq_nat @ N8 @ M5 )
% 9.53/5.31                   => ! [N9: nat] : ( ord_less_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ M5 @ N9 ) ) ) @ E ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7839_summable__partial__sum__bound,axiom,
% 9.53/5.31      ! [F: nat > real,E: real] :
% 9.53/5.31        ( ( summable_real @ F )
% 9.53/5.31       => ( ( ord_less_real @ zero_zero_real @ E )
% 9.53/5.31         => ~ ! [N8: nat] :
% 9.53/5.31                ~ ! [M5: nat] :
% 9.53/5.31                    ( ( ord_less_eq_nat @ N8 @ M5 )
% 9.53/5.31                   => ! [N9: nat] : ( ord_less_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ M5 @ N9 ) ) ) @ E ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7840_summable__power__series,axiom,
% 9.53/5.31      ! [F: nat > real,Z: real] :
% 9.53/5.31        ( ! [I4: nat] : ( ord_less_eq_real @ ( F @ I4 ) @ one_one_real )
% 9.53/5.31       => ( ! [I4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 9.53/5.31         => ( ( ord_less_eq_real @ zero_zero_real @ Z )
% 9.53/5.31           => ( ( ord_less_real @ Z @ one_one_real )
% 9.53/5.31             => ( summable_real
% 9.53/5.31                @ ^ [I3: nat] : ( times_times_real @ ( F @ I3 ) @ ( power_power_real @ Z @ I3 ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7841_Abel__lemma,axiom,
% 9.53/5.31      ! [R: real,R0: real,A: nat > complex,M7: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ zero_zero_real @ R )
% 9.53/5.31       => ( ( ord_less_real @ R @ R0 )
% 9.53/5.31         => ( ! [N3: nat] : ( ord_less_eq_real @ ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N3 ) ) @ ( power_power_real @ R0 @ N3 ) ) @ M7 )
% 9.53/5.31           => ( summable_real
% 9.53/5.31              @ ^ [N2: nat] : ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N2 ) ) @ ( power_power_real @ R @ N2 ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7842_powr__minus__divide,axiom,
% 9.53/5.31      ! [X: real,A: real] :
% 9.53/5.31        ( ( powr_real @ X @ ( uminus_uminus_real @ A ) )
% 9.53/5.31        = ( divide_divide_real @ one_one_real @ ( powr_real @ X @ A ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7843_summable__ratio__test,axiom,
% 9.53/5.31      ! [C: real,N4: nat,F: nat > real] :
% 9.53/5.31        ( ( ord_less_real @ C @ one_one_real )
% 9.53/5.31       => ( ! [N3: nat] :
% 9.53/5.31              ( ( ord_less_eq_nat @ N4 @ N3 )
% 9.53/5.31             => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ ( suc @ N3 ) ) ) @ ( times_times_real @ C @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) ) ) )
% 9.53/5.31         => ( summable_real @ F ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7844_summable__ratio__test,axiom,
% 9.53/5.31      ! [C: real,N4: nat,F: nat > complex] :
% 9.53/5.31        ( ( ord_less_real @ C @ one_one_real )
% 9.53/5.31       => ( ! [N3: nat] :
% 9.53/5.31              ( ( ord_less_eq_nat @ N4 @ N3 )
% 9.53/5.31             => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ ( suc @ N3 ) ) ) @ ( times_times_real @ C @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) ) ) )
% 9.53/5.31         => ( summable_complex @ F ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7845_powr__neg__one,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.31       => ( ( powr_real @ X @ ( uminus_uminus_real @ one_one_real ) )
% 9.53/5.31          = ( divide_divide_real @ one_one_real @ X ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7846_powr__mult__base,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.31       => ( ( times_times_real @ X @ ( powr_real @ X @ Y2 ) )
% 9.53/5.31          = ( powr_real @ X @ ( plus_plus_real @ one_one_real @ Y2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7847_le__log__iff,axiom,
% 9.53/5.31      ! [B: real,X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_real @ one_one_real @ B )
% 9.53/5.31       => ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.31         => ( ( ord_less_eq_real @ Y2 @ ( log @ B @ X ) )
% 9.53/5.31            = ( ord_less_eq_real @ ( powr_real @ B @ Y2 ) @ X ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7848_log__le__iff,axiom,
% 9.53/5.31      ! [B: real,X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_real @ one_one_real @ B )
% 9.53/5.31       => ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.31         => ( ( ord_less_eq_real @ ( log @ B @ X ) @ Y2 )
% 9.53/5.31            = ( ord_less_eq_real @ X @ ( powr_real @ B @ Y2 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7849_le__powr__iff,axiom,
% 9.53/5.31      ! [B: real,X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_real @ one_one_real @ B )
% 9.53/5.31       => ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.31         => ( ( ord_less_eq_real @ X @ ( powr_real @ B @ Y2 ) )
% 9.53/5.31            = ( ord_less_eq_real @ ( log @ B @ X ) @ Y2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7850_powr__le__iff,axiom,
% 9.53/5.31      ! [B: real,X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_real @ one_one_real @ B )
% 9.53/5.31       => ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.31         => ( ( ord_less_eq_real @ ( powr_real @ B @ Y2 ) @ X )
% 9.53/5.31            = ( ord_less_eq_real @ Y2 @ ( log @ B @ X ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7851_pi__half__neq__zero,axiom,
% 9.53/5.31      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 9.53/5.31     != zero_zero_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7852_pi__half__less__two,axiom,
% 9.53/5.31      ord_less_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7853_pi__half__le__two,axiom,
% 9.53/5.31      ord_less_eq_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7854_one__diff__power__eq,axiom,
% 9.53/5.31      ! [X: rat,N: nat] :
% 9.53/5.31        ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) )
% 9.53/5.31        = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7855_one__diff__power__eq,axiom,
% 9.53/5.31      ! [X: complex,N: nat] :
% 9.53/5.31        ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N ) )
% 9.53/5.31        = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7856_one__diff__power__eq,axiom,
% 9.53/5.31      ! [X: int,N: nat] :
% 9.53/5.31        ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N ) )
% 9.53/5.31        = ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7857_one__diff__power__eq,axiom,
% 9.53/5.31      ! [X: real,N: nat] :
% 9.53/5.31        ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N ) )
% 9.53/5.31        = ( times_times_real @ ( minus_minus_real @ one_one_real @ X ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7858_power__diff__1__eq,axiom,
% 9.53/5.31      ! [X: rat,N: nat] :
% 9.53/5.31        ( ( minus_minus_rat @ ( power_power_rat @ X @ N ) @ one_one_rat )
% 9.53/5.31        = ( times_times_rat @ ( minus_minus_rat @ X @ one_one_rat ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7859_power__diff__1__eq,axiom,
% 9.53/5.31      ! [X: complex,N: nat] :
% 9.53/5.31        ( ( minus_minus_complex @ ( power_power_complex @ X @ N ) @ one_one_complex )
% 9.53/5.31        = ( times_times_complex @ ( minus_minus_complex @ X @ one_one_complex ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7860_power__diff__1__eq,axiom,
% 9.53/5.31      ! [X: int,N: nat] :
% 9.53/5.31        ( ( minus_minus_int @ ( power_power_int @ X @ N ) @ one_one_int )
% 9.53/5.31        = ( times_times_int @ ( minus_minus_int @ X @ one_one_int ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7861_power__diff__1__eq,axiom,
% 9.53/5.31      ! [X: real,N: nat] :
% 9.53/5.31        ( ( minus_minus_real @ ( power_power_real @ X @ N ) @ one_one_real )
% 9.53/5.31        = ( times_times_real @ ( minus_minus_real @ X @ one_one_real ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7862_geometric__sum,axiom,
% 9.53/5.31      ! [X: complex,N: nat] :
% 9.53/5.31        ( ( X != one_one_complex )
% 9.53/5.31       => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.31          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X @ N ) @ one_one_complex ) @ ( minus_minus_complex @ X @ one_one_complex ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7863_geometric__sum,axiom,
% 9.53/5.31      ! [X: rat,N: nat] :
% 9.53/5.31        ( ( X != one_one_rat )
% 9.53/5.31       => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.31          = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ N ) @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7864_geometric__sum,axiom,
% 9.53/5.31      ! [X: real,N: nat] :
% 9.53/5.31        ( ( X != one_one_real )
% 9.53/5.31       => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.31          = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ N ) @ one_one_real ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7865_ln__powr__bound,axiom,
% 9.53/5.31      ! [X: real,A: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ one_one_real @ X )
% 9.53/5.31       => ( ( ord_less_real @ zero_zero_real @ A )
% 9.53/5.31         => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( divide_divide_real @ ( powr_real @ X @ A ) @ A ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7866_ln__powr__bound2,axiom,
% 9.53/5.31      ! [X: real,A: real] :
% 9.53/5.31        ( ( ord_less_real @ one_one_real @ X )
% 9.53/5.31       => ( ( ord_less_real @ zero_zero_real @ A )
% 9.53/5.31         => ( ord_less_eq_real @ ( powr_real @ ( ln_ln_real @ X ) @ A ) @ ( times_times_real @ ( powr_real @ A @ A ) @ X ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7867_log__add__eq__powr,axiom,
% 9.53/5.31      ! [B: real,X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_real @ zero_zero_real @ B )
% 9.53/5.31       => ( ( B != one_one_real )
% 9.53/5.31         => ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.31           => ( ( plus_plus_real @ ( log @ B @ X ) @ Y2 )
% 9.53/5.31              = ( log @ B @ ( times_times_real @ X @ ( powr_real @ B @ Y2 ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7868_add__log__eq__powr,axiom,
% 9.53/5.31      ! [B: real,X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_real @ zero_zero_real @ B )
% 9.53/5.31       => ( ( B != one_one_real )
% 9.53/5.31         => ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.31           => ( ( plus_plus_real @ Y2 @ ( log @ B @ X ) )
% 9.53/5.31              = ( log @ B @ ( times_times_real @ ( powr_real @ B @ Y2 ) @ X ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7869_minus__log__eq__powr,axiom,
% 9.53/5.31      ! [B: real,X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_real @ zero_zero_real @ B )
% 9.53/5.31       => ( ( B != one_one_real )
% 9.53/5.31         => ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.31           => ( ( minus_minus_real @ Y2 @ ( log @ B @ X ) )
% 9.53/5.31              = ( log @ B @ ( divide_divide_real @ ( powr_real @ B @ Y2 ) @ X ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7870_sum__gp__strict,axiom,
% 9.53/5.31      ! [X: rat,N: nat] :
% 9.53/5.31        ( ( ( X = one_one_rat )
% 9.53/5.31         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.31            = ( semiri681578069525770553at_rat @ N ) ) )
% 9.53/5.31        & ( ( X != one_one_rat )
% 9.53/5.31         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.31            = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7871_sum__gp__strict,axiom,
% 9.53/5.31      ! [X: complex,N: nat] :
% 9.53/5.31        ( ( ( X = one_one_complex )
% 9.53/5.31         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.31            = ( semiri8010041392384452111omplex @ N ) ) )
% 9.53/5.31        & ( ( X != one_one_complex )
% 9.53/5.31         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.31            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7872_sum__gp__strict,axiom,
% 9.53/5.31      ! [X: real,N: nat] :
% 9.53/5.31        ( ( ( X = one_one_real )
% 9.53/5.31         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.31            = ( semiri5074537144036343181t_real @ N ) ) )
% 9.53/5.31        & ( ( X != one_one_real )
% 9.53/5.31         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.31            = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7873_lemma__termdiff1,axiom,
% 9.53/5.31      ! [Z: rat,H2: rat,M: nat] :
% 9.53/5.31        ( ( groups2906978787729119204at_rat
% 9.53/5.31          @ ^ [P4: nat] : ( minus_minus_rat @ ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_rat @ Z @ P4 ) ) @ ( power_power_rat @ Z @ M ) )
% 9.53/5.31          @ ( set_ord_lessThan_nat @ M ) )
% 9.53/5.31        = ( groups2906978787729119204at_rat
% 9.53/5.31          @ ^ [P4: nat] : ( times_times_rat @ ( power_power_rat @ Z @ P4 ) @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ M @ P4 ) ) ) )
% 9.53/5.31          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7874_lemma__termdiff1,axiom,
% 9.53/5.31      ! [Z: complex,H2: complex,M: nat] :
% 9.53/5.31        ( ( groups2073611262835488442omplex
% 9.53/5.31          @ ^ [P4: nat] : ( minus_minus_complex @ ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_complex @ Z @ P4 ) ) @ ( power_power_complex @ Z @ M ) )
% 9.53/5.31          @ ( set_ord_lessThan_nat @ M ) )
% 9.53/5.31        = ( groups2073611262835488442omplex
% 9.53/5.31          @ ^ [P4: nat] : ( times_times_complex @ ( power_power_complex @ Z @ P4 ) @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ M @ P4 ) ) ) )
% 9.53/5.31          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7875_lemma__termdiff1,axiom,
% 9.53/5.31      ! [Z: int,H2: int,M: nat] :
% 9.53/5.31        ( ( groups3539618377306564664at_int
% 9.53/5.31          @ ^ [P4: nat] : ( minus_minus_int @ ( times_times_int @ ( power_power_int @ ( plus_plus_int @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_int @ Z @ P4 ) ) @ ( power_power_int @ Z @ M ) )
% 9.53/5.31          @ ( set_ord_lessThan_nat @ M ) )
% 9.53/5.31        = ( groups3539618377306564664at_int
% 9.53/5.31          @ ^ [P4: nat] : ( times_times_int @ ( power_power_int @ Z @ P4 ) @ ( minus_minus_int @ ( power_power_int @ ( plus_plus_int @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_int @ Z @ ( minus_minus_nat @ M @ P4 ) ) ) )
% 9.53/5.31          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7876_lemma__termdiff1,axiom,
% 9.53/5.31      ! [Z: real,H2: real,M: nat] :
% 9.53/5.31        ( ( groups6591440286371151544t_real
% 9.53/5.31          @ ^ [P4: nat] : ( minus_minus_real @ ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_real @ Z @ P4 ) ) @ ( power_power_real @ Z @ M ) )
% 9.53/5.31          @ ( set_ord_lessThan_nat @ M ) )
% 9.53/5.31        = ( groups6591440286371151544t_real
% 9.53/5.31          @ ^ [P4: nat] : ( times_times_real @ ( power_power_real @ Z @ P4 ) @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_real @ Z @ ( minus_minus_nat @ M @ P4 ) ) ) )
% 9.53/5.31          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7877_pi__half__gt__zero,axiom,
% 9.53/5.31      ord_less_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7878_pi__half__ge__zero,axiom,
% 9.53/5.31      ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7879_power__diff__sumr2,axiom,
% 9.53/5.31      ! [X: rat,N: nat,Y2: rat] :
% 9.53/5.31        ( ( minus_minus_rat @ ( power_power_rat @ X @ N ) @ ( power_power_rat @ Y2 @ N ) )
% 9.53/5.31        = ( times_times_rat @ ( minus_minus_rat @ X @ Y2 )
% 9.53/5.31          @ ( groups2906978787729119204at_rat
% 9.53/5.31            @ ^ [I3: nat] : ( times_times_rat @ ( power_power_rat @ Y2 @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) ) @ ( power_power_rat @ X @ I3 ) )
% 9.53/5.31            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7880_power__diff__sumr2,axiom,
% 9.53/5.31      ! [X: complex,N: nat,Y2: complex] :
% 9.53/5.31        ( ( minus_minus_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y2 @ N ) )
% 9.53/5.31        = ( times_times_complex @ ( minus_minus_complex @ X @ Y2 )
% 9.53/5.31          @ ( groups2073611262835488442omplex
% 9.53/5.31            @ ^ [I3: nat] : ( times_times_complex @ ( power_power_complex @ Y2 @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) ) @ ( power_power_complex @ X @ I3 ) )
% 9.53/5.31            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7881_power__diff__sumr2,axiom,
% 9.53/5.31      ! [X: int,N: nat,Y2: int] :
% 9.53/5.31        ( ( minus_minus_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y2 @ N ) )
% 9.53/5.31        = ( times_times_int @ ( minus_minus_int @ X @ Y2 )
% 9.53/5.31          @ ( groups3539618377306564664at_int
% 9.53/5.31            @ ^ [I3: nat] : ( times_times_int @ ( power_power_int @ Y2 @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) ) @ ( power_power_int @ X @ I3 ) )
% 9.53/5.31            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7882_power__diff__sumr2,axiom,
% 9.53/5.31      ! [X: real,N: nat,Y2: real] :
% 9.53/5.31        ( ( minus_minus_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y2 @ N ) )
% 9.53/5.31        = ( times_times_real @ ( minus_minus_real @ X @ Y2 )
% 9.53/5.31          @ ( groups6591440286371151544t_real
% 9.53/5.31            @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ Y2 @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) ) @ ( power_power_real @ X @ I3 ) )
% 9.53/5.31            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7883_diff__power__eq__sum,axiom,
% 9.53/5.31      ! [X: rat,N: nat,Y2: rat] :
% 9.53/5.31        ( ( minus_minus_rat @ ( power_power_rat @ X @ ( suc @ N ) ) @ ( power_power_rat @ Y2 @ ( suc @ N ) ) )
% 9.53/5.31        = ( times_times_rat @ ( minus_minus_rat @ X @ Y2 )
% 9.53/5.31          @ ( groups2906978787729119204at_rat
% 9.53/5.31            @ ^ [P4: nat] : ( times_times_rat @ ( power_power_rat @ X @ P4 ) @ ( power_power_rat @ Y2 @ ( minus_minus_nat @ N @ P4 ) ) )
% 9.53/5.31            @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7884_diff__power__eq__sum,axiom,
% 9.53/5.31      ! [X: complex,N: nat,Y2: complex] :
% 9.53/5.31        ( ( minus_minus_complex @ ( power_power_complex @ X @ ( suc @ N ) ) @ ( power_power_complex @ Y2 @ ( suc @ N ) ) )
% 9.53/5.31        = ( times_times_complex @ ( minus_minus_complex @ X @ Y2 )
% 9.53/5.31          @ ( groups2073611262835488442omplex
% 9.53/5.31            @ ^ [P4: nat] : ( times_times_complex @ ( power_power_complex @ X @ P4 ) @ ( power_power_complex @ Y2 @ ( minus_minus_nat @ N @ P4 ) ) )
% 9.53/5.31            @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7885_diff__power__eq__sum,axiom,
% 9.53/5.31      ! [X: int,N: nat,Y2: int] :
% 9.53/5.31        ( ( minus_minus_int @ ( power_power_int @ X @ ( suc @ N ) ) @ ( power_power_int @ Y2 @ ( suc @ N ) ) )
% 9.53/5.31        = ( times_times_int @ ( minus_minus_int @ X @ Y2 )
% 9.53/5.31          @ ( groups3539618377306564664at_int
% 9.53/5.31            @ ^ [P4: nat] : ( times_times_int @ ( power_power_int @ X @ P4 ) @ ( power_power_int @ Y2 @ ( minus_minus_nat @ N @ P4 ) ) )
% 9.53/5.31            @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7886_diff__power__eq__sum,axiom,
% 9.53/5.31      ! [X: real,N: nat,Y2: real] :
% 9.53/5.31        ( ( minus_minus_real @ ( power_power_real @ X @ ( suc @ N ) ) @ ( power_power_real @ Y2 @ ( suc @ N ) ) )
% 9.53/5.31        = ( times_times_real @ ( minus_minus_real @ X @ Y2 )
% 9.53/5.31          @ ( groups6591440286371151544t_real
% 9.53/5.31            @ ^ [P4: nat] : ( times_times_real @ ( power_power_real @ X @ P4 ) @ ( power_power_real @ Y2 @ ( minus_minus_nat @ N @ P4 ) ) )
% 9.53/5.31            @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7887_m2pi__less__pi,axiom,
% 9.53/5.31      ord_less_real @ ( uminus_uminus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) @ pi ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7888_powr__def,axiom,
% 9.53/5.31      ( powr_real
% 9.53/5.31      = ( ^ [X2: real,A3: real] : ( if_real @ ( X2 = zero_zero_real ) @ zero_zero_real @ ( exp_real @ ( times_times_real @ A3 @ ( ln_ln_real @ X2 ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7889_arctan__ubound,axiom,
% 9.53/5.31      ! [Y2: real] : ( ord_less_real @ ( arctan @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7890_arctan__one,axiom,
% 9.53/5.31      ( ( arctan @ one_one_real )
% 9.53/5.31      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7891_real__sum__nat__ivl__bounded2,axiom,
% 9.53/5.31      ! [N: nat,F: nat > rat,K5: rat,K: nat] :
% 9.53/5.31        ( ! [P7: nat] :
% 9.53/5.31            ( ( ord_less_nat @ P7 @ N )
% 9.53/5.31           => ( ord_less_eq_rat @ ( F @ P7 ) @ K5 ) )
% 9.53/5.31       => ( ( ord_less_eq_rat @ zero_zero_rat @ K5 )
% 9.53/5.31         => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ K5 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7892_real__sum__nat__ivl__bounded2,axiom,
% 9.53/5.31      ! [N: nat,F: nat > int,K5: int,K: nat] :
% 9.53/5.31        ( ! [P7: nat] :
% 9.53/5.31            ( ( ord_less_nat @ P7 @ N )
% 9.53/5.31           => ( ord_less_eq_int @ ( F @ P7 ) @ K5 ) )
% 9.53/5.31       => ( ( ord_less_eq_int @ zero_zero_int @ K5 )
% 9.53/5.31         => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ K5 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7893_real__sum__nat__ivl__bounded2,axiom,
% 9.53/5.31      ! [N: nat,F: nat > nat,K5: nat,K: nat] :
% 9.53/5.31        ( ! [P7: nat] :
% 9.53/5.31            ( ( ord_less_nat @ P7 @ N )
% 9.53/5.31           => ( ord_less_eq_nat @ ( F @ P7 ) @ K5 ) )
% 9.53/5.31       => ( ( ord_less_eq_nat @ zero_zero_nat @ K5 )
% 9.53/5.31         => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ K5 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7894_real__sum__nat__ivl__bounded2,axiom,
% 9.53/5.31      ! [N: nat,F: nat > real,K5: real,K: nat] :
% 9.53/5.31        ( ! [P7: nat] :
% 9.53/5.31            ( ( ord_less_nat @ P7 @ N )
% 9.53/5.31           => ( ord_less_eq_real @ ( F @ P7 ) @ K5 ) )
% 9.53/5.31       => ( ( ord_less_eq_real @ zero_zero_real @ K5 )
% 9.53/5.31         => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ K5 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7895_log__minus__eq__powr,axiom,
% 9.53/5.31      ! [B: real,X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_real @ zero_zero_real @ B )
% 9.53/5.31       => ( ( B != one_one_real )
% 9.53/5.31         => ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.31           => ( ( minus_minus_real @ ( log @ B @ X ) @ Y2 )
% 9.53/5.31              = ( log @ B @ ( times_times_real @ X @ ( powr_real @ B @ ( uminus_uminus_real @ Y2 ) ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7896_one__diff__power__eq_H,axiom,
% 9.53/5.31      ! [X: rat,N: nat] :
% 9.53/5.31        ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) )
% 9.53/5.31        = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X )
% 9.53/5.31          @ ( groups2906978787729119204at_rat
% 9.53/5.31            @ ^ [I3: nat] : ( power_power_rat @ X @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 9.53/5.31            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7897_one__diff__power__eq_H,axiom,
% 9.53/5.31      ! [X: complex,N: nat] :
% 9.53/5.31        ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N ) )
% 9.53/5.31        = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X )
% 9.53/5.31          @ ( groups2073611262835488442omplex
% 9.53/5.31            @ ^ [I3: nat] : ( power_power_complex @ X @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 9.53/5.31            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7898_one__diff__power__eq_H,axiom,
% 9.53/5.31      ! [X: int,N: nat] :
% 9.53/5.31        ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N ) )
% 9.53/5.31        = ( times_times_int @ ( minus_minus_int @ one_one_int @ X )
% 9.53/5.31          @ ( groups3539618377306564664at_int
% 9.53/5.31            @ ^ [I3: nat] : ( power_power_int @ X @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 9.53/5.31            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7899_one__diff__power__eq_H,axiom,
% 9.53/5.31      ! [X: real,N: nat] :
% 9.53/5.31        ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N ) )
% 9.53/5.31        = ( times_times_real @ ( minus_minus_real @ one_one_real @ X )
% 9.53/5.31          @ ( groups6591440286371151544t_real
% 9.53/5.31            @ ^ [I3: nat] : ( power_power_real @ X @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 9.53/5.31            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7900_minus__pi__half__less__zero,axiom,
% 9.53/5.31      ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ zero_zero_real ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7901_arctan__lbound,axiom,
% 9.53/5.31      ! [Y2: real] : ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y2 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7902_arctan__bounded,axiom,
% 9.53/5.31      ! [Y2: real] :
% 9.53/5.31        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y2 ) )
% 9.53/5.31        & ( ord_less_real @ ( arctan @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7903_powr__half__sqrt,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.31       => ( ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31          = ( sqrt @ X ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7904_powr__neg__numeral,axiom,
% 9.53/5.31      ! [X: real,N: num] :
% 9.53/5.31        ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.31       => ( ( powr_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 9.53/5.31          = ( divide_divide_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ N ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7905_sum__split__even__odd,axiom,
% 9.53/5.31      ! [F: nat > real,G: nat > real,N: nat] :
% 9.53/5.31        ( ( groups6591440286371151544t_real
% 9.53/5.31          @ ^ [I3: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( F @ I3 ) @ ( G @ I3 ) )
% 9.53/5.31          @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 9.53/5.31        = ( plus_plus_real
% 9.53/5.31          @ ( groups6591440286371151544t_real
% 9.53/5.31            @ ^ [I3: nat] : ( F @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) )
% 9.53/5.31            @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.31          @ ( groups6591440286371151544t_real
% 9.53/5.31            @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ one_one_nat ) )
% 9.53/5.31            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7906_machin__Euler,axiom,
% 9.53/5.31      ( ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ one ) ) ) @ ( arctan @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 9.53/5.31      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7907_machin,axiom,
% 9.53/5.31      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 9.53/5.31      = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( arctan @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( arctan @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7908_sum__bounds__lt__plus1,axiom,
% 9.53/5.31      ! [F: nat > nat,Mm: nat] :
% 9.53/5.31        ( ( groups3542108847815614940at_nat
% 9.53/5.31          @ ^ [K3: nat] : ( F @ ( suc @ K3 ) )
% 9.53/5.31          @ ( set_ord_lessThan_nat @ Mm ) )
% 9.53/5.31        = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7909_sum__bounds__lt__plus1,axiom,
% 9.53/5.31      ! [F: nat > real,Mm: nat] :
% 9.53/5.31        ( ( groups6591440286371151544t_real
% 9.53/5.31          @ ^ [K3: nat] : ( F @ ( suc @ K3 ) )
% 9.53/5.31          @ ( set_ord_lessThan_nat @ Mm ) )
% 9.53/5.31        = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7910_sin__cos__npi,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( sin_real @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31        = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7911_sumr__cos__zero__one,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( groups6591440286371151544t_real
% 9.53/5.31          @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ zero_zero_real @ M6 ) )
% 9.53/5.31          @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 9.53/5.31        = one_one_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7912_cos__pi__eq__zero,axiom,
% 9.53/5.31      ! [M: nat] :
% 9.53/5.31        ( ( cos_real @ ( divide_divide_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31        = zero_zero_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7913_arcosh__def,axiom,
% 9.53/5.31      ( arcosh_real
% 9.53/5.31      = ( ^ [X2: real] : ( ln_ln_real @ ( plus_plus_real @ X2 @ ( powr_real @ ( minus_minus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( real_V1803761363581548252l_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7914_cos__zero,axiom,
% 9.53/5.31      ( ( cos_complex @ zero_zero_complex )
% 9.53/5.31      = one_one_complex ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7915_cos__zero,axiom,
% 9.53/5.31      ( ( cos_real @ zero_zero_real )
% 9.53/5.31      = one_one_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7916_of__real__eq__1__iff,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ( real_V1803761363581548252l_real @ X )
% 9.53/5.31          = one_one_real )
% 9.53/5.31        = ( X = one_one_real ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7917_of__real__eq__1__iff,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ( real_V4546457046886955230omplex @ X )
% 9.53/5.31          = one_one_complex )
% 9.53/5.31        = ( X = one_one_real ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7918_of__real__1,axiom,
% 9.53/5.31      ( ( real_V1803761363581548252l_real @ one_one_real )
% 9.53/5.31      = one_one_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7919_of__real__1,axiom,
% 9.53/5.31      ( ( real_V4546457046886955230omplex @ one_one_real )
% 9.53/5.31      = one_one_complex ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7920_of__real__numeral,axiom,
% 9.53/5.31      ! [W: num] :
% 9.53/5.31        ( ( real_V1803761363581548252l_real @ ( numeral_numeral_real @ W ) )
% 9.53/5.31        = ( numeral_numeral_real @ W ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7921_of__real__numeral,axiom,
% 9.53/5.31      ! [W: num] :
% 9.53/5.31        ( ( real_V4546457046886955230omplex @ ( numeral_numeral_real @ W ) )
% 9.53/5.31        = ( numera6690914467698888265omplex @ W ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7922_of__real__mult,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( real_V1803761363581548252l_real @ ( times_times_real @ X @ Y2 ) )
% 9.53/5.31        = ( times_times_real @ ( real_V1803761363581548252l_real @ X ) @ ( real_V1803761363581548252l_real @ Y2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7923_of__real__mult,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( real_V4546457046886955230omplex @ ( times_times_real @ X @ Y2 ) )
% 9.53/5.31        = ( times_times_complex @ ( real_V4546457046886955230omplex @ X ) @ ( real_V4546457046886955230omplex @ Y2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7924_of__real__divide,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( real_V1803761363581548252l_real @ ( divide_divide_real @ X @ Y2 ) )
% 9.53/5.31        = ( divide_divide_real @ ( real_V1803761363581548252l_real @ X ) @ ( real_V1803761363581548252l_real @ Y2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7925_of__real__divide,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( real_V4546457046886955230omplex @ ( divide_divide_real @ X @ Y2 ) )
% 9.53/5.31        = ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ X ) @ ( real_V4546457046886955230omplex @ Y2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7926_of__real__add,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( real_V1803761363581548252l_real @ ( plus_plus_real @ X @ Y2 ) )
% 9.53/5.31        = ( plus_plus_real @ ( real_V1803761363581548252l_real @ X ) @ ( real_V1803761363581548252l_real @ Y2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7927_of__real__add,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( real_V4546457046886955230omplex @ ( plus_plus_real @ X @ Y2 ) )
% 9.53/5.31        = ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X ) @ ( real_V4546457046886955230omplex @ Y2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7928_of__real__power,axiom,
% 9.53/5.31      ! [X: real,N: nat] :
% 9.53/5.31        ( ( real_V1803761363581548252l_real @ ( power_power_real @ X @ N ) )
% 9.53/5.31        = ( power_power_real @ ( real_V1803761363581548252l_real @ X ) @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7929_of__real__power,axiom,
% 9.53/5.31      ! [X: real,N: nat] :
% 9.53/5.31        ( ( real_V4546457046886955230omplex @ ( power_power_real @ X @ N ) )
% 9.53/5.31        = ( power_power_complex @ ( real_V4546457046886955230omplex @ X ) @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7930_of__real__diff,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( real_V4546457046886955230omplex @ ( minus_minus_real @ X @ Y2 ) )
% 9.53/5.31        = ( minus_minus_complex @ ( real_V4546457046886955230omplex @ X ) @ ( real_V4546457046886955230omplex @ Y2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7931_sin__pi__minus,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( sin_real @ ( minus_minus_real @ pi @ X ) )
% 9.53/5.31        = ( sin_real @ X ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7932_cos__coeff__0,axiom,
% 9.53/5.31      ( ( cos_coeff @ zero_zero_nat )
% 9.53/5.31      = one_one_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7933_cos__pi,axiom,
% 9.53/5.31      ( ( cos_real @ pi )
% 9.53/5.31      = ( uminus_uminus_real @ one_one_real ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7934_cos__periodic__pi,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( cos_real @ ( plus_plus_real @ X @ pi ) )
% 9.53/5.31        = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7935_cos__periodic__pi2,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( cos_real @ ( plus_plus_real @ pi @ X ) )
% 9.53/5.31        = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7936_sin__periodic__pi,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( sin_real @ ( plus_plus_real @ X @ pi ) )
% 9.53/5.31        = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7937_sin__periodic__pi2,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( sin_real @ ( plus_plus_real @ pi @ X ) )
% 9.53/5.31        = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7938_cos__minus__pi,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( cos_real @ ( minus_minus_real @ X @ pi ) )
% 9.53/5.31        = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7939_cos__pi__minus,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( cos_real @ ( minus_minus_real @ pi @ X ) )
% 9.53/5.31        = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7940_sin__minus__pi,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( sin_real @ ( minus_minus_real @ X @ pi ) )
% 9.53/5.31        = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7941_sin__cos__squared__add3,axiom,
% 9.53/5.31      ! [X: complex] :
% 9.53/5.31        ( ( plus_plus_complex @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ X ) ) @ ( times_times_complex @ ( sin_complex @ X ) @ ( sin_complex @ X ) ) )
% 9.53/5.31        = one_one_complex ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7942_sin__cos__squared__add3,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( plus_plus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ X ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ X ) ) )
% 9.53/5.31        = one_one_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7943_of__real__neg__numeral,axiom,
% 9.53/5.31      ! [W: num] :
% 9.53/5.31        ( ( real_V1803761363581548252l_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 9.53/5.31        = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7944_of__real__neg__numeral,axiom,
% 9.53/5.31      ! [W: num] :
% 9.53/5.31        ( ( real_V4546457046886955230omplex @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 9.53/5.31        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7945_cos__of__real__pi,axiom,
% 9.53/5.31      ( ( cos_real @ ( real_V1803761363581548252l_real @ pi ) )
% 9.53/5.31      = ( uminus_uminus_real @ one_one_real ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7946_cos__of__real__pi,axiom,
% 9.53/5.31      ( ( cos_complex @ ( real_V4546457046886955230omplex @ pi ) )
% 9.53/5.31      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7947_sin__npi2,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( sin_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 9.53/5.31        = zero_zero_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7948_sin__npi,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 9.53/5.31        = zero_zero_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7949_sin__npi__int,axiom,
% 9.53/5.31      ! [N: int] :
% 9.53/5.31        ( ( sin_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 9.53/5.31        = zero_zero_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7950_cos__pi__half,axiom,
% 9.53/5.31      ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31      = zero_zero_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7951_sin__two__pi,axiom,
% 9.53/5.31      ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 9.53/5.31      = zero_zero_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7952_sin__pi__half,axiom,
% 9.53/5.31      ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31      = one_one_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7953_cos__two__pi,axiom,
% 9.53/5.31      ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 9.53/5.31      = one_one_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7954_norm__of__real__add1,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ X ) @ one_one_real ) )
% 9.53/5.31        = ( abs_abs_real @ ( plus_plus_real @ X @ one_one_real ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7955_norm__of__real__add1,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X ) @ one_one_complex ) )
% 9.53/5.31        = ( abs_abs_real @ ( plus_plus_real @ X @ one_one_real ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7956_norm__of__real__addn,axiom,
% 9.53/5.31      ! [X: real,B: num] :
% 9.53/5.31        ( ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ X ) @ ( numeral_numeral_real @ B ) ) )
% 9.53/5.31        = ( abs_abs_real @ ( plus_plus_real @ X @ ( numeral_numeral_real @ B ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7957_norm__of__real__addn,axiom,
% 9.53/5.31      ! [X: real,B: num] :
% 9.53/5.31        ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X ) @ ( numera6690914467698888265omplex @ B ) ) )
% 9.53/5.31        = ( abs_abs_real @ ( plus_plus_real @ X @ ( numeral_numeral_real @ B ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7958_cos__periodic,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( cos_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 9.53/5.31        = ( cos_real @ X ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7959_sin__periodic,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( sin_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 9.53/5.31        = ( sin_real @ X ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7960_cos__2pi__minus,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( cos_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X ) )
% 9.53/5.31        = ( cos_real @ X ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7961_cos__npi,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 9.53/5.31        = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7962_cos__npi2,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( cos_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 9.53/5.31        = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7963_sin__cos__squared__add2,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( plus_plus_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.53/5.31        = one_one_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7964_sin__cos__squared__add2,axiom,
% 9.53/5.31      ! [X: complex] :
% 9.53/5.31        ( ( plus_plus_complex @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.53/5.31        = one_one_complex ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7965_sin__cos__squared__add,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( plus_plus_real @ ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.53/5.31        = one_one_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7966_sin__cos__squared__add,axiom,
% 9.53/5.31      ! [X: complex] :
% 9.53/5.31        ( ( plus_plus_complex @ ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.53/5.31        = one_one_complex ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7967_cos__of__real__pi__half,axiom,
% 9.53/5.31      ( ( cos_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31      = zero_zero_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7968_cos__of__real__pi__half,axiom,
% 9.53/5.31      ( ( cos_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 9.53/5.31      = zero_zero_complex ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7969_sin__of__real__pi__half,axiom,
% 9.53/5.31      ( ( sin_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31      = one_one_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7970_sin__of__real__pi__half,axiom,
% 9.53/5.31      ( ( sin_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 9.53/5.31      = one_one_complex ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7971_sin__2npi,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 9.53/5.31        = zero_zero_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7972_cos__2npi,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 9.53/5.31        = one_one_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7973_sin__2pi__minus,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( sin_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X ) )
% 9.53/5.31        = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7974_sin__int__2pin,axiom,
% 9.53/5.31      ! [N: int] :
% 9.53/5.31        ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 9.53/5.31        = zero_zero_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7975_cos__int__2pin,axiom,
% 9.53/5.31      ! [N: int] :
% 9.53/5.31        ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 9.53/5.31        = one_one_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7976_cos__3over2__pi,axiom,
% 9.53/5.31      ( ( cos_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 9.53/5.31      = zero_zero_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7977_sin__3over2__pi,axiom,
% 9.53/5.31      ( ( sin_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 9.53/5.31      = ( uminus_uminus_real @ one_one_real ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7978_cos__npi__int,axiom,
% 9.53/5.31      ! [N: int] :
% 9.53/5.31        ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 9.53/5.31         => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 9.53/5.31            = one_one_real ) )
% 9.53/5.31        & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 9.53/5.31         => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 9.53/5.31            = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7979_sin__diff,axiom,
% 9.53/5.31      ! [X: complex,Y2: complex] :
% 9.53/5.31        ( ( sin_complex @ ( minus_minus_complex @ X @ Y2 ) )
% 9.53/5.31        = ( minus_minus_complex @ ( times_times_complex @ ( sin_complex @ X ) @ ( cos_complex @ Y2 ) ) @ ( times_times_complex @ ( cos_complex @ X ) @ ( sin_complex @ Y2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7980_sin__diff,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( sin_real @ ( minus_minus_real @ X @ Y2 ) )
% 9.53/5.31        = ( minus_minus_real @ ( times_times_real @ ( sin_real @ X ) @ ( cos_real @ Y2 ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( sin_real @ Y2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7981_polar__Ex,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31      ? [R3: real,A4: real] :
% 9.53/5.31        ( ( X
% 9.53/5.31          = ( times_times_real @ R3 @ ( cos_real @ A4 ) ) )
% 9.53/5.31        & ( Y2
% 9.53/5.31          = ( times_times_real @ R3 @ ( sin_real @ A4 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7982_cos__one__sin__zero,axiom,
% 9.53/5.31      ! [X: complex] :
% 9.53/5.31        ( ( ( cos_complex @ X )
% 9.53/5.31          = one_one_complex )
% 9.53/5.31       => ( ( sin_complex @ X )
% 9.53/5.31          = zero_zero_complex ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7983_cos__one__sin__zero,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ( cos_real @ X )
% 9.53/5.31          = one_one_real )
% 9.53/5.31       => ( ( sin_real @ X )
% 9.53/5.31          = zero_zero_real ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7984_cos__int__times__real,axiom,
% 9.53/5.31      ! [M: int,X: real] :
% 9.53/5.31        ( ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ ( real_V1803761363581548252l_real @ X ) ) )
% 9.53/5.31        = ( real_V1803761363581548252l_real @ ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7985_cos__int__times__real,axiom,
% 9.53/5.31      ! [M: int,X: real] :
% 9.53/5.31        ( ( cos_complex @ ( times_times_complex @ ( ring_17405671764205052669omplex @ M ) @ ( real_V4546457046886955230omplex @ X ) ) )
% 9.53/5.31        = ( real_V4546457046886955230omplex @ ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7986_sin__add,axiom,
% 9.53/5.31      ! [X: complex,Y2: complex] :
% 9.53/5.31        ( ( sin_complex @ ( plus_plus_complex @ X @ Y2 ) )
% 9.53/5.31        = ( plus_plus_complex @ ( times_times_complex @ ( sin_complex @ X ) @ ( cos_complex @ Y2 ) ) @ ( times_times_complex @ ( cos_complex @ X ) @ ( sin_complex @ Y2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7987_sin__add,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( sin_real @ ( plus_plus_real @ X @ Y2 ) )
% 9.53/5.31        = ( plus_plus_real @ ( times_times_real @ ( sin_real @ X ) @ ( cos_real @ Y2 ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( sin_real @ Y2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7988_sin__int__times__real,axiom,
% 9.53/5.31      ! [M: int,X: real] :
% 9.53/5.31        ( ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ ( real_V1803761363581548252l_real @ X ) ) )
% 9.53/5.31        = ( real_V1803761363581548252l_real @ ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7989_sin__int__times__real,axiom,
% 9.53/5.31      ! [M: int,X: real] :
% 9.53/5.31        ( ( sin_complex @ ( times_times_complex @ ( ring_17405671764205052669omplex @ M ) @ ( real_V4546457046886955230omplex @ X ) ) )
% 9.53/5.31        = ( real_V4546457046886955230omplex @ ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7990_cos__diff,axiom,
% 9.53/5.31      ! [X: complex,Y2: complex] :
% 9.53/5.31        ( ( cos_complex @ ( minus_minus_complex @ X @ Y2 ) )
% 9.53/5.31        = ( plus_plus_complex @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ Y2 ) ) @ ( times_times_complex @ ( sin_complex @ X ) @ ( sin_complex @ Y2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7991_cos__diff,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( cos_real @ ( minus_minus_real @ X @ Y2 ) )
% 9.53/5.31        = ( plus_plus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y2 ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7992_cos__add,axiom,
% 9.53/5.31      ! [X: complex,Y2: complex] :
% 9.53/5.31        ( ( cos_complex @ ( plus_plus_complex @ X @ Y2 ) )
% 9.53/5.31        = ( minus_minus_complex @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ Y2 ) ) @ ( times_times_complex @ ( sin_complex @ X ) @ ( sin_complex @ Y2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7993_cos__add,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( cos_real @ ( plus_plus_real @ X @ Y2 ) )
% 9.53/5.31        = ( minus_minus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y2 ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7994_sin__zero__norm__cos__one,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ( sin_real @ X )
% 9.53/5.31          = zero_zero_real )
% 9.53/5.31       => ( ( real_V7735802525324610683m_real @ ( cos_real @ X ) )
% 9.53/5.31          = one_one_real ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7995_sin__zero__norm__cos__one,axiom,
% 9.53/5.31      ! [X: complex] :
% 9.53/5.31        ( ( ( sin_complex @ X )
% 9.53/5.31          = zero_zero_complex )
% 9.53/5.31       => ( ( real_V1022390504157884413omplex @ ( cos_complex @ X ) )
% 9.53/5.31          = one_one_real ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7996_sin__zero__abs__cos__one,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ( sin_real @ X )
% 9.53/5.31          = zero_zero_real )
% 9.53/5.31       => ( ( abs_abs_real @ ( cos_real @ X ) )
% 9.53/5.31          = one_one_real ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7997_sin__cos__eq,axiom,
% 9.53/5.31      ( sin_real
% 9.53/5.31      = ( ^ [X2: real] : ( cos_real @ ( minus_minus_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7998_sin__cos__eq,axiom,
% 9.53/5.31      ( sin_complex
% 9.53/5.31      = ( ^ [X2: complex] : ( cos_complex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ X2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_7999_cos__sin__eq,axiom,
% 9.53/5.31      ( cos_real
% 9.53/5.31      = ( ^ [X2: real] : ( sin_real @ ( minus_minus_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8000_cos__sin__eq,axiom,
% 9.53/5.31      ( cos_complex
% 9.53/5.31      = ( ^ [X2: complex] : ( sin_complex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ X2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8001_sin__double,axiom,
% 9.53/5.31      ! [X: complex] :
% 9.53/5.31        ( ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 9.53/5.31        = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ X ) ) @ ( cos_complex @ X ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8002_sin__double,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 9.53/5.31        = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ X ) ) @ ( cos_real @ X ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8003_sincos__principal__value,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31      ? [Y3: real] :
% 9.53/5.31        ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ Y3 )
% 9.53/5.31        & ( ord_less_eq_real @ Y3 @ pi )
% 9.53/5.31        & ( ( sin_real @ Y3 )
% 9.53/5.31          = ( sin_real @ X ) )
% 9.53/5.31        & ( ( cos_real @ Y3 )
% 9.53/5.31          = ( cos_real @ X ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8004_sin__x__le__x,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.31       => ( ord_less_eq_real @ ( sin_real @ X ) @ X ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8005_minus__sin__cos__eq,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( uminus_uminus_real @ ( sin_real @ X ) )
% 9.53/5.31        = ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8006_minus__sin__cos__eq,axiom,
% 9.53/5.31      ! [X: complex] :
% 9.53/5.31        ( ( uminus1482373934393186551omplex @ ( sin_complex @ X ) )
% 9.53/5.31        = ( cos_complex @ ( plus_plus_complex @ X @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8007_sin__le__one,axiom,
% 9.53/5.31      ! [X: real] : ( ord_less_eq_real @ ( sin_real @ X ) @ one_one_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8008_cos__le__one,axiom,
% 9.53/5.31      ! [X: real] : ( ord_less_eq_real @ ( cos_real @ X ) @ one_one_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8009_abs__sin__x__le__abs__x,axiom,
% 9.53/5.31      ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X ) ) @ ( abs_abs_real @ X ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8010_sin__cos__le1,axiom,
% 9.53/5.31      ! [X: real,Y2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y2 ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y2 ) ) ) ) @ one_one_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8011_sin__squared__eq,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.53/5.31        = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8012_sin__squared__eq,axiom,
% 9.53/5.31      ! [X: complex] :
% 9.53/5.31        ( ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.53/5.31        = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8013_cos__squared__eq,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.53/5.31        = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8014_cos__squared__eq,axiom,
% 9.53/5.31      ! [X: complex] :
% 9.53/5.31        ( ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.53/5.31        = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8015_nonzero__of__real__divide,axiom,
% 9.53/5.31      ! [Y2: real,X: real] :
% 9.53/5.31        ( ( Y2 != zero_zero_real )
% 9.53/5.31       => ( ( real_V1803761363581548252l_real @ ( divide_divide_real @ X @ Y2 ) )
% 9.53/5.31          = ( divide_divide_real @ ( real_V1803761363581548252l_real @ X ) @ ( real_V1803761363581548252l_real @ Y2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8016_nonzero__of__real__divide,axiom,
% 9.53/5.31      ! [Y2: real,X: real] :
% 9.53/5.31        ( ( Y2 != zero_zero_real )
% 9.53/5.31       => ( ( real_V4546457046886955230omplex @ ( divide_divide_real @ X @ Y2 ) )
% 9.53/5.31          = ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ X ) @ ( real_V4546457046886955230omplex @ Y2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8017_sin__gt__zero,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.31       => ( ( ord_less_real @ X @ pi )
% 9.53/5.31         => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8018_sin__x__ge__neg__x,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.31       => ( ord_less_eq_real @ ( uminus_uminus_real @ X ) @ ( sin_real @ X ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8019_sin__ge__zero,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.31       => ( ( ord_less_eq_real @ X @ pi )
% 9.53/5.31         => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8020_sin__ge__minus__one,axiom,
% 9.53/5.31      ! [X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( sin_real @ X ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8021_cos__inj__pi,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.31       => ( ( ord_less_eq_real @ X @ pi )
% 9.53/5.31         => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 9.53/5.31           => ( ( ord_less_eq_real @ Y2 @ pi )
% 9.53/5.31             => ( ( ( cos_real @ X )
% 9.53/5.31                  = ( cos_real @ Y2 ) )
% 9.53/5.31               => ( X = Y2 ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8022_cos__mono__le__eq,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.31       => ( ( ord_less_eq_real @ X @ pi )
% 9.53/5.31         => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 9.53/5.31           => ( ( ord_less_eq_real @ Y2 @ pi )
% 9.53/5.31             => ( ( ord_less_eq_real @ ( cos_real @ X ) @ ( cos_real @ Y2 ) )
% 9.53/5.31                = ( ord_less_eq_real @ Y2 @ X ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8023_cos__monotone__0__pi__le,axiom,
% 9.53/5.31      ! [Y2: real,X: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 9.53/5.31       => ( ( ord_less_eq_real @ Y2 @ X )
% 9.53/5.31         => ( ( ord_less_eq_real @ X @ pi )
% 9.53/5.31           => ( ord_less_eq_real @ ( cos_real @ X ) @ ( cos_real @ Y2 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8024_cos__ge__minus__one,axiom,
% 9.53/5.31      ! [X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( cos_real @ X ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8025_abs__sin__le__one,axiom,
% 9.53/5.31      ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X ) ) @ one_one_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8026_abs__cos__le__one,axiom,
% 9.53/5.31      ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( cos_real @ X ) ) @ one_one_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8027_sin__times__sin,axiom,
% 9.53/5.31      ! [W: complex,Z: complex] :
% 9.53/5.31        ( ( times_times_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 9.53/5.31        = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8028_sin__times__sin,axiom,
% 9.53/5.31      ! [W: real,Z: real] :
% 9.53/5.31        ( ( times_times_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 9.53/5.31        = ( divide_divide_real @ ( minus_minus_real @ ( cos_real @ ( minus_minus_real @ W @ Z ) ) @ ( cos_real @ ( plus_plus_real @ W @ Z ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8029_sin__times__cos,axiom,
% 9.53/5.31      ! [W: complex,Z: complex] :
% 9.53/5.31        ( ( times_times_complex @ ( sin_complex @ W ) @ ( cos_complex @ Z ) )
% 9.53/5.31        = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8030_sin__times__cos,axiom,
% 9.53/5.31      ! [W: real,Z: real] :
% 9.53/5.31        ( ( times_times_real @ ( sin_real @ W ) @ ( cos_real @ Z ) )
% 9.53/5.31        = ( divide_divide_real @ ( plus_plus_real @ ( sin_real @ ( plus_plus_real @ W @ Z ) ) @ ( sin_real @ ( minus_minus_real @ W @ Z ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8031_cos__times__sin,axiom,
% 9.53/5.31      ! [W: complex,Z: complex] :
% 9.53/5.31        ( ( times_times_complex @ ( cos_complex @ W ) @ ( sin_complex @ Z ) )
% 9.53/5.31        = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8032_cos__times__sin,axiom,
% 9.53/5.31      ! [W: real,Z: real] :
% 9.53/5.31        ( ( times_times_real @ ( cos_real @ W ) @ ( sin_real @ Z ) )
% 9.53/5.31        = ( divide_divide_real @ ( minus_minus_real @ ( sin_real @ ( plus_plus_real @ W @ Z ) ) @ ( sin_real @ ( minus_minus_real @ W @ Z ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8033_sin__plus__sin,axiom,
% 9.53/5.31      ! [W: complex,Z: complex] :
% 9.53/5.31        ( ( plus_plus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 9.53/5.31        = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8034_sin__plus__sin,axiom,
% 9.53/5.31      ! [W: real,Z: real] :
% 9.53/5.31        ( ( plus_plus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 9.53/5.31        = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( minus_minus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8035_sin__diff__sin,axiom,
% 9.53/5.31      ! [W: complex,Z: complex] :
% 9.53/5.31        ( ( minus_minus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 9.53/5.31        = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8036_sin__diff__sin,axiom,
% 9.53/5.31      ! [W: real,Z: real] :
% 9.53/5.31        ( ( minus_minus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 9.53/5.31        = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( minus_minus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8037_cos__diff__cos,axiom,
% 9.53/5.31      ! [W: complex,Z: complex] :
% 9.53/5.31        ( ( minus_minus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 9.53/5.31        = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ Z @ W ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8038_cos__diff__cos,axiom,
% 9.53/5.31      ! [W: real,Z: real] :
% 9.53/5.31        ( ( minus_minus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 9.53/5.31        = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( sin_real @ ( divide_divide_real @ ( minus_minus_real @ Z @ W ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8039_cos__double,axiom,
% 9.53/5.31      ! [X: complex] :
% 9.53/5.31        ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 9.53/5.31        = ( minus_minus_complex @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8040_cos__double,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 9.53/5.31        = ( minus_minus_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8041_cos__double__sin,axiom,
% 9.53/5.31      ! [W: complex] :
% 9.53/5.31        ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 9.53/5.31        = ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( sin_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8042_cos__double__sin,axiom,
% 9.53/5.31      ! [W: real] :
% 9.53/5.31        ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 9.53/5.31        = ( minus_minus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( sin_real @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8043_norm__less__p1,axiom,
% 9.53/5.31      ! [X: real] : ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ ( real_V7735802525324610683m_real @ X ) ) @ one_one_real ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8044_norm__less__p1,axiom,
% 9.53/5.31      ! [X: complex] : ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( real_V1022390504157884413omplex @ X ) ) @ one_one_complex ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8045_cos__two__neq__zero,axiom,
% 9.53/5.31      ( ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 9.53/5.31     != zero_zero_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8046_cos__monotone__0__pi,axiom,
% 9.53/5.31      ! [Y2: real,X: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 9.53/5.31       => ( ( ord_less_real @ Y2 @ X )
% 9.53/5.31         => ( ( ord_less_eq_real @ X @ pi )
% 9.53/5.31           => ( ord_less_real @ ( cos_real @ X ) @ ( cos_real @ Y2 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8047_cos__mono__less__eq,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.31       => ( ( ord_less_eq_real @ X @ pi )
% 9.53/5.31         => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 9.53/5.31           => ( ( ord_less_eq_real @ Y2 @ pi )
% 9.53/5.31             => ( ( ord_less_real @ ( cos_real @ X ) @ ( cos_real @ Y2 ) )
% 9.53/5.31                = ( ord_less_real @ Y2 @ X ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8048_sin__eq__0__pi,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X )
% 9.53/5.31       => ( ( ord_less_real @ X @ pi )
% 9.53/5.31         => ( ( ( sin_real @ X )
% 9.53/5.31              = zero_zero_real )
% 9.53/5.31           => ( X = zero_zero_real ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8049_sin__zero__pi__iff,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_real @ ( abs_abs_real @ X ) @ pi )
% 9.53/5.31       => ( ( ( sin_real @ X )
% 9.53/5.31            = zero_zero_real )
% 9.53/5.31          = ( X = zero_zero_real ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8050_cos__monotone__minus__pi__0_H,axiom,
% 9.53/5.31      ! [Y2: real,X: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y2 )
% 9.53/5.31       => ( ( ord_less_eq_real @ Y2 @ X )
% 9.53/5.31         => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 9.53/5.31           => ( ord_less_eq_real @ ( cos_real @ Y2 ) @ ( cos_real @ X ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8051_sin__zero__iff__int2,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ( sin_real @ X )
% 9.53/5.31          = zero_zero_real )
% 9.53/5.31        = ( ? [I3: int] :
% 9.53/5.31              ( X
% 9.53/5.31              = ( times_times_real @ ( ring_1_of_int_real @ I3 ) @ pi ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8052_sincos__total__pi,axiom,
% 9.53/5.31      ! [Y2: real,X: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 9.53/5.31       => ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.53/5.31            = one_one_real )
% 9.53/5.31         => ? [T6: real] :
% 9.53/5.31              ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 9.53/5.31              & ( ord_less_eq_real @ T6 @ pi )
% 9.53/5.31              & ( X
% 9.53/5.31                = ( cos_real @ T6 ) )
% 9.53/5.31              & ( Y2
% 9.53/5.31                = ( sin_real @ T6 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8053_sin__cos__sqrt,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X ) )
% 9.53/5.31       => ( ( sin_real @ X )
% 9.53/5.31          = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8054_sin__expansion__lemma,axiom,
% 9.53/5.31      ! [X: real,M: nat] :
% 9.53/5.31        ( ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 9.53/5.31        = ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8055_cos__expansion__lemma,axiom,
% 9.53/5.31      ! [X: real,M: nat] :
% 9.53/5.31        ( ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 9.53/5.31        = ( uminus_uminus_real @ ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8056_sin__gt__zero__02,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.31       => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 9.53/5.31         => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8057_cos__two__less__zero,axiom,
% 9.53/5.31      ord_less_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8058_cos__is__zero,axiom,
% 9.53/5.31      ? [X3: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 9.53/5.31        & ( ord_less_eq_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 9.53/5.31        & ( ( cos_real @ X3 )
% 9.53/5.31          = zero_zero_real )
% 9.53/5.31        & ! [Y4: real] :
% 9.53/5.31            ( ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 9.53/5.31              & ( ord_less_eq_real @ Y4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 9.53/5.31              & ( ( cos_real @ Y4 )
% 9.53/5.31                = zero_zero_real ) )
% 9.53/5.31           => ( Y4 = X3 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8059_cos__two__le__zero,axiom,
% 9.53/5.31      ord_less_eq_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8060_norm__of__real__diff,axiom,
% 9.53/5.31      ! [B: real,A: real] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( real_V4546457046886955230omplex @ B ) @ ( real_V4546457046886955230omplex @ A ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8061_cos__monotone__minus__pi__0,axiom,
% 9.53/5.31      ! [Y2: real,X: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y2 )
% 9.53/5.31       => ( ( ord_less_real @ Y2 @ X )
% 9.53/5.31         => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 9.53/5.31           => ( ord_less_real @ ( cos_real @ Y2 ) @ ( cos_real @ X ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8062_cos__total,axiom,
% 9.53/5.31      ! [Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 9.53/5.31       => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 9.53/5.31         => ? [X3: real] :
% 9.53/5.31              ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 9.53/5.31              & ( ord_less_eq_real @ X3 @ pi )
% 9.53/5.31              & ( ( cos_real @ X3 )
% 9.53/5.31                = Y2 )
% 9.53/5.31              & ! [Y4: real] :
% 9.53/5.31                  ( ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 9.53/5.31                    & ( ord_less_eq_real @ Y4 @ pi )
% 9.53/5.31                    & ( ( cos_real @ Y4 )
% 9.53/5.31                      = Y2 ) )
% 9.53/5.31                 => ( Y4 = X3 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8063_sincos__total__pi__half,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.31       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 9.53/5.31         => ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.53/5.31              = one_one_real )
% 9.53/5.31           => ? [T6: real] :
% 9.53/5.31                ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 9.53/5.31                & ( ord_less_eq_real @ T6 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31                & ( X
% 9.53/5.31                  = ( cos_real @ T6 ) )
% 9.53/5.31                & ( Y2
% 9.53/5.31                  = ( sin_real @ T6 ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8064_sincos__total__2pi__le,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.53/5.31          = one_one_real )
% 9.53/5.31       => ? [T6: real] :
% 9.53/5.31            ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 9.53/5.31            & ( ord_less_eq_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 9.53/5.31            & ( X
% 9.53/5.31              = ( cos_real @ T6 ) )
% 9.53/5.31            & ( Y2
% 9.53/5.31              = ( sin_real @ T6 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8065_sincos__total__2pi,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.53/5.31          = one_one_real )
% 9.53/5.31       => ~ ! [T6: real] :
% 9.53/5.31              ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 9.53/5.31             => ( ( ord_less_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 9.53/5.31               => ( ( X
% 9.53/5.31                    = ( cos_real @ T6 ) )
% 9.53/5.31                 => ( Y2
% 9.53/5.31                   != ( sin_real @ T6 ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8066_sin__pi__divide__n__ge__0,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( N != zero_zero_nat )
% 9.53/5.31       => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8067_sin__45,axiom,
% 9.53/5.31      ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 9.53/5.31      = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8068_cos__45,axiom,
% 9.53/5.31      ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 9.53/5.31      = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8069_cos__times__cos,axiom,
% 9.53/5.31      ! [W: complex,Z: complex] :
% 9.53/5.31        ( ( times_times_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 9.53/5.31        = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8070_cos__times__cos,axiom,
% 9.53/5.31      ! [W: real,Z: real] :
% 9.53/5.31        ( ( times_times_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 9.53/5.31        = ( divide_divide_real @ ( plus_plus_real @ ( cos_real @ ( minus_minus_real @ W @ Z ) ) @ ( cos_real @ ( plus_plus_real @ W @ Z ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8071_cos__plus__cos,axiom,
% 9.53/5.31      ! [W: complex,Z: complex] :
% 9.53/5.31        ( ( plus_plus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 9.53/5.31        = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8072_cos__plus__cos,axiom,
% 9.53/5.31      ! [W: real,Z: real] :
% 9.53/5.31        ( ( plus_plus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 9.53/5.31        = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( cos_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( minus_minus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8073_sin__gt__zero2,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.31       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31         => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8074_sin__lt__zero,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_real @ pi @ X )
% 9.53/5.31       => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 9.53/5.31         => ( ord_less_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8075_cos__double__less__one,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.31       => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 9.53/5.31         => ( ord_less_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) @ one_one_real ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8076_sin__30,axiom,
% 9.53/5.31      ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 9.53/5.31      = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8077_cos__gt__zero,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.31       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31         => ( ord_less_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8078_sin__inj__pi,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 9.53/5.31       => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 9.53/5.31           => ( ( ord_less_eq_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31             => ( ( ( sin_real @ X )
% 9.53/5.31                  = ( sin_real @ Y2 ) )
% 9.53/5.31               => ( X = Y2 ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8079_sin__mono__le__eq,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 9.53/5.31       => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 9.53/5.31           => ( ( ord_less_eq_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31             => ( ( ord_less_eq_real @ ( sin_real @ X ) @ ( sin_real @ Y2 ) )
% 9.53/5.31                = ( ord_less_eq_real @ X @ Y2 ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8080_sin__monotone__2pi__le,axiom,
% 9.53/5.31      ! [Y2: real,X: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 9.53/5.31       => ( ( ord_less_eq_real @ Y2 @ X )
% 9.53/5.31         => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31           => ( ord_less_eq_real @ ( sin_real @ Y2 ) @ ( sin_real @ X ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8081_cos__60,axiom,
% 9.53/5.31      ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 9.53/5.31      = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8082_sin__60,axiom,
% 9.53/5.31      ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 9.53/5.31      = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8083_cos__30,axiom,
% 9.53/5.31      ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 9.53/5.31      = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8084_cos__one__2pi__int,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ( cos_real @ X )
% 9.53/5.31          = one_one_real )
% 9.53/5.31        = ( ? [X2: int] :
% 9.53/5.31              ( X
% 9.53/5.31              = ( times_times_real @ ( times_times_real @ ( ring_1_of_int_real @ X2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8085_cos__double__cos,axiom,
% 9.53/5.31      ! [W: complex] :
% 9.53/5.31        ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 9.53/5.31        = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( cos_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_complex ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8086_cos__double__cos,axiom,
% 9.53/5.31      ! [W: real] :
% 9.53/5.31        ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 9.53/5.31        = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( cos_real @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_real ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8087_cos__treble__cos,axiom,
% 9.53/5.31      ! [X: complex] :
% 9.53/5.31        ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ X ) )
% 9.53/5.31        = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ ( cos_complex @ X ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8088_cos__treble__cos,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ X ) )
% 9.53/5.31        = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( cos_real @ X ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8089_sin__le__zero,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ pi @ X )
% 9.53/5.31       => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 9.53/5.31         => ( ord_less_eq_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8090_sin__less__zero,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 9.53/5.31       => ( ( ord_less_real @ X @ zero_zero_real )
% 9.53/5.31         => ( ord_less_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8091_sin__mono__less__eq,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 9.53/5.31       => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 9.53/5.31           => ( ( ord_less_eq_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31             => ( ( ord_less_real @ ( sin_real @ X ) @ ( sin_real @ Y2 ) )
% 9.53/5.31                = ( ord_less_real @ X @ Y2 ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8092_sin__monotone__2pi,axiom,
% 9.53/5.31      ! [Y2: real,X: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 9.53/5.31       => ( ( ord_less_real @ Y2 @ X )
% 9.53/5.31         => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31           => ( ord_less_real @ ( sin_real @ Y2 ) @ ( sin_real @ X ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8093_sin__total,axiom,
% 9.53/5.31      ! [Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 9.53/5.31       => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 9.53/5.31         => ? [X3: real] :
% 9.53/5.31              ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 9.53/5.31              & ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31              & ( ( sin_real @ X3 )
% 9.53/5.31                = Y2 )
% 9.53/5.31              & ! [Y4: real] :
% 9.53/5.31                  ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 9.53/5.31                    & ( ord_less_eq_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31                    & ( ( sin_real @ Y4 )
% 9.53/5.31                      = Y2 ) )
% 9.53/5.31                 => ( Y4 = X3 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8094_cos__gt__zero__pi,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 9.53/5.31       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31         => ( ord_less_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8095_cos__ge__zero,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 9.53/5.31       => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31         => ( ord_less_eq_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8096_cos__one__2pi,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ( cos_real @ X )
% 9.53/5.31          = one_one_real )
% 9.53/5.31        = ( ? [X2: nat] :
% 9.53/5.31              ( X
% 9.53/5.31              = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 9.53/5.31          | ? [X2: nat] :
% 9.53/5.31              ( X
% 9.53/5.31              = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8097_sin__pi__divide__n__gt__0,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.53/5.31       => ( ord_less_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8098_sin__arctan,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( sin_real @ ( arctan @ X ) )
% 9.53/5.31        = ( divide_divide_real @ X @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8099_cos__arctan,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( cos_real @ ( arctan @ X ) )
% 9.53/5.31        = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8100_sin__zero__iff__int,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ( sin_real @ X )
% 9.53/5.31          = zero_zero_real )
% 9.53/5.31        = ( ? [I3: int] :
% 9.53/5.31              ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I3 )
% 9.53/5.31              & ( X
% 9.53/5.31                = ( times_times_real @ ( ring_1_of_int_real @ I3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8101_cos__zero__iff__int,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ( cos_real @ X )
% 9.53/5.31          = zero_zero_real )
% 9.53/5.31        = ( ? [I3: int] :
% 9.53/5.31              ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I3 )
% 9.53/5.31              & ( X
% 9.53/5.31                = ( times_times_real @ ( ring_1_of_int_real @ I3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8102_sin__zero__lemma,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.31       => ( ( ( sin_real @ X )
% 9.53/5.31            = zero_zero_real )
% 9.53/5.31         => ? [N3: nat] :
% 9.53/5.31              ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 9.53/5.31              & ( X
% 9.53/5.31                = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8103_sin__zero__iff,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ( sin_real @ X )
% 9.53/5.31          = zero_zero_real )
% 9.53/5.31        = ( ? [N2: nat] :
% 9.53/5.31              ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 9.53/5.31              & ( X
% 9.53/5.31                = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 9.53/5.31          | ? [N2: nat] :
% 9.53/5.31              ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 9.53/5.31              & ( X
% 9.53/5.31                = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8104_cos__zero__lemma,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.31       => ( ( ( cos_real @ X )
% 9.53/5.31            = zero_zero_real )
% 9.53/5.31         => ? [N3: nat] :
% 9.53/5.31              ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 9.53/5.31              & ( X
% 9.53/5.31                = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8105_cos__zero__iff,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ( cos_real @ X )
% 9.53/5.31          = zero_zero_real )
% 9.53/5.31        = ( ? [N2: nat] :
% 9.53/5.31              ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 9.53/5.31              & ( X
% 9.53/5.31                = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 9.53/5.31          | ? [N2: nat] :
% 9.53/5.31              ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 9.53/5.31              & ( X
% 9.53/5.31                = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8106_arsinh__def,axiom,
% 9.53/5.31      ( arsinh_real
% 9.53/5.31      = ( ^ [X2: real] : ( ln_ln_real @ ( plus_plus_real @ X2 @ ( powr_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( real_V1803761363581548252l_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8107_Maclaurin__cos__expansion2,axiom,
% 9.53/5.31      ! [X: real,N: nat] :
% 9.53/5.31        ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.31       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.31         => ? [T6: real] :
% 9.53/5.31              ( ( ord_less_real @ zero_zero_real @ T6 )
% 9.53/5.31              & ( ord_less_real @ T6 @ X )
% 9.53/5.31              & ( ( cos_real @ X )
% 9.53/5.31                = ( plus_plus_real
% 9.53/5.31                  @ ( groups6591440286371151544t_real
% 9.53/5.31                    @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 9.53/5.31                    @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.31                  @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8108_Maclaurin__minus__cos__expansion,axiom,
% 9.53/5.31      ! [N: nat,X: real] :
% 9.53/5.31        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.31       => ( ( ord_less_real @ X @ zero_zero_real )
% 9.53/5.31         => ? [T6: real] :
% 9.53/5.31              ( ( ord_less_real @ X @ T6 )
% 9.53/5.31              & ( ord_less_real @ T6 @ zero_zero_real )
% 9.53/5.31              & ( ( cos_real @ X )
% 9.53/5.31                = ( plus_plus_real
% 9.53/5.31                  @ ( groups6591440286371151544t_real
% 9.53/5.31                    @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 9.53/5.31                    @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.31                  @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8109_Maclaurin__cos__expansion,axiom,
% 9.53/5.31      ! [X: real,N: nat] :
% 9.53/5.31      ? [T6: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 9.53/5.31        & ( ( cos_real @ X )
% 9.53/5.31          = ( plus_plus_real
% 9.53/5.31            @ ( groups6591440286371151544t_real
% 9.53/5.31              @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 9.53/5.31              @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.31            @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8110_tan__double,axiom,
% 9.53/5.31      ! [X: complex] :
% 9.53/5.31        ( ( ( cos_complex @ X )
% 9.53/5.31         != zero_zero_complex )
% 9.53/5.31       => ( ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 9.53/5.31           != zero_zero_complex )
% 9.53/5.31         => ( ( tan_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 9.53/5.31            = ( divide1717551699836669952omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( tan_complex @ X ) ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( tan_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8111_tan__double,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ( cos_real @ X )
% 9.53/5.31         != zero_zero_real )
% 9.53/5.31       => ( ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 9.53/5.31           != zero_zero_real )
% 9.53/5.31         => ( ( tan_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 9.53/5.31            = ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( tan_real @ X ) ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8112_sin__tan,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31       => ( ( sin_real @ X )
% 9.53/5.31          = ( divide_divide_real @ ( tan_real @ X ) @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8113_fact__0,axiom,
% 9.53/5.31      ( ( semiri5044797733671781792omplex @ zero_zero_nat )
% 9.53/5.31      = one_one_complex ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8114_fact__0,axiom,
% 9.53/5.31      ( ( semiri773545260158071498ct_rat @ zero_zero_nat )
% 9.53/5.31      = one_one_rat ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8115_fact__0,axiom,
% 9.53/5.31      ( ( semiri1406184849735516958ct_int @ zero_zero_nat )
% 9.53/5.31      = one_one_int ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8116_fact__0,axiom,
% 9.53/5.31      ( ( semiri2265585572941072030t_real @ zero_zero_nat )
% 9.53/5.31      = one_one_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8117_fact__0,axiom,
% 9.53/5.31      ( ( semiri1408675320244567234ct_nat @ zero_zero_nat )
% 9.53/5.31      = one_one_nat ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8118_fact__1,axiom,
% 9.53/5.31      ( ( semiri5044797733671781792omplex @ one_one_nat )
% 9.53/5.31      = one_one_complex ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8119_fact__1,axiom,
% 9.53/5.31      ( ( semiri773545260158071498ct_rat @ one_one_nat )
% 9.53/5.31      = one_one_rat ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8120_fact__1,axiom,
% 9.53/5.31      ( ( semiri1406184849735516958ct_int @ one_one_nat )
% 9.53/5.31      = one_one_int ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8121_fact__1,axiom,
% 9.53/5.31      ( ( semiri2265585572941072030t_real @ one_one_nat )
% 9.53/5.31      = one_one_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8122_fact__1,axiom,
% 9.53/5.31      ( ( semiri1408675320244567234ct_nat @ one_one_nat )
% 9.53/5.31      = one_one_nat ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8123_tan__periodic__pi,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( tan_real @ ( plus_plus_real @ X @ pi ) )
% 9.53/5.31        = ( tan_real @ X ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8124_fact__Suc__0,axiom,
% 9.53/5.31      ( ( semiri5044797733671781792omplex @ ( suc @ zero_zero_nat ) )
% 9.53/5.31      = one_one_complex ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8125_fact__Suc__0,axiom,
% 9.53/5.31      ( ( semiri773545260158071498ct_rat @ ( suc @ zero_zero_nat ) )
% 9.53/5.31      = one_one_rat ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8126_fact__Suc__0,axiom,
% 9.53/5.31      ( ( semiri1406184849735516958ct_int @ ( suc @ zero_zero_nat ) )
% 9.53/5.31      = one_one_int ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8127_fact__Suc__0,axiom,
% 9.53/5.31      ( ( semiri2265585572941072030t_real @ ( suc @ zero_zero_nat ) )
% 9.53/5.31      = one_one_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8128_fact__Suc__0,axiom,
% 9.53/5.31      ( ( semiri1408675320244567234ct_nat @ ( suc @ zero_zero_nat ) )
% 9.53/5.31      = one_one_nat ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8129_fact__Suc,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( semiri1406184849735516958ct_int @ ( suc @ N ) )
% 9.53/5.31        = ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8130_fact__Suc,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( semiri5044797733671781792omplex @ ( suc @ N ) )
% 9.53/5.31        = ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N ) ) @ ( semiri5044797733671781792omplex @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8131_fact__Suc,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( semiri2265585572941072030t_real @ ( suc @ N ) )
% 9.53/5.31        = ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8132_fact__Suc,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( semiri1408675320244567234ct_nat @ ( suc @ N ) )
% 9.53/5.31        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( suc @ N ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8133_fact__2,axiom,
% 9.53/5.31      ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.53/5.31      = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8134_fact__2,axiom,
% 9.53/5.31      ( ( semiri773545260158071498ct_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.53/5.31      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8135_fact__2,axiom,
% 9.53/5.31      ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.53/5.31      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8136_fact__2,axiom,
% 9.53/5.31      ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.53/5.31      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8137_fact__2,axiom,
% 9.53/5.31      ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.53/5.31      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8138_tan__npi,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( tan_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 9.53/5.31        = zero_zero_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8139_tan__periodic__n,axiom,
% 9.53/5.31      ! [X: real,N: num] :
% 9.53/5.31        ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ N ) @ pi ) ) )
% 9.53/5.31        = ( tan_real @ X ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8140_tan__periodic__nat,axiom,
% 9.53/5.31      ! [X: real,N: nat] :
% 9.53/5.31        ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) ) )
% 9.53/5.31        = ( tan_real @ X ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8141_tan__periodic__int,axiom,
% 9.53/5.31      ! [X: real,I2: int] :
% 9.53/5.31        ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( ring_1_of_int_real @ I2 ) @ pi ) ) )
% 9.53/5.31        = ( tan_real @ X ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8142_tan__periodic,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 9.53/5.31        = ( tan_real @ X ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8143_fact__ge__zero,axiom,
% 9.53/5.31      ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8144_fact__ge__zero,axiom,
% 9.53/5.31      ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8145_fact__ge__zero,axiom,
% 9.53/5.31      ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8146_fact__ge__zero,axiom,
% 9.53/5.31      ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8147_fact__gt__zero,axiom,
% 9.53/5.31      ! [N: nat] : ( ord_less_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8148_fact__gt__zero,axiom,
% 9.53/5.31      ! [N: nat] : ( ord_less_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8149_fact__gt__zero,axiom,
% 9.53/5.31      ! [N: nat] : ( ord_less_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8150_fact__gt__zero,axiom,
% 9.53/5.31      ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8151_fact__not__neg,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ~ ( ord_less_rat @ ( semiri773545260158071498ct_rat @ N ) @ zero_zero_rat ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8152_fact__not__neg,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ~ ( ord_less_int @ ( semiri1406184849735516958ct_int @ N ) @ zero_zero_int ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8153_fact__not__neg,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ~ ( ord_less_real @ ( semiri2265585572941072030t_real @ N ) @ zero_zero_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8154_fact__not__neg,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ~ ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ N ) @ zero_zero_nat ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8155_fact__ge__1,axiom,
% 9.53/5.31      ! [N: nat] : ( ord_less_eq_rat @ one_one_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8156_fact__ge__1,axiom,
% 9.53/5.31      ! [N: nat] : ( ord_less_eq_int @ one_one_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8157_fact__ge__1,axiom,
% 9.53/5.31      ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8158_fact__ge__1,axiom,
% 9.53/5.31      ! [N: nat] : ( ord_less_eq_nat @ one_one_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8159_fact__mono,axiom,
% 9.53/5.31      ! [M: nat,N: nat] :
% 9.53/5.31        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.31       => ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8160_fact__mono,axiom,
% 9.53/5.31      ! [M: nat,N: nat] :
% 9.53/5.31        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.31       => ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ M ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8161_fact__mono,axiom,
% 9.53/5.31      ! [M: nat,N: nat] :
% 9.53/5.31        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.31       => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8162_fact__dvd,axiom,
% 9.53/5.31      ! [N: nat,M: nat] :
% 9.53/5.31        ( ( ord_less_eq_nat @ N @ M )
% 9.53/5.31       => ( dvd_dvd_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1406184849735516958ct_int @ M ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8163_fact__dvd,axiom,
% 9.53/5.31      ! [N: nat,M: nat] :
% 9.53/5.31        ( ( ord_less_eq_nat @ N @ M )
% 9.53/5.31       => ( dvd_dvd_Code_integer @ ( semiri3624122377584611663nteger @ N ) @ ( semiri3624122377584611663nteger @ M ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8164_fact__dvd,axiom,
% 9.53/5.31      ! [N: nat,M: nat] :
% 9.53/5.31        ( ( ord_less_eq_nat @ N @ M )
% 9.53/5.31       => ( dvd_dvd_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ M ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8165_fact__dvd,axiom,
% 9.53/5.31      ! [N: nat,M: nat] :
% 9.53/5.31        ( ( ord_less_eq_nat @ N @ M )
% 9.53/5.31       => ( dvd_dvd_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ M ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8166_fact__less__mono,axiom,
% 9.53/5.31      ! [M: nat,N: nat] :
% 9.53/5.31        ( ( ord_less_nat @ zero_zero_nat @ M )
% 9.53/5.31       => ( ( ord_less_nat @ M @ N )
% 9.53/5.31         => ( ord_less_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8167_fact__less__mono,axiom,
% 9.53/5.31      ! [M: nat,N: nat] :
% 9.53/5.31        ( ( ord_less_nat @ zero_zero_nat @ M )
% 9.53/5.31       => ( ( ord_less_nat @ M @ N )
% 9.53/5.31         => ( ord_less_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8168_fact__less__mono,axiom,
% 9.53/5.31      ! [M: nat,N: nat] :
% 9.53/5.31        ( ( ord_less_nat @ zero_zero_nat @ M )
% 9.53/5.31       => ( ( ord_less_nat @ M @ N )
% 9.53/5.31         => ( ord_less_real @ ( semiri2265585572941072030t_real @ M ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8169_fact__less__mono,axiom,
% 9.53/5.31      ! [M: nat,N: nat] :
% 9.53/5.31        ( ( ord_less_nat @ zero_zero_nat @ M )
% 9.53/5.31       => ( ( ord_less_nat @ M @ N )
% 9.53/5.31         => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8170_fact__fact__dvd__fact,axiom,
% 9.53/5.31      ! [K: nat,N: nat] : ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ N ) ) @ ( semiri3624122377584611663nteger @ ( plus_plus_nat @ K @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8171_fact__fact__dvd__fact,axiom,
% 9.53/5.31      ! [K: nat,N: nat] : ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ N ) ) @ ( semiri1406184849735516958ct_int @ ( plus_plus_nat @ K @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8172_fact__fact__dvd__fact,axiom,
% 9.53/5.31      ! [K: nat,N: nat] : ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ K @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8173_fact__fact__dvd__fact,axiom,
% 9.53/5.31      ! [K: nat,N: nat] : ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ N ) ) @ ( semiri1408675320244567234ct_nat @ ( plus_plus_nat @ K @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8174_fact__mod,axiom,
% 9.53/5.31      ! [M: nat,N: nat] :
% 9.53/5.31        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.31       => ( ( modulo_modulo_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1406184849735516958ct_int @ M ) )
% 9.53/5.31          = zero_zero_int ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8175_fact__mod,axiom,
% 9.53/5.31      ! [M: nat,N: nat] :
% 9.53/5.31        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.31       => ( ( modulo_modulo_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ M ) )
% 9.53/5.31          = zero_zero_nat ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8176_fact__le__power,axiom,
% 9.53/5.31      ! [N: nat] : ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1314217659103216013at_int @ ( power_power_nat @ N @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8177_fact__le__power,axiom,
% 9.53/5.31      ! [N: nat] : ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri5074537144036343181t_real @ ( power_power_nat @ N @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8178_fact__le__power,axiom,
% 9.53/5.31      ! [N: nat] : ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1316708129612266289at_nat @ ( power_power_nat @ N @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8179_tan__def,axiom,
% 9.53/5.31      ( tan_complex
% 9.53/5.31      = ( ^ [X2: complex] : ( divide1717551699836669952omplex @ ( sin_complex @ X2 ) @ ( cos_complex @ X2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8180_tan__def,axiom,
% 9.53/5.31      ( tan_real
% 9.53/5.31      = ( ^ [X2: real] : ( divide_divide_real @ ( sin_real @ X2 ) @ ( cos_real @ X2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8181_choose__dvd,axiom,
% 9.53/5.31      ! [K: nat,N: nat] :
% 9.53/5.31        ( ( ord_less_eq_nat @ K @ N )
% 9.53/5.31       => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8182_choose__dvd,axiom,
% 9.53/5.31      ! [K: nat,N: nat] :
% 9.53/5.31        ( ( ord_less_eq_nat @ K @ N )
% 9.53/5.31       => ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8183_choose__dvd,axiom,
% 9.53/5.31      ! [K: nat,N: nat] :
% 9.53/5.31        ( ( ord_less_eq_nat @ K @ N )
% 9.53/5.31       => ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8184_choose__dvd,axiom,
% 9.53/5.31      ! [K: nat,N: nat] :
% 9.53/5.31        ( ( ord_less_eq_nat @ K @ N )
% 9.53/5.31       => ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8185_fact__numeral,axiom,
% 9.53/5.31      ! [K: num] :
% 9.53/5.31        ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ K ) )
% 9.53/5.31        = ( times_times_complex @ ( numera6690914467698888265omplex @ K ) @ ( semiri5044797733671781792omplex @ ( pred_numeral @ K ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8186_fact__numeral,axiom,
% 9.53/5.31      ! [K: num] :
% 9.53/5.31        ( ( semiri773545260158071498ct_rat @ ( numeral_numeral_nat @ K ) )
% 9.53/5.31        = ( times_times_rat @ ( numeral_numeral_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( pred_numeral @ K ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8187_fact__numeral,axiom,
% 9.53/5.31      ! [K: num] :
% 9.53/5.31        ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ K ) )
% 9.53/5.31        = ( times_times_int @ ( numeral_numeral_int @ K ) @ ( semiri1406184849735516958ct_int @ ( pred_numeral @ K ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8188_fact__numeral,axiom,
% 9.53/5.31      ! [K: num] :
% 9.53/5.31        ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ K ) )
% 9.53/5.31        = ( times_times_real @ ( numeral_numeral_real @ K ) @ ( semiri2265585572941072030t_real @ ( pred_numeral @ K ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8189_fact__numeral,axiom,
% 9.53/5.31      ! [K: num] :
% 9.53/5.31        ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ K ) )
% 9.53/5.31        = ( times_times_nat @ ( numeral_numeral_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( pred_numeral @ K ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8190_square__fact__le__2__fact,axiom,
% 9.53/5.31      ! [N: nat] : ( ord_less_eq_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8191_tan__45,axiom,
% 9.53/5.31      ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 9.53/5.31      = one_one_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8192_tan__60,axiom,
% 9.53/5.31      ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 9.53/5.31      = ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8193_fact__num__eq__if,axiom,
% 9.53/5.31      ( semiri773545260158071498ct_rat
% 9.53/5.31      = ( ^ [M6: nat] : ( if_rat @ ( M6 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ M6 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8194_fact__num__eq__if,axiom,
% 9.53/5.31      ( semiri1406184849735516958ct_int
% 9.53/5.31      = ( ^ [M6: nat] : ( if_int @ ( M6 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8195_fact__num__eq__if,axiom,
% 9.53/5.31      ( semiri5044797733671781792omplex
% 9.53/5.31      = ( ^ [M6: nat] : ( if_complex @ ( M6 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ M6 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8196_fact__num__eq__if,axiom,
% 9.53/5.31      ( semiri2265585572941072030t_real
% 9.53/5.31      = ( ^ [M6: nat] : ( if_real @ ( M6 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M6 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8197_fact__num__eq__if,axiom,
% 9.53/5.31      ( semiri1408675320244567234ct_nat
% 9.53/5.31      = ( ^ [M6: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M6 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8198_fact__reduce,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.31       => ( ( semiri1406184849735516958ct_int @ N )
% 9.53/5.31          = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8199_fact__reduce,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.31       => ( ( semiri5044797733671781792omplex @ N )
% 9.53/5.31          = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8200_fact__reduce,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.31       => ( ( semiri2265585572941072030t_real @ N )
% 9.53/5.31          = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8201_fact__reduce,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.31       => ( ( semiri1408675320244567234ct_nat @ N )
% 9.53/5.31          = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8202_tan__gt__zero,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.31       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31         => ( ord_less_real @ zero_zero_real @ ( tan_real @ X ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8203_lemma__tan__total,axiom,
% 9.53/5.31      ! [Y2: real] :
% 9.53/5.31        ( ( ord_less_real @ zero_zero_real @ Y2 )
% 9.53/5.31       => ? [X3: real] :
% 9.53/5.31            ( ( ord_less_real @ zero_zero_real @ X3 )
% 9.53/5.31            & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31            & ( ord_less_real @ Y2 @ ( tan_real @ X3 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8204_lemma__tan__total1,axiom,
% 9.53/5.31      ! [Y2: real] :
% 9.53/5.31      ? [X3: real] :
% 9.53/5.31        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 9.53/5.31        & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31        & ( ( tan_real @ X3 )
% 9.53/5.31          = Y2 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8205_tan__mono__lt__eq,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 9.53/5.31       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 9.53/5.31           => ( ( ord_less_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31             => ( ( ord_less_real @ ( tan_real @ X ) @ ( tan_real @ Y2 ) )
% 9.53/5.31                = ( ord_less_real @ X @ Y2 ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8206_tan__monotone_H,axiom,
% 9.53/5.31      ! [Y2: real,X: real] :
% 9.53/5.31        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 9.53/5.31       => ( ( ord_less_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 9.53/5.31           => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31             => ( ( ord_less_real @ Y2 @ X )
% 9.53/5.31                = ( ord_less_real @ ( tan_real @ Y2 ) @ ( tan_real @ X ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8207_tan__monotone,axiom,
% 9.53/5.31      ! [Y2: real,X: real] :
% 9.53/5.31        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 9.53/5.31       => ( ( ord_less_real @ Y2 @ X )
% 9.53/5.31         => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31           => ( ord_less_real @ ( tan_real @ Y2 ) @ ( tan_real @ X ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8208_tan__total,axiom,
% 9.53/5.31      ! [Y2: real] :
% 9.53/5.31      ? [X3: real] :
% 9.53/5.31        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 9.53/5.31        & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31        & ( ( tan_real @ X3 )
% 9.53/5.31          = Y2 )
% 9.53/5.31        & ! [Y4: real] :
% 9.53/5.31            ( ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 9.53/5.31              & ( ord_less_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31              & ( ( tan_real @ Y4 )
% 9.53/5.31                = Y2 ) )
% 9.53/5.31           => ( Y4 = X3 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8209_tan__minus__45,axiom,
% 9.53/5.31      ( ( tan_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) )
% 9.53/5.31      = ( uminus_uminus_real @ one_one_real ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8210_tan__inverse,axiom,
% 9.53/5.31      ! [Y2: real] :
% 9.53/5.31        ( ( divide_divide_real @ one_one_real @ ( tan_real @ Y2 ) )
% 9.53/5.31        = ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8211_add__tan__eq,axiom,
% 9.53/5.31      ! [X: complex,Y2: complex] :
% 9.53/5.31        ( ( ( cos_complex @ X )
% 9.53/5.31         != zero_zero_complex )
% 9.53/5.31       => ( ( ( cos_complex @ Y2 )
% 9.53/5.31           != zero_zero_complex )
% 9.53/5.31         => ( ( plus_plus_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y2 ) )
% 9.53/5.31            = ( divide1717551699836669952omplex @ ( sin_complex @ ( plus_plus_complex @ X @ Y2 ) ) @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ Y2 ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8212_add__tan__eq,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( ( cos_real @ X )
% 9.53/5.31         != zero_zero_real )
% 9.53/5.31       => ( ( ( cos_real @ Y2 )
% 9.53/5.31           != zero_zero_real )
% 9.53/5.31         => ( ( plus_plus_real @ ( tan_real @ X ) @ ( tan_real @ Y2 ) )
% 9.53/5.31            = ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ X @ Y2 ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y2 ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8213_tan__total__pos,axiom,
% 9.53/5.31      ! [Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 9.53/5.31       => ? [X3: real] :
% 9.53/5.31            ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 9.53/5.31            & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31            & ( ( tan_real @ X3 )
% 9.53/5.31              = Y2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8214_tan__pos__pi2__le,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.31       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31         => ( ord_less_eq_real @ zero_zero_real @ ( tan_real @ X ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8215_tan__less__zero,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 9.53/5.31       => ( ( ord_less_real @ X @ zero_zero_real )
% 9.53/5.31         => ( ord_less_real @ ( tan_real @ X ) @ zero_zero_real ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8216_tan__mono__le__eq,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 9.53/5.31       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 9.53/5.31           => ( ( ord_less_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31             => ( ( ord_less_eq_real @ ( tan_real @ X ) @ ( tan_real @ Y2 ) )
% 9.53/5.31                = ( ord_less_eq_real @ X @ Y2 ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8217_tan__mono__le,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 9.53/5.31       => ( ( ord_less_eq_real @ X @ Y2 )
% 9.53/5.31         => ( ( ord_less_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31           => ( ord_less_eq_real @ ( tan_real @ X ) @ ( tan_real @ Y2 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8218_tan__bound__pi2,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 9.53/5.31       => ( ord_less_real @ ( abs_abs_real @ ( tan_real @ X ) ) @ one_one_real ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8219_tan__30,axiom,
% 9.53/5.31      ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 9.53/5.31      = ( divide_divide_real @ one_one_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8220_arctan__unique,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 9.53/5.31       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31         => ( ( ( tan_real @ X )
% 9.53/5.31              = Y2 )
% 9.53/5.31           => ( ( arctan @ Y2 )
% 9.53/5.31              = X ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8221_arctan__tan,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 9.53/5.31       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31         => ( ( arctan @ ( tan_real @ X ) )
% 9.53/5.31            = X ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8222_arctan,axiom,
% 9.53/5.31      ! [Y2: real] :
% 9.53/5.31        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y2 ) )
% 9.53/5.31        & ( ord_less_real @ ( arctan @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31        & ( ( tan_real @ ( arctan @ Y2 ) )
% 9.53/5.31          = Y2 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8223_Maclaurin__zero,axiom,
% 9.53/5.31      ! [X: real,N: nat,Diff: nat > complex > real] :
% 9.53/5.31        ( ( X = zero_zero_real )
% 9.53/5.31       => ( ( N != zero_zero_nat )
% 9.53/5.31         => ( ( groups6591440286371151544t_real
% 9.53/5.31              @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_complex ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 9.53/5.31              @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.31            = ( Diff @ zero_zero_nat @ zero_zero_complex ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8224_Maclaurin__zero,axiom,
% 9.53/5.31      ! [X: real,N: nat,Diff: nat > real > real] :
% 9.53/5.31        ( ( X = zero_zero_real )
% 9.53/5.31       => ( ( N != zero_zero_nat )
% 9.53/5.31         => ( ( groups6591440286371151544t_real
% 9.53/5.31              @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 9.53/5.31              @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.31            = ( Diff @ zero_zero_nat @ zero_zero_real ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8225_Maclaurin__zero,axiom,
% 9.53/5.31      ! [X: real,N: nat,Diff: nat > rat > real] :
% 9.53/5.31        ( ( X = zero_zero_real )
% 9.53/5.31       => ( ( N != zero_zero_nat )
% 9.53/5.31         => ( ( groups6591440286371151544t_real
% 9.53/5.31              @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_rat ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 9.53/5.31              @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.31            = ( Diff @ zero_zero_nat @ zero_zero_rat ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8226_Maclaurin__zero,axiom,
% 9.53/5.31      ! [X: real,N: nat,Diff: nat > nat > real] :
% 9.53/5.31        ( ( X = zero_zero_real )
% 9.53/5.31       => ( ( N != zero_zero_nat )
% 9.53/5.31         => ( ( groups6591440286371151544t_real
% 9.53/5.31              @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_nat ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 9.53/5.31              @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.31            = ( Diff @ zero_zero_nat @ zero_zero_nat ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8227_Maclaurin__zero,axiom,
% 9.53/5.31      ! [X: real,N: nat,Diff: nat > int > real] :
% 9.53/5.31        ( ( X = zero_zero_real )
% 9.53/5.31       => ( ( N != zero_zero_nat )
% 9.53/5.31         => ( ( groups6591440286371151544t_real
% 9.53/5.31              @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_int ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 9.53/5.31              @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.31            = ( Diff @ zero_zero_nat @ zero_zero_int ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8228_Maclaurin__lemma,axiom,
% 9.53/5.31      ! [H2: real,F: real > real,J: nat > real,N: nat] :
% 9.53/5.31        ( ( ord_less_real @ zero_zero_real @ H2 )
% 9.53/5.31       => ? [B8: real] :
% 9.53/5.31            ( ( F @ H2 )
% 9.53/5.31            = ( plus_plus_real
% 9.53/5.31              @ ( groups6591440286371151544t_real
% 9.53/5.31                @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( J @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 9.53/5.31                @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.31              @ ( times_times_real @ B8 @ ( divide_divide_real @ ( power_power_real @ H2 @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8229_lemma__tan__add1,axiom,
% 9.53/5.31      ! [X: complex,Y2: complex] :
% 9.53/5.31        ( ( ( cos_complex @ X )
% 9.53/5.31         != zero_zero_complex )
% 9.53/5.31       => ( ( ( cos_complex @ Y2 )
% 9.53/5.31           != zero_zero_complex )
% 9.53/5.31         => ( ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y2 ) ) )
% 9.53/5.31            = ( divide1717551699836669952omplex @ ( cos_complex @ ( plus_plus_complex @ X @ Y2 ) ) @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ Y2 ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8230_lemma__tan__add1,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( ( cos_real @ X )
% 9.53/5.31         != zero_zero_real )
% 9.53/5.31       => ( ( ( cos_real @ Y2 )
% 9.53/5.31           != zero_zero_real )
% 9.53/5.31         => ( ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X ) @ ( tan_real @ Y2 ) ) )
% 9.53/5.31            = ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ X @ Y2 ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y2 ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8231_tan__diff,axiom,
% 9.53/5.31      ! [X: complex,Y2: complex] :
% 9.53/5.31        ( ( ( cos_complex @ X )
% 9.53/5.31         != zero_zero_complex )
% 9.53/5.31       => ( ( ( cos_complex @ Y2 )
% 9.53/5.31           != zero_zero_complex )
% 9.53/5.31         => ( ( ( cos_complex @ ( minus_minus_complex @ X @ Y2 ) )
% 9.53/5.31             != zero_zero_complex )
% 9.53/5.31           => ( ( tan_complex @ ( minus_minus_complex @ X @ Y2 ) )
% 9.53/5.31              = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y2 ) ) @ ( plus_plus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y2 ) ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8232_tan__diff,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( ( cos_real @ X )
% 9.53/5.31         != zero_zero_real )
% 9.53/5.31       => ( ( ( cos_real @ Y2 )
% 9.53/5.31           != zero_zero_real )
% 9.53/5.31         => ( ( ( cos_real @ ( minus_minus_real @ X @ Y2 ) )
% 9.53/5.31             != zero_zero_real )
% 9.53/5.31           => ( ( tan_real @ ( minus_minus_real @ X @ Y2 ) )
% 9.53/5.31              = ( divide_divide_real @ ( minus_minus_real @ ( tan_real @ X ) @ ( tan_real @ Y2 ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X ) @ ( tan_real @ Y2 ) ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8233_tan__add,axiom,
% 9.53/5.31      ! [X: complex,Y2: complex] :
% 9.53/5.31        ( ( ( cos_complex @ X )
% 9.53/5.31         != zero_zero_complex )
% 9.53/5.31       => ( ( ( cos_complex @ Y2 )
% 9.53/5.31           != zero_zero_complex )
% 9.53/5.31         => ( ( ( cos_complex @ ( plus_plus_complex @ X @ Y2 ) )
% 9.53/5.31             != zero_zero_complex )
% 9.53/5.31           => ( ( tan_complex @ ( plus_plus_complex @ X @ Y2 ) )
% 9.53/5.31              = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y2 ) ) @ ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y2 ) ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8234_tan__add,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( ( cos_real @ X )
% 9.53/5.31         != zero_zero_real )
% 9.53/5.31       => ( ( ( cos_real @ Y2 )
% 9.53/5.31           != zero_zero_real )
% 9.53/5.31         => ( ( ( cos_real @ ( plus_plus_real @ X @ Y2 ) )
% 9.53/5.31             != zero_zero_real )
% 9.53/5.31           => ( ( tan_real @ ( plus_plus_real @ X @ Y2 ) )
% 9.53/5.31              = ( divide_divide_real @ ( plus_plus_real @ ( tan_real @ X ) @ ( tan_real @ Y2 ) ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X ) @ ( tan_real @ Y2 ) ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8235_tan__total__pi4,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 9.53/5.31       => ? [Z3: real] :
% 9.53/5.31            ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) @ Z3 )
% 9.53/5.31            & ( ord_less_real @ Z3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 9.53/5.31            & ( ( tan_real @ Z3 )
% 9.53/5.31              = X ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8236_Maclaurin__exp__le,axiom,
% 9.53/5.31      ! [X: real,N: nat] :
% 9.53/5.31      ? [T6: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 9.53/5.31        & ( ( exp_real @ X )
% 9.53/5.31          = ( plus_plus_real
% 9.53/5.31            @ ( groups6591440286371151544t_real
% 9.53/5.31              @ ^ [M6: nat] : ( divide_divide_real @ ( power_power_real @ X @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) )
% 9.53/5.31              @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.31            @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8237_tan__half,axiom,
% 9.53/5.31      ( tan_complex
% 9.53/5.31      = ( ^ [X2: complex] : ( divide1717551699836669952omplex @ ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) ) @ ( plus_plus_complex @ ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) ) @ one_one_complex ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8238_tan__half,axiom,
% 9.53/5.31      ( tan_real
% 9.53/5.31      = ( ^ [X2: real] : ( divide_divide_real @ ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) ) @ ( plus_plus_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) ) @ one_one_real ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8239_cos__coeff__def,axiom,
% 9.53/5.31      ( cos_coeff
% 9.53/5.31      = ( ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ zero_zero_real ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8240_Maclaurin__exp__lt,axiom,
% 9.53/5.31      ! [X: real,N: nat] :
% 9.53/5.31        ( ( X != zero_zero_real )
% 9.53/5.31       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.31         => ? [T6: real] :
% 9.53/5.31              ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T6 ) )
% 9.53/5.31              & ( ord_less_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 9.53/5.31              & ( ( exp_real @ X )
% 9.53/5.31                = ( plus_plus_real
% 9.53/5.31                  @ ( groups6591440286371151544t_real
% 9.53/5.31                    @ ^ [M6: nat] : ( divide_divide_real @ ( power_power_real @ X @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) )
% 9.53/5.31                    @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.31                  @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8241_cos__tan,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31       => ( ( cos_real @ X )
% 9.53/5.31          = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8242_Maclaurin__sin__expansion3,axiom,
% 9.53/5.31      ! [N: nat,X: real] :
% 9.53/5.31        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.31       => ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.31         => ? [T6: real] :
% 9.53/5.31              ( ( ord_less_real @ zero_zero_real @ T6 )
% 9.53/5.31              & ( ord_less_real @ T6 @ X )
% 9.53/5.31              & ( ( sin_real @ X )
% 9.53/5.31                = ( plus_plus_real
% 9.53/5.31                  @ ( groups6591440286371151544t_real
% 9.53/5.31                    @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 9.53/5.31                    @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.31                  @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8243_Maclaurin__sin__expansion4,axiom,
% 9.53/5.31      ! [X: real,N: nat] :
% 9.53/5.31        ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.31       => ? [T6: real] :
% 9.53/5.31            ( ( ord_less_real @ zero_zero_real @ T6 )
% 9.53/5.31            & ( ord_less_eq_real @ T6 @ X )
% 9.53/5.31            & ( ( sin_real @ X )
% 9.53/5.31              = ( plus_plus_real
% 9.53/5.31                @ ( groups6591440286371151544t_real
% 9.53/5.31                  @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 9.53/5.31                  @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.31                @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8244_Maclaurin__sin__expansion2,axiom,
% 9.53/5.31      ! [X: real,N: nat] :
% 9.53/5.31      ? [T6: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 9.53/5.31        & ( ( sin_real @ X )
% 9.53/5.31          = ( plus_plus_real
% 9.53/5.31            @ ( groups6591440286371151544t_real
% 9.53/5.31              @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 9.53/5.31              @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.31            @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8245_Maclaurin__sin__expansion,axiom,
% 9.53/5.31      ! [X: real,N: nat] :
% 9.53/5.31      ? [T6: real] :
% 9.53/5.31        ( ( sin_real @ X )
% 9.53/5.31        = ( plus_plus_real
% 9.53/5.31          @ ( groups6591440286371151544t_real
% 9.53/5.31            @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 9.53/5.31            @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.31          @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8246_sin__coeff__def,axiom,
% 9.53/5.31      ( sin_coeff
% 9.53/5.31      = ( ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ zero_zero_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8247_fact__ge__self,axiom,
% 9.53/5.31      ! [N: nat] : ( ord_less_eq_nat @ N @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8248_fact__mono__nat,axiom,
% 9.53/5.31      ! [M: nat,N: nat] :
% 9.53/5.31        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.31       => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8249_fact__less__mono__nat,axiom,
% 9.53/5.31      ! [M: nat,N: nat] :
% 9.53/5.31        ( ( ord_less_nat @ zero_zero_nat @ M )
% 9.53/5.31       => ( ( ord_less_nat @ M @ N )
% 9.53/5.31         => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8250_fact__ge__Suc__0__nat,axiom,
% 9.53/5.31      ! [N: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8251_dvd__fact,axiom,
% 9.53/5.31      ! [M: nat,N: nat] :
% 9.53/5.31        ( ( ord_less_eq_nat @ one_one_nat @ M )
% 9.53/5.31       => ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.31         => ( dvd_dvd_nat @ M @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8252_fact__diff__Suc,axiom,
% 9.53/5.31      ! [N: nat,M: nat] :
% 9.53/5.31        ( ( ord_less_nat @ N @ ( suc @ M ) )
% 9.53/5.31       => ( ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) )
% 9.53/5.31          = ( times_times_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M @ N ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8253_fact__div__fact__le__pow,axiom,
% 9.53/5.31      ! [R: nat,N: nat] :
% 9.53/5.31        ( ( ord_less_eq_nat @ R @ N )
% 9.53/5.31       => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ R ) ) ) @ ( power_power_nat @ N @ R ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8254_sin__coeff__Suc,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( sin_coeff @ ( suc @ N ) )
% 9.53/5.31        = ( divide_divide_real @ ( cos_coeff @ N ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8255_cos__coeff__Suc,axiom,
% 9.53/5.31      ! [N: nat] :
% 9.53/5.31        ( ( cos_coeff @ ( suc @ N ) )
% 9.53/5.31        = ( divide_divide_real @ ( uminus_uminus_real @ ( sin_coeff @ N ) ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8256_complex__unimodular__polar,axiom,
% 9.53/5.31      ! [Z: complex] :
% 9.53/5.31        ( ( ( real_V1022390504157884413omplex @ Z )
% 9.53/5.31          = one_one_real )
% 9.53/5.31       => ~ ! [T6: real] :
% 9.53/5.31              ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 9.53/5.31             => ( ( ord_less_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 9.53/5.31               => ( Z
% 9.53/5.31                 != ( complex2 @ ( cos_real @ T6 ) @ ( sin_real @ T6 ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8257_sin__paired,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( sums_real
% 9.53/5.31        @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 9.53/5.31        @ ( sin_real @ X ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8258_cos__arcsin,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 9.53/5.31       => ( ( ord_less_eq_real @ X @ one_one_real )
% 9.53/5.31         => ( ( cos_real @ ( arcsin @ X ) )
% 9.53/5.31            = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8259_sin__arccos__abs,axiom,
% 9.53/5.31      ! [Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 9.53/5.31       => ( ( sin_real @ ( arccos @ Y2 ) )
% 9.53/5.31          = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8260_arccos__1,axiom,
% 9.53/5.31      ( ( arccos @ one_one_real )
% 9.53/5.31      = zero_zero_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8261_arccos__minus__1,axiom,
% 9.53/5.31      ( ( arccos @ ( uminus_uminus_real @ one_one_real ) )
% 9.53/5.31      = pi ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8262_cos__arccos,axiom,
% 9.53/5.31      ! [Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 9.53/5.31       => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 9.53/5.31         => ( ( cos_real @ ( arccos @ Y2 ) )
% 9.53/5.31            = Y2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8263_sin__arcsin,axiom,
% 9.53/5.31      ! [Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 9.53/5.31       => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 9.53/5.31         => ( ( sin_real @ ( arcsin @ Y2 ) )
% 9.53/5.31            = Y2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8264_powser__sums__zero__iff,axiom,
% 9.53/5.31      ! [A: nat > complex,X: complex] :
% 9.53/5.31        ( ( sums_complex
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_complex @ ( A @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) )
% 9.53/5.31          @ X )
% 9.53/5.31        = ( ( A @ zero_zero_nat )
% 9.53/5.31          = X ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8265_powser__sums__zero__iff,axiom,
% 9.53/5.31      ! [A: nat > real,X: real] :
% 9.53/5.31        ( ( sums_real
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_real @ ( A @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) )
% 9.53/5.31          @ X )
% 9.53/5.31        = ( ( A @ zero_zero_nat )
% 9.53/5.31          = X ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8266_norm__cos__sin,axiom,
% 9.53/5.31      ! [T: real] :
% 9.53/5.31        ( ( real_V1022390504157884413omplex @ ( complex2 @ ( cos_real @ T ) @ ( sin_real @ T ) ) )
% 9.53/5.31        = one_one_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8267_arccos__0,axiom,
% 9.53/5.31      ( ( arccos @ zero_zero_real )
% 9.53/5.31      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8268_arcsin__1,axiom,
% 9.53/5.31      ( ( arcsin @ one_one_real )
% 9.53/5.31      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8269_arcsin__minus__1,axiom,
% 9.53/5.31      ( ( arcsin @ ( uminus_uminus_real @ one_one_real ) )
% 9.53/5.31      = ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8270_complex__of__real__mult__Complex,axiom,
% 9.53/5.31      ! [R: real,X: real,Y2: real] :
% 9.53/5.31        ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R ) @ ( complex2 @ X @ Y2 ) )
% 9.53/5.31        = ( complex2 @ ( times_times_real @ R @ X ) @ ( times_times_real @ R @ Y2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8271_Complex__mult__complex__of__real,axiom,
% 9.53/5.31      ! [X: real,Y2: real,R: real] :
% 9.53/5.31        ( ( times_times_complex @ ( complex2 @ X @ Y2 ) @ ( real_V4546457046886955230omplex @ R ) )
% 9.53/5.31        = ( complex2 @ ( times_times_real @ X @ R ) @ ( times_times_real @ Y2 @ R ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8272_complex__diff,axiom,
% 9.53/5.31      ! [A: real,B: real,C: real,D2: real] :
% 9.53/5.31        ( ( minus_minus_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D2 ) )
% 9.53/5.31        = ( complex2 @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8273_sums__le,axiom,
% 9.53/5.31      ! [F: nat > real,G: nat > real,S3: real,T: real] :
% 9.53/5.31        ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 9.53/5.31       => ( ( sums_real @ F @ S3 )
% 9.53/5.31         => ( ( sums_real @ G @ T )
% 9.53/5.31           => ( ord_less_eq_real @ S3 @ T ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8274_sums__le,axiom,
% 9.53/5.31      ! [F: nat > nat,G: nat > nat,S3: nat,T: nat] :
% 9.53/5.31        ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( G @ N3 ) )
% 9.53/5.31       => ( ( sums_nat @ F @ S3 )
% 9.53/5.31         => ( ( sums_nat @ G @ T )
% 9.53/5.31           => ( ord_less_eq_nat @ S3 @ T ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8275_sums__le,axiom,
% 9.53/5.31      ! [F: nat > int,G: nat > int,S3: int,T: int] :
% 9.53/5.31        ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( G @ N3 ) )
% 9.53/5.31       => ( ( sums_int @ F @ S3 )
% 9.53/5.31         => ( ( sums_int @ G @ T )
% 9.53/5.31           => ( ord_less_eq_int @ S3 @ T ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8276_sums__divide,axiom,
% 9.53/5.31      ! [F: nat > complex,A: complex,C: complex] :
% 9.53/5.31        ( ( sums_complex @ F @ A )
% 9.53/5.31       => ( sums_complex
% 9.53/5.31          @ ^ [N2: nat] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ C )
% 9.53/5.31          @ ( divide1717551699836669952omplex @ A @ C ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8277_sums__divide,axiom,
% 9.53/5.31      ! [F: nat > real,A: real,C: real] :
% 9.53/5.31        ( ( sums_real @ F @ A )
% 9.53/5.31       => ( sums_real
% 9.53/5.31          @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ C )
% 9.53/5.31          @ ( divide_divide_real @ A @ C ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8278_sums__diff,axiom,
% 9.53/5.31      ! [F: nat > real,A: real,G: nat > real,B: real] :
% 9.53/5.31        ( ( sums_real @ F @ A )
% 9.53/5.31       => ( ( sums_real @ G @ B )
% 9.53/5.31         => ( sums_real
% 9.53/5.31            @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 9.53/5.31            @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8279_sums__add,axiom,
% 9.53/5.31      ! [F: nat > real,A: real,G: nat > real,B: real] :
% 9.53/5.31        ( ( sums_real @ F @ A )
% 9.53/5.31       => ( ( sums_real @ G @ B )
% 9.53/5.31         => ( sums_real
% 9.53/5.31            @ ^ [N2: nat] : ( plus_plus_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 9.53/5.31            @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8280_sums__add,axiom,
% 9.53/5.31      ! [F: nat > nat,A: nat,G: nat > nat,B: nat] :
% 9.53/5.31        ( ( sums_nat @ F @ A )
% 9.53/5.31       => ( ( sums_nat @ G @ B )
% 9.53/5.31         => ( sums_nat
% 9.53/5.31            @ ^ [N2: nat] : ( plus_plus_nat @ ( F @ N2 ) @ ( G @ N2 ) )
% 9.53/5.31            @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8281_sums__add,axiom,
% 9.53/5.31      ! [F: nat > int,A: int,G: nat > int,B: int] :
% 9.53/5.31        ( ( sums_int @ F @ A )
% 9.53/5.31       => ( ( sums_int @ G @ B )
% 9.53/5.31         => ( sums_int
% 9.53/5.31            @ ^ [N2: nat] : ( plus_plus_int @ ( F @ N2 ) @ ( G @ N2 ) )
% 9.53/5.31            @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8282_sums__add,axiom,
% 9.53/5.31      ! [F: nat > complex,A: complex,G: nat > complex,B: complex] :
% 9.53/5.31        ( ( sums_complex @ F @ A )
% 9.53/5.31       => ( ( sums_complex @ G @ B )
% 9.53/5.31         => ( sums_complex
% 9.53/5.31            @ ^ [N2: nat] : ( plus_plus_complex @ ( F @ N2 ) @ ( G @ N2 ) )
% 9.53/5.31            @ ( plus_plus_complex @ A @ B ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8283_sums__mult,axiom,
% 9.53/5.31      ! [F: nat > complex,A: complex,C: complex] :
% 9.53/5.31        ( ( sums_complex @ F @ A )
% 9.53/5.31       => ( sums_complex
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) )
% 9.53/5.31          @ ( times_times_complex @ C @ A ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8284_sums__mult,axiom,
% 9.53/5.31      ! [F: nat > real,A: real,C: real] :
% 9.53/5.31        ( ( sums_real @ F @ A )
% 9.53/5.31       => ( sums_real
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) )
% 9.53/5.31          @ ( times_times_real @ C @ A ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8285_sums__mult2,axiom,
% 9.53/5.31      ! [F: nat > complex,A: complex,C: complex] :
% 9.53/5.31        ( ( sums_complex @ F @ A )
% 9.53/5.31       => ( sums_complex
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ C )
% 9.53/5.31          @ ( times_times_complex @ A @ C ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8286_sums__mult2,axiom,
% 9.53/5.31      ! [F: nat > real,A: real,C: real] :
% 9.53/5.31        ( ( sums_real @ F @ A )
% 9.53/5.31       => ( sums_real
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ C )
% 9.53/5.31          @ ( times_times_real @ A @ C ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8287_sums__mult2__iff,axiom,
% 9.53/5.31      ! [C: complex,F: nat > complex,D2: complex] :
% 9.53/5.31        ( ( C != zero_zero_complex )
% 9.53/5.31       => ( ( sums_complex
% 9.53/5.31            @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ C )
% 9.53/5.31            @ ( times_times_complex @ D2 @ C ) )
% 9.53/5.31          = ( sums_complex @ F @ D2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8288_sums__mult2__iff,axiom,
% 9.53/5.31      ! [C: real,F: nat > real,D2: real] :
% 9.53/5.31        ( ( C != zero_zero_real )
% 9.53/5.31       => ( ( sums_real
% 9.53/5.31            @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ C )
% 9.53/5.31            @ ( times_times_real @ D2 @ C ) )
% 9.53/5.31          = ( sums_real @ F @ D2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8289_sums__mult__iff,axiom,
% 9.53/5.31      ! [C: complex,F: nat > complex,D2: complex] :
% 9.53/5.31        ( ( C != zero_zero_complex )
% 9.53/5.31       => ( ( sums_complex
% 9.53/5.31            @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) )
% 9.53/5.31            @ ( times_times_complex @ C @ D2 ) )
% 9.53/5.31          = ( sums_complex @ F @ D2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8290_sums__mult__iff,axiom,
% 9.53/5.31      ! [C: real,F: nat > real,D2: real] :
% 9.53/5.31        ( ( C != zero_zero_real )
% 9.53/5.31       => ( ( sums_real
% 9.53/5.31            @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) )
% 9.53/5.31            @ ( times_times_real @ C @ D2 ) )
% 9.53/5.31          = ( sums_real @ F @ D2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8291_Complex__eq__numeral,axiom,
% 9.53/5.31      ! [A: real,B: real,W: num] :
% 9.53/5.31        ( ( ( complex2 @ A @ B )
% 9.53/5.31          = ( numera6690914467698888265omplex @ W ) )
% 9.53/5.31        = ( ( A
% 9.53/5.31            = ( numeral_numeral_real @ W ) )
% 9.53/5.31          & ( B = zero_zero_real ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8292_complex__add,axiom,
% 9.53/5.31      ! [A: real,B: real,C: real,D2: real] :
% 9.53/5.31        ( ( plus_plus_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D2 ) )
% 9.53/5.31        = ( complex2 @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8293_complex__of__real__add__Complex,axiom,
% 9.53/5.31      ! [R: real,X: real,Y2: real] :
% 9.53/5.31        ( ( plus_plus_complex @ ( real_V4546457046886955230omplex @ R ) @ ( complex2 @ X @ Y2 ) )
% 9.53/5.31        = ( complex2 @ ( plus_plus_real @ R @ X ) @ Y2 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8294_Complex__add__complex__of__real,axiom,
% 9.53/5.31      ! [X: real,Y2: real,R: real] :
% 9.53/5.31        ( ( plus_plus_complex @ ( complex2 @ X @ Y2 ) @ ( real_V4546457046886955230omplex @ R ) )
% 9.53/5.31        = ( complex2 @ ( plus_plus_real @ X @ R ) @ Y2 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8295_sums__mult__D,axiom,
% 9.53/5.31      ! [C: complex,F: nat > complex,A: complex] :
% 9.53/5.31        ( ( sums_complex
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) )
% 9.53/5.31          @ A )
% 9.53/5.31       => ( ( C != zero_zero_complex )
% 9.53/5.31         => ( sums_complex @ F @ ( divide1717551699836669952omplex @ A @ C ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8296_sums__mult__D,axiom,
% 9.53/5.31      ! [C: real,F: nat > real,A: real] :
% 9.53/5.31        ( ( sums_real
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) )
% 9.53/5.31          @ A )
% 9.53/5.31       => ( ( C != zero_zero_real )
% 9.53/5.31         => ( sums_real @ F @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8297_sums__Suc__imp,axiom,
% 9.53/5.31      ! [F: nat > complex,S3: complex] :
% 9.53/5.31        ( ( ( F @ zero_zero_nat )
% 9.53/5.31          = zero_zero_complex )
% 9.53/5.31       => ( ( sums_complex
% 9.53/5.31            @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 9.53/5.31            @ S3 )
% 9.53/5.31         => ( sums_complex @ F @ S3 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8298_sums__Suc__imp,axiom,
% 9.53/5.31      ! [F: nat > real,S3: real] :
% 9.53/5.31        ( ( ( F @ zero_zero_nat )
% 9.53/5.31          = zero_zero_real )
% 9.53/5.31       => ( ( sums_real
% 9.53/5.31            @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 9.53/5.31            @ S3 )
% 9.53/5.31         => ( sums_real @ F @ S3 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8299_sums__Suc,axiom,
% 9.53/5.31      ! [F: nat > real,L2: real] :
% 9.53/5.31        ( ( sums_real
% 9.53/5.31          @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 9.53/5.31          @ L2 )
% 9.53/5.31       => ( sums_real @ F @ ( plus_plus_real @ L2 @ ( F @ zero_zero_nat ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8300_sums__Suc,axiom,
% 9.53/5.31      ! [F: nat > nat,L2: nat] :
% 9.53/5.31        ( ( sums_nat
% 9.53/5.31          @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 9.53/5.31          @ L2 )
% 9.53/5.31       => ( sums_nat @ F @ ( plus_plus_nat @ L2 @ ( F @ zero_zero_nat ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8301_sums__Suc,axiom,
% 9.53/5.31      ! [F: nat > int,L2: int] :
% 9.53/5.31        ( ( sums_int
% 9.53/5.31          @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 9.53/5.31          @ L2 )
% 9.53/5.31       => ( sums_int @ F @ ( plus_plus_int @ L2 @ ( F @ zero_zero_nat ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8302_sums__Suc,axiom,
% 9.53/5.31      ! [F: nat > complex,L2: complex] :
% 9.53/5.31        ( ( sums_complex
% 9.53/5.31          @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 9.53/5.31          @ L2 )
% 9.53/5.31       => ( sums_complex @ F @ ( plus_plus_complex @ L2 @ ( F @ zero_zero_nat ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8303_sums__Suc__iff,axiom,
% 9.53/5.31      ! [F: nat > real,S3: real] :
% 9.53/5.31        ( ( sums_real
% 9.53/5.31          @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 9.53/5.31          @ S3 )
% 9.53/5.31        = ( sums_real @ F @ ( plus_plus_real @ S3 @ ( F @ zero_zero_nat ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8304_sums__Suc__iff,axiom,
% 9.53/5.31      ! [F: nat > complex,S3: complex] :
% 9.53/5.31        ( ( sums_complex
% 9.53/5.31          @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 9.53/5.31          @ S3 )
% 9.53/5.31        = ( sums_complex @ F @ ( plus_plus_complex @ S3 @ ( F @ zero_zero_nat ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8305_sums__zero__iff__shift,axiom,
% 9.53/5.31      ! [N: nat,F: nat > complex,S3: complex] :
% 9.53/5.31        ( ! [I4: nat] :
% 9.53/5.31            ( ( ord_less_nat @ I4 @ N )
% 9.53/5.31           => ( ( F @ I4 )
% 9.53/5.31              = zero_zero_complex ) )
% 9.53/5.31       => ( ( sums_complex
% 9.53/5.31            @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N ) )
% 9.53/5.31            @ S3 )
% 9.53/5.31          = ( sums_complex @ F @ S3 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8306_sums__zero__iff__shift,axiom,
% 9.53/5.31      ! [N: nat,F: nat > real,S3: real] :
% 9.53/5.31        ( ! [I4: nat] :
% 9.53/5.31            ( ( ord_less_nat @ I4 @ N )
% 9.53/5.31           => ( ( F @ I4 )
% 9.53/5.31              = zero_zero_real ) )
% 9.53/5.31       => ( ( sums_real
% 9.53/5.31            @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N ) )
% 9.53/5.31            @ S3 )
% 9.53/5.31          = ( sums_real @ F @ S3 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8307_Complex__eq__neg__numeral,axiom,
% 9.53/5.31      ! [A: real,B: real,W: num] :
% 9.53/5.31        ( ( ( complex2 @ A @ B )
% 9.53/5.31          = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 9.53/5.31        = ( ( A
% 9.53/5.31            = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 9.53/5.31          & ( B = zero_zero_real ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8308_complex__mult,axiom,
% 9.53/5.31      ! [A: real,B: real,C: real,D2: real] :
% 9.53/5.31        ( ( times_times_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D2 ) )
% 9.53/5.31        = ( complex2 @ ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) @ ( plus_plus_real @ ( times_times_real @ A @ D2 ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8309_Complex__eq__1,axiom,
% 9.53/5.31      ! [A: real,B: real] :
% 9.53/5.31        ( ( ( complex2 @ A @ B )
% 9.53/5.31          = one_one_complex )
% 9.53/5.31        = ( ( A = one_one_real )
% 9.53/5.31          & ( B = zero_zero_real ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8310_one__complex_Ocode,axiom,
% 9.53/5.31      ( one_one_complex
% 9.53/5.31      = ( complex2 @ one_one_real @ zero_zero_real ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8311_arccos__le__arccos,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 9.53/5.31       => ( ( ord_less_eq_real @ X @ Y2 )
% 9.53/5.31         => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 9.53/5.31           => ( ord_less_eq_real @ ( arccos @ Y2 ) @ ( arccos @ X ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8312_arccos__le__mono,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 9.53/5.31       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 9.53/5.31         => ( ( ord_less_eq_real @ ( arccos @ X ) @ ( arccos @ Y2 ) )
% 9.53/5.31            = ( ord_less_eq_real @ Y2 @ X ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8313_arccos__eq__iff,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 9.53/5.31          & ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real ) )
% 9.53/5.31       => ( ( ( arccos @ X )
% 9.53/5.31            = ( arccos @ Y2 ) )
% 9.53/5.31          = ( X = Y2 ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8314_arcsin__minus,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 9.53/5.31       => ( ( ord_less_eq_real @ X @ one_one_real )
% 9.53/5.31         => ( ( arcsin @ ( uminus_uminus_real @ X ) )
% 9.53/5.31            = ( uminus_uminus_real @ ( arcsin @ X ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8315_arcsin__le__arcsin,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 9.53/5.31       => ( ( ord_less_eq_real @ X @ Y2 )
% 9.53/5.31         => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 9.53/5.31           => ( ord_less_eq_real @ ( arcsin @ X ) @ ( arcsin @ Y2 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8316_arcsin__le__mono,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 9.53/5.31       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 9.53/5.31         => ( ( ord_less_eq_real @ ( arcsin @ X ) @ ( arcsin @ Y2 ) )
% 9.53/5.31            = ( ord_less_eq_real @ X @ Y2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8317_arcsin__eq__iff,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 9.53/5.31       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 9.53/5.31         => ( ( ( arcsin @ X )
% 9.53/5.31              = ( arcsin @ Y2 ) )
% 9.53/5.31            = ( X = Y2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8318_powser__sums__if,axiom,
% 9.53/5.31      ! [M: nat,Z: complex] :
% 9.53/5.31        ( sums_complex
% 9.53/5.31        @ ^ [N2: nat] : ( times_times_complex @ ( if_complex @ ( N2 = M ) @ one_one_complex @ zero_zero_complex ) @ ( power_power_complex @ Z @ N2 ) )
% 9.53/5.31        @ ( power_power_complex @ Z @ M ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8319_powser__sums__if,axiom,
% 9.53/5.31      ! [M: nat,Z: real] :
% 9.53/5.31        ( sums_real
% 9.53/5.31        @ ^ [N2: nat] : ( times_times_real @ ( if_real @ ( N2 = M ) @ one_one_real @ zero_zero_real ) @ ( power_power_real @ Z @ N2 ) )
% 9.53/5.31        @ ( power_power_real @ Z @ M ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8320_powser__sums__if,axiom,
% 9.53/5.31      ! [M: nat,Z: int] :
% 9.53/5.31        ( sums_int
% 9.53/5.31        @ ^ [N2: nat] : ( times_times_int @ ( if_int @ ( N2 = M ) @ one_one_int @ zero_zero_int ) @ ( power_power_int @ Z @ N2 ) )
% 9.53/5.31        @ ( power_power_int @ Z @ M ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8321_powser__sums__zero,axiom,
% 9.53/5.31      ! [A: nat > complex] :
% 9.53/5.31        ( sums_complex
% 9.53/5.31        @ ^ [N2: nat] : ( times_times_complex @ ( A @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) )
% 9.53/5.31        @ ( A @ zero_zero_nat ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8322_powser__sums__zero,axiom,
% 9.53/5.31      ! [A: nat > real] :
% 9.53/5.31        ( sums_real
% 9.53/5.31        @ ^ [N2: nat] : ( times_times_real @ ( A @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) )
% 9.53/5.31        @ ( A @ zero_zero_nat ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8323_sums__iff__shift,axiom,
% 9.53/5.31      ! [F: nat > complex,N: nat,S3: complex] :
% 9.53/5.31        ( ( sums_complex
% 9.53/5.31          @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N ) )
% 9.53/5.31          @ S3 )
% 9.53/5.31        = ( sums_complex @ F @ ( plus_plus_complex @ S3 @ ( groups2073611262835488442omplex @ F @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8324_sums__iff__shift,axiom,
% 9.53/5.31      ! [F: nat > real,N: nat,S3: real] :
% 9.53/5.31        ( ( sums_real
% 9.53/5.31          @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N ) )
% 9.53/5.31          @ S3 )
% 9.53/5.31        = ( sums_real @ F @ ( plus_plus_real @ S3 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8325_sums__split__initial__segment,axiom,
% 9.53/5.31      ! [F: nat > real,S3: real,N: nat] :
% 9.53/5.31        ( ( sums_real @ F @ S3 )
% 9.53/5.31       => ( sums_real
% 9.53/5.31          @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N ) )
% 9.53/5.31          @ ( minus_minus_real @ S3 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8326_sums__iff__shift_H,axiom,
% 9.53/5.31      ! [F: nat > real,N: nat,S3: real] :
% 9.53/5.31        ( ( sums_real
% 9.53/5.31          @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N ) )
% 9.53/5.31          @ ( minus_minus_real @ S3 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) ) )
% 9.53/5.31        = ( sums_real @ F @ S3 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8327_sums__If__finite__set_H,axiom,
% 9.53/5.31      ! [G: nat > complex,S2: complex,A2: set_nat,S5: complex,F: nat > complex] :
% 9.53/5.31        ( ( sums_complex @ G @ S2 )
% 9.53/5.31       => ( ( finite_finite_nat @ A2 )
% 9.53/5.31         => ( ( S5
% 9.53/5.31              = ( plus_plus_complex @ S2
% 9.53/5.31                @ ( groups2073611262835488442omplex
% 9.53/5.31                  @ ^ [N2: nat] : ( minus_minus_complex @ ( F @ N2 ) @ ( G @ N2 ) )
% 9.53/5.31                  @ A2 ) ) )
% 9.53/5.31           => ( sums_complex
% 9.53/5.31              @ ^ [N2: nat] : ( if_complex @ ( member_nat @ N2 @ A2 ) @ ( F @ N2 ) @ ( G @ N2 ) )
% 9.53/5.31              @ S5 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8328_sums__If__finite__set_H,axiom,
% 9.53/5.31      ! [G: nat > real,S2: real,A2: set_nat,S5: real,F: nat > real] :
% 9.53/5.31        ( ( sums_real @ G @ S2 )
% 9.53/5.31       => ( ( finite_finite_nat @ A2 )
% 9.53/5.31         => ( ( S5
% 9.53/5.31              = ( plus_plus_real @ S2
% 9.53/5.31                @ ( groups6591440286371151544t_real
% 9.53/5.31                  @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 9.53/5.31                  @ A2 ) ) )
% 9.53/5.31           => ( sums_real
% 9.53/5.31              @ ^ [N2: nat] : ( if_real @ ( member_nat @ N2 @ A2 ) @ ( F @ N2 ) @ ( G @ N2 ) )
% 9.53/5.31              @ S5 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8329_Complex__eq__neg__1,axiom,
% 9.53/5.31      ! [A: real,B: real] :
% 9.53/5.31        ( ( ( complex2 @ A @ B )
% 9.53/5.31          = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 9.53/5.31        = ( ( A
% 9.53/5.31            = ( uminus_uminus_real @ one_one_real ) )
% 9.53/5.31          & ( B = zero_zero_real ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8330_arccos__lbound,axiom,
% 9.53/5.31      ! [Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 9.53/5.31       => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 9.53/5.31         => ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8331_arccos__less__arccos,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 9.53/5.31       => ( ( ord_less_real @ X @ Y2 )
% 9.53/5.31         => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 9.53/5.31           => ( ord_less_real @ ( arccos @ Y2 ) @ ( arccos @ X ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8332_arccos__less__mono,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 9.53/5.31       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 9.53/5.31         => ( ( ord_less_real @ ( arccos @ X ) @ ( arccos @ Y2 ) )
% 9.53/5.31            = ( ord_less_real @ Y2 @ X ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8333_arccos__ubound,axiom,
% 9.53/5.31      ! [Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 9.53/5.31       => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 9.53/5.31         => ( ord_less_eq_real @ ( arccos @ Y2 ) @ pi ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8334_arccos__cos,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.31       => ( ( ord_less_eq_real @ X @ pi )
% 9.53/5.31         => ( ( arccos @ ( cos_real @ X ) )
% 9.53/5.31            = X ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8335_arcsin__less__arcsin,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 9.53/5.31       => ( ( ord_less_real @ X @ Y2 )
% 9.53/5.31         => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 9.53/5.31           => ( ord_less_real @ ( arcsin @ X ) @ ( arcsin @ Y2 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8336_arcsin__less__mono,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 9.53/5.31       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 9.53/5.31         => ( ( ord_less_real @ ( arcsin @ X ) @ ( arcsin @ Y2 ) )
% 9.53/5.31            = ( ord_less_real @ X @ Y2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8337_cos__arccos__abs,axiom,
% 9.53/5.31      ! [Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 9.53/5.31       => ( ( cos_real @ ( arccos @ Y2 ) )
% 9.53/5.31          = Y2 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8338_arccos__cos__eq__abs,axiom,
% 9.53/5.31      ! [Theta: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( abs_abs_real @ Theta ) @ pi )
% 9.53/5.31       => ( ( arccos @ ( cos_real @ Theta ) )
% 9.53/5.31          = ( abs_abs_real @ Theta ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8339_arccos__lt__bounded,axiom,
% 9.53/5.31      ! [Y2: real] :
% 9.53/5.31        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 9.53/5.31       => ( ( ord_less_real @ Y2 @ one_one_real )
% 9.53/5.31         => ( ( ord_less_real @ zero_zero_real @ ( arccos @ Y2 ) )
% 9.53/5.31            & ( ord_less_real @ ( arccos @ Y2 ) @ pi ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8340_arccos__bounded,axiom,
% 9.53/5.31      ! [Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 9.53/5.31       => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 9.53/5.31         => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y2 ) )
% 9.53/5.31            & ( ord_less_eq_real @ ( arccos @ Y2 ) @ pi ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8341_sin__arccos__nonzero,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 9.53/5.31       => ( ( ord_less_real @ X @ one_one_real )
% 9.53/5.31         => ( ( sin_real @ ( arccos @ X ) )
% 9.53/5.31           != zero_zero_real ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8342_arccos__cos2,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 9.53/5.31       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ X )
% 9.53/5.31         => ( ( arccos @ ( cos_real @ X ) )
% 9.53/5.31            = ( uminus_uminus_real @ X ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8343_arccos__minus,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 9.53/5.31       => ( ( ord_less_eq_real @ X @ one_one_real )
% 9.53/5.31         => ( ( arccos @ ( uminus_uminus_real @ X ) )
% 9.53/5.31            = ( minus_minus_real @ pi @ ( arccos @ X ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8344_cos__arcsin__nonzero,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 9.53/5.31       => ( ( ord_less_real @ X @ one_one_real )
% 9.53/5.31         => ( ( cos_real @ ( arcsin @ X ) )
% 9.53/5.31           != zero_zero_real ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8345_geometric__sums,axiom,
% 9.53/5.31      ! [C: real] :
% 9.53/5.31        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 9.53/5.31       => ( sums_real @ ( power_power_real @ C ) @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8346_geometric__sums,axiom,
% 9.53/5.31      ! [C: complex] :
% 9.53/5.31        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 9.53/5.31       => ( sums_complex @ ( power_power_complex @ C ) @ ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8347_power__half__series,axiom,
% 9.53/5.31      ( sums_real
% 9.53/5.31      @ ^ [N2: nat] : ( power_power_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( suc @ N2 ) )
% 9.53/5.31      @ one_one_real ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8348_arccos,axiom,
% 9.53/5.31      ! [Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 9.53/5.31       => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 9.53/5.31         => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y2 ) )
% 9.53/5.31            & ( ord_less_eq_real @ ( arccos @ Y2 ) @ pi )
% 9.53/5.31            & ( ( cos_real @ ( arccos @ Y2 ) )
% 9.53/5.31              = Y2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8349_complex__norm,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( real_V1022390504157884413omplex @ ( complex2 @ X @ Y2 ) )
% 9.53/5.31        = ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8350_arccos__minus__abs,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 9.53/5.31       => ( ( arccos @ ( uminus_uminus_real @ X ) )
% 9.53/5.31          = ( minus_minus_real @ pi @ ( arccos @ X ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8351_sums__if_H,axiom,
% 9.53/5.31      ! [G: nat > real,X: real] :
% 9.53/5.31        ( ( sums_real @ G @ X )
% 9.53/5.31       => ( sums_real
% 9.53/5.31          @ ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ zero_zero_real @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.53/5.31          @ X ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8352_sums__if,axiom,
% 9.53/5.31      ! [G: nat > real,X: real,F: nat > real,Y2: real] :
% 9.53/5.31        ( ( sums_real @ G @ X )
% 9.53/5.31       => ( ( sums_real @ F @ Y2 )
% 9.53/5.31         => ( sums_real
% 9.53/5.31            @ ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( F @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.53/5.31            @ ( plus_plus_real @ X @ Y2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8353_arccos__le__pi2,axiom,
% 9.53/5.31      ! [Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 9.53/5.31       => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 9.53/5.31         => ( ord_less_eq_real @ ( arccos @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8354_arcsin__lt__bounded,axiom,
% 9.53/5.31      ! [Y2: real] :
% 9.53/5.31        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 9.53/5.31       => ( ( ord_less_real @ Y2 @ one_one_real )
% 9.53/5.31         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y2 ) )
% 9.53/5.31            & ( ord_less_real @ ( arcsin @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8355_arcsin__lbound,axiom,
% 9.53/5.31      ! [Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 9.53/5.31       => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 9.53/5.31         => ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8356_arcsin__ubound,axiom,
% 9.53/5.31      ! [Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 9.53/5.31       => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 9.53/5.31         => ( ord_less_eq_real @ ( arcsin @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8357_arcsin__bounded,axiom,
% 9.53/5.31      ! [Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 9.53/5.31       => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 9.53/5.31         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y2 ) )
% 9.53/5.31            & ( ord_less_eq_real @ ( arcsin @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8358_arcsin__sin,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 9.53/5.31       => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31         => ( ( arcsin @ ( sin_real @ X ) )
% 9.53/5.31            = X ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8359_cos__paired,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( sums_real
% 9.53/5.31        @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( power_power_real @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 9.53/5.31        @ ( cos_real @ X ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8360_le__arcsin__iff,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 9.53/5.31       => ( ( ord_less_eq_real @ X @ one_one_real )
% 9.53/5.31         => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y2 )
% 9.53/5.31           => ( ( ord_less_eq_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31             => ( ( ord_less_eq_real @ Y2 @ ( arcsin @ X ) )
% 9.53/5.31                = ( ord_less_eq_real @ ( sin_real @ Y2 ) @ X ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8361_arcsin__le__iff,axiom,
% 9.53/5.31      ! [X: real,Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 9.53/5.31       => ( ( ord_less_eq_real @ X @ one_one_real )
% 9.53/5.31         => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y2 )
% 9.53/5.31           => ( ( ord_less_eq_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31             => ( ( ord_less_eq_real @ ( arcsin @ X ) @ Y2 )
% 9.53/5.31                = ( ord_less_eq_real @ X @ ( sin_real @ Y2 ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8362_arcsin__pi,axiom,
% 9.53/5.31      ! [Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 9.53/5.31       => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 9.53/5.31         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y2 ) )
% 9.53/5.31            & ( ord_less_eq_real @ ( arcsin @ Y2 ) @ pi )
% 9.53/5.31            & ( ( sin_real @ ( arcsin @ Y2 ) )
% 9.53/5.31              = Y2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8363_arcsin,axiom,
% 9.53/5.31      ! [Y2: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 9.53/5.31       => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 9.53/5.31         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y2 ) )
% 9.53/5.31            & ( ord_less_eq_real @ ( arcsin @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.31            & ( ( sin_real @ ( arcsin @ Y2 ) )
% 9.53/5.31              = Y2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8364_arccos__cos__eq__abs__2pi,axiom,
% 9.53/5.31      ! [Theta: real] :
% 9.53/5.31        ~ ! [K2: int] :
% 9.53/5.31            ( ( arccos @ ( cos_real @ Theta ) )
% 9.53/5.31           != ( abs_abs_real @ ( minus_minus_real @ Theta @ ( times_times_real @ ( ring_1_of_int_real @ K2 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8365_geometric__deriv__sums,axiom,
% 9.53/5.31      ! [Z: real] :
% 9.53/5.31        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 9.53/5.31       => ( sums_real
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) @ ( power_power_real @ Z @ N2 ) )
% 9.53/5.31          @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8366_geometric__deriv__sums,axiom,
% 9.53/5.31      ! [Z: complex] :
% 9.53/5.31        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 9.53/5.31       => ( sums_complex
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N2 ) ) @ ( power_power_complex @ Z @ N2 ) )
% 9.53/5.31          @ ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ ( minus_minus_complex @ one_one_complex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8367_sin__arccos,axiom,
% 9.53/5.31      ! [X: real] :
% 9.53/5.31        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 9.53/5.31       => ( ( ord_less_eq_real @ X @ one_one_real )
% 9.53/5.31         => ( ( sin_real @ ( arccos @ X ) )
% 9.53/5.31            = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8368_diffs__equiv,axiom,
% 9.53/5.31      ! [C: nat > real,X: real] :
% 9.53/5.31        ( ( summable_real
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_real @ ( diffs_real @ C @ N2 ) @ ( power_power_real @ X @ N2 ) ) )
% 9.53/5.31       => ( sums_real
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( C @ N2 ) ) @ ( power_power_real @ X @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) )
% 9.53/5.31          @ ( suminf_real
% 9.53/5.31            @ ^ [N2: nat] : ( times_times_real @ ( diffs_real @ C @ N2 ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8369_diffs__equiv,axiom,
% 9.53/5.31      ! [C: nat > complex,X: complex] :
% 9.53/5.31        ( ( summable_complex
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_complex @ ( diffs_complex @ C @ N2 ) @ ( power_power_complex @ X @ N2 ) ) )
% 9.53/5.31       => ( sums_complex
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( C @ N2 ) ) @ ( power_power_complex @ X @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) )
% 9.53/5.31          @ ( suminf_complex
% 9.53/5.31            @ ^ [N2: nat] : ( times_times_complex @ ( diffs_complex @ C @ N2 ) @ ( power_power_complex @ X @ N2 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8370_monoseq__def,axiom,
% 9.53/5.31      ( topolo6980174941875973593q_real
% 9.53/5.31      = ( ^ [X4: nat > real] :
% 9.53/5.31            ( ! [M6: nat,N2: nat] :
% 9.53/5.31                ( ( ord_less_eq_nat @ M6 @ N2 )
% 9.53/5.31               => ( ord_less_eq_real @ ( X4 @ M6 ) @ ( X4 @ N2 ) ) )
% 9.53/5.31            | ! [M6: nat,N2: nat] :
% 9.53/5.31                ( ( ord_less_eq_nat @ M6 @ N2 )
% 9.53/5.31               => ( ord_less_eq_real @ ( X4 @ N2 ) @ ( X4 @ M6 ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8371_monoseq__def,axiom,
% 9.53/5.31      ( topolo2489691266198938127t_real
% 9.53/5.31      = ( ^ [X4: nat > set_real] :
% 9.53/5.31            ( ! [M6: nat,N2: nat] :
% 9.53/5.31                ( ( ord_less_eq_nat @ M6 @ N2 )
% 9.53/5.31               => ( ord_less_eq_set_real @ ( X4 @ M6 ) @ ( X4 @ N2 ) ) )
% 9.53/5.31            | ! [M6: nat,N2: nat] :
% 9.53/5.31                ( ( ord_less_eq_nat @ M6 @ N2 )
% 9.53/5.31               => ( ord_less_eq_set_real @ ( X4 @ N2 ) @ ( X4 @ M6 ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8372_monoseq__def,axiom,
% 9.53/5.31      ( topolo7278393974255667507et_nat
% 9.53/5.31      = ( ^ [X4: nat > set_nat] :
% 9.53/5.31            ( ! [M6: nat,N2: nat] :
% 9.53/5.31                ( ( ord_less_eq_nat @ M6 @ N2 )
% 9.53/5.31               => ( ord_less_eq_set_nat @ ( X4 @ M6 ) @ ( X4 @ N2 ) ) )
% 9.53/5.31            | ! [M6: nat,N2: nat] :
% 9.53/5.31                ( ( ord_less_eq_nat @ M6 @ N2 )
% 9.53/5.31               => ( ord_less_eq_set_nat @ ( X4 @ N2 ) @ ( X4 @ M6 ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8373_monoseq__def,axiom,
% 9.53/5.31      ( topolo1459490580787246023eq_num
% 9.53/5.31      = ( ^ [X4: nat > num] :
% 9.53/5.31            ( ! [M6: nat,N2: nat] :
% 9.53/5.31                ( ( ord_less_eq_nat @ M6 @ N2 )
% 9.53/5.31               => ( ord_less_eq_num @ ( X4 @ M6 ) @ ( X4 @ N2 ) ) )
% 9.53/5.31            | ! [M6: nat,N2: nat] :
% 9.53/5.31                ( ( ord_less_eq_nat @ M6 @ N2 )
% 9.53/5.31               => ( ord_less_eq_num @ ( X4 @ N2 ) @ ( X4 @ M6 ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8374_monoseq__def,axiom,
% 9.53/5.31      ( topolo4902158794631467389eq_nat
% 9.53/5.31      = ( ^ [X4: nat > nat] :
% 9.53/5.31            ( ! [M6: nat,N2: nat] :
% 9.53/5.31                ( ( ord_less_eq_nat @ M6 @ N2 )
% 9.53/5.31               => ( ord_less_eq_nat @ ( X4 @ M6 ) @ ( X4 @ N2 ) ) )
% 9.53/5.31            | ! [M6: nat,N2: nat] :
% 9.53/5.31                ( ( ord_less_eq_nat @ M6 @ N2 )
% 9.53/5.31               => ( ord_less_eq_nat @ ( X4 @ N2 ) @ ( X4 @ M6 ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8375_monoseq__def,axiom,
% 9.53/5.31      ( topolo4899668324122417113eq_int
% 9.53/5.31      = ( ^ [X4: nat > int] :
% 9.53/5.31            ( ! [M6: nat,N2: nat] :
% 9.53/5.31                ( ( ord_less_eq_nat @ M6 @ N2 )
% 9.53/5.31               => ( ord_less_eq_int @ ( X4 @ M6 ) @ ( X4 @ N2 ) ) )
% 9.53/5.31            | ! [M6: nat,N2: nat] :
% 9.53/5.31                ( ( ord_less_eq_nat @ M6 @ N2 )
% 9.53/5.31               => ( ord_less_eq_int @ ( X4 @ N2 ) @ ( X4 @ M6 ) ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8376_monoI2,axiom,
% 9.53/5.31      ! [X8: nat > real] :
% 9.53/5.31        ( ! [M4: nat,N3: nat] :
% 9.53/5.31            ( ( ord_less_eq_nat @ M4 @ N3 )
% 9.53/5.31           => ( ord_less_eq_real @ ( X8 @ N3 ) @ ( X8 @ M4 ) ) )
% 9.53/5.31       => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8377_monoI2,axiom,
% 9.53/5.31      ! [X8: nat > set_real] :
% 9.53/5.31        ( ! [M4: nat,N3: nat] :
% 9.53/5.31            ( ( ord_less_eq_nat @ M4 @ N3 )
% 9.53/5.31           => ( ord_less_eq_set_real @ ( X8 @ N3 ) @ ( X8 @ M4 ) ) )
% 9.53/5.31       => ( topolo2489691266198938127t_real @ X8 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8378_monoI2,axiom,
% 9.53/5.31      ! [X8: nat > set_nat] :
% 9.53/5.31        ( ! [M4: nat,N3: nat] :
% 9.53/5.31            ( ( ord_less_eq_nat @ M4 @ N3 )
% 9.53/5.31           => ( ord_less_eq_set_nat @ ( X8 @ N3 ) @ ( X8 @ M4 ) ) )
% 9.53/5.31       => ( topolo7278393974255667507et_nat @ X8 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8379_monoI2,axiom,
% 9.53/5.31      ! [X8: nat > num] :
% 9.53/5.31        ( ! [M4: nat,N3: nat] :
% 9.53/5.31            ( ( ord_less_eq_nat @ M4 @ N3 )
% 9.53/5.31           => ( ord_less_eq_num @ ( X8 @ N3 ) @ ( X8 @ M4 ) ) )
% 9.53/5.31       => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8380_monoI2,axiom,
% 9.53/5.31      ! [X8: nat > nat] :
% 9.53/5.31        ( ! [M4: nat,N3: nat] :
% 9.53/5.31            ( ( ord_less_eq_nat @ M4 @ N3 )
% 9.53/5.31           => ( ord_less_eq_nat @ ( X8 @ N3 ) @ ( X8 @ M4 ) ) )
% 9.53/5.31       => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8381_monoI2,axiom,
% 9.53/5.31      ! [X8: nat > int] :
% 9.53/5.31        ( ! [M4: nat,N3: nat] :
% 9.53/5.31            ( ( ord_less_eq_nat @ M4 @ N3 )
% 9.53/5.31           => ( ord_less_eq_int @ ( X8 @ N3 ) @ ( X8 @ M4 ) ) )
% 9.53/5.31       => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8382_monoI1,axiom,
% 9.53/5.31      ! [X8: nat > real] :
% 9.53/5.31        ( ! [M4: nat,N3: nat] :
% 9.53/5.31            ( ( ord_less_eq_nat @ M4 @ N3 )
% 9.53/5.31           => ( ord_less_eq_real @ ( X8 @ M4 ) @ ( X8 @ N3 ) ) )
% 9.53/5.31       => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8383_monoI1,axiom,
% 9.53/5.31      ! [X8: nat > set_real] :
% 9.53/5.31        ( ! [M4: nat,N3: nat] :
% 9.53/5.31            ( ( ord_less_eq_nat @ M4 @ N3 )
% 9.53/5.31           => ( ord_less_eq_set_real @ ( X8 @ M4 ) @ ( X8 @ N3 ) ) )
% 9.53/5.31       => ( topolo2489691266198938127t_real @ X8 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8384_monoI1,axiom,
% 9.53/5.31      ! [X8: nat > set_nat] :
% 9.53/5.31        ( ! [M4: nat,N3: nat] :
% 9.53/5.31            ( ( ord_less_eq_nat @ M4 @ N3 )
% 9.53/5.31           => ( ord_less_eq_set_nat @ ( X8 @ M4 ) @ ( X8 @ N3 ) ) )
% 9.53/5.31       => ( topolo7278393974255667507et_nat @ X8 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8385_monoI1,axiom,
% 9.53/5.31      ! [X8: nat > num] :
% 9.53/5.31        ( ! [M4: nat,N3: nat] :
% 9.53/5.31            ( ( ord_less_eq_nat @ M4 @ N3 )
% 9.53/5.31           => ( ord_less_eq_num @ ( X8 @ M4 ) @ ( X8 @ N3 ) ) )
% 9.53/5.31       => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8386_monoI1,axiom,
% 9.53/5.31      ! [X8: nat > nat] :
% 9.53/5.31        ( ! [M4: nat,N3: nat] :
% 9.53/5.31            ( ( ord_less_eq_nat @ M4 @ N3 )
% 9.53/5.31           => ( ord_less_eq_nat @ ( X8 @ M4 ) @ ( X8 @ N3 ) ) )
% 9.53/5.31       => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8387_monoI1,axiom,
% 9.53/5.31      ! [X8: nat > int] :
% 9.53/5.31        ( ! [M4: nat,N3: nat] :
% 9.53/5.31            ( ( ord_less_eq_nat @ M4 @ N3 )
% 9.53/5.31           => ( ord_less_eq_int @ ( X8 @ M4 ) @ ( X8 @ N3 ) ) )
% 9.53/5.31       => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8388_diffs__def,axiom,
% 9.53/5.31      ( diffs_real
% 9.53/5.31      = ( ^ [C3: nat > real,N2: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) @ ( C3 @ ( suc @ N2 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8389_diffs__def,axiom,
% 9.53/5.31      ( diffs_int
% 9.53/5.31      = ( ^ [C3: nat > int,N2: nat] : ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) @ ( C3 @ ( suc @ N2 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8390_diffs__def,axiom,
% 9.53/5.31      ( diffs_complex
% 9.53/5.31      = ( ^ [C3: nat > complex,N2: nat] : ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N2 ) ) @ ( C3 @ ( suc @ N2 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8391_termdiff__converges__all,axiom,
% 9.53/5.31      ! [C: nat > complex,X: complex] :
% 9.53/5.31        ( ! [X3: complex] :
% 9.53/5.31            ( summable_complex
% 9.53/5.31            @ ^ [N2: nat] : ( times_times_complex @ ( C @ N2 ) @ ( power_power_complex @ X3 @ N2 ) ) )
% 9.53/5.31       => ( summable_complex
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_complex @ ( diffs_complex @ C @ N2 ) @ ( power_power_complex @ X @ N2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8392_termdiff__converges__all,axiom,
% 9.53/5.31      ! [C: nat > real,X: real] :
% 9.53/5.31        ( ! [X3: real] :
% 9.53/5.31            ( summable_real
% 9.53/5.31            @ ^ [N2: nat] : ( times_times_real @ ( C @ N2 ) @ ( power_power_real @ X3 @ N2 ) ) )
% 9.53/5.31       => ( summable_real
% 9.53/5.31          @ ^ [N2: nat] : ( times_times_real @ ( diffs_real @ C @ N2 ) @ ( power_power_real @ X @ N2 ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8393_termdiff__converges,axiom,
% 9.53/5.31      ! [X: real,K5: real,C: nat > real] :
% 9.53/5.31        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ K5 )
% 9.53/5.31       => ( ! [X3: real] :
% 9.53/5.31              ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X3 ) @ K5 )
% 9.53/5.31             => ( summable_real
% 9.53/5.31                @ ^ [N2: nat] : ( times_times_real @ ( C @ N2 ) @ ( power_power_real @ X3 @ N2 ) ) ) )
% 9.53/5.31         => ( summable_real
% 9.53/5.31            @ ^ [N2: nat] : ( times_times_real @ ( diffs_real @ C @ N2 ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8394_termdiff__converges,axiom,
% 9.53/5.31      ! [X: complex,K5: real,C: nat > complex] :
% 9.53/5.31        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ K5 )
% 9.53/5.31       => ( ! [X3: complex] :
% 9.53/5.31              ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X3 ) @ K5 )
% 9.53/5.31             => ( summable_complex
% 9.53/5.31                @ ^ [N2: nat] : ( times_times_complex @ ( C @ N2 ) @ ( power_power_complex @ X3 @ N2 ) ) ) )
% 9.53/5.31         => ( summable_complex
% 9.53/5.31            @ ^ [N2: nat] : ( times_times_complex @ ( diffs_complex @ C @ N2 ) @ ( power_power_complex @ X @ N2 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8395_mono__SucI1,axiom,
% 9.53/5.31      ! [X8: nat > real] :
% 9.53/5.31        ( ! [N3: nat] : ( ord_less_eq_real @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 9.53/5.31       => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8396_mono__SucI1,axiom,
% 9.53/5.31      ! [X8: nat > set_real] :
% 9.53/5.31        ( ! [N3: nat] : ( ord_less_eq_set_real @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 9.53/5.31       => ( topolo2489691266198938127t_real @ X8 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8397_mono__SucI1,axiom,
% 9.53/5.31      ! [X8: nat > set_nat] :
% 9.53/5.31        ( ! [N3: nat] : ( ord_less_eq_set_nat @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 9.53/5.31       => ( topolo7278393974255667507et_nat @ X8 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8398_mono__SucI1,axiom,
% 9.53/5.31      ! [X8: nat > num] :
% 9.53/5.31        ( ! [N3: nat] : ( ord_less_eq_num @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 9.53/5.31       => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8399_mono__SucI1,axiom,
% 9.53/5.31      ! [X8: nat > nat] :
% 9.53/5.31        ( ! [N3: nat] : ( ord_less_eq_nat @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 9.53/5.31       => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8400_mono__SucI1,axiom,
% 9.53/5.31      ! [X8: nat > int] :
% 9.53/5.31        ( ! [N3: nat] : ( ord_less_eq_int @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 9.53/5.31       => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8401_mono__SucI2,axiom,
% 9.53/5.31      ! [X8: nat > real] :
% 9.53/5.31        ( ! [N3: nat] : ( ord_less_eq_real @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 9.53/5.31       => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8402_mono__SucI2,axiom,
% 9.53/5.31      ! [X8: nat > set_real] :
% 9.53/5.31        ( ! [N3: nat] : ( ord_less_eq_set_real @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 9.53/5.31       => ( topolo2489691266198938127t_real @ X8 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8403_mono__SucI2,axiom,
% 9.53/5.31      ! [X8: nat > set_nat] :
% 9.53/5.31        ( ! [N3: nat] : ( ord_less_eq_set_nat @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 9.53/5.31       => ( topolo7278393974255667507et_nat @ X8 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8404_mono__SucI2,axiom,
% 9.53/5.31      ! [X8: nat > num] :
% 9.53/5.31        ( ! [N3: nat] : ( ord_less_eq_num @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 9.53/5.31       => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8405_mono__SucI2,axiom,
% 9.53/5.31      ! [X8: nat > nat] :
% 9.53/5.31        ( ! [N3: nat] : ( ord_less_eq_nat @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 9.53/5.31       => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8406_mono__SucI2,axiom,
% 9.53/5.31      ! [X8: nat > int] :
% 9.53/5.31        ( ! [N3: nat] : ( ord_less_eq_int @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 9.53/5.31       => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8407_monoseq__Suc,axiom,
% 9.53/5.31      ( topolo6980174941875973593q_real
% 9.53/5.31      = ( ^ [X4: nat > real] :
% 9.53/5.31            ( ! [N2: nat] : ( ord_less_eq_real @ ( X4 @ N2 ) @ ( X4 @ ( suc @ N2 ) ) )
% 9.53/5.31            | ! [N2: nat] : ( ord_less_eq_real @ ( X4 @ ( suc @ N2 ) ) @ ( X4 @ N2 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8408_monoseq__Suc,axiom,
% 9.53/5.31      ( topolo2489691266198938127t_real
% 9.53/5.31      = ( ^ [X4: nat > set_real] :
% 9.53/5.31            ( ! [N2: nat] : ( ord_less_eq_set_real @ ( X4 @ N2 ) @ ( X4 @ ( suc @ N2 ) ) )
% 9.53/5.31            | ! [N2: nat] : ( ord_less_eq_set_real @ ( X4 @ ( suc @ N2 ) ) @ ( X4 @ N2 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8409_monoseq__Suc,axiom,
% 9.53/5.31      ( topolo7278393974255667507et_nat
% 9.53/5.31      = ( ^ [X4: nat > set_nat] :
% 9.53/5.31            ( ! [N2: nat] : ( ord_less_eq_set_nat @ ( X4 @ N2 ) @ ( X4 @ ( suc @ N2 ) ) )
% 9.53/5.31            | ! [N2: nat] : ( ord_less_eq_set_nat @ ( X4 @ ( suc @ N2 ) ) @ ( X4 @ N2 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8410_monoseq__Suc,axiom,
% 9.53/5.31      ( topolo1459490580787246023eq_num
% 9.53/5.31      = ( ^ [X4: nat > num] :
% 9.53/5.31            ( ! [N2: nat] : ( ord_less_eq_num @ ( X4 @ N2 ) @ ( X4 @ ( suc @ N2 ) ) )
% 9.53/5.31            | ! [N2: nat] : ( ord_less_eq_num @ ( X4 @ ( suc @ N2 ) ) @ ( X4 @ N2 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8411_monoseq__Suc,axiom,
% 9.53/5.31      ( topolo4902158794631467389eq_nat
% 9.53/5.31      = ( ^ [X4: nat > nat] :
% 9.53/5.31            ( ! [N2: nat] : ( ord_less_eq_nat @ ( X4 @ N2 ) @ ( X4 @ ( suc @ N2 ) ) )
% 9.53/5.31            | ! [N2: nat] : ( ord_less_eq_nat @ ( X4 @ ( suc @ N2 ) ) @ ( X4 @ N2 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8412_monoseq__Suc,axiom,
% 9.53/5.31      ( topolo4899668324122417113eq_int
% 9.53/5.31      = ( ^ [X4: nat > int] :
% 9.53/5.31            ( ! [N2: nat] : ( ord_less_eq_int @ ( X4 @ N2 ) @ ( X4 @ ( suc @ N2 ) ) )
% 9.53/5.31            | ! [N2: nat] : ( ord_less_eq_int @ ( X4 @ ( suc @ N2 ) ) @ ( X4 @ N2 ) ) ) ) ) ).
% 9.53/5.31  
% 9.53/5.31  thf(fact_8413_or__minus__numerals_I1_J,axiom,
% 9.53/5.31      ! [N: num] :
% 9.53/5.31        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 9.53/5.31        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8414_or__minus__numerals_I5_J,axiom,
% 9.53/5.32      ! [N: num] :
% 9.53/5.32        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 9.53/5.32        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8415_pochhammer__double,axiom,
% 9.53/5.32      ! [Z: rat,N: nat] :
% 9.53/5.32        ( ( comm_s4028243227959126397er_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.53/5.32        = ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8416_pochhammer__double,axiom,
% 9.53/5.32      ! [Z: real,N: nat] :
% 9.53/5.32        ( ( comm_s7457072308508201937r_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.53/5.32        = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s7457072308508201937r_real @ Z @ N ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8417_pochhammer__double,axiom,
% 9.53/5.32      ! [Z: complex,N: nat] :
% 9.53/5.32        ( ( comm_s2602460028002588243omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.53/5.32        = ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s2602460028002588243omplex @ Z @ N ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8418_floor__log__nat__eq__powr__iff,axiom,
% 9.53/5.32      ! [B: nat,K: nat,N: nat] :
% 9.53/5.32        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 9.53/5.32       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 9.53/5.32         => ( ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 9.53/5.32              = ( semiri1314217659103216013at_int @ N ) )
% 9.53/5.32            = ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 9.53/5.32              & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8419_of__int__floor__cancel,axiom,
% 9.53/5.32      ! [X: real] :
% 9.53/5.32        ( ( ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) )
% 9.53/5.32          = X )
% 9.53/5.32        = ( ? [N2: int] :
% 9.53/5.32              ( X
% 9.53/5.32              = ( ring_1_of_int_real @ N2 ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8420_of__int__floor__cancel,axiom,
% 9.53/5.32      ! [X: rat] :
% 9.53/5.32        ( ( ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) )
% 9.53/5.32          = X )
% 9.53/5.32        = ( ? [N2: int] :
% 9.53/5.32              ( X
% 9.53/5.32              = ( ring_1_of_int_rat @ N2 ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8421_floor__numeral,axiom,
% 9.53/5.32      ! [V: num] :
% 9.53/5.32        ( ( archim6058952711729229775r_real @ ( numeral_numeral_real @ V ) )
% 9.53/5.32        = ( numeral_numeral_int @ V ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8422_floor__numeral,axiom,
% 9.53/5.32      ! [V: num] :
% 9.53/5.32        ( ( archim3151403230148437115or_rat @ ( numeral_numeral_rat @ V ) )
% 9.53/5.32        = ( numeral_numeral_int @ V ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8423_floor__one,axiom,
% 9.53/5.32      ( ( archim6058952711729229775r_real @ one_one_real )
% 9.53/5.32      = one_one_int ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8424_floor__one,axiom,
% 9.53/5.32      ( ( archim3151403230148437115or_rat @ one_one_rat )
% 9.53/5.32      = one_one_int ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8425_pochhammer__0,axiom,
% 9.53/5.32      ! [A: complex] :
% 9.53/5.32        ( ( comm_s2602460028002588243omplex @ A @ zero_zero_nat )
% 9.53/5.32        = one_one_complex ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8426_pochhammer__0,axiom,
% 9.53/5.32      ! [A: real] :
% 9.53/5.32        ( ( comm_s7457072308508201937r_real @ A @ zero_zero_nat )
% 9.53/5.32        = one_one_real ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8427_pochhammer__0,axiom,
% 9.53/5.32      ! [A: rat] :
% 9.53/5.32        ( ( comm_s4028243227959126397er_rat @ A @ zero_zero_nat )
% 9.53/5.32        = one_one_rat ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8428_pochhammer__0,axiom,
% 9.53/5.32      ! [A: nat] :
% 9.53/5.32        ( ( comm_s4663373288045622133er_nat @ A @ zero_zero_nat )
% 9.53/5.32        = one_one_nat ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8429_pochhammer__0,axiom,
% 9.53/5.32      ! [A: int] :
% 9.53/5.32        ( ( comm_s4660882817536571857er_int @ A @ zero_zero_nat )
% 9.53/5.32        = one_one_int ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8430_floor__diff__of__int,axiom,
% 9.53/5.32      ! [X: real,Z: int] :
% 9.53/5.32        ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X @ ( ring_1_of_int_real @ Z ) ) )
% 9.53/5.32        = ( minus_minus_int @ ( archim6058952711729229775r_real @ X ) @ Z ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8431_floor__diff__of__int,axiom,
% 9.53/5.32      ! [X: rat,Z: int] :
% 9.53/5.32        ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X @ ( ring_1_of_int_rat @ Z ) ) )
% 9.53/5.32        = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X ) @ Z ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8432_zero__le__floor,axiom,
% 9.53/5.32      ! [X: real] :
% 9.53/5.32        ( ( ord_less_eq_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X ) )
% 9.53/5.32        = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8433_zero__le__floor,axiom,
% 9.53/5.32      ! [X: rat] :
% 9.53/5.32        ( ( ord_less_eq_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X ) )
% 9.53/5.32        = ( ord_less_eq_rat @ zero_zero_rat @ X ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8434_floor__less__zero,axiom,
% 9.53/5.32      ! [X: real] :
% 9.53/5.32        ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ zero_zero_int )
% 9.53/5.32        = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8435_floor__less__zero,axiom,
% 9.53/5.32      ! [X: rat] :
% 9.53/5.32        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ zero_zero_int )
% 9.53/5.32        = ( ord_less_rat @ X @ zero_zero_rat ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8436_numeral__le__floor,axiom,
% 9.53/5.32      ! [V: num,X: real] :
% 9.53/5.32        ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X ) )
% 9.53/5.32        = ( ord_less_eq_real @ ( numeral_numeral_real @ V ) @ X ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8437_numeral__le__floor,axiom,
% 9.53/5.32      ! [V: num,X: rat] :
% 9.53/5.32        ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X ) )
% 9.53/5.32        = ( ord_less_eq_rat @ ( numeral_numeral_rat @ V ) @ X ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8438_zero__less__floor,axiom,
% 9.53/5.32      ! [X: real] :
% 9.53/5.32        ( ( ord_less_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X ) )
% 9.53/5.32        = ( ord_less_eq_real @ one_one_real @ X ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8439_zero__less__floor,axiom,
% 9.53/5.32      ! [X: rat] :
% 9.53/5.32        ( ( ord_less_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X ) )
% 9.53/5.32        = ( ord_less_eq_rat @ one_one_rat @ X ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8440_floor__le__zero,axiom,
% 9.53/5.32      ! [X: real] :
% 9.53/5.32        ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ zero_zero_int )
% 9.53/5.32        = ( ord_less_real @ X @ one_one_real ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8441_floor__le__zero,axiom,
% 9.53/5.32      ! [X: rat] :
% 9.53/5.32        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ zero_zero_int )
% 9.53/5.32        = ( ord_less_rat @ X @ one_one_rat ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8442_floor__less__numeral,axiom,
% 9.53/5.32      ! [X: real,V: num] :
% 9.53/5.32        ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ ( numeral_numeral_int @ V ) )
% 9.53/5.32        = ( ord_less_real @ X @ ( numeral_numeral_real @ V ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8443_floor__less__numeral,axiom,
% 9.53/5.32      ! [X: rat,V: num] :
% 9.53/5.32        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 9.53/5.32        = ( ord_less_rat @ X @ ( numeral_numeral_rat @ V ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8444_one__le__floor,axiom,
% 9.53/5.32      ! [X: real] :
% 9.53/5.32        ( ( ord_less_eq_int @ one_one_int @ ( archim6058952711729229775r_real @ X ) )
% 9.53/5.32        = ( ord_less_eq_real @ one_one_real @ X ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8445_one__le__floor,axiom,
% 9.53/5.32      ! [X: rat] :
% 9.53/5.32        ( ( ord_less_eq_int @ one_one_int @ ( archim3151403230148437115or_rat @ X ) )
% 9.53/5.32        = ( ord_less_eq_rat @ one_one_rat @ X ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8446_floor__less__one,axiom,
% 9.53/5.32      ! [X: real] :
% 9.53/5.32        ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int )
% 9.53/5.32        = ( ord_less_real @ X @ one_one_real ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8447_floor__less__one,axiom,
% 9.53/5.32      ! [X: rat] :
% 9.53/5.32        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int )
% 9.53/5.32        = ( ord_less_rat @ X @ one_one_rat ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8448_floor__neg__numeral,axiom,
% 9.53/5.32      ! [V: num] :
% 9.53/5.32        ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 9.53/5.32        = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8449_floor__neg__numeral,axiom,
% 9.53/5.32      ! [V: num] :
% 9.53/5.32        ( ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 9.53/5.32        = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8450_floor__diff__numeral,axiom,
% 9.53/5.32      ! [X: real,V: num] :
% 9.53/5.32        ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X @ ( numeral_numeral_real @ V ) ) )
% 9.53/5.32        = ( minus_minus_int @ ( archim6058952711729229775r_real @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8451_floor__diff__numeral,axiom,
% 9.53/5.32      ! [X: rat,V: num] :
% 9.53/5.32        ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X @ ( numeral_numeral_rat @ V ) ) )
% 9.53/5.32        = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8452_floor__diff__one,axiom,
% 9.53/5.32      ! [X: real] :
% 9.53/5.32        ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X @ one_one_real ) )
% 9.53/5.32        = ( minus_minus_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8453_floor__diff__one,axiom,
% 9.53/5.32      ! [X: rat] :
% 9.53/5.32        ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X @ one_one_rat ) )
% 9.53/5.32        = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8454_floor__numeral__power,axiom,
% 9.53/5.32      ! [X: num,N: nat] :
% 9.53/5.32        ( ( archim6058952711729229775r_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 9.53/5.32        = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8455_floor__numeral__power,axiom,
% 9.53/5.32      ! [X: num,N: nat] :
% 9.53/5.32        ( ( archim3151403230148437115or_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 9.53/5.32        = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8456_floor__divide__eq__div__numeral,axiom,
% 9.53/5.32      ! [A: num,B: num] :
% 9.53/5.32        ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 9.53/5.32        = ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8457_or__minus__numerals_I4_J,axiom,
% 9.53/5.32      ! [M: num,N: num] :
% 9.53/5.32        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 9.53/5.32        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8458_or__minus__numerals_I8_J,axiom,
% 9.53/5.32      ! [N: num,M: num] :
% 9.53/5.32        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 9.53/5.32        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8459_or__minus__numerals_I7_J,axiom,
% 9.53/5.32      ! [N: num,M: num] :
% 9.53/5.32        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 9.53/5.32        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8460_or__minus__numerals_I3_J,axiom,
% 9.53/5.32      ! [M: num,N: num] :
% 9.53/5.32        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 9.53/5.32        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8461_numeral__less__floor,axiom,
% 9.53/5.32      ! [V: num,X: real] :
% 9.53/5.32        ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X ) )
% 9.53/5.32        = ( ord_less_eq_real @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8462_numeral__less__floor,axiom,
% 9.53/5.32      ! [V: num,X: rat] :
% 9.53/5.32        ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X ) )
% 9.53/5.32        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8463_floor__le__numeral,axiom,
% 9.53/5.32      ! [X: real,V: num] :
% 9.53/5.32        ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ ( numeral_numeral_int @ V ) )
% 9.53/5.32        = ( ord_less_real @ X @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8464_floor__le__numeral,axiom,
% 9.53/5.32      ! [X: rat,V: num] :
% 9.53/5.32        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 9.53/5.32        = ( ord_less_rat @ X @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8465_one__less__floor,axiom,
% 9.53/5.32      ! [X: real] :
% 9.53/5.32        ( ( ord_less_int @ one_one_int @ ( archim6058952711729229775r_real @ X ) )
% 9.53/5.32        = ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8466_one__less__floor,axiom,
% 9.53/5.32      ! [X: rat] :
% 9.53/5.32        ( ( ord_less_int @ one_one_int @ ( archim3151403230148437115or_rat @ X ) )
% 9.53/5.32        = ( ord_less_eq_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8467_floor__le__one,axiom,
% 9.53/5.32      ! [X: real] :
% 9.53/5.32        ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int )
% 9.53/5.32        = ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8468_floor__le__one,axiom,
% 9.53/5.32      ! [X: rat] :
% 9.53/5.32        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int )
% 9.53/5.32        = ( ord_less_rat @ X @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8469_neg__numeral__le__floor,axiom,
% 9.53/5.32      ! [V: num,X: real] :
% 9.53/5.32        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X ) )
% 9.53/5.32        = ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8470_neg__numeral__le__floor,axiom,
% 9.53/5.32      ! [V: num,X: rat] :
% 9.53/5.32        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X ) )
% 9.53/5.32        = ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8471_floor__less__neg__numeral,axiom,
% 9.53/5.32      ! [X: real,V: num] :
% 9.53/5.32        ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 9.53/5.32        = ( ord_less_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8472_floor__less__neg__numeral,axiom,
% 9.53/5.32      ! [X: rat,V: num] :
% 9.53/5.32        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 9.53/5.32        = ( ord_less_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8473_floor__one__divide__eq__div__numeral,axiom,
% 9.53/5.32      ! [B: num] :
% 9.53/5.32        ( ( archim6058952711729229775r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) )
% 9.53/5.32        = ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ B ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8474_floor__minus__divide__eq__div__numeral,axiom,
% 9.53/5.32      ! [A: num,B: num] :
% 9.53/5.32        ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 9.53/5.32        = ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8475_neg__numeral__less__floor,axiom,
% 9.53/5.32      ! [V: num,X: real] :
% 9.53/5.32        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X ) )
% 9.53/5.32        = ( ord_less_eq_real @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8476_neg__numeral__less__floor,axiom,
% 9.53/5.32      ! [V: num,X: rat] :
% 9.53/5.32        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X ) )
% 9.53/5.32        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8477_floor__le__neg__numeral,axiom,
% 9.53/5.32      ! [X: real,V: num] :
% 9.53/5.32        ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 9.53/5.32        = ( ord_less_real @ X @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8478_floor__le__neg__numeral,axiom,
% 9.53/5.32      ! [X: rat,V: num] :
% 9.53/5.32        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 9.53/5.32        = ( ord_less_rat @ X @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8479_floor__minus__one__divide__eq__div__numeral,axiom,
% 9.53/5.32      ! [B: num] :
% 9.53/5.32        ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) ) )
% 9.53/5.32        = ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ B ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8480_or__not__num__neg_Osimps_I1_J,axiom,
% 9.53/5.32      ( ( bit_or_not_num_neg @ one @ one )
% 9.53/5.32      = one ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8481_floor__mono,axiom,
% 9.53/5.32      ! [X: real,Y2: real] :
% 9.53/5.32        ( ( ord_less_eq_real @ X @ Y2 )
% 9.53/5.32       => ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8482_floor__mono,axiom,
% 9.53/5.32      ! [X: rat,Y2: rat] :
% 9.53/5.32        ( ( ord_less_eq_rat @ X @ Y2 )
% 9.53/5.32       => ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8483_of__int__floor__le,axiom,
% 9.53/5.32      ! [X: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) ) @ X ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8484_of__int__floor__le,axiom,
% 9.53/5.32      ! [X: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) ) @ X ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8485_floor__less__cancel,axiom,
% 9.53/5.32      ! [X: real,Y2: real] :
% 9.53/5.32        ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y2 ) )
% 9.53/5.32       => ( ord_less_real @ X @ Y2 ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8486_floor__less__cancel,axiom,
% 9.53/5.32      ! [X: rat,Y2: rat] :
% 9.53/5.32        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y2 ) )
% 9.53/5.32       => ( ord_less_rat @ X @ Y2 ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8487_pochhammer__pos,axiom,
% 9.53/5.32      ! [X: real,N: nat] :
% 9.53/5.32        ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.32       => ( ord_less_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8488_pochhammer__pos,axiom,
% 9.53/5.32      ! [X: rat,N: nat] :
% 9.53/5.32        ( ( ord_less_rat @ zero_zero_rat @ X )
% 9.53/5.32       => ( ord_less_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8489_pochhammer__pos,axiom,
% 9.53/5.32      ! [X: nat,N: nat] :
% 9.53/5.32        ( ( ord_less_nat @ zero_zero_nat @ X )
% 9.53/5.32       => ( ord_less_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8490_pochhammer__pos,axiom,
% 9.53/5.32      ! [X: int,N: nat] :
% 9.53/5.32        ( ( ord_less_int @ zero_zero_int @ X )
% 9.53/5.32       => ( ord_less_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8491_pochhammer__eq__0__mono,axiom,
% 9.53/5.32      ! [A: complex,N: nat,M: nat] :
% 9.53/5.32        ( ( ( comm_s2602460028002588243omplex @ A @ N )
% 9.53/5.32          = zero_zero_complex )
% 9.53/5.32       => ( ( ord_less_eq_nat @ N @ M )
% 9.53/5.32         => ( ( comm_s2602460028002588243omplex @ A @ M )
% 9.53/5.32            = zero_zero_complex ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8492_pochhammer__eq__0__mono,axiom,
% 9.53/5.32      ! [A: real,N: nat,M: nat] :
% 9.53/5.32        ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 9.53/5.32          = zero_zero_real )
% 9.53/5.32       => ( ( ord_less_eq_nat @ N @ M )
% 9.53/5.32         => ( ( comm_s7457072308508201937r_real @ A @ M )
% 9.53/5.32            = zero_zero_real ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8493_pochhammer__eq__0__mono,axiom,
% 9.53/5.32      ! [A: rat,N: nat,M: nat] :
% 9.53/5.32        ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 9.53/5.32          = zero_zero_rat )
% 9.53/5.32       => ( ( ord_less_eq_nat @ N @ M )
% 9.53/5.32         => ( ( comm_s4028243227959126397er_rat @ A @ M )
% 9.53/5.32            = zero_zero_rat ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8494_pochhammer__neq__0__mono,axiom,
% 9.53/5.32      ! [A: complex,M: nat,N: nat] :
% 9.53/5.32        ( ( ( comm_s2602460028002588243omplex @ A @ M )
% 9.53/5.32         != zero_zero_complex )
% 9.53/5.32       => ( ( ord_less_eq_nat @ N @ M )
% 9.53/5.32         => ( ( comm_s2602460028002588243omplex @ A @ N )
% 9.53/5.32           != zero_zero_complex ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8495_pochhammer__neq__0__mono,axiom,
% 9.53/5.32      ! [A: real,M: nat,N: nat] :
% 9.53/5.32        ( ( ( comm_s7457072308508201937r_real @ A @ M )
% 9.53/5.32         != zero_zero_real )
% 9.53/5.32       => ( ( ord_less_eq_nat @ N @ M )
% 9.53/5.32         => ( ( comm_s7457072308508201937r_real @ A @ N )
% 9.53/5.32           != zero_zero_real ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8496_pochhammer__neq__0__mono,axiom,
% 9.53/5.32      ! [A: rat,M: nat,N: nat] :
% 9.53/5.32        ( ( ( comm_s4028243227959126397er_rat @ A @ M )
% 9.53/5.32         != zero_zero_rat )
% 9.53/5.32       => ( ( ord_less_eq_nat @ N @ M )
% 9.53/5.32         => ( ( comm_s4028243227959126397er_rat @ A @ N )
% 9.53/5.32           != zero_zero_rat ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8497_pochhammer__fact,axiom,
% 9.53/5.32      ( semiri5044797733671781792omplex
% 9.53/5.32      = ( comm_s2602460028002588243omplex @ one_one_complex ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8498_pochhammer__fact,axiom,
% 9.53/5.32      ( semiri773545260158071498ct_rat
% 9.53/5.32      = ( comm_s4028243227959126397er_rat @ one_one_rat ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8499_pochhammer__fact,axiom,
% 9.53/5.32      ( semiri1406184849735516958ct_int
% 9.53/5.32      = ( comm_s4660882817536571857er_int @ one_one_int ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8500_pochhammer__fact,axiom,
% 9.53/5.32      ( semiri2265585572941072030t_real
% 9.53/5.32      = ( comm_s7457072308508201937r_real @ one_one_real ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8501_pochhammer__fact,axiom,
% 9.53/5.32      ( semiri1408675320244567234ct_nat
% 9.53/5.32      = ( comm_s4663373288045622133er_nat @ one_one_nat ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8502_or__not__num__neg_Osimps_I4_J,axiom,
% 9.53/5.32      ! [N: num] :
% 9.53/5.32        ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ one )
% 9.53/5.32        = ( bit0 @ one ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8503_or__not__num__neg_Osimps_I6_J,axiom,
% 9.53/5.32      ! [N: num,M: num] :
% 9.53/5.32        ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit1 @ M ) )
% 9.53/5.32        = ( bit0 @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8504_or__not__num__neg_Osimps_I7_J,axiom,
% 9.53/5.32      ! [N: num] :
% 9.53/5.32        ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ one )
% 9.53/5.32        = one ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8505_or__not__num__neg_Osimps_I3_J,axiom,
% 9.53/5.32      ! [M: num] :
% 9.53/5.32        ( ( bit_or_not_num_neg @ one @ ( bit1 @ M ) )
% 9.53/5.32        = ( bit1 @ M ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8506_or__not__num__neg_Osimps_I5_J,axiom,
% 9.53/5.32      ! [N: num,M: num] :
% 9.53/5.32        ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit0 @ M ) )
% 9.53/5.32        = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8507_or__not__num__neg_Osimps_I9_J,axiom,
% 9.53/5.32      ! [N: num,M: num] :
% 9.53/5.32        ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ ( bit1 @ M ) )
% 9.53/5.32        = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8508_le__floor__iff,axiom,
% 9.53/5.32      ! [Z: int,X: real] :
% 9.53/5.32        ( ( ord_less_eq_int @ Z @ ( archim6058952711729229775r_real @ X ) )
% 9.53/5.32        = ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ X ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8509_le__floor__iff,axiom,
% 9.53/5.32      ! [Z: int,X: rat] :
% 9.53/5.32        ( ( ord_less_eq_int @ Z @ ( archim3151403230148437115or_rat @ X ) )
% 9.53/5.32        = ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8510_floor__less__iff,axiom,
% 9.53/5.32      ! [X: real,Z: int] :
% 9.53/5.32        ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ Z )
% 9.53/5.32        = ( ord_less_real @ X @ ( ring_1_of_int_real @ Z ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8511_floor__less__iff,axiom,
% 9.53/5.32      ! [X: rat,Z: int] :
% 9.53/5.32        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ Z )
% 9.53/5.32        = ( ord_less_rat @ X @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8512_le__floor__add,axiom,
% 9.53/5.32      ! [X: real,Y2: real] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y2 ) ) @ ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ Y2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8513_le__floor__add,axiom,
% 9.53/5.32      ! [X: rat,Y2: rat] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y2 ) ) @ ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ Y2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8514_int__add__floor,axiom,
% 9.53/5.32      ! [Z: int,X: real] :
% 9.53/5.32        ( ( plus_plus_int @ Z @ ( archim6058952711729229775r_real @ X ) )
% 9.53/5.32        = ( archim6058952711729229775r_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ X ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8515_int__add__floor,axiom,
% 9.53/5.32      ! [Z: int,X: rat] :
% 9.53/5.32        ( ( plus_plus_int @ Z @ ( archim3151403230148437115or_rat @ X ) )
% 9.53/5.32        = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ X ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8516_floor__add__int,axiom,
% 9.53/5.32      ! [X: real,Z: int] :
% 9.53/5.32        ( ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ Z )
% 9.53/5.32        = ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ ( ring_1_of_int_real @ Z ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8517_floor__add__int,axiom,
% 9.53/5.32      ! [X: rat,Z: int] :
% 9.53/5.32        ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ Z )
% 9.53/5.32        = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ ( ring_1_of_int_rat @ Z ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8518_floor__divide__of__int__eq,axiom,
% 9.53/5.32      ! [K: int,L2: int] :
% 9.53/5.32        ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( ring_1_of_int_real @ K ) @ ( ring_1_of_int_real @ L2 ) ) )
% 9.53/5.32        = ( divide_divide_int @ K @ L2 ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8519_floor__divide__of__int__eq,axiom,
% 9.53/5.32      ! [K: int,L2: int] :
% 9.53/5.32        ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ K ) @ ( ring_1_of_int_rat @ L2 ) ) )
% 9.53/5.32        = ( divide_divide_int @ K @ L2 ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8520_floor__power,axiom,
% 9.53/5.32      ! [X: real,N: nat] :
% 9.53/5.32        ( ( X
% 9.53/5.32          = ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) ) )
% 9.53/5.32       => ( ( archim6058952711729229775r_real @ ( power_power_real @ X @ N ) )
% 9.53/5.32          = ( power_power_int @ ( archim6058952711729229775r_real @ X ) @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8521_floor__power,axiom,
% 9.53/5.32      ! [X: rat,N: nat] :
% 9.53/5.32        ( ( X
% 9.53/5.32          = ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) ) )
% 9.53/5.32       => ( ( archim3151403230148437115or_rat @ ( power_power_rat @ X @ N ) )
% 9.53/5.32          = ( power_power_int @ ( archim3151403230148437115or_rat @ X ) @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8522_pochhammer__nonneg,axiom,
% 9.53/5.32      ! [X: real,N: nat] :
% 9.53/5.32        ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.32       => ( ord_less_eq_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8523_pochhammer__nonneg,axiom,
% 9.53/5.32      ! [X: rat,N: nat] :
% 9.53/5.32        ( ( ord_less_rat @ zero_zero_rat @ X )
% 9.53/5.32       => ( ord_less_eq_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8524_pochhammer__nonneg,axiom,
% 9.53/5.32      ! [X: nat,N: nat] :
% 9.53/5.32        ( ( ord_less_nat @ zero_zero_nat @ X )
% 9.53/5.32       => ( ord_less_eq_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8525_pochhammer__nonneg,axiom,
% 9.53/5.32      ! [X: int,N: nat] :
% 9.53/5.32        ( ( ord_less_int @ zero_zero_int @ X )
% 9.53/5.32       => ( ord_less_eq_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8526_pochhammer__0__left,axiom,
% 9.53/5.32      ! [N: nat] :
% 9.53/5.32        ( ( ( N = zero_zero_nat )
% 9.53/5.32         => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 9.53/5.32            = one_one_complex ) )
% 9.53/5.32        & ( ( N != zero_zero_nat )
% 9.53/5.32         => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 9.53/5.32            = zero_zero_complex ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8527_pochhammer__0__left,axiom,
% 9.53/5.32      ! [N: nat] :
% 9.53/5.32        ( ( ( N = zero_zero_nat )
% 9.53/5.32         => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 9.53/5.32            = one_one_real ) )
% 9.53/5.32        & ( ( N != zero_zero_nat )
% 9.53/5.32         => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 9.53/5.32            = zero_zero_real ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8528_pochhammer__0__left,axiom,
% 9.53/5.32      ! [N: nat] :
% 9.53/5.32        ( ( ( N = zero_zero_nat )
% 9.53/5.32         => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 9.53/5.32            = one_one_rat ) )
% 9.53/5.32        & ( ( N != zero_zero_nat )
% 9.53/5.32         => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 9.53/5.32            = zero_zero_rat ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8529_pochhammer__0__left,axiom,
% 9.53/5.32      ! [N: nat] :
% 9.53/5.32        ( ( ( N = zero_zero_nat )
% 9.53/5.32         => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 9.53/5.32            = one_one_nat ) )
% 9.53/5.32        & ( ( N != zero_zero_nat )
% 9.53/5.32         => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 9.53/5.32            = zero_zero_nat ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8530_pochhammer__0__left,axiom,
% 9.53/5.32      ! [N: nat] :
% 9.53/5.32        ( ( ( N = zero_zero_nat )
% 9.53/5.32         => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 9.53/5.32            = one_one_int ) )
% 9.53/5.32        & ( ( N != zero_zero_nat )
% 9.53/5.32         => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 9.53/5.32            = zero_zero_int ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8531_or__not__num__neg_Osimps_I2_J,axiom,
% 9.53/5.32      ! [M: num] :
% 9.53/5.32        ( ( bit_or_not_num_neg @ one @ ( bit0 @ M ) )
% 9.53/5.32        = ( bit1 @ M ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8532_one__add__floor,axiom,
% 9.53/5.32      ! [X: real] :
% 9.53/5.32        ( ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int )
% 9.53/5.32        = ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ one_one_real ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8533_one__add__floor,axiom,
% 9.53/5.32      ! [X: rat] :
% 9.53/5.32        ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int )
% 9.53/5.32        = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ one_one_rat ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8534_floor__divide__of__nat__eq,axiom,
% 9.53/5.32      ! [M: nat,N: nat] :
% 9.53/5.32        ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 9.53/5.32        = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8535_floor__divide__of__nat__eq,axiom,
% 9.53/5.32      ! [M: nat,N: nat] :
% 9.53/5.32        ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) )
% 9.53/5.32        = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8536_ceiling__diff__floor__le__1,axiom,
% 9.53/5.32      ! [X: real] : ( ord_less_eq_int @ ( minus_minus_int @ ( archim7802044766580827645g_real @ X ) @ ( archim6058952711729229775r_real @ X ) ) @ one_one_int ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8537_ceiling__diff__floor__le__1,axiom,
% 9.53/5.32      ! [X: rat] : ( ord_less_eq_int @ ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X ) @ ( archim3151403230148437115or_rat @ X ) ) @ one_one_int ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8538_real__of__int__floor__add__one__gt,axiom,
% 9.53/5.32      ! [R: real] : ( ord_less_real @ R @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) @ one_one_real ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8539_floor__eq,axiom,
% 9.53/5.32      ! [N: int,X: real] :
% 9.53/5.32        ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X )
% 9.53/5.32       => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 9.53/5.32         => ( ( archim6058952711729229775r_real @ X )
% 9.53/5.32            = N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8540_real__of__int__floor__add__one__ge,axiom,
% 9.53/5.32      ! [R: real] : ( ord_less_eq_real @ R @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) @ one_one_real ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8541_or__not__num__neg_Osimps_I8_J,axiom,
% 9.53/5.32      ! [N: num,M: num] :
% 9.53/5.32        ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ ( bit0 @ M ) )
% 9.53/5.32        = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8542_real__of__int__floor__gt__diff__one,axiom,
% 9.53/5.32      ! [R: real] : ( ord_less_real @ ( minus_minus_real @ R @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8543_real__of__int__floor__ge__diff__one,axiom,
% 9.53/5.32      ! [R: real] : ( ord_less_eq_real @ ( minus_minus_real @ R @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8544_pochhammer__rec,axiom,
% 9.53/5.32      ! [A: rat,N: nat] :
% 9.53/5.32        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 9.53/5.32        = ( times_times_rat @ A @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8545_pochhammer__rec,axiom,
% 9.53/5.32      ! [A: complex,N: nat] :
% 9.53/5.32        ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 9.53/5.32        = ( times_times_complex @ A @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8546_pochhammer__rec,axiom,
% 9.53/5.32      ! [A: real,N: nat] :
% 9.53/5.32        ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 9.53/5.32        = ( times_times_real @ A @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ one_one_real ) @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8547_pochhammer__rec,axiom,
% 9.53/5.32      ! [A: nat,N: nat] :
% 9.53/5.32        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 9.53/5.32        = ( times_times_nat @ A @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8548_pochhammer__rec,axiom,
% 9.53/5.32      ! [A: int,N: nat] :
% 9.53/5.32        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 9.53/5.32        = ( times_times_int @ A @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ one_one_int ) @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8549_pochhammer__rec_H,axiom,
% 9.53/5.32      ! [Z: rat,N: nat] :
% 9.53/5.32        ( ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N ) )
% 9.53/5.32        = ( times_times_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8550_pochhammer__rec_H,axiom,
% 9.53/5.32      ! [Z: real,N: nat] :
% 9.53/5.32        ( ( comm_s7457072308508201937r_real @ Z @ ( suc @ N ) )
% 9.53/5.32        = ( times_times_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N ) ) @ ( comm_s7457072308508201937r_real @ Z @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8551_pochhammer__rec_H,axiom,
% 9.53/5.32      ! [Z: int,N: nat] :
% 9.53/5.32        ( ( comm_s4660882817536571857er_int @ Z @ ( suc @ N ) )
% 9.53/5.32        = ( times_times_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N ) ) @ ( comm_s4660882817536571857er_int @ Z @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8552_pochhammer__rec_H,axiom,
% 9.53/5.32      ! [Z: nat,N: nat] :
% 9.53/5.32        ( ( comm_s4663373288045622133er_nat @ Z @ ( suc @ N ) )
% 9.53/5.32        = ( times_times_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N ) ) @ ( comm_s4663373288045622133er_nat @ Z @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8553_pochhammer__rec_H,axiom,
% 9.53/5.32      ! [Z: complex,N: nat] :
% 9.53/5.32        ( ( comm_s2602460028002588243omplex @ Z @ ( suc @ N ) )
% 9.53/5.32        = ( times_times_complex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ N ) ) @ ( comm_s2602460028002588243omplex @ Z @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8554_pochhammer__Suc,axiom,
% 9.53/5.32      ! [A: rat,N: nat] :
% 9.53/5.32        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 9.53/5.32        = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ A @ N ) @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8555_pochhammer__Suc,axiom,
% 9.53/5.32      ! [A: real,N: nat] :
% 9.53/5.32        ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 9.53/5.32        = ( times_times_real @ ( comm_s7457072308508201937r_real @ A @ N ) @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8556_pochhammer__Suc,axiom,
% 9.53/5.32      ! [A: int,N: nat] :
% 9.53/5.32        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 9.53/5.32        = ( times_times_int @ ( comm_s4660882817536571857er_int @ A @ N ) @ ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8557_pochhammer__Suc,axiom,
% 9.53/5.32      ! [A: nat,N: nat] :
% 9.53/5.32        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 9.53/5.32        = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ A @ N ) @ ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8558_pochhammer__Suc,axiom,
% 9.53/5.32      ! [A: complex,N: nat] :
% 9.53/5.32        ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 9.53/5.32        = ( times_times_complex @ ( comm_s2602460028002588243omplex @ A @ N ) @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ N ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8559_pochhammer__eq__0__iff,axiom,
% 9.53/5.32      ! [A: rat,N: nat] :
% 9.53/5.32        ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 9.53/5.32          = zero_zero_rat )
% 9.53/5.32        = ( ? [K3: nat] :
% 9.53/5.32              ( ( ord_less_nat @ K3 @ N )
% 9.53/5.32              & ( A
% 9.53/5.32                = ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K3 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8560_pochhammer__eq__0__iff,axiom,
% 9.53/5.32      ! [A: real,N: nat] :
% 9.53/5.32        ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 9.53/5.32          = zero_zero_real )
% 9.53/5.32        = ( ? [K3: nat] :
% 9.53/5.32              ( ( ord_less_nat @ K3 @ N )
% 9.53/5.32              & ( A
% 9.53/5.32                = ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K3 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8561_pochhammer__eq__0__iff,axiom,
% 9.53/5.32      ! [A: complex,N: nat] :
% 9.53/5.32        ( ( ( comm_s2602460028002588243omplex @ A @ N )
% 9.53/5.32          = zero_zero_complex )
% 9.53/5.32        = ( ? [K3: nat] :
% 9.53/5.32              ( ( ord_less_nat @ K3 @ N )
% 9.53/5.32              & ( A
% 9.53/5.32                = ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K3 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8562_pochhammer__of__nat__eq__0__iff,axiom,
% 9.53/5.32      ! [N: nat,K: nat] :
% 9.53/5.32        ( ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 9.53/5.32          = zero_z3403309356797280102nteger )
% 9.53/5.32        = ( ord_less_nat @ N @ K ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8563_pochhammer__of__nat__eq__0__iff,axiom,
% 9.53/5.32      ! [N: nat,K: nat] :
% 9.53/5.32        ( ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 9.53/5.32          = zero_zero_rat )
% 9.53/5.32        = ( ord_less_nat @ N @ K ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8564_pochhammer__of__nat__eq__0__iff,axiom,
% 9.53/5.32      ! [N: nat,K: nat] :
% 9.53/5.32        ( ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 9.53/5.32          = zero_zero_real )
% 9.53/5.32        = ( ord_less_nat @ N @ K ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8565_pochhammer__of__nat__eq__0__iff,axiom,
% 9.53/5.32      ! [N: nat,K: nat] :
% 9.53/5.32        ( ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 9.53/5.32          = zero_zero_int )
% 9.53/5.32        = ( ord_less_nat @ N @ K ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8566_pochhammer__of__nat__eq__0__iff,axiom,
% 9.53/5.32      ! [N: nat,K: nat] :
% 9.53/5.32        ( ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 9.53/5.32          = zero_zero_complex )
% 9.53/5.32        = ( ord_less_nat @ N @ K ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8567_pochhammer__of__nat__eq__0__lemma,axiom,
% 9.53/5.32      ! [N: nat,K: nat] :
% 9.53/5.32        ( ( ord_less_nat @ N @ K )
% 9.53/5.32       => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 9.53/5.32          = zero_z3403309356797280102nteger ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8568_pochhammer__of__nat__eq__0__lemma,axiom,
% 9.53/5.32      ! [N: nat,K: nat] :
% 9.53/5.32        ( ( ord_less_nat @ N @ K )
% 9.53/5.32       => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 9.53/5.32          = zero_zero_rat ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8569_pochhammer__of__nat__eq__0__lemma,axiom,
% 9.53/5.32      ! [N: nat,K: nat] :
% 9.53/5.32        ( ( ord_less_nat @ N @ K )
% 9.53/5.32       => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 9.53/5.32          = zero_zero_real ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8570_pochhammer__of__nat__eq__0__lemma,axiom,
% 9.53/5.32      ! [N: nat,K: nat] :
% 9.53/5.32        ( ( ord_less_nat @ N @ K )
% 9.53/5.32       => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 9.53/5.32          = zero_zero_int ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8571_pochhammer__of__nat__eq__0__lemma,axiom,
% 9.53/5.32      ! [N: nat,K: nat] :
% 9.53/5.32        ( ( ord_less_nat @ N @ K )
% 9.53/5.32       => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 9.53/5.32          = zero_zero_complex ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8572_pochhammer__product_H,axiom,
% 9.53/5.32      ! [Z: rat,N: nat,M: nat] :
% 9.53/5.32        ( ( comm_s4028243227959126397er_rat @ Z @ ( plus_plus_nat @ N @ M ) )
% 9.53/5.32        = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ N ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N ) ) @ M ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8573_pochhammer__product_H,axiom,
% 9.53/5.32      ! [Z: real,N: nat,M: nat] :
% 9.53/5.32        ( ( comm_s7457072308508201937r_real @ Z @ ( plus_plus_nat @ N @ M ) )
% 9.53/5.32        = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ N ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N ) ) @ M ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8574_pochhammer__product_H,axiom,
% 9.53/5.32      ! [Z: int,N: nat,M: nat] :
% 9.53/5.32        ( ( comm_s4660882817536571857er_int @ Z @ ( plus_plus_nat @ N @ M ) )
% 9.53/5.32        = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ N ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N ) ) @ M ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8575_pochhammer__product_H,axiom,
% 9.53/5.32      ! [Z: nat,N: nat,M: nat] :
% 9.53/5.32        ( ( comm_s4663373288045622133er_nat @ Z @ ( plus_plus_nat @ N @ M ) )
% 9.53/5.32        = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ N ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N ) ) @ M ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8576_pochhammer__product_H,axiom,
% 9.53/5.32      ! [Z: complex,N: nat,M: nat] :
% 9.53/5.32        ( ( comm_s2602460028002588243omplex @ Z @ ( plus_plus_nat @ N @ M ) )
% 9.53/5.32        = ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ N ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ N ) ) @ M ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8577_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 9.53/5.32      ! [K: nat,N: nat] :
% 9.53/5.32        ( ( ord_less_eq_nat @ K @ N )
% 9.53/5.32       => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 9.53/5.32         != zero_z3403309356797280102nteger ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8578_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 9.53/5.32      ! [K: nat,N: nat] :
% 9.53/5.32        ( ( ord_less_eq_nat @ K @ N )
% 9.53/5.32       => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 9.53/5.32         != zero_zero_rat ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8579_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 9.53/5.32      ! [K: nat,N: nat] :
% 9.53/5.32        ( ( ord_less_eq_nat @ K @ N )
% 9.53/5.32       => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 9.53/5.32         != zero_zero_real ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8580_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 9.53/5.32      ! [K: nat,N: nat] :
% 9.53/5.32        ( ( ord_less_eq_nat @ K @ N )
% 9.53/5.32       => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 9.53/5.32         != zero_zero_int ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8581_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 9.53/5.32      ! [K: nat,N: nat] :
% 9.53/5.32        ( ( ord_less_eq_nat @ K @ N )
% 9.53/5.32       => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 9.53/5.32         != zero_zero_complex ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8582_floor__unique,axiom,
% 9.53/5.32      ! [Z: int,X: real] :
% 9.53/5.32        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ X )
% 9.53/5.32       => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) )
% 9.53/5.32         => ( ( archim6058952711729229775r_real @ X )
% 9.53/5.32            = Z ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8583_floor__unique,axiom,
% 9.53/5.32      ! [Z: int,X: rat] :
% 9.53/5.32        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X )
% 9.53/5.32       => ( ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) )
% 9.53/5.32         => ( ( archim3151403230148437115or_rat @ X )
% 9.53/5.32            = Z ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8584_floor__eq__iff,axiom,
% 9.53/5.32      ! [X: real,A: int] :
% 9.53/5.32        ( ( ( archim6058952711729229775r_real @ X )
% 9.53/5.32          = A )
% 9.53/5.32        = ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ X )
% 9.53/5.32          & ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8585_floor__eq__iff,axiom,
% 9.53/5.32      ! [X: rat,A: int] :
% 9.53/5.32        ( ( ( archim3151403230148437115or_rat @ X )
% 9.53/5.32          = A )
% 9.53/5.32        = ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ X )
% 9.53/5.32          & ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8586_floor__split,axiom,
% 9.53/5.32      ! [P: int > $o,T: real] :
% 9.53/5.32        ( ( P @ ( archim6058952711729229775r_real @ T ) )
% 9.53/5.32        = ( ! [I3: int] :
% 9.53/5.32              ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ I3 ) @ T )
% 9.53/5.32                & ( ord_less_real @ T @ ( plus_plus_real @ ( ring_1_of_int_real @ I3 ) @ one_one_real ) ) )
% 9.53/5.32             => ( P @ I3 ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8587_floor__split,axiom,
% 9.53/5.32      ! [P: int > $o,T: rat] :
% 9.53/5.32        ( ( P @ ( archim3151403230148437115or_rat @ T ) )
% 9.53/5.32        = ( ! [I3: int] :
% 9.53/5.32              ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ I3 ) @ T )
% 9.53/5.32                & ( ord_less_rat @ T @ ( plus_plus_rat @ ( ring_1_of_int_rat @ I3 ) @ one_one_rat ) ) )
% 9.53/5.32             => ( P @ I3 ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8588_le__mult__floor,axiom,
% 9.53/5.32      ! [A: real,B: real] :
% 9.53/5.32        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 9.53/5.32       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 9.53/5.32         => ( ord_less_eq_int @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B ) ) @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8589_le__mult__floor,axiom,
% 9.53/5.32      ! [A: rat,B: rat] :
% 9.53/5.32        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.53/5.32       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 9.53/5.32         => ( ord_less_eq_int @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8590_less__floor__iff,axiom,
% 9.53/5.32      ! [Z: int,X: real] :
% 9.53/5.32        ( ( ord_less_int @ Z @ ( archim6058952711729229775r_real @ X ) )
% 9.53/5.32        = ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8591_less__floor__iff,axiom,
% 9.53/5.32      ! [Z: int,X: rat] :
% 9.53/5.32        ( ( ord_less_int @ Z @ ( archim3151403230148437115or_rat @ X ) )
% 9.53/5.32        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8592_floor__le__iff,axiom,
% 9.53/5.32      ! [X: real,Z: int] :
% 9.53/5.32        ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ Z )
% 9.53/5.32        = ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8593_floor__le__iff,axiom,
% 9.53/5.32      ! [X: rat,Z: int] :
% 9.53/5.32        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ Z )
% 9.53/5.32        = ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8594_floor__correct,axiom,
% 9.53/5.32      ! [X: real] :
% 9.53/5.32        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) ) @ X )
% 9.53/5.32        & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8595_floor__correct,axiom,
% 9.53/5.32      ! [X: rat] :
% 9.53/5.32        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) ) @ X )
% 9.53/5.32        & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8596_floor__eq2,axiom,
% 9.53/5.32      ! [N: int,X: real] :
% 9.53/5.32        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ N ) @ X )
% 9.53/5.32       => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 9.53/5.32         => ( ( archim6058952711729229775r_real @ X )
% 9.53/5.32            = N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8597_floor__divide__real__eq__div,axiom,
% 9.53/5.32      ! [B: int,A: real] :
% 9.53/5.32        ( ( ord_less_eq_int @ zero_zero_int @ B )
% 9.53/5.32       => ( ( archim6058952711729229775r_real @ ( divide_divide_real @ A @ ( ring_1_of_int_real @ B ) ) )
% 9.53/5.32          = ( divide_divide_int @ ( archim6058952711729229775r_real @ A ) @ B ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8598_or__not__num__neg_Oelims,axiom,
% 9.53/5.32      ! [X: num,Xa2: num,Y2: num] :
% 9.53/5.32        ( ( ( bit_or_not_num_neg @ X @ Xa2 )
% 9.53/5.32          = Y2 )
% 9.53/5.32       => ( ( ( X = one )
% 9.53/5.32           => ( ( Xa2 = one )
% 9.53/5.32             => ( Y2 != one ) ) )
% 9.53/5.32         => ( ( ( X = one )
% 9.53/5.32             => ! [M4: num] :
% 9.53/5.32                  ( ( Xa2
% 9.53/5.32                    = ( bit0 @ M4 ) )
% 9.53/5.32                 => ( Y2
% 9.53/5.32                   != ( bit1 @ M4 ) ) ) )
% 9.53/5.32           => ( ( ( X = one )
% 9.53/5.32               => ! [M4: num] :
% 9.53/5.32                    ( ( Xa2
% 9.53/5.32                      = ( bit1 @ M4 ) )
% 9.53/5.32                   => ( Y2
% 9.53/5.32                     != ( bit1 @ M4 ) ) ) )
% 9.53/5.32             => ( ( ? [N3: num] :
% 9.53/5.32                      ( X
% 9.53/5.32                      = ( bit0 @ N3 ) )
% 9.53/5.32                 => ( ( Xa2 = one )
% 9.53/5.32                   => ( Y2
% 9.53/5.32                     != ( bit0 @ one ) ) ) )
% 9.53/5.32               => ( ! [N3: num] :
% 9.53/5.32                      ( ( X
% 9.53/5.32                        = ( bit0 @ N3 ) )
% 9.53/5.32                     => ! [M4: num] :
% 9.53/5.32                          ( ( Xa2
% 9.53/5.32                            = ( bit0 @ M4 ) )
% 9.53/5.32                         => ( Y2
% 9.53/5.32                           != ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) ) ) )
% 9.53/5.32                 => ( ! [N3: num] :
% 9.53/5.32                        ( ( X
% 9.53/5.32                          = ( bit0 @ N3 ) )
% 9.53/5.32                       => ! [M4: num] :
% 9.53/5.32                            ( ( Xa2
% 9.53/5.32                              = ( bit1 @ M4 ) )
% 9.53/5.32                           => ( Y2
% 9.53/5.32                             != ( bit0 @ ( bit_or_not_num_neg @ N3 @ M4 ) ) ) ) )
% 9.53/5.32                   => ( ( ? [N3: num] :
% 9.53/5.32                            ( X
% 9.53/5.32                            = ( bit1 @ N3 ) )
% 9.53/5.32                       => ( ( Xa2 = one )
% 9.53/5.32                         => ( Y2 != one ) ) )
% 9.53/5.32                     => ( ! [N3: num] :
% 9.53/5.32                            ( ( X
% 9.53/5.32                              = ( bit1 @ N3 ) )
% 9.53/5.32                           => ! [M4: num] :
% 9.53/5.32                                ( ( Xa2
% 9.53/5.32                                  = ( bit0 @ M4 ) )
% 9.53/5.32                               => ( Y2
% 9.53/5.32                                 != ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) ) ) )
% 9.53/5.32                       => ~ ! [N3: num] :
% 9.53/5.32                              ( ( X
% 9.53/5.32                                = ( bit1 @ N3 ) )
% 9.53/5.32                             => ! [M4: num] :
% 9.53/5.32                                  ( ( Xa2
% 9.53/5.32                                    = ( bit1 @ M4 ) )
% 9.53/5.32                                 => ( Y2
% 9.53/5.32                                   != ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8599_pochhammer__product,axiom,
% 9.53/5.32      ! [M: nat,N: nat,Z: rat] :
% 9.53/5.32        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.32       => ( ( comm_s4028243227959126397er_rat @ Z @ N )
% 9.53/5.32          = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ M ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8600_pochhammer__product,axiom,
% 9.53/5.32      ! [M: nat,N: nat,Z: real] :
% 9.53/5.32        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.32       => ( ( comm_s7457072308508201937r_real @ Z @ N )
% 9.53/5.32          = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ M ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8601_pochhammer__product,axiom,
% 9.53/5.32      ! [M: nat,N: nat,Z: int] :
% 9.53/5.32        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.32       => ( ( comm_s4660882817536571857er_int @ Z @ N )
% 9.53/5.32          = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ M ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8602_pochhammer__product,axiom,
% 9.53/5.32      ! [M: nat,N: nat,Z: nat] :
% 9.53/5.32        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.32       => ( ( comm_s4663373288045622133er_nat @ Z @ N )
% 9.53/5.32          = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ M ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8603_pochhammer__product,axiom,
% 9.53/5.32      ! [M: nat,N: nat,Z: complex] :
% 9.53/5.32        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.32       => ( ( comm_s2602460028002588243omplex @ Z @ N )
% 9.53/5.32          = ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ M ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8604_floor__divide__lower,axiom,
% 9.53/5.32      ! [Q2: real,P6: real] :
% 9.53/5.32        ( ( ord_less_real @ zero_zero_real @ Q2 )
% 9.53/5.32       => ( ord_less_eq_real @ ( times_times_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P6 @ Q2 ) ) ) @ Q2 ) @ P6 ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8605_floor__divide__lower,axiom,
% 9.53/5.32      ! [Q2: rat,P6: rat] :
% 9.53/5.32        ( ( ord_less_rat @ zero_zero_rat @ Q2 )
% 9.53/5.32       => ( ord_less_eq_rat @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P6 @ Q2 ) ) ) @ Q2 ) @ P6 ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8606_pochhammer__absorb__comp,axiom,
% 9.53/5.32      ! [R: code_integer,K: nat] :
% 9.53/5.32        ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ R @ ( semiri4939895301339042750nteger @ K ) ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ R ) @ K ) )
% 9.53/5.32        = ( times_3573771949741848930nteger @ R @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ R ) @ one_one_Code_integer ) @ K ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8607_pochhammer__absorb__comp,axiom,
% 9.53/5.32      ! [R: rat,K: nat] :
% 9.53/5.32        ( ( times_times_rat @ ( minus_minus_rat @ R @ ( semiri681578069525770553at_rat @ K ) ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ R ) @ K ) )
% 9.53/5.32        = ( times_times_rat @ R @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ R ) @ one_one_rat ) @ K ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8608_pochhammer__absorb__comp,axiom,
% 9.53/5.32      ! [R: real,K: nat] :
% 9.53/5.32        ( ( times_times_real @ ( minus_minus_real @ R @ ( semiri5074537144036343181t_real @ K ) ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ R ) @ K ) )
% 9.53/5.32        = ( times_times_real @ R @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( uminus_uminus_real @ R ) @ one_one_real ) @ K ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8609_pochhammer__absorb__comp,axiom,
% 9.53/5.32      ! [R: int,K: nat] :
% 9.53/5.32        ( ( times_times_int @ ( minus_minus_int @ R @ ( semiri1314217659103216013at_int @ K ) ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ R ) @ K ) )
% 9.53/5.32        = ( times_times_int @ R @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( uminus_uminus_int @ R ) @ one_one_int ) @ K ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8610_pochhammer__absorb__comp,axiom,
% 9.53/5.32      ! [R: complex,K: nat] :
% 9.53/5.32        ( ( times_times_complex @ ( minus_minus_complex @ R @ ( semiri8010041392384452111omplex @ K ) ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ R ) @ K ) )
% 9.53/5.32        = ( times_times_complex @ R @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ R ) @ one_one_complex ) @ K ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8611_floor__divide__upper,axiom,
% 9.53/5.32      ! [Q2: real,P6: real] :
% 9.53/5.32        ( ( ord_less_real @ zero_zero_real @ Q2 )
% 9.53/5.32       => ( ord_less_real @ P6 @ ( times_times_real @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P6 @ Q2 ) ) ) @ one_one_real ) @ Q2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8612_floor__divide__upper,axiom,
% 9.53/5.32      ! [Q2: rat,P6: rat] :
% 9.53/5.32        ( ( ord_less_rat @ zero_zero_rat @ Q2 )
% 9.53/5.32       => ( ord_less_rat @ P6 @ ( times_times_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P6 @ Q2 ) ) ) @ one_one_rat ) @ Q2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8613_pochhammer__same,axiom,
% 9.53/5.32      ! [N: nat] :
% 9.53/5.32        ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ N )
% 9.53/5.32        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8614_pochhammer__same,axiom,
% 9.53/5.32      ! [N: nat] :
% 9.53/5.32        ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ N )
% 9.53/5.32        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8615_pochhammer__same,axiom,
% 9.53/5.32      ! [N: nat] :
% 9.53/5.32        ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ N )
% 9.53/5.32        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8616_pochhammer__same,axiom,
% 9.53/5.32      ! [N: nat] :
% 9.53/5.32        ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ N )
% 9.53/5.32        = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( semiri5044797733671781792omplex @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8617_pochhammer__same,axiom,
% 9.53/5.32      ! [N: nat] :
% 9.53/5.32        ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ N )
% 9.53/5.32        = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8618_round__def,axiom,
% 9.53/5.32      ( archim8280529875227126926d_real
% 9.53/5.32      = ( ^ [X2: real] : ( archim6058952711729229775r_real @ ( plus_plus_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8619_round__def,axiom,
% 9.53/5.32      ( archim7778729529865785530nd_rat
% 9.53/5.32      = ( ^ [X2: rat] : ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8620_pochhammer__minus_H,axiom,
% 9.53/5.32      ! [B: code_integer,K: nat] :
% 9.53/5.32        ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K )
% 9.53/5.32        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8621_pochhammer__minus_H,axiom,
% 9.53/5.32      ! [B: rat,K: nat] :
% 9.53/5.32        ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K )
% 9.53/5.32        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8622_pochhammer__minus_H,axiom,
% 9.53/5.32      ! [B: real,K: nat] :
% 9.53/5.32        ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K )
% 9.53/5.32        = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8623_pochhammer__minus_H,axiom,
% 9.53/5.32      ! [B: int,K: nat] :
% 9.53/5.32        ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K )
% 9.53/5.32        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8624_pochhammer__minus_H,axiom,
% 9.53/5.32      ! [B: complex,K: nat] :
% 9.53/5.32        ( ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K )
% 9.53/5.32        = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8625_pochhammer__minus,axiom,
% 9.53/5.32      ! [B: code_integer,K: nat] :
% 9.53/5.32        ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K )
% 9.53/5.32        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8626_pochhammer__minus,axiom,
% 9.53/5.32      ! [B: rat,K: nat] :
% 9.53/5.32        ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K )
% 9.53/5.32        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8627_pochhammer__minus,axiom,
% 9.53/5.32      ! [B: real,K: nat] :
% 9.53/5.32        ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K )
% 9.53/5.32        = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8628_pochhammer__minus,axiom,
% 9.53/5.32      ! [B: int,K: nat] :
% 9.53/5.32        ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K )
% 9.53/5.32        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8629_pochhammer__minus,axiom,
% 9.53/5.32      ! [B: complex,K: nat] :
% 9.53/5.32        ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K )
% 9.53/5.32        = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8630_floor__log__eq__powr__iff,axiom,
% 9.53/5.32      ! [X: real,B: real,K: int] :
% 9.53/5.32        ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.32       => ( ( ord_less_real @ one_one_real @ B )
% 9.53/5.32         => ( ( ( archim6058952711729229775r_real @ ( log @ B @ X ) )
% 9.53/5.32              = K )
% 9.53/5.32            = ( ( ord_less_eq_real @ ( powr_real @ B @ ( ring_1_of_int_real @ K ) ) @ X )
% 9.53/5.32              & ( ord_less_real @ X @ ( powr_real @ B @ ( ring_1_of_int_real @ ( plus_plus_int @ K @ one_one_int ) ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8631_floor__log2__div2,axiom,
% 9.53/5.32      ! [N: nat] :
% 9.53/5.32        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.53/5.32       => ( ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 9.53/5.32          = ( plus_plus_int @ ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_int ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8632_fact__double,axiom,
% 9.53/5.32      ! [N: nat] :
% 9.53/5.32        ( ( semiri5044797733671781792omplex @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.53/5.32        = ( times_times_complex @ ( times_times_complex @ ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( comm_s2602460028002588243omplex @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ N ) ) @ ( semiri5044797733671781792omplex @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8633_fact__double,axiom,
% 9.53/5.32      ! [N: nat] :
% 9.53/5.32        ( ( semiri773545260158071498ct_rat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.53/5.32        = ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ N ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8634_fact__double,axiom,
% 9.53/5.32      ! [N: nat] :
% 9.53/5.32        ( ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.53/5.32        = ( times_times_real @ ( times_times_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( comm_s7457072308508201937r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ N ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8635_floor__log__nat__eq__if,axiom,
% 9.53/5.32      ! [B: nat,N: nat,K: nat] :
% 9.53/5.32        ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 9.53/5.32       => ( ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 9.53/5.32         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 9.53/5.32           => ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 9.53/5.32              = ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8636_pochhammer__times__pochhammer__half,axiom,
% 9.53/5.32      ! [Z: rat,N: nat] :
% 9.53/5.32        ( ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 9.53/5.32        = ( groups73079841787564623at_rat
% 9.53/5.32          @ ^ [K3: nat] : ( plus_plus_rat @ Z @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ K3 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 9.53/5.32          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8637_pochhammer__times__pochhammer__half,axiom,
% 9.53/5.32      ! [Z: real,N: nat] :
% 9.53/5.32        ( ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ ( suc @ N ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 9.53/5.32        = ( groups129246275422532515t_real
% 9.53/5.32          @ ^ [K3: nat] : ( plus_plus_real @ Z @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ K3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.32          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8638_pochhammer__times__pochhammer__half,axiom,
% 9.53/5.32      ! [Z: complex,N: nat] :
% 9.53/5.32        ( ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ ( suc @ N ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 9.53/5.32        = ( groups6464643781859351333omplex
% 9.53/5.32          @ ^ [K3: nat] : ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ K3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 9.53/5.32          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8639_pochhammer__code,axiom,
% 9.53/5.32      ( comm_s4028243227959126397er_rat
% 9.53/5.32      = ( ^ [A3: rat,N2: nat] :
% 9.53/5.32            ( if_rat @ ( N2 = zero_zero_nat ) @ one_one_rat
% 9.53/5.32            @ ( set_fo1949268297981939178at_rat
% 9.53/5.32              @ ^ [O: nat] : ( times_times_rat @ ( plus_plus_rat @ A3 @ ( semiri681578069525770553at_rat @ O ) ) )
% 9.53/5.32              @ zero_zero_nat
% 9.53/5.32              @ ( minus_minus_nat @ N2 @ one_one_nat )
% 9.53/5.32              @ one_one_rat ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8640_pochhammer__code,axiom,
% 9.53/5.32      ( comm_s7457072308508201937r_real
% 9.53/5.32      = ( ^ [A3: real,N2: nat] :
% 9.53/5.32            ( if_real @ ( N2 = zero_zero_nat ) @ one_one_real
% 9.53/5.32            @ ( set_fo3111899725591712190t_real
% 9.53/5.32              @ ^ [O: nat] : ( times_times_real @ ( plus_plus_real @ A3 @ ( semiri5074537144036343181t_real @ O ) ) )
% 9.53/5.32              @ zero_zero_nat
% 9.53/5.32              @ ( minus_minus_nat @ N2 @ one_one_nat )
% 9.53/5.32              @ one_one_real ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8641_pochhammer__code,axiom,
% 9.53/5.32      ( comm_s4660882817536571857er_int
% 9.53/5.32      = ( ^ [A3: int,N2: nat] :
% 9.53/5.32            ( if_int @ ( N2 = zero_zero_nat ) @ one_one_int
% 9.53/5.32            @ ( set_fo2581907887559384638at_int
% 9.53/5.32              @ ^ [O: nat] : ( times_times_int @ ( plus_plus_int @ A3 @ ( semiri1314217659103216013at_int @ O ) ) )
% 9.53/5.32              @ zero_zero_nat
% 9.53/5.32              @ ( minus_minus_nat @ N2 @ one_one_nat )
% 9.53/5.32              @ one_one_int ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8642_pochhammer__code,axiom,
% 9.53/5.32      ( comm_s2602460028002588243omplex
% 9.53/5.32      = ( ^ [A3: complex,N2: nat] :
% 9.53/5.32            ( if_complex @ ( N2 = zero_zero_nat ) @ one_one_complex
% 9.53/5.32            @ ( set_fo1517530859248394432omplex
% 9.53/5.32              @ ^ [O: nat] : ( times_times_complex @ ( plus_plus_complex @ A3 @ ( semiri8010041392384452111omplex @ O ) ) )
% 9.53/5.32              @ zero_zero_nat
% 9.53/5.32              @ ( minus_minus_nat @ N2 @ one_one_nat )
% 9.53/5.32              @ one_one_complex ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8643_pochhammer__code,axiom,
% 9.53/5.32      ( comm_s4663373288045622133er_nat
% 9.53/5.32      = ( ^ [A3: nat,N2: nat] :
% 9.53/5.32            ( if_nat @ ( N2 = zero_zero_nat ) @ one_one_nat
% 9.53/5.32            @ ( set_fo2584398358068434914at_nat
% 9.53/5.32              @ ^ [O: nat] : ( times_times_nat @ ( plus_plus_nat @ A3 @ ( semiri1316708129612266289at_nat @ O ) ) )
% 9.53/5.32              @ zero_zero_nat
% 9.53/5.32              @ ( minus_minus_nat @ N2 @ one_one_nat )
% 9.53/5.32              @ one_one_nat ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8644_round__altdef,axiom,
% 9.53/5.32      ( archim8280529875227126926d_real
% 9.53/5.32      = ( ^ [X2: real] : ( if_int @ ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( archim2898591450579166408c_real @ X2 ) ) @ ( archim7802044766580827645g_real @ X2 ) @ ( archim6058952711729229775r_real @ X2 ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8645_round__altdef,axiom,
% 9.53/5.32      ( archim7778729529865785530nd_rat
% 9.53/5.32      = ( ^ [X2: rat] : ( if_int @ ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( archimedean_frac_rat @ X2 ) ) @ ( archim2889992004027027881ng_rat @ X2 ) @ ( archim3151403230148437115or_rat @ X2 ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8646_of__nat__code,axiom,
% 9.53/5.32      ( semiri681578069525770553at_rat
% 9.53/5.32      = ( ^ [N2: nat] :
% 9.53/5.32            ( semiri7787848453975740701ux_rat
% 9.53/5.32            @ ^ [I3: rat] : ( plus_plus_rat @ I3 @ one_one_rat )
% 9.53/5.32            @ N2
% 9.53/5.32            @ zero_zero_rat ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8647_of__nat__code,axiom,
% 9.53/5.32      ( semiri5074537144036343181t_real
% 9.53/5.32      = ( ^ [N2: nat] :
% 9.53/5.32            ( semiri7260567687927622513x_real
% 9.53/5.32            @ ^ [I3: real] : ( plus_plus_real @ I3 @ one_one_real )
% 9.53/5.32            @ N2
% 9.53/5.32            @ zero_zero_real ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8648_of__nat__code,axiom,
% 9.53/5.32      ( semiri1314217659103216013at_int
% 9.53/5.32      = ( ^ [N2: nat] :
% 9.53/5.32            ( semiri8420488043553186161ux_int
% 9.53/5.32            @ ^ [I3: int] : ( plus_plus_int @ I3 @ one_one_int )
% 9.53/5.32            @ N2
% 9.53/5.32            @ zero_zero_int ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8649_of__nat__code,axiom,
% 9.53/5.32      ( semiri1316708129612266289at_nat
% 9.53/5.32      = ( ^ [N2: nat] :
% 9.53/5.32            ( semiri8422978514062236437ux_nat
% 9.53/5.32            @ ^ [I3: nat] : ( plus_plus_nat @ I3 @ one_one_nat )
% 9.53/5.32            @ N2
% 9.53/5.32            @ zero_zero_nat ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8650_of__nat__code,axiom,
% 9.53/5.32      ( semiri8010041392384452111omplex
% 9.53/5.32      = ( ^ [N2: nat] :
% 9.53/5.32            ( semiri2816024913162550771omplex
% 9.53/5.32            @ ^ [I3: complex] : ( plus_plus_complex @ I3 @ one_one_complex )
% 9.53/5.32            @ N2
% 9.53/5.32            @ zero_zero_complex ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8651_prod_Oneutral__const,axiom,
% 9.53/5.32      ! [A2: set_nat] :
% 9.53/5.32        ( ( groups708209901874060359at_nat
% 9.53/5.32          @ ^ [Uu3: nat] : one_one_nat
% 9.53/5.32          @ A2 )
% 9.53/5.32        = one_one_nat ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8652_prod_Oneutral__const,axiom,
% 9.53/5.32      ! [A2: set_nat] :
% 9.53/5.32        ( ( groups705719431365010083at_int
% 9.53/5.32          @ ^ [Uu3: nat] : one_one_int
% 9.53/5.32          @ A2 )
% 9.53/5.32        = one_one_int ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8653_prod_Oneutral__const,axiom,
% 9.53/5.32      ! [A2: set_int] :
% 9.53/5.32        ( ( groups1705073143266064639nt_int
% 9.53/5.32          @ ^ [Uu3: int] : one_one_int
% 9.53/5.32          @ A2 )
% 9.53/5.32        = one_one_int ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8654_prod_Oempty,axiom,
% 9.53/5.32      ! [G: nat > complex] :
% 9.53/5.32        ( ( groups6464643781859351333omplex @ G @ bot_bot_set_nat )
% 9.53/5.32        = one_one_complex ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8655_prod_Oempty,axiom,
% 9.53/5.32      ! [G: nat > real] :
% 9.53/5.32        ( ( groups129246275422532515t_real @ G @ bot_bot_set_nat )
% 9.53/5.32        = one_one_real ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8656_prod_Oempty,axiom,
% 9.53/5.32      ! [G: nat > rat] :
% 9.53/5.32        ( ( groups73079841787564623at_rat @ G @ bot_bot_set_nat )
% 9.53/5.32        = one_one_rat ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8657_prod_Oempty,axiom,
% 9.53/5.32      ! [G: int > complex] :
% 9.53/5.32        ( ( groups7440179247065528705omplex @ G @ bot_bot_set_int )
% 9.53/5.32        = one_one_complex ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8658_prod_Oempty,axiom,
% 9.53/5.32      ! [G: int > real] :
% 9.53/5.32        ( ( groups2316167850115554303t_real @ G @ bot_bot_set_int )
% 9.53/5.32        = one_one_real ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8659_prod_Oempty,axiom,
% 9.53/5.32      ! [G: int > rat] :
% 9.53/5.32        ( ( groups1072433553688619179nt_rat @ G @ bot_bot_set_int )
% 9.53/5.32        = one_one_rat ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8660_prod_Oempty,axiom,
% 9.53/5.32      ! [G: int > nat] :
% 9.53/5.32        ( ( groups1707563613775114915nt_nat @ G @ bot_bot_set_int )
% 9.53/5.32        = one_one_nat ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8661_prod_Oempty,axiom,
% 9.53/5.32      ! [G: real > complex] :
% 9.53/5.32        ( ( groups713298508707869441omplex @ G @ bot_bot_set_real )
% 9.53/5.32        = one_one_complex ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8662_prod_Oempty,axiom,
% 9.53/5.32      ! [G: real > real] :
% 9.53/5.32        ( ( groups1681761925125756287l_real @ G @ bot_bot_set_real )
% 9.53/5.32        = one_one_real ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8663_prod_Oempty,axiom,
% 9.53/5.32      ! [G: real > rat] :
% 9.53/5.32        ( ( groups4061424788464935467al_rat @ G @ bot_bot_set_real )
% 9.53/5.32        = one_one_rat ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8664_prod_Oinfinite,axiom,
% 9.53/5.32      ! [A2: set_nat,G: nat > complex] :
% 9.53/5.32        ( ~ ( finite_finite_nat @ A2 )
% 9.53/5.32       => ( ( groups6464643781859351333omplex @ G @ A2 )
% 9.53/5.32          = one_one_complex ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8665_prod_Oinfinite,axiom,
% 9.53/5.32      ! [A2: set_complex,G: complex > complex] :
% 9.53/5.32        ( ~ ( finite3207457112153483333omplex @ A2 )
% 9.53/5.32       => ( ( groups3708469109370488835omplex @ G @ A2 )
% 9.53/5.32          = one_one_complex ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8666_prod_Oinfinite,axiom,
% 9.53/5.32      ! [A2: set_nat,G: nat > real] :
% 9.53/5.32        ( ~ ( finite_finite_nat @ A2 )
% 9.53/5.32       => ( ( groups129246275422532515t_real @ G @ A2 )
% 9.53/5.32          = one_one_real ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8667_prod_Oinfinite,axiom,
% 9.53/5.32      ! [A2: set_complex,G: complex > real] :
% 9.53/5.32        ( ~ ( finite3207457112153483333omplex @ A2 )
% 9.53/5.32       => ( ( groups766887009212190081x_real @ G @ A2 )
% 9.53/5.32          = one_one_real ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8668_prod_Oinfinite,axiom,
% 9.53/5.32      ! [A2: set_nat,G: nat > rat] :
% 9.53/5.32        ( ~ ( finite_finite_nat @ A2 )
% 9.53/5.32       => ( ( groups73079841787564623at_rat @ G @ A2 )
% 9.53/5.32          = one_one_rat ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8669_prod_Oinfinite,axiom,
% 9.53/5.32      ! [A2: set_complex,G: complex > rat] :
% 9.53/5.32        ( ~ ( finite3207457112153483333omplex @ A2 )
% 9.53/5.32       => ( ( groups225925009352817453ex_rat @ G @ A2 )
% 9.53/5.32          = one_one_rat ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8670_prod_Oinfinite,axiom,
% 9.53/5.32      ! [A2: set_complex,G: complex > nat] :
% 9.53/5.32        ( ~ ( finite3207457112153483333omplex @ A2 )
% 9.53/5.32       => ( ( groups861055069439313189ex_nat @ G @ A2 )
% 9.53/5.32          = one_one_nat ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8671_prod_Oinfinite,axiom,
% 9.53/5.32      ! [A2: set_complex,G: complex > int] :
% 9.53/5.32        ( ~ ( finite3207457112153483333omplex @ A2 )
% 9.53/5.32       => ( ( groups858564598930262913ex_int @ G @ A2 )
% 9.53/5.32          = one_one_int ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8672_prod_Oinfinite,axiom,
% 9.53/5.32      ! [A2: set_nat,G: nat > nat] :
% 9.53/5.32        ( ~ ( finite_finite_nat @ A2 )
% 9.53/5.32       => ( ( groups708209901874060359at_nat @ G @ A2 )
% 9.53/5.32          = one_one_nat ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8673_prod_Oinfinite,axiom,
% 9.53/5.32      ! [A2: set_nat,G: nat > int] :
% 9.53/5.32        ( ~ ( finite_finite_nat @ A2 )
% 9.53/5.32       => ( ( groups705719431365010083at_int @ G @ A2 )
% 9.53/5.32          = one_one_int ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8674_prod_Odelta_H,axiom,
% 9.53/5.32      ! [S2: set_real,A: real,B: real > complex] :
% 9.53/5.32        ( ( finite_finite_real @ S2 )
% 9.53/5.32       => ( ( ( member_real @ A @ S2 )
% 9.53/5.32           => ( ( groups713298508707869441omplex
% 9.53/5.32                @ ^ [K3: real] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( B @ A ) ) )
% 9.53/5.32          & ( ~ ( member_real @ A @ S2 )
% 9.53/5.32           => ( ( groups713298508707869441omplex
% 9.53/5.32                @ ^ [K3: real] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = one_one_complex ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8675_prod_Odelta_H,axiom,
% 9.53/5.32      ! [S2: set_int,A: int,B: int > complex] :
% 9.53/5.32        ( ( finite_finite_int @ S2 )
% 9.53/5.32       => ( ( ( member_int @ A @ S2 )
% 9.53/5.32           => ( ( groups7440179247065528705omplex
% 9.53/5.32                @ ^ [K3: int] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( B @ A ) ) )
% 9.53/5.32          & ( ~ ( member_int @ A @ S2 )
% 9.53/5.32           => ( ( groups7440179247065528705omplex
% 9.53/5.32                @ ^ [K3: int] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = one_one_complex ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8676_prod_Odelta_H,axiom,
% 9.53/5.32      ! [S2: set_nat,A: nat,B: nat > complex] :
% 9.53/5.32        ( ( finite_finite_nat @ S2 )
% 9.53/5.32       => ( ( ( member_nat @ A @ S2 )
% 9.53/5.32           => ( ( groups6464643781859351333omplex
% 9.53/5.32                @ ^ [K3: nat] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( B @ A ) ) )
% 9.53/5.32          & ( ~ ( member_nat @ A @ S2 )
% 9.53/5.32           => ( ( groups6464643781859351333omplex
% 9.53/5.32                @ ^ [K3: nat] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = one_one_complex ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8677_prod_Odelta_H,axiom,
% 9.53/5.32      ! [S2: set_complex,A: complex,B: complex > complex] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ S2 )
% 9.53/5.32       => ( ( ( member_complex @ A @ S2 )
% 9.53/5.32           => ( ( groups3708469109370488835omplex
% 9.53/5.32                @ ^ [K3: complex] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( B @ A ) ) )
% 9.53/5.32          & ( ~ ( member_complex @ A @ S2 )
% 9.53/5.32           => ( ( groups3708469109370488835omplex
% 9.53/5.32                @ ^ [K3: complex] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = one_one_complex ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8678_prod_Odelta_H,axiom,
% 9.53/5.32      ! [S2: set_real,A: real,B: real > real] :
% 9.53/5.32        ( ( finite_finite_real @ S2 )
% 9.53/5.32       => ( ( ( member_real @ A @ S2 )
% 9.53/5.32           => ( ( groups1681761925125756287l_real
% 9.53/5.32                @ ^ [K3: real] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( B @ A ) ) )
% 9.53/5.32          & ( ~ ( member_real @ A @ S2 )
% 9.53/5.32           => ( ( groups1681761925125756287l_real
% 9.53/5.32                @ ^ [K3: real] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = one_one_real ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8679_prod_Odelta_H,axiom,
% 9.53/5.32      ! [S2: set_int,A: int,B: int > real] :
% 9.53/5.32        ( ( finite_finite_int @ S2 )
% 9.53/5.32       => ( ( ( member_int @ A @ S2 )
% 9.53/5.32           => ( ( groups2316167850115554303t_real
% 9.53/5.32                @ ^ [K3: int] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( B @ A ) ) )
% 9.53/5.32          & ( ~ ( member_int @ A @ S2 )
% 9.53/5.32           => ( ( groups2316167850115554303t_real
% 9.53/5.32                @ ^ [K3: int] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = one_one_real ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8680_prod_Odelta_H,axiom,
% 9.53/5.32      ! [S2: set_nat,A: nat,B: nat > real] :
% 9.53/5.32        ( ( finite_finite_nat @ S2 )
% 9.53/5.32       => ( ( ( member_nat @ A @ S2 )
% 9.53/5.32           => ( ( groups129246275422532515t_real
% 9.53/5.32                @ ^ [K3: nat] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( B @ A ) ) )
% 9.53/5.32          & ( ~ ( member_nat @ A @ S2 )
% 9.53/5.32           => ( ( groups129246275422532515t_real
% 9.53/5.32                @ ^ [K3: nat] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = one_one_real ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8681_prod_Odelta_H,axiom,
% 9.53/5.32      ! [S2: set_complex,A: complex,B: complex > real] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ S2 )
% 9.53/5.32       => ( ( ( member_complex @ A @ S2 )
% 9.53/5.32           => ( ( groups766887009212190081x_real
% 9.53/5.32                @ ^ [K3: complex] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( B @ A ) ) )
% 9.53/5.32          & ( ~ ( member_complex @ A @ S2 )
% 9.53/5.32           => ( ( groups766887009212190081x_real
% 9.53/5.32                @ ^ [K3: complex] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = one_one_real ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8682_prod_Odelta_H,axiom,
% 9.53/5.32      ! [S2: set_real,A: real,B: real > rat] :
% 9.53/5.32        ( ( finite_finite_real @ S2 )
% 9.53/5.32       => ( ( ( member_real @ A @ S2 )
% 9.53/5.32           => ( ( groups4061424788464935467al_rat
% 9.53/5.32                @ ^ [K3: real] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ one_one_rat )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( B @ A ) ) )
% 9.53/5.32          & ( ~ ( member_real @ A @ S2 )
% 9.53/5.32           => ( ( groups4061424788464935467al_rat
% 9.53/5.32                @ ^ [K3: real] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ one_one_rat )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = one_one_rat ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8683_prod_Odelta_H,axiom,
% 9.53/5.32      ! [S2: set_int,A: int,B: int > rat] :
% 9.53/5.32        ( ( finite_finite_int @ S2 )
% 9.53/5.32       => ( ( ( member_int @ A @ S2 )
% 9.53/5.32           => ( ( groups1072433553688619179nt_rat
% 9.53/5.32                @ ^ [K3: int] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ one_one_rat )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( B @ A ) ) )
% 9.53/5.32          & ( ~ ( member_int @ A @ S2 )
% 9.53/5.32           => ( ( groups1072433553688619179nt_rat
% 9.53/5.32                @ ^ [K3: int] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ one_one_rat )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = one_one_rat ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8684_prod_Odelta,axiom,
% 9.53/5.32      ! [S2: set_real,A: real,B: real > complex] :
% 9.53/5.32        ( ( finite_finite_real @ S2 )
% 9.53/5.32       => ( ( ( member_real @ A @ S2 )
% 9.53/5.32           => ( ( groups713298508707869441omplex
% 9.53/5.32                @ ^ [K3: real] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( B @ A ) ) )
% 9.53/5.32          & ( ~ ( member_real @ A @ S2 )
% 9.53/5.32           => ( ( groups713298508707869441omplex
% 9.53/5.32                @ ^ [K3: real] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = one_one_complex ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8685_prod_Odelta,axiom,
% 9.53/5.32      ! [S2: set_int,A: int,B: int > complex] :
% 9.53/5.32        ( ( finite_finite_int @ S2 )
% 9.53/5.32       => ( ( ( member_int @ A @ S2 )
% 9.53/5.32           => ( ( groups7440179247065528705omplex
% 9.53/5.32                @ ^ [K3: int] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( B @ A ) ) )
% 9.53/5.32          & ( ~ ( member_int @ A @ S2 )
% 9.53/5.32           => ( ( groups7440179247065528705omplex
% 9.53/5.32                @ ^ [K3: int] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = one_one_complex ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8686_prod_Odelta,axiom,
% 9.53/5.32      ! [S2: set_nat,A: nat,B: nat > complex] :
% 9.53/5.32        ( ( finite_finite_nat @ S2 )
% 9.53/5.32       => ( ( ( member_nat @ A @ S2 )
% 9.53/5.32           => ( ( groups6464643781859351333omplex
% 9.53/5.32                @ ^ [K3: nat] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( B @ A ) ) )
% 9.53/5.32          & ( ~ ( member_nat @ A @ S2 )
% 9.53/5.32           => ( ( groups6464643781859351333omplex
% 9.53/5.32                @ ^ [K3: nat] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = one_one_complex ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8687_prod_Odelta,axiom,
% 9.53/5.32      ! [S2: set_complex,A: complex,B: complex > complex] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ S2 )
% 9.53/5.32       => ( ( ( member_complex @ A @ S2 )
% 9.53/5.32           => ( ( groups3708469109370488835omplex
% 9.53/5.32                @ ^ [K3: complex] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( B @ A ) ) )
% 9.53/5.32          & ( ~ ( member_complex @ A @ S2 )
% 9.53/5.32           => ( ( groups3708469109370488835omplex
% 9.53/5.32                @ ^ [K3: complex] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = one_one_complex ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8688_prod_Odelta,axiom,
% 9.53/5.32      ! [S2: set_real,A: real,B: real > real] :
% 9.53/5.32        ( ( finite_finite_real @ S2 )
% 9.53/5.32       => ( ( ( member_real @ A @ S2 )
% 9.53/5.32           => ( ( groups1681761925125756287l_real
% 9.53/5.32                @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( B @ A ) ) )
% 9.53/5.32          & ( ~ ( member_real @ A @ S2 )
% 9.53/5.32           => ( ( groups1681761925125756287l_real
% 9.53/5.32                @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = one_one_real ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8689_prod_Odelta,axiom,
% 9.53/5.32      ! [S2: set_int,A: int,B: int > real] :
% 9.53/5.32        ( ( finite_finite_int @ S2 )
% 9.53/5.32       => ( ( ( member_int @ A @ S2 )
% 9.53/5.32           => ( ( groups2316167850115554303t_real
% 9.53/5.32                @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( B @ A ) ) )
% 9.53/5.32          & ( ~ ( member_int @ A @ S2 )
% 9.53/5.32           => ( ( groups2316167850115554303t_real
% 9.53/5.32                @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = one_one_real ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8690_prod_Odelta,axiom,
% 9.53/5.32      ! [S2: set_nat,A: nat,B: nat > real] :
% 9.53/5.32        ( ( finite_finite_nat @ S2 )
% 9.53/5.32       => ( ( ( member_nat @ A @ S2 )
% 9.53/5.32           => ( ( groups129246275422532515t_real
% 9.53/5.32                @ ^ [K3: nat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( B @ A ) ) )
% 9.53/5.32          & ( ~ ( member_nat @ A @ S2 )
% 9.53/5.32           => ( ( groups129246275422532515t_real
% 9.53/5.32                @ ^ [K3: nat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = one_one_real ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8691_prod_Odelta,axiom,
% 9.53/5.32      ! [S2: set_complex,A: complex,B: complex > real] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ S2 )
% 9.53/5.32       => ( ( ( member_complex @ A @ S2 )
% 9.53/5.32           => ( ( groups766887009212190081x_real
% 9.53/5.32                @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( B @ A ) ) )
% 9.53/5.32          & ( ~ ( member_complex @ A @ S2 )
% 9.53/5.32           => ( ( groups766887009212190081x_real
% 9.53/5.32                @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = one_one_real ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8692_prod_Odelta,axiom,
% 9.53/5.32      ! [S2: set_real,A: real,B: real > rat] :
% 9.53/5.32        ( ( finite_finite_real @ S2 )
% 9.53/5.32       => ( ( ( member_real @ A @ S2 )
% 9.53/5.32           => ( ( groups4061424788464935467al_rat
% 9.53/5.32                @ ^ [K3: real] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ one_one_rat )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( B @ A ) ) )
% 9.53/5.32          & ( ~ ( member_real @ A @ S2 )
% 9.53/5.32           => ( ( groups4061424788464935467al_rat
% 9.53/5.32                @ ^ [K3: real] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ one_one_rat )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = one_one_rat ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8693_prod_Odelta,axiom,
% 9.53/5.32      ! [S2: set_int,A: int,B: int > rat] :
% 9.53/5.32        ( ( finite_finite_int @ S2 )
% 9.53/5.32       => ( ( ( member_int @ A @ S2 )
% 9.53/5.32           => ( ( groups1072433553688619179nt_rat
% 9.53/5.32                @ ^ [K3: int] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ one_one_rat )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( B @ A ) ) )
% 9.53/5.32          & ( ~ ( member_int @ A @ S2 )
% 9.53/5.32           => ( ( groups1072433553688619179nt_rat
% 9.53/5.32                @ ^ [K3: int] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ one_one_rat )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = one_one_rat ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8694_prod_Oinsert,axiom,
% 9.53/5.32      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > complex] :
% 9.53/5.32        ( ( finite5795047828879050333T_VEBT @ A2 )
% 9.53/5.32       => ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 9.53/5.32         => ( ( groups127312072573709053omplex @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 9.53/5.32            = ( times_times_complex @ ( G @ X ) @ ( groups127312072573709053omplex @ G @ A2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8695_prod_Oinsert,axiom,
% 9.53/5.32      ! [A2: set_real,X: real,G: real > complex] :
% 9.53/5.32        ( ( finite_finite_real @ A2 )
% 9.53/5.32       => ( ~ ( member_real @ X @ A2 )
% 9.53/5.32         => ( ( groups713298508707869441omplex @ G @ ( insert_real @ X @ A2 ) )
% 9.53/5.32            = ( times_times_complex @ ( G @ X ) @ ( groups713298508707869441omplex @ G @ A2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8696_prod_Oinsert,axiom,
% 9.53/5.32      ! [A2: set_int,X: int,G: int > complex] :
% 9.53/5.32        ( ( finite_finite_int @ A2 )
% 9.53/5.32       => ( ~ ( member_int @ X @ A2 )
% 9.53/5.32         => ( ( groups7440179247065528705omplex @ G @ ( insert_int @ X @ A2 ) )
% 9.53/5.32            = ( times_times_complex @ ( G @ X ) @ ( groups7440179247065528705omplex @ G @ A2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8697_prod_Oinsert,axiom,
% 9.53/5.32      ! [A2: set_nat,X: nat,G: nat > complex] :
% 9.53/5.32        ( ( finite_finite_nat @ A2 )
% 9.53/5.32       => ( ~ ( member_nat @ X @ A2 )
% 9.53/5.32         => ( ( groups6464643781859351333omplex @ G @ ( insert_nat @ X @ A2 ) )
% 9.53/5.32            = ( times_times_complex @ ( G @ X ) @ ( groups6464643781859351333omplex @ G @ A2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8698_prod_Oinsert,axiom,
% 9.53/5.32      ! [A2: set_complex,X: complex,G: complex > complex] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.32       => ( ~ ( member_complex @ X @ A2 )
% 9.53/5.32         => ( ( groups3708469109370488835omplex @ G @ ( insert_complex @ X @ A2 ) )
% 9.53/5.32            = ( times_times_complex @ ( G @ X ) @ ( groups3708469109370488835omplex @ G @ A2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8699_prod_Oinsert,axiom,
% 9.53/5.32      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > real] :
% 9.53/5.32        ( ( finite5795047828879050333T_VEBT @ A2 )
% 9.53/5.32       => ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 9.53/5.32         => ( ( groups2703838992350267259T_real @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 9.53/5.32            = ( times_times_real @ ( G @ X ) @ ( groups2703838992350267259T_real @ G @ A2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8700_prod_Oinsert,axiom,
% 9.53/5.32      ! [A2: set_real,X: real,G: real > real] :
% 9.53/5.32        ( ( finite_finite_real @ A2 )
% 9.53/5.32       => ( ~ ( member_real @ X @ A2 )
% 9.53/5.32         => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X @ A2 ) )
% 9.53/5.32            = ( times_times_real @ ( G @ X ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8701_prod_Oinsert,axiom,
% 9.53/5.32      ! [A2: set_int,X: int,G: int > real] :
% 9.53/5.32        ( ( finite_finite_int @ A2 )
% 9.53/5.32       => ( ~ ( member_int @ X @ A2 )
% 9.53/5.32         => ( ( groups2316167850115554303t_real @ G @ ( insert_int @ X @ A2 ) )
% 9.53/5.32            = ( times_times_real @ ( G @ X ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8702_prod_Oinsert,axiom,
% 9.53/5.32      ! [A2: set_nat,X: nat,G: nat > real] :
% 9.53/5.32        ( ( finite_finite_nat @ A2 )
% 9.53/5.32       => ( ~ ( member_nat @ X @ A2 )
% 9.53/5.32         => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X @ A2 ) )
% 9.53/5.32            = ( times_times_real @ ( G @ X ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8703_prod_Oinsert,axiom,
% 9.53/5.32      ! [A2: set_complex,X: complex,G: complex > real] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.32       => ( ~ ( member_complex @ X @ A2 )
% 9.53/5.32         => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X @ A2 ) )
% 9.53/5.32            = ( times_times_real @ ( G @ X ) @ ( groups766887009212190081x_real @ G @ A2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8704_prod_OlessThan__Suc,axiom,
% 9.53/5.32      ! [G: nat > complex,N: nat] :
% 9.53/5.32        ( ( groups6464643781859351333omplex @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 9.53/5.32        = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8705_prod_OlessThan__Suc,axiom,
% 9.53/5.32      ! [G: nat > real,N: nat] :
% 9.53/5.32        ( ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 9.53/5.32        = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8706_prod_OlessThan__Suc,axiom,
% 9.53/5.32      ! [G: nat > nat,N: nat] :
% 9.53/5.32        ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 9.53/5.32        = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8707_prod_OlessThan__Suc,axiom,
% 9.53/5.32      ! [G: nat > int,N: nat] :
% 9.53/5.32        ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 9.53/5.32        = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8708_prod_Ocl__ivl__Suc,axiom,
% 9.53/5.32      ! [N: nat,M: nat,G: nat > rat] :
% 9.53/5.32        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 9.53/5.32         => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.53/5.32            = one_one_rat ) )
% 9.53/5.32        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 9.53/5.32         => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.53/5.32            = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8709_prod_Ocl__ivl__Suc,axiom,
% 9.53/5.32      ! [N: nat,M: nat,G: nat > complex] :
% 9.53/5.32        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 9.53/5.32         => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.53/5.32            = one_one_complex ) )
% 9.53/5.32        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 9.53/5.32         => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.53/5.32            = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8710_prod_Ocl__ivl__Suc,axiom,
% 9.53/5.32      ! [N: nat,M: nat,G: nat > real] :
% 9.53/5.32        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 9.53/5.32         => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.53/5.32            = one_one_real ) )
% 9.53/5.32        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 9.53/5.32         => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.53/5.32            = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8711_prod_Ocl__ivl__Suc,axiom,
% 9.53/5.32      ! [N: nat,M: nat,G: nat > nat] :
% 9.53/5.32        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 9.53/5.32         => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.53/5.32            = one_one_nat ) )
% 9.53/5.32        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 9.53/5.32         => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.53/5.32            = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8712_prod_Ocl__ivl__Suc,axiom,
% 9.53/5.32      ! [N: nat,M: nat,G: nat > int] :
% 9.53/5.32        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 9.53/5.32         => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.53/5.32            = one_one_int ) )
% 9.53/5.32        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 9.53/5.32         => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.53/5.32            = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8713_prod_Oneutral,axiom,
% 9.53/5.32      ! [A2: set_nat,G: nat > nat] :
% 9.53/5.32        ( ! [X3: nat] :
% 9.53/5.32            ( ( member_nat @ X3 @ A2 )
% 9.53/5.32           => ( ( G @ X3 )
% 9.53/5.32              = one_one_nat ) )
% 9.53/5.32       => ( ( groups708209901874060359at_nat @ G @ A2 )
% 9.53/5.32          = one_one_nat ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8714_prod_Oneutral,axiom,
% 9.53/5.32      ! [A2: set_nat,G: nat > int] :
% 9.53/5.32        ( ! [X3: nat] :
% 9.53/5.32            ( ( member_nat @ X3 @ A2 )
% 9.53/5.32           => ( ( G @ X3 )
% 9.53/5.32              = one_one_int ) )
% 9.53/5.32       => ( ( groups705719431365010083at_int @ G @ A2 )
% 9.53/5.32          = one_one_int ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8715_prod_Oneutral,axiom,
% 9.53/5.32      ! [A2: set_int,G: int > int] :
% 9.53/5.32        ( ! [X3: int] :
% 9.53/5.32            ( ( member_int @ X3 @ A2 )
% 9.53/5.32           => ( ( G @ X3 )
% 9.53/5.32              = one_one_int ) )
% 9.53/5.32       => ( ( groups1705073143266064639nt_int @ G @ A2 )
% 9.53/5.32          = one_one_int ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8716_prod_Onot__neutral__contains__not__neutral,axiom,
% 9.53/5.32      ! [G: complex > complex,A2: set_complex] :
% 9.53/5.32        ( ( ( groups3708469109370488835omplex @ G @ A2 )
% 9.53/5.32         != one_one_complex )
% 9.53/5.32       => ~ ! [A4: complex] :
% 9.53/5.32              ( ( member_complex @ A4 @ A2 )
% 9.53/5.32             => ( ( G @ A4 )
% 9.53/5.32                = one_one_complex ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8717_prod_Onot__neutral__contains__not__neutral,axiom,
% 9.53/5.32      ! [G: real > complex,A2: set_real] :
% 9.53/5.32        ( ( ( groups713298508707869441omplex @ G @ A2 )
% 9.53/5.32         != one_one_complex )
% 9.53/5.32       => ~ ! [A4: real] :
% 9.53/5.32              ( ( member_real @ A4 @ A2 )
% 9.53/5.32             => ( ( G @ A4 )
% 9.53/5.32                = one_one_complex ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8718_prod_Onot__neutral__contains__not__neutral,axiom,
% 9.53/5.32      ! [G: nat > complex,A2: set_nat] :
% 9.53/5.32        ( ( ( groups6464643781859351333omplex @ G @ A2 )
% 9.53/5.32         != one_one_complex )
% 9.53/5.32       => ~ ! [A4: nat] :
% 9.53/5.32              ( ( member_nat @ A4 @ A2 )
% 9.53/5.32             => ( ( G @ A4 )
% 9.53/5.32                = one_one_complex ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8719_prod_Onot__neutral__contains__not__neutral,axiom,
% 9.53/5.32      ! [G: int > complex,A2: set_int] :
% 9.53/5.32        ( ( ( groups7440179247065528705omplex @ G @ A2 )
% 9.53/5.32         != one_one_complex )
% 9.53/5.32       => ~ ! [A4: int] :
% 9.53/5.32              ( ( member_int @ A4 @ A2 )
% 9.53/5.32             => ( ( G @ A4 )
% 9.53/5.32                = one_one_complex ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8720_prod_Onot__neutral__contains__not__neutral,axiom,
% 9.53/5.32      ! [G: complex > real,A2: set_complex] :
% 9.53/5.32        ( ( ( groups766887009212190081x_real @ G @ A2 )
% 9.53/5.32         != one_one_real )
% 9.53/5.32       => ~ ! [A4: complex] :
% 9.53/5.32              ( ( member_complex @ A4 @ A2 )
% 9.53/5.32             => ( ( G @ A4 )
% 9.53/5.32                = one_one_real ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8721_prod_Onot__neutral__contains__not__neutral,axiom,
% 9.53/5.32      ! [G: real > real,A2: set_real] :
% 9.53/5.32        ( ( ( groups1681761925125756287l_real @ G @ A2 )
% 9.53/5.32         != one_one_real )
% 9.53/5.32       => ~ ! [A4: real] :
% 9.53/5.32              ( ( member_real @ A4 @ A2 )
% 9.53/5.32             => ( ( G @ A4 )
% 9.53/5.32                = one_one_real ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8722_prod_Onot__neutral__contains__not__neutral,axiom,
% 9.53/5.32      ! [G: nat > real,A2: set_nat] :
% 9.53/5.32        ( ( ( groups129246275422532515t_real @ G @ A2 )
% 9.53/5.32         != one_one_real )
% 9.53/5.32       => ~ ! [A4: nat] :
% 9.53/5.32              ( ( member_nat @ A4 @ A2 )
% 9.53/5.32             => ( ( G @ A4 )
% 9.53/5.32                = one_one_real ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8723_prod_Onot__neutral__contains__not__neutral,axiom,
% 9.53/5.32      ! [G: int > real,A2: set_int] :
% 9.53/5.32        ( ( ( groups2316167850115554303t_real @ G @ A2 )
% 9.53/5.32         != one_one_real )
% 9.53/5.32       => ~ ! [A4: int] :
% 9.53/5.32              ( ( member_int @ A4 @ A2 )
% 9.53/5.32             => ( ( G @ A4 )
% 9.53/5.32                = one_one_real ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8724_prod_Onot__neutral__contains__not__neutral,axiom,
% 9.53/5.32      ! [G: complex > rat,A2: set_complex] :
% 9.53/5.32        ( ( ( groups225925009352817453ex_rat @ G @ A2 )
% 9.53/5.32         != one_one_rat )
% 9.53/5.32       => ~ ! [A4: complex] :
% 9.53/5.32              ( ( member_complex @ A4 @ A2 )
% 9.53/5.32             => ( ( G @ A4 )
% 9.53/5.32                = one_one_rat ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8725_prod_Onot__neutral__contains__not__neutral,axiom,
% 9.53/5.32      ! [G: real > rat,A2: set_real] :
% 9.53/5.32        ( ( ( groups4061424788464935467al_rat @ G @ A2 )
% 9.53/5.32         != one_one_rat )
% 9.53/5.32       => ~ ! [A4: real] :
% 9.53/5.32              ( ( member_real @ A4 @ A2 )
% 9.53/5.32             => ( ( G @ A4 )
% 9.53/5.32                = one_one_rat ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8726_prod__power__distrib,axiom,
% 9.53/5.32      ! [F: nat > nat,A2: set_nat,N: nat] :
% 9.53/5.32        ( ( power_power_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ N )
% 9.53/5.32        = ( groups708209901874060359at_nat
% 9.53/5.32          @ ^ [X2: nat] : ( power_power_nat @ ( F @ X2 ) @ N )
% 9.53/5.32          @ A2 ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8727_prod__power__distrib,axiom,
% 9.53/5.32      ! [F: nat > int,A2: set_nat,N: nat] :
% 9.53/5.32        ( ( power_power_int @ ( groups705719431365010083at_int @ F @ A2 ) @ N )
% 9.53/5.32        = ( groups705719431365010083at_int
% 9.53/5.32          @ ^ [X2: nat] : ( power_power_int @ ( F @ X2 ) @ N )
% 9.53/5.32          @ A2 ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8728_prod__power__distrib,axiom,
% 9.53/5.32      ! [F: int > int,A2: set_int,N: nat] :
% 9.53/5.32        ( ( power_power_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ N )
% 9.53/5.32        = ( groups1705073143266064639nt_int
% 9.53/5.32          @ ^ [X2: int] : ( power_power_int @ ( F @ X2 ) @ N )
% 9.53/5.32          @ A2 ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8729_prod_Odistrib,axiom,
% 9.53/5.32      ! [G: nat > nat,H2: nat > nat,A2: set_nat] :
% 9.53/5.32        ( ( groups708209901874060359at_nat
% 9.53/5.32          @ ^ [X2: nat] : ( times_times_nat @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 9.53/5.32          @ A2 )
% 9.53/5.32        = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ A2 ) @ ( groups708209901874060359at_nat @ H2 @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8730_prod_Odistrib,axiom,
% 9.53/5.32      ! [G: nat > int,H2: nat > int,A2: set_nat] :
% 9.53/5.32        ( ( groups705719431365010083at_int
% 9.53/5.32          @ ^ [X2: nat] : ( times_times_int @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 9.53/5.32          @ A2 )
% 9.53/5.32        = ( times_times_int @ ( groups705719431365010083at_int @ G @ A2 ) @ ( groups705719431365010083at_int @ H2 @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8731_prod_Odistrib,axiom,
% 9.53/5.32      ! [G: int > int,H2: int > int,A2: set_int] :
% 9.53/5.32        ( ( groups1705073143266064639nt_int
% 9.53/5.32          @ ^ [X2: int] : ( times_times_int @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 9.53/5.32          @ A2 )
% 9.53/5.32        = ( times_times_int @ ( groups1705073143266064639nt_int @ G @ A2 ) @ ( groups1705073143266064639nt_int @ H2 @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8732_mod__prod__eq,axiom,
% 9.53/5.32      ! [F: nat > nat,A: nat,A2: set_nat] :
% 9.53/5.32        ( ( modulo_modulo_nat
% 9.53/5.32          @ ( groups708209901874060359at_nat
% 9.53/5.32            @ ^ [I3: nat] : ( modulo_modulo_nat @ ( F @ I3 ) @ A )
% 9.53/5.32            @ A2 )
% 9.53/5.32          @ A )
% 9.53/5.32        = ( modulo_modulo_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ A ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8733_mod__prod__eq,axiom,
% 9.53/5.32      ! [F: nat > int,A: int,A2: set_nat] :
% 9.53/5.32        ( ( modulo_modulo_int
% 9.53/5.32          @ ( groups705719431365010083at_int
% 9.53/5.32            @ ^ [I3: nat] : ( modulo_modulo_int @ ( F @ I3 ) @ A )
% 9.53/5.32            @ A2 )
% 9.53/5.32          @ A )
% 9.53/5.32        = ( modulo_modulo_int @ ( groups705719431365010083at_int @ F @ A2 ) @ A ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8734_mod__prod__eq,axiom,
% 9.53/5.32      ! [F: int > int,A: int,A2: set_int] :
% 9.53/5.32        ( ( modulo_modulo_int
% 9.53/5.32          @ ( groups1705073143266064639nt_int
% 9.53/5.32            @ ^ [I3: int] : ( modulo_modulo_int @ ( F @ I3 ) @ A )
% 9.53/5.32            @ A2 )
% 9.53/5.32          @ A )
% 9.53/5.32        = ( modulo_modulo_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ A ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8735_prod__nonneg,axiom,
% 9.53/5.32      ! [A2: set_nat,F: nat > nat] :
% 9.53/5.32        ( ! [X3: nat] :
% 9.53/5.32            ( ( member_nat @ X3 @ A2 )
% 9.53/5.32           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 9.53/5.32       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8736_prod__nonneg,axiom,
% 9.53/5.32      ! [A2: set_nat,F: nat > int] :
% 9.53/5.32        ( ! [X3: nat] :
% 9.53/5.32            ( ( member_nat @ X3 @ A2 )
% 9.53/5.32           => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 9.53/5.32       => ( ord_less_eq_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8737_prod__nonneg,axiom,
% 9.53/5.32      ! [A2: set_int,F: int > int] :
% 9.53/5.32        ( ! [X3: int] :
% 9.53/5.32            ( ( member_int @ X3 @ A2 )
% 9.53/5.32           => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 9.53/5.32       => ( ord_less_eq_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8738_prod__mono,axiom,
% 9.53/5.32      ! [A2: set_complex,F: complex > real,G: complex > real] :
% 9.53/5.32        ( ! [I4: complex] :
% 9.53/5.32            ( ( member_complex @ I4 @ A2 )
% 9.53/5.32           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 9.53/5.32              & ( ord_less_eq_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 9.53/5.32       => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ( groups766887009212190081x_real @ G @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8739_prod__mono,axiom,
% 9.53/5.32      ! [A2: set_real,F: real > real,G: real > real] :
% 9.53/5.32        ( ! [I4: real] :
% 9.53/5.32            ( ( member_real @ I4 @ A2 )
% 9.53/5.32           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 9.53/5.32              & ( ord_less_eq_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 9.53/5.32       => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8740_prod__mono,axiom,
% 9.53/5.32      ! [A2: set_nat,F: nat > real,G: nat > real] :
% 9.53/5.32        ( ! [I4: nat] :
% 9.53/5.32            ( ( member_nat @ I4 @ A2 )
% 9.53/5.32           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 9.53/5.32              & ( ord_less_eq_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 9.53/5.32       => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8741_prod__mono,axiom,
% 9.53/5.32      ! [A2: set_int,F: int > real,G: int > real] :
% 9.53/5.32        ( ! [I4: int] :
% 9.53/5.32            ( ( member_int @ I4 @ A2 )
% 9.53/5.32           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 9.53/5.32              & ( ord_less_eq_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 9.53/5.32       => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8742_prod__mono,axiom,
% 9.53/5.32      ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 9.53/5.32        ( ! [I4: complex] :
% 9.53/5.32            ( ( member_complex @ I4 @ A2 )
% 9.53/5.32           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) )
% 9.53/5.32              & ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 9.53/5.32       => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ ( groups225925009352817453ex_rat @ G @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8743_prod__mono,axiom,
% 9.53/5.32      ! [A2: set_real,F: real > rat,G: real > rat] :
% 9.53/5.32        ( ! [I4: real] :
% 9.53/5.32            ( ( member_real @ I4 @ A2 )
% 9.53/5.32           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) )
% 9.53/5.32              & ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 9.53/5.32       => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ ( groups4061424788464935467al_rat @ G @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8744_prod__mono,axiom,
% 9.53/5.32      ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 9.53/5.32        ( ! [I4: nat] :
% 9.53/5.32            ( ( member_nat @ I4 @ A2 )
% 9.53/5.32           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) )
% 9.53/5.32              & ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 9.53/5.32       => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ ( groups73079841787564623at_rat @ G @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8745_prod__mono,axiom,
% 9.53/5.32      ! [A2: set_int,F: int > rat,G: int > rat] :
% 9.53/5.32        ( ! [I4: int] :
% 9.53/5.32            ( ( member_int @ I4 @ A2 )
% 9.53/5.32           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) )
% 9.53/5.32              & ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 9.53/5.32       => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ ( groups1072433553688619179nt_rat @ G @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8746_prod__mono,axiom,
% 9.53/5.32      ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 9.53/5.32        ( ! [I4: complex] :
% 9.53/5.32            ( ( member_complex @ I4 @ A2 )
% 9.53/5.32           => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) )
% 9.53/5.32              & ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 9.53/5.32       => ( ord_less_eq_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) @ ( groups861055069439313189ex_nat @ G @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8747_prod__mono,axiom,
% 9.53/5.32      ! [A2: set_real,F: real > nat,G: real > nat] :
% 9.53/5.32        ( ! [I4: real] :
% 9.53/5.32            ( ( member_real @ I4 @ A2 )
% 9.53/5.32           => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) )
% 9.53/5.32              & ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 9.53/5.32       => ( ord_less_eq_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) @ ( groups4696554848551431203al_nat @ G @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8748_prod__pos,axiom,
% 9.53/5.32      ! [A2: set_nat,F: nat > nat] :
% 9.53/5.32        ( ! [X3: nat] :
% 9.53/5.32            ( ( member_nat @ X3 @ A2 )
% 9.53/5.32           => ( ord_less_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 9.53/5.32       => ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8749_prod__pos,axiom,
% 9.53/5.32      ! [A2: set_nat,F: nat > int] :
% 9.53/5.32        ( ! [X3: nat] :
% 9.53/5.32            ( ( member_nat @ X3 @ A2 )
% 9.53/5.32           => ( ord_less_int @ zero_zero_int @ ( F @ X3 ) ) )
% 9.53/5.32       => ( ord_less_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8750_prod__pos,axiom,
% 9.53/5.32      ! [A2: set_int,F: int > int] :
% 9.53/5.32        ( ! [X3: int] :
% 9.53/5.32            ( ( member_int @ X3 @ A2 )
% 9.53/5.32           => ( ord_less_int @ zero_zero_int @ ( F @ X3 ) ) )
% 9.53/5.32       => ( ord_less_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8751_prod__ge__1,axiom,
% 9.53/5.32      ! [A2: set_complex,F: complex > real] :
% 9.53/5.32        ( ! [X3: complex] :
% 9.53/5.32            ( ( member_complex @ X3 @ A2 )
% 9.53/5.32           => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 9.53/5.32       => ( ord_less_eq_real @ one_one_real @ ( groups766887009212190081x_real @ F @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8752_prod__ge__1,axiom,
% 9.53/5.32      ! [A2: set_real,F: real > real] :
% 9.53/5.32        ( ! [X3: real] :
% 9.53/5.32            ( ( member_real @ X3 @ A2 )
% 9.53/5.32           => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 9.53/5.32       => ( ord_less_eq_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8753_prod__ge__1,axiom,
% 9.53/5.32      ! [A2: set_nat,F: nat > real] :
% 9.53/5.32        ( ! [X3: nat] :
% 9.53/5.32            ( ( member_nat @ X3 @ A2 )
% 9.53/5.32           => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 9.53/5.32       => ( ord_less_eq_real @ one_one_real @ ( groups129246275422532515t_real @ F @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8754_prod__ge__1,axiom,
% 9.53/5.32      ! [A2: set_int,F: int > real] :
% 9.53/5.32        ( ! [X3: int] :
% 9.53/5.32            ( ( member_int @ X3 @ A2 )
% 9.53/5.32           => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 9.53/5.32       => ( ord_less_eq_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8755_prod__ge__1,axiom,
% 9.53/5.32      ! [A2: set_complex,F: complex > rat] :
% 9.53/5.32        ( ! [X3: complex] :
% 9.53/5.32            ( ( member_complex @ X3 @ A2 )
% 9.53/5.32           => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 9.53/5.32       => ( ord_less_eq_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8756_prod__ge__1,axiom,
% 9.53/5.32      ! [A2: set_real,F: real > rat] :
% 9.53/5.32        ( ! [X3: real] :
% 9.53/5.32            ( ( member_real @ X3 @ A2 )
% 9.53/5.32           => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 9.53/5.32       => ( ord_less_eq_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8757_prod__ge__1,axiom,
% 9.53/5.32      ! [A2: set_nat,F: nat > rat] :
% 9.53/5.32        ( ! [X3: nat] :
% 9.53/5.32            ( ( member_nat @ X3 @ A2 )
% 9.53/5.32           => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 9.53/5.32       => ( ord_less_eq_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8758_prod__ge__1,axiom,
% 9.53/5.32      ! [A2: set_int,F: int > rat] :
% 9.53/5.32        ( ! [X3: int] :
% 9.53/5.32            ( ( member_int @ X3 @ A2 )
% 9.53/5.32           => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 9.53/5.32       => ( ord_less_eq_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8759_prod__ge__1,axiom,
% 9.53/5.32      ! [A2: set_complex,F: complex > nat] :
% 9.53/5.32        ( ! [X3: complex] :
% 9.53/5.32            ( ( member_complex @ X3 @ A2 )
% 9.53/5.32           => ( ord_less_eq_nat @ one_one_nat @ ( F @ X3 ) ) )
% 9.53/5.32       => ( ord_less_eq_nat @ one_one_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8760_prod__ge__1,axiom,
% 9.53/5.32      ! [A2: set_real,F: real > nat] :
% 9.53/5.32        ( ! [X3: real] :
% 9.53/5.32            ( ( member_real @ X3 @ A2 )
% 9.53/5.32           => ( ord_less_eq_nat @ one_one_nat @ ( F @ X3 ) ) )
% 9.53/5.32       => ( ord_less_eq_nat @ one_one_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8761_prod__atLeastAtMost__code,axiom,
% 9.53/5.32      ! [F: nat > rat,A: nat,B: nat] :
% 9.53/5.32        ( ( groups73079841787564623at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 9.53/5.32        = ( set_fo1949268297981939178at_rat
% 9.53/5.32          @ ^ [A3: nat] : ( times_times_rat @ ( F @ A3 ) )
% 9.53/5.32          @ A
% 9.53/5.32          @ B
% 9.53/5.32          @ one_one_rat ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8762_prod__atLeastAtMost__code,axiom,
% 9.53/5.32      ! [F: nat > complex,A: nat,B: nat] :
% 9.53/5.32        ( ( groups6464643781859351333omplex @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 9.53/5.32        = ( set_fo1517530859248394432omplex
% 9.53/5.32          @ ^ [A3: nat] : ( times_times_complex @ ( F @ A3 ) )
% 9.53/5.32          @ A
% 9.53/5.32          @ B
% 9.53/5.32          @ one_one_complex ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8763_prod__atLeastAtMost__code,axiom,
% 9.53/5.32      ! [F: nat > real,A: nat,B: nat] :
% 9.53/5.32        ( ( groups129246275422532515t_real @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 9.53/5.32        = ( set_fo3111899725591712190t_real
% 9.53/5.32          @ ^ [A3: nat] : ( times_times_real @ ( F @ A3 ) )
% 9.53/5.32          @ A
% 9.53/5.32          @ B
% 9.53/5.32          @ one_one_real ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8764_prod__atLeastAtMost__code,axiom,
% 9.53/5.32      ! [F: nat > nat,A: nat,B: nat] :
% 9.53/5.32        ( ( groups708209901874060359at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 9.53/5.32        = ( set_fo2584398358068434914at_nat
% 9.53/5.32          @ ^ [A3: nat] : ( times_times_nat @ ( F @ A3 ) )
% 9.53/5.32          @ A
% 9.53/5.32          @ B
% 9.53/5.32          @ one_one_nat ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8765_prod__atLeastAtMost__code,axiom,
% 9.53/5.32      ! [F: nat > int,A: nat,B: nat] :
% 9.53/5.32        ( ( groups705719431365010083at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 9.53/5.32        = ( set_fo2581907887559384638at_int
% 9.53/5.32          @ ^ [A3: nat] : ( times_times_int @ ( F @ A3 ) )
% 9.53/5.32          @ A
% 9.53/5.32          @ B
% 9.53/5.32          @ one_one_int ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8766_prod_Ointer__filter,axiom,
% 9.53/5.32      ! [A2: set_int,G: int > complex,P: int > $o] :
% 9.53/5.32        ( ( finite_finite_int @ A2 )
% 9.53/5.32       => ( ( groups7440179247065528705omplex @ G
% 9.53/5.32            @ ( collect_int
% 9.53/5.32              @ ^ [X2: int] :
% 9.53/5.32                  ( ( member_int @ X2 @ A2 )
% 9.53/5.32                  & ( P @ X2 ) ) ) )
% 9.53/5.32          = ( groups7440179247065528705omplex
% 9.53/5.32            @ ^ [X2: int] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_complex )
% 9.53/5.32            @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8767_prod_Ointer__filter,axiom,
% 9.53/5.32      ! [A2: set_real,G: real > complex,P: real > $o] :
% 9.53/5.32        ( ( finite_finite_real @ A2 )
% 9.53/5.32       => ( ( groups713298508707869441omplex @ G
% 9.53/5.32            @ ( collect_real
% 9.53/5.32              @ ^ [X2: real] :
% 9.53/5.32                  ( ( member_real @ X2 @ A2 )
% 9.53/5.32                  & ( P @ X2 ) ) ) )
% 9.53/5.32          = ( groups713298508707869441omplex
% 9.53/5.32            @ ^ [X2: real] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_complex )
% 9.53/5.32            @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8768_prod_Ointer__filter,axiom,
% 9.53/5.32      ! [A2: set_nat,G: nat > complex,P: nat > $o] :
% 9.53/5.32        ( ( finite_finite_nat @ A2 )
% 9.53/5.32       => ( ( groups6464643781859351333omplex @ G
% 9.53/5.32            @ ( collect_nat
% 9.53/5.32              @ ^ [X2: nat] :
% 9.53/5.32                  ( ( member_nat @ X2 @ A2 )
% 9.53/5.32                  & ( P @ X2 ) ) ) )
% 9.53/5.32          = ( groups6464643781859351333omplex
% 9.53/5.32            @ ^ [X2: nat] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_complex )
% 9.53/5.32            @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8769_prod_Ointer__filter,axiom,
% 9.53/5.32      ! [A2: set_complex,G: complex > complex,P: complex > $o] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.32       => ( ( groups3708469109370488835omplex @ G
% 9.53/5.32            @ ( collect_complex
% 9.53/5.32              @ ^ [X2: complex] :
% 9.53/5.32                  ( ( member_complex @ X2 @ A2 )
% 9.53/5.32                  & ( P @ X2 ) ) ) )
% 9.53/5.32          = ( groups3708469109370488835omplex
% 9.53/5.32            @ ^ [X2: complex] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_complex )
% 9.53/5.32            @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8770_prod_Ointer__filter,axiom,
% 9.53/5.32      ! [A2: set_int,G: int > real,P: int > $o] :
% 9.53/5.32        ( ( finite_finite_int @ A2 )
% 9.53/5.32       => ( ( groups2316167850115554303t_real @ G
% 9.53/5.32            @ ( collect_int
% 9.53/5.32              @ ^ [X2: int] :
% 9.53/5.32                  ( ( member_int @ X2 @ A2 )
% 9.53/5.32                  & ( P @ X2 ) ) ) )
% 9.53/5.32          = ( groups2316167850115554303t_real
% 9.53/5.32            @ ^ [X2: int] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_real )
% 9.53/5.32            @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8771_prod_Ointer__filter,axiom,
% 9.53/5.32      ! [A2: set_real,G: real > real,P: real > $o] :
% 9.53/5.32        ( ( finite_finite_real @ A2 )
% 9.53/5.32       => ( ( groups1681761925125756287l_real @ G
% 9.53/5.32            @ ( collect_real
% 9.53/5.32              @ ^ [X2: real] :
% 9.53/5.32                  ( ( member_real @ X2 @ A2 )
% 9.53/5.32                  & ( P @ X2 ) ) ) )
% 9.53/5.32          = ( groups1681761925125756287l_real
% 9.53/5.32            @ ^ [X2: real] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_real )
% 9.53/5.32            @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8772_prod_Ointer__filter,axiom,
% 9.53/5.32      ! [A2: set_nat,G: nat > real,P: nat > $o] :
% 9.53/5.32        ( ( finite_finite_nat @ A2 )
% 9.53/5.32       => ( ( groups129246275422532515t_real @ G
% 9.53/5.32            @ ( collect_nat
% 9.53/5.32              @ ^ [X2: nat] :
% 9.53/5.32                  ( ( member_nat @ X2 @ A2 )
% 9.53/5.32                  & ( P @ X2 ) ) ) )
% 9.53/5.32          = ( groups129246275422532515t_real
% 9.53/5.32            @ ^ [X2: nat] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_real )
% 9.53/5.32            @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8773_prod_Ointer__filter,axiom,
% 9.53/5.32      ! [A2: set_complex,G: complex > real,P: complex > $o] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.32       => ( ( groups766887009212190081x_real @ G
% 9.53/5.32            @ ( collect_complex
% 9.53/5.32              @ ^ [X2: complex] :
% 9.53/5.32                  ( ( member_complex @ X2 @ A2 )
% 9.53/5.32                  & ( P @ X2 ) ) ) )
% 9.53/5.32          = ( groups766887009212190081x_real
% 9.53/5.32            @ ^ [X2: complex] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_real )
% 9.53/5.32            @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8774_prod_Ointer__filter,axiom,
% 9.53/5.32      ! [A2: set_int,G: int > rat,P: int > $o] :
% 9.53/5.32        ( ( finite_finite_int @ A2 )
% 9.53/5.32       => ( ( groups1072433553688619179nt_rat @ G
% 9.53/5.32            @ ( collect_int
% 9.53/5.32              @ ^ [X2: int] :
% 9.53/5.32                  ( ( member_int @ X2 @ A2 )
% 9.53/5.32                  & ( P @ X2 ) ) ) )
% 9.53/5.32          = ( groups1072433553688619179nt_rat
% 9.53/5.32            @ ^ [X2: int] : ( if_rat @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_rat )
% 9.53/5.32            @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8775_prod_Ointer__filter,axiom,
% 9.53/5.32      ! [A2: set_real,G: real > rat,P: real > $o] :
% 9.53/5.32        ( ( finite_finite_real @ A2 )
% 9.53/5.32       => ( ( groups4061424788464935467al_rat @ G
% 9.53/5.32            @ ( collect_real
% 9.53/5.32              @ ^ [X2: real] :
% 9.53/5.32                  ( ( member_real @ X2 @ A2 )
% 9.53/5.32                  & ( P @ X2 ) ) ) )
% 9.53/5.32          = ( groups4061424788464935467al_rat
% 9.53/5.32            @ ^ [X2: real] : ( if_rat @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_rat )
% 9.53/5.32            @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8776_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 9.53/5.32      ! [G: nat > nat,M: nat,N: nat] :
% 9.53/5.32        ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 9.53/5.32        = ( groups708209901874060359at_nat
% 9.53/5.32          @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.53/5.32          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8777_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 9.53/5.32      ! [G: nat > int,M: nat,N: nat] :
% 9.53/5.32        ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 9.53/5.32        = ( groups705719431365010083at_int
% 9.53/5.32          @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.53/5.32          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8778_power__sum,axiom,
% 9.53/5.32      ! [C: real,F: nat > nat,A2: set_nat] :
% 9.53/5.32        ( ( power_power_real @ C @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 9.53/5.32        = ( groups129246275422532515t_real
% 9.53/5.32          @ ^ [A3: nat] : ( power_power_real @ C @ ( F @ A3 ) )
% 9.53/5.32          @ A2 ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8779_power__sum,axiom,
% 9.53/5.32      ! [C: complex,F: nat > nat,A2: set_nat] :
% 9.53/5.32        ( ( power_power_complex @ C @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 9.53/5.32        = ( groups6464643781859351333omplex
% 9.53/5.32          @ ^ [A3: nat] : ( power_power_complex @ C @ ( F @ A3 ) )
% 9.53/5.32          @ A2 ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8780_power__sum,axiom,
% 9.53/5.32      ! [C: nat,F: nat > nat,A2: set_nat] :
% 9.53/5.32        ( ( power_power_nat @ C @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 9.53/5.32        = ( groups708209901874060359at_nat
% 9.53/5.32          @ ^ [A3: nat] : ( power_power_nat @ C @ ( F @ A3 ) )
% 9.53/5.32          @ A2 ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8781_power__sum,axiom,
% 9.53/5.32      ! [C: int,F: nat > nat,A2: set_nat] :
% 9.53/5.32        ( ( power_power_int @ C @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 9.53/5.32        = ( groups705719431365010083at_int
% 9.53/5.32          @ ^ [A3: nat] : ( power_power_int @ C @ ( F @ A3 ) )
% 9.53/5.32          @ A2 ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8782_power__sum,axiom,
% 9.53/5.32      ! [C: int,F: int > nat,A2: set_int] :
% 9.53/5.32        ( ( power_power_int @ C @ ( groups4541462559716669496nt_nat @ F @ A2 ) )
% 9.53/5.32        = ( groups1705073143266064639nt_int
% 9.53/5.32          @ ^ [A3: int] : ( power_power_int @ C @ ( F @ A3 ) )
% 9.53/5.32          @ A2 ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8783_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 9.53/5.32      ! [G: nat > nat,M: nat,K: nat,N: nat] :
% 9.53/5.32        ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 9.53/5.32        = ( groups708209901874060359at_nat
% 9.53/5.32          @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 9.53/5.32          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8784_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 9.53/5.32      ! [G: nat > int,M: nat,K: nat,N: nat] :
% 9.53/5.32        ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 9.53/5.32        = ( groups705719431365010083at_int
% 9.53/5.32          @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 9.53/5.32          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8785_frac__ge__0,axiom,
% 9.53/5.32      ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( archim2898591450579166408c_real @ X ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8786_frac__ge__0,axiom,
% 9.53/5.32      ! [X: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( archimedean_frac_rat @ X ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8787_frac__lt__1,axiom,
% 9.53/5.32      ! [X: real] : ( ord_less_real @ ( archim2898591450579166408c_real @ X ) @ one_one_real ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8788_frac__lt__1,axiom,
% 9.53/5.32      ! [X: rat] : ( ord_less_rat @ ( archimedean_frac_rat @ X ) @ one_one_rat ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8789_prod__le__1,axiom,
% 9.53/5.32      ! [A2: set_complex,F: complex > real] :
% 9.53/5.32        ( ! [X3: complex] :
% 9.53/5.32            ( ( member_complex @ X3 @ A2 )
% 9.53/5.32           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 9.53/5.32              & ( ord_less_eq_real @ ( F @ X3 ) @ one_one_real ) ) )
% 9.53/5.32       => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A2 ) @ one_one_real ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8790_prod__le__1,axiom,
% 9.53/5.32      ! [A2: set_real,F: real > real] :
% 9.53/5.32        ( ! [X3: real] :
% 9.53/5.32            ( ( member_real @ X3 @ A2 )
% 9.53/5.32           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 9.53/5.32              & ( ord_less_eq_real @ ( F @ X3 ) @ one_one_real ) ) )
% 9.53/5.32       => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ one_one_real ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8791_prod__le__1,axiom,
% 9.53/5.32      ! [A2: set_nat,F: nat > real] :
% 9.53/5.32        ( ! [X3: nat] :
% 9.53/5.32            ( ( member_nat @ X3 @ A2 )
% 9.53/5.32           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 9.53/5.32              & ( ord_less_eq_real @ ( F @ X3 ) @ one_one_real ) ) )
% 9.53/5.32       => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ one_one_real ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8792_prod__le__1,axiom,
% 9.53/5.32      ! [A2: set_int,F: int > real] :
% 9.53/5.32        ( ! [X3: int] :
% 9.53/5.32            ( ( member_int @ X3 @ A2 )
% 9.53/5.32           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 9.53/5.32              & ( ord_less_eq_real @ ( F @ X3 ) @ one_one_real ) ) )
% 9.53/5.32       => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ one_one_real ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8793_prod__le__1,axiom,
% 9.53/5.32      ! [A2: set_complex,F: complex > rat] :
% 9.53/5.32        ( ! [X3: complex] :
% 9.53/5.32            ( ( member_complex @ X3 @ A2 )
% 9.53/5.32           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 9.53/5.32              & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 9.53/5.32       => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8794_prod__le__1,axiom,
% 9.53/5.32      ! [A2: set_real,F: real > rat] :
% 9.53/5.32        ( ! [X3: real] :
% 9.53/5.32            ( ( member_real @ X3 @ A2 )
% 9.53/5.32           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 9.53/5.32              & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 9.53/5.32       => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8795_prod__le__1,axiom,
% 9.53/5.32      ! [A2: set_nat,F: nat > rat] :
% 9.53/5.32        ( ! [X3: nat] :
% 9.53/5.32            ( ( member_nat @ X3 @ A2 )
% 9.53/5.32           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 9.53/5.32              & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 9.53/5.32       => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8796_prod__le__1,axiom,
% 9.53/5.32      ! [A2: set_int,F: int > rat] :
% 9.53/5.32        ( ! [X3: int] :
% 9.53/5.32            ( ( member_int @ X3 @ A2 )
% 9.53/5.32           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 9.53/5.32              & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 9.53/5.32       => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8797_prod__le__1,axiom,
% 9.53/5.32      ! [A2: set_complex,F: complex > nat] :
% 9.53/5.32        ( ! [X3: complex] :
% 9.53/5.32            ( ( member_complex @ X3 @ A2 )
% 9.53/5.32           => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) )
% 9.53/5.32              & ( ord_less_eq_nat @ ( F @ X3 ) @ one_one_nat ) ) )
% 9.53/5.32       => ( ord_less_eq_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) @ one_one_nat ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8798_prod__le__1,axiom,
% 9.53/5.32      ! [A2: set_real,F: real > nat] :
% 9.53/5.32        ( ! [X3: real] :
% 9.53/5.32            ( ( member_real @ X3 @ A2 )
% 9.53/5.32           => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) )
% 9.53/5.32              & ( ord_less_eq_nat @ ( F @ X3 ) @ one_one_nat ) ) )
% 9.53/5.32       => ( ord_less_eq_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) @ one_one_nat ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8799_frac__1__eq,axiom,
% 9.53/5.32      ! [X: real] :
% 9.53/5.32        ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X @ one_one_real ) )
% 9.53/5.32        = ( archim2898591450579166408c_real @ X ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8800_frac__1__eq,axiom,
% 9.53/5.32      ! [X: rat] :
% 9.53/5.32        ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ one_one_rat ) )
% 9.53/5.32        = ( archimedean_frac_rat @ X ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8801_prod_Orelated,axiom,
% 9.53/5.32      ! [R2: rat > rat > $o,S2: set_nat,H2: nat > rat,G: nat > rat] :
% 9.53/5.32        ( ( R2 @ one_one_rat @ one_one_rat )
% 9.53/5.32       => ( ! [X15: rat,Y15: rat,X22: rat,Y23: rat] :
% 9.53/5.32              ( ( ( R2 @ X15 @ X22 )
% 9.53/5.32                & ( R2 @ Y15 @ Y23 ) )
% 9.53/5.32             => ( R2 @ ( times_times_rat @ X15 @ Y15 ) @ ( times_times_rat @ X22 @ Y23 ) ) )
% 9.53/5.32         => ( ( finite_finite_nat @ S2 )
% 9.53/5.32           => ( ! [X3: nat] :
% 9.53/5.32                  ( ( member_nat @ X3 @ S2 )
% 9.53/5.32                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 9.53/5.32             => ( R2 @ ( groups73079841787564623at_rat @ H2 @ S2 ) @ ( groups73079841787564623at_rat @ G @ S2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8802_prod_Orelated,axiom,
% 9.53/5.32      ! [R2: rat > rat > $o,S2: set_complex,H2: complex > rat,G: complex > rat] :
% 9.53/5.32        ( ( R2 @ one_one_rat @ one_one_rat )
% 9.53/5.32       => ( ! [X15: rat,Y15: rat,X22: rat,Y23: rat] :
% 9.53/5.32              ( ( ( R2 @ X15 @ X22 )
% 9.53/5.32                & ( R2 @ Y15 @ Y23 ) )
% 9.53/5.32             => ( R2 @ ( times_times_rat @ X15 @ Y15 ) @ ( times_times_rat @ X22 @ Y23 ) ) )
% 9.53/5.32         => ( ( finite3207457112153483333omplex @ S2 )
% 9.53/5.32           => ( ! [X3: complex] :
% 9.53/5.32                  ( ( member_complex @ X3 @ S2 )
% 9.53/5.32                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 9.53/5.32             => ( R2 @ ( groups225925009352817453ex_rat @ H2 @ S2 ) @ ( groups225925009352817453ex_rat @ G @ S2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8803_prod_Orelated,axiom,
% 9.53/5.32      ! [R2: complex > complex > $o,S2: set_nat,H2: nat > complex,G: nat > complex] :
% 9.53/5.32        ( ( R2 @ one_one_complex @ one_one_complex )
% 9.53/5.32       => ( ! [X15: complex,Y15: complex,X22: complex,Y23: complex] :
% 9.53/5.32              ( ( ( R2 @ X15 @ X22 )
% 9.53/5.32                & ( R2 @ Y15 @ Y23 ) )
% 9.53/5.32             => ( R2 @ ( times_times_complex @ X15 @ Y15 ) @ ( times_times_complex @ X22 @ Y23 ) ) )
% 9.53/5.32         => ( ( finite_finite_nat @ S2 )
% 9.53/5.32           => ( ! [X3: nat] :
% 9.53/5.32                  ( ( member_nat @ X3 @ S2 )
% 9.53/5.32                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 9.53/5.32             => ( R2 @ ( groups6464643781859351333omplex @ H2 @ S2 ) @ ( groups6464643781859351333omplex @ G @ S2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8804_prod_Orelated,axiom,
% 9.53/5.32      ! [R2: complex > complex > $o,S2: set_complex,H2: complex > complex,G: complex > complex] :
% 9.53/5.32        ( ( R2 @ one_one_complex @ one_one_complex )
% 9.53/5.32       => ( ! [X15: complex,Y15: complex,X22: complex,Y23: complex] :
% 9.53/5.32              ( ( ( R2 @ X15 @ X22 )
% 9.53/5.32                & ( R2 @ Y15 @ Y23 ) )
% 9.53/5.32             => ( R2 @ ( times_times_complex @ X15 @ Y15 ) @ ( times_times_complex @ X22 @ Y23 ) ) )
% 9.53/5.32         => ( ( finite3207457112153483333omplex @ S2 )
% 9.53/5.32           => ( ! [X3: complex] :
% 9.53/5.32                  ( ( member_complex @ X3 @ S2 )
% 9.53/5.32                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 9.53/5.32             => ( R2 @ ( groups3708469109370488835omplex @ H2 @ S2 ) @ ( groups3708469109370488835omplex @ G @ S2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8805_prod_Orelated,axiom,
% 9.53/5.32      ! [R2: real > real > $o,S2: set_nat,H2: nat > real,G: nat > real] :
% 9.53/5.32        ( ( R2 @ one_one_real @ one_one_real )
% 9.53/5.32       => ( ! [X15: real,Y15: real,X22: real,Y23: real] :
% 9.53/5.32              ( ( ( R2 @ X15 @ X22 )
% 9.53/5.32                & ( R2 @ Y15 @ Y23 ) )
% 9.53/5.32             => ( R2 @ ( times_times_real @ X15 @ Y15 ) @ ( times_times_real @ X22 @ Y23 ) ) )
% 9.53/5.32         => ( ( finite_finite_nat @ S2 )
% 9.53/5.32           => ( ! [X3: nat] :
% 9.53/5.32                  ( ( member_nat @ X3 @ S2 )
% 9.53/5.32                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 9.53/5.32             => ( R2 @ ( groups129246275422532515t_real @ H2 @ S2 ) @ ( groups129246275422532515t_real @ G @ S2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8806_prod_Orelated,axiom,
% 9.53/5.32      ! [R2: real > real > $o,S2: set_complex,H2: complex > real,G: complex > real] :
% 9.53/5.32        ( ( R2 @ one_one_real @ one_one_real )
% 9.53/5.32       => ( ! [X15: real,Y15: real,X22: real,Y23: real] :
% 9.53/5.32              ( ( ( R2 @ X15 @ X22 )
% 9.53/5.32                & ( R2 @ Y15 @ Y23 ) )
% 9.53/5.32             => ( R2 @ ( times_times_real @ X15 @ Y15 ) @ ( times_times_real @ X22 @ Y23 ) ) )
% 9.53/5.32         => ( ( finite3207457112153483333omplex @ S2 )
% 9.53/5.32           => ( ! [X3: complex] :
% 9.53/5.32                  ( ( member_complex @ X3 @ S2 )
% 9.53/5.32                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 9.53/5.32             => ( R2 @ ( groups766887009212190081x_real @ H2 @ S2 ) @ ( groups766887009212190081x_real @ G @ S2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8807_prod_Orelated,axiom,
% 9.53/5.32      ! [R2: nat > nat > $o,S2: set_complex,H2: complex > nat,G: complex > nat] :
% 9.53/5.32        ( ( R2 @ one_one_nat @ one_one_nat )
% 9.53/5.32       => ( ! [X15: nat,Y15: nat,X22: nat,Y23: nat] :
% 9.53/5.32              ( ( ( R2 @ X15 @ X22 )
% 9.53/5.32                & ( R2 @ Y15 @ Y23 ) )
% 9.53/5.32             => ( R2 @ ( times_times_nat @ X15 @ Y15 ) @ ( times_times_nat @ X22 @ Y23 ) ) )
% 9.53/5.32         => ( ( finite3207457112153483333omplex @ S2 )
% 9.53/5.32           => ( ! [X3: complex] :
% 9.53/5.32                  ( ( member_complex @ X3 @ S2 )
% 9.53/5.32                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 9.53/5.32             => ( R2 @ ( groups861055069439313189ex_nat @ H2 @ S2 ) @ ( groups861055069439313189ex_nat @ G @ S2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8808_prod_Orelated,axiom,
% 9.53/5.32      ! [R2: int > int > $o,S2: set_complex,H2: complex > int,G: complex > int] :
% 9.53/5.32        ( ( R2 @ one_one_int @ one_one_int )
% 9.53/5.32       => ( ! [X15: int,Y15: int,X22: int,Y23: int] :
% 9.53/5.32              ( ( ( R2 @ X15 @ X22 )
% 9.53/5.32                & ( R2 @ Y15 @ Y23 ) )
% 9.53/5.32             => ( R2 @ ( times_times_int @ X15 @ Y15 ) @ ( times_times_int @ X22 @ Y23 ) ) )
% 9.53/5.32         => ( ( finite3207457112153483333omplex @ S2 )
% 9.53/5.32           => ( ! [X3: complex] :
% 9.53/5.32                  ( ( member_complex @ X3 @ S2 )
% 9.53/5.32                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 9.53/5.32             => ( R2 @ ( groups858564598930262913ex_int @ H2 @ S2 ) @ ( groups858564598930262913ex_int @ G @ S2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8809_prod_Orelated,axiom,
% 9.53/5.32      ! [R2: nat > nat > $o,S2: set_nat,H2: nat > nat,G: nat > nat] :
% 9.53/5.32        ( ( R2 @ one_one_nat @ one_one_nat )
% 9.53/5.32       => ( ! [X15: nat,Y15: nat,X22: nat,Y23: nat] :
% 9.53/5.32              ( ( ( R2 @ X15 @ X22 )
% 9.53/5.32                & ( R2 @ Y15 @ Y23 ) )
% 9.53/5.32             => ( R2 @ ( times_times_nat @ X15 @ Y15 ) @ ( times_times_nat @ X22 @ Y23 ) ) )
% 9.53/5.32         => ( ( finite_finite_nat @ S2 )
% 9.53/5.32           => ( ! [X3: nat] :
% 9.53/5.32                  ( ( member_nat @ X3 @ S2 )
% 9.53/5.32                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 9.53/5.32             => ( R2 @ ( groups708209901874060359at_nat @ H2 @ S2 ) @ ( groups708209901874060359at_nat @ G @ S2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8810_prod_Orelated,axiom,
% 9.53/5.32      ! [R2: int > int > $o,S2: set_nat,H2: nat > int,G: nat > int] :
% 9.53/5.32        ( ( R2 @ one_one_int @ one_one_int )
% 9.53/5.32       => ( ! [X15: int,Y15: int,X22: int,Y23: int] :
% 9.53/5.32              ( ( ( R2 @ X15 @ X22 )
% 9.53/5.32                & ( R2 @ Y15 @ Y23 ) )
% 9.53/5.32             => ( R2 @ ( times_times_int @ X15 @ Y15 ) @ ( times_times_int @ X22 @ Y23 ) ) )
% 9.53/5.32         => ( ( finite_finite_nat @ S2 )
% 9.53/5.32           => ( ! [X3: nat] :
% 9.53/5.32                  ( ( member_nat @ X3 @ S2 )
% 9.53/5.32                 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 9.53/5.32             => ( R2 @ ( groups705719431365010083at_int @ H2 @ S2 ) @ ( groups705719431365010083at_int @ G @ S2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8811_prod_Oinsert__if,axiom,
% 9.53/5.32      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > complex] :
% 9.53/5.32        ( ( finite5795047828879050333T_VEBT @ A2 )
% 9.53/5.32       => ( ( ( member_VEBT_VEBT @ X @ A2 )
% 9.53/5.32           => ( ( groups127312072573709053omplex @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 9.53/5.32              = ( groups127312072573709053omplex @ G @ A2 ) ) )
% 9.53/5.32          & ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 9.53/5.32           => ( ( groups127312072573709053omplex @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 9.53/5.32              = ( times_times_complex @ ( G @ X ) @ ( groups127312072573709053omplex @ G @ A2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8812_prod_Oinsert__if,axiom,
% 9.53/5.32      ! [A2: set_real,X: real,G: real > complex] :
% 9.53/5.32        ( ( finite_finite_real @ A2 )
% 9.53/5.32       => ( ( ( member_real @ X @ A2 )
% 9.53/5.32           => ( ( groups713298508707869441omplex @ G @ ( insert_real @ X @ A2 ) )
% 9.53/5.32              = ( groups713298508707869441omplex @ G @ A2 ) ) )
% 9.53/5.32          & ( ~ ( member_real @ X @ A2 )
% 9.53/5.32           => ( ( groups713298508707869441omplex @ G @ ( insert_real @ X @ A2 ) )
% 9.53/5.32              = ( times_times_complex @ ( G @ X ) @ ( groups713298508707869441omplex @ G @ A2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8813_prod_Oinsert__if,axiom,
% 9.53/5.32      ! [A2: set_int,X: int,G: int > complex] :
% 9.53/5.32        ( ( finite_finite_int @ A2 )
% 9.53/5.32       => ( ( ( member_int @ X @ A2 )
% 9.53/5.32           => ( ( groups7440179247065528705omplex @ G @ ( insert_int @ X @ A2 ) )
% 9.53/5.32              = ( groups7440179247065528705omplex @ G @ A2 ) ) )
% 9.53/5.32          & ( ~ ( member_int @ X @ A2 )
% 9.53/5.32           => ( ( groups7440179247065528705omplex @ G @ ( insert_int @ X @ A2 ) )
% 9.53/5.32              = ( times_times_complex @ ( G @ X ) @ ( groups7440179247065528705omplex @ G @ A2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8814_prod_Oinsert__if,axiom,
% 9.53/5.32      ! [A2: set_nat,X: nat,G: nat > complex] :
% 9.53/5.32        ( ( finite_finite_nat @ A2 )
% 9.53/5.32       => ( ( ( member_nat @ X @ A2 )
% 9.53/5.32           => ( ( groups6464643781859351333omplex @ G @ ( insert_nat @ X @ A2 ) )
% 9.53/5.32              = ( groups6464643781859351333omplex @ G @ A2 ) ) )
% 9.53/5.32          & ( ~ ( member_nat @ X @ A2 )
% 9.53/5.32           => ( ( groups6464643781859351333omplex @ G @ ( insert_nat @ X @ A2 ) )
% 9.53/5.32              = ( times_times_complex @ ( G @ X ) @ ( groups6464643781859351333omplex @ G @ A2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8815_prod_Oinsert__if,axiom,
% 9.53/5.32      ! [A2: set_complex,X: complex,G: complex > complex] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.32       => ( ( ( member_complex @ X @ A2 )
% 9.53/5.32           => ( ( groups3708469109370488835omplex @ G @ ( insert_complex @ X @ A2 ) )
% 9.53/5.32              = ( groups3708469109370488835omplex @ G @ A2 ) ) )
% 9.53/5.32          & ( ~ ( member_complex @ X @ A2 )
% 9.53/5.32           => ( ( groups3708469109370488835omplex @ G @ ( insert_complex @ X @ A2 ) )
% 9.53/5.32              = ( times_times_complex @ ( G @ X ) @ ( groups3708469109370488835omplex @ G @ A2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8816_prod_Oinsert__if,axiom,
% 9.53/5.32      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > real] :
% 9.53/5.32        ( ( finite5795047828879050333T_VEBT @ A2 )
% 9.53/5.32       => ( ( ( member_VEBT_VEBT @ X @ A2 )
% 9.53/5.32           => ( ( groups2703838992350267259T_real @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 9.53/5.32              = ( groups2703838992350267259T_real @ G @ A2 ) ) )
% 9.53/5.32          & ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 9.53/5.32           => ( ( groups2703838992350267259T_real @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 9.53/5.32              = ( times_times_real @ ( G @ X ) @ ( groups2703838992350267259T_real @ G @ A2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8817_prod_Oinsert__if,axiom,
% 9.53/5.32      ! [A2: set_real,X: real,G: real > real] :
% 9.53/5.32        ( ( finite_finite_real @ A2 )
% 9.53/5.32       => ( ( ( member_real @ X @ A2 )
% 9.53/5.32           => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X @ A2 ) )
% 9.53/5.32              = ( groups1681761925125756287l_real @ G @ A2 ) ) )
% 9.53/5.32          & ( ~ ( member_real @ X @ A2 )
% 9.53/5.32           => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X @ A2 ) )
% 9.53/5.32              = ( times_times_real @ ( G @ X ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8818_prod_Oinsert__if,axiom,
% 9.53/5.32      ! [A2: set_int,X: int,G: int > real] :
% 9.53/5.32        ( ( finite_finite_int @ A2 )
% 9.53/5.32       => ( ( ( member_int @ X @ A2 )
% 9.53/5.32           => ( ( groups2316167850115554303t_real @ G @ ( insert_int @ X @ A2 ) )
% 9.53/5.32              = ( groups2316167850115554303t_real @ G @ A2 ) ) )
% 9.53/5.32          & ( ~ ( member_int @ X @ A2 )
% 9.53/5.32           => ( ( groups2316167850115554303t_real @ G @ ( insert_int @ X @ A2 ) )
% 9.53/5.32              = ( times_times_real @ ( G @ X ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8819_prod_Oinsert__if,axiom,
% 9.53/5.32      ! [A2: set_nat,X: nat,G: nat > real] :
% 9.53/5.32        ( ( finite_finite_nat @ A2 )
% 9.53/5.32       => ( ( ( member_nat @ X @ A2 )
% 9.53/5.32           => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X @ A2 ) )
% 9.53/5.32              = ( groups129246275422532515t_real @ G @ A2 ) ) )
% 9.53/5.32          & ( ~ ( member_nat @ X @ A2 )
% 9.53/5.32           => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X @ A2 ) )
% 9.53/5.32              = ( times_times_real @ ( G @ X ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8820_prod_Oinsert__if,axiom,
% 9.53/5.32      ! [A2: set_complex,X: complex,G: complex > real] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.32       => ( ( ( member_complex @ X @ A2 )
% 9.53/5.32           => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X @ A2 ) )
% 9.53/5.32              = ( groups766887009212190081x_real @ G @ A2 ) ) )
% 9.53/5.32          & ( ~ ( member_complex @ X @ A2 )
% 9.53/5.32           => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X @ A2 ) )
% 9.53/5.32              = ( times_times_real @ ( G @ X ) @ ( groups766887009212190081x_real @ G @ A2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8821_prod_Oreindex__bij__witness__not__neutral,axiom,
% 9.53/5.32      ! [S5: set_real,T5: set_real,S2: set_real,I2: real > real,J: real > real,T4: set_real,G: real > complex,H2: real > complex] :
% 9.53/5.32        ( ( finite_finite_real @ S5 )
% 9.53/5.32       => ( ( finite_finite_real @ T5 )
% 9.53/5.32         => ( ! [A4: real] :
% 9.53/5.32                ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 9.53/5.32               => ( ( I2 @ ( J @ A4 ) )
% 9.53/5.32                  = A4 ) )
% 9.53/5.32           => ( ! [A4: real] :
% 9.53/5.32                  ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 9.53/5.32                 => ( member_real @ ( J @ A4 ) @ ( minus_minus_set_real @ T4 @ T5 ) ) )
% 9.53/5.32             => ( ! [B3: real] :
% 9.53/5.32                    ( ( member_real @ B3 @ ( minus_minus_set_real @ T4 @ T5 ) )
% 9.53/5.32                   => ( ( J @ ( I2 @ B3 ) )
% 9.53/5.32                      = B3 ) )
% 9.53/5.32               => ( ! [B3: real] :
% 9.53/5.32                      ( ( member_real @ B3 @ ( minus_minus_set_real @ T4 @ T5 ) )
% 9.53/5.32                     => ( member_real @ ( I2 @ B3 ) @ ( minus_minus_set_real @ S2 @ S5 ) ) )
% 9.53/5.32                 => ( ! [A4: real] :
% 9.53/5.32                        ( ( member_real @ A4 @ S5 )
% 9.53/5.32                       => ( ( G @ A4 )
% 9.53/5.32                          = one_one_complex ) )
% 9.53/5.32                   => ( ! [B3: real] :
% 9.53/5.32                          ( ( member_real @ B3 @ T5 )
% 9.53/5.32                         => ( ( H2 @ B3 )
% 9.53/5.32                            = one_one_complex ) )
% 9.53/5.32                     => ( ! [A4: real] :
% 9.53/5.32                            ( ( member_real @ A4 @ S2 )
% 9.53/5.32                           => ( ( H2 @ ( J @ A4 ) )
% 9.53/5.32                              = ( G @ A4 ) ) )
% 9.53/5.32                       => ( ( groups713298508707869441omplex @ G @ S2 )
% 9.53/5.32                          = ( groups713298508707869441omplex @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8822_prod_Oreindex__bij__witness__not__neutral,axiom,
% 9.53/5.32      ! [S5: set_real,T5: set_int,S2: set_real,I2: int > real,J: real > int,T4: set_int,G: real > complex,H2: int > complex] :
% 9.53/5.32        ( ( finite_finite_real @ S5 )
% 9.53/5.32       => ( ( finite_finite_int @ T5 )
% 9.53/5.32         => ( ! [A4: real] :
% 9.53/5.32                ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 9.53/5.32               => ( ( I2 @ ( J @ A4 ) )
% 9.53/5.32                  = A4 ) )
% 9.53/5.32           => ( ! [A4: real] :
% 9.53/5.32                  ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 9.53/5.32                 => ( member_int @ ( J @ A4 ) @ ( minus_minus_set_int @ T4 @ T5 ) ) )
% 9.53/5.32             => ( ! [B3: int] :
% 9.53/5.32                    ( ( member_int @ B3 @ ( minus_minus_set_int @ T4 @ T5 ) )
% 9.53/5.32                   => ( ( J @ ( I2 @ B3 ) )
% 9.53/5.32                      = B3 ) )
% 9.53/5.32               => ( ! [B3: int] :
% 9.53/5.32                      ( ( member_int @ B3 @ ( minus_minus_set_int @ T4 @ T5 ) )
% 9.53/5.32                     => ( member_real @ ( I2 @ B3 ) @ ( minus_minus_set_real @ S2 @ S5 ) ) )
% 9.53/5.32                 => ( ! [A4: real] :
% 9.53/5.32                        ( ( member_real @ A4 @ S5 )
% 9.53/5.32                       => ( ( G @ A4 )
% 9.53/5.32                          = one_one_complex ) )
% 9.53/5.32                   => ( ! [B3: int] :
% 9.53/5.32                          ( ( member_int @ B3 @ T5 )
% 9.53/5.32                         => ( ( H2 @ B3 )
% 9.53/5.32                            = one_one_complex ) )
% 9.53/5.32                     => ( ! [A4: real] :
% 9.53/5.32                            ( ( member_real @ A4 @ S2 )
% 9.53/5.32                           => ( ( H2 @ ( J @ A4 ) )
% 9.53/5.32                              = ( G @ A4 ) ) )
% 9.53/5.32                       => ( ( groups713298508707869441omplex @ G @ S2 )
% 9.53/5.32                          = ( groups7440179247065528705omplex @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8823_prod_Oreindex__bij__witness__not__neutral,axiom,
% 9.53/5.32      ! [S5: set_int,T5: set_real,S2: set_int,I2: real > int,J: int > real,T4: set_real,G: int > complex,H2: real > complex] :
% 9.53/5.32        ( ( finite_finite_int @ S5 )
% 9.53/5.32       => ( ( finite_finite_real @ T5 )
% 9.53/5.32         => ( ! [A4: int] :
% 9.53/5.32                ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 9.53/5.32               => ( ( I2 @ ( J @ A4 ) )
% 9.53/5.32                  = A4 ) )
% 9.53/5.32           => ( ! [A4: int] :
% 9.53/5.32                  ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 9.53/5.32                 => ( member_real @ ( J @ A4 ) @ ( minus_minus_set_real @ T4 @ T5 ) ) )
% 9.53/5.32             => ( ! [B3: real] :
% 9.53/5.32                    ( ( member_real @ B3 @ ( minus_minus_set_real @ T4 @ T5 ) )
% 9.53/5.32                   => ( ( J @ ( I2 @ B3 ) )
% 9.53/5.32                      = B3 ) )
% 9.53/5.32               => ( ! [B3: real] :
% 9.53/5.32                      ( ( member_real @ B3 @ ( minus_minus_set_real @ T4 @ T5 ) )
% 9.53/5.32                     => ( member_int @ ( I2 @ B3 ) @ ( minus_minus_set_int @ S2 @ S5 ) ) )
% 9.53/5.32                 => ( ! [A4: int] :
% 9.53/5.32                        ( ( member_int @ A4 @ S5 )
% 9.53/5.32                       => ( ( G @ A4 )
% 9.53/5.32                          = one_one_complex ) )
% 9.53/5.32                   => ( ! [B3: real] :
% 9.53/5.32                          ( ( member_real @ B3 @ T5 )
% 9.53/5.32                         => ( ( H2 @ B3 )
% 9.53/5.32                            = one_one_complex ) )
% 9.53/5.32                     => ( ! [A4: int] :
% 9.53/5.32                            ( ( member_int @ A4 @ S2 )
% 9.53/5.32                           => ( ( H2 @ ( J @ A4 ) )
% 9.53/5.32                              = ( G @ A4 ) ) )
% 9.53/5.32                       => ( ( groups7440179247065528705omplex @ G @ S2 )
% 9.53/5.32                          = ( groups713298508707869441omplex @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8824_prod_Oreindex__bij__witness__not__neutral,axiom,
% 9.53/5.32      ! [S5: set_int,T5: set_int,S2: set_int,I2: int > int,J: int > int,T4: set_int,G: int > complex,H2: int > complex] :
% 9.53/5.32        ( ( finite_finite_int @ S5 )
% 9.53/5.32       => ( ( finite_finite_int @ T5 )
% 9.53/5.32         => ( ! [A4: int] :
% 9.53/5.32                ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 9.53/5.32               => ( ( I2 @ ( J @ A4 ) )
% 9.53/5.32                  = A4 ) )
% 9.53/5.32           => ( ! [A4: int] :
% 9.53/5.32                  ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 9.53/5.32                 => ( member_int @ ( J @ A4 ) @ ( minus_minus_set_int @ T4 @ T5 ) ) )
% 9.53/5.32             => ( ! [B3: int] :
% 9.53/5.32                    ( ( member_int @ B3 @ ( minus_minus_set_int @ T4 @ T5 ) )
% 9.53/5.32                   => ( ( J @ ( I2 @ B3 ) )
% 9.53/5.32                      = B3 ) )
% 9.53/5.32               => ( ! [B3: int] :
% 9.53/5.32                      ( ( member_int @ B3 @ ( minus_minus_set_int @ T4 @ T5 ) )
% 9.53/5.32                     => ( member_int @ ( I2 @ B3 ) @ ( minus_minus_set_int @ S2 @ S5 ) ) )
% 9.53/5.32                 => ( ! [A4: int] :
% 9.53/5.32                        ( ( member_int @ A4 @ S5 )
% 9.53/5.32                       => ( ( G @ A4 )
% 9.53/5.32                          = one_one_complex ) )
% 9.53/5.32                   => ( ! [B3: int] :
% 9.53/5.32                          ( ( member_int @ B3 @ T5 )
% 9.53/5.32                         => ( ( H2 @ B3 )
% 9.53/5.32                            = one_one_complex ) )
% 9.53/5.32                     => ( ! [A4: int] :
% 9.53/5.32                            ( ( member_int @ A4 @ S2 )
% 9.53/5.32                           => ( ( H2 @ ( J @ A4 ) )
% 9.53/5.32                              = ( G @ A4 ) ) )
% 9.53/5.32                       => ( ( groups7440179247065528705omplex @ G @ S2 )
% 9.53/5.32                          = ( groups7440179247065528705omplex @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8825_prod_Oreindex__bij__witness__not__neutral,axiom,
% 9.53/5.32      ! [S5: set_real,T5: set_complex,S2: set_real,I2: complex > real,J: real > complex,T4: set_complex,G: real > complex,H2: complex > complex] :
% 9.53/5.32        ( ( finite_finite_real @ S5 )
% 9.53/5.32       => ( ( finite3207457112153483333omplex @ T5 )
% 9.53/5.32         => ( ! [A4: real] :
% 9.53/5.32                ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 9.53/5.32               => ( ( I2 @ ( J @ A4 ) )
% 9.53/5.32                  = A4 ) )
% 9.53/5.32           => ( ! [A4: real] :
% 9.53/5.32                  ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 9.53/5.32                 => ( member_complex @ ( J @ A4 ) @ ( minus_811609699411566653omplex @ T4 @ T5 ) ) )
% 9.53/5.32             => ( ! [B3: complex] :
% 9.53/5.32                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T4 @ T5 ) )
% 9.53/5.32                   => ( ( J @ ( I2 @ B3 ) )
% 9.53/5.32                      = B3 ) )
% 9.53/5.32               => ( ! [B3: complex] :
% 9.53/5.32                      ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T4 @ T5 ) )
% 9.53/5.32                     => ( member_real @ ( I2 @ B3 ) @ ( minus_minus_set_real @ S2 @ S5 ) ) )
% 9.53/5.32                 => ( ! [A4: real] :
% 9.53/5.32                        ( ( member_real @ A4 @ S5 )
% 9.53/5.32                       => ( ( G @ A4 )
% 9.53/5.32                          = one_one_complex ) )
% 9.53/5.32                   => ( ! [B3: complex] :
% 9.53/5.32                          ( ( member_complex @ B3 @ T5 )
% 9.53/5.32                         => ( ( H2 @ B3 )
% 9.53/5.32                            = one_one_complex ) )
% 9.53/5.32                     => ( ! [A4: real] :
% 9.53/5.32                            ( ( member_real @ A4 @ S2 )
% 9.53/5.32                           => ( ( H2 @ ( J @ A4 ) )
% 9.53/5.32                              = ( G @ A4 ) ) )
% 9.53/5.32                       => ( ( groups713298508707869441omplex @ G @ S2 )
% 9.53/5.32                          = ( groups3708469109370488835omplex @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8826_prod_Oreindex__bij__witness__not__neutral,axiom,
% 9.53/5.32      ! [S5: set_int,T5: set_complex,S2: set_int,I2: complex > int,J: int > complex,T4: set_complex,G: int > complex,H2: complex > complex] :
% 9.53/5.32        ( ( finite_finite_int @ S5 )
% 9.53/5.32       => ( ( finite3207457112153483333omplex @ T5 )
% 9.53/5.32         => ( ! [A4: int] :
% 9.53/5.32                ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 9.53/5.32               => ( ( I2 @ ( J @ A4 ) )
% 9.53/5.32                  = A4 ) )
% 9.53/5.32           => ( ! [A4: int] :
% 9.53/5.32                  ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 9.53/5.32                 => ( member_complex @ ( J @ A4 ) @ ( minus_811609699411566653omplex @ T4 @ T5 ) ) )
% 9.53/5.32             => ( ! [B3: complex] :
% 9.53/5.32                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T4 @ T5 ) )
% 9.53/5.32                   => ( ( J @ ( I2 @ B3 ) )
% 9.53/5.32                      = B3 ) )
% 9.53/5.32               => ( ! [B3: complex] :
% 9.53/5.32                      ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T4 @ T5 ) )
% 9.53/5.32                     => ( member_int @ ( I2 @ B3 ) @ ( minus_minus_set_int @ S2 @ S5 ) ) )
% 9.53/5.32                 => ( ! [A4: int] :
% 9.53/5.32                        ( ( member_int @ A4 @ S5 )
% 9.53/5.32                       => ( ( G @ A4 )
% 9.53/5.32                          = one_one_complex ) )
% 9.53/5.32                   => ( ! [B3: complex] :
% 9.53/5.32                          ( ( member_complex @ B3 @ T5 )
% 9.53/5.32                         => ( ( H2 @ B3 )
% 9.53/5.32                            = one_one_complex ) )
% 9.53/5.32                     => ( ! [A4: int] :
% 9.53/5.32                            ( ( member_int @ A4 @ S2 )
% 9.53/5.32                           => ( ( H2 @ ( J @ A4 ) )
% 9.53/5.32                              = ( G @ A4 ) ) )
% 9.53/5.32                       => ( ( groups7440179247065528705omplex @ G @ S2 )
% 9.53/5.32                          = ( groups3708469109370488835omplex @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8827_prod_Oreindex__bij__witness__not__neutral,axiom,
% 9.53/5.32      ! [S5: set_complex,T5: set_real,S2: set_complex,I2: real > complex,J: complex > real,T4: set_real,G: complex > complex,H2: real > complex] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ S5 )
% 9.53/5.32       => ( ( finite_finite_real @ T5 )
% 9.53/5.32         => ( ! [A4: complex] :
% 9.53/5.32                ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ S2 @ S5 ) )
% 9.53/5.32               => ( ( I2 @ ( J @ A4 ) )
% 9.53/5.32                  = A4 ) )
% 9.53/5.32           => ( ! [A4: complex] :
% 9.53/5.32                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ S2 @ S5 ) )
% 9.53/5.32                 => ( member_real @ ( J @ A4 ) @ ( minus_minus_set_real @ T4 @ T5 ) ) )
% 9.53/5.32             => ( ! [B3: real] :
% 9.53/5.32                    ( ( member_real @ B3 @ ( minus_minus_set_real @ T4 @ T5 ) )
% 9.53/5.32                   => ( ( J @ ( I2 @ B3 ) )
% 9.53/5.32                      = B3 ) )
% 9.53/5.32               => ( ! [B3: real] :
% 9.53/5.32                      ( ( member_real @ B3 @ ( minus_minus_set_real @ T4 @ T5 ) )
% 9.53/5.32                     => ( member_complex @ ( I2 @ B3 ) @ ( minus_811609699411566653omplex @ S2 @ S5 ) ) )
% 9.53/5.32                 => ( ! [A4: complex] :
% 9.53/5.32                        ( ( member_complex @ A4 @ S5 )
% 9.53/5.32                       => ( ( G @ A4 )
% 9.53/5.32                          = one_one_complex ) )
% 9.53/5.32                   => ( ! [B3: real] :
% 9.53/5.32                          ( ( member_real @ B3 @ T5 )
% 9.53/5.32                         => ( ( H2 @ B3 )
% 9.53/5.32                            = one_one_complex ) )
% 9.53/5.32                     => ( ! [A4: complex] :
% 9.53/5.32                            ( ( member_complex @ A4 @ S2 )
% 9.53/5.32                           => ( ( H2 @ ( J @ A4 ) )
% 9.53/5.32                              = ( G @ A4 ) ) )
% 9.53/5.32                       => ( ( groups3708469109370488835omplex @ G @ S2 )
% 9.53/5.32                          = ( groups713298508707869441omplex @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8828_prod_Oreindex__bij__witness__not__neutral,axiom,
% 9.53/5.32      ! [S5: set_complex,T5: set_int,S2: set_complex,I2: int > complex,J: complex > int,T4: set_int,G: complex > complex,H2: int > complex] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ S5 )
% 9.53/5.32       => ( ( finite_finite_int @ T5 )
% 9.53/5.32         => ( ! [A4: complex] :
% 9.53/5.32                ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ S2 @ S5 ) )
% 9.53/5.32               => ( ( I2 @ ( J @ A4 ) )
% 9.53/5.32                  = A4 ) )
% 9.53/5.32           => ( ! [A4: complex] :
% 9.53/5.32                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ S2 @ S5 ) )
% 9.53/5.32                 => ( member_int @ ( J @ A4 ) @ ( minus_minus_set_int @ T4 @ T5 ) ) )
% 9.53/5.32             => ( ! [B3: int] :
% 9.53/5.32                    ( ( member_int @ B3 @ ( minus_minus_set_int @ T4 @ T5 ) )
% 9.53/5.32                   => ( ( J @ ( I2 @ B3 ) )
% 9.53/5.32                      = B3 ) )
% 9.53/5.32               => ( ! [B3: int] :
% 9.53/5.32                      ( ( member_int @ B3 @ ( minus_minus_set_int @ T4 @ T5 ) )
% 9.53/5.32                     => ( member_complex @ ( I2 @ B3 ) @ ( minus_811609699411566653omplex @ S2 @ S5 ) ) )
% 9.53/5.32                 => ( ! [A4: complex] :
% 9.53/5.32                        ( ( member_complex @ A4 @ S5 )
% 9.53/5.32                       => ( ( G @ A4 )
% 9.53/5.32                          = one_one_complex ) )
% 9.53/5.32                   => ( ! [B3: int] :
% 9.53/5.32                          ( ( member_int @ B3 @ T5 )
% 9.53/5.32                         => ( ( H2 @ B3 )
% 9.53/5.32                            = one_one_complex ) )
% 9.53/5.32                     => ( ! [A4: complex] :
% 9.53/5.32                            ( ( member_complex @ A4 @ S2 )
% 9.53/5.32                           => ( ( H2 @ ( J @ A4 ) )
% 9.53/5.32                              = ( G @ A4 ) ) )
% 9.53/5.32                       => ( ( groups3708469109370488835omplex @ G @ S2 )
% 9.53/5.32                          = ( groups7440179247065528705omplex @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8829_prod_Oreindex__bij__witness__not__neutral,axiom,
% 9.53/5.32      ! [S5: set_complex,T5: set_complex,S2: set_complex,I2: complex > complex,J: complex > complex,T4: set_complex,G: complex > complex,H2: complex > complex] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ S5 )
% 9.53/5.32       => ( ( finite3207457112153483333omplex @ T5 )
% 9.53/5.32         => ( ! [A4: complex] :
% 9.53/5.32                ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ S2 @ S5 ) )
% 9.53/5.32               => ( ( I2 @ ( J @ A4 ) )
% 9.53/5.32                  = A4 ) )
% 9.53/5.32           => ( ! [A4: complex] :
% 9.53/5.32                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ S2 @ S5 ) )
% 9.53/5.32                 => ( member_complex @ ( J @ A4 ) @ ( minus_811609699411566653omplex @ T4 @ T5 ) ) )
% 9.53/5.32             => ( ! [B3: complex] :
% 9.53/5.32                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T4 @ T5 ) )
% 9.53/5.32                   => ( ( J @ ( I2 @ B3 ) )
% 9.53/5.32                      = B3 ) )
% 9.53/5.32               => ( ! [B3: complex] :
% 9.53/5.32                      ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T4 @ T5 ) )
% 9.53/5.32                     => ( member_complex @ ( I2 @ B3 ) @ ( minus_811609699411566653omplex @ S2 @ S5 ) ) )
% 9.53/5.32                 => ( ! [A4: complex] :
% 9.53/5.32                        ( ( member_complex @ A4 @ S5 )
% 9.53/5.32                       => ( ( G @ A4 )
% 9.53/5.32                          = one_one_complex ) )
% 9.53/5.32                   => ( ! [B3: complex] :
% 9.53/5.32                          ( ( member_complex @ B3 @ T5 )
% 9.53/5.32                         => ( ( H2 @ B3 )
% 9.53/5.32                            = one_one_complex ) )
% 9.53/5.32                     => ( ! [A4: complex] :
% 9.53/5.32                            ( ( member_complex @ A4 @ S2 )
% 9.53/5.32                           => ( ( H2 @ ( J @ A4 ) )
% 9.53/5.32                              = ( G @ A4 ) ) )
% 9.53/5.32                       => ( ( groups3708469109370488835omplex @ G @ S2 )
% 9.53/5.32                          = ( groups3708469109370488835omplex @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8830_prod_Oreindex__bij__witness__not__neutral,axiom,
% 9.53/5.32      ! [S5: set_real,T5: set_real,S2: set_real,I2: real > real,J: real > real,T4: set_real,G: real > real,H2: real > real] :
% 9.53/5.32        ( ( finite_finite_real @ S5 )
% 9.53/5.32       => ( ( finite_finite_real @ T5 )
% 9.53/5.32         => ( ! [A4: real] :
% 9.53/5.32                ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 9.53/5.32               => ( ( I2 @ ( J @ A4 ) )
% 9.53/5.32                  = A4 ) )
% 9.53/5.32           => ( ! [A4: real] :
% 9.53/5.32                  ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 9.53/5.32                 => ( member_real @ ( J @ A4 ) @ ( minus_minus_set_real @ T4 @ T5 ) ) )
% 9.53/5.32             => ( ! [B3: real] :
% 9.53/5.32                    ( ( member_real @ B3 @ ( minus_minus_set_real @ T4 @ T5 ) )
% 9.53/5.32                   => ( ( J @ ( I2 @ B3 ) )
% 9.53/5.32                      = B3 ) )
% 9.53/5.32               => ( ! [B3: real] :
% 9.53/5.32                      ( ( member_real @ B3 @ ( minus_minus_set_real @ T4 @ T5 ) )
% 9.53/5.32                     => ( member_real @ ( I2 @ B3 ) @ ( minus_minus_set_real @ S2 @ S5 ) ) )
% 9.53/5.32                 => ( ! [A4: real] :
% 9.53/5.32                        ( ( member_real @ A4 @ S5 )
% 9.53/5.32                       => ( ( G @ A4 )
% 9.53/5.32                          = one_one_real ) )
% 9.53/5.32                   => ( ! [B3: real] :
% 9.53/5.32                          ( ( member_real @ B3 @ T5 )
% 9.53/5.32                         => ( ( H2 @ B3 )
% 9.53/5.32                            = one_one_real ) )
% 9.53/5.32                     => ( ! [A4: real] :
% 9.53/5.32                            ( ( member_real @ A4 @ S2 )
% 9.53/5.32                           => ( ( H2 @ ( J @ A4 ) )
% 9.53/5.32                              = ( G @ A4 ) ) )
% 9.53/5.32                       => ( ( groups1681761925125756287l_real @ G @ S2 )
% 9.53/5.32                          = ( groups1681761925125756287l_real @ H2 @ T4 ) ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8831_prod_Osetdiff__irrelevant,axiom,
% 9.53/5.32      ! [A2: set_real,G: real > complex] :
% 9.53/5.32        ( ( finite_finite_real @ A2 )
% 9.53/5.32       => ( ( groups713298508707869441omplex @ G
% 9.53/5.32            @ ( minus_minus_set_real @ A2
% 9.53/5.32              @ ( collect_real
% 9.53/5.32                @ ^ [X2: real] :
% 9.53/5.32                    ( ( G @ X2 )
% 9.53/5.32                    = one_one_complex ) ) ) )
% 9.53/5.32          = ( groups713298508707869441omplex @ G @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8832_prod_Osetdiff__irrelevant,axiom,
% 9.53/5.32      ! [A2: set_complex,G: complex > complex] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.32       => ( ( groups3708469109370488835omplex @ G
% 9.53/5.32            @ ( minus_811609699411566653omplex @ A2
% 9.53/5.32              @ ( collect_complex
% 9.53/5.32                @ ^ [X2: complex] :
% 9.53/5.32                    ( ( G @ X2 )
% 9.53/5.32                    = one_one_complex ) ) ) )
% 9.53/5.32          = ( groups3708469109370488835omplex @ G @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8833_prod_Osetdiff__irrelevant,axiom,
% 9.53/5.32      ! [A2: set_real,G: real > real] :
% 9.53/5.32        ( ( finite_finite_real @ A2 )
% 9.53/5.32       => ( ( groups1681761925125756287l_real @ G
% 9.53/5.32            @ ( minus_minus_set_real @ A2
% 9.53/5.32              @ ( collect_real
% 9.53/5.32                @ ^ [X2: real] :
% 9.53/5.32                    ( ( G @ X2 )
% 9.53/5.32                    = one_one_real ) ) ) )
% 9.53/5.32          = ( groups1681761925125756287l_real @ G @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8834_prod_Osetdiff__irrelevant,axiom,
% 9.53/5.32      ! [A2: set_complex,G: complex > real] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.32       => ( ( groups766887009212190081x_real @ G
% 9.53/5.32            @ ( minus_811609699411566653omplex @ A2
% 9.53/5.32              @ ( collect_complex
% 9.53/5.32                @ ^ [X2: complex] :
% 9.53/5.32                    ( ( G @ X2 )
% 9.53/5.32                    = one_one_real ) ) ) )
% 9.53/5.32          = ( groups766887009212190081x_real @ G @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8835_prod_Osetdiff__irrelevant,axiom,
% 9.53/5.32      ! [A2: set_real,G: real > rat] :
% 9.53/5.32        ( ( finite_finite_real @ A2 )
% 9.53/5.32       => ( ( groups4061424788464935467al_rat @ G
% 9.53/5.32            @ ( minus_minus_set_real @ A2
% 9.53/5.32              @ ( collect_real
% 9.53/5.32                @ ^ [X2: real] :
% 9.53/5.32                    ( ( G @ X2 )
% 9.53/5.32                    = one_one_rat ) ) ) )
% 9.53/5.32          = ( groups4061424788464935467al_rat @ G @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8836_prod_Osetdiff__irrelevant,axiom,
% 9.53/5.32      ! [A2: set_complex,G: complex > rat] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.32       => ( ( groups225925009352817453ex_rat @ G
% 9.53/5.32            @ ( minus_811609699411566653omplex @ A2
% 9.53/5.32              @ ( collect_complex
% 9.53/5.32                @ ^ [X2: complex] :
% 9.53/5.32                    ( ( G @ X2 )
% 9.53/5.32                    = one_one_rat ) ) ) )
% 9.53/5.32          = ( groups225925009352817453ex_rat @ G @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8837_prod_Osetdiff__irrelevant,axiom,
% 9.53/5.32      ! [A2: set_real,G: real > nat] :
% 9.53/5.32        ( ( finite_finite_real @ A2 )
% 9.53/5.32       => ( ( groups4696554848551431203al_nat @ G
% 9.53/5.32            @ ( minus_minus_set_real @ A2
% 9.53/5.32              @ ( collect_real
% 9.53/5.32                @ ^ [X2: real] :
% 9.53/5.32                    ( ( G @ X2 )
% 9.53/5.32                    = one_one_nat ) ) ) )
% 9.53/5.32          = ( groups4696554848551431203al_nat @ G @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8838_prod_Osetdiff__irrelevant,axiom,
% 9.53/5.32      ! [A2: set_complex,G: complex > nat] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.32       => ( ( groups861055069439313189ex_nat @ G
% 9.53/5.32            @ ( minus_811609699411566653omplex @ A2
% 9.53/5.32              @ ( collect_complex
% 9.53/5.32                @ ^ [X2: complex] :
% 9.53/5.32                    ( ( G @ X2 )
% 9.53/5.32                    = one_one_nat ) ) ) )
% 9.53/5.32          = ( groups861055069439313189ex_nat @ G @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8839_prod_Osetdiff__irrelevant,axiom,
% 9.53/5.32      ! [A2: set_real,G: real > int] :
% 9.53/5.32        ( ( finite_finite_real @ A2 )
% 9.53/5.32       => ( ( groups4694064378042380927al_int @ G
% 9.53/5.32            @ ( minus_minus_set_real @ A2
% 9.53/5.32              @ ( collect_real
% 9.53/5.32                @ ^ [X2: real] :
% 9.53/5.32                    ( ( G @ X2 )
% 9.53/5.32                    = one_one_int ) ) ) )
% 9.53/5.32          = ( groups4694064378042380927al_int @ G @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8840_prod_Osetdiff__irrelevant,axiom,
% 9.53/5.32      ! [A2: set_complex,G: complex > int] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.32       => ( ( groups858564598930262913ex_int @ G
% 9.53/5.32            @ ( minus_811609699411566653omplex @ A2
% 9.53/5.32              @ ( collect_complex
% 9.53/5.32                @ ^ [X2: complex] :
% 9.53/5.32                    ( ( G @ X2 )
% 9.53/5.32                    = one_one_int ) ) ) )
% 9.53/5.32          = ( groups858564598930262913ex_int @ G @ A2 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8841_prod_Onat__diff__reindex,axiom,
% 9.53/5.32      ! [G: nat > nat,N: nat] :
% 9.53/5.32        ( ( groups708209901874060359at_nat
% 9.53/5.32          @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 9.53/5.32          @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.32        = ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8842_prod_Onat__diff__reindex,axiom,
% 9.53/5.32      ! [G: nat > int,N: nat] :
% 9.53/5.32        ( ( groups705719431365010083at_int
% 9.53/5.32          @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 9.53/5.32          @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.32        = ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8843_prod_OatLeastAtMost__rev,axiom,
% 9.53/5.32      ! [G: nat > nat,N: nat,M: nat] :
% 9.53/5.32        ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 9.53/5.32        = ( groups708209901874060359at_nat
% 9.53/5.32          @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I3 ) )
% 9.53/5.32          @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8844_prod_OatLeastAtMost__rev,axiom,
% 9.53/5.32      ! [G: nat > int,N: nat,M: nat] :
% 9.53/5.32        ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 9.53/5.32        = ( groups705719431365010083at_int
% 9.53/5.32          @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I3 ) )
% 9.53/5.32          @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8845_less__1__prod2,axiom,
% 9.53/5.32      ! [I6: set_real,I2: real,F: real > real] :
% 9.53/5.32        ( ( finite_finite_real @ I6 )
% 9.53/5.32       => ( ( member_real @ I2 @ I6 )
% 9.53/5.32         => ( ( ord_less_real @ one_one_real @ ( F @ I2 ) )
% 9.53/5.32           => ( ! [I4: real] :
% 9.53/5.32                  ( ( member_real @ I4 @ I6 )
% 9.53/5.32                 => ( ord_less_eq_real @ one_one_real @ ( F @ I4 ) ) )
% 9.53/5.32             => ( ord_less_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ I6 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8846_less__1__prod2,axiom,
% 9.53/5.32      ! [I6: set_int,I2: int,F: int > real] :
% 9.53/5.32        ( ( finite_finite_int @ I6 )
% 9.53/5.32       => ( ( member_int @ I2 @ I6 )
% 9.53/5.32         => ( ( ord_less_real @ one_one_real @ ( F @ I2 ) )
% 9.53/5.32           => ( ! [I4: int] :
% 9.53/5.32                  ( ( member_int @ I4 @ I6 )
% 9.53/5.32                 => ( ord_less_eq_real @ one_one_real @ ( F @ I4 ) ) )
% 9.53/5.32             => ( ord_less_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ I6 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8847_less__1__prod2,axiom,
% 9.53/5.32      ! [I6: set_nat,I2: nat,F: nat > real] :
% 9.53/5.32        ( ( finite_finite_nat @ I6 )
% 9.53/5.32       => ( ( member_nat @ I2 @ I6 )
% 9.53/5.32         => ( ( ord_less_real @ one_one_real @ ( F @ I2 ) )
% 9.53/5.32           => ( ! [I4: nat] :
% 9.53/5.32                  ( ( member_nat @ I4 @ I6 )
% 9.53/5.32                 => ( ord_less_eq_real @ one_one_real @ ( F @ I4 ) ) )
% 9.53/5.32             => ( ord_less_real @ one_one_real @ ( groups129246275422532515t_real @ F @ I6 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8848_less__1__prod2,axiom,
% 9.53/5.32      ! [I6: set_complex,I2: complex,F: complex > real] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ I6 )
% 9.53/5.32       => ( ( member_complex @ I2 @ I6 )
% 9.53/5.32         => ( ( ord_less_real @ one_one_real @ ( F @ I2 ) )
% 9.53/5.32           => ( ! [I4: complex] :
% 9.53/5.32                  ( ( member_complex @ I4 @ I6 )
% 9.53/5.32                 => ( ord_less_eq_real @ one_one_real @ ( F @ I4 ) ) )
% 9.53/5.32             => ( ord_less_real @ one_one_real @ ( groups766887009212190081x_real @ F @ I6 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8849_less__1__prod2,axiom,
% 9.53/5.32      ! [I6: set_real,I2: real,F: real > rat] :
% 9.53/5.32        ( ( finite_finite_real @ I6 )
% 9.53/5.32       => ( ( member_real @ I2 @ I6 )
% 9.53/5.32         => ( ( ord_less_rat @ one_one_rat @ ( F @ I2 ) )
% 9.53/5.32           => ( ! [I4: real] :
% 9.53/5.32                  ( ( member_real @ I4 @ I6 )
% 9.53/5.32                 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I4 ) ) )
% 9.53/5.32             => ( ord_less_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ I6 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8850_less__1__prod2,axiom,
% 9.53/5.32      ! [I6: set_int,I2: int,F: int > rat] :
% 9.53/5.32        ( ( finite_finite_int @ I6 )
% 9.53/5.32       => ( ( member_int @ I2 @ I6 )
% 9.53/5.32         => ( ( ord_less_rat @ one_one_rat @ ( F @ I2 ) )
% 9.53/5.32           => ( ! [I4: int] :
% 9.53/5.32                  ( ( member_int @ I4 @ I6 )
% 9.53/5.32                 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I4 ) ) )
% 9.53/5.32             => ( ord_less_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ I6 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8851_less__1__prod2,axiom,
% 9.53/5.32      ! [I6: set_nat,I2: nat,F: nat > rat] :
% 9.53/5.32        ( ( finite_finite_nat @ I6 )
% 9.53/5.32       => ( ( member_nat @ I2 @ I6 )
% 9.53/5.32         => ( ( ord_less_rat @ one_one_rat @ ( F @ I2 ) )
% 9.53/5.32           => ( ! [I4: nat] :
% 9.53/5.32                  ( ( member_nat @ I4 @ I6 )
% 9.53/5.32                 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I4 ) ) )
% 9.53/5.32             => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ I6 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8852_less__1__prod2,axiom,
% 9.53/5.32      ! [I6: set_complex,I2: complex,F: complex > rat] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ I6 )
% 9.53/5.32       => ( ( member_complex @ I2 @ I6 )
% 9.53/5.32         => ( ( ord_less_rat @ one_one_rat @ ( F @ I2 ) )
% 9.53/5.32           => ( ! [I4: complex] :
% 9.53/5.32                  ( ( member_complex @ I4 @ I6 )
% 9.53/5.32                 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I4 ) ) )
% 9.53/5.32             => ( ord_less_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F @ I6 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8853_less__1__prod2,axiom,
% 9.53/5.32      ! [I6: set_real,I2: real,F: real > int] :
% 9.53/5.32        ( ( finite_finite_real @ I6 )
% 9.53/5.32       => ( ( member_real @ I2 @ I6 )
% 9.53/5.32         => ( ( ord_less_int @ one_one_int @ ( F @ I2 ) )
% 9.53/5.32           => ( ! [I4: real] :
% 9.53/5.32                  ( ( member_real @ I4 @ I6 )
% 9.53/5.32                 => ( ord_less_eq_int @ one_one_int @ ( F @ I4 ) ) )
% 9.53/5.32             => ( ord_less_int @ one_one_int @ ( groups4694064378042380927al_int @ F @ I6 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8854_less__1__prod2,axiom,
% 9.53/5.32      ! [I6: set_complex,I2: complex,F: complex > int] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ I6 )
% 9.53/5.32       => ( ( member_complex @ I2 @ I6 )
% 9.53/5.32         => ( ( ord_less_int @ one_one_int @ ( F @ I2 ) )
% 9.53/5.32           => ( ! [I4: complex] :
% 9.53/5.32                  ( ( member_complex @ I4 @ I6 )
% 9.53/5.32                 => ( ord_less_eq_int @ one_one_int @ ( F @ I4 ) ) )
% 9.53/5.32             => ( ord_less_int @ one_one_int @ ( groups858564598930262913ex_int @ F @ I6 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8855_less__1__prod,axiom,
% 9.53/5.32      ! [I6: set_complex,F: complex > real] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ I6 )
% 9.53/5.32       => ( ( I6 != bot_bot_set_complex )
% 9.53/5.32         => ( ! [I4: complex] :
% 9.53/5.32                ( ( member_complex @ I4 @ I6 )
% 9.53/5.32               => ( ord_less_real @ one_one_real @ ( F @ I4 ) ) )
% 9.53/5.32           => ( ord_less_real @ one_one_real @ ( groups766887009212190081x_real @ F @ I6 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8856_less__1__prod,axiom,
% 9.53/5.32      ! [I6: set_nat,F: nat > real] :
% 9.53/5.32        ( ( finite_finite_nat @ I6 )
% 9.53/5.32       => ( ( I6 != bot_bot_set_nat )
% 9.53/5.32         => ( ! [I4: nat] :
% 9.53/5.32                ( ( member_nat @ I4 @ I6 )
% 9.53/5.32               => ( ord_less_real @ one_one_real @ ( F @ I4 ) ) )
% 9.53/5.32           => ( ord_less_real @ one_one_real @ ( groups129246275422532515t_real @ F @ I6 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8857_less__1__prod,axiom,
% 9.53/5.32      ! [I6: set_int,F: int > real] :
% 9.53/5.32        ( ( finite_finite_int @ I6 )
% 9.53/5.32       => ( ( I6 != bot_bot_set_int )
% 9.53/5.32         => ( ! [I4: int] :
% 9.53/5.32                ( ( member_int @ I4 @ I6 )
% 9.53/5.32               => ( ord_less_real @ one_one_real @ ( F @ I4 ) ) )
% 9.53/5.32           => ( ord_less_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ I6 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8858_less__1__prod,axiom,
% 9.53/5.32      ! [I6: set_real,F: real > real] :
% 9.53/5.32        ( ( finite_finite_real @ I6 )
% 9.53/5.32       => ( ( I6 != bot_bot_set_real )
% 9.53/5.32         => ( ! [I4: real] :
% 9.53/5.32                ( ( member_real @ I4 @ I6 )
% 9.53/5.32               => ( ord_less_real @ one_one_real @ ( F @ I4 ) ) )
% 9.53/5.32           => ( ord_less_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ I6 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8859_less__1__prod,axiom,
% 9.53/5.32      ! [I6: set_complex,F: complex > rat] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ I6 )
% 9.53/5.32       => ( ( I6 != bot_bot_set_complex )
% 9.53/5.32         => ( ! [I4: complex] :
% 9.53/5.32                ( ( member_complex @ I4 @ I6 )
% 9.53/5.32               => ( ord_less_rat @ one_one_rat @ ( F @ I4 ) ) )
% 9.53/5.32           => ( ord_less_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F @ I6 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8860_less__1__prod,axiom,
% 9.53/5.32      ! [I6: set_nat,F: nat > rat] :
% 9.53/5.32        ( ( finite_finite_nat @ I6 )
% 9.53/5.32       => ( ( I6 != bot_bot_set_nat )
% 9.53/5.32         => ( ! [I4: nat] :
% 9.53/5.32                ( ( member_nat @ I4 @ I6 )
% 9.53/5.32               => ( ord_less_rat @ one_one_rat @ ( F @ I4 ) ) )
% 9.53/5.32           => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ I6 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8861_less__1__prod,axiom,
% 9.53/5.32      ! [I6: set_int,F: int > rat] :
% 9.53/5.32        ( ( finite_finite_int @ I6 )
% 9.53/5.32       => ( ( I6 != bot_bot_set_int )
% 9.53/5.32         => ( ! [I4: int] :
% 9.53/5.32                ( ( member_int @ I4 @ I6 )
% 9.53/5.32               => ( ord_less_rat @ one_one_rat @ ( F @ I4 ) ) )
% 9.53/5.32           => ( ord_less_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ I6 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8862_less__1__prod,axiom,
% 9.53/5.32      ! [I6: set_real,F: real > rat] :
% 9.53/5.32        ( ( finite_finite_real @ I6 )
% 9.53/5.32       => ( ( I6 != bot_bot_set_real )
% 9.53/5.32         => ( ! [I4: real] :
% 9.53/5.32                ( ( member_real @ I4 @ I6 )
% 9.53/5.32               => ( ord_less_rat @ one_one_rat @ ( F @ I4 ) ) )
% 9.53/5.32           => ( ord_less_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ I6 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8863_less__1__prod,axiom,
% 9.53/5.32      ! [I6: set_complex,F: complex > int] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ I6 )
% 9.53/5.32       => ( ( I6 != bot_bot_set_complex )
% 9.53/5.32         => ( ! [I4: complex] :
% 9.53/5.32                ( ( member_complex @ I4 @ I6 )
% 9.53/5.32               => ( ord_less_int @ one_one_int @ ( F @ I4 ) ) )
% 9.53/5.32           => ( ord_less_int @ one_one_int @ ( groups858564598930262913ex_int @ F @ I6 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8864_less__1__prod,axiom,
% 9.53/5.32      ! [I6: set_real,F: real > int] :
% 9.53/5.32        ( ( finite_finite_real @ I6 )
% 9.53/5.32       => ( ( I6 != bot_bot_set_real )
% 9.53/5.32         => ( ! [I4: real] :
% 9.53/5.32                ( ( member_real @ I4 @ I6 )
% 9.53/5.32               => ( ord_less_int @ one_one_int @ ( F @ I4 ) ) )
% 9.53/5.32           => ( ord_less_int @ one_one_int @ ( groups4694064378042380927al_int @ F @ I6 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8865_prod_Osubset__diff,axiom,
% 9.53/5.32      ! [B2: set_complex,A2: set_complex,G: complex > complex] :
% 9.53/5.32        ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 9.53/5.32       => ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.32         => ( ( groups3708469109370488835omplex @ G @ A2 )
% 9.53/5.32            = ( times_times_complex @ ( groups3708469109370488835omplex @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups3708469109370488835omplex @ G @ B2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8866_prod_Osubset__diff,axiom,
% 9.53/5.32      ! [B2: set_complex,A2: set_complex,G: complex > real] :
% 9.53/5.32        ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 9.53/5.32       => ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.32         => ( ( groups766887009212190081x_real @ G @ A2 )
% 9.53/5.32            = ( times_times_real @ ( groups766887009212190081x_real @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups766887009212190081x_real @ G @ B2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8867_prod_Osubset__diff,axiom,
% 9.53/5.32      ! [B2: set_complex,A2: set_complex,G: complex > nat] :
% 9.53/5.32        ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 9.53/5.32       => ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.32         => ( ( groups861055069439313189ex_nat @ G @ A2 )
% 9.53/5.32            = ( times_times_nat @ ( groups861055069439313189ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups861055069439313189ex_nat @ G @ B2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8868_prod_Osubset__diff,axiom,
% 9.53/5.32      ! [B2: set_complex,A2: set_complex,G: complex > int] :
% 9.53/5.32        ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 9.53/5.32       => ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.32         => ( ( groups858564598930262913ex_int @ G @ A2 )
% 9.53/5.32            = ( times_times_int @ ( groups858564598930262913ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups858564598930262913ex_int @ G @ B2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8869_prod_Osubset__diff,axiom,
% 9.53/5.32      ! [B2: set_real,A2: set_real,G: real > complex] :
% 9.53/5.32        ( ( ord_less_eq_set_real @ B2 @ A2 )
% 9.53/5.32       => ( ( finite_finite_real @ A2 )
% 9.53/5.32         => ( ( groups713298508707869441omplex @ G @ A2 )
% 9.53/5.32            = ( times_times_complex @ ( groups713298508707869441omplex @ G @ ( minus_minus_set_real @ A2 @ B2 ) ) @ ( groups713298508707869441omplex @ G @ B2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8870_prod_Osubset__diff,axiom,
% 9.53/5.32      ! [B2: set_real,A2: set_real,G: real > real] :
% 9.53/5.32        ( ( ord_less_eq_set_real @ B2 @ A2 )
% 9.53/5.32       => ( ( finite_finite_real @ A2 )
% 9.53/5.32         => ( ( groups1681761925125756287l_real @ G @ A2 )
% 9.53/5.32            = ( times_times_real @ ( groups1681761925125756287l_real @ G @ ( minus_minus_set_real @ A2 @ B2 ) ) @ ( groups1681761925125756287l_real @ G @ B2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8871_prod_Osubset__diff,axiom,
% 9.53/5.32      ! [B2: set_real,A2: set_real,G: real > nat] :
% 9.53/5.32        ( ( ord_less_eq_set_real @ B2 @ A2 )
% 9.53/5.32       => ( ( finite_finite_real @ A2 )
% 9.53/5.32         => ( ( groups4696554848551431203al_nat @ G @ A2 )
% 9.53/5.32            = ( times_times_nat @ ( groups4696554848551431203al_nat @ G @ ( minus_minus_set_real @ A2 @ B2 ) ) @ ( groups4696554848551431203al_nat @ G @ B2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8872_prod_Osubset__diff,axiom,
% 9.53/5.32      ! [B2: set_real,A2: set_real,G: real > int] :
% 9.53/5.32        ( ( ord_less_eq_set_real @ B2 @ A2 )
% 9.53/5.32       => ( ( finite_finite_real @ A2 )
% 9.53/5.32         => ( ( groups4694064378042380927al_int @ G @ A2 )
% 9.53/5.32            = ( times_times_int @ ( groups4694064378042380927al_int @ G @ ( minus_minus_set_real @ A2 @ B2 ) ) @ ( groups4694064378042380927al_int @ G @ B2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8873_prod_Osubset__diff,axiom,
% 9.53/5.32      ! [B2: set_nat,A2: set_nat,G: nat > complex] :
% 9.53/5.32        ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 9.53/5.32       => ( ( finite_finite_nat @ A2 )
% 9.53/5.32         => ( ( groups6464643781859351333omplex @ G @ A2 )
% 9.53/5.32            = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups6464643781859351333omplex @ G @ B2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8874_prod_Osubset__diff,axiom,
% 9.53/5.32      ! [B2: set_nat,A2: set_nat,G: nat > real] :
% 9.53/5.32        ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 9.53/5.32       => ( ( finite_finite_nat @ A2 )
% 9.53/5.32         => ( ( groups129246275422532515t_real @ G @ A2 )
% 9.53/5.32            = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups129246275422532515t_real @ G @ B2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8875_prod_Omono__neutral__cong__right,axiom,
% 9.53/5.32      ! [T4: set_int,S2: set_int,G: int > complex,H2: int > complex] :
% 9.53/5.32        ( ( finite_finite_int @ T4 )
% 9.53/5.32       => ( ( ord_less_eq_set_int @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: int] :
% 9.53/5.32                ( ( member_int @ X3 @ ( minus_minus_set_int @ T4 @ S2 ) )
% 9.53/5.32               => ( ( G @ X3 )
% 9.53/5.32                  = one_one_complex ) )
% 9.53/5.32           => ( ! [X3: int] :
% 9.53/5.32                  ( ( member_int @ X3 @ S2 )
% 9.53/5.32                 => ( ( G @ X3 )
% 9.53/5.32                    = ( H2 @ X3 ) ) )
% 9.53/5.32             => ( ( groups7440179247065528705omplex @ G @ T4 )
% 9.53/5.32                = ( groups7440179247065528705omplex @ H2 @ S2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8876_prod_Omono__neutral__cong__right,axiom,
% 9.53/5.32      ! [T4: set_complex,S2: set_complex,G: complex > complex,H2: complex > complex] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ T4 )
% 9.53/5.32       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: complex] :
% 9.53/5.32                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 9.53/5.32               => ( ( G @ X3 )
% 9.53/5.32                  = one_one_complex ) )
% 9.53/5.32           => ( ! [X3: complex] :
% 9.53/5.32                  ( ( member_complex @ X3 @ S2 )
% 9.53/5.32                 => ( ( G @ X3 )
% 9.53/5.32                    = ( H2 @ X3 ) ) )
% 9.53/5.32             => ( ( groups3708469109370488835omplex @ G @ T4 )
% 9.53/5.32                = ( groups3708469109370488835omplex @ H2 @ S2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8877_prod_Omono__neutral__cong__right,axiom,
% 9.53/5.32      ! [T4: set_int,S2: set_int,G: int > real,H2: int > real] :
% 9.53/5.32        ( ( finite_finite_int @ T4 )
% 9.53/5.32       => ( ( ord_less_eq_set_int @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: int] :
% 9.53/5.32                ( ( member_int @ X3 @ ( minus_minus_set_int @ T4 @ S2 ) )
% 9.53/5.32               => ( ( G @ X3 )
% 9.53/5.32                  = one_one_real ) )
% 9.53/5.32           => ( ! [X3: int] :
% 9.53/5.32                  ( ( member_int @ X3 @ S2 )
% 9.53/5.32                 => ( ( G @ X3 )
% 9.53/5.32                    = ( H2 @ X3 ) ) )
% 9.53/5.32             => ( ( groups2316167850115554303t_real @ G @ T4 )
% 9.53/5.32                = ( groups2316167850115554303t_real @ H2 @ S2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8878_prod_Omono__neutral__cong__right,axiom,
% 9.53/5.32      ! [T4: set_complex,S2: set_complex,G: complex > real,H2: complex > real] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ T4 )
% 9.53/5.32       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: complex] :
% 9.53/5.32                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 9.53/5.32               => ( ( G @ X3 )
% 9.53/5.32                  = one_one_real ) )
% 9.53/5.32           => ( ! [X3: complex] :
% 9.53/5.32                  ( ( member_complex @ X3 @ S2 )
% 9.53/5.32                 => ( ( G @ X3 )
% 9.53/5.32                    = ( H2 @ X3 ) ) )
% 9.53/5.32             => ( ( groups766887009212190081x_real @ G @ T4 )
% 9.53/5.32                = ( groups766887009212190081x_real @ H2 @ S2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8879_prod_Omono__neutral__cong__right,axiom,
% 9.53/5.32      ! [T4: set_int,S2: set_int,G: int > rat,H2: int > rat] :
% 9.53/5.32        ( ( finite_finite_int @ T4 )
% 9.53/5.32       => ( ( ord_less_eq_set_int @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: int] :
% 9.53/5.32                ( ( member_int @ X3 @ ( minus_minus_set_int @ T4 @ S2 ) )
% 9.53/5.32               => ( ( G @ X3 )
% 9.53/5.32                  = one_one_rat ) )
% 9.53/5.32           => ( ! [X3: int] :
% 9.53/5.32                  ( ( member_int @ X3 @ S2 )
% 9.53/5.32                 => ( ( G @ X3 )
% 9.53/5.32                    = ( H2 @ X3 ) ) )
% 9.53/5.32             => ( ( groups1072433553688619179nt_rat @ G @ T4 )
% 9.53/5.32                = ( groups1072433553688619179nt_rat @ H2 @ S2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8880_prod_Omono__neutral__cong__right,axiom,
% 9.53/5.32      ! [T4: set_complex,S2: set_complex,G: complex > rat,H2: complex > rat] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ T4 )
% 9.53/5.32       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: complex] :
% 9.53/5.32                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 9.53/5.32               => ( ( G @ X3 )
% 9.53/5.32                  = one_one_rat ) )
% 9.53/5.32           => ( ! [X3: complex] :
% 9.53/5.32                  ( ( member_complex @ X3 @ S2 )
% 9.53/5.32                 => ( ( G @ X3 )
% 9.53/5.32                    = ( H2 @ X3 ) ) )
% 9.53/5.32             => ( ( groups225925009352817453ex_rat @ G @ T4 )
% 9.53/5.32                = ( groups225925009352817453ex_rat @ H2 @ S2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8881_prod_Omono__neutral__cong__right,axiom,
% 9.53/5.32      ! [T4: set_int,S2: set_int,G: int > nat,H2: int > nat] :
% 9.53/5.32        ( ( finite_finite_int @ T4 )
% 9.53/5.32       => ( ( ord_less_eq_set_int @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: int] :
% 9.53/5.32                ( ( member_int @ X3 @ ( minus_minus_set_int @ T4 @ S2 ) )
% 9.53/5.32               => ( ( G @ X3 )
% 9.53/5.32                  = one_one_nat ) )
% 9.53/5.32           => ( ! [X3: int] :
% 9.53/5.32                  ( ( member_int @ X3 @ S2 )
% 9.53/5.32                 => ( ( G @ X3 )
% 9.53/5.32                    = ( H2 @ X3 ) ) )
% 9.53/5.32             => ( ( groups1707563613775114915nt_nat @ G @ T4 )
% 9.53/5.32                = ( groups1707563613775114915nt_nat @ H2 @ S2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8882_prod_Omono__neutral__cong__right,axiom,
% 9.53/5.32      ! [T4: set_complex,S2: set_complex,G: complex > nat,H2: complex > nat] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ T4 )
% 9.53/5.32       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: complex] :
% 9.53/5.32                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 9.53/5.32               => ( ( G @ X3 )
% 9.53/5.32                  = one_one_nat ) )
% 9.53/5.32           => ( ! [X3: complex] :
% 9.53/5.32                  ( ( member_complex @ X3 @ S2 )
% 9.53/5.32                 => ( ( G @ X3 )
% 9.53/5.32                    = ( H2 @ X3 ) ) )
% 9.53/5.32             => ( ( groups861055069439313189ex_nat @ G @ T4 )
% 9.53/5.32                = ( groups861055069439313189ex_nat @ H2 @ S2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8883_prod_Omono__neutral__cong__right,axiom,
% 9.53/5.32      ! [T4: set_complex,S2: set_complex,G: complex > int,H2: complex > int] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ T4 )
% 9.53/5.32       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: complex] :
% 9.53/5.32                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 9.53/5.32               => ( ( G @ X3 )
% 9.53/5.32                  = one_one_int ) )
% 9.53/5.32           => ( ! [X3: complex] :
% 9.53/5.32                  ( ( member_complex @ X3 @ S2 )
% 9.53/5.32                 => ( ( G @ X3 )
% 9.53/5.32                    = ( H2 @ X3 ) ) )
% 9.53/5.32             => ( ( groups858564598930262913ex_int @ G @ T4 )
% 9.53/5.32                = ( groups858564598930262913ex_int @ H2 @ S2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8884_prod_Omono__neutral__cong__right,axiom,
% 9.53/5.32      ! [T4: set_real,S2: set_real,G: real > complex,H2: real > complex] :
% 9.53/5.32        ( ( finite_finite_real @ T4 )
% 9.53/5.32       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: real] :
% 9.53/5.32                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 9.53/5.32               => ( ( G @ X3 )
% 9.53/5.32                  = one_one_complex ) )
% 9.53/5.32           => ( ! [X3: real] :
% 9.53/5.32                  ( ( member_real @ X3 @ S2 )
% 9.53/5.32                 => ( ( G @ X3 )
% 9.53/5.32                    = ( H2 @ X3 ) ) )
% 9.53/5.32             => ( ( groups713298508707869441omplex @ G @ T4 )
% 9.53/5.32                = ( groups713298508707869441omplex @ H2 @ S2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8885_prod_Omono__neutral__cong__left,axiom,
% 9.53/5.32      ! [T4: set_int,S2: set_int,H2: int > complex,G: int > complex] :
% 9.53/5.32        ( ( finite_finite_int @ T4 )
% 9.53/5.32       => ( ( ord_less_eq_set_int @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: int] :
% 9.53/5.32                ( ( member_int @ X3 @ ( minus_minus_set_int @ T4 @ S2 ) )
% 9.53/5.32               => ( ( H2 @ X3 )
% 9.53/5.32                  = one_one_complex ) )
% 9.53/5.32           => ( ! [X3: int] :
% 9.53/5.32                  ( ( member_int @ X3 @ S2 )
% 9.53/5.32                 => ( ( G @ X3 )
% 9.53/5.32                    = ( H2 @ X3 ) ) )
% 9.53/5.32             => ( ( groups7440179247065528705omplex @ G @ S2 )
% 9.53/5.32                = ( groups7440179247065528705omplex @ H2 @ T4 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8886_prod_Omono__neutral__cong__left,axiom,
% 9.53/5.32      ! [T4: set_complex,S2: set_complex,H2: complex > complex,G: complex > complex] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ T4 )
% 9.53/5.32       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: complex] :
% 9.53/5.32                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 9.53/5.32               => ( ( H2 @ X3 )
% 9.53/5.32                  = one_one_complex ) )
% 9.53/5.32           => ( ! [X3: complex] :
% 9.53/5.32                  ( ( member_complex @ X3 @ S2 )
% 9.53/5.32                 => ( ( G @ X3 )
% 9.53/5.32                    = ( H2 @ X3 ) ) )
% 9.53/5.32             => ( ( groups3708469109370488835omplex @ G @ S2 )
% 9.53/5.32                = ( groups3708469109370488835omplex @ H2 @ T4 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8887_prod_Omono__neutral__cong__left,axiom,
% 9.53/5.32      ! [T4: set_int,S2: set_int,H2: int > real,G: int > real] :
% 9.53/5.32        ( ( finite_finite_int @ T4 )
% 9.53/5.32       => ( ( ord_less_eq_set_int @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: int] :
% 9.53/5.32                ( ( member_int @ X3 @ ( minus_minus_set_int @ T4 @ S2 ) )
% 9.53/5.32               => ( ( H2 @ X3 )
% 9.53/5.32                  = one_one_real ) )
% 9.53/5.32           => ( ! [X3: int] :
% 9.53/5.32                  ( ( member_int @ X3 @ S2 )
% 9.53/5.32                 => ( ( G @ X3 )
% 9.53/5.32                    = ( H2 @ X3 ) ) )
% 9.53/5.32             => ( ( groups2316167850115554303t_real @ G @ S2 )
% 9.53/5.32                = ( groups2316167850115554303t_real @ H2 @ T4 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8888_prod_Omono__neutral__cong__left,axiom,
% 9.53/5.32      ! [T4: set_complex,S2: set_complex,H2: complex > real,G: complex > real] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ T4 )
% 9.53/5.32       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: complex] :
% 9.53/5.32                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 9.53/5.32               => ( ( H2 @ X3 )
% 9.53/5.32                  = one_one_real ) )
% 9.53/5.32           => ( ! [X3: complex] :
% 9.53/5.32                  ( ( member_complex @ X3 @ S2 )
% 9.53/5.32                 => ( ( G @ X3 )
% 9.53/5.32                    = ( H2 @ X3 ) ) )
% 9.53/5.32             => ( ( groups766887009212190081x_real @ G @ S2 )
% 9.53/5.32                = ( groups766887009212190081x_real @ H2 @ T4 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8889_prod_Omono__neutral__cong__left,axiom,
% 9.53/5.32      ! [T4: set_int,S2: set_int,H2: int > rat,G: int > rat] :
% 9.53/5.32        ( ( finite_finite_int @ T4 )
% 9.53/5.32       => ( ( ord_less_eq_set_int @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: int] :
% 9.53/5.32                ( ( member_int @ X3 @ ( minus_minus_set_int @ T4 @ S2 ) )
% 9.53/5.32               => ( ( H2 @ X3 )
% 9.53/5.32                  = one_one_rat ) )
% 9.53/5.32           => ( ! [X3: int] :
% 9.53/5.32                  ( ( member_int @ X3 @ S2 )
% 9.53/5.32                 => ( ( G @ X3 )
% 9.53/5.32                    = ( H2 @ X3 ) ) )
% 9.53/5.32             => ( ( groups1072433553688619179nt_rat @ G @ S2 )
% 9.53/5.32                = ( groups1072433553688619179nt_rat @ H2 @ T4 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8890_prod_Omono__neutral__cong__left,axiom,
% 9.53/5.32      ! [T4: set_complex,S2: set_complex,H2: complex > rat,G: complex > rat] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ T4 )
% 9.53/5.32       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: complex] :
% 9.53/5.32                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 9.53/5.32               => ( ( H2 @ X3 )
% 9.53/5.32                  = one_one_rat ) )
% 9.53/5.32           => ( ! [X3: complex] :
% 9.53/5.32                  ( ( member_complex @ X3 @ S2 )
% 9.53/5.32                 => ( ( G @ X3 )
% 9.53/5.32                    = ( H2 @ X3 ) ) )
% 9.53/5.32             => ( ( groups225925009352817453ex_rat @ G @ S2 )
% 9.53/5.32                = ( groups225925009352817453ex_rat @ H2 @ T4 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8891_prod_Omono__neutral__cong__left,axiom,
% 9.53/5.32      ! [T4: set_int,S2: set_int,H2: int > nat,G: int > nat] :
% 9.53/5.32        ( ( finite_finite_int @ T4 )
% 9.53/5.32       => ( ( ord_less_eq_set_int @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: int] :
% 9.53/5.32                ( ( member_int @ X3 @ ( minus_minus_set_int @ T4 @ S2 ) )
% 9.53/5.32               => ( ( H2 @ X3 )
% 9.53/5.32                  = one_one_nat ) )
% 9.53/5.32           => ( ! [X3: int] :
% 9.53/5.32                  ( ( member_int @ X3 @ S2 )
% 9.53/5.32                 => ( ( G @ X3 )
% 9.53/5.32                    = ( H2 @ X3 ) ) )
% 9.53/5.32             => ( ( groups1707563613775114915nt_nat @ G @ S2 )
% 9.53/5.32                = ( groups1707563613775114915nt_nat @ H2 @ T4 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8892_prod_Omono__neutral__cong__left,axiom,
% 9.53/5.32      ! [T4: set_complex,S2: set_complex,H2: complex > nat,G: complex > nat] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ T4 )
% 9.53/5.32       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: complex] :
% 9.53/5.32                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 9.53/5.32               => ( ( H2 @ X3 )
% 9.53/5.32                  = one_one_nat ) )
% 9.53/5.32           => ( ! [X3: complex] :
% 9.53/5.32                  ( ( member_complex @ X3 @ S2 )
% 9.53/5.32                 => ( ( G @ X3 )
% 9.53/5.32                    = ( H2 @ X3 ) ) )
% 9.53/5.32             => ( ( groups861055069439313189ex_nat @ G @ S2 )
% 9.53/5.32                = ( groups861055069439313189ex_nat @ H2 @ T4 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8893_prod_Omono__neutral__cong__left,axiom,
% 9.53/5.32      ! [T4: set_complex,S2: set_complex,H2: complex > int,G: complex > int] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ T4 )
% 9.53/5.32       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: complex] :
% 9.53/5.32                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 9.53/5.32               => ( ( H2 @ X3 )
% 9.53/5.32                  = one_one_int ) )
% 9.53/5.32           => ( ! [X3: complex] :
% 9.53/5.32                  ( ( member_complex @ X3 @ S2 )
% 9.53/5.32                 => ( ( G @ X3 )
% 9.53/5.32                    = ( H2 @ X3 ) ) )
% 9.53/5.32             => ( ( groups858564598930262913ex_int @ G @ S2 )
% 9.53/5.32                = ( groups858564598930262913ex_int @ H2 @ T4 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8894_prod_Omono__neutral__cong__left,axiom,
% 9.53/5.32      ! [T4: set_real,S2: set_real,H2: real > complex,G: real > complex] :
% 9.53/5.32        ( ( finite_finite_real @ T4 )
% 9.53/5.32       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: real] :
% 9.53/5.32                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 9.53/5.32               => ( ( H2 @ X3 )
% 9.53/5.32                  = one_one_complex ) )
% 9.53/5.32           => ( ! [X3: real] :
% 9.53/5.32                  ( ( member_real @ X3 @ S2 )
% 9.53/5.32                 => ( ( G @ X3 )
% 9.53/5.32                    = ( H2 @ X3 ) ) )
% 9.53/5.32             => ( ( groups713298508707869441omplex @ G @ S2 )
% 9.53/5.32                = ( groups713298508707869441omplex @ H2 @ T4 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8895_prod_Omono__neutral__right,axiom,
% 9.53/5.32      ! [T4: set_complex,S2: set_complex,G: complex > complex] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ T4 )
% 9.53/5.32       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: complex] :
% 9.53/5.32                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 9.53/5.32               => ( ( G @ X3 )
% 9.53/5.32                  = one_one_complex ) )
% 9.53/5.32           => ( ( groups3708469109370488835omplex @ G @ T4 )
% 9.53/5.32              = ( groups3708469109370488835omplex @ G @ S2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8896_prod_Omono__neutral__right,axiom,
% 9.53/5.32      ! [T4: set_complex,S2: set_complex,G: complex > real] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ T4 )
% 9.53/5.32       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: complex] :
% 9.53/5.32                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 9.53/5.32               => ( ( G @ X3 )
% 9.53/5.32                  = one_one_real ) )
% 9.53/5.32           => ( ( groups766887009212190081x_real @ G @ T4 )
% 9.53/5.32              = ( groups766887009212190081x_real @ G @ S2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8897_prod_Omono__neutral__right,axiom,
% 9.53/5.32      ! [T4: set_complex,S2: set_complex,G: complex > rat] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ T4 )
% 9.53/5.32       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: complex] :
% 9.53/5.32                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 9.53/5.32               => ( ( G @ X3 )
% 9.53/5.32                  = one_one_rat ) )
% 9.53/5.32           => ( ( groups225925009352817453ex_rat @ G @ T4 )
% 9.53/5.32              = ( groups225925009352817453ex_rat @ G @ S2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8898_prod_Omono__neutral__right,axiom,
% 9.53/5.32      ! [T4: set_complex,S2: set_complex,G: complex > nat] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ T4 )
% 9.53/5.32       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: complex] :
% 9.53/5.32                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 9.53/5.32               => ( ( G @ X3 )
% 9.53/5.32                  = one_one_nat ) )
% 9.53/5.32           => ( ( groups861055069439313189ex_nat @ G @ T4 )
% 9.53/5.32              = ( groups861055069439313189ex_nat @ G @ S2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8899_prod_Omono__neutral__right,axiom,
% 9.53/5.32      ! [T4: set_complex,S2: set_complex,G: complex > int] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ T4 )
% 9.53/5.32       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: complex] :
% 9.53/5.32                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 9.53/5.32               => ( ( G @ X3 )
% 9.53/5.32                  = one_one_int ) )
% 9.53/5.32           => ( ( groups858564598930262913ex_int @ G @ T4 )
% 9.53/5.32              = ( groups858564598930262913ex_int @ G @ S2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8900_prod_Omono__neutral__right,axiom,
% 9.53/5.32      ! [T4: set_real,S2: set_real,G: real > complex] :
% 9.53/5.32        ( ( finite_finite_real @ T4 )
% 9.53/5.32       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: real] :
% 9.53/5.32                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 9.53/5.32               => ( ( G @ X3 )
% 9.53/5.32                  = one_one_complex ) )
% 9.53/5.32           => ( ( groups713298508707869441omplex @ G @ T4 )
% 9.53/5.32              = ( groups713298508707869441omplex @ G @ S2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8901_prod_Omono__neutral__right,axiom,
% 9.53/5.32      ! [T4: set_real,S2: set_real,G: real > real] :
% 9.53/5.32        ( ( finite_finite_real @ T4 )
% 9.53/5.32       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: real] :
% 9.53/5.32                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 9.53/5.32               => ( ( G @ X3 )
% 9.53/5.32                  = one_one_real ) )
% 9.53/5.32           => ( ( groups1681761925125756287l_real @ G @ T4 )
% 9.53/5.32              = ( groups1681761925125756287l_real @ G @ S2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8902_prod_Omono__neutral__right,axiom,
% 9.53/5.32      ! [T4: set_real,S2: set_real,G: real > rat] :
% 9.53/5.32        ( ( finite_finite_real @ T4 )
% 9.53/5.32       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: real] :
% 9.53/5.32                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 9.53/5.32               => ( ( G @ X3 )
% 9.53/5.32                  = one_one_rat ) )
% 9.53/5.32           => ( ( groups4061424788464935467al_rat @ G @ T4 )
% 9.53/5.32              = ( groups4061424788464935467al_rat @ G @ S2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8903_prod_Omono__neutral__right,axiom,
% 9.53/5.32      ! [T4: set_real,S2: set_real,G: real > nat] :
% 9.53/5.32        ( ( finite_finite_real @ T4 )
% 9.53/5.32       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: real] :
% 9.53/5.32                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 9.53/5.32               => ( ( G @ X3 )
% 9.53/5.32                  = one_one_nat ) )
% 9.53/5.32           => ( ( groups4696554848551431203al_nat @ G @ T4 )
% 9.53/5.32              = ( groups4696554848551431203al_nat @ G @ S2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8904_prod_Omono__neutral__right,axiom,
% 9.53/5.32      ! [T4: set_real,S2: set_real,G: real > int] :
% 9.53/5.32        ( ( finite_finite_real @ T4 )
% 9.53/5.32       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: real] :
% 9.53/5.32                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 9.53/5.32               => ( ( G @ X3 )
% 9.53/5.32                  = one_one_int ) )
% 9.53/5.32           => ( ( groups4694064378042380927al_int @ G @ T4 )
% 9.53/5.32              = ( groups4694064378042380927al_int @ G @ S2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8905_prod_Omono__neutral__left,axiom,
% 9.53/5.32      ! [T4: set_complex,S2: set_complex,G: complex > complex] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ T4 )
% 9.53/5.32       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: complex] :
% 9.53/5.32                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 9.53/5.32               => ( ( G @ X3 )
% 9.53/5.32                  = one_one_complex ) )
% 9.53/5.32           => ( ( groups3708469109370488835omplex @ G @ S2 )
% 9.53/5.32              = ( groups3708469109370488835omplex @ G @ T4 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8906_prod_Omono__neutral__left,axiom,
% 9.53/5.32      ! [T4: set_complex,S2: set_complex,G: complex > real] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ T4 )
% 9.53/5.32       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: complex] :
% 9.53/5.32                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 9.53/5.32               => ( ( G @ X3 )
% 9.53/5.32                  = one_one_real ) )
% 9.53/5.32           => ( ( groups766887009212190081x_real @ G @ S2 )
% 9.53/5.32              = ( groups766887009212190081x_real @ G @ T4 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8907_prod_Omono__neutral__left,axiom,
% 9.53/5.32      ! [T4: set_complex,S2: set_complex,G: complex > rat] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ T4 )
% 9.53/5.32       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: complex] :
% 9.53/5.32                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 9.53/5.32               => ( ( G @ X3 )
% 9.53/5.32                  = one_one_rat ) )
% 9.53/5.32           => ( ( groups225925009352817453ex_rat @ G @ S2 )
% 9.53/5.32              = ( groups225925009352817453ex_rat @ G @ T4 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8908_prod_Omono__neutral__left,axiom,
% 9.53/5.32      ! [T4: set_complex,S2: set_complex,G: complex > nat] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ T4 )
% 9.53/5.32       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: complex] :
% 9.53/5.32                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 9.53/5.32               => ( ( G @ X3 )
% 9.53/5.32                  = one_one_nat ) )
% 9.53/5.32           => ( ( groups861055069439313189ex_nat @ G @ S2 )
% 9.53/5.32              = ( groups861055069439313189ex_nat @ G @ T4 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8909_prod_Omono__neutral__left,axiom,
% 9.53/5.32      ! [T4: set_complex,S2: set_complex,G: complex > int] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ T4 )
% 9.53/5.32       => ( ( ord_le211207098394363844omplex @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: complex] :
% 9.53/5.32                ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T4 @ S2 ) )
% 9.53/5.32               => ( ( G @ X3 )
% 9.53/5.32                  = one_one_int ) )
% 9.53/5.32           => ( ( groups858564598930262913ex_int @ G @ S2 )
% 9.53/5.32              = ( groups858564598930262913ex_int @ G @ T4 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8910_prod_Omono__neutral__left,axiom,
% 9.53/5.32      ! [T4: set_real,S2: set_real,G: real > complex] :
% 9.53/5.32        ( ( finite_finite_real @ T4 )
% 9.53/5.32       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: real] :
% 9.53/5.32                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 9.53/5.32               => ( ( G @ X3 )
% 9.53/5.32                  = one_one_complex ) )
% 9.53/5.32           => ( ( groups713298508707869441omplex @ G @ S2 )
% 9.53/5.32              = ( groups713298508707869441omplex @ G @ T4 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8911_prod_Omono__neutral__left,axiom,
% 9.53/5.32      ! [T4: set_real,S2: set_real,G: real > real] :
% 9.53/5.32        ( ( finite_finite_real @ T4 )
% 9.53/5.32       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: real] :
% 9.53/5.32                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 9.53/5.32               => ( ( G @ X3 )
% 9.53/5.32                  = one_one_real ) )
% 9.53/5.32           => ( ( groups1681761925125756287l_real @ G @ S2 )
% 9.53/5.32              = ( groups1681761925125756287l_real @ G @ T4 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8912_prod_Omono__neutral__left,axiom,
% 9.53/5.32      ! [T4: set_real,S2: set_real,G: real > rat] :
% 9.53/5.32        ( ( finite_finite_real @ T4 )
% 9.53/5.32       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: real] :
% 9.53/5.32                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 9.53/5.32               => ( ( G @ X3 )
% 9.53/5.32                  = one_one_rat ) )
% 9.53/5.32           => ( ( groups4061424788464935467al_rat @ G @ S2 )
% 9.53/5.32              = ( groups4061424788464935467al_rat @ G @ T4 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8913_prod_Omono__neutral__left,axiom,
% 9.53/5.32      ! [T4: set_real,S2: set_real,G: real > nat] :
% 9.53/5.32        ( ( finite_finite_real @ T4 )
% 9.53/5.32       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: real] :
% 9.53/5.32                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 9.53/5.32               => ( ( G @ X3 )
% 9.53/5.32                  = one_one_nat ) )
% 9.53/5.32           => ( ( groups4696554848551431203al_nat @ G @ S2 )
% 9.53/5.32              = ( groups4696554848551431203al_nat @ G @ T4 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8914_prod_Omono__neutral__left,axiom,
% 9.53/5.32      ! [T4: set_real,S2: set_real,G: real > int] :
% 9.53/5.32        ( ( finite_finite_real @ T4 )
% 9.53/5.32       => ( ( ord_less_eq_set_real @ S2 @ T4 )
% 9.53/5.32         => ( ! [X3: real] :
% 9.53/5.32                ( ( member_real @ X3 @ ( minus_minus_set_real @ T4 @ S2 ) )
% 9.53/5.32               => ( ( G @ X3 )
% 9.53/5.32                  = one_one_int ) )
% 9.53/5.32           => ( ( groups4694064378042380927al_int @ G @ S2 )
% 9.53/5.32              = ( groups4694064378042380927al_int @ G @ T4 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8915_prod_Osame__carrierI,axiom,
% 9.53/5.32      ! [C4: set_int,A2: set_int,B2: set_int,G: int > complex,H2: int > complex] :
% 9.53/5.32        ( ( finite_finite_int @ C4 )
% 9.53/5.32       => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 9.53/5.32         => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 9.53/5.32           => ( ! [A4: int] :
% 9.53/5.32                  ( ( member_int @ A4 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 9.53/5.32                 => ( ( G @ A4 )
% 9.53/5.32                    = one_one_complex ) )
% 9.53/5.32             => ( ! [B3: int] :
% 9.53/5.32                    ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 9.53/5.32                   => ( ( H2 @ B3 )
% 9.53/5.32                      = one_one_complex ) )
% 9.53/5.32               => ( ( ( groups7440179247065528705omplex @ G @ C4 )
% 9.53/5.32                    = ( groups7440179247065528705omplex @ H2 @ C4 ) )
% 9.53/5.32                 => ( ( groups7440179247065528705omplex @ G @ A2 )
% 9.53/5.32                    = ( groups7440179247065528705omplex @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8916_prod_Osame__carrierI,axiom,
% 9.53/5.32      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > complex,H2: complex > complex] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ C4 )
% 9.53/5.32       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 9.53/5.32         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 9.53/5.32           => ( ! [A4: complex] :
% 9.53/5.32                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 9.53/5.32                 => ( ( G @ A4 )
% 9.53/5.32                    = one_one_complex ) )
% 9.53/5.32             => ( ! [B3: complex] :
% 9.53/5.32                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 9.53/5.32                   => ( ( H2 @ B3 )
% 9.53/5.32                      = one_one_complex ) )
% 9.53/5.32               => ( ( ( groups3708469109370488835omplex @ G @ C4 )
% 9.53/5.32                    = ( groups3708469109370488835omplex @ H2 @ C4 ) )
% 9.53/5.32                 => ( ( groups3708469109370488835omplex @ G @ A2 )
% 9.53/5.32                    = ( groups3708469109370488835omplex @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8917_prod_Osame__carrierI,axiom,
% 9.53/5.32      ! [C4: set_int,A2: set_int,B2: set_int,G: int > real,H2: int > real] :
% 9.53/5.32        ( ( finite_finite_int @ C4 )
% 9.53/5.32       => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 9.53/5.32         => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 9.53/5.32           => ( ! [A4: int] :
% 9.53/5.32                  ( ( member_int @ A4 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 9.53/5.32                 => ( ( G @ A4 )
% 9.53/5.32                    = one_one_real ) )
% 9.53/5.32             => ( ! [B3: int] :
% 9.53/5.32                    ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 9.53/5.32                   => ( ( H2 @ B3 )
% 9.53/5.32                      = one_one_real ) )
% 9.53/5.32               => ( ( ( groups2316167850115554303t_real @ G @ C4 )
% 9.53/5.32                    = ( groups2316167850115554303t_real @ H2 @ C4 ) )
% 9.53/5.32                 => ( ( groups2316167850115554303t_real @ G @ A2 )
% 9.53/5.32                    = ( groups2316167850115554303t_real @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8918_prod_Osame__carrierI,axiom,
% 9.53/5.32      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > real,H2: complex > real] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ C4 )
% 9.53/5.32       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 9.53/5.32         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 9.53/5.32           => ( ! [A4: complex] :
% 9.53/5.32                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 9.53/5.32                 => ( ( G @ A4 )
% 9.53/5.32                    = one_one_real ) )
% 9.53/5.32             => ( ! [B3: complex] :
% 9.53/5.32                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 9.53/5.32                   => ( ( H2 @ B3 )
% 9.53/5.32                      = one_one_real ) )
% 9.53/5.32               => ( ( ( groups766887009212190081x_real @ G @ C4 )
% 9.53/5.32                    = ( groups766887009212190081x_real @ H2 @ C4 ) )
% 9.53/5.32                 => ( ( groups766887009212190081x_real @ G @ A2 )
% 9.53/5.32                    = ( groups766887009212190081x_real @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8919_prod_Osame__carrierI,axiom,
% 9.53/5.32      ! [C4: set_int,A2: set_int,B2: set_int,G: int > rat,H2: int > rat] :
% 9.53/5.32        ( ( finite_finite_int @ C4 )
% 9.53/5.32       => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 9.53/5.32         => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 9.53/5.32           => ( ! [A4: int] :
% 9.53/5.32                  ( ( member_int @ A4 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 9.53/5.32                 => ( ( G @ A4 )
% 9.53/5.32                    = one_one_rat ) )
% 9.53/5.32             => ( ! [B3: int] :
% 9.53/5.32                    ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 9.53/5.32                   => ( ( H2 @ B3 )
% 9.53/5.32                      = one_one_rat ) )
% 9.53/5.32               => ( ( ( groups1072433553688619179nt_rat @ G @ C4 )
% 9.53/5.32                    = ( groups1072433553688619179nt_rat @ H2 @ C4 ) )
% 9.53/5.32                 => ( ( groups1072433553688619179nt_rat @ G @ A2 )
% 9.53/5.32                    = ( groups1072433553688619179nt_rat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8920_prod_Osame__carrierI,axiom,
% 9.53/5.32      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > rat,H2: complex > rat] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ C4 )
% 9.53/5.32       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 9.53/5.32         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 9.53/5.32           => ( ! [A4: complex] :
% 9.53/5.32                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 9.53/5.32                 => ( ( G @ A4 )
% 9.53/5.32                    = one_one_rat ) )
% 9.53/5.32             => ( ! [B3: complex] :
% 9.53/5.32                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 9.53/5.32                   => ( ( H2 @ B3 )
% 9.53/5.32                      = one_one_rat ) )
% 9.53/5.32               => ( ( ( groups225925009352817453ex_rat @ G @ C4 )
% 9.53/5.32                    = ( groups225925009352817453ex_rat @ H2 @ C4 ) )
% 9.53/5.32                 => ( ( groups225925009352817453ex_rat @ G @ A2 )
% 9.53/5.32                    = ( groups225925009352817453ex_rat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8921_prod_Osame__carrierI,axiom,
% 9.53/5.32      ! [C4: set_int,A2: set_int,B2: set_int,G: int > nat,H2: int > nat] :
% 9.53/5.32        ( ( finite_finite_int @ C4 )
% 9.53/5.32       => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 9.53/5.32         => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 9.53/5.32           => ( ! [A4: int] :
% 9.53/5.32                  ( ( member_int @ A4 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 9.53/5.32                 => ( ( G @ A4 )
% 9.53/5.32                    = one_one_nat ) )
% 9.53/5.32             => ( ! [B3: int] :
% 9.53/5.32                    ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 9.53/5.32                   => ( ( H2 @ B3 )
% 9.53/5.32                      = one_one_nat ) )
% 9.53/5.32               => ( ( ( groups1707563613775114915nt_nat @ G @ C4 )
% 9.53/5.32                    = ( groups1707563613775114915nt_nat @ H2 @ C4 ) )
% 9.53/5.32                 => ( ( groups1707563613775114915nt_nat @ G @ A2 )
% 9.53/5.32                    = ( groups1707563613775114915nt_nat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8922_prod_Osame__carrierI,axiom,
% 9.53/5.32      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > nat,H2: complex > nat] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ C4 )
% 9.53/5.32       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 9.53/5.32         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 9.53/5.32           => ( ! [A4: complex] :
% 9.53/5.32                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 9.53/5.32                 => ( ( G @ A4 )
% 9.53/5.32                    = one_one_nat ) )
% 9.53/5.32             => ( ! [B3: complex] :
% 9.53/5.32                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 9.53/5.32                   => ( ( H2 @ B3 )
% 9.53/5.32                      = one_one_nat ) )
% 9.53/5.32               => ( ( ( groups861055069439313189ex_nat @ G @ C4 )
% 9.53/5.32                    = ( groups861055069439313189ex_nat @ H2 @ C4 ) )
% 9.53/5.32                 => ( ( groups861055069439313189ex_nat @ G @ A2 )
% 9.53/5.32                    = ( groups861055069439313189ex_nat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8923_prod_Osame__carrierI,axiom,
% 9.53/5.32      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > int,H2: complex > int] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ C4 )
% 9.53/5.32       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 9.53/5.32         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 9.53/5.32           => ( ! [A4: complex] :
% 9.53/5.32                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 9.53/5.32                 => ( ( G @ A4 )
% 9.53/5.32                    = one_one_int ) )
% 9.53/5.32             => ( ! [B3: complex] :
% 9.53/5.32                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 9.53/5.32                   => ( ( H2 @ B3 )
% 9.53/5.32                      = one_one_int ) )
% 9.53/5.32               => ( ( ( groups858564598930262913ex_int @ G @ C4 )
% 9.53/5.32                    = ( groups858564598930262913ex_int @ H2 @ C4 ) )
% 9.53/5.32                 => ( ( groups858564598930262913ex_int @ G @ A2 )
% 9.53/5.32                    = ( groups858564598930262913ex_int @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8924_prod_Osame__carrierI,axiom,
% 9.53/5.32      ! [C4: set_real,A2: set_real,B2: set_real,G: real > complex,H2: real > complex] :
% 9.53/5.32        ( ( finite_finite_real @ C4 )
% 9.53/5.32       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 9.53/5.32         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 9.53/5.32           => ( ! [A4: real] :
% 9.53/5.32                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 9.53/5.32                 => ( ( G @ A4 )
% 9.53/5.32                    = one_one_complex ) )
% 9.53/5.32             => ( ! [B3: real] :
% 9.53/5.32                    ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 9.53/5.32                   => ( ( H2 @ B3 )
% 9.53/5.32                      = one_one_complex ) )
% 9.53/5.32               => ( ( ( groups713298508707869441omplex @ G @ C4 )
% 9.53/5.32                    = ( groups713298508707869441omplex @ H2 @ C4 ) )
% 9.53/5.32                 => ( ( groups713298508707869441omplex @ G @ A2 )
% 9.53/5.32                    = ( groups713298508707869441omplex @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8925_prod_Osame__carrier,axiom,
% 9.53/5.32      ! [C4: set_int,A2: set_int,B2: set_int,G: int > complex,H2: int > complex] :
% 9.53/5.32        ( ( finite_finite_int @ C4 )
% 9.53/5.32       => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 9.53/5.32         => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 9.53/5.32           => ( ! [A4: int] :
% 9.53/5.32                  ( ( member_int @ A4 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 9.53/5.32                 => ( ( G @ A4 )
% 9.53/5.32                    = one_one_complex ) )
% 9.53/5.32             => ( ! [B3: int] :
% 9.53/5.32                    ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 9.53/5.32                   => ( ( H2 @ B3 )
% 9.53/5.32                      = one_one_complex ) )
% 9.53/5.32               => ( ( ( groups7440179247065528705omplex @ G @ A2 )
% 9.53/5.32                    = ( groups7440179247065528705omplex @ H2 @ B2 ) )
% 9.53/5.32                  = ( ( groups7440179247065528705omplex @ G @ C4 )
% 9.53/5.32                    = ( groups7440179247065528705omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8926_prod_Osame__carrier,axiom,
% 9.53/5.32      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > complex,H2: complex > complex] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ C4 )
% 9.53/5.32       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 9.53/5.32         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 9.53/5.32           => ( ! [A4: complex] :
% 9.53/5.32                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 9.53/5.32                 => ( ( G @ A4 )
% 9.53/5.32                    = one_one_complex ) )
% 9.53/5.32             => ( ! [B3: complex] :
% 9.53/5.32                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 9.53/5.32                   => ( ( H2 @ B3 )
% 9.53/5.32                      = one_one_complex ) )
% 9.53/5.32               => ( ( ( groups3708469109370488835omplex @ G @ A2 )
% 9.53/5.32                    = ( groups3708469109370488835omplex @ H2 @ B2 ) )
% 9.53/5.32                  = ( ( groups3708469109370488835omplex @ G @ C4 )
% 9.53/5.32                    = ( groups3708469109370488835omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8927_prod_Osame__carrier,axiom,
% 9.53/5.32      ! [C4: set_int,A2: set_int,B2: set_int,G: int > real,H2: int > real] :
% 9.53/5.32        ( ( finite_finite_int @ C4 )
% 9.53/5.32       => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 9.53/5.32         => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 9.53/5.32           => ( ! [A4: int] :
% 9.53/5.32                  ( ( member_int @ A4 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 9.53/5.32                 => ( ( G @ A4 )
% 9.53/5.32                    = one_one_real ) )
% 9.53/5.32             => ( ! [B3: int] :
% 9.53/5.32                    ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 9.53/5.32                   => ( ( H2 @ B3 )
% 9.53/5.32                      = one_one_real ) )
% 9.53/5.32               => ( ( ( groups2316167850115554303t_real @ G @ A2 )
% 9.53/5.32                    = ( groups2316167850115554303t_real @ H2 @ B2 ) )
% 9.53/5.32                  = ( ( groups2316167850115554303t_real @ G @ C4 )
% 9.53/5.32                    = ( groups2316167850115554303t_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8928_prod_Osame__carrier,axiom,
% 9.53/5.32      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > real,H2: complex > real] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ C4 )
% 9.53/5.32       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 9.53/5.32         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 9.53/5.32           => ( ! [A4: complex] :
% 9.53/5.32                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 9.53/5.32                 => ( ( G @ A4 )
% 9.53/5.32                    = one_one_real ) )
% 9.53/5.32             => ( ! [B3: complex] :
% 9.53/5.32                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 9.53/5.32                   => ( ( H2 @ B3 )
% 9.53/5.32                      = one_one_real ) )
% 9.53/5.32               => ( ( ( groups766887009212190081x_real @ G @ A2 )
% 9.53/5.32                    = ( groups766887009212190081x_real @ H2 @ B2 ) )
% 9.53/5.32                  = ( ( groups766887009212190081x_real @ G @ C4 )
% 9.53/5.32                    = ( groups766887009212190081x_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8929_prod_Osame__carrier,axiom,
% 9.53/5.32      ! [C4: set_int,A2: set_int,B2: set_int,G: int > rat,H2: int > rat] :
% 9.53/5.32        ( ( finite_finite_int @ C4 )
% 9.53/5.32       => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 9.53/5.32         => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 9.53/5.32           => ( ! [A4: int] :
% 9.53/5.32                  ( ( member_int @ A4 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 9.53/5.32                 => ( ( G @ A4 )
% 9.53/5.32                    = one_one_rat ) )
% 9.53/5.32             => ( ! [B3: int] :
% 9.53/5.32                    ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 9.53/5.32                   => ( ( H2 @ B3 )
% 9.53/5.32                      = one_one_rat ) )
% 9.53/5.32               => ( ( ( groups1072433553688619179nt_rat @ G @ A2 )
% 9.53/5.32                    = ( groups1072433553688619179nt_rat @ H2 @ B2 ) )
% 9.53/5.32                  = ( ( groups1072433553688619179nt_rat @ G @ C4 )
% 9.53/5.32                    = ( groups1072433553688619179nt_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8930_prod_Osame__carrier,axiom,
% 9.53/5.32      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > rat,H2: complex > rat] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ C4 )
% 9.53/5.32       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 9.53/5.32         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 9.53/5.32           => ( ! [A4: complex] :
% 9.53/5.32                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 9.53/5.32                 => ( ( G @ A4 )
% 9.53/5.32                    = one_one_rat ) )
% 9.53/5.32             => ( ! [B3: complex] :
% 9.53/5.32                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 9.53/5.32                   => ( ( H2 @ B3 )
% 9.53/5.32                      = one_one_rat ) )
% 9.53/5.32               => ( ( ( groups225925009352817453ex_rat @ G @ A2 )
% 9.53/5.32                    = ( groups225925009352817453ex_rat @ H2 @ B2 ) )
% 9.53/5.32                  = ( ( groups225925009352817453ex_rat @ G @ C4 )
% 9.53/5.32                    = ( groups225925009352817453ex_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8931_prod_Osame__carrier,axiom,
% 9.53/5.32      ! [C4: set_int,A2: set_int,B2: set_int,G: int > nat,H2: int > nat] :
% 9.53/5.32        ( ( finite_finite_int @ C4 )
% 9.53/5.32       => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 9.53/5.32         => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 9.53/5.32           => ( ! [A4: int] :
% 9.53/5.32                  ( ( member_int @ A4 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 9.53/5.32                 => ( ( G @ A4 )
% 9.53/5.32                    = one_one_nat ) )
% 9.53/5.32             => ( ! [B3: int] :
% 9.53/5.32                    ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 9.53/5.32                   => ( ( H2 @ B3 )
% 9.53/5.32                      = one_one_nat ) )
% 9.53/5.32               => ( ( ( groups1707563613775114915nt_nat @ G @ A2 )
% 9.53/5.32                    = ( groups1707563613775114915nt_nat @ H2 @ B2 ) )
% 9.53/5.32                  = ( ( groups1707563613775114915nt_nat @ G @ C4 )
% 9.53/5.32                    = ( groups1707563613775114915nt_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8932_prod_Osame__carrier,axiom,
% 9.53/5.32      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > nat,H2: complex > nat] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ C4 )
% 9.53/5.32       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 9.53/5.32         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 9.53/5.32           => ( ! [A4: complex] :
% 9.53/5.32                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 9.53/5.32                 => ( ( G @ A4 )
% 9.53/5.32                    = one_one_nat ) )
% 9.53/5.32             => ( ! [B3: complex] :
% 9.53/5.32                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 9.53/5.32                   => ( ( H2 @ B3 )
% 9.53/5.32                      = one_one_nat ) )
% 9.53/5.32               => ( ( ( groups861055069439313189ex_nat @ G @ A2 )
% 9.53/5.32                    = ( groups861055069439313189ex_nat @ H2 @ B2 ) )
% 9.53/5.32                  = ( ( groups861055069439313189ex_nat @ G @ C4 )
% 9.53/5.32                    = ( groups861055069439313189ex_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8933_prod_Osame__carrier,axiom,
% 9.53/5.32      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > int,H2: complex > int] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ C4 )
% 9.53/5.32       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 9.53/5.32         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 9.53/5.32           => ( ! [A4: complex] :
% 9.53/5.32                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 9.53/5.32                 => ( ( G @ A4 )
% 9.53/5.32                    = one_one_int ) )
% 9.53/5.32             => ( ! [B3: complex] :
% 9.53/5.32                    ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 9.53/5.32                   => ( ( H2 @ B3 )
% 9.53/5.32                      = one_one_int ) )
% 9.53/5.32               => ( ( ( groups858564598930262913ex_int @ G @ A2 )
% 9.53/5.32                    = ( groups858564598930262913ex_int @ H2 @ B2 ) )
% 9.53/5.32                  = ( ( groups858564598930262913ex_int @ G @ C4 )
% 9.53/5.32                    = ( groups858564598930262913ex_int @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8934_prod_Osame__carrier,axiom,
% 9.53/5.32      ! [C4: set_real,A2: set_real,B2: set_real,G: real > complex,H2: real > complex] :
% 9.53/5.32        ( ( finite_finite_real @ C4 )
% 9.53/5.32       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 9.53/5.32         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 9.53/5.32           => ( ! [A4: real] :
% 9.53/5.32                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 9.53/5.32                 => ( ( G @ A4 )
% 9.53/5.32                    = one_one_complex ) )
% 9.53/5.32             => ( ! [B3: real] :
% 9.53/5.32                    ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 9.53/5.32                   => ( ( H2 @ B3 )
% 9.53/5.32                      = one_one_complex ) )
% 9.53/5.32               => ( ( ( groups713298508707869441omplex @ G @ A2 )
% 9.53/5.32                    = ( groups713298508707869441omplex @ H2 @ B2 ) )
% 9.53/5.32                  = ( ( groups713298508707869441omplex @ G @ C4 )
% 9.53/5.32                    = ( groups713298508707869441omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8935_prod_OatLeast0__atMost__Suc,axiom,
% 9.53/5.32      ! [G: nat > complex,N: nat] :
% 9.53/5.32        ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 9.53/5.32        = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8936_prod_OatLeast0__atMost__Suc,axiom,
% 9.53/5.32      ! [G: nat > real,N: nat] :
% 9.53/5.32        ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 9.53/5.32        = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8937_prod_OatLeast0__atMost__Suc,axiom,
% 9.53/5.32      ! [G: nat > nat,N: nat] :
% 9.53/5.32        ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 9.53/5.32        = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8938_prod_OatLeast0__atMost__Suc,axiom,
% 9.53/5.32      ! [G: nat > int,N: nat] :
% 9.53/5.32        ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 9.53/5.32        = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8939_prod_OatLeast__Suc__atMost,axiom,
% 9.53/5.32      ! [M: nat,N: nat,G: nat > complex] :
% 9.53/5.32        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.32       => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.53/5.32          = ( times_times_complex @ ( G @ M ) @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8940_prod_OatLeast__Suc__atMost,axiom,
% 9.53/5.32      ! [M: nat,N: nat,G: nat > real] :
% 9.53/5.32        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.32       => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.53/5.32          = ( times_times_real @ ( G @ M ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8941_prod_OatLeast__Suc__atMost,axiom,
% 9.53/5.32      ! [M: nat,N: nat,G: nat > nat] :
% 9.53/5.32        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.32       => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.53/5.32          = ( times_times_nat @ ( G @ M ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8942_prod_OatLeast__Suc__atMost,axiom,
% 9.53/5.32      ! [M: nat,N: nat,G: nat > int] :
% 9.53/5.32        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.32       => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.53/5.32          = ( times_times_int @ ( G @ M ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8943_prod_Onat__ivl__Suc_H,axiom,
% 9.53/5.32      ! [M: nat,N: nat,G: nat > complex] :
% 9.53/5.32        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 9.53/5.32       => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.53/5.32          = ( times_times_complex @ ( G @ ( suc @ N ) ) @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8944_prod_Onat__ivl__Suc_H,axiom,
% 9.53/5.32      ! [M: nat,N: nat,G: nat > real] :
% 9.53/5.32        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 9.53/5.32       => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.53/5.32          = ( times_times_real @ ( G @ ( suc @ N ) ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8945_prod_Onat__ivl__Suc_H,axiom,
% 9.53/5.32      ! [M: nat,N: nat,G: nat > nat] :
% 9.53/5.32        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 9.53/5.32       => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.53/5.32          = ( times_times_nat @ ( G @ ( suc @ N ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8946_prod_Onat__ivl__Suc_H,axiom,
% 9.53/5.32      ! [M: nat,N: nat,G: nat > int] :
% 9.53/5.32        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 9.53/5.32       => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.53/5.32          = ( times_times_int @ ( G @ ( suc @ N ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8947_prod_OlessThan__Suc__shift,axiom,
% 9.53/5.32      ! [G: nat > complex,N: nat] :
% 9.53/5.32        ( ( groups6464643781859351333omplex @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 9.53/5.32        = ( times_times_complex @ ( G @ zero_zero_nat )
% 9.53/5.32          @ ( groups6464643781859351333omplex
% 9.53/5.32            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.53/5.32            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8948_prod_OlessThan__Suc__shift,axiom,
% 9.53/5.32      ! [G: nat > real,N: nat] :
% 9.53/5.32        ( ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 9.53/5.32        = ( times_times_real @ ( G @ zero_zero_nat )
% 9.53/5.32          @ ( groups129246275422532515t_real
% 9.53/5.32            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.53/5.32            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8949_prod_OlessThan__Suc__shift,axiom,
% 9.53/5.32      ! [G: nat > nat,N: nat] :
% 9.53/5.32        ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 9.53/5.32        = ( times_times_nat @ ( G @ zero_zero_nat )
% 9.53/5.32          @ ( groups708209901874060359at_nat
% 9.53/5.32            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.53/5.32            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8950_prod_OlessThan__Suc__shift,axiom,
% 9.53/5.32      ! [G: nat > int,N: nat] :
% 9.53/5.32        ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 9.53/5.32        = ( times_times_int @ ( G @ zero_zero_nat )
% 9.53/5.32          @ ( groups705719431365010083at_int
% 9.53/5.32            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.53/5.32            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8951_prod_OSuc__reindex__ivl,axiom,
% 9.53/5.32      ! [M: nat,N: nat,G: nat > complex] :
% 9.53/5.32        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.32       => ( ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 9.53/5.32          = ( times_times_complex @ ( G @ M )
% 9.53/5.32            @ ( groups6464643781859351333omplex
% 9.53/5.32              @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.53/5.32              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8952_prod_OSuc__reindex__ivl,axiom,
% 9.53/5.32      ! [M: nat,N: nat,G: nat > real] :
% 9.53/5.32        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.32       => ( ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 9.53/5.32          = ( times_times_real @ ( G @ M )
% 9.53/5.32            @ ( groups129246275422532515t_real
% 9.53/5.32              @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.53/5.32              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8953_prod_OSuc__reindex__ivl,axiom,
% 9.53/5.32      ! [M: nat,N: nat,G: nat > nat] :
% 9.53/5.32        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.32       => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 9.53/5.32          = ( times_times_nat @ ( G @ M )
% 9.53/5.32            @ ( groups708209901874060359at_nat
% 9.53/5.32              @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.53/5.32              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8954_prod_OSuc__reindex__ivl,axiom,
% 9.53/5.32      ! [M: nat,N: nat,G: nat > int] :
% 9.53/5.32        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.32       => ( ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 9.53/5.32          = ( times_times_int @ ( G @ M )
% 9.53/5.32            @ ( groups705719431365010083at_int
% 9.53/5.32              @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.53/5.32              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8955_frac__def,axiom,
% 9.53/5.32      ( archim2898591450579166408c_real
% 9.53/5.32      = ( ^ [X2: real] : ( minus_minus_real @ X2 @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8956_frac__def,axiom,
% 9.53/5.32      ( archimedean_frac_rat
% 9.53/5.32      = ( ^ [X2: rat] : ( minus_minus_rat @ X2 @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8957_prod_OatLeast1__atMost__eq,axiom,
% 9.53/5.32      ! [G: nat > nat,N: nat] :
% 9.53/5.32        ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 9.53/5.32        = ( groups708209901874060359at_nat
% 9.53/5.32          @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 9.53/5.32          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8958_prod_OatLeast1__atMost__eq,axiom,
% 9.53/5.32      ! [G: nat > int,N: nat] :
% 9.53/5.32        ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 9.53/5.32        = ( groups705719431365010083at_int
% 9.53/5.32          @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 9.53/5.32          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8959_fact__prod,axiom,
% 9.53/5.32      ( semiri1406184849735516958ct_int
% 9.53/5.32      = ( ^ [N2: nat] :
% 9.53/5.32            ( semiri1314217659103216013at_int
% 9.53/5.32            @ ( groups708209901874060359at_nat
% 9.53/5.32              @ ^ [X2: nat] : X2
% 9.53/5.32              @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8960_fact__prod,axiom,
% 9.53/5.32      ( semiri5044797733671781792omplex
% 9.53/5.32      = ( ^ [N2: nat] :
% 9.53/5.32            ( semiri8010041392384452111omplex
% 9.53/5.32            @ ( groups708209901874060359at_nat
% 9.53/5.32              @ ^ [X2: nat] : X2
% 9.53/5.32              @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8961_fact__prod,axiom,
% 9.53/5.32      ( semiri2265585572941072030t_real
% 9.53/5.32      = ( ^ [N2: nat] :
% 9.53/5.32            ( semiri5074537144036343181t_real
% 9.53/5.32            @ ( groups708209901874060359at_nat
% 9.53/5.32              @ ^ [X2: nat] : X2
% 9.53/5.32              @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8962_fact__prod,axiom,
% 9.53/5.32      ( semiri1408675320244567234ct_nat
% 9.53/5.32      = ( ^ [N2: nat] :
% 9.53/5.32            ( semiri1316708129612266289at_nat
% 9.53/5.32            @ ( groups708209901874060359at_nat
% 9.53/5.32              @ ^ [X2: nat] : X2
% 9.53/5.32              @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8963_prod__mono__strict,axiom,
% 9.53/5.32      ! [A2: set_complex,F: complex > real,G: complex > real] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.32       => ( ! [I4: complex] :
% 9.53/5.32              ( ( member_complex @ I4 @ A2 )
% 9.53/5.32             => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 9.53/5.32                & ( ord_less_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 9.53/5.32         => ( ( A2 != bot_bot_set_complex )
% 9.53/5.32           => ( ord_less_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ( groups766887009212190081x_real @ G @ A2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8964_prod__mono__strict,axiom,
% 9.53/5.32      ! [A2: set_nat,F: nat > real,G: nat > real] :
% 9.53/5.32        ( ( finite_finite_nat @ A2 )
% 9.53/5.32       => ( ! [I4: nat] :
% 9.53/5.32              ( ( member_nat @ I4 @ A2 )
% 9.53/5.32             => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 9.53/5.32                & ( ord_less_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 9.53/5.32         => ( ( A2 != bot_bot_set_nat )
% 9.53/5.32           => ( ord_less_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8965_prod__mono__strict,axiom,
% 9.53/5.32      ! [A2: set_int,F: int > real,G: int > real] :
% 9.53/5.32        ( ( finite_finite_int @ A2 )
% 9.53/5.32       => ( ! [I4: int] :
% 9.53/5.32              ( ( member_int @ I4 @ A2 )
% 9.53/5.32             => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 9.53/5.32                & ( ord_less_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 9.53/5.32         => ( ( A2 != bot_bot_set_int )
% 9.53/5.32           => ( ord_less_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8966_prod__mono__strict,axiom,
% 9.53/5.32      ! [A2: set_real,F: real > real,G: real > real] :
% 9.53/5.32        ( ( finite_finite_real @ A2 )
% 9.53/5.32       => ( ! [I4: real] :
% 9.53/5.32              ( ( member_real @ I4 @ A2 )
% 9.53/5.32             => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 9.53/5.32                & ( ord_less_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 9.53/5.32         => ( ( A2 != bot_bot_set_real )
% 9.53/5.32           => ( ord_less_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8967_prod__mono__strict,axiom,
% 9.53/5.32      ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.32       => ( ! [I4: complex] :
% 9.53/5.32              ( ( member_complex @ I4 @ A2 )
% 9.53/5.32             => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) )
% 9.53/5.32                & ( ord_less_rat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 9.53/5.32         => ( ( A2 != bot_bot_set_complex )
% 9.53/5.32           => ( ord_less_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ ( groups225925009352817453ex_rat @ G @ A2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8968_prod__mono__strict,axiom,
% 9.53/5.32      ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 9.53/5.32        ( ( finite_finite_nat @ A2 )
% 9.53/5.32       => ( ! [I4: nat] :
% 9.53/5.32              ( ( member_nat @ I4 @ A2 )
% 9.53/5.32             => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) )
% 9.53/5.32                & ( ord_less_rat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 9.53/5.32         => ( ( A2 != bot_bot_set_nat )
% 9.53/5.32           => ( ord_less_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ ( groups73079841787564623at_rat @ G @ A2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8969_prod__mono__strict,axiom,
% 9.53/5.32      ! [A2: set_int,F: int > rat,G: int > rat] :
% 9.53/5.32        ( ( finite_finite_int @ A2 )
% 9.53/5.32       => ( ! [I4: int] :
% 9.53/5.32              ( ( member_int @ I4 @ A2 )
% 9.53/5.32             => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) )
% 9.53/5.32                & ( ord_less_rat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 9.53/5.32         => ( ( A2 != bot_bot_set_int )
% 9.53/5.32           => ( ord_less_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ ( groups1072433553688619179nt_rat @ G @ A2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8970_prod__mono__strict,axiom,
% 9.53/5.32      ! [A2: set_real,F: real > rat,G: real > rat] :
% 9.53/5.32        ( ( finite_finite_real @ A2 )
% 9.53/5.32       => ( ! [I4: real] :
% 9.53/5.32              ( ( member_real @ I4 @ A2 )
% 9.53/5.32             => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) )
% 9.53/5.32                & ( ord_less_rat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 9.53/5.32         => ( ( A2 != bot_bot_set_real )
% 9.53/5.32           => ( ord_less_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ ( groups4061424788464935467al_rat @ G @ A2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8971_prod__mono__strict,axiom,
% 9.53/5.32      ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.32       => ( ! [I4: complex] :
% 9.53/5.32              ( ( member_complex @ I4 @ A2 )
% 9.53/5.32             => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) )
% 9.53/5.32                & ( ord_less_nat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 9.53/5.32         => ( ( A2 != bot_bot_set_complex )
% 9.53/5.32           => ( ord_less_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) @ ( groups861055069439313189ex_nat @ G @ A2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8972_prod__mono__strict,axiom,
% 9.53/5.32      ! [A2: set_int,F: int > nat,G: int > nat] :
% 9.53/5.32        ( ( finite_finite_int @ A2 )
% 9.53/5.32       => ( ! [I4: int] :
% 9.53/5.32              ( ( member_int @ I4 @ A2 )
% 9.53/5.32             => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) )
% 9.53/5.32                & ( ord_less_nat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 9.53/5.32         => ( ( A2 != bot_bot_set_int )
% 9.53/5.32           => ( ord_less_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ ( groups1707563613775114915nt_nat @ G @ A2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8973_even__prod__iff,axiom,
% 9.53/5.32      ! [A2: set_nat,F: nat > code_integer] :
% 9.53/5.32        ( ( finite_finite_nat @ A2 )
% 9.53/5.32       => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups3455450783089532116nteger @ F @ A2 ) )
% 9.53/5.32          = ( ? [X2: nat] :
% 9.53/5.32                ( ( member_nat @ X2 @ A2 )
% 9.53/5.32                & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8974_even__prod__iff,axiom,
% 9.53/5.32      ! [A2: set_complex,F: complex > code_integer] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.32       => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups8682486955453173170nteger @ F @ A2 ) )
% 9.53/5.32          = ( ? [X2: complex] :
% 9.53/5.32                ( ( member_complex @ X2 @ A2 )
% 9.53/5.32                & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8975_even__prod__iff,axiom,
% 9.53/5.32      ! [A2: set_complex,F: complex > nat] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.32       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups861055069439313189ex_nat @ F @ A2 ) )
% 9.53/5.32          = ( ? [X2: complex] :
% 9.53/5.32                ( ( member_complex @ X2 @ A2 )
% 9.53/5.32                & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8976_even__prod__iff,axiom,
% 9.53/5.32      ! [A2: set_complex,F: complex > int] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.32       => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups858564598930262913ex_int @ F @ A2 ) )
% 9.53/5.32          = ( ? [X2: complex] :
% 9.53/5.32                ( ( member_complex @ X2 @ A2 )
% 9.53/5.32                & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8977_even__prod__iff,axiom,
% 9.53/5.32      ! [A2: set_nat,F: nat > nat] :
% 9.53/5.32        ( ( finite_finite_nat @ A2 )
% 9.53/5.32       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 9.53/5.32          = ( ? [X2: nat] :
% 9.53/5.32                ( ( member_nat @ X2 @ A2 )
% 9.53/5.32                & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8978_even__prod__iff,axiom,
% 9.53/5.32      ! [A2: set_nat,F: nat > int] :
% 9.53/5.32        ( ( finite_finite_nat @ A2 )
% 9.53/5.32       => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups705719431365010083at_int @ F @ A2 ) )
% 9.53/5.32          = ( ? [X2: nat] :
% 9.53/5.32                ( ( member_nat @ X2 @ A2 )
% 9.53/5.32                & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8979_even__prod__iff,axiom,
% 9.53/5.32      ! [A2: set_int,F: int > int] :
% 9.53/5.32        ( ( finite_finite_int @ A2 )
% 9.53/5.32       => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups1705073143266064639nt_int @ F @ A2 ) )
% 9.53/5.32          = ( ? [X2: int] :
% 9.53/5.32                ( ( member_int @ X2 @ A2 )
% 9.53/5.32                & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8980_prod_Oremove,axiom,
% 9.53/5.32      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > complex] :
% 9.53/5.32        ( ( finite5795047828879050333T_VEBT @ A2 )
% 9.53/5.32       => ( ( member_VEBT_VEBT @ X @ A2 )
% 9.53/5.32         => ( ( groups127312072573709053omplex @ G @ A2 )
% 9.53/5.32            = ( times_times_complex @ ( G @ X ) @ ( groups127312072573709053omplex @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8981_prod_Oremove,axiom,
% 9.53/5.32      ! [A2: set_complex,X: complex,G: complex > complex] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.32       => ( ( member_complex @ X @ A2 )
% 9.53/5.32         => ( ( groups3708469109370488835omplex @ G @ A2 )
% 9.53/5.32            = ( times_times_complex @ ( G @ X ) @ ( groups3708469109370488835omplex @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8982_prod_Oremove,axiom,
% 9.53/5.32      ! [A2: set_int,X: int,G: int > complex] :
% 9.53/5.32        ( ( finite_finite_int @ A2 )
% 9.53/5.32       => ( ( member_int @ X @ A2 )
% 9.53/5.32         => ( ( groups7440179247065528705omplex @ G @ A2 )
% 9.53/5.32            = ( times_times_complex @ ( G @ X ) @ ( groups7440179247065528705omplex @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8983_prod_Oremove,axiom,
% 9.53/5.32      ! [A2: set_real,X: real,G: real > complex] :
% 9.53/5.32        ( ( finite_finite_real @ A2 )
% 9.53/5.32       => ( ( member_real @ X @ A2 )
% 9.53/5.32         => ( ( groups713298508707869441omplex @ G @ A2 )
% 9.53/5.32            = ( times_times_complex @ ( G @ X ) @ ( groups713298508707869441omplex @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8984_prod_Oremove,axiom,
% 9.53/5.32      ! [A2: set_nat,X: nat,G: nat > complex] :
% 9.53/5.32        ( ( finite_finite_nat @ A2 )
% 9.53/5.32       => ( ( member_nat @ X @ A2 )
% 9.53/5.32         => ( ( groups6464643781859351333omplex @ G @ A2 )
% 9.53/5.32            = ( times_times_complex @ ( G @ X ) @ ( groups6464643781859351333omplex @ G @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8985_prod_Oremove,axiom,
% 9.53/5.32      ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > real] :
% 9.53/5.32        ( ( finite5795047828879050333T_VEBT @ A2 )
% 9.53/5.32       => ( ( member_VEBT_VEBT @ X @ A2 )
% 9.53/5.32         => ( ( groups2703838992350267259T_real @ G @ A2 )
% 9.53/5.32            = ( times_times_real @ ( G @ X ) @ ( groups2703838992350267259T_real @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8986_prod_Oremove,axiom,
% 9.53/5.32      ! [A2: set_complex,X: complex,G: complex > real] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.32       => ( ( member_complex @ X @ A2 )
% 9.53/5.32         => ( ( groups766887009212190081x_real @ G @ A2 )
% 9.53/5.32            = ( times_times_real @ ( G @ X ) @ ( groups766887009212190081x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8987_prod_Oremove,axiom,
% 9.53/5.32      ! [A2: set_int,X: int,G: int > real] :
% 9.53/5.32        ( ( finite_finite_int @ A2 )
% 9.53/5.32       => ( ( member_int @ X @ A2 )
% 9.53/5.32         => ( ( groups2316167850115554303t_real @ G @ A2 )
% 9.53/5.32            = ( times_times_real @ ( G @ X ) @ ( groups2316167850115554303t_real @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8988_prod_Oremove,axiom,
% 9.53/5.32      ! [A2: set_real,X: real,G: real > real] :
% 9.53/5.32        ( ( finite_finite_real @ A2 )
% 9.53/5.32       => ( ( member_real @ X @ A2 )
% 9.53/5.32         => ( ( groups1681761925125756287l_real @ G @ A2 )
% 9.53/5.32            = ( times_times_real @ ( G @ X ) @ ( groups1681761925125756287l_real @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8989_prod_Oremove,axiom,
% 9.53/5.32      ! [A2: set_nat,X: nat,G: nat > real] :
% 9.53/5.32        ( ( finite_finite_nat @ A2 )
% 9.53/5.32       => ( ( member_nat @ X @ A2 )
% 9.53/5.32         => ( ( groups129246275422532515t_real @ G @ A2 )
% 9.53/5.32            = ( times_times_real @ ( G @ X ) @ ( groups129246275422532515t_real @ G @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8990_prod_Oinsert__remove,axiom,
% 9.53/5.32      ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > complex,X: vEBT_VEBT] :
% 9.53/5.32        ( ( finite5795047828879050333T_VEBT @ A2 )
% 9.53/5.32       => ( ( groups127312072573709053omplex @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 9.53/5.32          = ( times_times_complex @ ( G @ X ) @ ( groups127312072573709053omplex @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8991_prod_Oinsert__remove,axiom,
% 9.53/5.32      ! [A2: set_complex,G: complex > complex,X: complex] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.32       => ( ( groups3708469109370488835omplex @ G @ ( insert_complex @ X @ A2 ) )
% 9.53/5.32          = ( times_times_complex @ ( G @ X ) @ ( groups3708469109370488835omplex @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8992_prod_Oinsert__remove,axiom,
% 9.53/5.32      ! [A2: set_int,G: int > complex,X: int] :
% 9.53/5.32        ( ( finite_finite_int @ A2 )
% 9.53/5.32       => ( ( groups7440179247065528705omplex @ G @ ( insert_int @ X @ A2 ) )
% 9.53/5.32          = ( times_times_complex @ ( G @ X ) @ ( groups7440179247065528705omplex @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8993_prod_Oinsert__remove,axiom,
% 9.53/5.32      ! [A2: set_real,G: real > complex,X: real] :
% 9.53/5.32        ( ( finite_finite_real @ A2 )
% 9.53/5.32       => ( ( groups713298508707869441omplex @ G @ ( insert_real @ X @ A2 ) )
% 9.53/5.32          = ( times_times_complex @ ( G @ X ) @ ( groups713298508707869441omplex @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8994_prod_Oinsert__remove,axiom,
% 9.53/5.32      ! [A2: set_nat,G: nat > complex,X: nat] :
% 9.53/5.32        ( ( finite_finite_nat @ A2 )
% 9.53/5.32       => ( ( groups6464643781859351333omplex @ G @ ( insert_nat @ X @ A2 ) )
% 9.53/5.32          = ( times_times_complex @ ( G @ X ) @ ( groups6464643781859351333omplex @ G @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8995_prod_Oinsert__remove,axiom,
% 9.53/5.32      ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > real,X: vEBT_VEBT] :
% 9.53/5.32        ( ( finite5795047828879050333T_VEBT @ A2 )
% 9.53/5.32       => ( ( groups2703838992350267259T_real @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 9.53/5.32          = ( times_times_real @ ( G @ X ) @ ( groups2703838992350267259T_real @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8996_prod_Oinsert__remove,axiom,
% 9.53/5.32      ! [A2: set_complex,G: complex > real,X: complex] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.32       => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X @ A2 ) )
% 9.53/5.32          = ( times_times_real @ ( G @ X ) @ ( groups766887009212190081x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8997_prod_Oinsert__remove,axiom,
% 9.53/5.32      ! [A2: set_int,G: int > real,X: int] :
% 9.53/5.32        ( ( finite_finite_int @ A2 )
% 9.53/5.32       => ( ( groups2316167850115554303t_real @ G @ ( insert_int @ X @ A2 ) )
% 9.53/5.32          = ( times_times_real @ ( G @ X ) @ ( groups2316167850115554303t_real @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8998_prod_Oinsert__remove,axiom,
% 9.53/5.32      ! [A2: set_real,G: real > real,X: real] :
% 9.53/5.32        ( ( finite_finite_real @ A2 )
% 9.53/5.32       => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X @ A2 ) )
% 9.53/5.32          = ( times_times_real @ ( G @ X ) @ ( groups1681761925125756287l_real @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_8999_prod_Oinsert__remove,axiom,
% 9.53/5.32      ! [A2: set_nat,G: nat > real,X: nat] :
% 9.53/5.32        ( ( finite_finite_nat @ A2 )
% 9.53/5.32       => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X @ A2 ) )
% 9.53/5.32          = ( times_times_real @ ( G @ X ) @ ( groups129246275422532515t_real @ G @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9000_prod_Oub__add__nat,axiom,
% 9.53/5.32      ! [M: nat,N: nat,G: nat > complex,P6: nat] :
% 9.53/5.32        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 9.53/5.32       => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 9.53/5.32          = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9001_prod_Oub__add__nat,axiom,
% 9.53/5.32      ! [M: nat,N: nat,G: nat > real,P6: nat] :
% 9.53/5.32        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 9.53/5.32       => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 9.53/5.32          = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9002_prod_Oub__add__nat,axiom,
% 9.53/5.32      ! [M: nat,N: nat,G: nat > nat,P6: nat] :
% 9.53/5.32        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 9.53/5.32       => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 9.53/5.32          = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9003_prod_Oub__add__nat,axiom,
% 9.53/5.32      ! [M: nat,N: nat,G: nat > int,P6: nat] :
% 9.53/5.32        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 9.53/5.32       => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 9.53/5.32          = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9004_fold__atLeastAtMost__nat_Osimps,axiom,
% 9.53/5.32      ( set_fo2584398358068434914at_nat
% 9.53/5.32      = ( ^ [F3: nat > nat > nat,A3: nat,B4: nat,Acc2: nat] : ( if_nat @ ( ord_less_nat @ B4 @ A3 ) @ Acc2 @ ( set_fo2584398358068434914at_nat @ F3 @ ( plus_plus_nat @ A3 @ one_one_nat ) @ B4 @ ( F3 @ A3 @ Acc2 ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9005_fold__atLeastAtMost__nat_Oelims,axiom,
% 9.53/5.32      ! [X: nat > nat > nat,Xa2: nat,Xb: nat,Xc: nat,Y2: nat] :
% 9.53/5.32        ( ( ( set_fo2584398358068434914at_nat @ X @ Xa2 @ Xb @ Xc )
% 9.53/5.32          = Y2 )
% 9.53/5.32       => ( ( ( ord_less_nat @ Xb @ Xa2 )
% 9.53/5.32           => ( Y2 = Xc ) )
% 9.53/5.32          & ( ~ ( ord_less_nat @ Xb @ Xa2 )
% 9.53/5.32           => ( Y2
% 9.53/5.32              = ( set_fo2584398358068434914at_nat @ X @ ( plus_plus_nat @ Xa2 @ one_one_nat ) @ Xb @ ( X @ Xa2 @ Xc ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9006_prod_Odelta__remove,axiom,
% 9.53/5.32      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > complex,C: vEBT_VEBT > complex] :
% 9.53/5.32        ( ( finite5795047828879050333T_VEBT @ S2 )
% 9.53/5.32       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 9.53/5.32           => ( ( groups127312072573709053omplex
% 9.53/5.32                @ ^ [K3: vEBT_VEBT] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( times_times_complex @ ( B @ A ) @ ( groups127312072573709053omplex @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 9.53/5.32          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 9.53/5.32           => ( ( groups127312072573709053omplex
% 9.53/5.32                @ ^ [K3: vEBT_VEBT] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( groups127312072573709053omplex @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9007_prod_Odelta__remove,axiom,
% 9.53/5.32      ! [S2: set_complex,A: complex,B: complex > complex,C: complex > complex] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ S2 )
% 9.53/5.32       => ( ( ( member_complex @ A @ S2 )
% 9.53/5.32           => ( ( groups3708469109370488835omplex
% 9.53/5.32                @ ^ [K3: complex] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( times_times_complex @ ( B @ A ) @ ( groups3708469109370488835omplex @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 9.53/5.32          & ( ~ ( member_complex @ A @ S2 )
% 9.53/5.32           => ( ( groups3708469109370488835omplex
% 9.53/5.32                @ ^ [K3: complex] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( groups3708469109370488835omplex @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9008_prod_Odelta__remove,axiom,
% 9.53/5.32      ! [S2: set_int,A: int,B: int > complex,C: int > complex] :
% 9.53/5.32        ( ( finite_finite_int @ S2 )
% 9.53/5.32       => ( ( ( member_int @ A @ S2 )
% 9.53/5.32           => ( ( groups7440179247065528705omplex
% 9.53/5.32                @ ^ [K3: int] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( times_times_complex @ ( B @ A ) @ ( groups7440179247065528705omplex @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 9.53/5.32          & ( ~ ( member_int @ A @ S2 )
% 9.53/5.32           => ( ( groups7440179247065528705omplex
% 9.53/5.32                @ ^ [K3: int] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( groups7440179247065528705omplex @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9009_prod_Odelta__remove,axiom,
% 9.53/5.32      ! [S2: set_real,A: real,B: real > complex,C: real > complex] :
% 9.53/5.32        ( ( finite_finite_real @ S2 )
% 9.53/5.32       => ( ( ( member_real @ A @ S2 )
% 9.53/5.32           => ( ( groups713298508707869441omplex
% 9.53/5.32                @ ^ [K3: real] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( times_times_complex @ ( B @ A ) @ ( groups713298508707869441omplex @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 9.53/5.32          & ( ~ ( member_real @ A @ S2 )
% 9.53/5.32           => ( ( groups713298508707869441omplex
% 9.53/5.32                @ ^ [K3: real] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( groups713298508707869441omplex @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9010_prod_Odelta__remove,axiom,
% 9.53/5.32      ! [S2: set_nat,A: nat,B: nat > complex,C: nat > complex] :
% 9.53/5.32        ( ( finite_finite_nat @ S2 )
% 9.53/5.32       => ( ( ( member_nat @ A @ S2 )
% 9.53/5.32           => ( ( groups6464643781859351333omplex
% 9.53/5.32                @ ^ [K3: nat] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( times_times_complex @ ( B @ A ) @ ( groups6464643781859351333omplex @ C @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 9.53/5.32          & ( ~ ( member_nat @ A @ S2 )
% 9.53/5.32           => ( ( groups6464643781859351333omplex
% 9.53/5.32                @ ^ [K3: nat] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( groups6464643781859351333omplex @ C @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9011_prod_Odelta__remove,axiom,
% 9.53/5.32      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > real,C: vEBT_VEBT > real] :
% 9.53/5.32        ( ( finite5795047828879050333T_VEBT @ S2 )
% 9.53/5.32       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 9.53/5.32           => ( ( groups2703838992350267259T_real
% 9.53/5.32                @ ^ [K3: vEBT_VEBT] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( times_times_real @ ( B @ A ) @ ( groups2703838992350267259T_real @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 9.53/5.32          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 9.53/5.32           => ( ( groups2703838992350267259T_real
% 9.53/5.32                @ ^ [K3: vEBT_VEBT] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( groups2703838992350267259T_real @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9012_prod_Odelta__remove,axiom,
% 9.53/5.32      ! [S2: set_complex,A: complex,B: complex > real,C: complex > real] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ S2 )
% 9.53/5.32       => ( ( ( member_complex @ A @ S2 )
% 9.53/5.32           => ( ( groups766887009212190081x_real
% 9.53/5.32                @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( times_times_real @ ( B @ A ) @ ( groups766887009212190081x_real @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 9.53/5.32          & ( ~ ( member_complex @ A @ S2 )
% 9.53/5.32           => ( ( groups766887009212190081x_real
% 9.53/5.32                @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( groups766887009212190081x_real @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9013_prod_Odelta__remove,axiom,
% 9.53/5.32      ! [S2: set_int,A: int,B: int > real,C: int > real] :
% 9.53/5.32        ( ( finite_finite_int @ S2 )
% 9.53/5.32       => ( ( ( member_int @ A @ S2 )
% 9.53/5.32           => ( ( groups2316167850115554303t_real
% 9.53/5.32                @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( times_times_real @ ( B @ A ) @ ( groups2316167850115554303t_real @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 9.53/5.32          & ( ~ ( member_int @ A @ S2 )
% 9.53/5.32           => ( ( groups2316167850115554303t_real
% 9.53/5.32                @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( groups2316167850115554303t_real @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9014_prod_Odelta__remove,axiom,
% 9.53/5.32      ! [S2: set_real,A: real,B: real > real,C: real > real] :
% 9.53/5.32        ( ( finite_finite_real @ S2 )
% 9.53/5.32       => ( ( ( member_real @ A @ S2 )
% 9.53/5.32           => ( ( groups1681761925125756287l_real
% 9.53/5.32                @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( times_times_real @ ( B @ A ) @ ( groups1681761925125756287l_real @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 9.53/5.32          & ( ~ ( member_real @ A @ S2 )
% 9.53/5.32           => ( ( groups1681761925125756287l_real
% 9.53/5.32                @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( groups1681761925125756287l_real @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9015_prod_Odelta__remove,axiom,
% 9.53/5.32      ! [S2: set_nat,A: nat,B: nat > real,C: nat > real] :
% 9.53/5.32        ( ( finite_finite_nat @ S2 )
% 9.53/5.32       => ( ( ( member_nat @ A @ S2 )
% 9.53/5.32           => ( ( groups129246275422532515t_real
% 9.53/5.32                @ ^ [K3: nat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( times_times_real @ ( B @ A ) @ ( groups129246275422532515t_real @ C @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 9.53/5.32          & ( ~ ( member_nat @ A @ S2 )
% 9.53/5.32           => ( ( groups129246275422532515t_real
% 9.53/5.32                @ ^ [K3: nat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 9.53/5.32                @ S2 )
% 9.53/5.32              = ( groups129246275422532515t_real @ C @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9016_frac__eq,axiom,
% 9.53/5.32      ! [X: real] :
% 9.53/5.32        ( ( ( archim2898591450579166408c_real @ X )
% 9.53/5.32          = X )
% 9.53/5.32        = ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.32          & ( ord_less_real @ X @ one_one_real ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9017_frac__eq,axiom,
% 9.53/5.32      ! [X: rat] :
% 9.53/5.32        ( ( ( archimedean_frac_rat @ X )
% 9.53/5.32          = X )
% 9.53/5.32        = ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 9.53/5.32          & ( ord_less_rat @ X @ one_one_rat ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9018_norm__prod__diff,axiom,
% 9.53/5.32      ! [I6: set_Pr1261947904930325089at_nat,Z: product_prod_nat_nat > complex,W: product_prod_nat_nat > complex] :
% 9.53/5.32        ( ! [I4: product_prod_nat_nat] :
% 9.53/5.32            ( ( member8440522571783428010at_nat @ I4 @ I6 )
% 9.53/5.32           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I4 ) ) @ one_one_real ) )
% 9.53/5.32       => ( ! [I4: product_prod_nat_nat] :
% 9.53/5.32              ( ( member8440522571783428010at_nat @ I4 @ I6 )
% 9.53/5.32             => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I4 ) ) @ one_one_real ) )
% 9.53/5.32         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups8110221916422527690omplex @ Z @ I6 ) @ ( groups8110221916422527690omplex @ W @ I6 ) ) )
% 9.53/5.32            @ ( groups4567486121110086003t_real
% 9.53/5.32              @ ^ [I3: product_prod_nat_nat] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I3 ) @ ( W @ I3 ) ) )
% 9.53/5.32              @ I6 ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9019_norm__prod__diff,axiom,
% 9.53/5.32      ! [I6: set_complex,Z: complex > complex,W: complex > complex] :
% 9.53/5.32        ( ! [I4: complex] :
% 9.53/5.32            ( ( member_complex @ I4 @ I6 )
% 9.53/5.32           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I4 ) ) @ one_one_real ) )
% 9.53/5.32       => ( ! [I4: complex] :
% 9.53/5.32              ( ( member_complex @ I4 @ I6 )
% 9.53/5.32             => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I4 ) ) @ one_one_real ) )
% 9.53/5.32         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups3708469109370488835omplex @ Z @ I6 ) @ ( groups3708469109370488835omplex @ W @ I6 ) ) )
% 9.53/5.32            @ ( groups5808333547571424918x_real
% 9.53/5.32              @ ^ [I3: complex] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I3 ) @ ( W @ I3 ) ) )
% 9.53/5.32              @ I6 ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9020_norm__prod__diff,axiom,
% 9.53/5.32      ! [I6: set_real,Z: real > complex,W: real > complex] :
% 9.53/5.32        ( ! [I4: real] :
% 9.53/5.32            ( ( member_real @ I4 @ I6 )
% 9.53/5.32           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I4 ) ) @ one_one_real ) )
% 9.53/5.32       => ( ! [I4: real] :
% 9.53/5.32              ( ( member_real @ I4 @ I6 )
% 9.53/5.32             => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I4 ) ) @ one_one_real ) )
% 9.53/5.32         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups713298508707869441omplex @ Z @ I6 ) @ ( groups713298508707869441omplex @ W @ I6 ) ) )
% 9.53/5.32            @ ( groups8097168146408367636l_real
% 9.53/5.32              @ ^ [I3: real] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I3 ) @ ( W @ I3 ) ) )
% 9.53/5.32              @ I6 ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9021_norm__prod__diff,axiom,
% 9.53/5.32      ! [I6: set_int,Z: int > complex,W: int > complex] :
% 9.53/5.32        ( ! [I4: int] :
% 9.53/5.32            ( ( member_int @ I4 @ I6 )
% 9.53/5.32           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I4 ) ) @ one_one_real ) )
% 9.53/5.32       => ( ! [I4: int] :
% 9.53/5.32              ( ( member_int @ I4 @ I6 )
% 9.53/5.32             => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I4 ) ) @ one_one_real ) )
% 9.53/5.32         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups7440179247065528705omplex @ Z @ I6 ) @ ( groups7440179247065528705omplex @ W @ I6 ) ) )
% 9.53/5.32            @ ( groups8778361861064173332t_real
% 9.53/5.32              @ ^ [I3: int] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I3 ) @ ( W @ I3 ) ) )
% 9.53/5.32              @ I6 ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9022_norm__prod__diff,axiom,
% 9.53/5.32      ! [I6: set_nat,Z: nat > complex,W: nat > complex] :
% 9.53/5.32        ( ! [I4: nat] :
% 9.53/5.32            ( ( member_nat @ I4 @ I6 )
% 9.53/5.32           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I4 ) ) @ one_one_real ) )
% 9.53/5.32       => ( ! [I4: nat] :
% 9.53/5.32              ( ( member_nat @ I4 @ I6 )
% 9.53/5.32             => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I4 ) ) @ one_one_real ) )
% 9.53/5.32         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups6464643781859351333omplex @ Z @ I6 ) @ ( groups6464643781859351333omplex @ W @ I6 ) ) )
% 9.53/5.32            @ ( groups6591440286371151544t_real
% 9.53/5.32              @ ^ [I3: nat] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I3 ) @ ( W @ I3 ) ) )
% 9.53/5.32              @ I6 ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9023_frac__add,axiom,
% 9.53/5.32      ! [X: real,Y2: real] :
% 9.53/5.32        ( ( ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y2 ) ) @ one_one_real )
% 9.53/5.32         => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X @ Y2 ) )
% 9.53/5.32            = ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y2 ) ) ) )
% 9.53/5.32        & ( ~ ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y2 ) ) @ one_one_real )
% 9.53/5.32         => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X @ Y2 ) )
% 9.53/5.32            = ( minus_minus_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y2 ) ) @ one_one_real ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9024_frac__add,axiom,
% 9.53/5.32      ! [X: rat,Y2: rat] :
% 9.53/5.32        ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y2 ) ) @ one_one_rat )
% 9.53/5.32         => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ Y2 ) )
% 9.53/5.32            = ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y2 ) ) ) )
% 9.53/5.32        & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y2 ) ) @ one_one_rat )
% 9.53/5.32         => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ Y2 ) )
% 9.53/5.32            = ( minus_minus_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y2 ) ) @ one_one_rat ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9025_fact__eq__fact__times,axiom,
% 9.53/5.32      ! [N: nat,M: nat] :
% 9.53/5.32        ( ( ord_less_eq_nat @ N @ M )
% 9.53/5.32       => ( ( semiri1408675320244567234ct_nat @ M )
% 9.53/5.32          = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N )
% 9.53/5.32            @ ( groups708209901874060359at_nat
% 9.53/5.32              @ ^ [X2: nat] : X2
% 9.53/5.32              @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9026_prod__mono2,axiom,
% 9.53/5.32      ! [B2: set_int,A2: set_int,F: int > real] :
% 9.53/5.32        ( ( finite_finite_int @ B2 )
% 9.53/5.32       => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 9.53/5.32         => ( ! [B3: int] :
% 9.53/5.32                ( ( member_int @ B3 @ ( minus_minus_set_int @ B2 @ A2 ) )
% 9.53/5.32               => ( ord_less_eq_real @ one_one_real @ ( F @ B3 ) ) )
% 9.53/5.32           => ( ! [A4: int] :
% 9.53/5.32                  ( ( member_int @ A4 @ A2 )
% 9.53/5.32                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A4 ) ) )
% 9.53/5.32             => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ( groups2316167850115554303t_real @ F @ B2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9027_prod__mono2,axiom,
% 9.53/5.32      ! [B2: set_complex,A2: set_complex,F: complex > real] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ B2 )
% 9.53/5.32       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 9.53/5.32         => ( ! [B3: complex] :
% 9.53/5.32                ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 9.53/5.32               => ( ord_less_eq_real @ one_one_real @ ( F @ B3 ) ) )
% 9.53/5.32           => ( ! [A4: complex] :
% 9.53/5.32                  ( ( member_complex @ A4 @ A2 )
% 9.53/5.32                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A4 ) ) )
% 9.53/5.32             => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ( groups766887009212190081x_real @ F @ B2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9028_prod__mono2,axiom,
% 9.53/5.32      ! [B2: set_int,A2: set_int,F: int > rat] :
% 9.53/5.32        ( ( finite_finite_int @ B2 )
% 9.53/5.32       => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 9.53/5.32         => ( ! [B3: int] :
% 9.53/5.32                ( ( member_int @ B3 @ ( minus_minus_set_int @ B2 @ A2 ) )
% 9.53/5.32               => ( ord_less_eq_rat @ one_one_rat @ ( F @ B3 ) ) )
% 9.53/5.32           => ( ! [A4: int] :
% 9.53/5.32                  ( ( member_int @ A4 @ A2 )
% 9.53/5.32                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A4 ) ) )
% 9.53/5.32             => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ ( groups1072433553688619179nt_rat @ F @ B2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9029_prod__mono2,axiom,
% 9.53/5.32      ! [B2: set_complex,A2: set_complex,F: complex > rat] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ B2 )
% 9.53/5.32       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 9.53/5.32         => ( ! [B3: complex] :
% 9.53/5.32                ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 9.53/5.32               => ( ord_less_eq_rat @ one_one_rat @ ( F @ B3 ) ) )
% 9.53/5.32           => ( ! [A4: complex] :
% 9.53/5.32                  ( ( member_complex @ A4 @ A2 )
% 9.53/5.32                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A4 ) ) )
% 9.53/5.32             => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ ( groups225925009352817453ex_rat @ F @ B2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9030_prod__mono2,axiom,
% 9.53/5.32      ! [B2: set_complex,A2: set_complex,F: complex > int] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ B2 )
% 9.53/5.32       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 9.53/5.32         => ( ! [B3: complex] :
% 9.53/5.32                ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 9.53/5.32               => ( ord_less_eq_int @ one_one_int @ ( F @ B3 ) ) )
% 9.53/5.32           => ( ! [A4: complex] :
% 9.53/5.32                  ( ( member_complex @ A4 @ A2 )
% 9.53/5.32                 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A4 ) ) )
% 9.53/5.32             => ( ord_less_eq_int @ ( groups858564598930262913ex_int @ F @ A2 ) @ ( groups858564598930262913ex_int @ F @ B2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9031_prod__mono2,axiom,
% 9.53/5.32      ! [B2: set_real,A2: set_real,F: real > real] :
% 9.53/5.32        ( ( finite_finite_real @ B2 )
% 9.53/5.32       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 9.53/5.32         => ( ! [B3: real] :
% 9.53/5.32                ( ( member_real @ B3 @ ( minus_minus_set_real @ B2 @ A2 ) )
% 9.53/5.32               => ( ord_less_eq_real @ one_one_real @ ( F @ B3 ) ) )
% 9.53/5.32           => ( ! [A4: real] :
% 9.53/5.32                  ( ( member_real @ A4 @ A2 )
% 9.53/5.32                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A4 ) ) )
% 9.53/5.32             => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( groups1681761925125756287l_real @ F @ B2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9032_prod__mono2,axiom,
% 9.53/5.32      ! [B2: set_real,A2: set_real,F: real > rat] :
% 9.53/5.32        ( ( finite_finite_real @ B2 )
% 9.53/5.32       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 9.53/5.32         => ( ! [B3: real] :
% 9.53/5.32                ( ( member_real @ B3 @ ( minus_minus_set_real @ B2 @ A2 ) )
% 9.53/5.32               => ( ord_less_eq_rat @ one_one_rat @ ( F @ B3 ) ) )
% 9.53/5.32           => ( ! [A4: real] :
% 9.53/5.32                  ( ( member_real @ A4 @ A2 )
% 9.53/5.32                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A4 ) ) )
% 9.53/5.32             => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ ( groups4061424788464935467al_rat @ F @ B2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9033_prod__mono2,axiom,
% 9.53/5.32      ! [B2: set_real,A2: set_real,F: real > int] :
% 9.53/5.32        ( ( finite_finite_real @ B2 )
% 9.53/5.32       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 9.53/5.32         => ( ! [B3: real] :
% 9.53/5.32                ( ( member_real @ B3 @ ( minus_minus_set_real @ B2 @ A2 ) )
% 9.53/5.32               => ( ord_less_eq_int @ one_one_int @ ( F @ B3 ) ) )
% 9.53/5.32           => ( ! [A4: real] :
% 9.53/5.32                  ( ( member_real @ A4 @ A2 )
% 9.53/5.32                 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A4 ) ) )
% 9.53/5.32             => ( ord_less_eq_int @ ( groups4694064378042380927al_int @ F @ A2 ) @ ( groups4694064378042380927al_int @ F @ B2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9034_prod__mono2,axiom,
% 9.53/5.32      ! [B2: set_nat,A2: set_nat,F: nat > real] :
% 9.53/5.32        ( ( finite_finite_nat @ B2 )
% 9.53/5.32       => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 9.53/5.32         => ( ! [B3: nat] :
% 9.53/5.32                ( ( member_nat @ B3 @ ( minus_minus_set_nat @ B2 @ A2 ) )
% 9.53/5.32               => ( ord_less_eq_real @ one_one_real @ ( F @ B3 ) ) )
% 9.53/5.32           => ( ! [A4: nat] :
% 9.53/5.32                  ( ( member_nat @ A4 @ A2 )
% 9.53/5.32                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A4 ) ) )
% 9.53/5.32             => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( groups129246275422532515t_real @ F @ B2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9035_prod__mono2,axiom,
% 9.53/5.32      ! [B2: set_nat,A2: set_nat,F: nat > rat] :
% 9.53/5.32        ( ( finite_finite_nat @ B2 )
% 9.53/5.32       => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 9.53/5.32         => ( ! [B3: nat] :
% 9.53/5.32                ( ( member_nat @ B3 @ ( minus_minus_set_nat @ B2 @ A2 ) )
% 9.53/5.32               => ( ord_less_eq_rat @ one_one_rat @ ( F @ B3 ) ) )
% 9.53/5.32           => ( ! [A4: nat] :
% 9.53/5.32                  ( ( member_nat @ A4 @ A2 )
% 9.53/5.32                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A4 ) ) )
% 9.53/5.32             => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ ( groups73079841787564623at_rat @ F @ B2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9036_prod__diff1,axiom,
% 9.53/5.32      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > complex,A: vEBT_VEBT] :
% 9.53/5.32        ( ( finite5795047828879050333T_VEBT @ A2 )
% 9.53/5.32       => ( ( ( F @ A )
% 9.53/5.32           != zero_zero_complex )
% 9.53/5.32         => ( ( ( member_VEBT_VEBT @ A @ A2 )
% 9.53/5.32             => ( ( groups127312072573709053omplex @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 9.53/5.32                = ( divide1717551699836669952omplex @ ( groups127312072573709053omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 9.53/5.32            & ( ~ ( member_VEBT_VEBT @ A @ A2 )
% 9.53/5.32             => ( ( groups127312072573709053omplex @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 9.53/5.32                = ( groups127312072573709053omplex @ F @ A2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9037_prod__diff1,axiom,
% 9.53/5.32      ! [A2: set_complex,F: complex > complex,A: complex] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.32       => ( ( ( F @ A )
% 9.53/5.32           != zero_zero_complex )
% 9.53/5.32         => ( ( ( member_complex @ A @ A2 )
% 9.53/5.32             => ( ( groups3708469109370488835omplex @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 9.53/5.32                = ( divide1717551699836669952omplex @ ( groups3708469109370488835omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 9.53/5.32            & ( ~ ( member_complex @ A @ A2 )
% 9.53/5.32             => ( ( groups3708469109370488835omplex @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 9.53/5.32                = ( groups3708469109370488835omplex @ F @ A2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9038_prod__diff1,axiom,
% 9.53/5.32      ! [A2: set_int,F: int > complex,A: int] :
% 9.53/5.32        ( ( finite_finite_int @ A2 )
% 9.53/5.32       => ( ( ( F @ A )
% 9.53/5.32           != zero_zero_complex )
% 9.53/5.32         => ( ( ( member_int @ A @ A2 )
% 9.53/5.32             => ( ( groups7440179247065528705omplex @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 9.53/5.32                = ( divide1717551699836669952omplex @ ( groups7440179247065528705omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 9.53/5.32            & ( ~ ( member_int @ A @ A2 )
% 9.53/5.32             => ( ( groups7440179247065528705omplex @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 9.53/5.32                = ( groups7440179247065528705omplex @ F @ A2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9039_prod__diff1,axiom,
% 9.53/5.32      ! [A2: set_real,F: real > complex,A: real] :
% 9.53/5.32        ( ( finite_finite_real @ A2 )
% 9.53/5.32       => ( ( ( F @ A )
% 9.53/5.32           != zero_zero_complex )
% 9.53/5.32         => ( ( ( member_real @ A @ A2 )
% 9.53/5.32             => ( ( groups713298508707869441omplex @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 9.53/5.32                = ( divide1717551699836669952omplex @ ( groups713298508707869441omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 9.53/5.32            & ( ~ ( member_real @ A @ A2 )
% 9.53/5.32             => ( ( groups713298508707869441omplex @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 9.53/5.32                = ( groups713298508707869441omplex @ F @ A2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9040_prod__diff1,axiom,
% 9.53/5.32      ! [A2: set_nat,F: nat > complex,A: nat] :
% 9.53/5.32        ( ( finite_finite_nat @ A2 )
% 9.53/5.32       => ( ( ( F @ A )
% 9.53/5.32           != zero_zero_complex )
% 9.53/5.32         => ( ( ( member_nat @ A @ A2 )
% 9.53/5.32             => ( ( groups6464643781859351333omplex @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 9.53/5.32                = ( divide1717551699836669952omplex @ ( groups6464643781859351333omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 9.53/5.32            & ( ~ ( member_nat @ A @ A2 )
% 9.53/5.32             => ( ( groups6464643781859351333omplex @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 9.53/5.32                = ( groups6464643781859351333omplex @ F @ A2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9041_prod__diff1,axiom,
% 9.53/5.32      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > real,A: vEBT_VEBT] :
% 9.53/5.32        ( ( finite5795047828879050333T_VEBT @ A2 )
% 9.53/5.32       => ( ( ( F @ A )
% 9.53/5.32           != zero_zero_real )
% 9.53/5.32         => ( ( ( member_VEBT_VEBT @ A @ A2 )
% 9.53/5.32             => ( ( groups2703838992350267259T_real @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 9.53/5.32                = ( divide_divide_real @ ( groups2703838992350267259T_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 9.53/5.32            & ( ~ ( member_VEBT_VEBT @ A @ A2 )
% 9.53/5.32             => ( ( groups2703838992350267259T_real @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 9.53/5.32                = ( groups2703838992350267259T_real @ F @ A2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9042_prod__diff1,axiom,
% 9.53/5.32      ! [A2: set_complex,F: complex > real,A: complex] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.32       => ( ( ( F @ A )
% 9.53/5.32           != zero_zero_real )
% 9.53/5.32         => ( ( ( member_complex @ A @ A2 )
% 9.53/5.32             => ( ( groups766887009212190081x_real @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 9.53/5.32                = ( divide_divide_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 9.53/5.32            & ( ~ ( member_complex @ A @ A2 )
% 9.53/5.32             => ( ( groups766887009212190081x_real @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 9.53/5.32                = ( groups766887009212190081x_real @ F @ A2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9043_prod__diff1,axiom,
% 9.53/5.32      ! [A2: set_int,F: int > real,A: int] :
% 9.53/5.32        ( ( finite_finite_int @ A2 )
% 9.53/5.32       => ( ( ( F @ A )
% 9.53/5.32           != zero_zero_real )
% 9.53/5.32         => ( ( ( member_int @ A @ A2 )
% 9.53/5.32             => ( ( groups2316167850115554303t_real @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 9.53/5.32                = ( divide_divide_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 9.53/5.32            & ( ~ ( member_int @ A @ A2 )
% 9.53/5.32             => ( ( groups2316167850115554303t_real @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 9.53/5.32                = ( groups2316167850115554303t_real @ F @ A2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9044_prod__diff1,axiom,
% 9.53/5.32      ! [A2: set_real,F: real > real,A: real] :
% 9.53/5.32        ( ( finite_finite_real @ A2 )
% 9.53/5.32       => ( ( ( F @ A )
% 9.53/5.32           != zero_zero_real )
% 9.53/5.32         => ( ( ( member_real @ A @ A2 )
% 9.53/5.32             => ( ( groups1681761925125756287l_real @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 9.53/5.32                = ( divide_divide_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 9.53/5.32            & ( ~ ( member_real @ A @ A2 )
% 9.53/5.32             => ( ( groups1681761925125756287l_real @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 9.53/5.32                = ( groups1681761925125756287l_real @ F @ A2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9045_prod__diff1,axiom,
% 9.53/5.32      ! [A2: set_nat,F: nat > real,A: nat] :
% 9.53/5.32        ( ( finite_finite_nat @ A2 )
% 9.53/5.32       => ( ( ( F @ A )
% 9.53/5.32           != zero_zero_real )
% 9.53/5.32         => ( ( ( member_nat @ A @ A2 )
% 9.53/5.32             => ( ( groups129246275422532515t_real @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 9.53/5.32                = ( divide_divide_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 9.53/5.32            & ( ~ ( member_nat @ A @ A2 )
% 9.53/5.32             => ( ( groups129246275422532515t_real @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 9.53/5.32                = ( groups129246275422532515t_real @ F @ A2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9046_pochhammer__Suc__prod,axiom,
% 9.53/5.32      ! [A: rat,N: nat] :
% 9.53/5.32        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 9.53/5.32        = ( groups73079841787564623at_rat
% 9.53/5.32          @ ^ [I3: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ I3 ) )
% 9.53/5.32          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9047_pochhammer__Suc__prod,axiom,
% 9.53/5.32      ! [A: real,N: nat] :
% 9.53/5.32        ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 9.53/5.32        = ( groups129246275422532515t_real
% 9.53/5.32          @ ^ [I3: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ I3 ) )
% 9.53/5.32          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9048_pochhammer__Suc__prod,axiom,
% 9.53/5.32      ! [A: complex,N: nat] :
% 9.53/5.32        ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 9.53/5.32        = ( groups6464643781859351333omplex
% 9.53/5.32          @ ^ [I3: nat] : ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ I3 ) )
% 9.53/5.32          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9049_pochhammer__Suc__prod,axiom,
% 9.53/5.32      ! [A: nat,N: nat] :
% 9.53/5.32        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 9.53/5.32        = ( groups708209901874060359at_nat
% 9.53/5.32          @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ I3 ) )
% 9.53/5.32          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9050_pochhammer__Suc__prod,axiom,
% 9.53/5.32      ! [A: int,N: nat] :
% 9.53/5.32        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 9.53/5.32        = ( groups705719431365010083at_int
% 9.53/5.32          @ ^ [I3: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ I3 ) )
% 9.53/5.32          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9051_pochhammer__prod__rev,axiom,
% 9.53/5.32      ( comm_s4028243227959126397er_rat
% 9.53/5.32      = ( ^ [A3: rat,N2: nat] :
% 9.53/5.32            ( groups73079841787564623at_rat
% 9.53/5.32            @ ^ [I3: nat] : ( plus_plus_rat @ A3 @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 9.53/5.32            @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9052_pochhammer__prod__rev,axiom,
% 9.53/5.32      ( comm_s7457072308508201937r_real
% 9.53/5.32      = ( ^ [A3: real,N2: nat] :
% 9.53/5.32            ( groups129246275422532515t_real
% 9.53/5.32            @ ^ [I3: nat] : ( plus_plus_real @ A3 @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 9.53/5.32            @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9053_pochhammer__prod__rev,axiom,
% 9.53/5.32      ( comm_s2602460028002588243omplex
% 9.53/5.32      = ( ^ [A3: complex,N2: nat] :
% 9.53/5.32            ( groups6464643781859351333omplex
% 9.53/5.32            @ ^ [I3: nat] : ( plus_plus_complex @ A3 @ ( semiri8010041392384452111omplex @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 9.53/5.32            @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9054_pochhammer__prod__rev,axiom,
% 9.53/5.32      ( comm_s4663373288045622133er_nat
% 9.53/5.32      = ( ^ [A3: nat,N2: nat] :
% 9.53/5.32            ( groups708209901874060359at_nat
% 9.53/5.32            @ ^ [I3: nat] : ( plus_plus_nat @ A3 @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 9.53/5.32            @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9055_pochhammer__prod__rev,axiom,
% 9.53/5.32      ( comm_s4660882817536571857er_int
% 9.53/5.32      = ( ^ [A3: int,N2: nat] :
% 9.53/5.32            ( groups705719431365010083at_int
% 9.53/5.32            @ ^ [I3: nat] : ( plus_plus_int @ A3 @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 9.53/5.32            @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9056_fact__div__fact,axiom,
% 9.53/5.32      ! [N: nat,M: nat] :
% 9.53/5.32        ( ( ord_less_eq_nat @ N @ M )
% 9.53/5.32       => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) )
% 9.53/5.32          = ( groups708209901874060359at_nat
% 9.53/5.32            @ ^ [X2: nat] : X2
% 9.53/5.32            @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9057_prod_Oin__pairs,axiom,
% 9.53/5.32      ! [G: nat > complex,M: nat,N: nat] :
% 9.53/5.32        ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 9.53/5.32        = ( groups6464643781859351333omplex
% 9.53/5.32          @ ^ [I3: nat] : ( times_times_complex @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.53/5.32          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9058_prod_Oin__pairs,axiom,
% 9.53/5.32      ! [G: nat > real,M: nat,N: nat] :
% 9.53/5.32        ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 9.53/5.32        = ( groups129246275422532515t_real
% 9.53/5.32          @ ^ [I3: nat] : ( times_times_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.53/5.32          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9059_prod_Oin__pairs,axiom,
% 9.53/5.32      ! [G: nat > nat,M: nat,N: nat] :
% 9.53/5.32        ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 9.53/5.32        = ( groups708209901874060359at_nat
% 9.53/5.32          @ ^ [I3: nat] : ( times_times_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.53/5.32          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9060_prod_Oin__pairs,axiom,
% 9.53/5.32      ! [G: nat > int,M: nat,N: nat] :
% 9.53/5.32        ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 9.53/5.32        = ( groups705719431365010083at_int
% 9.53/5.32          @ ^ [I3: nat] : ( times_times_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.53/5.32          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9061_sum__atLeastAtMost__code,axiom,
% 9.53/5.32      ! [F: nat > complex,A: nat,B: nat] :
% 9.53/5.32        ( ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 9.53/5.32        = ( set_fo1517530859248394432omplex
% 9.53/5.32          @ ^ [A3: nat] : ( plus_plus_complex @ ( F @ A3 ) )
% 9.53/5.32          @ A
% 9.53/5.32          @ B
% 9.53/5.32          @ zero_zero_complex ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9062_sum__atLeastAtMost__code,axiom,
% 9.53/5.32      ! [F: nat > rat,A: nat,B: nat] :
% 9.53/5.32        ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 9.53/5.32        = ( set_fo1949268297981939178at_rat
% 9.53/5.32          @ ^ [A3: nat] : ( plus_plus_rat @ ( F @ A3 ) )
% 9.53/5.32          @ A
% 9.53/5.32          @ B
% 9.53/5.32          @ zero_zero_rat ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9063_sum__atLeastAtMost__code,axiom,
% 9.53/5.32      ! [F: nat > int,A: nat,B: nat] :
% 9.53/5.32        ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 9.53/5.32        = ( set_fo2581907887559384638at_int
% 9.53/5.32          @ ^ [A3: nat] : ( plus_plus_int @ ( F @ A3 ) )
% 9.53/5.32          @ A
% 9.53/5.32          @ B
% 9.53/5.32          @ zero_zero_int ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9064_sum__atLeastAtMost__code,axiom,
% 9.53/5.32      ! [F: nat > nat,A: nat,B: nat] :
% 9.53/5.32        ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 9.53/5.32        = ( set_fo2584398358068434914at_nat
% 9.53/5.32          @ ^ [A3: nat] : ( plus_plus_nat @ ( F @ A3 ) )
% 9.53/5.32          @ A
% 9.53/5.32          @ B
% 9.53/5.32          @ zero_zero_nat ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9065_sum__atLeastAtMost__code,axiom,
% 9.53/5.32      ! [F: nat > real,A: nat,B: nat] :
% 9.53/5.32        ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 9.53/5.32        = ( set_fo3111899725591712190t_real
% 9.53/5.32          @ ^ [A3: nat] : ( plus_plus_real @ ( F @ A3 ) )
% 9.53/5.32          @ A
% 9.53/5.32          @ B
% 9.53/5.32          @ zero_zero_real ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9066_pochhammer__Suc__prod__rev,axiom,
% 9.53/5.32      ! [A: rat,N: nat] :
% 9.53/5.32        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 9.53/5.32        = ( groups73079841787564623at_rat
% 9.53/5.32          @ ^ [I3: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N @ I3 ) ) )
% 9.53/5.32          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9067_pochhammer__Suc__prod__rev,axiom,
% 9.53/5.32      ! [A: real,N: nat] :
% 9.53/5.32        ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 9.53/5.32        = ( groups129246275422532515t_real
% 9.53/5.32          @ ^ [I3: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ I3 ) ) )
% 9.53/5.32          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9068_pochhammer__Suc__prod__rev,axiom,
% 9.53/5.32      ! [A: complex,N: nat] :
% 9.53/5.32        ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 9.53/5.32        = ( groups6464643781859351333omplex
% 9.53/5.32          @ ^ [I3: nat] : ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ ( minus_minus_nat @ N @ I3 ) ) )
% 9.53/5.32          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9069_pochhammer__Suc__prod__rev,axiom,
% 9.53/5.32      ! [A: nat,N: nat] :
% 9.53/5.32        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 9.53/5.32        = ( groups708209901874060359at_nat
% 9.53/5.32          @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N @ I3 ) ) )
% 9.53/5.32          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9070_pochhammer__Suc__prod__rev,axiom,
% 9.53/5.32      ! [A: int,N: nat] :
% 9.53/5.32        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 9.53/5.32        = ( groups705719431365010083at_int
% 9.53/5.32          @ ^ [I3: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ I3 ) ) )
% 9.53/5.32          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9071_floor__add,axiom,
% 9.53/5.32      ! [X: real,Y2: real] :
% 9.53/5.32        ( ( ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y2 ) ) @ one_one_real )
% 9.53/5.32         => ( ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ Y2 ) )
% 9.53/5.32            = ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y2 ) ) ) )
% 9.53/5.32        & ( ~ ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y2 ) ) @ one_one_real )
% 9.53/5.32         => ( ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ Y2 ) )
% 9.53/5.32            = ( plus_plus_int @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y2 ) ) @ one_one_int ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9072_floor__add,axiom,
% 9.53/5.32      ! [X: rat,Y2: rat] :
% 9.53/5.32        ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y2 ) ) @ one_one_rat )
% 9.53/5.32         => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ Y2 ) )
% 9.53/5.32            = ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y2 ) ) ) )
% 9.53/5.32        & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y2 ) ) @ one_one_rat )
% 9.53/5.32         => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ Y2 ) )
% 9.53/5.32            = ( plus_plus_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y2 ) ) @ one_one_int ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9073_fact__code,axiom,
% 9.53/5.32      ( semiri1406184849735516958ct_int
% 9.53/5.32      = ( ^ [N2: nat] : ( semiri1314217659103216013at_int @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 @ one_one_nat ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9074_fact__code,axiom,
% 9.53/5.32      ( semiri5044797733671781792omplex
% 9.53/5.32      = ( ^ [N2: nat] : ( semiri8010041392384452111omplex @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 @ one_one_nat ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9075_fact__code,axiom,
% 9.53/5.32      ( semiri2265585572941072030t_real
% 9.53/5.32      = ( ^ [N2: nat] : ( semiri5074537144036343181t_real @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 @ one_one_nat ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9076_fact__code,axiom,
% 9.53/5.32      ( semiri1408675320244567234ct_nat
% 9.53/5.32      = ( ^ [N2: nat] : ( semiri1316708129612266289at_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 @ one_one_nat ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9077_gchoose__row__sum__weighted,axiom,
% 9.53/5.32      ! [R: rat,M: nat] :
% 9.53/5.32        ( ( groups2906978787729119204at_rat
% 9.53/5.32          @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ R @ K3 ) @ ( minus_minus_rat @ ( divide_divide_rat @ R @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K3 ) ) )
% 9.53/5.32          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 9.53/5.32        = ( times_times_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ ( suc @ M ) ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ R @ ( suc @ M ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9078_gchoose__row__sum__weighted,axiom,
% 9.53/5.32      ! [R: complex,M: nat] :
% 9.53/5.32        ( ( groups2073611262835488442omplex
% 9.53/5.32          @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ R @ K3 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ R @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K3 ) ) )
% 9.53/5.32          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 9.53/5.32        = ( times_times_complex @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ ( suc @ M ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( gbinomial_complex @ R @ ( suc @ M ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9079_gchoose__row__sum__weighted,axiom,
% 9.53/5.32      ! [R: real,M: nat] :
% 9.53/5.32        ( ( groups6591440286371151544t_real
% 9.53/5.32          @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ R @ K3 ) @ ( minus_minus_real @ ( divide_divide_real @ R @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K3 ) ) )
% 9.53/5.32          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 9.53/5.32        = ( times_times_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( gbinomial_real @ R @ ( suc @ M ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9080_Maclaurin__sin__bound,axiom,
% 9.53/5.32      ! [X: real,N: nat] :
% 9.53/5.32        ( ord_less_eq_real
% 9.53/5.32        @ ( abs_abs_real
% 9.53/5.32          @ ( minus_minus_real @ ( sin_real @ X )
% 9.53/5.32            @ ( groups6591440286371151544t_real
% 9.53/5.32              @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 9.53/5.32              @ ( set_ord_lessThan_nat @ N ) ) ) )
% 9.53/5.32        @ ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( abs_abs_real @ X ) @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9081_central__binomial__lower__bound,axiom,
% 9.53/5.32      ! [N: nat] :
% 9.53/5.32        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.32       => ( ord_less_eq_real @ ( divide_divide_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ N ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9082_exp__two__pi__i,axiom,
% 9.53/5.32      ( ( exp_complex @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( real_V4546457046886955230omplex @ pi ) ) @ imaginary_unit ) )
% 9.53/5.32      = one_one_complex ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9083_inverse__mult__distrib,axiom,
% 9.53/5.32      ! [A: real,B: real] :
% 9.53/5.32        ( ( inverse_inverse_real @ ( times_times_real @ A @ B ) )
% 9.53/5.32        = ( times_times_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9084_inverse__mult__distrib,axiom,
% 9.53/5.32      ! [A: complex,B: complex] :
% 9.53/5.32        ( ( invers8013647133539491842omplex @ ( times_times_complex @ A @ B ) )
% 9.53/5.32        = ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9085_inverse__1,axiom,
% 9.53/5.32      ( ( inverse_inverse_rat @ one_one_rat )
% 9.53/5.32      = one_one_rat ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9086_inverse__1,axiom,
% 9.53/5.32      ( ( inverse_inverse_real @ one_one_real )
% 9.53/5.32      = one_one_real ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9087_inverse__1,axiom,
% 9.53/5.32      ( ( invers8013647133539491842omplex @ one_one_complex )
% 9.53/5.32      = one_one_complex ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9088_inverse__eq__1__iff,axiom,
% 9.53/5.32      ! [X: rat] :
% 9.53/5.32        ( ( ( inverse_inverse_rat @ X )
% 9.53/5.32          = one_one_rat )
% 9.53/5.32        = ( X = one_one_rat ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9089_inverse__eq__1__iff,axiom,
% 9.53/5.32      ! [X: real] :
% 9.53/5.32        ( ( ( inverse_inverse_real @ X )
% 9.53/5.32          = one_one_real )
% 9.53/5.32        = ( X = one_one_real ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9090_inverse__eq__1__iff,axiom,
% 9.53/5.32      ! [X: complex] :
% 9.53/5.32        ( ( ( invers8013647133539491842omplex @ X )
% 9.53/5.32          = one_one_complex )
% 9.53/5.32        = ( X = one_one_complex ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9091_inverse__divide,axiom,
% 9.53/5.32      ! [A: rat,B: rat] :
% 9.53/5.32        ( ( inverse_inverse_rat @ ( divide_divide_rat @ A @ B ) )
% 9.53/5.32        = ( divide_divide_rat @ B @ A ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9092_inverse__divide,axiom,
% 9.53/5.32      ! [A: real,B: real] :
% 9.53/5.32        ( ( inverse_inverse_real @ ( divide_divide_real @ A @ B ) )
% 9.53/5.32        = ( divide_divide_real @ B @ A ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9093_inverse__divide,axiom,
% 9.53/5.32      ! [A: complex,B: complex] :
% 9.53/5.32        ( ( invers8013647133539491842omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 9.53/5.32        = ( divide1717551699836669952omplex @ B @ A ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9094_binomial__Suc__n,axiom,
% 9.53/5.32      ! [N: nat] :
% 9.53/5.32        ( ( binomial @ ( suc @ N ) @ N )
% 9.53/5.32        = ( suc @ N ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9095_binomial__n__n,axiom,
% 9.53/5.32      ! [N: nat] :
% 9.53/5.32        ( ( binomial @ N @ N )
% 9.53/5.32        = one_one_nat ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9096_inverse__nonnegative__iff__nonnegative,axiom,
% 9.53/5.32      ! [A: rat] :
% 9.53/5.32        ( ( ord_less_eq_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 9.53/5.32        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9097_inverse__nonnegative__iff__nonnegative,axiom,
% 9.53/5.32      ! [A: real] :
% 9.53/5.32        ( ( ord_less_eq_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 9.53/5.32        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9098_inverse__nonpositive__iff__nonpositive,axiom,
% 9.53/5.32      ! [A: rat] :
% 9.53/5.32        ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 9.53/5.32        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9099_inverse__nonpositive__iff__nonpositive,axiom,
% 9.53/5.32      ! [A: real] :
% 9.53/5.32        ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 9.53/5.32        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9100_inverse__less__iff__less,axiom,
% 9.53/5.32      ! [A: rat,B: rat] :
% 9.53/5.32        ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.53/5.32       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 9.53/5.32         => ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 9.53/5.32            = ( ord_less_rat @ B @ A ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9101_inverse__less__iff__less,axiom,
% 9.53/5.32      ! [A: real,B: real] :
% 9.53/5.32        ( ( ord_less_real @ zero_zero_real @ A )
% 9.53/5.32       => ( ( ord_less_real @ zero_zero_real @ B )
% 9.53/5.32         => ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 9.53/5.32            = ( ord_less_real @ B @ A ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9102_inverse__less__iff__less__neg,axiom,
% 9.53/5.32      ! [A: rat,B: rat] :
% 9.53/5.32        ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.53/5.32       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 9.53/5.32         => ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 9.53/5.32            = ( ord_less_rat @ B @ A ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9103_inverse__less__iff__less__neg,axiom,
% 9.53/5.32      ! [A: real,B: real] :
% 9.53/5.32        ( ( ord_less_real @ A @ zero_zero_real )
% 9.53/5.32       => ( ( ord_less_real @ B @ zero_zero_real )
% 9.53/5.32         => ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 9.53/5.32            = ( ord_less_real @ B @ A ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9104_inverse__negative__iff__negative,axiom,
% 9.53/5.32      ! [A: rat] :
% 9.53/5.32        ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 9.53/5.32        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9105_inverse__negative__iff__negative,axiom,
% 9.53/5.32      ! [A: real] :
% 9.53/5.32        ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 9.53/5.32        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9106_inverse__positive__iff__positive,axiom,
% 9.53/5.32      ! [A: rat] :
% 9.53/5.32        ( ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 9.53/5.32        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9107_inverse__positive__iff__positive,axiom,
% 9.53/5.32      ! [A: real] :
% 9.53/5.32        ( ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 9.53/5.32        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9108_gbinomial__0_I2_J,axiom,
% 9.53/5.32      ! [K: nat] :
% 9.53/5.32        ( ( gbinomial_complex @ zero_zero_complex @ ( suc @ K ) )
% 9.53/5.32        = zero_zero_complex ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9109_gbinomial__0_I2_J,axiom,
% 9.53/5.32      ! [K: nat] :
% 9.53/5.32        ( ( gbinomial_real @ zero_zero_real @ ( suc @ K ) )
% 9.53/5.32        = zero_zero_real ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9110_gbinomial__0_I2_J,axiom,
% 9.53/5.32      ! [K: nat] :
% 9.53/5.32        ( ( gbinomial_rat @ zero_zero_rat @ ( suc @ K ) )
% 9.53/5.32        = zero_zero_rat ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9111_gbinomial__0_I2_J,axiom,
% 9.53/5.32      ! [K: nat] :
% 9.53/5.32        ( ( gbinomial_nat @ zero_zero_nat @ ( suc @ K ) )
% 9.53/5.32        = zero_zero_nat ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9112_gbinomial__0_I2_J,axiom,
% 9.53/5.32      ! [K: nat] :
% 9.53/5.32        ( ( gbinomial_int @ zero_zero_int @ ( suc @ K ) )
% 9.53/5.32        = zero_zero_int ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9113_binomial__1,axiom,
% 9.53/5.32      ! [N: nat] :
% 9.53/5.32        ( ( binomial @ N @ ( suc @ zero_zero_nat ) )
% 9.53/5.32        = N ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9114_binomial__0__Suc,axiom,
% 9.53/5.32      ! [K: nat] :
% 9.53/5.32        ( ( binomial @ zero_zero_nat @ ( suc @ K ) )
% 9.53/5.32        = zero_zero_nat ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9115_binomial__Suc__Suc,axiom,
% 9.53/5.32      ! [N: nat,K: nat] :
% 9.53/5.32        ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 9.53/5.32        = ( plus_plus_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9116_binomial__eq__0__iff,axiom,
% 9.53/5.32      ! [N: nat,K: nat] :
% 9.53/5.32        ( ( ( binomial @ N @ K )
% 9.53/5.32          = zero_zero_nat )
% 9.53/5.32        = ( ord_less_nat @ N @ K ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9117_gbinomial__0_I1_J,axiom,
% 9.53/5.32      ! [A: complex] :
% 9.53/5.32        ( ( gbinomial_complex @ A @ zero_zero_nat )
% 9.53/5.32        = one_one_complex ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9118_gbinomial__0_I1_J,axiom,
% 9.53/5.32      ! [A: real] :
% 9.53/5.32        ( ( gbinomial_real @ A @ zero_zero_nat )
% 9.53/5.32        = one_one_real ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9119_gbinomial__0_I1_J,axiom,
% 9.53/5.32      ! [A: rat] :
% 9.53/5.32        ( ( gbinomial_rat @ A @ zero_zero_nat )
% 9.53/5.32        = one_one_rat ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9120_gbinomial__0_I1_J,axiom,
% 9.53/5.32      ! [A: nat] :
% 9.53/5.32        ( ( gbinomial_nat @ A @ zero_zero_nat )
% 9.53/5.32        = one_one_nat ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9121_gbinomial__0_I1_J,axiom,
% 9.53/5.32      ! [A: int] :
% 9.53/5.32        ( ( gbinomial_int @ A @ zero_zero_nat )
% 9.53/5.32        = one_one_int ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9122_binomial__n__0,axiom,
% 9.53/5.32      ! [N: nat] :
% 9.53/5.32        ( ( binomial @ N @ zero_zero_nat )
% 9.53/5.32        = one_one_nat ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9123_norm__ii,axiom,
% 9.53/5.32      ( ( real_V1022390504157884413omplex @ imaginary_unit )
% 9.53/5.32      = one_one_real ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9124_prod__eq__1__iff,axiom,
% 9.53/5.32      ! [A2: set_complex,F: complex > nat] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.32       => ( ( ( groups861055069439313189ex_nat @ F @ A2 )
% 9.53/5.32            = one_one_nat )
% 9.53/5.32          = ( ! [X2: complex] :
% 9.53/5.32                ( ( member_complex @ X2 @ A2 )
% 9.53/5.32               => ( ( F @ X2 )
% 9.53/5.32                  = one_one_nat ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9125_prod__eq__1__iff,axiom,
% 9.53/5.32      ! [A2: set_nat,F: nat > nat] :
% 9.53/5.32        ( ( finite_finite_nat @ A2 )
% 9.53/5.32       => ( ( ( groups708209901874060359at_nat @ F @ A2 )
% 9.53/5.32            = one_one_nat )
% 9.53/5.32          = ( ! [X2: nat] :
% 9.53/5.32                ( ( member_nat @ X2 @ A2 )
% 9.53/5.32               => ( ( F @ X2 )
% 9.53/5.32                  = one_one_nat ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9126_inverse__le__iff__le__neg,axiom,
% 9.53/5.32      ! [A: rat,B: rat] :
% 9.53/5.32        ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.53/5.32       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 9.53/5.32         => ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 9.53/5.32            = ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9127_inverse__le__iff__le__neg,axiom,
% 9.53/5.32      ! [A: real,B: real] :
% 9.53/5.32        ( ( ord_less_real @ A @ zero_zero_real )
% 9.53/5.32       => ( ( ord_less_real @ B @ zero_zero_real )
% 9.53/5.32         => ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 9.53/5.32            = ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9128_inverse__le__iff__le,axiom,
% 9.53/5.32      ! [A: rat,B: rat] :
% 9.53/5.32        ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.53/5.32       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 9.53/5.32         => ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 9.53/5.32            = ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9129_inverse__le__iff__le,axiom,
% 9.53/5.32      ! [A: real,B: real] :
% 9.53/5.32        ( ( ord_less_real @ zero_zero_real @ A )
% 9.53/5.32       => ( ( ord_less_real @ zero_zero_real @ B )
% 9.53/5.32         => ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 9.53/5.32            = ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9130_right__inverse,axiom,
% 9.53/5.32      ! [A: rat] :
% 9.53/5.32        ( ( A != zero_zero_rat )
% 9.53/5.32       => ( ( times_times_rat @ A @ ( inverse_inverse_rat @ A ) )
% 9.53/5.32          = one_one_rat ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9131_right__inverse,axiom,
% 9.53/5.32      ! [A: real] :
% 9.53/5.32        ( ( A != zero_zero_real )
% 9.53/5.32       => ( ( times_times_real @ A @ ( inverse_inverse_real @ A ) )
% 9.53/5.32          = one_one_real ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9132_right__inverse,axiom,
% 9.53/5.32      ! [A: complex] :
% 9.53/5.32        ( ( A != zero_zero_complex )
% 9.53/5.32       => ( ( times_times_complex @ A @ ( invers8013647133539491842omplex @ A ) )
% 9.53/5.32          = one_one_complex ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9133_left__inverse,axiom,
% 9.53/5.32      ! [A: rat] :
% 9.53/5.32        ( ( A != zero_zero_rat )
% 9.53/5.32       => ( ( times_times_rat @ ( inverse_inverse_rat @ A ) @ A )
% 9.53/5.32          = one_one_rat ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9134_left__inverse,axiom,
% 9.53/5.32      ! [A: real] :
% 9.53/5.32        ( ( A != zero_zero_real )
% 9.53/5.32       => ( ( times_times_real @ ( inverse_inverse_real @ A ) @ A )
% 9.53/5.32          = one_one_real ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9135_left__inverse,axiom,
% 9.53/5.32      ! [A: complex] :
% 9.53/5.32        ( ( A != zero_zero_complex )
% 9.53/5.32       => ( ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ A )
% 9.53/5.32          = one_one_complex ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9136_inverse__eq__divide__numeral,axiom,
% 9.53/5.32      ! [W: num] :
% 9.53/5.32        ( ( inverse_inverse_rat @ ( numeral_numeral_rat @ W ) )
% 9.53/5.32        = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ W ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9137_inverse__eq__divide__numeral,axiom,
% 9.53/5.32      ! [W: num] :
% 9.53/5.32        ( ( inverse_inverse_real @ ( numeral_numeral_real @ W ) )
% 9.53/5.32        = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ W ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9138_inverse__eq__divide__numeral,axiom,
% 9.53/5.32      ! [W: num] :
% 9.53/5.32        ( ( invers8013647133539491842omplex @ ( numera6690914467698888265omplex @ W ) )
% 9.53/5.32        = ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9139_zero__less__binomial__iff,axiom,
% 9.53/5.32      ! [N: nat,K: nat] :
% 9.53/5.32        ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) )
% 9.53/5.32        = ( ord_less_eq_nat @ K @ N ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9140_prod__pos__nat__iff,axiom,
% 9.53/5.32      ! [A2: set_complex,F: complex > nat] :
% 9.53/5.32        ( ( finite3207457112153483333omplex @ A2 )
% 9.53/5.32       => ( ( ord_less_nat @ zero_zero_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) )
% 9.53/5.32          = ( ! [X2: complex] :
% 9.53/5.32                ( ( member_complex @ X2 @ A2 )
% 9.53/5.32               => ( ord_less_nat @ zero_zero_nat @ ( F @ X2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9141_prod__pos__nat__iff,axiom,
% 9.53/5.32      ! [A2: set_nat,F: nat > nat] :
% 9.53/5.32        ( ( finite_finite_nat @ A2 )
% 9.53/5.32       => ( ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 9.53/5.32          = ( ! [X2: nat] :
% 9.53/5.32                ( ( member_nat @ X2 @ A2 )
% 9.53/5.32               => ( ord_less_nat @ zero_zero_nat @ ( F @ X2 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9142_inverse__eq__divide__neg__numeral,axiom,
% 9.53/5.32      ! [W: num] :
% 9.53/5.32        ( ( inverse_inverse_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 9.53/5.32        = ( divide_divide_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9143_inverse__eq__divide__neg__numeral,axiom,
% 9.53/5.32      ! [W: num] :
% 9.53/5.32        ( ( inverse_inverse_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 9.53/5.32        = ( divide_divide_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9144_inverse__eq__divide__neg__numeral,axiom,
% 9.53/5.32      ! [W: num] :
% 9.53/5.32        ( ( invers8013647133539491842omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 9.53/5.32        = ( divide1717551699836669952omplex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9145_power2__i,axiom,
% 9.53/5.32      ( ( power_power_complex @ imaginary_unit @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.53/5.32      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9146_i__even__power,axiom,
% 9.53/5.32      ! [N: nat] :
% 9.53/5.32        ( ( power_power_complex @ imaginary_unit @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.53/5.32        = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9147_exp__two__pi__i_H,axiom,
% 9.53/5.32      ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) )
% 9.53/5.32      = one_one_complex ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9148_mult__commute__imp__mult__inverse__commute,axiom,
% 9.53/5.32      ! [Y2: real,X: real] :
% 9.53/5.32        ( ( ( times_times_real @ Y2 @ X )
% 9.53/5.32          = ( times_times_real @ X @ Y2 ) )
% 9.53/5.32       => ( ( times_times_real @ ( inverse_inverse_real @ Y2 ) @ X )
% 9.53/5.32          = ( times_times_real @ X @ ( inverse_inverse_real @ Y2 ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9149_mult__commute__imp__mult__inverse__commute,axiom,
% 9.53/5.32      ! [Y2: complex,X: complex] :
% 9.53/5.32        ( ( ( times_times_complex @ Y2 @ X )
% 9.53/5.32          = ( times_times_complex @ X @ Y2 ) )
% 9.53/5.32       => ( ( times_times_complex @ ( invers8013647133539491842omplex @ Y2 ) @ X )
% 9.53/5.32          = ( times_times_complex @ X @ ( invers8013647133539491842omplex @ Y2 ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9150_choose__one,axiom,
% 9.53/5.32      ! [N: nat] :
% 9.53/5.32        ( ( binomial @ N @ one_one_nat )
% 9.53/5.32        = N ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9151_power__inverse,axiom,
% 9.53/5.32      ! [A: real,N: nat] :
% 9.53/5.32        ( ( power_power_real @ ( inverse_inverse_real @ A ) @ N )
% 9.53/5.32        = ( inverse_inverse_real @ ( power_power_real @ A @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9152_power__inverse,axiom,
% 9.53/5.32      ! [A: complex,N: nat] :
% 9.53/5.32        ( ( power_power_complex @ ( invers8013647133539491842omplex @ A ) @ N )
% 9.53/5.32        = ( invers8013647133539491842omplex @ ( power_power_complex @ A @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9153_real__sqrt__inverse,axiom,
% 9.53/5.32      ! [X: real] :
% 9.53/5.32        ( ( sqrt @ ( inverse_inverse_real @ X ) )
% 9.53/5.32        = ( inverse_inverse_real @ ( sqrt @ X ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9154_norm__inverse__le__norm,axiom,
% 9.53/5.32      ! [R: real,X: real] :
% 9.53/5.32        ( ( ord_less_eq_real @ R @ ( real_V7735802525324610683m_real @ X ) )
% 9.53/5.32       => ( ( ord_less_real @ zero_zero_real @ R )
% 9.53/5.32         => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( inverse_inverse_real @ X ) ) @ ( inverse_inverse_real @ R ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9155_norm__inverse__le__norm,axiom,
% 9.53/5.32      ! [R: real,X: complex] :
% 9.53/5.32        ( ( ord_less_eq_real @ R @ ( real_V1022390504157884413omplex @ X ) )
% 9.53/5.32       => ( ( ord_less_real @ zero_zero_real @ R )
% 9.53/5.32         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( invers8013647133539491842omplex @ X ) ) @ ( inverse_inverse_real @ R ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9156_binomial__eq__0,axiom,
% 9.53/5.32      ! [N: nat,K: nat] :
% 9.53/5.32        ( ( ord_less_nat @ N @ K )
% 9.53/5.32       => ( ( binomial @ N @ K )
% 9.53/5.32          = zero_zero_nat ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9157_positive__imp__inverse__positive,axiom,
% 9.53/5.32      ! [A: rat] :
% 9.53/5.32        ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.53/5.32       => ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9158_positive__imp__inverse__positive,axiom,
% 9.53/5.32      ! [A: real] :
% 9.53/5.32        ( ( ord_less_real @ zero_zero_real @ A )
% 9.53/5.32       => ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9159_negative__imp__inverse__negative,axiom,
% 9.53/5.32      ! [A: rat] :
% 9.53/5.32        ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.53/5.32       => ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9160_negative__imp__inverse__negative,axiom,
% 9.53/5.32      ! [A: real] :
% 9.53/5.32        ( ( ord_less_real @ A @ zero_zero_real )
% 9.53/5.32       => ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9161_inverse__positive__imp__positive,axiom,
% 9.53/5.32      ! [A: rat] :
% 9.53/5.32        ( ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 9.53/5.32       => ( ( A != zero_zero_rat )
% 9.53/5.32         => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9162_inverse__positive__imp__positive,axiom,
% 9.53/5.32      ! [A: real] :
% 9.53/5.32        ( ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 9.53/5.32       => ( ( A != zero_zero_real )
% 9.53/5.32         => ( ord_less_real @ zero_zero_real @ A ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9163_inverse__negative__imp__negative,axiom,
% 9.53/5.32      ! [A: rat] :
% 9.53/5.32        ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 9.53/5.32       => ( ( A != zero_zero_rat )
% 9.53/5.32         => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9164_inverse__negative__imp__negative,axiom,
% 9.53/5.32      ! [A: real] :
% 9.53/5.32        ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 9.53/5.32       => ( ( A != zero_zero_real )
% 9.53/5.32         => ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9165_less__imp__inverse__less__neg,axiom,
% 9.53/5.32      ! [A: rat,B: rat] :
% 9.53/5.32        ( ( ord_less_rat @ A @ B )
% 9.53/5.32       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 9.53/5.32         => ( ord_less_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9166_less__imp__inverse__less__neg,axiom,
% 9.53/5.32      ! [A: real,B: real] :
% 9.53/5.32        ( ( ord_less_real @ A @ B )
% 9.53/5.32       => ( ( ord_less_real @ B @ zero_zero_real )
% 9.53/5.32         => ( ord_less_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9167_inverse__less__imp__less__neg,axiom,
% 9.53/5.32      ! [A: rat,B: rat] :
% 9.53/5.32        ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 9.53/5.32       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 9.53/5.32         => ( ord_less_rat @ B @ A ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9168_inverse__less__imp__less__neg,axiom,
% 9.53/5.32      ! [A: real,B: real] :
% 9.53/5.32        ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 9.53/5.32       => ( ( ord_less_real @ B @ zero_zero_real )
% 9.53/5.32         => ( ord_less_real @ B @ A ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9169_less__imp__inverse__less,axiom,
% 9.53/5.32      ! [A: rat,B: rat] :
% 9.53/5.32        ( ( ord_less_rat @ A @ B )
% 9.53/5.32       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.53/5.32         => ( ord_less_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9170_less__imp__inverse__less,axiom,
% 9.53/5.32      ! [A: real,B: real] :
% 9.53/5.32        ( ( ord_less_real @ A @ B )
% 9.53/5.32       => ( ( ord_less_real @ zero_zero_real @ A )
% 9.53/5.32         => ( ord_less_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9171_inverse__less__imp__less,axiom,
% 9.53/5.32      ! [A: rat,B: rat] :
% 9.53/5.32        ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 9.53/5.32       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.53/5.32         => ( ord_less_rat @ B @ A ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9172_inverse__less__imp__less,axiom,
% 9.53/5.32      ! [A: real,B: real] :
% 9.53/5.32        ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 9.53/5.32       => ( ( ord_less_real @ zero_zero_real @ A )
% 9.53/5.32         => ( ord_less_real @ B @ A ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9173_nonzero__inverse__mult__distrib,axiom,
% 9.53/5.32      ! [A: rat,B: rat] :
% 9.53/5.32        ( ( A != zero_zero_rat )
% 9.53/5.32       => ( ( B != zero_zero_rat )
% 9.53/5.32         => ( ( inverse_inverse_rat @ ( times_times_rat @ A @ B ) )
% 9.53/5.32            = ( times_times_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9174_nonzero__inverse__mult__distrib,axiom,
% 9.53/5.32      ! [A: real,B: real] :
% 9.53/5.32        ( ( A != zero_zero_real )
% 9.53/5.32       => ( ( B != zero_zero_real )
% 9.53/5.32         => ( ( inverse_inverse_real @ ( times_times_real @ A @ B ) )
% 9.53/5.32            = ( times_times_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9175_nonzero__inverse__mult__distrib,axiom,
% 9.53/5.32      ! [A: complex,B: complex] :
% 9.53/5.32        ( ( A != zero_zero_complex )
% 9.53/5.32       => ( ( B != zero_zero_complex )
% 9.53/5.32         => ( ( invers8013647133539491842omplex @ ( times_times_complex @ A @ B ) )
% 9.53/5.32            = ( times_times_complex @ ( invers8013647133539491842omplex @ B ) @ ( invers8013647133539491842omplex @ A ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9176_Suc__times__binomial__eq,axiom,
% 9.53/5.32      ! [N: nat,K: nat] :
% 9.53/5.32        ( ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) )
% 9.53/5.32        = ( times_times_nat @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) @ ( suc @ K ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9177_Suc__times__binomial,axiom,
% 9.53/5.32      ! [K: nat,N: nat] :
% 9.53/5.32        ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) )
% 9.53/5.32        = ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9178_inverse__numeral__1,axiom,
% 9.53/5.32      ( ( inverse_inverse_rat @ ( numeral_numeral_rat @ one ) )
% 9.53/5.32      = ( numeral_numeral_rat @ one ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9179_inverse__numeral__1,axiom,
% 9.53/5.32      ( ( inverse_inverse_real @ ( numeral_numeral_real @ one ) )
% 9.53/5.32      = ( numeral_numeral_real @ one ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9180_inverse__numeral__1,axiom,
% 9.53/5.32      ( ( invers8013647133539491842omplex @ ( numera6690914467698888265omplex @ one ) )
% 9.53/5.32      = ( numera6690914467698888265omplex @ one ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9181_inverse__unique,axiom,
% 9.53/5.32      ! [A: rat,B: rat] :
% 9.53/5.32        ( ( ( times_times_rat @ A @ B )
% 9.53/5.32          = one_one_rat )
% 9.53/5.32       => ( ( inverse_inverse_rat @ A )
% 9.53/5.32          = B ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9182_inverse__unique,axiom,
% 9.53/5.32      ! [A: real,B: real] :
% 9.53/5.32        ( ( ( times_times_real @ A @ B )
% 9.53/5.32          = one_one_real )
% 9.53/5.32       => ( ( inverse_inverse_real @ A )
% 9.53/5.32          = B ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9183_inverse__unique,axiom,
% 9.53/5.32      ! [A: complex,B: complex] :
% 9.53/5.32        ( ( ( times_times_complex @ A @ B )
% 9.53/5.32          = one_one_complex )
% 9.53/5.32       => ( ( invers8013647133539491842omplex @ A )
% 9.53/5.32          = B ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9184_choose__mult__lemma,axiom,
% 9.53/5.32      ! [M: nat,R: nat,K: nat] :
% 9.53/5.32        ( ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R ) @ K ) @ ( plus_plus_nat @ M @ K ) ) @ ( binomial @ ( plus_plus_nat @ M @ K ) @ K ) )
% 9.53/5.32        = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R ) @ K ) @ K ) @ ( binomial @ ( plus_plus_nat @ M @ R ) @ M ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9185_divide__inverse__commute,axiom,
% 9.53/5.32      ( divide1717551699836669952omplex
% 9.53/5.32      = ( ^ [A3: complex,B4: complex] : ( times_times_complex @ ( invers8013647133539491842omplex @ B4 ) @ A3 ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9186_binomial__symmetric,axiom,
% 9.53/5.32      ! [K: nat,N: nat] :
% 9.53/5.32        ( ( ord_less_eq_nat @ K @ N )
% 9.53/5.32       => ( ( binomial @ N @ K )
% 9.53/5.32          = ( binomial @ N @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9187_binomial__le__pow,axiom,
% 9.53/5.32      ! [R: nat,N: nat] :
% 9.53/5.32        ( ( ord_less_eq_nat @ R @ N )
% 9.53/5.32       => ( ord_less_eq_nat @ ( binomial @ N @ R ) @ ( power_power_nat @ N @ R ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9188_divide__real__def,axiom,
% 9.53/5.32      ( divide_divide_real
% 9.53/5.32      = ( ^ [X2: real,Y: real] : ( times_times_real @ X2 @ ( inverse_inverse_real @ Y ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9189_zero__less__binomial,axiom,
% 9.53/5.32      ! [K: nat,N: nat] :
% 9.53/5.32        ( ( ord_less_eq_nat @ K @ N )
% 9.53/5.32       => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9190_Suc__times__binomial__add,axiom,
% 9.53/5.32      ! [A: nat,B: nat] :
% 9.53/5.32        ( ( times_times_nat @ ( suc @ A ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ ( suc @ A ) ) )
% 9.53/5.32        = ( times_times_nat @ ( suc @ B ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ A ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9191_binomial__Suc__Suc__eq__times,axiom,
% 9.53/5.32      ! [N: nat,K: nat] :
% 9.53/5.32        ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 9.53/5.32        = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) @ ( suc @ K ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9192_choose__mult,axiom,
% 9.53/5.32      ! [K: nat,M: nat,N: nat] :
% 9.53/5.32        ( ( ord_less_eq_nat @ K @ M )
% 9.53/5.32       => ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.32         => ( ( times_times_nat @ ( binomial @ N @ M ) @ ( binomial @ M @ K ) )
% 9.53/5.32            = ( times_times_nat @ ( binomial @ N @ K ) @ ( binomial @ ( minus_minus_nat @ N @ K ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9193_binomial__absorb__comp,axiom,
% 9.53/5.32      ! [N: nat,K: nat] :
% 9.53/5.32        ( ( times_times_nat @ ( minus_minus_nat @ N @ K ) @ ( binomial @ N @ K ) )
% 9.53/5.32        = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9194_inverse__powr,axiom,
% 9.53/5.32      ! [Y2: real,A: real] :
% 9.53/5.32        ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 9.53/5.32       => ( ( powr_real @ ( inverse_inverse_real @ Y2 ) @ A )
% 9.53/5.32          = ( inverse_inverse_real @ ( powr_real @ Y2 @ A ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9195_imaginary__unit_Ocode,axiom,
% 9.53/5.32      ( imaginary_unit
% 9.53/5.32      = ( complex2 @ zero_zero_real @ one_one_real ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9196_Complex__eq__i,axiom,
% 9.53/5.32      ! [X: real,Y2: real] :
% 9.53/5.32        ( ( ( complex2 @ X @ Y2 )
% 9.53/5.32          = imaginary_unit )
% 9.53/5.32        = ( ( X = zero_zero_real )
% 9.53/5.32          & ( Y2 = one_one_real ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9197_binomial__absorption,axiom,
% 9.53/5.32      ! [K: nat,N: nat] :
% 9.53/5.32        ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ N @ ( suc @ K ) ) )
% 9.53/5.32        = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9198_forall__pos__mono__1,axiom,
% 9.53/5.32      ! [P: real > $o,E: real] :
% 9.53/5.32        ( ! [D3: real,E2: real] :
% 9.53/5.32            ( ( ord_less_real @ D3 @ E2 )
% 9.53/5.32           => ( ( P @ D3 )
% 9.53/5.32             => ( P @ E2 ) ) )
% 9.53/5.32       => ( ! [N3: nat] : ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) )
% 9.53/5.32         => ( ( ord_less_real @ zero_zero_real @ E )
% 9.53/5.32           => ( P @ E ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9199_binomial__fact__lemma,axiom,
% 9.53/5.32      ! [K: nat,N: nat] :
% 9.53/5.32        ( ( ord_less_eq_nat @ K @ N )
% 9.53/5.32       => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( binomial @ N @ K ) )
% 9.53/5.32          = ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9200_real__arch__inverse,axiom,
% 9.53/5.32      ! [E: real] :
% 9.53/5.32        ( ( ord_less_real @ zero_zero_real @ E )
% 9.53/5.32        = ( ? [N2: nat] :
% 9.53/5.32              ( ( N2 != zero_zero_nat )
% 9.53/5.32              & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 9.53/5.32              & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ E ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9201_forall__pos__mono,axiom,
% 9.53/5.32      ! [P: real > $o,E: real] :
% 9.53/5.32        ( ! [D3: real,E2: real] :
% 9.53/5.32            ( ( ord_less_real @ D3 @ E2 )
% 9.53/5.32           => ( ( P @ D3 )
% 9.53/5.32             => ( P @ E2 ) ) )
% 9.53/5.32       => ( ! [N3: nat] :
% 9.53/5.32              ( ( N3 != zero_zero_nat )
% 9.53/5.32             => ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) ) )
% 9.53/5.32         => ( ( ord_less_real @ zero_zero_real @ E )
% 9.53/5.32           => ( P @ E ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9202_sqrt__divide__self__eq,axiom,
% 9.53/5.32      ! [X: real] :
% 9.53/5.32        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.32       => ( ( divide_divide_real @ ( sqrt @ X ) @ X )
% 9.53/5.32          = ( inverse_inverse_real @ ( sqrt @ X ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9203_ln__inverse,axiom,
% 9.53/5.32      ! [X: real] :
% 9.53/5.32        ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.32       => ( ( ln_ln_real @ ( inverse_inverse_real @ X ) )
% 9.53/5.32          = ( uminus_uminus_real @ ( ln_ln_real @ X ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9204_prod__int__plus__eq,axiom,
% 9.53/5.32      ! [I2: nat,J: nat] :
% 9.53/5.32        ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I2 @ ( plus_plus_nat @ I2 @ J ) ) )
% 9.53/5.32        = ( groups1705073143266064639nt_int
% 9.53/5.32          @ ^ [X2: int] : X2
% 9.53/5.32          @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I2 @ J ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9205_binomial__maximum,axiom,
% 9.53/5.32      ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9206_binomial__antimono,axiom,
% 9.53/5.32      ! [K: nat,K6: nat,N: nat] :
% 9.53/5.32        ( ( ord_less_eq_nat @ K @ K6 )
% 9.53/5.32       => ( ( ord_less_eq_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ K )
% 9.53/5.32         => ( ( ord_less_eq_nat @ K6 @ N )
% 9.53/5.32           => ( ord_less_eq_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9207_binomial__mono,axiom,
% 9.53/5.32      ! [K: nat,K6: nat,N: nat] :
% 9.53/5.32        ( ( ord_less_eq_nat @ K @ K6 )
% 9.53/5.32       => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 9.53/5.32         => ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9208_binomial__maximum_H,axiom,
% 9.53/5.32      ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ K ) @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9209_binomial__le__pow2,axiom,
% 9.53/5.32      ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9210_choose__reduce__nat,axiom,
% 9.53/5.32      ! [N: nat,K: nat] :
% 9.53/5.32        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.32       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 9.53/5.32         => ( ( binomial @ N @ K )
% 9.53/5.32            = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9211_times__binomial__minus1__eq,axiom,
% 9.53/5.32      ! [K: nat,N: nat] :
% 9.53/5.32        ( ( ord_less_nat @ zero_zero_nat @ K )
% 9.53/5.32       => ( ( times_times_nat @ K @ ( binomial @ N @ K ) )
% 9.53/5.32          = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9212_binomial__altdef__nat,axiom,
% 9.53/5.32      ! [K: nat,N: nat] :
% 9.53/5.32        ( ( ord_less_eq_nat @ K @ N )
% 9.53/5.32       => ( ( binomial @ N @ K )
% 9.53/5.32          = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9213_log__inverse,axiom,
% 9.53/5.32      ! [A: real,X: real] :
% 9.53/5.32        ( ( ord_less_real @ zero_zero_real @ A )
% 9.53/5.32       => ( ( A != one_one_real )
% 9.53/5.32         => ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.32           => ( ( log @ A @ ( inverse_inverse_real @ X ) )
% 9.53/5.32              = ( uminus_uminus_real @ ( log @ A @ X ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9214_binomial__less__binomial__Suc,axiom,
% 9.53/5.32      ! [K: nat,N: nat] :
% 9.53/5.32        ( ( ord_less_nat @ K @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.53/5.32       => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9215_binomial__strict__mono,axiom,
% 9.53/5.32      ! [K: nat,K6: nat,N: nat] :
% 9.53/5.32        ( ( ord_less_nat @ K @ K6 )
% 9.53/5.32       => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 9.53/5.32         => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9216_binomial__strict__antimono,axiom,
% 9.53/5.32      ! [K: nat,K6: nat,N: nat] :
% 9.53/5.32        ( ( ord_less_nat @ K @ K6 )
% 9.53/5.32       => ( ( ord_less_eq_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) )
% 9.53/5.32         => ( ( ord_less_eq_nat @ K6 @ N )
% 9.53/5.32           => ( ord_less_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9217_central__binomial__odd,axiom,
% 9.53/5.32      ! [N: nat] :
% 9.53/5.32        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.53/5.32       => ( ( binomial @ N @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.53/5.32          = ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9218_binomial__addition__formula,axiom,
% 9.53/5.32      ! [N: nat,K: nat] :
% 9.53/5.32        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.32       => ( ( binomial @ N @ ( suc @ K ) )
% 9.53/5.32          = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9219_exp__plus__inverse__exp,axiom,
% 9.53/5.32      ! [X: real] : ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9220_choose__two,axiom,
% 9.53/5.32      ! [N: nat] :
% 9.53/5.32        ( ( binomial @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.53/5.32        = ( divide_divide_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9221_plus__inverse__ge__2,axiom,
% 9.53/5.32      ! [X: real] :
% 9.53/5.32        ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.32       => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ X @ ( inverse_inverse_real @ X ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9222_real__inv__sqrt__pow2,axiom,
% 9.53/5.32      ! [X: real] :
% 9.53/5.32        ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.32       => ( ( power_power_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.53/5.32          = ( inverse_inverse_real @ X ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9223_tan__cot,axiom,
% 9.53/5.32      ! [X: real] :
% 9.53/5.32        ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) )
% 9.53/5.32        = ( inverse_inverse_real @ ( tan_real @ X ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9224_real__le__x__sinh,axiom,
% 9.53/5.32      ! [X: real] :
% 9.53/5.32        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.32       => ( ord_less_eq_real @ X @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9225_real__le__abs__sinh,axiom,
% 9.53/5.32      ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9226_cmod__unit__one,axiom,
% 9.53/5.32      ! [A: real] :
% 9.53/5.32        ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A ) ) ) ) )
% 9.53/5.32        = one_one_real ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9227_binomial__code,axiom,
% 9.53/5.32      ( binomial
% 9.53/5.32      = ( ^ [N2: nat,K3: nat] : ( if_nat @ ( ord_less_nat @ N2 @ K3 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K3 ) ) @ ( binomial @ N2 @ ( minus_minus_nat @ N2 @ K3 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N2 @ K3 ) @ one_one_nat ) @ N2 @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K3 ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9228_Arg__minus__ii,axiom,
% 9.53/5.32      ( ( arg @ ( uminus1482373934393186551omplex @ imaginary_unit ) )
% 9.53/5.32      = ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9229_csqrt__ii,axiom,
% 9.53/5.32      ( ( csqrt @ imaginary_unit )
% 9.53/5.32      = ( divide1717551699836669952omplex @ ( plus_plus_complex @ one_one_complex @ imaginary_unit ) @ ( real_V4546457046886955230omplex @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9230_Arg__ii,axiom,
% 9.53/5.32      ( ( arg @ imaginary_unit )
% 9.53/5.32      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9231_power2__csqrt,axiom,
% 9.53/5.32      ! [Z: complex] :
% 9.53/5.32        ( ( power_power_complex @ ( csqrt @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.53/5.32        = Z ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9232_lessThan__Suc__atMost,axiom,
% 9.53/5.32      ! [K: nat] :
% 9.53/5.32        ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 9.53/5.32        = ( set_ord_atMost_nat @ K ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9233_atMost__Suc,axiom,
% 9.53/5.32      ! [K: nat] :
% 9.53/5.32        ( ( set_ord_atMost_nat @ ( suc @ K ) )
% 9.53/5.32        = ( insert_nat @ ( suc @ K ) @ ( set_ord_atMost_nat @ K ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9234_atMost__nat__numeral,axiom,
% 9.53/5.32      ! [K: num] :
% 9.53/5.32        ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K ) )
% 9.53/5.32        = ( insert_nat @ ( numeral_numeral_nat @ K ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K ) ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9235_sum__choose__upper,axiom,
% 9.53/5.32      ! [M: nat,N: nat] :
% 9.53/5.32        ( ( groups3542108847815614940at_nat
% 9.53/5.32          @ ^ [K3: nat] : ( binomial @ K3 @ M )
% 9.53/5.32          @ ( set_ord_atMost_nat @ N ) )
% 9.53/5.32        = ( binomial @ ( suc @ N ) @ ( suc @ M ) ) ) ).
% 9.53/5.32  
% 9.53/5.32  thf(fact_9236_sum__choose__lower,axiom,
% 9.53/5.33      ! [R: nat,N: nat] :
% 9.53/5.33        ( ( groups3542108847815614940at_nat
% 9.53/5.33          @ ^ [K3: nat] : ( binomial @ ( plus_plus_nat @ R @ K3 ) @ K3 )
% 9.53/5.33          @ ( set_ord_atMost_nat @ N ) )
% 9.53/5.33        = ( binomial @ ( suc @ ( plus_plus_nat @ R @ N ) ) @ N ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9237_choose__rising__sum_I1_J,axiom,
% 9.53/5.33      ! [N: nat,M: nat] :
% 9.53/5.33        ( ( groups3542108847815614940at_nat
% 9.53/5.33          @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 9.53/5.33          @ ( set_ord_atMost_nat @ M ) )
% 9.53/5.33        = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9238_choose__rising__sum_I2_J,axiom,
% 9.53/5.33      ! [N: nat,M: nat] :
% 9.53/5.33        ( ( groups3542108847815614940at_nat
% 9.53/5.33          @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 9.53/5.33          @ ( set_ord_atMost_nat @ M ) )
% 9.53/5.33        = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ M ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9239_sum__choose__diagonal,axiom,
% 9.53/5.33      ! [M: nat,N: nat] :
% 9.53/5.33        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.33       => ( ( groups3542108847815614940at_nat
% 9.53/5.33            @ ^ [K3: nat] : ( binomial @ ( minus_minus_nat @ N @ K3 ) @ ( minus_minus_nat @ M @ K3 ) )
% 9.53/5.33            @ ( set_ord_atMost_nat @ M ) )
% 9.53/5.33          = ( binomial @ ( suc @ N ) @ M ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9240_vandermonde,axiom,
% 9.53/5.33      ! [M: nat,N: nat,R: nat] :
% 9.53/5.33        ( ( groups3542108847815614940at_nat
% 9.53/5.33          @ ^ [K3: nat] : ( times_times_nat @ ( binomial @ M @ K3 ) @ ( binomial @ N @ ( minus_minus_nat @ R @ K3 ) ) )
% 9.53/5.33          @ ( set_ord_atMost_nat @ R ) )
% 9.53/5.33        = ( binomial @ ( plus_plus_nat @ M @ N ) @ R ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9241_of__real__sqrt,axiom,
% 9.53/5.33      ! [X: real] :
% 9.53/5.33        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.33       => ( ( real_V4546457046886955230omplex @ ( sqrt @ X ) )
% 9.53/5.33          = ( csqrt @ ( real_V4546457046886955230omplex @ X ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9242_choose__row__sum,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( groups3542108847815614940at_nat @ ( binomial @ N ) @ ( set_ord_atMost_nat @ N ) )
% 9.53/5.33        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9243_Arg__bounded,axiom,
% 9.53/5.33      ! [Z: complex] :
% 9.53/5.33        ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 9.53/5.33        & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9244_binomial,axiom,
% 9.53/5.33      ! [A: nat,B: nat,N: nat] :
% 9.53/5.33        ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 9.53/5.33        = ( groups3542108847815614940at_nat
% 9.53/5.33          @ ^ [K3: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N @ K3 ) ) @ ( power_power_nat @ A @ K3 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 9.53/5.33          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9245_atLeast1__atMost__eq__remove0,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N )
% 9.53/5.33        = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9246_polynomial__product__nat,axiom,
% 9.53/5.33      ! [M: nat,A: nat > nat,N: nat,B: nat > nat,X: nat] :
% 9.53/5.33        ( ! [I4: nat] :
% 9.53/5.33            ( ( ord_less_nat @ M @ I4 )
% 9.53/5.33           => ( ( A @ I4 )
% 9.53/5.33              = zero_zero_nat ) )
% 9.53/5.33       => ( ! [J2: nat] :
% 9.53/5.33              ( ( ord_less_nat @ N @ J2 )
% 9.53/5.33             => ( ( B @ J2 )
% 9.53/5.33                = zero_zero_nat ) )
% 9.53/5.33         => ( ( times_times_nat
% 9.53/5.33              @ ( groups3542108847815614940at_nat
% 9.53/5.33                @ ^ [I3: nat] : ( times_times_nat @ ( A @ I3 ) @ ( power_power_nat @ X @ I3 ) )
% 9.53/5.33                @ ( set_ord_atMost_nat @ M ) )
% 9.53/5.33              @ ( groups3542108847815614940at_nat
% 9.53/5.33                @ ^ [J3: nat] : ( times_times_nat @ ( B @ J3 ) @ ( power_power_nat @ X @ J3 ) )
% 9.53/5.33                @ ( set_ord_atMost_nat @ N ) ) )
% 9.53/5.33            = ( groups3542108847815614940at_nat
% 9.53/5.33              @ ^ [R5: nat] :
% 9.53/5.33                  ( times_times_nat
% 9.53/5.33                  @ ( groups3542108847815614940at_nat
% 9.53/5.33                    @ ^ [K3: nat] : ( times_times_nat @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 9.53/5.33                    @ ( set_ord_atMost_nat @ R5 ) )
% 9.53/5.33                  @ ( power_power_nat @ X @ R5 ) )
% 9.53/5.33              @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9247_choose__square__sum,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( groups3542108847815614940at_nat
% 9.53/5.33          @ ^ [K3: nat] : ( power_power_nat @ ( binomial @ N @ K3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.53/5.33          @ ( set_ord_atMost_nat @ N ) )
% 9.53/5.33        = ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9248_complex__inverse,axiom,
% 9.53/5.33      ! [A: real,B: real] :
% 9.53/5.33        ( ( invers8013647133539491842omplex @ ( complex2 @ A @ B ) )
% 9.53/5.33        = ( complex2 @ ( divide_divide_real @ A @ ( plus_plus_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( uminus_uminus_real @ B ) @ ( plus_plus_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9249_binomial__r__part__sum,axiom,
% 9.53/5.33      ! [M: nat] :
% 9.53/5.33        ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M ) )
% 9.53/5.33        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9250_choose__linear__sum,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( groups3542108847815614940at_nat
% 9.53/5.33          @ ^ [I3: nat] : ( times_times_nat @ I3 @ ( binomial @ N @ I3 ) )
% 9.53/5.33          @ ( set_ord_atMost_nat @ N ) )
% 9.53/5.33        = ( times_times_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9251_cis__minus__pi__half,axiom,
% 9.53/5.33      ( ( cis @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 9.53/5.33      = ( uminus1482373934393186551omplex @ imaginary_unit ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9252_of__nat__id,axiom,
% 9.53/5.33      ( semiri1316708129612266289at_nat
% 9.53/5.33      = ( ^ [N2: nat] : N2 ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9253_norm__cis,axiom,
% 9.53/5.33      ! [A: real] :
% 9.53/5.33        ( ( real_V1022390504157884413omplex @ ( cis @ A ) )
% 9.53/5.33        = one_one_real ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9254_cis__pi__half,axiom,
% 9.53/5.33      ( ( cis @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.33      = imaginary_unit ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9255_cis__2pi,axiom,
% 9.53/5.33      ( ( cis @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 9.53/5.33      = one_one_complex ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9256_real__scaleR__def,axiom,
% 9.53/5.33      real_V1485227260804924795R_real = times_times_real ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9257_complex__scaleR,axiom,
% 9.53/5.33      ! [R: real,A: real,B: real] :
% 9.53/5.33        ( ( real_V2046097035970521341omplex @ R @ ( complex2 @ A @ B ) )
% 9.53/5.33        = ( complex2 @ ( times_times_real @ R @ A ) @ ( times_times_real @ R @ B ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9258_cis__mult,axiom,
% 9.53/5.33      ! [A: real,B: real] :
% 9.53/5.33        ( ( times_times_complex @ ( cis @ A ) @ ( cis @ B ) )
% 9.53/5.33        = ( cis @ ( plus_plus_real @ A @ B ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9259_cis__divide,axiom,
% 9.53/5.33      ! [A: real,B: real] :
% 9.53/5.33        ( ( divide1717551699836669952omplex @ ( cis @ A ) @ ( cis @ B ) )
% 9.53/5.33        = ( cis @ ( minus_minus_real @ A @ B ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9260_DeMoivre,axiom,
% 9.53/5.33      ! [A: real,N: nat] :
% 9.53/5.33        ( ( power_power_complex @ ( cis @ A ) @ N )
% 9.53/5.33        = ( cis @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9261_bij__betw__roots__unity,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( bij_betw_nat_complex
% 9.53/5.33          @ ^ [K3: nat] : ( cis @ ( divide_divide_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( semiri5074537144036343181t_real @ K3 ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 9.53/5.33          @ ( set_ord_lessThan_nat @ N )
% 9.53/5.33          @ ( collect_complex
% 9.53/5.33            @ ^ [Z4: complex] :
% 9.53/5.33                ( ( power_power_complex @ Z4 @ N )
% 9.53/5.33                = one_one_complex ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9262_cot__less__zero,axiom,
% 9.53/5.33      ! [X: real] :
% 9.53/5.33        ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 9.53/5.33       => ( ( ord_less_real @ X @ zero_zero_real )
% 9.53/5.33         => ( ord_less_real @ ( cot_real @ X ) @ zero_zero_real ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9263_sinh__real__less__iff,axiom,
% 9.53/5.33      ! [X: real,Y2: real] :
% 9.53/5.33        ( ( ord_less_real @ ( sinh_real @ X ) @ ( sinh_real @ Y2 ) )
% 9.53/5.33        = ( ord_less_real @ X @ Y2 ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9264_sinh__real__le__iff,axiom,
% 9.53/5.33      ! [X: real,Y2: real] :
% 9.53/5.33        ( ( ord_less_eq_real @ ( sinh_real @ X ) @ ( sinh_real @ Y2 ) )
% 9.53/5.33        = ( ord_less_eq_real @ X @ Y2 ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9265_sinh__real__neg__iff,axiom,
% 9.53/5.33      ! [X: real] :
% 9.53/5.33        ( ( ord_less_real @ ( sinh_real @ X ) @ zero_zero_real )
% 9.53/5.33        = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9266_sinh__real__pos__iff,axiom,
% 9.53/5.33      ! [X: real] :
% 9.53/5.33        ( ( ord_less_real @ zero_zero_real @ ( sinh_real @ X ) )
% 9.53/5.33        = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9267_sinh__real__nonneg__iff,axiom,
% 9.53/5.33      ! [X: real] :
% 9.53/5.33        ( ( ord_less_eq_real @ zero_zero_real @ ( sinh_real @ X ) )
% 9.53/5.33        = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9268_sinh__real__nonpos__iff,axiom,
% 9.53/5.33      ! [X: real] :
% 9.53/5.33        ( ( ord_less_eq_real @ ( sinh_real @ X ) @ zero_zero_real )
% 9.53/5.33        = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9269_cot__npi,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( cot_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 9.53/5.33        = zero_zero_real ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9270_cot__periodic,axiom,
% 9.53/5.33      ! [X: real] :
% 9.53/5.33        ( ( cot_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 9.53/5.33        = ( cot_real @ X ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9271_sinh__le__cosh__real,axiom,
% 9.53/5.33      ! [X: real] : ( ord_less_eq_real @ ( sinh_real @ X ) @ ( cosh_real @ X ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9272_sinh__less__cosh__real,axiom,
% 9.53/5.33      ! [X: real] : ( ord_less_real @ ( sinh_real @ X ) @ ( cosh_real @ X ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9273_cosh__real__pos,axiom,
% 9.53/5.33      ! [X: real] : ( ord_less_real @ zero_zero_real @ ( cosh_real @ X ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9274_cosh__real__nonpos__le__iff,axiom,
% 9.53/5.33      ! [X: real,Y2: real] :
% 9.53/5.33        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 9.53/5.33       => ( ( ord_less_eq_real @ Y2 @ zero_zero_real )
% 9.53/5.33         => ( ( ord_less_eq_real @ ( cosh_real @ X ) @ ( cosh_real @ Y2 ) )
% 9.53/5.33            = ( ord_less_eq_real @ Y2 @ X ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9275_cosh__real__nonneg__le__iff,axiom,
% 9.53/5.33      ! [X: real,Y2: real] :
% 9.53/5.33        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.33       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 9.53/5.33         => ( ( ord_less_eq_real @ ( cosh_real @ X ) @ ( cosh_real @ Y2 ) )
% 9.53/5.33            = ( ord_less_eq_real @ X @ Y2 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9276_cosh__real__nonneg,axiom,
% 9.53/5.33      ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( cosh_real @ X ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9277_cosh__real__ge__1,axiom,
% 9.53/5.33      ! [X: real] : ( ord_less_eq_real @ one_one_real @ ( cosh_real @ X ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9278_cosh__real__nonpos__less__iff,axiom,
% 9.53/5.33      ! [X: real,Y2: real] :
% 9.53/5.33        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 9.53/5.33       => ( ( ord_less_eq_real @ Y2 @ zero_zero_real )
% 9.53/5.33         => ( ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y2 ) )
% 9.53/5.33            = ( ord_less_real @ Y2 @ X ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9279_cosh__real__nonneg__less__iff,axiom,
% 9.53/5.33      ! [X: real,Y2: real] :
% 9.53/5.33        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.33       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 9.53/5.33         => ( ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y2 ) )
% 9.53/5.33            = ( ord_less_real @ X @ Y2 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9280_cosh__real__strict__mono,axiom,
% 9.53/5.33      ! [X: real,Y2: real] :
% 9.53/5.33        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.33       => ( ( ord_less_real @ X @ Y2 )
% 9.53/5.33         => ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y2 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9281_arcosh__cosh__real,axiom,
% 9.53/5.33      ! [X: real] :
% 9.53/5.33        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.33       => ( ( arcosh_real @ ( cosh_real @ X ) )
% 9.53/5.33          = X ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9282_cosh__ln__real,axiom,
% 9.53/5.33      ! [X: real] :
% 9.53/5.33        ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.33       => ( ( cosh_real @ ( ln_ln_real @ X ) )
% 9.53/5.33          = ( divide_divide_real @ ( plus_plus_real @ X @ ( inverse_inverse_real @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9283_cot__gt__zero,axiom,
% 9.53/5.33      ! [X: real] :
% 9.53/5.33        ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.33       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.33         => ( ord_less_real @ zero_zero_real @ ( cot_real @ X ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9284_sinh__ln__real,axiom,
% 9.53/5.33      ! [X: real] :
% 9.53/5.33        ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.33       => ( ( sinh_real @ ( ln_ln_real @ X ) )
% 9.53/5.33          = ( divide_divide_real @ ( minus_minus_real @ X @ ( inverse_inverse_real @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9285_tan__cot_H,axiom,
% 9.53/5.33      ! [X: real] :
% 9.53/5.33        ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) )
% 9.53/5.33        = ( cot_real @ X ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9286_arctan__def,axiom,
% 9.53/5.33      ( arctan
% 9.53/5.33      = ( ^ [Y: real] :
% 9.53/5.33            ( the_real
% 9.53/5.33            @ ^ [X2: real] :
% 9.53/5.33                ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 9.53/5.33                & ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.33                & ( ( tan_real @ X2 )
% 9.53/5.33                  = Y ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9287_arcsin__def,axiom,
% 9.53/5.33      ( arcsin
% 9.53/5.33      = ( ^ [Y: real] :
% 9.53/5.33            ( the_real
% 9.53/5.33            @ ^ [X2: real] :
% 9.53/5.33                ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 9.53/5.33                & ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.33                & ( ( sin_real @ X2 )
% 9.53/5.33                  = Y ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9288_signed__take__bit__eq__take__bit__minus,axiom,
% 9.53/5.33      ( bit_ri631733984087533419it_int
% 9.53/5.33      = ( ^ [N2: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ K3 ) @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N2 ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9289_signed__take__bit__nonnegative__iff,axiom,
% 9.53/5.33      ! [N: nat,K: int] :
% 9.53/5.33        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 9.53/5.33        = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9290_signed__take__bit__negative__iff,axiom,
% 9.53/5.33      ! [N: nat,K: int] :
% 9.53/5.33        ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ zero_zero_int )
% 9.53/5.33        = ( bit_se1146084159140164899it_int @ K @ N ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9291_bit__minus__numeral__Bit0__Suc__iff,axiom,
% 9.53/5.33      ! [W: num,N: nat] :
% 9.53/5.33        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( suc @ N ) )
% 9.53/5.33        = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ N ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9292_bit__minus__numeral__Bit1__Suc__iff,axiom,
% 9.53/5.33      ! [W: num,N: nat] :
% 9.53/5.33        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( suc @ N ) )
% 9.53/5.33        = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9293_bit__minus__numeral__int_I1_J,axiom,
% 9.53/5.33      ! [W: num,N: num] :
% 9.53/5.33        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 9.53/5.33        = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ ( pred_numeral @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9294_bit__minus__numeral__int_I2_J,axiom,
% 9.53/5.33      ! [W: num,N: num] :
% 9.53/5.33        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 9.53/5.33        = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9295_bit__and__int__iff,axiom,
% 9.53/5.33      ! [K: int,L2: int,N: nat] :
% 9.53/5.33        ( ( bit_se1146084159140164899it_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) @ N )
% 9.53/5.33        = ( ( bit_se1146084159140164899it_int @ K @ N )
% 9.53/5.33          & ( bit_se1146084159140164899it_int @ L2 @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9296_bit__or__int__iff,axiom,
% 9.53/5.33      ! [K: int,L2: int,N: nat] :
% 9.53/5.33        ( ( bit_se1146084159140164899it_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) @ N )
% 9.53/5.33        = ( ( bit_se1146084159140164899it_int @ K @ N )
% 9.53/5.33          | ( bit_se1146084159140164899it_int @ L2 @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9297_bit__not__int__iff_H,axiom,
% 9.53/5.33      ! [K: int,N: nat] :
% 9.53/5.33        ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ ( uminus_uminus_int @ K ) @ one_one_int ) @ N )
% 9.53/5.33        = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9298_ln__neg__is__const,axiom,
% 9.53/5.33      ! [X: real] :
% 9.53/5.33        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 9.53/5.33       => ( ( ln_ln_real @ X )
% 9.53/5.33          = ( the_real
% 9.53/5.33            @ ^ [X2: real] : $false ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9299_bit__imp__take__bit__positive,axiom,
% 9.53/5.33      ! [N: nat,M: nat,K: int] :
% 9.53/5.33        ( ( ord_less_nat @ N @ M )
% 9.53/5.33       => ( ( bit_se1146084159140164899it_int @ K @ N )
% 9.53/5.33         => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M @ K ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9300_bit__concat__bit__iff,axiom,
% 9.53/5.33      ! [M: nat,K: int,L2: int,N: nat] :
% 9.53/5.33        ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M @ K @ L2 ) @ N )
% 9.53/5.33        = ( ( ( ord_less_nat @ N @ M )
% 9.53/5.33            & ( bit_se1146084159140164899it_int @ K @ N ) )
% 9.53/5.33          | ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.33            & ( bit_se1146084159140164899it_int @ L2 @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9301_signed__take__bit__eq__concat__bit,axiom,
% 9.53/5.33      ( bit_ri631733984087533419it_int
% 9.53/5.33      = ( ^ [N2: nat,K3: int] : ( bit_concat_bit @ N2 @ K3 @ ( uminus_uminus_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N2 ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9302_int__bit__bound,axiom,
% 9.53/5.33      ! [K: int] :
% 9.53/5.33        ~ ! [N3: nat] :
% 9.53/5.33            ( ! [M5: nat] :
% 9.53/5.33                ( ( ord_less_eq_nat @ N3 @ M5 )
% 9.53/5.33               => ( ( bit_se1146084159140164899it_int @ K @ M5 )
% 9.53/5.33                  = ( bit_se1146084159140164899it_int @ K @ N3 ) ) )
% 9.53/5.33           => ~ ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 9.53/5.33               => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N3 @ one_one_nat ) )
% 9.53/5.33                  = ( ~ ( bit_se1146084159140164899it_int @ K @ N3 ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9303_bit__int__def,axiom,
% 9.53/5.33      ( bit_se1146084159140164899it_int
% 9.53/5.33      = ( ^ [K3: int,N2: nat] :
% 9.53/5.33            ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9304_arccos__def,axiom,
% 9.53/5.33      ( arccos
% 9.53/5.33      = ( ^ [Y: real] :
% 9.53/5.33            ( the_real
% 9.53/5.33            @ ^ [X2: real] :
% 9.53/5.33                ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 9.53/5.33                & ( ord_less_eq_real @ X2 @ pi )
% 9.53/5.33                & ( ( cos_real @ X2 )
% 9.53/5.33                  = Y ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9305_set__bit__eq,axiom,
% 9.53/5.33      ( bit_se7879613467334960850it_int
% 9.53/5.33      = ( ^ [N2: nat,K3: int] :
% 9.53/5.33            ( plus_plus_int @ K3
% 9.53/5.33            @ ( times_times_int
% 9.53/5.33              @ ( zero_n2684676970156552555ol_int
% 9.53/5.33                @ ~ ( bit_se1146084159140164899it_int @ K3 @ N2 ) )
% 9.53/5.33              @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9306_unset__bit__eq,axiom,
% 9.53/5.33      ( bit_se4203085406695923979it_int
% 9.53/5.33      = ( ^ [N2: nat,K3: int] : ( minus_minus_int @ K3 @ ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9307_pi__half,axiom,
% 9.53/5.33      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 9.53/5.33      = ( the_real
% 9.53/5.33        @ ^ [X2: real] :
% 9.53/5.33            ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 9.53/5.33            & ( ord_less_eq_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 9.53/5.33            & ( ( cos_real @ X2 )
% 9.53/5.33              = zero_zero_real ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9308_pi__def,axiom,
% 9.53/5.33      ( pi
% 9.53/5.33      = ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 9.53/5.33        @ ( the_real
% 9.53/5.33          @ ^ [X2: real] :
% 9.53/5.33              ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 9.53/5.33              & ( ord_less_eq_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 9.53/5.33              & ( ( cos_real @ X2 )
% 9.53/5.33                = zero_zero_real ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9309_take__bit__Suc__from__most,axiom,
% 9.53/5.33      ! [N: nat,K: int] :
% 9.53/5.33        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ K )
% 9.53/5.33        = ( plus_plus_int @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K @ N ) ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9310_bij__betw__nth__root__unity,axiom,
% 9.53/5.33      ! [C: complex,N: nat] :
% 9.53/5.33        ( ( C != zero_zero_complex )
% 9.53/5.33       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33         => ( bij_be1856998921033663316omplex @ ( times_times_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ ( root @ N @ ( real_V1022390504157884413omplex @ C ) ) ) @ ( cis @ ( divide_divide_real @ ( arg @ C ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) )
% 9.53/5.33            @ ( collect_complex
% 9.53/5.33              @ ^ [Z4: complex] :
% 9.53/5.33                  ( ( power_power_complex @ Z4 @ N )
% 9.53/5.33                  = one_one_complex ) )
% 9.53/5.33            @ ( collect_complex
% 9.53/5.33              @ ^ [Z4: complex] :
% 9.53/5.33                  ( ( power_power_complex @ Z4 @ N )
% 9.53/5.33                  = C ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9311_modulo__int__unfold,axiom,
% 9.53/5.33      ! [L2: int,K: int,N: nat,M: nat] :
% 9.53/5.33        ( ( ( ( ( sgn_sgn_int @ L2 )
% 9.53/5.33              = zero_zero_int )
% 9.53/5.33            | ( ( sgn_sgn_int @ K )
% 9.53/5.33              = zero_zero_int )
% 9.53/5.33            | ( N = zero_zero_nat ) )
% 9.53/5.33         => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 9.53/5.33            = ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) ) )
% 9.53/5.33        & ( ~ ( ( ( sgn_sgn_int @ L2 )
% 9.53/5.33                = zero_zero_int )
% 9.53/5.33              | ( ( sgn_sgn_int @ K )
% 9.53/5.33                = zero_zero_int )
% 9.53/5.33              | ( N = zero_zero_nat ) )
% 9.53/5.33         => ( ( ( ( sgn_sgn_int @ K )
% 9.53/5.33                = ( sgn_sgn_int @ L2 ) )
% 9.53/5.33             => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 9.53/5.33                = ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) )
% 9.53/5.33            & ( ( ( sgn_sgn_int @ K )
% 9.53/5.33               != ( sgn_sgn_int @ L2 ) )
% 9.53/5.33             => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 9.53/5.33                = ( times_times_int @ ( sgn_sgn_int @ L2 )
% 9.53/5.33                  @ ( minus_minus_int
% 9.53/5.33                    @ ( semiri1314217659103216013at_int
% 9.53/5.33                      @ ( times_times_nat @ N
% 9.53/5.33                        @ ( zero_n2687167440665602831ol_nat
% 9.53/5.33                          @ ~ ( dvd_dvd_nat @ N @ M ) ) ) )
% 9.53/5.33                    @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9312_powr__int,axiom,
% 9.53/5.33      ! [X: real,I2: int] :
% 9.53/5.33        ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.33       => ( ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 9.53/5.33           => ( ( powr_real @ X @ ( ring_1_of_int_real @ I2 ) )
% 9.53/5.33              = ( power_power_real @ X @ ( nat2 @ I2 ) ) ) )
% 9.53/5.33          & ( ~ ( ord_less_eq_int @ zero_zero_int @ I2 )
% 9.53/5.33           => ( ( powr_real @ X @ ( ring_1_of_int_real @ I2 ) )
% 9.53/5.33              = ( divide_divide_real @ one_one_real @ ( power_power_real @ X @ ( nat2 @ ( uminus_uminus_int @ I2 ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9313_divide__int__unfold,axiom,
% 9.53/5.33      ! [L2: int,K: int,N: nat,M: nat] :
% 9.53/5.33        ( ( ( ( ( sgn_sgn_int @ L2 )
% 9.53/5.33              = zero_zero_int )
% 9.53/5.33            | ( ( sgn_sgn_int @ K )
% 9.53/5.33              = zero_zero_int )
% 9.53/5.33            | ( N = zero_zero_nat ) )
% 9.53/5.33         => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 9.53/5.33            = zero_zero_int ) )
% 9.53/5.33        & ( ~ ( ( ( sgn_sgn_int @ L2 )
% 9.53/5.33                = zero_zero_int )
% 9.53/5.33              | ( ( sgn_sgn_int @ K )
% 9.53/5.33                = zero_zero_int )
% 9.53/5.33              | ( N = zero_zero_nat ) )
% 9.53/5.33         => ( ( ( ( sgn_sgn_int @ K )
% 9.53/5.33                = ( sgn_sgn_int @ L2 ) )
% 9.53/5.33             => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 9.53/5.33                = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) )
% 9.53/5.33            & ( ( ( sgn_sgn_int @ K )
% 9.53/5.33               != ( sgn_sgn_int @ L2 ) )
% 9.53/5.33             => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 9.53/5.33                = ( uminus_uminus_int
% 9.53/5.33                  @ ( semiri1314217659103216013at_int
% 9.53/5.33                    @ ( plus_plus_nat @ ( divide_divide_nat @ M @ N )
% 9.53/5.33                      @ ( zero_n2687167440665602831ol_nat
% 9.53/5.33                        @ ~ ( dvd_dvd_nat @ N @ M ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9314_real__root__zero,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( root @ N @ zero_zero_real )
% 9.53/5.33        = zero_zero_real ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9315_nat__numeral,axiom,
% 9.53/5.33      ! [K: num] :
% 9.53/5.33        ( ( nat2 @ ( numeral_numeral_int @ K ) )
% 9.53/5.33        = ( numeral_numeral_nat @ K ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9316_real__root__Suc__0,axiom,
% 9.53/5.33      ! [X: real] :
% 9.53/5.33        ( ( root @ ( suc @ zero_zero_nat ) @ X )
% 9.53/5.33        = X ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9317_real__root__eq__iff,axiom,
% 9.53/5.33      ! [N: nat,X: real,Y2: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( ( root @ N @ X )
% 9.53/5.33            = ( root @ N @ Y2 ) )
% 9.53/5.33          = ( X = Y2 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9318_root__0,axiom,
% 9.53/5.33      ! [X: real] :
% 9.53/5.33        ( ( root @ zero_zero_nat @ X )
% 9.53/5.33        = zero_zero_real ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9319_nat__1,axiom,
% 9.53/5.33      ( ( nat2 @ one_one_int )
% 9.53/5.33      = ( suc @ zero_zero_nat ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9320_real__root__eq__0__iff,axiom,
% 9.53/5.33      ! [N: nat,X: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( ( root @ N @ X )
% 9.53/5.33            = zero_zero_real )
% 9.53/5.33          = ( X = zero_zero_real ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9321_real__root__less__iff,axiom,
% 9.53/5.33      ! [N: nat,X: real,Y2: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( ord_less_real @ ( root @ N @ X ) @ ( root @ N @ Y2 ) )
% 9.53/5.33          = ( ord_less_real @ X @ Y2 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9322_real__root__le__iff,axiom,
% 9.53/5.33      ! [N: nat,X: real,Y2: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N @ Y2 ) )
% 9.53/5.33          = ( ord_less_eq_real @ X @ Y2 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9323_zless__nat__conj,axiom,
% 9.53/5.33      ! [W: int,Z: int] :
% 9.53/5.33        ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 9.53/5.33        = ( ( ord_less_int @ zero_zero_int @ Z )
% 9.53/5.33          & ( ord_less_int @ W @ Z ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9324_real__root__eq__1__iff,axiom,
% 9.53/5.33      ! [N: nat,X: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( ( root @ N @ X )
% 9.53/5.33            = one_one_real )
% 9.53/5.33          = ( X = one_one_real ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9325_real__root__one,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( root @ N @ one_one_real )
% 9.53/5.33          = one_one_real ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9326_nat__neg__numeral,axiom,
% 9.53/5.33      ! [K: num] :
% 9.53/5.33        ( ( nat2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 9.53/5.33        = zero_zero_nat ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9327_real__root__gt__0__iff,axiom,
% 9.53/5.33      ! [N: nat,Y2: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( ord_less_real @ zero_zero_real @ ( root @ N @ Y2 ) )
% 9.53/5.33          = ( ord_less_real @ zero_zero_real @ Y2 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9328_real__root__lt__0__iff,axiom,
% 9.53/5.33      ! [N: nat,X: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( ord_less_real @ ( root @ N @ X ) @ zero_zero_real )
% 9.53/5.33          = ( ord_less_real @ X @ zero_zero_real ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9329_real__root__ge__0__iff,axiom,
% 9.53/5.33      ! [N: nat,Y2: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ Y2 ) )
% 9.53/5.33          = ( ord_less_eq_real @ zero_zero_real @ Y2 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9330_real__root__le__0__iff,axiom,
% 9.53/5.33      ! [N: nat,X: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( ord_less_eq_real @ ( root @ N @ X ) @ zero_zero_real )
% 9.53/5.33          = ( ord_less_eq_real @ X @ zero_zero_real ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9331_zero__less__nat__eq,axiom,
% 9.53/5.33      ! [Z: int] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z ) )
% 9.53/5.33        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9332_real__root__lt__1__iff,axiom,
% 9.53/5.33      ! [N: nat,X: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( ord_less_real @ ( root @ N @ X ) @ one_one_real )
% 9.53/5.33          = ( ord_less_real @ X @ one_one_real ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9333_real__root__gt__1__iff,axiom,
% 9.53/5.33      ! [N: nat,Y2: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( ord_less_real @ one_one_real @ ( root @ N @ Y2 ) )
% 9.53/5.33          = ( ord_less_real @ one_one_real @ Y2 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9334_real__root__le__1__iff,axiom,
% 9.53/5.33      ! [N: nat,X: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( ord_less_eq_real @ ( root @ N @ X ) @ one_one_real )
% 9.53/5.33          = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9335_real__root__ge__1__iff,axiom,
% 9.53/5.33      ! [N: nat,Y2: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( ord_less_eq_real @ one_one_real @ ( root @ N @ Y2 ) )
% 9.53/5.33          = ( ord_less_eq_real @ one_one_real @ Y2 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9336_diff__nat__numeral,axiom,
% 9.53/5.33      ! [V: num,V3: num] :
% 9.53/5.33        ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ ( numeral_numeral_nat @ V3 ) )
% 9.53/5.33        = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ V3 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9337_nat__eq__numeral__power__cancel__iff,axiom,
% 9.53/5.33      ! [Y2: int,X: num,N: nat] :
% 9.53/5.33        ( ( ( nat2 @ Y2 )
% 9.53/5.33          = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 9.53/5.33        = ( Y2
% 9.53/5.33          = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9338_numeral__power__eq__nat__cancel__iff,axiom,
% 9.53/5.33      ! [X: num,N: nat,Y2: int] :
% 9.53/5.33        ( ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 9.53/5.33          = ( nat2 @ Y2 ) )
% 9.53/5.33        = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 9.53/5.33          = Y2 ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9339_nat__ceiling__le__eq,axiom,
% 9.53/5.33      ! [X: real,A: nat] :
% 9.53/5.33        ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) @ A )
% 9.53/5.33        = ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ A ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9340_one__less__nat__eq,axiom,
% 9.53/5.33      ! [Z: int] :
% 9.53/5.33        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z ) )
% 9.53/5.33        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9341_real__root__pow__pos2,axiom,
% 9.53/5.33      ! [N: nat,X: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.33         => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 9.53/5.33            = X ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9342_nat__numeral__diff__1,axiom,
% 9.53/5.33      ! [V: num] :
% 9.53/5.33        ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat )
% 9.53/5.33        = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ one_one_int ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9343_nat__less__numeral__power__cancel__iff,axiom,
% 9.53/5.33      ! [A: int,X: num,N: nat] :
% 9.53/5.33        ( ( ord_less_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 9.53/5.33        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9344_numeral__power__less__nat__cancel__iff,axiom,
% 9.53/5.33      ! [X: num,N: nat,A: int] :
% 9.53/5.33        ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) @ ( nat2 @ A ) )
% 9.53/5.33        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9345_nat__le__numeral__power__cancel__iff,axiom,
% 9.53/5.33      ! [A: int,X: num,N: nat] :
% 9.53/5.33        ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 9.53/5.33        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9346_numeral__power__le__nat__cancel__iff,axiom,
% 9.53/5.33      ! [X: num,N: nat,A: int] :
% 9.53/5.33        ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) @ ( nat2 @ A ) )
% 9.53/5.33        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9347_bit__nat__iff,axiom,
% 9.53/5.33      ! [K: int,N: nat] :
% 9.53/5.33        ( ( bit_se1148574629649215175it_nat @ ( nat2 @ K ) @ N )
% 9.53/5.33        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 9.53/5.33          & ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9348_real__root__inverse,axiom,
% 9.53/5.33      ! [N: nat,X: real] :
% 9.53/5.33        ( ( root @ N @ ( inverse_inverse_real @ X ) )
% 9.53/5.33        = ( inverse_inverse_real @ ( root @ N @ X ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9349_real__root__commute,axiom,
% 9.53/5.33      ! [M: nat,N: nat,X: real] :
% 9.53/5.33        ( ( root @ M @ ( root @ N @ X ) )
% 9.53/5.33        = ( root @ N @ ( root @ M @ X ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9350_real__root__minus,axiom,
% 9.53/5.33      ! [N: nat,X: real] :
% 9.53/5.33        ( ( root @ N @ ( uminus_uminus_real @ X ) )
% 9.53/5.33        = ( uminus_uminus_real @ ( root @ N @ X ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9351_real__root__mult__exp,axiom,
% 9.53/5.33      ! [M: nat,N: nat,X: real] :
% 9.53/5.33        ( ( root @ ( times_times_nat @ M @ N ) @ X )
% 9.53/5.33        = ( root @ M @ ( root @ N @ X ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9352_real__root__mult,axiom,
% 9.53/5.33      ! [N: nat,X: real,Y2: real] :
% 9.53/5.33        ( ( root @ N @ ( times_times_real @ X @ Y2 ) )
% 9.53/5.33        = ( times_times_real @ ( root @ N @ X ) @ ( root @ N @ Y2 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9353_real__root__divide,axiom,
% 9.53/5.33      ! [N: nat,X: real,Y2: real] :
% 9.53/5.33        ( ( root @ N @ ( divide_divide_real @ X @ Y2 ) )
% 9.53/5.33        = ( divide_divide_real @ ( root @ N @ X ) @ ( root @ N @ Y2 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9354_not__bit__Suc__0__Suc,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9355_bit__Suc__0__iff,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N )
% 9.53/5.33        = ( N = zero_zero_nat ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9356_real__root__pos__pos__le,axiom,
% 9.53/5.33      ! [X: real,N: nat] :
% 9.53/5.33        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.33       => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9357_nat__numeral__as__int,axiom,
% 9.53/5.33      ( numeral_numeral_nat
% 9.53/5.33      = ( ^ [I3: num] : ( nat2 @ ( numeral_numeral_int @ I3 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9358_nat__mono,axiom,
% 9.53/5.33      ! [X: int,Y2: int] :
% 9.53/5.33        ( ( ord_less_eq_int @ X @ Y2 )
% 9.53/5.33       => ( ord_less_eq_nat @ ( nat2 @ X ) @ ( nat2 @ Y2 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9359_nat__one__as__int,axiom,
% 9.53/5.33      ( one_one_nat
% 9.53/5.33      = ( nat2 @ one_one_int ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9360_div__eq__sgn__abs,axiom,
% 9.53/5.33      ! [K: int,L2: int] :
% 9.53/5.33        ( ( ( sgn_sgn_int @ K )
% 9.53/5.33          = ( sgn_sgn_int @ L2 ) )
% 9.53/5.33       => ( ( divide_divide_int @ K @ L2 )
% 9.53/5.33          = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9361_unset__bit__nat__def,axiom,
% 9.53/5.33      ( bit_se4205575877204974255it_nat
% 9.53/5.33      = ( ^ [M6: nat,N2: nat] : ( nat2 @ ( bit_se4203085406695923979it_int @ M6 @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9362_nat__mask__eq,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( nat2 @ ( bit_se2000444600071755411sk_int @ N ) )
% 9.53/5.33        = ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9363_not__bit__Suc__0__numeral,axiom,
% 9.53/5.33      ! [N: num] :
% 9.53/5.33        ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9364_real__root__less__mono,axiom,
% 9.53/5.33      ! [N: nat,X: real,Y2: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( ord_less_real @ X @ Y2 )
% 9.53/5.33         => ( ord_less_real @ ( root @ N @ X ) @ ( root @ N @ Y2 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9365_real__root__le__mono,axiom,
% 9.53/5.33      ! [N: nat,X: real,Y2: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( ord_less_eq_real @ X @ Y2 )
% 9.53/5.33         => ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N @ Y2 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9366_real__root__power,axiom,
% 9.53/5.33      ! [N: nat,X: real,K: nat] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( root @ N @ ( power_power_real @ X @ K ) )
% 9.53/5.33          = ( power_power_real @ ( root @ N @ X ) @ K ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9367_real__root__abs,axiom,
% 9.53/5.33      ! [N: nat,X: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( root @ N @ ( abs_abs_real @ X ) )
% 9.53/5.33          = ( abs_abs_real @ ( root @ N @ X ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9368_nat__mono__iff,axiom,
% 9.53/5.33      ! [Z: int,W: int] :
% 9.53/5.33        ( ( ord_less_int @ zero_zero_int @ Z )
% 9.53/5.33       => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 9.53/5.33          = ( ord_less_int @ W @ Z ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9369_zless__nat__eq__int__zless,axiom,
% 9.53/5.33      ! [M: nat,Z: int] :
% 9.53/5.33        ( ( ord_less_nat @ M @ ( nat2 @ Z ) )
% 9.53/5.33        = ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ Z ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9370_nat__le__iff,axiom,
% 9.53/5.33      ! [X: int,N: nat] :
% 9.53/5.33        ( ( ord_less_eq_nat @ ( nat2 @ X ) @ N )
% 9.53/5.33        = ( ord_less_eq_int @ X @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9371_nat__int__add,axiom,
% 9.53/5.33      ! [A: nat,B: nat] :
% 9.53/5.33        ( ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) )
% 9.53/5.33        = ( plus_plus_nat @ A @ B ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9372_sgn__mod,axiom,
% 9.53/5.33      ! [L2: int,K: int] :
% 9.53/5.33        ( ( L2 != zero_zero_int )
% 9.53/5.33       => ( ~ ( dvd_dvd_int @ L2 @ K )
% 9.53/5.33         => ( ( sgn_sgn_int @ ( modulo_modulo_int @ K @ L2 ) )
% 9.53/5.33            = ( sgn_sgn_int @ L2 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9373_int__minus,axiom,
% 9.53/5.33      ! [N: nat,M: nat] :
% 9.53/5.33        ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ M ) )
% 9.53/5.33        = ( semiri1314217659103216013at_int @ ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9374_nat__abs__mult__distrib,axiom,
% 9.53/5.33      ! [W: int,Z: int] :
% 9.53/5.33        ( ( nat2 @ ( abs_abs_int @ ( times_times_int @ W @ Z ) ) )
% 9.53/5.33        = ( times_times_nat @ ( nat2 @ ( abs_abs_int @ W ) ) @ ( nat2 @ ( abs_abs_int @ Z ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9375_real__nat__ceiling__ge,axiom,
% 9.53/5.33      ! [X: real] : ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9376_nat__plus__as__int,axiom,
% 9.53/5.33      ( plus_plus_nat
% 9.53/5.33      = ( ^ [A3: nat,B4: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9377_and__nat__def,axiom,
% 9.53/5.33      ( bit_se727722235901077358nd_nat
% 9.53/5.33      = ( ^ [M6: nat,N2: nat] : ( nat2 @ ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9378_nat__times__as__int,axiom,
% 9.53/5.33      ( times_times_nat
% 9.53/5.33      = ( ^ [A3: nat,B4: nat] : ( nat2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9379_or__nat__def,axiom,
% 9.53/5.33      ( bit_se1412395901928357646or_nat
% 9.53/5.33      = ( ^ [M6: nat,N2: nat] : ( nat2 @ ( bit_se1409905431419307370or_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9380_nat__minus__as__int,axiom,
% 9.53/5.33      ( minus_minus_nat
% 9.53/5.33      = ( ^ [A3: nat,B4: nat] : ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9381_nat__div__as__int,axiom,
% 9.53/5.33      ( divide_divide_nat
% 9.53/5.33      = ( ^ [A3: nat,B4: nat] : ( nat2 @ ( divide_divide_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9382_real__root__gt__zero,axiom,
% 9.53/5.33      ! [N: nat,X: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.33         => ( ord_less_real @ zero_zero_real @ ( root @ N @ X ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9383_real__root__strict__decreasing,axiom,
% 9.53/5.33      ! [N: nat,N4: nat,X: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( ord_less_nat @ N @ N4 )
% 9.53/5.33         => ( ( ord_less_real @ one_one_real @ X )
% 9.53/5.33           => ( ord_less_real @ ( root @ N4 @ X ) @ ( root @ N @ X ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9384_sqrt__def,axiom,
% 9.53/5.33      ( sqrt
% 9.53/5.33      = ( root @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9385_root__abs__power,axiom,
% 9.53/5.33      ! [N: nat,Y2: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( abs_abs_real @ ( root @ N @ ( power_power_real @ Y2 @ N ) ) )
% 9.53/5.33          = ( abs_abs_real @ Y2 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9386_nat__less__eq__zless,axiom,
% 9.53/5.33      ! [W: int,Z: int] :
% 9.53/5.33        ( ( ord_less_eq_int @ zero_zero_int @ W )
% 9.53/5.33       => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 9.53/5.33          = ( ord_less_int @ W @ Z ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9387_nat__le__eq__zle,axiom,
% 9.53/5.33      ! [W: int,Z: int] :
% 9.53/5.33        ( ( ( ord_less_int @ zero_zero_int @ W )
% 9.53/5.33          | ( ord_less_eq_int @ zero_zero_int @ Z ) )
% 9.53/5.33       => ( ( ord_less_eq_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 9.53/5.33          = ( ord_less_eq_int @ W @ Z ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9388_nat__add__distrib,axiom,
% 9.53/5.33      ! [Z: int,Z6: int] :
% 9.53/5.33        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 9.53/5.33       => ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 9.53/5.33         => ( ( nat2 @ ( plus_plus_int @ Z @ Z6 ) )
% 9.53/5.33            = ( plus_plus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9389_le__nat__iff,axiom,
% 9.53/5.33      ! [K: int,N: nat] :
% 9.53/5.33        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 9.53/5.33       => ( ( ord_less_eq_nat @ N @ ( nat2 @ K ) )
% 9.53/5.33          = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9390_div__sgn__abs__cancel,axiom,
% 9.53/5.33      ! [V: int,K: int,L2: int] :
% 9.53/5.33        ( ( V != zero_zero_int )
% 9.53/5.33       => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ K ) ) @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ L2 ) ) )
% 9.53/5.33          = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9391_Suc__as__int,axiom,
% 9.53/5.33      ( suc
% 9.53/5.33      = ( ^ [A3: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ one_one_int ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9392_nat__mult__distrib,axiom,
% 9.53/5.33      ! [Z: int,Z6: int] :
% 9.53/5.33        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 9.53/5.33       => ( ( nat2 @ ( times_times_int @ Z @ Z6 ) )
% 9.53/5.33          = ( times_times_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9393_nat__abs__triangle__ineq,axiom,
% 9.53/5.33      ! [K: int,L2: int] : ( ord_less_eq_nat @ ( nat2 @ ( abs_abs_int @ ( plus_plus_int @ K @ L2 ) ) ) @ ( plus_plus_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9394_nat__diff__distrib,axiom,
% 9.53/5.33      ! [Z6: int,Z: int] :
% 9.53/5.33        ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 9.53/5.33       => ( ( ord_less_eq_int @ Z6 @ Z )
% 9.53/5.33         => ( ( nat2 @ ( minus_minus_int @ Z @ Z6 ) )
% 9.53/5.33            = ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9395_nat__diff__distrib_H,axiom,
% 9.53/5.33      ! [X: int,Y2: int] :
% 9.53/5.33        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 9.53/5.33       => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 9.53/5.33         => ( ( nat2 @ ( minus_minus_int @ X @ Y2 ) )
% 9.53/5.33            = ( minus_minus_nat @ ( nat2 @ X ) @ ( nat2 @ Y2 ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9396_nat__div__distrib_H,axiom,
% 9.53/5.33      ! [Y2: int,X: int] :
% 9.53/5.33        ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 9.53/5.33       => ( ( nat2 @ ( divide_divide_int @ X @ Y2 ) )
% 9.53/5.33          = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y2 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9397_nat__div__distrib,axiom,
% 9.53/5.33      ! [X: int,Y2: int] :
% 9.53/5.33        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 9.53/5.33       => ( ( nat2 @ ( divide_divide_int @ X @ Y2 ) )
% 9.53/5.33          = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y2 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9398_div__dvd__sgn__abs,axiom,
% 9.53/5.33      ! [L2: int,K: int] :
% 9.53/5.33        ( ( dvd_dvd_int @ L2 @ K )
% 9.53/5.33       => ( ( divide_divide_int @ K @ L2 )
% 9.53/5.33          = ( times_times_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( sgn_sgn_int @ L2 ) ) @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9399_nat__power__eq,axiom,
% 9.53/5.33      ! [Z: int,N: nat] :
% 9.53/5.33        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 9.53/5.33       => ( ( nat2 @ ( power_power_int @ Z @ N ) )
% 9.53/5.33          = ( power_power_nat @ ( nat2 @ Z ) @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9400_nat__floor__neg,axiom,
% 9.53/5.33      ! [X: real] :
% 9.53/5.33        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 9.53/5.33       => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 9.53/5.33          = zero_zero_nat ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9401_div__abs__eq__div__nat,axiom,
% 9.53/5.33      ! [K: int,L2: int] :
% 9.53/5.33        ( ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) )
% 9.53/5.33        = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9402_nat__mod__distrib,axiom,
% 9.53/5.33      ! [X: int,Y2: int] :
% 9.53/5.33        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 9.53/5.33       => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 9.53/5.33         => ( ( nat2 @ ( modulo_modulo_int @ X @ Y2 ) )
% 9.53/5.33            = ( modulo_modulo_nat @ ( nat2 @ X ) @ ( nat2 @ Y2 ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9403_floor__eq3,axiom,
% 9.53/5.33      ! [N: nat,X: real] :
% 9.53/5.33        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ X )
% 9.53/5.33       => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 9.53/5.33         => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 9.53/5.33            = N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9404_le__nat__floor,axiom,
% 9.53/5.33      ! [X: nat,A: real] :
% 9.53/5.33        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ A )
% 9.53/5.33       => ( ord_less_eq_nat @ X @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9405_mod__abs__eq__div__nat,axiom,
% 9.53/5.33      ! [K: int,L2: int] :
% 9.53/5.33        ( ( modulo_modulo_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) )
% 9.53/5.33        = ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9406_nat__take__bit__eq,axiom,
% 9.53/5.33      ! [K: int,N: nat] :
% 9.53/5.33        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 9.53/5.33       => ( ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 9.53/5.33          = ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9407_take__bit__nat__eq,axiom,
% 9.53/5.33      ! [K: int,N: nat] :
% 9.53/5.33        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 9.53/5.33       => ( ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) )
% 9.53/5.33          = ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9408_divide__int__def,axiom,
% 9.53/5.33      ( divide_divide_int
% 9.53/5.33      = ( ^ [K3: int,L: int] :
% 9.53/5.33            ( if_int @ ( L = zero_zero_int ) @ zero_zero_int
% 9.53/5.33            @ ( if_int
% 9.53/5.33              @ ( ( sgn_sgn_int @ K3 )
% 9.53/5.33                = ( sgn_sgn_int @ L ) )
% 9.53/5.33              @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) )
% 9.53/5.33              @ ( uminus_uminus_int
% 9.53/5.33                @ ( semiri1314217659103216013at_int
% 9.53/5.33                  @ ( plus_plus_nat @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) )
% 9.53/5.33                    @ ( zero_n2687167440665602831ol_nat
% 9.53/5.33                      @ ~ ( dvd_dvd_int @ L @ K3 ) ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9409_modulo__int__def,axiom,
% 9.53/5.33      ( modulo_modulo_int
% 9.53/5.33      = ( ^ [K3: int,L: int] :
% 9.53/5.33            ( if_int @ ( L = zero_zero_int ) @ K3
% 9.53/5.33            @ ( if_int
% 9.53/5.33              @ ( ( sgn_sgn_int @ K3 )
% 9.53/5.33                = ( sgn_sgn_int @ L ) )
% 9.53/5.33              @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) )
% 9.53/5.33              @ ( times_times_int @ ( sgn_sgn_int @ L )
% 9.53/5.33                @ ( minus_minus_int
% 9.53/5.33                  @ ( times_times_int @ ( abs_abs_int @ L )
% 9.53/5.33                    @ ( zero_n2684676970156552555ol_int
% 9.53/5.33                      @ ~ ( dvd_dvd_int @ L @ K3 ) ) )
% 9.53/5.33                  @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9410_real__root__pos__pos,axiom,
% 9.53/5.33      ! [N: nat,X: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.33         => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9411_real__root__strict__increasing,axiom,
% 9.53/5.33      ! [N: nat,N4: nat,X: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( ord_less_nat @ N @ N4 )
% 9.53/5.33         => ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.33           => ( ( ord_less_real @ X @ one_one_real )
% 9.53/5.33             => ( ord_less_real @ ( root @ N @ X ) @ ( root @ N4 @ X ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9412_real__root__decreasing,axiom,
% 9.53/5.33      ! [N: nat,N4: nat,X: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( ord_less_eq_nat @ N @ N4 )
% 9.53/5.33         => ( ( ord_less_eq_real @ one_one_real @ X )
% 9.53/5.33           => ( ord_less_eq_real @ ( root @ N4 @ X ) @ ( root @ N @ X ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9413_odd__real__root__power__cancel,axiom,
% 9.53/5.33      ! [N: nat,X: real] :
% 9.53/5.33        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.53/5.33       => ( ( root @ N @ ( power_power_real @ X @ N ) )
% 9.53/5.33          = X ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9414_odd__real__root__unique,axiom,
% 9.53/5.33      ! [N: nat,Y2: real,X: real] :
% 9.53/5.33        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.53/5.33       => ( ( ( power_power_real @ Y2 @ N )
% 9.53/5.33            = X )
% 9.53/5.33         => ( ( root @ N @ X )
% 9.53/5.33            = Y2 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9415_odd__real__root__pow,axiom,
% 9.53/5.33      ! [N: nat,X: real] :
% 9.53/5.33        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.53/5.33       => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 9.53/5.33          = X ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9416_real__root__pow__pos,axiom,
% 9.53/5.33      ! [N: nat,X: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.33         => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 9.53/5.33            = X ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9417_real__root__pos__unique,axiom,
% 9.53/5.33      ! [N: nat,Y2: real,X: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 9.53/5.33         => ( ( ( power_power_real @ Y2 @ N )
% 9.53/5.33              = X )
% 9.53/5.33           => ( ( root @ N @ X )
% 9.53/5.33              = Y2 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9418_real__root__power__cancel,axiom,
% 9.53/5.33      ! [N: nat,X: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.33         => ( ( root @ N @ ( power_power_real @ X @ N ) )
% 9.53/5.33            = X ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9419_nat__2,axiom,
% 9.53/5.33      ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.53/5.33      = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9420_Suc__nat__eq__nat__zadd1,axiom,
% 9.53/5.33      ! [Z: int] :
% 9.53/5.33        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 9.53/5.33       => ( ( suc @ ( nat2 @ Z ) )
% 9.53/5.33          = ( nat2 @ ( plus_plus_int @ one_one_int @ Z ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9421_nat__less__iff,axiom,
% 9.53/5.33      ! [W: int,M: nat] :
% 9.53/5.33        ( ( ord_less_eq_int @ zero_zero_int @ W )
% 9.53/5.33       => ( ( ord_less_nat @ ( nat2 @ W ) @ M )
% 9.53/5.33          = ( ord_less_int @ W @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9422_nat__mult__distrib__neg,axiom,
% 9.53/5.33      ! [Z: int,Z6: int] :
% 9.53/5.33        ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 9.53/5.33       => ( ( nat2 @ ( times_times_int @ Z @ Z6 ) )
% 9.53/5.33          = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z ) ) @ ( nat2 @ ( uminus_uminus_int @ Z6 ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9423_nat__abs__int__diff,axiom,
% 9.53/5.33      ! [A: nat,B: nat] :
% 9.53/5.33        ( ( ( ord_less_eq_nat @ A @ B )
% 9.53/5.33         => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 9.53/5.33            = ( minus_minus_nat @ B @ A ) ) )
% 9.53/5.33        & ( ~ ( ord_less_eq_nat @ A @ B )
% 9.53/5.33         => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 9.53/5.33            = ( minus_minus_nat @ A @ B ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9424_floor__eq4,axiom,
% 9.53/5.33      ! [N: nat,X: real] :
% 9.53/5.33        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ X )
% 9.53/5.33       => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 9.53/5.33         => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 9.53/5.33            = N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9425_diff__nat__eq__if,axiom,
% 9.53/5.33      ! [Z6: int,Z: int] :
% 9.53/5.33        ( ( ( ord_less_int @ Z6 @ zero_zero_int )
% 9.53/5.33         => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) )
% 9.53/5.33            = ( nat2 @ Z ) ) )
% 9.53/5.33        & ( ~ ( ord_less_int @ Z6 @ zero_zero_int )
% 9.53/5.33         => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) )
% 9.53/5.33            = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z @ Z6 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z @ Z6 ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9426_real__root__increasing,axiom,
% 9.53/5.33      ! [N: nat,N4: nat,X: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( ord_less_eq_nat @ N @ N4 )
% 9.53/5.33         => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.33           => ( ( ord_less_eq_real @ X @ one_one_real )
% 9.53/5.33             => ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N4 @ X ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9427_bit__nat__def,axiom,
% 9.53/5.33      ( bit_se1148574629649215175it_nat
% 9.53/5.33      = ( ^ [M6: nat,N2: nat] :
% 9.53/5.33            ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9428_eucl__rel__int__remainderI,axiom,
% 9.53/5.33      ! [R: int,L2: int,K: int,Q2: int] :
% 9.53/5.33        ( ( ( sgn_sgn_int @ R )
% 9.53/5.33          = ( sgn_sgn_int @ L2 ) )
% 9.53/5.33       => ( ( ord_less_int @ ( abs_abs_int @ R ) @ ( abs_abs_int @ L2 ) )
% 9.53/5.33         => ( ( K
% 9.53/5.33              = ( plus_plus_int @ ( times_times_int @ Q2 @ L2 ) @ R ) )
% 9.53/5.33           => ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9429_log__root,axiom,
% 9.53/5.33      ! [N: nat,A: real,B: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( ord_less_real @ zero_zero_real @ A )
% 9.53/5.33         => ( ( log @ B @ ( root @ N @ A ) )
% 9.53/5.33            = ( divide_divide_real @ ( log @ B @ A ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9430_log__base__root,axiom,
% 9.53/5.33      ! [N: nat,B: real,X: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( ord_less_real @ zero_zero_real @ B )
% 9.53/5.33         => ( ( log @ ( root @ N @ B ) @ X )
% 9.53/5.33            = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9431_ln__root,axiom,
% 9.53/5.33      ! [N: nat,B: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( ord_less_real @ zero_zero_real @ B )
% 9.53/5.33         => ( ( ln_ln_real @ ( root @ N @ B ) )
% 9.53/5.33            = ( divide_divide_real @ ( ln_ln_real @ B ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9432_eucl__rel__int_Osimps,axiom,
% 9.53/5.33      ( eucl_rel_int
% 9.53/5.33      = ( ^ [A1: int,A22: int,A32: product_prod_int_int] :
% 9.53/5.33            ( ? [K3: int] :
% 9.53/5.33                ( ( A1 = K3 )
% 9.53/5.33                & ( A22 = zero_zero_int )
% 9.53/5.33                & ( A32
% 9.53/5.33                  = ( product_Pair_int_int @ zero_zero_int @ K3 ) ) )
% 9.53/5.33            | ? [L: int,K3: int,Q4: int] :
% 9.53/5.33                ( ( A1 = K3 )
% 9.53/5.33                & ( A22 = L )
% 9.53/5.33                & ( A32
% 9.53/5.33                  = ( product_Pair_int_int @ Q4 @ zero_zero_int ) )
% 9.53/5.33                & ( L != zero_zero_int )
% 9.53/5.33                & ( K3
% 9.53/5.33                  = ( times_times_int @ Q4 @ L ) ) )
% 9.53/5.33            | ? [R5: int,L: int,K3: int,Q4: int] :
% 9.53/5.33                ( ( A1 = K3 )
% 9.53/5.33                & ( A22 = L )
% 9.53/5.33                & ( A32
% 9.53/5.33                  = ( product_Pair_int_int @ Q4 @ R5 ) )
% 9.53/5.33                & ( ( sgn_sgn_int @ R5 )
% 9.53/5.33                  = ( sgn_sgn_int @ L ) )
% 9.53/5.33                & ( ord_less_int @ ( abs_abs_int @ R5 ) @ ( abs_abs_int @ L ) )
% 9.53/5.33                & ( K3
% 9.53/5.33                  = ( plus_plus_int @ ( times_times_int @ Q4 @ L ) @ R5 ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9433_eucl__rel__int_Ocases,axiom,
% 9.53/5.33      ! [A12: int,A23: int,A33: product_prod_int_int] :
% 9.53/5.33        ( ( eucl_rel_int @ A12 @ A23 @ A33 )
% 9.53/5.33       => ( ( ( A23 = zero_zero_int )
% 9.53/5.33           => ( A33
% 9.53/5.33             != ( product_Pair_int_int @ zero_zero_int @ A12 ) ) )
% 9.53/5.33         => ( ! [Q3: int] :
% 9.53/5.33                ( ( A33
% 9.53/5.33                  = ( product_Pair_int_int @ Q3 @ zero_zero_int ) )
% 9.53/5.33               => ( ( A23 != zero_zero_int )
% 9.53/5.33                 => ( A12
% 9.53/5.33                   != ( times_times_int @ Q3 @ A23 ) ) ) )
% 9.53/5.33           => ~ ! [R3: int,Q3: int] :
% 9.53/5.33                  ( ( A33
% 9.53/5.33                    = ( product_Pair_int_int @ Q3 @ R3 ) )
% 9.53/5.33                 => ( ( ( sgn_sgn_int @ R3 )
% 9.53/5.33                      = ( sgn_sgn_int @ A23 ) )
% 9.53/5.33                   => ( ( ord_less_int @ ( abs_abs_int @ R3 ) @ ( abs_abs_int @ A23 ) )
% 9.53/5.33                     => ( A12
% 9.53/5.33                       != ( plus_plus_int @ ( times_times_int @ Q3 @ A23 ) @ R3 ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9434_div__noneq__sgn__abs,axiom,
% 9.53/5.33      ! [L2: int,K: int] :
% 9.53/5.33        ( ( L2 != zero_zero_int )
% 9.53/5.33       => ( ( ( sgn_sgn_int @ K )
% 9.53/5.33           != ( sgn_sgn_int @ L2 ) )
% 9.53/5.33         => ( ( divide_divide_int @ K @ L2 )
% 9.53/5.33            = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) ) )
% 9.53/5.33              @ ( zero_n2684676970156552555ol_int
% 9.53/5.33                @ ~ ( dvd_dvd_int @ L2 @ K ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9435_root__powr__inverse,axiom,
% 9.53/5.33      ! [N: nat,X: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.33         => ( ( root @ N @ X )
% 9.53/5.33            = ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9436_even__nat__iff,axiom,
% 9.53/5.33      ! [K: int] :
% 9.53/5.33        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 9.53/5.33       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat2 @ K ) )
% 9.53/5.33          = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9437_powr__real__of__int,axiom,
% 9.53/5.33      ! [X: real,N: int] :
% 9.53/5.33        ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.33       => ( ( ( ord_less_eq_int @ zero_zero_int @ N )
% 9.53/5.33           => ( ( powr_real @ X @ ( ring_1_of_int_real @ N ) )
% 9.53/5.33              = ( power_power_real @ X @ ( nat2 @ N ) ) ) )
% 9.53/5.33          & ( ~ ( ord_less_eq_int @ zero_zero_int @ N )
% 9.53/5.33           => ( ( powr_real @ X @ ( ring_1_of_int_real @ N ) )
% 9.53/5.33              = ( inverse_inverse_real @ ( power_power_real @ X @ ( nat2 @ ( uminus_uminus_int @ N ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9438_arctan__inverse,axiom,
% 9.53/5.33      ! [X: real] :
% 9.53/5.33        ( ( X != zero_zero_real )
% 9.53/5.33       => ( ( arctan @ ( divide_divide_real @ one_one_real @ X ) )
% 9.53/5.33          = ( minus_minus_real @ ( divide_divide_real @ ( times_times_real @ ( sgn_sgn_real @ X ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( arctan @ X ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9439_cis__multiple__2pi,axiom,
% 9.53/5.33      ! [N: real] :
% 9.53/5.33        ( ( member_real @ N @ ring_1_Ints_real )
% 9.53/5.33       => ( ( cis @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 9.53/5.33          = one_one_complex ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9440_setceilmax,axiom,
% 9.53/5.33      ! [S3: vEBT_VEBT,M: nat,Listy: list_VEBT_VEBT,N: nat] :
% 9.53/5.33        ( ( vEBT_invar_vebt @ S3 @ M )
% 9.53/5.33       => ( ! [X3: vEBT_VEBT] :
% 9.53/5.33              ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Listy ) )
% 9.53/5.33             => ( vEBT_invar_vebt @ X3 @ N ) )
% 9.53/5.33         => ( ( M
% 9.53/5.33              = ( suc @ N ) )
% 9.53/5.33           => ( ! [X3: vEBT_VEBT] :
% 9.53/5.33                  ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Listy ) )
% 9.53/5.33                 => ( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ X3 ) )
% 9.53/5.33                    = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) )
% 9.53/5.33             => ( ( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ S3 ) )
% 9.53/5.33                  = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) )
% 9.53/5.33               => ( ( semiri1314217659103216013at_int @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ S3 @ ( set_VEBT_VEBT2 @ Listy ) ) ) ) )
% 9.53/5.33                  = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9441_height__compose__list,axiom,
% 9.53/5.33      ! [T: vEBT_VEBT,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 9.53/5.33        ( ( member_VEBT_VEBT @ T @ ( set_VEBT_VEBT2 @ TreeList ) )
% 9.53/5.33       => ( ord_less_eq_nat @ ( vEBT_VEBT_height @ T ) @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary @ ( set_VEBT_VEBT2 @ TreeList ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9442_max__ins__scaled,axiom,
% 9.53/5.33      ! [N: nat,X14: vEBT_VEBT,M: nat,X13: list_VEBT_VEBT] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( vEBT_VEBT_height @ X14 ) ) @ ( plus_plus_nat @ M @ ( times_times_nat @ N @ ( lattic8265883725875713057ax_nat @ ( insert_nat @ ( vEBT_VEBT_height @ X14 ) @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( set_VEBT_VEBT2 @ X13 ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9443_height__i__max,axiom,
% 9.53/5.33      ! [I2: nat,X13: list_VEBT_VEBT,Foo: nat] :
% 9.53/5.33        ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ X13 ) )
% 9.53/5.33       => ( ord_less_eq_nat @ ( vEBT_VEBT_height @ ( nth_VEBT_VEBT @ X13 @ I2 ) ) @ ( ord_max_nat @ Foo @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( set_VEBT_VEBT2 @ X13 ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9444_max__idx__list,axiom,
% 9.53/5.33      ! [I2: nat,X13: list_VEBT_VEBT,N: nat,X14: vEBT_VEBT] :
% 9.53/5.33        ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ X13 ) )
% 9.53/5.33       => ( ord_less_eq_nat @ ( times_times_nat @ N @ ( vEBT_VEBT_height @ ( nth_VEBT_VEBT @ X13 @ I2 ) ) ) @ ( suc @ ( suc @ ( times_times_nat @ N @ ( ord_max_nat @ ( vEBT_VEBT_height @ X14 ) @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( set_VEBT_VEBT2 @ X13 ) ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9445_sgn__le__0__iff,axiom,
% 9.53/5.33      ! [X: real] :
% 9.53/5.33        ( ( ord_less_eq_real @ ( sgn_sgn_real @ X ) @ zero_zero_real )
% 9.53/5.33        = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9446_zero__le__sgn__iff,axiom,
% 9.53/5.33      ! [X: real] :
% 9.53/5.33        ( ( ord_less_eq_real @ zero_zero_real @ ( sgn_sgn_real @ X ) )
% 9.53/5.33        = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9447_real__sgn__eq,axiom,
% 9.53/5.33      ( sgn_sgn_real
% 9.53/5.33      = ( ^ [X2: real] : ( divide_divide_real @ X2 @ ( abs_abs_real @ X2 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9448_sgn__root,axiom,
% 9.53/5.33      ! [N: nat,X: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( sgn_sgn_real @ ( root @ N @ X ) )
% 9.53/5.33          = ( sgn_sgn_real @ X ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9449_VEBT__internal_Oheight_Osimps_I2_J,axiom,
% 9.53/5.33      ! [Uu: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 9.53/5.33        ( ( vEBT_VEBT_height @ ( vEBT_Node @ Uu @ Deg @ TreeList @ Summary ) )
% 9.53/5.33        = ( plus_plus_nat @ one_one_nat @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary @ ( set_VEBT_VEBT2 @ TreeList ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9450_sgn__real__def,axiom,
% 9.53/5.33      ( sgn_sgn_real
% 9.53/5.33      = ( ^ [A3: real] : ( if_real @ ( A3 = zero_zero_real ) @ zero_zero_real @ ( if_real @ ( ord_less_real @ zero_zero_real @ A3 ) @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9451_VEBT__internal_Oheight_Oelims,axiom,
% 9.53/5.33      ! [X: vEBT_VEBT,Y2: nat] :
% 9.53/5.33        ( ( ( vEBT_VEBT_height @ X )
% 9.53/5.33          = Y2 )
% 9.53/5.33       => ( ( ? [A4: $o,B3: $o] :
% 9.53/5.33                ( X
% 9.53/5.33                = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.53/5.33           => ( Y2 != zero_zero_nat ) )
% 9.53/5.33         => ~ ! [Uu2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.53/5.33                ( ( X
% 9.53/5.33                  = ( vEBT_Node @ Uu2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 9.53/5.33               => ( Y2
% 9.53/5.33                 != ( plus_plus_nat @ one_one_nat @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary2 @ ( set_VEBT_VEBT2 @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9452_sin__times__pi__eq__0,axiom,
% 9.53/5.33      ! [X: real] :
% 9.53/5.33        ( ( ( sin_real @ ( times_times_real @ X @ pi ) )
% 9.53/5.33          = zero_zero_real )
% 9.53/5.33        = ( member_real @ X @ ring_1_Ints_real ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9453_divide__nat__def,axiom,
% 9.53/5.33      ( divide_divide_nat
% 9.53/5.33      = ( ^ [M6: nat,N2: nat] :
% 9.53/5.33            ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat
% 9.53/5.33            @ ( lattic8265883725875713057ax_nat
% 9.53/5.33              @ ( collect_nat
% 9.53/5.33                @ ^ [K3: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K3 @ N2 ) @ M6 ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9454_sgn__power__injE,axiom,
% 9.53/5.33      ! [A: real,N: nat,X: real,B: real] :
% 9.53/5.33        ( ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 9.53/5.33          = X )
% 9.53/5.33       => ( ( X
% 9.53/5.33            = ( times_times_real @ ( sgn_sgn_real @ B ) @ ( power_power_real @ ( abs_abs_real @ B ) @ N ) ) )
% 9.53/5.33         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33           => ( A = B ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9455_sgn__power__root,axiom,
% 9.53/5.33      ! [N: nat,X: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( times_times_real @ ( sgn_sgn_real @ ( root @ N @ X ) ) @ ( power_power_real @ ( abs_abs_real @ ( root @ N @ X ) ) @ N ) )
% 9.53/5.33          = X ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9456_root__sgn__power,axiom,
% 9.53/5.33      ! [N: nat,Y2: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( root @ N @ ( times_times_real @ ( sgn_sgn_real @ Y2 ) @ ( power_power_real @ ( abs_abs_real @ Y2 ) @ N ) ) )
% 9.53/5.33          = Y2 ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9457_cis__Arg__unique,axiom,
% 9.53/5.33      ! [Z: complex,X: real] :
% 9.53/5.33        ( ( ( sgn_sgn_complex @ Z )
% 9.53/5.33          = ( cis @ X ) )
% 9.53/5.33       => ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X )
% 9.53/5.33         => ( ( ord_less_eq_real @ X @ pi )
% 9.53/5.33           => ( ( arg @ Z )
% 9.53/5.33              = X ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9458_split__root,axiom,
% 9.53/5.33      ! [P: real > $o,N: nat,X: real] :
% 9.53/5.33        ( ( P @ ( root @ N @ X ) )
% 9.53/5.33        = ( ( ( N = zero_zero_nat )
% 9.53/5.33           => ( P @ zero_zero_real ) )
% 9.53/5.33          & ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33           => ! [Y: real] :
% 9.53/5.33                ( ( ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N ) )
% 9.53/5.33                  = X )
% 9.53/5.33               => ( P @ Y ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9459_sin__integer__2pi,axiom,
% 9.53/5.33      ! [N: real] :
% 9.53/5.33        ( ( member_real @ N @ ring_1_Ints_real )
% 9.53/5.33       => ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 9.53/5.33          = zero_zero_real ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9460_cos__integer__2pi,axiom,
% 9.53/5.33      ! [N: real] :
% 9.53/5.33        ( ( member_real @ N @ ring_1_Ints_real )
% 9.53/5.33       => ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 9.53/5.33          = one_one_real ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9461_Arg__correct,axiom,
% 9.53/5.33      ! [Z: complex] :
% 9.53/5.33        ( ( Z != zero_zero_complex )
% 9.53/5.33       => ( ( ( sgn_sgn_complex @ Z )
% 9.53/5.33            = ( cis @ ( arg @ Z ) ) )
% 9.53/5.33          & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 9.53/5.33          & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9462_bij__betw__Suc,axiom,
% 9.53/5.33      ! [M7: set_nat,N4: set_nat] :
% 9.53/5.33        ( ( bij_betw_nat_nat @ suc @ M7 @ N4 )
% 9.53/5.33        = ( ( image_nat_nat @ suc @ M7 )
% 9.53/5.33          = N4 ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9463_image__Suc__atLeastAtMost,axiom,
% 9.53/5.33      ! [I2: nat,J: nat] :
% 9.53/5.33        ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I2 @ J ) )
% 9.53/5.33        = ( set_or1269000886237332187st_nat @ ( suc @ I2 ) @ ( suc @ J ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9464_zero__notin__Suc__image,axiom,
% 9.53/5.33      ! [A2: set_nat] :
% 9.53/5.33        ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A2 ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9465_image__Suc__lessThan,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.33        = ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9466_image__Suc__atMost,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) )
% 9.53/5.33        = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9467_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 9.53/5.33        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9468_lessThan__Suc__eq__insert__0,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( set_ord_lessThan_nat @ ( suc @ N ) )
% 9.53/5.33        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9469_atMost__Suc__eq__insert__0,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( set_ord_atMost_nat @ ( suc @ N ) )
% 9.53/5.33        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9470_Arg__def,axiom,
% 9.53/5.33      ( arg
% 9.53/5.33      = ( ^ [Z4: complex] :
% 9.53/5.33            ( if_real @ ( Z4 = zero_zero_complex ) @ zero_zero_real
% 9.53/5.33            @ ( fChoice_real
% 9.53/5.33              @ ^ [A3: real] :
% 9.53/5.33                  ( ( ( sgn_sgn_complex @ Z4 )
% 9.53/5.33                    = ( cis @ A3 ) )
% 9.53/5.33                  & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ A3 )
% 9.53/5.33                  & ( ord_less_eq_real @ A3 @ pi ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9471_horner__sum__of__bool__2__less,axiom,
% 9.53/5.33      ! [Bs: list_o] : ( ord_less_int @ ( groups9116527308978886569_o_int @ zero_n2684676970156552555ol_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Bs ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( size_size_list_o @ Bs ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9472_xor__Suc__0__eq,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( bit_se6528837805403552850or_nat @ N @ ( suc @ zero_zero_nat ) )
% 9.53/5.33        = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 9.53/5.33          @ ( zero_n2687167440665602831ol_nat
% 9.53/5.33            @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9473_xor__nat__numerals_I4_J,axiom,
% 9.53/5.33      ! [X: num] :
% 9.53/5.33        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 9.53/5.33        = ( numeral_numeral_nat @ ( bit0 @ X ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9474_xor__nat__numerals_I3_J,axiom,
% 9.53/5.33      ! [X: num] :
% 9.53/5.33        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 9.53/5.33        = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9475_xor__nat__numerals_I2_J,axiom,
% 9.53/5.33      ! [Y2: num] :
% 9.53/5.33        ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) )
% 9.53/5.33        = ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9476_xor__nat__numerals_I1_J,axiom,
% 9.53/5.33      ! [Y2: num] :
% 9.53/5.33        ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) )
% 9.53/5.33        = ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9477_xor__nat__unfold,axiom,
% 9.53/5.33      ( bit_se6528837805403552850or_nat
% 9.53/5.33      = ( ^ [M6: nat,N2: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N2 @ ( if_nat @ ( N2 = zero_zero_nat ) @ M6 @ ( plus_plus_nat @ ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9478_xor__nat__rec,axiom,
% 9.53/5.33      ( bit_se6528837805403552850or_nat
% 9.53/5.33      = ( ^ [M6: nat,N2: nat] :
% 9.53/5.33            ( plus_plus_nat
% 9.53/5.33            @ ( zero_n2687167440665602831ol_nat
% 9.53/5.33              @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 ) )
% 9.53/5.33               != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 9.53/5.33            @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9479_Suc__0__xor__eq,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N )
% 9.53/5.33        = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 9.53/5.33          @ ( zero_n2687167440665602831ol_nat
% 9.53/5.33            @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9480_push__bit__nonnegative__int__iff,axiom,
% 9.53/5.33      ! [N: nat,K: int] :
% 9.53/5.33        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se545348938243370406it_int @ N @ K ) )
% 9.53/5.33        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9481_push__bit__negative__int__iff,axiom,
% 9.53/5.33      ! [N: nat,K: int] :
% 9.53/5.33        ( ( ord_less_int @ ( bit_se545348938243370406it_int @ N @ K ) @ zero_zero_int )
% 9.53/5.33        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9482_concat__bit__of__zero__1,axiom,
% 9.53/5.33      ! [N: nat,L2: int] :
% 9.53/5.33        ( ( bit_concat_bit @ N @ zero_zero_int @ L2 )
% 9.53/5.33        = ( bit_se545348938243370406it_int @ N @ L2 ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9483_xor__nonnegative__int__iff,axiom,
% 9.53/5.33      ! [K: int,L2: int] :
% 9.53/5.33        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ K @ L2 ) )
% 9.53/5.33        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 9.53/5.33          = ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9484_xor__negative__int__iff,axiom,
% 9.53/5.33      ! [K: int,L2: int] :
% 9.53/5.33        ( ( ord_less_int @ ( bit_se6526347334894502574or_int @ K @ L2 ) @ zero_zero_int )
% 9.53/5.33        = ( ( ord_less_int @ K @ zero_zero_int )
% 9.53/5.33         != ( ord_less_int @ L2 @ zero_zero_int ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9485_push__bit__of__Suc__0,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( bit_se547839408752420682it_nat @ N @ ( suc @ zero_zero_nat ) )
% 9.53/5.33        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9486_bit__xor__int__iff,axiom,
% 9.53/5.33      ! [K: int,L2: int,N: nat] :
% 9.53/5.33        ( ( bit_se1146084159140164899it_int @ ( bit_se6526347334894502574or_int @ K @ L2 ) @ N )
% 9.53/5.33        = ( ( bit_se1146084159140164899it_int @ K @ N )
% 9.53/5.33         != ( bit_se1146084159140164899it_int @ L2 @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9487_flip__bit__int__def,axiom,
% 9.53/5.33      ( bit_se2159334234014336723it_int
% 9.53/5.33      = ( ^ [N2: nat,K3: int] : ( bit_se6526347334894502574or_int @ K3 @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9488_push__bit__nat__eq,axiom,
% 9.53/5.33      ! [N: nat,K: int] :
% 9.53/5.33        ( ( bit_se547839408752420682it_nat @ N @ ( nat2 @ K ) )
% 9.53/5.33        = ( nat2 @ ( bit_se545348938243370406it_int @ N @ K ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9489_XOR__lower,axiom,
% 9.53/5.33      ! [X: int,Y2: int] :
% 9.53/5.33        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 9.53/5.33       => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 9.53/5.33         => ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ X @ Y2 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9490_set__bit__nat__def,axiom,
% 9.53/5.33      ( bit_se7882103937844011126it_nat
% 9.53/5.33      = ( ^ [M6: nat,N2: nat] : ( bit_se1412395901928357646or_nat @ N2 @ ( bit_se547839408752420682it_nat @ M6 @ one_one_nat ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9491_flip__bit__nat__def,axiom,
% 9.53/5.33      ( bit_se2161824704523386999it_nat
% 9.53/5.33      = ( ^ [M6: nat,N2: nat] : ( bit_se6528837805403552850or_nat @ N2 @ ( bit_se547839408752420682it_nat @ M6 @ one_one_nat ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9492_bit__push__bit__iff__int,axiom,
% 9.53/5.33      ! [M: nat,K: int,N: nat] :
% 9.53/5.33        ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M @ K ) @ N )
% 9.53/5.33        = ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.33          & ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9493_xor__nat__def,axiom,
% 9.53/5.33      ( bit_se6528837805403552850or_nat
% 9.53/5.33      = ( ^ [M6: nat,N2: nat] : ( nat2 @ ( bit_se6526347334894502574or_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9494_bit__push__bit__iff__nat,axiom,
% 9.53/5.33      ! [M: nat,Q2: nat,N: nat] :
% 9.53/5.33        ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M @ Q2 ) @ N )
% 9.53/5.33        = ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.33          & ( bit_se1148574629649215175it_nat @ Q2 @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9495_concat__bit__eq,axiom,
% 9.53/5.33      ( bit_concat_bit
% 9.53/5.33      = ( ^ [N2: nat,K3: int,L: int] : ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N2 @ K3 ) @ ( bit_se545348938243370406it_int @ N2 @ L ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9496_concat__bit__def,axiom,
% 9.53/5.33      ( bit_concat_bit
% 9.53/5.33      = ( ^ [N2: nat,K3: int,L: int] : ( bit_se1409905431419307370or_int @ ( bit_se2923211474154528505it_int @ N2 @ K3 ) @ ( bit_se545348938243370406it_int @ N2 @ L ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9497_set__bit__int__def,axiom,
% 9.53/5.33      ( bit_se7879613467334960850it_int
% 9.53/5.33      = ( ^ [N2: nat,K3: int] : ( bit_se1409905431419307370or_int @ K3 @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9498_push__bit__nat__def,axiom,
% 9.53/5.33      ( bit_se547839408752420682it_nat
% 9.53/5.33      = ( ^ [N2: nat,M6: nat] : ( times_times_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9499_push__bit__int__def,axiom,
% 9.53/5.33      ( bit_se545348938243370406it_int
% 9.53/5.33      = ( ^ [N2: nat,K3: int] : ( times_times_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9500_push__bit__minus__one,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 9.53/5.33        = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9501_XOR__upper,axiom,
% 9.53/5.33      ! [X: int,N: nat,Y2: int] :
% 9.53/5.33        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 9.53/5.33       => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 9.53/5.33         => ( ( ord_less_int @ Y2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 9.53/5.33           => ( ord_less_int @ ( bit_se6526347334894502574or_int @ X @ Y2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9502_xor__int__rec,axiom,
% 9.53/5.33      ( bit_se6526347334894502574or_int
% 9.53/5.33      = ( ^ [K3: int,L: int] :
% 9.53/5.33            ( plus_plus_int
% 9.53/5.33            @ ( zero_n2684676970156552555ol_int
% 9.53/5.33              @ ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) )
% 9.53/5.33               != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) )
% 9.53/5.33            @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9503_xor__int__unfold,axiom,
% 9.53/5.33      ( bit_se6526347334894502574or_int
% 9.53/5.33      = ( ^ [K3: int,L: int] :
% 9.53/5.33            ( if_int
% 9.53/5.33            @ ( K3
% 9.53/5.33              = ( uminus_uminus_int @ one_one_int ) )
% 9.53/5.33            @ ( bit_ri7919022796975470100ot_int @ L )
% 9.53/5.33            @ ( if_int
% 9.53/5.33              @ ( L
% 9.53/5.33                = ( uminus_uminus_int @ one_one_int ) )
% 9.53/5.33              @ ( bit_ri7919022796975470100ot_int @ K3 )
% 9.53/5.33              @ ( if_int @ ( K3 = zero_zero_int ) @ L @ ( if_int @ ( L = zero_zero_int ) @ K3 @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9504_VEBT__internal_Oheight_Opelims,axiom,
% 9.53/5.33      ! [X: vEBT_VEBT,Y2: nat] :
% 9.53/5.33        ( ( ( vEBT_VEBT_height @ X )
% 9.53/5.33          = Y2 )
% 9.53/5.33       => ( ( accp_VEBT_VEBT @ vEBT_VEBT_height_rel @ X )
% 9.53/5.33         => ( ! [A4: $o,B3: $o] :
% 9.53/5.33                ( ( X
% 9.53/5.33                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.53/5.33               => ( ( Y2 = zero_zero_nat )
% 9.53/5.33                 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_height_rel @ ( vEBT_Leaf @ A4 @ B3 ) ) ) )
% 9.53/5.33           => ~ ! [Uu2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.53/5.33                  ( ( X
% 9.53/5.33                    = ( vEBT_Node @ Uu2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 9.53/5.33                 => ( ( Y2
% 9.53/5.33                      = ( plus_plus_nat @ one_one_nat @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary2 @ ( set_VEBT_VEBT2 @ TreeList2 ) ) ) ) ) )
% 9.53/5.33                   => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_height_rel @ ( vEBT_Node @ Uu2 @ Deg2 @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9505_Cauchy__iff2,axiom,
% 9.53/5.33      ( topolo4055970368930404560y_real
% 9.53/5.33      = ( ^ [X4: nat > real] :
% 9.53/5.33          ! [J3: nat] :
% 9.53/5.33          ? [M8: nat] :
% 9.53/5.33          ! [M6: nat] :
% 9.53/5.33            ( ( ord_less_eq_nat @ M8 @ M6 )
% 9.53/5.33           => ! [N2: nat] :
% 9.53/5.33                ( ( ord_less_eq_nat @ M8 @ N2 )
% 9.53/5.33               => ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ ( X4 @ M6 ) @ ( X4 @ N2 ) ) ) @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ J3 ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9506_not__negative__int__iff,axiom,
% 9.53/5.33      ! [K: int] :
% 9.53/5.33        ( ( ord_less_int @ ( bit_ri7919022796975470100ot_int @ K ) @ zero_zero_int )
% 9.53/5.33        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9507_not__nonnegative__int__iff,axiom,
% 9.53/5.33      ! [K: int] :
% 9.53/5.33        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 9.53/5.33        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9508_or__minus__minus__numerals,axiom,
% 9.53/5.33      ! [M: num,N: num] :
% 9.53/5.33        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.53/5.33        = ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9509_and__minus__minus__numerals,axiom,
% 9.53/5.33      ! [M: num,N: num] :
% 9.53/5.33        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.53/5.33        = ( bit_ri7919022796975470100ot_int @ ( bit_se1409905431419307370or_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9510_bit__not__int__iff,axiom,
% 9.53/5.33      ! [K: int,N: nat] :
% 9.53/5.33        ( ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ K ) @ N )
% 9.53/5.33        = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9511_or__int__def,axiom,
% 9.53/5.33      ( bit_se1409905431419307370or_int
% 9.53/5.33      = ( ^ [K3: int,L: int] : ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K3 ) @ ( bit_ri7919022796975470100ot_int @ L ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9512_not__int__def,axiom,
% 9.53/5.33      ( bit_ri7919022796975470100ot_int
% 9.53/5.33      = ( ^ [K3: int] : ( minus_minus_int @ ( uminus_uminus_int @ K3 ) @ one_one_int ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9513_and__not__numerals_I1_J,axiom,
% 9.53/5.33      ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 9.53/5.33      = zero_zero_int ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9514_or__not__numerals_I1_J,axiom,
% 9.53/5.33      ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 9.53/5.33      = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9515_unset__bit__int__def,axiom,
% 9.53/5.33      ( bit_se4203085406695923979it_int
% 9.53/5.33      = ( ^ [N2: nat,K3: int] : ( bit_se725231765392027082nd_int @ K3 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9516_xor__int__def,axiom,
% 9.53/5.33      ( bit_se6526347334894502574or_int
% 9.53/5.33      = ( ^ [K3: int,L: int] : ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ K3 @ ( bit_ri7919022796975470100ot_int @ L ) ) @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K3 ) @ L ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9517_not__int__div__2,axiom,
% 9.53/5.33      ! [K: int] :
% 9.53/5.33        ( ( divide_divide_int @ ( bit_ri7919022796975470100ot_int @ K ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.53/5.33        = ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9518_even__not__iff__int,axiom,
% 9.53/5.33      ! [K: int] :
% 9.53/5.33        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ K ) )
% 9.53/5.33        = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9519_and__not__numerals_I4_J,axiom,
% 9.53/5.33      ! [M: num] :
% 9.53/5.33        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 9.53/5.33        = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9520_and__not__numerals_I2_J,axiom,
% 9.53/5.33      ! [N: num] :
% 9.53/5.33        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 9.53/5.33        = one_one_int ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9521_or__not__numerals_I4_J,axiom,
% 9.53/5.33      ! [M: num] :
% 9.53/5.33        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 9.53/5.33        = ( bit_ri7919022796975470100ot_int @ one_one_int ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9522_or__not__numerals_I2_J,axiom,
% 9.53/5.33      ! [N: num] :
% 9.53/5.33        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 9.53/5.33        = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9523_bit__minus__int__iff,axiom,
% 9.53/5.33      ! [K: int,N: nat] :
% 9.53/5.33        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ K ) @ N )
% 9.53/5.33        = ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ K @ one_one_int ) ) @ N ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9524_numeral__or__not__num__eq,axiom,
% 9.53/5.33      ! [M: num,N: num] :
% 9.53/5.33        ( ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N ) )
% 9.53/5.33        = ( uminus_uminus_int @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9525_int__numeral__not__or__num__neg,axiom,
% 9.53/5.33      ! [M: num,N: num] :
% 9.53/5.33        ( ( bit_se1409905431419307370or_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 9.53/5.33        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ N @ M ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9526_int__numeral__or__not__num__neg,axiom,
% 9.53/5.33      ! [M: num,N: num] :
% 9.53/5.33        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 9.53/5.33        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9527_and__not__numerals_I5_J,axiom,
% 9.53/5.33      ! [M: num,N: num] :
% 9.53/5.33        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 9.53/5.33        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9528_and__not__numerals_I7_J,axiom,
% 9.53/5.33      ! [M: num] :
% 9.53/5.33        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 9.53/5.33        = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9529_or__not__numerals_I3_J,axiom,
% 9.53/5.33      ! [N: num] :
% 9.53/5.33        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 9.53/5.33        = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9530_and__not__numerals_I3_J,axiom,
% 9.53/5.33      ! [N: num] :
% 9.53/5.33        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 9.53/5.33        = zero_zero_int ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9531_or__not__numerals_I7_J,axiom,
% 9.53/5.33      ! [M: num] :
% 9.53/5.33        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 9.53/5.33        = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9532_and__not__numerals_I9_J,axiom,
% 9.53/5.33      ! [M: num,N: num] :
% 9.53/5.33        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 9.53/5.33        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9533_and__not__numerals_I6_J,axiom,
% 9.53/5.33      ! [M: num,N: num] :
% 9.53/5.33        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 9.53/5.33        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9534_or__not__numerals_I6_J,axiom,
% 9.53/5.33      ! [M: num,N: num] :
% 9.53/5.33        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 9.53/5.33        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9535_or__not__numerals_I5_J,axiom,
% 9.53/5.33      ! [M: num,N: num] :
% 9.53/5.33        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 9.53/5.33        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9536_and__not__numerals_I8_J,axiom,
% 9.53/5.33      ! [M: num,N: num] :
% 9.53/5.33        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 9.53/5.33        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9537_or__not__numerals_I8_J,axiom,
% 9.53/5.33      ! [M: num,N: num] :
% 9.53/5.33        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 9.53/5.33        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9538_or__not__numerals_I9_J,axiom,
% 9.53/5.33      ! [M: num,N: num] :
% 9.53/5.33        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 9.53/5.33        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9539_not__int__rec,axiom,
% 9.53/5.33      ( bit_ri7919022796975470100ot_int
% 9.53/5.33      = ( ^ [K3: int] : ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9540_vebt__maxt_Opelims,axiom,
% 9.53/5.33      ! [X: vEBT_VEBT,Y2: option_nat] :
% 9.53/5.33        ( ( ( vEBT_vebt_maxt @ X )
% 9.53/5.33          = Y2 )
% 9.53/5.33       => ( ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ X )
% 9.53/5.33         => ( ! [A4: $o,B3: $o] :
% 9.53/5.33                ( ( X
% 9.53/5.33                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.53/5.33               => ( ( ( B3
% 9.53/5.33                     => ( Y2
% 9.53/5.33                        = ( some_nat @ one_one_nat ) ) )
% 9.53/5.33                    & ( ~ B3
% 9.53/5.33                     => ( ( A4
% 9.53/5.33                         => ( Y2
% 9.53/5.33                            = ( some_nat @ zero_zero_nat ) ) )
% 9.53/5.33                        & ( ~ A4
% 9.53/5.33                         => ( Y2 = none_nat ) ) ) ) )
% 9.53/5.33                 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Leaf @ A4 @ B3 ) ) ) )
% 9.53/5.33           => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 9.53/5.33                  ( ( X
% 9.53/5.33                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 9.53/5.33                 => ( ( Y2 = none_nat )
% 9.53/5.33                   => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 9.53/5.33             => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 9.53/5.33                    ( ( X
% 9.53/5.33                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 9.53/5.33                   => ( ( Y2
% 9.53/5.33                        = ( some_nat @ Ma2 ) )
% 9.53/5.33                     => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9541_vebt__mint_Opelims,axiom,
% 9.53/5.33      ! [X: vEBT_VEBT,Y2: option_nat] :
% 9.53/5.33        ( ( ( vEBT_vebt_mint @ X )
% 9.53/5.33          = Y2 )
% 9.53/5.33       => ( ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ X )
% 9.53/5.33         => ( ! [A4: $o,B3: $o] :
% 9.53/5.33                ( ( X
% 9.53/5.33                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.53/5.33               => ( ( ( A4
% 9.53/5.33                     => ( Y2
% 9.53/5.33                        = ( some_nat @ zero_zero_nat ) ) )
% 9.53/5.33                    & ( ~ A4
% 9.53/5.33                     => ( ( B3
% 9.53/5.33                         => ( Y2
% 9.53/5.33                            = ( some_nat @ one_one_nat ) ) )
% 9.53/5.33                        & ( ~ B3
% 9.53/5.33                         => ( Y2 = none_nat ) ) ) ) )
% 9.53/5.33                 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Leaf @ A4 @ B3 ) ) ) )
% 9.53/5.33           => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 9.53/5.33                  ( ( X
% 9.53/5.33                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 9.53/5.33                 => ( ( Y2 = none_nat )
% 9.53/5.33                   => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 9.53/5.33             => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 9.53/5.33                    ( ( X
% 9.53/5.33                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 9.53/5.33                   => ( ( Y2
% 9.53/5.33                        = ( some_nat @ Mi2 ) )
% 9.53/5.33                     => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9542_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Opelims,axiom,
% 9.53/5.33      ! [X: vEBT_VEBT,Y2: nat] :
% 9.53/5.33        ( ( ( vEBT_T_m_i_n_t @ X )
% 9.53/5.33          = Y2 )
% 9.53/5.33       => ( ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ X )
% 9.53/5.33         => ( ! [A4: $o,B3: $o] :
% 9.53/5.33                ( ( X
% 9.53/5.33                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.53/5.33               => ( ( Y2
% 9.53/5.33                    = ( plus_plus_nat @ one_one_nat @ ( if_nat @ A4 @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 9.53/5.33                 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ ( vEBT_Leaf @ A4 @ B3 ) ) ) )
% 9.53/5.33           => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 9.53/5.33                  ( ( X
% 9.53/5.33                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 9.53/5.33                 => ( ( Y2 = one_one_nat )
% 9.53/5.33                   => ~ ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 9.53/5.33             => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 9.53/5.33                    ( ( X
% 9.53/5.33                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 9.53/5.33                   => ( ( Y2 = one_one_nat )
% 9.53/5.33                     => ~ ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9543_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Opelims,axiom,
% 9.53/5.33      ! [X: vEBT_VEBT,Y2: nat] :
% 9.53/5.33        ( ( ( vEBT_T_m_a_x_t @ X )
% 9.53/5.33          = Y2 )
% 9.53/5.33       => ( ( accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ X )
% 9.53/5.33         => ( ! [A4: $o,B3: $o] :
% 9.53/5.33                ( ( X
% 9.53/5.33                  = ( vEBT_Leaf @ A4 @ B3 ) )
% 9.53/5.33               => ( ( Y2
% 9.53/5.33                    = ( plus_plus_nat @ one_one_nat @ ( if_nat @ B3 @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 9.53/5.33                 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ ( vEBT_Leaf @ A4 @ B3 ) ) ) )
% 9.53/5.33           => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 9.53/5.33                  ( ( X
% 9.53/5.33                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 9.53/5.33                 => ( ( Y2 = one_one_nat )
% 9.53/5.33                   => ~ ( accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 9.53/5.33             => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 9.53/5.33                    ( ( X
% 9.53/5.33                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 9.53/5.33                   => ( ( Y2 = one_one_nat )
% 9.53/5.33                     => ~ ( accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9544_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Opelims,axiom,
% 9.53/5.33      ! [X: vEBT_VEBT,Y2: nat] :
% 9.53/5.33        ( ( ( vEBT_T_m_i_n_N_u_l_l @ X )
% 9.53/5.33          = Y2 )
% 9.53/5.33       => ( ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ X )
% 9.53/5.33         => ( ( ( X
% 9.53/5.33                = ( vEBT_Leaf @ $false @ $false ) )
% 9.53/5.33             => ( ( Y2 = one_one_nat )
% 9.53/5.33               => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Leaf @ $false @ $false ) ) ) )
% 9.53/5.33           => ( ! [Uv2: $o] :
% 9.53/5.33                  ( ( X
% 9.53/5.33                    = ( vEBT_Leaf @ $true @ Uv2 ) )
% 9.53/5.33                 => ( ( Y2 = one_one_nat )
% 9.53/5.33                   => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) ) )
% 9.53/5.33             => ( ! [Uu2: $o] :
% 9.53/5.33                    ( ( X
% 9.53/5.33                      = ( vEBT_Leaf @ Uu2 @ $true ) )
% 9.53/5.33                   => ( ( Y2 = one_one_nat )
% 9.53/5.33                     => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) ) )
% 9.53/5.33               => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 9.53/5.33                      ( ( X
% 9.53/5.33                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 9.53/5.33                     => ( ( Y2 = one_one_nat )
% 9.53/5.33                       => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) )
% 9.53/5.33                 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 9.53/5.33                        ( ( X
% 9.53/5.33                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 9.53/5.33                       => ( ( Y2 = one_one_nat )
% 9.53/5.33                         => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9545_VEBT__internal_OminNull_Opelims_I1_J,axiom,
% 9.53/5.33      ! [X: vEBT_VEBT,Y2: $o] :
% 9.53/5.33        ( ( ( vEBT_VEBT_minNull @ X )
% 9.53/5.33          = Y2 )
% 9.53/5.33       => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 9.53/5.33         => ( ( ( X
% 9.53/5.33                = ( vEBT_Leaf @ $false @ $false ) )
% 9.53/5.33             => ( Y2
% 9.53/5.33               => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) ) )
% 9.53/5.33           => ( ! [Uv2: $o] :
% 9.53/5.33                  ( ( X
% 9.53/5.33                    = ( vEBT_Leaf @ $true @ Uv2 ) )
% 9.53/5.33                 => ( ~ Y2
% 9.53/5.33                   => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) ) )
% 9.53/5.33             => ( ! [Uu2: $o] :
% 9.53/5.33                    ( ( X
% 9.53/5.33                      = ( vEBT_Leaf @ Uu2 @ $true ) )
% 9.53/5.33                   => ( ~ Y2
% 9.53/5.33                     => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) ) )
% 9.53/5.33               => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 9.53/5.33                      ( ( X
% 9.53/5.33                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 9.53/5.33                     => ( Y2
% 9.53/5.33                       => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) )
% 9.53/5.33                 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 9.53/5.33                        ( ( X
% 9.53/5.33                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 9.53/5.33                       => ( ~ Y2
% 9.53/5.33                         => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9546_VEBT__internal_OminNull_Opelims_I3_J,axiom,
% 9.53/5.33      ! [X: vEBT_VEBT] :
% 9.53/5.33        ( ~ ( vEBT_VEBT_minNull @ X )
% 9.53/5.33       => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 9.53/5.33         => ( ! [Uv2: $o] :
% 9.53/5.33                ( ( X
% 9.53/5.33                  = ( vEBT_Leaf @ $true @ Uv2 ) )
% 9.53/5.33               => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) )
% 9.53/5.33           => ( ! [Uu2: $o] :
% 9.53/5.33                  ( ( X
% 9.53/5.33                    = ( vEBT_Leaf @ Uu2 @ $true ) )
% 9.53/5.33                 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) )
% 9.53/5.33             => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 9.53/5.33                    ( ( X
% 9.53/5.33                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 9.53/5.33                   => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9547_VEBT__internal_OminNull_Opelims_I2_J,axiom,
% 9.53/5.33      ! [X: vEBT_VEBT] :
% 9.53/5.33        ( ( vEBT_VEBT_minNull @ X )
% 9.53/5.33       => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 9.53/5.33         => ( ( ( X
% 9.53/5.33                = ( vEBT_Leaf @ $false @ $false ) )
% 9.53/5.33             => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) )
% 9.53/5.33           => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 9.53/5.33                  ( ( X
% 9.53/5.33                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 9.53/5.33                 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9548_Sum__Ico__nat,axiom,
% 9.53/5.33      ! [M: nat,N: nat] :
% 9.53/5.33        ( ( groups3542108847815614940at_nat
% 9.53/5.33          @ ^ [X2: nat] : X2
% 9.53/5.33          @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 9.53/5.33        = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9549_sum__power2,axiom,
% 9.53/5.33      ! [K: nat] :
% 9.53/5.33        ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 9.53/5.33        = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9550_VEBT_Osize_I3_J,axiom,
% 9.53/5.33      ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 9.53/5.33        ( ( size_size_VEBT_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 9.53/5.33        = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ size_size_VEBT_VEBT @ X13 ) @ ( size_size_VEBT_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9551_image__Suc__atLeastLessThan,axiom,
% 9.53/5.33      ! [I2: nat,J: nat] :
% 9.53/5.33        ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I2 @ J ) )
% 9.53/5.33        = ( set_or4665077453230672383an_nat @ ( suc @ I2 ) @ ( suc @ J ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9552_atLeastLessThan__singleton,axiom,
% 9.53/5.33      ! [M: nat] :
% 9.53/5.33        ( ( set_or4665077453230672383an_nat @ M @ ( suc @ M ) )
% 9.53/5.33        = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9553_all__nat__less__eq,axiom,
% 9.53/5.33      ! [N: nat,P: nat > $o] :
% 9.53/5.33        ( ( ! [M6: nat] :
% 9.53/5.33              ( ( ord_less_nat @ M6 @ N )
% 9.53/5.33             => ( P @ M6 ) ) )
% 9.53/5.33        = ( ! [X2: nat] :
% 9.53/5.33              ( ( member_nat @ X2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 9.53/5.33             => ( P @ X2 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9554_ex__nat__less__eq,axiom,
% 9.53/5.33      ! [N: nat,P: nat > $o] :
% 9.53/5.33        ( ( ? [M6: nat] :
% 9.53/5.33              ( ( ord_less_nat @ M6 @ N )
% 9.53/5.33              & ( P @ M6 ) ) )
% 9.53/5.33        = ( ? [X2: nat] :
% 9.53/5.33              ( ( member_nat @ X2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 9.53/5.33              & ( P @ X2 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9555_atLeastLessThanSuc__atLeastAtMost,axiom,
% 9.53/5.33      ! [L2: nat,U: nat] :
% 9.53/5.33        ( ( set_or4665077453230672383an_nat @ L2 @ ( suc @ U ) )
% 9.53/5.33        = ( set_or1269000886237332187st_nat @ L2 @ U ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9556_atLeast0__lessThan__Suc,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 9.53/5.33        = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9557_atLeastLessThanSuc,axiom,
% 9.53/5.33      ! [M: nat,N: nat] :
% 9.53/5.33        ( ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.33         => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 9.53/5.33            = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) )
% 9.53/5.33        & ( ~ ( ord_less_eq_nat @ M @ N )
% 9.53/5.33         => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 9.53/5.33            = bot_bot_set_nat ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9558_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 9.53/5.33        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9559_prod__Suc__Suc__fact,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 9.53/5.33        = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9560_prod__Suc__fact,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 9.53/5.33        = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9561_atLeastLessThan__nat__numeral,axiom,
% 9.53/5.33      ! [M: nat,K: num] :
% 9.53/5.33        ( ( ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 9.53/5.33         => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 9.53/5.33            = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M @ ( pred_numeral @ K ) ) ) ) )
% 9.53/5.33        & ( ~ ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 9.53/5.33         => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 9.53/5.33            = bot_bot_set_nat ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9562_atLeast1__lessThan__eq__remove0,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N )
% 9.53/5.33        = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9563_image__minus__const__atLeastLessThan__nat,axiom,
% 9.53/5.33      ! [C: nat,Y2: nat,X: nat] :
% 9.53/5.33        ( ( ( ord_less_nat @ C @ Y2 )
% 9.53/5.33         => ( ( image_nat_nat
% 9.53/5.33              @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 9.53/5.33              @ ( set_or4665077453230672383an_nat @ X @ Y2 ) )
% 9.53/5.33            = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X @ C ) @ ( minus_minus_nat @ Y2 @ C ) ) ) )
% 9.53/5.33        & ( ~ ( ord_less_nat @ C @ Y2 )
% 9.53/5.33         => ( ( ( ord_less_nat @ X @ Y2 )
% 9.53/5.33             => ( ( image_nat_nat
% 9.53/5.33                  @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 9.53/5.33                  @ ( set_or4665077453230672383an_nat @ X @ Y2 ) )
% 9.53/5.33                = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 9.53/5.33            & ( ~ ( ord_less_nat @ X @ Y2 )
% 9.53/5.33             => ( ( image_nat_nat
% 9.53/5.33                  @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 9.53/5.33                  @ ( set_or4665077453230672383an_nat @ X @ Y2 ) )
% 9.53/5.33                = bot_bot_set_nat ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9564_Chebyshev__sum__upper__nat,axiom,
% 9.53/5.33      ! [N: nat,A: nat > nat,B: nat > nat] :
% 9.53/5.33        ( ! [I4: nat,J2: nat] :
% 9.53/5.33            ( ( ord_less_eq_nat @ I4 @ J2 )
% 9.53/5.33           => ( ( ord_less_nat @ J2 @ N )
% 9.53/5.33             => ( ord_less_eq_nat @ ( A @ I4 ) @ ( A @ J2 ) ) ) )
% 9.53/5.33       => ( ! [I4: nat,J2: nat] :
% 9.53/5.33              ( ( ord_less_eq_nat @ I4 @ J2 )
% 9.53/5.33             => ( ( ord_less_nat @ J2 @ N )
% 9.53/5.33               => ( ord_less_eq_nat @ ( B @ J2 ) @ ( B @ I4 ) ) ) )
% 9.53/5.33         => ( ord_less_eq_nat
% 9.53/5.33            @ ( times_times_nat @ N
% 9.53/5.33              @ ( groups3542108847815614940at_nat
% 9.53/5.33                @ ^ [I3: nat] : ( times_times_nat @ ( A @ I3 ) @ ( B @ I3 ) )
% 9.53/5.33                @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 9.53/5.33            @ ( times_times_nat @ ( groups3542108847815614940at_nat @ A @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( groups3542108847815614940at_nat @ B @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9565_image__add__int__atLeastLessThan,axiom,
% 9.53/5.33      ! [L2: int,U: int] :
% 9.53/5.33        ( ( image_int_int
% 9.53/5.33          @ ^ [X2: int] : ( plus_plus_int @ X2 @ L2 )
% 9.53/5.33          @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L2 ) ) )
% 9.53/5.33        = ( set_or4662586982721622107an_int @ L2 @ U ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9566_VEBT_Osize__gen_I1_J,axiom,
% 9.53/5.33      ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 9.53/5.33        ( ( vEBT_size_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 9.53/5.33        = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ vEBT_size_VEBT @ X13 ) @ ( vEBT_size_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9567_valid__eq,axiom,
% 9.53/5.33      vEBT_VEBT_valid = vEBT_invar_vebt ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9568_valid__eq1,axiom,
% 9.53/5.33      ! [T: vEBT_VEBT,D2: nat] :
% 9.53/5.33        ( ( vEBT_invar_vebt @ T @ D2 )
% 9.53/5.33       => ( vEBT_VEBT_valid @ T @ D2 ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9569_valid__eq2,axiom,
% 9.53/5.33      ! [T: vEBT_VEBT,D2: nat] :
% 9.53/5.33        ( ( vEBT_VEBT_valid @ T @ D2 )
% 9.53/5.33       => ( vEBT_invar_vebt @ T @ D2 ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9570_VEBT__internal_Ovalid_H_Osimps_I1_J,axiom,
% 9.53/5.33      ! [Uu: $o,Uv: $o,D2: nat] :
% 9.53/5.33        ( ( vEBT_VEBT_valid @ ( vEBT_Leaf @ Uu @ Uv ) @ D2 )
% 9.53/5.33        = ( D2 = one_one_nat ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9571_VEBT_Osize__gen_I2_J,axiom,
% 9.53/5.33      ! [X21: $o,X222: $o] :
% 9.53/5.33        ( ( vEBT_size_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 9.53/5.33        = zero_zero_nat ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9572_Code__Target__Int_Opositive__def,axiom,
% 9.53/5.33      code_Target_positive = numeral_numeral_int ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9573_csqrt_Osimps_I1_J,axiom,
% 9.53/5.33      ! [Z: complex] :
% 9.53/5.33        ( ( re @ ( csqrt @ Z ) )
% 9.53/5.33        = ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9574_complex__Re__numeral,axiom,
% 9.53/5.33      ! [V: num] :
% 9.53/5.33        ( ( re @ ( numera6690914467698888265omplex @ V ) )
% 9.53/5.33        = ( numeral_numeral_real @ V ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9575_Re__divide__of__nat,axiom,
% 9.53/5.33      ! [Z: complex,N: nat] :
% 9.53/5.33        ( ( re @ ( divide1717551699836669952omplex @ Z @ ( semiri8010041392384452111omplex @ N ) ) )
% 9.53/5.33        = ( divide_divide_real @ ( re @ Z ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9576_Re__divide__of__real,axiom,
% 9.53/5.33      ! [Z: complex,R: real] :
% 9.53/5.33        ( ( re @ ( divide1717551699836669952omplex @ Z @ ( real_V4546457046886955230omplex @ R ) ) )
% 9.53/5.33        = ( divide_divide_real @ ( re @ Z ) @ R ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9577_Re__sgn,axiom,
% 9.53/5.33      ! [Z: complex] :
% 9.53/5.33        ( ( re @ ( sgn_sgn_complex @ Z ) )
% 9.53/5.33        = ( divide_divide_real @ ( re @ Z ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9578_Re__divide__numeral,axiom,
% 9.53/5.33      ! [Z: complex,W: num] :
% 9.53/5.33        ( ( re @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 9.53/5.33        = ( divide_divide_real @ ( re @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9579_complex__Re__le__cmod,axiom,
% 9.53/5.33      ! [X: complex] : ( ord_less_eq_real @ ( re @ X ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9580_one__complex_Osimps_I1_J,axiom,
% 9.53/5.33      ( ( re @ one_one_complex )
% 9.53/5.33      = one_one_real ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9581_plus__complex_Osimps_I1_J,axiom,
% 9.53/5.33      ! [X: complex,Y2: complex] :
% 9.53/5.33        ( ( re @ ( plus_plus_complex @ X @ Y2 ) )
% 9.53/5.33        = ( plus_plus_real @ ( re @ X ) @ ( re @ Y2 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9582_scaleR__complex_Osimps_I1_J,axiom,
% 9.53/5.33      ! [R: real,X: complex] :
% 9.53/5.33        ( ( re @ ( real_V2046097035970521341omplex @ R @ X ) )
% 9.53/5.33        = ( times_times_real @ R @ ( re @ X ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9583_minus__complex_Osimps_I1_J,axiom,
% 9.53/5.33      ! [X: complex,Y2: complex] :
% 9.53/5.33        ( ( re @ ( minus_minus_complex @ X @ Y2 ) )
% 9.53/5.33        = ( minus_minus_real @ ( re @ X ) @ ( re @ Y2 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9584_abs__Re__le__cmod,axiom,
% 9.53/5.33      ! [X: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9585_Re__csqrt,axiom,
% 9.53/5.33      ! [Z: complex] : ( ord_less_eq_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9586_cmod__plus__Re__le__0__iff,axiom,
% 9.53/5.33      ! [Z: complex] :
% 9.53/5.33        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ zero_zero_real )
% 9.53/5.33        = ( ( re @ Z )
% 9.53/5.33          = ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9587_cos__n__Re__cis__pow__n,axiom,
% 9.53/5.33      ! [N: nat,A: real] :
% 9.53/5.33        ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 9.53/5.33        = ( re @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9588_csqrt_Ocode,axiom,
% 9.53/5.33      ( csqrt
% 9.53/5.33      = ( ^ [Z4: complex] :
% 9.53/5.33            ( complex2 @ ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z4 ) @ ( re @ Z4 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.33            @ ( times_times_real
% 9.53/5.33              @ ( if_real
% 9.53/5.33                @ ( ( im @ Z4 )
% 9.53/5.33                  = zero_zero_real )
% 9.53/5.33                @ one_one_real
% 9.53/5.33                @ ( sgn_sgn_real @ ( im @ Z4 ) ) )
% 9.53/5.33              @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z4 ) @ ( re @ Z4 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9589_csqrt_Osimps_I2_J,axiom,
% 9.53/5.33      ! [Z: complex] :
% 9.53/5.33        ( ( im @ ( csqrt @ Z ) )
% 9.53/5.33        = ( times_times_real
% 9.53/5.33          @ ( if_real
% 9.53/5.33            @ ( ( im @ Z )
% 9.53/5.33              = zero_zero_real )
% 9.53/5.33            @ one_one_real
% 9.53/5.33            @ ( sgn_sgn_real @ ( im @ Z ) ) )
% 9.53/5.33          @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9590_csqrt__of__real__nonpos,axiom,
% 9.53/5.33      ! [X: complex] :
% 9.53/5.33        ( ( ( im @ X )
% 9.53/5.33          = zero_zero_real )
% 9.53/5.33       => ( ( ord_less_eq_real @ ( re @ X ) @ zero_zero_real )
% 9.53/5.33         => ( ( csqrt @ X )
% 9.53/5.33            = ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sqrt @ ( abs_abs_real @ ( re @ X ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9591_Im__divide__of__real,axiom,
% 9.53/5.33      ! [Z: complex,R: real] :
% 9.53/5.33        ( ( im @ ( divide1717551699836669952omplex @ Z @ ( real_V4546457046886955230omplex @ R ) ) )
% 9.53/5.33        = ( divide_divide_real @ ( im @ Z ) @ R ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9592_Im__sgn,axiom,
% 9.53/5.33      ! [Z: complex] :
% 9.53/5.33        ( ( im @ ( sgn_sgn_complex @ Z ) )
% 9.53/5.33        = ( divide_divide_real @ ( im @ Z ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9593_Re__power__real,axiom,
% 9.53/5.33      ! [X: complex,N: nat] :
% 9.53/5.33        ( ( ( im @ X )
% 9.53/5.33          = zero_zero_real )
% 9.53/5.33       => ( ( re @ ( power_power_complex @ X @ N ) )
% 9.53/5.33          = ( power_power_real @ ( re @ X ) @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9594_Im__divide__numeral,axiom,
% 9.53/5.33      ! [Z: complex,W: num] :
% 9.53/5.33        ( ( im @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 9.53/5.33        = ( divide_divide_real @ ( im @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9595_Im__divide__of__nat,axiom,
% 9.53/5.33      ! [Z: complex,N: nat] :
% 9.53/5.33        ( ( im @ ( divide1717551699836669952omplex @ Z @ ( semiri8010041392384452111omplex @ N ) ) )
% 9.53/5.33        = ( divide_divide_real @ ( im @ Z ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9596_csqrt__of__real__nonneg,axiom,
% 9.53/5.33      ! [X: complex] :
% 9.53/5.33        ( ( ( im @ X )
% 9.53/5.33          = zero_zero_real )
% 9.53/5.33       => ( ( ord_less_eq_real @ zero_zero_real @ ( re @ X ) )
% 9.53/5.33         => ( ( csqrt @ X )
% 9.53/5.33            = ( real_V4546457046886955230omplex @ ( sqrt @ ( re @ X ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9597_csqrt__minus,axiom,
% 9.53/5.33      ! [X: complex] :
% 9.53/5.33        ( ( ( ord_less_real @ ( im @ X ) @ zero_zero_real )
% 9.53/5.33          | ( ( ( im @ X )
% 9.53/5.33              = zero_zero_real )
% 9.53/5.33            & ( ord_less_eq_real @ zero_zero_real @ ( re @ X ) ) ) )
% 9.53/5.33       => ( ( csqrt @ ( uminus1482373934393186551omplex @ X ) )
% 9.53/5.33          = ( times_times_complex @ imaginary_unit @ ( csqrt @ X ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9598_imaginary__unit_Osimps_I2_J,axiom,
% 9.53/5.33      ( ( im @ imaginary_unit )
% 9.53/5.33      = one_one_real ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9599_plus__complex_Osimps_I2_J,axiom,
% 9.53/5.33      ! [X: complex,Y2: complex] :
% 9.53/5.33        ( ( im @ ( plus_plus_complex @ X @ Y2 ) )
% 9.53/5.33        = ( plus_plus_real @ ( im @ X ) @ ( im @ Y2 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9600_scaleR__complex_Osimps_I2_J,axiom,
% 9.53/5.33      ! [R: real,X: complex] :
% 9.53/5.33        ( ( im @ ( real_V2046097035970521341omplex @ R @ X ) )
% 9.53/5.33        = ( times_times_real @ R @ ( im @ X ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9601_minus__complex_Osimps_I2_J,axiom,
% 9.53/5.33      ! [X: complex,Y2: complex] :
% 9.53/5.33        ( ( im @ ( minus_minus_complex @ X @ Y2 ) )
% 9.53/5.33        = ( minus_minus_real @ ( im @ X ) @ ( im @ Y2 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9602_abs__Im__le__cmod,axiom,
% 9.53/5.33      ! [X: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9603_times__complex_Osimps_I2_J,axiom,
% 9.53/5.33      ! [X: complex,Y2: complex] :
% 9.53/5.33        ( ( im @ ( times_times_complex @ X @ Y2 ) )
% 9.53/5.33        = ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( im @ Y2 ) ) @ ( times_times_real @ ( im @ X ) @ ( re @ Y2 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9604_cmod__Re__le__iff,axiom,
% 9.53/5.33      ! [X: complex,Y2: complex] :
% 9.53/5.33        ( ( ( im @ X )
% 9.53/5.33          = ( im @ Y2 ) )
% 9.53/5.33       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y2 ) )
% 9.53/5.33          = ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X ) ) @ ( abs_abs_real @ ( re @ Y2 ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9605_cmod__Im__le__iff,axiom,
% 9.53/5.33      ! [X: complex,Y2: complex] :
% 9.53/5.33        ( ( ( re @ X )
% 9.53/5.33          = ( re @ Y2 ) )
% 9.53/5.33       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y2 ) )
% 9.53/5.33          = ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X ) ) @ ( abs_abs_real @ ( im @ Y2 ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9606_times__complex_Osimps_I1_J,axiom,
% 9.53/5.33      ! [X: complex,Y2: complex] :
% 9.53/5.33        ( ( re @ ( times_times_complex @ X @ Y2 ) )
% 9.53/5.33        = ( minus_minus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y2 ) ) @ ( times_times_real @ ( im @ X ) @ ( im @ Y2 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9607_plus__complex_Ocode,axiom,
% 9.53/5.33      ( plus_plus_complex
% 9.53/5.33      = ( ^ [X2: complex,Y: complex] : ( complex2 @ ( plus_plus_real @ ( re @ X2 ) @ ( re @ Y ) ) @ ( plus_plus_real @ ( im @ X2 ) @ ( im @ Y ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9608_scaleR__complex_Ocode,axiom,
% 9.53/5.33      ( real_V2046097035970521341omplex
% 9.53/5.33      = ( ^ [R5: real,X2: complex] : ( complex2 @ ( times_times_real @ R5 @ ( re @ X2 ) ) @ ( times_times_real @ R5 @ ( im @ X2 ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9609_minus__complex_Ocode,axiom,
% 9.53/5.33      ( minus_minus_complex
% 9.53/5.33      = ( ^ [X2: complex,Y: complex] : ( complex2 @ ( minus_minus_real @ ( re @ X2 ) @ ( re @ Y ) ) @ ( minus_minus_real @ ( im @ X2 ) @ ( im @ Y ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9610_csqrt__principal,axiom,
% 9.53/5.33      ! [Z: complex] :
% 9.53/5.33        ( ( ord_less_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) )
% 9.53/5.33        | ( ( ( re @ ( csqrt @ Z ) )
% 9.53/5.33            = zero_zero_real )
% 9.53/5.33          & ( ord_less_eq_real @ zero_zero_real @ ( im @ ( csqrt @ Z ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9611_cmod__le,axiom,
% 9.53/5.33      ! [Z: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( plus_plus_real @ ( abs_abs_real @ ( re @ Z ) ) @ ( abs_abs_real @ ( im @ Z ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9612_sin__n__Im__cis__pow__n,axiom,
% 9.53/5.33      ! [N: nat,A: real] :
% 9.53/5.33        ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 9.53/5.33        = ( im @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9613_Re__exp,axiom,
% 9.53/5.33      ! [Z: complex] :
% 9.53/5.33        ( ( re @ ( exp_complex @ Z ) )
% 9.53/5.33        = ( times_times_real @ ( exp_real @ ( re @ Z ) ) @ ( cos_real @ ( im @ Z ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9614_Im__exp,axiom,
% 9.53/5.33      ! [Z: complex] :
% 9.53/5.33        ( ( im @ ( exp_complex @ Z ) )
% 9.53/5.33        = ( times_times_real @ ( exp_real @ ( re @ Z ) ) @ ( sin_real @ ( im @ Z ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9615_times__complex_Ocode,axiom,
% 9.53/5.33      ( times_times_complex
% 9.53/5.33      = ( ^ [X2: complex,Y: complex] : ( complex2 @ ( minus_minus_real @ ( times_times_real @ ( re @ X2 ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X2 ) @ ( im @ Y ) ) ) @ ( plus_plus_real @ ( times_times_real @ ( re @ X2 ) @ ( im @ Y ) ) @ ( times_times_real @ ( im @ X2 ) @ ( re @ Y ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9616_cmod__power2,axiom,
% 9.53/5.33      ! [Z: complex] :
% 9.53/5.33        ( ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.53/5.33        = ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9617_Im__power2,axiom,
% 9.53/5.33      ! [X: complex] :
% 9.53/5.33        ( ( im @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.53/5.33        = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ X ) ) @ ( im @ X ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9618_Re__power2,axiom,
% 9.53/5.33      ! [X: complex] :
% 9.53/5.33        ( ( re @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.53/5.33        = ( minus_minus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9619_complex__eq__0,axiom,
% 9.53/5.33      ! [Z: complex] :
% 9.53/5.33        ( ( Z = zero_zero_complex )
% 9.53/5.33        = ( ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.53/5.33          = zero_zero_real ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9620_norm__complex__def,axiom,
% 9.53/5.33      ( real_V1022390504157884413omplex
% 9.53/5.33      = ( ^ [Z4: complex] : ( sqrt @ ( plus_plus_real @ ( power_power_real @ ( re @ Z4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9621_inverse__complex_Osimps_I1_J,axiom,
% 9.53/5.33      ! [X: complex] :
% 9.53/5.33        ( ( re @ ( invers8013647133539491842omplex @ X ) )
% 9.53/5.33        = ( divide_divide_real @ ( re @ X ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9622_complex__neq__0,axiom,
% 9.53/5.33      ! [Z: complex] :
% 9.53/5.33        ( ( Z != zero_zero_complex )
% 9.53/5.33        = ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9623_Re__divide,axiom,
% 9.53/5.33      ! [X: complex,Y2: complex] :
% 9.53/5.33        ( ( re @ ( divide1717551699836669952omplex @ X @ Y2 ) )
% 9.53/5.33        = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y2 ) ) @ ( times_times_real @ ( im @ X ) @ ( im @ Y2 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9624_csqrt__square,axiom,
% 9.53/5.33      ! [B: complex] :
% 9.53/5.33        ( ( ( ord_less_real @ zero_zero_real @ ( re @ B ) )
% 9.53/5.33          | ( ( ( re @ B )
% 9.53/5.33              = zero_zero_real )
% 9.53/5.33            & ( ord_less_eq_real @ zero_zero_real @ ( im @ B ) ) ) )
% 9.53/5.33       => ( ( csqrt @ ( power_power_complex @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.53/5.33          = B ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9625_csqrt__unique,axiom,
% 9.53/5.33      ! [W: complex,Z: complex] :
% 9.53/5.33        ( ( ( power_power_complex @ W @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.53/5.33          = Z )
% 9.53/5.33       => ( ( ( ord_less_real @ zero_zero_real @ ( re @ W ) )
% 9.53/5.33            | ( ( ( re @ W )
% 9.53/5.33                = zero_zero_real )
% 9.53/5.33              & ( ord_less_eq_real @ zero_zero_real @ ( im @ W ) ) ) )
% 9.53/5.33         => ( ( csqrt @ Z )
% 9.53/5.33            = W ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9626_inverse__complex_Osimps_I2_J,axiom,
% 9.53/5.33      ! [X: complex] :
% 9.53/5.33        ( ( im @ ( invers8013647133539491842omplex @ X ) )
% 9.53/5.33        = ( divide_divide_real @ ( uminus_uminus_real @ ( im @ X ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9627_Im__divide,axiom,
% 9.53/5.33      ! [X: complex,Y2: complex] :
% 9.53/5.33        ( ( im @ ( divide1717551699836669952omplex @ X @ Y2 ) )
% 9.53/5.33        = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X ) @ ( re @ Y2 ) ) @ ( times_times_real @ ( re @ X ) @ ( im @ Y2 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9628_complex__abs__le__norm,axiom,
% 9.53/5.33      ! [Z: complex] : ( ord_less_eq_real @ ( plus_plus_real @ ( abs_abs_real @ ( re @ Z ) ) @ ( abs_abs_real @ ( im @ Z ) ) ) @ ( times_times_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9629_complex__unit__circle,axiom,
% 9.53/5.33      ! [Z: complex] :
% 9.53/5.33        ( ( Z != zero_zero_complex )
% 9.53/5.33       => ( ( plus_plus_real @ ( power_power_real @ ( divide_divide_real @ ( re @ Z ) @ ( real_V1022390504157884413omplex @ Z ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( divide_divide_real @ ( im @ Z ) @ ( real_V1022390504157884413omplex @ Z ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.53/5.33          = one_one_real ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9630_inverse__complex_Ocode,axiom,
% 9.53/5.33      ( invers8013647133539491842omplex
% 9.53/5.33      = ( ^ [X2: complex] : ( complex2 @ ( divide_divide_real @ ( re @ X2 ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( uminus_uminus_real @ ( im @ X2 ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9631_Complex__divide,axiom,
% 9.53/5.33      ( divide1717551699836669952omplex
% 9.53/5.33      = ( ^ [X2: complex,Y: complex] : ( complex2 @ ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X2 ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X2 ) @ ( im @ Y ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X2 ) @ ( re @ Y ) ) @ ( times_times_real @ ( re @ X2 ) @ ( im @ Y ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9632_Im__Reals__divide,axiom,
% 9.53/5.33      ! [R: complex,Z: complex] :
% 9.53/5.33        ( ( member_complex @ R @ real_V2521375963428798218omplex )
% 9.53/5.33       => ( ( im @ ( divide1717551699836669952omplex @ R @ Z ) )
% 9.53/5.33          = ( divide_divide_real @ ( times_times_real @ ( uminus_uminus_real @ ( re @ R ) ) @ ( im @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9633_Re__Reals__divide,axiom,
% 9.53/5.33      ! [R: complex,Z: complex] :
% 9.53/5.33        ( ( member_complex @ R @ real_V2521375963428798218omplex )
% 9.53/5.33       => ( ( re @ ( divide1717551699836669952omplex @ R @ Z ) )
% 9.53/5.33          = ( divide_divide_real @ ( times_times_real @ ( re @ R ) @ ( re @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9634_Re__divide__Reals,axiom,
% 9.53/5.33      ! [R: complex,Z: complex] :
% 9.53/5.33        ( ( member_complex @ R @ real_V2521375963428798218omplex )
% 9.53/5.33       => ( ( re @ ( divide1717551699836669952omplex @ Z @ R ) )
% 9.53/5.33          = ( divide_divide_real @ ( re @ Z ) @ ( re @ R ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9635_Im__divide__Reals,axiom,
% 9.53/5.33      ! [R: complex,Z: complex] :
% 9.53/5.33        ( ( member_complex @ R @ real_V2521375963428798218omplex )
% 9.53/5.33       => ( ( im @ ( divide1717551699836669952omplex @ Z @ R ) )
% 9.53/5.33          = ( divide_divide_real @ ( im @ Z ) @ ( re @ R ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9636_complex__diff__cnj,axiom,
% 9.53/5.33      ! [Z: complex] :
% 9.53/5.33        ( ( minus_minus_complex @ Z @ ( cnj @ Z ) )
% 9.53/5.33        = ( times_times_complex @ ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( im @ Z ) ) ) @ imaginary_unit ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9637_complex__mult__cnj,axiom,
% 9.53/5.33      ! [Z: complex] :
% 9.53/5.33        ( ( times_times_complex @ Z @ ( cnj @ Z ) )
% 9.53/5.33        = ( real_V4546457046886955230omplex @ ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9638_complex__cnj__diff,axiom,
% 9.53/5.33      ! [X: complex,Y2: complex] :
% 9.53/5.33        ( ( cnj @ ( minus_minus_complex @ X @ Y2 ) )
% 9.53/5.33        = ( minus_minus_complex @ ( cnj @ X ) @ ( cnj @ Y2 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9639_Re__complex__div__gt__0,axiom,
% 9.53/5.33      ! [A: complex,B: complex] :
% 9.53/5.33        ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 9.53/5.33        = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9640_Re__complex__div__lt__0,axiom,
% 9.53/5.33      ! [A: complex,B: complex] :
% 9.53/5.33        ( ( ord_less_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 9.53/5.33        = ( ord_less_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9641_Re__complex__div__ge__0,axiom,
% 9.53/5.33      ! [A: complex,B: complex] :
% 9.53/5.33        ( ( ord_less_eq_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 9.53/5.33        = ( ord_less_eq_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9642_Re__complex__div__le__0,axiom,
% 9.53/5.33      ! [A: complex,B: complex] :
% 9.53/5.33        ( ( ord_less_eq_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 9.53/5.33        = ( ord_less_eq_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9643_Im__complex__div__gt__0,axiom,
% 9.53/5.33      ! [A: complex,B: complex] :
% 9.53/5.33        ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 9.53/5.33        = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9644_Im__complex__div__lt__0,axiom,
% 9.53/5.33      ! [A: complex,B: complex] :
% 9.53/5.33        ( ( ord_less_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 9.53/5.33        = ( ord_less_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9645_Im__complex__div__ge__0,axiom,
% 9.53/5.33      ! [A: complex,B: complex] :
% 9.53/5.33        ( ( ord_less_eq_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 9.53/5.33        = ( ord_less_eq_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9646_Im__complex__div__le__0,axiom,
% 9.53/5.33      ! [A: complex,B: complex] :
% 9.53/5.33        ( ( ord_less_eq_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 9.53/5.33        = ( ord_less_eq_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9647_complex__mod__mult__cnj,axiom,
% 9.53/5.33      ! [Z: complex] :
% 9.53/5.33        ( ( real_V1022390504157884413omplex @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 9.53/5.33        = ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9648_complex__div__gt__0,axiom,
% 9.53/5.33      ! [A: complex,B: complex] :
% 9.53/5.33        ( ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 9.53/5.33          = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) )
% 9.53/5.33        & ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 9.53/5.33          = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9649_complex__norm__square,axiom,
% 9.53/5.33      ! [Z: complex] :
% 9.53/5.33        ( ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.53/5.33        = ( times_times_complex @ Z @ ( cnj @ Z ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9650_complex__add__cnj,axiom,
% 9.53/5.33      ! [Z: complex] :
% 9.53/5.33        ( ( plus_plus_complex @ Z @ ( cnj @ Z ) )
% 9.53/5.33        = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ Z ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9651_complex__div__cnj,axiom,
% 9.53/5.33      ( divide1717551699836669952omplex
% 9.53/5.33      = ( ^ [A3: complex,B4: complex] : ( divide1717551699836669952omplex @ ( times_times_complex @ A3 @ ( cnj @ B4 ) ) @ ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ B4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9652_cnj__add__mult__eq__Re,axiom,
% 9.53/5.33      ! [Z: complex,W: complex] :
% 9.53/5.33        ( ( plus_plus_complex @ ( times_times_complex @ Z @ ( cnj @ W ) ) @ ( times_times_complex @ ( cnj @ Z ) @ W ) )
% 9.53/5.33        = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ ( times_times_complex @ Z @ ( cnj @ W ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9653_divmod__step__integer__def,axiom,
% 9.53/5.33      ( unique4921790084139445826nteger
% 9.53/5.33      = ( ^ [L: num] :
% 9.53/5.33            ( produc6916734918728496179nteger
% 9.53/5.33            @ ^ [Q4: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9654_card__Collect__less__nat,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( finite_card_nat
% 9.53/5.33          @ ( collect_nat
% 9.53/5.33            @ ^ [I3: nat] : ( ord_less_nat @ I3 @ N ) ) )
% 9.53/5.33        = N ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9655_card__atMost,axiom,
% 9.53/5.33      ! [U: nat] :
% 9.53/5.33        ( ( finite_card_nat @ ( set_ord_atMost_nat @ U ) )
% 9.53/5.33        = ( suc @ U ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9656_card__atLeastLessThan,axiom,
% 9.53/5.33      ! [L2: nat,U: nat] :
% 9.53/5.33        ( ( finite_card_nat @ ( set_or4665077453230672383an_nat @ L2 @ U ) )
% 9.53/5.33        = ( minus_minus_nat @ U @ L2 ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9657_card__Collect__le__nat,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( finite_card_nat
% 9.53/5.33          @ ( collect_nat
% 9.53/5.33            @ ^ [I3: nat] : ( ord_less_eq_nat @ I3 @ N ) ) )
% 9.53/5.33        = ( suc @ N ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9658_card__atLeastAtMost,axiom,
% 9.53/5.33      ! [L2: nat,U: nat] :
% 9.53/5.33        ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L2 @ U ) )
% 9.53/5.33        = ( minus_minus_nat @ ( suc @ U ) @ L2 ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9659_card__atLeastLessThan__int,axiom,
% 9.53/5.33      ! [L2: int,U: int] :
% 9.53/5.33        ( ( finite_card_int @ ( set_or4662586982721622107an_int @ L2 @ U ) )
% 9.53/5.33        = ( nat2 @ ( minus_minus_int @ U @ L2 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9660_card__atLeastAtMost__int,axiom,
% 9.53/5.33      ! [L2: int,U: int] :
% 9.53/5.33        ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L2 @ U ) )
% 9.53/5.33        = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L2 ) @ one_one_int ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9661_minus__integer__code_I2_J,axiom,
% 9.53/5.33      ! [L2: code_integer] :
% 9.53/5.33        ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ L2 )
% 9.53/5.33        = ( uminus1351360451143612070nteger @ L2 ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9662_minus__integer__code_I1_J,axiom,
% 9.53/5.33      ! [K: code_integer] :
% 9.53/5.33        ( ( minus_8373710615458151222nteger @ K @ zero_z3403309356797280102nteger )
% 9.53/5.33        = K ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9663_card__less,axiom,
% 9.53/5.33      ! [M7: set_nat,I2: nat] :
% 9.53/5.33        ( ( member_nat @ zero_zero_nat @ M7 )
% 9.53/5.33       => ( ( finite_card_nat
% 9.53/5.33            @ ( collect_nat
% 9.53/5.33              @ ^ [K3: nat] :
% 9.53/5.33                  ( ( member_nat @ K3 @ M7 )
% 9.53/5.33                  & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) )
% 9.53/5.33         != zero_zero_nat ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9664_card__less__Suc,axiom,
% 9.53/5.33      ! [M7: set_nat,I2: nat] :
% 9.53/5.33        ( ( member_nat @ zero_zero_nat @ M7 )
% 9.53/5.33       => ( ( suc
% 9.53/5.33            @ ( finite_card_nat
% 9.53/5.33              @ ( collect_nat
% 9.53/5.33                @ ^ [K3: nat] :
% 9.53/5.33                    ( ( member_nat @ ( suc @ K3 ) @ M7 )
% 9.53/5.33                    & ( ord_less_nat @ K3 @ I2 ) ) ) ) )
% 9.53/5.33          = ( finite_card_nat
% 9.53/5.33            @ ( collect_nat
% 9.53/5.33              @ ^ [K3: nat] :
% 9.53/5.33                  ( ( member_nat @ K3 @ M7 )
% 9.53/5.33                  & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9665_card__less__Suc2,axiom,
% 9.53/5.33      ! [M7: set_nat,I2: nat] :
% 9.53/5.33        ( ~ ( member_nat @ zero_zero_nat @ M7 )
% 9.53/5.33       => ( ( finite_card_nat
% 9.53/5.33            @ ( collect_nat
% 9.53/5.33              @ ^ [K3: nat] :
% 9.53/5.33                  ( ( member_nat @ ( suc @ K3 ) @ M7 )
% 9.53/5.33                  & ( ord_less_nat @ K3 @ I2 ) ) ) )
% 9.53/5.33          = ( finite_card_nat
% 9.53/5.33            @ ( collect_nat
% 9.53/5.33              @ ^ [K3: nat] :
% 9.53/5.33                  ( ( member_nat @ K3 @ M7 )
% 9.53/5.33                  & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9666_one__natural_Orsp,axiom,
% 9.53/5.33      one_one_nat = one_one_nat ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9667_subset__card__intvl__is__intvl,axiom,
% 9.53/5.33      ! [A2: set_nat,K: nat] :
% 9.53/5.33        ( ( ord_less_eq_set_nat @ A2 @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) )
% 9.53/5.33       => ( A2
% 9.53/5.33          = ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9668_card__le__Suc__Max,axiom,
% 9.53/5.33      ! [S2: set_nat] :
% 9.53/5.33        ( ( finite_finite_nat @ S2 )
% 9.53/5.33       => ( ord_less_eq_nat @ ( finite_card_nat @ S2 ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S2 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9669_subset__eq__atLeast0__lessThan__card,axiom,
% 9.53/5.33      ! [N4: set_nat,N: nat] :
% 9.53/5.33        ( ( ord_less_eq_set_nat @ N4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 9.53/5.33       => ( ord_less_eq_nat @ ( finite_card_nat @ N4 ) @ N ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9670_card__sum__le__nat__sum,axiom,
% 9.53/5.33      ! [S2: set_nat] :
% 9.53/5.33        ( ord_less_eq_nat
% 9.53/5.33        @ ( groups3542108847815614940at_nat
% 9.53/5.33          @ ^ [X2: nat] : X2
% 9.53/5.33          @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S2 ) ) )
% 9.53/5.33        @ ( groups3542108847815614940at_nat
% 9.53/5.33          @ ^ [X2: nat] : X2
% 9.53/5.33          @ S2 ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9671_card__nth__roots,axiom,
% 9.53/5.33      ! [C: complex,N: nat] :
% 9.53/5.33        ( ( C != zero_zero_complex )
% 9.53/5.33       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33         => ( ( finite_card_complex
% 9.53/5.33              @ ( collect_complex
% 9.53/5.33                @ ^ [Z4: complex] :
% 9.53/5.33                    ( ( power_power_complex @ Z4 @ N )
% 9.53/5.33                    = C ) ) )
% 9.53/5.33            = N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9672_card__roots__unity__eq,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( finite_card_complex
% 9.53/5.33            @ ( collect_complex
% 9.53/5.33              @ ^ [Z4: complex] :
% 9.53/5.33                  ( ( power_power_complex @ Z4 @ N )
% 9.53/5.33                  = one_one_complex ) ) )
% 9.53/5.33          = N ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9673_integer__of__int__code,axiom,
% 9.53/5.33      ( code_integer_of_int
% 9.53/5.33      = ( ^ [K3: int] :
% 9.53/5.33            ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K3 ) ) )
% 9.53/5.33            @ ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 9.53/5.33              @ ( if_Code_integer
% 9.53/5.33                @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.53/5.33                  = zero_zero_int )
% 9.53/5.33                @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 9.53/5.33                @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9674_divide__integer_Oabs__eq,axiom,
% 9.53/5.33      ! [Xa2: int,X: int] :
% 9.53/5.33        ( ( divide6298287555418463151nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 9.53/5.33        = ( code_integer_of_int @ ( divide_divide_int @ Xa2 @ X ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9675_minus__integer_Oabs__eq,axiom,
% 9.53/5.33      ! [Xa2: int,X: int] :
% 9.53/5.33        ( ( minus_8373710615458151222nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 9.53/5.33        = ( code_integer_of_int @ ( minus_minus_int @ Xa2 @ X ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9676_integer__of__num_I3_J,axiom,
% 9.53/5.33      ! [N: num] :
% 9.53/5.33        ( ( code_integer_of_num @ ( bit1 @ N ) )
% 9.53/5.33        = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) @ one_one_Code_integer ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9677_num__of__integer__code,axiom,
% 9.53/5.33      ( code_num_of_integer
% 9.53/5.33      = ( ^ [K3: code_integer] :
% 9.53/5.33            ( if_num @ ( ord_le3102999989581377725nteger @ K3 @ one_one_Code_integer ) @ one
% 9.53/5.33            @ ( produc7336495610019696514er_num
% 9.53/5.33              @ ^ [L: code_integer,J3: code_integer] : ( if_num @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_num @ ( code_num_of_integer @ L ) @ ( code_num_of_integer @ L ) ) @ ( plus_plus_num @ ( plus_plus_num @ ( code_num_of_integer @ L ) @ ( code_num_of_integer @ L ) ) @ one ) )
% 9.53/5.33              @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9678_integer__of__num__triv_I1_J,axiom,
% 9.53/5.33      ( ( code_integer_of_num @ one )
% 9.53/5.33      = one_one_Code_integer ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9679_integer__of__num_I2_J,axiom,
% 9.53/5.33      ! [N: num] :
% 9.53/5.33        ( ( code_integer_of_num @ ( bit0 @ N ) )
% 9.53/5.33        = ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9680_integer__of__num__triv_I2_J,axiom,
% 9.53/5.33      ( ( code_integer_of_num @ ( bit0 @ one ) )
% 9.53/5.33      = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9681_nat__of__integer__code,axiom,
% 9.53/5.33      ( code_nat_of_integer
% 9.53/5.33      = ( ^ [K3: code_integer] :
% 9.53/5.33            ( if_nat @ ( ord_le3102999989581377725nteger @ K3 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 9.53/5.33            @ ( produc1555791787009142072er_nat
% 9.53/5.33              @ ^ [L: code_integer,J3: code_integer] : ( if_nat @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_nat @ ( code_nat_of_integer @ L ) @ ( code_nat_of_integer @ L ) ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( code_nat_of_integer @ L ) @ ( code_nat_of_integer @ L ) ) @ one_one_nat ) )
% 9.53/5.33              @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9682_int__of__integer__code,axiom,
% 9.53/5.33      ( code_int_of_integer
% 9.53/5.33      = ( ^ [K3: code_integer] :
% 9.53/5.33            ( if_int @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K3 ) ) )
% 9.53/5.33            @ ( if_int @ ( K3 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 9.53/5.33              @ ( produc1553301316500091796er_int
% 9.53/5.33                @ ^ [L: code_integer,J3: code_integer] : ( if_int @ ( J3 = zero_z3403309356797280102nteger ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L ) ) @ one_one_int ) )
% 9.53/5.33                @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9683_int__of__integer__numeral,axiom,
% 9.53/5.33      ! [K: num] :
% 9.53/5.33        ( ( code_int_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 9.53/5.33        = ( numeral_numeral_int @ K ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9684_minus__integer_Orep__eq,axiom,
% 9.53/5.33      ! [X: code_integer,Xa2: code_integer] :
% 9.53/5.33        ( ( code_int_of_integer @ ( minus_8373710615458151222nteger @ X @ Xa2 ) )
% 9.53/5.33        = ( minus_minus_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9685_divide__integer_Orep__eq,axiom,
% 9.53/5.33      ! [X: code_integer,Xa2: code_integer] :
% 9.53/5.33        ( ( code_int_of_integer @ ( divide6298287555418463151nteger @ X @ Xa2 ) )
% 9.53/5.33        = ( divide_divide_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9686_nat__of__integer__code__post_I3_J,axiom,
% 9.53/5.33      ! [K: num] :
% 9.53/5.33        ( ( code_nat_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 9.53/5.33        = ( numeral_numeral_nat @ K ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9687_nat__of__integer__code__post_I2_J,axiom,
% 9.53/5.33      ( ( code_nat_of_integer @ one_one_Code_integer )
% 9.53/5.33      = one_one_nat ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9688_floor__real__def,axiom,
% 9.53/5.33      ( archim6058952711729229775r_real
% 9.53/5.33      = ( ^ [X2: real] :
% 9.53/5.33            ( the_int
% 9.53/5.33            @ ^ [Z4: int] :
% 9.53/5.33                ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z4 ) @ X2 )
% 9.53/5.33                & ( ord_less_real @ X2 @ ( ring_1_of_int_real @ ( plus_plus_int @ Z4 @ one_one_int ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9689_bit__cut__integer__def,axiom,
% 9.53/5.33      ( code_bit_cut_integer
% 9.53/5.33      = ( ^ [K3: code_integer] :
% 9.53/5.33            ( produc6677183202524767010eger_o @ ( divide6298287555418463151nteger @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.53/5.33            @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ K3 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9690_nat_Odisc__eq__case_I2_J,axiom,
% 9.53/5.33      ! [Nat: nat] :
% 9.53/5.33        ( ( Nat != zero_zero_nat )
% 9.53/5.33        = ( case_nat_o @ $false
% 9.53/5.33          @ ^ [Uu3: nat] : $true
% 9.53/5.33          @ Nat ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9691_nat_Odisc__eq__case_I1_J,axiom,
% 9.53/5.33      ! [Nat: nat] :
% 9.53/5.33        ( ( Nat = zero_zero_nat )
% 9.53/5.33        = ( case_nat_o @ $true
% 9.53/5.33          @ ^ [Uu3: nat] : $false
% 9.53/5.33          @ Nat ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9692_less__eq__nat_Osimps_I2_J,axiom,
% 9.53/5.33      ! [M: nat,N: nat] :
% 9.53/5.33        ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 9.53/5.33        = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M ) @ N ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9693_max__Suc2,axiom,
% 9.53/5.33      ! [M: nat,N: nat] :
% 9.53/5.33        ( ( ord_max_nat @ M @ ( suc @ N ) )
% 9.53/5.33        = ( case_nat_nat @ ( suc @ N )
% 9.53/5.33          @ ^ [M2: nat] : ( suc @ ( ord_max_nat @ M2 @ N ) )
% 9.53/5.33          @ M ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9694_max__Suc1,axiom,
% 9.53/5.33      ! [N: nat,M: nat] :
% 9.53/5.33        ( ( ord_max_nat @ ( suc @ N ) @ M )
% 9.53/5.33        = ( case_nat_nat @ ( suc @ N )
% 9.53/5.33          @ ^ [M2: nat] : ( suc @ ( ord_max_nat @ N @ M2 ) )
% 9.53/5.33          @ M ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9695_diff__Suc,axiom,
% 9.53/5.33      ! [M: nat,N: nat] :
% 9.53/5.33        ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 9.53/5.33        = ( case_nat_nat @ zero_zero_nat
% 9.53/5.33          @ ^ [K3: nat] : K3
% 9.53/5.33          @ ( minus_minus_nat @ M @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9696_bit__cut__integer__code,axiom,
% 9.53/5.33      ( code_bit_cut_integer
% 9.53/5.33      = ( ^ [K3: code_integer] :
% 9.53/5.33            ( if_Pro5737122678794959658eger_o @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 9.53/5.33            @ ( produc9125791028180074456eger_o
% 9.53/5.33              @ ^ [R5: code_integer,S6: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ R5 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ S6 ) ) @ ( S6 = one_one_Code_integer ) )
% 9.53/5.33              @ ( code_divmod_abs @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9697_pred__def,axiom,
% 9.53/5.33      ( pred
% 9.53/5.33      = ( case_nat_nat @ zero_zero_nat
% 9.53/5.33        @ ^ [X24: nat] : X24 ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9698_divmod__integer__code,axiom,
% 9.53/5.33      ( code_divmod_integer
% 9.53/5.33      = ( ^ [K3: code_integer,L: code_integer] :
% 9.53/5.33            ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 9.53/5.33            @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L )
% 9.53/5.33              @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ ( code_divmod_abs @ K3 @ L )
% 9.53/5.33                @ ( produc6916734918728496179nteger
% 9.53/5.33                  @ ^ [R5: code_integer,S6: code_integer] : ( if_Pro6119634080678213985nteger @ ( S6 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L @ S6 ) ) )
% 9.53/5.33                  @ ( code_divmod_abs @ K3 @ L ) ) )
% 9.53/5.33              @ ( if_Pro6119634080678213985nteger @ ( L = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 9.53/5.33                @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 9.53/5.33                  @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K3 @ L )
% 9.53/5.33                    @ ( produc6916734918728496179nteger
% 9.53/5.33                      @ ^ [R5: code_integer,S6: code_integer] : ( if_Pro6119634080678213985nteger @ ( S6 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L ) @ S6 ) ) )
% 9.53/5.33                      @ ( code_divmod_abs @ K3 @ L ) ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9699_drop__bit__numeral__minus__bit1,axiom,
% 9.53/5.33      ! [L2: num,K: num] :
% 9.53/5.33        ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 9.53/5.33        = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9700_Suc__0__mod__numeral,axiom,
% 9.53/5.33      ! [K: num] :
% 9.53/5.33        ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 9.53/5.33        = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9701_drop__bit__nonnegative__int__iff,axiom,
% 9.53/5.33      ! [N: nat,K: int] :
% 9.53/5.33        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se8568078237143864401it_int @ N @ K ) )
% 9.53/5.33        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9702_drop__bit__negative__int__iff,axiom,
% 9.53/5.33      ! [N: nat,K: int] :
% 9.53/5.33        ( ( ord_less_int @ ( bit_se8568078237143864401it_int @ N @ K ) @ zero_zero_int )
% 9.53/5.33        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9703_drop__bit__minus__one,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 9.53/5.33        = ( uminus_uminus_int @ one_one_int ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9704_snd__divmod__nat,axiom,
% 9.53/5.33      ! [M: nat,N: nat] :
% 9.53/5.33        ( ( product_snd_nat_nat @ ( divmod_nat @ M @ N ) )
% 9.53/5.33        = ( modulo_modulo_nat @ M @ N ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9705_drop__bit__Suc__minus__bit0,axiom,
% 9.53/5.33      ! [N: nat,K: num] :
% 9.53/5.33        ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 9.53/5.33        = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9706_drop__bit__numeral__minus__bit0,axiom,
% 9.53/5.33      ! [L2: num,K: num] :
% 9.53/5.33        ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 9.53/5.33        = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9707_drop__bit__Suc__minus__bit1,axiom,
% 9.53/5.33      ! [N: nat,K: num] :
% 9.53/5.33        ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 9.53/5.33        = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9708_drop__bit__push__bit__int,axiom,
% 9.53/5.33      ! [M: nat,N: nat,K: int] :
% 9.53/5.33        ( ( bit_se8568078237143864401it_int @ M @ ( bit_se545348938243370406it_int @ N @ K ) )
% 9.53/5.33        = ( bit_se8568078237143864401it_int @ ( minus_minus_nat @ M @ N ) @ ( bit_se545348938243370406it_int @ ( minus_minus_nat @ N @ M ) @ K ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9709_drop__bit__int__def,axiom,
% 9.53/5.33      ( bit_se8568078237143864401it_int
% 9.53/5.33      = ( ^ [N2: nat,K3: int] : ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9710_Suc__0__div__numeral,axiom,
% 9.53/5.33      ! [K: num] :
% 9.53/5.33        ( ( divide_divide_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 9.53/5.33        = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9711_prod__decode__aux_Oelims,axiom,
% 9.53/5.33      ! [X: nat,Xa2: nat,Y2: product_prod_nat_nat] :
% 9.53/5.33        ( ( ( nat_prod_decode_aux @ X @ Xa2 )
% 9.53/5.33          = Y2 )
% 9.53/5.33       => ( ( ( ord_less_eq_nat @ Xa2 @ X )
% 9.53/5.33           => ( Y2
% 9.53/5.33              = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X @ Xa2 ) ) ) )
% 9.53/5.33          & ( ~ ( ord_less_eq_nat @ Xa2 @ X )
% 9.53/5.33           => ( Y2
% 9.53/5.33              = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9712_prod__decode__aux_Osimps,axiom,
% 9.53/5.33      ( nat_prod_decode_aux
% 9.53/5.33      = ( ^ [K3: nat,M6: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M6 @ K3 ) @ ( product_Pair_nat_nat @ M6 @ ( minus_minus_nat @ K3 @ M6 ) ) @ ( nat_prod_decode_aux @ ( suc @ K3 ) @ ( minus_minus_nat @ M6 @ ( suc @ K3 ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9713_drop__bit__of__Suc__0,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( bit_se8570568707652914677it_nat @ N @ ( suc @ zero_zero_nat ) )
% 9.53/5.33        = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9714_fst__divmod__nat,axiom,
% 9.53/5.33      ! [M: nat,N: nat] :
% 9.53/5.33        ( ( product_fst_nat_nat @ ( divmod_nat @ M @ N ) )
% 9.53/5.33        = ( divide_divide_nat @ M @ N ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9715_drop__bit__nat__eq,axiom,
% 9.53/5.33      ! [N: nat,K: int] :
% 9.53/5.33        ( ( bit_se8570568707652914677it_nat @ N @ ( nat2 @ K ) )
% 9.53/5.33        = ( nat2 @ ( bit_se8568078237143864401it_int @ N @ K ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9716_drop__bit__nat__def,axiom,
% 9.53/5.33      ( bit_se8570568707652914677it_nat
% 9.53/5.33      = ( ^ [N2: nat,M6: nat] : ( divide_divide_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9717_minus__one__mod__numeral,axiom,
% 9.53/5.33      ! [N: num] :
% 9.53/5.33        ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 9.53/5.33        = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9718_one__mod__minus__numeral,axiom,
% 9.53/5.33      ! [N: num] :
% 9.53/5.33        ( ( modulo_modulo_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.53/5.33        = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9719_minus__numeral__mod__numeral,axiom,
% 9.53/5.33      ! [M: num,N: num] :
% 9.53/5.33        ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 9.53/5.33        = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9720_numeral__mod__minus__numeral,axiom,
% 9.53/5.33      ! [M: num,N: num] :
% 9.53/5.33        ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.53/5.33        = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9721_Divides_Oadjust__mod__def,axiom,
% 9.53/5.33      ( adjust_mod
% 9.53/5.33      = ( ^ [L: int,R5: int] : ( if_int @ ( R5 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ L @ R5 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9722_bezw_Oelims,axiom,
% 9.53/5.33      ! [X: nat,Xa2: nat,Y2: product_prod_int_int] :
% 9.53/5.33        ( ( ( bezw @ X @ Xa2 )
% 9.53/5.33          = Y2 )
% 9.53/5.33       => ( ( ( Xa2 = zero_zero_nat )
% 9.53/5.33           => ( Y2
% 9.53/5.33              = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 9.53/5.33          & ( ( Xa2 != zero_zero_nat )
% 9.53/5.33           => ( Y2
% 9.53/5.33              = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa2 ) ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9723_bezw_Osimps,axiom,
% 9.53/5.33      ( bezw
% 9.53/5.33      = ( ^ [X2: nat,Y: nat] : ( if_Pro3027730157355071871nt_int @ ( Y = zero_zero_nat ) @ ( product_Pair_int_int @ one_one_int @ zero_zero_int ) @ ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X2 @ Y ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X2 @ Y ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X2 @ Y ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X2 @ Y ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9724_bezw__non__0,axiom,
% 9.53/5.33      ! [Y2: nat,X: nat] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ Y2 )
% 9.53/5.33       => ( ( bezw @ X @ Y2 )
% 9.53/5.33          = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y2 @ ( modulo_modulo_nat @ X @ Y2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y2 @ ( modulo_modulo_nat @ X @ Y2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y2 @ ( modulo_modulo_nat @ X @ Y2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Y2 ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9725_bezw_Opelims,axiom,
% 9.53/5.33      ! [X: nat,Xa2: nat,Y2: product_prod_int_int] :
% 9.53/5.33        ( ( ( bezw @ X @ Xa2 )
% 9.53/5.33          = Y2 )
% 9.53/5.33       => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 9.53/5.33         => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 9.53/5.33                 => ( Y2
% 9.53/5.33                    = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 9.53/5.33                & ( ( Xa2 != zero_zero_nat )
% 9.53/5.33                 => ( Y2
% 9.53/5.33                    = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa2 ) ) ) ) ) ) ) )
% 9.53/5.33             => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9726_prod__decode__aux_Opelims,axiom,
% 9.53/5.33      ! [X: nat,Xa2: nat,Y2: product_prod_nat_nat] :
% 9.53/5.33        ( ( ( nat_prod_decode_aux @ X @ Xa2 )
% 9.53/5.33          = Y2 )
% 9.53/5.33       => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 9.53/5.33         => ~ ( ( ( ( ord_less_eq_nat @ Xa2 @ X )
% 9.53/5.33                 => ( Y2
% 9.53/5.33                    = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X @ Xa2 ) ) ) )
% 9.53/5.33                & ( ~ ( ord_less_eq_nat @ Xa2 @ X )
% 9.53/5.33                 => ( Y2
% 9.53/5.33                    = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X ) ) ) ) ) )
% 9.53/5.33             => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9727_nat__descend__induct,axiom,
% 9.53/5.33      ! [N: nat,P: nat > $o,M: nat] :
% 9.53/5.33        ( ! [K2: nat] :
% 9.53/5.33            ( ( ord_less_nat @ N @ K2 )
% 9.53/5.33           => ( P @ K2 ) )
% 9.53/5.33       => ( ! [K2: nat] :
% 9.53/5.33              ( ( ord_less_eq_nat @ K2 @ N )
% 9.53/5.33             => ( ! [I: nat] :
% 9.53/5.33                    ( ( ord_less_nat @ K2 @ I )
% 9.53/5.33                   => ( P @ I ) )
% 9.53/5.33               => ( P @ K2 ) ) )
% 9.53/5.33         => ( P @ M ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9728_card__greaterThanLessThan__int,axiom,
% 9.53/5.33      ! [L2: int,U: int] :
% 9.53/5.33        ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L2 @ U ) )
% 9.53/5.33        = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L2 @ one_one_int ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9729_infinite__nat__iff__unbounded__le,axiom,
% 9.53/5.33      ! [S2: set_nat] :
% 9.53/5.33        ( ( ~ ( finite_finite_nat @ S2 ) )
% 9.53/5.33        = ( ! [M6: nat] :
% 9.53/5.33            ? [N2: nat] :
% 9.53/5.33              ( ( ord_less_eq_nat @ M6 @ N2 )
% 9.53/5.33              & ( member_nat @ N2 @ S2 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9730_infinite__nat__iff__unbounded,axiom,
% 9.53/5.33      ! [S2: set_nat] :
% 9.53/5.33        ( ( ~ ( finite_finite_nat @ S2 ) )
% 9.53/5.33        = ( ! [M6: nat] :
% 9.53/5.33            ? [N2: nat] :
% 9.53/5.33              ( ( ord_less_nat @ M6 @ N2 )
% 9.53/5.33              & ( member_nat @ N2 @ S2 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9731_unbounded__k__infinite,axiom,
% 9.53/5.33      ! [K: nat,S2: set_nat] :
% 9.53/5.33        ( ! [M4: nat] :
% 9.53/5.33            ( ( ord_less_nat @ K @ M4 )
% 9.53/5.33           => ? [N9: nat] :
% 9.53/5.33                ( ( ord_less_nat @ M4 @ N9 )
% 9.53/5.33                & ( member_nat @ N9 @ S2 ) ) )
% 9.53/5.33       => ~ ( finite_finite_nat @ S2 ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9732_finite__enumerate,axiom,
% 9.53/5.33      ! [S2: set_nat] :
% 9.53/5.33        ( ( finite_finite_nat @ S2 )
% 9.53/5.33       => ? [R3: nat > nat] :
% 9.53/5.33            ( ( strict1292158309912662752at_nat @ R3 @ ( set_ord_lessThan_nat @ ( finite_card_nat @ S2 ) ) )
% 9.53/5.33            & ! [N9: nat] :
% 9.53/5.33                ( ( ord_less_nat @ N9 @ ( finite_card_nat @ S2 ) )
% 9.53/5.33               => ( member_nat @ ( R3 @ N9 ) @ S2 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9733_xor__minus__numerals_I1_J,axiom,
% 9.53/5.33      ! [N: num,K: int] :
% 9.53/5.33        ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ K )
% 9.53/5.33        = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ ( neg_numeral_sub_int @ N @ one ) @ K ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9734_xor__minus__numerals_I2_J,axiom,
% 9.53/5.33      ! [K: int,N: num] :
% 9.53/5.33        ( ( bit_se6526347334894502574or_int @ K @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.53/5.33        = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ K @ ( neg_numeral_sub_int @ N @ one ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9735_card__greaterThanLessThan,axiom,
% 9.53/5.33      ! [L2: nat,U: nat] :
% 9.53/5.33        ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L2 @ U ) )
% 9.53/5.33        = ( minus_minus_nat @ U @ ( suc @ L2 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9736_atLeastSucLessThan__greaterThanLessThan,axiom,
% 9.53/5.33      ! [L2: nat,U: nat] :
% 9.53/5.33        ( ( set_or4665077453230672383an_nat @ ( suc @ L2 ) @ U )
% 9.53/5.33        = ( set_or5834768355832116004an_nat @ L2 @ U ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9737_tanh__real__bounds,axiom,
% 9.53/5.33      ! [X: real] : ( member_real @ ( tanh_real @ X ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9738_sub__BitM__One__eq,axiom,
% 9.53/5.33      ! [N: num] :
% 9.53/5.33        ( ( neg_numeral_sub_int @ ( bitM @ N ) @ one )
% 9.53/5.33        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( neg_numeral_sub_int @ N @ one ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9739_Suc__funpow,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( compow_nat_nat @ N @ suc )
% 9.53/5.33        = ( plus_plus_nat @ N ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9740_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 9.53/5.33      ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 9.53/5.33      @ ^ [X2: nat,Y: nat] : ( ord_less_eq_nat @ Y @ X2 )
% 9.53/5.33      @ ^ [X2: nat,Y: nat] : ( ord_less_nat @ Y @ X2 ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9741_times__int_Oabs__eq,axiom,
% 9.53/5.33      ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 9.53/5.33        ( ( times_times_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 9.53/5.33        = ( abs_Integ
% 9.53/5.33          @ ( produc27273713700761075at_nat
% 9.53/5.33            @ ^ [X2: nat,Y: nat] :
% 9.53/5.33                ( produc2626176000494625587at_nat
% 9.53/5.33                @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U2 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y @ U2 ) ) ) )
% 9.53/5.33            @ Xa2
% 9.53/5.33            @ X ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9742_eq__Abs__Integ,axiom,
% 9.53/5.33      ! [Z: int] :
% 9.53/5.33        ~ ! [X3: nat,Y3: nat] :
% 9.53/5.33            ( Z
% 9.53/5.33           != ( abs_Integ @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9743_nat_Oabs__eq,axiom,
% 9.53/5.33      ! [X: product_prod_nat_nat] :
% 9.53/5.33        ( ( nat2 @ ( abs_Integ @ X ) )
% 9.53/5.33        = ( produc6842872674320459806at_nat @ minus_minus_nat @ X ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9744_zero__int__def,axiom,
% 9.53/5.33      ( zero_zero_int
% 9.53/5.33      = ( abs_Integ @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9745_int__def,axiom,
% 9.53/5.33      ( semiri1314217659103216013at_int
% 9.53/5.33      = ( ^ [N2: nat] : ( abs_Integ @ ( product_Pair_nat_nat @ N2 @ zero_zero_nat ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9746_uminus__int_Oabs__eq,axiom,
% 9.53/5.33      ! [X: product_prod_nat_nat] :
% 9.53/5.33        ( ( uminus_uminus_int @ ( abs_Integ @ X ) )
% 9.53/5.33        = ( abs_Integ
% 9.53/5.33          @ ( produc2626176000494625587at_nat
% 9.53/5.33            @ ^ [X2: nat,Y: nat] : ( product_Pair_nat_nat @ Y @ X2 )
% 9.53/5.33            @ X ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9747_one__int__def,axiom,
% 9.53/5.33      ( one_one_int
% 9.53/5.33      = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9748_less__int_Oabs__eq,axiom,
% 9.53/5.33      ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 9.53/5.33        ( ( ord_less_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 9.53/5.33        = ( produc8739625826339149834_nat_o
% 9.53/5.33          @ ^ [X2: nat,Y: nat] :
% 9.53/5.33              ( produc6081775807080527818_nat_o
% 9.53/5.33              @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) )
% 9.53/5.33          @ Xa2
% 9.53/5.33          @ X ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9749_less__eq__int_Oabs__eq,axiom,
% 9.53/5.33      ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 9.53/5.33        ( ( ord_less_eq_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 9.53/5.33        = ( produc8739625826339149834_nat_o
% 9.53/5.33          @ ^ [X2: nat,Y: nat] :
% 9.53/5.33              ( produc6081775807080527818_nat_o
% 9.53/5.33              @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) )
% 9.53/5.33          @ Xa2
% 9.53/5.33          @ X ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9750_plus__int_Oabs__eq,axiom,
% 9.53/5.33      ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 9.53/5.33        ( ( plus_plus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 9.53/5.33        = ( abs_Integ
% 9.53/5.33          @ ( produc27273713700761075at_nat
% 9.53/5.33            @ ^ [X2: nat,Y: nat] :
% 9.53/5.33                ( produc2626176000494625587at_nat
% 9.53/5.33                @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ U2 ) @ ( plus_plus_nat @ Y @ V4 ) ) )
% 9.53/5.33            @ Xa2
% 9.53/5.33            @ X ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9751_minus__int_Oabs__eq,axiom,
% 9.53/5.33      ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 9.53/5.33        ( ( minus_minus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 9.53/5.33        = ( abs_Integ
% 9.53/5.33          @ ( produc27273713700761075at_nat
% 9.53/5.33            @ ^ [X2: nat,Y: nat] :
% 9.53/5.33                ( produc2626176000494625587at_nat
% 9.53/5.33                @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ Y @ U2 ) ) )
% 9.53/5.33            @ Xa2
% 9.53/5.33            @ X ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9752_num__of__nat_Osimps_I2_J,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33         => ( ( num_of_nat @ ( suc @ N ) )
% 9.53/5.33            = ( inc @ ( num_of_nat @ N ) ) ) )
% 9.53/5.33        & ( ~ ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33         => ( ( num_of_nat @ ( suc @ N ) )
% 9.53/5.33            = one ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9753_num__of__nat__numeral__eq,axiom,
% 9.53/5.33      ! [Q2: num] :
% 9.53/5.33        ( ( num_of_nat @ ( numeral_numeral_nat @ Q2 ) )
% 9.53/5.33        = Q2 ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9754_num__of__nat_Osimps_I1_J,axiom,
% 9.53/5.33      ( ( num_of_nat @ zero_zero_nat )
% 9.53/5.33      = one ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9755_numeral__num__of__nat,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( numeral_numeral_nat @ ( num_of_nat @ N ) )
% 9.53/5.33          = N ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9756_num__of__nat__One,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( ord_less_eq_nat @ N @ one_one_nat )
% 9.53/5.33       => ( ( num_of_nat @ N )
% 9.53/5.33          = one ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9757_num__of__nat__double,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( num_of_nat @ ( plus_plus_nat @ N @ N ) )
% 9.53/5.33          = ( bit0 @ ( num_of_nat @ N ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9758_num__of__nat__plus__distrib,axiom,
% 9.53/5.33      ! [M: nat,N: nat] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ M )
% 9.53/5.33       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33         => ( ( num_of_nat @ ( plus_plus_nat @ M @ N ) )
% 9.53/5.33            = ( plus_plus_num @ ( num_of_nat @ M ) @ ( num_of_nat @ N ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9759_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 9.53/5.33      ! [N: nat,J: nat,I2: nat] :
% 9.53/5.33        ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ ( suc @ I2 ) ) )
% 9.53/5.33       => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I2 @ J ) ) @ N )
% 9.53/5.33          = ( suc @ ( plus_plus_nat @ I2 @ N ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9760_less__eq__int_Orep__eq,axiom,
% 9.53/5.33      ( ord_less_eq_int
% 9.53/5.33      = ( ^ [X2: int,Xa4: int] :
% 9.53/5.33            ( produc8739625826339149834_nat_o
% 9.53/5.33            @ ^ [Y: nat,Z4: nat] :
% 9.53/5.33                ( produc6081775807080527818_nat_o
% 9.53/5.33                @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y @ V4 ) @ ( plus_plus_nat @ U2 @ Z4 ) ) )
% 9.53/5.33            @ ( rep_Integ @ X2 )
% 9.53/5.33            @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9761_less__int_Orep__eq,axiom,
% 9.53/5.33      ( ord_less_int
% 9.53/5.33      = ( ^ [X2: int,Xa4: int] :
% 9.53/5.33            ( produc8739625826339149834_nat_o
% 9.53/5.33            @ ^ [Y: nat,Z4: nat] :
% 9.53/5.33                ( produc6081775807080527818_nat_o
% 9.53/5.33                @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y @ V4 ) @ ( plus_plus_nat @ U2 @ Z4 ) ) )
% 9.53/5.33            @ ( rep_Integ @ X2 )
% 9.53/5.33            @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9762_nat_Orep__eq,axiom,
% 9.53/5.33      ( nat2
% 9.53/5.33      = ( ^ [X2: int] : ( produc6842872674320459806at_nat @ minus_minus_nat @ ( rep_Integ @ X2 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9763_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 9.53/5.33      ! [N: nat,J: nat,I2: nat] :
% 9.53/5.33        ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ I2 ) )
% 9.53/5.33       => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I2 @ J ) ) @ N )
% 9.53/5.33          = ( suc @ ( plus_plus_nat @ I2 @ N ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9764_prod__encode__def,axiom,
% 9.53/5.33      ( nat_prod_encode
% 9.53/5.33      = ( produc6842872674320459806at_nat
% 9.53/5.33        @ ^ [M6: nat,N2: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M6 @ N2 ) ) @ M6 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9765_uminus__int__def,axiom,
% 9.53/5.33      ( uminus_uminus_int
% 9.53/5.33      = ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ
% 9.53/5.33        @ ( produc2626176000494625587at_nat
% 9.53/5.33          @ ^ [X2: nat,Y: nat] : ( product_Pair_nat_nat @ Y @ X2 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9766_card__greaterThanAtMost,axiom,
% 9.53/5.33      ! [L2: nat,U: nat] :
% 9.53/5.33        ( ( finite_card_nat @ ( set_or6659071591806873216st_nat @ L2 @ U ) )
% 9.53/5.33        = ( minus_minus_nat @ U @ L2 ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9767_atLeastSucAtMost__greaterThanAtMost,axiom,
% 9.53/5.33      ! [L2: nat,U: nat] :
% 9.53/5.33        ( ( set_or1269000886237332187st_nat @ ( suc @ L2 ) @ U )
% 9.53/5.33        = ( set_or6659071591806873216st_nat @ L2 @ U ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9768_le__prod__encode__2,axiom,
% 9.53/5.33      ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9769_le__prod__encode__1,axiom,
% 9.53/5.33      ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9770_prod__encode__prod__decode__aux,axiom,
% 9.53/5.33      ! [K: nat,M: nat] :
% 9.53/5.33        ( ( nat_prod_encode @ ( nat_prod_decode_aux @ K @ M ) )
% 9.53/5.33        = ( plus_plus_nat @ ( nat_triangle @ K ) @ M ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9771_times__int__def,axiom,
% 9.53/5.33      ( times_times_int
% 9.53/5.33      = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 9.53/5.33        @ ( produc27273713700761075at_nat
% 9.53/5.33          @ ^ [X2: nat,Y: nat] :
% 9.53/5.33              ( produc2626176000494625587at_nat
% 9.53/5.33              @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U2 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y @ U2 ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9772_minus__int__def,axiom,
% 9.53/5.33      ( minus_minus_int
% 9.53/5.33      = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 9.53/5.33        @ ( produc27273713700761075at_nat
% 9.53/5.33          @ ^ [X2: nat,Y: nat] :
% 9.53/5.33              ( produc2626176000494625587at_nat
% 9.53/5.33              @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ Y @ U2 ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9773_plus__int__def,axiom,
% 9.53/5.33      ( plus_plus_int
% 9.53/5.33      = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 9.53/5.33        @ ( produc27273713700761075at_nat
% 9.53/5.33          @ ^ [X2: nat,Y: nat] :
% 9.53/5.33              ( produc2626176000494625587at_nat
% 9.53/5.33              @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ U2 ) @ ( plus_plus_nat @ Y @ V4 ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9774_card__greaterThanAtMost__int,axiom,
% 9.53/5.33      ! [L2: int,U: int] :
% 9.53/5.33        ( ( finite_card_int @ ( set_or6656581121297822940st_int @ L2 @ U ) )
% 9.53/5.33        = ( nat2 @ ( minus_minus_int @ U @ L2 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9775_Gcd__remove0__nat,axiom,
% 9.53/5.33      ! [M7: set_nat] :
% 9.53/5.33        ( ( finite_finite_nat @ M7 )
% 9.53/5.33       => ( ( gcd_Gcd_nat @ M7 )
% 9.53/5.33          = ( gcd_Gcd_nat @ ( minus_minus_set_nat @ M7 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9776_pow_Osimps_I3_J,axiom,
% 9.53/5.33      ! [X: num,Y2: num] :
% 9.53/5.33        ( ( pow @ X @ ( bit1 @ Y2 ) )
% 9.53/5.33        = ( times_times_num @ ( sqr @ ( pow @ X @ Y2 ) ) @ X ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9777_Gcd__nat__eq__one,axiom,
% 9.53/5.33      ! [N4: set_nat] :
% 9.53/5.33        ( ( member_nat @ one_one_nat @ N4 )
% 9.53/5.33       => ( ( gcd_Gcd_nat @ N4 )
% 9.53/5.33          = one_one_nat ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9778_sqr_Osimps_I2_J,axiom,
% 9.53/5.33      ! [N: num] :
% 9.53/5.33        ( ( sqr @ ( bit0 @ N ) )
% 9.53/5.33        = ( bit0 @ ( bit0 @ ( sqr @ N ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9779_sqr_Osimps_I1_J,axiom,
% 9.53/5.33      ( ( sqr @ one )
% 9.53/5.33      = one ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9780_sqr__conv__mult,axiom,
% 9.53/5.33      ( sqr
% 9.53/5.33      = ( ^ [X2: num] : ( times_times_num @ X2 @ X2 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9781_pow_Osimps_I2_J,axiom,
% 9.53/5.33      ! [X: num,Y2: num] :
% 9.53/5.33        ( ( pow @ X @ ( bit0 @ Y2 ) )
% 9.53/5.33        = ( sqr @ ( pow @ X @ Y2 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9782_sqr_Osimps_I3_J,axiom,
% 9.53/5.33      ! [N: num] :
% 9.53/5.33        ( ( sqr @ ( bit1 @ N ) )
% 9.53/5.33        = ( bit1 @ ( bit0 @ ( plus_plus_num @ ( sqr @ N ) @ N ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9783_take__bit__numeral__minus__numeral__int,axiom,
% 9.53/5.33      ! [M: num,N: num] :
% 9.53/5.33        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.53/5.33        = ( case_option_int_num @ zero_zero_int
% 9.53/5.33          @ ^ [Q4: num] : ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_int @ Q4 ) ) )
% 9.53/5.33          @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9784_of__nat__eq__id,axiom,
% 9.53/5.33      semiri1316708129612266289at_nat = id_nat ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9785_take__bit__num__simps_I1_J,axiom,
% 9.53/5.33      ! [M: num] :
% 9.53/5.33        ( ( bit_take_bit_num @ zero_zero_nat @ M )
% 9.53/5.33        = none_num ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9786_take__bit__num__simps_I2_J,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( bit_take_bit_num @ ( suc @ N ) @ one )
% 9.53/5.33        = ( some_num @ one ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9787_take__bit__num__simps_I5_J,axiom,
% 9.53/5.33      ! [R: num] :
% 9.53/5.33        ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R ) @ one )
% 9.53/5.33        = ( some_num @ one ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9788_Code__Abstract__Nat_Otake__bit__num__code_I1_J,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( bit_take_bit_num @ N @ one )
% 9.53/5.33        = ( case_nat_option_num @ none_num
% 9.53/5.33          @ ^ [N2: nat] : ( some_num @ one )
% 9.53/5.33          @ N ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9789_less__int__def,axiom,
% 9.53/5.33      ( ord_less_int
% 9.53/5.33      = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 9.53/5.33        @ ( produc8739625826339149834_nat_o
% 9.53/5.33          @ ^ [X2: nat,Y: nat] :
% 9.53/5.33              ( produc6081775807080527818_nat_o
% 9.53/5.33              @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9790_less__eq__int__def,axiom,
% 9.53/5.33      ( ord_less_eq_int
% 9.53/5.33      = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 9.53/5.33        @ ( produc8739625826339149834_nat_o
% 9.53/5.33          @ ^ [X2: nat,Y: nat] :
% 9.53/5.33              ( produc6081775807080527818_nat_o
% 9.53/5.33              @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9791_nat__def,axiom,
% 9.53/5.33      ( nat2
% 9.53/5.33      = ( map_fu2345160673673942751at_nat @ rep_Integ @ id_nat @ ( produc6842872674320459806at_nat @ minus_minus_nat ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9792_take__bit__num__def,axiom,
% 9.53/5.33      ( bit_take_bit_num
% 9.53/5.33      = ( ^ [N2: nat,M6: num] :
% 9.53/5.33            ( if_option_num
% 9.53/5.33            @ ( ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ M6 ) )
% 9.53/5.33              = zero_zero_nat )
% 9.53/5.33            @ none_num
% 9.53/5.33            @ ( some_num @ ( num_of_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ M6 ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9793_and__minus__numerals_I3_J,axiom,
% 9.53/5.33      ! [M: num,N: num] :
% 9.53/5.33        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 9.53/5.33        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9794_and__minus__numerals_I7_J,axiom,
% 9.53/5.33      ! [N: num,M: num] :
% 9.53/5.33        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 9.53/5.33        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9795_and__minus__numerals_I4_J,axiom,
% 9.53/5.33      ! [M: num,N: num] :
% 9.53/5.33        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 9.53/5.33        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9796_take__bit__num__simps_I4_J,axiom,
% 9.53/5.33      ! [N: nat,M: num] :
% 9.53/5.33        ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit1 @ M ) )
% 9.53/5.33        = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N @ M ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9797_take__bit__num__simps_I3_J,axiom,
% 9.53/5.33      ! [N: nat,M: num] :
% 9.53/5.33        ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit0 @ M ) )
% 9.53/5.33        = ( case_o6005452278849405969um_num @ none_num
% 9.53/5.33          @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 9.53/5.33          @ ( bit_take_bit_num @ N @ M ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9798_take__bit__num__simps_I7_J,axiom,
% 9.53/5.33      ! [R: num,M: num] :
% 9.53/5.33        ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R ) @ ( bit1 @ M ) )
% 9.53/5.33        = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ ( pred_numeral @ R ) @ M ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9799_take__bit__num__simps_I6_J,axiom,
% 9.53/5.33      ! [R: num,M: num] :
% 9.53/5.33        ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R ) @ ( bit0 @ M ) )
% 9.53/5.33        = ( case_o6005452278849405969um_num @ none_num
% 9.53/5.33          @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 9.53/5.33          @ ( bit_take_bit_num @ ( pred_numeral @ R ) @ M ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9800_and__minus__numerals_I8_J,axiom,
% 9.53/5.33      ! [N: num,M: num] :
% 9.53/5.33        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 9.53/5.33        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9801_and__not__num_Osimps_I8_J,axiom,
% 9.53/5.33      ! [M: num,N: num] :
% 9.53/5.33        ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 9.53/5.33        = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 9.53/5.33          @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 9.53/5.33          @ ( bit_and_not_num @ M @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9802_and__not__num_Osimps_I1_J,axiom,
% 9.53/5.33      ( ( bit_and_not_num @ one @ one )
% 9.53/5.33      = none_num ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9803_and__not__num_Osimps_I4_J,axiom,
% 9.53/5.33      ! [M: num] :
% 9.53/5.33        ( ( bit_and_not_num @ ( bit0 @ M ) @ one )
% 9.53/5.33        = ( some_num @ ( bit0 @ M ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9804_and__not__num_Osimps_I2_J,axiom,
% 9.53/5.33      ! [N: num] :
% 9.53/5.33        ( ( bit_and_not_num @ one @ ( bit0 @ N ) )
% 9.53/5.33        = ( some_num @ one ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9805_and__not__num_Osimps_I3_J,axiom,
% 9.53/5.33      ! [N: num] :
% 9.53/5.33        ( ( bit_and_not_num @ one @ ( bit1 @ N ) )
% 9.53/5.33        = none_num ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9806_Code__Abstract__Nat_Otake__bit__num__code_I2_J,axiom,
% 9.53/5.33      ! [N: nat,M: num] :
% 9.53/5.33        ( ( bit_take_bit_num @ N @ ( bit0 @ M ) )
% 9.53/5.33        = ( case_nat_option_num @ none_num
% 9.53/5.33          @ ^ [N2: nat] :
% 9.53/5.33              ( case_o6005452278849405969um_num @ none_num
% 9.53/5.33              @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 9.53/5.33              @ ( bit_take_bit_num @ N2 @ M ) )
% 9.53/5.33          @ N ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9807_and__not__num_Osimps_I7_J,axiom,
% 9.53/5.33      ! [M: num] :
% 9.53/5.33        ( ( bit_and_not_num @ ( bit1 @ M ) @ one )
% 9.53/5.33        = ( some_num @ ( bit0 @ M ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9808_and__not__num__eq__Some__iff,axiom,
% 9.53/5.33      ! [M: num,N: num,Q2: num] :
% 9.53/5.33        ( ( ( bit_and_not_num @ M @ N )
% 9.53/5.33          = ( some_num @ Q2 ) )
% 9.53/5.33        = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 9.53/5.33          = ( numeral_numeral_int @ Q2 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9809_Code__Abstract__Nat_Otake__bit__num__code_I3_J,axiom,
% 9.53/5.33      ! [N: nat,M: num] :
% 9.53/5.33        ( ( bit_take_bit_num @ N @ ( bit1 @ M ) )
% 9.53/5.33        = ( case_nat_option_num @ none_num
% 9.53/5.33          @ ^ [N2: nat] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N2 @ M ) ) )
% 9.53/5.33          @ N ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9810_and__not__num__eq__None__iff,axiom,
% 9.53/5.33      ! [M: num,N: num] :
% 9.53/5.33        ( ( ( bit_and_not_num @ M @ N )
% 9.53/5.33          = none_num )
% 9.53/5.33        = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 9.53/5.33          = zero_zero_int ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9811_int__numeral__and__not__num,axiom,
% 9.53/5.33      ! [M: num,N: num] :
% 9.53/5.33        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 9.53/5.33        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9812_int__numeral__not__and__num,axiom,
% 9.53/5.33      ! [M: num,N: num] :
% 9.53/5.33        ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 9.53/5.33        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ N @ M ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9813_Bit__Operations_Otake__bit__num__code,axiom,
% 9.53/5.33      ( bit_take_bit_num
% 9.53/5.33      = ( ^ [N2: nat,M6: num] :
% 9.53/5.33            ( produc478579273971653890on_num
% 9.53/5.33            @ ^ [A3: nat,X2: num] :
% 9.53/5.33                ( case_nat_option_num @ none_num
% 9.53/5.33                @ ^ [O: nat] :
% 9.53/5.33                    ( case_num_option_num @ ( some_num @ one )
% 9.53/5.33                    @ ^ [P4: num] :
% 9.53/5.33                        ( case_o6005452278849405969um_num @ none_num
% 9.53/5.33                        @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 9.53/5.33                        @ ( bit_take_bit_num @ O @ P4 ) )
% 9.53/5.33                    @ ^ [P4: num] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ O @ P4 ) ) )
% 9.53/5.33                    @ X2 )
% 9.53/5.33                @ A3 )
% 9.53/5.33            @ ( product_Pair_nat_num @ N2 @ M6 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9814_and__not__num_Oelims,axiom,
% 9.53/5.33      ! [X: num,Xa2: num,Y2: option_num] :
% 9.53/5.33        ( ( ( bit_and_not_num @ X @ Xa2 )
% 9.53/5.33          = Y2 )
% 9.53/5.33       => ( ( ( X = one )
% 9.53/5.33           => ( ( Xa2 = one )
% 9.53/5.33             => ( Y2 != none_num ) ) )
% 9.53/5.33         => ( ( ( X = one )
% 9.53/5.33             => ( ? [N3: num] :
% 9.53/5.33                    ( Xa2
% 9.53/5.33                    = ( bit0 @ N3 ) )
% 9.53/5.33               => ( Y2
% 9.53/5.33                 != ( some_num @ one ) ) ) )
% 9.53/5.33           => ( ( ( X = one )
% 9.53/5.33               => ( ? [N3: num] :
% 9.53/5.33                      ( Xa2
% 9.53/5.33                      = ( bit1 @ N3 ) )
% 9.53/5.33                 => ( Y2 != none_num ) ) )
% 9.53/5.33             => ( ! [M4: num] :
% 9.53/5.33                    ( ( X
% 9.53/5.33                      = ( bit0 @ M4 ) )
% 9.53/5.33                   => ( ( Xa2 = one )
% 9.53/5.33                     => ( Y2
% 9.53/5.33                       != ( some_num @ ( bit0 @ M4 ) ) ) ) )
% 9.53/5.33               => ( ! [M4: num] :
% 9.53/5.33                      ( ( X
% 9.53/5.33                        = ( bit0 @ M4 ) )
% 9.53/5.33                     => ! [N3: num] :
% 9.53/5.33                          ( ( Xa2
% 9.53/5.33                            = ( bit0 @ N3 ) )
% 9.53/5.33                         => ( Y2
% 9.53/5.33                           != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N3 ) ) ) ) )
% 9.53/5.33                 => ( ! [M4: num] :
% 9.53/5.33                        ( ( X
% 9.53/5.33                          = ( bit0 @ M4 ) )
% 9.53/5.33                       => ! [N3: num] :
% 9.53/5.33                            ( ( Xa2
% 9.53/5.33                              = ( bit1 @ N3 ) )
% 9.53/5.33                           => ( Y2
% 9.53/5.33                             != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N3 ) ) ) ) )
% 9.53/5.33                   => ( ! [M4: num] :
% 9.53/5.33                          ( ( X
% 9.53/5.33                            = ( bit1 @ M4 ) )
% 9.53/5.33                         => ( ( Xa2 = one )
% 9.53/5.33                           => ( Y2
% 9.53/5.33                             != ( some_num @ ( bit0 @ M4 ) ) ) ) )
% 9.53/5.33                     => ( ! [M4: num] :
% 9.53/5.33                            ( ( X
% 9.53/5.33                              = ( bit1 @ M4 ) )
% 9.53/5.33                           => ! [N3: num] :
% 9.53/5.33                                ( ( Xa2
% 9.53/5.33                                  = ( bit0 @ N3 ) )
% 9.53/5.33                               => ( Y2
% 9.53/5.33                                 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 9.53/5.33                                    @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 9.53/5.33                                    @ ( bit_and_not_num @ M4 @ N3 ) ) ) ) )
% 9.53/5.33                       => ~ ! [M4: num] :
% 9.53/5.33                              ( ( X
% 9.53/5.33                                = ( bit1 @ M4 ) )
% 9.53/5.33                             => ! [N3: num] :
% 9.53/5.33                                  ( ( Xa2
% 9.53/5.33                                    = ( bit1 @ N3 ) )
% 9.53/5.33                                 => ( Y2
% 9.53/5.33                                   != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9815_and__not__num_Osimps_I5_J,axiom,
% 9.53/5.33      ! [M: num,N: num] :
% 9.53/5.33        ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 9.53/5.33        = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9816_and__not__num_Osimps_I6_J,axiom,
% 9.53/5.33      ! [M: num,N: num] :
% 9.53/5.33        ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 9.53/5.33        = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9817_and__not__num_Osimps_I9_J,axiom,
% 9.53/5.33      ! [M: num,N: num] :
% 9.53/5.33        ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 9.53/5.33        = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9818_and__num_Oelims,axiom,
% 9.53/5.33      ! [X: num,Xa2: num,Y2: option_num] :
% 9.53/5.33        ( ( ( bit_un7362597486090784418nd_num @ X @ Xa2 )
% 9.53/5.33          = Y2 )
% 9.53/5.33       => ( ( ( X = one )
% 9.53/5.33           => ( ( Xa2 = one )
% 9.53/5.33             => ( Y2
% 9.53/5.33               != ( some_num @ one ) ) ) )
% 9.53/5.33         => ( ( ( X = one )
% 9.53/5.33             => ( ? [N3: num] :
% 9.53/5.33                    ( Xa2
% 9.53/5.33                    = ( bit0 @ N3 ) )
% 9.53/5.33               => ( Y2 != none_num ) ) )
% 9.53/5.33           => ( ( ( X = one )
% 9.53/5.33               => ( ? [N3: num] :
% 9.53/5.33                      ( Xa2
% 9.53/5.33                      = ( bit1 @ N3 ) )
% 9.53/5.33                 => ( Y2
% 9.53/5.33                   != ( some_num @ one ) ) ) )
% 9.53/5.33             => ( ( ? [M4: num] :
% 9.53/5.33                      ( X
% 9.53/5.33                      = ( bit0 @ M4 ) )
% 9.53/5.33                 => ( ( Xa2 = one )
% 9.53/5.33                   => ( Y2 != none_num ) ) )
% 9.53/5.33               => ( ! [M4: num] :
% 9.53/5.33                      ( ( X
% 9.53/5.33                        = ( bit0 @ M4 ) )
% 9.53/5.33                     => ! [N3: num] :
% 9.53/5.33                          ( ( Xa2
% 9.53/5.33                            = ( bit0 @ N3 ) )
% 9.53/5.33                         => ( Y2
% 9.53/5.33                           != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) ) ) )
% 9.53/5.33                 => ( ! [M4: num] :
% 9.53/5.33                        ( ( X
% 9.53/5.33                          = ( bit0 @ M4 ) )
% 9.53/5.33                       => ! [N3: num] :
% 9.53/5.33                            ( ( Xa2
% 9.53/5.33                              = ( bit1 @ N3 ) )
% 9.53/5.33                           => ( Y2
% 9.53/5.33                             != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) ) ) )
% 9.53/5.33                   => ( ( ? [M4: num] :
% 9.53/5.33                            ( X
% 9.53/5.33                            = ( bit1 @ M4 ) )
% 9.53/5.33                       => ( ( Xa2 = one )
% 9.53/5.33                         => ( Y2
% 9.53/5.33                           != ( some_num @ one ) ) ) )
% 9.53/5.33                     => ( ! [M4: num] :
% 9.53/5.33                            ( ( X
% 9.53/5.33                              = ( bit1 @ M4 ) )
% 9.53/5.33                           => ! [N3: num] :
% 9.53/5.33                                ( ( Xa2
% 9.53/5.33                                  = ( bit0 @ N3 ) )
% 9.53/5.33                               => ( Y2
% 9.53/5.33                                 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) ) ) )
% 9.53/5.33                       => ~ ! [M4: num] :
% 9.53/5.33                              ( ( X
% 9.53/5.33                                = ( bit1 @ M4 ) )
% 9.53/5.33                             => ! [N3: num] :
% 9.53/5.33                                  ( ( Xa2
% 9.53/5.33                                    = ( bit1 @ N3 ) )
% 9.53/5.33                                 => ( Y2
% 9.53/5.33                                   != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 9.53/5.33                                      @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 9.53/5.33                                      @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9819_xor__num_Oelims,axiom,
% 9.53/5.33      ! [X: num,Xa2: num,Y2: option_num] :
% 9.53/5.33        ( ( ( bit_un2480387367778600638or_num @ X @ Xa2 )
% 9.53/5.33          = Y2 )
% 9.53/5.33       => ( ( ( X = one )
% 9.53/5.33           => ( ( Xa2 = one )
% 9.53/5.33             => ( Y2 != none_num ) ) )
% 9.53/5.33         => ( ( ( X = one )
% 9.53/5.33             => ! [N3: num] :
% 9.53/5.33                  ( ( Xa2
% 9.53/5.33                    = ( bit0 @ N3 ) )
% 9.53/5.33                 => ( Y2
% 9.53/5.33                   != ( some_num @ ( bit1 @ N3 ) ) ) ) )
% 9.53/5.33           => ( ( ( X = one )
% 9.53/5.33               => ! [N3: num] :
% 9.53/5.33                    ( ( Xa2
% 9.53/5.33                      = ( bit1 @ N3 ) )
% 9.53/5.33                   => ( Y2
% 9.53/5.33                     != ( some_num @ ( bit0 @ N3 ) ) ) ) )
% 9.53/5.33             => ( ! [M4: num] :
% 9.53/5.33                    ( ( X
% 9.53/5.33                      = ( bit0 @ M4 ) )
% 9.53/5.33                   => ( ( Xa2 = one )
% 9.53/5.33                     => ( Y2
% 9.53/5.33                       != ( some_num @ ( bit1 @ M4 ) ) ) ) )
% 9.53/5.33               => ( ! [M4: num] :
% 9.53/5.33                      ( ( X
% 9.53/5.33                        = ( bit0 @ M4 ) )
% 9.53/5.33                     => ! [N3: num] :
% 9.53/5.33                          ( ( Xa2
% 9.53/5.33                            = ( bit0 @ N3 ) )
% 9.53/5.33                         => ( Y2
% 9.53/5.33                           != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) ) ) )
% 9.53/5.33                 => ( ! [M4: num] :
% 9.53/5.33                        ( ( X
% 9.53/5.33                          = ( bit0 @ M4 ) )
% 9.53/5.33                       => ! [N3: num] :
% 9.53/5.33                            ( ( Xa2
% 9.53/5.33                              = ( bit1 @ N3 ) )
% 9.53/5.33                           => ( Y2
% 9.53/5.33                             != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) ) ) ) )
% 9.53/5.33                   => ( ! [M4: num] :
% 9.53/5.33                          ( ( X
% 9.53/5.33                            = ( bit1 @ M4 ) )
% 9.53/5.33                         => ( ( Xa2 = one )
% 9.53/5.33                           => ( Y2
% 9.53/5.33                             != ( some_num @ ( bit0 @ M4 ) ) ) ) )
% 9.53/5.33                     => ( ! [M4: num] :
% 9.53/5.33                            ( ( X
% 9.53/5.33                              = ( bit1 @ M4 ) )
% 9.53/5.33                           => ! [N3: num] :
% 9.53/5.33                                ( ( Xa2
% 9.53/5.33                                  = ( bit0 @ N3 ) )
% 9.53/5.33                               => ( Y2
% 9.53/5.33                                 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) ) ) ) )
% 9.53/5.33                       => ~ ! [M4: num] :
% 9.53/5.33                              ( ( X
% 9.53/5.33                                = ( bit1 @ M4 ) )
% 9.53/5.33                             => ! [N3: num] :
% 9.53/5.33                                  ( ( Xa2
% 9.53/5.33                                    = ( bit1 @ N3 ) )
% 9.53/5.33                                 => ( Y2
% 9.53/5.33                                   != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9820_xor__num_Osimps_I8_J,axiom,
% 9.53/5.33      ! [M: num,N: num] :
% 9.53/5.33        ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 9.53/5.33        = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9821_and__num_Osimps_I1_J,axiom,
% 9.53/5.33      ( ( bit_un7362597486090784418nd_num @ one @ one )
% 9.53/5.33      = ( some_num @ one ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9822_xor__num_Osimps_I1_J,axiom,
% 9.53/5.33      ( ( bit_un2480387367778600638or_num @ one @ one )
% 9.53/5.33      = none_num ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9823_xor__num_Osimps_I5_J,axiom,
% 9.53/5.33      ! [M: num,N: num] :
% 9.53/5.33        ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 9.53/5.33        = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9824_and__num_Osimps_I5_J,axiom,
% 9.53/5.33      ! [M: num,N: num] :
% 9.53/5.33        ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 9.53/5.33        = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9825_and__num_Osimps_I3_J,axiom,
% 9.53/5.33      ! [N: num] :
% 9.53/5.33        ( ( bit_un7362597486090784418nd_num @ one @ ( bit1 @ N ) )
% 9.53/5.33        = ( some_num @ one ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9826_and__num_Osimps_I7_J,axiom,
% 9.53/5.33      ! [M: num] :
% 9.53/5.33        ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ one )
% 9.53/5.33        = ( some_num @ one ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9827_and__num_Osimps_I2_J,axiom,
% 9.53/5.33      ! [N: num] :
% 9.53/5.33        ( ( bit_un7362597486090784418nd_num @ one @ ( bit0 @ N ) )
% 9.53/5.33        = none_num ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9828_and__num_Osimps_I4_J,axiom,
% 9.53/5.33      ! [M: num] :
% 9.53/5.33        ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ one )
% 9.53/5.33        = none_num ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9829_and__num_Osimps_I8_J,axiom,
% 9.53/5.33      ! [M: num,N: num] :
% 9.53/5.33        ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 9.53/5.33        = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9830_and__num_Osimps_I6_J,axiom,
% 9.53/5.33      ! [M: num,N: num] :
% 9.53/5.33        ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 9.53/5.33        = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9831_xor__num_Osimps_I9_J,axiom,
% 9.53/5.33      ! [M: num,N: num] :
% 9.53/5.33        ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 9.53/5.33        = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9832_xor__num_Osimps_I2_J,axiom,
% 9.53/5.33      ! [N: num] :
% 9.53/5.33        ( ( bit_un2480387367778600638or_num @ one @ ( bit0 @ N ) )
% 9.53/5.33        = ( some_num @ ( bit1 @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9833_xor__num_Osimps_I3_J,axiom,
% 9.53/5.33      ! [N: num] :
% 9.53/5.33        ( ( bit_un2480387367778600638or_num @ one @ ( bit1 @ N ) )
% 9.53/5.33        = ( some_num @ ( bit0 @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9834_xor__num_Osimps_I4_J,axiom,
% 9.53/5.33      ! [M: num] :
% 9.53/5.33        ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ one )
% 9.53/5.33        = ( some_num @ ( bit1 @ M ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9835_xor__num_Osimps_I7_J,axiom,
% 9.53/5.33      ! [M: num] :
% 9.53/5.33        ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ one )
% 9.53/5.33        = ( some_num @ ( bit0 @ M ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9836_and__num_Osimps_I9_J,axiom,
% 9.53/5.33      ! [M: num,N: num] :
% 9.53/5.33        ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 9.53/5.33        = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 9.53/5.33          @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 9.53/5.33          @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9837_xor__num_Osimps_I6_J,axiom,
% 9.53/5.33      ! [M: num,N: num] :
% 9.53/5.33        ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 9.53/5.33        = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9838_xor__num__dict,axiom,
% 9.53/5.33      bit_un2480387367778600638or_num = bit_un6178654185764691216or_num ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9839_and__num__dict,axiom,
% 9.53/5.33      bit_un7362597486090784418nd_num = bit_un1837492267222099188nd_num ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9840_min__Suc__Suc,axiom,
% 9.53/5.33      ! [M: nat,N: nat] :
% 9.53/5.33        ( ( ord_min_nat @ ( suc @ M ) @ ( suc @ N ) )
% 9.53/5.33        = ( suc @ ( ord_min_nat @ M @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9841_min__0R,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( ord_min_nat @ N @ zero_zero_nat )
% 9.53/5.33        = zero_zero_nat ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9842_min__0L,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( ord_min_nat @ zero_zero_nat @ N )
% 9.53/5.33        = zero_zero_nat ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9843_min__numeral__Suc,axiom,
% 9.53/5.33      ! [K: num,N: nat] :
% 9.53/5.33        ( ( ord_min_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 9.53/5.33        = ( suc @ ( ord_min_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9844_min__Suc__numeral,axiom,
% 9.53/5.33      ! [N: nat,K: num] :
% 9.53/5.33        ( ( ord_min_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 9.53/5.33        = ( suc @ ( ord_min_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9845_min__diff,axiom,
% 9.53/5.33      ! [M: nat,I2: nat,N: nat] :
% 9.53/5.33        ( ( ord_min_nat @ ( minus_minus_nat @ M @ I2 ) @ ( minus_minus_nat @ N @ I2 ) )
% 9.53/5.33        = ( minus_minus_nat @ ( ord_min_nat @ M @ N ) @ I2 ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9846_nat__mult__min__right,axiom,
% 9.53/5.33      ! [M: nat,N: nat,Q2: nat] :
% 9.53/5.33        ( ( times_times_nat @ M @ ( ord_min_nat @ N @ Q2 ) )
% 9.53/5.33        = ( ord_min_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q2 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9847_nat__mult__min__left,axiom,
% 9.53/5.33      ! [M: nat,N: nat,Q2: nat] :
% 9.53/5.33        ( ( times_times_nat @ ( ord_min_nat @ M @ N ) @ Q2 )
% 9.53/5.33        = ( ord_min_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N @ Q2 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9848_concat__bit__assoc__sym,axiom,
% 9.53/5.33      ! [M: nat,N: nat,K: int,L2: int,R: int] :
% 9.53/5.33        ( ( bit_concat_bit @ M @ ( bit_concat_bit @ N @ K @ L2 ) @ R )
% 9.53/5.33        = ( bit_concat_bit @ ( ord_min_nat @ M @ N ) @ K @ ( bit_concat_bit @ ( minus_minus_nat @ M @ N ) @ L2 @ R ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9849_take__bit__concat__bit__eq,axiom,
% 9.53/5.33      ! [M: nat,N: nat,K: int,L2: int] :
% 9.53/5.33        ( ( bit_se2923211474154528505it_int @ M @ ( bit_concat_bit @ N @ K @ L2 ) )
% 9.53/5.33        = ( bit_concat_bit @ ( ord_min_nat @ M @ N ) @ K @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ M @ N ) @ L2 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9850_min__Suc2,axiom,
% 9.53/5.33      ! [M: nat,N: nat] :
% 9.53/5.33        ( ( ord_min_nat @ M @ ( suc @ N ) )
% 9.53/5.33        = ( case_nat_nat @ zero_zero_nat
% 9.53/5.33          @ ^ [M2: nat] : ( suc @ ( ord_min_nat @ M2 @ N ) )
% 9.53/5.33          @ M ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9851_min__Suc1,axiom,
% 9.53/5.33      ! [N: nat,M: nat] :
% 9.53/5.33        ( ( ord_min_nat @ ( suc @ N ) @ M )
% 9.53/5.33        = ( case_nat_nat @ zero_zero_nat
% 9.53/5.33          @ ^ [M2: nat] : ( suc @ ( ord_min_nat @ N @ M2 ) )
% 9.53/5.33          @ M ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9852_min__enat__simps_I2_J,axiom,
% 9.53/5.33      ! [Q2: extended_enat] :
% 9.53/5.33        ( ( ord_mi8085742599997312461d_enat @ Q2 @ zero_z5237406670263579293d_enat )
% 9.53/5.33        = zero_z5237406670263579293d_enat ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9853_min__enat__simps_I3_J,axiom,
% 9.53/5.33      ! [Q2: extended_enat] :
% 9.53/5.33        ( ( ord_mi8085742599997312461d_enat @ zero_z5237406670263579293d_enat @ Q2 )
% 9.53/5.33        = zero_z5237406670263579293d_enat ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9854_divmod__integer__eq__cases,axiom,
% 9.53/5.33      ( code_divmod_integer
% 9.53/5.33      = ( ^ [K3: code_integer,L: code_integer] :
% 9.53/5.33            ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 9.53/5.33            @ ( if_Pro6119634080678213985nteger @ ( L = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 9.53/5.33              @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L
% 9.53/5.33                @ ( if_Pro6119634080678213985nteger
% 9.53/5.33                  @ ( ( sgn_sgn_Code_integer @ K3 )
% 9.53/5.33                    = ( sgn_sgn_Code_integer @ L ) )
% 9.53/5.33                  @ ( code_divmod_abs @ K3 @ L )
% 9.53/5.33                  @ ( produc6916734918728496179nteger
% 9.53/5.33                    @ ^ [R5: code_integer,S6: code_integer] : ( if_Pro6119634080678213985nteger @ ( S6 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ L ) @ S6 ) ) )
% 9.53/5.33                    @ ( code_divmod_abs @ K3 @ L ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9855_sorted__list__of__set__greaterThanAtMost,axiom,
% 9.53/5.33      ! [I2: nat,J: nat] :
% 9.53/5.33        ( ( ord_less_eq_nat @ ( suc @ I2 ) @ J )
% 9.53/5.33       => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I2 @ J ) )
% 9.53/5.33          = ( cons_nat @ ( suc @ I2 ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I2 ) @ J ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9856_sorted__list__of__set__greaterThanLessThan,axiom,
% 9.53/5.33      ! [I2: nat,J: nat] :
% 9.53/5.33        ( ( ord_less_nat @ ( suc @ I2 ) @ J )
% 9.53/5.33       => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I2 @ J ) )
% 9.53/5.33          = ( cons_nat @ ( suc @ I2 ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I2 ) @ J ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9857_card_Ocomp__fun__commute__on,axiom,
% 9.53/5.33      ( ( comp_nat_nat_nat @ suc @ suc )
% 9.53/5.33      = ( comp_nat_nat_nat @ suc @ suc ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9858_Code__Target__Int_Onegative__def,axiom,
% 9.53/5.33      ( code_Target_negative
% 9.53/5.33      = ( comp_int_int_num @ uminus_uminus_int @ numeral_numeral_int ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9859_upto__aux__rec,axiom,
% 9.53/5.33      ( upto_aux
% 9.53/5.33      = ( ^ [I3: int,J3: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J3 @ I3 ) @ Js @ ( upto_aux @ I3 @ ( minus_minus_int @ J3 @ one_one_int ) @ ( cons_int @ J3 @ Js ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9860_Inf__real__def,axiom,
% 9.53/5.33      ( comple4887499456419720421f_real
% 9.53/5.33      = ( ^ [X4: set_real] : ( uminus_uminus_real @ ( comple1385675409528146559p_real @ ( image_real_real @ uminus_uminus_real @ X4 ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9861_range__mod,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( image_nat_nat
% 9.53/5.33            @ ^ [M6: nat] : ( modulo_modulo_nat @ M6 @ N )
% 9.53/5.33            @ top_top_set_nat )
% 9.53/5.33          = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9862_suminf__eq__SUP__real,axiom,
% 9.53/5.33      ! [X8: nat > real] :
% 9.53/5.33        ( ( summable_real @ X8 )
% 9.53/5.33       => ( ! [I4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( X8 @ I4 ) )
% 9.53/5.33         => ( ( suminf_real @ X8 )
% 9.53/5.33            = ( comple1385675409528146559p_real
% 9.53/5.33              @ ( image_nat_real
% 9.53/5.33                @ ^ [I3: nat] : ( groups6591440286371151544t_real @ X8 @ ( set_ord_lessThan_nat @ I3 ) )
% 9.53/5.33                @ top_top_set_nat ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9863_UNIV__nat__eq,axiom,
% 9.53/5.33      ( top_top_set_nat
% 9.53/5.33      = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ top_top_set_nat ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9864_card__UNIV__unit,axiom,
% 9.53/5.33      ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 9.53/5.33      = one_one_nat ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9865_card__UNIV__bool,axiom,
% 9.53/5.33      ( ( finite_card_o @ top_top_set_o )
% 9.53/5.33      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9866_range__mult,axiom,
% 9.53/5.33      ! [A: real] :
% 9.53/5.33        ( ( ( A = zero_zero_real )
% 9.53/5.33         => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 9.53/5.33            = ( insert_real @ zero_zero_real @ bot_bot_set_real ) ) )
% 9.53/5.33        & ( ( A != zero_zero_real )
% 9.53/5.33         => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 9.53/5.33            = top_top_set_real ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9867_root__def,axiom,
% 9.53/5.33      ( root
% 9.53/5.33      = ( ^ [N2: nat,X2: real] :
% 9.53/5.33            ( if_real @ ( N2 = zero_zero_nat ) @ zero_zero_real
% 9.53/5.33            @ ( the_in5290026491893676941l_real @ top_top_set_real
% 9.53/5.33              @ ^ [Y: real] : ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N2 ) )
% 9.53/5.33              @ X2 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9868_inf__enat__def,axiom,
% 9.53/5.33      inf_in1870772243966228564d_enat = ord_mi8085742599997312461d_enat ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9869_inf__nat__def,axiom,
% 9.53/5.33      inf_inf_nat = ord_min_nat ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9870_card__UNIV__char,axiom,
% 9.53/5.33      ( ( finite_card_char @ top_top_set_char )
% 9.53/5.33      = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9871_UNIV__char__of__nat,axiom,
% 9.53/5.33      ( top_top_set_char
% 9.53/5.33      = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9872_sorted__list__of__set__lessThan__Suc,axiom,
% 9.53/5.33      ! [K: nat] :
% 9.53/5.33        ( ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ ( suc @ K ) ) )
% 9.53/5.33        = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ K ) ) @ ( cons_nat @ K @ nil_nat ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9873_sorted__list__of__set__atMost__Suc,axiom,
% 9.53/5.33      ! [K: nat] :
% 9.53/5.33        ( ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ ( suc @ K ) ) )
% 9.53/5.33        = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ K ) ) @ ( cons_nat @ ( suc @ K ) @ nil_nat ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9874_nat__of__char__less__256,axiom,
% 9.53/5.33      ! [C: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9875_range__nat__of__char,axiom,
% 9.53/5.33      ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 9.53/5.33      = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9876_integer__of__char__code,axiom,
% 9.53/5.33      ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B72: $o] :
% 9.53/5.33        ( ( integer_of_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B72 ) )
% 9.53/5.33        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ B72 ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B62 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B52 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B42 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B32 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B22 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B1 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B0 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9877_list__encode_Oelims,axiom,
% 9.53/5.33      ! [X: list_nat,Y2: nat] :
% 9.53/5.33        ( ( ( nat_list_encode @ X )
% 9.53/5.33          = Y2 )
% 9.53/5.33       => ( ( ( X = nil_nat )
% 9.53/5.33           => ( Y2 != zero_zero_nat ) )
% 9.53/5.33         => ~ ! [X3: nat,Xs3: list_nat] :
% 9.53/5.33                ( ( X
% 9.53/5.33                  = ( cons_nat @ X3 @ Xs3 ) )
% 9.53/5.33               => ( Y2
% 9.53/5.33                 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X3 @ ( nat_list_encode @ Xs3 ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9878_list__encode_Osimps_I2_J,axiom,
% 9.53/5.33      ! [X: nat,Xs2: list_nat] :
% 9.53/5.33        ( ( nat_list_encode @ ( cons_nat @ X @ Xs2 ) )
% 9.53/5.33        = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X @ ( nat_list_encode @ Xs2 ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9879_String_Ochar__of__ascii__of,axiom,
% 9.53/5.33      ! [C: char] :
% 9.53/5.33        ( ( comm_s629917340098488124ar_nat @ ( ascii_of @ C ) )
% 9.53/5.33        = ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( comm_s629917340098488124ar_nat @ C ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9880_upto__rec__numeral_I4_J,axiom,
% 9.53/5.33      ! [M: num,N: num] :
% 9.53/5.33        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.53/5.33         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.53/5.33            = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 9.53/5.33        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.53/5.33         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.53/5.33            = nil_int ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9881_length__upto,axiom,
% 9.53/5.33      ! [I2: int,J: int] :
% 9.53/5.33        ( ( size_size_list_int @ ( upto @ I2 @ J ) )
% 9.53/5.33        = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J @ I2 ) @ one_one_int ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9882_upto__rec__numeral_I1_J,axiom,
% 9.53/5.33      ! [M: num,N: num] :
% 9.53/5.33        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 9.53/5.33         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 9.53/5.33            = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 9.53/5.33        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 9.53/5.33         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 9.53/5.33            = nil_int ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9883_upto__rec__numeral_I2_J,axiom,
% 9.53/5.33      ! [M: num,N: num] :
% 9.53/5.33        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.53/5.33         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.53/5.33            = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 9.53/5.33        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.53/5.33         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.53/5.33            = nil_int ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9884_upto__rec__numeral_I3_J,axiom,
% 9.53/5.33      ! [M: num,N: num] :
% 9.53/5.33        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 9.53/5.33         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 9.53/5.33            = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 9.53/5.33        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 9.53/5.33         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 9.53/5.33            = nil_int ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9885_upto__split1,axiom,
% 9.53/5.33      ! [I2: int,J: int,K: int] :
% 9.53/5.33        ( ( ord_less_eq_int @ I2 @ J )
% 9.53/5.33       => ( ( ord_less_eq_int @ J @ K )
% 9.53/5.33         => ( ( upto @ I2 @ K )
% 9.53/5.33            = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9886_atLeastLessThan__upto,axiom,
% 9.53/5.33      ( set_or4662586982721622107an_int
% 9.53/5.33      = ( ^ [I3: int,J3: int] : ( set_int2 @ ( upto @ I3 @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9887_upto__rec2,axiom,
% 9.53/5.33      ! [I2: int,J: int] :
% 9.53/5.33        ( ( ord_less_eq_int @ I2 @ J )
% 9.53/5.33       => ( ( upto @ I2 @ J )
% 9.53/5.33          = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9888_greaterThanLessThan__upto,axiom,
% 9.53/5.33      ( set_or5832277885323065728an_int
% 9.53/5.33      = ( ^ [I3: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9889_upto__split3,axiom,
% 9.53/5.33      ! [I2: int,J: int,K: int] :
% 9.53/5.33        ( ( ord_less_eq_int @ I2 @ J )
% 9.53/5.33       => ( ( ord_less_eq_int @ J @ K )
% 9.53/5.33         => ( ( upto @ I2 @ K )
% 9.53/5.33            = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9890_DERIV__real__root__generic,axiom,
% 9.53/5.33      ! [N: nat,X: real,D4: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( X != zero_zero_real )
% 9.53/5.33         => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.53/5.33             => ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.33               => ( D4
% 9.53/5.33                  = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) )
% 9.53/5.33           => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.53/5.33               => ( ( ord_less_real @ X @ zero_zero_real )
% 9.53/5.33                 => ( D4
% 9.53/5.33                    = ( uminus_uminus_real @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ) )
% 9.53/5.33             => ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.53/5.33                 => ( D4
% 9.53/5.33                    = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) )
% 9.53/5.33               => ( has_fi5821293074295781190e_real @ ( root @ N ) @ D4 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9891_DERIV__pos__imp__increasing,axiom,
% 9.53/5.33      ! [A: real,B: real,F: real > real] :
% 9.53/5.33        ( ( ord_less_real @ A @ B )
% 9.53/5.33       => ( ! [X3: real] :
% 9.53/5.33              ( ( ord_less_eq_real @ A @ X3 )
% 9.53/5.33             => ( ( ord_less_eq_real @ X3 @ B )
% 9.53/5.33               => ? [Y4: real] :
% 9.53/5.33                    ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 9.53/5.33                    & ( ord_less_real @ zero_zero_real @ Y4 ) ) ) )
% 9.53/5.33         => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9892_DERIV__neg__imp__decreasing,axiom,
% 9.53/5.33      ! [A: real,B: real,F: real > real] :
% 9.53/5.33        ( ( ord_less_real @ A @ B )
% 9.53/5.33       => ( ! [X3: real] :
% 9.53/5.33              ( ( ord_less_eq_real @ A @ X3 )
% 9.53/5.33             => ( ( ord_less_eq_real @ X3 @ B )
% 9.53/5.33               => ? [Y4: real] :
% 9.53/5.33                    ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 9.53/5.33                    & ( ord_less_real @ Y4 @ zero_zero_real ) ) ) )
% 9.53/5.33         => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9893_deriv__nonneg__imp__mono,axiom,
% 9.53/5.33      ! [A: real,B: real,G: real > real,G2: real > real] :
% 9.53/5.33        ( ! [X3: real] :
% 9.53/5.33            ( ( member_real @ X3 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 9.53/5.33           => ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 9.53/5.33       => ( ! [X3: real] :
% 9.53/5.33              ( ( member_real @ X3 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 9.53/5.33             => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X3 ) ) )
% 9.53/5.33         => ( ( ord_less_eq_real @ A @ B )
% 9.53/5.33           => ( ord_less_eq_real @ ( G @ A ) @ ( G @ B ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9894_DERIV__nonneg__imp__nondecreasing,axiom,
% 9.53/5.33      ! [A: real,B: real,F: real > real] :
% 9.53/5.33        ( ( ord_less_eq_real @ A @ B )
% 9.53/5.33       => ( ! [X3: real] :
% 9.53/5.33              ( ( ord_less_eq_real @ A @ X3 )
% 9.53/5.33             => ( ( ord_less_eq_real @ X3 @ B )
% 9.53/5.33               => ? [Y4: real] :
% 9.53/5.33                    ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 9.53/5.33                    & ( ord_less_eq_real @ zero_zero_real @ Y4 ) ) ) )
% 9.53/5.33         => ( ord_less_eq_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9895_DERIV__nonpos__imp__nonincreasing,axiom,
% 9.53/5.33      ! [A: real,B: real,F: real > real] :
% 9.53/5.33        ( ( ord_less_eq_real @ A @ B )
% 9.53/5.33       => ( ! [X3: real] :
% 9.53/5.33              ( ( ord_less_eq_real @ A @ X3 )
% 9.53/5.33             => ( ( ord_less_eq_real @ X3 @ B )
% 9.53/5.33               => ? [Y4: real] :
% 9.53/5.33                    ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 9.53/5.33                    & ( ord_less_eq_real @ Y4 @ zero_zero_real ) ) ) )
% 9.53/5.33         => ( ord_less_eq_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9896_DERIV__pos__inc__left,axiom,
% 9.53/5.33      ! [F: real > real,L2: real,X: real] :
% 9.53/5.33        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 9.53/5.33       => ( ( ord_less_real @ zero_zero_real @ L2 )
% 9.53/5.33         => ? [D3: real] :
% 9.53/5.33              ( ( ord_less_real @ zero_zero_real @ D3 )
% 9.53/5.33              & ! [H4: real] :
% 9.53/5.33                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 9.53/5.33                 => ( ( ord_less_real @ H4 @ D3 )
% 9.53/5.33                   => ( ord_less_real @ ( F @ ( minus_minus_real @ X @ H4 ) ) @ ( F @ X ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9897_DERIV__neg__dec__left,axiom,
% 9.53/5.33      ! [F: real > real,L2: real,X: real] :
% 9.53/5.33        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 9.53/5.33       => ( ( ord_less_real @ L2 @ zero_zero_real )
% 9.53/5.33         => ? [D3: real] :
% 9.53/5.33              ( ( ord_less_real @ zero_zero_real @ D3 )
% 9.53/5.33              & ! [H4: real] :
% 9.53/5.33                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 9.53/5.33                 => ( ( ord_less_real @ H4 @ D3 )
% 9.53/5.33                   => ( ord_less_real @ ( F @ X ) @ ( F @ ( minus_minus_real @ X @ H4 ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9898_DERIV__pos__inc__right,axiom,
% 9.53/5.33      ! [F: real > real,L2: real,X: real] :
% 9.53/5.33        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 9.53/5.33       => ( ( ord_less_real @ zero_zero_real @ L2 )
% 9.53/5.33         => ? [D3: real] :
% 9.53/5.33              ( ( ord_less_real @ zero_zero_real @ D3 )
% 9.53/5.33              & ! [H4: real] :
% 9.53/5.33                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 9.53/5.33                 => ( ( ord_less_real @ H4 @ D3 )
% 9.53/5.33                   => ( ord_less_real @ ( F @ X ) @ ( F @ ( plus_plus_real @ X @ H4 ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9899_DERIV__neg__dec__right,axiom,
% 9.53/5.33      ! [F: real > real,L2: real,X: real] :
% 9.53/5.33        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 9.53/5.33       => ( ( ord_less_real @ L2 @ zero_zero_real )
% 9.53/5.33         => ? [D3: real] :
% 9.53/5.33              ( ( ord_less_real @ zero_zero_real @ D3 )
% 9.53/5.33              & ! [H4: real] :
% 9.53/5.33                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 9.53/5.33                 => ( ( ord_less_real @ H4 @ D3 )
% 9.53/5.33                   => ( ord_less_real @ ( F @ ( plus_plus_real @ X @ H4 ) ) @ ( F @ X ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9900_DERIV__const__ratio__const,axiom,
% 9.53/5.33      ! [A: real,B: real,F: real > real,K: real] :
% 9.53/5.33        ( ( A != B )
% 9.53/5.33       => ( ! [X3: real] : ( has_fi5821293074295781190e_real @ F @ K @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 9.53/5.33         => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 9.53/5.33            = ( times_times_real @ ( minus_minus_real @ B @ A ) @ K ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9901_DERIV__const__ratio__const2,axiom,
% 9.53/5.33      ! [A: real,B: real,F: real > real,K: real] :
% 9.53/5.33        ( ( A != B )
% 9.53/5.33       => ( ! [X3: real] : ( has_fi5821293074295781190e_real @ F @ K @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 9.53/5.33         => ( ( divide_divide_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( minus_minus_real @ B @ A ) )
% 9.53/5.33            = K ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9902_DERIV__isconst3,axiom,
% 9.53/5.33      ! [A: real,B: real,X: real,Y2: real,F: real > real] :
% 9.53/5.33        ( ( ord_less_real @ A @ B )
% 9.53/5.33       => ( ( member_real @ X @ ( set_or1633881224788618240n_real @ A @ B ) )
% 9.53/5.33         => ( ( member_real @ Y2 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 9.53/5.33           => ( ! [X3: real] :
% 9.53/5.33                  ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 9.53/5.33                 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 9.53/5.33             => ( ( F @ X )
% 9.53/5.33                = ( F @ Y2 ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9903_has__real__derivative__pos__inc__left,axiom,
% 9.53/5.33      ! [F: real > real,L2: real,X: real,S2: set_real] :
% 9.53/5.33        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ S2 ) )
% 9.53/5.33       => ( ( ord_less_real @ zero_zero_real @ L2 )
% 9.53/5.33         => ? [D3: real] :
% 9.53/5.33              ( ( ord_less_real @ zero_zero_real @ D3 )
% 9.53/5.33              & ! [H4: real] :
% 9.53/5.33                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 9.53/5.33                 => ( ( member_real @ ( minus_minus_real @ X @ H4 ) @ S2 )
% 9.53/5.33                   => ( ( ord_less_real @ H4 @ D3 )
% 9.53/5.33                     => ( ord_less_real @ ( F @ ( minus_minus_real @ X @ H4 ) ) @ ( F @ X ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9904_has__real__derivative__neg__dec__left,axiom,
% 9.53/5.33      ! [F: real > real,L2: real,X: real,S2: set_real] :
% 9.53/5.33        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ S2 ) )
% 9.53/5.33       => ( ( ord_less_real @ L2 @ zero_zero_real )
% 9.53/5.33         => ? [D3: real] :
% 9.53/5.33              ( ( ord_less_real @ zero_zero_real @ D3 )
% 9.53/5.33              & ! [H4: real] :
% 9.53/5.33                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 9.53/5.33                 => ( ( member_real @ ( minus_minus_real @ X @ H4 ) @ S2 )
% 9.53/5.33                   => ( ( ord_less_real @ H4 @ D3 )
% 9.53/5.33                     => ( ord_less_real @ ( F @ X ) @ ( F @ ( minus_minus_real @ X @ H4 ) ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9905_has__real__derivative__neg__dec__right,axiom,
% 9.53/5.33      ! [F: real > real,L2: real,X: real,S2: set_real] :
% 9.53/5.33        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ S2 ) )
% 9.53/5.33       => ( ( ord_less_real @ L2 @ zero_zero_real )
% 9.53/5.33         => ? [D3: real] :
% 9.53/5.33              ( ( ord_less_real @ zero_zero_real @ D3 )
% 9.53/5.33              & ! [H4: real] :
% 9.53/5.33                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 9.53/5.33                 => ( ( member_real @ ( plus_plus_real @ X @ H4 ) @ S2 )
% 9.53/5.33                   => ( ( ord_less_real @ H4 @ D3 )
% 9.53/5.33                     => ( ord_less_real @ ( F @ ( plus_plus_real @ X @ H4 ) ) @ ( F @ X ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9906_has__real__derivative__pos__inc__right,axiom,
% 9.53/5.33      ! [F: real > real,L2: real,X: real,S2: set_real] :
% 9.53/5.33        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ S2 ) )
% 9.53/5.33       => ( ( ord_less_real @ zero_zero_real @ L2 )
% 9.53/5.33         => ? [D3: real] :
% 9.53/5.33              ( ( ord_less_real @ zero_zero_real @ D3 )
% 9.53/5.33              & ! [H4: real] :
% 9.53/5.33                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 9.53/5.33                 => ( ( member_real @ ( plus_plus_real @ X @ H4 ) @ S2 )
% 9.53/5.33                   => ( ( ord_less_real @ H4 @ D3 )
% 9.53/5.33                     => ( ord_less_real @ ( F @ X ) @ ( F @ ( plus_plus_real @ X @ H4 ) ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9907_MVT2,axiom,
% 9.53/5.33      ! [A: real,B: real,F: real > real,F4: real > real] :
% 9.53/5.33        ( ( ord_less_real @ A @ B )
% 9.53/5.33       => ( ! [X3: real] :
% 9.53/5.33              ( ( ord_less_eq_real @ A @ X3 )
% 9.53/5.33             => ( ( ord_less_eq_real @ X3 @ B )
% 9.53/5.33               => ( has_fi5821293074295781190e_real @ F @ ( F4 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 9.53/5.33         => ? [Z3: real] :
% 9.53/5.33              ( ( ord_less_real @ A @ Z3 )
% 9.53/5.33              & ( ord_less_real @ Z3 @ B )
% 9.53/5.33              & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 9.53/5.33                = ( times_times_real @ ( minus_minus_real @ B @ A ) @ ( F4 @ Z3 ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9908_DERIV__local__const,axiom,
% 9.53/5.33      ! [F: real > real,L2: real,X: real,D2: real] :
% 9.53/5.33        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 9.53/5.33       => ( ( ord_less_real @ zero_zero_real @ D2 )
% 9.53/5.33         => ( ! [Y3: real] :
% 9.53/5.33                ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y3 ) ) @ D2 )
% 9.53/5.33               => ( ( F @ X )
% 9.53/5.33                  = ( F @ Y3 ) ) )
% 9.53/5.33           => ( L2 = zero_zero_real ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9909_DERIV__ln,axiom,
% 9.53/5.33      ! [X: real] :
% 9.53/5.33        ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.33       => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( inverse_inverse_real @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9910_DERIV__const__average,axiom,
% 9.53/5.33      ! [A: real,B: real,V: real > real,K: real] :
% 9.53/5.33        ( ( A != B )
% 9.53/5.33       => ( ! [X3: real] : ( has_fi5821293074295781190e_real @ V @ K @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 9.53/5.33         => ( ( V @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 9.53/5.33            = ( divide_divide_real @ ( plus_plus_real @ ( V @ A ) @ ( V @ B ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9911_DERIV__local__min,axiom,
% 9.53/5.33      ! [F: real > real,L2: real,X: real,D2: real] :
% 9.53/5.33        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 9.53/5.33       => ( ( ord_less_real @ zero_zero_real @ D2 )
% 9.53/5.33         => ( ! [Y3: real] :
% 9.53/5.33                ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y3 ) ) @ D2 )
% 9.53/5.33               => ( ord_less_eq_real @ ( F @ X ) @ ( F @ Y3 ) ) )
% 9.53/5.33           => ( L2 = zero_zero_real ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9912_DERIV__local__max,axiom,
% 9.53/5.33      ! [F: real > real,L2: real,X: real,D2: real] :
% 9.53/5.33        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 9.53/5.33       => ( ( ord_less_real @ zero_zero_real @ D2 )
% 9.53/5.33         => ( ! [Y3: real] :
% 9.53/5.33                ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y3 ) ) @ D2 )
% 9.53/5.33               => ( ord_less_eq_real @ ( F @ Y3 ) @ ( F @ X ) ) )
% 9.53/5.33           => ( L2 = zero_zero_real ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9913_DERIV__ln__divide,axiom,
% 9.53/5.33      ! [X: real] :
% 9.53/5.33        ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.33       => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( divide_divide_real @ one_one_real @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9914_DERIV__pow,axiom,
% 9.53/5.33      ! [N: nat,X: real,S3: set_real] :
% 9.53/5.33        ( has_fi5821293074295781190e_real
% 9.53/5.33        @ ^ [X2: real] : ( power_power_real @ X2 @ N )
% 9.53/5.33        @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ X @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 9.53/5.33        @ ( topolo2177554685111907308n_real @ X @ S3 ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9915_DERIV__fun__pow,axiom,
% 9.53/5.33      ! [G: real > real,M: real,X: real,N: nat] :
% 9.53/5.33        ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 9.53/5.33       => ( has_fi5821293074295781190e_real
% 9.53/5.33          @ ^ [X2: real] : ( power_power_real @ ( G @ X2 ) @ N )
% 9.53/5.33          @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( G @ X ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) @ M )
% 9.53/5.33          @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9916_has__real__derivative__powr,axiom,
% 9.53/5.33      ! [Z: real,R: real] :
% 9.53/5.33        ( ( ord_less_real @ zero_zero_real @ Z )
% 9.53/5.33       => ( has_fi5821293074295781190e_real
% 9.53/5.33          @ ^ [Z4: real] : ( powr_real @ Z4 @ R )
% 9.53/5.33          @ ( times_times_real @ R @ ( powr_real @ Z @ ( minus_minus_real @ R @ one_one_real ) ) )
% 9.53/5.33          @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9917_DERIV__fun__powr,axiom,
% 9.53/5.33      ! [G: real > real,M: real,X: real,R: real] :
% 9.53/5.33        ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 9.53/5.33       => ( ( ord_less_real @ zero_zero_real @ ( G @ X ) )
% 9.53/5.33         => ( has_fi5821293074295781190e_real
% 9.53/5.33            @ ^ [X2: real] : ( powr_real @ ( G @ X2 ) @ R )
% 9.53/5.33            @ ( times_times_real @ ( times_times_real @ R @ ( powr_real @ ( G @ X ) @ ( minus_minus_real @ R @ ( semiri5074537144036343181t_real @ one_one_nat ) ) ) ) @ M )
% 9.53/5.33            @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9918_DERIV__log,axiom,
% 9.53/5.33      ! [X: real,B: real] :
% 9.53/5.33        ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.33       => ( has_fi5821293074295781190e_real @ ( log @ B ) @ ( divide_divide_real @ one_one_real @ ( times_times_real @ ( ln_ln_real @ B ) @ X ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9919_DERIV__powr,axiom,
% 9.53/5.33      ! [G: real > real,M: real,X: real,F: real > real,R: real] :
% 9.53/5.33        ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 9.53/5.33       => ( ( ord_less_real @ zero_zero_real @ ( G @ X ) )
% 9.53/5.33         => ( ( has_fi5821293074295781190e_real @ F @ R @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 9.53/5.33           => ( has_fi5821293074295781190e_real
% 9.53/5.33              @ ^ [X2: real] : ( powr_real @ ( G @ X2 ) @ ( F @ X2 ) )
% 9.53/5.33              @ ( times_times_real @ ( powr_real @ ( G @ X ) @ ( F @ X ) ) @ ( plus_plus_real @ ( times_times_real @ R @ ( ln_ln_real @ ( G @ X ) ) ) @ ( divide_divide_real @ ( times_times_real @ M @ ( F @ X ) ) @ ( G @ X ) ) ) )
% 9.53/5.33              @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9920_DERIV__real__sqrt,axiom,
% 9.53/5.33      ! [X: real] :
% 9.53/5.33        ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.33       => ( has_fi5821293074295781190e_real @ sqrt @ ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9921_DERIV__arctan,axiom,
% 9.53/5.33      ! [X: real] : ( has_fi5821293074295781190e_real @ arctan @ ( inverse_inverse_real @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9922_DERIV__series_H,axiom,
% 9.53/5.33      ! [F: real > nat > real,F4: real > nat > real,X0: real,A: real,B: real,L5: nat > real] :
% 9.53/5.33        ( ! [N3: nat] :
% 9.53/5.33            ( has_fi5821293074295781190e_real
% 9.53/5.33            @ ^ [X2: real] : ( F @ X2 @ N3 )
% 9.53/5.33            @ ( F4 @ X0 @ N3 )
% 9.53/5.33            @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) )
% 9.53/5.33       => ( ! [X3: real] :
% 9.53/5.33              ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 9.53/5.33             => ( summable_real @ ( F @ X3 ) ) )
% 9.53/5.33         => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 9.53/5.33           => ( ( summable_real @ ( F4 @ X0 ) )
% 9.53/5.33             => ( ( summable_real @ L5 )
% 9.53/5.33               => ( ! [N3: nat,X3: real,Y3: real] :
% 9.53/5.33                      ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 9.53/5.33                     => ( ( member_real @ Y3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 9.53/5.33                       => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( F @ X3 @ N3 ) @ ( F @ Y3 @ N3 ) ) ) @ ( times_times_real @ ( L5 @ N3 ) @ ( abs_abs_real @ ( minus_minus_real @ X3 @ Y3 ) ) ) ) ) )
% 9.53/5.33                 => ( has_fi5821293074295781190e_real
% 9.53/5.33                    @ ^ [X2: real] : ( suminf_real @ ( F @ X2 ) )
% 9.53/5.33                    @ ( suminf_real @ ( F4 @ X0 ) )
% 9.53/5.33                    @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9923_arsinh__real__has__field__derivative,axiom,
% 9.53/5.33      ! [X: real,A2: set_real] : ( has_fi5821293074295781190e_real @ arsinh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X @ A2 ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9924_DERIV__real__sqrt__generic,axiom,
% 9.53/5.33      ! [X: real,D4: real] :
% 9.53/5.33        ( ( X != zero_zero_real )
% 9.53/5.33       => ( ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.33           => ( D4
% 9.53/5.33              = ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 9.53/5.33         => ( ( ( ord_less_real @ X @ zero_zero_real )
% 9.53/5.33             => ( D4
% 9.53/5.33                = ( divide_divide_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 9.53/5.33           => ( has_fi5821293074295781190e_real @ sqrt @ D4 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9925_arcosh__real__has__field__derivative,axiom,
% 9.53/5.33      ! [X: real,A2: set_real] :
% 9.53/5.33        ( ( ord_less_real @ one_one_real @ X )
% 9.53/5.33       => ( has_fi5821293074295781190e_real @ arcosh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X @ A2 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9926_artanh__real__has__field__derivative,axiom,
% 9.53/5.33      ! [X: real,A2: set_real] :
% 9.53/5.33        ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 9.53/5.33       => ( has_fi5821293074295781190e_real @ artanh_real @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ A2 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9927_DERIV__power__series_H,axiom,
% 9.53/5.33      ! [R2: real,F: nat > real,X0: real] :
% 9.53/5.33        ( ! [X3: real] :
% 9.53/5.33            ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R2 ) @ R2 ) )
% 9.53/5.33           => ( summable_real
% 9.53/5.33              @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( F @ N2 ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) @ ( power_power_real @ X3 @ N2 ) ) ) )
% 9.53/5.33       => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R2 ) @ R2 ) )
% 9.53/5.33         => ( ( ord_less_real @ zero_zero_real @ R2 )
% 9.53/5.33           => ( has_fi5821293074295781190e_real
% 9.53/5.33              @ ^ [X2: real] :
% 9.53/5.33                  ( suminf_real
% 9.53/5.33                  @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ X2 @ ( suc @ N2 ) ) ) )
% 9.53/5.33              @ ( suminf_real
% 9.53/5.33                @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( F @ N2 ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) @ ( power_power_real @ X0 @ N2 ) ) )
% 9.53/5.33              @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9928_DERIV__real__root,axiom,
% 9.53/5.33      ! [N: nat,X: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( ord_less_real @ zero_zero_real @ X )
% 9.53/5.33         => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9929_DERIV__arccos,axiom,
% 9.53/5.33      ! [X: real] :
% 9.53/5.33        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 9.53/5.33       => ( ( ord_less_real @ X @ one_one_real )
% 9.53/5.33         => ( has_fi5821293074295781190e_real @ arccos @ ( inverse_inverse_real @ ( uminus_uminus_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9930_DERIV__arcsin,axiom,
% 9.53/5.33      ! [X: real] :
% 9.53/5.33        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 9.53/5.33       => ( ( ord_less_real @ X @ one_one_real )
% 9.53/5.33         => ( has_fi5821293074295781190e_real @ arcsin @ ( inverse_inverse_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9931_Maclaurin__all__le,axiom,
% 9.53/5.33      ! [Diff: nat > real > real,F: real > real,X: real,N: nat] :
% 9.53/5.33        ( ( ( Diff @ zero_zero_nat )
% 9.53/5.33          = F )
% 9.53/5.33       => ( ! [M4: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 9.53/5.33         => ? [T6: real] :
% 9.53/5.33              ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 9.53/5.33              & ( ( F @ X )
% 9.53/5.33                = ( plus_plus_real
% 9.53/5.33                  @ ( groups6591440286371151544t_real
% 9.53/5.33                    @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 9.53/5.33                    @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.33                  @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9932_Maclaurin__all__le__objl,axiom,
% 9.53/5.33      ! [Diff: nat > real > real,F: real > real,X: real,N: nat] :
% 9.53/5.33        ( ( ( ( Diff @ zero_zero_nat )
% 9.53/5.33            = F )
% 9.53/5.33          & ! [M4: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 9.53/5.33       => ? [T6: real] :
% 9.53/5.33            ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 9.53/5.33            & ( ( F @ X )
% 9.53/5.33              = ( plus_plus_real
% 9.53/5.33                @ ( groups6591440286371151544t_real
% 9.53/5.33                  @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 9.53/5.33                  @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.33                @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9933_DERIV__odd__real__root,axiom,
% 9.53/5.33      ! [N: nat,X: real] :
% 9.53/5.33        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.53/5.33       => ( ( X != zero_zero_real )
% 9.53/5.33         => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9934_Maclaurin__minus,axiom,
% 9.53/5.33      ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 9.53/5.33        ( ( ord_less_real @ H2 @ zero_zero_real )
% 9.53/5.33       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33         => ( ( ( Diff @ zero_zero_nat )
% 9.53/5.33              = F )
% 9.53/5.33           => ( ! [M4: nat,T6: real] :
% 9.53/5.33                  ( ( ( ord_less_nat @ M4 @ N )
% 9.53/5.33                    & ( ord_less_eq_real @ H2 @ T6 )
% 9.53/5.33                    & ( ord_less_eq_real @ T6 @ zero_zero_real ) )
% 9.53/5.33                 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 9.53/5.33             => ? [T6: real] :
% 9.53/5.33                  ( ( ord_less_real @ H2 @ T6 )
% 9.53/5.33                  & ( ord_less_real @ T6 @ zero_zero_real )
% 9.53/5.33                  & ( ( F @ H2 )
% 9.53/5.33                    = ( plus_plus_real
% 9.53/5.33                      @ ( groups6591440286371151544t_real
% 9.53/5.33                        @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 9.53/5.33                        @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.33                      @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9935_Maclaurin2,axiom,
% 9.53/5.33      ! [H2: real,Diff: nat > real > real,F: real > real,N: nat] :
% 9.53/5.33        ( ( ord_less_real @ zero_zero_real @ H2 )
% 9.53/5.33       => ( ( ( Diff @ zero_zero_nat )
% 9.53/5.33            = F )
% 9.53/5.33         => ( ! [M4: nat,T6: real] :
% 9.53/5.33                ( ( ( ord_less_nat @ M4 @ N )
% 9.53/5.33                  & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 9.53/5.33                  & ( ord_less_eq_real @ T6 @ H2 ) )
% 9.53/5.33               => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 9.53/5.33           => ? [T6: real] :
% 9.53/5.33                ( ( ord_less_real @ zero_zero_real @ T6 )
% 9.53/5.33                & ( ord_less_eq_real @ T6 @ H2 )
% 9.53/5.33                & ( ( F @ H2 )
% 9.53/5.33                  = ( plus_plus_real
% 9.53/5.33                    @ ( groups6591440286371151544t_real
% 9.53/5.33                      @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 9.53/5.33                      @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.33                    @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9936_Maclaurin,axiom,
% 9.53/5.33      ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 9.53/5.33        ( ( ord_less_real @ zero_zero_real @ H2 )
% 9.53/5.33       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33         => ( ( ( Diff @ zero_zero_nat )
% 9.53/5.33              = F )
% 9.53/5.33           => ( ! [M4: nat,T6: real] :
% 9.53/5.33                  ( ( ( ord_less_nat @ M4 @ N )
% 9.53/5.33                    & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 9.53/5.33                    & ( ord_less_eq_real @ T6 @ H2 ) )
% 9.53/5.33                 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 9.53/5.33             => ? [T6: real] :
% 9.53/5.33                  ( ( ord_less_real @ zero_zero_real @ T6 )
% 9.53/5.33                  & ( ord_less_real @ T6 @ H2 )
% 9.53/5.33                  & ( ( F @ H2 )
% 9.53/5.33                    = ( plus_plus_real
% 9.53/5.33                      @ ( groups6591440286371151544t_real
% 9.53/5.33                        @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 9.53/5.33                        @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.33                      @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9937_Maclaurin__all__lt,axiom,
% 9.53/5.33      ! [Diff: nat > real > real,F: real > real,N: nat,X: real] :
% 9.53/5.33        ( ( ( Diff @ zero_zero_nat )
% 9.53/5.33          = F )
% 9.53/5.33       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33         => ( ( X != zero_zero_real )
% 9.53/5.33           => ( ! [M4: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 9.53/5.33             => ? [T6: real] :
% 9.53/5.33                  ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T6 ) )
% 9.53/5.33                  & ( ord_less_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 9.53/5.33                  & ( ( F @ X )
% 9.53/5.33                    = ( plus_plus_real
% 9.53/5.33                      @ ( groups6591440286371151544t_real
% 9.53/5.33                        @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 9.53/5.33                        @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.33                      @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9938_Maclaurin__bi__le,axiom,
% 9.53/5.33      ! [Diff: nat > real > real,F: real > real,N: nat,X: real] :
% 9.53/5.33        ( ( ( Diff @ zero_zero_nat )
% 9.53/5.33          = F )
% 9.53/5.33       => ( ! [M4: nat,T6: real] :
% 9.53/5.33              ( ( ( ord_less_nat @ M4 @ N )
% 9.53/5.33                & ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) ) )
% 9.53/5.33             => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 9.53/5.33         => ? [T6: real] :
% 9.53/5.33              ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 9.53/5.33              & ( ( F @ X )
% 9.53/5.33                = ( plus_plus_real
% 9.53/5.33                  @ ( groups6591440286371151544t_real
% 9.53/5.33                    @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 9.53/5.33                    @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.33                  @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9939_Taylor__down,axiom,
% 9.53/5.33      ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( ( Diff @ zero_zero_nat )
% 9.53/5.33            = F )
% 9.53/5.33         => ( ! [M4: nat,T6: real] :
% 9.53/5.33                ( ( ( ord_less_nat @ M4 @ N )
% 9.53/5.33                  & ( ord_less_eq_real @ A @ T6 )
% 9.53/5.33                  & ( ord_less_eq_real @ T6 @ B ) )
% 9.53/5.33               => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 9.53/5.33           => ( ( ord_less_real @ A @ C )
% 9.53/5.33             => ( ( ord_less_eq_real @ C @ B )
% 9.53/5.33               => ? [T6: real] :
% 9.53/5.33                    ( ( ord_less_real @ A @ T6 )
% 9.53/5.33                    & ( ord_less_real @ T6 @ C )
% 9.53/5.33                    & ( ( F @ A )
% 9.53/5.33                      = ( plus_plus_real
% 9.53/5.33                        @ ( groups6591440286371151544t_real
% 9.53/5.33                          @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ M6 ) )
% 9.53/5.33                          @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.33                        @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9940_Taylor__up,axiom,
% 9.53/5.33      ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( ( Diff @ zero_zero_nat )
% 9.53/5.33            = F )
% 9.53/5.33         => ( ! [M4: nat,T6: real] :
% 9.53/5.33                ( ( ( ord_less_nat @ M4 @ N )
% 9.53/5.33                  & ( ord_less_eq_real @ A @ T6 )
% 9.53/5.33                  & ( ord_less_eq_real @ T6 @ B ) )
% 9.53/5.33               => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 9.53/5.33           => ( ( ord_less_eq_real @ A @ C )
% 9.53/5.33             => ( ( ord_less_real @ C @ B )
% 9.53/5.33               => ? [T6: real] :
% 9.53/5.33                    ( ( ord_less_real @ C @ T6 )
% 9.53/5.33                    & ( ord_less_real @ T6 @ B )
% 9.53/5.33                    & ( ( F @ B )
% 9.53/5.33                      = ( plus_plus_real
% 9.53/5.33                        @ ( groups6591440286371151544t_real
% 9.53/5.33                          @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ M6 ) )
% 9.53/5.33                          @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.33                        @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9941_Taylor,axiom,
% 9.53/5.33      ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real,X: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( ( Diff @ zero_zero_nat )
% 9.53/5.33            = F )
% 9.53/5.33         => ( ! [M4: nat,T6: real] :
% 9.53/5.33                ( ( ( ord_less_nat @ M4 @ N )
% 9.53/5.33                  & ( ord_less_eq_real @ A @ T6 )
% 9.53/5.33                  & ( ord_less_eq_real @ T6 @ B ) )
% 9.53/5.33               => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 9.53/5.33           => ( ( ord_less_eq_real @ A @ C )
% 9.53/5.33             => ( ( ord_less_eq_real @ C @ B )
% 9.53/5.33               => ( ( ord_less_eq_real @ A @ X )
% 9.53/5.33                 => ( ( ord_less_eq_real @ X @ B )
% 9.53/5.33                   => ( ( X != C )
% 9.53/5.33                     => ? [T6: real] :
% 9.53/5.33                          ( ( ( ord_less_real @ X @ C )
% 9.53/5.33                           => ( ( ord_less_real @ X @ T6 )
% 9.53/5.33                              & ( ord_less_real @ T6 @ C ) ) )
% 9.53/5.33                          & ( ~ ( ord_less_real @ X @ C )
% 9.53/5.33                           => ( ( ord_less_real @ C @ T6 )
% 9.53/5.33                              & ( ord_less_real @ T6 @ X ) ) )
% 9.53/5.33                          & ( ( F @ X )
% 9.53/5.33                            = ( plus_plus_real
% 9.53/5.33                              @ ( groups6591440286371151544t_real
% 9.53/5.33                                @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C ) @ M6 ) )
% 9.53/5.33                                @ ( set_ord_lessThan_nat @ N ) )
% 9.53/5.33                              @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C ) @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9942_Maclaurin__lemma2,axiom,
% 9.53/5.33      ! [N: nat,H2: real,Diff: nat > real > real,K: nat,B2: real] :
% 9.53/5.33        ( ! [M4: nat,T6: real] :
% 9.53/5.33            ( ( ( ord_less_nat @ M4 @ N )
% 9.53/5.33              & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 9.53/5.33              & ( ord_less_eq_real @ T6 @ H2 ) )
% 9.53/5.33           => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 9.53/5.33       => ( ( N
% 9.53/5.33            = ( suc @ K ) )
% 9.53/5.33         => ! [M5: nat,T7: real] :
% 9.53/5.33              ( ( ( ord_less_nat @ M5 @ N )
% 9.53/5.33                & ( ord_less_eq_real @ zero_zero_real @ T7 )
% 9.53/5.33                & ( ord_less_eq_real @ T7 @ H2 ) )
% 9.53/5.33             => ( has_fi5821293074295781190e_real
% 9.53/5.33                @ ^ [U2: real] :
% 9.53/5.33                    ( minus_minus_real @ ( Diff @ M5 @ U2 )
% 9.53/5.33                    @ ( plus_plus_real
% 9.53/5.33                      @ ( groups6591440286371151544t_real
% 9.53/5.33                        @ ^ [P4: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ M5 @ P4 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P4 ) ) @ ( power_power_real @ U2 @ P4 ) )
% 9.53/5.33                        @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ M5 ) ) )
% 9.53/5.33                      @ ( times_times_real @ B2 @ ( divide_divide_real @ ( power_power_real @ U2 @ ( minus_minus_nat @ N @ M5 ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ M5 ) ) ) ) ) )
% 9.53/5.33                @ ( minus_minus_real @ ( Diff @ ( suc @ M5 ) @ T7 )
% 9.53/5.33                  @ ( plus_plus_real
% 9.53/5.33                    @ ( groups6591440286371151544t_real
% 9.53/5.33                      @ ^ [P4: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ ( suc @ M5 ) @ P4 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P4 ) ) @ ( power_power_real @ T7 @ P4 ) )
% 9.53/5.33                      @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ M5 ) ) ) )
% 9.53/5.33                    @ ( times_times_real @ B2 @ ( divide_divide_real @ ( power_power_real @ T7 @ ( minus_minus_nat @ N @ ( suc @ M5 ) ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ ( suc @ M5 ) ) ) ) ) ) )
% 9.53/5.33                @ ( topolo2177554685111907308n_real @ T7 @ top_top_set_real ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9943_DERIV__arctan__series,axiom,
% 9.53/5.33      ! [X: real] :
% 9.53/5.33        ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 9.53/5.33       => ( has_fi5821293074295781190e_real
% 9.53/5.33          @ ^ [X9: real] :
% 9.53/5.33              ( suminf_real
% 9.53/5.33              @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X9 @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) )
% 9.53/5.33          @ ( suminf_real
% 9.53/5.33            @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( power_power_real @ X @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.53/5.33          @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9944_DERIV__even__real__root,axiom,
% 9.53/5.33      ! [N: nat,X: real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.53/5.33         => ( ( ord_less_real @ X @ zero_zero_real )
% 9.53/5.33           => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9945_isCont__Lb__Ub,axiom,
% 9.53/5.33      ! [A: real,B: real,F: real > real] :
% 9.53/5.33        ( ( ord_less_eq_real @ A @ B )
% 9.53/5.33       => ( ! [X3: real] :
% 9.53/5.33              ( ( ( ord_less_eq_real @ A @ X3 )
% 9.53/5.33                & ( ord_less_eq_real @ X3 @ B ) )
% 9.53/5.33             => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ F ) )
% 9.53/5.33         => ? [L6: real,M9: real] :
% 9.53/5.33              ( ! [X5: real] :
% 9.53/5.33                  ( ( ( ord_less_eq_real @ A @ X5 )
% 9.53/5.33                    & ( ord_less_eq_real @ X5 @ B ) )
% 9.53/5.33                 => ( ( ord_less_eq_real @ L6 @ ( F @ X5 ) )
% 9.53/5.33                    & ( ord_less_eq_real @ ( F @ X5 ) @ M9 ) ) )
% 9.53/5.33              & ! [Y4: real] :
% 9.53/5.33                  ( ( ( ord_less_eq_real @ L6 @ Y4 )
% 9.53/5.33                    & ( ord_less_eq_real @ Y4 @ M9 ) )
% 9.53/5.33                 => ? [X3: real] :
% 9.53/5.33                      ( ( ord_less_eq_real @ A @ X3 )
% 9.53/5.33                      & ( ord_less_eq_real @ X3 @ B )
% 9.53/5.33                      & ( ( F @ X3 )
% 9.53/5.33                        = Y4 ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9946_LIM__fun__less__zero,axiom,
% 9.53/5.33      ! [F: real > real,L2: real,C: real] :
% 9.53/5.33        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 9.53/5.33       => ( ( ord_less_real @ L2 @ zero_zero_real )
% 9.53/5.33         => ? [R3: real] :
% 9.53/5.33              ( ( ord_less_real @ zero_zero_real @ R3 )
% 9.53/5.33              & ! [X5: real] :
% 9.53/5.33                  ( ( ( X5 != C )
% 9.53/5.33                    & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X5 ) ) @ R3 ) )
% 9.53/5.33                 => ( ord_less_real @ ( F @ X5 ) @ zero_zero_real ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9947_LIM__fun__not__zero,axiom,
% 9.53/5.33      ! [F: real > real,L2: real,C: real] :
% 9.53/5.33        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 9.53/5.33       => ( ( L2 != zero_zero_real )
% 9.53/5.33         => ? [R3: real] :
% 9.53/5.33              ( ( ord_less_real @ zero_zero_real @ R3 )
% 9.53/5.33              & ! [X5: real] :
% 9.53/5.33                  ( ( ( X5 != C )
% 9.53/5.33                    & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X5 ) ) @ R3 ) )
% 9.53/5.33                 => ( ( F @ X5 )
% 9.53/5.33                   != zero_zero_real ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9948_LIM__fun__gt__zero,axiom,
% 9.53/5.33      ! [F: real > real,L2: real,C: real] :
% 9.53/5.33        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 9.53/5.33       => ( ( ord_less_real @ zero_zero_real @ L2 )
% 9.53/5.33         => ? [R3: real] :
% 9.53/5.33              ( ( ord_less_real @ zero_zero_real @ R3 )
% 9.53/5.33              & ! [X5: real] :
% 9.53/5.33                  ( ( ( X5 != C )
% 9.53/5.33                    & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X5 ) ) @ R3 ) )
% 9.53/5.33                 => ( ord_less_real @ zero_zero_real @ ( F @ X5 ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9949_isCont__real__sqrt,axiom,
% 9.53/5.33      ! [X: real] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ sqrt ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9950_isCont__real__root,axiom,
% 9.53/5.33      ! [X: real,N: nat] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ ( root @ N ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9951_isCont__inverse__function2,axiom,
% 9.53/5.33      ! [A: real,X: real,B: real,G: real > real,F: real > real] :
% 9.53/5.33        ( ( ord_less_real @ A @ X )
% 9.53/5.33       => ( ( ord_less_real @ X @ B )
% 9.53/5.33         => ( ! [Z3: real] :
% 9.53/5.33                ( ( ord_less_eq_real @ A @ Z3 )
% 9.53/5.33               => ( ( ord_less_eq_real @ Z3 @ B )
% 9.53/5.33                 => ( ( G @ ( F @ Z3 ) )
% 9.53/5.33                    = Z3 ) ) )
% 9.53/5.33           => ( ! [Z3: real] :
% 9.53/5.33                  ( ( ord_less_eq_real @ A @ Z3 )
% 9.53/5.33                 => ( ( ord_less_eq_real @ Z3 @ B )
% 9.53/5.33                   => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) ) )
% 9.53/5.33             => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X ) @ top_top_set_real ) @ G ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9952_isCont__arcosh,axiom,
% 9.53/5.33      ! [X: real] :
% 9.53/5.33        ( ( ord_less_real @ one_one_real @ X )
% 9.53/5.33       => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ arcosh_real ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9953_LIM__cos__div__sin,axiom,
% 9.53/5.33      ( filterlim_real_real
% 9.53/5.33      @ ^ [X2: real] : ( divide_divide_real @ ( cos_real @ X2 ) @ ( sin_real @ X2 ) )
% 9.53/5.33      @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 9.53/5.33      @ ( topolo2177554685111907308n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ top_top_set_real ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9954_DERIV__inverse__function,axiom,
% 9.53/5.33      ! [F: real > real,D4: real,G: real > real,X: real,A: real,B: real] :
% 9.53/5.33        ( ( has_fi5821293074295781190e_real @ F @ D4 @ ( topolo2177554685111907308n_real @ ( G @ X ) @ top_top_set_real ) )
% 9.53/5.33       => ( ( D4 != zero_zero_real )
% 9.53/5.33         => ( ( ord_less_real @ A @ X )
% 9.53/5.33           => ( ( ord_less_real @ X @ B )
% 9.53/5.33             => ( ! [Y3: real] :
% 9.53/5.33                    ( ( ord_less_real @ A @ Y3 )
% 9.53/5.33                   => ( ( ord_less_real @ Y3 @ B )
% 9.53/5.33                     => ( ( F @ ( G @ Y3 ) )
% 9.53/5.33                        = Y3 ) ) )
% 9.53/5.33               => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ G )
% 9.53/5.33                 => ( has_fi5821293074295781190e_real @ G @ ( inverse_inverse_real @ D4 ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9955_isCont__arccos,axiom,
% 9.53/5.33      ! [X: real] :
% 9.53/5.33        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 9.53/5.33       => ( ( ord_less_real @ X @ one_one_real )
% 9.53/5.33         => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ arccos ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9956_isCont__arcsin,axiom,
% 9.53/5.33      ! [X: real] :
% 9.53/5.33        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 9.53/5.33       => ( ( ord_less_real @ X @ one_one_real )
% 9.53/5.33         => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ arcsin ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9957_LIM__less__bound,axiom,
% 9.53/5.33      ! [B: real,X: real,F: real > real] :
% 9.53/5.33        ( ( ord_less_real @ B @ X )
% 9.53/5.33       => ( ! [X3: real] :
% 9.53/5.33              ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ B @ X ) )
% 9.53/5.33             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 9.53/5.33         => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ F )
% 9.53/5.33           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9958_isCont__artanh,axiom,
% 9.53/5.33      ! [X: real] :
% 9.53/5.33        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 9.53/5.33       => ( ( ord_less_real @ X @ one_one_real )
% 9.53/5.33         => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ artanh_real ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9959_isCont__inverse__function,axiom,
% 9.53/5.33      ! [D2: real,X: real,G: real > real,F: real > real] :
% 9.53/5.33        ( ( ord_less_real @ zero_zero_real @ D2 )
% 9.53/5.33       => ( ! [Z3: real] :
% 9.53/5.33              ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z3 @ X ) ) @ D2 )
% 9.53/5.33             => ( ( G @ ( F @ Z3 ) )
% 9.53/5.33                = Z3 ) )
% 9.53/5.33         => ( ! [Z3: real] :
% 9.53/5.33                ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z3 @ X ) ) @ D2 )
% 9.53/5.33               => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) )
% 9.53/5.33           => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X ) @ top_top_set_real ) @ G ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9960_GMVT_H,axiom,
% 9.53/5.33      ! [A: real,B: real,F: real > real,G: real > real,G2: real > real,F4: real > real] :
% 9.53/5.33        ( ( ord_less_real @ A @ B )
% 9.53/5.33       => ( ! [Z3: real] :
% 9.53/5.33              ( ( ord_less_eq_real @ A @ Z3 )
% 9.53/5.33             => ( ( ord_less_eq_real @ Z3 @ B )
% 9.53/5.33               => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) ) )
% 9.53/5.33         => ( ! [Z3: real] :
% 9.53/5.33                ( ( ord_less_eq_real @ A @ Z3 )
% 9.53/5.33               => ( ( ord_less_eq_real @ Z3 @ B )
% 9.53/5.33                 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ G ) ) )
% 9.53/5.33           => ( ! [Z3: real] :
% 9.53/5.33                  ( ( ord_less_real @ A @ Z3 )
% 9.53/5.33                 => ( ( ord_less_real @ Z3 @ B )
% 9.53/5.33                   => ( has_fi5821293074295781190e_real @ G @ ( G2 @ Z3 ) @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) )
% 9.53/5.33             => ( ! [Z3: real] :
% 9.53/5.33                    ( ( ord_less_real @ A @ Z3 )
% 9.53/5.33                   => ( ( ord_less_real @ Z3 @ B )
% 9.53/5.33                     => ( has_fi5821293074295781190e_real @ F @ ( F4 @ Z3 ) @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) )
% 9.53/5.33               => ? [C2: real] :
% 9.53/5.33                    ( ( ord_less_real @ A @ C2 )
% 9.53/5.33                    & ( ord_less_real @ C2 @ B )
% 9.53/5.33                    & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( G2 @ C2 ) )
% 9.53/5.33                      = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ ( F4 @ C2 ) ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9961_summable__Leibniz_I2_J,axiom,
% 9.53/5.33      ! [A: nat > real] :
% 9.53/5.33        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 9.53/5.33       => ( ( topolo6980174941875973593q_real @ A )
% 9.53/5.33         => ( ( ord_less_real @ zero_zero_real @ ( A @ zero_zero_nat ) )
% 9.53/5.33           => ! [N9: nat] :
% 9.53/5.33                ( member_real
% 9.53/5.33                @ ( suminf_real
% 9.53/5.33                  @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) )
% 9.53/5.33                @ ( set_or1222579329274155063t_real
% 9.53/5.33                  @ ( groups6591440286371151544t_real
% 9.53/5.33                    @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 9.53/5.33                    @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) ) )
% 9.53/5.33                  @ ( groups6591440286371151544t_real
% 9.53/5.33                    @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 9.53/5.33                    @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) @ one_one_nat ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9962_summable__Leibniz_I3_J,axiom,
% 9.53/5.33      ! [A: nat > real] :
% 9.53/5.33        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 9.53/5.33       => ( ( topolo6980174941875973593q_real @ A )
% 9.53/5.33         => ( ( ord_less_real @ ( A @ zero_zero_nat ) @ zero_zero_real )
% 9.53/5.33           => ! [N9: nat] :
% 9.53/5.33                ( member_real
% 9.53/5.33                @ ( suminf_real
% 9.53/5.33                  @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) )
% 9.53/5.33                @ ( set_or1222579329274155063t_real
% 9.53/5.33                  @ ( groups6591440286371151544t_real
% 9.53/5.33                    @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 9.53/5.33                    @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) @ one_one_nat ) ) )
% 9.53/5.33                  @ ( groups6591440286371151544t_real
% 9.53/5.33                    @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 9.53/5.33                    @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9963_mult__nat__right__at__top,axiom,
% 9.53/5.33      ! [C: nat] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ C )
% 9.53/5.33       => ( filterlim_nat_nat
% 9.53/5.33          @ ^ [X2: nat] : ( times_times_nat @ X2 @ C )
% 9.53/5.33          @ at_top_nat
% 9.53/5.33          @ at_top_nat ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9964_mult__nat__left__at__top,axiom,
% 9.53/5.33      ! [C: nat] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ C )
% 9.53/5.33       => ( filterlim_nat_nat @ ( times_times_nat @ C ) @ at_top_nat @ at_top_nat ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9965_monoseq__convergent,axiom,
% 9.53/5.33      ! [X8: nat > real,B2: real] :
% 9.53/5.33        ( ( topolo6980174941875973593q_real @ X8 )
% 9.53/5.33       => ( ! [I4: nat] : ( ord_less_eq_real @ ( abs_abs_real @ ( X8 @ I4 ) ) @ B2 )
% 9.53/5.33         => ~ ! [L6: real] :
% 9.53/5.33                ~ ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9966_LIMSEQ__root,axiom,
% 9.53/5.33      ( filterlim_nat_real
% 9.53/5.33      @ ^ [N2: nat] : ( root @ N2 @ ( semiri5074537144036343181t_real @ N2 ) )
% 9.53/5.33      @ ( topolo2815343760600316023s_real @ one_one_real )
% 9.53/5.33      @ at_top_nat ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9967_nested__sequence__unique,axiom,
% 9.53/5.33      ! [F: nat > real,G: nat > real] :
% 9.53/5.33        ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 9.53/5.33       => ( ! [N3: nat] : ( ord_less_eq_real @ ( G @ ( suc @ N3 ) ) @ ( G @ N3 ) )
% 9.53/5.33         => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 9.53/5.33           => ( ( filterlim_nat_real
% 9.53/5.33                @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 9.53/5.33                @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 9.53/5.33                @ at_top_nat )
% 9.53/5.33             => ? [L4: real] :
% 9.53/5.33                  ( ! [N9: nat] : ( ord_less_eq_real @ ( F @ N9 ) @ L4 )
% 9.53/5.33                  & ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat )
% 9.53/5.33                  & ! [N9: nat] : ( ord_less_eq_real @ L4 @ ( G @ N9 ) )
% 9.53/5.33                  & ( filterlim_nat_real @ G @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9968_LIMSEQ__inverse__zero,axiom,
% 9.53/5.33      ! [X8: nat > real] :
% 9.53/5.33        ( ! [R3: real] :
% 9.53/5.33          ? [N7: nat] :
% 9.53/5.33          ! [N3: nat] :
% 9.53/5.33            ( ( ord_less_eq_nat @ N7 @ N3 )
% 9.53/5.33           => ( ord_less_real @ R3 @ ( X8 @ N3 ) ) )
% 9.53/5.33       => ( filterlim_nat_real
% 9.53/5.33          @ ^ [N2: nat] : ( inverse_inverse_real @ ( X8 @ N2 ) )
% 9.53/5.33          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 9.53/5.33          @ at_top_nat ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9969_lim__inverse__n_H,axiom,
% 9.53/5.33      ( filterlim_nat_real
% 9.53/5.33      @ ^ [N2: nat] : ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N2 ) )
% 9.53/5.33      @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 9.53/5.33      @ at_top_nat ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9970_LIMSEQ__root__const,axiom,
% 9.53/5.33      ! [C: real] :
% 9.53/5.33        ( ( ord_less_real @ zero_zero_real @ C )
% 9.53/5.33       => ( filterlim_nat_real
% 9.53/5.33          @ ^ [N2: nat] : ( root @ N2 @ C )
% 9.53/5.33          @ ( topolo2815343760600316023s_real @ one_one_real )
% 9.53/5.33          @ at_top_nat ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9971_LIMSEQ__inverse__real__of__nat,axiom,
% 9.53/5.33      ( filterlim_nat_real
% 9.53/5.33      @ ^ [N2: nat] : ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) )
% 9.53/5.33      @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 9.53/5.33      @ at_top_nat ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9972_LIMSEQ__inverse__real__of__nat__add,axiom,
% 9.53/5.33      ! [R: real] :
% 9.53/5.33        ( filterlim_nat_real
% 9.53/5.33        @ ^ [N2: nat] : ( plus_plus_real @ R @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) )
% 9.53/5.33        @ ( topolo2815343760600316023s_real @ R )
% 9.53/5.33        @ at_top_nat ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9973_increasing__LIMSEQ,axiom,
% 9.53/5.33      ! [F: nat > real,L2: real] :
% 9.53/5.33        ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 9.53/5.33       => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ L2 )
% 9.53/5.33         => ( ! [E2: real] :
% 9.53/5.33                ( ( ord_less_real @ zero_zero_real @ E2 )
% 9.53/5.33               => ? [N9: nat] : ( ord_less_eq_real @ L2 @ ( plus_plus_real @ ( F @ N9 ) @ E2 ) ) )
% 9.53/5.33           => ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ at_top_nat ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9974_LIMSEQ__realpow__zero,axiom,
% 9.53/5.33      ! [X: real] :
% 9.53/5.33        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.33       => ( ( ord_less_real @ X @ one_one_real )
% 9.53/5.33         => ( filterlim_nat_real @ ( power_power_real @ X ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9975_LIMSEQ__divide__realpow__zero,axiom,
% 9.53/5.33      ! [X: real,A: real] :
% 9.53/5.33        ( ( ord_less_real @ one_one_real @ X )
% 9.53/5.33       => ( filterlim_nat_real
% 9.53/5.33          @ ^ [N2: nat] : ( divide_divide_real @ A @ ( power_power_real @ X @ N2 ) )
% 9.53/5.33          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 9.53/5.33          @ at_top_nat ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9976_LIMSEQ__abs__realpow__zero,axiom,
% 9.53/5.33      ! [C: real] :
% 9.53/5.33        ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 9.53/5.33       => ( filterlim_nat_real @ ( power_power_real @ ( abs_abs_real @ C ) ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9977_LIMSEQ__abs__realpow__zero2,axiom,
% 9.53/5.33      ! [C: real] :
% 9.53/5.33        ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 9.53/5.33       => ( filterlim_nat_real @ ( power_power_real @ C ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9978_LIMSEQ__inverse__realpow__zero,axiom,
% 9.53/5.33      ! [X: real] :
% 9.53/5.33        ( ( ord_less_real @ one_one_real @ X )
% 9.53/5.33       => ( filterlim_nat_real
% 9.53/5.33          @ ^ [N2: nat] : ( inverse_inverse_real @ ( power_power_real @ X @ N2 ) )
% 9.53/5.33          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 9.53/5.33          @ at_top_nat ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9979_LIMSEQ__inverse__real__of__nat__add__minus,axiom,
% 9.53/5.33      ! [R: real] :
% 9.53/5.33        ( filterlim_nat_real
% 9.53/5.33        @ ^ [N2: nat] : ( plus_plus_real @ R @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) )
% 9.53/5.33        @ ( topolo2815343760600316023s_real @ R )
% 9.53/5.33        @ at_top_nat ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9980_tendsto__exp__limit__sequentially,axiom,
% 9.53/5.33      ! [X: real] :
% 9.53/5.33        ( filterlim_nat_real
% 9.53/5.33        @ ^ [N2: nat] : ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 )
% 9.53/5.33        @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 9.53/5.33        @ at_top_nat ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9981_LIMSEQ__inverse__real__of__nat__add__minus__mult,axiom,
% 9.53/5.33      ! [R: real] :
% 9.53/5.33        ( filterlim_nat_real
% 9.53/5.33        @ ^ [N2: nat] : ( times_times_real @ R @ ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) ) )
% 9.53/5.33        @ ( topolo2815343760600316023s_real @ R )
% 9.53/5.33        @ at_top_nat ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9982_summable__Leibniz_I1_J,axiom,
% 9.53/5.33      ! [A: nat > real] :
% 9.53/5.33        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 9.53/5.33       => ( ( topolo6980174941875973593q_real @ A )
% 9.53/5.33         => ( summable_real
% 9.53/5.33            @ ^ [N2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( A @ N2 ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9983_summable,axiom,
% 9.53/5.33      ! [A: nat > real] :
% 9.53/5.33        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 9.53/5.33       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 9.53/5.33         => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 9.53/5.33           => ( summable_real
% 9.53/5.33              @ ^ [N2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( A @ N2 ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9984_cos__diff__limit__1,axiom,
% 9.53/5.33      ! [Theta: nat > real,Theta2: real] :
% 9.53/5.33        ( ( filterlim_nat_real
% 9.53/5.33          @ ^ [J3: nat] : ( cos_real @ ( minus_minus_real @ ( Theta @ J3 ) @ Theta2 ) )
% 9.53/5.33          @ ( topolo2815343760600316023s_real @ one_one_real )
% 9.53/5.33          @ at_top_nat )
% 9.53/5.33       => ~ ! [K2: nat > int] :
% 9.53/5.33              ~ ( filterlim_nat_real
% 9.53/5.33                @ ^ [J3: nat] : ( minus_minus_real @ ( Theta @ J3 ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K2 @ J3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 9.53/5.33                @ ( topolo2815343760600316023s_real @ Theta2 )
% 9.53/5.33                @ at_top_nat ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9985_cos__limit__1,axiom,
% 9.53/5.33      ! [Theta: nat > real] :
% 9.53/5.33        ( ( filterlim_nat_real
% 9.53/5.33          @ ^ [J3: nat] : ( cos_real @ ( Theta @ J3 ) )
% 9.53/5.33          @ ( topolo2815343760600316023s_real @ one_one_real )
% 9.53/5.33          @ at_top_nat )
% 9.53/5.33       => ? [K2: nat > int] :
% 9.53/5.33            ( filterlim_nat_real
% 9.53/5.33            @ ^ [J3: nat] : ( minus_minus_real @ ( Theta @ J3 ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K2 @ J3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 9.53/5.33            @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 9.53/5.33            @ at_top_nat ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9986_summable__Leibniz_I4_J,axiom,
% 9.53/5.33      ! [A: nat > real] :
% 9.53/5.33        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 9.53/5.33       => ( ( topolo6980174941875973593q_real @ A )
% 9.53/5.33         => ( filterlim_nat_real
% 9.53/5.33            @ ^ [N2: nat] :
% 9.53/5.33                ( groups6591440286371151544t_real
% 9.53/5.33                @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 9.53/5.33                @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 9.53/5.33            @ ( topolo2815343760600316023s_real
% 9.53/5.33              @ ( suminf_real
% 9.53/5.33                @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 9.53/5.33            @ at_top_nat ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9987_zeroseq__arctan__series,axiom,
% 9.53/5.33      ! [X: real] :
% 9.53/5.33        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 9.53/5.33       => ( filterlim_nat_real
% 9.53/5.33          @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) )
% 9.53/5.33          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 9.53/5.33          @ at_top_nat ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9988_summable__Leibniz_H_I2_J,axiom,
% 9.53/5.33      ! [A: nat > real,N: nat] :
% 9.53/5.33        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 9.53/5.33       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 9.53/5.33         => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 9.53/5.33           => ( ord_less_eq_real
% 9.53/5.33              @ ( groups6591440286371151544t_real
% 9.53/5.33                @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 9.53/5.33                @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 9.53/5.33              @ ( suminf_real
% 9.53/5.33                @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9989_summable__Leibniz_H_I3_J,axiom,
% 9.53/5.33      ! [A: nat > real] :
% 9.53/5.33        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 9.53/5.33       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 9.53/5.33         => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 9.53/5.33           => ( filterlim_nat_real
% 9.53/5.33              @ ^ [N2: nat] :
% 9.53/5.33                  ( groups6591440286371151544t_real
% 9.53/5.33                  @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 9.53/5.33                  @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 9.53/5.33              @ ( topolo2815343760600316023s_real
% 9.53/5.33                @ ( suminf_real
% 9.53/5.33                  @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 9.53/5.33              @ at_top_nat ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9990_sums__alternating__upper__lower,axiom,
% 9.53/5.33      ! [A: nat > real] :
% 9.53/5.33        ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 9.53/5.33       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 9.53/5.33         => ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 9.53/5.33           => ? [L4: real] :
% 9.53/5.33                ( ! [N9: nat] :
% 9.53/5.33                    ( ord_less_eq_real
% 9.53/5.33                    @ ( groups6591440286371151544t_real
% 9.53/5.33                      @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 9.53/5.33                      @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) ) )
% 9.53/5.33                    @ L4 )
% 9.53/5.33                & ( filterlim_nat_real
% 9.53/5.33                  @ ^ [N2: nat] :
% 9.53/5.33                      ( groups6591440286371151544t_real
% 9.53/5.33                      @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 9.53/5.33                      @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 9.53/5.33                  @ ( topolo2815343760600316023s_real @ L4 )
% 9.53/5.33                  @ at_top_nat )
% 9.53/5.33                & ! [N9: nat] :
% 9.53/5.33                    ( ord_less_eq_real @ L4
% 9.53/5.33                    @ ( groups6591440286371151544t_real
% 9.53/5.33                      @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 9.53/5.33                      @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) @ one_one_nat ) ) ) )
% 9.53/5.33                & ( filterlim_nat_real
% 9.53/5.33                  @ ^ [N2: nat] :
% 9.53/5.33                      ( groups6591440286371151544t_real
% 9.53/5.33                      @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 9.53/5.33                      @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 9.53/5.33                  @ ( topolo2815343760600316023s_real @ L4 )
% 9.53/5.33                  @ at_top_nat ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9991_summable__Leibniz_I5_J,axiom,
% 9.53/5.33      ! [A: nat > real] :
% 9.53/5.33        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 9.53/5.33       => ( ( topolo6980174941875973593q_real @ A )
% 9.53/5.33         => ( filterlim_nat_real
% 9.53/5.33            @ ^ [N2: nat] :
% 9.53/5.33                ( groups6591440286371151544t_real
% 9.53/5.33                @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 9.53/5.33                @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 9.53/5.33            @ ( topolo2815343760600316023s_real
% 9.53/5.33              @ ( suminf_real
% 9.53/5.33                @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 9.53/5.33            @ at_top_nat ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9992_summable__Leibniz_H_I4_J,axiom,
% 9.53/5.33      ! [A: nat > real,N: nat] :
% 9.53/5.33        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 9.53/5.33       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 9.53/5.33         => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 9.53/5.33           => ( ord_less_eq_real
% 9.53/5.33              @ ( suminf_real
% 9.53/5.33                @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) )
% 9.53/5.33              @ ( groups6591440286371151544t_real
% 9.53/5.33                @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 9.53/5.33                @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9993_summable__Leibniz_H_I5_J,axiom,
% 9.53/5.33      ! [A: nat > real] :
% 9.53/5.33        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 9.53/5.33       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 9.53/5.33         => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 9.53/5.33           => ( filterlim_nat_real
% 9.53/5.33              @ ^ [N2: nat] :
% 9.53/5.33                  ( groups6591440286371151544t_real
% 9.53/5.33                  @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 9.53/5.33                  @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 9.53/5.33              @ ( topolo2815343760600316023s_real
% 9.53/5.33                @ ( suminf_real
% 9.53/5.33                  @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 9.53/5.33              @ at_top_nat ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9994_real__bounded__linear,axiom,
% 9.53/5.33      ( real_V5970128139526366754l_real
% 9.53/5.33      = ( ^ [F3: real > real] :
% 9.53/5.33          ? [C3: real] :
% 9.53/5.33            ( F3
% 9.53/5.33            = ( ^ [X2: real] : ( times_times_real @ X2 @ C3 ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9995_filterlim__Suc,axiom,
% 9.53/5.33      filterlim_nat_nat @ suc @ at_top_nat @ at_top_nat ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9996_dist__complex__def,axiom,
% 9.53/5.33      ( real_V3694042436643373181omplex
% 9.53/5.33      = ( ^ [X2: complex,Y: complex] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Y ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9997_dist__real__def,axiom,
% 9.53/5.33      ( real_V975177566351809787t_real
% 9.53/5.33      = ( ^ [X2: real,Y: real] : ( abs_abs_real @ ( minus_minus_real @ X2 @ Y ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9998_tendsto__exp__limit__at__right,axiom,
% 9.53/5.33      ! [X: real] :
% 9.53/5.33        ( filterlim_real_real
% 9.53/5.33        @ ^ [Y: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ X @ Y ) ) @ ( divide_divide_real @ one_one_real @ Y ) )
% 9.53/5.33        @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 9.53/5.33        @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_9999_tendsto__arcosh__at__left__1,axiom,
% 9.53/5.33      filterlim_real_real @ arcosh_real @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5849166863359141190n_real @ one_one_real ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10000_filterlim__tan__at__right,axiom,
% 9.53/5.33      filterlim_real_real @ tan_real @ at_bot_real @ ( topolo2177554685111907308n_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( set_or5849166863359141190n_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10001_atLeast__Suc__greaterThan,axiom,
% 9.53/5.33      ! [K: nat] :
% 9.53/5.33        ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 9.53/5.33        = ( set_or1210151606488870762an_nat @ K ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10002_greaterThan__0,axiom,
% 9.53/5.33      ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 9.53/5.33      = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10003_greaterThan__Suc,axiom,
% 9.53/5.33      ! [K: nat] :
% 9.53/5.33        ( ( set_or1210151606488870762an_nat @ ( suc @ K ) )
% 9.53/5.33        = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K ) @ ( insert_nat @ ( suc @ K ) @ bot_bot_set_nat ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10004_atLeast__Suc,axiom,
% 9.53/5.33      ! [K: nat] :
% 9.53/5.33        ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 9.53/5.33        = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K ) @ ( insert_nat @ K @ bot_bot_set_nat ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10005_tanh__real__at__bot,axiom,
% 9.53/5.33      filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ one_one_real ) ) @ at_bot_real ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10006_artanh__real__at__right__1,axiom,
% 9.53/5.33      filterlim_real_real @ artanh_real @ at_bot_real @ ( topolo2177554685111907308n_real @ ( uminus_uminus_real @ one_one_real ) @ ( set_or5849166863359141190n_real @ ( uminus_uminus_real @ one_one_real ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10007_DERIV__pos__imp__increasing__at__bot,axiom,
% 9.53/5.33      ! [B: real,F: real > real,Flim: real] :
% 9.53/5.33        ( ! [X3: real] :
% 9.53/5.33            ( ( ord_less_eq_real @ X3 @ B )
% 9.53/5.33           => ? [Y4: real] :
% 9.53/5.33                ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 9.53/5.33                & ( ord_less_real @ zero_zero_real @ Y4 ) ) )
% 9.53/5.33       => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_bot_real )
% 9.53/5.33         => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10008_filterlim__pow__at__bot__odd,axiom,
% 9.53/5.33      ! [N: nat,F: real > real,F5: filter_real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( filterlim_real_real @ F @ at_bot_real @ F5 )
% 9.53/5.33         => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.53/5.33           => ( filterlim_real_real
% 9.53/5.33              @ ^ [X2: real] : ( power_power_real @ ( F @ X2 ) @ N )
% 9.53/5.33              @ at_bot_real
% 9.53/5.33              @ F5 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10009_tendsto__arctan__at__bot,axiom,
% 9.53/5.33      filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ at_bot_real ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10010_filterlim__pow__at__bot__even,axiom,
% 9.53/5.33      ! [N: nat,F: real > real,F5: filter_real] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( ( filterlim_real_real @ F @ at_bot_real @ F5 )
% 9.53/5.33         => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.53/5.33           => ( filterlim_real_real
% 9.53/5.33              @ ^ [X2: real] : ( power_power_real @ ( F @ X2 ) @ N )
% 9.53/5.33              @ at_top_real
% 9.53/5.33              @ F5 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10011_sqrt__at__top,axiom,
% 9.53/5.33      filterlim_real_real @ sqrt @ at_top_real @ at_top_real ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10012_tanh__real__at__top,axiom,
% 9.53/5.33      filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ one_one_real ) @ at_top_real ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10013_artanh__real__at__left__1,axiom,
% 9.53/5.33      filterlim_real_real @ artanh_real @ at_top_real @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5984915006950818249n_real @ one_one_real ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10014_ln__x__over__x__tendsto__0,axiom,
% 9.53/5.33      ( filterlim_real_real
% 9.53/5.33      @ ^ [X2: real] : ( divide_divide_real @ ( ln_ln_real @ X2 ) @ X2 )
% 9.53/5.33      @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 9.53/5.33      @ at_top_real ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10015_tendsto__power__div__exp__0,axiom,
% 9.53/5.33      ! [K: nat] :
% 9.53/5.33        ( filterlim_real_real
% 9.53/5.33        @ ^ [X2: real] : ( divide_divide_real @ ( power_power_real @ X2 @ K ) @ ( exp_real @ X2 ) )
% 9.53/5.33        @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 9.53/5.33        @ at_top_real ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10016_tendsto__exp__limit__at__top,axiom,
% 9.53/5.33      ! [X: real] :
% 9.53/5.33        ( filterlim_real_real
% 9.53/5.33        @ ^ [Y: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ Y ) ) @ Y )
% 9.53/5.33        @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 9.53/5.33        @ at_top_real ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10017_filterlim__tan__at__left,axiom,
% 9.53/5.33      filterlim_real_real @ tan_real @ at_top_real @ ( topolo2177554685111907308n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( set_or5984915006950818249n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10018_tendsto__arctan__at__top,axiom,
% 9.53/5.33      filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ at_top_real ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10019_DERIV__neg__imp__decreasing__at__top,axiom,
% 9.53/5.33      ! [B: real,F: real > real,Flim: real] :
% 9.53/5.33        ( ! [X3: real] :
% 9.53/5.33            ( ( ord_less_eq_real @ B @ X3 )
% 9.53/5.33           => ? [Y4: real] :
% 9.53/5.33                ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 9.53/5.33                & ( ord_less_real @ Y4 @ zero_zero_real ) ) )
% 9.53/5.33       => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_top_real )
% 9.53/5.33         => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10020_lhopital__right__at__top,axiom,
% 9.53/5.33      ! [G: real > real,X: real,G2: real > real,F: real > real,F4: real > real,Y2: real] :
% 9.53/5.33        ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 9.53/5.33       => ( ( eventually_real
% 9.53/5.33            @ ^ [X2: real] :
% 9.53/5.33                ( ( G2 @ X2 )
% 9.53/5.33               != zero_zero_real )
% 9.53/5.33            @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 9.53/5.33         => ( ( eventually_real
% 9.53/5.33              @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 9.53/5.33              @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 9.53/5.33           => ( ( eventually_real
% 9.53/5.33                @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 9.53/5.33                @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 9.53/5.33             => ( ( filterlim_real_real
% 9.53/5.33                  @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 9.53/5.33                  @ ( topolo2815343760600316023s_real @ Y2 )
% 9.53/5.33                  @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 9.53/5.33               => ( filterlim_real_real
% 9.53/5.33                  @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 9.53/5.33                  @ ( topolo2815343760600316023s_real @ Y2 )
% 9.53/5.33                  @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10021_eventually__sequentially__Suc,axiom,
% 9.53/5.33      ! [P: nat > $o] :
% 9.53/5.33        ( ( eventually_nat
% 9.53/5.33          @ ^ [I3: nat] : ( P @ ( suc @ I3 ) )
% 9.53/5.33          @ at_top_nat )
% 9.53/5.33        = ( eventually_nat @ P @ at_top_nat ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10022_eventually__sequentially__seg,axiom,
% 9.53/5.33      ! [P: nat > $o,K: nat] :
% 9.53/5.33        ( ( eventually_nat
% 9.53/5.33          @ ^ [N2: nat] : ( P @ ( plus_plus_nat @ N2 @ K ) )
% 9.53/5.33          @ at_top_nat )
% 9.53/5.33        = ( eventually_nat @ P @ at_top_nat ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10023_eventually__sequentially,axiom,
% 9.53/5.33      ! [P: nat > $o] :
% 9.53/5.33        ( ( eventually_nat @ P @ at_top_nat )
% 9.53/5.33        = ( ? [N6: nat] :
% 9.53/5.33            ! [N2: nat] :
% 9.53/5.33              ( ( ord_less_eq_nat @ N6 @ N2 )
% 9.53/5.33             => ( P @ N2 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10024_eventually__sequentiallyI,axiom,
% 9.53/5.33      ! [C: nat,P: nat > $o] :
% 9.53/5.33        ( ! [X3: nat] :
% 9.53/5.33            ( ( ord_less_eq_nat @ C @ X3 )
% 9.53/5.33           => ( P @ X3 ) )
% 9.53/5.33       => ( eventually_nat @ P @ at_top_nat ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10025_le__sequentially,axiom,
% 9.53/5.33      ! [F5: filter_nat] :
% 9.53/5.33        ( ( ord_le2510731241096832064er_nat @ F5 @ at_top_nat )
% 9.53/5.33        = ( ! [N6: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N6 ) @ F5 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10026_sequentially__offset,axiom,
% 9.53/5.33      ! [P: nat > $o,K: nat] :
% 9.53/5.33        ( ( eventually_nat @ P @ at_top_nat )
% 9.53/5.33       => ( eventually_nat
% 9.53/5.33          @ ^ [I3: nat] : ( P @ ( plus_plus_nat @ I3 @ K ) )
% 9.53/5.33          @ at_top_nat ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10027_eventually__at__left__real,axiom,
% 9.53/5.33      ! [B: real,A: real] :
% 9.53/5.33        ( ( ord_less_real @ B @ A )
% 9.53/5.33       => ( eventually_real
% 9.53/5.33          @ ^ [X2: real] : ( member_real @ X2 @ ( set_or1633881224788618240n_real @ B @ A ) )
% 9.53/5.33          @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10028_eventually__at__right__to__0,axiom,
% 9.53/5.33      ! [P: real > $o,A: real] :
% 9.53/5.33        ( ( eventually_real @ P @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 9.53/5.33        = ( eventually_real
% 9.53/5.33          @ ^ [X2: real] : ( P @ ( plus_plus_real @ X2 @ A ) )
% 9.53/5.33          @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10029_eventually__at__right__real,axiom,
% 9.53/5.33      ! [A: real,B: real] :
% 9.53/5.33        ( ( ord_less_real @ A @ B )
% 9.53/5.33       => ( eventually_real
% 9.53/5.33          @ ^ [X2: real] : ( member_real @ X2 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 9.53/5.33          @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10030_lhopital__left__at__top__at__top,axiom,
% 9.53/5.33      ! [F: real > real,A: real,G: real > real,F4: real > real,G2: real > real] :
% 9.53/5.33        ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 9.53/5.33       => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 9.53/5.33         => ( ( eventually_real
% 9.53/5.33              @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 9.53/5.33              @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 9.53/5.33           => ( ( eventually_real
% 9.53/5.33                @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 9.53/5.33                @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 9.53/5.33             => ( ( filterlim_real_real
% 9.53/5.33                  @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 9.53/5.33                  @ at_top_real
% 9.53/5.33                  @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 9.53/5.33               => ( filterlim_real_real
% 9.53/5.33                  @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 9.53/5.33                  @ at_top_real
% 9.53/5.33                  @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10031_lhopital__at__top__at__top,axiom,
% 9.53/5.33      ! [F: real > real,A: real,G: real > real,F4: real > real,G2: real > real] :
% 9.53/5.33        ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 9.53/5.33       => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 9.53/5.33         => ( ( eventually_real
% 9.53/5.33              @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 9.53/5.33              @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 9.53/5.33           => ( ( eventually_real
% 9.53/5.33                @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 9.53/5.33                @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 9.53/5.33             => ( ( filterlim_real_real
% 9.53/5.33                  @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 9.53/5.33                  @ at_top_real
% 9.53/5.33                  @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 9.53/5.33               => ( filterlim_real_real
% 9.53/5.33                  @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 9.53/5.33                  @ at_top_real
% 9.53/5.33                  @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10032_lhopital__left,axiom,
% 9.53/5.33      ! [F: real > real,X: real,G: real > real,G2: real > real,F4: real > real,F5: filter_real] :
% 9.53/5.33        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 9.53/5.33       => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 9.53/5.33         => ( ( eventually_real
% 9.53/5.33              @ ^ [X2: real] :
% 9.53/5.33                  ( ( G @ X2 )
% 9.53/5.33                 != zero_zero_real )
% 9.53/5.33              @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 9.53/5.33           => ( ( eventually_real
% 9.53/5.33                @ ^ [X2: real] :
% 9.53/5.33                    ( ( G2 @ X2 )
% 9.53/5.33                   != zero_zero_real )
% 9.53/5.33                @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 9.53/5.33             => ( ( eventually_real
% 9.53/5.33                  @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 9.53/5.33                  @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 9.53/5.33               => ( ( eventually_real
% 9.53/5.33                    @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 9.53/5.33                    @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 9.53/5.33                 => ( ( filterlim_real_real
% 9.53/5.33                      @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 9.53/5.33                      @ F5
% 9.53/5.33                      @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 9.53/5.33                   => ( filterlim_real_real
% 9.53/5.33                      @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 9.53/5.33                      @ F5
% 9.53/5.33                      @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10033_lhopital,axiom,
% 9.53/5.33      ! [F: real > real,X: real,G: real > real,G2: real > real,F4: real > real,F5: filter_real] :
% 9.53/5.33        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 9.53/5.33       => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 9.53/5.33         => ( ( eventually_real
% 9.53/5.33              @ ^ [X2: real] :
% 9.53/5.33                  ( ( G @ X2 )
% 9.53/5.33                 != zero_zero_real )
% 9.53/5.33              @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 9.53/5.33           => ( ( eventually_real
% 9.53/5.33                @ ^ [X2: real] :
% 9.53/5.33                    ( ( G2 @ X2 )
% 9.53/5.33                   != zero_zero_real )
% 9.53/5.33                @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 9.53/5.33             => ( ( eventually_real
% 9.53/5.33                  @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 9.53/5.33                  @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 9.53/5.33               => ( ( eventually_real
% 9.53/5.33                    @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 9.53/5.33                    @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 9.53/5.33                 => ( ( filterlim_real_real
% 9.53/5.33                      @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 9.53/5.33                      @ F5
% 9.53/5.33                      @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 9.53/5.33                   => ( filterlim_real_real
% 9.53/5.33                      @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 9.53/5.33                      @ F5
% 9.53/5.33                      @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10034_lhopital__right__at__top__at__top,axiom,
% 9.53/5.33      ! [F: real > real,A: real,G: real > real,F4: real > real,G2: real > real] :
% 9.53/5.33        ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 9.53/5.33       => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 9.53/5.33         => ( ( eventually_real
% 9.53/5.33              @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 9.53/5.33              @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 9.53/5.33           => ( ( eventually_real
% 9.53/5.33                @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 9.53/5.33                @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 9.53/5.33             => ( ( filterlim_real_real
% 9.53/5.33                  @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 9.53/5.33                  @ at_top_real
% 9.53/5.33                  @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 9.53/5.33               => ( filterlim_real_real
% 9.53/5.33                  @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 9.53/5.33                  @ at_top_real
% 9.53/5.33                  @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10035_lhopital__left__at__top__at__bot,axiom,
% 9.53/5.33      ! [F: real > real,A: real,G: real > real,F4: real > real,G2: real > real] :
% 9.53/5.33        ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 9.53/5.33       => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 9.53/5.33         => ( ( eventually_real
% 9.53/5.33              @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 9.53/5.33              @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 9.53/5.33           => ( ( eventually_real
% 9.53/5.33                @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 9.53/5.33                @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 9.53/5.33             => ( ( filterlim_real_real
% 9.53/5.33                  @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 9.53/5.33                  @ at_bot_real
% 9.53/5.33                  @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 9.53/5.33               => ( filterlim_real_real
% 9.53/5.33                  @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 9.53/5.33                  @ at_bot_real
% 9.53/5.33                  @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10036_lhopital__at__top__at__bot,axiom,
% 9.53/5.33      ! [F: real > real,A: real,G: real > real,F4: real > real,G2: real > real] :
% 9.53/5.33        ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 9.53/5.33       => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 9.53/5.33         => ( ( eventually_real
% 9.53/5.33              @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 9.53/5.33              @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 9.53/5.33           => ( ( eventually_real
% 9.53/5.33                @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 9.53/5.33                @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 9.53/5.33             => ( ( filterlim_real_real
% 9.53/5.33                  @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 9.53/5.33                  @ at_bot_real
% 9.53/5.33                  @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 9.53/5.33               => ( filterlim_real_real
% 9.53/5.33                  @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 9.53/5.33                  @ at_bot_real
% 9.53/5.33                  @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10037_lhopital__left__at__top,axiom,
% 9.53/5.33      ! [G: real > real,X: real,G2: real > real,F: real > real,F4: real > real,Y2: real] :
% 9.53/5.33        ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 9.53/5.33       => ( ( eventually_real
% 9.53/5.33            @ ^ [X2: real] :
% 9.53/5.33                ( ( G2 @ X2 )
% 9.53/5.33               != zero_zero_real )
% 9.53/5.33            @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 9.53/5.33         => ( ( eventually_real
% 9.53/5.33              @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 9.53/5.33              @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 9.53/5.33           => ( ( eventually_real
% 9.53/5.33                @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 9.53/5.33                @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 9.53/5.33             => ( ( filterlim_real_real
% 9.53/5.33                  @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 9.53/5.33                  @ ( topolo2815343760600316023s_real @ Y2 )
% 9.53/5.33                  @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 9.53/5.33               => ( filterlim_real_real
% 9.53/5.33                  @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 9.53/5.33                  @ ( topolo2815343760600316023s_real @ Y2 )
% 9.53/5.33                  @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10038_lhopital__at__top,axiom,
% 9.53/5.33      ! [G: real > real,X: real,G2: real > real,F: real > real,F4: real > real,Y2: real] :
% 9.53/5.33        ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 9.53/5.33       => ( ( eventually_real
% 9.53/5.33            @ ^ [X2: real] :
% 9.53/5.33                ( ( G2 @ X2 )
% 9.53/5.33               != zero_zero_real )
% 9.53/5.33            @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 9.53/5.33         => ( ( eventually_real
% 9.53/5.33              @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 9.53/5.33              @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 9.53/5.33           => ( ( eventually_real
% 9.53/5.33                @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 9.53/5.33                @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 9.53/5.33             => ( ( filterlim_real_real
% 9.53/5.33                  @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 9.53/5.33                  @ ( topolo2815343760600316023s_real @ Y2 )
% 9.53/5.33                  @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 9.53/5.33               => ( filterlim_real_real
% 9.53/5.33                  @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 9.53/5.33                  @ ( topolo2815343760600316023s_real @ Y2 )
% 9.53/5.33                  @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10039_lhospital__at__top__at__top,axiom,
% 9.53/5.33      ! [G: real > real,G2: real > real,F: real > real,F4: real > real,X: real] :
% 9.53/5.33        ( ( filterlim_real_real @ G @ at_top_real @ at_top_real )
% 9.53/5.33       => ( ( eventually_real
% 9.53/5.33            @ ^ [X2: real] :
% 9.53/5.33                ( ( G2 @ X2 )
% 9.53/5.33               != zero_zero_real )
% 9.53/5.33            @ at_top_real )
% 9.53/5.33         => ( ( eventually_real
% 9.53/5.33              @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 9.53/5.33              @ at_top_real )
% 9.53/5.33           => ( ( eventually_real
% 9.53/5.33                @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 9.53/5.33                @ at_top_real )
% 9.53/5.33             => ( ( filterlim_real_real
% 9.53/5.33                  @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 9.53/5.33                  @ ( topolo2815343760600316023s_real @ X )
% 9.53/5.33                  @ at_top_real )
% 9.53/5.33               => ( filterlim_real_real
% 9.53/5.33                  @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 9.53/5.33                  @ ( topolo2815343760600316023s_real @ X )
% 9.53/5.33                  @ at_top_real ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10040_lhopital__right,axiom,
% 9.53/5.33      ! [F: real > real,X: real,G: real > real,G2: real > real,F4: real > real,F5: filter_real] :
% 9.53/5.33        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 9.53/5.33       => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 9.53/5.33         => ( ( eventually_real
% 9.53/5.33              @ ^ [X2: real] :
% 9.53/5.33                  ( ( G @ X2 )
% 9.53/5.33                 != zero_zero_real )
% 9.53/5.33              @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 9.53/5.33           => ( ( eventually_real
% 9.53/5.33                @ ^ [X2: real] :
% 9.53/5.33                    ( ( G2 @ X2 )
% 9.53/5.33                   != zero_zero_real )
% 9.53/5.33                @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 9.53/5.33             => ( ( eventually_real
% 9.53/5.33                  @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 9.53/5.33                  @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 9.53/5.33               => ( ( eventually_real
% 9.53/5.33                    @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 9.53/5.33                    @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 9.53/5.33                 => ( ( filterlim_real_real
% 9.53/5.33                      @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 9.53/5.33                      @ F5
% 9.53/5.33                      @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 9.53/5.33                   => ( filterlim_real_real
% 9.53/5.33                      @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 9.53/5.33                      @ F5
% 9.53/5.33                      @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10041_lhopital__right__0,axiom,
% 9.53/5.33      ! [F0: real > real,G0: real > real,G2: real > real,F4: real > real,F5: filter_real] :
% 9.53/5.33        ( ( filterlim_real_real @ F0 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 9.53/5.33       => ( ( filterlim_real_real @ G0 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 9.53/5.33         => ( ( eventually_real
% 9.53/5.33              @ ^ [X2: real] :
% 9.53/5.33                  ( ( G0 @ X2 )
% 9.53/5.33                 != zero_zero_real )
% 9.53/5.33              @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 9.53/5.33           => ( ( eventually_real
% 9.53/5.33                @ ^ [X2: real] :
% 9.53/5.33                    ( ( G2 @ X2 )
% 9.53/5.33                   != zero_zero_real )
% 9.53/5.33                @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 9.53/5.33             => ( ( eventually_real
% 9.53/5.33                  @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F0 @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 9.53/5.33                  @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 9.53/5.33               => ( ( eventually_real
% 9.53/5.33                    @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G0 @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 9.53/5.33                    @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 9.53/5.33                 => ( ( filterlim_real_real
% 9.53/5.33                      @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 9.53/5.33                      @ F5
% 9.53/5.33                      @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 9.53/5.33                   => ( filterlim_real_real
% 9.53/5.33                      @ ^ [X2: real] : ( divide_divide_real @ ( F0 @ X2 ) @ ( G0 @ X2 ) )
% 9.53/5.33                      @ F5
% 9.53/5.33                      @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10042_lhopital__right__at__top__at__bot,axiom,
% 9.53/5.33      ! [F: real > real,A: real,G: real > real,F4: real > real,G2: real > real] :
% 9.53/5.33        ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 9.53/5.33       => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 9.53/5.33         => ( ( eventually_real
% 9.53/5.33              @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 9.53/5.33              @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 9.53/5.33           => ( ( eventually_real
% 9.53/5.33                @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 9.53/5.33                @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 9.53/5.33             => ( ( filterlim_real_real
% 9.53/5.33                  @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 9.53/5.33                  @ at_bot_real
% 9.53/5.33                  @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 9.53/5.33               => ( filterlim_real_real
% 9.53/5.33                  @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 9.53/5.33                  @ at_bot_real
% 9.53/5.33                  @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10043_lhopital__right__0__at__top,axiom,
% 9.53/5.33      ! [G: real > real,G2: real > real,F: real > real,F4: real > real,X: real] :
% 9.53/5.33        ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 9.53/5.33       => ( ( eventually_real
% 9.53/5.33            @ ^ [X2: real] :
% 9.53/5.33                ( ( G2 @ X2 )
% 9.53/5.33               != zero_zero_real )
% 9.53/5.33            @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 9.53/5.33         => ( ( eventually_real
% 9.53/5.33              @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 9.53/5.33              @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 9.53/5.33           => ( ( eventually_real
% 9.53/5.33                @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 9.53/5.33                @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 9.53/5.33             => ( ( filterlim_real_real
% 9.53/5.33                  @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 9.53/5.33                  @ ( topolo2815343760600316023s_real @ X )
% 9.53/5.33                  @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 9.53/5.33               => ( filterlim_real_real
% 9.53/5.33                  @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 9.53/5.33                  @ ( topolo2815343760600316023s_real @ X )
% 9.53/5.33                  @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10044_GreatestI__nat,axiom,
% 9.53/5.33      ! [P: nat > $o,K: nat,B: nat] :
% 9.53/5.33        ( ( P @ K )
% 9.53/5.33       => ( ! [Y3: nat] :
% 9.53/5.33              ( ( P @ Y3 )
% 9.53/5.33             => ( ord_less_eq_nat @ Y3 @ B ) )
% 9.53/5.33         => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10045_Greatest__le__nat,axiom,
% 9.53/5.33      ! [P: nat > $o,K: nat,B: nat] :
% 9.53/5.33        ( ( P @ K )
% 9.53/5.33       => ( ! [Y3: nat] :
% 9.53/5.33              ( ( P @ Y3 )
% 9.53/5.33             => ( ord_less_eq_nat @ Y3 @ B ) )
% 9.53/5.33         => ( ord_less_eq_nat @ K @ ( order_Greatest_nat @ P ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10046_GreatestI__ex__nat,axiom,
% 9.53/5.33      ! [P: nat > $o,B: nat] :
% 9.53/5.33        ( ? [X_1: nat] : ( P @ X_1 )
% 9.53/5.33       => ( ! [Y3: nat] :
% 9.53/5.33              ( ( P @ Y3 )
% 9.53/5.33             => ( ord_less_eq_nat @ Y3 @ B ) )
% 9.53/5.33         => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10047_Bseq__realpow,axiom,
% 9.53/5.33      ! [X: real] :
% 9.53/5.33        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.33       => ( ( ord_less_eq_real @ X @ one_one_real )
% 9.53/5.33         => ( bfun_nat_real @ ( power_power_real @ X ) @ at_top_nat ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10048_VEBT__internal_Ovalid_H_Oelims_I1_J,axiom,
% 9.53/5.33      ! [X: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 9.53/5.33        ( ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 9.53/5.33          = Y2 )
% 9.53/5.33       => ( ( ? [Uu2: $o,Uv2: $o] :
% 9.53/5.33                ( X
% 9.53/5.33                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 9.53/5.33           => ( Y2
% 9.53/5.33              = ( Xa2 != one_one_nat ) ) )
% 9.53/5.33         => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.53/5.33                ( ( X
% 9.53/5.33                  = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 9.53/5.33               => ( Y2
% 9.53/5.33                  = ( ~ ( ( Deg2 = Xa2 )
% 9.53/5.33                        & ! [X2: vEBT_VEBT] :
% 9.53/5.33                            ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 9.53/5.33                           => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.53/5.33                        & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.53/5.33                        & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 9.53/5.33                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.53/5.33                        & ( case_o184042715313410164at_nat
% 9.53/5.33                          @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 9.53/5.33                            & ! [X2: vEBT_VEBT] :
% 9.53/5.33                                ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 9.53/5.33                               => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 9.53/5.33                          @ ( produc6081775807080527818_nat_o
% 9.53/5.33                            @ ^ [Mi3: nat,Ma3: nat] :
% 9.53/5.33                                ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 9.53/5.33                                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 9.53/5.33                                & ! [I3: nat] :
% 9.53/5.33                                    ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.53/5.33                                   => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X4 ) )
% 9.53/5.33                                      = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 9.53/5.33                                & ( ( Mi3 = Ma3 )
% 9.53/5.33                                 => ! [X2: vEBT_VEBT] :
% 9.53/5.33                                      ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 9.53/5.33                                     => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 9.53/5.33                                & ( ( Mi3 != Ma3 )
% 9.53/5.33                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 9.53/5.33                                    & ! [X2: nat] :
% 9.53/5.33                                        ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 9.53/5.33                                       => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X2 )
% 9.53/5.33                                         => ( ( ord_less_nat @ Mi3 @ X2 )
% 9.53/5.33                                            & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 9.53/5.33                          @ Mima ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10049_decseq__bounded,axiom,
% 9.53/5.33      ! [X8: nat > real,B2: real] :
% 9.53/5.33        ( ( order_9091379641038594480t_real @ X8 )
% 9.53/5.33       => ( ! [I4: nat] : ( ord_less_eq_real @ B2 @ ( X8 @ I4 ) )
% 9.53/5.33         => ( bfun_nat_real @ X8 @ at_top_nat ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10050_decseq__convergent,axiom,
% 9.53/5.33      ! [X8: nat > real,B2: real] :
% 9.53/5.33        ( ( order_9091379641038594480t_real @ X8 )
% 9.53/5.33       => ( ! [I4: nat] : ( ord_less_eq_real @ B2 @ ( X8 @ I4 ) )
% 9.53/5.33         => ~ ! [L6: real] :
% 9.53/5.33                ( ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 9.53/5.33               => ~ ! [I: nat] : ( ord_less_eq_real @ L6 @ ( X8 @ I ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10051_VEBT__internal_Ovalid_H_Osimps_I2_J,axiom,
% 9.53/5.33      ! [Mima2: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Deg4: nat] :
% 9.53/5.33        ( ( vEBT_VEBT_valid @ ( vEBT_Node @ Mima2 @ Deg @ TreeList @ Summary ) @ Deg4 )
% 9.53/5.33        = ( ( Deg = Deg4 )
% 9.53/5.33          & ! [X2: vEBT_VEBT] :
% 9.53/5.33              ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 9.53/5.33             => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.53/5.33          & ( vEBT_VEBT_valid @ Summary @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.53/5.33          & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 9.53/5.33            = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.53/5.33          & ( case_o184042715313410164at_nat
% 9.53/5.33            @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X4 )
% 9.53/5.33              & ! [X2: vEBT_VEBT] :
% 9.53/5.33                  ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 9.53/5.33                 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 9.53/5.33            @ ( produc6081775807080527818_nat_o
% 9.53/5.33              @ ^ [Mi3: nat,Ma3: nat] :
% 9.53/5.33                  ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 9.53/5.33                  & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 9.53/5.33                  & ! [I3: nat] :
% 9.53/5.33                      ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.53/5.33                     => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ X4 ) )
% 9.53/5.33                        = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 9.53/5.33                  & ( ( Mi3 = Ma3 )
% 9.53/5.33                   => ! [X2: vEBT_VEBT] :
% 9.53/5.33                        ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 9.53/5.33                       => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 9.53/5.33                  & ( ( Mi3 != Ma3 )
% 9.53/5.33                   => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 9.53/5.33                      & ! [X2: nat] :
% 9.53/5.33                          ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 9.53/5.33                         => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X2 )
% 9.53/5.33                           => ( ( ord_less_nat @ Mi3 @ X2 )
% 9.53/5.33                              & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 9.53/5.33            @ Mima2 ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10052_VEBT__internal_Ovalid_H_Oelims_I3_J,axiom,
% 9.53/5.33      ! [X: vEBT_VEBT,Xa2: nat] :
% 9.53/5.33        ( ~ ( vEBT_VEBT_valid @ X @ Xa2 )
% 9.53/5.33       => ( ( ? [Uu2: $o,Uv2: $o] :
% 9.53/5.33                ( X
% 9.53/5.33                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 9.53/5.33           => ( Xa2 = one_one_nat ) )
% 9.53/5.33         => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.53/5.33                ( ( X
% 9.53/5.33                  = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 9.53/5.33               => ( ( Deg2 = Xa2 )
% 9.53/5.33                  & ! [X3: vEBT_VEBT] :
% 9.53/5.33                      ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 9.53/5.33                     => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.53/5.33                  & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.53/5.33                  & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 9.53/5.33                    = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.53/5.33                  & ( case_o184042715313410164at_nat
% 9.53/5.33                    @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 9.53/5.33                      & ! [X2: vEBT_VEBT] :
% 9.53/5.33                          ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 9.53/5.33                         => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 9.53/5.33                    @ ( produc6081775807080527818_nat_o
% 9.53/5.33                      @ ^ [Mi3: nat,Ma3: nat] :
% 9.53/5.33                          ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 9.53/5.33                          & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 9.53/5.33                          & ! [I3: nat] :
% 9.53/5.33                              ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.53/5.33                             => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X4 ) )
% 9.53/5.33                                = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 9.53/5.33                          & ( ( Mi3 = Ma3 )
% 9.53/5.33                           => ! [X2: vEBT_VEBT] :
% 9.53/5.33                                ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 9.53/5.33                               => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 9.53/5.33                          & ( ( Mi3 != Ma3 )
% 9.53/5.33                           => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 9.53/5.33                              & ! [X2: nat] :
% 9.53/5.33                                  ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 9.53/5.33                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X2 )
% 9.53/5.33                                   => ( ( ord_less_nat @ Mi3 @ X2 )
% 9.53/5.33                                      & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 9.53/5.33                    @ Mima ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10053_VEBT__internal_Ovalid_H_Oelims_I2_J,axiom,
% 9.53/5.33      ! [X: vEBT_VEBT,Xa2: nat] :
% 9.53/5.33        ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 9.53/5.33       => ( ( ? [Uu2: $o,Uv2: $o] :
% 9.53/5.33                ( X
% 9.53/5.33                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 9.53/5.33           => ( Xa2 != one_one_nat ) )
% 9.53/5.33         => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.53/5.33                ( ( X
% 9.53/5.33                  = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 9.53/5.33               => ~ ( ( Deg2 = Xa2 )
% 9.53/5.33                    & ! [X5: vEBT_VEBT] :
% 9.53/5.33                        ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 9.53/5.33                       => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.53/5.33                    & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.53/5.33                    & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 9.53/5.33                      = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.53/5.33                    & ( case_o184042715313410164at_nat
% 9.53/5.33                      @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 9.53/5.33                        & ! [X2: vEBT_VEBT] :
% 9.53/5.33                            ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 9.53/5.33                           => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 9.53/5.33                      @ ( produc6081775807080527818_nat_o
% 9.53/5.33                        @ ^ [Mi3: nat,Ma3: nat] :
% 9.53/5.33                            ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 9.53/5.33                            & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 9.53/5.33                            & ! [I3: nat] :
% 9.53/5.33                                ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.53/5.33                               => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X4 ) )
% 9.53/5.33                                  = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 9.53/5.33                            & ( ( Mi3 = Ma3 )
% 9.53/5.33                             => ! [X2: vEBT_VEBT] :
% 9.53/5.33                                  ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 9.53/5.33                                 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 9.53/5.33                            & ( ( Mi3 != Ma3 )
% 9.53/5.33                             => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 9.53/5.33                                & ! [X2: nat] :
% 9.53/5.33                                    ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 9.53/5.33                                   => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X2 )
% 9.53/5.33                                     => ( ( ord_less_nat @ Mi3 @ X2 )
% 9.53/5.33                                        & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 9.53/5.33                      @ Mima ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10054_VEBT__internal_Ovalid_H_Opelims_I3_J,axiom,
% 9.53/5.33      ! [X: vEBT_VEBT,Xa2: nat] :
% 9.53/5.33        ( ~ ( vEBT_VEBT_valid @ X @ Xa2 )
% 9.53/5.33       => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 9.53/5.33         => ( ! [Uu2: $o,Uv2: $o] :
% 9.53/5.33                ( ( X
% 9.53/5.33                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 9.53/5.33               => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 9.53/5.33                 => ( Xa2 = one_one_nat ) ) )
% 9.53/5.33           => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.53/5.33                  ( ( X
% 9.53/5.33                    = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 9.53/5.33                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) )
% 9.53/5.33                   => ( ( Deg2 = Xa2 )
% 9.53/5.33                      & ! [X3: vEBT_VEBT] :
% 9.53/5.33                          ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 9.53/5.33                         => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.53/5.33                      & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.53/5.33                      & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 9.53/5.33                        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.53/5.33                      & ( case_o184042715313410164at_nat
% 9.53/5.33                        @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 9.53/5.33                          & ! [X2: vEBT_VEBT] :
% 9.53/5.33                              ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 9.53/5.33                             => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 9.53/5.33                        @ ( produc6081775807080527818_nat_o
% 9.53/5.33                          @ ^ [Mi3: nat,Ma3: nat] :
% 9.53/5.33                              ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 9.53/5.33                              & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 9.53/5.33                              & ! [I3: nat] :
% 9.53/5.33                                  ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.53/5.33                                 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X4 ) )
% 9.53/5.33                                    = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 9.53/5.33                              & ( ( Mi3 = Ma3 )
% 9.53/5.33                               => ! [X2: vEBT_VEBT] :
% 9.53/5.33                                    ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 9.53/5.33                                   => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 9.53/5.33                              & ( ( Mi3 != Ma3 )
% 9.53/5.33                               => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 9.53/5.33                                  & ! [X2: nat] :
% 9.53/5.33                                      ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 9.53/5.33                                     => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X2 )
% 9.53/5.33                                       => ( ( ord_less_nat @ Mi3 @ X2 )
% 9.53/5.33                                          & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 9.53/5.33                        @ Mima ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10055_VEBT__internal_Ovalid_H_Opelims_I2_J,axiom,
% 9.53/5.33      ! [X: vEBT_VEBT,Xa2: nat] :
% 9.53/5.33        ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 9.53/5.33       => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 9.53/5.33         => ( ! [Uu2: $o,Uv2: $o] :
% 9.53/5.33                ( ( X
% 9.53/5.33                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 9.53/5.33               => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 9.53/5.33                 => ( Xa2 != one_one_nat ) ) )
% 9.53/5.33           => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.53/5.33                  ( ( X
% 9.53/5.33                    = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 9.53/5.33                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) )
% 9.53/5.33                   => ~ ( ( Deg2 = Xa2 )
% 9.53/5.33                        & ! [X5: vEBT_VEBT] :
% 9.53/5.33                            ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 9.53/5.33                           => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.53/5.33                        & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.53/5.33                        & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 9.53/5.33                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.53/5.33                        & ( case_o184042715313410164at_nat
% 9.53/5.33                          @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 9.53/5.33                            & ! [X2: vEBT_VEBT] :
% 9.53/5.33                                ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 9.53/5.33                               => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 9.53/5.33                          @ ( produc6081775807080527818_nat_o
% 9.53/5.33                            @ ^ [Mi3: nat,Ma3: nat] :
% 9.53/5.33                                ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 9.53/5.33                                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 9.53/5.33                                & ! [I3: nat] :
% 9.53/5.33                                    ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.53/5.33                                   => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X4 ) )
% 9.53/5.33                                      = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 9.53/5.33                                & ( ( Mi3 = Ma3 )
% 9.53/5.33                                 => ! [X2: vEBT_VEBT] :
% 9.53/5.33                                      ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 9.53/5.33                                     => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 9.53/5.33                                & ( ( Mi3 != Ma3 )
% 9.53/5.33                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 9.53/5.33                                    & ! [X2: nat] :
% 9.53/5.33                                        ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 9.53/5.33                                       => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X2 )
% 9.53/5.33                                         => ( ( ord_less_nat @ Mi3 @ X2 )
% 9.53/5.33                                            & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 9.53/5.33                          @ Mima ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10056_VEBT__internal_Ovalid_H_Opelims_I1_J,axiom,
% 9.53/5.33      ! [X: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 9.53/5.33        ( ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 9.53/5.33          = Y2 )
% 9.53/5.33       => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 9.53/5.33         => ( ! [Uu2: $o,Uv2: $o] :
% 9.53/5.33                ( ( X
% 9.53/5.33                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 9.53/5.33               => ( ( Y2
% 9.53/5.33                    = ( Xa2 = one_one_nat ) )
% 9.53/5.33                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 9.53/5.33           => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 9.53/5.33                  ( ( X
% 9.53/5.33                    = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 9.53/5.33                 => ( ( Y2
% 9.53/5.33                      = ( ( Deg2 = Xa2 )
% 9.53/5.33                        & ! [X2: vEBT_VEBT] :
% 9.53/5.33                            ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 9.53/5.33                           => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.53/5.33                        & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.53/5.33                        & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 9.53/5.33                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.53/5.33                        & ( case_o184042715313410164at_nat
% 9.53/5.33                          @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 9.53/5.33                            & ! [X2: vEBT_VEBT] :
% 9.53/5.33                                ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 9.53/5.33                               => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 9.53/5.33                          @ ( produc6081775807080527818_nat_o
% 9.53/5.33                            @ ^ [Mi3: nat,Ma3: nat] :
% 9.53/5.33                                ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 9.53/5.33                                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 9.53/5.33                                & ! [I3: nat] :
% 9.53/5.33                                    ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 9.53/5.33                                   => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X4 ) )
% 9.53/5.33                                      = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 9.53/5.33                                & ( ( Mi3 = Ma3 )
% 9.53/5.33                                 => ! [X2: vEBT_VEBT] :
% 9.53/5.33                                      ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 9.53/5.33                                     => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 9.53/5.33                                & ( ( Mi3 != Ma3 )
% 9.53/5.33                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 9.53/5.33                                    & ! [X2: nat] :
% 9.53/5.33                                        ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 9.53/5.33                                       => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X2 )
% 9.53/5.33                                         => ( ( ord_less_nat @ Mi3 @ X2 )
% 9.53/5.33                                            & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 9.53/5.33                          @ Mima ) ) )
% 9.53/5.33                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10057_GMVT,axiom,
% 9.53/5.33      ! [A: real,B: real,F: real > real,G: real > real] :
% 9.53/5.33        ( ( ord_less_real @ A @ B )
% 9.53/5.33       => ( ! [X3: real] :
% 9.53/5.33              ( ( ( ord_less_eq_real @ A @ X3 )
% 9.53/5.33                & ( ord_less_eq_real @ X3 @ B ) )
% 9.53/5.33             => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ F ) )
% 9.53/5.33         => ( ! [X3: real] :
% 9.53/5.33                ( ( ( ord_less_real @ A @ X3 )
% 9.53/5.33                  & ( ord_less_real @ X3 @ B ) )
% 9.53/5.33               => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 9.53/5.33           => ( ! [X3: real] :
% 9.53/5.33                  ( ( ( ord_less_eq_real @ A @ X3 )
% 9.53/5.33                    & ( ord_less_eq_real @ X3 @ B ) )
% 9.53/5.33                 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ G ) )
% 9.53/5.33             => ( ! [X3: real] :
% 9.53/5.33                    ( ( ( ord_less_real @ A @ X3 )
% 9.53/5.33                      & ( ord_less_real @ X3 @ B ) )
% 9.53/5.33                   => ( differ6690327859849518006l_real @ G @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 9.53/5.33               => ? [G_c: real,F_c: real,C2: real] :
% 9.53/5.33                    ( ( has_fi5821293074295781190e_real @ G @ G_c @ ( topolo2177554685111907308n_real @ C2 @ top_top_set_real ) )
% 9.53/5.33                    & ( has_fi5821293074295781190e_real @ F @ F_c @ ( topolo2177554685111907308n_real @ C2 @ top_top_set_real ) )
% 9.53/5.33                    & ( ord_less_real @ A @ C2 )
% 9.53/5.33                    & ( ord_less_real @ C2 @ B )
% 9.53/5.33                    & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ G_c )
% 9.53/5.33                      = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ F_c ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10058_MVT,axiom,
% 9.53/5.33      ! [A: real,B: real,F: real > real] :
% 9.53/5.33        ( ( ord_less_real @ A @ B )
% 9.53/5.33       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 9.53/5.33         => ( ! [X3: real] :
% 9.53/5.33                ( ( ord_less_real @ A @ X3 )
% 9.53/5.33               => ( ( ord_less_real @ X3 @ B )
% 9.53/5.33                 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 9.53/5.33           => ? [L4: real,Z3: real] :
% 9.53/5.33                ( ( ord_less_real @ A @ Z3 )
% 9.53/5.33                & ( ord_less_real @ Z3 @ B )
% 9.53/5.33                & ( has_fi5821293074295781190e_real @ F @ L4 @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) )
% 9.53/5.33                & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 9.53/5.33                  = ( times_times_real @ ( minus_minus_real @ B @ A ) @ L4 ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10059_continuous__on__arcosh,axiom,
% 9.53/5.33      ! [A2: set_real] :
% 9.53/5.33        ( ( ord_less_eq_set_real @ A2 @ ( set_ord_atLeast_real @ one_one_real ) )
% 9.53/5.33       => ( topolo5044208981011980120l_real @ A2 @ arcosh_real ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10060_continuous__on__arcosh_H,axiom,
% 9.53/5.33      ! [A2: set_real,F: real > real] :
% 9.53/5.33        ( ( topolo5044208981011980120l_real @ A2 @ F )
% 9.53/5.33       => ( ! [X3: real] :
% 9.53/5.33              ( ( member_real @ X3 @ A2 )
% 9.53/5.33             => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 9.53/5.33         => ( topolo5044208981011980120l_real @ A2
% 9.53/5.33            @ ^ [X2: real] : ( arcosh_real @ ( F @ X2 ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10061_continuous__image__closed__interval,axiom,
% 9.53/5.33      ! [A: real,B: real,F: real > real] :
% 9.53/5.33        ( ( ord_less_eq_real @ A @ B )
% 9.53/5.33       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 9.53/5.33         => ? [C2: real,D3: real] :
% 9.53/5.33              ( ( ( image_real_real @ F @ ( set_or1222579329274155063t_real @ A @ B ) )
% 9.53/5.33                = ( set_or1222579329274155063t_real @ C2 @ D3 ) )
% 9.53/5.33              & ( ord_less_eq_real @ C2 @ D3 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10062_continuous__on__arccos_H,axiom,
% 9.53/5.33      topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arccos ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10063_continuous__on__arcsin_H,axiom,
% 9.53/5.33      topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arcsin ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10064_continuous__on__artanh,axiom,
% 9.53/5.33      ! [A2: set_real] :
% 9.53/5.33        ( ( ord_less_eq_set_real @ A2 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) )
% 9.53/5.33       => ( topolo5044208981011980120l_real @ A2 @ artanh_real ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10065_continuous__on__artanh_H,axiom,
% 9.53/5.33      ! [A2: set_real,F: real > real] :
% 9.53/5.33        ( ( topolo5044208981011980120l_real @ A2 @ F )
% 9.53/5.33       => ( ! [X3: real] :
% 9.53/5.33              ( ( member_real @ X3 @ A2 )
% 9.53/5.33             => ( member_real @ ( F @ X3 ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) )
% 9.53/5.33         => ( topolo5044208981011980120l_real @ A2
% 9.53/5.33            @ ^ [X2: real] : ( artanh_real @ ( F @ X2 ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10066_Rolle__deriv,axiom,
% 9.53/5.33      ! [A: real,B: real,F: real > real,F4: real > real > real] :
% 9.53/5.33        ( ( ord_less_real @ A @ B )
% 9.53/5.33       => ( ( ( F @ A )
% 9.53/5.33            = ( F @ B ) )
% 9.53/5.33         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 9.53/5.33           => ( ! [X3: real] :
% 9.53/5.33                  ( ( ord_less_real @ A @ X3 )
% 9.53/5.33                 => ( ( ord_less_real @ X3 @ B )
% 9.53/5.33                   => ( has_de1759254742604945161l_real @ F @ ( F4 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 9.53/5.33             => ? [Z3: real] :
% 9.53/5.33                  ( ( ord_less_real @ A @ Z3 )
% 9.53/5.33                  & ( ord_less_real @ Z3 @ B )
% 9.53/5.33                  & ( ( F4 @ Z3 )
% 9.53/5.33                    = ( ^ [V4: real] : zero_zero_real ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10067_mvt,axiom,
% 9.53/5.33      ! [A: real,B: real,F: real > real,F4: real > real > real] :
% 9.53/5.33        ( ( ord_less_real @ A @ B )
% 9.53/5.33       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 9.53/5.33         => ( ! [X3: real] :
% 9.53/5.33                ( ( ord_less_real @ A @ X3 )
% 9.53/5.33               => ( ( ord_less_real @ X3 @ B )
% 9.53/5.33                 => ( has_de1759254742604945161l_real @ F @ ( F4 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 9.53/5.33           => ~ ! [Xi: real] :
% 9.53/5.33                  ( ( ord_less_real @ A @ Xi )
% 9.53/5.33                 => ( ( ord_less_real @ Xi @ B )
% 9.53/5.33                   => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 9.53/5.33                     != ( F4 @ Xi @ ( minus_minus_real @ B @ A ) ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10068_DERIV__isconst__end,axiom,
% 9.53/5.33      ! [A: real,B: real,F: real > real] :
% 9.53/5.33        ( ( ord_less_real @ A @ B )
% 9.53/5.33       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 9.53/5.33         => ( ! [X3: real] :
% 9.53/5.33                ( ( ord_less_real @ A @ X3 )
% 9.53/5.33               => ( ( ord_less_real @ X3 @ B )
% 9.53/5.33                 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 9.53/5.33           => ( ( F @ B )
% 9.53/5.33              = ( F @ A ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10069_DERIV__neg__imp__decreasing__open,axiom,
% 9.53/5.33      ! [A: real,B: real,F: real > real] :
% 9.53/5.33        ( ( ord_less_real @ A @ B )
% 9.53/5.33       => ( ! [X3: real] :
% 9.53/5.33              ( ( ord_less_real @ A @ X3 )
% 9.53/5.33             => ( ( ord_less_real @ X3 @ B )
% 9.53/5.33               => ? [Y4: real] :
% 9.53/5.33                    ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 9.53/5.33                    & ( ord_less_real @ Y4 @ zero_zero_real ) ) ) )
% 9.53/5.33         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 9.53/5.33           => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10070_DERIV__pos__imp__increasing__open,axiom,
% 9.53/5.33      ! [A: real,B: real,F: real > real] :
% 9.53/5.33        ( ( ord_less_real @ A @ B )
% 9.53/5.33       => ( ! [X3: real] :
% 9.53/5.33              ( ( ord_less_real @ A @ X3 )
% 9.53/5.33             => ( ( ord_less_real @ X3 @ B )
% 9.53/5.33               => ? [Y4: real] :
% 9.53/5.33                    ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 9.53/5.33                    & ( ord_less_real @ zero_zero_real @ Y4 ) ) ) )
% 9.53/5.33         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 9.53/5.33           => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10071_DERIV__isconst2,axiom,
% 9.53/5.33      ! [A: real,B: real,F: real > real,X: real] :
% 9.53/5.33        ( ( ord_less_real @ A @ B )
% 9.53/5.33       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 9.53/5.33         => ( ! [X3: real] :
% 9.53/5.33                ( ( ord_less_real @ A @ X3 )
% 9.53/5.33               => ( ( ord_less_real @ X3 @ B )
% 9.53/5.33                 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 9.53/5.33           => ( ( ord_less_eq_real @ A @ X )
% 9.53/5.33             => ( ( ord_less_eq_real @ X @ B )
% 9.53/5.33               => ( ( F @ X )
% 9.53/5.33                  = ( F @ A ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10072_Rolle,axiom,
% 9.53/5.33      ! [A: real,B: real,F: real > real] :
% 9.53/5.33        ( ( ord_less_real @ A @ B )
% 9.53/5.33       => ( ( ( F @ A )
% 9.53/5.33            = ( F @ B ) )
% 9.53/5.33         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 9.53/5.33           => ( ! [X3: real] :
% 9.53/5.33                  ( ( ord_less_real @ A @ X3 )
% 9.53/5.33                 => ( ( ord_less_real @ X3 @ B )
% 9.53/5.33                   => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 9.53/5.33             => ? [Z3: real] :
% 9.53/5.33                  ( ( ord_less_real @ A @ Z3 )
% 9.53/5.33                  & ( ord_less_real @ Z3 @ B )
% 9.53/5.33                  & ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10073_uniformity__real__def,axiom,
% 9.53/5.33      ( topolo1511823702728130853y_real
% 9.53/5.33      = ( comple2936214249959783750l_real
% 9.53/5.33        @ ( image_2178119161166701260l_real
% 9.53/5.33          @ ^ [E3: real] :
% 9.53/5.33              ( princi6114159922880469582l_real
% 9.53/5.33              @ ( collec3799799289383736868l_real
% 9.53/5.33                @ ( produc5414030515140494994real_o
% 9.53/5.33                  @ ^ [X2: real,Y: real] : ( ord_less_real @ ( real_V975177566351809787t_real @ X2 @ Y ) @ E3 ) ) ) )
% 9.53/5.33          @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10074_uniformity__complex__def,axiom,
% 9.53/5.33      ( topolo896644834953643431omplex
% 9.53/5.33      = ( comple8358262395181532106omplex
% 9.53/5.33        @ ( image_5971271580939081552omplex
% 9.53/5.33          @ ^ [E3: real] :
% 9.53/5.33              ( princi3496590319149328850omplex
% 9.53/5.33              @ ( collec8663557070575231912omplex
% 9.53/5.33                @ ( produc6771430404735790350plex_o
% 9.53/5.33                  @ ^ [X2: complex,Y: complex] : ( ord_less_real @ ( real_V3694042436643373181omplex @ X2 @ Y ) @ E3 ) ) ) )
% 9.53/5.33          @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10075_mono__Suc,axiom,
% 9.53/5.33      order_mono_nat_nat @ suc ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10076_mono__times__nat,axiom,
% 9.53/5.33      ! [N: nat] :
% 9.53/5.33        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.33       => ( order_mono_nat_nat @ ( times_times_nat @ N ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10077_incseq__bounded,axiom,
% 9.53/5.33      ! [X8: nat > real,B2: real] :
% 9.53/5.33        ( ( order_mono_nat_real @ X8 )
% 9.53/5.33       => ( ! [I4: nat] : ( ord_less_eq_real @ ( X8 @ I4 ) @ B2 )
% 9.53/5.33         => ( bfun_nat_real @ X8 @ at_top_nat ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10078_incseq__convergent,axiom,
% 9.53/5.33      ! [X8: nat > real,B2: real] :
% 9.53/5.33        ( ( order_mono_nat_real @ X8 )
% 9.53/5.33       => ( ! [I4: nat] : ( ord_less_eq_real @ ( X8 @ I4 ) @ B2 )
% 9.53/5.33         => ~ ! [L6: real] :
% 9.53/5.33                ( ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 9.53/5.33               => ~ ! [I: nat] : ( ord_less_eq_real @ ( X8 @ I ) @ L6 ) ) ) ) ).
% 9.53/5.33  
% 9.53/5.33  thf(fact_10079_mono__ge2__power__minus__self,axiom,
% 9.53/5.33      ! [K: nat] :
% 9.53/5.33        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 9.53/5.33       => ( order_mono_nat_nat
% 9.53/5.33          @ ^ [M6: nat] : ( minus_minus_nat @ ( power_power_nat @ K @ M6 ) @ M6 ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10080_eventually__prod__sequentially,axiom,
% 9.53/5.34      ! [P: product_prod_nat_nat > $o] :
% 9.53/5.34        ( ( eventu1038000079068216329at_nat @ P @ ( prod_filter_nat_nat @ at_top_nat @ at_top_nat ) )
% 9.53/5.34        = ( ? [N6: nat] :
% 9.53/5.34            ! [M6: nat] :
% 9.53/5.34              ( ( ord_less_eq_nat @ N6 @ M6 )
% 9.53/5.34             => ! [N2: nat] :
% 9.53/5.34                  ( ( ord_less_eq_nat @ N6 @ N2 )
% 9.53/5.34                 => ( P @ ( product_Pair_nat_nat @ N2 @ M6 ) ) ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10081_filtermap__at__right__shift,axiom,
% 9.53/5.34      ! [D2: real,A: real] :
% 9.53/5.34        ( ( filtermap_real_real
% 9.53/5.34          @ ^ [X2: real] : ( minus_minus_real @ X2 @ D2 )
% 9.53/5.34          @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 9.53/5.34        = ( topolo2177554685111907308n_real @ ( minus_minus_real @ A @ D2 ) @ ( set_or5849166863359141190n_real @ ( minus_minus_real @ A @ D2 ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10082_at__right__to__0,axiom,
% 9.53/5.34      ! [A: real] :
% 9.53/5.34        ( ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) )
% 9.53/5.34        = ( filtermap_real_real
% 9.53/5.34          @ ^ [X2: real] : ( plus_plus_real @ X2 @ A )
% 9.53/5.34          @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10083_nonneg__incseq__Bseq__subseq__iff,axiom,
% 9.53/5.34      ! [F: nat > real,G: nat > nat] :
% 9.53/5.34        ( ! [X3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 9.53/5.34       => ( ( order_mono_nat_real @ F )
% 9.53/5.34         => ( ( order_5726023648592871131at_nat @ G )
% 9.53/5.34           => ( ( bfun_nat_real
% 9.53/5.34                @ ^ [X2: nat] : ( F @ ( G @ X2 ) )
% 9.53/5.34                @ at_top_nat )
% 9.53/5.34              = ( bfun_nat_real @ F @ at_top_nat ) ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10084_inj__sgn__power,axiom,
% 9.53/5.34      ! [N: nat] :
% 9.53/5.34        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.34       => ( inj_on_real_real
% 9.53/5.34          @ ^ [Y: real] : ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N ) )
% 9.53/5.34          @ top_top_set_real ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10085_strict__mono__imp__increasing,axiom,
% 9.53/5.34      ! [F: nat > nat,N: nat] :
% 9.53/5.34        ( ( order_5726023648592871131at_nat @ F )
% 9.53/5.34       => ( ord_less_eq_nat @ N @ ( F @ N ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10086_log__inj,axiom,
% 9.53/5.34      ! [B: real] :
% 9.53/5.34        ( ( ord_less_real @ one_one_real @ B )
% 9.53/5.34       => ( inj_on_real_real @ ( log @ B ) @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10087_inj__on__diff__nat,axiom,
% 9.53/5.34      ! [N4: set_nat,K: nat] :
% 9.53/5.34        ( ! [N3: nat] :
% 9.53/5.34            ( ( member_nat @ N3 @ N4 )
% 9.53/5.34           => ( ord_less_eq_nat @ K @ N3 ) )
% 9.53/5.34       => ( inj_on_nat_nat
% 9.53/5.34          @ ^ [N2: nat] : ( minus_minus_nat @ N2 @ K )
% 9.53/5.34          @ N4 ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10088_inj__Suc,axiom,
% 9.53/5.34      ! [N4: set_nat] : ( inj_on_nat_nat @ suc @ N4 ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10089_summable__reindex,axiom,
% 9.53/5.34      ! [F: nat > real,G: nat > nat] :
% 9.53/5.34        ( ( summable_real @ F )
% 9.53/5.34       => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 9.53/5.34         => ( ! [X3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 9.53/5.34           => ( summable_real @ ( comp_nat_real_nat @ F @ G ) ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10090_suminf__reindex__mono,axiom,
% 9.53/5.34      ! [F: nat > real,G: nat > nat] :
% 9.53/5.34        ( ( summable_real @ F )
% 9.53/5.34       => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 9.53/5.34         => ( ! [X3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 9.53/5.34           => ( ord_less_eq_real @ ( suminf_real @ ( comp_nat_real_nat @ F @ G ) ) @ ( suminf_real @ F ) ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10091_inj__on__char__of__nat,axiom,
% 9.53/5.34      inj_on_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10092_suminf__reindex,axiom,
% 9.53/5.34      ! [F: nat > real,G: nat > nat] :
% 9.53/5.34        ( ( summable_real @ F )
% 9.53/5.34       => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 9.53/5.34         => ( ! [X3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 9.53/5.34           => ( ! [X3: nat] :
% 9.53/5.34                  ( ~ ( member_nat @ X3 @ ( image_nat_nat @ G @ top_top_set_nat ) )
% 9.53/5.34                 => ( ( F @ X3 )
% 9.53/5.34                    = zero_zero_real ) )
% 9.53/5.34             => ( ( suminf_real @ ( comp_nat_real_nat @ F @ G ) )
% 9.53/5.34                = ( suminf_real @ F ) ) ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10093_pos__deriv__imp__strict__mono,axiom,
% 9.53/5.34      ! [F: real > real,F4: real > real] :
% 9.53/5.34        ( ! [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 9.53/5.34       => ( ! [X3: real] : ( ord_less_real @ zero_zero_real @ ( F4 @ X3 ) )
% 9.53/5.34         => ( order_7092887310737990675l_real @ F ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10094_powr__real__of__int_H,axiom,
% 9.53/5.34      ! [X: real,N: int] :
% 9.53/5.34        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.34       => ( ( ( X != zero_zero_real )
% 9.53/5.34            | ( ord_less_int @ zero_zero_int @ N ) )
% 9.53/5.34         => ( ( powr_real @ X @ ( ring_1_of_int_real @ N ) )
% 9.53/5.34            = ( power_int_real @ X @ N ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10095_pred__nat__def,axiom,
% 9.53/5.34      ( pred_nat
% 9.53/5.34      = ( collec3392354462482085612at_nat
% 9.53/5.34        @ ( produc6081775807080527818_nat_o
% 9.53/5.34          @ ^ [M6: nat,N2: nat] :
% 9.53/5.34              ( N2
% 9.53/5.34              = ( suc @ M6 ) ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10096_atLeastLessThan__add__Un,axiom,
% 9.53/5.34      ! [I2: nat,J: nat,K: nat] :
% 9.53/5.34        ( ( ord_less_eq_nat @ I2 @ J )
% 9.53/5.34       => ( ( set_or4665077453230672383an_nat @ I2 @ ( plus_plus_nat @ J @ K ) )
% 9.53/5.34          = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I2 @ J ) @ ( set_or4665077453230672383an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10097_sup__enat__def,axiom,
% 9.53/5.34      sup_su3973961784419623482d_enat = ord_ma741700101516333627d_enat ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10098_sup__nat__def,axiom,
% 9.53/5.34      sup_sup_nat = ord_max_nat ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10099_Rats__eq__int__div__nat,axiom,
% 9.53/5.34      ( field_5140801741446780682s_real
% 9.53/5.34      = ( collect_real
% 9.53/5.34        @ ^ [Uu3: real] :
% 9.53/5.34          ? [I3: int,N2: nat] :
% 9.53/5.34            ( ( Uu3
% 9.53/5.34              = ( divide_divide_real @ ( ring_1_of_int_real @ I3 ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 9.53/5.34            & ( N2 != zero_zero_nat ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10100_Rats__abs__iff,axiom,
% 9.53/5.34      ! [X: real] :
% 9.53/5.34        ( ( member_real @ ( abs_abs_real @ X ) @ field_5140801741446780682s_real )
% 9.53/5.34        = ( member_real @ X @ field_5140801741446780682s_real ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10101_Rats__dense__in__real,axiom,
% 9.53/5.34      ! [X: real,Y2: real] :
% 9.53/5.34        ( ( ord_less_real @ X @ Y2 )
% 9.53/5.34       => ? [X3: real] :
% 9.53/5.34            ( ( member_real @ X3 @ field_5140801741446780682s_real )
% 9.53/5.34            & ( ord_less_real @ X @ X3 )
% 9.53/5.34            & ( ord_less_real @ X3 @ Y2 ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10102_Rats__no__bot__less,axiom,
% 9.53/5.34      ! [X: real] :
% 9.53/5.34      ? [X3: real] :
% 9.53/5.34        ( ( member_real @ X3 @ field_5140801741446780682s_real )
% 9.53/5.34        & ( ord_less_real @ X3 @ X ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10103_Rats__no__top__le,axiom,
% 9.53/5.34      ! [X: real] :
% 9.53/5.34      ? [X3: real] :
% 9.53/5.34        ( ( member_real @ X3 @ field_5140801741446780682s_real )
% 9.53/5.34        & ( ord_less_eq_real @ X @ X3 ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10104_Rats__eq__int__div__int,axiom,
% 9.53/5.34      ( field_5140801741446780682s_real
% 9.53/5.34      = ( collect_real
% 9.53/5.34        @ ^ [Uu3: real] :
% 9.53/5.34          ? [I3: int,J3: int] :
% 9.53/5.34            ( ( Uu3
% 9.53/5.34              = ( divide_divide_real @ ( ring_1_of_int_real @ I3 ) @ ( ring_1_of_int_real @ J3 ) ) )
% 9.53/5.34            & ( J3 != zero_zero_int ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10105_less__eq,axiom,
% 9.53/5.34      ! [M: nat,N: nat] :
% 9.53/5.34        ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N ) @ ( transi6264000038957366511cl_nat @ pred_nat ) )
% 9.53/5.34        = ( ord_less_nat @ M @ N ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10106_pred__nat__trancl__eq__le,axiom,
% 9.53/5.34      ! [M: nat,N: nat] :
% 9.53/5.34        ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N ) @ ( transi2905341329935302413cl_nat @ pred_nat ) )
% 9.53/5.34        = ( ord_less_eq_nat @ M @ N ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10107_tl__upt,axiom,
% 9.53/5.34      ! [M: nat,N: nat] :
% 9.53/5.34        ( ( tl_nat @ ( upt @ M @ N ) )
% 9.53/5.34        = ( upt @ ( suc @ M ) @ N ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10108_hd__upt,axiom,
% 9.53/5.34      ! [I2: nat,J: nat] :
% 9.53/5.34        ( ( ord_less_nat @ I2 @ J )
% 9.53/5.34       => ( ( hd_nat @ ( upt @ I2 @ J ) )
% 9.53/5.34          = I2 ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10109_drop__upt,axiom,
% 9.53/5.34      ! [M: nat,I2: nat,J: nat] :
% 9.53/5.34        ( ( drop_nat @ M @ ( upt @ I2 @ J ) )
% 9.53/5.34        = ( upt @ ( plus_plus_nat @ I2 @ M ) @ J ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10110_length__upt,axiom,
% 9.53/5.34      ! [I2: nat,J: nat] :
% 9.53/5.34        ( ( size_size_list_nat @ ( upt @ I2 @ J ) )
% 9.53/5.34        = ( minus_minus_nat @ J @ I2 ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10111_take__upt,axiom,
% 9.53/5.34      ! [I2: nat,M: nat,N: nat] :
% 9.53/5.34        ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ M ) @ N )
% 9.53/5.34       => ( ( take_nat @ M @ ( upt @ I2 @ N ) )
% 9.53/5.34          = ( upt @ I2 @ ( plus_plus_nat @ I2 @ M ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10112_upt__conv__Nil,axiom,
% 9.53/5.34      ! [J: nat,I2: nat] :
% 9.53/5.34        ( ( ord_less_eq_nat @ J @ I2 )
% 9.53/5.34       => ( ( upt @ I2 @ J )
% 9.53/5.34          = nil_nat ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10113_upt__eq__Nil__conv,axiom,
% 9.53/5.34      ! [I2: nat,J: nat] :
% 9.53/5.34        ( ( ( upt @ I2 @ J )
% 9.53/5.34          = nil_nat )
% 9.53/5.34        = ( ( J = zero_zero_nat )
% 9.53/5.34          | ( ord_less_eq_nat @ J @ I2 ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10114_nth__upt,axiom,
% 9.53/5.34      ! [I2: nat,K: nat,J: nat] :
% 9.53/5.34        ( ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ J )
% 9.53/5.34       => ( ( nth_nat @ ( upt @ I2 @ J ) @ K )
% 9.53/5.34          = ( plus_plus_nat @ I2 @ K ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10115_upt__rec__numeral,axiom,
% 9.53/5.34      ! [M: num,N: num] :
% 9.53/5.34        ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 9.53/5.34         => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 9.53/5.34            = ( cons_nat @ ( numeral_numeral_nat @ M ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) ) ) ) )
% 9.53/5.34        & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 9.53/5.34         => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 9.53/5.34            = nil_nat ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10116_map__Suc__upt,axiom,
% 9.53/5.34      ! [M: nat,N: nat] :
% 9.53/5.34        ( ( map_nat_nat @ suc @ ( upt @ M @ N ) )
% 9.53/5.34        = ( upt @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10117_map__add__upt,axiom,
% 9.53/5.34      ! [N: nat,M: nat] :
% 9.53/5.34        ( ( map_nat_nat
% 9.53/5.34          @ ^ [I3: nat] : ( plus_plus_nat @ I3 @ N )
% 9.53/5.34          @ ( upt @ zero_zero_nat @ M ) )
% 9.53/5.34        = ( upt @ N @ ( plus_plus_nat @ M @ N ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10118_upt__conv__Cons__Cons,axiom,
% 9.53/5.34      ! [M: nat,N: nat,Ns: list_nat,Q2: nat] :
% 9.53/5.34        ( ( ( cons_nat @ M @ ( cons_nat @ N @ Ns ) )
% 9.53/5.34          = ( upt @ M @ Q2 ) )
% 9.53/5.34        = ( ( cons_nat @ N @ Ns )
% 9.53/5.34          = ( upt @ ( suc @ M ) @ Q2 ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10119_greaterThanLessThan__upt,axiom,
% 9.53/5.34      ( set_or5834768355832116004an_nat
% 9.53/5.34      = ( ^ [N2: nat,M6: nat] : ( set_nat2 @ ( upt @ ( suc @ N2 ) @ M6 ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10120_greaterThanAtMost__upt,axiom,
% 9.53/5.34      ( set_or6659071591806873216st_nat
% 9.53/5.34      = ( ^ [N2: nat,M6: nat] : ( set_nat2 @ ( upt @ ( suc @ N2 ) @ ( suc @ M6 ) ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10121_atLeastAtMost__upt,axiom,
% 9.53/5.34      ( set_or1269000886237332187st_nat
% 9.53/5.34      = ( ^ [N2: nat,M6: nat] : ( set_nat2 @ ( upt @ N2 @ ( suc @ M6 ) ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10122_atMost__upto,axiom,
% 9.53/5.34      ( set_ord_atMost_nat
% 9.53/5.34      = ( ^ [N2: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ ( suc @ N2 ) ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10123_upt__conv__Cons,axiom,
% 9.53/5.34      ! [I2: nat,J: nat] :
% 9.53/5.34        ( ( ord_less_nat @ I2 @ J )
% 9.53/5.34       => ( ( upt @ I2 @ J )
% 9.53/5.34          = ( cons_nat @ I2 @ ( upt @ ( suc @ I2 ) @ J ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10124_map__decr__upt,axiom,
% 9.53/5.34      ! [M: nat,N: nat] :
% 9.53/5.34        ( ( map_nat_nat
% 9.53/5.34          @ ^ [N2: nat] : ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 9.53/5.34          @ ( upt @ ( suc @ M ) @ ( suc @ N ) ) )
% 9.53/5.34        = ( upt @ M @ N ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10125_upt__add__eq__append,axiom,
% 9.53/5.34      ! [I2: nat,J: nat,K: nat] :
% 9.53/5.34        ( ( ord_less_eq_nat @ I2 @ J )
% 9.53/5.34       => ( ( upt @ I2 @ ( plus_plus_nat @ J @ K ) )
% 9.53/5.34          = ( append_nat @ ( upt @ I2 @ J ) @ ( upt @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10126_upt__eq__Cons__conv,axiom,
% 9.53/5.34      ! [I2: nat,J: nat,X: nat,Xs2: list_nat] :
% 9.53/5.34        ( ( ( upt @ I2 @ J )
% 9.53/5.34          = ( cons_nat @ X @ Xs2 ) )
% 9.53/5.34        = ( ( ord_less_nat @ I2 @ J )
% 9.53/5.34          & ( I2 = X )
% 9.53/5.34          & ( ( upt @ ( plus_plus_nat @ I2 @ one_one_nat ) @ J )
% 9.53/5.34            = Xs2 ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10127_upt__rec,axiom,
% 9.53/5.34      ( upt
% 9.53/5.34      = ( ^ [I3: nat,J3: nat] : ( if_list_nat @ ( ord_less_nat @ I3 @ J3 ) @ ( cons_nat @ I3 @ ( upt @ ( suc @ I3 ) @ J3 ) ) @ nil_nat ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10128_upt__Suc__append,axiom,
% 9.53/5.34      ! [I2: nat,J: nat] :
% 9.53/5.34        ( ( ord_less_eq_nat @ I2 @ J )
% 9.53/5.34       => ( ( upt @ I2 @ ( suc @ J ) )
% 9.53/5.34          = ( append_nat @ ( upt @ I2 @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10129_upt__Suc,axiom,
% 9.53/5.34      ! [I2: nat,J: nat] :
% 9.53/5.34        ( ( ( ord_less_eq_nat @ I2 @ J )
% 9.53/5.34         => ( ( upt @ I2 @ ( suc @ J ) )
% 9.53/5.34            = ( append_nat @ ( upt @ I2 @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) )
% 9.53/5.34        & ( ~ ( ord_less_eq_nat @ I2 @ J )
% 9.53/5.34         => ( ( upt @ I2 @ ( suc @ J ) )
% 9.53/5.34            = nil_nat ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10130_sum__list__upt,axiom,
% 9.53/5.34      ! [M: nat,N: nat] :
% 9.53/5.34        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.34       => ( ( groups4561878855575611511st_nat @ ( upt @ M @ N ) )
% 9.53/5.34          = ( groups3542108847815614940at_nat
% 9.53/5.34            @ ^ [X2: nat] : X2
% 9.53/5.34            @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10131_card__length__sum__list__rec,axiom,
% 9.53/5.34      ! [M: nat,N4: nat] :
% 9.53/5.34        ( ( ord_less_eq_nat @ one_one_nat @ M )
% 9.53/5.34       => ( ( finite_card_list_nat
% 9.53/5.34            @ ( collect_list_nat
% 9.53/5.34              @ ^ [L: list_nat] :
% 9.53/5.34                  ( ( ( size_size_list_nat @ L )
% 9.53/5.34                    = M )
% 9.53/5.34                  & ( ( groups4561878855575611511st_nat @ L )
% 9.53/5.34                    = N4 ) ) ) )
% 9.53/5.34          = ( plus_plus_nat
% 9.53/5.34            @ ( finite_card_list_nat
% 9.53/5.34              @ ( collect_list_nat
% 9.53/5.34                @ ^ [L: list_nat] :
% 9.53/5.34                    ( ( ( size_size_list_nat @ L )
% 9.53/5.34                      = ( minus_minus_nat @ M @ one_one_nat ) )
% 9.53/5.34                    & ( ( groups4561878855575611511st_nat @ L )
% 9.53/5.34                      = N4 ) ) ) )
% 9.53/5.34            @ ( finite_card_list_nat
% 9.53/5.34              @ ( collect_list_nat
% 9.53/5.34                @ ^ [L: list_nat] :
% 9.53/5.34                    ( ( ( size_size_list_nat @ L )
% 9.53/5.34                      = M )
% 9.53/5.34                    & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L ) @ one_one_nat )
% 9.53/5.34                      = N4 ) ) ) ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10132_card__length__sum__list,axiom,
% 9.53/5.34      ! [M: nat,N4: nat] :
% 9.53/5.34        ( ( finite_card_list_nat
% 9.53/5.34          @ ( collect_list_nat
% 9.53/5.34            @ ^ [L: list_nat] :
% 9.53/5.34                ( ( ( size_size_list_nat @ L )
% 9.53/5.34                  = M )
% 9.53/5.34                & ( ( groups4561878855575611511st_nat @ L )
% 9.53/5.34                  = N4 ) ) ) )
% 9.53/5.34        = ( binomial @ ( minus_minus_nat @ ( plus_plus_nat @ N4 @ M ) @ one_one_nat ) @ N4 ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10133_sorted__wrt__upt,axiom,
% 9.53/5.34      ! [M: nat,N: nat] : ( sorted_wrt_nat @ ord_less_nat @ ( upt @ M @ N ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10134_sorted__upt,axiom,
% 9.53/5.34      ! [M: nat,N: nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( upt @ M @ N ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10135_sorted__wrt__less__idx,axiom,
% 9.53/5.34      ! [Ns: list_nat,I2: nat] :
% 9.53/5.34        ( ( sorted_wrt_nat @ ord_less_nat @ Ns )
% 9.53/5.34       => ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Ns ) )
% 9.53/5.34         => ( ord_less_eq_nat @ I2 @ ( nth_nat @ Ns @ I2 ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10136_list__encode_Opelims,axiom,
% 9.53/5.34      ! [X: list_nat,Y2: nat] :
% 9.53/5.34        ( ( ( nat_list_encode @ X )
% 9.53/5.34          = Y2 )
% 9.53/5.34       => ( ( accp_list_nat @ nat_list_encode_rel @ X )
% 9.53/5.34         => ( ( ( X = nil_nat )
% 9.53/5.34             => ( ( Y2 = zero_zero_nat )
% 9.53/5.34               => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 9.53/5.34           => ~ ! [X3: nat,Xs3: list_nat] :
% 9.53/5.34                  ( ( X
% 9.53/5.34                    = ( cons_nat @ X3 @ Xs3 ) )
% 9.53/5.34                 => ( ( Y2
% 9.53/5.34                      = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X3 @ ( nat_list_encode @ Xs3 ) ) ) ) )
% 9.53/5.34                   => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X3 @ Xs3 ) ) ) ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10137_and__not__num_Opelims,axiom,
% 9.53/5.34      ! [X: num,Xa2: num,Y2: option_num] :
% 9.53/5.34        ( ( ( bit_and_not_num @ X @ Xa2 )
% 9.53/5.34          = Y2 )
% 9.53/5.34       => ( ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ X @ Xa2 ) )
% 9.53/5.34         => ( ( ( X = one )
% 9.53/5.34             => ( ( Xa2 = one )
% 9.53/5.34               => ( ( Y2 = none_num )
% 9.53/5.34                 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 9.53/5.34           => ( ( ( X = one )
% 9.53/5.34               => ! [N3: num] :
% 9.53/5.34                    ( ( Xa2
% 9.53/5.34                      = ( bit0 @ N3 ) )
% 9.53/5.34                   => ( ( Y2
% 9.53/5.34                        = ( some_num @ one ) )
% 9.53/5.34                     => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 9.53/5.34             => ( ( ( X = one )
% 9.53/5.34                 => ! [N3: num] :
% 9.53/5.34                      ( ( Xa2
% 9.53/5.34                        = ( bit1 @ N3 ) )
% 9.53/5.34                     => ( ( Y2 = none_num )
% 9.53/5.34                       => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 9.53/5.34               => ( ! [M4: num] :
% 9.53/5.34                      ( ( X
% 9.53/5.34                        = ( bit0 @ M4 ) )
% 9.53/5.34                     => ( ( Xa2 = one )
% 9.53/5.34                       => ( ( Y2
% 9.53/5.34                            = ( some_num @ ( bit0 @ M4 ) ) )
% 9.53/5.34                         => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) ) ) ) )
% 9.53/5.34                 => ( ! [M4: num] :
% 9.53/5.34                        ( ( X
% 9.53/5.34                          = ( bit0 @ M4 ) )
% 9.53/5.34                       => ! [N3: num] :
% 9.53/5.34                            ( ( Xa2
% 9.53/5.34                              = ( bit0 @ N3 ) )
% 9.53/5.34                           => ( ( Y2
% 9.53/5.34                                = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N3 ) ) )
% 9.53/5.34                             => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 9.53/5.34                   => ( ! [M4: num] :
% 9.53/5.34                          ( ( X
% 9.53/5.34                            = ( bit0 @ M4 ) )
% 9.53/5.34                         => ! [N3: num] :
% 9.53/5.34                              ( ( Xa2
% 9.53/5.34                                = ( bit1 @ N3 ) )
% 9.53/5.34                             => ( ( Y2
% 9.53/5.34                                  = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N3 ) ) )
% 9.53/5.34                               => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 9.53/5.34                     => ( ! [M4: num] :
% 9.53/5.34                            ( ( X
% 9.53/5.34                              = ( bit1 @ M4 ) )
% 9.53/5.34                           => ( ( Xa2 = one )
% 9.53/5.34                             => ( ( Y2
% 9.53/5.34                                  = ( some_num @ ( bit0 @ M4 ) ) )
% 9.53/5.34                               => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) ) ) ) )
% 9.53/5.34                       => ( ! [M4: num] :
% 9.53/5.34                              ( ( X
% 9.53/5.34                                = ( bit1 @ M4 ) )
% 9.53/5.34                             => ! [N3: num] :
% 9.53/5.34                                  ( ( Xa2
% 9.53/5.34                                    = ( bit0 @ N3 ) )
% 9.53/5.34                                 => ( ( Y2
% 9.53/5.34                                      = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 9.53/5.34                                        @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 9.53/5.34                                        @ ( bit_and_not_num @ M4 @ N3 ) ) )
% 9.53/5.34                                   => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 9.53/5.34                         => ~ ! [M4: num] :
% 9.53/5.34                                ( ( X
% 9.53/5.34                                  = ( bit1 @ M4 ) )
% 9.53/5.34                               => ! [N3: num] :
% 9.53/5.34                                    ( ( Xa2
% 9.53/5.34                                      = ( bit1 @ N3 ) )
% 9.53/5.34                                   => ( ( Y2
% 9.53/5.34                                        = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N3 ) ) )
% 9.53/5.34                                     => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10138_and__num_Opelims,axiom,
% 9.53/5.34      ! [X: num,Xa2: num,Y2: option_num] :
% 9.53/5.34        ( ( ( bit_un7362597486090784418nd_num @ X @ Xa2 )
% 9.53/5.34          = Y2 )
% 9.53/5.34       => ( ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ X @ Xa2 ) )
% 9.53/5.34         => ( ( ( X = one )
% 9.53/5.34             => ( ( Xa2 = one )
% 9.53/5.34               => ( ( Y2
% 9.53/5.34                    = ( some_num @ one ) )
% 9.53/5.34                 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 9.53/5.34           => ( ( ( X = one )
% 9.53/5.34               => ! [N3: num] :
% 9.53/5.34                    ( ( Xa2
% 9.53/5.34                      = ( bit0 @ N3 ) )
% 9.53/5.34                   => ( ( Y2 = none_num )
% 9.53/5.34                     => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 9.53/5.34             => ( ( ( X = one )
% 9.53/5.34                 => ! [N3: num] :
% 9.53/5.34                      ( ( Xa2
% 9.53/5.34                        = ( bit1 @ N3 ) )
% 9.53/5.34                     => ( ( Y2
% 9.53/5.34                          = ( some_num @ one ) )
% 9.53/5.34                       => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 9.53/5.34               => ( ! [M4: num] :
% 9.53/5.34                      ( ( X
% 9.53/5.34                        = ( bit0 @ M4 ) )
% 9.53/5.34                     => ( ( Xa2 = one )
% 9.53/5.34                       => ( ( Y2 = none_num )
% 9.53/5.34                         => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) ) ) ) )
% 9.53/5.34                 => ( ! [M4: num] :
% 9.53/5.34                        ( ( X
% 9.53/5.34                          = ( bit0 @ M4 ) )
% 9.53/5.34                       => ! [N3: num] :
% 9.53/5.34                            ( ( Xa2
% 9.53/5.34                              = ( bit0 @ N3 ) )
% 9.53/5.34                           => ( ( Y2
% 9.53/5.34                                = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) )
% 9.53/5.34                             => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 9.53/5.34                   => ( ! [M4: num] :
% 9.53/5.34                          ( ( X
% 9.53/5.34                            = ( bit0 @ M4 ) )
% 9.53/5.34                         => ! [N3: num] :
% 9.53/5.34                              ( ( Xa2
% 9.53/5.34                                = ( bit1 @ N3 ) )
% 9.53/5.34                             => ( ( Y2
% 9.53/5.34                                  = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) )
% 9.53/5.34                               => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 9.53/5.34                     => ( ! [M4: num] :
% 9.53/5.34                            ( ( X
% 9.53/5.34                              = ( bit1 @ M4 ) )
% 9.53/5.34                           => ( ( Xa2 = one )
% 9.53/5.34                             => ( ( Y2
% 9.53/5.34                                  = ( some_num @ one ) )
% 9.53/5.34                               => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) ) ) ) )
% 9.53/5.34                       => ( ! [M4: num] :
% 9.53/5.34                              ( ( X
% 9.53/5.34                                = ( bit1 @ M4 ) )
% 9.53/5.34                             => ! [N3: num] :
% 9.53/5.34                                  ( ( Xa2
% 9.53/5.34                                    = ( bit0 @ N3 ) )
% 9.53/5.34                                 => ( ( Y2
% 9.53/5.34                                      = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) )
% 9.53/5.34                                   => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 9.53/5.34                         => ~ ! [M4: num] :
% 9.53/5.34                                ( ( X
% 9.53/5.34                                  = ( bit1 @ M4 ) )
% 9.53/5.34                               => ! [N3: num] :
% 9.53/5.34                                    ( ( Xa2
% 9.53/5.34                                      = ( bit1 @ N3 ) )
% 9.53/5.34                                   => ( ( Y2
% 9.53/5.34                                        = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 9.53/5.34                                          @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 9.53/5.34                                          @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) )
% 9.53/5.34                                     => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10139_xor__num_Opelims,axiom,
% 9.53/5.34      ! [X: num,Xa2: num,Y2: option_num] :
% 9.53/5.34        ( ( ( bit_un2480387367778600638or_num @ X @ Xa2 )
% 9.53/5.34          = Y2 )
% 9.53/5.34       => ( ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ X @ Xa2 ) )
% 9.53/5.34         => ( ( ( X = one )
% 9.53/5.34             => ( ( Xa2 = one )
% 9.53/5.34               => ( ( Y2 = none_num )
% 9.53/5.34                 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 9.53/5.34           => ( ( ( X = one )
% 9.53/5.34               => ! [N3: num] :
% 9.53/5.34                    ( ( Xa2
% 9.53/5.34                      = ( bit0 @ N3 ) )
% 9.53/5.34                   => ( ( Y2
% 9.53/5.34                        = ( some_num @ ( bit1 @ N3 ) ) )
% 9.53/5.34                     => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 9.53/5.34             => ( ( ( X = one )
% 9.53/5.34                 => ! [N3: num] :
% 9.53/5.34                      ( ( Xa2
% 9.53/5.34                        = ( bit1 @ N3 ) )
% 9.53/5.34                     => ( ( Y2
% 9.53/5.34                          = ( some_num @ ( bit0 @ N3 ) ) )
% 9.53/5.34                       => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 9.53/5.34               => ( ! [M4: num] :
% 9.53/5.34                      ( ( X
% 9.53/5.34                        = ( bit0 @ M4 ) )
% 9.53/5.34                     => ( ( Xa2 = one )
% 9.53/5.34                       => ( ( Y2
% 9.53/5.34                            = ( some_num @ ( bit1 @ M4 ) ) )
% 9.53/5.34                         => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) ) ) ) )
% 9.53/5.34                 => ( ! [M4: num] :
% 9.53/5.34                        ( ( X
% 9.53/5.34                          = ( bit0 @ M4 ) )
% 9.53/5.34                       => ! [N3: num] :
% 9.53/5.34                            ( ( Xa2
% 9.53/5.34                              = ( bit0 @ N3 ) )
% 9.53/5.34                           => ( ( Y2
% 9.53/5.34                                = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) )
% 9.53/5.34                             => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 9.53/5.34                   => ( ! [M4: num] :
% 9.53/5.34                          ( ( X
% 9.53/5.34                            = ( bit0 @ M4 ) )
% 9.53/5.34                         => ! [N3: num] :
% 9.53/5.34                              ( ( Xa2
% 9.53/5.34                                = ( bit1 @ N3 ) )
% 9.53/5.34                             => ( ( Y2
% 9.53/5.34                                  = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) ) )
% 9.53/5.34                               => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 9.53/5.34                     => ( ! [M4: num] :
% 9.53/5.34                            ( ( X
% 9.53/5.34                              = ( bit1 @ M4 ) )
% 9.53/5.34                           => ( ( Xa2 = one )
% 9.53/5.34                             => ( ( Y2
% 9.53/5.34                                  = ( some_num @ ( bit0 @ M4 ) ) )
% 9.53/5.34                               => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) ) ) ) )
% 9.53/5.34                       => ( ! [M4: num] :
% 9.53/5.34                              ( ( X
% 9.53/5.34                                = ( bit1 @ M4 ) )
% 9.53/5.34                             => ! [N3: num] :
% 9.53/5.34                                  ( ( Xa2
% 9.53/5.34                                    = ( bit0 @ N3 ) )
% 9.53/5.34                                 => ( ( Y2
% 9.53/5.34                                      = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) ) )
% 9.53/5.34                                   => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 9.53/5.34                         => ~ ! [M4: num] :
% 9.53/5.34                                ( ( X
% 9.53/5.34                                  = ( bit1 @ M4 ) )
% 9.53/5.34                               => ! [N3: num] :
% 9.53/5.34                                    ( ( Xa2
% 9.53/5.34                                      = ( bit1 @ N3 ) )
% 9.53/5.34                                   => ( ( Y2
% 9.53/5.34                                        = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) )
% 9.53/5.34                                     => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10140_or__not__num__neg_Opelims,axiom,
% 9.53/5.34      ! [X: num,Xa2: num,Y2: num] :
% 9.53/5.34        ( ( ( bit_or_not_num_neg @ X @ Xa2 )
% 9.53/5.34          = Y2 )
% 9.53/5.34       => ( ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ X @ Xa2 ) )
% 9.53/5.34         => ( ( ( X = one )
% 9.53/5.34             => ( ( Xa2 = one )
% 9.53/5.34               => ( ( Y2 = one )
% 9.53/5.34                 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 9.53/5.34           => ( ( ( X = one )
% 9.53/5.34               => ! [M4: num] :
% 9.53/5.34                    ( ( Xa2
% 9.53/5.34                      = ( bit0 @ M4 ) )
% 9.53/5.34                   => ( ( Y2
% 9.53/5.34                        = ( bit1 @ M4 ) )
% 9.53/5.34                     => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit0 @ M4 ) ) ) ) ) )
% 9.53/5.34             => ( ( ( X = one )
% 9.53/5.34                 => ! [M4: num] :
% 9.53/5.34                      ( ( Xa2
% 9.53/5.34                        = ( bit1 @ M4 ) )
% 9.53/5.34                     => ( ( Y2
% 9.53/5.34                          = ( bit1 @ M4 ) )
% 9.53/5.34                       => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit1 @ M4 ) ) ) ) ) )
% 9.53/5.34               => ( ! [N3: num] :
% 9.53/5.34                      ( ( X
% 9.53/5.34                        = ( bit0 @ N3 ) )
% 9.53/5.34                     => ( ( Xa2 = one )
% 9.53/5.34                       => ( ( Y2
% 9.53/5.34                            = ( bit0 @ one ) )
% 9.53/5.34                         => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ one ) ) ) ) )
% 9.53/5.34                 => ( ! [N3: num] :
% 9.53/5.34                        ( ( X
% 9.53/5.34                          = ( bit0 @ N3 ) )
% 9.53/5.34                       => ! [M4: num] :
% 9.53/5.34                            ( ( Xa2
% 9.53/5.34                              = ( bit0 @ M4 ) )
% 9.53/5.34                           => ( ( Y2
% 9.53/5.34                                = ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) )
% 9.53/5.34                             => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ ( bit0 @ M4 ) ) ) ) ) )
% 9.53/5.34                   => ( ! [N3: num] :
% 9.53/5.34                          ( ( X
% 9.53/5.34                            = ( bit0 @ N3 ) )
% 9.53/5.34                         => ! [M4: num] :
% 9.53/5.34                              ( ( Xa2
% 9.53/5.34                                = ( bit1 @ M4 ) )
% 9.53/5.34                             => ( ( Y2
% 9.53/5.34                                  = ( bit0 @ ( bit_or_not_num_neg @ N3 @ M4 ) ) )
% 9.53/5.34                               => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ ( bit1 @ M4 ) ) ) ) ) )
% 9.53/5.34                     => ( ! [N3: num] :
% 9.53/5.34                            ( ( X
% 9.53/5.34                              = ( bit1 @ N3 ) )
% 9.53/5.34                           => ( ( Xa2 = one )
% 9.53/5.34                             => ( ( Y2 = one )
% 9.53/5.34                               => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ one ) ) ) ) )
% 9.53/5.34                       => ( ! [N3: num] :
% 9.53/5.34                              ( ( X
% 9.53/5.34                                = ( bit1 @ N3 ) )
% 9.53/5.34                             => ! [M4: num] :
% 9.53/5.34                                  ( ( Xa2
% 9.53/5.34                                    = ( bit0 @ M4 ) )
% 9.53/5.34                                 => ( ( Y2
% 9.53/5.34                                      = ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) )
% 9.53/5.34                                   => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ ( bit0 @ M4 ) ) ) ) ) )
% 9.53/5.34                         => ~ ! [N3: num] :
% 9.53/5.34                                ( ( X
% 9.53/5.34                                  = ( bit1 @ N3 ) )
% 9.53/5.34                               => ! [M4: num] :
% 9.53/5.34                                    ( ( Xa2
% 9.53/5.34                                      = ( bit1 @ M4 ) )
% 9.53/5.34                                   => ( ( Y2
% 9.53/5.34                                        = ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) )
% 9.53/5.34                                     => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ ( bit1 @ M4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10141_and__num__rel__dict,axiom,
% 9.53/5.34      bit_un4731106466462545111um_rel = bit_un5425074673868309765um_rel ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10142_xor__num__rel__dict,axiom,
% 9.53/5.34      bit_un2901131394128224187um_rel = bit_un3595099601533988841um_rel ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10143_rcis__inverse,axiom,
% 9.53/5.34      ! [R: real,A: real] :
% 9.53/5.34        ( ( invers8013647133539491842omplex @ ( rcis @ R @ A ) )
% 9.53/5.34        = ( rcis @ ( divide_divide_real @ one_one_real @ R ) @ ( uminus_uminus_real @ A ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10144_Re__rcis,axiom,
% 9.53/5.34      ! [R: real,A: real] :
% 9.53/5.34        ( ( re @ ( rcis @ R @ A ) )
% 9.53/5.34        = ( times_times_real @ R @ ( cos_real @ A ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10145_Im__rcis,axiom,
% 9.53/5.34      ! [R: real,A: real] :
% 9.53/5.34        ( ( im @ ( rcis @ R @ A ) )
% 9.53/5.34        = ( times_times_real @ R @ ( sin_real @ A ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10146_cis__rcis__eq,axiom,
% 9.53/5.34      ( cis
% 9.53/5.34      = ( rcis @ one_one_real ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10147_rcis__mult,axiom,
% 9.53/5.34      ! [R1: real,A: real,R22: real,B: real] :
% 9.53/5.34        ( ( times_times_complex @ ( rcis @ R1 @ A ) @ ( rcis @ R22 @ B ) )
% 9.53/5.34        = ( rcis @ ( times_times_real @ R1 @ R22 ) @ ( plus_plus_real @ A @ B ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10148_rcis__divide,axiom,
% 9.53/5.34      ! [R1: real,A: real,R22: real,B: real] :
% 9.53/5.34        ( ( divide1717551699836669952omplex @ ( rcis @ R1 @ A ) @ ( rcis @ R22 @ B ) )
% 9.53/5.34        = ( rcis @ ( divide_divide_real @ R1 @ R22 ) @ ( minus_minus_real @ A @ B ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10149_DeMoivre2,axiom,
% 9.53/5.34      ! [R: real,A: real,N: nat] :
% 9.53/5.34        ( ( power_power_complex @ ( rcis @ R @ A ) @ N )
% 9.53/5.34        = ( rcis @ ( power_power_real @ R @ N ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10150_Field__natLeq__on,axiom,
% 9.53/5.34      ! [N: nat] :
% 9.53/5.34        ( ( field_nat
% 9.53/5.34          @ ( collec3392354462482085612at_nat
% 9.53/5.34            @ ( produc6081775807080527818_nat_o
% 9.53/5.34              @ ^ [X2: nat,Y: nat] :
% 9.53/5.34                  ( ( ord_less_nat @ X2 @ N )
% 9.53/5.34                  & ( ord_less_nat @ Y @ N )
% 9.53/5.34                  & ( ord_less_eq_nat @ X2 @ Y ) ) ) ) )
% 9.53/5.34        = ( collect_nat
% 9.53/5.34          @ ^ [X2: nat] : ( ord_less_nat @ X2 @ N ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10151_natLess__def,axiom,
% 9.53/5.34      ( bNF_Ca8459412986667044542atLess
% 9.53/5.34      = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10152_wf__less,axiom,
% 9.53/5.34      wf_nat @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10153_product__atMost__eq__Un,axiom,
% 9.53/5.34      ! [A2: set_nat,M: nat] :
% 9.53/5.34        ( ( produc457027306803732586at_nat @ A2
% 9.53/5.34          @ ^ [Uu3: nat] : ( set_ord_atMost_nat @ M ) )
% 9.53/5.34        = ( sup_su6327502436637775413at_nat
% 9.53/5.34          @ ( produc457027306803732586at_nat @ A2
% 9.53/5.34            @ ^ [I3: nat] : ( set_ord_atMost_nat @ ( minus_minus_nat @ M @ I3 ) ) )
% 9.53/5.34          @ ( produc457027306803732586at_nat @ A2
% 9.53/5.34            @ ^ [I3: nat] : ( set_or6659071591806873216st_nat @ ( minus_minus_nat @ M @ I3 ) @ M ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10154_pairs__le__eq__Sigma,axiom,
% 9.53/5.34      ! [M: nat] :
% 9.53/5.34        ( ( collec3392354462482085612at_nat
% 9.53/5.34          @ ( produc6081775807080527818_nat_o
% 9.53/5.34            @ ^ [I3: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ J3 ) @ M ) ) )
% 9.53/5.34        = ( produc457027306803732586at_nat @ ( set_ord_atMost_nat @ M )
% 9.53/5.34          @ ^ [R5: nat] : ( set_ord_atMost_nat @ ( minus_minus_nat @ M @ R5 ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10155_finite__vimage__Suc__iff,axiom,
% 9.53/5.34      ! [F5: set_nat] :
% 9.53/5.34        ( ( finite_finite_nat @ ( vimage_nat_nat @ suc @ F5 ) )
% 9.53/5.34        = ( finite_finite_nat @ F5 ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10156_le__enumerate,axiom,
% 9.53/5.34      ! [S2: set_nat,N: nat] :
% 9.53/5.34        ( ~ ( finite_finite_nat @ S2 )
% 9.53/5.34       => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S2 @ N ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10157_vimage__Suc__insert__Suc,axiom,
% 9.53/5.34      ! [N: nat,A2: set_nat] :
% 9.53/5.34        ( ( vimage_nat_nat @ suc @ ( insert_nat @ ( suc @ N ) @ A2 ) )
% 9.53/5.34        = ( insert_nat @ N @ ( vimage_nat_nat @ suc @ A2 ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10158_vimage__Suc__insert__0,axiom,
% 9.53/5.34      ! [A2: set_nat] :
% 9.53/5.34        ( ( vimage_nat_nat @ suc @ ( insert_nat @ zero_zero_nat @ A2 ) )
% 9.53/5.34        = ( vimage_nat_nat @ suc @ A2 ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10159_finite__le__enumerate,axiom,
% 9.53/5.34      ! [S2: set_nat,N: nat] :
% 9.53/5.34        ( ( finite_finite_nat @ S2 )
% 9.53/5.34       => ( ( ord_less_nat @ N @ ( finite_card_nat @ S2 ) )
% 9.53/5.34         => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S2 @ N ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10160_set__decode__div__2,axiom,
% 9.53/5.34      ! [X: nat] :
% 9.53/5.34        ( ( nat_set_decode @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.53/5.34        = ( vimage_nat_nat @ suc @ ( nat_set_decode @ X ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10161_set__encode__vimage__Suc,axiom,
% 9.53/5.34      ! [A2: set_nat] :
% 9.53/5.34        ( ( nat_set_encode @ ( vimage_nat_nat @ suc @ A2 ) )
% 9.53/5.34        = ( divide_divide_nat @ ( nat_set_encode @ A2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10162_Least__eq__0,axiom,
% 9.53/5.34      ! [P: nat > $o] :
% 9.53/5.34        ( ( P @ zero_zero_nat )
% 9.53/5.34       => ( ( ord_Least_nat @ P )
% 9.53/5.34          = zero_zero_nat ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10163_Least__Suc,axiom,
% 9.53/5.34      ! [P: nat > $o,N: nat] :
% 9.53/5.34        ( ( P @ N )
% 9.53/5.34       => ( ~ ( P @ zero_zero_nat )
% 9.53/5.34         => ( ( ord_Least_nat @ P )
% 9.53/5.34            = ( suc
% 9.53/5.34              @ ( ord_Least_nat
% 9.53/5.34                @ ^ [M6: nat] : ( P @ ( suc @ M6 ) ) ) ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10164_Least__Suc2,axiom,
% 9.53/5.34      ! [P: nat > $o,N: nat,Q: nat > $o,M: nat] :
% 9.53/5.34        ( ( P @ N )
% 9.53/5.34       => ( ( Q @ M )
% 9.53/5.34         => ( ~ ( P @ zero_zero_nat )
% 9.53/5.34           => ( ! [K2: nat] :
% 9.53/5.34                  ( ( P @ ( suc @ K2 ) )
% 9.53/5.34                  = ( Q @ K2 ) )
% 9.53/5.34             => ( ( ord_Least_nat @ P )
% 9.53/5.34                = ( suc @ ( ord_Least_nat @ Q ) ) ) ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10165_Sup__real__def,axiom,
% 9.53/5.34      ( comple1385675409528146559p_real
% 9.53/5.34      = ( ^ [X4: set_real] :
% 9.53/5.34            ( ord_Least_real
% 9.53/5.34            @ ^ [Z4: real] :
% 9.53/5.34              ! [X2: real] :
% 9.53/5.34                ( ( member_real @ X2 @ X4 )
% 9.53/5.34               => ( ord_less_eq_real @ X2 @ Z4 ) ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10166_Restr__natLeq,axiom,
% 9.53/5.34      ! [N: nat] :
% 9.53/5.34        ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 9.53/5.34          @ ( produc457027306803732586at_nat
% 9.53/5.34            @ ( collect_nat
% 9.53/5.34              @ ^ [X2: nat] : ( ord_less_nat @ X2 @ N ) )
% 9.53/5.34            @ ^ [Uu3: nat] :
% 9.53/5.34                ( collect_nat
% 9.53/5.34                @ ^ [X2: nat] : ( ord_less_nat @ X2 @ N ) ) ) )
% 9.53/5.34        = ( collec3392354462482085612at_nat
% 9.53/5.34          @ ( produc6081775807080527818_nat_o
% 9.53/5.34            @ ^ [X2: nat,Y: nat] :
% 9.53/5.34                ( ( ord_less_nat @ X2 @ N )
% 9.53/5.34                & ( ord_less_nat @ Y @ N )
% 9.53/5.34                & ( ord_less_eq_nat @ X2 @ Y ) ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10167_natLeq__natLess__Id,axiom,
% 9.53/5.34      ( bNF_Ca8459412986667044542atLess
% 9.53/5.34      = ( minus_1356011639430497352at_nat @ bNF_Ca8665028551170535155natLeq @ id_nat2 ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10168_natLeq__def,axiom,
% 9.53/5.34      ( bNF_Ca8665028551170535155natLeq
% 9.53/5.34      = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_eq_nat ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10169_Restr__natLeq2,axiom,
% 9.53/5.34      ! [N: nat] :
% 9.53/5.34        ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 9.53/5.34          @ ( produc457027306803732586at_nat @ ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N )
% 9.53/5.34            @ ^ [Uu3: nat] : ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N ) ) )
% 9.53/5.34        = ( collec3392354462482085612at_nat
% 9.53/5.34          @ ( produc6081775807080527818_nat_o
% 9.53/5.34            @ ^ [X2: nat,Y: nat] :
% 9.53/5.34                ( ( ord_less_nat @ X2 @ N )
% 9.53/5.34                & ( ord_less_nat @ Y @ N )
% 9.53/5.34                & ( ord_less_eq_nat @ X2 @ Y ) ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10170_natLeq__underS__less,axiom,
% 9.53/5.34      ! [N: nat] :
% 9.53/5.34        ( ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N )
% 9.53/5.34        = ( collect_nat
% 9.53/5.34          @ ^ [X2: nat] : ( ord_less_nat @ X2 @ N ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10171_quotient__of__number_I5_J,axiom,
% 9.53/5.34      ! [K: num] :
% 9.53/5.34        ( ( quotient_of @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 9.53/5.34        = ( product_Pair_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10172_quotient__of__number_I3_J,axiom,
% 9.53/5.34      ! [K: num] :
% 9.53/5.34        ( ( quotient_of @ ( numeral_numeral_rat @ K ) )
% 9.53/5.34        = ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10173_diff__rat__def,axiom,
% 9.53/5.34      ( minus_minus_rat
% 9.53/5.34      = ( ^ [Q4: rat,R5: rat] : ( plus_plus_rat @ Q4 @ ( uminus_uminus_rat @ R5 ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10174_rat__floor__code,axiom,
% 9.53/5.34      ( archim3151403230148437115or_rat
% 9.53/5.34      = ( ^ [P4: rat] : ( produc8211389475949308722nt_int @ divide_divide_int @ ( quotient_of @ P4 ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10175_rat__minus__code,axiom,
% 9.53/5.34      ! [P6: rat,Q2: rat] :
% 9.53/5.34        ( ( quotient_of @ ( minus_minus_rat @ P6 @ Q2 ) )
% 9.53/5.34        = ( produc4245557441103728435nt_int
% 9.53/5.34          @ ^ [A3: int,C3: int] :
% 9.53/5.34              ( produc4245557441103728435nt_int
% 9.53/5.34              @ ^ [B4: int,D: int] : ( normalize @ ( product_Pair_int_int @ ( minus_minus_int @ ( times_times_int @ A3 @ D ) @ ( times_times_int @ B4 @ C3 ) ) @ ( times_times_int @ C3 @ D ) ) )
% 9.53/5.34              @ ( quotient_of @ Q2 ) )
% 9.53/5.34          @ ( quotient_of @ P6 ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10176_Frct__code__post_I4_J,axiom,
% 9.53/5.34      ! [K: num] :
% 9.53/5.34        ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) )
% 9.53/5.34        = ( numeral_numeral_rat @ K ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10177_obtain__pos__sum,axiom,
% 9.53/5.34      ! [R: rat] :
% 9.53/5.34        ( ( ord_less_rat @ zero_zero_rat @ R )
% 9.53/5.34       => ~ ! [S: rat] :
% 9.53/5.34              ( ( ord_less_rat @ zero_zero_rat @ S )
% 9.53/5.34             => ! [T6: rat] :
% 9.53/5.34                  ( ( ord_less_rat @ zero_zero_rat @ T6 )
% 9.53/5.34                 => ( R
% 9.53/5.34                   != ( plus_plus_rat @ S @ T6 ) ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10178_Frct__code__post_I6_J,axiom,
% 9.53/5.34      ! [K: num,L2: num] :
% 9.53/5.34        ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_int @ L2 ) ) )
% 9.53/5.34        = ( divide_divide_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_rat @ L2 ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10179_Frct__code__post_I5_J,axiom,
% 9.53/5.34      ! [K: num] :
% 9.53/5.34        ( ( frct @ ( product_Pair_int_int @ one_one_int @ ( numeral_numeral_int @ K ) ) )
% 9.53/5.34        = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10180_normalize__def,axiom,
% 9.53/5.34      ( normalize
% 9.53/5.34      = ( ^ [P4: product_prod_int_int] :
% 9.53/5.34            ( if_Pro3027730157355071871nt_int @ ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ P4 ) ) @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P4 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P4 ) @ ( product_snd_int_int @ P4 ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P4 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P4 ) @ ( product_snd_int_int @ P4 ) ) ) )
% 9.53/5.34            @ ( if_Pro3027730157355071871nt_int
% 9.53/5.34              @ ( ( product_snd_int_int @ P4 )
% 9.53/5.34                = zero_zero_int )
% 9.53/5.34              @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 9.53/5.34              @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P4 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P4 ) @ ( product_snd_int_int @ P4 ) ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P4 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P4 ) @ ( product_snd_int_int @ P4 ) ) ) ) ) ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10181_gcd__neg__numeral__2__int,axiom,
% 9.53/5.34      ! [X: int,N: num] :
% 9.53/5.34        ( ( gcd_gcd_int @ X @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.53/5.34        = ( gcd_gcd_int @ X @ ( numeral_numeral_int @ N ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10182_gcd__neg__numeral__1__int,axiom,
% 9.53/5.34      ! [N: num,X: int] :
% 9.53/5.34        ( ( gcd_gcd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ X )
% 9.53/5.34        = ( gcd_gcd_int @ ( numeral_numeral_int @ N ) @ X ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10183_gcd__1__nat,axiom,
% 9.53/5.34      ! [M: nat] :
% 9.53/5.34        ( ( gcd_gcd_nat @ M @ one_one_nat )
% 9.53/5.34        = one_one_nat ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10184_gcd__Suc__0,axiom,
% 9.53/5.34      ! [M: nat] :
% 9.53/5.34        ( ( gcd_gcd_nat @ M @ ( suc @ zero_zero_nat ) )
% 9.53/5.34        = ( suc @ zero_zero_nat ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10185_gcd__pos__nat,axiom,
% 9.53/5.34      ! [M: nat,N: nat] :
% 9.53/5.34        ( ( ord_less_nat @ zero_zero_nat @ ( gcd_gcd_nat @ M @ N ) )
% 9.53/5.34        = ( ( M != zero_zero_nat )
% 9.53/5.34          | ( N != zero_zero_nat ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10186_last__upt,axiom,
% 9.53/5.34      ! [I2: nat,J: nat] :
% 9.53/5.34        ( ( ord_less_nat @ I2 @ J )
% 9.53/5.34       => ( ( last_nat @ ( upt @ I2 @ J ) )
% 9.53/5.34          = ( minus_minus_nat @ J @ one_one_nat ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10187_bezout__nat,axiom,
% 9.53/5.34      ! [A: nat,B: nat] :
% 9.53/5.34        ( ( A != zero_zero_nat )
% 9.53/5.34       => ? [X3: nat,Y3: nat] :
% 9.53/5.34            ( ( times_times_nat @ A @ X3 )
% 9.53/5.34            = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10188_bezout__gcd__nat_H,axiom,
% 9.53/5.34      ! [B: nat,A: nat] :
% 9.53/5.34      ? [X3: nat,Y3: nat] :
% 9.53/5.34        ( ( ( ord_less_eq_nat @ ( times_times_nat @ B @ Y3 ) @ ( times_times_nat @ A @ X3 ) )
% 9.53/5.34          & ( ( minus_minus_nat @ ( times_times_nat @ A @ X3 ) @ ( times_times_nat @ B @ Y3 ) )
% 9.53/5.34            = ( gcd_gcd_nat @ A @ B ) ) )
% 9.53/5.34        | ( ( ord_less_eq_nat @ ( times_times_nat @ A @ Y3 ) @ ( times_times_nat @ B @ X3 ) )
% 9.53/5.34          & ( ( minus_minus_nat @ ( times_times_nat @ B @ X3 ) @ ( times_times_nat @ A @ Y3 ) )
% 9.53/5.34            = ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10189_gcd__diff1__nat,axiom,
% 9.53/5.34      ! [N: nat,M: nat] :
% 9.53/5.34        ( ( ord_less_eq_nat @ N @ M )
% 9.53/5.34       => ( ( gcd_gcd_nat @ ( minus_minus_nat @ M @ N ) @ N )
% 9.53/5.34          = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10190_gcd__diff2__nat,axiom,
% 9.53/5.34      ! [M: nat,N: nat] :
% 9.53/5.34        ( ( ord_less_eq_nat @ M @ N )
% 9.53/5.34       => ( ( gcd_gcd_nat @ ( minus_minus_nat @ N @ M ) @ N )
% 9.53/5.34          = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10191_gcd__le2__nat,axiom,
% 9.53/5.34      ! [B: nat,A: nat] :
% 9.53/5.34        ( ( B != zero_zero_nat )
% 9.53/5.34       => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ B ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10192_gcd__le1__nat,axiom,
% 9.53/5.34      ! [A: nat,B: nat] :
% 9.53/5.34        ( ( A != zero_zero_nat )
% 9.53/5.34       => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ A ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10193_gcd__mult__distrib__nat,axiom,
% 9.53/5.34      ! [K: nat,M: nat,N: nat] :
% 9.53/5.34        ( ( times_times_nat @ K @ ( gcd_gcd_nat @ M @ N ) )
% 9.53/5.34        = ( gcd_gcd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10194_gcd__is__Max__divisors__nat,axiom,
% 9.53/5.34      ! [N: nat,M: nat] :
% 9.53/5.34        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.53/5.34       => ( ( gcd_gcd_nat @ M @ N )
% 9.53/5.34          = ( lattic8265883725875713057ax_nat
% 9.53/5.34            @ ( collect_nat
% 9.53/5.34              @ ^ [D: nat] :
% 9.53/5.34                  ( ( dvd_dvd_nat @ D @ M )
% 9.53/5.34                  & ( dvd_dvd_nat @ D @ N ) ) ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10195_gcd__nat_Opelims,axiom,
% 9.53/5.34      ! [X: nat,Xa2: nat,Y2: nat] :
% 9.53/5.34        ( ( ( gcd_gcd_nat @ X @ Xa2 )
% 9.53/5.34          = Y2 )
% 9.53/5.34       => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 9.53/5.34         => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 9.53/5.34                 => ( Y2 = X ) )
% 9.53/5.34                & ( ( Xa2 != zero_zero_nat )
% 9.53/5.34                 => ( Y2
% 9.53/5.34                    = ( gcd_gcd_nat @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) ) )
% 9.53/5.34             => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10196_natLeq__on__wo__rel,axiom,
% 9.53/5.34      ! [N: nat] :
% 9.53/5.34        ( bNF_We3818239936649020644el_nat
% 9.53/5.34        @ ( collec3392354462482085612at_nat
% 9.53/5.34          @ ( produc6081775807080527818_nat_o
% 9.53/5.34            @ ^ [X2: nat,Y: nat] :
% 9.53/5.34                ( ( ord_less_nat @ X2 @ N )
% 9.53/5.34                & ( ord_less_nat @ Y @ N )
% 9.53/5.34                & ( ord_less_eq_nat @ X2 @ Y ) ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10197_Bseq__monoseq__convergent_H__inc,axiom,
% 9.53/5.34      ! [F: nat > real,M7: nat] :
% 9.53/5.34        ( ( bfun_nat_real
% 9.53/5.34          @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ M7 ) )
% 9.53/5.34          @ at_top_nat )
% 9.53/5.34       => ( ! [M4: nat,N3: nat] :
% 9.53/5.34              ( ( ord_less_eq_nat @ M7 @ M4 )
% 9.53/5.34             => ( ( ord_less_eq_nat @ M4 @ N3 )
% 9.53/5.34               => ( ord_less_eq_real @ ( F @ M4 ) @ ( F @ N3 ) ) ) )
% 9.53/5.34         => ( topolo7531315842566124627t_real @ F ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10198_Bseq__monoseq__convergent_H__dec,axiom,
% 9.53/5.34      ! [F: nat > real,M7: nat] :
% 9.53/5.34        ( ( bfun_nat_real
% 9.53/5.34          @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ M7 ) )
% 9.53/5.34          @ at_top_nat )
% 9.53/5.34       => ( ! [M4: nat,N3: nat] :
% 9.53/5.34              ( ( ord_less_eq_nat @ M7 @ M4 )
% 9.53/5.34             => ( ( ord_less_eq_nat @ M4 @ N3 )
% 9.53/5.34               => ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ M4 ) ) ) )
% 9.53/5.34         => ( topolo7531315842566124627t_real @ F ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10199_Bseq__mono__convergent,axiom,
% 9.53/5.34      ! [X8: nat > real] :
% 9.53/5.34        ( ( bfun_nat_real @ X8 @ at_top_nat )
% 9.53/5.34       => ( ! [M4: nat,N3: nat] :
% 9.53/5.34              ( ( ord_less_eq_nat @ M4 @ N3 )
% 9.53/5.34             => ( ord_less_eq_real @ ( X8 @ M4 ) @ ( X8 @ N3 ) ) )
% 9.53/5.34         => ( topolo7531315842566124627t_real @ X8 ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10200_convergent__realpow,axiom,
% 9.53/5.34      ! [X: real] :
% 9.53/5.34        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 9.53/5.34       => ( ( ord_less_eq_real @ X @ one_one_real )
% 9.53/5.34         => ( topolo7531315842566124627t_real @ ( power_power_real @ X ) ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10201_bot__nat__0_Oordering__top__axioms,axiom,
% 9.53/5.34      ( ordering_top_nat
% 9.53/5.34      @ ^ [X2: nat,Y: nat] : ( ord_less_eq_nat @ Y @ X2 )
% 9.53/5.34      @ ^ [X2: nat,Y: nat] : ( ord_less_nat @ Y @ X2 )
% 9.53/5.34      @ zero_zero_nat ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10202_pair__lessI2,axiom,
% 9.53/5.34      ! [A: nat,B: nat,S3: nat,T: nat] :
% 9.53/5.34        ( ( ord_less_eq_nat @ A @ B )
% 9.53/5.34       => ( ( ord_less_nat @ S3 @ T )
% 9.53/5.34         => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S3 ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_less ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10203_pair__less__iff1,axiom,
% 9.53/5.34      ! [X: nat,Y2: nat,Z: nat] :
% 9.53/5.34        ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ X @ Y2 ) @ ( product_Pair_nat_nat @ X @ Z ) ) @ fun_pair_less )
% 9.53/5.34        = ( ord_less_nat @ Y2 @ Z ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10204_pair__lessI1,axiom,
% 9.53/5.34      ! [A: nat,B: nat,S3: nat,T: nat] :
% 9.53/5.34        ( ( ord_less_nat @ A @ B )
% 9.53/5.34       => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S3 ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_less ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10205_pair__leqI2,axiom,
% 9.53/5.34      ! [A: nat,B: nat,S3: nat,T: nat] :
% 9.53/5.34        ( ( ord_less_eq_nat @ A @ B )
% 9.53/5.34       => ( ( ord_less_eq_nat @ S3 @ T )
% 9.53/5.34         => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S3 ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_leq ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10206_pair__leqI1,axiom,
% 9.53/5.34      ! [A: nat,B: nat,S3: nat,T: nat] :
% 9.53/5.34        ( ( ord_less_nat @ A @ B )
% 9.53/5.34       => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S3 ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_leq ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10207_of__rat__dense,axiom,
% 9.53/5.34      ! [X: real,Y2: real] :
% 9.53/5.34        ( ( ord_less_real @ X @ Y2 )
% 9.53/5.34       => ? [Q3: rat] :
% 9.53/5.34            ( ( ord_less_real @ X @ ( field_7254667332652039916t_real @ Q3 ) )
% 9.53/5.34            & ( ord_less_real @ ( field_7254667332652039916t_real @ Q3 ) @ Y2 ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10208_euclidean__size__int__def,axiom,
% 9.53/5.34      ( euclid4774559944035922753ze_int
% 9.53/5.34      = ( comp_int_nat_int @ nat2 @ abs_abs_int ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10209_euclidean__size__nat__def,axiom,
% 9.53/5.34      euclid4777050414544973029ze_nat = id_nat ).
% 9.53/5.34  
% 9.53/5.34  thf(fact_10210_abs__division__segment,axiom,
% 9.53/5.34      ! [K: int] :
% 9.53/5.34        ( ( abs_abs_int @ ( euclid3395696857347342551nt_int @ K ) )
% 9.53/5.34        = one_one_int ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 9.53/5.34      ! [X: int,Y2: int] :
% 9.53/5.34        ( ( if_int @ $false @ X @ Y2 )
% 9.53/5.34        = Y2 ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 9.53/5.34      ! [X: int,Y2: int] :
% 9.53/5.34        ( ( if_int @ $true @ X @ Y2 )
% 9.53/5.34        = X ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 9.53/5.34      ! [X: nat,Y2: nat] :
% 9.53/5.34        ( ( if_nat @ $false @ X @ Y2 )
% 9.53/5.34        = Y2 ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 9.53/5.34      ! [X: nat,Y2: nat] :
% 9.53/5.34        ( ( if_nat @ $true @ X @ Y2 )
% 9.53/5.34        = X ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 9.53/5.34      ! [X: num,Y2: num] :
% 9.53/5.34        ( ( if_num @ $false @ X @ Y2 )
% 9.53/5.34        = Y2 ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 9.53/5.34      ! [X: num,Y2: num] :
% 9.53/5.34        ( ( if_num @ $true @ X @ Y2 )
% 9.53/5.34        = X ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 9.53/5.34      ! [X: rat,Y2: rat] :
% 9.53/5.34        ( ( if_rat @ $false @ X @ Y2 )
% 9.53/5.34        = Y2 ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 9.53/5.34      ! [X: rat,Y2: rat] :
% 9.53/5.34        ( ( if_rat @ $true @ X @ Y2 )
% 9.53/5.34        = X ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 9.53/5.34      ! [X: real,Y2: real] :
% 9.53/5.34        ( ( if_real @ $false @ X @ Y2 )
% 9.53/5.34        = Y2 ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 9.53/5.34      ! [X: real,Y2: real] :
% 9.53/5.34        ( ( if_real @ $true @ X @ Y2 )
% 9.53/5.34        = X ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_fChoice_1_1_fChoice_001t__Real__Oreal_T,axiom,
% 9.53/5.34      ! [P: real > $o] :
% 9.53/5.34        ( ( P @ ( fChoice_real @ P ) )
% 9.53/5.34        = ( ? [X4: real] : ( P @ X4 ) ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_2_1_If_001t__Complex__Ocomplex_T,axiom,
% 9.53/5.34      ! [X: complex,Y2: complex] :
% 9.53/5.34        ( ( if_complex @ $false @ X @ Y2 )
% 9.53/5.34        = Y2 ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_1_1_If_001t__Complex__Ocomplex_T,axiom,
% 9.53/5.34      ! [X: complex,Y2: complex] :
% 9.53/5.34        ( ( if_complex @ $true @ X @ Y2 )
% 9.53/5.34        = X ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_2_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 9.53/5.34      ! [X: extended_enat,Y2: extended_enat] :
% 9.53/5.34        ( ( if_Extended_enat @ $false @ X @ Y2 )
% 9.53/5.34        = Y2 ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_1_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 9.53/5.34      ! [X: extended_enat,Y2: extended_enat] :
% 9.53/5.34        ( ( if_Extended_enat @ $true @ X @ Y2 )
% 9.53/5.34        = X ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 9.53/5.34      ! [X: code_integer,Y2: code_integer] :
% 9.53/5.34        ( ( if_Code_integer @ $false @ X @ Y2 )
% 9.53/5.34        = Y2 ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 9.53/5.34      ! [X: code_integer,Y2: code_integer] :
% 9.53/5.34        ( ( if_Code_integer @ $true @ X @ Y2 )
% 9.53/5.34        = X ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_2_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 9.53/5.34      ! [X: set_nat,Y2: set_nat] :
% 9.53/5.34        ( ( if_set_nat @ $false @ X @ Y2 )
% 9.53/5.34        = Y2 ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_1_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 9.53/5.34      ! [X: set_nat,Y2: set_nat] :
% 9.53/5.34        ( ( if_set_nat @ $true @ X @ Y2 )
% 9.53/5.34        = X ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_2_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 9.53/5.34      ! [X: vEBT_VEBT,Y2: vEBT_VEBT] :
% 9.53/5.34        ( ( if_VEBT_VEBT @ $false @ X @ Y2 )
% 9.53/5.34        = Y2 ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_1_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 9.53/5.34      ! [X: vEBT_VEBT,Y2: vEBT_VEBT] :
% 9.53/5.34        ( ( if_VEBT_VEBT @ $true @ X @ Y2 )
% 9.53/5.34        = X ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 9.53/5.34      ! [X: list_int,Y2: list_int] :
% 9.53/5.34        ( ( if_list_int @ $false @ X @ Y2 )
% 9.53/5.34        = Y2 ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 9.53/5.34      ! [X: list_int,Y2: list_int] :
% 9.53/5.34        ( ( if_list_int @ $true @ X @ Y2 )
% 9.53/5.34        = X ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 9.53/5.34      ! [X: list_nat,Y2: list_nat] :
% 9.53/5.34        ( ( if_list_nat @ $false @ X @ Y2 )
% 9.53/5.34        = Y2 ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 9.53/5.34      ! [X: list_nat,Y2: list_nat] :
% 9.53/5.34        ( ( if_list_nat @ $true @ X @ Y2 )
% 9.53/5.34        = X ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_2_1_If_001t__Set__Oset_It__Real__Oreal_J_T,axiom,
% 9.53/5.34      ! [X: set_real,Y2: set_real] :
% 9.53/5.34        ( ( if_set_real @ $false @ X @ Y2 )
% 9.53/5.34        = Y2 ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_1_1_If_001t__Set__Oset_It__Real__Oreal_J_T,axiom,
% 9.53/5.34      ! [X: set_real,Y2: set_real] :
% 9.53/5.34        ( ( if_set_real @ $true @ X @ Y2 )
% 9.53/5.34        = X ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_2_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 9.53/5.34      ! [X: int > int,Y2: int > int] :
% 9.53/5.34        ( ( if_int_int @ $false @ X @ Y2 )
% 9.53/5.34        = Y2 ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_1_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 9.53/5.34      ! [X: int > int,Y2: int > int] :
% 9.53/5.34        ( ( if_int_int @ $true @ X @ Y2 )
% 9.53/5.34        = X ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_2_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 9.53/5.34      ! [X: option_nat,Y2: option_nat] :
% 9.53/5.34        ( ( if_option_nat @ $false @ X @ Y2 )
% 9.53/5.34        = Y2 ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_1_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 9.53/5.34      ! [X: option_nat,Y2: option_nat] :
% 9.53/5.34        ( ( if_option_nat @ $true @ X @ Y2 )
% 9.53/5.34        = X ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 9.53/5.34      ! [X: option_num,Y2: option_num] :
% 9.53/5.34        ( ( if_option_num @ $false @ X @ Y2 )
% 9.53/5.34        = Y2 ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 9.53/5.34      ! [X: option_num,Y2: option_num] :
% 9.53/5.34        ( ( if_option_num @ $true @ X @ Y2 )
% 9.53/5.34        = X ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 9.53/5.34      ! [X: product_prod_int_int,Y2: product_prod_int_int] :
% 9.53/5.34        ( ( if_Pro3027730157355071871nt_int @ $false @ X @ Y2 )
% 9.53/5.34        = Y2 ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 9.53/5.34      ! [X: product_prod_int_int,Y2: product_prod_int_int] :
% 9.53/5.34        ( ( if_Pro3027730157355071871nt_int @ $true @ X @ Y2 )
% 9.53/5.34        = X ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 9.53/5.34      ! [X: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 9.53/5.34        ( ( if_Pro6206227464963214023at_nat @ $false @ X @ Y2 )
% 9.53/5.34        = Y2 ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 9.53/5.34      ! [X: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 9.53/5.34        ( ( if_Pro6206227464963214023at_nat @ $true @ X @ Y2 )
% 9.53/5.34        = X ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 9.53/5.34      ! [X: produc6271795597528267376eger_o,Y2: produc6271795597528267376eger_o] :
% 9.53/5.34        ( ( if_Pro5737122678794959658eger_o @ $false @ X @ Y2 )
% 9.53/5.34        = Y2 ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 9.53/5.34      ! [X: produc6271795597528267376eger_o,Y2: produc6271795597528267376eger_o] :
% 9.53/5.34        ( ( if_Pro5737122678794959658eger_o @ $true @ X @ Y2 )
% 9.53/5.34        = X ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 9.53/5.34      ! [P: $o] :
% 9.53/5.34        ( ( P = $true )
% 9.53/5.34        | ( P = $false ) ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 9.53/5.34      ! [X: produc8923325533196201883nteger,Y2: produc8923325533196201883nteger] :
% 9.53/5.34        ( ( if_Pro6119634080678213985nteger @ $false @ X @ Y2 )
% 9.53/5.34        = Y2 ) ).
% 9.53/5.34  
% 9.53/5.34  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 9.53/5.34      ! [X: produc8923325533196201883nteger,Y2: produc8923325533196201883nteger] :
% 9.53/5.34        ( ( if_Pro6119634080678213985nteger @ $true @ X @ Y2 )
% 9.53/5.34        = X ) ).
% 9.53/5.34  
% 9.53/5.34  thf(conj_0,conjecture,
% 9.53/5.34      ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 9.53/5.34      = ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_t @ summary ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat ) @ one_one_nat ) ) ).
% 9.53/5.34  ------------------------
% 9.53/5.89  % (21772)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21656 for (2994ds/2Mi)
% 9.53/5.89  % (21769)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21656 for (2994ds/183Mi)
% 9.53/5.89  % (21771)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_21656 for (2994ds/27Mi)
% 9.53/5.89  % (21770)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_21656 for (2994ds/4Mi)
% 9.53/5.89  % (21773)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_21656 for (2994ds/2Mi)
% 9.53/5.90  % (21773)Instruction limit reached!
% 9.53/5.90  % (21773)------------------------------
% 9.53/5.90  % (21773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/5.90  % (21773)Termination reason: Unknown
% 9.53/5.90  % (21773)Termination phase: shuffling
% 9.53/5.90  
% 9.53/5.90  % (21773)Memory used [KB]: 13304
% 9.53/5.90  % (21773)Time elapsed: 0.003 s
% 9.53/5.90  % (21773)Instructions burned: 2 (million)
% 9.53/5.90  % (21773)------------------------------
% 9.53/5.90  % (21773)------------------------------
% 9.53/5.90  % (21772)Instruction limit reached!
% 9.53/5.90  % (21772)------------------------------
% 9.53/5.90  % (21772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/5.90  % (21772)Termination reason: Unknown
% 9.53/5.90  % (21772)Termination phase: shuffling
% 9.53/5.90  
% 9.53/5.90  % (21772)Memory used [KB]: 13304
% 9.53/5.90  % (21772)Time elapsed: 0.004 s
% 9.53/5.90  % (21772)Instructions burned: 2 (million)
% 9.53/5.90  % (21772)------------------------------
% 9.53/5.90  % (21772)------------------------------
% 9.53/5.90  % (21774)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_21656 for (2994ds/275Mi)
% 9.53/5.90  % (21770)Instruction limit reached!
% 9.53/5.90  % (21770)------------------------------
% 9.53/5.90  % (21770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/5.90  % (21770)Termination reason: Unknown
% 9.53/5.90  % (21770)Termination phase: shuffling
% 9.53/5.90  
% 9.53/5.90  % (21770)Memory used [KB]: 13432
% 9.53/5.90  % (21770)Time elapsed: 0.007 s
% 9.53/5.90  % (21770)Instructions burned: 4 (million)
% 9.53/5.90  % (21770)------------------------------
% 9.53/5.90  % (21770)------------------------------
% 9.53/5.91  % (21775)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21656 for (2994ds/18Mi)
% 9.53/5.92  % (21776)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_21656 for (2994ds/3Mi)
% 9.53/5.92  % (21777)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_21656 for (2994ds/37Mi)
% 9.53/5.92  % (21776)Instruction limit reached!
% 9.53/5.92  % (21776)------------------------------
% 9.53/5.92  % (21776)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/5.92  % (21776)Termination reason: Unknown
% 9.53/5.92  % (21776)Termination phase: shuffling
% 9.53/5.92  
% 9.53/5.92  % (21776)Memory used [KB]: 13304
% 9.53/5.92  % (21776)Time elapsed: 0.005 s
% 9.53/5.92  % (21776)Instructions burned: 3 (million)
% 9.53/5.92  % (21776)------------------------------
% 9.53/5.92  % (21776)------------------------------
% 9.53/5.92  % (21778)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_21656 for (2994ds/15Mi)
% 9.53/5.92  % (21771)Instruction limit reached!
% 9.53/5.92  % (21771)------------------------------
% 9.53/5.92  % (21771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/5.92  % (21771)Termination reason: Unknown
% 9.53/5.92  % (21771)Termination phase: shuffling
% 9.53/5.92  
% 9.53/5.92  % (21771)Memory used [KB]: 14328
% 9.53/5.92  % (21771)Time elapsed: 0.030 s
% 9.53/5.92  % (21771)Instructions burned: 27 (million)
% 9.53/5.92  % (21771)------------------------------
% 9.53/5.92  % (21771)------------------------------
% 9.53/5.93  % (21775)Instruction limit reached!
% 9.53/5.93  % (21775)------------------------------
% 9.53/5.93  % (21775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/5.93  % (21775)Termination reason: Unknown
% 9.53/5.93  % (21775)Termination phase: shuffling
% 9.53/5.93  
% 9.53/5.93  % (21775)Memory used [KB]: 14200
% 9.53/5.93  % (21775)Time elapsed: 0.024 s
% 9.53/5.93  % (21775)Instructions burned: 18 (million)
% 9.53/5.93  % (21775)------------------------------
% 9.53/5.93  % (21775)------------------------------
% 9.53/5.94  % (21779)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_21656 for (2994ds/3Mi)
% 9.53/5.94  % (21778)Instruction limit reached!
% 9.53/5.94  % (21778)------------------------------
% 9.53/5.94  % (21778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/5.94  % (21778)Termination reason: Unknown
% 9.53/5.94  % (21778)Termination phase: shuffling
% 9.53/5.94  
% 9.53/5.94  % (21778)Memory used [KB]: 14200
% 9.53/5.94  % (21778)Time elapsed: 0.022 s
% 9.53/5.94  % (21778)Instructions burned: 16 (million)
% 9.53/5.94  % (21778)------------------------------
% 9.53/5.94  % (21778)------------------------------
% 9.53/5.94  % (21779)Instruction limit reached!
% 9.53/5.94  % (21779)------------------------------
% 9.53/5.94  % (21779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/5.94  % (21779)Termination reason: Unknown
% 9.53/5.94  % (21779)Termination phase: shuffling
% 9.53/5.94  
% 9.53/5.94  % (21779)Memory used [KB]: 13304
% 9.53/5.94  % (21779)Time elapsed: 0.005 s
% 9.53/5.94  % (21779)Instructions burned: 3 (million)
% 9.53/5.94  % (21779)------------------------------
% 9.53/5.94  % (21779)------------------------------
% 9.53/5.94  % (21780)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_21656 for (2994ds/1041Mi)
% 9.53/5.95  % (21777)Instruction limit reached!
% 9.53/5.95  % (21777)------------------------------
% 9.53/5.95  % (21777)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/5.95  % (21777)Termination reason: Unknown
% 9.53/5.95  % (21777)Termination phase: shuffling
% 9.53/5.95  
% 9.53/5.95  % (21777)Memory used [KB]: 14456
% 9.53/5.95  % (21777)Time elapsed: 0.034 s
% 9.53/5.95  % (21777)Instructions burned: 37 (million)
% 9.53/5.95  % (21777)------------------------------
% 9.53/5.95  % (21777)------------------------------
% 9.53/5.95  % (21781)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_21656 for (2994ds/7Mi)
% 9.53/5.96  % (21781)Instruction limit reached!
% 9.53/5.96  % (21781)------------------------------
% 9.53/5.96  % (21781)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/5.96  % (21781)Termination reason: Unknown
% 9.53/5.96  % (21781)Termination phase: shuffling
% 9.53/5.96  
% 9.53/5.96  % (21781)Memory used [KB]: 13688
% 9.53/5.96  % (21781)Time elapsed: 0.011 s
% 9.53/5.96  % (21781)Instructions burned: 7 (million)
% 9.53/5.96  % (21781)------------------------------
% 9.53/5.96  % (21781)------------------------------
% 9.53/5.96  % (21782)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_21656 for (2994ds/16Mi)
% 9.53/5.96  % (21783)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_21656 for (2994ds/3Mi)
% 9.53/5.96  % (21783)Instruction limit reached!
% 9.53/5.96  % (21783)------------------------------
% 9.53/5.96  % (21783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/5.96  % (21783)Termination reason: Unknown
% 9.53/5.96  % (21783)Termination phase: shuffling
% 9.53/5.96  
% 9.53/5.96  % (21783)Memory used [KB]: 13304
% 9.53/5.96  % (21783)Time elapsed: 0.005 s
% 9.53/5.96  % (21783)Instructions burned: 3 (million)
% 9.53/5.96  % (21783)------------------------------
% 9.53/5.96  % (21783)------------------------------
% 9.53/5.97  % (21784)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_21656 for (2993ds/3Mi)
% 9.53/5.97  % (21784)Instruction limit reached!
% 9.53/5.97  % (21784)------------------------------
% 9.53/5.97  % (21784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/5.97  % (21784)Termination reason: Unknown
% 9.53/5.97  % (21784)Termination phase: shuffling
% 9.53/5.97  
% 9.53/5.97  % (21784)Memory used [KB]: 13304
% 9.53/5.97  % (21784)Time elapsed: 0.005 s
% 9.53/5.97  % (21784)Instructions burned: 3 (million)
% 9.53/5.97  % (21784)------------------------------
% 9.53/5.97  % (21784)------------------------------
% 9.53/5.98  % (21785)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_21656 for (2993ds/7Mi)
% 9.53/5.98  % (21782)Instruction limit reached!
% 9.53/5.98  % (21782)------------------------------
% 9.53/5.98  % (21782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/5.98  % (21782)Termination reason: Unknown
% 9.53/5.98  % (21782)Termination phase: shuffling
% 9.53/5.98  
% 9.53/5.98  % (21782)Memory used [KB]: 14200
% 9.53/5.98  % (21782)Time elapsed: 0.023 s
% 9.53/5.98  % (21782)Instructions burned: 17 (million)
% 9.53/5.98  % (21782)------------------------------
% 9.53/5.98  % (21782)------------------------------
% 9.53/5.98  % (21786)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_21656 for (2993ds/3Mi)
% 9.53/5.99  % (21786)Instruction limit reached!
% 9.53/5.99  % (21786)------------------------------
% 9.53/5.99  % (21786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/5.99  % (21786)Termination reason: Unknown
% 9.53/5.99  % (21786)Termination phase: shuffling
% 9.53/5.99  
% 9.53/5.99  % (21786)Memory used [KB]: 13304
% 9.53/5.99  % (21786)Time elapsed: 0.005 s
% 9.53/5.99  % (21786)Instructions burned: 3 (million)
% 9.53/5.99  % (21786)------------------------------
% 9.53/5.99  % (21786)------------------------------
% 9.53/5.99  % (21785)Instruction limit reached!
% 9.53/5.99  % (21785)------------------------------
% 9.53/5.99  % (21785)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/5.99  % (21785)Termination reason: Unknown
% 9.53/5.99  % (21785)Termination phase: shuffling
% 9.53/5.99  
% 9.53/5.99  % (21785)Memory used [KB]: 13688
% 9.53/5.99  % (21785)Time elapsed: 0.011 s
% 9.53/5.99  % (21785)Instructions burned: 7 (million)
% 9.53/5.99  % (21785)------------------------------
% 9.53/5.99  % (21785)------------------------------
% 9.53/5.99  % (21787)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_21656 for (2993ds/4Mi)
% 9.53/5.99  % (21774)Instruction limit reached!
% 9.53/5.99  % (21774)------------------------------
% 9.53/5.99  % (21774)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/5.99  % (21774)Termination reason: Unknown
% 9.53/5.99  % (21774)Termination phase: shuffling
% 9.53/5.99  
% 9.53/5.99  % (21774)Memory used [KB]: 17270
% 9.53/5.99  % (21774)Time elapsed: 0.097 s
% 9.53/5.99  % (21774)Instructions burned: 276 (million)
% 9.53/5.99  % (21774)------------------------------
% 9.53/5.99  % (21774)------------------------------
% 9.53/5.99  % (21787)Instruction limit reached!
% 9.53/5.99  % (21787)------------------------------
% 9.53/5.99  % (21787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/5.99  % (21787)Termination reason: Unknown
% 9.53/5.99  % (21787)Termination phase: shuffling
% 9.53/5.99  
% 9.53/5.99  % (21787)Memory used [KB]: 13432
% 9.53/5.99  % (21787)Time elapsed: 0.006 s
% 9.53/5.99  % (21787)Instructions burned: 4 (million)
% 9.53/5.99  % (21787)------------------------------
% 9.53/5.99  % (21787)------------------------------
% 9.53/6.00  % (21788)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_21656 for (2993ds/18Mi)
% 9.53/6.00  % (21789)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_21656 for (2993ds/710Mi)
% 9.53/6.00  % (21791)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_21656 for (2993ds/902Mi)
% 9.53/6.01  % (21790)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_21656 for (2993ds/6Mi)
% 9.53/6.01  % (21790)Instruction limit reached!
% 9.53/6.01  % (21790)------------------------------
% 9.53/6.01  % (21790)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/6.01  % (21790)Termination reason: Unknown
% 9.53/6.01  % (21790)Termination phase: shuffling
% 9.53/6.01  
% 9.53/6.01  % (21790)Memory used [KB]: 13560
% 9.53/6.01  % (21790)Time elapsed: 0.007 s
% 9.53/6.01  % (21790)Instructions burned: 6 (million)
% 9.53/6.01  % (21790)------------------------------
% 9.53/6.01  % (21790)------------------------------
% 9.53/6.01  % (21769)Instruction limit reached!
% 9.53/6.01  % (21769)------------------------------
% 9.53/6.01  % (21769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/6.01  % (21769)Termination reason: Unknown
% 9.53/6.01  % (21769)Termination phase: shuffling
% 9.53/6.01  
% 9.53/6.01  % (21769)Memory used [KB]: 16375
% 9.53/6.01  % (21769)Time elapsed: 0.121 s
% 9.53/6.01  % (21769)Instructions burned: 185 (million)
% 9.53/6.01  % (21769)------------------------------
% 9.53/6.01  % (21769)------------------------------
% 9.53/6.01  % (21788)Instruction limit reached!
% 9.53/6.01  % (21788)------------------------------
% 9.53/6.01  % (21788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/6.01  % (21788)Termination reason: Unknown
% 9.53/6.01  % (21788)Termination phase: shuffling
% 9.53/6.01  
% 9.53/6.01  % (21788)Memory used [KB]: 14200
% 9.53/6.01  % (21788)Time elapsed: 0.016 s
% 9.53/6.01  % (21788)Instructions burned: 18 (million)
% 9.53/6.01  % (21788)------------------------------
% 9.53/6.01  % (21788)------------------------------
% 9.53/6.02  % (21793)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_21656 for (2993ds/5Mi)
% 9.53/6.02  % (21794)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_21656 for (2993ds/6Mi)
% 9.53/6.03  % (21795)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_21656 for (2993ds/377Mi)
% 10.98/6.03  % (21793)Instruction limit reached!
% 10.98/6.03  % (21793)------------------------------
% 10.98/6.03  % (21793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.98/6.03  % (21793)Termination reason: Unknown
% 10.98/6.03  % (21793)Termination phase: shuffling
% 10.98/6.03  
% 10.98/6.03  % (21793)Memory used [KB]: 13560
% 10.98/6.03  % (21793)Time elapsed: 0.006 s
% 10.98/6.03  % (21793)Instructions burned: 5 (million)
% 10.98/6.03  % (21793)------------------------------
% 10.98/6.03  % (21793)------------------------------
% 10.98/6.03  % (21794)Instruction limit reached!
% 10.98/6.03  % (21794)------------------------------
% 10.98/6.03  % (21794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.98/6.03  % (21794)Termination reason: Unknown
% 10.98/6.03  % (21794)Termination phase: shuffling
% 10.98/6.03  
% 10.98/6.03  % (21794)Memory used [KB]: 13560
% 10.98/6.03  % (21794)Time elapsed: 0.006 s
% 10.98/6.03  % (21794)Instructions burned: 6 (million)
% 10.98/6.03  % (21794)------------------------------
% 10.98/6.03  % (21794)------------------------------
% 10.98/6.03  % (21792)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_21656 for (2993ds/21Mi)
% 10.98/6.04  % (21797)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_21656 for (2993ds/19Mi)
% 10.98/6.05  % (21796)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_21656 for (2993ds/779Mi)
% 10.98/6.05  % (21792)Instruction limit reached!
% 10.98/6.05  % (21792)------------------------------
% 10.98/6.05  % (21792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.98/6.05  % (21792)Termination reason: Unknown
% 10.98/6.05  % (21792)Termination phase: shuffling
% 10.98/6.05  
% 10.98/6.05  % (21792)Memory used [KB]: 14200
% 10.98/6.05  % (21792)Time elapsed: 0.022 s
% 10.98/6.05  % (21792)Instructions burned: 22 (million)
% 10.98/6.05  % (21792)------------------------------
% 10.98/6.05  % (21792)------------------------------
% 10.98/6.05  % (21797)Instruction limit reached!
% 10.98/6.05  % (21797)------------------------------
% 10.98/6.05  % (21797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.98/6.05  % (21797)Termination reason: Unknown
% 10.98/6.05  % (21797)Termination phase: shuffling
% 10.98/6.05  
% 10.98/6.05  % (21797)Memory used [KB]: 14200
% 10.98/6.05  % (21797)Time elapsed: 0.016 s
% 10.98/6.05  % (21797)Instructions burned: 21 (million)
% 10.98/6.05  % (21797)------------------------------
% 10.98/6.05  % (21797)------------------------------
% 10.98/6.06  % (21798)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_21656 for (2992ds/879Mi)
% 10.98/6.07  % (21799)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_21656 for (2992ds/17Mi)
% 10.98/6.08  % (21799)Instruction limit reached!
% 10.98/6.08  % (21799)------------------------------
% 10.98/6.08  % (21799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.98/6.08  % (21799)Termination reason: Unknown
% 10.98/6.08  % (21799)Termination phase: shuffling
% 10.98/6.08  
% 10.98/6.08  % (21799)Memory used [KB]: 14200
% 10.98/6.08  % (21799)Time elapsed: 0.015 s
% 10.98/6.08  % (21799)Instructions burned: 17 (million)
% 10.98/6.08  % (21799)------------------------------
% 10.98/6.08  % (21799)------------------------------
% 10.98/6.10  % (21800)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_21656 for (2992ds/3Mi)
% 10.98/6.10  % (21800)Instruction limit reached!
% 10.98/6.10  % (21800)------------------------------
% 10.98/6.10  % (21800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.98/6.10  % (21800)Termination reason: Unknown
% 10.98/6.10  % (21800)Termination phase: shuffling
% 10.98/6.10  
% 10.98/6.10  % (21800)Memory used [KB]: 13432
% 10.98/6.10  % (21800)Time elapsed: 0.004 s
% 10.98/6.10  % (21800)Instructions burned: 3 (million)
% 10.98/6.10  % (21800)------------------------------
% 10.98/6.10  % (21800)------------------------------
% 10.98/6.11  % (21801)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_21656 for (2992ds/30Mi)
% 10.98/6.13  % (21801)Instruction limit reached!
% 10.98/6.13  % (21801)------------------------------
% 10.98/6.13  % (21801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.98/6.13  % (21801)Termination reason: Unknown
% 10.98/6.13  % (21801)Termination phase: shuffling
% 10.98/6.13  
% 10.98/6.13  % (21801)Memory used [KB]: 14328
% 10.98/6.13  % (21801)Time elapsed: 0.019 s
% 10.98/6.13  % (21801)Instructions burned: 31 (million)
% 10.98/6.13  % (21801)------------------------------
% 10.98/6.13  % (21801)------------------------------
% 11.47/6.14  % (21802)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_21656 for (2992ds/127Mi)
% 11.47/6.18  % (21802)Instruction limit reached!
% 11.47/6.18  % (21802)------------------------------
% 11.47/6.18  % (21802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.47/6.18  % (21802)Termination reason: Unknown
% 11.47/6.18  % (21802)Termination phase: shuffling
% 11.47/6.18  
% 11.47/6.18  % (21802)Memory used [KB]: 15735
% 11.47/6.18  % (21802)Time elapsed: 0.050 s
% 11.47/6.18  % (21802)Instructions burned: 128 (million)
% 11.47/6.18  % (21802)------------------------------
% 11.47/6.18  % (21802)------------------------------
% 11.73/6.20  % (21803)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_21656 for (2991ds/100Mi)
% 11.73/6.21  % (21795)Instruction limit reached!
% 11.73/6.21  % (21795)------------------------------
% 11.73/6.21  % (21795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.73/6.21  % (21795)Termination reason: Unknown
% 11.73/6.21  % (21795)Termination phase: shuffling
% 11.73/6.21  
% 11.73/6.21  % (21795)Memory used [KB]: 18677
% 11.73/6.21  % (21795)Time elapsed: 0.190 s
% 11.73/6.21  % (21795)Instructions burned: 378 (million)
% 11.73/6.21  % (21795)------------------------------
% 11.73/6.21  % (21795)------------------------------
% 11.73/6.23  % (21804)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_21656 for (2991ds/3Mi)
% 11.73/6.23  % (21804)Instruction limit reached!
% 11.73/6.23  % (21804)------------------------------
% 11.73/6.23  % (21804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.73/6.23  % (21804)Termination reason: Unknown
% 11.73/6.23  % (21804)Termination phase: shuffling
% 11.73/6.23  
% 11.73/6.23  % (21804)Memory used [KB]: 13432
% 11.73/6.23  % (21804)Time elapsed: 0.004 s
% 11.73/6.23  % (21804)Instructions burned: 3 (million)
% 11.73/6.23  % (21804)------------------------------
% 11.73/6.23  % (21804)------------------------------
% 11.73/6.23  % (21803)Instruction limit reached!
% 11.73/6.23  % (21803)------------------------------
% 11.73/6.23  % (21803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.73/6.23  % (21803)Termination reason: Unknown
% 11.73/6.23  % (21803)Termination phase: shuffling
% 11.73/6.23  
% 11.73/6.23  % (21803)Memory used [KB]: 15351
% 11.73/6.23  % (21803)Time elapsed: 0.038 s
% 11.73/6.23  % (21803)Instructions burned: 103 (million)
% 11.73/6.23  % (21803)------------------------------
% 11.73/6.23  % (21803)------------------------------
% 11.73/6.24  % (21805)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_21656 for (2991ds/20Mi)
% 11.73/6.24  % (21806)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_21656 for (2991ds/86Mi)
% 11.73/6.26  % (21805)Instruction limit reached!
% 11.73/6.26  % (21805)------------------------------
% 11.73/6.26  % (21805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.73/6.26  % (21805)Termination reason: Unknown
% 11.73/6.26  % (21805)Termination phase: shuffling
% 11.73/6.26  
% 11.73/6.26  % (21805)Memory used [KB]: 14200
% 11.73/6.26  % (21805)Time elapsed: 0.017 s
% 11.73/6.26  % (21805)Instructions burned: 21 (million)
% 11.73/6.26  % (21805)------------------------------
% 11.73/6.26  % (21805)------------------------------
% 11.73/6.27  % (21807)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_21656 for (2990ds/107Mi)
% 11.73/6.27  % (21789)Instruction limit reached!
% 11.73/6.27  % (21789)------------------------------
% 11.73/6.27  % (21789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.73/6.27  % (21789)Termination reason: Unknown
% 11.73/6.27  % (21789)Termination phase: shuffling
% 11.73/6.27  
% 11.73/6.27  % (21789)Memory used [KB]: 24434
% 11.73/6.27  % (21789)Time elapsed: 0.269 s
% 11.73/6.27  % (21789)Instructions burned: 711 (million)
% 11.73/6.27  % (21789)------------------------------
% 11.73/6.27  % (21789)------------------------------
% 11.73/6.28  % (21806)Instruction limit reached!
% 11.73/6.28  % (21806)------------------------------
% 11.73/6.28  % (21806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.73/6.28  % (21806)Termination reason: Unknown
% 11.73/6.28  % (21806)Termination phase: shuffling
% 11.73/6.28  
% 11.73/6.28  % (21806)Memory used [KB]: 15223
% 11.73/6.28  % (21806)Time elapsed: 0.037 s
% 11.73/6.28  % (21806)Instructions burned: 88 (million)
% 11.73/6.28  % (21806)------------------------------
% 11.73/6.28  % (21806)------------------------------
% 11.73/6.28  % (21808)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_21656 for (2990ds/39Mi)
% 12.35/6.30  % (21796)Instruction limit reached!
% 12.35/6.30  % (21796)------------------------------
% 12.35/6.30  % (21796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.35/6.30  % (21796)Termination reason: Unknown
% 12.35/6.30  % (21796)Termination phase: shuffling
% 12.35/6.30  
% 12.35/6.30  % (21796)Memory used [KB]: 26481
% 12.35/6.30  % (21796)Time elapsed: 0.254 s
% 12.35/6.30  % (21796)Instructions burned: 779 (million)
% 12.35/6.30  % (21796)------------------------------
% 12.35/6.30  % (21796)------------------------------
% 12.35/6.30  % (21780)Instruction limit reached!
% 12.35/6.30  % (21780)------------------------------
% 12.35/6.30  % (21780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.35/6.30  % (21780)Termination reason: Unknown
% 12.35/6.30  % (21780)Termination phase: shuffling
% 12.35/6.30  
% 12.35/6.30  % (21780)Memory used [KB]: 33901
% 12.35/6.30  % (21780)Time elapsed: 0.364 s
% 12.35/6.30  % (21780)Instructions burned: 1041 (million)
% 12.35/6.30  % (21780)------------------------------
% 12.35/6.30  % (21780)------------------------------
% 12.35/6.31  % (21808)Instruction limit reached!
% 12.35/6.31  % (21808)------------------------------
% 12.35/6.31  % (21808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.35/6.31  % (21808)Termination reason: Unknown
% 12.35/6.31  % (21808)Termination phase: shuffling
% 12.35/6.31  
% 12.35/6.31  % (21808)Memory used [KB]: 14583
% 12.35/6.31  % (21808)Time elapsed: 0.023 s
% 12.35/6.31  % (21808)Instructions burned: 41 (million)
% 12.35/6.31  % (21808)------------------------------
% 12.35/6.31  % (21808)------------------------------
% 12.35/6.31  % (21810)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_21656 for (2990ds/46Mi)
% 12.35/6.31  % (21791)Instruction limit reached!
% 12.35/6.31  % (21791)------------------------------
% 12.35/6.31  % (21791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.35/6.31  % (21791)Termination reason: Unknown
% 12.35/6.31  % (21791)Termination phase: shuffling
% 12.35/6.31  
% 12.35/6.31  % (21791)Memory used [KB]: 26737
% 12.35/6.31  % (21791)Time elapsed: 0.308 s
% 12.35/6.31  % (21791)Instructions burned: 902 (million)
% 12.35/6.31  % (21791)------------------------------
% 12.35/6.31  % (21791)------------------------------
% 12.35/6.31  % (21809)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_21656 for (2990ds/448Mi)
% 12.35/6.31  % (21807)Instruction limit reached!
% 12.35/6.31  % (21807)------------------------------
% 12.35/6.31  % (21807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.35/6.31  % (21807)Termination reason: Unknown
% 12.35/6.31  % (21807)Termination phase: shuffling
% 12.35/6.31  
% 12.35/6.31  % (21807)Memory used [KB]: 15351
% 12.35/6.31  % (21807)Time elapsed: 0.047 s
% 12.35/6.31  % (21807)Instructions burned: 107 (million)
% 12.35/6.31  % (21807)------------------------------
% 12.35/6.31  % (21807)------------------------------
% 12.35/6.32  % (21811)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_21656 for (2990ds/98Mi)
% 12.35/6.32  % (21812)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_21656 for (2990ds/507Mi)
% 12.35/6.32  % (21813)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_21656 for (2990ds/149Mi)
% 12.35/6.33  % (21814)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_21656 for (2990ds/39Mi)
% 12.35/6.34  % (21810)Instruction limit reached!
% 12.35/6.34  % (21810)------------------------------
% 12.35/6.34  % (21810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.35/6.34  % (21810)Termination reason: Unknown
% 12.35/6.34  % (21810)Termination phase: shuffling
% 12.35/6.34  
% 12.35/6.34  % (21810)Memory used [KB]: 14583
% 12.35/6.34  % (21810)Time elapsed: 0.027 s
% 12.35/6.34  % (21810)Instructions burned: 49 (million)
% 12.35/6.34  % (21810)------------------------------
% 12.35/6.34  % (21810)------------------------------
% 12.35/6.35  % (21815)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_21656 for (2990ds/6Mi)
% 12.35/6.35  % (21814)Instruction limit reached!
% 12.35/6.35  % (21814)------------------------------
% 12.35/6.35  % (21814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.35/6.35  % (21814)Termination reason: Unknown
% 12.35/6.35  % (21814)Termination phase: shuffling
% 12.35/6.35  
% 12.35/6.35  % (21814)Memory used [KB]: 14456
% 12.35/6.35  % (21814)Time elapsed: 0.024 s
% 12.35/6.35  % (21814)Instructions burned: 40 (million)
% 12.35/6.35  % (21814)------------------------------
% 12.35/6.35  % (21814)------------------------------
% 12.35/6.35  % (21815)Instruction limit reached!
% 12.35/6.35  % (21815)------------------------------
% 12.35/6.35  % (21815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.35/6.35  % (21815)Termination reason: Unknown
% 12.35/6.35  % (21815)Termination phase: shuffling
% 12.35/6.35  
% 12.35/6.35  % (21815)Memory used [KB]: 13560
% 12.35/6.35  % (21815)Time elapsed: 0.006 s
% 12.35/6.35  % (21815)Instructions burned: 6 (million)
% 12.35/6.35  % (21815)------------------------------
% 12.35/6.35  % (21815)------------------------------
% 12.35/6.36  % (21811)Instruction limit reached!
% 12.35/6.36  % (21811)------------------------------
% 12.35/6.36  % (21811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.35/6.36  % (21811)Termination reason: Unknown
% 12.35/6.36  % (21811)Termination phase: shuffling
% 12.35/6.36  
% 12.35/6.36  % (21811)Memory used [KB]: 15479
% 12.35/6.36  % (21811)Time elapsed: 0.040 s
% 12.35/6.36  % (21811)Instructions burned: 99 (million)
% 12.35/6.36  % (21811)------------------------------
% 12.35/6.36  % (21811)------------------------------
% 12.35/6.36  % (21816)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_21656 for (2989ds/1087Mi)
% 12.35/6.36  % (21817)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_21656 for (2989ds/47Mi)
% 12.35/6.37  % (21818)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_21656 for (2989ds/44Mi)
% 12.35/6.38  % (21813)Instruction limit reached!
% 12.35/6.38  % (21813)------------------------------
% 12.35/6.38  % (21813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.35/6.38  % (21813)Termination reason: Unknown
% 12.35/6.38  % (21813)Termination phase: shuffling
% 12.35/6.38  
% 12.35/6.38  % (21813)Memory used [KB]: 15991
% 12.35/6.38  % (21813)Time elapsed: 0.060 s
% 12.35/6.38  % (21813)Instructions burned: 151 (million)
% 12.35/6.38  % (21813)------------------------------
% 12.35/6.38  % (21813)------------------------------
% 12.35/6.38  % (21798)Instruction limit reached!
% 12.35/6.38  % (21798)------------------------------
% 12.35/6.38  % (21798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.35/6.38  % (21798)Termination reason: Unknown
% 12.35/6.38  % (21798)Termination phase: shuffling
% 12.35/6.38  
% 12.35/6.38  % (21798)Memory used [KB]: 26097
% 12.35/6.38  % (21798)Time elapsed: 0.322 s
% 12.35/6.38  % (21798)Instructions burned: 879 (million)
% 12.35/6.38  % (21798)------------------------------
% 12.35/6.38  % (21798)------------------------------
% 12.35/6.39  % (21818)Instruction limit reached!
% 12.35/6.39  % (21818)------------------------------
% 12.35/6.39  % (21818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.35/6.39  % (21818)Termination reason: Unknown
% 12.35/6.39  % (21818)Termination phase: shuffling
% 12.35/6.39  
% 12.35/6.39  % (21818)Memory used [KB]: 14583
% 12.35/6.39  % (21818)Time elapsed: 0.022 s
% 12.35/6.39  % (21818)Instructions burned: 44 (million)
% 12.35/6.39  % (21818)------------------------------
% 12.35/6.39  % (21818)------------------------------
% 12.35/6.39  % (21817)Instruction limit reached!
% 12.35/6.39  % (21817)------------------------------
% 12.35/6.39  % (21817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.35/6.39  % (21817)Termination reason: Unknown
% 12.35/6.39  % (21817)Termination phase: shuffling
% 12.35/6.39  
% 12.35/6.39  % (21817)Memory used [KB]: 14583
% 12.35/6.39  % (21817)Time elapsed: 0.025 s
% 12.35/6.39  % (21817)Instructions burned: 49 (million)
% 12.35/6.39  % (21817)------------------------------
% 12.35/6.39  % (21817)------------------------------
% 12.35/6.39  % (21819)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_21656 for (2989ds/432Mi)
% 13.36/6.40  % (21820)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_21656 for (2989ds/62Mi)
% 13.36/6.40  % (21821)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_21656 for (2989ds/31Mi)
% 13.36/6.40  % (21822)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_21656 for (2989ds/96Mi)
% 13.36/6.42  % (21821)Instruction limit reached!
% 13.36/6.42  % (21821)------------------------------
% 13.36/6.42  % (21821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.36/6.42  % (21821)Termination reason: Unknown
% 13.36/6.42  % (21821)Termination phase: shuffling
% 13.36/6.42  
% 13.36/6.42  % (21821)Memory used [KB]: 14328
% 13.36/6.42  % (21821)Time elapsed: 0.020 s
% 13.36/6.42  % (21821)Instructions burned: 31 (million)
% 13.36/6.42  % (21821)------------------------------
% 13.36/6.42  % (21821)------------------------------
% 13.36/6.42  % (21820)Instruction limit reached!
% 13.36/6.42  % (21820)------------------------------
% 13.36/6.42  % (21820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.36/6.42  % (21820)Termination reason: Unknown
% 13.36/6.42  % (21820)Termination phase: shuffling
% 13.36/6.42  
% 13.36/6.42  % (21820)Memory used [KB]: 14839
% 13.36/6.42  % (21820)Time elapsed: 0.029 s
% 13.36/6.42  % (21820)Instructions burned: 65 (million)
% 13.36/6.42  % (21820)------------------------------
% 13.36/6.42  % (21820)------------------------------
% 13.36/6.43  % (21823)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_21656 for (2989ds/453Mi)
% 13.36/6.44  % (21824)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_21656 for (2989ds/71Mi)
% 13.36/6.44  % (21822)Instruction limit reached!
% 13.36/6.44  % (21822)------------------------------
% 13.36/6.44  % (21822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.36/6.44  % (21822)Termination reason: Unknown
% 13.36/6.44  % (21822)Termination phase: shuffling
% 13.36/6.44  
% 13.36/6.44  % (21822)Memory used [KB]: 15223
% 13.36/6.44  % (21822)Time elapsed: 0.040 s
% 13.36/6.44  % (21822)Instructions burned: 96 (million)
% 13.36/6.44  % (21822)------------------------------
% 13.36/6.44  % (21822)------------------------------
% 13.36/6.45  % (21825)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_21656 for (2989ds/83Mi)
% 13.36/6.47  % (21824)Instruction limit reached!
% 13.36/6.47  % (21824)------------------------------
% 13.36/6.47  % (21824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.36/6.47  % (21824)Termination reason: Unknown
% 13.36/6.47  % (21824)Termination phase: shuffling
% 13.36/6.47  
% 13.36/6.47  % (21824)Memory used [KB]: 14967
% 13.36/6.47  % (21824)Time elapsed: 0.033 s
% 13.36/6.47  % (21824)Instructions burned: 73 (million)
% 13.36/6.47  % (21824)------------------------------
% 13.36/6.47  % (21824)------------------------------
% 13.36/6.48  % (21826)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_21656 for (2988ds/11Mi)
% 13.36/6.48  % (21825)Instruction limit reached!
% 13.36/6.48  % (21825)------------------------------
% 13.36/6.48  % (21825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.36/6.48  % (21825)Termination reason: Unknown
% 13.36/6.48  % (21825)Termination phase: shuffling
% 13.36/6.48  
% 13.36/6.48  % (21825)Memory used [KB]: 15095
% 13.36/6.48  % (21825)Time elapsed: 0.036 s
% 13.36/6.48  % (21825)Instructions burned: 83 (million)
% 13.36/6.48  % (21825)------------------------------
% 13.36/6.48  % (21825)------------------------------
% 13.36/6.49  % (21826)Instruction limit reached!
% 13.36/6.49  % (21826)------------------------------
% 13.36/6.49  % (21826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.36/6.49  % (21826)Termination reason: Unknown
% 13.36/6.49  % (21826)Termination phase: shuffling
% 13.36/6.49  
% 13.36/6.49  % (21826)Memory used [KB]: 14072
% 13.36/6.49  % (21826)Time elapsed: 0.012 s
% 13.36/6.49  % (21826)Instructions burned: 11 (million)
% 13.36/6.49  % (21826)------------------------------
% 13.36/6.49  % (21826)------------------------------
% 13.36/6.49  % (21812)Instruction limit reached!
% 13.36/6.49  % (21812)------------------------------
% 13.36/6.49  % (21812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.36/6.49  % (21812)Termination reason: Unknown
% 13.36/6.49  % (21812)Termination phase: shuffling
% 13.36/6.49  
% 13.36/6.49  % (21812)Memory used [KB]: 19829
% 13.36/6.49  % (21812)Time elapsed: 0.176 s
% 13.36/6.49  % (21812)Instructions burned: 507 (million)
% 13.36/6.49  % (21812)------------------------------
% 13.36/6.49  % (21812)------------------------------
% 13.36/6.50  % (21827)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_21656 for (2988ds/41Mi)
% 13.79/6.50  % (21828)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_21656 for (2988ds/6Mi)
% 13.79/6.50  % (21829)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_21656 for (2988ds/150Mi)
% 13.79/6.50  % (21828)Instruction limit reached!
% 13.79/6.50  % (21828)------------------------------
% 13.79/6.50  % (21828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.79/6.50  % (21828)Termination reason: Unknown
% 13.79/6.50  % (21828)Termination phase: shuffling
% 13.79/6.50  
% 13.79/6.50  % (21828)Memory used [KB]: 13560
% 13.79/6.50  % (21828)Time elapsed: 0.006 s
% 13.79/6.50  % (21828)Instructions burned: 6 (million)
% 13.79/6.50  % (21828)------------------------------
% 13.79/6.50  % (21828)------------------------------
% 13.79/6.52  % (21830)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_21656 for (2988ds/343Mi)
% 13.79/6.52  % (21827)Instruction limit reached!
% 13.79/6.52  % (21827)------------------------------
% 13.79/6.52  % (21827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.79/6.52  % (21827)Termination reason: Unknown
% 13.79/6.52  % (21827)Termination phase: shuffling
% 13.79/6.52  
% 13.79/6.52  % (21827)Memory used [KB]: 14583
% 13.79/6.52  % (21827)Time elapsed: 0.022 s
% 13.79/6.52  % (21827)Instructions burned: 43 (million)
% 13.79/6.52  % (21827)------------------------------
% 13.79/6.52  % (21827)------------------------------
% 13.79/6.52  % (21809)Instruction limit reached!
% 13.79/6.52  % (21809)------------------------------
% 13.79/6.52  % (21809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.79/6.52  % (21809)Termination reason: Unknown
% 13.79/6.52  % (21809)Termination phase: shuffling
% 13.79/6.52  
% 13.79/6.52  % (21809)Memory used [KB]: 22259
% 13.79/6.52  % (21809)Time elapsed: 0.208 s
% 13.79/6.52  % (21809)Instructions burned: 448 (million)
% 13.79/6.52  % (21809)------------------------------
% 13.79/6.52  % (21809)------------------------------
% 13.79/6.53  % (21831)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_21656 for (2988ds/109Mi)
% 13.79/6.53  % (21819)Instruction limit reached!
% 13.79/6.53  % (21819)------------------------------
% 13.79/6.53  % (21819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.79/6.53  % (21819)Termination reason: Unknown
% 13.79/6.53  % (21819)Termination phase: shuffling
% 13.79/6.53  
% 13.79/6.53  % (21819)Memory used [KB]: 21875
% 13.79/6.53  % (21819)Time elapsed: 0.135 s
% 13.79/6.53  % (21819)Instructions burned: 432 (million)
% 13.79/6.53  % (21819)------------------------------
% 13.79/6.53  % (21819)------------------------------
% 13.79/6.53  % (21832)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_21656 for (2988ds/253Mi)
% 13.79/6.54  % (21833)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_21656 for (2988ds/140Mi)
% 13.79/6.56  % (21829)Instruction limit reached!
% 13.79/6.56  % (21829)------------------------------
% 13.79/6.56  % (21829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.79/6.56  % (21829)Termination reason: Unknown
% 13.79/6.56  % (21829)Termination phase: shuffling
% 13.79/6.56  
% 13.79/6.56  % (21829)Memory used [KB]: 15863
% 13.79/6.56  % (21829)Time elapsed: 0.057 s
% 13.79/6.56  % (21829)Instructions burned: 151 (million)
% 13.79/6.56  % (21829)------------------------------
% 13.79/6.56  % (21829)------------------------------
% 13.79/6.57  % (21823)Instruction limit reached!
% 13.79/6.57  % (21823)------------------------------
% 13.79/6.57  % (21823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.79/6.57  % (21823)Termination reason: Unknown
% 13.79/6.57  % (21823)Termination phase: shuffling
% 13.79/6.57  
% 13.79/6.57  % (21823)Memory used [KB]: 22259
% 13.79/6.57  % (21823)Time elapsed: 0.139 s
% 13.79/6.57  % (21823)Instructions burned: 453 (million)
% 13.79/6.57  % (21823)------------------------------
% 13.79/6.57  % (21823)------------------------------
% 13.79/6.57  % (21831)Instruction limit reached!
% 13.79/6.57  % (21831)------------------------------
% 13.79/6.57  % (21831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.79/6.57  % (21831)Termination reason: Unknown
% 13.79/6.57  % (21831)Termination phase: shuffling
% 13.79/6.57  
% 13.79/6.57  % (21831)Memory used [KB]: 15351
% 13.79/6.57  % (21831)Time elapsed: 0.044 s
% 13.79/6.57  % (21831)Instructions burned: 109 (million)
% 13.79/6.57  % (21831)------------------------------
% 13.79/6.57  % (21831)------------------------------
% 13.79/6.57  % (21834)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_21656 for (2987ds/614Mi)
% 13.79/6.58  % (21835)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_21656 for (2987ds/202Mi)
% 13.79/6.58  % (21836)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_21656 for (2987ds/339Mi)
% 13.79/6.59  % (21833)Instruction limit reached!
% 13.79/6.59  % (21833)------------------------------
% 13.79/6.59  % (21833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.79/6.59  % (21833)Termination reason: Unknown
% 13.79/6.59  % (21833)Termination phase: shuffling
% 13.79/6.59  
% 13.79/6.59  % (21833)Memory used [KB]: 15607
% 13.79/6.59  % (21833)Time elapsed: 0.052 s
% 13.79/6.59  % (21833)Instructions burned: 140 (million)
% 13.79/6.59  % (21833)------------------------------
% 13.79/6.59  % (21833)------------------------------
% 14.55/6.60  % (21837)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_21656 for (2987ds/283Mi)
% 14.55/6.62  % (21832)Instruction limit reached!
% 14.55/6.62  % (21832)------------------------------
% 14.55/6.62  % (21832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.55/6.62  % (21832)Termination reason: Unknown
% 14.55/6.62  % (21832)Termination phase: shuffling
% 14.55/6.62  
% 14.55/6.62  % (21832)Memory used [KB]: 17014
% 14.55/6.62  % (21832)Time elapsed: 0.090 s
% 14.55/6.62  % (21832)Instructions burned: 253 (million)
% 14.55/6.62  % (21832)------------------------------
% 14.55/6.62  % (21832)------------------------------
% 14.55/6.63  % (21838)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_21656 for (2987ds/134Mi)
% 14.55/6.63  % (21830)Instruction limit reached!
% 14.55/6.63  % (21830)------------------------------
% 14.55/6.63  % (21830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.55/6.63  % (21830)Termination reason: Unknown
% 14.55/6.63  % (21830)Termination phase: shuffling
% 14.55/6.63  
% 14.55/6.63  % (21830)Memory used [KB]: 18166
% 14.55/6.63  % (21830)Time elapsed: 0.120 s
% 14.55/6.63  % (21830)Instructions burned: 343 (million)
% 14.55/6.63  % (21830)------------------------------
% 14.55/6.63  % (21830)------------------------------
% 14.55/6.65  % (21839)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_21656 for (2987ds/298Mi)
% 14.55/6.65  % (21835)Instruction limit reached!
% 14.55/6.65  % (21835)------------------------------
% 14.55/6.65  % (21835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.55/6.65  % (21835)Termination reason: Unknown
% 14.55/6.65  % (21835)Termination phase: shuffling
% 14.55/6.65  
% 14.55/6.65  % (21835)Memory used [KB]: 16502
% 14.55/6.65  % (21835)Time elapsed: 0.075 s
% 14.55/6.65  % (21835)Instructions burned: 204 (million)
% 14.55/6.65  % (21835)------------------------------
% 14.55/6.65  % (21835)------------------------------
% 14.55/6.66  % (21840)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_21656 for (2986ds/192Mi)
% 14.55/6.68  % (21838)Instruction limit reached!
% 14.55/6.68  % (21838)------------------------------
% 14.55/6.68  % (21838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.55/6.68  % (21838)Termination reason: Unknown
% 14.55/6.68  % (21838)Termination phase: shuffling
% 14.55/6.68  
% 14.55/6.68  % (21838)Memory used [KB]: 15479
% 14.55/6.68  % (21838)Time elapsed: 0.052 s
% 14.55/6.68  % (21838)Instructions burned: 136 (million)
% 14.55/6.68  % (21838)------------------------------
% 14.55/6.68  % (21838)------------------------------
% 14.55/6.69  % (21837)Instruction limit reached!
% 14.55/6.69  % (21837)------------------------------
% 14.55/6.69  % (21837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.55/6.69  % (21837)Termination reason: Unknown
% 14.55/6.69  % (21837)Termination phase: shuffling
% 14.55/6.69  
% 14.55/6.69  % (21837)Memory used [KB]: 19957
% 14.55/6.69  % (21837)Time elapsed: 0.089 s
% 14.55/6.69  % (21837)Instructions burned: 285 (million)
% 14.55/6.69  % (21837)------------------------------
% 14.55/6.69  % (21837)------------------------------
% 14.55/6.69  % (21841)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_21656 for (2986ds/258Mi)
% 15.02/6.70  % (21836)Instruction limit reached!
% 15.02/6.70  % (21836)------------------------------
% 15.02/6.70  % (21836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.02/6.70  % (21836)Termination reason: Unknown
% 15.02/6.70  % (21836)Termination phase: shuffling
% 15.02/6.70  
% 15.02/6.70  % (21836)Memory used [KB]: 18038
% 15.02/6.70  % (21836)Time elapsed: 0.117 s
% 15.02/6.70  % (21836)Instructions burned: 340 (million)
% 15.02/6.70  % (21836)------------------------------
% 15.02/6.70  % (21836)------------------------------
% 15.02/6.70  % (21842)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_21656 for (2986ds/90Mi)
% 15.02/6.71  % (21843)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_21656 for (2986ds/231Mi)
% 15.02/6.72  % (21816)Instruction limit reached!
% 15.02/6.72  % (21816)------------------------------
% 15.02/6.72  % (21816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.02/6.72  % (21816)Termination reason: Unknown
% 15.02/6.72  % (21816)Termination phase: Property scanning
% 15.02/6.72  
% 15.02/6.72  % (21816)Memory used [KB]: 27888
% 15.02/6.72  % (21816)Time elapsed: 0.363 s
% 15.02/6.72  % (21816)Instructions burned: 1087 (million)
% 15.02/6.72  % (21816)------------------------------
% 15.02/6.72  % (21816)------------------------------
% 15.02/6.73  % (21840)Instruction limit reached!
% 15.02/6.73  % (21840)------------------------------
% 15.02/6.73  % (21840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.02/6.73  % (21840)Termination reason: Unknown
% 15.02/6.73  % (21840)Termination phase: shuffling
% 15.02/6.73  
% 15.02/6.73  % (21840)Memory used [KB]: 16375
% 15.02/6.73  % (21840)Time elapsed: 0.071 s
% 15.02/6.73  % (21840)Instructions burned: 194 (million)
% 15.02/6.73  % (21840)------------------------------
% 15.02/6.73  % (21840)------------------------------
% 15.02/6.73  % (21844)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_21656 for (2986ds/458Mi)
% 15.02/6.74  % (21842)Instruction limit reached!
% 15.02/6.74  % (21842)------------------------------
% 15.02/6.74  % (21842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.02/6.74  % (21842)Termination reason: Unknown
% 15.02/6.74  % (21842)Termination phase: shuffling
% 15.02/6.74  
% 15.02/6.74  % (21842)Memory used [KB]: 15223
% 15.02/6.74  % (21842)Time elapsed: 0.039 s
% 15.02/6.74  % (21842)Instructions burned: 93 (million)
% 15.02/6.74  % (21842)------------------------------
% 15.02/6.74  % (21842)------------------------------
% 15.02/6.74  % (21839)Instruction limit reached!
% 15.02/6.74  % (21839)------------------------------
% 15.02/6.74  % (21839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.02/6.74  % (21839)Termination reason: Unknown
% 15.02/6.74  % (21839)Termination phase: shuffling
% 15.02/6.74  
% 15.02/6.74  % (21839)Memory used [KB]: 20212
% 15.02/6.74  % (21839)Time elapsed: 0.095 s
% 15.02/6.74  % (21839)Instructions burned: 300 (million)
% 15.02/6.74  % (21839)------------------------------
% 15.02/6.74  % (21839)------------------------------
% 15.02/6.74  % (21845)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_21656 for (2986ds/31Mi)
% 15.02/6.75  % (21846)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_21656 for (2985ds/297Mi)
% 15.02/6.75  % (21847)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_21656 for (2985ds/987Mi)
% 15.02/6.76  % (21845)Instruction limit reached!
% 15.02/6.76  % (21845)------------------------------
% 15.02/6.76  % (21845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.02/6.76  % (21845)Termination reason: Unknown
% 15.02/6.76  % (21845)Termination phase: shuffling
% 15.02/6.76  
% 15.02/6.76  % (21845)Memory used [KB]: 14328
% 15.02/6.76  % (21845)Time elapsed: 0.020 s
% 15.02/6.76  % (21845)Instructions burned: 32 (million)
% 15.02/6.76  % (21845)------------------------------
% 15.02/6.76  % (21845)------------------------------
% 15.02/6.77  % (21848)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_21656 for (2985ds/182Mi)
% 15.02/6.78  % (21843)Instruction limit reached!
% 15.02/6.78  % (21843)------------------------------
% 15.02/6.78  % (21843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.02/6.78  % (21843)Termination reason: Unknown
% 15.02/6.78  % (21843)Termination phase: shuffling
% 15.02/6.78  
% 15.02/6.78  % (21843)Memory used [KB]: 17270
% 15.02/6.78  % (21843)Time elapsed: 0.074 s
% 15.02/6.78  % (21843)Instructions burned: 232 (million)
% 15.02/6.78  % (21843)------------------------------
% 15.02/6.78  % (21843)------------------------------
% 15.02/6.78  % (21834)Instruction limit reached!
% 15.02/6.78  % (21834)------------------------------
% 15.02/6.78  % (21834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.02/6.78  % (21834)Termination reason: Unknown
% 15.02/6.78  % (21834)Termination phase: shuffling
% 15.02/6.78  
% 15.02/6.78  % (21834)Memory used [KB]: 23666
% 15.02/6.78  % (21834)Time elapsed: 0.212 s
% 15.02/6.78  % (21834)Instructions burned: 616 (million)
% 15.02/6.78  % (21834)------------------------------
% 15.02/6.78  % (21834)------------------------------
% 15.02/6.78  % (21841)Instruction limit reached!
% 15.02/6.78  % (21841)------------------------------
% 15.02/6.78  % (21841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.02/6.78  % (21841)Termination reason: Unknown
% 15.02/6.78  % (21841)Termination phase: shuffling
% 15.02/6.78  
% 15.02/6.78  % (21841)Memory used [KB]: 17398
% 15.02/6.78  % (21841)Time elapsed: 0.094 s
% 15.02/6.78  % (21841)Instructions burned: 260 (million)
% 15.02/6.78  % (21841)------------------------------
% 15.02/6.78  % (21841)------------------------------
% 15.02/6.79  % (21849)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_21656 for (2985ds/182Mi)
% 15.02/6.79  % (21850)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_21656 for (2985ds/154Mi)
% 15.02/6.80  % (21851)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_21656 for (2985ds/79Mi)
% 16.21/6.83  % (21851)Instruction limit reached!
% 16.21/6.83  % (21851)------------------------------
% 16.21/6.83  % (21851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.21/6.83  % (21851)Termination reason: Unknown
% 16.21/6.83  % (21851)Termination phase: shuffling
% 16.21/6.83  
% 16.21/6.83  % (21851)Memory used [KB]: 14967
% 16.21/6.83  % (21851)Time elapsed: 0.033 s
% 16.21/6.83  % (21851)Instructions burned: 80 (million)
% 16.21/6.83  % (21851)------------------------------
% 16.21/6.83  % (21851)------------------------------
% 16.21/6.84  % (21852)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_21656 for (2985ds/216Mi)
% 16.21/6.84  % (21848)Instruction limit reached!
% 16.21/6.84  % (21848)------------------------------
% 16.21/6.84  % (21848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.21/6.84  % (21848)Termination reason: Unknown
% 16.21/6.84  % (21848)Termination phase: shuffling
% 16.21/6.84  
% 16.21/6.84  % (21848)Memory used [KB]: 16247
% 16.21/6.84  % (21848)Time elapsed: 0.068 s
% 16.21/6.84  % (21848)Instructions burned: 183 (million)
% 16.21/6.84  % (21848)------------------------------
% 16.21/6.84  % (21848)------------------------------
% 16.21/6.84  % (21846)Instruction limit reached!
% 16.21/6.84  % (21846)------------------------------
% 16.21/6.84  % (21846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.21/6.84  % (21846)Termination reason: Unknown
% 16.21/6.84  % (21846)Termination phase: shuffling
% 16.21/6.84  
% 16.21/6.84  % (21846)Memory used [KB]: 20084
% 16.21/6.84  % (21846)Time elapsed: 0.094 s
% 16.21/6.84  % (21846)Instructions burned: 298 (million)
% 16.21/6.84  % (21846)------------------------------
% 16.21/6.84  % (21846)------------------------------
% 16.21/6.84  % (21850)Instruction limit reached!
% 16.21/6.84  % (21850)------------------------------
% 16.21/6.84  % (21850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.21/6.84  % (21850)Termination reason: Unknown
% 16.21/6.84  % (21850)Termination phase: shuffling
% 16.21/6.84  
% 16.21/6.84  % (21850)Memory used [KB]: 16247
% 16.21/6.84  % (21850)Time elapsed: 0.052 s
% 16.21/6.84  % (21850)Instructions burned: 157 (million)
% 16.21/6.84  % (21850)------------------------------
% 16.21/6.84  % (21850)------------------------------
% 16.21/6.85  % (21853)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_21656 for (2984ds/114Mi)
% 16.21/6.85  % (21854)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_21656 for (2984ds/922Mi)
% 16.21/6.86  % (21855)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_21656 for (2984ds/182Mi)
% 16.21/6.86  % (21849)Instruction limit reached!
% 16.21/6.86  % (21849)------------------------------
% 16.21/6.86  % (21849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.21/6.86  % (21849)Termination reason: Unknown
% 16.21/6.86  % (21849)Termination phase: shuffling
% 16.21/6.86  
% 16.21/6.86  % (21849)Memory used [KB]: 16247
% 16.21/6.86  % (21849)Time elapsed: 0.069 s
% 16.21/6.86  % (21849)Instructions burned: 183 (million)
% 16.21/6.86  % (21849)------------------------------
% 16.21/6.86  % (21849)------------------------------
% 16.21/6.87  % (21856)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_21656 for (2984ds/164Mi)
% 16.21/6.89  % (21844)Instruction limit reached!
% 16.21/6.89  % (21844)------------------------------
% 16.21/6.89  % (21844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.21/6.89  % (21844)Termination reason: Unknown
% 16.21/6.89  % (21844)Termination phase: shuffling
% 16.21/6.89  
% 16.21/6.89  % (21844)Memory used [KB]: 19061
% 16.21/6.89  % (21844)Time elapsed: 0.153 s
% 16.21/6.89  % (21844)Instructions burned: 459 (million)
% 16.21/6.89  % (21844)------------------------------
% 16.21/6.89  % (21844)------------------------------
% 16.21/6.90  % (21853)Instruction limit reached!
% 16.21/6.90  % (21853)------------------------------
% 16.21/6.90  % (21853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.21/6.90  % (21853)Termination reason: Unknown
% 16.21/6.90  % (21853)Termination phase: shuffling
% 16.21/6.90  
% 16.21/6.90  % (21853)Memory used [KB]: 15479
% 16.21/6.90  % (21853)Time elapsed: 0.046 s
% 16.21/6.90  % (21853)Instructions burned: 115 (million)
% 16.21/6.90  % (21853)------------------------------
% 16.21/6.90  % (21853)------------------------------
% 16.73/6.90  % (21857)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_21656 for (2984ds/50Mi)
% 16.73/6.91  % (21858)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_21656 for (2984ds/368Mi)
% 16.73/6.91  % (21852)Instruction limit reached!
% 16.73/6.91  % (21852)------------------------------
% 16.73/6.91  % (21852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.73/6.91  % (21852)Termination reason: Unknown
% 16.73/6.91  % (21852)Termination phase: shuffling
% 16.73/6.91  
% 16.73/6.91  % (21852)Memory used [KB]: 17142
% 16.73/6.91  % (21852)Time elapsed: 0.071 s
% 16.73/6.91  % (21852)Instructions burned: 219 (million)
% 16.73/6.91  % (21852)------------------------------
% 16.73/6.91  % (21852)------------------------------
% 16.73/6.91  % (21855)Instruction limit reached!
% 16.73/6.91  % (21855)------------------------------
% 16.73/6.91  % (21855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.73/6.91  % (21855)Termination reason: Unknown
% 16.73/6.91  % (21855)Termination phase: shuffling
% 16.73/6.91  
% 16.73/6.91  % (21855)Memory used [KB]: 16630
% 16.73/6.91  % (21855)Time elapsed: 0.060 s
% 16.73/6.91  % (21855)Instructions burned: 184 (million)
% 16.73/6.91  % (21855)------------------------------
% 16.73/6.91  % (21855)------------------------------
% 16.73/6.92  % (21857)Instruction limit reached!
% 16.73/6.92  % (21857)------------------------------
% 16.73/6.92  % (21857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.73/6.92  % (21857)Termination reason: Unknown
% 16.73/6.92  % (21857)Termination phase: shuffling
% 16.73/6.92  
% 16.73/6.92  % (21857)Memory used [KB]: 14711
% 16.73/6.92  % (21857)Time elapsed: 0.024 s
% 16.73/6.92  % (21857)Instructions burned: 50 (million)
% 16.73/6.92  % (21857)------------------------------
% 16.73/6.92  % (21857)------------------------------
% 16.73/6.92  % (21859)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_21656 for (2984ds/1021Mi)
% 16.73/6.93  % (21856)Instruction limit reached!
% 16.73/6.93  % (21856)------------------------------
% 16.73/6.93  % (21856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.73/6.93  % (21856)Termination reason: Unknown
% 16.73/6.93  % (21856)Termination phase: shuffling
% 16.73/6.93  
% 16.73/6.93  % (21856)Memory used [KB]: 16247
% 16.73/6.93  % (21856)Time elapsed: 0.056 s
% 16.73/6.93  % (21856)Instructions burned: 165 (million)
% 16.73/6.93  % (21856)------------------------------
% 16.73/6.93  % (21856)------------------------------
% 16.73/6.93  % (21860)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_21656 for (2984ds/267Mi)
% 16.73/6.93  % (21861)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_21656 for (2984ds/204Mi)
% 16.73/6.94  % (21862)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_21656 for (2984ds/26Mi)
% 16.73/6.95  % (21862)Instruction limit reached!
% 16.73/6.95  % (21862)------------------------------
% 16.73/6.95  % (21862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.73/6.95  % (21862)Termination reason: Unknown
% 16.73/6.95  % (21862)Termination phase: shuffling
% 16.73/6.95  
% 16.73/6.95  % (21862)Memory used [KB]: 14328
% 16.73/6.95  % (21862)Time elapsed: 0.017 s
% 16.73/6.95  % (21862)Instructions burned: 26 (million)
% 16.73/6.95  % (21862)------------------------------
% 16.73/6.95  % (21862)------------------------------
% 16.73/6.96  % (21863)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_21656 for (2983ds/53Mi)
% 16.73/6.99  % (21863)Instruction limit reached!
% 16.73/6.99  % (21863)------------------------------
% 16.73/6.99  % (21863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.73/6.99  % (21863)Termination reason: Unknown
% 16.73/6.99  % (21863)Termination phase: shuffling
% 16.73/6.99  
% 16.73/6.99  % (21863)Memory used [KB]: 14711
% 16.73/6.99  % (21863)Time elapsed: 0.024 s
% 16.73/6.99  % (21863)Instructions burned: 53 (million)
% 16.73/6.99  % (21863)------------------------------
% 16.73/6.99  % (21863)------------------------------
% 16.73/7.01  % (21864)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_21656 for (2983ds/4436Mi)
% 16.73/7.01  % (21861)Instruction limit reached!
% 16.73/7.01  % (21861)------------------------------
% 16.73/7.01  % (21861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.73/7.01  % (21861)Termination reason: Unknown
% 16.73/7.01  % (21861)Termination phase: shuffling
% 16.73/7.01  
% 16.73/7.01  % (21861)Memory used [KB]: 16630
% 16.73/7.01  % (21861)Time elapsed: 0.075 s
% 16.73/7.01  % (21861)Instructions burned: 206 (million)
% 16.73/7.01  % (21861)------------------------------
% 16.73/7.01  % (21861)------------------------------
% 16.73/7.01  % (21860)Instruction limit reached!
% 16.73/7.01  % (21860)------------------------------
% 16.73/7.01  % (21860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.73/7.01  % (21860)Termination reason: Unknown
% 16.73/7.01  % (21860)Termination phase: shuffling
% 16.73/7.01  
% 16.73/7.01  % (21860)Memory used [KB]: 19701
% 16.73/7.01  % (21860)Time elapsed: 0.085 s
% 16.73/7.01  % (21860)Instructions burned: 269 (million)
% 16.73/7.01  % (21860)------------------------------
% 16.73/7.01  % (21860)------------------------------
% 16.73/7.02  % (21866)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_21656 for (2983ds/1539Mi)
% 17.93/7.02  % (21867)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_21656 for (2983ds/408Mi)
% 17.93/7.03  % (21858)Instruction limit reached!
% 17.93/7.03  % (21858)------------------------------
% 17.93/7.03  % (21858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.93/7.03  % (21858)Termination reason: Unknown
% 17.93/7.03  % (21858)Termination phase: shuffling
% 17.93/7.03  
% 17.93/7.03  % (21858)Memory used [KB]: 18549
% 17.93/7.03  % (21858)Time elapsed: 0.129 s
% 17.93/7.03  % (21858)Instructions burned: 370 (million)
% 17.93/7.03  % (21858)------------------------------
% 17.93/7.03  % (21858)------------------------------
% 17.93/7.04  % (21847)Instruction limit reached!
% 17.93/7.04  % (21847)------------------------------
% 17.93/7.04  % (21847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.93/7.04  % (21847)Termination reason: Unknown
% 17.93/7.04  % (21847)Termination phase: shuffling
% 17.93/7.04  
% 17.93/7.04  % (21847)Memory used [KB]: 33261
% 17.93/7.04  % (21847)Time elapsed: 0.293 s
% 17.93/7.04  % (21847)Instructions burned: 988 (million)
% 17.93/7.04  % (21847)------------------------------
% 17.93/7.04  % (21847)------------------------------
% 17.93/7.05  % (21868)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_21656 for (2983ds/5205Mi)
% 17.93/7.06  % (21869)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_21656 for (2983ds/1913Mi)
% 18.31/7.16  % (21867)Instruction limit reached!
% 18.31/7.16  % (21867)------------------------------
% 18.31/7.16  % (21867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.31/7.16  % (21867)Termination reason: Unknown
% 18.31/7.16  % (21867)Termination phase: shuffling
% 18.31/7.16  
% 18.31/7.16  % (21867)Memory used [KB]: 19189
% 18.31/7.16  % (21867)Time elapsed: 0.144 s
% 18.31/7.16  % (21867)Instructions burned: 409 (million)
% 18.31/7.16  % (21867)------------------------------
% 18.31/7.16  % (21867)------------------------------
% 18.31/7.17  % (21854)Instruction limit reached!
% 18.31/7.17  % (21854)------------------------------
% 18.31/7.17  % (21854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.31/7.17  % (21854)Termination reason: Unknown
% 18.31/7.17  % (21854)Termination phase: shuffling
% 18.31/7.17  
% 18.31/7.17  % (21854)Memory used [KB]: 26993
% 18.31/7.17  % (21854)Time elapsed: 0.314 s
% 18.31/7.17  % (21854)Instructions burned: 924 (million)
% 18.31/7.17  % (21854)------------------------------
% 18.31/7.17  % (21854)------------------------------
% 18.31/7.18  % (21870)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_21656 for (2981ds/4350Mi)
% 18.31/7.18  % (21871)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_21656 for (2981ds/68Mi)
% 18.68/7.21  % (21871)Instruction limit reached!
% 18.68/7.21  % (21871)------------------------------
% 18.68/7.21  % (21871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.68/7.21  % (21871)Termination reason: Unknown
% 18.68/7.21  % (21871)Termination phase: shuffling
% 18.68/7.21  
% 18.68/7.21  % (21871)Memory used [KB]: 14839
% 18.68/7.21  % (21871)Time elapsed: 0.030 s
% 18.68/7.21  % (21871)Instructions burned: 68 (million)
% 18.68/7.21  % (21871)------------------------------
% 18.68/7.21  % (21871)------------------------------
% 18.68/7.22  % (21872)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_21656 for (2981ds/358Mi)
% 18.68/7.26  % (21859)Instruction limit reached!
% 18.68/7.26  % (21859)------------------------------
% 18.68/7.26  % (21859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.68/7.26  % (21859)Termination reason: Unknown
% 18.68/7.26  % (21859)Termination phase: Property scanning
% 18.68/7.26  
% 18.68/7.26  % (21859)Memory used [KB]: 27888
% 18.68/7.26  % (21859)Time elapsed: 0.344 s
% 18.68/7.26  % (21859)Instructions burned: 1024 (million)
% 18.68/7.26  % (21859)------------------------------
% 18.68/7.26  % (21859)------------------------------
% 18.68/7.28  % (21873)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_21656 for (2980ds/31Mi)
% 18.68/7.29  % (21873)Instruction limit reached!
% 18.68/7.29  % (21873)------------------------------
% 18.68/7.29  % (21873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.68/7.29  % (21873)Termination reason: Unknown
% 18.68/7.29  % (21873)Termination phase: shuffling
% 18.68/7.29  
% 18.68/7.29  % (21873)Memory used [KB]: 14328
% 18.68/7.29  % (21873)Time elapsed: 0.020 s
% 18.68/7.29  % (21873)Instructions burned: 32 (million)
% 18.68/7.29  % (21873)------------------------------
% 18.68/7.29  % (21873)------------------------------
% 18.92/7.30  % (21874)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_21656 for (2980ds/279Mi)
% 18.92/7.34  % (21872)Instruction limit reached!
% 18.92/7.34  % (21872)------------------------------
% 18.92/7.34  % (21872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.92/7.34  % (21872)Termination reason: Unknown
% 18.92/7.34  % (21872)Termination phase: shuffling
% 18.92/7.34  
% 18.92/7.34  % (21872)Memory used [KB]: 18421
% 18.92/7.34  % (21872)Time elapsed: 0.124 s
% 18.92/7.34  % (21872)Instructions burned: 360 (million)
% 18.92/7.34  % (21872)------------------------------
% 18.92/7.34  % (21872)------------------------------
% 18.92/7.35  % (21875)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_21656 for (2979ds/258Mi)
% 18.92/7.39  % (21874)Instruction limit reached!
% 18.92/7.39  % (21874)------------------------------
% 18.92/7.39  % (21874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.92/7.39  % (21874)Termination reason: Unknown
% 18.92/7.39  % (21874)Termination phase: shuffling
% 18.92/7.39  
% 18.92/7.39  % (21874)Memory used [KB]: 19957
% 18.92/7.39  % (21874)Time elapsed: 0.088 s
% 18.92/7.39  % (21874)Instructions burned: 281 (million)
% 18.92/7.39  % (21874)------------------------------
% 18.92/7.39  % (21874)------------------------------
% 19.26/7.40  % (21876)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_21656 for (2979ds/26Mi)
% 19.26/7.42  % (21876)Instruction limit reached!
% 19.26/7.42  % (21876)------------------------------
% 19.26/7.42  % (21876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.26/7.42  % (21876)Termination reason: Unknown
% 19.26/7.42  % (21876)Termination phase: shuffling
% 19.26/7.42  
% 19.26/7.42  % (21876)Memory used [KB]: 14328
% 19.26/7.42  % (21876)Time elapsed: 0.017 s
% 19.26/7.42  % (21876)Instructions burned: 26 (million)
% 19.26/7.42  % (21876)------------------------------
% 19.26/7.42  % (21876)------------------------------
% 19.26/7.43  % (21877)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_21656 for (2979ds/995Mi)
% 19.26/7.44  % (21875)Instruction limit reached!
% 19.26/7.44  % (21875)------------------------------
% 19.26/7.44  % (21875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.26/7.44  % (21875)Termination reason: Unknown
% 19.26/7.44  % (21875)Termination phase: shuffling
% 19.26/7.44  
% 19.26/7.44  % (21875)Memory used [KB]: 17142
% 19.26/7.44  % (21875)Time elapsed: 0.090 s
% 19.26/7.44  % (21875)Instructions burned: 259 (million)
% 19.26/7.44  % (21875)------------------------------
% 19.26/7.44  % (21875)------------------------------
% 19.26/7.45  % (21878)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_21656 for (2978ds/373Mi)
% 19.26/7.48  % (21866)Instruction limit reached!
% 19.26/7.48  % (21866)------------------------------
% 19.26/7.48  % (21866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.26/7.48  % (21866)Termination reason: Unknown
% 19.26/7.48  % (21866)Termination phase: Property scanning
% 19.26/7.48  
% 19.26/7.48  % (21866)Memory used [KB]: 27760
% 19.26/7.48  % (21866)Time elapsed: 0.470 s
% 19.26/7.48  % (21866)Instructions burned: 1539 (million)
% 19.26/7.48  % (21866)------------------------------
% 19.26/7.48  % (21866)------------------------------
% 19.98/7.50  % (21879)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_21656 for (2978ds/253Mi)
% 19.98/7.57  % (21879)Instruction limit reached!
% 19.98/7.57  % (21879)------------------------------
% 19.98/7.57  % (21879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.98/7.57  % (21879)Termination reason: Unknown
% 19.98/7.57  % (21879)Termination phase: shuffling
% 19.98/7.57  
% 19.98/7.58  % (21879)Memory used [KB]: 19573
% 19.98/7.58  % (21879)Time elapsed: 0.080 s
% 19.98/7.58  % (21879)Instructions burned: 254 (million)
% 19.98/7.58  % (21879)------------------------------
% 19.98/7.58  % (21879)------------------------------
% 19.98/7.58  % (21878)Instruction limit reached!
% 19.98/7.58  % (21878)------------------------------
% 19.98/7.58  % (21878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.98/7.58  % (21878)Termination reason: Unknown
% 19.98/7.58  % (21878)Termination phase: shuffling
% 19.98/7.58  
% 19.98/7.58  % (21878)Memory used [KB]: 18421
% 19.98/7.58  % (21878)Time elapsed: 0.126 s
% 19.98/7.58  % (21878)Instructions burned: 375 (million)
% 19.98/7.58  % (21878)------------------------------
% 19.98/7.58  % (21878)------------------------------
% 19.98/7.59  % (21880)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_21656 for (2977ds/832Mi)
% 19.98/7.59  % (21881)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_21656 for (2977ds/668Mi)
% 20.30/7.63  % (21869)Instruction limit reached!
% 20.30/7.63  % (21869)------------------------------
% 20.30/7.63  % (21869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.30/7.63  % (21869)Termination reason: Unknown
% 20.30/7.63  % (21869)Termination phase: SInE selection
% 20.30/7.63  
% 20.30/7.63  % (21869)Memory used [KB]: 27888
% 20.30/7.63  % (21869)Time elapsed: 0.575 s
% 20.30/7.63  % (21869)Instructions burned: 1913 (million)
% 20.30/7.63  % (21869)------------------------------
% 20.30/7.63  % (21869)------------------------------
% 20.30/7.64  % (21882)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_21656 for (2977ds/40Mi)
% 20.30/7.66  % (21882)Instruction limit reached!
% 20.30/7.66  % (21882)------------------------------
% 20.30/7.66  % (21882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.30/7.66  % (21882)Termination reason: Unknown
% 20.30/7.66  % (21882)Termination phase: shuffling
% 20.30/7.66  
% 20.30/7.66  % (21882)Memory used [KB]: 14583
% 20.30/7.66  % (21882)Time elapsed: 0.021 s
% 20.30/7.66  % (21882)Instructions burned: 41 (million)
% 20.30/7.66  % (21882)------------------------------
% 20.30/7.66  % (21882)------------------------------
% 20.30/7.67  % (21883)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_21656 for (2976ds/294Mi)
% 21.02/7.72  % (21877)Instruction limit reached!
% 21.02/7.72  % (21877)------------------------------
% 21.02/7.72  % (21877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.02/7.72  % (21877)Termination reason: Unknown
% 21.02/7.72  % (21877)Termination phase: shuffling
% 21.02/7.72  
% 21.02/7.72  % (21877)Memory used [KB]: 33261
% 21.02/7.72  % (21877)Time elapsed: 0.291 s
% 21.02/7.72  % (21877)Instructions burned: 997 (million)
% 21.02/7.72  % (21877)------------------------------
% 21.02/7.72  % (21877)------------------------------
% 21.02/7.73  % (21884)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_21656 for (2976ds/187Mi)
% 21.02/7.76  % (21883)Instruction limit reached!
% 21.02/7.76  % (21883)------------------------------
% 21.02/7.76  % (21883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.02/7.76  % (21883)Termination reason: Unknown
% 21.02/7.76  % (21883)Termination phase: shuffling
% 21.02/7.76  
% 21.02/7.76  % (21883)Memory used [KB]: 20084
% 21.02/7.76  % (21883)Time elapsed: 0.091 s
% 21.02/7.76  % (21883)Instructions burned: 295 (million)
% 21.02/7.76  % (21883)------------------------------
% 21.02/7.76  % (21883)------------------------------
% 21.02/7.77  % (21885)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_21656 for (2975ds/371Mi)
% 21.02/7.78  % (21881)Instruction limit reached!
% 21.02/7.78  % (21881)------------------------------
% 21.02/7.78  % (21881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.02/7.78  % (21881)Termination reason: Unknown
% 21.02/7.78  % (21881)Termination phase: shuffling
% 21.02/7.78  
% 21.02/7.78  % (21881)Memory used [KB]: 25074
% 21.02/7.78  % (21881)Time elapsed: 0.196 s
% 21.02/7.78  % (21881)Instructions burned: 669 (million)
% 21.02/7.78  % (21881)------------------------------
% 21.02/7.78  % (21881)------------------------------
% 21.02/7.79  % (21886)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_21656 for (2975ds/1827Mi)
% 21.72/7.80  % (21884)Instruction limit reached!
% 21.72/7.80  % (21884)------------------------------
% 21.72/7.80  % (21884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.72/7.80  % (21884)Termination reason: Unknown
% 21.72/7.80  % (21884)Termination phase: shuffling
% 21.72/7.80  
% 21.72/7.80  % (21884)Memory used [KB]: 16247
% 21.72/7.80  % (21884)Time elapsed: 0.068 s
% 21.72/7.80  % (21884)Instructions burned: 188 (million)
% 21.72/7.80  % (21884)------------------------------
% 21.72/7.80  % (21884)------------------------------
% 21.72/7.81  % (21887)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_21656 for (2975ds/70Mi)
% 21.72/7.84  % (21887)Instruction limit reached!
% 21.72/7.84  % (21887)------------------------------
% 21.72/7.84  % (21887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.72/7.84  % (21887)Termination reason: Unknown
% 21.72/7.84  % (21887)Termination phase: shuffling
% 21.72/7.84  
% 21.72/7.84  % (21887)Memory used [KB]: 14967
% 21.72/7.84  % (21887)Time elapsed: 0.029 s
% 21.72/7.84  % (21887)Instructions burned: 70 (million)
% 21.72/7.84  % (21887)------------------------------
% 21.72/7.84  % (21887)------------------------------
% 21.72/7.85  % (21888)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_21656 for (2975ds/316Mi)
% 21.72/7.87  % (21880)Instruction limit reached!
% 21.72/7.87  % (21880)------------------------------
% 21.72/7.87  % (21880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.72/7.87  % (21880)Termination reason: Unknown
% 21.72/7.87  % (21880)Termination phase: shuffling
% 21.72/7.87  
% 21.72/7.87  % (21880)Memory used [KB]: 25841
% 21.72/7.87  % (21880)Time elapsed: 0.281 s
% 21.72/7.87  % (21880)Instructions burned: 835 (million)
% 21.72/7.87  % (21880)------------------------------
% 21.72/7.87  % (21880)------------------------------
% 21.72/7.88  % (21889)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_21656 for (2974ds/932Mi)
% 22.25/7.90  % (21885)Instruction limit reached!
% 22.25/7.90  % (21885)------------------------------
% 22.25/7.90  % (21885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.25/7.90  % (21885)Termination reason: Unknown
% 22.25/7.90  % (21885)Termination phase: shuffling
% 22.25/7.90  
% 22.25/7.90  % (21885)Memory used [KB]: 18293
% 22.25/7.90  % (21885)Time elapsed: 0.126 s
% 22.25/7.90  % (21885)Instructions burned: 373 (million)
% 22.25/7.90  % (21885)------------------------------
% 22.25/7.90  % (21885)------------------------------
% 22.25/7.91  % (21890)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_21656 for (2974ds/4714Mi)
% 22.25/7.94  % (21888)Instruction limit reached!
% 22.25/7.94  % (21888)------------------------------
% 22.25/7.94  % (21888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.25/7.94  % (21888)Termination reason: Unknown
% 22.25/7.94  % (21888)Termination phase: shuffling
% 22.25/7.94  
% 22.25/7.94  % (21888)Memory used [KB]: 20340
% 22.25/7.94  % (21888)Time elapsed: 0.097 s
% 22.25/7.94  % (21888)Instructions burned: 316 (million)
% 22.25/7.94  % (21888)------------------------------
% 22.25/7.94  % (21888)------------------------------
% 22.25/7.95  % (21891)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_21656 for (2974ds/8250Mi)
% 25.71/8.15  % (21889)Instruction limit reached!
% 25.71/8.15  % (21889)------------------------------
% 25.71/8.15  % (21889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.71/8.15  % (21889)Termination reason: Unknown
% 25.71/8.15  % (21889)Termination phase: shuffling
% 25.71/8.15  
% 25.71/8.15  % (21889)Memory used [KB]: 32494
% 25.71/8.15  % (21889)Time elapsed: 0.278 s
% 25.71/8.15  % (21889)Instructions burned: 933 (million)
% 25.71/8.15  % (21889)------------------------------
% 25.71/8.15  % (21889)------------------------------
% 25.71/8.17  % (21892)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_21656 for (2971ds/770Mi)
% 26.77/8.34  % (21886)Instruction limit reached!
% 26.77/8.34  % (21886)------------------------------
% 26.77/8.34  % (21886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.77/8.34  % (21886)Termination reason: Unknown
% 26.77/8.34  % (21886)Termination phase: Preprocessing 1
% 26.77/8.34  
% 26.77/8.34  % (21886)Memory used [KB]: 29040
% 26.77/8.34  % (21886)Time elapsed: 0.549 s
% 26.77/8.34  % (21886)Instructions burned: 1829 (million)
% 26.77/8.34  % (21886)------------------------------
% 26.77/8.34  % (21886)------------------------------
% 26.77/8.35  % (21894)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_21656 for (2969ds/794Mi)
% 27.33/8.40  % (21864)Instruction limit reached!
% 27.33/8.40  % (21864)------------------------------
% 27.33/8.40  % (21864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.33/8.40  % (21864)Termination reason: Unknown
% 27.33/8.40  % (21864)Termination phase: Saturation
% 27.33/8.40  
% 27.33/8.40  % (21864)Memory used [KB]: 35436
% 27.33/8.40  % (21864)Time elapsed: 1.404 s
% 27.33/8.40  % (21864)Instructions burned: 4437 (million)
% 27.33/8.40  % (21864)------------------------------
% 27.33/8.40  % (21864)------------------------------
% 27.33/8.41  % (21895)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_21656 for (2969ds/464Mi)
% 27.33/8.42  % (21892)Instruction limit reached!
% 27.33/8.42  % (21892)------------------------------
% 27.33/8.42  % (21892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.33/8.42  % (21892)Termination reason: Unknown
% 27.33/8.42  % (21892)Termination phase: shuffling
% 27.33/8.42  
% 27.33/8.42  % (21892)Memory used [KB]: 24818
% 27.33/8.42  % (21892)Time elapsed: 0.253 s
% 27.33/8.42  % (21892)Instructions burned: 770 (million)
% 27.33/8.42  % (21892)------------------------------
% 27.33/8.42  % (21892)------------------------------
% 27.33/8.43  % (21870)Instruction limit reached!
% 27.33/8.43  % (21870)------------------------------
% 27.33/8.43  % (21870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.33/8.43  % (21870)Termination reason: Unknown
% 27.33/8.43  % (21870)Termination phase: Saturation
% 27.33/8.43  
% 27.33/8.43  % (21870)Memory used [KB]: 37739
% 27.33/8.43  % (21870)Time elapsed: 1.274 s
% 27.33/8.43  % (21870)Instructions burned: 4350 (million)
% 27.33/8.43  % (21870)------------------------------
% 27.33/8.43  % (21870)------------------------------
% 27.33/8.43  % (21896)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_21656 for (2969ds/1376Mi)
% 27.33/8.44  % (21897)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_21656 for (2969ds/906Mi)
% 27.33/8.45  % (21868)Instruction limit reached!
% 27.33/8.45  % (21868)------------------------------
% 27.33/8.45  % (21868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.33/8.45  % (21868)Termination reason: Unknown
% 27.33/8.45  % (21868)Termination phase: Function definition elimination
% 27.33/8.45  
% 27.33/8.45  % (21868)Memory used [KB]: 61022
% 27.33/8.45  % (21868)Time elapsed: 1.407 s
% 27.33/8.45  % (21868)Instructions burned: 5206 (million)
% 27.33/8.45  % (21868)------------------------------
% 27.33/8.45  % (21868)------------------------------
% 27.33/8.47  % (21898)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_21656 for (2968ds/434Mi)
% 27.92/8.57  % (21895)Instruction limit reached!
% 27.92/8.57  % (21895)------------------------------
% 27.92/8.57  % (21895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.92/8.57  % (21895)Termination reason: Unknown
% 27.92/8.57  % (21895)Termination phase: shuffling
% 27.92/8.57  
% 27.92/8.57  % (21895)Memory used [KB]: 19701
% 27.92/8.57  % (21895)Time elapsed: 0.157 s
% 27.92/8.57  % (21895)Instructions burned: 464 (million)
% 27.92/8.57  % (21895)------------------------------
% 27.92/8.57  % (21895)------------------------------
% 27.92/8.58  % (21899)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_21656 for (2967ds/865Mi)
% 28.29/8.61  % (21898)Instruction limit reached!
% 28.29/8.61  % (21898)------------------------------
% 28.29/8.61  % (21898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.29/8.61  % (21898)Termination reason: Unknown
% 28.29/8.61  % (21898)Termination phase: shuffling
% 28.29/8.61  
% 28.29/8.61  % (21898)Memory used [KB]: 19061
% 28.29/8.61  % (21898)Time elapsed: 0.148 s
% 28.29/8.61  % (21898)Instructions burned: 436 (million)
% 28.29/8.61  % (21898)------------------------------
% 28.29/8.61  % (21898)------------------------------
% 28.29/8.61  % (21894)Instruction limit reached!
% 28.29/8.61  % (21894)------------------------------
% 28.29/8.61  % (21894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.29/8.61  % (21894)Termination reason: Unknown
% 28.29/8.61  % (21894)Termination phase: shuffling
% 28.29/8.61  
% 28.29/8.61  % (21894)Memory used [KB]: 25074
% 28.29/8.61  % (21894)Time elapsed: 0.262 s
% 28.29/8.61  % (21894)Instructions burned: 794 (million)
% 28.29/8.61  % (21894)------------------------------
% 28.29/8.61  % (21894)------------------------------
% 28.29/8.62  % (21900)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_21656 for (2967ds/593Mi)
% 28.29/8.63  % (21901)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_21656 for (2967ds/443Mi)
% 28.92/8.74  % (21897)Instruction limit reached!
% 28.92/8.74  % (21897)------------------------------
% 28.92/8.74  % (21897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.92/8.74  % (21897)Termination reason: Unknown
% 28.92/8.74  % (21897)Termination phase: shuffling
% 28.92/8.74  
% 28.92/8.74  % (21897)Memory used [KB]: 26353
% 28.92/8.74  % (21897)Time elapsed: 0.299 s
% 28.92/8.74  % (21897)Instructions burned: 908 (million)
% 28.92/8.74  % (21897)------------------------------
% 28.92/8.74  % (21897)------------------------------
% 28.92/8.75  % (21902)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_21656 for (2966ds/594Mi)
% 28.92/8.77  % (21901)Instruction limit reached!
% 28.92/8.77  % (21901)------------------------------
% 28.92/8.77  % (21901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.92/8.77  % (21901)Termination reason: Unknown
% 28.92/8.77  % (21901)Termination phase: shuffling
% 28.92/8.77  
% 28.92/8.77  % (21901)Memory used [KB]: 19061
% 28.92/8.77  % (21901)Time elapsed: 0.148 s
% 28.92/8.77  % (21901)Instructions burned: 443 (million)
% 28.92/8.77  % (21901)------------------------------
% 28.92/8.77  % (21901)------------------------------
% 28.92/8.79  % (21903)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_21656 for (2965ds/327Mi)
% 29.59/8.80  % (21900)Instruction limit reached!
% 29.59/8.80  % (21900)------------------------------
% 29.59/8.80  % (21900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.59/8.80  % (21900)Termination reason: Unknown
% 29.59/8.80  % (21900)Termination phase: shuffling
% 29.59/8.80  
% 29.59/8.80  % (21900)Memory used [KB]: 24178
% 29.59/8.80  % (21900)Time elapsed: 0.178 s
% 29.59/8.80  % (21900)Instructions burned: 593 (million)
% 29.59/8.80  % (21900)------------------------------
% 29.59/8.80  % (21900)------------------------------
% 29.59/8.81  % (21904)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_21656 for (2965ds/5411Mi)
% 29.59/8.83  % (21896)Instruction limit reached!
% 29.59/8.83  % (21896)------------------------------
% 29.59/8.83  % (21896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.59/8.83  % (21896)Termination reason: Unknown
% 29.59/8.83  % (21896)Termination phase: shuffling
% 29.59/8.83  
% 29.59/8.83  % (21896)Memory used [KB]: 38123
% 29.59/8.83  % (21896)Time elapsed: 0.401 s
% 29.59/8.83  % (21896)Instructions burned: 1378 (million)
% 29.59/8.83  % (21896)------------------------------
% 29.59/8.83  % (21896)------------------------------
% 29.59/8.83  % (21899)Instruction limit reached!
% 29.59/8.83  % (21899)------------------------------
% 29.59/8.83  % (21899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.59/8.83  % (21899)Termination reason: Unknown
% 29.59/8.83  % (21899)Termination phase: shuffling
% 29.59/8.83  
% 29.59/8.83  % (21899)Memory used [KB]: 31726
% 29.59/8.83  % (21899)Time elapsed: 0.255 s
% 29.59/8.83  % (21899)Instructions burned: 865 (million)
% 29.59/8.83  % (21899)------------------------------
% 29.59/8.83  % (21899)------------------------------
% 29.59/8.84  % (21905)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_21656 for (2965ds/1762Mi)
% 29.59/8.85  % (21906)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_21656 for (2965ds/96Mi)
% 29.59/8.88  % (21906)Instruction limit reached!
% 29.59/8.88  % (21906)------------------------------
% 29.59/8.88  % (21906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.59/8.88  % (21906)Termination reason: Unknown
% 29.59/8.88  % (21906)Termination phase: shuffling
% 29.59/8.88  
% 29.59/8.88  % (21906)Memory used [KB]: 15351
% 29.59/8.88  % (21906)Time elapsed: 0.036 s
% 29.59/8.88  % (21906)Instructions burned: 97 (million)
% 29.59/8.88  % (21906)------------------------------
% 29.59/8.88  % (21906)------------------------------
% 29.59/8.89  % (21907)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_21656 for (2964ds/503Mi)
% 30.70/8.90  % (21903)Instruction limit reached!
% 30.70/8.90  % (21903)------------------------------
% 30.70/8.90  % (21903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.70/8.90  % (21903)Termination reason: Unknown
% 30.70/8.90  % (21903)Termination phase: shuffling
% 30.70/8.90  
% 30.70/8.90  % (21903)Memory used [KB]: 17910
% 30.70/8.90  % (21903)Time elapsed: 0.114 s
% 30.70/8.90  % (21903)Instructions burned: 329 (million)
% 30.70/8.90  % (21903)------------------------------
% 30.70/8.90  % (21903)------------------------------
% 30.70/8.91  % (21908)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_21656 for (2964ds/90Mi)
% 30.70/8.95  % (21908)Instruction limit reached!
% 30.70/8.95  % (21908)------------------------------
% 30.70/8.95  % (21908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.70/8.95  % (21902)Instruction limit reached!
% 30.70/8.95  % (21902)------------------------------
% 30.70/8.95  % (21902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.70/8.95  % (21902)Termination reason: Unknown
% 30.70/8.95  % (21902)Termination phase: shuffling
% 30.70/8.95  
% 30.70/8.95  % (21902)Memory used [KB]: 22899
% 30.70/8.95  % (21902)Time elapsed: 0.199 s
% 30.70/8.95  % (21902)Instructions burned: 594 (million)
% 30.70/8.95  % (21902)------------------------------
% 30.70/8.95  % (21902)------------------------------
% 30.70/8.95  % (21908)Termination reason: Unknown
% 30.70/8.95  % (21908)Termination phase: shuffling
% 30.70/8.95  
% 30.70/8.95  % (21908)Memory used [KB]: 15223
% 30.70/8.95  % (21908)Time elapsed: 0.038 s
% 30.70/8.95  % (21908)Instructions burned: 90 (million)
% 30.70/8.95  % (21908)------------------------------
% 30.70/8.95  % (21908)------------------------------
% 30.70/8.96  % (21909)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_21656 for (2964ds/593Mi)
% 30.70/8.96  % (21910)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_21656 for (2964ds/1512Mi)
% 31.99/9.06  % (21907)Instruction limit reached!
% 31.99/9.06  % (21907)------------------------------
% 31.99/9.06  % (21907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.99/9.06  % (21907)Termination reason: Unknown
% 31.99/9.06  % (21907)Termination phase: shuffling
% 31.99/9.06  
% 31.99/9.06  % (21907)Memory used [KB]: 20084
% 31.99/9.06  % (21907)Time elapsed: 0.169 s
% 31.99/9.06  % (21907)Instructions burned: 503 (million)
% 31.99/9.06  % (21907)------------------------------
% 31.99/9.06  % (21907)------------------------------
% 31.99/9.07  % (21911)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_21656 for (2962ds/569Mi)
% 32.67/9.16  % (21909)Instruction limit reached!
% 32.67/9.16  % (21909)------------------------------
% 32.67/9.16  % (21909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.67/9.16  % (21909)Termination reason: Unknown
% 32.67/9.16  % (21909)Termination phase: shuffling
% 32.67/9.16  
% 32.67/9.16  % (21909)Memory used [KB]: 23155
% 32.67/9.16  % (21909)Time elapsed: 0.200 s
% 32.67/9.16  % (21909)Instructions burned: 594 (million)
% 32.67/9.16  % (21909)------------------------------
% 32.67/9.16  % (21909)------------------------------
% 32.67/9.17  % (21912)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_21656 for (2961ds/501Mi)
% 32.67/9.18  % (21890)Instruction limit reached!
% 32.67/9.18  % (21890)------------------------------
% 32.67/9.18  % (21890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.67/9.18  % (21890)Termination reason: Unknown
% 32.67/9.18  % (21890)Termination phase: Function definition elimination
% 32.67/9.18  
% 32.67/9.18  % (21890)Memory used [KB]: 56544
% 32.67/9.18  % (21890)Time elapsed: 1.269 s
% 32.67/9.18  % (21890)Instructions burned: 4714 (million)
% 32.67/9.18  % (21890)------------------------------
% 32.67/9.18  % (21890)------------------------------
% 32.67/9.19  % (21913)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_21656 for (2961ds/562Mi)
% 33.06/9.24  % (21911)Instruction limit reached!
% 33.06/9.24  % (21911)------------------------------
% 33.06/9.24  % (21911)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.06/9.24  % (21911)Termination reason: Unknown
% 33.06/9.24  % (21911)Termination phase: shuffling
% 33.06/9.24  
% 33.06/9.24  % (21911)Memory used [KB]: 23794
% 33.06/9.24  % (21911)Time elapsed: 0.169 s
% 33.06/9.24  % (21911)Instructions burned: 571 (million)
% 33.06/9.24  % (21911)------------------------------
% 33.06/9.24  % (21911)------------------------------
% 33.06/9.25  % (21914)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_21656 for (2960ds/406Mi)
% 33.66/9.33  % (21912)Instruction limit reached!
% 33.66/9.33  % (21912)------------------------------
% 33.66/9.33  % (21912)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.66/9.33  % (21912)Termination reason: Unknown
% 33.66/9.33  % (21912)Termination phase: shuffling
% 33.66/9.33  
% 33.66/9.33  % (21912)Memory used [KB]: 19701
% 33.66/9.33  % (21912)Time elapsed: 0.167 s
% 33.66/9.33  % (21912)Instructions burned: 501 (million)
% 33.66/9.33  % (21912)------------------------------
% 33.66/9.33  % (21912)------------------------------
% 33.66/9.35  % (21915)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_21656 for (2960ds/582Mi)
% 33.66/9.35  % (21905)Instruction limit reached!
% 33.66/9.35  % (21905)------------------------------
% 33.66/9.35  % (21905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.66/9.35  % (21905)Termination reason: Unknown
% 33.66/9.35  % (21905)Termination phase: shuffling
% 33.66/9.35  
% 33.66/9.35  % (21905)Memory used [KB]: 43112
% 33.66/9.35  % (21905)Time elapsed: 0.511 s
% 33.66/9.35  % (21905)Instructions burned: 1764 (million)
% 33.66/9.35  % (21905)------------------------------
% 33.66/9.35  % (21905)------------------------------
% 33.66/9.35  % (21913)Instruction limit reached!
% 33.66/9.35  % (21913)------------------------------
% 33.66/9.35  % (21913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.66/9.35  % (21913)Termination reason: Unknown
% 33.66/9.35  % (21913)Termination phase: shuffling
% 33.66/9.35  
% 33.66/9.35  % (21913)Memory used [KB]: 23666
% 33.66/9.35  % (21913)Time elapsed: 0.166 s
% 33.66/9.35  % (21913)Instructions burned: 562 (million)
% 33.66/9.35  % (21913)------------------------------
% 33.66/9.35  % (21913)------------------------------
% 33.66/9.37  % (21916)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_21656 for (2959ds/456Mi)
% 33.66/9.37  % (21917)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_21656 for (2959ds/393Mi)
% 33.66/9.39  % (21914)Instruction limit reached!
% 33.66/9.39  % (21914)------------------------------
% 33.66/9.39  % (21914)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.66/9.39  % (21914)Termination reason: Unknown
% 33.66/9.39  % (21914)Termination phase: shuffling
% 33.66/9.39  
% 33.66/9.39  % (21914)Memory used [KB]: 19061
% 33.66/9.39  % (21914)Time elapsed: 0.139 s
% 33.66/9.39  % (21914)Instructions burned: 406 (million)
% 33.66/9.39  % (21914)------------------------------
% 33.66/9.39  % (21914)------------------------------
% 34.53/9.40  % (21918)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_21656 for (2959ds/1335Mi)
% 34.53/9.44  % (21910)Instruction limit reached!
% 34.53/9.44  % (21910)------------------------------
% 34.53/9.44  % (21910)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.53/9.44  % (21910)Termination reason: Unknown
% 34.53/9.44  % (21910)Termination phase: Property scanning
% 34.53/9.44  
% 34.53/9.44  % (21910)Memory used [KB]: 30447
% 34.53/9.44  % (21910)Time elapsed: 0.482 s
% 34.53/9.44  % (21910)Instructions burned: 1514 (million)
% 34.53/9.44  % (21910)------------------------------
% 34.53/9.44  % (21910)------------------------------
% 34.53/9.45  % (21919)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_21656 for (2958ds/3373Mi)
% 34.53/9.48  % (21917)Instruction limit reached!
% 34.53/9.48  % (21917)------------------------------
% 34.53/9.48  % (21917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.53/9.48  % (21917)Termination reason: Unknown
% 34.53/9.48  % (21917)Termination phase: shuffling
% 34.53/9.48  
% 34.53/9.48  % (21917)Memory used [KB]: 21492
% 34.53/9.48  % (21917)Time elapsed: 0.120 s
% 34.53/9.48  % (21917)Instructions burned: 395 (million)
% 34.53/9.48  % (21917)------------------------------
% 34.53/9.48  % (21917)------------------------------
% 34.53/9.50  % (21920)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_21656 for (2958ds/474Mi)
% 34.90/9.52  % (21916)Instruction limit reached!
% 34.90/9.52  % (21916)------------------------------
% 34.90/9.52  % (21916)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.90/9.52  % (21916)Termination reason: Unknown
% 34.90/9.52  % (21916)Termination phase: shuffling
% 34.90/9.52  
% 34.90/9.52  % (21916)Memory used [KB]: 19573
% 34.90/9.52  % (21916)Time elapsed: 0.156 s
% 34.90/9.52  % (21916)Instructions burned: 457 (million)
% 34.90/9.52  % (21916)------------------------------
% 34.90/9.52  % (21916)------------------------------
% 34.90/9.53  % (21922)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_21656 for (2958ds/157Mi)
% 34.90/9.54  % (21915)Instruction limit reached!
% 34.90/9.54  % (21915)------------------------------
% 34.90/9.54  % (21915)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.90/9.54  % (21915)Termination reason: Unknown
% 34.90/9.54  % (21915)Termination phase: shuffling
% 34.90/9.54  
% 34.90/9.54  % (21915)Memory used [KB]: 21364
% 34.90/9.54  % (21915)Time elapsed: 0.200 s
% 34.90/9.54  % (21915)Instructions burned: 583 (million)
% 34.90/9.54  % (21915)------------------------------
% 34.90/9.54  % (21915)------------------------------
% 34.90/9.56  % (21923)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_21656 for (2957ds/590Mi)
% 34.90/9.58  % (21922)Instruction limit reached!
% 34.90/9.58  % (21922)------------------------------
% 34.90/9.58  % (21922)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.90/9.58  % (21922)Termination reason: Unknown
% 34.90/9.58  % (21922)Termination phase: shuffling
% 34.90/9.58  
% 34.90/9.58  % (21922)Memory used [KB]: 16247
% 34.90/9.58  % (21922)Time elapsed: 0.053 s
% 34.90/9.58  % (21922)Instructions burned: 157 (million)
% 34.90/9.58  % (21922)------------------------------
% 34.90/9.58  % (21922)------------------------------
% 34.90/9.60  % (21924)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_21656 for (2957ds/104Mi)
% 35.54/9.64  % (21924)Instruction limit reached!
% 35.54/9.64  % (21924)------------------------------
% 35.54/9.64  % (21924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.54/9.64  % (21924)Termination reason: Unknown
% 35.54/9.64  % (21924)Termination phase: shuffling
% 35.54/9.64  
% 35.54/9.64  % (21924)Memory used [KB]: 15223
% 35.54/9.64  % (21924)Time elapsed: 0.042 s
% 35.54/9.64  % (21924)Instructions burned: 105 (million)
% 35.54/9.64  % (21924)------------------------------
% 35.54/9.64  % (21924)------------------------------
% 35.54/9.64  % (21920)Instruction limit reached!
% 35.54/9.64  % (21920)------------------------------
% 35.54/9.64  % (21920)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.54/9.64  % (21920)Termination reason: Unknown
% 35.54/9.64  % (21920)Termination phase: shuffling
% 35.54/9.64  
% 35.54/9.64  % (21920)Memory used [KB]: 22387
% 35.54/9.64  % (21920)Time elapsed: 0.143 s
% 35.54/9.64  % (21920)Instructions burned: 474 (million)
% 35.54/9.64  % (21920)------------------------------
% 35.54/9.64  % (21920)------------------------------
% 35.54/9.65  % (21925)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_21656 for (2957ds/414Mi)
% 35.54/9.65  % (21926)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_21656 for (2957ds/715Mi)
% 35.95/9.75  % (21923)Instruction limit reached!
% 35.95/9.75  % (21923)------------------------------
% 35.95/9.75  % (21923)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.95/9.75  % (21923)Termination reason: Unknown
% 35.95/9.75  % (21923)Termination phase: shuffling
% 35.95/9.75  
% 35.95/9.75  % (21923)Memory used [KB]: 23155
% 35.95/9.75  % (21923)Time elapsed: 0.199 s
% 35.95/9.75  % (21923)Instructions burned: 590 (million)
% 35.95/9.75  % (21923)------------------------------
% 35.95/9.75  % (21923)------------------------------
% 35.95/9.77  % (21927)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_21656 for (2955ds/961Mi)
% 35.95/9.77  % (21925)Instruction limit reached!
% 35.95/9.77  % (21925)------------------------------
% 35.95/9.77  % (21925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.95/9.77  % (21925)Termination reason: Unknown
% 35.95/9.77  % (21925)Termination phase: shuffling
% 35.95/9.77  
% 35.95/9.77  % (21925)Memory used [KB]: 21748
% 35.95/9.77  % (21925)Time elapsed: 0.125 s
% 35.95/9.77  % (21925)Instructions burned: 414 (million)
% 35.95/9.77  % (21925)------------------------------
% 35.95/9.77  % (21925)------------------------------
% 35.95/9.78  % (21928)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_21656 for (2955ds/1213Mi)
% 35.95/9.79  % (21918)Instruction limit reached!
% 35.95/9.79  % (21918)------------------------------
% 35.95/9.79  % (21918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.95/9.79  % (21918)Termination reason: Unknown
% 35.95/9.79  % (21918)Termination phase: shuffling
% 35.95/9.79  
% 35.95/9.79  % (21918)Memory used [KB]: 37611
% 35.95/9.79  % (21918)Time elapsed: 0.388 s
% 35.95/9.79  % (21918)Instructions burned: 1336 (million)
% 35.95/9.79  % (21918)------------------------------
% 35.95/9.79  % (21918)------------------------------
% 36.88/9.80  % (21929)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_21656 for (2955ds/1979Mi)
% 36.88/9.85  % (21904)Refutation not found, incomplete strategy
% 36.88/9.85  % (21904)------------------------------
% 36.88/9.85  % (21904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.88/9.85  % (21904)Termination reason: Refutation not found, incomplete strategy
% 36.88/9.85  
% 36.88/9.85  
% 36.88/9.85  % (21904)Memory used [KB]: 42216
% 36.88/9.85  % (21904)Time elapsed: 1.039 s
% 36.88/9.85  % (21904)Instructions burned: 3479 (million)
% 36.88/9.85  % (21904)------------------------------
% 36.88/9.85  % (21904)------------------------------
% 36.88/9.87  % (21930)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_21656 for (2954ds/481Mi)
% 36.88/9.89  % (21926)Instruction limit reached!
% 36.88/9.89  % (21926)------------------------------
% 36.88/9.89  % (21926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.88/9.89  % (21926)Termination reason: Unknown
% 36.88/9.89  % (21926)Termination phase: shuffling
% 36.88/9.89  
% 36.88/9.89  % (21926)Memory used [KB]: 24434
% 36.88/9.89  % (21926)Time elapsed: 0.239 s
% 36.88/9.89  % (21926)Instructions burned: 717 (million)
% 36.88/9.89  % (21926)------------------------------
% 36.88/9.89  % (21926)------------------------------
% 37.30/9.90  % (21931)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_21656 for (2954ds/783Mi)
% 37.30/10.01  % (21930)Instruction limit reached!
% 37.30/10.01  % (21930)------------------------------
% 37.30/10.01  % (21930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.30/10.01  % (21930)Termination reason: Unknown
% 37.30/10.01  % (21930)Termination phase: shuffling
% 37.30/10.01  
% 37.30/10.01  % (21930)Memory used [KB]: 22515
% 37.30/10.01  % (21930)Time elapsed: 0.145 s
% 37.30/10.01  % (21930)Instructions burned: 482 (million)
% 37.30/10.01  % (21930)------------------------------
% 37.30/10.01  % (21930)------------------------------
% 39.04/10.03  % (21932)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_21656 for (2953ds/432Mi)
% 39.04/10.11  % (21927)Instruction limit reached!
% 39.04/10.11  % (21927)------------------------------
% 39.04/10.11  % (21927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.04/10.11  % (21927)Termination reason: Unknown
% 39.04/10.11  % (21927)Termination phase: shuffling
% 39.04/10.11  
% 39.04/10.11  % (21927)Memory used [KB]: 27121
% 39.04/10.11  % (21927)Time elapsed: 0.342 s
% 39.04/10.11  % (21927)Instructions burned: 961 (million)
% 39.04/10.11  % (21927)------------------------------
% 39.04/10.11  % (21927)------------------------------
% 39.04/10.12  % (21933)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_21656 for (2952ds/1670Mi)
% 39.62/10.16  % (21931)Instruction limit reached!
% 39.62/10.16  % (21931)------------------------------
% 39.62/10.16  % (21931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.62/10.16  % (21931)Termination reason: Unknown
% 39.62/10.16  % (21931)Termination phase: shuffling
% 39.62/10.16  
% 39.62/10.16  % (21931)Memory used [KB]: 25202
% 39.62/10.16  % (21931)Time elapsed: 0.262 s
% 39.62/10.16  % (21931)Instructions burned: 783 (million)
% 39.62/10.16  % (21931)------------------------------
% 39.62/10.16  % (21931)------------------------------
% 39.62/10.17  % (21928)Instruction limit reached!
% 39.62/10.17  % (21928)------------------------------
% 39.62/10.17  % (21928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.62/10.17  % (21928)Termination reason: Unknown
% 39.62/10.17  % (21928)Termination phase: Property scanning
% 39.62/10.17  
% 39.62/10.17  % (21928)Memory used [KB]: 27888
% 39.62/10.17  % (21928)Time elapsed: 0.390 s
% 39.62/10.17  % (21928)Instructions burned: 1215 (million)
% 39.62/10.17  % (21928)------------------------------
% 39.62/10.17  % (21928)------------------------------
% 39.62/10.17  % (21934)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_21656 for (2951ds/90Mi)
% 39.62/10.18  % (21932)Instruction limit reached!
% 39.62/10.18  % (21932)------------------------------
% 39.62/10.18  % (21932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.62/10.18  % (21932)Termination reason: Unknown
% 39.62/10.18  % (21932)Termination phase: shuffling
% 39.62/10.18  
% 39.62/10.18  % (21932)Memory used [KB]: 19061
% 39.62/10.18  % (21932)Time elapsed: 0.146 s
% 39.62/10.18  % (21932)Instructions burned: 433 (million)
% 39.62/10.18  % (21932)------------------------------
% 39.62/10.18  % (21932)------------------------------
% 39.62/10.18  % (21935)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_21656 for (2951ds/346Mi)
% 39.62/10.19  % (21936)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_21656 for (2951ds/401Mi)
% 40.11/10.21  % (21934)Instruction limit reached!
% 40.11/10.21  % (21934)------------------------------
% 40.11/10.21  % (21934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.11/10.21  % (21934)Termination reason: Unknown
% 40.11/10.21  % (21934)Termination phase: shuffling
% 40.11/10.21  
% 40.11/10.21  % (21934)Memory used [KB]: 15095
% 40.11/10.21  % (21934)Time elapsed: 0.038 s
% 40.11/10.21  % (21934)Instructions burned: 90 (million)
% 40.11/10.21  % (21934)------------------------------
% 40.11/10.21  % (21934)------------------------------
% 40.11/10.22  % (21937)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_21656 for (2951ds/6454Mi)
% 40.11/10.29  % (21935)Instruction limit reached!
% 40.11/10.29  % (21935)------------------------------
% 40.11/10.29  % (21935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.11/10.29  % (21935)Termination reason: Unknown
% 40.11/10.29  % (21935)Termination phase: shuffling
% 40.11/10.29  
% 40.11/10.29  % (21935)Memory used [KB]: 20724
% 40.11/10.29  % (21935)Time elapsed: 0.106 s
% 40.11/10.29  % (21935)Instructions burned: 346 (million)
% 40.11/10.29  % (21935)------------------------------
% 40.11/10.29  % (21935)------------------------------
% 40.57/10.30  % (21938)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_21656 for (2950ds/283Mi)
% 40.57/10.31  % (21936)Instruction limit reached!
% 40.57/10.31  % (21936)------------------------------
% 40.57/10.31  % (21936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.57/10.31  % (21936)Termination reason: Unknown
% 40.57/10.31  % (21936)Termination phase: shuffling
% 40.57/10.31  
% 40.57/10.31  % (21936)Memory used [KB]: 21620
% 40.57/10.31  % (21936)Time elapsed: 0.122 s
% 40.57/10.31  % (21936)Instructions burned: 403 (million)
% 40.57/10.31  % (21936)------------------------------
% 40.57/10.31  % (21936)------------------------------
% 40.57/10.32  % (21939)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_21656 for (2950ds/865Mi)
% 41.01/10.40  % (21938)Instruction limit reached!
% 41.01/10.40  % (21938)------------------------------
% 41.01/10.40  % (21938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.01/10.40  % (21938)Termination reason: Unknown
% 41.01/10.40  % (21938)Termination phase: shuffling
% 41.01/10.40  
% 41.01/10.40  % (21938)Memory used [KB]: 17526
% 41.01/10.40  % (21938)Time elapsed: 0.099 s
% 41.01/10.40  % (21938)Instructions burned: 283 (million)
% 41.01/10.40  % (21938)------------------------------
% 41.01/10.40  % (21938)------------------------------
% 41.01/10.41  % (21940)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_21656 for (2949ds/4528Mi)
% 41.01/10.41  % (21929)Instruction limit reached!
% 41.01/10.41  % (21929)------------------------------
% 41.01/10.41  % (21929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.01/10.41  % (21929)Termination reason: Unknown
% 41.01/10.41  % (21929)Termination phase: Preprocessing 3
% 41.01/10.41  
% 41.01/10.41  % (21929)Memory used [KB]: 33773
% 41.01/10.41  % (21929)Time elapsed: 0.611 s
% 41.01/10.41  % (21929)Instructions burned: 1979 (million)
% 41.01/10.41  % (21929)------------------------------
% 41.01/10.41  % (21929)------------------------------
% 41.01/10.42  % (21941)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_21656 for (2949ds/1001Mi)
% 41.01/10.44  % (21919)Instruction limit reached!
% 41.01/10.44  % (21919)------------------------------
% 41.01/10.44  % (21919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.01/10.44  % (21919)Termination reason: Unknown
% 41.01/10.44  % (21919)Termination phase: Function definition elimination
% 41.01/10.44  
% 41.01/10.44  % (21919)Memory used [KB]: 40297
% 41.01/10.44  % (21919)Time elapsed: 0.987 s
% 41.01/10.44  % (21919)Instructions burned: 3375 (million)
% 41.01/10.44  % (21919)------------------------------
% 41.01/10.44  % (21919)------------------------------
% 41.01/10.45  % (21942)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_21656 for (2949ds/102Mi)
% 41.01/10.49  % (21942)Instruction limit reached!
% 41.01/10.49  % (21942)------------------------------
% 41.01/10.49  % (21942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.01/10.49  % (21942)Termination reason: Unknown
% 41.01/10.49  % (21942)Termination phase: shuffling
% 41.01/10.49  
% 41.01/10.49  % (21942)Memory used [KB]: 15479
% 41.01/10.49  % (21942)Time elapsed: 0.038 s
% 41.01/10.49  % (21942)Instructions burned: 103 (million)
% 41.01/10.49  % (21942)------------------------------
% 41.01/10.49  % (21942)------------------------------
% 41.33/10.50  % (21943)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_21656 for (2948ds/952Mi)
% 41.33/10.52  % (21891)Instruction limit reached!
% 41.33/10.52  % (21891)------------------------------
% 41.33/10.52  % (21891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.33/10.52  % (21891)Termination reason: Unknown
% 41.33/10.52  % (21891)Termination phase: Saturation
% 41.33/10.52  
% 41.33/10.52  % (21891)Memory used [KB]: 59871
% 41.33/10.52  % (21891)Time elapsed: 2.569 s
% 41.33/10.52  % (21891)Instructions burned: 8251 (million)
% 41.33/10.52  % (21891)------------------------------
% 41.33/10.52  % (21891)------------------------------
% 41.33/10.54  % (21944)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_21656 for (2948ds/578Mi)
% 41.38/10.60  % (21933)Instruction limit reached!
% 41.38/10.60  % (21933)------------------------------
% 41.38/10.60  % (21933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.38/10.60  % (21933)Termination reason: Unknown
% 41.38/10.60  % (21933)Termination phase: shuffling
% 41.38/10.60  
% 41.38/10.60  % (21933)Memory used [KB]: 41960
% 41.38/10.60  % (21933)Time elapsed: 0.484 s
% 41.38/10.60  % (21933)Instructions burned: 1671 (million)
% 41.38/10.60  % (21933)------------------------------
% 41.38/10.60  % (21933)------------------------------
% 41.38/10.60  % (21939)Instruction limit reached!
% 41.38/10.60  % (21939)------------------------------
% 41.38/10.60  % (21939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.38/10.60  % (21939)Termination reason: Unknown
% 41.38/10.60  % (21939)Termination phase: shuffling
% 41.38/10.60  
% 41.38/10.60  % (21939)Memory used [KB]: 25841
% 41.38/10.60  % (21939)Time elapsed: 0.286 s
% 41.38/10.60  % (21939)Instructions burned: 865 (million)
% 41.38/10.60  % (21939)------------------------------
% 41.38/10.60  % (21939)------------------------------
% 41.38/10.61  % (21945)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_21656 for (2947ds/643Mi)
% 41.38/10.62  % (21946)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_21656 for (2947ds/865Mi)
% 42.17/10.71  % (21944)Instruction limit reached!
% 42.17/10.71  % (21944)------------------------------
% 42.17/10.71  % (21944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.17/10.71  % (21944)Termination reason: Unknown
% 42.17/10.71  % (21944)Termination phase: shuffling
% 42.17/10.71  
% 42.17/10.71  % (21944)Memory used [KB]: 24050
% 42.17/10.71  % (21944)Time elapsed: 0.171 s
% 42.17/10.71  % (21944)Instructions burned: 580 (million)
% 42.17/10.71  % (21944)------------------------------
% 42.17/10.71  % (21944)------------------------------
% 42.17/10.72  % (21947)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_21656 for (2946ds/1174Mi)
% 42.17/10.75  % (21941)Instruction limit reached!
% 42.17/10.75  % (21941)------------------------------
% 42.17/10.75  % (21941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.17/10.75  % (21941)Termination reason: Unknown
% 42.17/10.75  % (21941)Termination phase: shuffling
% 42.17/10.75  
% 42.17/10.75  % (21941)Memory used [KB]: 27504
% 42.17/10.75  % (21941)Time elapsed: 0.332 s
% 42.17/10.75  % (21941)Instructions burned: 1003 (million)
% 42.17/10.75  % (21941)------------------------------
% 42.17/10.75  % (21941)------------------------------
% 42.17/10.77  % (21949)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_21656 for (2945ds/644Mi)
% 42.69/10.80  % (21945)Instruction limit reached!
% 42.69/10.80  % (21945)------------------------------
% 42.69/10.80  % (21945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.69/10.80  % (21945)Termination reason: Unknown
% 42.69/10.80  % (21945)Termination phase: shuffling
% 42.69/10.80  
% 42.69/10.80  % (21945)Memory used [KB]: 24818
% 42.69/10.80  % (21945)Time elapsed: 0.190 s
% 42.69/10.80  % (21945)Instructions burned: 644 (million)
% 42.69/10.80  % (21945)------------------------------
% 42.69/10.80  % (21945)------------------------------
% 42.69/10.81  % (21943)Instruction limit reached!
% 42.69/10.81  % (21943)------------------------------
% 42.69/10.81  % (21943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.69/10.81  % (21943)Termination reason: Unknown
% 42.69/10.81  % (21943)Termination phase: shuffling
% 42.69/10.81  
% 42.69/10.81  % (21943)Memory used [KB]: 26993
% 42.69/10.81  % (21943)Time elapsed: 0.314 s
% 42.69/10.81  % (21943)Instructions burned: 954 (million)
% 42.69/10.81  % (21943)------------------------------
% 42.69/10.81  % (21943)------------------------------
% 42.69/10.82  % (21950)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_21656 for (2945ds/1201Mi)
% 42.69/10.82  % (21951)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_21656 for (2945ds/1046Mi)
% 43.21/10.90  % (21946)Instruction limit reached!
% 43.21/10.90  % (21946)------------------------------
% 43.21/10.90  % (21946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.21/10.90  % (21946)Termination reason: Unknown
% 43.21/10.90  % (21946)Termination phase: shuffling
% 43.21/10.90  
% 43.21/10.90  % (21946)Memory used [KB]: 25969
% 43.21/10.90  % (21946)Time elapsed: 0.286 s
% 43.21/10.90  % (21946)Instructions burned: 866 (million)
% 43.21/10.90  % (21946)------------------------------
% 43.21/10.90  % (21946)------------------------------
% 43.21/10.91  % (21952)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_21656 for (2944ds/222Mi)
% 43.21/10.98  % (21949)Instruction limit reached!
% 43.21/10.98  % (21949)------------------------------
% 43.21/10.98  % (21949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.21/10.98  % (21949)Termination reason: Unknown
% 43.21/10.98  % (21949)Termination phase: shuffling
% 43.21/10.98  
% 43.21/10.98  % (21949)Memory used [KB]: 23539
% 43.21/10.98  % (21949)Time elapsed: 0.214 s
% 43.21/10.98  % (21949)Instructions burned: 644 (million)
% 43.21/10.98  % (21949)------------------------------
% 43.21/10.98  % (21949)------------------------------
% 43.21/10.98  % (21952)Instruction limit reached!
% 43.21/10.98  % (21952)------------------------------
% 43.21/10.98  % (21952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.21/10.98  % (21952)Termination reason: Unknown
% 43.21/10.98  % (21952)Termination phase: shuffling
% 43.21/10.98  
% 43.21/10.98  % (21952)Memory used [KB]: 17142
% 43.21/10.98  % (21952)Time elapsed: 0.071 s
% 43.21/10.98  % (21952)Instructions burned: 224 (million)
% 43.21/10.98  % (21952)------------------------------
% 43.21/10.98  % (21952)------------------------------
% 43.21/10.99  % (21953)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_21656 for (2943ds/68Mi)
% 43.21/10.99  % (21954)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_21656 for (2943ds/454Mi)
% 43.21/11.02  % (21953)Instruction limit reached!
% 43.21/11.02  % (21953)------------------------------
% 43.21/11.02  % (21953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.21/11.02  % (21953)Termination reason: Unknown
% 43.21/11.02  % (21953)Termination phase: shuffling
% 43.21/11.02  
% 43.21/11.02  % (21953)Memory used [KB]: 14967
% 43.21/11.02  % (21953)Time elapsed: 0.032 s
% 43.21/11.02  % (21953)Instructions burned: 69 (million)
% 43.21/11.02  % (21953)------------------------------
% 43.21/11.02  % (21953)------------------------------
% 46.00/11.03  % (21955)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_21656 for (2943ds/360Mi)
% 46.00/11.09  % (21947)Instruction limit reached!
% 46.00/11.09  % (21947)------------------------------
% 46.00/11.09  % (21947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 46.00/11.09  % (21947)Termination reason: Unknown
% 46.00/11.09  % (21947)Termination phase: Property scanning
% 46.00/11.09  
% 46.00/11.09  % (21947)Memory used [KB]: 27760
% 46.00/11.09  % (21947)Time elapsed: 0.377 s
% 46.00/11.09  % (21947)Instructions burned: 1175 (million)
% 46.00/11.09  % (21947)------------------------------
% 46.00/11.09  % (21947)------------------------------
% 46.00/11.11  % (21956)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_21656 for (2942ds/157Mi)
% 46.00/11.13  % (21951)Instruction limit reached!
% 46.00/11.13  % (21951)------------------------------
% 46.00/11.13  % (21951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 46.00/11.13  % (21951)Termination reason: Unknown
% 46.00/11.13  % (21951)Termination phase: shuffling
% 46.00/11.13  
% 46.00/11.13  % (21951)Memory used [KB]: 33901
% 46.00/11.13  % (21951)Time elapsed: 0.306 s
% 46.00/11.13  % (21951)Instructions burned: 1049 (million)
% 46.00/11.13  % (21951)------------------------------
% 46.00/11.13  % (21951)------------------------------
% 46.32/11.13  % (21954)Instruction limit reached!
% 46.32/11.13  % (21954)------------------------------
% 46.32/11.13  % (21954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 46.32/11.13  % (21954)Termination reason: Unknown
% 46.32/11.13  % (21954)Termination phase: shuffling
% 46.32/11.13  
% 46.32/11.13  % (21954)Memory used [KB]: 22131
% 46.32/11.13  % (21954)Time elapsed: 0.137 s
% 46.32/11.13  % (21954)Instructions burned: 454 (million)
% 46.32/11.13  % (21954)------------------------------
% 46.32/11.13  % (21954)------------------------------
% 46.32/11.14  % (21957)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_21656 for (2942ds/5061Mi)
% 46.32/11.14  % (21958)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_21656 for (2942ds/2401Mi)
% 46.32/11.14  % (21955)Instruction limit reached!
% 46.32/11.14  % (21955)------------------------------
% 46.32/11.14  % (21955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 46.32/11.14  % (21955)Termination reason: Unknown
% 46.32/11.14  % (21955)Termination phase: shuffling
% 46.32/11.14  
% 46.32/11.14  % (21955)Memory used [KB]: 20852
% 46.32/11.14  % (21955)Time elapsed: 0.111 s
% 46.32/11.14  % (21955)Instructions burned: 361 (million)
% 46.32/11.14  % (21955)------------------------------
% 46.32/11.14  % (21955)------------------------------
% 46.32/11.15  % (21959)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_21656 for (2941ds/5798Mi)
% 46.32/11.16  % (21956)Instruction limit reached!
% 46.32/11.16  % (21956)------------------------------
% 46.32/11.16  % (21956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 46.32/11.16  % (21956)Termination reason: Unknown
% 46.32/11.16  % (21956)Termination phase: shuffling
% 46.32/11.16  
% 46.32/11.16  % (21956)Memory used [KB]: 16247
% 46.32/11.16  % (21956)Time elapsed: 0.054 s
% 46.32/11.16  % (21956)Instructions burned: 160 (million)
% 46.32/11.16  % (21956)------------------------------
% 46.32/11.16  % (21956)------------------------------
% 46.32/11.17  % (21960)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_21656 for (2941ds/346Mi)
% 47.05/11.20  % (21950)Instruction limit reached!
% 47.05/11.20  % (21950)------------------------------
% 47.05/11.20  % (21950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.05/11.20  % (21950)Termination reason: Unknown
% 47.05/11.20  % (21950)Termination phase: Property scanning
% 47.05/11.20  
% 47.05/11.20  % (21950)Memory used [KB]: 27760
% 47.05/11.20  % (21950)Time elapsed: 0.384 s
% 47.05/11.20  % (21950)Instructions burned: 1202 (million)
% 47.05/11.20  % (21950)------------------------------
% 47.05/11.20  % (21950)------------------------------
% 47.05/11.21  % (21961)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_21656 for (2941ds/1321Mi)
% 47.05/11.27  % (21960)Instruction limit reached!
% 47.05/11.27  % (21960)------------------------------
% 47.05/11.27  % (21960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.05/11.27  % (21960)Termination reason: Unknown
% 47.05/11.27  % (21960)Termination phase: shuffling
% 47.05/11.27  
% 47.05/11.27  % (21960)Memory used [KB]: 20852
% 47.05/11.27  % (21960)Time elapsed: 0.106 s
% 47.05/11.27  % (21960)Instructions burned: 347 (million)
% 47.05/11.27  % (21960)------------------------------
% 47.05/11.27  % (21960)------------------------------
% 47.05/11.29  % (21962)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_21656 for (2940ds/1312Mi)
% 47.99/11.62  % (21961)Instruction limit reached!
% 47.99/11.62  % (21961)------------------------------
% 47.99/11.62  % (21961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.99/11.62  % (21961)Termination reason: Unknown
% 47.99/11.62  % (21961)Termination phase: Property scanning
% 47.99/11.62  
% 47.99/11.62  % (21961)Memory used [KB]: 27888
% 47.99/11.62  % (21961)Time elapsed: 0.414 s
% 47.99/11.62  % (21961)Instructions burned: 1321 (million)
% 47.99/11.62  % (21961)------------------------------
% 47.99/11.62  % (21961)------------------------------
% 47.99/11.64  % (21963)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_21656 for (2937ds/672Mi)
% 47.99/11.66  % (21962)Instruction limit reached!
% 47.99/11.66  % (21962)------------------------------
% 47.99/11.66  % (21962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.99/11.66  % (21962)Termination reason: Unknown
% 47.99/11.66  % (21962)Termination phase: shuffling
% 47.99/11.66  
% 47.99/11.66  % (21962)Memory used [KB]: 37355
% 47.99/11.66  % (21962)Time elapsed: 0.378 s
% 47.99/11.66  % (21962)Instructions burned: 1313 (million)
% 47.99/11.66  % (21962)------------------------------
% 47.99/11.66  % (21962)------------------------------
% 47.99/11.68  % (21964)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_21656 for (2936ds/1897Mi)
% 48.99/11.75  % (21940)Instruction limit reached!
% 48.99/11.75  % (21940)------------------------------
% 48.99/11.75  % (21940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.99/11.75  % (21940)Termination reason: Unknown
% 48.99/11.75  % (21940)Termination phase: Saturation
% 48.99/11.75  
% 48.99/11.75  % (21940)Memory used [KB]: 39914
% 48.99/11.75  % (21940)Time elapsed: 1.339 s
% 48.99/11.75  % (21940)Instructions burned: 4528 (million)
% 48.99/11.75  % (21940)------------------------------
% 48.99/11.75  % (21940)------------------------------
% 48.99/11.76  % (21965)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_21656 for (2935ds/1202Mi)
% 49.15/11.86  % (21963)Instruction limit reached!
% 49.15/11.86  % (21963)------------------------------
% 49.15/11.86  % (21963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.15/11.86  % (21963)Termination reason: Unknown
% 49.15/11.86  % (21963)Termination phase: shuffling
% 49.15/11.86  
% 49.15/11.86  % (21963)Memory used [KB]: 21748
% 49.15/11.86  % (21963)Time elapsed: 0.225 s
% 49.15/11.86  % (21963)Instructions burned: 674 (million)
% 49.15/11.86  % (21963)------------------------------
% 49.15/11.86  % (21963)------------------------------
% 49.15/11.87  % (21966)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on DTF2THF_21656 for (2934ds/1493Mi)
% 49.15/11.88  % (21958)Instruction limit reached!
% 49.15/11.88  % (21958)------------------------------
% 49.15/11.88  % (21958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.15/11.88  % (21958)Termination reason: Unknown
% 49.15/11.88  % (21958)Termination phase: Property scanning
% 49.15/11.88  
% 49.15/11.88  % (21958)Memory used [KB]: 40041
% 49.15/11.88  % (21958)Time elapsed: 0.741 s
% 49.15/11.88  % (21958)Instructions burned: 2404 (million)
% 49.15/11.88  % (21958)------------------------------
% 49.15/11.88  % (21958)------------------------------
% 49.15/11.89  % (21967)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on DTF2THF_21656 for (2934ds/7679Mi)
% 53.02/12.05  % (21937)Instruction limit reached!
% 53.02/12.05  % (21937)------------------------------
% 53.02/12.05  % (21937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.02/12.05  % (21937)Termination reason: Unknown
% 53.02/12.05  % (21937)Termination phase: Saturation
% 53.02/12.05  
% 53.02/12.05  % (21937)Memory used [KB]: 40425
% 53.02/12.05  % (21937)Time elapsed: 1.831 s
% 53.02/12.05  % (21937)Instructions burned: 6454 (million)
% 53.02/12.05  % (21937)------------------------------
% 53.02/12.05  % (21937)------------------------------
% 53.02/12.06  % (21969)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on DTF2THF_21656 for (2932ds/340Mi)
% 53.71/12.15  % (21965)Instruction limit reached!
% 53.71/12.15  % (21965)------------------------------
% 53.71/12.15  % (21965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.71/12.15  % (21965)Termination reason: Unknown
% 53.71/12.15  % (21965)Termination phase: Property scanning
% 53.71/12.15  
% 53.71/12.15  % (21965)Memory used [KB]: 27760
% 53.71/12.15  % (21965)Time elapsed: 0.396 s
% 53.71/12.15  % (21965)Instructions burned: 1202 (million)
% 53.71/12.15  % (21965)------------------------------
% 53.71/12.15  % (21965)------------------------------
% 53.71/12.17  % (21970)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on DTF2THF_21656 for (2931ds/3672Mi)
% 53.71/12.18  % (21969)Instruction limit reached!
% 53.71/12.18  % (21969)------------------------------
% 53.71/12.18  % (21969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.71/12.18  % (21969)Termination reason: Unknown
% 53.71/12.18  % (21969)Termination phase: shuffling
% 53.71/12.18  
% 53.71/12.18  % (21969)Memory used [KB]: 18166
% 53.71/12.18  % (21969)Time elapsed: 0.118 s
% 53.71/12.18  % (21969)Instructions burned: 342 (million)
% 53.71/12.18  % (21969)------------------------------
% 53.71/12.18  % (21969)------------------------------
% 53.71/12.19  % (21971)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on DTF2THF_21656 for (2931ds/1535Mi)
% 54.24/12.26  % (21964)Instruction limit reached!
% 54.24/12.26  % (21964)------------------------------
% 54.24/12.26  % (21964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.24/12.26  % (21964)Termination reason: Unknown
% 54.24/12.26  % (21964)Termination phase: SInE selection
% 54.24/12.26  
% 54.24/12.26  % (21964)Memory used [KB]: 28016
% 54.24/12.26  % (21964)Time elapsed: 0.585 s
% 54.24/12.26  % (21964)Instructions burned: 1898 (million)
% 54.24/12.26  % (21964)------------------------------
% 54.24/12.26  % (21964)------------------------------
% 54.24/12.27  % (21972)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=4637:si=on:rtra=on_0 on DTF2THF_21656 for (2930ds/4637Mi)
% 54.66/12.30  % (21966)Instruction limit reached!
% 54.66/12.30  % (21966)------------------------------
% 54.66/12.30  % (21966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.66/12.30  % (21966)Termination reason: Unknown
% 54.66/12.30  % (21966)Termination phase: shuffling
% 54.66/12.30  
% 54.66/12.30  % (21966)Memory used [KB]: 39658
% 54.66/12.30  % (21966)Time elapsed: 0.433 s
% 54.66/12.30  % (21966)Instructions burned: 1494 (million)
% 54.66/12.30  % (21966)------------------------------
% 54.66/12.30  % (21966)------------------------------
% 54.66/12.32  % (21973)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_21656 for (2930ds/3174Mi)
% 55.00/12.48  % (21957)Instruction limit reached!
% 55.00/12.48  % (21957)------------------------------
% 55.00/12.48  % (21957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.00/12.48  % (21957)Termination reason: Unknown
% 55.00/12.48  % (21957)Termination phase: Function definition elimination
% 55.00/12.48  
% 55.00/12.48  % (21957)Memory used [KB]: 58080
% 55.00/12.48  % (21957)Time elapsed: 1.346 s
% 55.00/12.48  % (21957)Instructions burned: 5062 (million)
% 55.00/12.48  % (21957)------------------------------
% 55.00/12.48  % (21957)------------------------------
% 55.31/12.50  % (21974)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_21656 for (2928ds/307Mi)
% 55.31/12.59  % (21974)Instruction limit reached!
% 55.31/12.59  % (21974)------------------------------
% 55.31/12.59  % (21974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.31/12.59  % (21974)Termination reason: Unknown
% 55.31/12.59  % (21974)Termination phase: shuffling
% 55.31/12.59  
% 55.31/12.59  % (21974)Memory used [KB]: 20212
% 55.31/12.59  % (21974)Time elapsed: 0.096 s
% 55.31/12.59  % (21974)Instructions burned: 310 (million)
% 55.31/12.59  % (21974)------------------------------
% 55.31/12.59  % (21974)------------------------------
% 55.61/12.60  % (21975)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=3619:si=on:rtra=on_0 on DTF2THF_21656 for (2927ds/3619Mi)
% 55.61/12.64  % (21971)Instruction limit reached!
% 55.61/12.64  % (21971)------------------------------
% 55.61/12.64  % (21971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.61/12.64  % (21971)Termination reason: Unknown
% 55.61/12.64  % (21971)Termination phase: shuffling
% 55.61/12.64  
% 55.61/12.64  % (21971)Memory used [KB]: 40041
% 55.61/12.64  % (21971)Time elapsed: 0.447 s
% 55.61/12.64  % (21971)Instructions burned: 1536 (million)
% 55.61/12.64  % (21971)------------------------------
% 55.61/12.64  % (21971)------------------------------
% 55.61/12.65  % (21976)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_21656 for (2926ds/2325Mi)
% 56.28/12.72  % (21959)Instruction limit reached!
% 56.28/12.72  % (21959)------------------------------
% 56.28/12.72  % (21959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.28/12.72  % (21959)Termination reason: Unknown
% 56.28/12.72  % (21959)Termination phase: Property scanning
% 56.28/12.72  
% 56.28/12.72  % (21959)Memory used [KB]: 54881
% 56.28/12.72  % (21959)Time elapsed: 1.565 s
% 56.28/12.72  % (21959)Instructions burned: 5799 (million)
% 56.28/12.72  % (21959)------------------------------
% 56.28/12.72  % (21959)------------------------------
% 56.28/12.73  % (21977)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2341:si=on:rtra=on_0 on DTF2THF_21656 for (2926ds/2341Mi)
% 61.23/13.23  % (21973)Instruction limit reached!
% 61.23/13.23  % (21973)------------------------------
% 61.23/13.23  % (21973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 61.23/13.23  % (21973)Termination reason: Unknown
% 61.23/13.23  % (21973)Termination phase: Saturation
% 61.23/13.23  
% 61.23/13.23  % (21973)Memory used [KB]: 37611
% 61.23/13.23  % (21973)Time elapsed: 0.919 s
% 61.23/13.23  % (21973)Instructions burned: 3176 (million)
% 61.23/13.23  % (21973)------------------------------
% 61.23/13.23  % (21973)------------------------------
% 61.23/13.25  % (21970)Instruction limit reached!
% 61.23/13.25  % (21970)------------------------------
% 61.23/13.25  % (21970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 61.23/13.25  % (21970)Termination reason: Unknown
% 61.23/13.25  % (21970)Termination phase: Function definition elimination
% 61.23/13.25  
% 61.23/13.25  % (21970)Memory used [KB]: 38506
% 61.23/13.25  % (21970)Time elapsed: 1.080 s
% 61.23/13.25  % (21970)Instructions burned: 3674 (million)
% 61.23/13.25  % (21970)------------------------------
% 61.23/13.25  % (21970)------------------------------
% 61.23/13.25  % (21978)lrs+1010_1:16_apa=on:bsd=on:cnfonf=off:hud=10:sac=on:sos=on:ss=axioms:i=7257:si=on:rtra=on_0 on DTF2THF_21656 for (2921ds/7257Mi)
% 61.23/13.26  % (21980)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=3710:si=on:rtra=on_0 on DTF2THF_21656 for (2920ds/3710Mi)
% 61.86/13.36  % (21976)Instruction limit reached!
% 61.86/13.36  % (21976)------------------------------
% 61.86/13.36  % (21976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 61.86/13.36  % (21976)Termination reason: Unknown
% 61.86/13.36  % (21976)Termination phase: Preprocessing 3
% 61.86/13.36  
% 61.86/13.36  % (21976)Memory used [KB]: 37867
% 61.86/13.36  % (21976)Time elapsed: 0.712 s
% 61.86/13.36  % (21976)Instructions burned: 2325 (million)
% 61.86/13.36  % (21976)------------------------------
% 61.86/13.36  % (21976)------------------------------
% 61.86/13.37  % (21981)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=326:si=on:rtra=on_0 on DTF2THF_21656 for (2919ds/326Mi)
% 62.35/13.44  % (21977)Instruction limit reached!
% 62.35/13.44  % (21977)------------------------------
% 62.35/13.44  % (21977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.35/13.44  % (21977)Termination reason: Unknown
% 62.35/13.44  % (21977)Termination phase: SInE selection
% 62.35/13.44  
% 62.35/13.44  % (21977)Memory used [KB]: 28400
% 62.35/13.44  % (21977)Time elapsed: 0.708 s
% 62.35/13.44  % (21977)Instructions burned: 2343 (million)
% 62.35/13.44  % (21977)------------------------------
% 62.35/13.44  % (21977)------------------------------
% 62.35/13.45  % (21982)lrs+1010_1:64_au=on:c=on:e2e=on:flr=on:hfsq=on:hfsql=off:hfsqr=4,1:ins=1:ntd=on:sp=occurrence:i=1100:si=on:rtra=on_0 on DTF2THF_21656 for (2919ds/1100Mi)
% 62.35/13.48  % (21981)Instruction limit reached!
% 62.35/13.48  % (21981)------------------------------
% 62.35/13.48  % (21981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.35/13.48  % (21981)Termination reason: Unknown
% 62.35/13.48  % (21981)Termination phase: shuffling
% 62.35/13.48  
% 62.35/13.48  % (21981)Memory used [KB]: 18038
% 62.35/13.48  % (21981)Time elapsed: 0.112 s
% 62.35/13.48  % (21981)Instructions burned: 326 (million)
% 62.35/13.48  % (21981)------------------------------
% 62.35/13.48  % (21981)------------------------------
% 62.35/13.50  % (21983)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_21656 for (2918ds/406Mi)
% 63.12/13.63  % (21983)Instruction limit reached!
% 63.12/13.63  % (21983)------------------------------
% 63.12/13.63  % (21983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.12/13.63  % (21983)Termination reason: Unknown
% 63.12/13.63  % (21983)Termination phase: shuffling
% 63.12/13.63  
% 63.12/13.63  % (21983)Memory used [KB]: 18805
% 63.12/13.63  % (21983)Time elapsed: 0.136 s
% 63.12/13.63  % (21983)Instructions burned: 406 (million)
% 63.12/13.63  % (21983)------------------------------
% 63.12/13.63  % (21983)------------------------------
% 63.12/13.64  % (21984)dis+1010_1:1_aac=none:bd=preordered:e2e=on:fde=none:fe=axiom:nm=16:nwc=10.0:prag=on:i=1871:si=on:rtra=on_0 on DTF2THF_21656 for (2917ds/1871Mi)
% 63.12/13.66  % (21975)Instruction limit reached!
% 63.12/13.66  % (21975)------------------------------
% 63.12/13.66  % (21975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.12/13.66  % (21975)Termination reason: Unknown
% 63.12/13.66  % (21975)Termination phase: Property scanning
% 63.12/13.66  
% 63.12/13.66  % (21975)Memory used [KB]: 43879
% 63.12/13.66  % (21975)Time elapsed: 1.060 s
% 63.12/13.66  % (21975)Instructions burned: 3622 (million)
% 63.12/13.66  % (21975)------------------------------
% 63.12/13.66  % (21975)------------------------------
% 63.12/13.67  % (21972)Instruction limit reached!
% 63.12/13.67  % (21972)------------------------------
% 63.12/13.67  % (21972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.12/13.67  % (21972)Termination reason: Unknown
% 63.12/13.67  % (21972)Termination phase: Saturation
% 63.12/13.67  
% 63.12/13.67  % (21972)Memory used [KB]: 36971
% 63.12/13.67  % (21972)Time elapsed: 1.403 s
% 63.12/13.67  % (21972)Instructions burned: 4639 (million)
% 63.12/13.67  % (21972)------------------------------
% 63.12/13.67  % (21972)------------------------------
% 63.12/13.68  % (21985)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1194:si=on:rtra=on_0 on DTF2THF_21656 for (2916ds/1194Mi)
% 63.12/13.68  % (21986)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_21656 for (2916ds/474Mi)
% 63.63/13.81  % (21982)Instruction limit reached!
% 63.63/13.81  % (21982)------------------------------
% 63.63/13.81  % (21982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.63/13.81  % (21982)Termination reason: Unknown
% 63.63/13.81  % (21982)Termination phase: Property scanning
% 63.63/13.81  
% 63.63/13.81  % (21982)Memory used [KB]: 27888
% 63.63/13.81  % (21982)Time elapsed: 0.358 s
% 63.63/13.81  % (21982)Instructions burned: 1100 (million)
% 63.63/13.81  % (21982)------------------------------
% 63.63/13.81  % (21982)------------------------------
% 63.63/13.82  % (21987)dis+1010_1:1_au=on:cnfonf=lazy_gen:ins=3:plsq=on:plsqc=1:plsqr=15142123,262144:sp=reverse_arity:i=3115:si=on:rtra=on_0 on DTF2THF_21656 for (2915ds/3115Mi)
% 63.63/13.83  % (21986)Instruction limit reached!
% 63.63/13.83  % (21986)------------------------------
% 63.63/13.83  % (21986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.63/13.83  % (21986)Termination reason: Unknown
% 63.63/13.83  % (21986)Termination phase: shuffling
% 63.63/13.83  
% 63.63/13.83  % (21986)Memory used [KB]: 22515
% 63.63/13.83  % (21986)Time elapsed: 0.142 s
% 63.63/13.83  % (21986)Instructions burned: 475 (million)
% 63.63/13.83  % (21986)------------------------------
% 63.63/13.83  % (21986)------------------------------
% 63.63/13.84  % (21988)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_21656 for (2915ds/831Mi)
% 67.03/14.06  % (21985)Instruction limit reached!
% 67.03/14.06  % (21985)------------------------------
% 67.03/14.06  % (21985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 67.03/14.06  % (21985)Termination reason: Unknown
% 67.03/14.06  % (21985)Termination phase: Property scanning
% 67.03/14.06  
% 67.03/14.06  % (21985)Memory used [KB]: 27888
% 67.03/14.06  % (21985)Time elapsed: 0.382 s
% 67.03/14.06  % (21985)Instructions burned: 1195 (million)
% 67.03/14.06  % (21985)------------------------------
% 67.03/14.06  % (21985)------------------------------
% 67.03/14.07  % (21989)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_21656 for (2912ds/1188Mi)
% 67.03/14.11  % (21988)Instruction limit reached!
% 67.03/14.11  % (21988)------------------------------
% 67.03/14.11  % (21988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 67.03/14.11  % (21988)Termination reason: Unknown
% 67.03/14.11  % (21988)Termination phase: shuffling
% 67.03/14.11  
% 67.03/14.11  % (21988)Memory used [KB]: 25585
% 67.03/14.11  % (21988)Time elapsed: 0.273 s
% 67.03/14.11  % (21988)Instructions burned: 833 (million)
% 67.03/14.11  % (21988)------------------------------
% 67.03/14.11  % (21988)------------------------------
% 67.03/14.12  % (21990)ott+1010_1:20_cnfonf=lazy_pi_sigma_gen:fe=axiom:plsq=on:plsqc=2:plsqr=32,1:sac=on:sos=all:i=2868:si=on:rtra=on_0 on DTF2THF_21656 for (2912ds/2868Mi)
% 67.71/14.15  % (21967)Instruction limit reached!
% 67.71/14.15  % (21967)------------------------------
% 67.71/14.15  % (21967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 67.71/14.15  % (21967)Termination reason: Unknown
% 67.71/14.15  % (21967)Termination phase: Saturation
% 67.71/14.15  
% 67.71/14.15  % (21967)Memory used [KB]: 41577
% 67.71/14.15  % (21967)Time elapsed: 2.253 s
% 67.71/14.15  % (21967)Instructions burned: 7681 (million)
% 67.71/14.15  % (21967)------------------------------
% 67.71/14.15  % (21967)------------------------------
% 67.71/14.16  % (21991)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1516:si=on:rtra=on_0 on DTF2THF_21656 for (2912ds/1516Mi)
% 68.03/14.23  % (21984)Instruction limit reached!
% 68.03/14.23  % (21984)------------------------------
% 68.03/14.23  % (21984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 68.03/14.23  % (21984)Termination reason: Unknown
% 68.03/14.23  % (21984)Termination phase: Naming
% 68.03/14.23  
% 68.03/14.23  % (21984)Memory used [KB]: 33517
% 68.03/14.23  % (21984)Time elapsed: 0.595 s
% 68.03/14.23  % (21984)Instructions burned: 1872 (million)
% 68.03/14.23  % (21984)------------------------------
% 68.03/14.23  % (21984)------------------------------
% 68.03/14.25  % (21992)lrs+1002_1:20_afp=1000:au=on:bsd=on:cnfonf=lazy_not_gen_be_off:sos=all:sp=const_max:i=2321:si=on:rtra=on_0 on DTF2THF_21656 for (2911ds/2321Mi)
% 68.03/14.28  % (21980)Instruction limit reached!
% 68.03/14.28  % (21980)------------------------------
% 68.03/14.28  % (21980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 68.03/14.29  % (21980)Termination reason: Unknown
% 68.03/14.29  % (21980)Termination phase: Property scanning
% 68.03/14.29  
% 68.03/14.29  % (21980)Memory used [KB]: 44903
% 68.03/14.29  % (21980)Time elapsed: 1.028 s
% 68.03/14.29  % (21980)Instructions burned: 3713 (million)
% 68.03/14.29  % (21980)------------------------------
% 68.03/14.29  % (21980)------------------------------
% 68.37/14.30  % (21993)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_21656 for (2910ds/2812Mi)
% 68.58/14.41  % (21989)Instruction limit reached!
% 68.58/14.41  % (21989)------------------------------
% 68.58/14.41  % (21989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 68.58/14.41  % (21989)Termination reason: Unknown
% 68.58/14.41  % (21989)Termination phase: shuffling
% 68.58/14.41  
% 68.58/14.41  % (21989)Memory used [KB]: 35692
% 68.58/14.41  % (21989)Time elapsed: 0.346 s
% 68.58/14.41  % (21989)Instructions burned: 1188 (million)
% 68.58/14.41  % (21989)------------------------------
% 68.58/14.41  % (21989)------------------------------
% 68.58/14.43  % (21994)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_21656 for (2909ds/4604Mi)
% 69.33/14.63  % (21991)Instruction limit reached!
% 69.33/14.63  % (21991)------------------------------
% 69.33/14.63  % (21991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.33/14.63  % (21991)Termination reason: Unknown
% 69.33/14.63  % (21991)Termination phase: Property scanning
% 69.33/14.63  
% 69.33/14.63  % (21991)Memory used [KB]: 27888
% 69.33/14.63  % (21991)Time elapsed: 0.469 s
% 69.33/14.63  % (21991)Instructions burned: 1517 (million)
% 69.33/14.63  % (21991)------------------------------
% 69.33/14.63  % (21991)------------------------------
% 69.33/14.64  % (21996)ott+1002_1:4_c=on:chr=on:cnfonf=lazy_not_be_gen:hud=10:nm=10:piset=all_but_not_eq:rp=on:spb=goal:uhcvi=on:i=2678:si=on:rtra=on_0 on DTF2THF_21656 for (2907ds/2678Mi)
% 69.33/14.67  % (21987)Instruction limit reached!
% 69.33/14.67  % (21987)------------------------------
% 69.33/14.67  % (21987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.33/14.67  % (21987)Termination reason: Unknown
% 69.33/14.67  % (21987)Termination phase: Property scanning
% 69.33/14.67  
% 69.33/14.67  % (21987)Memory used [KB]: 44903
% 69.33/14.67  % (21987)Time elapsed: 0.854 s
% 69.33/14.67  % (21987)Instructions burned: 3117 (million)
% 69.33/14.67  % (21987)------------------------------
% 69.33/14.67  % (21987)------------------------------
% 69.33/14.69  % (21997)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_21656 for (2906ds/643Mi)
% 70.10/14.87  % (21997)Instruction limit reached!
% 70.10/14.87  % (21997)------------------------------
% 70.10/14.87  % (21997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.10/14.87  % (21997)Termination reason: Unknown
% 70.10/14.87  % (21997)Termination phase: shuffling
% 70.10/14.87  
% 70.10/14.87  % (21997)Memory used [KB]: 24818
% 70.10/14.87  % (21997)Time elapsed: 0.189 s
% 70.10/14.87  % (21997)Instructions burned: 645 (million)
% 70.10/14.87  % (21997)------------------------------
% 70.10/14.87  % (21997)------------------------------
% 70.10/14.89  % (21998)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=458:si=on:rtra=on_0 on DTF2THF_21656 for (2904ds/458Mi)
% 70.42/14.90  % (21992)Instruction limit reached!
% 70.42/14.90  % (21992)------------------------------
% 70.42/14.90  % (21992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.42/14.90  % (21992)Termination reason: Unknown
% 70.42/14.90  % (21992)Termination phase: Property scanning
% 70.42/14.90  
% 70.42/14.90  % (21992)Memory used [KB]: 43368
% 70.42/14.90  % (21992)Time elapsed: 0.651 s
% 70.42/14.90  % (21992)Instructions burned: 2323 (million)
% 70.42/14.90  % (21992)------------------------------
% 70.42/14.90  % (21992)------------------------------
% 70.42/14.90  % (21990)Instruction limit reached!
% 70.42/14.90  % (21990)------------------------------
% 70.42/14.90  % (21990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.42/14.90  % (21990)Termination reason: Unknown
% 70.42/14.90  % (21990)Termination phase: Property scanning
% 70.42/14.90  
% 70.42/14.90  % (21990)Memory used [KB]: 43368
% 70.42/14.90  % (21990)Time elapsed: 0.782 s
% 70.42/14.90  % (21990)Instructions burned: 2868 (million)
% 70.42/14.90  % (21990)------------------------------
% 70.42/14.90  % (21990)------------------------------
% 70.42/14.91  % (21999)lrs+1010_1:1_anc=all_dependent:apa=on:au=on:bd=off:c=on:cnfonf=off:ntd=on:i=2546:si=on:rtra=on_0 on DTF2THF_21656 for (2904ds/2546Mi)
% 70.42/14.91  % (22000)dis+21_1:1_acc=model:au=on:cnfonf=lazy_gen:ins=2:plsq=on:plsqc=1:plsqr=32,1:i=1432:si=on:rtra=on_0 on DTF2THF_21656 for (2904ds/1432Mi)
% 70.42/15.02  % (21998)Instruction limit reached!
% 70.42/15.02  % (21998)------------------------------
% 70.42/15.02  % (21998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.42/15.02  % (21998)Termination reason: Unknown
% 70.42/15.02  % (21998)Termination phase: shuffling
% 70.42/15.02  
% 70.42/15.02  % (21998)Memory used [KB]: 22259
% 70.42/15.02  % (21998)Time elapsed: 0.139 s
% 70.42/15.02  % (21998)Instructions burned: 459 (million)
% 70.42/15.02  % (21998)------------------------------
% 70.42/15.02  % (21998)------------------------------
% 73.90/15.04  % (22001)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=386:si=on:rtra=on_0 on DTF2THF_21656 for (2903ds/386Mi)
% 74.71/15.14  % (21993)Instruction limit reached!
% 74.71/15.14  % (21993)------------------------------
% 74.71/15.14  % (21993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 74.71/15.14  % (21993)Termination reason: Unknown
% 74.71/15.14  % (21993)Termination phase: Property scanning
% 74.71/15.14  
% 74.71/15.14  % (21993)Memory used [KB]: 40041
% 74.71/15.14  % (21993)Time elapsed: 0.843 s
% 74.71/15.14  % (21993)Instructions burned: 2812 (million)
% 74.71/15.14  % (21993)------------------------------
% 74.71/15.14  % (21993)------------------------------
% 74.71/15.15  % (22001)Instruction limit reached!
% 74.71/15.15  % (22001)------------------------------
% 74.71/15.15  % (22001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 74.71/15.15  % (22001)Termination reason: Unknown
% 74.71/15.15  % (22001)Termination phase: shuffling
% 74.71/15.15  
% 74.71/15.15  % (22001)Memory used [KB]: 21364
% 74.71/15.15  % (22001)Time elapsed: 0.118 s
% 74.71/15.15  % (22001)Instructions burned: 387 (million)
% 74.71/15.15  % (22001)------------------------------
% 74.71/15.15  % (22001)------------------------------
% 74.71/15.15  % (22002)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_21656 for (2901ds/360Mi)
% 74.71/15.16  % (22003)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=5446:si=on:rtra=on_0 on DTF2THF_21656 for (2901ds/5446Mi)
% 75.21/15.26  % (22002)Instruction limit reached!
% 75.21/15.26  % (22002)------------------------------
% 75.21/15.26  % (22002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 75.21/15.26  % (22002)Termination reason: Unknown
% 75.21/15.26  % (22002)Termination phase: shuffling
% 75.21/15.26  
% 75.21/15.26  % (22002)Memory used [KB]: 20980
% 75.21/15.26  % (22002)Time elapsed: 0.110 s
% 75.21/15.26  % (22002)Instructions burned: 360 (million)
% 75.21/15.26  % (22002)------------------------------
% 75.21/15.26  % (22002)------------------------------
% 75.21/15.27  % (22004)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=2573:si=on:rtra=on_0 on DTF2THF_21656 for (2900ds/2573Mi)
% 75.83/15.33  % (22000)Instruction limit reached!
% 75.83/15.33  % (22000)------------------------------
% 75.83/15.33  % (22000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 75.83/15.33  % (22000)Termination reason: Unknown
% 75.83/15.33  % (22000)Termination phase: shuffling
% 75.83/15.33  
% 75.83/15.33  % (22000)Memory used [KB]: 38762
% 75.83/15.33  % (22000)Time elapsed: 0.414 s
% 75.83/15.33  % (22000)Instructions burned: 1433 (million)
% 75.83/15.33  % (22000)------------------------------
% 75.83/15.33  % (22000)------------------------------
% 75.83/15.34  % (22005)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=2655:si=on:rtra=on_0 on DTF2THF_21656 for (2900ds/2655Mi)
% 75.83/15.38  % (21978)Refutation not found, incomplete strategy
% 75.83/15.38  % (21978)------------------------------
% 75.83/15.38  % (21978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 75.83/15.38  % (21978)Termination reason: Refutation not found, incomplete strategy
% 75.83/15.38  
% 75.83/15.38  
% 75.83/15.38  % (21978)Memory used [KB]: 73559
% 75.83/15.38  % (21978)Time elapsed: 2.138 s
% 75.83/15.38  % (21978)Instructions burned: 7184 (million)
% 75.83/15.38  % (21978)------------------------------
% 75.83/15.38  % (21978)------------------------------
% 76.27/15.40  % (22006)dis+1002_16:1_apa=on:au=on:av=off:cnfonf=off:e2e=on:nm=0:nwc=10.0:i=2781:si=on:rtra=on_0 on DTF2THF_21656 for (2899ds/2781Mi)
% 76.27/15.43  % (21996)Instruction limit reached!
% 76.27/15.43  % (21996)------------------------------
% 76.27/15.43  % (21996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.27/15.43  % (21996)Termination reason: Unknown
% 76.27/15.43  % (21996)Termination phase: Property scanning
% 76.27/15.43  
% 76.27/15.43  % (21996)Memory used [KB]: 43240
% 76.27/15.43  % (21996)Time elapsed: 0.794 s
% 76.27/15.43  % (21996)Instructions burned: 2680 (million)
% 76.27/15.43  % (21996)------------------------------
% 76.27/15.43  % (21996)------------------------------
% 76.27/15.44  % (22007)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_21656 for (2899ds/307Mi)
% 76.52/15.54  % (22007)Instruction limit reached!
% 76.52/15.54  % (22007)------------------------------
% 76.52/15.54  % (22007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.52/15.54  % (22007)Termination reason: Unknown
% 76.52/15.54  % (22007)Termination phase: shuffling
% 76.52/15.54  
% 76.52/15.54  % (22007)Memory used [KB]: 20212
% 76.52/15.54  % (22007)Time elapsed: 0.096 s
% 76.52/15.54  % (22007)Instructions burned: 310 (million)
% 76.52/15.54  % (22007)------------------------------
% 76.52/15.54  % (22007)------------------------------
% 76.52/15.55  % (22008)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=1548:si=on:rtra=on_0 on DTF2THF_21656 for (2898ds/1548Mi)
% 77.04/15.70  % (21999)Instruction limit reached!
% 77.04/15.70  % (21999)------------------------------
% 77.04/15.70  % (21999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.04/15.70  % (21999)Termination reason: Unknown
% 77.04/15.70  % (21999)Termination phase: Preprocessing 3
% 77.04/15.70  
% 77.04/15.70  % (21999)Memory used [KB]: 39402
% 77.04/15.70  % (21999)Time elapsed: 0.788 s
% 77.04/15.70  % (21999)Instructions burned: 2548 (million)
% 77.04/15.70  % (21999)------------------------------
% 77.04/15.70  % (21999)------------------------------
% 77.04/15.71  % (22009)lrs+10_1:3_alpa=true:hud=3:ins=1:ntd=on:plsq=on:plsqc=1:plsqr=32,1:prag=on:s2a=on:s2agt=10:i=5214:si=on:rtra=on_0 on DTF2THF_21656 for (2896ds/5214Mi)
% 77.14/15.83  % (21994)Instruction limit reached!
% 77.14/15.83  % (21994)------------------------------
% 77.14/15.83  % (21994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.14/15.83  % (21994)Termination reason: Unknown
% 77.14/15.83  % (21994)Termination phase: Saturation
% 77.14/15.83  
% 77.14/15.83  % (21994)Memory used [KB]: 36204
% 77.14/15.83  % (21994)Time elapsed: 1.428 s
% 77.14/15.83  % (21994)Instructions burned: 4607 (million)
% 77.14/15.83  % (21994)------------------------------
% 77.14/15.83  % (21994)------------------------------
% 77.14/15.84  % (22011)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_21656 for (2895ds/3201Mi)
% 77.19/15.98  % (22004)Instruction limit reached!
% 77.19/15.98  % (22004)------------------------------
% 77.19/15.98  % (22004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.19/15.98  % (22004)Termination reason: Unknown
% 77.19/15.98  % (22004)Termination phase: Property scanning
% 77.19/15.98  
% 77.19/15.98  % (22004)Memory used [KB]: 43368
% 77.19/15.98  % (22004)Time elapsed: 0.711 s
% 77.19/15.98  % (22004)Instructions burned: 2575 (million)
% 77.19/15.98  % (22004)------------------------------
% 77.19/15.98  % (22004)------------------------------
% 77.19/16.00  % (22012)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_21656 for (2893ds/454Mi)
% 81.09/16.03  % (22008)Instruction limit reached!
% 81.09/16.03  % (22008)------------------------------
% 81.09/16.03  % (22008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 81.09/16.03  % (22008)Termination reason: Unknown
% 81.09/16.03  % (22008)Termination phase: Property scanning
% 81.09/16.03  
% 81.09/16.03  % (22008)Memory used [KB]: 27760
% 81.09/16.03  % (22008)Time elapsed: 0.481 s
% 81.09/16.03  % (22008)Instructions burned: 1549 (million)
% 81.09/16.03  % (22008)------------------------------
% 81.09/16.03  % (22008)------------------------------
% 81.09/16.04  % (22013)lrs+1002_1:32_au=on:ins=2:nm=16:ntd=on:piset=all_but_not_eq:sp=occurrence:i=3049:si=on:rtra=on_0 on DTF2THF_21656 for (2893ds/3049Mi)
% 81.09/16.07  % (22005)Instruction limit reached!
% 81.09/16.07  % (22005)------------------------------
% 81.09/16.07  % (22005)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 81.09/16.07  % (22005)Termination reason: Unknown
% 81.09/16.07  % (22005)Termination phase: Property scanning
% 81.09/16.07  
% 81.09/16.07  % (22005)Memory used [KB]: 43368
% 81.09/16.07  % (22005)Time elapsed: 0.729 s
% 81.09/16.07  % (22005)Instructions burned: 2657 (million)
% 81.09/16.07  % (22005)------------------------------
% 81.09/16.07  % (22005)------------------------------
% 81.09/16.08  % (22014)lrs+1010_1:1_bd=preordered:cnfonf=off:e2e=on:kws=inv_precedence:lwlo=on:sd=2:ss=axioms:i=7311:si=on:rtra=on_0 on DTF2THF_21656 for (2892ds/7311Mi)
% 81.68/16.13  % (22012)Instruction limit reached!
% 81.68/16.13  % (22012)------------------------------
% 81.68/16.13  % (22012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 81.68/16.13  % (22012)Termination reason: Unknown
% 81.68/16.13  % (22012)Termination phase: shuffling
% 81.68/16.13  
% 81.68/16.13  % (22012)Memory used [KB]: 22259
% 81.68/16.13  % (22012)Time elapsed: 0.138 s
% 81.68/16.13  % (22012)Instructions burned: 454 (million)
% 81.68/16.13  % (22012)------------------------------
% 81.68/16.13  % (22012)------------------------------
% 81.68/16.15  % (22015)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=6804:si=on:rtra=on_0 on DTF2THF_21656 for (2891ds/6804Mi)
% 81.96/16.29  % (22006)Instruction limit reached!
% 81.96/16.29  % (22006)------------------------------
% 81.96/16.29  % (22006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 81.96/16.29  % (22006)Termination reason: Unknown
% 81.96/16.29  % (22006)Termination phase: Clausification
% 81.96/16.29  
% 81.96/16.29  % (22006)Memory used [KB]: 152875
% 81.96/16.29  % (22006)Time elapsed: 0.893 s
% 81.96/16.29  % (22006)Instructions burned: 2782 (million)
% 81.96/16.29  % (22006)------------------------------
% 81.96/16.29  % (22006)------------------------------
% 81.46/16.31  % (22016)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on DTF2THF_21656 for (2890ds/1683Mi)
% 83.28/16.64  % (22003)Instruction limit reached!
% 83.28/16.64  % (22003)------------------------------
% 83.28/16.64  % (22003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 83.28/16.64  % (22003)Termination reason: Unknown
% 83.28/16.64  % (22003)Termination phase: Function definition elimination
% 83.28/16.64  
% 83.28/16.64  % (22003)Memory used [KB]: 49380
% 83.28/16.64  % (22003)Time elapsed: 1.480 s
% 83.28/16.64  % (22003)Instructions burned: 5448 (million)
% 83.28/16.64  % (22003)------------------------------
% 83.28/16.64  % (22003)------------------------------
% 83.28/16.66  % (22017)lrs+10_8:1_au=on:av=off:bd=off:cs=on:e2e=on:hfsq=on:hfsqc=50:hfsql=off:nm=0:i=4688:si=on:rtra=on_0 on DTF2THF_21656 for (2886ds/4688Mi)
% 83.76/16.80  % (22011)Instruction limit reached!
% 83.76/16.80  % (22011)------------------------------
% 83.76/16.80  % (22011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 83.76/16.80  % (22011)Termination reason: Unknown
% 83.76/16.80  % (22011)Termination phase: Property scanning
% 83.76/16.80  
% 83.76/16.80  % (22011)Memory used [KB]: 40169
% 83.76/16.80  % (22011)Time elapsed: 0.957 s
% 83.76/16.80  % (22011)Instructions burned: 3201 (million)
% 83.76/16.80  % (22011)------------------------------
% 83.76/16.80  % (22011)------------------------------
% 83.76/16.81  % (22018)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on DTF2THF_21656 for (2885ds/2207Mi)
% 83.76/16.82  % (22016)Instruction limit reached!
% 83.76/16.82  % (22016)------------------------------
% 83.76/16.82  % (22016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 83.76/16.82  % (22016)Termination reason: Unknown
% 83.76/16.82  % (22016)Termination phase: Property scanning
% 83.76/16.82  
% 83.76/16.82  % (22016)Memory used [KB]: 27760
% 83.76/16.82  % (22016)Time elapsed: 0.511 s
% 83.76/16.82  % (22016)Instructions burned: 1684 (million)
% 83.76/16.82  % (22016)------------------------------
% 83.76/16.82  % (22016)------------------------------
% 83.76/16.84  % (22019)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=8216:si=on:rtra=on_0 on DTF2THF_21656 for (2885ds/8216Mi)
% 84.38/16.95  % (22013)Instruction limit reached!
% 84.38/16.95  % (22013)------------------------------
% 84.38/16.95  % (22013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 84.38/16.95  % (22013)Termination reason: Unknown
% 84.38/16.95  % (22013)Termination phase: Property scanning
% 84.38/16.95  
% 84.38/16.95  % (22013)Memory used [KB]: 39914
% 84.38/16.95  % (22013)Time elapsed: 0.904 s
% 84.38/16.95  % (22013)Instructions burned: 3049 (million)
% 84.38/16.95  % (22013)------------------------------
% 84.38/16.95  % (22013)------------------------------
% 84.38/16.96  % (22020)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=430:si=on:rtra=on_0 on DTF2THF_21656 for (2883ds/430Mi)
% 87.97/17.10  % (22020)Instruction limit reached!
% 87.97/17.10  % (22020)------------------------------
% 87.97/17.10  % (22020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 87.97/17.10  % (22020)Termination reason: Unknown
% 87.97/17.10  % (22020)Termination phase: shuffling
% 87.97/17.10  
% 87.97/17.10  % (22020)Memory used [KB]: 22003
% 87.97/17.10  % (22020)Time elapsed: 0.133 s
% 87.97/17.10  % (22020)Instructions burned: 432 (million)
% 87.97/17.10  % (22020)------------------------------
% 87.97/17.10  % (22020)------------------------------
% 87.97/17.12  % (22022)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=2012:si=on:rtra=on_0 on DTF2THF_21656 for (2882ds/2012Mi)
% 88.69/17.18  % (22009)Instruction limit reached!
% 88.69/17.18  % (22009)------------------------------
% 88.69/17.18  % (22009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 88.69/17.18  % (22009)Termination reason: Unknown
% 88.69/17.18  % (22009)Termination phase: Property scanning
% 88.69/17.18  
% 88.69/17.18  % (22009)Memory used [KB]: 63069
% 88.69/17.18  % (22009)Time elapsed: 1.471 s
% 88.69/17.18  % (22009)Instructions burned: 5216 (million)
% 88.69/17.18  % (22009)------------------------------
% 88.69/17.18  % (22009)------------------------------
% 88.69/17.20  % (22023)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=631:si=on:rtra=on_0 on DTF2THF_21656 for (2881ds/631Mi)
% 90.19/17.41  % (22023)Instruction limit reached!
% 90.19/17.41  % (22023)------------------------------
% 90.19/17.41  % (22023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 90.19/17.41  % (22023)Termination reason: Unknown
% 90.19/17.41  % (22023)Termination phase: shuffling
% 90.19/17.41  
% 90.19/17.41  % (22023)Memory used [KB]: 23539
% 90.19/17.41  % (22023)Time elapsed: 0.213 s
% 90.19/17.41  % (22023)Instructions burned: 633 (million)
% 90.19/17.41  % (22023)------------------------------
% 90.19/17.41  % (22023)------------------------------
% 90.19/17.42  % (22024)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=8785:si=on:rtra=on_0 on DTF2THF_21656 for (2879ds/8785Mi)
% 90.19/17.49  % (22018)Instruction limit reached!
% 90.19/17.49  % (22018)------------------------------
% 90.19/17.49  % (22018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 90.19/17.49  % (22018)Termination reason: Unknown
% 90.19/17.49  % (22018)Termination phase: Preprocessing 3
% 90.19/17.49  
% 90.19/17.49  % (22018)Memory used [KB]: 36459
% 90.19/17.49  % (22018)Time elapsed: 0.685 s
% 90.19/17.49  % (22018)Instructions burned: 2208 (million)
% 90.19/17.49  % (22018)------------------------------
% 90.19/17.49  % (22018)------------------------------
% 90.23/17.51  % (22025)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=739:si=on:rtra=on_0 on DTF2THF_21656 for (2878ds/739Mi)
% 91.32/17.69  % (22022)Instruction limit reached!
% 91.32/17.69  % (22022)------------------------------
% 91.32/17.69  % (22022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 91.32/17.69  % (22022)Termination reason: Unknown
% 91.32/17.69  % (22022)Termination phase: Property scanning
% 91.32/17.69  
% 91.32/17.69  % (22022)Memory used [KB]: 43368
% 91.32/17.69  % (22022)Time elapsed: 0.580 s
% 91.32/17.69  % (22022)Instructions burned: 2014 (million)
% 91.32/17.69  % (22022)------------------------------
% 91.32/17.69  % (22022)------------------------------
% 91.72/17.71  % (22026)dis+1002_1:1024_fe=off:hud=5:prag=on:i=5473:si=on:rtra=on_0 on DTF2THF_21656 for (2876ds/5473Mi)
% 91.72/17.76  % (22025)Instruction limit reached!
% 91.72/17.76  % (22025)------------------------------
% 91.72/17.76  % (22025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 91.72/17.76  % (22025)Termination reason: Unknown
% 91.72/17.76  % (22025)Termination phase: shuffling
% 91.72/17.76  
% 91.72/17.76  % (22025)Memory used [KB]: 24946
% 91.72/17.76  % (22025)Time elapsed: 0.252 s
% 91.72/17.76  % (22025)Instructions burned: 739 (million)
% 91.72/17.76  % (22025)------------------------------
% 91.72/17.76  % (22025)------------------------------
% 91.72/17.77  % (22027)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=43570:si=on:rtra=on_0 on DTF2THF_21656 for (2875ds/43570Mi)
% 95.06/18.06  % (22017)Instruction limit reached!
% 95.06/18.06  % (22017)------------------------------
% 95.06/18.06  % (22017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 95.06/18.06  % (22017)Termination reason: Unknown
% 95.06/18.06  % (22017)Termination phase: Property scanning
% 95.06/18.06  
% 95.06/18.06  % (22017)Memory used [KB]: 303705
% 95.06/18.06  % (22017)Time elapsed: 1.409 s
% 95.06/18.06  % (22017)Instructions burned: 4688 (million)
% 95.06/18.06  % (22017)------------------------------
% 95.06/18.06  % (22017)------------------------------
% 95.06/18.09  % (22028)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=8382:si=on:rtra=on_0 on DTF2THF_21656 for (2872ds/8382Mi)
% 96.17/18.20  % (22015)Instruction limit reached!
% 96.17/18.20  % (22015)------------------------------
% 96.17/18.20  % (22015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 96.17/18.20  % (22015)Termination reason: Unknown
% 96.17/18.20  % (22015)Termination phase: Saturation
% 96.17/18.20  
% 96.17/18.20  % (22015)Memory used [KB]: 75990
% 96.17/18.20  % (22015)Time elapsed: 2.057 s
% 96.17/18.20  % (22015)Instructions burned: 6804 (million)
% 96.17/18.20  % (22015)------------------------------
% 96.17/18.20  % (22015)------------------------------
% 96.17/18.22  % (22029)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=407:si=on:rtra=on_0 on DTF2THF_21656 for (2871ds/407Mi)
% 96.17/18.29  % (22014)Instruction limit reached!
% 96.17/18.29  % (22014)------------------------------
% 96.17/18.29  % (22014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 96.17/18.29  % (22014)Termination reason: Unknown
% 96.17/18.29  % (22014)Termination phase: Saturation
% 96.17/18.29  
% 96.17/18.29  % (22014)Memory used [KB]: 44263
% 96.17/18.29  % (22014)Time elapsed: 2.207 s
% 96.17/18.29  % (22014)Instructions burned: 7312 (million)
% 96.17/18.29  % (22014)------------------------------
% 96.17/18.29  % (22014)------------------------------
% 96.70/18.30  % (22031)lrs+10_1:50_cbe=off:cnfonf=lazy_pi_sigma_gen:fe=off:hud=5:plsq=on:plsqr=1,32:sos=all:i=2971:si=on:rtra=on_0 on DTF2THF_21656 for (2870ds/2971Mi)
% 96.70/18.35  % (22029)Instruction limit reached!
% 96.70/18.35  % (22029)------------------------------
% 96.70/18.35  % (22029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 96.70/18.35  % (22029)Termination reason: Unknown
% 96.70/18.35  % (22029)Termination phase: shuffling
% 96.70/18.35  
% 96.70/18.35  % (22029)Memory used [KB]: 18805
% 96.70/18.35  % (22029)Time elapsed: 0.138 s
% 96.70/18.35  % (22029)Instructions burned: 409 (million)
% 96.70/18.35  % (22029)------------------------------
% 96.70/18.35  % (22029)------------------------------
% 96.70/18.37  % (22032)lrs+1002_1:1_aac=none:bd=off:e2e=on:fde=none:fe=off:piset=or:prag=on:rawr=on:sos=on:updr=off:i=9822:si=on:rtra=on_0 on DTF2THF_21656 for (2869ds/9822Mi)
% 98.47/18.78  % (22027)Refutation not found, incomplete strategy
% 98.47/18.78  % (22027)------------------------------
% 98.47/18.78  % (22027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 98.47/18.78  % (22027)Termination reason: Refutation not found, incomplete strategy
% 98.47/18.78  
% 98.47/18.78  
% 98.47/18.78  % (22027)Memory used [KB]: 42472
% 98.47/18.78  % (22027)Time elapsed: 1.010 s
% 98.47/18.78  % (22027)Instructions burned: 3311 (million)
% 98.47/18.78  % (22027)------------------------------
% 98.47/18.78  % (22027)------------------------------
% 98.47/18.80  % (22033)dis+10_5:1_av=off:ntd=on:s2a=on:s2at=3.0:sgt=16:sp=unary_frequency:ss=axioms:i=8425:si=on:rtra=on_0 on DTF2THF_21656 for (2865ds/8425Mi)
% 102.08/19.03  % (22019)Instruction limit reached!
% 102.08/19.03  % (22019)------------------------------
% 102.08/19.03  % (22019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 102.08/19.03  % (22019)Termination reason: Unknown
% 102.08/19.03  % (22019)Termination phase: Saturation
% 102.08/19.03  
% 102.08/19.03  % (22019)Memory used [KB]: 63964
% 102.08/19.03  % (22019)Time elapsed: 2.197 s
% 102.08/19.03  % (22019)Instructions burned: 8218 (million)
% 102.08/19.03  % (22019)------------------------------
% 102.08/19.03  % (22019)------------------------------
% 102.08/19.05  % (22034)lrs+30_1:1_aac=none:au=on:cbe=off:cs=on:nm=2:rawr=on:sos=on:i=3107:si=on:rtra=on_0 on DTF2THF_21656 for (2863ds/3107Mi)
% 102.08/19.12  % (22031)Instruction limit reached!
% 102.08/19.12  % (22031)------------------------------
% 102.08/19.12  % (22031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 102.08/19.12  % (22031)Termination reason: Unknown
% 102.08/19.12  % (22031)Termination phase: Preprocessing 2
% 102.08/19.12  
% 102.08/19.12  % (22031)Memory used [KB]: 43624
% 102.08/19.12  % (22031)Time elapsed: 0.819 s
% 102.08/19.12  % (22031)Instructions burned: 2971 (million)
% 102.08/19.12  % (22031)------------------------------
% 102.08/19.12  % (22031)------------------------------
% 102.75/19.13  % (22035)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=7967:si=on:rtra=on_0 on DTF2THF_21656 for (2862ds/7967Mi)
% 103.08/19.23  % (22026)Instruction limit reached!
% 103.08/19.23  % (22026)------------------------------
% 103.08/19.23  % (22026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 103.08/19.23  % (22026)Termination reason: Unknown
% 103.08/19.23  % (22026)Termination phase: Property scanning
% 103.08/19.23  
% 103.08/19.23  % (22026)Memory used [KB]: 50148
% 103.08/19.23  % (22026)Time elapsed: 1.520 s
% 103.08/19.23  % (22026)Instructions burned: 5476 (million)
% 103.08/19.23  % (22026)------------------------------
% 103.08/19.23  % (22026)------------------------------
% 103.08/19.24  % (22036)lrs+1010_10:959_abs=on:acc=on:bd=off:ccuc=small_ones:cha=on:cnfonf=lazy_simp:fd=preordered:fe=off:hud=3:ile=on:kws=inv_frequency:nm=2:piset=and:sd=5:sp=frequency:spb=goal_then_units:ss=axioms:st=4.5:i=3629:si=on:rtra=on_0 on DTF2THF_21656 for (2861ds/3629Mi)
% 104.72/19.67  % (22024)Instruction limit reached!
% 104.72/19.67  % (22024)------------------------------
% 104.72/19.67  % (22024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 104.72/19.67  % (22024)Termination reason: Unknown
% 104.72/19.67  % (22024)Termination phase: Property scanning
% 104.72/19.67  
% 104.72/19.67  % (22024)Memory used [KB]: 55777
% 104.72/19.67  % (22024)Time elapsed: 2.253 s
% 104.72/19.67  % (22024)Instructions burned: 8787 (million)
% 104.72/19.67  % (22024)------------------------------
% 104.72/19.67  % (22024)------------------------------
% 104.72/19.68  % (22038)lrs+1010_1:1024_au=on:fe=axiom:lwlo=on:nm=0:ntd=on:nwc=10.0:spb=non_intro:uhcvi=on:i=939:si=on:rtra=on_0 on DTF2THF_21656 for (2856ds/939Mi)
% 105.71/19.97  % (22034)Instruction limit reached!
% 105.71/19.97  % (22034)------------------------------
% 105.71/19.97  % (22034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 105.71/19.97  % (22034)Termination reason: Unknown
% 105.71/19.97  % (22034)Termination phase: Property scanning
% 105.71/19.97  
% 105.71/19.97  % (22034)Memory used [KB]: 45542
% 105.71/19.97  % (22034)Time elapsed: 0.922 s
% 105.71/19.97  % (22034)Instructions burned: 3107 (million)
% 105.71/19.97  % (22034)------------------------------
% 105.71/19.97  % (22034)------------------------------
% 105.71/19.98  % (22039)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_21656 for (2853ds/1188Mi)
% 105.71/19.99  % (22038)Instruction limit reached!
% 105.71/19.99  % (22038)------------------------------
% 105.71/19.99  % (22038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 105.71/19.99  % (22038)Termination reason: Unknown
% 105.71/19.99  % (22038)Termination phase: shuffling
% 105.71/19.99  
% 105.71/19.99  % (22038)Memory used [KB]: 26737
% 105.71/19.99  % (22038)Time elapsed: 0.308 s
% 105.71/19.99  % (22038)Instructions burned: 941 (million)
% 105.71/19.99  % (22038)------------------------------
% 105.71/19.99  % (22038)------------------------------
% 105.71/20.00  % (22040)dis+21_3:2_avsq=on:cbe=off:e2e=on:flr=on:ile=on:nwc=5.0:piset=or:rawr=on:sp=occurrence:i=3205:si=on:rtra=on_0 on DTF2THF_21656 for (2853ds/3205Mi)
% 110.32/20.24  % (22036)Instruction limit reached!
% 110.32/20.24  % (22036)------------------------------
% 110.32/20.24  % (22036)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 110.32/20.24  % (22036)Termination reason: Unknown
% 110.32/20.24  % (22036)Termination phase: SInE selection
% 110.32/20.24  
% 110.32/20.24  % (22036)Memory used [KB]: 44263
% 110.32/20.24  % (22036)Time elapsed: 1.004 s
% 110.32/20.24  % (22036)Instructions burned: 3630 (million)
% 110.32/20.24  % (22036)------------------------------
% 110.32/20.24  % (22036)------------------------------
% 110.32/20.26  % (22041)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_21656 for (2851ds/865Mi)
% 110.97/20.32  % (22039)Instruction limit reached!
% 110.97/20.32  % (22039)------------------------------
% 110.97/20.32  % (22039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 110.97/20.32  % (22039)Termination reason: Unknown
% 110.97/20.32  % (22039)Termination phase: shuffling
% 110.97/20.32  
% 110.97/20.32  % (22039)Memory used [KB]: 35692
% 110.97/20.32  % (22039)Time elapsed: 0.345 s
% 110.97/20.32  % (22039)Instructions burned: 1190 (million)
% 110.97/20.32  % (22039)------------------------------
% 110.97/20.32  % (22039)------------------------------
% 110.97/20.34  % (22042)ott+1002_1:1_au=on:bd=off:cbe=off:cha=on:cnfonf=lazy_pi_sigma_gen:fd=off:fe=off:ntd=on:sp=const_frequency:i=7469:si=on:rtra=on_0 on DTF2THF_21656 for (2850ds/7469Mi)
% 110.97/20.35  % (22028)Instruction limit reached!
% 110.97/20.35  % (22028)------------------------------
% 110.97/20.35  % (22028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 110.97/20.35  % (22028)Termination reason: Unknown
% 110.97/20.35  % (22028)Termination phase: Property scanning
% 110.97/20.35  
% 110.97/20.35  % (22028)Memory used [KB]: 298715
% 110.97/20.35  % (22028)Time elapsed: 2.258 s
% 110.97/20.35  % (22028)Instructions burned: 8385 (million)
% 110.97/20.35  % (22028)------------------------------
% 110.97/20.35  % (22028)------------------------------
% 110.97/20.38  % (22043)dis+10_1:10_bd=preordered:e2e=on:fde=none:fe=axiom:hud=3:kws=precedence:nwc=3.0:prag=on:sp=const_max:tgt=full:i=4165:si=on:rtra=on_0 on DTF2THF_21656 for (2849ds/4165Mi)
% 111.89/20.54  % (22041)Instruction limit reached!
% 111.89/20.54  % (22041)------------------------------
% 111.89/20.54  % (22041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 111.89/20.54  % (22041)Termination reason: Unknown
% 111.89/20.54  % (22041)Termination phase: shuffling
% 111.89/20.54  
% 111.89/20.54  % (22041)Memory used [KB]: 26225
% 111.89/20.54  % (22041)Time elapsed: 0.289 s
% 111.89/20.54  % (22041)Instructions burned: 867 (million)
% 111.89/20.54  % (22041)------------------------------
% 111.89/20.54  % (22041)------------------------------
% 111.89/20.56  % (22044)dis+1010_1:1_au=on:avsq=on:cnfonf=lazy_simp:fsr=off:ntd=on:nwc=10.0:sp=reverse_frequency:ss=axioms:st=1.5:i=13468:si=on:rtra=on_0 on DTF2THF_21656 for (2847ds/13468Mi)
% 113.82/20.96  % (22040)Instruction limit reached!
% 113.82/20.96  % (22040)------------------------------
% 113.82/20.96  % (22040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 113.82/20.96  % (22040)Termination reason: Unknown
% 113.82/20.96  % (22040)Termination phase: Property scanning
% 113.82/20.96  
% 113.82/20.96  % (22040)Memory used [KB]: 42984
% 113.82/20.96  % (22040)Time elapsed: 0.955 s
% 113.82/20.96  % (22040)Instructions burned: 3209 (million)
% 113.82/20.96  % (22040)------------------------------
% 113.82/20.96  % (22040)------------------------------
% 113.82/20.97  % (22046)dis+1002_1:1_au=on:bsr=unit_only:cbe=off:fe=off:fsr=off:nm=10:nwc=6.0:plsq=on:plsqc=1:plsqr=32,1:sos=all:i=2635:si=on:rtra=on_0 on DTF2THF_21656 for (2843ds/2635Mi)
% 116.85/21.13  % (22035)Instruction limit reached!
% 116.85/21.13  % (22035)------------------------------
% 116.85/21.13  % (22035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 116.85/21.13  % (22035)Termination reason: Unknown
% 116.85/21.13  % (22035)Termination phase: Property scanning
% 116.85/21.13  
% 116.85/21.13  % (22035)Memory used [KB]: 61790
% 116.85/21.13  % (22035)Time elapsed: 2.003 s
% 116.85/21.13  % (22035)Instructions burned: 7968 (million)
% 116.85/21.13  % (22035)------------------------------
% 116.85/21.13  % (22035)------------------------------
% 116.85/21.15  % (22047)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=631:si=on:rtra=on_0 on DTF2THF_21656 for (2841ds/631Mi)
% 117.27/21.26  % (22033)Instruction limit reached!
% 117.27/21.26  % (22033)------------------------------
% 117.27/21.26  % (22033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 117.27/21.26  % (22033)Termination reason: Unknown
% 117.27/21.26  % (22033)Termination phase: Saturation
% 117.27/21.26  
% 117.27/21.26  % (22033)Memory used [KB]: 46822
% 117.27/21.26  % (22033)Time elapsed: 2.466 s
% 117.27/21.26  % (22033)Instructions burned: 8425 (million)
% 117.27/21.26  % (22033)------------------------------
% 117.27/21.26  % (22033)------------------------------
% 117.27/21.27  % (22048)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=15557:si=on:rtra=on_0 on DTF2THF_21656 for (2840ds/15557Mi)
% 117.27/21.29  % (22032)Instruction limit reached!
% 117.27/21.29  % (22032)------------------------------
% 117.27/21.29  % (22032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 117.27/21.29  % (22032)Termination reason: Unknown
% 117.27/21.29  % (22032)Termination phase: Saturation
% 117.27/21.29  
% 117.27/21.29  % (22032)Memory used [KB]: 91597
% 117.27/21.29  % (22032)Time elapsed: 2.928 s
% 117.27/21.29  % (22032)Instructions burned: 9823 (million)
% 117.27/21.29  % (22032)------------------------------
% 117.27/21.29  % (22032)------------------------------
% 114.91/21.31  % (22049)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2142:si=on:rtra=on_0 on DTF2THF_21656 for (2840ds/2142Mi)
% 114.91/21.33  % (22047)Instruction limit reached!
% 114.91/21.33  % (22047)------------------------------
% 114.91/21.33  % (22047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 114.91/21.33  % (22047)Termination reason: Unknown
% 114.91/21.33  % (22047)Termination phase: shuffling
% 114.91/21.33  
% 114.91/21.33  % (22047)Memory used [KB]: 24434
% 114.91/21.33  % (22047)Time elapsed: 0.186 s
% 114.91/21.33  % (22047)Instructions burned: 632 (million)
% 114.91/21.33  % (22047)------------------------------
% 114.91/21.33  % (22047)------------------------------
% 114.91/21.35  % (22050)dis+1002_1:1_aac=none:au=on:bd=off:cnfonf=conj_eager:nwc=5.0:sgt=5:sp=reverse_arity:ss=axioms:i=5624:si=on:rtra=on_0 on DTF2THF_21656 for (2840ds/5624Mi)
% 118.86/21.58  % (22043)Instruction limit reached!
% 118.86/21.58  % (22043)------------------------------
% 118.86/21.58  % (22043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 118.86/21.58  % (22043)Termination reason: Unknown
% 118.86/21.58  % (22043)Termination phase: Property scanning
% 118.86/21.58  
% 118.86/21.58  % (22043)Memory used [KB]: 44007
% 118.86/21.58  % (22043)Time elapsed: 1.197 s
% 118.86/21.58  % (22043)Instructions burned: 4167 (million)
% 118.86/21.58  % (22043)------------------------------
% 118.86/21.58  % (22043)------------------------------
% 118.86/21.59  % (22051)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=1665:si=on:rtra=on_0 on DTF2THF_21656 for (2837ds/1665Mi)
% 119.57/21.77  % (22046)Instruction limit reached!
% 119.57/21.77  % (22046)------------------------------
% 119.57/21.77  % (22046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 119.57/21.77  % (22046)Termination reason: Unknown
% 119.57/21.77  % (22046)Termination phase: Property scanning
% 119.57/21.77  
% 119.57/21.77  % (22046)Memory used [KB]: 39914
% 119.57/21.77  % (22046)Time elapsed: 0.798 s
% 119.57/21.77  % (22046)Instructions burned: 2635 (million)
% 119.57/21.77  % (22046)------------------------------
% 119.57/21.77  % (22046)------------------------------
% 119.57/21.78  % (22052)dis+1002_1:1_av=off:prag=on:sd=1:sos=on:sp=occurrence:ss=axioms:i=64912:si=on:rtra=on_0 on DTF2THF_21656 for (2835ds/64912Mi)
% 120.03/21.96  % (22049)Instruction limit reached!
% 120.03/21.96  % (22049)------------------------------
% 120.03/21.96  % (22049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 120.03/21.96  % (22049)Termination reason: Unknown
% 120.03/21.96  % (22049)Termination phase: SInE selection
% 120.03/21.96  
% 120.03/21.96  % (22049)Memory used [KB]: 28144
% 120.03/21.96  % (22049)Time elapsed: 0.651 s
% 120.03/21.96  % (22049)Instructions burned: 2142 (million)
% 120.03/21.96  % (22049)------------------------------
% 120.03/21.96  % (22049)------------------------------
% 120.03/21.97  % (22053)lrs+10_1:32_atotf=0.1:avsq=on:bsr=on:cnfonf=lazy_gen:fde=unused:i=7801:si=on:rtra=on_0 on DTF2THF_21656 for (2833ds/7801Mi)
% 123.11/22.07  % (22051)Instruction limit reached!
% 123.11/22.07  % (22051)------------------------------
% 123.11/22.07  % (22051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 123.11/22.07  % (22051)Termination reason: Unknown
% 123.11/22.07  % (22051)Termination phase: shuffling
% 123.11/22.07  
% 123.11/22.07  % (22051)Memory used [KB]: 41833
% 123.11/22.07  % (22051)Time elapsed: 0.480 s
% 123.11/22.07  % (22051)Instructions burned: 1666 (million)
% 123.11/22.07  % (22051)------------------------------
% 123.11/22.07  % (22051)------------------------------
% 123.11/22.08  % (22055)ott+2_1:1_au=on:hfsq=on:hfsqc=5:hfsql=off:nwc=5.0:sd=3:ss=axioms:st=5.0:i=15194:si=on:rtra=on_0 on DTF2THF_21656 for (2832ds/15194Mi)
% 124.22/22.28  % (22042)Instruction limit reached!
% 124.22/22.28  % (22042)------------------------------
% 124.22/22.28  % (22042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 124.22/22.28  % (22042)Termination reason: Unknown
% 124.22/22.28  % (22042)Termination phase: Property scanning
% 124.22/22.28  
% 124.22/22.28  % (22042)Memory used [KB]: 61917
% 124.22/22.28  % (22042)Time elapsed: 1.941 s
% 124.22/22.28  % (22042)Instructions burned: 7472 (million)
% 124.22/22.28  % (22042)------------------------------
% 124.22/22.28  % (22042)------------------------------
% 124.22/22.29  % (22056)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=6753:si=on:rtra=on_0 on DTF2THF_21656 for (2830ds/6753Mi)
% 126.31/22.62  % (22052)Refutation not found, incomplete strategy
% 126.31/22.62  % (22052)------------------------------
% 126.31/22.62  % (22052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 126.31/22.62  % (22052)Termination reason: Refutation not found, incomplete strategy
% 126.31/22.62  
% 126.31/22.62  
% 126.31/22.62  % (22052)Memory used [KB]: 32238
% 126.31/22.62  % (22052)Time elapsed: 0.843 s
% 126.31/22.62  % (22052)Instructions burned: 2853 (million)
% 126.31/22.62  % (22052)------------------------------
% 126.31/22.62  % (22052)------------------------------
% 126.31/22.64  % (22057)lrs+1002_1:28_bd=off:cnfonf=lazy_simp:plsq=on:plsqr=1,1:prag=on:i=1003:si=on:rtra=on_0 on DTF2THF_21656 for (2827ds/1003Mi)
% 127.15/22.86  % (22050)Instruction limit reached!
% 127.15/22.86  % (22050)------------------------------
% 127.15/22.86  % (22050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 127.15/22.86  % (22050)Termination reason: Unknown
% 127.15/22.86  % (22050)Termination phase: Saturation
% 127.15/22.86  
% 127.15/22.86  % (22050)Memory used [KB]: 61917
% 127.15/22.86  % (22050)Time elapsed: 1.519 s
% 127.15/22.86  % (22050)Instructions burned: 5627 (million)
% 127.15/22.86  % (22050)------------------------------
% 127.15/22.86  % (22050)------------------------------
% 127.15/22.88  % (22058)ott-21_5:4_atotf=0.3:e2e=on:hud=15:ins=1:plsq=on:plsqc=1:plsqr=32,1:sp=unary_frequency:tnu=2:i=13018:si=on:rtra=on_0 on DTF2THF_21656 for (2824ds/13018Mi)
% 127.54/22.93  % (22057)Instruction limit reached!
% 127.54/22.93  % (22057)------------------------------
% 127.54/22.93  % (22057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 127.54/22.93  % (22057)Termination reason: Unknown
% 127.54/22.93  % (22057)Termination phase: shuffling
% 127.54/22.93  
% 127.54/22.93  % (22057)Memory used [KB]: 33517
% 127.54/22.93  % (22057)Time elapsed: 0.292 s
% 127.54/22.93  % (22057)Instructions burned: 1005 (million)
% 127.54/22.93  % (22057)------------------------------
% 127.54/22.93  % (22057)------------------------------
% 127.54/22.94  % (22059)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1267:si=on:rtra=on_0 on DTF2THF_21656 for (2824ds/1267Mi)
% 132.05/23.34  % (22059)Instruction limit reached!
% 132.05/23.34  % (22059)------------------------------
% 132.05/23.34  % (22059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 132.05/23.34  % (22059)Termination reason: Unknown
% 132.05/23.34  % (22059)Termination phase: Property scanning
% 132.05/23.34  
% 132.05/23.34  % (22059)Memory used [KB]: 27888
% 132.05/23.34  % (22059)Time elapsed: 0.399 s
% 132.05/23.34  % (22059)Instructions burned: 1268 (million)
% 132.05/23.34  % (22059)------------------------------
% 132.05/23.34  % (22059)------------------------------
% 132.05/23.35  % (22061)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=2570:si=on:rtra=on_0 on DTF2THF_21656 for (2820ds/2570Mi)
% 137.15/24.05  % (22061)Instruction limit reached!
% 137.15/24.05  % (22061)------------------------------
% 137.15/24.05  % (22061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 137.15/24.05  % (22061)Termination reason: Unknown
% 137.15/24.05  % (22061)Termination phase: Property scanning
% 137.15/24.05  
% 137.15/24.05  % (22061)Memory used [KB]: 43368
% 137.15/24.05  % (22061)Time elapsed: 0.700 s
% 137.15/24.05  % (22061)Instructions burned: 2571 (million)
% 137.15/24.05  % (22061)------------------------------
% 137.15/24.05  % (22061)------------------------------
% 137.15/24.06  % (22062)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=13163:si=on:rtra=on_0 on DTF2THF_21656 for (2812ds/13163Mi)
% 137.15/24.07  % (22053)Instruction limit reached!
% 137.15/24.07  % (22053)------------------------------
% 137.15/24.07  % (22053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 137.15/24.07  % (22053)Termination reason: Unknown
% 137.15/24.07  % (22053)Termination phase: Saturation
% 137.15/24.07  
% 137.15/24.07  % (22053)Memory used [KB]: 52323
% 137.15/24.07  % (22053)Time elapsed: 2.105 s
% 137.15/24.07  % (22053)Instructions burned: 7801 (million)
% 137.15/24.07  % (22053)------------------------------
% 137.15/24.07  % (22053)------------------------------
% 137.15/24.09  % (22063)lrs+1666_1:1_au=on:s2a=on:sd=2:ss=axioms:st=5.0:i=5087:si=on:rtra=on_0 on DTF2THF_21656 for (2812ds/5087Mi)
% 137.77/24.18  % (22044)Instruction limit reached!
% 137.77/24.18  % (22044)------------------------------
% 137.77/24.18  % (22044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 137.77/24.18  % (22044)Termination reason: Unknown
% 137.77/24.18  % (22044)Termination phase: Saturation
% 137.77/24.18  
% 137.77/24.18  % (22044)Memory used [KB]: 81491
% 137.77/24.18  % (22044)Time elapsed: 3.626 s
% 137.77/24.18  % (22044)Instructions burned: 13469 (million)
% 137.77/24.18  % (22044)------------------------------
% 137.77/24.18  % (22044)------------------------------
% 137.77/24.20  % (22064)lrs+1002_1:1_aac=none:au=on:bd=off:cnfonf=lazy_pi_sigma_gen:s2a=on:sac=on:sd=1:sgt=20:ss=axioms:i=10380:si=on:rtra=on_0 on DTF2THF_21656 for (2811ds/10380Mi)
% 138.11/24.28  % (22056)Instruction limit reached!
% 138.11/24.28  % (22056)------------------------------
% 138.11/24.28  % (22056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 138.11/24.28  % (22056)Termination reason: Unknown
% 138.11/24.28  % (22056)Termination phase: Saturation
% 138.11/24.28  
% 138.11/24.28  % (22056)Memory used [KB]: 72536
% 138.11/24.28  % (22056)Time elapsed: 1.988 s
% 138.11/24.28  % (22056)Instructions burned: 6755 (million)
% 138.11/24.28  % (22056)------------------------------
% 138.11/24.28  % (22056)------------------------------
% 138.11/24.29  % (22065)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4218:si=on:rtra=on_0 on DTF2THF_21656 for (2810ds/4218Mi)
% 144.89/25.17  % (22048)Instruction limit reached!
% 144.89/25.17  % (22048)------------------------------
% 144.89/25.17  % (22048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 144.89/25.17  % (22048)Termination reason: Unknown
% 144.89/25.17  % (22048)Termination phase: Saturation
% 144.89/25.17  
% 144.89/25.17  % (22048)Memory used [KB]: 69082
% 144.89/25.17  % (22048)Time elapsed: 3.903 s
% 144.89/25.17  % (22048)Instructions burned: 15560 (million)
% 144.89/25.17  % (22048)------------------------------
% 144.89/25.17  % (22048)------------------------------
% 144.89/25.19  % (22067)ott+1666_1:1_hfaw=0:hfsq=on:hfsql=off:hfsqr=1,16:hud=15:slsq=on:slsqr=1,2:tnu=2:i=3971:si=on:rtra=on_0 on DTF2THF_21656 for (2801ds/3971Mi)
% 147.18/25.50  % (22065)Instruction limit reached!
% 147.18/25.50  % (22065)------------------------------
% 147.18/25.50  % (22065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 147.18/25.50  % (22065)Termination reason: Unknown
% 147.18/25.50  % (22065)Termination phase: Saturation
% 147.18/25.50  
% 147.18/25.50  % (22065)Memory used [KB]: 37611
% 147.18/25.50  % (22065)Time elapsed: 1.207 s
% 147.18/25.50  % (22065)Instructions burned: 4218 (million)
% 147.18/25.50  % (22065)------------------------------
% 147.18/25.50  % (22065)------------------------------
% 147.18/25.50  % (22063)Instruction limit reached!
% 147.18/25.50  % (22063)------------------------------
% 147.18/25.50  % (22063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 147.18/25.50  % (22063)Termination reason: Unknown
% 147.18/25.50  % (22063)Termination phase: Saturation
% 147.18/25.50  
% 147.18/25.50  % (22063)Memory used [KB]: 46182
% 147.18/25.50  % (22063)Time elapsed: 1.418 s
% 147.18/25.50  % (22063)Instructions burned: 5090 (million)
% 147.18/25.50  % (22063)------------------------------
% 147.18/25.50  % (22063)------------------------------
% 147.18/25.51  % (22068)dis+1010_1:1_anc=all_dependent:au=on:bs=on:sd=5:sp=occurrence:ss=axioms:st=2.0:i=14014:si=on:rtra=on_0 on DTF2THF_21656 for (2798ds/14014Mi)
% 147.18/25.52  % (22069)lrs+10_1:1_ins=1:sgt=8:ss=axioms:i=8517:si=on:rtra=on_0 on DTF2THF_21656 for (2798ds/8517Mi)
% 151.19/26.07  % (22055)Instruction limit reached!
% 151.19/26.07  % (22055)------------------------------
% 151.19/26.07  % (22055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 151.19/26.07  % (22055)Termination reason: Unknown
% 151.19/26.07  % (22055)Termination phase: Saturation
% 151.19/26.07  
% 151.19/26.07  % (22055)Memory used [KB]: 72280
% 151.19/26.07  % (22055)Time elapsed: 3.990 s
% 151.19/26.07  % (22055)Instructions burned: 15194 (million)
% 151.19/26.07  % (22055)------------------------------
% 151.19/26.07  % (22055)------------------------------
% 151.19/26.09  % (22071)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=10148:si=on:rtra=on_0 on DTF2THF_21656 for (2792ds/10148Mi)
% 151.86/26.19  % (22058)Instruction limit reached!
% 151.86/26.19  % (22058)------------------------------
% 151.86/26.19  % (22058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 151.86/26.19  % (22058)Termination reason: Unknown
% 151.86/26.19  % (22058)Termination phase: Property scanning
% 151.86/26.19  
% 151.86/26.19  % (22058)Memory used [KB]: 70873
% 151.86/26.19  % (22058)Time elapsed: 3.315 s
% 151.86/26.19  % (22058)Instructions burned: 13019 (million)
% 151.86/26.19  % (22058)------------------------------
% 151.86/26.19  % (22058)------------------------------
% 152.27/26.21  % (22072)lrs+10_1:2_ntd=on:nwc=10.0:plsq=on:plsqc=1:plsqr=2,1:ss=axioms:i=9078:si=on:rtra=on_0 on DTF2THF_21656 for (2791ds/9078Mi)
% 153.29/26.44  % (22067)Instruction limit reached!
% 153.29/26.44  % (22067)------------------------------
% 153.29/26.44  % (22067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 153.29/26.44  % (22067)Termination reason: Unknown
% 153.29/26.44  % (22067)Termination phase: Function definition elimination
% 153.29/26.44  
% 153.29/26.44  % (22067)Memory used [KB]: 45159
% 153.29/26.44  % (22067)Time elapsed: 1.249 s
% 153.29/26.44  % (22067)Instructions burned: 3972 (million)
% 153.29/26.44  % (22067)------------------------------
% 153.29/26.44  % (22067)------------------------------
% 153.29/26.45  % (22073)lrs+2_1:1_bet=on:bsr=on:cnfonf=lazy_pi_sigma_gen:er=filter:kws=inv_frequency:ntd=on:sd=3:ss=axioms:i=16164:si=on:rtra=on_0 on DTF2THF_21656 for (2788ds/16164Mi)
% 159.41/27.25  % (22064)Instruction limit reached!
% 159.41/27.25  % (22064)------------------------------
% 159.41/27.25  % (22064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 159.41/27.25  % (22064)Termination reason: Unknown
% 159.41/27.25  % (22064)Termination phase: Saturation
% 159.41/27.25  
% 159.41/27.25  % (22064)Memory used [KB]: 51299
% 159.41/27.25  % (22064)Time elapsed: 3.055 s
% 159.41/27.25  % (22064)Instructions burned: 10380 (million)
% 159.41/27.25  % (22064)------------------------------
% 159.41/27.25  % (22064)------------------------------
% 159.41/27.26  % (22075)lrs+32_1:1_au=on:bet=on:cbe=off:cs=on:ins=3:i=6102:si=on:rtra=on_0 on DTF2THF_21656 for (2780ds/6102Mi)
% 160.68/27.41  % (22062)Instruction limit reached!
% 160.68/27.41  % (22062)------------------------------
% 160.68/27.41  % (22062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 160.68/27.41  % (22062)Termination reason: Unknown
% 160.68/27.41  % (22062)Termination phase: Property scanning
% 160.68/27.41  
% 160.68/27.41  % (22062)Memory used [KB]: 53602
% 160.68/27.41  % (22062)Time elapsed: 3.354 s
% 160.68/27.41  % (22062)Instructions burned: 13164 (million)
% 160.68/27.41  % (22062)------------------------------
% 160.68/27.41  % (22062)------------------------------
% 160.68/27.43  % (22076)lrs+1010_1:1_au=on:bd=off:e2e=on:fde=unused:nm=4:s2a=on:sos=all:sp=const_frequency:i=10308:si=on:rtra=on_0 on DTF2THF_21656 for (2779ds/10308Mi)
% 163.19/28.00  % (22069)Instruction limit reached!
% 163.19/28.00  % (22069)------------------------------
% 163.19/28.00  % (22069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 163.19/28.00  % (22069)Termination reason: Unknown
% 163.19/28.00  % (22069)Termination phase: Saturation
% 163.19/28.00  
% 163.19/28.00  % (22069)Memory used [KB]: 55521
% 163.19/28.00  % (22069)Time elapsed: 2.483 s
% 163.19/28.00  % (22069)Instructions burned: 8519 (million)
% 163.19/28.00  % (22069)------------------------------
% 163.19/28.00  % (22069)------------------------------
% 163.19/28.01  % (22077)dis+1010_1:1_au=on:avsq=on:bd=off:cbe=off:cnfonf=off:cs=on:hud=5:nm=0:plsq=on:plsqc=1:plsqr=7,1:ss=axioms:tgt=full:i=4041:si=on:rtra=on_0 on DTF2THF_21656 for (2773ds/4041Mi)
% 167.43/28.49  % (22073)First to succeed.
% 168.03/28.52  % (22073)Refutation found. Thanks to Tanya!
% 168.03/28.52  % SZS status Theorem for DTF2THF_21656
% 168.03/28.52  % SZS output start Proof for DTF2THF_21656
% 168.03/28.52  thf(type_def_5, type, rat: $tType).
% 168.03/28.52  thf(type_def_6, type, int: $tType).
% 168.03/28.52  thf(type_def_8, type, real: $tType).
% 168.03/28.52  thf(type_def_9, type, set_Pr1261947904930325089at_nat: $tType).
% 168.03/28.52  thf(type_def_10, type, nat: $tType).
% 168.03/28.52  thf(type_def_11, type, complex: $tType).
% 168.03/28.52  thf(type_def_12, type, product_prod_int_int: $tType).
% 168.03/28.52  thf(type_def_13, type, num: $tType).
% 168.03/28.52  thf(type_def_14, type, option_num: $tType).
% 168.03/28.52  thf(type_def_15, type, product_prod_num_num: $tType).
% 168.03/28.52  thf(type_def_16, type, code_integer: $tType).
% 168.03/28.52  thf(type_def_17, type, produc6271795597528267376eger_o: $tType).
% 168.03/28.52  thf(type_def_18, type, produc8923325533196201883nteger: $tType).
% 168.03/28.52  thf(type_def_19, type, set_fi4554929511873752355omplex: $tType).
% 168.03/28.52  thf(type_def_20, type, filter6041513312241820739omplex: $tType).
% 168.03/28.52  thf(type_def_21, type, set_fi7789364187291644575l_real: $tType).
% 168.03/28.52  thf(type_def_22, type, filter2146258269922977983l_real: $tType).
% 168.03/28.52  thf(type_def_23, type, set_real: $tType).
% 168.03/28.52  thf(type_def_24, type, filter_real: $tType).
% 168.03/28.52  thf(type_def_25, type, product_prod_nat_nat: $tType).
% 168.03/28.52  thf(type_def_26, type, filter_nat: $tType).
% 168.03/28.52  thf(type_def_27, type, filter1242075044329608583at_nat: $tType).
% 168.03/28.52  thf(type_def_28, type, set_Pr5085853215250843933omplex: $tType).
% 168.03/28.52  thf(type_def_29, type, set_Pr6218003697084177305l_real: $tType).
% 168.03/28.52  thf(type_def_30, type, set_o: $tType).
% 168.03/28.52  thf(type_def_31, type, set_complex: $tType).
% 168.03/28.52  thf(type_def_32, type, set_int: $tType).
% 168.03/28.52  thf(type_def_33, type, set_list_nat: $tType).
% 168.03/28.52  thf(type_def_34, type, set_nat: $tType).
% 168.03/28.52  thf(type_def_35, type, set_Product_unit: $tType).
% 168.03/28.52  thf(type_def_36, type, set_char: $tType).
% 168.03/28.52  thf(type_def_37, type, set_list_o: $tType).
% 168.03/28.52  thf(type_def_38, type, set_list_complex: $tType).
% 168.03/28.52  thf(type_def_39, type, set_list_int: $tType).
% 168.03/28.52  thf(type_def_40, type, set_list_real: $tType).
% 168.03/28.52  thf(type_def_41, type, set_list_VEBT_VEBT: $tType).
% 168.03/28.52  thf(type_def_42, type, set_num: $tType).
% 168.03/28.52  thf(type_def_43, type, set_rat: $tType).
% 168.03/28.52  thf(type_def_44, type, set_set_nat: $tType).
% 168.03/28.52  thf(type_def_45, type, set_set_real: $tType).
% 168.03/28.52  thf(type_def_46, type, set_VEBT_VEBT: $tType).
% 168.03/28.52  thf(type_def_47, type, char: $tType).
% 168.03/28.52  thf(type_def_48, type, set_Pr8693737435421807431at_nat: $tType).
% 168.03/28.52  thf(type_def_49, type, list_nat: $tType).
% 168.03/28.52  thf(type_def_50, type, extended_enat: $tType).
% 168.03/28.52  thf(type_def_51, type, vEBT_VEBT: $tType).
% 168.03/28.52  thf(type_def_52, type, list_o: $tType).
% 168.03/28.52  thf(type_def_53, type, list_int: $tType).
% 168.03/28.52  thf(type_def_54, type, option_nat: $tType).
% 168.03/28.52  thf(type_def_55, type, list_complex: $tType).
% 168.03/28.52  thf(type_def_56, type, list_P6011104703257516679at_nat: $tType).
% 168.03/28.52  thf(type_def_57, type, list_real: $tType).
% 168.03/28.52  thf(type_def_58, type, list_VEBT_VEBT: $tType).
% 168.03/28.52  thf(type_def_59, type, list_num: $tType).
% 168.03/28.52  thf(type_def_60, type, list_P4002435161011370285od_o_o: $tType).
% 168.03/28.52  thf(type_def_61, type, product_prod_o_o: $tType).
% 168.03/28.52  thf(type_def_62, type, list_P3795440434834930179_o_int: $tType).
% 168.03/28.52  thf(type_def_63, type, product_prod_o_int: $tType).
% 168.03/28.52  thf(type_def_64, type, list_P6285523579766656935_o_nat: $tType).
% 168.03/28.52  thf(type_def_65, type, product_prod_o_nat: $tType).
% 168.03/28.52  thf(type_def_66, type, list_P7495141550334521929T_VEBT: $tType).
% 168.03/28.52  thf(type_def_67, type, produc2504756804600209347T_VEBT: $tType).
% 168.03/28.52  thf(type_def_68, type, list_P1726324292696863441at_num: $tType).
% 168.03/28.52  thf(type_def_69, type, product_prod_nat_num: $tType).
% 168.03/28.52  thf(type_def_70, type, list_P3744719386663036955um_num: $tType).
% 168.03/28.52  thf(type_def_71, type, list_P3126845725202233233VEBT_o: $tType).
% 168.03/28.52  thf(type_def_72, type, produc334124729049499915VEBT_o: $tType).
% 168.03/28.52  thf(type_def_73, type, list_P4547456442757143711BT_int: $tType).
% 168.03/28.52  thf(type_def_74, type, produc4894624898956917775BT_int: $tType).
% 168.03/28.52  thf(type_def_75, type, list_P7037539587688870467BT_nat: $tType).
% 168.03/28.52  thf(type_def_76, type, produc9072475918466114483BT_nat: $tType).
% 168.03/28.52  thf(type_def_77, type, list_P7413028617227757229T_VEBT: $tType).
% 168.03/28.52  thf(type_def_78, type, produc8243902056947475879T_VEBT: $tType).
% 168.03/28.52  thf(type_def_79, type, list_P7333126701944960589_nat_o: $tType).
% 168.03/28.52  thf(type_def_80, type, list_P5647936690300460905T_VEBT: $tType).
% 168.03/28.52  thf(type_def_81, type, option4927543243414619207at_nat: $tType).
% 168.03/28.52  thf(type_def_82, type, produc4953844613479565601on_nat: $tType).
% 168.03/28.52  thf(type_def_83, type, produc2233624965454879586on_nat: $tType).
% 168.03/28.52  thf(type_def_84, type, produc7248412053542808358at_nat: $tType).
% 168.03/28.52  thf(type_def_85, type, produc4471711990508489141at_nat: $tType).
% 168.03/28.52  thf(type_def_86, type, produc8306885398267862888on_nat: $tType).
% 168.03/28.52  thf(type_def_87, type, produc2963631642982155120at_num: $tType).
% 168.03/28.52  thf(type_def_88, type, produc3368934014287244435at_num: $tType).
% 168.03/28.52  thf(type_def_89, type, produc3447558737645232053on_num: $tType).
% 168.03/28.52  thf(type_def_90, type, produc7036089656553540234on_num: $tType).
% 168.03/28.52  thf(type_def_91, type, produc1193250871479095198on_num: $tType).
% 168.03/28.52  thf(type_def_92, type, produc6121120109295599847at_nat: $tType).
% 168.03/28.52  thf(type_def_93, type, produc5491161045314408544at_nat: $tType).
% 168.03/28.52  thf(type_def_94, type, produc5542196010084753463at_nat: $tType).
% 168.03/28.52  thf(type_def_95, type, produc859450856879609959at_nat: $tType).
% 168.03/28.52  thf(type_def_96, type, produc4411394909380815293omplex: $tType).
% 168.03/28.52  thf(type_def_97, type, produc2422161461964618553l_real: $tType).
% 168.03/28.52  thf(func_def_0, type, produc5542196010084753463at_nat: $tType).
% 168.03/28.52  thf(func_def_1, type, produc5491161045314408544at_nat: $tType).
% 168.03/28.52  thf(func_def_2, type, produc1193250871479095198on_num: $tType).
% 168.03/28.52  thf(func_def_3, type, produc8306885398267862888on_nat: $tType).
% 168.03/28.52  thf(func_def_4, type, produc6121120109295599847at_nat: $tType).
% 168.03/28.52  thf(func_def_5, type, produc3368934014287244435at_num: $tType).
% 168.03/28.52  thf(func_def_6, type, produc4471711990508489141at_nat: $tType).
% 168.03/28.52  thf(func_def_7, type, produc7036089656553540234on_num: $tType).
% 168.03/28.52  thf(func_def_8, type, produc2233624965454879586on_nat: $tType).
% 168.03/28.52  thf(func_def_9, type, set_Pr8693737435421807431at_nat: $tType).
% 168.03/28.52  thf(func_def_10, type, produc859450856879609959at_nat: $tType).
% 168.03/28.52  thf(func_def_11, type, set_fi4554929511873752355omplex: $tType).
% 168.03/28.52  thf(func_def_12, type, list_P7413028617227757229T_VEBT: $tType).
% 168.03/28.52  thf(func_def_13, type, produc3447558737645232053on_num: $tType).
% 168.03/28.52  thf(func_def_14, type, produc4953844613479565601on_nat: $tType).
% 168.03/28.52  thf(func_def_15, type, produc2963631642982155120at_num: $tType).
% 168.03/28.52  thf(func_def_16, type, produc7248412053542808358at_nat: $tType).
% 168.03/28.52  thf(func_def_17, type, set_fi7789364187291644575l_real: $tType).
% 168.03/28.52  thf(func_def_18, type, filter6041513312241820739omplex: $tType).
% 168.03/28.52  thf(func_def_19, type, list_P7037539587688870467BT_nat: $tType).
% 168.03/28.52  thf(func_def_20, type, list_P4547456442757143711BT_int: $tType).
% 168.03/28.52  thf(func_def_21, type, list_P5647936690300460905T_VEBT: $tType).
% 168.03/28.52  thf(func_def_22, type, produc8243902056947475879T_VEBT: $tType).
% 168.03/28.52  thf(func_def_23, type, set_Pr5085853215250843933omplex: $tType).
% 168.03/28.52  thf(func_def_24, type, produc8923325533196201883nteger: $tType).
% 168.03/28.52  thf(func_def_25, type, list_P3126845725202233233VEBT_o: $tType).
% 168.03/28.52  thf(func_def_26, type, list_P7495141550334521929T_VEBT: $tType).
% 168.03/28.52  thf(func_def_27, type, filter2146258269922977983l_real: $tType).
% 168.03/28.52  thf(func_def_28, type, option4927543243414619207at_nat: $tType).
% 168.03/28.52  thf(func_def_29, type, filter1242075044329608583at_nat: $tType).
% 168.03/28.52  thf(func_def_30, type, set_Pr6218003697084177305l_real: $tType).
% 168.03/28.52  thf(func_def_31, type, list_P3744719386663036955um_num: $tType).
% 168.03/28.52  thf(func_def_32, type, list_P1726324292696863441at_num: $tType).
% 168.03/28.52  thf(func_def_33, type, list_P6011104703257516679at_nat: $tType).
% 168.03/28.52  thf(func_def_34, type, produc9072475918466114483BT_nat: $tType).
% 168.03/28.52  thf(func_def_35, type, produc4894624898956917775BT_int: $tType).
% 168.03/28.52  thf(func_def_36, type, set_Pr1261947904930325089at_nat: $tType).
% 168.03/28.52  thf(func_def_37, type, produc4411394909380815293omplex: $tType).
% 168.03/28.52  thf(func_def_38, type, list_P7333126701944960589_nat_o: $tType).
% 168.03/28.52  thf(func_def_39, type, list_P6285523579766656935_o_nat: $tType).
% 168.03/28.52  thf(func_def_40, type, list_P3795440434834930179_o_int: $tType).
% 168.03/28.52  thf(func_def_41, type, set_list_VEBT_VEBT: $tType).
% 168.03/28.52  thf(func_def_42, type, produc334124729049499915VEBT_o: $tType).
% 168.03/28.52  thf(func_def_43, type, produc2504756804600209347T_VEBT: $tType).
% 168.03/28.52  thf(func_def_44, type, produc6271795597528267376eger_o: $tType).
% 168.03/28.52  thf(func_def_45, type, produc2422161461964618553l_real: $tType).
% 168.03/28.52  thf(func_def_46, type, product_prod_num_num: $tType).
% 168.03/28.52  thf(func_def_47, type, product_prod_nat_num: $tType).
% 168.03/28.52  thf(func_def_48, type, product_prod_nat_nat: $tType).
% 168.03/28.52  thf(func_def_49, type, product_prod_int_int: $tType).
% 168.03/28.52  thf(func_def_50, type, list_P4002435161011370285od_o_o: $tType).
% 168.03/28.52  thf(func_def_51, type, set_list_complex: $tType).
% 168.03/28.52  thf(func_def_52, type, set_list_real: $tType).
% 168.03/28.52  thf(func_def_53, type, list_VEBT_VEBT: $tType).
% 168.03/28.52  thf(func_def_54, type, set_set_real: $tType).
% 168.03/28.52  thf(func_def_55, type, set_list_nat: $tType).
% 168.03/28.52  thf(func_def_56, type, set_list_int: $tType).
% 168.03/28.52  thf(func_def_57, type, product_prod_o_nat: $tType).
% 168.03/28.52  thf(func_def_58, type, product_prod_o_int: $tType).
% 168.03/28.52  thf(func_def_59, type, set_VEBT_VEBT: $tType).
% 168.03/28.52  thf(func_def_60, type, set_set_nat: $tType).
% 168.03/28.52  thf(func_def_61, type, set_Product_unit: $tType).
% 168.03/28.52  thf(func_def_62, type, list_complex: $tType).
% 168.03/28.52  thf(func_def_63, type, set_list_o: $tType).
% 168.03/28.52  thf(func_def_64, type, product_prod_o_o: $tType).
% 168.03/28.52  thf(func_def_65, type, set_complex: $tType).
% 168.03/28.52  thf(func_def_66, type, filter_real: $tType).
% 168.03/28.52  thf(func_def_67, type, option_num: $tType).
% 168.03/28.52  thf(func_def_68, type, option_nat: $tType).
% 168.03/28.52  thf(func_def_69, type, filter_nat: $tType).
% 168.03/28.52  thf(func_def_70, type, set_char: $tType).
% 168.03/28.52  thf(func_def_71, type, list_real: $tType).
% 168.03/28.52  thf(func_def_72, type, set_real: $tType).
% 168.03/28.52  thf(func_def_73, type, list_num: $tType).
% 168.03/28.52  thf(func_def_74, type, list_nat: $tType).
% 168.03/28.52  thf(func_def_75, type, list_int: $tType).
% 168.03/28.52  thf(func_def_76, type, vEBT_VEBT: $tType).
% 168.03/28.52  thf(func_def_77, type, set_rat: $tType).
% 168.03/28.52  thf(func_def_78, type, set_num: $tType).
% 168.03/28.52  thf(func_def_79, type, set_nat: $tType).
% 168.03/28.52  thf(func_def_80, type, set_int: $tType).
% 168.03/28.52  thf(func_def_81, type, code_integer: $tType).
% 168.03/28.52  thf(func_def_82, type, extended_enat: $tType).
% 168.03/28.52  thf(func_def_83, type, list_o: $tType).
% 168.03/28.52  thf(func_def_84, type, complex: $tType).
% 168.03/28.52  thf(func_def_85, type, set_o: $tType).
% 168.03/28.52  thf(func_def_86, type, char: $tType).
% 168.03/28.52  thf(func_def_87, type, real: $tType).
% 168.03/28.52  thf(func_def_88, type, rat: $tType).
% 168.03/28.52  thf(func_def_89, type, num: $tType).
% 168.03/28.52  thf(func_def_90, type, nat: $tType).
% 168.03/28.52  thf(func_def_91, type, int: $tType).
% 168.03/28.52  thf(func_def_92, type, archim2889992004027027881ng_rat: rat > int).
% 168.03/28.52  thf(func_def_93, type, archim7802044766580827645g_real: real > int).
% 168.03/28.52  thf(func_def_94, type, archim3151403230148437115or_rat: rat > int).
% 168.03/28.52  thf(func_def_95, type, archim6058952711729229775r_real: real > int).
% 168.03/28.52  thf(func_def_96, type, archimedean_frac_rat: rat > rat).
% 168.03/28.52  thf(func_def_97, type, archim2898591450579166408c_real: real > real).
% 168.03/28.52  thf(func_def_98, type, archim7778729529865785530nd_rat: rat > int).
% 168.03/28.52  thf(func_def_99, type, archim8280529875227126926d_real: real > int).
% 168.03/28.52  thf(func_def_100, type, bNF_Ca8665028551170535155natLeq: set_Pr1261947904930325089at_nat).
% 168.03/28.52  thf(func_def_101, type, bNF_Ca8459412986667044542atLess: set_Pr1261947904930325089at_nat).
% 168.03/28.52  thf(func_def_102, type, bNF_We3818239936649020644el_nat: set_Pr1261947904930325089at_nat > $o).
% 168.03/28.52  thf(func_def_103, type, binomial: nat > nat > nat).
% 168.03/28.52  thf(func_def_104, type, gbinomial_complex: complex > nat > complex).
% 168.03/28.52  thf(func_def_105, type, gbinomial_int: int > nat > int).
% 168.03/28.52  thf(func_def_106, type, gbinomial_nat: nat > nat > nat).
% 168.03/28.52  thf(func_def_107, type, gbinomial_rat: rat > nat > rat).
% 168.03/28.52  thf(func_def_108, type, gbinomial_real: real > nat > real).
% 168.03/28.52  thf(func_def_109, type, bit_and_int_rel: product_prod_int_int > product_prod_int_int > $o).
% 168.03/28.52  thf(func_def_110, type, bit_and_not_num: num > num > option_num).
% 168.03/28.52  thf(func_def_111, type, bit_and_not_num_rel: product_prod_num_num > product_prod_num_num > $o).
% 168.03/28.52  thf(func_def_112, type, bit_concat_bit: nat > int > int > int).
% 168.03/28.52  thf(func_def_113, type, bit_or_not_num_neg: num > num > num).
% 168.03/28.52  thf(func_def_114, type, bit_or3848514188828904588eg_rel: product_prod_num_num > product_prod_num_num > $o).
% 168.03/28.52  thf(func_def_115, type, bit_ri7919022796975470100ot_int: int > int).
% 168.03/28.52  thf(func_def_116, type, bit_ri6519982836138164636nteger: nat > code_integer > code_integer).
% 168.03/28.52  thf(func_def_117, type, bit_ri631733984087533419it_int: nat > int > int).
% 168.03/28.52  thf(func_def_118, type, bit_se3949692690581998587nteger: code_integer > code_integer > code_integer).
% 168.03/28.52  thf(func_def_119, type, bit_se725231765392027082nd_int: int > int > int).
% 168.03/28.52  thf(func_def_120, type, bit_se727722235901077358nd_nat: nat > nat > nat).
% 168.03/28.52  thf(func_def_121, type, bit_se8568078237143864401it_int: nat > int > int).
% 168.03/28.52  thf(func_def_122, type, bit_se8570568707652914677it_nat: nat > nat > nat).
% 168.03/28.52  thf(func_def_123, type, bit_se1345352211410354436nteger: nat > code_integer > code_integer).
% 168.03/28.52  thf(func_def_124, type, bit_se2159334234014336723it_int: nat > int > int).
% 168.03/28.52  thf(func_def_125, type, bit_se2161824704523386999it_nat: nat > nat > nat).
% 168.03/28.52  thf(func_def_126, type, bit_se2119862282449309892nteger: nat > code_integer).
% 168.03/28.52  thf(func_def_127, type, bit_se2000444600071755411sk_int: nat > int).
% 168.03/28.52  thf(func_def_128, type, bit_se2002935070580805687sk_nat: nat > nat).
% 168.03/28.52  thf(func_def_129, type, bit_se1080825931792720795nteger: code_integer > code_integer > code_integer).
% 168.03/28.52  thf(func_def_130, type, bit_se1409905431419307370or_int: int > int > int).
% 168.03/28.52  thf(func_def_131, type, bit_se1412395901928357646or_nat: nat > nat > nat).
% 168.03/28.52  thf(func_def_132, type, bit_se545348938243370406it_int: nat > int > int).
% 168.03/28.52  thf(func_def_133, type, bit_se547839408752420682it_nat: nat > nat > nat).
% 168.03/28.52  thf(func_def_134, type, bit_se2793503036327961859nteger: nat > code_integer > code_integer).
% 168.03/28.52  thf(func_def_135, type, bit_se7879613467334960850it_int: nat > int > int).
% 168.03/28.52  thf(func_def_136, type, bit_se7882103937844011126it_nat: nat > nat > nat).
% 168.03/28.52  thf(func_def_137, type, bit_se1745604003318907178nteger: nat > code_integer > code_integer).
% 168.03/28.52  thf(func_def_138, type, bit_se2923211474154528505it_int: nat > int > int).
% 168.03/28.52  thf(func_def_139, type, bit_se2925701944663578781it_nat: nat > nat > nat).
% 168.03/28.52  thf(func_def_140, type, bit_se8260200283734997820nteger: nat > code_integer > code_integer).
% 168.03/28.52  thf(func_def_141, type, bit_se4203085406695923979it_int: nat > int > int).
% 168.03/28.52  thf(func_def_142, type, bit_se4205575877204974255it_nat: nat > nat > nat).
% 168.03/28.52  thf(func_def_143, type, bit_se6526347334894502574or_int: int > int > int).
% 168.03/28.52  thf(func_def_144, type, bit_se6528837805403552850or_nat: nat > nat > nat).
% 168.03/28.52  thf(func_def_145, type, bit_se1146084159140164899it_int: int > nat > $o).
% 168.03/28.52  thf(func_def_146, type, bit_se1148574629649215175it_nat: nat > nat > $o).
% 168.03/28.52  thf(func_def_147, type, bit_take_bit_num: nat > num > option_num).
% 168.03/28.52  thf(func_def_148, type, bit_un1837492267222099188nd_num: num > num > option_num).
% 168.03/28.52  thf(func_def_149, type, bit_un5425074673868309765um_rel: product_prod_num_num > product_prod_num_num > $o).
% 168.03/28.52  thf(func_def_150, type, bit_un6178654185764691216or_num: num > num > option_num).
% 168.03/28.52  thf(func_def_151, type, bit_un3595099601533988841um_rel: product_prod_num_num > product_prod_num_num > $o).
% 168.03/28.52  thf(func_def_152, type, bit_un7362597486090784418nd_num: num > num > option_num).
% 168.03/28.52  thf(func_def_153, type, bit_un4731106466462545111um_rel: product_prod_num_num > product_prod_num_num > $o).
% 168.03/28.52  thf(func_def_154, type, bit_un2480387367778600638or_num: num > num > option_num).
% 168.03/28.52  thf(func_def_155, type, bit_un2901131394128224187um_rel: product_prod_num_num > product_prod_num_num > $o).
% 168.03/28.52  thf(func_def_156, type, code_bit_cut_integer: code_integer > produc6271795597528267376eger_o).
% 168.03/28.52  thf(func_def_157, type, code_divmod_abs: code_integer > code_integer > produc8923325533196201883nteger).
% 168.03/28.52  thf(func_def_158, type, code_divmod_integer: code_integer > code_integer > produc8923325533196201883nteger).
% 168.03/28.52  thf(func_def_159, type, code_int_of_integer: code_integer > int).
% 168.03/28.52  thf(func_def_160, type, code_integer_of_int: int > code_integer).
% 168.03/28.52  thf(func_def_161, type, code_integer_of_num: num > code_integer).
% 168.03/28.52  thf(func_def_162, type, code_nat_of_integer: code_integer > nat).
% 168.03/28.52  thf(func_def_163, type, code_num_of_integer: code_integer > num).
% 168.03/28.52  thf(func_def_164, type, code_Target_negative: num > int).
% 168.03/28.52  thf(func_def_165, type, code_Target_positive: num > int).
% 168.03/28.52  thf(func_def_166, type, comple8358262395181532106omplex: set_fi4554929511873752355omplex > filter6041513312241820739omplex).
% 168.03/28.52  thf(func_def_167, type, comple2936214249959783750l_real: set_fi7789364187291644575l_real > filter2146258269922977983l_real).
% 168.03/28.52  thf(func_def_168, type, comple4887499456419720421f_real: set_real > real).
% 168.03/28.52  thf(func_def_169, type, comple1385675409528146559p_real: set_real > real).
% 168.03/28.52  thf(func_def_170, type, arg: complex > real).
% 168.03/28.52  thf(func_def_171, type, cis: real > complex).
% 168.03/28.52  thf(func_def_172, type, cnj: complex > complex).
% 168.03/28.52  thf(func_def_173, type, complex2: real > real > complex).
% 168.03/28.52  thf(func_def_174, type, im: complex > real).
% 168.03/28.52  thf(func_def_175, type, re: complex > real).
% 168.03/28.52  thf(func_def_176, type, csqrt: complex > complex).
% 168.03/28.52  thf(func_def_177, type, imaginary_unit: complex).
% 168.03/28.52  thf(func_def_178, type, rcis: real > real > complex).
% 168.03/28.52  thf(func_def_179, type, differ6690327859849518006l_real: (real > real) > filter_real > $o).
% 168.03/28.52  thf(func_def_180, type, has_de1759254742604945161l_real: (real > real) > (real > real) > filter_real > $o).
% 168.03/28.52  thf(func_def_181, type, has_fi5821293074295781190e_real: (real > real) > real > filter_real > $o).
% 168.03/28.52  thf(func_def_182, type, adjust_div: product_prod_int_int > int).
% 168.03/28.52  thf(func_def_183, type, adjust_mod: int > int > int).
% 168.03/28.52  thf(func_def_184, type, divmod_nat: nat > nat > product_prod_nat_nat).
% 168.03/28.52  thf(func_def_185, type, eucl_rel_int: int > int > product_prod_int_int > $o).
% 168.03/28.52  thf(func_def_186, type, unique5706413561485394159nteger: produc8923325533196201883nteger > $o).
% 168.03/28.52  thf(func_def_187, type, unique6319869463603278526ux_int: product_prod_int_int > $o).
% 168.03/28.52  thf(func_def_188, type, unique6322359934112328802ux_nat: product_prod_nat_nat > $o).
% 168.03/28.52  thf(func_def_189, type, unique3479559517661332726nteger: num > num > produc8923325533196201883nteger).
% 168.03/28.52  thf(func_def_190, type, unique5052692396658037445od_int: num > num > product_prod_int_int).
% 168.03/28.52  thf(func_def_191, type, unique5055182867167087721od_nat: num > num > product_prod_nat_nat).
% 168.03/28.52  thf(func_def_192, type, unique4921790084139445826nteger: num > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 168.03/28.52  thf(func_def_193, type, unique5024387138958732305ep_int: num > product_prod_int_int > product_prod_int_int).
% 168.03/28.52  thf(func_def_194, type, unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat).
% 168.03/28.52  thf(func_def_195, type, euclid4774559944035922753ze_int: int > nat).
% 168.03/28.52  thf(func_def_196, type, euclid4777050414544973029ze_nat: nat > nat).
% 168.03/28.52  thf(func_def_197, type, euclid3395696857347342551nt_int: int > int).
% 168.03/28.52  thf(func_def_198, type, comm_s8582702949713902594nteger: code_integer > nat > code_integer).
% 168.03/28.52  thf(func_def_199, type, comm_s2602460028002588243omplex: complex > nat > complex).
% 168.03/28.52  thf(func_def_200, type, comm_s4660882817536571857er_int: int > nat > int).
% 168.03/28.52  thf(func_def_201, type, comm_s4663373288045622133er_nat: nat > nat > nat).
% 168.03/28.52  thf(func_def_202, type, comm_s4028243227959126397er_rat: rat > nat > rat).
% 168.03/28.52  thf(func_def_203, type, comm_s7457072308508201937r_real: real > nat > real).
% 168.03/28.52  thf(func_def_204, type, semiri3624122377584611663nteger: nat > code_integer).
% 168.03/28.52  thf(func_def_205, type, semiri5044797733671781792omplex: nat > complex).
% 168.03/28.52  thf(func_def_206, type, semiri1406184849735516958ct_int: nat > int).
% 168.03/28.52  thf(func_def_207, type, semiri1408675320244567234ct_nat: nat > nat).
% 168.03/28.52  thf(func_def_208, type, semiri773545260158071498ct_rat: nat > rat).
% 168.03/28.52  thf(func_def_209, type, semiri2265585572941072030t_real: nat > real).
% 168.03/28.52  thf(func_def_210, type, invers8013647133539491842omplex: complex > complex).
% 168.03/28.52  thf(func_def_211, type, inverse_inverse_rat: rat > rat).
% 168.03/28.52  thf(func_def_212, type, inverse_inverse_real: real > real).
% 168.03/28.52  thf(func_def_213, type, at_bot_real: filter_real).
% 168.03/28.52  thf(func_def_214, type, at_top_nat: filter_nat).
% 168.03/28.52  thf(func_def_215, type, at_top_real: filter_real).
% 168.03/28.52  thf(func_def_216, type, eventually_nat: (nat > $o) > filter_nat > $o).
% 168.03/28.52  thf(func_def_217, type, eventu1038000079068216329at_nat: (product_prod_nat_nat > $o) > filter1242075044329608583at_nat > $o).
% 168.03/28.52  thf(func_def_218, type, eventually_real: (real > $o) > filter_real > $o).
% 168.03/28.52  thf(func_def_219, type, filterlim_nat_nat: (nat > nat) > filter_nat > filter_nat > $o).
% 168.03/28.52  thf(func_def_220, type, filterlim_nat_real: (nat > real) > filter_real > filter_nat > $o).
% 168.03/28.52  thf(func_def_221, type, filterlim_real_real: (real > real) > filter_real > filter_real > $o).
% 168.03/28.52  thf(func_def_222, type, filtermap_real_real: (real > real) > filter_real > filter_real).
% 168.03/28.52  thf(func_def_223, type, princi3496590319149328850omplex: set_Pr5085853215250843933omplex > filter6041513312241820739omplex).
% 168.03/28.52  thf(func_def_224, type, princi6114159922880469582l_real: set_Pr6218003697084177305l_real > filter2146258269922977983l_real).
% 168.03/28.52  thf(func_def_225, type, prod_filter_nat_nat: filter_nat > filter_nat > filter1242075044329608583at_nat).
% 168.03/28.52  thf(func_def_226, type, finite_card_o: set_o > nat).
% 168.03/28.52  thf(func_def_227, type, finite_card_complex: set_complex > nat).
% 168.03/28.52  thf(func_def_228, type, finite_card_int: set_int > nat).
% 168.03/28.52  thf(func_def_229, type, finite_card_list_nat: set_list_nat > nat).
% 168.03/28.52  thf(func_def_230, type, finite_card_nat: set_nat > nat).
% 168.03/28.52  thf(func_def_231, type, finite410649719033368117t_unit: set_Product_unit > nat).
% 168.03/28.52  thf(func_def_232, type, finite_card_char: set_char > nat).
% 168.03/28.52  thf(func_def_233, type, finite_finite_o: set_o > $o).
% 168.03/28.52  thf(func_def_234, type, finite3207457112153483333omplex: set_complex > $o).
% 168.03/28.52  thf(func_def_235, type, finite_finite_int: set_int > $o).
% 168.03/28.52  thf(func_def_236, type, finite_finite_list_o: set_list_o > $o).
% 168.03/28.52  thf(func_def_237, type, finite8712137658972009173omplex: set_list_complex > $o).
% 168.03/28.52  thf(func_def_238, type, finite3922522038869484883st_int: set_list_int > $o).
% 168.03/28.52  thf(func_def_239, type, finite8100373058378681591st_nat: set_list_nat > $o).
% 168.03/28.52  thf(func_def_240, type, finite306553202115118035t_real: set_list_real > $o).
% 168.03/28.52  thf(func_def_241, type, finite3004134309566078307T_VEBT: set_list_VEBT_VEBT > $o).
% 168.03/28.52  thf(func_def_242, type, finite_finite_nat: set_nat > $o).
% 168.03/28.52  thf(func_def_243, type, finite_finite_num: set_num > $o).
% 168.03/28.52  thf(func_def_244, type, finite6177210948735845034at_nat: set_Pr1261947904930325089at_nat > $o).
% 168.03/28.52  thf(func_def_245, type, finite_finite_rat: set_rat > $o).
% 168.03/28.52  thf(func_def_246, type, finite_finite_real: set_real > $o).
% 168.03/28.52  thf(func_def_247, type, finite1152437895449049373et_nat: set_set_nat > $o).
% 168.03/28.52  thf(func_def_248, type, finite9007344921179782393t_real: set_set_real > $o).
% 168.03/28.52  thf(func_def_249, type, finite5795047828879050333T_VEBT: set_VEBT_VEBT > $o).
% 168.03/28.52  thf(func_def_250, type, bij_be1856998921033663316omplex: (complex > complex) > set_complex > set_complex > $o).
% 168.03/28.52  thf(func_def_251, type, bij_betw_nat_complex: (nat > complex) > set_nat > set_complex > $o).
% 168.03/28.52  thf(func_def_252, type, bij_betw_nat_nat: (nat > nat) > set_nat > set_nat > $o).
% 168.03/28.52  thf(func_def_253, type, comp_C8797469213163452608nteger: ((code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > code_integer > code_integer) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 168.03/28.52  thf(func_def_254, type, comp_C1593894019821074884nteger: (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > code_integer) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 168.03/28.52  thf(func_def_255, type, comp_int_int_num: (int > int) > (num > int) > num > int).
% 168.03/28.52  thf(func_def_256, type, comp_int_nat_int: (int > nat) > (int > int) > int > nat).
% 168.03/28.52  thf(func_def_257, type, comp_nat_nat_nat: (nat > nat) > (nat > nat) > nat > nat).
% 168.03/28.52  thf(func_def_258, type, comp_nat_real_nat: (nat > real) > (nat > nat) > nat > real).
% 168.03/28.52  thf(func_def_259, type, id_o: $o > $o).
% 168.03/28.52  thf(func_def_260, type, id_nat: nat > nat).
% 168.03/28.52  thf(func_def_261, type, inj_on_nat_nat: (nat > nat) > set_nat > $o).
% 168.03/28.52  thf(func_def_262, type, inj_on_nat_char: (nat > char) > set_nat > $o).
% 168.03/28.52  thf(func_def_263, type, inj_on_real_real: (real > real) > set_real > $o).
% 168.03/28.52  thf(func_def_264, type, map_fu434086159418415080_int_o: (int > product_prod_nat_nat) > ((product_prod_nat_nat > $o) > int > $o) > (product_prod_nat_nat > product_prod_nat_nat > $o) > int > int > $o).
% 168.03/28.52  thf(func_def_265, type, map_fu4960017516451851995nt_int: (int > product_prod_nat_nat) > ((product_prod_nat_nat > product_prod_nat_nat) > int > int) > (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > int > int > int).
% 168.03/28.52  thf(func_def_266, type, map_fu4826362097070443709at_o_o: (int > product_prod_nat_nat) > ($o > $o) > (product_prod_nat_nat > $o) > int > $o).
% 168.03/28.52  thf(func_def_267, type, map_fu2345160673673942751at_nat: (int > product_prod_nat_nat) > (nat > nat) > (product_prod_nat_nat > nat) > int > nat).
% 168.03/28.52  thf(func_def_268, type, map_fu3667384564859982768at_int: (int > product_prod_nat_nat) > (product_prod_nat_nat > int) > (product_prod_nat_nat > product_prod_nat_nat) > int > int).
% 168.03/28.52  thf(func_def_269, type, strict1292158309912662752at_nat: (nat > nat) > set_nat > $o).
% 168.03/28.52  thf(func_def_270, type, the_in5290026491893676941l_real: set_real > (real > real) > real > real).
% 168.03/28.52  thf(func_def_271, type, fun_pair_leq: set_Pr8693737435421807431at_nat).
% 168.03/28.52  thf(func_def_272, type, fun_pair_less: set_Pr8693737435421807431at_nat).
% 168.03/28.52  thf(func_def_273, type, gcd_Gcd_nat: set_nat > nat).
% 168.03/28.52  thf(func_def_274, type, bezw: nat > nat > product_prod_int_int).
% 168.03/28.52  thf(func_def_275, type, bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o).
% 168.03/28.52  thf(func_def_276, type, gcd_gcd_int: int > int > int).
% 168.03/28.52  thf(func_def_277, type, gcd_gcd_nat: nat > nat > nat).
% 168.03/28.52  thf(func_def_278, type, gcd_nat_rel: product_prod_nat_nat > product_prod_nat_nat > $o).
% 168.03/28.52  thf(func_def_279, type, abs_abs_Code_integer: code_integer > code_integer).
% 168.03/28.52  thf(func_def_280, type, abs_abs_complex: complex > complex).
% 168.03/28.52  thf(func_def_281, type, abs_abs_int: int > int).
% 168.03/28.52  thf(func_def_282, type, abs_abs_rat: rat > rat).
% 168.03/28.52  thf(func_def_283, type, abs_abs_real: real > real).
% 168.03/28.52  thf(func_def_284, type, minus_8727706125548526216plex_o: (complex > $o) > (complex > $o) > complex > $o).
% 168.03/28.52  thf(func_def_285, type, minus_minus_int_o: (int > $o) > (int > $o) > int > $o).
% 168.03/28.52  thf(func_def_286, type, minus_1139252259498527702_nat_o: (list_nat > $o) > (list_nat > $o) > list_nat > $o).
% 168.03/28.52  thf(func_def_287, type, minus_minus_nat_o: (nat > $o) > (nat > $o) > nat > $o).
% 168.03/28.52  thf(func_def_288, type, minus_2270307095948843157_nat_o: (product_prod_nat_nat > $o) > (product_prod_nat_nat > $o) > product_prod_nat_nat > $o).
% 168.03/28.52  thf(func_def_289, type, minus_minus_real_o: (real > $o) > (real > $o) > real > $o).
% 168.03/28.52  thf(func_def_290, type, minus_8373710615458151222nteger: code_integer > code_integer > code_integer).
% 168.03/28.52  thf(func_def_291, type, minus_minus_complex: complex > complex > complex).
% 168.03/28.52  thf(func_def_292, type, minus_3235023915231533773d_enat: extended_enat > extended_enat > extended_enat).
% 168.03/28.52  thf(func_def_293, type, minus_minus_int: int > int > int).
% 168.03/28.52  thf(func_def_294, type, minus_minus_nat: nat > nat > nat).
% 168.03/28.52  thf(func_def_295, type, minus_minus_rat: rat > rat > rat).
% 168.03/28.52  thf(func_def_296, type, minus_minus_real: real > real > real).
% 168.03/28.52  thf(func_def_297, type, minus_811609699411566653omplex: set_complex > set_complex > set_complex).
% 168.03/28.52  thf(func_def_298, type, minus_minus_set_int: set_int > set_int > set_int).
% 168.03/28.52  thf(func_def_299, type, minus_7954133019191499631st_nat: set_list_nat > set_list_nat > set_list_nat).
% 168.03/28.52  thf(func_def_300, type, minus_minus_set_nat: set_nat > set_nat > set_nat).
% 168.03/28.52  thf(func_def_301, type, minus_1356011639430497352at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 168.03/28.52  thf(func_def_302, type, minus_minus_set_real: set_real > set_real > set_real).
% 168.03/28.52  thf(func_def_303, type, minus_5127226145743854075T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > set_VEBT_VEBT).
% 168.03/28.52  thf(func_def_304, type, one_one_Code_integer: code_integer).
% 168.03/28.52  thf(func_def_305, type, one_one_complex: complex).
% 168.03/28.52  thf(func_def_306, type, one_on7984719198319812577d_enat: extended_enat).
% 168.03/28.52  thf(func_def_307, type, one_one_int: int).
% 168.03/28.52  thf(func_def_308, type, one_one_nat: nat).
% 168.03/28.52  thf(func_def_309, type, one_one_rat: rat).
% 168.03/28.52  thf(func_def_310, type, one_one_real: real).
% 168.03/28.52  thf(func_def_311, type, plus_p5714425477246183910nteger: code_integer > code_integer > code_integer).
% 168.03/28.52  thf(func_def_312, type, plus_plus_complex: complex > complex > complex).
% 168.03/28.52  thf(func_def_313, type, plus_p3455044024723400733d_enat: extended_enat > extended_enat > extended_enat).
% 168.03/28.52  thf(func_def_314, type, plus_plus_int: int > int > int).
% 168.03/28.52  thf(func_def_315, type, plus_plus_nat: nat > nat > nat).
% 168.03/28.52  thf(func_def_316, type, plus_plus_num: num > num > num).
% 168.03/28.52  thf(func_def_317, type, plus_plus_rat: rat > rat > rat).
% 168.03/28.52  thf(func_def_318, type, plus_plus_real: real > real > real).
% 168.03/28.52  thf(func_def_319, type, sgn_sgn_Code_integer: code_integer > code_integer).
% 168.03/28.52  thf(func_def_320, type, sgn_sgn_complex: complex > complex).
% 168.03/28.52  thf(func_def_321, type, sgn_sgn_int: int > int).
% 168.03/28.52  thf(func_def_322, type, sgn_sgn_real: real > real).
% 168.03/28.52  thf(func_def_323, type, times_3573771949741848930nteger: code_integer > code_integer > code_integer).
% 168.03/28.52  thf(func_def_324, type, times_times_complex: complex > complex > complex).
% 168.03/28.52  thf(func_def_325, type, times_7803423173614009249d_enat: extended_enat > extended_enat > extended_enat).
% 168.03/28.52  thf(func_def_326, type, times_times_int: int > int > int).
% 168.03/28.52  thf(func_def_327, type, times_times_nat: nat > nat > nat).
% 168.03/28.52  thf(func_def_328, type, times_times_num: num > num > num).
% 168.03/28.52  thf(func_def_329, type, times_times_rat: rat > rat > rat).
% 168.03/28.52  thf(func_def_330, type, times_times_real: real > real > real).
% 168.03/28.52  thf(func_def_331, type, uminus1351360451143612070nteger: code_integer > code_integer).
% 168.03/28.52  thf(func_def_332, type, uminus1482373934393186551omplex: complex > complex).
% 168.03/28.52  thf(func_def_333, type, uminus_uminus_int: int > int).
% 168.03/28.52  thf(func_def_334, type, uminus_uminus_rat: rat > rat).
% 168.03/28.52  thf(func_def_335, type, uminus_uminus_real: real > real).
% 168.03/28.52  thf(func_def_336, type, uminus1532241313380277803et_int: set_int > set_int).
% 168.03/28.52  thf(func_def_337, type, uminus5710092332889474511et_nat: set_nat > set_nat).
% 168.03/28.52  thf(func_def_338, type, uminus6524753893492686040at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 168.03/28.52  thf(func_def_339, type, uminus612125837232591019t_real: set_real > set_real).
% 168.03/28.52  thf(func_def_340, type, uminus8041839845116263051T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT).
% 168.03/28.52  thf(func_def_341, type, zero_z3403309356797280102nteger: code_integer).
% 168.03/28.52  thf(func_def_342, type, zero_zero_complex: complex).
% 168.03/28.52  thf(func_def_343, type, zero_z5237406670263579293d_enat: extended_enat).
% 168.03/28.52  thf(func_def_344, type, zero_zero_int: int).
% 168.03/28.52  thf(func_def_345, type, zero_zero_nat: nat).
% 168.03/28.52  thf(func_def_346, type, zero_zero_rat: rat).
% 168.03/28.52  thf(func_def_347, type, zero_zero_real: real).
% 168.03/28.52  thf(func_def_348, type, groups6621422865394947399nteger: (complex > code_integer) > set_complex > code_integer).
% 168.03/28.52  thf(func_def_349, type, groups7754918857620584856omplex: (complex > complex) > set_complex > complex).
% 168.03/28.52  thf(func_def_350, type, groups5690904116761175830ex_int: (complex > int) > set_complex > int).
% 168.03/28.52  thf(func_def_351, type, groups5693394587270226106ex_nat: (complex > nat) > set_complex > nat).
% 168.03/28.52  thf(func_def_352, type, groups5058264527183730370ex_rat: (complex > rat) > set_complex > rat).
% 168.03/28.52  thf(func_def_353, type, groups5808333547571424918x_real: (complex > real) > set_complex > real).
% 168.03/28.52  thf(func_def_354, type, groups7873554091576472773nteger: (int > code_integer) > set_int > code_integer).
% 168.03/28.52  thf(func_def_355, type, groups3049146728041665814omplex: (int > complex) > set_int > complex).
% 168.03/28.52  thf(func_def_356, type, groups4538972089207619220nt_int: (int > int) > set_int > int).
% 168.03/28.52  thf(func_def_357, type, groups4541462559716669496nt_nat: (int > nat) > set_int > nat).
% 168.03/28.52  thf(func_def_358, type, groups3906332499630173760nt_rat: (int > rat) > set_int > rat).
% 168.03/28.52  thf(func_def_359, type, groups8778361861064173332t_real: (int > real) > set_int > real).
% 168.03/28.52  thf(func_def_360, type, groups7501900531339628137nteger: (nat > code_integer) > set_nat > code_integer).
% 168.03/28.52  thf(func_def_361, type, groups2073611262835488442omplex: (nat > complex) > set_nat > complex).
% 168.03/28.52  thf(func_def_362, type, groups3539618377306564664at_int: (nat > int) > set_nat > int).
% 168.03/28.52  thf(func_def_363, type, groups3542108847815614940at_nat: (nat > nat) > set_nat > nat).
% 168.03/28.52  thf(func_def_364, type, groups2906978787729119204at_rat: (nat > rat) > set_nat > rat).
% 168.03/28.52  thf(func_def_365, type, groups6591440286371151544t_real: (nat > real) > set_nat > real).
% 168.03/28.52  thf(func_def_366, type, groups6381953495645901045omplex: (product_prod_nat_nat > complex) > set_Pr1261947904930325089at_nat > complex).
% 168.03/28.52  thf(func_def_367, type, groups977919841031483927at_nat: (product_prod_nat_nat > nat) > set_Pr1261947904930325089at_nat > nat).
% 168.03/28.52  thf(func_def_368, type, groups342789780944988191at_rat: (product_prod_nat_nat > rat) > set_Pr1261947904930325089at_nat > rat).
% 168.03/28.52  thf(func_def_369, type, groups4567486121110086003t_real: (product_prod_nat_nat > real) > set_Pr1261947904930325089at_nat > real).
% 168.03/28.52  thf(func_def_370, type, groups7713935264441627589nteger: (real > code_integer) > set_real > code_integer).
% 168.03/28.52  thf(func_def_371, type, groups5754745047067104278omplex: (real > complex) > set_real > complex).
% 168.03/28.52  thf(func_def_372, type, groups1932886352136224148al_int: (real > int) > set_real > int).
% 168.03/28.52  thf(func_def_373, type, groups1935376822645274424al_nat: (real > nat) > set_real > nat).
% 168.03/28.52  thf(func_def_374, type, groups1300246762558778688al_rat: (real > rat) > set_real > rat).
% 168.03/28.52  thf(func_def_375, type, groups8097168146408367636l_real: (real > real) > set_real > real).
% 168.03/28.52  thf(func_def_376, type, groups1794756597179926696omplex: (vEBT_VEBT > complex) > set_VEBT_VEBT > complex).
% 168.03/28.52  thf(func_def_377, type, groups769130701875090982BT_int: (vEBT_VEBT > int) > set_VEBT_VEBT > int).
% 168.03/28.52  thf(func_def_378, type, groups771621172384141258BT_nat: (vEBT_VEBT > nat) > set_VEBT_VEBT > nat).
% 168.03/28.52  thf(func_def_379, type, groups136491112297645522BT_rat: (vEBT_VEBT > rat) > set_VEBT_VEBT > rat).
% 168.03/28.52  thf(func_def_380, type, groups2240296850493347238T_real: (vEBT_VEBT > real) > set_VEBT_VEBT > real).
% 168.03/28.52  thf(func_def_381, type, groups8682486955453173170nteger: (complex > code_integer) > set_complex > code_integer).
% 168.03/28.52  thf(func_def_382, type, groups3708469109370488835omplex: (complex > complex) > set_complex > complex).
% 168.03/28.52  thf(func_def_383, type, groups858564598930262913ex_int: (complex > int) > set_complex > int).
% 168.03/28.52  thf(func_def_384, type, groups861055069439313189ex_nat: (complex > nat) > set_complex > nat).
% 168.03/28.52  thf(func_def_385, type, groups225925009352817453ex_rat: (complex > rat) > set_complex > rat).
% 168.03/28.52  thf(func_def_386, type, groups766887009212190081x_real: (complex > real) > set_complex > real).
% 168.03/28.52  thf(func_def_387, type, groups7440179247065528705omplex: (int > complex) > set_int > complex).
% 168.03/28.52  thf(func_def_388, type, groups1705073143266064639nt_int: (int > int) > set_int > int).
% 168.03/28.52  thf(func_def_389, type, groups1707563613775114915nt_nat: (int > nat) > set_int > nat).
% 168.03/28.52  thf(func_def_390, type, groups1072433553688619179nt_rat: (int > rat) > set_int > rat).
% 168.03/28.52  thf(func_def_391, type, groups2316167850115554303t_real: (int > real) > set_int > real).
% 168.03/28.52  thf(func_def_392, type, groups3455450783089532116nteger: (nat > code_integer) > set_nat > code_integer).
% 168.03/28.52  thf(func_def_393, type, groups6464643781859351333omplex: (nat > complex) > set_nat > complex).
% 168.03/28.52  thf(func_def_394, type, groups705719431365010083at_int: (nat > int) > set_nat > int).
% 168.03/28.52  thf(func_def_395, type, groups708209901874060359at_nat: (nat > nat) > set_nat > nat).
% 168.03/28.52  thf(func_def_396, type, groups73079841787564623at_rat: (nat > rat) > set_nat > rat).
% 168.03/28.52  thf(func_def_397, type, groups129246275422532515t_real: (nat > real) > set_nat > real).
% 168.03/28.52  thf(func_def_398, type, groups8110221916422527690omplex: (product_prod_nat_nat > complex) > set_Pr1261947904930325089at_nat > complex).
% 168.03/28.52  thf(func_def_399, type, groups713298508707869441omplex: (real > complex) > set_real > complex).
% 168.03/28.52  thf(func_def_400, type, groups4694064378042380927al_int: (real > int) > set_real > int).
% 168.03/28.52  thf(func_def_401, type, groups4696554848551431203al_nat: (real > nat) > set_real > nat).
% 168.03/28.52  thf(func_def_402, type, groups4061424788464935467al_rat: (real > rat) > set_real > rat).
% 168.03/28.52  thf(func_def_403, type, groups1681761925125756287l_real: (real > real) > set_real > real).
% 168.03/28.52  thf(func_def_404, type, groups127312072573709053omplex: (vEBT_VEBT > complex) > set_VEBT_VEBT > complex).
% 168.03/28.52  thf(func_def_405, type, groups2703838992350267259T_real: (vEBT_VEBT > real) > set_VEBT_VEBT > real).
% 168.03/28.52  thf(func_def_406, type, groups9116527308978886569_o_int: ($o > int) > int > list_o > int).
% 168.03/28.52  thf(func_def_407, type, groups4561878855575611511st_nat: list_nat > nat).
% 168.03/28.52  thf(func_def_408, type, the_int: (int > $o) > int).
% 168.03/28.52  thf(func_def_409, type, the_real: (real > $o) > real).
% 168.03/28.52  thf(func_def_410, type, if_int_int: $o > (int > int) > (int > int) > int > int).
% 168.03/28.52  thf(func_def_411, type, if_Code_integer: $o > code_integer > code_integer > code_integer).
% 168.03/28.52  thf(func_def_412, type, if_complex: $o > complex > complex > complex).
% 168.03/28.52  thf(func_def_413, type, if_Extended_enat: $o > extended_enat > extended_enat > extended_enat).
% 168.03/28.52  thf(func_def_414, type, if_int: $o > int > int > int).
% 168.03/28.52  thf(func_def_415, type, if_list_int: $o > list_int > list_int > list_int).
% 168.03/28.52  thf(func_def_416, type, if_list_nat: $o > list_nat > list_nat > list_nat).
% 168.03/28.52  thf(func_def_417, type, if_nat: $o > nat > nat > nat).
% 168.03/28.52  thf(func_def_418, type, if_num: $o > num > num > num).
% 168.03/28.52  thf(func_def_419, type, if_option_nat: $o > option_nat > option_nat > option_nat).
% 168.03/28.52  thf(func_def_420, type, if_option_num: $o > option_num > option_num > option_num).
% 168.03/28.52  thf(func_def_421, type, if_Pro5737122678794959658eger_o: $o > produc6271795597528267376eger_o > produc6271795597528267376eger_o > produc6271795597528267376eger_o).
% 168.03/28.52  thf(func_def_422, type, if_Pro6119634080678213985nteger: $o > produc8923325533196201883nteger > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 168.03/28.52  thf(func_def_423, type, if_Pro3027730157355071871nt_int: $o > product_prod_int_int > product_prod_int_int > product_prod_int_int).
% 168.03/28.52  thf(func_def_424, type, if_Pro6206227464963214023at_nat: $o > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat).
% 168.03/28.52  thf(func_def_425, type, if_rat: $o > rat > rat > rat).
% 168.03/28.52  thf(func_def_426, type, if_real: $o > real > real > real).
% 168.03/28.52  thf(func_def_427, type, if_set_nat: $o > set_nat > set_nat > set_nat).
% 168.03/28.52  thf(func_def_428, type, if_set_real: $o > set_real > set_real > set_real).
% 168.03/28.52  thf(func_def_429, type, if_VEBT_VEBT: $o > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT).
% 168.03/28.52  thf(func_def_430, type, infini8530281810654367211te_nat: set_nat > nat > nat).
% 168.03/28.52  thf(func_def_431, type, abs_Integ: product_prod_nat_nat > int).
% 168.03/28.52  thf(func_def_432, type, rep_Integ: int > product_prod_nat_nat).
% 168.03/28.52  thf(func_def_433, type, nat2: int > nat).
% 168.03/28.52  thf(func_def_434, type, power_int_real: real > int > real).
% 168.03/28.52  thf(func_def_435, type, ring_1_Ints_real: set_real).
% 168.03/28.52  thf(func_def_436, type, ring_18347121197199848620nteger: int > code_integer).
% 168.03/28.52  thf(func_def_437, type, ring_17405671764205052669omplex: int > complex).
% 168.03/28.52  thf(func_def_438, type, ring_1_of_int_int: int > int).
% 168.03/28.52  thf(func_def_439, type, ring_1_of_int_rat: int > rat).
% 168.03/28.52  thf(func_def_440, type, ring_1_of_int_real: int > real).
% 168.03/28.52  thf(func_def_441, type, inf_in1870772243966228564d_enat: extended_enat > extended_enat > extended_enat).
% 168.03/28.52  thf(func_def_442, type, inf_inf_nat: nat > nat > nat).
% 168.03/28.52  thf(func_def_443, type, inf_in2572325071724192079at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 168.03/28.52  thf(func_def_444, type, semila1623282765462674594er_nat: (nat > nat > nat) > nat > (nat > nat > $o) > (nat > nat > $o) > $o).
% 168.03/28.52  thf(func_def_445, type, sup_su3973961784419623482d_enat: extended_enat > extended_enat > extended_enat).
% 168.03/28.52  thf(func_def_446, type, sup_sup_nat: nat > nat > nat).
% 168.03/28.52  thf(func_def_447, type, sup_sup_set_nat: set_nat > set_nat > set_nat).
% 168.03/28.52  thf(func_def_448, type, sup_su6327502436637775413at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 168.03/28.52  thf(func_def_449, type, lattic8265883725875713057ax_nat: set_nat > nat).
% 168.03/28.52  thf(func_def_450, type, bfun_nat_real: (nat > real) > filter_nat > $o).
% 168.03/28.52  thf(func_def_451, type, append_int: list_int > list_int > list_int).
% 168.03/28.52  thf(func_def_452, type, append_nat: list_nat > list_nat > list_nat).
% 168.03/28.52  thf(func_def_453, type, drop_nat: nat > list_nat > list_nat).
% 168.03/28.52  thf(func_def_454, type, last_nat: list_nat > nat).
% 168.03/28.52  thf(func_def_455, type, linord2614967742042102400et_nat: set_nat > list_nat).
% 168.03/28.52  thf(func_def_456, type, cons_int: int > list_int > list_int).
% 168.03/28.52  thf(func_def_457, type, cons_nat: nat > list_nat > list_nat).
% 168.03/28.52  thf(func_def_458, type, nil_int: list_int).
% 168.03/28.52  thf(func_def_459, type, nil_nat: list_nat).
% 168.03/28.52  thf(func_def_460, type, hd_nat: list_nat > nat).
% 168.03/28.52  thf(func_def_461, type, map_nat_nat: (nat > nat) > list_nat > list_nat).
% 168.03/28.52  thf(func_def_462, type, set_o2: list_o > set_o).
% 168.03/28.52  thf(func_def_463, type, set_complex2: list_complex > set_complex).
% 168.03/28.52  thf(func_def_464, type, set_int2: list_int > set_int).
% 168.03/28.52  thf(func_def_465, type, set_nat2: list_nat > set_nat).
% 168.03/28.52  thf(func_def_466, type, set_Pr5648618587558075414at_nat: list_P6011104703257516679at_nat > set_Pr1261947904930325089at_nat).
% 168.03/28.52  thf(func_def_467, type, set_real2: list_real > set_real).
% 168.03/28.52  thf(func_def_468, type, set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT).
% 168.03/28.52  thf(func_def_469, type, size_list_VEBT_VEBT: (vEBT_VEBT > nat) > list_VEBT_VEBT > nat).
% 168.03/28.52  thf(func_def_470, type, tl_nat: list_nat > list_nat).
% 168.03/28.52  thf(func_def_471, type, list_update_o: list_o > nat > $o > list_o).
% 168.03/28.52  thf(func_def_472, type, list_update_complex: list_complex > nat > complex > list_complex).
% 168.03/28.52  thf(func_def_473, type, list_update_int: list_int > nat > int > list_int).
% 168.03/28.52  thf(func_def_474, type, list_update_nat: list_nat > nat > nat > list_nat).
% 168.03/28.52  thf(func_def_475, type, list_u6180841689913720943at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat > list_P6011104703257516679at_nat).
% 168.03/28.52  thf(func_def_476, type, list_update_real: list_real > nat > real > list_real).
% 168.03/28.52  thf(func_def_477, type, list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT).
% 168.03/28.52  thf(func_def_478, type, nth_o: list_o > nat > $o).
% 168.03/28.52  thf(func_def_479, type, nth_complex: list_complex > nat > complex).
% 168.03/28.52  thf(func_def_480, type, nth_int: list_int > nat > int).
% 168.03/28.52  thf(func_def_481, type, nth_nat: list_nat > nat > nat).
% 168.03/28.52  thf(func_def_482, type, nth_num: list_num > nat > num).
% 168.03/28.52  thf(func_def_483, type, nth_Product_prod_o_o: list_P4002435161011370285od_o_o > nat > product_prod_o_o).
% 168.03/28.52  thf(func_def_484, type, nth_Pr1649062631805364268_o_int: list_P3795440434834930179_o_int > nat > product_prod_o_int).
% 168.03/28.52  thf(func_def_485, type, nth_Pr5826913651314560976_o_nat: list_P6285523579766656935_o_nat > nat > product_prod_o_nat).
% 168.03/28.52  thf(func_def_486, type, nth_Pr6777367263587873994T_VEBT: list_P7495141550334521929T_VEBT > nat > produc2504756804600209347T_VEBT).
% 168.03/28.52  thf(func_def_487, type, nth_Pr7617993195940197384at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat).
% 168.03/28.52  thf(func_def_488, type, nth_Pr8326237132889035090at_num: list_P1726324292696863441at_num > nat > product_prod_nat_num).
% 168.03/28.52  thf(func_def_489, type, nth_Pr6456567536196504476um_num: list_P3744719386663036955um_num > nat > product_prod_num_num).
% 168.03/28.52  thf(func_def_490, type, nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o).
% 168.03/28.52  thf(func_def_491, type, nth_Pr6837108013167703752BT_int: list_P4547456442757143711BT_int > nat > produc4894624898956917775BT_int).
% 168.03/28.52  thf(func_def_492, type, nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat).
% 168.03/28.52  thf(func_def_493, type, nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT).
% 168.03/28.52  thf(func_def_494, type, nth_real: list_real > nat > real).
% 168.03/28.52  thf(func_def_495, type, nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT).
% 168.03/28.52  thf(func_def_496, type, product_o_o: list_o > list_o > list_P4002435161011370285od_o_o).
% 168.03/28.52  thf(func_def_497, type, product_o_int: list_o > list_int > list_P3795440434834930179_o_int).
% 168.03/28.52  thf(func_def_498, type, product_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat).
% 168.03/28.52  thf(func_def_499, type, product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT).
% 168.03/28.52  thf(func_def_500, type, product_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o).
% 168.03/28.52  thf(func_def_501, type, product_nat_num: list_nat > list_num > list_P1726324292696863441at_num).
% 168.03/28.52  thf(func_def_502, type, produc7156399406898700509T_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT).
% 168.03/28.52  thf(func_def_503, type, product_num_num: list_num > list_num > list_P3744719386663036955um_num).
% 168.03/28.52  thf(func_def_504, type, product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o).
% 168.03/28.52  thf(func_def_505, type, produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int).
% 168.03/28.52  thf(func_def_506, type, produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat).
% 168.03/28.52  thf(func_def_507, type, produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT).
% 168.03/28.52  thf(func_def_508, type, replicate_o: nat > $o > list_o).
% 168.03/28.52  thf(func_def_509, type, replicate_complex: nat > complex > list_complex).
% 168.03/28.52  thf(func_def_510, type, replicate_int: nat > int > list_int).
% 168.03/28.52  thf(func_def_511, type, replicate_nat: nat > nat > list_nat).
% 168.03/28.52  thf(func_def_512, type, replic4235873036481779905at_nat: nat > product_prod_nat_nat > list_P6011104703257516679at_nat).
% 168.03/28.52  thf(func_def_513, type, replicate_real: nat > real > list_real).
% 168.03/28.52  thf(func_def_514, type, replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT).
% 168.03/28.52  thf(func_def_515, type, sorted_wrt_nat: (nat > nat > $o) > list_nat > $o).
% 168.03/28.52  thf(func_def_516, type, take_nat: nat > list_nat > list_nat).
% 168.03/28.52  thf(func_def_517, type, upt: nat > nat > list_nat).
% 168.03/28.52  thf(func_def_518, type, upto: int > int > list_int).
% 168.03/28.52  thf(func_def_519, type, upto_aux: int > int > list_int > list_int).
% 168.03/28.52  thf(func_def_520, type, suc: nat > nat).
% 168.03/28.52  thf(func_def_521, type, compow_nat_nat: nat > (nat > nat) > nat > nat).
% 168.03/28.52  thf(func_def_522, type, case_nat_o: $o > (nat > $o) > nat > $o).
% 168.03/28.52  thf(func_def_523, type, case_nat_nat: nat > (nat > nat) > nat > nat).
% 168.03/28.52  thf(func_def_524, type, case_nat_option_num: option_num > (nat > option_num) > nat > option_num).
% 168.03/28.52  thf(func_def_525, type, pred: nat > nat).
% 168.03/28.52  thf(func_def_526, type, semiri4939895301339042750nteger: nat > code_integer).
% 168.03/28.52  thf(func_def_527, type, semiri8010041392384452111omplex: nat > complex).
% 168.03/28.52  thf(func_def_528, type, semiri4216267220026989637d_enat: nat > extended_enat).
% 168.03/28.52  thf(func_def_529, type, semiri1314217659103216013at_int: nat > int).
% 168.03/28.52  thf(func_def_530, type, semiri1316708129612266289at_nat: nat > nat).
% 168.03/28.52  thf(func_def_531, type, semiri681578069525770553at_rat: nat > rat).
% 168.03/28.52  thf(func_def_532, type, semiri5074537144036343181t_real: nat > real).
% 168.03/28.52  thf(func_def_533, type, semiri2816024913162550771omplex: (complex > complex) > nat > complex > complex).
% 168.03/28.52  thf(func_def_534, type, semiri8420488043553186161ux_int: (int > int) > nat > int > int).
% 168.03/28.52  thf(func_def_535, type, semiri8422978514062236437ux_nat: (nat > nat) > nat > nat > nat).
% 168.03/28.52  thf(func_def_536, type, semiri7787848453975740701ux_rat: (rat > rat) > nat > rat > rat).
% 168.03/28.52  thf(func_def_537, type, semiri7260567687927622513x_real: (real > real) > nat > real > real).
% 168.03/28.52  thf(func_def_538, type, size_size_list_o: list_o > nat).
% 168.03/28.52  thf(func_def_539, type, size_s3451745648224563538omplex: list_complex > nat).
% 168.03/28.52  thf(func_def_540, type, size_size_list_int: list_int > nat).
% 168.03/28.52  thf(func_def_541, type, size_size_list_nat: list_nat > nat).
% 168.03/28.52  thf(func_def_542, type, size_size_list_num: list_num > nat).
% 168.03/28.52  thf(func_def_543, type, size_s1515746228057227161od_o_o: list_P4002435161011370285od_o_o > nat).
% 168.03/28.52  thf(func_def_544, type, size_s2953683556165314199_o_int: list_P3795440434834930179_o_int > nat).
% 168.03/28.52  thf(func_def_545, type, size_s5443766701097040955_o_nat: list_P6285523579766656935_o_nat > nat).
% 168.03/28.52  thf(func_def_546, type, size_s4313452262239582901T_VEBT: list_P7495141550334521929T_VEBT > nat).
% 168.03/28.52  thf(func_def_547, type, size_s6491369823275344609_nat_o: list_P7333126701944960589_nat_o > nat).
% 168.03/28.52  thf(func_def_548, type, size_s5460976970255530739at_nat: list_P6011104703257516679at_nat > nat).
% 168.03/28.52  thf(func_def_549, type, size_s4762443039079500285T_VEBT: list_P5647936690300460905T_VEBT > nat).
% 168.03/28.52  thf(func_def_550, type, size_s9168528473962070013VEBT_o: list_P3126845725202233233VEBT_o > nat).
% 168.03/28.52  thf(func_def_551, type, size_s3661962791536183091BT_int: list_P4547456442757143711BT_int > nat).
% 168.03/28.52  thf(func_def_552, type, size_s6152045936467909847BT_nat: list_P7037539587688870467BT_nat > nat).
% 168.03/28.52  thf(func_def_553, type, size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat).
% 168.03/28.52  thf(func_def_554, type, size_size_list_real: list_real > nat).
% 168.03/28.52  thf(func_def_555, type, size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat).
% 168.03/28.52  thf(func_def_556, type, size_size_num: num > nat).
% 168.03/28.52  thf(func_def_557, type, size_size_option_nat: option_nat > nat).
% 168.03/28.52  thf(func_def_558, type, size_size_option_num: option_num > nat).
% 168.03/28.52  thf(func_def_559, type, size_s170228958280169651at_nat: option4927543243414619207at_nat > nat).
% 168.03/28.52  thf(func_def_560, type, size_size_VEBT_VEBT: vEBT_VEBT > nat).
% 168.03/28.52  thf(func_def_561, type, nat_list_encode: list_nat > nat).
% 168.03/28.52  thf(func_def_562, type, nat_list_encode_rel: list_nat > list_nat > $o).
% 168.03/28.52  thf(func_def_563, type, nat_prod_decode_aux: nat > nat > product_prod_nat_nat).
% 168.03/28.52  thf(func_def_564, type, nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o).
% 168.03/28.52  thf(func_def_565, type, nat_prod_encode: product_prod_nat_nat > nat).
% 168.03/28.52  thf(func_def_566, type, nat_set_decode: nat > set_nat).
% 168.03/28.52  thf(func_def_567, type, nat_set_encode: set_nat > nat).
% 168.03/28.52  thf(func_def_568, type, nat_triangle: nat > nat).
% 168.03/28.52  thf(func_def_569, type, root: nat > real > real).
% 168.03/28.52  thf(func_def_570, type, sqrt: real > real).
% 168.03/28.52  thf(func_def_571, type, bitM: num > num).
% 168.03/28.52  thf(func_def_572, type, inc: num > num).
% 168.03/28.52  thf(func_def_573, type, neg_nu8804712462038260780nteger: code_integer > code_integer).
% 168.03/28.52  thf(func_def_574, type, neg_nu7009210354673126013omplex: complex > complex).
% 168.03/28.52  thf(func_def_575, type, neg_numeral_dbl_int: int > int).
% 168.03/28.52  thf(func_def_576, type, neg_numeral_dbl_rat: rat > rat).
% 168.03/28.52  thf(func_def_577, type, neg_numeral_dbl_real: real > real).
% 168.03/28.52  thf(func_def_578, type, neg_nu7757733837767384882nteger: code_integer > code_integer).
% 168.03/28.52  thf(func_def_579, type, neg_nu6511756317524482435omplex: complex > complex).
% 168.03/28.52  thf(func_def_580, type, neg_nu3811975205180677377ec_int: int > int).
% 168.03/28.52  thf(func_def_581, type, neg_nu3179335615603231917ec_rat: rat > rat).
% 168.03/28.52  thf(func_def_582, type, neg_nu6075765906172075777c_real: real > real).
% 168.03/28.52  thf(func_def_583, type, neg_nu5831290666863070958nteger: code_integer > code_integer).
% 168.03/28.52  thf(func_def_584, type, neg_nu8557863876264182079omplex: complex > complex).
% 168.03/28.52  thf(func_def_585, type, neg_nu5851722552734809277nc_int: int > int).
% 168.03/28.52  thf(func_def_586, type, neg_nu5219082963157363817nc_rat: rat > rat).
% 168.03/28.52  thf(func_def_587, type, neg_nu8295874005876285629c_real: real > real).
% 168.03/28.52  thf(func_def_588, type, neg_numeral_sub_int: num > num > int).
% 168.03/28.52  thf(func_def_589, type, bit0: num > num).
% 168.03/28.52  thf(func_def_590, type, bit1: num > num).
% 168.03/28.52  thf(func_def_591, type, one: num).
% 168.03/28.52  thf(func_def_592, type, case_num_option_num: option_num > (num > option_num) > (num > option_num) > num > option_num).
% 168.03/28.52  thf(func_def_593, type, size_num: num > nat).
% 168.03/28.52  thf(func_def_594, type, num_of_nat: nat > num).
% 168.03/28.52  thf(func_def_595, type, numera6620942414471956472nteger: num > code_integer).
% 168.03/28.52  thf(func_def_596, type, numera6690914467698888265omplex: num > complex).
% 168.03/28.52  thf(func_def_597, type, numera1916890842035813515d_enat: num > extended_enat).
% 168.03/28.52  thf(func_def_598, type, numeral_numeral_int: num > int).
% 168.03/28.52  thf(func_def_599, type, numeral_numeral_nat: num > nat).
% 168.03/28.52  thf(func_def_600, type, numeral_numeral_rat: num > rat).
% 168.03/28.52  thf(func_def_601, type, numeral_numeral_real: num > real).
% 168.03/28.52  thf(func_def_602, type, pow: num > num > num).
% 168.03/28.52  thf(func_def_603, type, pred_numeral: num > nat).
% 168.03/28.52  thf(func_def_604, type, sqr: num > num).
% 168.03/28.52  thf(func_def_605, type, none_nat: option_nat).
% 168.03/28.52  thf(func_def_606, type, none_num: option_num).
% 168.03/28.52  thf(func_def_607, type, none_P5556105721700978146at_nat: option4927543243414619207at_nat).
% 168.03/28.52  thf(func_def_608, type, some_nat: nat > option_nat).
% 168.03/28.52  thf(func_def_609, type, some_num: num > option_num).
% 168.03/28.52  thf(func_def_610, type, some_P7363390416028606310at_nat: product_prod_nat_nat > option4927543243414619207at_nat).
% 168.03/28.52  thf(func_def_611, type, case_o184042715313410164at_nat: $o > (product_prod_nat_nat > $o) > option4927543243414619207at_nat > $o).
% 168.03/28.52  thf(func_def_612, type, case_option_int_num: int > (num > int) > option_num > int).
% 168.03/28.52  thf(func_def_613, type, case_option_num_num: num > (num > num) > option_num > num).
% 168.03/28.52  thf(func_def_614, type, case_o6005452278849405969um_num: option_num > (num > option_num) > option_num > option_num).
% 168.03/28.52  thf(func_def_615, type, map_option_num_num: (num > num) > option_num > option_num).
% 168.03/28.52  thf(func_def_616, type, size_option_nat: (nat > nat) > option_nat > nat).
% 168.03/28.52  thf(func_def_617, type, size_option_num: (num > nat) > option_num > nat).
% 168.03/28.52  thf(func_def_618, type, size_o8335143837870341156at_nat: (product_prod_nat_nat > nat) > option4927543243414619207at_nat > nat).
% 168.03/28.52  thf(func_def_619, type, the_nat: option_nat > nat).
% 168.03/28.52  thf(func_def_620, type, the_num: option_num > num).
% 168.03/28.52  thf(func_def_621, type, the_Pr8591224930841456533at_nat: option4927543243414619207at_nat > product_prod_nat_nat).
% 168.03/28.52  thf(func_def_622, type, order_underS_nat: set_Pr1261947904930325089at_nat > nat > set_nat).
% 168.03/28.52  thf(func_def_623, type, bot_bo4199563552545308370d_enat: extended_enat).
% 168.03/28.52  thf(func_def_624, type, bot_bot_nat: nat).
% 168.03/28.52  thf(func_def_625, type, bot_bot_set_complex: set_complex).
% 168.03/28.52  thf(func_def_626, type, bot_bot_set_int: set_int).
% 168.03/28.52  thf(func_def_627, type, bot_bot_set_nat: set_nat).
% 168.03/28.52  thf(func_def_628, type, bot_bot_set_num: set_num).
% 168.03/28.52  thf(func_def_629, type, bot_bo2099793752762293965at_nat: set_Pr1261947904930325089at_nat).
% 168.03/28.52  thf(func_def_630, type, bot_bot_set_rat: set_rat).
% 168.03/28.52  thf(func_def_631, type, bot_bot_set_real: set_real).
% 168.03/28.52  thf(func_def_632, type, bot_bot_set_set_nat: set_set_nat).
% 168.03/28.52  thf(func_def_633, type, bot_bot_set_set_real: set_set_real).
% 168.03/28.52  thf(func_def_634, type, bot_bo8194388402131092736T_VEBT: set_VEBT_VEBT).
% 168.03/28.52  thf(func_def_635, type, ord_Least_nat: (nat > $o) > nat).
% 168.03/28.52  thf(func_def_636, type, ord_Least_real: (real > $o) > real).
% 168.03/28.52  thf(func_def_637, type, ord_le6747313008572928689nteger: code_integer > code_integer > $o).
% 168.03/28.52  thf(func_def_638, type, ord_le72135733267957522d_enat: extended_enat > extended_enat > $o).
% 168.03/28.52  thf(func_def_639, type, ord_less_int: int > int > $o).
% 168.03/28.52  thf(func_def_640, type, ord_less_nat: nat > nat > $o).
% 168.03/28.52  thf(func_def_641, type, ord_less_num: num > num > $o).
% 168.03/28.52  thf(func_def_642, type, ord_less_rat: rat > rat > $o).
% 168.03/28.52  thf(func_def_643, type, ord_less_real: real > real > $o).
% 168.03/28.52  thf(func_def_644, type, ord_less_set_complex: set_complex > set_complex > $o).
% 168.03/28.52  thf(func_def_645, type, ord_less_set_int: set_int > set_int > $o).
% 168.03/28.52  thf(func_def_646, type, ord_less_set_nat: set_nat > set_nat > $o).
% 168.03/28.52  thf(func_def_647, type, ord_less_set_num: set_num > set_num > $o).
% 168.03/28.52  thf(func_def_648, type, ord_le7866589430770878221at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o).
% 168.03/28.52  thf(func_def_649, type, ord_less_set_rat: set_rat > set_rat > $o).
% 168.03/28.52  thf(func_def_650, type, ord_less_set_real: set_real > set_real > $o).
% 168.03/28.52  thf(func_def_651, type, ord_less_set_set_nat: set_set_nat > set_set_nat > $o).
% 168.03/28.52  thf(func_def_652, type, ord_le7926960851185191020t_real: set_set_real > set_set_real > $o).
% 168.03/28.52  thf(func_def_653, type, ord_le3480810397992357184T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > $o).
% 168.03/28.52  thf(func_def_654, type, ord_le3102999989581377725nteger: code_integer > code_integer > $o).
% 168.03/28.52  thf(func_def_655, type, ord_le2932123472753598470d_enat: extended_enat > extended_enat > $o).
% 168.03/28.52  thf(func_def_656, type, ord_le2510731241096832064er_nat: filter_nat > filter_nat > $o).
% 168.03/28.52  thf(func_def_657, type, ord_less_eq_int: int > int > $o).
% 168.03/28.52  thf(func_def_658, type, ord_less_eq_nat: nat > nat > $o).
% 168.03/28.52  thf(func_def_659, type, ord_less_eq_num: num > num > $o).
% 168.03/28.52  thf(func_def_660, type, ord_less_eq_rat: rat > rat > $o).
% 168.03/28.52  thf(func_def_661, type, ord_less_eq_real: real > real > $o).
% 168.03/28.52  thf(func_def_662, type, ord_less_eq_set_o: set_o > set_o > $o).
% 168.03/28.52  thf(func_def_663, type, ord_le211207098394363844omplex: set_complex > set_complex > $o).
% 168.03/28.52  thf(func_def_664, type, ord_less_eq_set_int: set_int > set_int > $o).
% 168.03/28.52  thf(func_def_665, type, ord_less_eq_set_nat: set_nat > set_nat > $o).
% 168.03/28.52  thf(func_def_666, type, ord_less_eq_set_num: set_num > set_num > $o).
% 168.03/28.52  thf(func_def_667, type, ord_le3146513528884898305at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o).
% 168.03/28.52  thf(func_def_668, type, ord_less_eq_set_real: set_real > set_real > $o).
% 168.03/28.52  thf(func_def_669, type, ord_le6893508408891458716et_nat: set_set_nat > set_set_nat > $o).
% 168.03/28.52  thf(func_def_670, type, ord_le3558479182127378552t_real: set_set_real > set_set_real > $o).
% 168.03/28.52  thf(func_def_671, type, ord_le4337996190870823476T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > $o).
% 168.03/28.52  thf(func_def_672, type, ord_max_Code_integer: code_integer > code_integer > code_integer).
% 168.03/28.52  thf(func_def_673, type, ord_ma741700101516333627d_enat: extended_enat > extended_enat > extended_enat).
% 168.03/28.52  thf(func_def_674, type, ord_max_int: int > int > int).
% 168.03/28.52  thf(func_def_675, type, ord_max_nat: nat > nat > nat).
% 168.03/28.52  thf(func_def_676, type, ord_max_num: num > num > num).
% 168.03/28.52  thf(func_def_677, type, ord_max_rat: rat > rat > rat).
% 168.03/28.52  thf(func_def_678, type, ord_max_real: real > real > real).
% 168.03/28.52  thf(func_def_679, type, ord_max_set_nat: set_nat > set_nat > set_nat).
% 168.03/28.52  thf(func_def_680, type, ord_max_set_real: set_real > set_real > set_real).
% 168.03/28.52  thf(func_def_681, type, ord_mi8085742599997312461d_enat: extended_enat > extended_enat > extended_enat).
% 168.03/28.52  thf(func_def_682, type, ord_min_nat: nat > nat > nat).
% 168.03/28.52  thf(func_def_683, type, order_Greatest_nat: (nat > $o) > nat).
% 168.03/28.52  thf(func_def_684, type, order_9091379641038594480t_real: (nat > real) > $o).
% 168.03/28.52  thf(func_def_685, type, order_mono_nat_nat: (nat > nat) > $o).
% 168.03/28.52  thf(func_def_686, type, order_mono_nat_real: (nat > real) > $o).
% 168.03/28.52  thf(func_def_687, type, order_5726023648592871131at_nat: (nat > nat) > $o).
% 168.03/28.52  thf(func_def_688, type, order_7092887310737990675l_real: (real > real) > $o).
% 168.03/28.52  thf(func_def_689, type, ordering_top_nat: (nat > nat > $o) > (nat > nat > $o) > nat > $o).
% 168.03/28.52  thf(func_def_690, type, top_top_set_o: set_o).
% 168.03/28.52  thf(func_def_691, type, top_top_set_nat: set_nat).
% 168.03/28.52  thf(func_def_692, type, top_to1996260823553986621t_unit: set_Product_unit).
% 168.03/28.52  thf(func_def_693, type, top_top_set_real: set_real).
% 168.03/28.52  thf(func_def_694, type, top_top_set_char: set_char).
% 168.03/28.52  thf(func_def_695, type, power_8256067586552552935nteger: code_integer > nat > code_integer).
% 168.03/28.52  thf(func_def_696, type, power_power_complex: complex > nat > complex).
% 168.03/28.52  thf(func_def_697, type, power_power_int: int > nat > int).
% 168.03/28.52  thf(func_def_698, type, power_power_nat: nat > nat > nat).
% 168.03/28.52  thf(func_def_699, type, power_power_rat: rat > nat > rat).
% 168.03/28.52  thf(func_def_700, type, power_power_real: real > nat > real).
% 168.03/28.52  thf(func_def_701, type, produc4035269172776083154on_nat: (nat > nat > $o) > produc4953844613479565601on_nat > produc2233624965454879586on_nat).
% 168.03/28.52  thf(func_def_702, type, produc3209952032786966637at_nat: (nat > nat > nat) > produc7248412053542808358at_nat > produc4471711990508489141at_nat).
% 168.03/28.52  thf(func_def_703, type, produc8929957630744042906on_nat: (nat > nat > nat) > produc4953844613479565601on_nat > produc8306885398267862888on_nat).
% 168.03/28.52  thf(func_def_704, type, produc851828971589881931at_num: (nat > num > num) > produc2963631642982155120at_num > produc3368934014287244435at_num).
% 168.03/28.52  thf(func_def_705, type, produc3576312749637752826on_num: (num > num > $o) > produc3447558737645232053on_num > produc7036089656553540234on_num).
% 168.03/28.52  thf(func_def_706, type, produc5778274026573060048on_num: (num > num > num) > produc3447558737645232053on_num > produc1193250871479095198on_num).
% 168.03/28.52  thf(func_def_707, type, produc3994169339658061776at_nat: (product_prod_nat_nat > product_prod_nat_nat > $o) > produc6121120109295599847at_nat > produc5491161045314408544at_nat).
% 168.03/28.52  thf(func_def_708, type, produc2899441246263362727at_nat: (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > produc6121120109295599847at_nat > produc5542196010084753463at_nat).
% 168.03/28.52  thf(func_def_709, type, product_Pair_o_o: $o > $o > product_prod_o_o).
% 168.03/28.52  thf(func_def_710, type, product_Pair_o_int: $o > int > product_prod_o_int).
% 168.03/28.52  thf(func_def_711, type, product_Pair_o_nat: $o > nat > product_prod_o_nat).
% 168.03/28.52  thf(func_def_712, type, produc2982872950893828659T_VEBT: $o > vEBT_VEBT > produc2504756804600209347T_VEBT).
% 168.03/28.52  thf(func_def_713, type, produc6677183202524767010eger_o: code_integer > $o > produc6271795597528267376eger_o).
% 168.03/28.52  thf(func_def_714, type, produc1086072967326762835nteger: code_integer > code_integer > produc8923325533196201883nteger).
% 168.03/28.52  thf(func_def_715, type, product_Pair_int_int: int > int > product_prod_int_int).
% 168.03/28.52  thf(func_def_716, type, product_Pair_nat_nat: nat > nat > product_prod_nat_nat).
% 168.03/28.52  thf(func_def_717, type, product_Pair_nat_num: nat > num > product_prod_nat_num).
% 168.03/28.52  thf(func_def_718, type, produc487386426758144856at_nat: nat > product_prod_nat_nat > produc7248412053542808358at_nat).
% 168.03/28.52  thf(func_def_719, type, produc1195630363706982562at_num: nat > product_prod_nat_num > produc2963631642982155120at_num).
% 168.03/28.52  thf(func_def_720, type, product_Pair_num_num: num > num > product_prod_num_num).
% 168.03/28.52  thf(func_def_721, type, produc5098337634421038937on_nat: option_nat > option_nat > produc4953844613479565601on_nat).
% 168.03/28.52  thf(func_def_722, type, produc8585076106096196333on_num: option_num > option_num > produc3447558737645232053on_num).
% 168.03/28.52  thf(func_def_723, type, produc488173922507101015at_nat: option4927543243414619207at_nat > option4927543243414619207at_nat > produc6121120109295599847at_nat).
% 168.03/28.52  thf(func_def_724, type, produc6161850002892822231at_nat: product_prod_nat_nat > product_prod_nat_nat > produc859450856879609959at_nat).
% 168.03/28.52  thf(func_def_725, type, produc8721562602347293563VEBT_o: vEBT_VEBT > $o > produc334124729049499915VEBT_o).
% 168.03/28.52  thf(func_def_726, type, produc736041933913180425BT_int: vEBT_VEBT > int > produc4894624898956917775BT_int).
% 168.03/28.52  thf(func_def_727, type, produc738532404422230701BT_nat: vEBT_VEBT > nat > produc9072475918466114483BT_nat).
% 168.03/28.52  thf(func_def_728, type, produc537772716801021591T_VEBT: vEBT_VEBT > vEBT_VEBT > produc8243902056947475879T_VEBT).
% 168.03/28.52  thf(func_def_729, type, produc457027306803732586at_nat: set_nat > (nat > set_nat) > set_Pr1261947904930325089at_nat).
% 168.03/28.52  thf(func_def_730, type, produc6499014454317279255nteger: (code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 168.03/28.52  thf(func_def_731, type, produc1553301316500091796er_int: (code_integer > code_integer > int) > produc8923325533196201883nteger > int).
% 168.03/28.52  thf(func_def_732, type, produc1555791787009142072er_nat: (code_integer > code_integer > nat) > produc8923325533196201883nteger > nat).
% 168.03/28.52  thf(func_def_733, type, produc7336495610019696514er_num: (code_integer > code_integer > num) > produc8923325533196201883nteger > num).
% 168.03/28.52  thf(func_def_734, type, produc9125791028180074456eger_o: (code_integer > code_integer > produc6271795597528267376eger_o) > produc8923325533196201883nteger > produc6271795597528267376eger_o).
% 168.03/28.52  thf(func_def_735, type, produc6916734918728496179nteger: (code_integer > code_integer > produc8923325533196201883nteger) > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 168.03/28.52  thf(func_def_736, type, produc6771430404735790350plex_o: (complex > complex > $o) > produc4411394909380815293omplex > $o).
% 168.03/28.52  thf(func_def_737, type, produc4947309494688390418_int_o: (int > int > $o) > product_prod_int_int > $o).
% 168.03/28.52  thf(func_def_738, type, produc8211389475949308722nt_int: (int > int > int) > product_prod_int_int > int).
% 168.03/28.52  thf(func_def_739, type, produc4245557441103728435nt_int: (int > int > product_prod_int_int) > product_prod_int_int > product_prod_int_int).
% 168.03/28.52  thf(func_def_740, type, produc8739625826339149834_nat_o: (nat > nat > product_prod_nat_nat > $o) > product_prod_nat_nat > product_prod_nat_nat > $o).
% 168.03/28.52  thf(func_def_741, type, produc27273713700761075at_nat: (nat > nat > product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat).
% 168.03/28.52  thf(func_def_742, type, produc6081775807080527818_nat_o: (nat > nat > $o) > product_prod_nat_nat > $o).
% 168.03/28.52  thf(func_def_743, type, produc1917071388513777916omplex: (nat > nat > complex) > product_prod_nat_nat > complex).
% 168.03/28.52  thf(func_def_744, type, produc6840382203811409530at_int: (nat > nat > int) > product_prod_nat_nat > int).
% 168.03/28.52  thf(func_def_745, type, produc6842872674320459806at_nat: (nat > nat > nat) > product_prod_nat_nat > nat).
% 168.03/28.52  thf(func_def_746, type, produc2626176000494625587at_nat: (nat > nat > product_prod_nat_nat) > product_prod_nat_nat > product_prod_nat_nat).
% 168.03/28.52  thf(func_def_747, type, produc6207742614233964070at_rat: (nat > nat > rat) > product_prod_nat_nat > rat).
% 168.03/28.52  thf(func_def_748, type, produc1703576794950452218t_real: (nat > nat > real) > product_prod_nat_nat > real).
% 168.03/28.52  thf(func_def_749, type, produc3453488052772718514omplex: (nat > nat > set_complex) > product_prod_nat_nat > set_complex).
% 168.03/28.52  thf(func_def_750, type, produc3668448655016342576t_real: (nat > nat > set_real) > product_prod_nat_nat > set_real).
% 168.03/28.52  thf(func_def_751, type, produc4927758841916487424_num_o: (nat > num > $o) > product_prod_nat_num > $o).
% 168.03/28.52  thf(func_def_752, type, produc478579273971653890on_num: (nat > num > option_num) > product_prod_nat_num > option_num).
% 168.03/28.52  thf(func_def_753, type, produc6231982587499038204omplex: (nat > num > set_complex) > product_prod_nat_num > set_complex).
% 168.03/28.52  thf(func_def_754, type, produc9175805072616146554et_int: (nat > num > set_int) > product_prod_nat_num > set_int).
% 168.03/28.52  thf(func_def_755, type, produc4130284055270567454et_nat: (nat > num > set_nat) > product_prod_nat_num > set_nat).
% 168.03/28.52  thf(func_def_756, type, produc1435849484188172666t_real: (nat > num > set_real) > product_prod_nat_num > set_real).
% 168.03/28.52  thf(func_def_757, type, produc5703948589228662326_num_o: (num > num > $o) > product_prod_num_num > $o).
% 168.03/28.52  thf(func_def_758, type, produc2866383454006189126omplex: (num > num > set_complex) > product_prod_num_num > set_complex).
% 168.03/28.52  thf(func_def_759, type, produc6406642877701697732et_int: (num > num > set_int) > product_prod_num_num > set_int).
% 168.03/28.52  thf(func_def_760, type, produc1361121860356118632et_nat: (num > num > set_nat) > product_prod_num_num > set_nat).
% 168.03/28.52  thf(func_def_761, type, produc8296048397933160132t_real: (num > num > set_real) > product_prod_num_num > set_real).
% 168.03/28.52  thf(func_def_762, type, produc6590410687421337004_nat_o: (product_prod_nat_nat > product_prod_nat_nat > $o) > produc859450856879609959at_nat > $o).
% 168.03/28.52  thf(func_def_763, type, produc5414030515140494994real_o: (real > real > $o) > produc2422161461964618553l_real > $o).
% 168.03/28.52  thf(func_def_764, type, product_fst_int_int: product_prod_int_int > int).
% 168.03/28.52  thf(func_def_765, type, product_fst_nat_nat: product_prod_nat_nat > nat).
% 168.03/28.52  thf(func_def_766, type, product_snd_int_int: product_prod_int_int > int).
% 168.03/28.52  thf(func_def_767, type, product_snd_nat_nat: product_prod_nat_nat > nat).
% 168.03/28.52  thf(func_def_768, type, frct: product_prod_int_int > rat).
% 168.03/28.52  thf(func_def_769, type, field_5140801741446780682s_real: set_real).
% 168.03/28.52  thf(func_def_770, type, field_7254667332652039916t_real: rat > real).
% 168.03/28.52  thf(func_def_771, type, normalize: product_prod_int_int > product_prod_int_int).
% 168.03/28.52  thf(func_def_772, type, quotient_of: rat > product_prod_int_int).
% 168.03/28.52  thf(func_def_773, type, real_V2521375963428798218omplex: set_complex).
% 168.03/28.52  thf(func_def_774, type, real_V5970128139526366754l_real: (real > real) > $o).
% 168.03/28.52  thf(func_def_775, type, real_V3694042436643373181omplex: complex > complex > real).
% 168.03/28.52  thf(func_def_776, type, real_V975177566351809787t_real: real > real > real).
% 168.03/28.52  thf(func_def_777, type, real_V1022390504157884413omplex: complex > real).
% 168.03/28.52  thf(func_def_778, type, real_V7735802525324610683m_real: real > real).
% 168.03/28.52  thf(func_def_779, type, real_V4546457046886955230omplex: real > complex).
% 168.03/28.52  thf(func_def_780, type, real_V1803761363581548252l_real: real > real).
% 168.03/28.52  thf(func_def_781, type, real_V2046097035970521341omplex: real > complex > complex).
% 168.03/28.52  thf(func_def_782, type, real_V1485227260804924795R_real: real > real > real).
% 168.03/28.52  thf(func_def_783, type, field_nat: set_Pr1261947904930325089at_nat > set_nat).
% 168.03/28.52  thf(func_def_784, type, id_nat2: set_Pr1261947904930325089at_nat).
% 168.03/28.52  thf(func_def_785, type, divide6298287555418463151nteger: code_integer > code_integer > code_integer).
% 168.03/28.52  thf(func_def_786, type, divide1717551699836669952omplex: complex > complex > complex).
% 168.03/28.52  thf(func_def_787, type, divide_divide_int: int > int > int).
% 168.03/28.52  thf(func_def_788, type, divide_divide_nat: nat > nat > nat).
% 168.03/28.52  thf(func_def_789, type, divide_divide_rat: rat > rat > rat).
% 168.03/28.52  thf(func_def_790, type, divide_divide_real: real > real > real).
% 168.03/28.52  thf(func_def_791, type, dvd_dvd_Code_integer: code_integer > code_integer > $o).
% 168.03/28.52  thf(func_def_792, type, dvd_dvd_complex: complex > complex > $o).
% 168.03/28.52  thf(func_def_793, type, dvd_dvd_int: int > int > $o).
% 168.03/28.52  thf(func_def_794, type, dvd_dvd_nat: nat > nat > $o).
% 168.03/28.52  thf(func_def_795, type, dvd_dvd_rat: rat > rat > $o).
% 168.03/28.52  thf(func_def_796, type, dvd_dvd_real: real > real > $o).
% 168.03/28.52  thf(func_def_797, type, modulo364778990260209775nteger: code_integer > code_integer > code_integer).
% 168.03/28.52  thf(func_def_798, type, modulo_modulo_int: int > int > int).
% 168.03/28.52  thf(func_def_799, type, modulo_modulo_nat: nat > nat > nat).
% 168.03/28.52  thf(func_def_800, type, zero_n356916108424825756nteger: $o > code_integer).
% 168.03/28.52  thf(func_def_801, type, zero_n1201886186963655149omplex: $o > complex).
% 168.03/28.52  thf(func_def_802, type, zero_n2684676970156552555ol_int: $o > int).
% 168.03/28.52  thf(func_def_803, type, zero_n2687167440665602831ol_nat: $o > nat).
% 168.03/28.52  thf(func_def_804, type, zero_n2052037380579107095ol_rat: $o > rat).
% 168.03/28.52  thf(func_def_805, type, zero_n3304061248610475627l_real: $o > real).
% 168.03/28.52  thf(func_def_806, type, suminf_complex: (nat > complex) > complex).
% 168.03/28.52  thf(func_def_807, type, suminf_int: (nat > int) > int).
% 168.03/28.52  thf(func_def_808, type, suminf_nat: (nat > nat) > nat).
% 168.03/28.52  thf(func_def_809, type, suminf_real: (nat > real) > real).
% 168.03/28.52  thf(func_def_810, type, summable_complex: (nat > complex) > $o).
% 168.03/28.52  thf(func_def_811, type, summable_int: (nat > int) > $o).
% 168.03/28.52  thf(func_def_812, type, summable_nat: (nat > nat) > $o).
% 168.03/28.52  thf(func_def_813, type, summable_real: (nat > real) > $o).
% 168.03/28.52  thf(func_def_814, type, sums_complex: (nat > complex) > complex > $o).
% 168.03/28.52  thf(func_def_815, type, sums_int: (nat > int) > int > $o).
% 168.03/28.52  thf(func_def_816, type, sums_nat: (nat > nat) > nat > $o).
% 168.03/28.52  thf(func_def_817, type, sums_real: (nat > real) > real > $o).
% 168.03/28.52  thf(func_def_818, type, collect_complex: (complex > $o) > set_complex).
% 168.03/28.52  thf(func_def_819, type, collect_int: (int > $o) > set_int).
% 168.03/28.52  thf(func_def_820, type, collect_list_o: (list_o > $o) > set_list_o).
% 168.03/28.52  thf(func_def_821, type, collect_list_complex: (list_complex > $o) > set_list_complex).
% 168.03/28.52  thf(func_def_822, type, collect_list_int: (list_int > $o) > set_list_int).
% 168.03/28.52  thf(func_def_823, type, collect_list_nat: (list_nat > $o) > set_list_nat).
% 168.03/28.52  thf(func_def_824, type, collect_list_real: (list_real > $o) > set_list_real).
% 168.03/28.52  thf(func_def_825, type, collec5608196760682091941T_VEBT: (list_VEBT_VEBT > $o) > set_list_VEBT_VEBT).
% 168.03/28.52  thf(func_def_826, type, collect_nat: (nat > $o) > set_nat).
% 168.03/28.52  thf(func_def_827, type, collect_num: (num > $o) > set_num).
% 168.03/28.52  thf(func_def_828, type, collec8663557070575231912omplex: (produc4411394909380815293omplex > $o) > set_Pr5085853215250843933omplex).
% 168.03/28.52  thf(func_def_829, type, collec3392354462482085612at_nat: (product_prod_nat_nat > $o) > set_Pr1261947904930325089at_nat).
% 168.03/28.52  thf(func_def_830, type, collec3799799289383736868l_real: (produc2422161461964618553l_real > $o) > set_Pr6218003697084177305l_real).
% 168.03/28.52  thf(func_def_831, type, collect_rat: (rat > $o) > set_rat).
% 168.03/28.52  thf(func_def_832, type, collect_real: (real > $o) > set_real).
% 168.03/28.52  thf(func_def_833, type, image_int_int: (int > int) > set_int > set_int).
% 168.03/28.52  thf(func_def_834, type, image_nat_nat: (nat > nat) > set_nat > set_nat).
% 168.03/28.52  thf(func_def_835, type, image_nat_real: (nat > real) > set_nat > set_real).
% 168.03/28.52  thf(func_def_836, type, image_nat_char: (nat > char) > set_nat > set_char).
% 168.03/28.52  thf(func_def_837, type, image_5971271580939081552omplex: (real > filter6041513312241820739omplex) > set_real > set_fi4554929511873752355omplex).
% 168.03/28.52  thf(func_def_838, type, image_2178119161166701260l_real: (real > filter2146258269922977983l_real) > set_real > set_fi7789364187291644575l_real).
% 168.03/28.52  thf(func_def_839, type, image_real_real: (real > real) > set_real > set_real).
% 168.03/28.52  thf(func_def_840, type, image_char_nat: (char > nat) > set_char > set_nat).
% 168.03/28.52  thf(func_def_841, type, image_VEBT_VEBT_nat: (vEBT_VEBT > nat) > set_VEBT_VEBT > set_nat).
% 168.03/28.52  thf(func_def_842, type, insert_complex: complex > set_complex > set_complex).
% 168.03/28.52  thf(func_def_843, type, insert_int: int > set_int > set_int).
% 168.03/28.52  thf(func_def_844, type, insert_nat: nat > set_nat > set_nat).
% 168.03/28.52  thf(func_def_845, type, insert_num: num > set_num > set_num).
% 168.03/28.52  thf(func_def_846, type, insert8211810215607154385at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 168.03/28.52  thf(func_def_847, type, insert_rat: rat > set_rat > set_rat).
% 168.03/28.52  thf(func_def_848, type, insert_real: real > set_real > set_real).
% 168.03/28.52  thf(func_def_849, type, insert_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > set_VEBT_VEBT).
% 168.03/28.52  thf(func_def_850, type, vimage_nat_nat: (nat > nat) > set_nat > set_nat).
% 168.03/28.52  thf(func_def_851, type, set_fo1517530859248394432omplex: (nat > complex > complex) > nat > nat > complex > complex).
% 168.03/28.52  thf(func_def_852, type, set_fo2581907887559384638at_int: (nat > int > int) > nat > nat > int > int).
% 168.03/28.52  thf(func_def_853, type, set_fo2584398358068434914at_nat: (nat > nat > nat) > nat > nat > nat > nat).
% 168.03/28.52  thf(func_def_854, type, set_fo1949268297981939178at_rat: (nat > rat > rat) > nat > nat > rat > rat).
% 168.03/28.52  thf(func_def_855, type, set_fo3111899725591712190t_real: (nat > real > real) > nat > nat > real > real).
% 168.03/28.52  thf(func_def_856, type, set_or1266510415728281911st_int: int > int > set_int).
% 168.03/28.52  thf(func_def_857, type, set_or1269000886237332187st_nat: nat > nat > set_nat).
% 168.03/28.52  thf(func_def_858, type, set_or7049704709247886629st_num: num > num > set_num).
% 168.03/28.52  thf(func_def_859, type, set_or633870826150836451st_rat: rat > rat > set_rat).
% 168.03/28.52  thf(func_def_860, type, set_or1222579329274155063t_real: real > real > set_real).
% 168.03/28.52  thf(func_def_861, type, set_or4548717258645045905et_nat: set_nat > set_nat > set_set_nat).
% 168.03/28.52  thf(func_def_862, type, set_or7743017856606604397t_real: set_real > set_real > set_set_real).
% 168.03/28.52  thf(func_def_863, type, set_or4662586982721622107an_int: int > int > set_int).
% 168.03/28.52  thf(func_def_864, type, set_or4665077453230672383an_nat: nat > nat > set_nat).
% 168.03/28.52  thf(func_def_865, type, set_ord_atLeast_nat: nat > set_nat).
% 168.03/28.52  thf(func_def_866, type, set_ord_atLeast_real: real > set_real).
% 168.03/28.52  thf(func_def_867, type, set_ord_atMost_nat: nat > set_nat).
% 168.03/28.52  thf(func_def_868, type, set_or6656581121297822940st_int: int > int > set_int).
% 168.03/28.52  thf(func_def_869, type, set_or6659071591806873216st_nat: nat > nat > set_nat).
% 168.03/28.52  thf(func_def_870, type, set_or5832277885323065728an_int: int > int > set_int).
% 168.03/28.52  thf(func_def_871, type, set_or5834768355832116004an_nat: nat > nat > set_nat).
% 168.03/28.52  thf(func_def_872, type, set_or1633881224788618240n_real: real > real > set_real).
% 168.03/28.52  thf(func_def_873, type, set_or1210151606488870762an_nat: nat > set_nat).
% 168.03/28.52  thf(func_def_874, type, set_or5849166863359141190n_real: real > set_real).
% 168.03/28.52  thf(func_def_875, type, set_ord_lessThan_int: int > set_int).
% 168.03/28.52  thf(func_def_876, type, set_ord_lessThan_nat: nat > set_nat).
% 168.03/28.52  thf(func_def_877, type, set_ord_lessThan_num: num > set_num).
% 168.03/28.52  thf(func_def_878, type, set_ord_lessThan_rat: rat > set_rat).
% 168.03/28.52  thf(func_def_879, type, set_or5984915006950818249n_real: real > set_real).
% 168.03/28.52  thf(func_def_880, type, ascii_of: char > char).
% 168.03/28.52  thf(func_def_881, type, char2: $o > $o > $o > $o > $o > $o > $o > $o > char).
% 168.03/28.52  thf(func_def_882, type, comm_s629917340098488124ar_nat: char > nat).
% 168.03/28.52  thf(func_def_883, type, integer_of_char: char > code_integer).
% 168.03/28.52  thf(func_def_884, type, unique3096191561947761185of_nat: nat > char).
% 168.03/28.52  thf(func_def_885, type, topolo4422821103128117721l_real: filter_real > (real > real) > $o).
% 168.03/28.52  thf(func_def_886, type, topolo5044208981011980120l_real: set_real > (real > real) > $o).
% 168.03/28.52  thf(func_def_887, type, topolo4899668324122417113eq_int: (nat > int) > $o).
% 168.03/28.52  thf(func_def_888, type, topolo4902158794631467389eq_nat: (nat > nat) > $o).
% 168.03/28.52  thf(func_def_889, type, topolo1459490580787246023eq_num: (nat > num) > $o).
% 168.03/28.52  thf(func_def_890, type, topolo6980174941875973593q_real: (nat > real) > $o).
% 168.03/28.52  thf(func_def_891, type, topolo7278393974255667507et_nat: (nat > set_nat) > $o).
% 168.03/28.52  thf(func_def_892, type, topolo2489691266198938127t_real: (nat > set_real) > $o).
% 168.03/28.52  thf(func_def_893, type, topolo2177554685111907308n_real: real > set_real > filter_real).
% 168.03/28.52  thf(func_def_894, type, topolo7531315842566124627t_real: (nat > real) > $o).
% 168.03/28.52  thf(func_def_895, type, topolo2815343760600316023s_real: real > filter_real).
% 168.03/28.52  thf(func_def_896, type, topolo4055970368930404560y_real: (nat > real) > $o).
% 168.03/28.52  thf(func_def_897, type, topolo896644834953643431omplex: filter6041513312241820739omplex).
% 168.03/28.52  thf(func_def_898, type, topolo1511823702728130853y_real: filter2146258269922977983l_real).
% 168.03/28.52  thf(func_def_899, type, arccos: real > real).
% 168.03/28.52  thf(func_def_900, type, arcosh_real: real > real).
% 168.03/28.52  thf(func_def_901, type, arcsin: real > real).
% 168.03/28.52  thf(func_def_902, type, arctan: real > real).
% 168.03/28.52  thf(func_def_903, type, arsinh_real: real > real).
% 168.03/28.52  thf(func_def_904, type, artanh_real: real > real).
% 168.03/28.52  thf(func_def_905, type, cos_complex: complex > complex).
% 168.03/28.52  thf(func_def_906, type, cos_real: real > real).
% 168.03/28.52  thf(func_def_907, type, cos_coeff: nat > real).
% 168.03/28.52  thf(func_def_908, type, cosh_real: real > real).
% 168.03/28.52  thf(func_def_909, type, cot_real: real > real).
% 168.03/28.52  thf(func_def_910, type, diffs_complex: (nat > complex) > nat > complex).
% 168.03/28.52  thf(func_def_911, type, diffs_int: (nat > int) > nat > int).
% 168.03/28.52  thf(func_def_912, type, diffs_real: (nat > real) > nat > real).
% 168.03/28.52  thf(func_def_913, type, exp_complex: complex > complex).
% 168.03/28.52  thf(func_def_914, type, exp_real: real > real).
% 168.03/28.52  thf(func_def_915, type, ln_ln_real: real > real).
% 168.03/28.52  thf(func_def_916, type, log: real > real > real).
% 168.03/28.52  thf(func_def_917, type, pi: real).
% 168.03/28.52  thf(func_def_918, type, powr_real: real > real > real).
% 168.03/28.52  thf(func_def_919, type, sin_complex: complex > complex).
% 168.03/28.52  thf(func_def_920, type, sin_real: real > real).
% 168.03/28.52  thf(func_def_921, type, sin_coeff: nat > real).
% 168.03/28.52  thf(func_def_922, type, sinh_real: real > real).
% 168.03/28.52  thf(func_def_923, type, tan_complex: complex > complex).
% 168.03/28.52  thf(func_def_924, type, tan_real: real > real).
% 168.03/28.52  thf(func_def_925, type, tanh_complex: complex > complex).
% 168.03/28.52  thf(func_def_926, type, tanh_real: real > real).
% 168.03/28.52  thf(func_def_927, type, transi2905341329935302413cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 168.03/28.52  thf(func_def_928, type, transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 168.03/28.52  thf(func_def_929, type, vEBT_T_i_n_s_e_r_t: vEBT_VEBT > nat > nat).
% 168.03/28.52  thf(func_def_930, type, vEBT_T_i_n_s_e_r_t2: vEBT_VEBT > nat > nat).
% 168.03/28.52  thf(func_def_931, type, vEBT_T5076183648494686801_t_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 168.03/28.52  thf(func_def_932, type, vEBT_T9217963907923527482_t_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 168.03/28.52  thf(func_def_933, type, vEBT_T_m_a_x_t: vEBT_VEBT > nat).
% 168.03/28.52  thf(func_def_934, type, vEBT_T_m_a_x_t_rel: vEBT_VEBT > vEBT_VEBT > $o).
% 168.03/28.52  thf(func_def_935, type, vEBT_T_m_e_m_b_e_r: vEBT_VEBT > nat > nat).
% 168.03/28.52  thf(func_def_936, type, vEBT_T_m_e_m_b_e_r2: vEBT_VEBT > nat > nat).
% 168.03/28.52  thf(func_def_937, type, vEBT_T8099345112685741742_r_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 168.03/28.52  thf(func_def_938, type, vEBT_T5837161174952499735_r_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 168.03/28.52  thf(func_def_939, type, vEBT_T_m_i_n_N_u_l_l: vEBT_VEBT > nat).
% 168.03/28.52  thf(func_def_940, type, vEBT_T5462971552011256508_l_rel: vEBT_VEBT > vEBT_VEBT > $o).
% 168.03/28.52  thf(func_def_941, type, vEBT_T_m_i_n_t: vEBT_VEBT > nat).
% 168.03/28.52  thf(func_def_942, type, vEBT_T_m_i_n_t_rel: vEBT_VEBT > vEBT_VEBT > $o).
% 168.03/28.52  thf(func_def_943, type, vEBT_T_p_r_e_d: vEBT_VEBT > nat > nat).
% 168.03/28.52  thf(func_def_944, type, vEBT_T_p_r_e_d2: vEBT_VEBT > nat > nat).
% 168.03/28.52  thf(func_def_945, type, vEBT_T_p_r_e_d_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 168.03/28.52  thf(func_def_946, type, vEBT_T_p_r_e_d_rel2: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 168.03/28.52  thf(func_def_947, type, vEBT_T_s_u_c_c: vEBT_VEBT > nat > nat).
% 168.03/28.52  thf(func_def_948, type, vEBT_T_s_u_c_c2: vEBT_VEBT > nat > nat).
% 168.03/28.52  thf(func_def_949, type, vEBT_T_s_u_c_c_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 168.03/28.52  thf(func_def_950, type, vEBT_T_s_u_c_c_rel2: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 168.03/28.52  thf(func_def_951, type, vEBT_Leaf: $o > $o > vEBT_VEBT).
% 168.03/28.52  thf(func_def_952, type, vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT).
% 168.03/28.52  thf(func_def_953, type, vEBT_size_VEBT: vEBT_VEBT > nat).
% 168.03/28.52  thf(func_def_954, type, vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o).
% 168.03/28.52  thf(func_def_955, type, vEBT_VEBT_high: nat > nat > nat).
% 168.03/28.52  thf(func_def_956, type, vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o).
% 168.03/28.52  thf(func_def_957, type, vEBT_VEBT_low: nat > nat > nat).
% 168.03/28.52  thf(func_def_958, type, vEBT_VEBT_membermima: vEBT_VEBT > nat > $o).
% 168.03/28.52  thf(func_def_959, type, vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 168.03/28.52  thf(func_def_960, type, vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o).
% 168.03/28.52  thf(func_def_961, type, vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 168.03/28.52  thf(func_def_962, type, vEBT_VEBT_valid: vEBT_VEBT > nat > $o).
% 168.03/28.52  thf(func_def_963, type, vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 168.03/28.52  thf(func_def_964, type, vEBT_invar_vebt: vEBT_VEBT > nat > $o).
% 168.03/28.52  thf(func_def_965, type, vEBT_set_vebt: vEBT_VEBT > set_nat).
% 168.03/28.52  thf(func_def_966, type, vEBT_vebt_buildup: nat > vEBT_VEBT).
% 168.03/28.52  thf(func_def_967, type, vEBT_v4011308405150292612up_rel: nat > nat > $o).
% 168.03/28.52  thf(func_def_968, type, vEBT_T_d_e_l_e_t_e: vEBT_VEBT > nat > nat).
% 168.03/28.52  thf(func_def_969, type, vEBT_T8441311223069195367_e_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 168.03/28.52  thf(func_def_970, type, vEBT_vebt_delete: vEBT_VEBT > nat > vEBT_VEBT).
% 168.03/28.52  thf(func_def_971, type, vEBT_vebt_delete_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 168.03/28.52  thf(func_def_972, type, vEBT_VEBT_height: vEBT_VEBT > nat).
% 168.03/28.52  thf(func_def_973, type, vEBT_VEBT_height_rel: vEBT_VEBT > vEBT_VEBT > $o).
% 168.03/28.52  thf(func_def_974, type, vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT).
% 168.03/28.52  thf(func_def_975, type, vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 168.03/28.52  thf(func_def_976, type, vEBT_VEBT_bit_concat: nat > nat > nat > nat).
% 168.03/28.52  thf(func_def_977, type, vEBT_VEBT_minNull: vEBT_VEBT > $o).
% 168.03/28.52  thf(func_def_978, type, vEBT_V6963167321098673237ll_rel: vEBT_VEBT > vEBT_VEBT > $o).
% 168.03/28.52  thf(func_def_979, type, vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat).
% 168.03/28.52  thf(func_def_980, type, vEBT_vebt_member: vEBT_VEBT > nat > $o).
% 168.03/28.52  thf(func_def_981, type, vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 168.03/28.52  thf(func_def_982, type, vEBT_VEBT_add: option_nat > option_nat > option_nat).
% 168.03/28.52  thf(func_def_983, type, vEBT_VEBT_greater: option_nat > option_nat > $o).
% 168.03/28.52  thf(func_def_984, type, vEBT_VEBT_less: option_nat > option_nat > $o).
% 168.03/28.52  thf(func_def_985, type, vEBT_VEBT_lesseq: option_nat > option_nat > $o).
% 168.03/28.52  thf(func_def_986, type, vEBT_VEBT_max_in_set: set_nat > nat > $o).
% 168.03/28.52  thf(func_def_987, type, vEBT_VEBT_min_in_set: set_nat > nat > $o).
% 168.03/28.52  thf(func_def_988, type, vEBT_VEBT_mul: option_nat > option_nat > option_nat).
% 168.03/28.52  thf(func_def_989, type, vEBT_V4262088993061758097ft_nat: (nat > nat > nat) > option_nat > option_nat > option_nat).
% 168.03/28.52  thf(func_def_990, type, vEBT_V819420779217536731ft_num: (num > num > num) > option_num > option_num > option_num).
% 168.03/28.52  thf(func_def_991, type, vEBT_V1502963449132264192at_nat: (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > option4927543243414619207at_nat > option4927543243414619207at_nat > option4927543243414619207at_nat).
% 168.03/28.52  thf(func_def_992, type, vEBT_VEBT_power: option_nat > option_nat > option_nat).
% 168.03/28.52  thf(func_def_993, type, vEBT_vebt_maxt: vEBT_VEBT > option_nat).
% 168.03/28.52  thf(func_def_994, type, vEBT_vebt_maxt_rel: vEBT_VEBT > vEBT_VEBT > $o).
% 168.03/28.52  thf(func_def_995, type, vEBT_vebt_mint: vEBT_VEBT > option_nat).
% 168.03/28.52  thf(func_def_996, type, vEBT_vebt_mint_rel: vEBT_VEBT > vEBT_VEBT > $o).
% 168.03/28.52  thf(func_def_997, type, vEBT_is_pred_in_set: set_nat > nat > nat > $o).
% 168.03/28.52  thf(func_def_998, type, vEBT_vebt_pred: vEBT_VEBT > nat > option_nat).
% 168.03/28.52  thf(func_def_999, type, vEBT_vebt_pred_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 168.03/28.52  thf(func_def_1000, type, vEBT_is_succ_in_set: set_nat > nat > nat > $o).
% 168.03/28.52  thf(func_def_1001, type, vEBT_vebt_succ: vEBT_VEBT > nat > option_nat).
% 168.03/28.52  thf(func_def_1002, type, vEBT_vebt_succ_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 168.03/28.52  thf(func_def_1003, type, accp_list_nat: (list_nat > list_nat > $o) > list_nat > $o).
% 168.03/28.52  thf(func_def_1004, type, accp_nat: (nat > nat > $o) > nat > $o).
% 168.03/28.52  thf(func_def_1005, type, accp_P1096762738010456898nt_int: (product_prod_int_int > product_prod_int_int > $o) > product_prod_int_int > $o).
% 168.03/28.52  thf(func_def_1006, type, accp_P4275260045618599050at_nat: (product_prod_nat_nat > product_prod_nat_nat > $o) > product_prod_nat_nat > $o).
% 168.03/28.52  thf(func_def_1007, type, accp_P3113834385874906142um_num: (product_prod_num_num > product_prod_num_num > $o) > product_prod_num_num > $o).
% 168.03/28.52  thf(func_def_1008, type, accp_P2887432264394892906BT_nat: (produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o) > produc9072475918466114483BT_nat > $o).
% 168.03/28.52  thf(func_def_1009, type, accp_VEBT_VEBT: (vEBT_VEBT > vEBT_VEBT > $o) > vEBT_VEBT > $o).
% 168.03/28.52  thf(func_def_1010, type, pred_nat: set_Pr1261947904930325089at_nat).
% 168.03/28.52  thf(func_def_1011, type, wf_nat: set_Pr1261947904930325089at_nat > $o).
% 168.03/28.52  thf(func_def_1012, type, fChoice_real: (real > $o) > real).
% 168.03/28.52  thf(func_def_1013, type, member_o: $o > set_o > $o).
% 168.03/28.52  thf(func_def_1014, type, member_complex: complex > set_complex > $o).
% 168.03/28.52  thf(func_def_1015, type, member_int: int > set_int > $o).
% 168.03/28.52  thf(func_def_1016, type, member_list_o: list_o > set_list_o > $o).
% 168.03/28.52  thf(func_def_1017, type, member_list_int: list_int > set_list_int > $o).
% 168.03/28.52  thf(func_def_1018, type, member_list_nat: list_nat > set_list_nat > $o).
% 168.03/28.52  thf(func_def_1019, type, member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o).
% 168.03/28.52  thf(func_def_1020, type, member_nat: nat > set_nat > $o).
% 168.03/28.52  thf(func_def_1021, type, member_num: num > set_num > $o).
% 168.03/28.52  thf(func_def_1022, type, member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o).
% 168.03/28.52  thf(func_def_1023, type, member8206827879206165904at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > $o).
% 168.03/28.52  thf(func_def_1024, type, member_rat: rat > set_rat > $o).
% 168.03/28.52  thf(func_def_1025, type, member_real: real > set_real > $o).
% 168.03/28.52  thf(func_def_1026, type, member_set_nat: set_nat > set_set_nat > $o).
% 168.03/28.52  thf(func_def_1027, type, member_set_real: set_real > set_set_real > $o).
% 168.03/28.52  thf(func_def_1028, type, member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o).
% 168.03/28.52  thf(func_def_1029, type, deg: nat).
% 168.03/28.52  thf(func_def_1030, type, m: nat).
% 168.03/28.52  thf(func_def_1031, type, ma: nat).
% 168.03/28.52  thf(func_def_1032, type, mi: nat).
% 168.03/28.52  thf(func_def_1033, type, na: nat).
% 168.03/28.52  thf(func_def_1034, type, summary: vEBT_VEBT).
% 168.03/28.52  thf(func_def_1035, type, treeList: list_VEBT_VEBT).
% 168.03/28.52  thf(func_def_1036, type, xa: nat).
% 168.03/28.52  thf(func_def_1061, type, ph1: !>[X0: $tType]:(X0)).
% 168.03/28.52  thf(func_def_1062, type, sK2: rat > rat).
% 168.03/28.52  thf(func_def_1063, type, sK3: real > real).
% 168.03/28.52  thf(func_def_1064, type, sK4: rat > rat).
% 168.03/28.52  thf(func_def_1065, type, sK5: real > real).
% 168.03/28.52  thf(func_def_1066, type, sK6: real > nat).
% 168.03/28.52  thf(func_def_1067, type, sK7: int).
% 168.03/28.52  thf(func_def_1068, type, sK8: int).
% 168.03/28.52  thf(func_def_1069, type, sK9: int).
% 168.03/28.52  thf(func_def_1070, type, sK10: int).
% 168.03/28.52  thf(func_def_1071, type, sK11: int).
% 168.03/28.52  thf(func_def_1072, type, sK12: nat > list_VEBT_VEBT).
% 168.03/28.52  thf(func_def_1073, type, sK13: nat).
% 168.03/28.52  thf(func_def_1074, type, sK14: nat).
% 168.03/28.52  thf(func_def_1075, type, sK15: nat).
% 168.03/28.52  thf(func_def_1076, type, sK16: nat).
% 168.03/28.52  thf(func_def_1077, type, sK17: nat).
% 168.03/28.52  thf(func_def_1078, type, sK18: nat).
% 168.03/28.52  thf(func_def_1079, type, sK19: nat).
% 168.03/28.52  thf(func_def_1080, type, sK20: nat).
% 168.03/28.52  thf(func_def_1081, type, sK21: real).
% 168.03/28.52  thf(func_def_1082, type, sK22: real).
% 168.03/28.52  thf(func_def_1083, type, sK23: real).
% 168.03/28.52  thf(func_def_1084, type, sK24: real).
% 168.03/28.52  thf(func_def_1085, type, sK25: real).
% 168.03/28.52  thf(func_def_1086, type, sK26: real).
% 168.03/28.52  thf(func_def_1087, type, sK27: vEBT_VEBT > nat).
% 168.03/28.52  thf(func_def_1088, type, sK28: nat > nat).
% 168.03/28.52  thf(func_def_1089, type, sK29: nat > nat).
% 168.03/28.52  thf(func_def_1090, type, sK30: int > int).
% 168.03/28.52  thf(func_def_1091, type, sK31: int > int).
% 168.03/28.52  thf(func_def_1092, type, sK32: real > real).
% 168.03/28.52  thf(func_def_1093, type, sK33: nat > nat).
% 168.03/28.52  thf(func_def_1094, type, sK34: nat).
% 168.03/28.52  thf(func_def_1095, type, sK35: nat).
% 168.03/28.52  thf(func_def_1096, type, sK36: real > real).
% 168.03/28.52  thf(f37304,plain,(
% 168.03/28.52    $false),
% 168.03/28.52    inference(subsumption_resolution,[status(thm)],[f37303,f36976])).
% 168.03/28.52  thf(f36976,plain,(
% 168.03/28.52    ((plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ (bit1 @ one))) @ (plus_plus_nat @ (vEBT_T_m_i_n_t @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))) @ (plus_plus_nat @ (vEBT_T_m_i_n_t @ summary) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit1 @ one))) @ (numeral_numeral_nat @ (bit1 @ (bit0 @ (bit1 @ one))))))))) @ (numeral_numeral_nat @ one)) != (vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ mi))),
% 168.03/28.52    inference(forward_demodulation,[status(thm)],[f36975,f36213])).
% 168.03/28.52  thf(f36213,plain,(
% 168.03/28.52    ( ! [X2 : nat,X1 : nat] : (((plus_plus_nat @ X1 @ X2) = (plus_plus_nat @ X2 @ X1))) )),
% 168.03/28.52    inference(beta_eta_normalization,[status(thm)],[f36209])).
% 168.03/28.52  thf(f36209,plain,(
% 168.03/28.52    ( ! [X2 : nat,X1 : nat] : ((((^[Y0 : nat]: (plus_plus_nat @ Y0 @ X1)) @ X2) = (plus_plus_nat @ X1 @ X2))) )),
% 168.03/28.52    inference(argument_congruence,[status(thm)],[f36208])).
% 168.03/28.52  thf(f36208,plain,(
% 168.03/28.52    ( ! [X1 : nat] : (((plus_plus_nat @ X1) = (^[Y0 : nat]: (plus_plus_nat @ Y0 @ X1)))) )),
% 168.03/28.52    inference(beta_eta_normalization,[status(thm)],[f36207])).
% 168.03/28.52  thf(f36207,plain,(
% 168.03/28.52    ( ! [X1 : nat] : (((plus_plus_nat @ X1) = ((^[Y0 : nat]: ((^[Y1 : nat]: (plus_plus_nat @ Y1 @ Y0)))) @ X1))) )),
% 168.03/28.52    inference(argument_congruence,[status(thm)],[f30366])).
% 168.03/28.52  thf(f30366,plain,(
% 168.03/28.52    (plus_plus_nat = (^[Y0 : nat]: ((^[Y1 : nat]: (plus_plus_nat @ Y1 @ Y0)))))),
% 168.03/28.52    inference(cnf_transformation,[status(thm)],[f15701])).
% 168.03/28.52  thf(f15701,plain,(
% 168.03/28.52    (plus_plus_nat = (^[Y0 : nat]: ((^[Y1 : nat]: (plus_plus_nat @ Y1 @ Y0)))))),
% 168.03/28.52    inference(fool_elimination,[status(thm)],[f15700])).
% 168.03/28.52  thf(f15700,plain,(
% 168.03/28.52    (plus_plus_nat = (^[X0 : nat, X1 : nat] : (plus_plus_nat @ X1 @ X0)))),
% 168.03/28.52    inference(rectify,[status(thm)],[f1291])).
% 168.03/28.52  thf(f1291,axiom,(
% 168.03/28.52    (plus_plus_nat = (^[X93 : nat, X118 : nat] : (plus_plus_nat @ X118 @ X93)))),
% 168.03/28.52    file('/export/starexec/sandbox2/tmp/tmp.T5XVM49IAI/DTF2THF_21656.p',fact_1290_add_Ocommute)).
% 168.03/28.52  thf(f36975,plain,(
% 168.03/28.52    ((plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ (bit1 @ one))) @ (plus_plus_nat @ (vEBT_T_m_i_n_t @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))) @ (plus_plus_nat @ (vEBT_T_m_i_n_t @ summary) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ (bit0 @ (bit1 @ one)))) @ (numeral_numeral_nat @ (bit0 @ (bit1 @ one)))))))) @ (numeral_numeral_nat @ one)) != (vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ mi))),
% 168.03/28.52    inference(backward_demodulation,[status(thm)],[f36249,f36971])).
% 168.03/28.52  thf(f36971,plain,(
% 168.03/28.52    ( ! [X1 : num] : (((plus_plus_nat @ (numeral_numeral_nat @ X1) @ (numeral_numeral_nat @ X1)) = (numeral_numeral_nat @ (bit0 @ X1)))) )),
% 168.03/28.52    inference(equality_proxy_clausification,[status(thm)],[f36970])).
% 168.03/28.52  thf(f36970,plain,(
% 168.03/28.52    ( ! [X1 : num] : (($true = ((numeral_numeral_nat @ (bit0 @ X1)) = (plus_plus_nat @ (numeral_numeral_nat @ X1) @ (numeral_numeral_nat @ X1))))) )),
% 168.03/28.52    inference(beta_eta_normalization,[status(thm)],[f36969])).
% 168.03/28.52  thf(f36969,plain,(
% 168.03/28.52    ( ! [X1 : num] : ((((^[Y0 : num]: ((numeral_numeral_nat @ (bit0 @ Y0)) = (plus_plus_nat @ (numeral_numeral_nat @ Y0) @ (numeral_numeral_nat @ Y0)))) @ X1) = $true)) )),
% 168.03/28.52    inference(pi_clausification,[status(thm)],[f30340])).
% 168.03/28.52  thf(f30340,plain,(
% 168.03/28.52    ((!! @ num @ (^[Y0 : num]: ((numeral_numeral_nat @ (bit0 @ Y0)) = (plus_plus_nat @ (numeral_numeral_nat @ Y0) @ (numeral_numeral_nat @ Y0))))) = $true)),
% 168.03/28.52    inference(cnf_transformation,[status(thm)],[f19285])).
% 168.03/28.52  thf(f19285,plain,(
% 168.03/28.52    ((!! @ num @ (^[Y0 : num]: ((numeral_numeral_nat @ (bit0 @ Y0)) = (plus_plus_nat @ (numeral_numeral_nat @ Y0) @ (numeral_numeral_nat @ Y0))))) = $true)),
% 168.03/28.52    inference(fool_elimination,[status(thm)],[f19284])).
% 168.03/28.52  thf(f19284,plain,(
% 168.03/28.52    ! [X0 : num] : ((numeral_numeral_nat @ (bit0 @ X0)) = (plus_plus_nat @ (numeral_numeral_nat @ X0) @ (numeral_numeral_nat @ X0)))),
% 168.03/28.52    inference(rectify,[status(thm)],[f1547])).
% 168.03/28.52  thf(f1547,axiom,(
% 168.03/28.52    ! [X2 : num] : ((numeral_numeral_nat @ (bit0 @ X2)) = (plus_plus_nat @ (numeral_numeral_nat @ X2) @ (numeral_numeral_nat @ X2)))),
% 168.03/28.52    file('/export/starexec/sandbox2/tmp/tmp.T5XVM49IAI/DTF2THF_21656.p',fact_1546_numeral__code_I2_J)).
% 168.03/28.52  thf(f36249,plain,(
% 168.03/28.52    ((plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ (bit1 @ one))) @ (plus_plus_nat @ (vEBT_T_m_i_n_t @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))) @ (plus_plus_nat @ (vEBT_T_m_i_n_t @ summary) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ (bit0 @ (bit1 @ one)))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ (numeral_numeral_nat @ (bit1 @ one)))))))) @ (numeral_numeral_nat @ one)) != (vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ mi))),
% 168.03/28.52    inference(forward_demodulation,[status(thm)],[f36248,f36213])).
% 168.03/28.52  thf(f36248,plain,(
% 168.03/28.52    ((vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ mi) != (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ (bit1 @ one))) @ (plus_plus_nat @ (vEBT_T_m_i_n_t @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))) @ (plus_plus_nat @ (vEBT_T_m_i_n_t @ summary) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ (numeral_numeral_nat @ (bit1 @ one))) @ (numeral_numeral_nat @ (bit1 @ (bit0 @ (bit1 @ one))))))))) @ (numeral_numeral_nat @ one)))),
% 168.03/28.52    inference(forward_demodulation,[status(thm)],[f36247,f36213])).
% 168.03/28.52  thf(f36247,plain,(
% 168.03/28.52    ((vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ mi) != (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ (bit1 @ one))) @ (plus_plus_nat @ (vEBT_T_m_i_n_t @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))) @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ (numeral_numeral_nat @ (bit1 @ one))) @ (numeral_numeral_nat @ (bit1 @ (bit0 @ (bit1 @ one))))) @ (vEBT_T_m_i_n_t @ summary))))) @ (numeral_numeral_nat @ one)))),
% 168.03/28.52    inference(forward_demodulation,[status(thm)],[f36246,f36213])).
% 168.03/28.52  thf(f36246,plain,(
% 168.03/28.52    ((plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ (bit1 @ one))) @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ (numeral_numeral_nat @ (bit1 @ one))) @ (numeral_numeral_nat @ (bit1 @ (bit0 @ (bit1 @ one))))) @ (vEBT_T_m_i_n_t @ summary)) @ (vEBT_T_m_i_n_t @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))))) @ (numeral_numeral_nat @ one)) != (vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ mi))),
% 168.03/28.52    inference(forward_demodulation,[status(thm)],[f36222,f36213])).
% 168.03/28.52  thf(f36222,plain,(
% 168.03/28.52    ((vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ mi) != (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ (numeral_numeral_nat @ (bit1 @ one))) @ (numeral_numeral_nat @ (bit1 @ (bit0 @ (bit1 @ one))))) @ (vEBT_T_m_i_n_t @ summary)) @ (vEBT_T_m_i_n_t @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (numeral_numeral_nat @ (bit1 @ (bit1 @ one))))) @ (numeral_numeral_nat @ one)))),
% 168.03/28.52    inference(backward_demodulation,[status(thm)],[f36124,f36213])).
% 168.03/28.52  thf(f36124,plain,(
% 168.03/28.52    ((plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ (numeral_numeral_nat @ (bit1 @ one))) @ (numeral_numeral_nat @ (bit1 @ (bit0 @ (bit1 @ one))))) @ (vEBT_T_m_i_n_t @ summary)) @ (vEBT_T_m_i_n_t @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (numeral_numeral_nat @ (bit1 @ (bit1 @ one)))) @ (numeral_numeral_nat @ one)) @ (numeral_numeral_nat @ one)) != (vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ mi))),
% 168.03/28.52    inference(equality_proxy_clausification,[status(thm)],[f36123])).
% 168.03/28.52  thf(f36123,plain,(
% 168.03/28.52    (((vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ mi) = (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ (numeral_numeral_nat @ (bit1 @ one))) @ (numeral_numeral_nat @ (bit1 @ (bit0 @ (bit1 @ one))))) @ (vEBT_T_m_i_n_t @ summary)) @ (vEBT_T_m_i_n_t @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (numeral_numeral_nat @ (bit1 @ (bit1 @ one)))) @ (numeral_numeral_nat @ one)) @ (numeral_numeral_nat @ one))) = $false)),
% 168.03/28.52    inference(not_proxy_clausification,[status(thm)],[f33948])).
% 168.03/28.52  thf(f33948,plain,(
% 168.03/28.52    ($true = (~ ((vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ mi) = (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ (numeral_numeral_nat @ (bit1 @ one))) @ (numeral_numeral_nat @ (bit1 @ (bit0 @ (bit1 @ one))))) @ (vEBT_T_m_i_n_t @ summary)) @ (vEBT_T_m_i_n_t @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (numeral_numeral_nat @ (bit1 @ (bit1 @ one)))) @ (numeral_numeral_nat @ one)) @ (numeral_numeral_nat @ one)))))),
% 168.03/28.52    inference(definition_unfolding,[status(thm)],[f31669,f30958,f30783,f30783])).
% 168.03/28.52  thf(f30783,plain,(
% 168.03/28.52    (one_one_nat = (numeral_numeral_nat @ one))),
% 168.03/28.52    inference(cnf_transformation,[status(thm)],[f28081])).
% 168.03/28.52  thf(f28081,plain,(
% 168.03/28.52    (one_one_nat = (numeral_numeral_nat @ one))),
% 168.03/28.52    inference(fool_elimination,[status(thm)],[f206])).
% 168.03/28.52  thf(f206,axiom,(
% 168.03/28.52    (one_one_nat = (numeral_numeral_nat @ one))),
% 168.03/28.52    file('/export/starexec/sandbox2/tmp/tmp.T5XVM49IAI/DTF2THF_21656.p',fact_205_numerals_I1_J)).
% 168.03/28.52  thf(f30958,plain,(
% 168.03/28.52    (xa = mi)),
% 168.03/28.52    inference(cnf_transformation,[status(thm)],[f27728])).
% 168.03/28.52  thf(f27728,plain,(
% 168.03/28.52    (xa = mi)),
% 168.03/28.52    inference(fool_elimination,[status(thm)],[f1])).
% 168.03/28.52  thf(f1,axiom,(
% 168.03/28.52    (xa = mi)),
% 168.03/28.52    file('/export/starexec/sandbox2/tmp/tmp.T5XVM49IAI/DTF2THF_21656.p',fact_0_True)).
% 168.03/28.52  thf(f31669,plain,(
% 168.03/28.52    ($true = (~ ((vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ xa) = (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ (numeral_numeral_nat @ (bit1 @ one))) @ (numeral_numeral_nat @ (bit1 @ (bit0 @ (bit1 @ one))))) @ (vEBT_T_m_i_n_t @ summary)) @ (vEBT_T_m_i_n_t @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (numeral_numeral_nat @ (bit1 @ (bit1 @ one)))) @ one_one_nat) @ one_one_nat))))),
% 168.03/28.52    inference(cnf_transformation,[status(thm)],[f17484])).
% 168.03/28.52  thf(f17484,plain,(
% 168.03/28.52    ($true = (~ ((vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ xa) = (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ (numeral_numeral_nat @ (bit1 @ one))) @ (numeral_numeral_nat @ (bit1 @ (bit0 @ (bit1 @ one))))) @ (vEBT_T_m_i_n_t @ summary)) @ (vEBT_T_m_i_n_t @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (numeral_numeral_nat @ (bit1 @ (bit1 @ one)))) @ one_one_nat) @ one_one_nat))))),
% 168.03/28.52    inference(fool_elimination,[status(thm)],[f10255])).
% 168.03/28.52  thf(f10255,negated_conjecture,(
% 168.03/28.52    ~((vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ xa) = (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ (numeral_numeral_nat @ (bit1 @ one))) @ (numeral_numeral_nat @ (bit1 @ (bit0 @ (bit1 @ one))))) @ (vEBT_T_m_i_n_t @ summary)) @ (vEBT_T_m_i_n_t @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (numeral_numeral_nat @ (bit1 @ (bit1 @ one)))) @ one_one_nat) @ one_one_nat))),
% 168.03/28.52    inference(negated_conjecture,[status(cth)],[f10254])).
% 168.03/28.52  thf(f10254,conjecture,(
% 168.03/28.52    ((vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ xa) = (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ (numeral_numeral_nat @ (bit1 @ one))) @ (numeral_numeral_nat @ (bit1 @ (bit0 @ (bit1 @ one))))) @ (vEBT_T_m_i_n_t @ summary)) @ (vEBT_T_m_i_n_t @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (numeral_numeral_nat @ (bit1 @ (bit1 @ one)))) @ one_one_nat) @ one_one_nat))),
% 168.03/28.52    file('/export/starexec/sandbox2/tmp/tmp.T5XVM49IAI/DTF2THF_21656.p',conj_0)).
% 168.03/28.52  thf(f37303,plain,(
% 168.03/28.52    ((plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ (bit1 @ one))) @ (plus_plus_nat @ (vEBT_T_m_i_n_t @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))) @ (plus_plus_nat @ (vEBT_T_m_i_n_t @ summary) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit1 @ one))) @ (numeral_numeral_nat @ (bit1 @ (bit0 @ (bit1 @ one))))))))) @ (numeral_numeral_nat @ one)) = (vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ mi))),
% 168.03/28.52    inference(backward_demodulation,[status(thm)],[f36978,f37302])).
% 168.03/28.52  thf(f37302,plain,(
% 168.03/28.52    ( ! [X2 : nat,X1 : nat] : (((if_nat @ $false @ X1 @ X2) = X2)) )),
% 168.03/28.52    inference(equality_proxy_clausification,[status(thm)],[f37301])).
% 168.03/28.52  thf(f37301,plain,(
% 168.03/28.52    ( ! [X2 : nat,X1 : nat] : (($true = ((if_nat @ $false @ X1 @ X2) = X2))) )),
% 168.03/28.52    inference(beta_eta_normalization,[status(thm)],[f37300])).
% 168.03/28.52  thf(f37300,plain,(
% 168.03/28.52    ( ! [X2 : nat,X1 : nat] : (($true = ((^[Y0 : nat]: ((if_nat @ $false @ X1 @ Y0) = Y0)) @ X2))) )),
% 168.03/28.52    inference(pi_clausification,[status(thm)],[f37297])).
% 168.03/28.52  thf(f37297,plain,(
% 168.03/28.52    ( ! [X1 : nat] : (((!! @ nat @ (^[Y0 : nat]: ((if_nat @ $false @ X1 @ Y0) = Y0))) = $true)) )),
% 168.03/28.52    inference(beta_eta_normalization,[status(thm)],[f37296])).
% 168.03/28.52  thf(f37296,plain,(
% 168.03/28.52    ( ! [X1 : nat] : (($true = ((^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((if_nat @ $false @ Y0 @ Y1) = Y1)))) @ X1))) )),
% 168.03/28.52    inference(pi_clausification,[status(thm)],[f29963])).
% 168.03/28.52  thf(f29963,plain,(
% 168.03/28.52    ((!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((if_nat @ $false @ Y0 @ Y1) = Y1))))) = $true)),
% 168.03/28.52    inference(cnf_transformation,[status(thm)],[f24490])).
% 168.03/28.52  thf(f24490,plain,(
% 168.03/28.52    ((!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((if_nat @ $false @ Y0 @ Y1) = Y1))))) = $true)),
% 168.03/28.52    inference(fool_elimination,[status(thm)],[f24489])).
% 168.03/28.52  thf(f24489,plain,(
% 168.03/28.52    ! [X0 : nat,X1 : nat] : ((if_nat @ $false @ X1 @ X0) = X0)),
% 168.03/28.52    inference(rectify,[status(thm)],[f10214])).
% 168.03/28.52  thf(f10214,axiom,(
% 168.03/28.52    ! [X20 : nat,X12 : nat] : ((if_nat @ $false @ X12 @ X20) = X20)),
% 168.03/28.52    file('/export/starexec/sandbox2/tmp/tmp.T5XVM49IAI/DTF2THF_21656.p',help_If_2_1_If_001t__Nat__Onat_T)).
% 168.03/28.52  thf(f36978,plain,(
% 168.03/28.52    ((vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ mi) = (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ (bit1 @ one))) @ (plus_plus_nat @ (vEBT_T_m_i_n_t @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))) @ (plus_plus_nat @ (vEBT_T_m_i_n_t @ summary) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit1 @ one))) @ (numeral_numeral_nat @ (bit1 @ (bit0 @ (bit1 @ one))))))))) @ (if_nat @ $false @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one))) @ (vEBT_T_d_e_l_e_t_e @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))))) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (vEBT_T_m_i_n_N_u_l_l @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))))) @ (if_nat @ (vEBT_VEBT_minNull @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))))) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (vEBT_T_d_e_l_e_t_e @ summary @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (if_nat @ (ma = (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (vEBT_T_m_a_x_t @ (vEBT_vebt_delete @ summary @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (if_nat @ (none_nat = (vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (numeral_numeral_nat @ one) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ (bit0 @ one)))) @ (vEBT_T_m_a_x_t @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))))))))) @ (numeral_numeral_nat @ one)))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (if_nat @ (ma = (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit1 @ one))) @ (vEBT_T_m_a_x_t @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))))) @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (numeral_numeral_nat @ one)))))) @ (numeral_numeral_nat @ one))))),
% 168.03/28.52    inference(forward_demodulation,[status(thm)],[f36974,f36213])).
% 168.03/28.52  thf(f36974,plain,(
% 168.03/28.52    ((vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ mi) = (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ (bit1 @ one))) @ (plus_plus_nat @ (vEBT_T_m_i_n_t @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))) @ (plus_plus_nat @ (vEBT_T_m_i_n_t @ summary) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ (bit0 @ (bit1 @ one)))) @ (numeral_numeral_nat @ (bit0 @ (bit1 @ one)))))))) @ (if_nat @ $false @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one))) @ (vEBT_T_d_e_l_e_t_e @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))))) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (vEBT_T_m_i_n_N_u_l_l @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))))) @ (if_nat @ (vEBT_VEBT_minNull @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))))) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (vEBT_T_d_e_l_e_t_e @ summary @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (if_nat @ (ma = (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (vEBT_T_m_a_x_t @ (vEBT_vebt_delete @ summary @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (if_nat @ (none_nat = (vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (numeral_numeral_nat @ one) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ (bit0 @ one)))) @ (vEBT_T_m_a_x_t @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))))))))) @ (numeral_numeral_nat @ one)))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (if_nat @ (ma = (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit1 @ one))) @ (vEBT_T_m_a_x_t @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))))) @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (numeral_numeral_nat @ one)))))) @ (numeral_numeral_nat @ one))))),
% 168.03/28.52    inference(backward_demodulation,[status(thm)],[f36390,f36971])).
% 168.03/28.52  thf(f36390,plain,(
% 168.03/28.52    ((plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ (bit1 @ one))) @ (plus_plus_nat @ (vEBT_T_m_i_n_t @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))) @ (plus_plus_nat @ (vEBT_T_m_i_n_t @ summary) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ (bit0 @ (bit1 @ one)))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ (numeral_numeral_nat @ (bit1 @ one)))))))) @ (if_nat @ $false @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one))) @ (vEBT_T_d_e_l_e_t_e @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))))) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (vEBT_T_m_i_n_N_u_l_l @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))))) @ (if_nat @ (vEBT_VEBT_minNull @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))))) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (vEBT_T_d_e_l_e_t_e @ summary @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (if_nat @ (ma = (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (vEBT_T_m_a_x_t @ (vEBT_vebt_delete @ summary @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (if_nat @ (none_nat = (vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (numeral_numeral_nat @ one) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ (bit0 @ one)))) @ (vEBT_T_m_a_x_t @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))))))))) @ (numeral_numeral_nat @ one)))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (if_nat @ (ma = (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit1 @ one))) @ (vEBT_T_m_a_x_t @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))))) @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (numeral_numeral_nat @ one)))))) @ (numeral_numeral_nat @ one))) = (vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ mi))),
% 168.03/28.52    inference(backward_demodulation,[status(thm)],[f36237,f36385])).
% 168.03/28.52  thf(f36385,plain,(
% 168.03/28.52    ( ! [X2 : nat,X1 : nat] : (((times_times_nat @ X1 @ X2) = (times_times_nat @ X2 @ X1))) )),
% 168.03/28.52    inference(beta_eta_normalization,[status(thm)],[f36379])).
% 168.03/28.52  thf(f36379,plain,(
% 168.03/28.52    ( ! [X2 : nat,X1 : nat] : ((((^[Y0 : nat]: (times_times_nat @ Y0 @ X1)) @ X2) = (times_times_nat @ X1 @ X2))) )),
% 168.03/28.52    inference(argument_congruence,[status(thm)],[f36287])).
% 168.03/28.52  thf(f36287,plain,(
% 168.03/28.52    ( ! [X1 : nat] : (((times_times_nat @ X1) = (^[Y0 : nat]: (times_times_nat @ Y0 @ X1)))) )),
% 168.03/28.52    inference(beta_eta_normalization,[status(thm)],[f36284])).
% 168.03/28.52  thf(f36284,plain,(
% 168.03/28.52    ( ! [X1 : nat] : (((times_times_nat @ X1) = ((^[Y0 : nat]: ((^[Y1 : nat]: (times_times_nat @ Y1 @ Y0)))) @ X1))) )),
% 168.03/28.52    inference(argument_congruence,[status(thm)],[f31577])).
% 168.03/28.52  thf(f31577,plain,(
% 168.03/28.52    (times_times_nat = (^[Y0 : nat]: ((^[Y1 : nat]: (times_times_nat @ Y1 @ Y0)))))),
% 168.03/28.52    inference(cnf_transformation,[status(thm)],[f15240])).
% 168.03/28.52  thf(f15240,plain,(
% 168.03/28.52    (times_times_nat = (^[Y0 : nat]: ((^[Y1 : nat]: (times_times_nat @ Y1 @ Y0)))))),
% 168.03/28.52    inference(fool_elimination,[status(thm)],[f15239])).
% 168.03/28.52  thf(f15239,plain,(
% 168.03/28.52    ((^[X0 : nat, X1 : nat] : (times_times_nat @ X1 @ X0)) = times_times_nat)),
% 168.03/28.52    inference(rectify,[status(thm)],[f1242])).
% 168.03/28.52  thf(f1242,axiom,(
% 168.03/28.52    ((^[X93 : nat, X118 : nat] : (times_times_nat @ X118 @ X93)) = times_times_nat)),
% 168.03/28.52    file('/export/starexec/sandbox2/tmp/tmp.T5XVM49IAI/DTF2THF_21656.p',fact_1241_mult_Ocommute)).
% 168.03/28.52  thf(f36237,plain,(
% 168.03/28.52    ((vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ mi) = (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ (bit1 @ one))) @ (plus_plus_nat @ (vEBT_T_m_i_n_t @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))) @ (plus_plus_nat @ (vEBT_T_m_i_n_t @ summary) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ (bit0 @ (bit1 @ one)))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ (numeral_numeral_nat @ (bit1 @ one)))))))) @ (if_nat @ $false @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one))) @ (vEBT_T_d_e_l_e_t_e @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (vEBT_T_m_i_n_N_u_l_l @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))))) @ (if_nat @ (vEBT_VEBT_minNull @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (vEBT_T_d_e_l_e_t_e @ summary @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (if_nat @ (ma = (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (vEBT_T_m_a_x_t @ (vEBT_vebt_delete @ summary @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (if_nat @ (none_nat = (vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (numeral_numeral_nat @ one) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ (bit0 @ one)))) @ (vEBT_T_m_a_x_t @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))))))))) @ (numeral_numeral_nat @ one)))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (if_nat @ (ma = (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit1 @ one))) @ (vEBT_T_m_a_x_t @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (divide_divide_nat @ (plus_plus_nat @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (numeral_numeral_nat @ one)))))) @ (numeral_numeral_nat @ one))))),
% 168.03/28.52    inference(forward_demodulation,[status(thm)],[f36236,f36213])).
% 168.03/28.52  thf(f36236,plain,(
% 168.03/28.52    ((plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ (bit1 @ one))) @ (plus_plus_nat @ (vEBT_T_m_i_n_t @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))) @ (plus_plus_nat @ (vEBT_T_m_i_n_t @ summary) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ (bit0 @ (bit1 @ one)))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ (numeral_numeral_nat @ (bit1 @ one)))))))) @ (if_nat @ $false @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one))) @ (vEBT_T_d_e_l_e_t_e @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (vEBT_T_m_i_n_N_u_l_l @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))))) @ (if_nat @ (vEBT_VEBT_minNull @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (vEBT_T_d_e_l_e_t_e @ summary @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (if_nat @ (ma = (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))))) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (vEBT_T_m_a_x_t @ (vEBT_vebt_delete @ summary @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (if_nat @ (none_nat = (vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (numeral_numeral_nat @ one) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ (bit0 @ one)))) @ (vEBT_T_m_a_x_t @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))))))))) @ (numeral_numeral_nat @ one)))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (if_nat @ (ma = (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit1 @ one))) @ (vEBT_T_m_a_x_t @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (numeral_numeral_nat @ one)))))) @ (numeral_numeral_nat @ one))) = (vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ mi))),
% 168.03/28.52    inference(forward_demodulation,[status(thm)],[f36235,f36213])).
% 168.03/28.52  thf(f36235,plain,(
% 168.03/28.52    ((plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ (bit1 @ one))) @ (plus_plus_nat @ (vEBT_T_m_i_n_t @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))) @ (plus_plus_nat @ (vEBT_T_m_i_n_t @ summary) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ (numeral_numeral_nat @ (bit1 @ one))) @ (numeral_numeral_nat @ (bit1 @ (bit0 @ (bit1 @ one))))))))) @ (if_nat @ $false @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one))) @ (vEBT_T_d_e_l_e_t_e @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (vEBT_T_m_i_n_N_u_l_l @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))))) @ (if_nat @ (vEBT_VEBT_minNull @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (vEBT_T_d_e_l_e_t_e @ summary @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (if_nat @ (ma = (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))))) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (vEBT_T_m_a_x_t @ (vEBT_vebt_delete @ summary @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (if_nat @ (none_nat = (vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (numeral_numeral_nat @ one) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ (bit0 @ one)))) @ (vEBT_T_m_a_x_t @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))))))))) @ (numeral_numeral_nat @ one)))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (if_nat @ (ma = (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit1 @ one))) @ (vEBT_T_m_a_x_t @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (numeral_numeral_nat @ one)))))) @ (numeral_numeral_nat @ one))) = (vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ mi))),
% 168.03/28.52    inference(forward_demodulation,[status(thm)],[f36234,f36213])).
% 168.03/28.52  thf(f36234,plain,(
% 168.03/28.52    ((plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ (bit1 @ one))) @ (plus_plus_nat @ (vEBT_T_m_i_n_t @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))) @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ (numeral_numeral_nat @ (bit1 @ one))) @ (numeral_numeral_nat @ (bit1 @ (bit0 @ (bit1 @ one))))) @ (vEBT_T_m_i_n_t @ summary))))) @ (if_nat @ $false @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one))) @ (vEBT_T_d_e_l_e_t_e @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (vEBT_T_m_i_n_N_u_l_l @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))))) @ (if_nat @ (vEBT_VEBT_minNull @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (vEBT_T_d_e_l_e_t_e @ summary @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (if_nat @ (ma = (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))))) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (vEBT_T_m_a_x_t @ (vEBT_vebt_delete @ summary @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (if_nat @ (none_nat = (vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (numeral_numeral_nat @ one) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ (bit0 @ one)))) @ (vEBT_T_m_a_x_t @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))))))))) @ (numeral_numeral_nat @ one)))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (if_nat @ (ma = (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit1 @ one))) @ (vEBT_T_m_a_x_t @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (numeral_numeral_nat @ one)))))) @ (numeral_numeral_nat @ one))) = (vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ mi))),
% 168.03/28.52    inference(forward_demodulation,[status(thm)],[f36233,f36213])).
% 168.03/28.52  thf(f36233,plain,(
% 168.03/28.52    ((vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ mi) = (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ (bit1 @ one))) @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ (numeral_numeral_nat @ (bit1 @ one))) @ (numeral_numeral_nat @ (bit1 @ (bit0 @ (bit1 @ one))))) @ (vEBT_T_m_i_n_t @ summary)) @ (vEBT_T_m_i_n_t @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))))) @ (if_nat @ $false @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one))) @ (vEBT_T_d_e_l_e_t_e @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (vEBT_T_m_i_n_N_u_l_l @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))))) @ (if_nat @ (vEBT_VEBT_minNull @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (vEBT_T_d_e_l_e_t_e @ summary @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (if_nat @ (ma = (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))))) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (vEBT_T_m_a_x_t @ (vEBT_vebt_delete @ summary @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (if_nat @ (none_nat = (vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (numeral_numeral_nat @ one) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ (bit0 @ one)))) @ (vEBT_T_m_a_x_t @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))))))))) @ (numeral_numeral_nat @ one)))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (if_nat @ (ma = (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit1 @ one))) @ (vEBT_T_m_a_x_t @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (numeral_numeral_nat @ one)))))) @ (numeral_numeral_nat @ one))))),
% 168.03/28.52    inference(forward_demodulation,[status(thm)],[f36223,f36213])).
% 168.03/28.52  thf(f36223,plain,(
% 168.03/28.52    ((vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ mi) = (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ (numeral_numeral_nat @ (bit1 @ one))) @ (numeral_numeral_nat @ (bit1 @ (bit0 @ (bit1 @ one))))) @ (vEBT_T_m_i_n_t @ summary)) @ (vEBT_T_m_i_n_t @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (numeral_numeral_nat @ (bit1 @ (bit1 @ one))))) @ (if_nat @ $false @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one))) @ (vEBT_T_d_e_l_e_t_e @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (vEBT_T_m_i_n_N_u_l_l @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))))) @ (if_nat @ (vEBT_VEBT_minNull @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (vEBT_T_d_e_l_e_t_e @ summary @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (if_nat @ (ma = (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))))) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (vEBT_T_m_a_x_t @ (vEBT_vebt_delete @ summary @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (if_nat @ (none_nat = (vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (numeral_numeral_nat @ one) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ (bit0 @ one)))) @ (vEBT_T_m_a_x_t @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))))))))) @ (numeral_numeral_nat @ one)))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (if_nat @ (ma = (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit1 @ one))) @ (vEBT_T_m_a_x_t @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (numeral_numeral_nat @ one)))))) @ (numeral_numeral_nat @ one))))),
% 168.03/28.52    inference(backward_demodulation,[status(thm)],[f36069,f36213])).
% 168.03/28.52  thf(f36069,plain,(
% 168.03/28.52    ((plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ (numeral_numeral_nat @ (bit1 @ one))) @ (numeral_numeral_nat @ (bit1 @ (bit0 @ (bit1 @ one))))) @ (vEBT_T_m_i_n_t @ summary)) @ (vEBT_T_m_i_n_t @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (numeral_numeral_nat @ (bit1 @ (bit1 @ one)))) @ (numeral_numeral_nat @ one)) @ (if_nat @ $false @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one))) @ (vEBT_T_d_e_l_e_t_e @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (vEBT_T_m_i_n_N_u_l_l @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))))) @ (if_nat @ (vEBT_VEBT_minNull @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (vEBT_T_d_e_l_e_t_e @ summary @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (if_nat @ (ma = (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))))) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (vEBT_T_m_a_x_t @ (vEBT_vebt_delete @ summary @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (if_nat @ (none_nat = (vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (numeral_numeral_nat @ one) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ (bit0 @ one)))) @ (vEBT_T_m_a_x_t @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))))))))) @ (numeral_numeral_nat @ one)))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (if_nat @ (ma = (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit1 @ one))) @ (vEBT_T_m_a_x_t @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (numeral_numeral_nat @ one)))))) @ (numeral_numeral_nat @ one))) = (vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ mi))),
% 168.03/28.52    inference(forward_demodulation,[status(thm)],[f35323,f36015])).
% 168.03/28.52  thf(f36015,plain,(
% 168.03/28.52    ((ord_less_real @ (semiri5074537144036343181t_real @ (plus_plus_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (numeral_numeral_nat @ one))) @ (plus_plus_real @ (semiri5074537144036343181t_real @ (size_s6755466524823107622T_VEBT @ treeList)) @ (numeral_numeral_real @ one))) = $false)),
% 168.03/28.52    inference(not_proxy_clausification,[status(thm)],[f35757])).
% 168.03/28.52  thf(f35757,plain,(
% 168.03/28.52    ((~ (ord_less_real @ (semiri5074537144036343181t_real @ (plus_plus_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (numeral_numeral_nat @ one))) @ (plus_plus_real @ (semiri5074537144036343181t_real @ (size_s6755466524823107622T_VEBT @ treeList)) @ (numeral_numeral_real @ one)))) = $true)),
% 168.03/28.52    inference(beta_eta_normalization,[status(thm)],[f33566])).
% 168.03/28.52  thf(f33566,plain,(
% 168.03/28.52    ($true = (~ ((^[Y0 : nat]: ((^[Y1 : nat]: ((^[Y2 : nat]: (ord_less_real @ (semiri5074537144036343181t_real @ Y1) @ (plus_plus_real @ (semiri5074537144036343181t_real @ Y2) @ (numeral_numeral_real @ one)))))) @ (plus_plus_nat @ Y0 @ (numeral_numeral_nat @ one)))) @ ((^[Y0 : nat]: ((^[Y1 : nat]: (divide_divide_nat @ Y0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ Y1))))) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ treeList))))),
% 168.03/28.52    inference(definition_unfolding,[status(thm)],[f31231,f32416,f30037])).
% 168.03/28.52  thf(f30037,plain,(
% 168.03/28.52    (vEBT_VEBT_high = (^[Y0 : nat]: ((^[Y1 : nat]: (divide_divide_nat @ Y0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ Y1))))))),
% 168.03/28.52    inference(cnf_transformation,[status(thm)],[f29609])).
% 168.03/28.52  thf(f29609,plain,(
% 168.03/28.52    (vEBT_VEBT_high = (^[Y0 : nat]: ((^[Y1 : nat]: (divide_divide_nat @ Y0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ Y1))))))),
% 168.03/28.52    inference(fool_elimination,[status(thm)],[f29608])).
% 168.03/28.52  thf(f29608,plain,(
% 168.03/28.52    (vEBT_VEBT_high = (^[X0 : nat, X1 : nat] : (divide_divide_nat @ X0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ X1))))),
% 168.03/28.52    inference(rectify,[status(thm)],[f35])).
% 168.03/28.52  thf(f35,axiom,(
% 168.03/28.52    (vEBT_VEBT_high = (^[X13 : nat, X14 : nat] : (divide_divide_nat @ X13 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ X14))))),
% 168.03/28.52    file('/export/starexec/sandbox2/tmp/tmp.T5XVM49IAI/DTF2THF_21656.p',fact_34_high__def)).
% 168.03/28.52  thf(f32416,plain,(
% 168.03/28.52    (ord_less_nat = (^[Y0 : nat]: ((^[Y1 : nat]: ((^[Y2 : nat]: (ord_less_real @ (semiri5074537144036343181t_real @ Y1) @ (plus_plus_real @ (semiri5074537144036343181t_real @ Y2) @ (numeral_numeral_real @ one)))))) @ (plus_plus_nat @ Y0 @ (numeral_numeral_nat @ one)))))),
% 168.03/28.52    inference(definition_unfolding,[status(thm)],[f29859,f32415,f30783])).
% 168.03/28.52  thf(f32415,plain,(
% 168.03/28.52    (ord_less_eq_nat = (^[Y0 : nat]: ((^[Y1 : nat]: (ord_less_real @ (semiri5074537144036343181t_real @ Y0) @ (plus_plus_real @ (semiri5074537144036343181t_real @ Y1) @ (numeral_numeral_real @ one)))))))),
% 168.03/28.52    inference(definition_unfolding,[status(thm)],[f30830,f30031])).
% 168.03/28.52  thf(f30031,plain,(
% 168.03/28.52    (one_one_real = (numeral_numeral_real @ one))),
% 168.03/28.52    inference(cnf_transformation,[status(thm)],[f21614])).
% 168.03/28.52  thf(f21614,plain,(
% 168.03/28.52    (one_one_real = (numeral_numeral_real @ one))),
% 168.03/28.52    inference(fool_elimination,[status(thm)],[f201])).
% 168.03/28.52  thf(f201,axiom,(
% 168.03/28.52    (one_one_real = (numeral_numeral_real @ one))),
% 168.03/28.52    file('/export/starexec/sandbox2/tmp/tmp.T5XVM49IAI/DTF2THF_21656.p',fact_200_numeral__One)).
% 168.03/28.52  thf(f30830,plain,(
% 168.03/28.52    (ord_less_eq_nat = (^[Y0 : nat]: ((^[Y1 : nat]: (ord_less_real @ (semiri5074537144036343181t_real @ Y0) @ (plus_plus_real @ (semiri5074537144036343181t_real @ Y1) @ one_one_real))))))),
% 168.03/28.52    inference(cnf_transformation,[status(thm)],[f27880])).
% 168.03/28.52  thf(f27880,plain,(
% 168.03/28.52    (ord_less_eq_nat = (^[Y0 : nat]: ((^[Y1 : nat]: (ord_less_real @ (semiri5074537144036343181t_real @ Y0) @ (plus_plus_real @ (semiri5074537144036343181t_real @ Y1) @ one_one_real))))))),
% 168.03/28.52    inference(fool_elimination,[status(thm)],[f27879])).
% 168.03/28.52  thf(f27879,plain,(
% 168.03/28.52    (ord_less_eq_nat = (^[X0 : nat, X1 : nat] : (ord_less_real @ (semiri5074537144036343181t_real @ X0) @ (plus_plus_real @ (semiri5074537144036343181t_real @ X1) @ one_one_real))))),
% 168.03/28.52    inference(rectify,[status(thm)],[f7407])).
% 168.03/28.52  thf(f7407,axiom,(
% 168.03/28.52    (ord_less_eq_nat = (^[X14 : nat, X73 : nat] : (ord_less_real @ (semiri5074537144036343181t_real @ X14) @ (plus_plus_real @ (semiri5074537144036343181t_real @ X73) @ one_one_real))))),
% 168.03/28.52    file('/export/starexec/sandbox2/tmp/tmp.T5XVM49IAI/DTF2THF_21656.p',fact_7406_nat__le__real__less)).
% 168.03/28.52  thf(f29859,plain,(
% 168.03/28.52    (ord_less_nat = (^[Y0 : nat]: (ord_less_eq_nat @ (plus_plus_nat @ Y0 @ one_one_nat))))),
% 168.03/28.52    inference(cnf_transformation,[status(thm)],[f16609])).
% 168.03/28.52  thf(f16609,plain,(
% 168.03/28.52    (ord_less_nat = (^[Y0 : nat]: (ord_less_eq_nat @ (plus_plus_nat @ Y0 @ one_one_nat))))),
% 168.03/28.52    inference(fool_elimination,[status(thm)],[f16608])).
% 168.03/28.52  thf(f16608,plain,(
% 168.03/28.52    (ord_less_nat = (^[X0 : nat] : (ord_less_eq_nat @ (plus_plus_nat @ X0 @ one_one_nat))))),
% 168.03/28.52    inference(rectify,[status(thm)],[f625])).
% 168.03/28.52  thf(f625,axiom,(
% 168.03/28.52    (ord_less_nat = (^[X93 : nat] : (ord_less_eq_nat @ (plus_plus_nat @ X93 @ one_one_nat))))),
% 168.03/28.52    file('/export/starexec/sandbox2/tmp/tmp.T5XVM49IAI/DTF2THF_21656.p',fact_624_discrete)).
% 168.03/28.52  thf(f31231,plain,(
% 168.03/28.52    ((~ (ord_less_nat @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ treeList))) = $true)),
% 168.03/28.52    inference(cnf_transformation,[status(thm)],[f24835])).
% 168.03/28.52  thf(f24835,plain,(
% 168.03/28.52    ((~ (ord_less_nat @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ treeList))) = $true)),
% 168.03/28.52    inference(fool_elimination,[status(thm)],[f24834])).
% 168.03/28.52  thf(f24834,plain,(
% 168.03/28.52    ~(ord_less_nat @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ treeList))),
% 168.03/28.52    inference(rectify,[status(thm)],[f5])).
% 168.03/28.52  thf(f5,axiom,(
% 168.03/28.52    ~(ord_less_nat @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ treeList))),
% 168.03/28.52    file('/export/starexec/sandbox2/tmp/tmp.T5XVM49IAI/DTF2THF_21656.p',fact_4_False)).
% 168.03/28.52  thf(f35323,plain,(
% 168.03/28.52    ((plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ (numeral_numeral_nat @ (bit1 @ one))) @ (numeral_numeral_nat @ (bit1 @ (bit0 @ (bit1 @ one))))) @ (vEBT_T_m_i_n_t @ summary)) @ (vEBT_T_m_i_n_t @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (numeral_numeral_nat @ (bit1 @ (bit1 @ one)))) @ (numeral_numeral_nat @ one)) @ (if_nat @ (ord_less_real @ (semiri5074537144036343181t_real @ (plus_plus_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (numeral_numeral_nat @ one))) @ (plus_plus_real @ (semiri5074537144036343181t_real @ (size_s6755466524823107622T_VEBT @ treeList)) @ (numeral_numeral_real @ one))) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one))) @ (vEBT_T_d_e_l_e_t_e @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (vEBT_T_m_i_n_N_u_l_l @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))))) @ (if_nat @ (vEBT_VEBT_minNull @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (vEBT_T_d_e_l_e_t_e @ summary @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (if_nat @ (ma = (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))))) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (vEBT_T_m_a_x_t @ (vEBT_vebt_delete @ summary @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (if_nat @ (none_nat = (vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (numeral_numeral_nat @ one) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ (bit0 @ one)))) @ (vEBT_T_m_a_x_t @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))))))))) @ (numeral_numeral_nat @ one)))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (if_nat @ (ma = (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit1 @ one))) @ (vEBT_T_m_a_x_t @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (times_times_nat @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (numeral_numeral_nat @ one)))))) @ (numeral_numeral_nat @ one))) = (vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ mi))),
% 168.03/28.52    inference(beta_eta_normalization,[status(thm)],[f33334])).
% 168.03/28.52  thf(f33334,plain,(
% 168.03/28.52    ((plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ (numeral_numeral_nat @ (bit1 @ one))) @ (numeral_numeral_nat @ (bit1 @ (bit0 @ (bit1 @ one))))) @ (vEBT_T_m_i_n_t @ summary)) @ (vEBT_T_m_i_n_t @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (numeral_numeral_nat @ (bit1 @ (bit1 @ one)))) @ (numeral_numeral_nat @ one)) @ (if_nat @ ((^[Y0 : nat]: ((^[Y1 : nat]: ((^[Y2 : nat]: (ord_less_real @ (semiri5074537144036343181t_real @ Y1) @ (plus_plus_real @ (semiri5074537144036343181t_real @ Y2) @ (numeral_numeral_real @ one)))))) @ (plus_plus_nat @ Y0 @ (numeral_numeral_nat @ one)))) @ ((^[Y0 : nat]: ((^[Y1 : nat]: (divide_divide_nat @ Y0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ Y1))))) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ treeList)) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one))) @ (vEBT_T_d_e_l_e_t_e @ (nth_VEBT_VEBT @ treeList @ ((^[Y0 : nat]: ((^[Y1 : nat]: (divide_divide_nat @ Y0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ Y1))))) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ ((^[Y0 : nat]: ((^[Y1 : nat]: ((^[Y2 : nat]: ((^[Y3 : nat]: (minus_minus_nat @ Y2 @ (times_times_nat @ (divide_divide_nat @ Y2 @ Y3) @ Y3))))) @ Y0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ Y1))))) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (vEBT_T_m_i_n_N_u_l_l @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ ((^[Y0 : nat]: ((^[Y1 : nat]: (divide_divide_nat @ Y0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ Y1))))) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ ((^[Y0 : nat]: ((^[Y1 : nat]: ((^[Y2 : nat]: ((^[Y3 : nat]: (minus_minus_nat @ Y2 @ (times_times_nat @ (divide_divide_nat @ Y2 @ Y3) @ Y3))))) @ Y0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ Y1))))) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ (if_nat @ (vEBT_VEBT_minNull @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ ((^[Y0 : nat]: ((^[Y1 : nat]: (divide_divide_nat @ Y0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ Y1))))) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ ((^[Y0 : nat]: ((^[Y1 : nat]: ((^[Y2 : nat]: ((^[Y3 : nat]: (minus_minus_nat @ Y2 @ (times_times_nat @ (divide_divide_nat @ Y2 @ Y3) @ Y3))))) @ Y0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ Y1))))) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (vEBT_T_d_e_l_e_t_e @ summary @ ((^[Y0 : nat]: ((^[Y1 : nat]: (divide_divide_nat @ Y0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ Y1))))) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (if_nat @ (ma = (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))))) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (vEBT_T_m_a_x_t @ (vEBT_vebt_delete @ summary @ ((^[Y0 : nat]: ((^[Y1 : nat]: (divide_divide_nat @ Y0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ Y1))))) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ one) @ (if_nat @ (none_nat = (vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ ((^[Y0 : nat]: ((^[Y1 : nat]: (divide_divide_nat @ Y0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ Y1))))) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ (numeral_numeral_nat @ one) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ (bit0 @ one)))) @ (vEBT_T_m_a_x_t @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ ((^[Y0 : nat]: ((^[Y1 : nat]: (divide_divide_nat @ Y0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ Y1))))) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ ((^[Y0 : nat]: ((^[Y1 : nat]: (divide_divide_nat @ Y0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ Y1))))) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ ((^[Y0 : nat]: ((^[Y1 : nat]: ((^[Y2 : nat]: ((^[Y3 : nat]: (minus_minus_nat @ Y2 @ (times_times_nat @ (divide_divide_nat @ Y2 @ Y3) @ Y3))))) @ Y0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ Y1))))) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ ((^[Y0 : nat]: ((^[Y1 : nat]: (divide_divide_nat @ Y0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ Y1))))) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))))))))) @ (numeral_numeral_nat @ one)))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (if_nat @ (ma = (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit1 @ one))) @ (vEBT_T_m_a_x_t @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ ((^[Y0 : nat]: ((^[Y1 : nat]: (divide_divide_nat @ Y0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ Y1))))) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ ((^[Y0 : nat]: ((^[Y1 : nat]: (divide_divide_nat @ Y0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ Y1))))) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ ((^[Y0 : nat]: ((^[Y1 : nat]: ((^[Y2 : nat]: ((^[Y3 : nat]: (minus_minus_nat @ Y2 @ (times_times_nat @ (divide_divide_nat @ Y2 @ Y3) @ Y3))))) @ Y0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ Y1))))) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ ((^[Y0 : nat]: ((^[Y1 : nat]: (divide_divide_nat @ Y0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ Y1))))) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ (numeral_numeral_nat @ one)))))) @ (numeral_numeral_nat @ one))) = (vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ mi))),
% 168.03/28.52    inference(definition_unfolding,[status(thm)],[f30946,f30958,f30783,f32416,f30037,f30037,f32420,f30783,f30037,f32420,f30037,f32420,f30783,f30037,f30783,f30037,f30783,f30037,f30783,f30037,f30037,f32420,f30037,f30783,f30037,f30037,f32420,f30037,f30783,f30783])).
% 168.03/28.52  thf(f32420,plain,(
% 168.03/28.52    (vEBT_VEBT_low = (^[Y0 : nat]: ((^[Y1 : nat]: ((^[Y2 : nat]: ((^[Y3 : nat]: (minus_minus_nat @ Y2 @ (times_times_nat @ (divide_divide_nat @ Y2 @ Y3) @ Y3))))) @ Y0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ Y1))))))),
% 168.03/28.52    inference(definition_unfolding,[status(thm)],[f31018,f30425])).
% 168.03/28.52  thf(f30425,plain,(
% 168.03/28.52    (modulo_modulo_nat = (^[Y0 : nat]: ((^[Y1 : nat]: (minus_minus_nat @ Y0 @ (times_times_nat @ (divide_divide_nat @ Y0 @ Y1) @ Y1))))))),
% 168.03/28.52    inference(cnf_transformation,[status(thm)],[f29241])).
% 168.03/28.52  thf(f29241,plain,(
% 168.03/28.52    (modulo_modulo_nat = (^[Y0 : nat]: ((^[Y1 : nat]: (minus_minus_nat @ Y0 @ (times_times_nat @ (divide_divide_nat @ Y0 @ Y1) @ Y1))))))),
% 168.03/28.52    inference(fool_elimination,[status(thm)],[f29240])).
% 168.03/28.52  thf(f29240,plain,(
% 168.03/28.52    (modulo_modulo_nat = (^[X0 : nat, X1 : nat] : (minus_minus_nat @ X0 @ (times_times_nat @ (divide_divide_nat @ X0 @ X1) @ X1))))),
% 168.03/28.52    inference(rectify,[status(thm)],[f3655])).
% 168.03/28.52  thf(f3655,axiom,(
% 168.03/28.52    (modulo_modulo_nat = (^[X73 : nat, X14 : nat] : (minus_minus_nat @ X73 @ (times_times_nat @ (divide_divide_nat @ X73 @ X14) @ X14))))),
% 168.03/28.52    file('/export/starexec/sandbox2/tmp/tmp.T5XVM49IAI/DTF2THF_21656.p',fact_3654_modulo__nat__def)).
% 168.03/28.52  thf(f31018,plain,(
% 168.03/28.52    (vEBT_VEBT_low = (^[Y0 : nat]: ((^[Y1 : nat]: (modulo_modulo_nat @ Y0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ Y1))))))),
% 168.03/28.52    inference(cnf_transformation,[status(thm)],[f18603])).
% 168.03/28.52  thf(f18603,plain,(
% 168.03/28.52    (vEBT_VEBT_low = (^[Y0 : nat]: ((^[Y1 : nat]: (modulo_modulo_nat @ Y0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ Y1))))))),
% 168.03/28.52    inference(fool_elimination,[status(thm)],[f18602])).
% 168.03/28.52  thf(f18602,plain,(
% 168.03/28.52    ((^[X0 : nat, X1 : nat] : (modulo_modulo_nat @ X0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ X1))) = vEBT_VEBT_low)),
% 168.03/28.52    inference(rectify,[status(thm)],[f3448])).
% 168.03/28.52  thf(f3448,axiom,(
% 168.03/28.52    ((^[X13 : nat, X14 : nat] : (modulo_modulo_nat @ X13 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ X14))) = vEBT_VEBT_low)),
% 168.03/28.52    file('/export/starexec/sandbox2/tmp/tmp.T5XVM49IAI/DTF2THF_21656.p',fact_3447_low__def)).
% 168.03/28.52  thf(f30946,plain,(
% 168.03/28.52    ((vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ xa) = (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ (numeral_numeral_nat @ (bit1 @ one))) @ (numeral_numeral_nat @ (bit1 @ (bit0 @ (bit1 @ one))))) @ (vEBT_T_m_i_n_t @ summary)) @ (vEBT_T_m_i_n_t @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (numeral_numeral_nat @ (bit1 @ (bit1 @ one)))) @ one_one_nat) @ (if_nat @ (ord_less_nat @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ treeList)) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one))) @ (vEBT_T_d_e_l_e_t_e @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (plus_plus_nat @ (plus_plus_nat @ one_one_nat @ (vEBT_T_m_i_n_N_u_l_l @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ (if_nat @ (vEBT_VEBT_minNull @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (plus_plus_nat @ (plus_plus_nat @ one_one_nat @ (vEBT_T_d_e_l_e_t_e @ summary @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (if_nat @ (ma = (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))))) @ (plus_plus_nat @ (plus_plus_nat @ one_one_nat @ (vEBT_T_m_a_x_t @ (vEBT_vebt_delete @ summary @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ (plus_plus_nat @ one_one_nat @ (if_nat @ (none_nat = (vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ one_one_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ (bit0 @ one)))) @ (vEBT_T_m_a_x_t @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))))))))) @ one_one_nat))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (if_nat @ (ma = (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit1 @ one))) @ (vEBT_T_m_a_x_t @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ one_one_nat))))) @ one_one_nat)))),
% 168.03/28.52    inference(cnf_transformation,[status(thm)],[f19767])).
% 168.03/28.52  thf(f19767,plain,(
% 168.03/28.52    ((vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ xa) = (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ (numeral_numeral_nat @ (bit1 @ one))) @ (numeral_numeral_nat @ (bit1 @ (bit0 @ (bit1 @ one))))) @ (vEBT_T_m_i_n_t @ summary)) @ (vEBT_T_m_i_n_t @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (numeral_numeral_nat @ (bit1 @ (bit1 @ one)))) @ one_one_nat) @ (if_nat @ (ord_less_nat @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ treeList)) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one))) @ (vEBT_T_d_e_l_e_t_e @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (plus_plus_nat @ (plus_plus_nat @ one_one_nat @ (vEBT_T_m_i_n_N_u_l_l @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ (if_nat @ (vEBT_VEBT_minNull @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (plus_plus_nat @ (plus_plus_nat @ one_one_nat @ (vEBT_T_d_e_l_e_t_e @ summary @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (if_nat @ (ma = (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))))) @ (plus_plus_nat @ (plus_plus_nat @ one_one_nat @ (vEBT_T_m_a_x_t @ (vEBT_vebt_delete @ summary @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ (plus_plus_nat @ one_one_nat @ (if_nat @ (none_nat = (vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ one_one_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ (bit0 @ one)))) @ (vEBT_T_m_a_x_t @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))))))))) @ one_one_nat))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (if_nat @ (ma = (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit1 @ one))) @ (vEBT_T_m_a_x_t @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ one_one_nat))))) @ one_one_nat)))),
% 168.03/28.52    inference(fool_elimination,[status(thm)],[f1572])).
% 168.03/28.52  thf(f1572,axiom,(
% 168.03/28.52    ((plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ (numeral_numeral_nat @ (bit1 @ one))) @ (numeral_numeral_nat @ (bit1 @ (bit0 @ (bit1 @ one))))) @ (vEBT_T_m_i_n_t @ summary)) @ (vEBT_T_m_i_n_t @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))) @ (numeral_numeral_nat @ (bit1 @ (bit1 @ one)))) @ one_one_nat) @ (if_nat @ (ord_less_nat @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ treeList)) @ (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one))) @ (vEBT_T_d_e_l_e_t_e @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (plus_plus_nat @ (plus_plus_nat @ one_one_nat @ (vEBT_T_m_i_n_N_u_l_l @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ (if_nat @ (vEBT_VEBT_minNull @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (plus_plus_nat @ (plus_plus_nat @ one_one_nat @ (vEBT_T_d_e_l_e_t_e @ summary @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (if_nat @ (ma = (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))))) @ (plus_plus_nat @ (plus_plus_nat @ one_one_nat @ (vEBT_T_m_a_x_t @ (vEBT_vebt_delete @ summary @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ (plus_plus_nat @ one_one_nat @ (if_nat @ (none_nat = (vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ one_one_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ (bit0 @ one)))) @ (vEBT_T_m_a_x_t @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))))))))) @ one_one_nat))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (if_nat @ (ma = (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary))))))) @ (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ (bit1 @ one))) @ (vEBT_T_m_a_x_t @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ one_one_nat))))) @ one_one_nat)) = (vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ xa))),
% 168.03/28.52    file('/export/starexec/sandbox2/tmp/tmp.T5XVM49IAI/DTF2THF_21656.p',fact_1571__C3_C)).
% 168.03/28.52  % SZS output end Proof for DTF2THF_21656
% 168.03/28.52  % (22073)------------------------------
% 168.03/28.52  % (22073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 168.03/28.52  % (22073)Termination reason: Refutation
% 168.03/28.52  
% 168.03/28.52  % (22073)Memory used [KB]: 65500
% 168.03/28.52  % (22073)Time elapsed: 2.061 s
% 168.03/28.52  % (22073)Instructions burned: 7427 (million)
% 168.03/28.52  % (22073)------------------------------
% 168.03/28.52  % (22073)------------------------------
% 168.03/28.52  % (21767)Success in time 23.187 s
%------------------------------------------------------------------------------